Isidore of Seville: ETYMOLOGIARVM SIVE ORIGINVM LIBRI XX

MATHEMATICA Latine dicitur doctrinalis scientia, quae abstractam considerat quantitatem. Abstracta enim quantitas est, quam intellectu a materia separantes vel ab aliis accidentibus, ut est par, inpar, vel ab aliis huiuscemodi in sola ratiocinatione tractamus. Cuius species sunt quattuor: id est Arithmetica, Musica, Geometria et Astronomia.

MATHEMATICS is called in Latin a doctrinal science, which considers abstract quantity. For abstract quantity is that which, separating by the intellect from matter or from other accidents—such as even, odd—or from others of this kind, we handle in reasoning alone. Its species are four: that is, Arithmetic, Music, Geometry, and Astronomy.

Arithmetica est disciplina quantitatis numerabilis secundum se. Musica est disciplina quae de numeris loquitur, qui inveniuntur in sonis. Geometria est disciplina magnitudinis et formarum. Astronomia est disciplina quae cursus caelestium siderum atque figuras contemplatur omnes atque habitudines stellarum.

Arithmetic is the discipline of countable quantity in itself. Music is the discipline that speaks about numbers which are found in sounds. Geometry is the discipline of magnitude and forms. Astronomy is the discipline that contemplates the courses of the heavenly stars and all the figures and the relations (habitudes) of the stars.

Quas disciplinas deinceps paulo latius indicamus, ut earum causae conpetenter possint ostendi.

These disciplines we next indicate somewhat more broadly, so that their causes may be able to be shown competently.

I. DE VOCABVLO ARITHMETICAE DISCIPLINAE.

1. ON THE VOCABLE OF THE DISCIPLINE OF ARITHMETIC.

[1] Arithmetica est disciplina numerorum. Graeci enim numerum ARITHMON dicunt. Quam scriptores saecularium litterarum inter disciplinas mathematicas ideo primam esse voluerunt, quoniam ipsa ut sit nullam aliam indiget disciplinam.

[1] Arithmetic is the discipline of numbers. For the Greeks call “number” ARITHMON. The writers of secular literature therefore wished it to be first among the mathematical disciplines, since it, in order to be, needs no other discipline.

[2] Musica autem et Geometria et Astronomia, quae sequuntur, ut sint atque subsistant istius egent auxilium.

[2] But Music and Geometry and Astronomy, which follow, in order that they may exist and subsist, need the aid of this discipline.

II. DE AVCTORIBVS EIVS.

2. ON ITS AUTHORS.

[1] Numeri disciplinam apud Graecos primum Pythagoram autumant conscripsisse, ac deinde a Nicomacho diffusius esse dispositam; quam apud Latinos primus Apuleius, deinde Boetius transtulerunt.

[1] They aver that Pythagoras was the first among the Greeks to have conscribed the discipline of Number, and then that it was more diffusely disposed by Nicomachus; which among the Latins Apuleius first, then Boethius, translated.

III. QVID SIT NVMERVS.

3. WHAT A NUMBER IS.

[1] Numerus autem est multitudo ex unitatibus constituta. Nam unum semen numeri esse, non numerum. Numero nummus nomen dedit, et a sui frequentatione vocabulum indidit.

[1] Number, moreover, is a multitude constituted from units. For the one is the seed of number, not a number. The coin gave its name to number, and from its own frequent use it imposed the word.

Vnus a Graeco nomen trahit; Graeci enim unum ENA dicunt: sic duo et tres, quos illi DUO et TRIA appellant.

One draws its name from Greek; for the Greeks say ENA for “one”: so too two and three, which they call DUO and TRIA.

[2] Quattuor vero a figura quadrata nomen sumpserunt. Quinque autem non secundum naturam, sed secundum placitum voluntatis vocabulum acceperunt ab eo, qui numeris nomina indidit. Sex autem et septem a Graeco veniunt.

[2] Four indeed took their name from the square figure. But five received its appellation not according to nature, but according to the pleasure of the will, from him who imposed names upon the numbers. But six and seven come from the Greek.

[3] In multis enim nominibus quae in Graeco aspirationem habent, nos pro aspiratione S ponimus. Inde est pro EX sex, [et] pro EPTA septem, sicut pro herpillo herba serpillum. Octo vero per translationem, sicut illi et nos: ita illi ENNEA, nos novem: illi DEKA, nos decem.

[3] For in many names which in Greek have aspiration, we put S in place of the aspiration. Hence, for EX, six, and for EPTA, seven, just as, in place of herpillus, the herb serpillum. But eight, indeed, is by translation, as both they and we: thus they ENNEA, we nine; they DEKA, we ten.

[4] Dicti autem decem a Graeca etymologia, eo quod ligent et coniungant infra iacentes numeros. Nam DESMOS coniungere vel ligare apud eos dicitur. Porro viginti dicti quod sint decem bis geniti, U pro B littera posita.

[4] However, ten are said from Greek etymology, because they bind and conjoin the numbers lying beneath. For DESMOS among them is said to mean to join or to bind. Furthermore, twenty are said so because they are ten begotten twice, with the letter U set in place of B.

Triginta, quod a ternario denario gignantur: sic usque ad nonaginta.

Thirty, because they are generated from a ternary denary: thus up to ninety.

[5] Centum vero vocati a cantho, quod est circulum; ducenti a duo centum. Sic et reliqui usque ad mille. Mille autem a multitudine, unde et militia, quasi multitia: inde et milia, quae Graeci mutata littera myriada vocant.

[5] But a hundred are called from canthus, which is a circle; two hundred from duo centum. Thus also the rest up to a thousand. A thousand, moreover, is from multitude, whence also militia, as if “multitude-ness”; and from this also milia, which the Greeks, with a letter changed, call myriada.

IV. QVID PRAESTENT NVMERI.

4. WHAT NUMBERS AFFORD.

[1] Ratio numerorum contemnenda non est. In multis enim sanctarum scripturarum locis quantum mysterium habent elucet. Non enim frustra in laudibus Dei dictum est (Sap.

[1] The rationale of numbers is not to be contemned. For in many places of the holy Scriptures it shines forth how much mystery they have. For not in vain, in the praises of God, it was said (Wis.

11,21): 'Omnia in mensura et numero et pondere fecisti.'

(11,21): 'You have made all things in measure and number and weight.'

[2] Senarius namque [numerus] qui partibus suis perfectus est, perfectionem mundi quadam numeri [sui] significatione declarat. Similiter et quadraginta dies, quibus Moyses et Helias et ipse Dominus ieiunaverunt, sine numerorum cognitione non intelleguntur.

[2] For the senary [number], which is perfect by its own parts, declares the perfection of the world by a certain signification of its [own] number. Likewise also the forty days during which Moses and Elijah and the Lord himself fasted are not understood without knowledge of numbers.

[3] Sic et alii in scripturis sacris numeri existunt, quorum figuras nonnisi noti huius artis scientiae solvere possunt. Datum est etiam nobis ex aliqua parte sub numerorum consistere disciplina, quando horas per eam dicimus, quando de mensuum curriculo disputamus, quando spatium anni redeuntis agnoscimus.

[3] Thus also other numbers exist in the sacred scriptures, whose figures only those skilled in the science of this art are able to resolve. It has also been granted to us in some part to stand under the discipline of numbers, when we tell the hours by it, when we discourse about the course (curriculum) of the months, when we recognize the span of the returning year.

[4] Per numerum siquidem ne confundamur instruimur. Tolle numerum in rebus omnibus, et omnia pereunt. Adime saeculo conputum, et cuncta ignorantia caeca conplectitur, nec differri potest a ceteris animalibus, qui calculi nesciunt rationem.

[4] Indeed, by number we are instructed, lest we be confounded. Take away number from all things, and all things perish. Remove computation from the world, and blind ignorance embraces everything, nor can it be distinguished from the other animals, who do not know calculation.

V. DE PRIMA DIVISIONE PARIVM ET INPARIVM.

5. ON THE FIRST DIVISION OF EVENS AND ODDS.

[1] Numerus dividitur in [his] paribus et inparibus. Par numerus dividitur in his: pariter par, pariter inpar, et inpariter par. Inpar numerus dividitur in his: primum et simplum, secundum et conpositum, tertium mediocrem; qui quodammodo primus et incompositus est, alio vero modo secundus et conpositus est.

[1] Number is divided into [these] even and odd. An even number is divided into these: evenly even, evenly odd, and oddly even. An odd number is divided into these: first and simple, second and composite, third mediocre; which in a certain manner is first and incomposite, but in another manner second and composite.

[2] Par numerus est, qui in duabus aequis partibus dividi potest, ut II, IV et VIII. Inpar vero numerus est, qui dividi aequis partibus nequit, uno medio vel deficiente vel superante, ut III, V, VII, IX et reliqui.

[2] An even number is that which can be divided into two equal parts, as 2, 4, and 8. An odd number, however, is that which cannot be divided into equal parts, with a single middle either deficient or exceeding, as 3, 5, 7, 9, and the rest.

[3] Pariter par numerus est, qui secundum parem numerum pariter dividitur, quousque ad indivisibilem perveniat unitatem; ut puta LXIV habet medietate XXXII, hic autem XVI, XVI vero VIII, octonarius IV, quaternarius II, binarius unum, qui singularis indivisibilis est.

[3] An evenly even number is that which is divided evenly according to an even number, until it reaches the indivisible unity; for instance, 64 has by halving 32, this moreover 16, 16 indeed 8, the octonary 4, the quaternary 2, the binary 1, which is singular and indivisible.

[4] Pariter inpar est, qui in partes aequas recipit sectionem, sed partes eius mox indissecabiles permanent, ut VI, X et XXXVIII, L. Mox enim hunc numerum divideris, incurris in numerum quem secare non possis.

[4] The evenly-odd is that which receives a section into equal parts, but its parts at once remain indivisible, as 6, 10 and 38, 50. For as soon as you divide this number, you encounter a number which you cannot cut.

[5] Inpariter par numerus est, cuius partes etiam dividi possunt, sed usque ad unitatem non perveniunt, ut XXIV. Hi enim in medietatem divisi XII faciunt rursumque in aliam medietatem VI, deinde in aliam tres; et ultra divisionem non recipit sectio illa, sed ante unitatem invenitur terminus, quem secare non possis.

[5] An oddly even number is that whose parts also can be divided, but do not reach to unity, as 24. For these, divided into a half, make 12, and again into another half 6, then into another, three; and beyond that division the section does not admit further division, but before unity a terminus is found which you cannot cut.

[6] Inpariter inpar est, qui ab inpari numero inpariter mensuratur, ut XXV, XLIX; qui dum sint inpares numeri, ab inparibus etiam partibus dividuntur, ut septies septeni XLIX et quinquies quini XXV. Inparium numerorum alii simplices sunt, alii conpositi, alii mediocres.

[6] Oddly odd is that which is measured by an odd number in an odd fashion, as 25, 49; which, since they are odd numbers, are also divided by odd parts, as seven times seven [is] 49 and five times five [is] 25. Of odd numbers, some are simple, others composite, others middle.

[7] Simplices sunt, qui nullam aliam partem habent nisi solam unitatem, ut ternarius solam tertiam, et quinarius solam quintam, et septenarius solam septimam. His enim una pars sola est. Conpositi sunt, qui non solum unitate metiuntur, sed etiam alieno numero procreantur, ut novem, XV et XXI.

[7] Simple are those which have no other part except the unit alone, as the ternary has only the third, the quinary only the fifth, and the septenary only the seventh. For to these there is one part alone. Composite are those which are measured not only by the unit, but are also procreated by another number, as nine, 15, and 21.

Dicimus enim ter terni, et septies terni, ter quini, et quinquies quini.

For we say thrice three, and seven times three, thrice five, and five times five.

[8] Mediocres numeri sunt, qui quodammodo simplices et inconpositi esse videntur, alio vero modo et conpositi; [ut] verbi gratia, novem ad XXV dum conparatus fuerit, primus est et inconpositus, quia non habet communem numerum nisi solum monadicum: ad quindecim vero si conparatus fuerit, secundus est et compositus, quoniam inest illi communis numerus praeter monadicum, id est ternarius numerus; qui(a) novem mensurat ter terni, et quindecim ter quini.

[8] Middle numbers are those which seem in a certain manner to be simple and uncompounded, but in another manner also compounded; [for] for example, when nine has been compared to 25, in the first case it is simple and uncompounded, because it has no common number except only the monadic; but if it has been compared to fifteen, in the second case it is compounded, since there is in it a common number besides the monadic, that is, the ternary number; beca(u)se nine is measured by three threes, and fifteen by three fives.

[9] Item parium numerorum alii sunt superflui, alii diminutivi, alii perfecti. Superflui sunt, quorum partes simul ductae plenitudinem suam excedunt, ut puta duodenarius. Habet enim partes quinque: duodecimam, quod est unum; sextam, quod duo; quartam, quod tria; tertiam, quod quattuor; dimidiam, quod sex.

[9] Likewise, of even numbers, some are superfluous, others diminutive (deficient), others perfect. Superfluous are those whose parts, drawn together, exceed their own plenitude, as, for instance, the duodenary. For it has five parts: the twelfth, which is one; the sixth, which is two; the fourth, which is three; the third, which is four; the half, which is six.

Vnum enim et duo, et tria, et quattuor, et sex simul ducta XVI faciunt et longe a duodenario excedunt: sic et alii similes plurimi, ut duodevicesimus, et multi tales.

For one and two and three and four and six, when taken together, make 16 and far exceed the duodenary: so too very many similar others, such as the eighteenth, and many such.

[10] Diminutivi numeri sunt, qui partibus suis computati minorem summam efficiunt, utputa denarius, cuius partes sunt tres: decima, quod est unum; quinta, quod duo; dimidia, quod quinque. Vnum enim et duo et quinque simul ducta octonarium faciunt, longe a denario minorem. Similis est huic octonarius, vel alii plurimi qui in partes redacti infra consistunt.

[10] Deficient numbers are those which, computed by their parts, make a lesser sum, for instance the ten, whose parts are three: the tenth, which is one; the fifth, which two; the half, which five. For one and two and five, taken together, make eight, far less than the ten. Similar to this is the eight, as also very many others which, when reduced into parts, fall short.

[11] Perfectus numerus est, qui suis partibus adinpletur, ut senarius; habet enim tres partes, sextam, tertiam, [et] dimidiam: sexta eius unum est, tertia duo, dimidia tres. Haec partes in summam ductae, id est unum et duo et tria simul eundem consummant perficiuntque senarium. Sunt autem perfecti numeri intra denarium VI, intra centenarium XXVIII, intra millenarium CCCCXCVI.

[11] A perfect number is that which is filled up by its own parts, as the senary (six); for it has three parts, the sixth, the third, and the half: its sixth is one, its third two, its half three. These parts, led into a sum—that is, one and two and three together—consummate and perfect the same six. Now the perfect numbers within ten are 6, within one hundred 28, within one thousand 496.

VI. DE SECVNDA DIVISIONE TOTIVS NVMERI.

6. ON THE SECOND DIVISION OF THE WHOLE NUMBER.

[1] Omnis numerus (1) aut secundum se consideratur, (2) aut ad aliquid. (1) Iste dividitur sic: alii enim sunt aequales, alii inaequales. (2) Iste dividitur sic: alii sunt maiores, alii sunt minores.

[1] Every number (1) either is considered according to itself, (2) or in relation to something. (1) This is divided thus: some are equal, others unequal. (2) This is divided thus: some are greater, others lesser.

Maiores dividuntur sic: multiplices, superparticulares, superpartientes, multiplices superparticulares, multiplices superpartientes. Minores dividuntur sic: submultiplices, subsuperparticulares, subsuperpartientes, submultiplices subsuperparticulares, submultiplices subsuperpartientes.

The greater are divided thus: multiple, superparticular, superpartient, multiple superparticular, multiple superpartient. The lesser are divided thus: submultiple, subsuperparticular, subsuperpartient, submultiple subsuperparticular, submultiple subsuperpartient.

[2] Per se numerus est, qui sine relatione aliqua dicitur, ut III. IV. V. VI, et ceteri similes. Ad aliquid numerus est, qui relative ad alios conparatur; ut verbi gratia IV ad II dum conparatus fuerit, duplex dicitur [et multiplex], VI ad III, VIII ad IV, X ad V; et iterum III ad unum triplex, VI ad II, IX ad III et ceteri.

[2] A number in itself is that which is said without any relation, as 3. 4. 5. 6, and other similar ones. A number in relation is that which is compared relatively to others; for example, when 4 has been compared to 2, it is called double [and multiple], 6 to 3, 8 to 4, 10 to 5; and again 3 to 1 is triple, 6 to 2, 9 to 3, and the rest.

[3] Aequales numeri dicuntur, qui secundum quantitatem aequales sunt, ut verbi gratia II ad II, III ad III, X ad X, C ad C. Inaequales numeri sunt, qui ad invicem conparati inaequalitatem demonstrant, ut III ad II, IV ad III, V ad IV, X ad VI; et universaliter maior minori aut minor maiori huiusmodi dum conparatus fuerit, inaequalis dicitur.

[3] Equal numbers are said to be those which are equal according to quantity, as, for example, 2 to 2, 3 to 3, 10 to 10, 100 to 100. Unequal numbers are those which, when compared to one another, demonstrate inequality, as 3 to 2, 4 to 3, 5 to 4, 10 to 6; and universally, when the greater is compared to the lesser or the lesser to the greater in this manner, it is called unequal.

[4] Maior numerus est, qui habet in se illum minorem numerum, ad quem conparatur, et aliquid plus; ut verbi gratia quinarius numerus trinario numero fortior est, eo quod habet quinarius numerus in se trinarium numerum et alias partes eius duas, et reliqui tales.

[4] A greater number is that which has within itself that lesser number to which it is compared, and something more; for example, the quinary number is stronger than the ternary number, because the quinary number has within itself the ternary number and two other parts of it, and the rest are such.

[5] [Minor numerus est, qui continetur a maiori, ad quem conparatur, cum aliqua parte sui, ut ternarius ad quinarium. Continetur enim ab eo cum duabus partibus suis.] Multiplex numerus est, qui habet in se minorem numerum bis, aut ter, aut quater, aut multipliciter; ut verbi gratia II ad unum dum conparati fuerint, duplex est; III ad unum, triplex; IV quadruplex, et reliqui.

[5] [A lesser number is that which is contained by the greater, to which it is compared, together with some part of itself, as the ternary to the quinary. For it is contained by it with two of its own parts.] A multiple number is that which has within itself the lesser number twice, or thrice, or four times, or multiply; for example, 2 to one, when compared, is double; 3 to one, triple; 4 to one, quadruple; and the rest.

[6] Econtra submultiplex numerus est, qui intra multiplicem continetur bis, aut ter, aut quater, aut multipliciter; ut verbi gratia unus a II bis continetur, a III ter, a IV quater, a V quinquies, et ab aliis multipliciter.

[6] Conversely, a submultiple number is that which is contained within a multiple twice, or thrice, or four times, or manifoldly; for example, one is contained by 2 twice, by 3 thrice, by 4 four times, by 5 five times, and by others manifoldly.

[7] Superparticularis numerus est, dum fortior continet intra se inferiorem numerum, circa quem conparatur, similiter et unam partem eius; ut verbi gratia III ad II dum conparati fuerint, continent intra se II et alium unum, qui media pars est duorum; IV ad III dum conparati fuerint, continent in se III, et alium unum, qui est tertia pars trium. Iterum V ad IV dum conparati fuerint, habent in se quaternarium numerum, et alium unum, qui quarta pars esse dicitur quaternarii numeri, et ceteri tales.

[7] A superparticular number is, when the stronger contains within itself the lower number, with respect to which it is compared, and likewise one part of it; for example, when 3 to 2 have been compared, they contain within themselves 2 and another 1, which is the half of two; when 4 to 3 have been compared, they contain in themselves 3 and another 1, which is a third part of three. Again, when 5 to 4 have been compared, they have in themselves the number 4, and another 1, which is said to be the fourth part of the quaternary number, and others of this kind.

[8] Superpartiens numerus est, qui in se inferiorem numerum totum continet, et super hoc alteras partes eius II, aut III, aut IV, aut V, aut alias; ut verbi gratia V ad III dum conparati fuerint, habent in se quinarius numerus trinarium, et super hoc alias partes eius II; VII ad IV dum conparati fuerint, habent in se IV, et alias III partes eius; IX ad V dum conparati fuerint, habent in se V, et alias IV partes eius.

[8] A superpartient number is that which contains within itself the whole lower number, and over and above this other parts of it 2, or 3, or 4, or 5, or others; for example, when 5 to 3 have been compared, the quinary number has the ternary within itself, and over this other 2 of its parts; when 7 to 4 have been compared, they have within themselves 4, and other 3 of its parts; when 9 to 5 have been compared, they have within themselves 5, and other 4 of its parts.

[9] Subsuperpartiens numerus est, qui continetur in numero superpartienti cum aliquibus partibus suis duabus aut tribus aut pluribus; [ut] verbi gratia III continentur a V cum aliis II partibus suis; V a IX cum IV partibus suis.

[9] A subsuperpartient number is that which is contained in a superpartient number together with some of its own parts, two or three or more; [as], for example, 3 is contained by 5 with a further 2 of its parts; 5 by 9 with 4 of its parts.

[10] Subsuperparticularis numerus est minor, qui continetur in fortiori numero cum alia una parte sua, aut media, aut tertia, aut quarta, aut quinta; ut verbi gratia II ad III, III ad IV, IV ad V, et ceteri.

[10] The subsuperparticular number is the lesser, which is contained in the stronger (greater) number together with one other part of itself, whether the half, or the third, or the fourth, or the fifth; for example, 2 to 3, 3 to 4, 4 to 5, and the rest.

[11] Multiplex superparticularis numerus est, qui, dum conparatus ad inferiorem sibi numerum fuerit, continet in se totum inferiorem numerum multipliciter cum aliqua parte eius; ut verbi gratia V ad II dum conparati fuerint, continent in se bis II, IV, et unam partem eius; IX ad IV dum conparati fuerint, continent in se bis IV, VIII, et unam partem eius.

[11] A multiple superparticular number is that which, when compared to the number inferior to itself, contains within itself the whole inferior number, multiplied, together with some part of it; for example, 5 to 2, when they have been compared, contain within themselves twice 2, 4, and one part of it; 9 to 4, when they have been compared, contain within themselves twice 4, 8, and one part of it.

[12] [Submultiplex [sub]superparticularis numerus est qui, dum ad fortiorem sibi numerum conparatus fuerit, continetur ab eo multipliciter cum alia una parte sua; ut verbi gratia II ad V dum conparati fuerint, continentur ab eo bis cum una parte sua.] Multiplex superpartionalis numerus est, qui dum conparatus ad inferiorem sibi numerum fuerit, continet eum multipliciter cum aliis partibus eius; ut verbi gratia VIII ad III dum conparati fuerint, continent in se bis III, cum aliis II partibus eius; XIV ad VI dum conparati fuerint, continent intra se bis VI cum aliis II partibus eius; [XVI ad VII dum conparati fuerint, continent eum bis cum aliis II partibus eius; XXI ad IX dum conparati fuerint, continent intra se bis IX cum aliis III partibus eius].

[12] [A submultiple [sub]superparticular number is that which, when compared to a stronger number than itself, is contained by it multiply with one other of its parts; for example, 2 to 5 when they have been compared, are contained by it twice with one of its parts.] A multiple superpartient number is that which, when compared to a lower number than itself, contains it multiply with other parts of it; for example, 8 to 3 when they have been compared, contain within themselves twice 3, with two other parts of it; 14 to 6 when they have been compared, contain within themselves twice 6 with two other parts of it; [16 to 7 when they have been compared, contain it twice with two other parts of it; 21 to 9 when they have been compared, contain within themselves twice 9 with three other parts of it].

[13] Submultiplex superpartionalis numerus est, qui dum ad fortiorem sibi conparatus fuerit, continetur ab eo multipliciter cum aliquibus partibus suis; ut verbi gratia III ad VIII continentur bis cum II partibus suis; IV ad XI continentur bis cum III partibus suis.

[13] The submultiple superpartional number is that which, when compared to a stronger number than itself, is contained by it multiply together with some of its parts; as, for example, 3 to 8 are contained twice with its 2 parts; 4 to 11 are contained twice with its 3 parts.

VII. DE TERTIA DIVISIONE TOTIVS NVMERI.

7. ON THE THIRD DIVISION OF THE WHOLE NUMBER.

[1] Numeri (1) aut discreti sunt, (2) aut continentes. Iste dividitur sic: (1) lineales, (2) superficiosi, (3) solidi. Discretus numerus est, qui a discretis monadibus continetur, ut verbi gratia III.

[1] Numbers (1) are either discrete, (2) or continuous. The latter is divided thus: (1) linear, (2) superficial, (3) solid. A discrete number is that which is composed of discrete monads, for example 3.

IV. V. VI. et reliqui.

4. 5. 6. and the rest.

[2] Continens numerus est, qui coniunctis monadibus continetur; [ut] verbi gratia ternarius numerus in magnitudine intellegatur, id est in linea, aut spatium aut solidum dicitur continens: similiter quaternarius et quinarius numeri.

[2] A continuous number is that which is contained by conjoined monads; [as] for example, let the ternary number be understood in magnitude, that is, in a line, or a space or a solid is called continuous: similarly the quaternary and quinary numbers.

[3] Linealis numerus est, qui inchoans a monade linealiter scribitur usque ad infinitum. Vnde alpha ponitur pro designatione linearum, quoniam haec littera unum significat apud Graecos (sequitur figura).

[3] A lineal number is that which, beginning from the monad, is written lineally up to infinity. Whence alpha is set for the designation of lines, since this letter signifies one among the Greeks (the figure follows).

[4] Superficialis numerus est, qui non solum longitudine, sed et latitudine continetur, ut trigonus, quadratus, quinqueangulus vel circulatus numeri, et ceteri, qui semper in plano pede, id est superficie continentur. Trigonus numerus est ita (seq. figura). Quadratus numerus est ita (seq.

[4] A superficial number is that which is contained not only by length but also by breadth, such as trigonal, quadrate, quinquangular, or circular numbers, and the rest, which are always contained on a flat footing, that is, on a surface. A trigonal number is thus (figure follows). A quadrate number is thus (follows

figura). Quinqueangulus ita (seq. figura).

figure). Five-angled thus (the figure follows).

[5] Circularis numerus est ita, qui dum similiter multiplicatus fuerit, a se inchoans ad se convertitur, ut verbi gratia quinquies quini XXV, ita (seq. figura). Solidus numerus est, qui longitudine et latitudine vel altitudine continetur, ut sunt pyramides, qui in modum flammae consurgunt, ita (seq. figura).

[5] A circular number is thus: which, when it has been similarly multiplied, beginning from itself it is turned back to itself, for example, five times five 25, thus (seq. figura). A solid number is that which is contained by length and breadth or height, as are pyramids, which rise in the manner of a flame, thus (seq. figura).

[6] Cubus, ut sunt tesserae, ita (seq. figura). Sphaerae, quibus est aequalis undique rotunditas, ita (seq. figura). Sphaericus autem numerus est, qui a circulato numero multiplicatus a se inchoat et in se convertitur.

[6] The cube, as dice are, thus (the figure follows). Spheres, which have an equal roundness on every side, thus (the figure follows). But a spherical number is that which, when multiplied by the circular number, begins from itself and turns back into itself.

Quinquies quini XXV. Hic circulus dum in se ipsum multiplicatus fuerit, facit sphaeram, id est quinquies XXV CXXV.

Five times five is 25. This circle, when it has been multiplied into itself, makes a sphere, that is, five times 25 is 125.

VIII. DE DIFFERENTIA ARITHMETICAE, GEOMETRIAE ET MVSICAE.

8. ON THE DIFFERENCE OF ARITHMETIC, GEOMETRY, AND MUSIC.

[1] Inter Arithmeticam [autem] et Geometriam et Musicam hoc interest, ut media invenias. In Arithmetica primo sic quaeris. Coniungis extrema, et dividis, et facis medium: utputa fac extrema esse VI et XII, simul iungis et faciunt X et VIII: partiris media et facis IX, quod est analogicum arithmeticae, ut medius quot monadibus superat primum, his superetur ab extremo.

[1] Between Arithmetic [however] and Geometry and Music this is the difference: that you find the means. In Arithmetic first you inquire thus. You join the extremes, and you divide, and you make the mean: for example, make the extremes be 6 and 12; you join them together and they make 18; you halve them and you make 9, which is arithmetical, namely that the middle exceeds the first by as many monads as it is exceeded by the last.

Superant enim IX VI tribus monadibus, his superatur a XII.

For 9 surpasses 6 by three monads, and by these it is surpassed by 12.

[2] Secundum geometriam vero ita quaeris. Extrema multiplicata tantum faciunt, quantum et media duplicata, utputa VI et XII multiplicata facient septuagies dipondius, media VIII et IX multiplicata tantundem faciunt.

[2] According to geometry, indeed, thus you inquire. The extremes, when multiplied, make as much as likewise the means taken twofold (as a pair), for example 6 and 12, when multiplied, will make 72, the means 8 and 9, when multiplied, make just as much.

[3] Secundum musicam ita: Qua parte superat medius primum, eadem parte superatur medius ab extremo. Vtputa VI et VIII; duabus partibus superant, quae duae partes tertia media, VII[I], superatur ab ultima nona.

[3] According to music thus: By whatever part the mean surpasses the first, by the same part the mean is surpassed by the last. For example 6 and 8; they surpass by two parts, which two parts are a third; the mean, 7[1], is surpassed by the last, the ninth.

IX. QVOT NVMERI INFINITI EXISTVNT.

9. HOW MANY INFINITE NUMBERS EXIST.

[1] Numeros autem infinitos esse certissimum est, quoniam in quocumque numero finem faciendum putaveris, idem ipse non dico uno addito augeri, sed quamlibet sit magnus, et quamlibet ingentem multitudinem continens, in ipsa ratione atque scientia numerorum non solum duplicari, verum etiam multiplicari potest.

[1] That numbers are infinite is most certain, since at whatever number you think an end ought to be made, that very same number—I do not merely say increased by adding one—but however great it may be, and however immense a multitude it contains, can, in the very rationale and science of numbers, not only be duplicated but even multiplied.

[2] Ita vero suis quisque numerus proprietatibus terminatur, ut nullus eorum par esse cuicumque alteri possit. Ergo et dispares inter se atque diversi sunt, et singuli quique finiti sunt, et omnes infiniti sunt.

[2] Thus indeed each number is terminated by its own properties, so that none of them can be equal to any other. Therefore they are disparate among themselves and diverse, and each individual is finite, and all are infinite.

X. DE INVENTORIBVS GEOMETRIAE ET VOCABVLO EIVS.

10. ON THE INVENTORS OF GEOMETRY AND ITS VOCABLE.

[1] Geometriae disciplina primum ab Aegyptiis reperta dicitur, quod, inundante Nilo et omnium possessionibus limo obductis, initium terrae dividendae per lineas et mensuras nomen arti dedit. Quae deinde longius acumine sapientium profecta et maris et caeli et aeris spatia metiuntur.

[1] The discipline of geometry is said to have been first discovered by the Egyptians, because, when the Nile overflowed and the possessions of all were overlaid with mud, the beginning of dividing the land by lines and measures gave the art its name. Which then, having advanced further by the acumen of the wise, measures the spaces of sea and sky and air.

[2] Nam provocati studio sic coeperunt post terrae dimensionem et caeli spatia quaerere: quanto intervallo luna a terris, a luna sol ipse distaret, et usque ad verticem caeli quanta se mensura distenderet, sicque intervalla ipsa caeli orbisque ambitum per numerum stadiorum ratione probabili distinxerunt.

[2] For, provoked by zeal, thus they began after the measurement of the earth to inquire also into the spaces of the sky: by what interval the moon was distant from the lands, from the moon the sun itself, and by how great a measure it extended itself up to the summit of the sky; and thus they distinguished the intervals themselves of the heaven and the circuit of the orb by the number of stadia, with probable reason.

[3] Sed quia ex terrae dimensione haec disciplina coepit, ex initio sui et nomen servavit. Nam geometria de terra et de mensura nuncupata est. Terra enim Graece GE vocatur, METRA mensura.

[3] But since from the dimension of the earth this discipline began, from its beginning it also preserved the name. For geometry is named from earth and from measure. For earth in Greek is called GE, METRA measure.

Huius disciplinae ars continet in se lineamenta, intervalla, magnitudines et figuras, et in figuris dimensiones et numeros.

The art of this discipline contains within itself lineaments, intervals, magnitudes and figures, and in the figures dimensions and numbers.

XI. DE QVADRIPERTITA DIVISIONE GEOMETRIAE.

11. ON THE QUADRIPARTITE DIVISION OF GEOMETRY.

[1] Geometriae quadripertita divisio est, in planum, in magnitudinem numerabilem, in magnitudinem rationalem, et in figuras solidas.

[1] The quadripartite division of geometry is: into the plane, into numerable magnitude, into rational magnitude, and into solid figures.

[2] Planae figurae sunt, quae longitudine et latitudine continentur, quae sunt iuxta Platonem numero quinque. Numerabilis magnitudo est, quae numeris arithmeticae dividi potest.

[2] Plane figures are those which are contained by length and breadth, which, according to Plato, are five in number. A numerable magnitude is that which can be divided by the numbers of arithmetic.

[3] Magnitudines rationales sunt, quorum mensuram scire possumus, inrationales vero, quorum mensurae quantitas cognita non habetur.

[3] Rational magnitudes are those whose measure we can know, but irrational, on the other hand, are those whose quantity of measure is not held as known.

XII. DE FIGVRIS GEOMETRIAE.

12. ON THE FIGURES OF GEOMETRY.

[1] Figurae solidae sunt, quae longitudine, latitudine et altitudine continentur, ut est cubus, cuius species quinque in plano. Quarum prima circulus est figura plana, quae vocatur circumducta; cuius in medio punctus est, quo cuncta convergunt, quod centrum geometriae vocant, Latini punctum circuli nuncupant (sequitur figura).

[1] Solid figures are those which are contained by length, latitude, and altitude, as is the cube, whose species are five on the plane. Of these the first is the circle, a plane figure, which is called circumducted; in the middle of which there is a point, to which all things converge, which they call the center of geometry; the Latins name it the point of the circle (a figure follows).

[2] Quadrilatera figura est in plano quadrata; quae sub quattuor rectis lineis iacet, ita (seq. figura). Dianatheton grammon figura plana, [ita] (seq. figura). Orthogonium, id est rectiangulum figura plana.

[2] A quadrilateral is a figure squared in the plane; which lies under four straight lines, thus (seq. figura). Dianatheton grammon, a plane figure, [thus] (seq. figura). Orthogonium, that is, a rectangle, a plane figure.

Est enim triangulum et habet angulum rectum (seq. figura). Isopleuros figura plana, recta et subter constituta (seq. figura).

For it is a triangle and has a right angle (figure follows). Isopleuros is a plane figure, straight and constituted beneath (figure follows).

[3] Sphaera est figura in rotundum formata, partibus cunctis aequalis (seq. figura). Cubus est figura propria solida, quae longitudine, latitudine et altitudine continetur (seq. figura).

[3] A sphere is a figure formed into the round, equal in all its parts (seq. figura). A cube is a proper solid figure, which is contained by length, breadth, and height (seq. figura).

[4] Cylindrus est figura quadrata, habens superius semicirculum (seq. figura).

[4] A cylinder is a quadrate figure, having above a semicircle (see figure).

[5] Conon, figura quae ab amplo in angustum finit, sicut orthogonium (seq. figura).

[5] Cone, a figure which tapers from the ample into the narrow, like an orthogonium (following figure).

[6] Pyramis est figura, quae in modum ignis ab amplo in acumen consurgit; ignis enim apud Graecos PUR appellatur (seq. figura).

[6] A pyramid is a figure which, in the manner of fire, rises from broad to a point; for fire among the Greeks is called PUR (the figure follows).

[7] Sicut autem infra X omnis est numerus, ita intra hunc circulum omnium figurarum concluditur ambitus (seq. figura). Prima autem figura huius artis punctus est, cuius pars nulla est. Secunda linea, praeter latitudinem longitudo.

[7] And just as every number is within 10, so within this circle the ambit of all figures is enclosed (seq. figura). But the first figure of this art is the point, which has no part. The second is the line, length without breadth.

Recta linea est, quae ex aequo in suis punctis iacet. Superficies vero, quod longitudines et latitudines solas habet. Superficiei vero fines lineae sunt, quorum formae ideo in superioribus decem figuris positae non sunt, quia inter eas inveniuntur.

A straight line is that which lies evenly with respect to its points. A surface, moreover, is that which has lengths and breadths only. But the boundaries of a surface are lines, the forms of which for that reason were not set among the ten figures above, because they are found among them.

XIII. DE NVMERIS GEOMETRIAE.

13. ON THE NUMBERS OF GEOMETRY.

[1] Numeros autem secundum Geometriam ita quaeris. Extrema quippe eius multiplicata tantum faciunt, quantum et media duplicata: utputa VI et XII multiplicata faciunt septuagies dipondius, media VIII et IX multiplicata tantundem faciunt.

[1] But you inquire about numbers according to Geometry thus: indeed, the extremes of it, when multiplied, make as much as the means taken as a pair: for example, 6 and 12, when multiplied, make seventy-two; the means, 8 and 9, when multiplied, make the same amount.

[XIV. EXPOSITIO FIGVRARVM INFRA SCRIPTARVM.

[14. EXPOSITION OF THE FIGURES WRITTEN BELOW.

[1] Alia ratio in motu stellarum similiter octo figuris colligitur: aut quod diametra sint aut quadrata aut trigona aut hexagona aut asyndeta aut simul aut circumferens, id est superferens aut superfertur. Diametra sunt quando quinque signa intersunt. Tetragona, quando duo.

[1] Another reckoning in the motion of the stars likewise is collected by eight figures: either that they are diametral, or quadrate, or trigonal, or hexagonal, or asyndetic, or together, or circumferent, that is superferent, or are superborne. Diametral they are when five signs intervene. Tetragonal, when two.

Hexagona, quando unum. Asyndeton, quando nullum. Simul, quando in eadem particula sunt.

Hexagonal, when one. Asyndeton, when none. Simultaneous, when they are in the same part.

Superferens, quando supervenit aut actum facit. Superfertur quando antecedit. Trigona, quando tria media.

Superferens, when it supervenes or brings the act to completion. Superfertur, when it precedes. Trigons, when there are three intervening.

[2] Item secundum rationem aliam sunt octo differentiae, id est: signum, partes, fines, conventu, retrogradu an recto itinere, latitudo et longitudo.

[2] Likewise, according to another rationale, there are eight differences, that is: sign, parts, limits, conjunction, by retrograde or by straight course, latitude and longitude.

[3] Ratio interioris formae. Posset huius loci talis quaestio nasci. Cum in ordine numeri prius VIII sint, hic prius IX posuit, quoniam in ratione arithmeticae vel geometriae plus sunt VIII quam IX. VIII enim cubus est vel solidum, id est corpus quod plus invenire non potest.

[3] Rationale of the inner form. Such a question could arise about this place: since in the order of numbers 8 come earlier, here he has set 9 first, because in the rationale of arithmetic or geometry 8 are greater than 9. For 8 is a cube or a solid, that is, a body beyond which nothing more can be found.

IX vero superficies sunt, id est res quae plena non est, sed indigeat perfectionem.

9, however, are surfaces, that is, a thing which is not full, but stands in need of perfection.

[4] Hic duo cubi, id est duae soliditates, hoc modo inveniuntur. Senarius primus perfectus est; dividitur enim paribus numeris sic: sexta per as; in tertia per dupondios; ter bini, sex; in dimidium, id est bis terni, sex. Aliud quod ita dividas per pares numeros invenies, quod a proposito conveniens sit.

[4] Here two cubes, that is, two solidities, are found in this way. The senary (six) is the first perfect [number]; for it is divided by equal numbers thus: in a sixth by asses (ones); in a third by dupondii (twos); three times two, six; in the half, that is, twice three, six. You will find another thing which you may thus divide by equal numbers, which will be suitable to the proposed purpose.

[5] Inter primum in ordine, id est X, qui propter primum perfectum numerum cum primo versu multiplicans sexies noveni, LIV; novies seni, LIV. ÝFacitque materia tot partes habuisse cognoscitur non inmerito duobus,Ý (e) quibus habet unum in tali ordine: I, II, III, IV, IX, VIII, alios simul XXVII.]

[5] Among the first in the order, that is 10, which, on account of the first perfect number, multiplying with the first line: six times nine, 54; nine times six, 54. ÝAnd so the material is known to have had so many parts, not without merit by two,Ý (from) which it has one in such an order: 1, 2, 3, 4, 9, 8, others together 27.]

DE MVSICA

ON MUSIC

XV. DE MVSICA ET EIVS NOMINE.

15. ON MUSIC AND ITS NAME.

[1] Musica est peritia modulationis sono cantuque consistens. Et dicta Musica per derivationem a Musis. Musae autem appellatae APO TOU MASAI, id est a quaerendo, quod per eas, sicut antiqui voluerunt, vis carminum et vocis modulatio quaereretur.

[1] Music is expertise of modulation, consisting in sound and song. And it is called Music by derivation from the Muses. The Muses, moreover, are named APO TOU MASAI, that is, from seeking, because through them, as the ancients wished, the force of songs and the modulation of the voice were sought.

[2] Quarum sonus, quia sensibilis res est, praeterfluit in praeteritum tempus, inprimiturque memoriae. Inde a poetis Iovis et Memoriae filias Musas esse confictum est. Nisi enim ab homine memoria teneantur soni, pereunt, quia scribi non possunt.

[2] The sound of which, because it is a sensible thing, flows past into past time, and is imprinted upon memory. Hence it has been fashioned by the poets that the Muses are the daughters of Jove and Memory. For unless sounds are held by human memory, they perish, because they cannot be written.

XVI. DE INVENTORIBVS EIVS.

16. ON ITS INVENTORS.

[1] Moyses dicit repertorem musicae artis fuisse Tubal, qui fuit de stirpe Cain ante diluvium. Graeci vero Pythagoram dicunt huius artis invenisse primordia ex malleorum sonitu et cordarum extensione percussa. Alii Linum Thebaeum et Zetum et Amphion in musica arte primos claruisse ferunt.

[1] Moses says the discoverer of the musical art was Tubal, who was of the stock of Cain before the Deluge. The Greeks, however, say that Pythagoras discovered the primordia of this art from the sound of hammers and from the extension of strings when struck. Others report that Linus the Theban and Zetus and Amphion were the first to shine in the musical art.

[2] Post quos paulatim directa est praecipue haec disciplina et aucta multis modis, eratque tam turpe Musicam nescire quam litteras. Interponebatur autem non modo sacris, sed et omnibus sollemnibus, omnibusque laetis, vel tristioribus rebus.

[2] After whom this discipline was gradually set in order especially and augmented in many ways, and it was as shameful not to know Music as letters. Moreover, it was interposed not only in sacred rites, but also in all solemnities, and in all joyful, or more sorrowful, affairs.

[3] Vt enim in veneratione divina hymni, ita in nuptiis Hymenaei, et in funeribus threni, et lamenta ad tibias canebantur. In conviviis vero lyra vel cithara circumferebatur, et accubantibus singulis ordinabatur conviviale genus canticorum.

[3] For just as, in divine veneration, there were hymns, so at weddings, Hymenaeals, and at funerals, threnodies; and laments were sung to the pipes. At banquets, indeed, the lyre or cithara was carried around, and for each of those reclining in turn a convivial kind of songs was arranged.

XVII. QVID POSSIT MVSICA.

17. WHAT MUSIC CAN DO.

[1] Itaque sine Musica nulla disciplina potest esse perfecta, nihil enim sine illa. Nam et ipse mundus quadam harmonia sonorum fertur esse conpositus, et coelum ipsud sub harmoniae modulatione revolvi. Musica movet affectus, provocat in diversum habitum sensus.

[1] And so without Music no discipline can be perfect, for nothing is without her. For the world itself is said to be composed by a certain harmony of sounds, and the heaven itself to be revolved under the modulation of harmony. Music moves the affections, it provokes the senses into a different disposition.

[2] In proeliis quoque tubae concentus pugnantes accendit, et quanto vehementior fuerit clangor, tanto fit ad certamen animus fortior. Siquidem et remiges cantus hortatur, ad tolerandos quoque labores musica animum mulcet, et singulorum operum fatigationem modulatio vocis solatur.

[2] In battles too the concert of trumpets enkindles the combatants, and the more vehement the clangor is, by so much the stronger the spirit becomes for the contest. Indeed, song exhorts the rowers; music also soothes the mind for bearing labors, and the modulation of the voice consoles the fatigue of individual works.

[3] Excitos quoque animos musica sedat, sicut de David legitur, qui ab spiritu inmundo Saulem arte modulationis eripuit. Ipsas quoque bestias, necnon et serpentes, volucres atque delphinas ad auditum suae modulationis musica provocat. Sed et quidquid loquimur, vel intrinsecus venarum pulsibus commovemur, per musicos rhythmos harmoniae virtutibus probatur esse sociatum.

[3] Music also soothes aroused spirits, as is read about David, who by the art of modulation rescued Saul from an unclean spirit. Music even provokes the very beasts, and likewise serpents, birds, and dolphins to the hearing of its modulation. But also whatever we speak, or when we are inwardly stirred by the pulses of the veins, is proved to be associated, through musical rhythms, with the virtues of harmony.

XVIII. DE TRIBVS PARTIBVS MVSICAE.

18. ON THE THREE PARTS OF MUSIC.

[1] Musicae partes sunt tres, id est, harmonica, rhythmica, metrica. Harmonica est, quae decernit in sonis acutum et gravem. Rhythmica est, quae requirit incursionem verborum, utrum bene sonus an male cohaereat.

[1] The parts of music are three, that is, harmonic, rhythmic, metric. Harmonic is that which determines in sounds the acute and the grave. Rhythmic is that which requires the incursion of words, whether the sound cohere well or ill.

[2] Metrica est, quae mensuram diversorum metrorum probabili ratione cognoscit, ut verbi gratia heroicon, iambicon, elegiacon, et cetera.

[2] The metrical is that which, by a probable rationale, recognizes the measure of diverse meters, as, for example, the heroic, iambic, elegiac, and the rest.

XIX. DE TRIFORMI MVSICAE DIVISIONE.

19. ON THE TRIFORM DIVISION OF MUSIC.

[1] Ad omnem autem sonum, quae materies cantilenarum est, triformem constat esse naturam. Prima est harmonica, quae ex vocum cantibus constat. Secunda organica, quae ex flatu consistit.

[1] Now as to every sound, which is the material of songs, it is agreed to have a threefold nature. The first is harmonica, which consists of the songs of voices. The second is organica, which consists by breath.

Tertia rhythmica, quae pulsu digitorum numeros recipit.

The third is rhythmical, which receives numbers by the tapping of the fingers.

[2] Nam aut voce editur sonus, sicut per fauces, aut flatu, sicut per tubam vel tibiam, aut pulsu, sicut per citharam, aut per quodlibet aliud, quod percutiendo canorum est.

[2] For sound is produced either by the voice, as through the throat, or by breath, as through the tuba or the tibia, or by striking, as through the cithara, or through whatever other thing which, by being struck, is canorous.

XX. DE PRIMA DIVISIONE MVSICAE QVAE HARMONICA DICITVR.

20. ON THE FIRST DIVISION OF MUSIC WHICH IS CALLED HARMONIC.

[1] Prima divisio Musicae, quae harmonica dicitur, id est, modulatio vocis, pertinet ad comoedos, tragoedos, vel choros, vel ad omnes qui voce propria canunt. Haec ex animo et corpore motum facit, et ex motu sonum, ex quo colligitur Musica, quae in homine vox appellatur.

[1] The first division of Music, which is called harmonica, that is, the modulation of the voice, pertains to comic actors, tragic actors, or choruses, or to all who sing with their own voice. This makes motion from mind and body, and from motion sound, from which Music is gathered, which in a human is called voice.

[2] Vox est aer spiritu verberatus, unde et verba sunt nuncupata. Proprie autem vox hominum est, seu inrationabilium animantium. Nam in aliis abusive non proprie sonitum vocem vocari, ut: 'vox tubae infremuit', (Virg.

[2] Voice is air beaten by spirit/breath, whence even words are named. Properly, however, voice belongs to human beings, or to irrational animals. For in other things, abusively and not properly, a sound is called a voice, as: 'the voice of the trumpet roared,' (Verg.

Aen. 3,556):

Aeneid 3,556):

Fractasque ad litore voces.

And the voices fractured at the shore.

Nam proprium est ut litorei sonent scopuli, et (Virg. Aen. 9,503):

For it is characteristic that littoral crags resound, and (Virgil, Aeneid 9,503):

At tuba terribilem sonitum procul aere canoro.

But the trumpet, with sonorous bronze, gave forth a terrible sound from afar.

Harmonia est modulatio vocis, et concordantia plurimorum sonorum, vel coaptatio.

Harmony is modulation of the voice, and concordance of very many sounds, or coaptation.

[3] Symphonia est modulationis temperamentum ex gravi et acuto concordantibus sonis, sive in voce, sive in flatu, sive in pulsu. Per hanc quippe voces acutiores gravioresque concordant, ita ut quisquis ab ea dissonuerit, sensum auditus offendat. Cujus contraria est diaphonia, id est voces discrepantes, vel dissonae.

[3] Symphony is the tempering of modulation from grave and acute, concordant sounds, whether in voice, or in breath, or in beating. Through this, indeed, the sharper and the graver voices concord, such that whoever departs from it into dissonance offends the sense of hearing. Its contrary is diaphony, that is, discrepant, or dissonant, voices.

[4] Euphonia est suavitas vocis. Haec et melos a suavitate et melle dicta.

[4] Euphony is the sweetness of the voice. This and melos are said to be named from sweetness and honey.

[5] Diastema est vocis spatium ex duobus vel pluribus sonis aptatum.

[5] Diastema is the interval of the voice adapted from two or more sounds.

[6] Diesis est spatia quaedam et deductiones modulandi atque vergentes de uno in altero sono.

[6] A diesis is certain spaces and leadings of modulation, and inclinations from one sound into another.

[7] Tonus est acuta enuntiatio vocis. Est enim harmoniae differentia et quantitas, quae in vocis accentu vel tenore consistit: cuius genera in quindecim partibus musici dividerunt, ex quibus hyperlydius novissimus et acutissimus, hypodorius omnium gravissimus.

[7] Tone is an acute enunciation of the voice. For it is a difference and a quantity of harmony, which consists in the voice’s accent or tenor: whose kinds the musicians divided into fifteen parts, of which the Hyper-Lydian is the last and most acute, the Hypo-Dorian the gravest of all.

[8] Cantus est inflexio vocis, nam sonus directus est; praecedit autem sonus cantum.

[8] Chant is an inflection of the voice, for sound is direct; however, sound precedes chant.

[9] Arsis est vocis elevatio, hoc est initium. Thesis vocis positio, hoc est finis.

[9] Arsis is the elevation of the voice, that is, the beginning. Thesis is the position of the voice, that is, the end.

[10] Suaves voces sunt subtiles et spissae, clarae atque acutae. Perspicuae voces sunt, quae longius protrahuntur, ita ut omnem inpleant continuo locum, sicut clangor tubarum.

[10] Sweet voices are subtle and thick, clear and sharp. Perspicuous voices are those which are prolonged farther, such that they fill the whole place continuously, just like the clangor of trumpets.

[11] Subtiles voces sunt, quibus non est spiritus, qualis est infantium, vel mulierum, vel aegrotantium, sicut in nervis. Quae enim subtilissimae cordae sunt, subtiles ac tenues sonos emittunt.

[11] Subtle voices are those that lack breath, such as that of infants, or of women, or of the sick, as on strings. For the strings that are most subtle emit subtle and tenuous sounds.

[12] Pingues sunt voces, quando spiritus multus simul egreditur, sicut virorum. Acuta vox tenuis, alta, sicut in cordis videmus. Dura vox est, quae violenter emittit sonos, sicut tonitruum, sicut incudis sonus, quotiens in durum malleus percutitur ferrum.

[12] Voices are full(-bodied) when much breath goes out at once, as with men. An acute voice is thin, high, as we see on strings. A hard voice is one that emits sounds forcibly, like thunder, like the sound of the anvil, whenever the hammer strikes hard iron.

[13] Aspera vox est rauca, et quae dispergitur per minutos et indissimiles pulsus. Caeca vox est, quae, mox emissa fuerit, conticescit, atque suffocata nequaquam longius producitur, sicut est in fictilibus. Vinnola est vox mollis atque flexibilis.

[13] A rough voice is hoarse, and one that is dispersed through minute and dissimilar pulses. A blind voice is one which, as soon as it has been emitted, falls silent, and, being suffocated, is by no means prolonged farther, as it is in earthenware. Vinnola is a voice soft and flexible.

Et vinnola dicta a vinno, hoc est cincinno molliter flexo.

And “vinnola” is said from “vinno,” that is, from a curl gently flexed.

[14] Perfecta autem vox est alta, suavis et clara: alta, ut in sublime sufficiat; clara, ut aures adinpleat; suavis, ut animos audientium blandiat. Si ex his aliquid defuerit, vox perfecta non est.

[14] But a perfect voice is high, suave, and clear: high, so that it may suffice unto the sublime; clear, so that it may fill the ears; suave, so that it may blandish the minds of the hearers. If anything of these is lacking, the voice is not perfect.

XXI. DE SECVNDA DIVISIONE, QVAE ORGANICA DICITVR.

21. ON THE SECOND DIVISION, WHICH IS CALLED ORGANIC.

[1] Secunda est divisio organica in his, quae spiritu reflante completa in sonum vocis animantur, ut sunt tubae, calami, fistulae, organa, pandoria, et his similia instrumenta.

[1] The second division is organical, in those things which, filled as the breath blows back, are animated into the sound of voice, such as tubas, reeds, pipes (fistulae), organs, pandoria, and instruments similar to these.

[2] Organum vocabulum est generale vasorum omnium musicorum. Hoc autem, cui folles adhibentur, alio Graeci nomine appellant. Vt autem organum dicatur, magis ea vulgaris est Graecorum consuetudo.

[2] Organum is the general term for all musical instruments. This one, however, to which bellows are applied, the Greeks call by another name. But its being called organum is rather the vulgar (common) custom of the Greeks.

[3] Tuba primum a Tyrrhenis inventa, de quibus Vergilius (Aen. 8,526):

[3] The trumpet was first invented by the Tyrrhenians, about whom Vergil (Aen. 8,526):

Tyrrhenusque tubae mugire per aethera clangor.

And the Tyrrhenian clangor of the trumpet bellowed through the ether.

Adhibebatur autem non solum in proeliis, sed in omnibus festis diebus propter laudis vel gaudii claritatem. Vnde et in Psalterio dicitur (81,4): 'Canite in initio mensis tuba, in die insignis sollemnitatis vestrae.' Praeceptum enim fuerat Iudaeis ut in initio novae lunae tuba clangerent, quod etiam et hucusque faciunt.

It was employed not only in battles, but on all festal days on account of the clarity of praise or of joy. Whence also in the Psalter it is said (81,4): 'Blow the trumpet at the beginning of the month, on the day of your notable solemnity.' For it had been commanded to the Jews that at the beginning of the new moon they should sound the trumpet, which even to this day they do.

[4] Tibias excogitatas in Phrygia ferunt: has diu quidem funeribus tantum adhibitas, mox et sacris gentilium. Tibias autem appellatas putant, quod primum de cervinis tibiis cruribusque hinnulorum fierent, deinde per abusionem ita coeptas vocari etiam quae non de cruribus ossibusque essent. Hinc et tibicen, quasi tibiarum cantus.

[4] They report that the tibiae were devised in Phrygia: for a long time these were employed only at funerals, later also in the rites of the gentiles. They think, moreover, that they were called tibiae because at first they were made from the shin-bones of deer and the legs of fawns; then, by abuse, those which were not from legs and bones also began to be so called. Hence too tibicen, as if “the singing of tibiae.”

[5] Calamus nomen est proprium arboris a calendo, id est fundendo voces vocatus.

[5] Calamus is the proper name of a tree, called from “calendo,” that is, from pouring out voices.

[6] Fistulam quidam putant a Mercurio inventam, alii a Fauno, quem Graeci vocant Pan. Nonnulli eam ab Idi pastore Agrigentino ex Sicilia. Fistula autem dicta, quod vocem emittat.

[6] Some think the fistula (shepherd’s pipe) was invented by Mercury, others by Faunus, whom the Greeks call Pan. Some [say it was] by Idi, a shepherd of Agrigentum from Sicily. But it is called “fistula” because it emits a voice.

Nam FOS Graece vox, STOLIA missa appellatur.

For FOS in Greek is “voice,” STOLIA is called “Mass.”

[7] Sambuca in musicis species est symphoniarum. Est enim genus ligni fragilis, unde et tibiae conponuntur.

[7] The sambuca, in music, is a species of symphonies. For it is a kind of brittle wood, whence pipes also are composed.

[8] Pandorius ab inventore vocata. De quo Vergilius (Ecl. 2,32):

[8] called ‘Pandorius’ from its inventor. About which Vergil (Ecl. 2,32):

Pan primus calamos cera coniungere plures
instituit, Pan curat ovis oviumque magistros.

Pan first instituted to join together several reeds with wax,
Pan cares for the sheep and the masters of the sheep.

Fuit enim apud gentiles deus pastoralis, qui primus dispares calamos ad cantum aptavit, et studiosa arte conposuit.

For there was among the pagans a pastoral god, who first adapted unequal reeds for song, and composed them with studious art.

XXII. DE TERTIA DIVISIONE, QVAE RYTHMICA NVNCVPATVR.

22. ON THE THIRD DIVISION, WHICH IS CALLED RHYTHMIC.

[1] Tertia est divisio rythmica, pertinens ad nervos et pulsum, cui dantur species cithararum diversarum, tympanum quoque, cymbalum, sistrum, acetabula aenea et argentea, vel alia quae metallico rigore percussa reddunt cum suavitate tinnitum et cetera huiuscemodi.

[1] The third division is rhythmic, pertaining to strings and to the pulse, to which are assigned the kinds of diverse citharas, the tympanum also, the cymbal, the sistrum, bronze and silver acetabula, or other things which, when struck with metallic rigidity, render a ringing with sweetness, and other things of this sort.

[2] Citharae ac psalterii repertor Tubal, ut praedictum est, perhibetur. Iuxta opinionem autem Graecorum citharae usus repertus fuisse ab Apolline creditur. Forma citharae initio similis fuisse traditur pectori humano, quo uti vox a pectore, ita ex ipsa cantus ederetur, appellatamque eadem de causa.

[2] The inventor of the cithara and the psaltery is held to be Tubal, as was said above. But according to the opinion of the Greeks, the use of the cithara is believed to have been discovered by Apollo. The form of the cithara is handed down to have been at the beginning similar to the human breast, so that, just as the voice is from the breast, thus from it the song might be produced, and for the same reason it was so named.

Nam pectus Dorica lingua KITHARA vocari.

For the breast is called KITHARA in the Doric tongue.

[3] Paulatim autem plures eius species extiterunt, ut psalteria, lyrae, barbitae, phoenices et pectides, et quae dicuntur Indicae, et feriuntur a duobus simul. Item aliae atque aliae, et quadrata forma vel trigonali. [4 Chordarum etiam numerus multiplicatus, et conmutatum genus.

[3] Gradually, however, more of its species came forth, such as psalteries, lyres, barbitae, phoenices, and pectides, and the ones called Indian, which are struck by two at the same time. Likewise still others and others, in a square form or a triangular one. [4 Chordarum the number too has been multiplied, and the kind altered.

Veteres autem citharam fidiculam vel fidicem nominaverunt, quia tam concinunt inter se chordae eius, quam bene conveniat inter quos fides sit. Antiqua autem cithara septemchordis erat. Vnde et Vergilius (Aen.

Moreover, the ancients named the cithara “fidicula” or “fidicen,” because its strings harmonize among themselves just as well as those among whom faith prevails agree. But the ancient cithara was seven‑stringed. Whence also Vergil (Aen.

6,646):

Septem discrimina vocum.

Seven discriminations of tones.

[5] Discrimina autem ideo, quod nulla chorda vicinae chordae similem sonum reddat. Sed ideo septem chordae, vel quia totam vocem implent, vel quia septem motibus sonat caelum.

[5] The discriminations, moreover, are for this reason: that no string renders a similar sound to the neighboring string. But for this reason there are seven strings, either because they fill the whole voice, or because heaven sounds with seven motions.

[6] Chordas autem dictas a corde, quia sicut pulsus est cordis in pectore, ita pulsus chordae in cithara. Has primus Mercurius excogitavit; idemque prior in nervos sonum strinxit.

[6] The strings are said to be named from the heart (cor), because just as there is the pulse of the heart in the breast, so the pulse of the string on the cithara. Mercury first devised these; and he likewise was the first to draw sound taut upon the sinews (strings).

[7] Psalterium, quod vulgo canticum dicitur, a psallendo nominatum, quod ad eius vocem chorus consonando respondeat. Est autem similitudo citharae barbaricae in modum DELTA literae; sed psalterii et citharae haec differentia est, quod psalterium lignum illud concavum, unde sonus redditur, superius habet, et deorsum feriuntur chordae, et desuper sonant. Cithara vero concavitatem ligni inferius habet.

[7] The psaltery, which in common speech is called a canticle, is named from psalling, since to its voice the chorus responds in consonance. There is moreover a likeness to a barbarian cithara in the shape of the letter DELTA; but the difference between psaltery and cithara is this: that the psaltery has that hollow piece of wood, whence the sound is rendered, above, and the strings are struck from below, and they sound from above. The cithara, however, has the concavity of the wood beneath.

Psalterium autem Hebraei decachordon usi sunt propter numerum Decalogi legis.

Moreover, the Hebrews used a decachord psaltery on account of the number of the Law’s Decalogue.

[8] Lyra dicta APO TOU LUREIN, id est a varietate vocum, quod diversos sonos efficiat. Lyram primum a Mercurio inventam fuisse dicunt, hoc modo. Cum regrediens Nilus in suos meatus varia in campis reliquisset animalia, relicta etiam testudo est.

[8] The lyre is called APO TOU LUREIN, that is, from the variety of voices, because it produces diverse sounds. They say the lyre was first invented by Mercury, in this way: when the Nile, returning back into its channels, had left various animals in the fields, a tortoise too was left behind.

Quae cum putrefacta esset, et nervi eius remansissent extenti intra corium, percussa a Mercurio sonitum dedit; ad cuius speciem Mercurius lyram fecit et Orpheo tradidit, qui eius rei maxime erat studiosus.

When it had putrefied, and its sinews had remained stretched within the hide, struck by Mercury it gave a sound; at the sight of which Mercury made a lyre and handed it over to Orpheus, who was most studious of that matter.

[9] Vnde existimatur eadem arte non feras tantum, sed et saxa atque silvas cantus modulatione adplicuisse. Hanc musici propter studii amorem, et carminis laudem etiam inter sidera suarum fabularum commentis conlocatam esse finxerunt.

[9] Whence it is supposed that by the same art he drew not only wild beasts, but even rocks and forests by the modulation of song. Musicians, for love of study and for the praise of song, also feigned that it was placed among the stars by the inventions of their fables.

[10] Tympanum est pellis vel corium ligno ex una parte extentum. Est enim pars media symphoniae in similitudinem cribri. Tympanum autem dictum quod medium est, unde et margaritum medium tympanum dicitur; et ipsud, ut symphonia, ad virgulam percutitur.

[10] A tympanum is a skin or hide stretched on wood on one side. For it is the middle part of the symphonia, in the likeness of a sieve. And it is called a tympanum because it is in the middle, whence also the margaritum is called the middle tympanum; and it itself, like the symphonia, is struck with a little rod.

[11] Cymbala acitabula quaedam sunt, quae percussa invicem se tangunt et faciunt sonum. Dicta autem cymbala, quia cum ballematia simul percutiuntur; cum enim Graeci dicunt SUN, BALA ballematia.

[11] Cymbals are certain acitabula, which, when struck, touch one another and make a sound. They are called cymbals because they are struck together with ballematia; for when the Greeks say SUN, BALA—ballematia.

[12] Sistrum ab inventrice vocatum. Isis enim regina Aegyptiorum id genus invenisse probatur. Iuvenalis (13,93):

[12] The sistrum was named from its inventress. For Isis, queen of the Egyptians, is proved to have invented that kind. Juvenal (13,93):

Isis et irato feriat mea lumina sistro.

May Isis even strike my eyes with her irate sistrum.

Inde et hoc mulieres percutiunt, quia inventrix huius generis mulier. Vnde et apud Amazonas sistro ad bellum feminarum exercitus vocabatur.

Thence women also strike this, because the inventress of this kind was a woman. Whence also among the Amazons, by the sistrum the army of women was called to war.

[13] Tintinabulum de sono vocis nomen habet, sicut [et] plausus manuum, stridor valvarum.

[13] The tintinnabulum has its name from the sound of a voice, just as also the applause of hands, the creaking of doors.

[14] Symphonia vulgo appellatur lignum cavum ex utraque parte pelle extenta, quam virgulis hinc et inde musici feriunt, fitque in ea ex concordia gravis et acuti suavissimus cantus.

[14] Symphonia is commonly called a hollow piece of wood with skin stretched on both sides, which musicians strike with little rods on this side and that, and upon it from the concord of the grave and the acute there is produced a most sweet song.

XXIII. DE NVMERIS MVSICIS.

23. ON MUSICAL NUMBERS.

[1] Numeros autem secundum musicam ita quaeris. Positis extremis, utputa VI et decas dipondius, vides quot monadibus superetur VI a XII, et est VI monadibus: ducis per quadratum, sexies seni faciunt XXXVI. Coniungis extrema illa prima, VI ad XII, simul efficiunt XVIII.

[1] As for the numbers according to music, you seek them thus. With the extremes set, for instance 6 and the two-pound decade (that is, 12), you see by how many monads 6 is surpassed by 12, and it is by 6 monads: you take it through the square, six times six make 36. You join those first extremes, 6 to 12, together they make 18.

Partiris tricies sexies per decas octo, efficit dipondius. Hos iungis cum summa minore, id est sexies, erunt VIII et erit medium inter VI et XII. Quapropter VIII superant VI duabus monadibus, id est tertia de VI, et superantur VIII a XII quattuor monadibus, tertia portione.

You divide thirty-six by the eighteen; it yields a dupondius (two). You join this with the lesser sum, that is, sixfold; they will be 8, and it will be the mean between 6 and 12. Wherefore 8 surpass 6 by two monads, that is, a third of 6; and 8 are surpassed by 12 by four monads, by a third portion.

Qua parte ergo superat, eadem superatur.

Therefore, by whatever part it surpasses, by the same it is surpassed.

[2] Sed haec ratio quemadmodum in mundo est ex volubilitate circulorum, ita et in microcosmo in tantum praeter vocem valet, ut sine ipsius perfectione etiam homo symphoniis carens non constet. Eiusdem musicae perfectione etiam metra consistunt in arsi et thesi, id est elevatione et positione.

[2] But this ratio, just as in the world it is from the revolution of the circles, so also in the microcosm prevails to such an extent beyond voice that, without its perfection, even a man lacking harmonies (symphonies) does not hold together. By the perfection of this same music, even meters consist in arsis and thesis, that is, elevation and position.

DE ASTRONOMIA

ON ASTRONOMY

XXIV. DE ASTRONOMIAE NOMINE.

24. ON THE NAME OF ASTRONOMY.

[1] Astronomia est astrorum lex, quae cursus siderum et figuras et habitudines stellarum circa se et circa terram indagabili ratione percurrit.

[1] Astronomy is the law of the stars, which, by an investigable reasoning, runs through the courses of the stars, their figures, and the habitudes of the stars around themselves and around the earth.

XXV. DE INVENTORIBVS EIVS.

25. ON ITS INVENTORS.

[1] Astronomiam primi Aegyptii invenerunt. Astrologiam vero et nativitatis observantiam Chaldaei primi docuerunt. Abraham autem instituisse Aegyptios Astrologiam Iosephus auctor adseverat.

[1] The first Egyptians invented Astronomy. But Astrology and the observation of nativities the Chaldeans were the first to teach. Moreover Josephus, the authority, asserts that Abraham instituted Astrology for the Egyptians.

Graeci autem dicunt hanc artem ab Atlante prius excogitatam, ideoque dictus est sustinuisse caelum.

The Greeks, however, say that this art was previously devised by Atlas, and for that reason he was said to have sustained the heaven.

[2] Quisquis autem ille fuit, motu caeli et ratione animi excitatus per temporum vices, per astrorum ratos definitosque cursus, per intervallorum spatia moderata, consideravit dimensiones quasdam et numeros, quae definiendo ac secernendo in ordinem nectens Astrologiam repperit.

[2] Whoever he was, stirred by the motion of the heaven and by the reason of the mind, through the vicissitudes of times, through the fixed and defined courses of the stars, through the moderated spaces of intervals, he considered certain dimensions and numbers, which, by defining and separating, connecting into order, he discovered Astrology.

XXVI. DE INSTITVTORIBVS EIVS.

26. ON ITS INSTITUTORS.

[1] In utraque autem lingua diversorum quidem sunt de astronomia scripta volumina, inter quos tamen Ptolemaeus rex Alexandriae apud Graecos praecipuus habetur: hic etiam et canones instituit, quibus cursus astrorum inveniatur.

[1] In both tongues, indeed, there are volumes of diverse writings on astronomy, among whom, however, Ptolemy, king of Alexandria, is held as preeminent among the Greeks: he also instituted canons by which the courses of the stars are found.

XXVII. DE DIFFERENTIA ASTRONOMIAE ET ASTROLOGIAE.

27. ON THE DIFFERENCE OF ASTRONOMY AND ASTROLOGY.

[1] Inter Astronomiam autem et Astrologiam aliquid differt. Nam Astronomia caeli conversionem, ortus, obitus motusque siderum continet, vel qua ex causa ita vocentur. Astrologia vero partim naturalis, partim superstitiosa est.

[1] Between Astronomy, however, and Astrology there is some difference. For Astronomy contains the conversion of the heaven, the risings, settings, and motions of the stars, or by what cause they are so called. Astrology, indeed, is partly natural, partly superstitious.

[2] Naturalis, dum exequitur solis et lunae cursus, vel stellarum certas temporum stationes. Superstitiosa vero est illa quam mathematici sequuntur, qui in stellis auguriantur, quique etiam duodecim caeli signa per singula animae vel corporis membra disponunt, siderumque cursu nativitates hominum et mores praedicare conantur.

[2] The natural, when it sets forth the courses of the sun and moon, or the fixed stations of the stars in the seasons. The superstitious, however, is that which the mathematicians (astrologers) follow, who take augury from the stars, and who even assign the twelve signs of heaven to the several members of the soul or of the body, and who try to predict, by the course of the stars, the nativities of men and their characters.

XXVIII. DE ASTRONOMIAE RATIONE.

28. ON THE RATIONALE OF ASTRONOMY.

[1] Astronomiae ratio modis plurimis constat. Definit enim quid sit mundus, quid [sit] caelum, quid sphaerae situs et cursus, quid axis caeli et poli, quae sint climata caeli, qui cursus solis et lunae atque astrorum, et cetera.

[1] The rationale of astronomy consists in very many modes. For it defines what the world is, what [is] the heaven, what the sphere’s position and course are, what the axis of heaven and the poles are, what the climates of the sky are, what the courses of the sun and moon and of the stars are, and the rest.

XXIX. DE MVNDO ET EIVS NOMINE.

29. ON THE WORLD AND ITS NAME.

[1] Mundus est is qui constat ex caelo, [et] terra et mare cunctisque sideribus. Qui ideo mundus est appellatus, quia semper in motu est; nulla enim requies eius elementis concessa est.

[1] The world is that which consists of heaven, [and] earth and sea and all the stars. Which for that reason has been called the world, because it is always in motion; for no rest has been granted to its elements.

XXX. DE FORMA MVNDI.

30. ON THE FORM OF THE WORLD.

[1] Forma mundi ita demonstratur. Nam quemadmodum erigitur mundus in septentrionalem plagam, ita declinatur in australem. Caput autem eius et quasi facies orientalis regio est, ultima pars septentrionalis est.

[1] The form of the world is thus demonstrated. For just as the world is erected toward the septentrional region, so it declines toward the austral. Its head, moreover, and as it were its face, is the oriental region; the farthest part is the septentrional.

XXXI. DE CAELO ET EIVS NOMINE.

31. ON HEAVEN AND ITS NAME.

[1] Caelum philosophi rotundum, volubile atque ardens esse dixerunt; vocatumque hoc nomine, eo quod tamquam vas caelatum inpressa signa habeat stellarum.

[1] The philosophers said that the heaven is rotund, revolving, and ardent; and that it is called by this name because, as if it were a chased vessel, it has the impressed signs of the stars.

[2] Distinxit enim eum Deus claris luminibus, et inplevit sole scilicet et lunae orbe fulgenti, et astrorum micantium splendentibus signis adornavit. Hoc autem Graece OURANOS dicitur APO TOU ORASTHAI, id est a videndo, eo quod aer perspicuus sit et ad speculandum purior.

[2] For God distinguished it with bright luminaries, and filled it with the sun, to wit, and the shining orb of the moon, and adorned it with the shining signs of the twinkling stars. But this in Greek is called OURANOS from APO TOU ORASTHAI, that is, from seeing, because the air is transparent and purer for observing.

XXXII. DE SPHAERAE CAELESTIS SITV.

32. ON THE POSITION OF THE CELESTIAL SPHERE.

[1] Sphaera caeli est species quaedam in rotundo formata, cuius centrum terra est ex omnibus partibus aequaliter conclusa. Hanc sphaeram nec principium habere dicunt nec terminum, ideo quod in rotundum, quasi circulus, unde incipiat vel ubi desinat non facile conprehendatur.

[1] The sphere of heaven is a certain form, fashioned in the round, whose center is the earth, enclosed equally on all sides. They say that this sphere has neither beginning nor terminus, for the reason that, being rotund, like a circle, where it begins or where it ceases is not easily comprehended.

[2] Philosophi autem mundi septem caelos, id est planetas, globorum consono motu introduxerunt, quorum orbibus conexa memorant omnia, quos sibi innexos et velut insertos versari retro, et [e] contrario ceteris motu ferri arbitrantur.

[2] But the philosophers of the world have introduced seven heavens, that is, the planets, by the consonant (harmonious) motion of the globes, and they recount that all things are connected to their orbits; they judge that these, linked to them and as if inserted, revolve backward, and, [e] on the contrary, are borne by a motion opposite to the rest.

XXXIII. DE EIVSDEM SPHAERAE MOTV.

33. ON THE MOTION OF THE SAME SPHERE.

[1] Sphaerae motus duobus axibus volvitur, quorum unus est septentrionalis, qui numquam occidit, appellaturque Boreus; alter Australis, qui numquam videtur, et Austronotius dicitur.

[1] The motion of the sphere revolves on two axes, of which one is septentrional, which never sets and is called Boreus; the other austral, which is never seen and is called Austronotius.

[2] His duobus polis moveri sphaeram caeli dicunt, et cum motu eius sidera in ea fixa ab oriente usque ad occidentem circuire, septentrionibus breviores gyros iuxta cardinem peragentibus.

[2] They say the sphere of heaven is moved by these two poles, and that, with its motion, the stars fixed in it circle from the orient to the occident, the northern ones performing shorter gyres near the axis.

XXXIV. DE EIVSDEM SPHAERAE CVRSV.

34. ON THE COURSE OF THE SAME SPHERE.

[1] Sphaera caeli ab oriente et occidente semel in die et nocte vertitur viginti quattuor horarum spatiis, quibus sol cursum suum super terras et sub terras sua volubilitate concludit.

[1] The sphere of the sky is turned from the east to the west once in a day and night, in spans of twenty-four hours, within which the sun, by its own volubility, concludes its course over the lands and under the lands.

XXXV. DE CELERITATE CAELI.

35. ON THE CELERITY OF HEAVEN.

[1] Tanta celeritate sphaera caeli dicitur currere ut, nisi adversus praecipitem eius cursum astra currerent, qui eam remorarent, mundi ruinam faceret.

[1] The sphere of heaven is said to run with such celerity that, unless the stars were running against its headlong course to retard it, it would make the ruin of the world.

XXXVI. DE AXE CAELI.

36. ON THE AXIS OF HEAVEN.

[1] Axis est septentrionis linea recta, quae per mediam pilam sphaerae tendit; et dicta axis quod in ea sphaera ut rota volvitur, vel quia ibi plaustrum est.

[1] The axis is the straight line of the Septentrion, which stretches through the middle of the globe of the sphere; and it is called “axis” because on it the sphere is turned like a wheel, or because the Wagon (Wain) is there.

XXXVII. DE CAELESTIBVS POLIS.

37. ON THE HEAVENLY POLES.

[1] Poli sunt circuli, qui currunt per axem. Horum alter est Septentrionalis, qui numquam occidit, appellaturque Boreus; alter Australis, qui numquam videtur, et Austronotius dicitur; et dicti poli quod sint axium cycli ex usu plaustrorum, a poliendo scilicet nominati; sed polus Boreus semper videtur, Austronotius numquam, quia dextra caeli altiora sunt, pressa Austri.

[1] The poles are circles which run along the axis. Of these, one is the Northern (Septentrional), which never sets, and is called Boreal; the other, the Southern, which is never seen, and is called Austronotian; and they are called poles because they are cycles of axles from the use of wagons, namely named from polishing; but the Boreal pole is always seen, the Austronotian never, because the right-hand parts of the heaven are higher, those of the South pressed down.

XXXVIII. DE CARDINIBVS CAELI.

38. ON THE CARDINAL POINTS OF THE SKY.

[1] Cardines caeli extremae partes sunt axis. Et dictae cardines eo, quod per eos vertitur caelum, vel quia sicut cor volvuntur.

[1] The cardines of the sky are the extreme parts of the axis. And they are called cardines because through them the heaven is turned, or because, like a heart, they revolve.

XXXIX. DE CONVEXIS CAELI.

39. ON THE CONVEXITIES OF THE SKY.

[1] Convexa autem caeli extrema eius sunt, a curvitate dicta, ut est illud:

[1] The convexities of the sky are its extremities, named from curvature, as is that saying:

Convexum quotiens cludit nox humida caelum.

Whenever the humid night closes the convex heaven.

Convexum enim curvum est, quasi conversum seu inclinatum, et in modum circuli flexum.

For the convex is curved, as if turned or inclined, and bent in the manner of a circle.

XL. DE IANVIS CAELI.

40. ON THE DOORS OF HEAVEN.

[1] Ianuae caeli duae sunt, oriens et occasus. Nam una porta sol procedit, alia se recipit.

[1] The gates of heaven are two, the Orient and the Occident. For by one gate the sun proceeds, by the other it withdraws itself.

XLI. DE GEMINA FACIE CAELI.

41. ON THE TWIN FACE OF HEAVEN.

[1] Facies caeli vel caput orientalis regio, ultima septentrionalis. De qua Lucanus (4,106):

[1] The face of the sky, or its head, is the oriental region; the farthest, the septentrional. Concerning which Lucan (4,106):

Sic mundi pars ima iacet, quam Zona nivalis
perpetuaeque premunt hiemes.

Thus the lowest part of the world lies, which the Snowy Zone
and perpetual winters press.

XLII. DE QVATTVOR PARTIBVS CAELI.

42. ON THE FOUR PARTS OF THE SKY.

[1] Climata caeli, id est plagae vel partes, quattuor sunt, ex quibus prima pars orientalis est, unde aliquae stellae oriuntur. Secunda occidentalis, ubi nobis aliquae stellae occidunt. Tertia septentrionalis, ubi sol pervenit in diebus maioribus.

[1] The climates of the sky, that is, the regions or parts, are four, of which the first part is the oriental, whence some stars arise. The second is occidental, where for us some stars set. The third is septentrional (northern), where the sun comes in the longer days.

Quarta australis, ubi sol pervenit noctibus maioribus.

Fourth, the southern, where the sun reaches in the longer nights.

[2] Oriens autem ab exortu solis est nuncupatus. Occidens, quod diem faciat occidere atque interire. Abscondit enim lumen mundo et tenebras supcrinducit.

[2] The Orient, moreover, has been named from the rising of the sun. The Occident, because it makes the day to set and to perish. For it hides the light from the world and superinduces darkness.

Septentrio autem a septem stellis axis vocatus, quae in ipso revolutae rotantur. Hic proprie et vertex dicitur eo quod vertitur.

The Septentrion, moreover, is called from the seven stars of the axis, which, revolved upon it, are rotated. This is properly also called the vertex, because it is turned.

[3] Meridies autem vocata, vel quia ibi sol facit medium diem quasi medidies, vel quia tunc purius micat aether. Merum enim purum dicitur.

[3] Meridies, moreover, is called thus, either because there the sun makes the middle of the day, as if “mediday,” or because then the ether gleams more purely. For merum is called pure.

[4] Sunt et alia septem climata caeli, quasi septem lineae ab oriente in occidentem, sub quibus et mores hominum dispares atque animalia specialiter diversa nascuntur, quae vocata sunt a locis quibusdam famosis; quorum primum est Merois, secundum Syene, tertium Catachoras, id est Africa, quartum Rhodus, quintum Hellespontus, sextum Mesopontum, septimum Borusthenes.

[4] There are also another seven climates of the sky, as if seven lines from east to west, under which both the mores of men are disparate and animals specially diverse are born, which have been named from certain famous places; of which the first is Merois, the second Syene, the third Catachoras, that is Africa, the fourth Rhodes, the fifth the Hellespont, the sixth Mesopontum, the seventh Borusthenes.

XLIII. DE HEMISPHAERIIS.

43. ON HEMISPHERES.

[1] Haemisphaeria dimidia pars sphaerae est. Hemisphaerion supra terra est ea pars caeli quae a nobis tota videtur; Hemisphaerion sub terra est quae videri non potest, quam diu sub terra fuerit.

[1] A hemisphere is a half part of a sphere. The Hemisphaerion above the earth is that part of the heaven which is seen by us in its entirety; the Hemisphaerion under the earth is that which cannot be seen, for as long as it is under the earth.

XLIV. DE QVINQVE CIRCVLIS CAELI.

44. ON THE FIVE CIRCLES OF THE SKY.

[1] Zonae caeli quinque sunt, quarum distinctionibus quaedam partes temperie sua incoluntur, quaedam inmanitate frigoris aut caloris inhabitabiles existunt. Quae ideo zonae vel circuli appellantur, eo quod in circumductione sphaerae existunt.

[1] There are five zones of the sky, by the distinctions of which certain parts, by their own temperateness, are inhabited, while certain others, by the immanity of cold or of heat, are uninhabitable. Which therefore are called zones or circles, for the reason that they exist in the circumduction of the sphere.

[2] Quorum primus circulus ideo ARKTIKOS appellatur, eo quod intra eum Arctorum signa inclusa prospiciuntur. Secundus circulus, THERINOS qui TROPIKOS dicitur, quia in eo circulo sol Aquilonis finibus aestatem faciens ultra eum circulum non transit, sed statim revertitur; et inde TROPIKOS appellatur.

[2] Of which the first circle is therefore called ARKTIKOS, because within it the Bears’ constellations are seen enclosed. The second circle, THERINOS which is called TROPIKOS, because in that circle the sun, making summer at the boundaries of the North, does not pass beyond that circle, but immediately turns back; and from that it is called TROPIKOS.

[3] Tertius circulus EMERINOS, qui a Latinis ideo aequinoctialis appellatur, eo quod sol, cum ad eum orbem pervenerit, aequinoctium facit. EMERINOS enim Latine dies dicitur atque nox, quo circulo dimidia sphaerae pars constituta prespicitur. Quartus autem circulus ANTARKTIKOS vocatus eo quod contrarius sit circulo, quem ARKTIKON nominamus.

[3] The third circle, EMERINOS, which by the Latins is therefore called the equinoctial, because the sun, when it has reached that orb, makes the equinox. For EMERINOS in Latin is called “day and night,” at which circle the half of the sphere is clearly seen. But the fourth circle is called ANTARKTIKOS because it is opposite to the circle which we name ARKTIKON.

[4] Quintus circulus CHEIMERINOS TROPIKOS, qui a Latinis hiemalis sive brumalis appellatur, ideo quia sol cum ad eum circulum pervenerit, hiemem his, qui ad Aquilonem sunt, facit, et aestatem his, qui in Austri partibus conmorantur.

[4] The fifth circle, CHEIMERINOS TROPIKOS, which in Latin is called winter or brumal, is so called because when the sun has reached that circle, it makes winter for those who are toward the North, and summer for those who dwell in the austral parts.

XLV. DE ZODIACO CIRCVLO.

45. ON THE ZODIAC CIRCLE.

[1] Zodiacus [autem] circulus [est], qui ex linearum quinque angulis, [et] ex una linea constat.

[1] The Zodiac [however] circle [is], which consists of five angles of lines, [and] of a single line.

XLVI. DE CANDIDO CIRCVLO.

46. ON THE WHITE CIRCLE.

[1] Lacteus circulus via est, quae in sphaera videtur, a candore dicta, quia alba est. Quam aliqui dicunt viam esse qua circuit sol, et ex splendoris ipsius transitu ita lucere.

[1] The Milky circle is a way which is seen on the sphere, so called from candor, because it is white. Some say it is the way by which the sun circuits, and that from the transit of its own splendor it thus shines.

XLVII. DE MAGNITVDINE SOLIS.

47. ON THE MAGNITUDE OF THE SUN.

[1] Magnitudo solis fortior terrae est, unde et eodem momento, quum oritur, et orienti simul et occidenti aequaliter apparet. Quod vero tamquam cubitalis nobis videtur, considerare oportet quantum sol distat a terris, quae longitudo facit ut parvus videatur a nobis.

[1] The magnitude of the sun is greater than the earth’s, whence also at the same moment, when it rises, it appears equally to both the east and the west at the same time. But as to its seeming to us as if cubital, one ought to consider how far the sun is distant from the earth; that length causes it to appear small to us.

XLVIII. DE MAGNITVDINE LVNAE.

48. ON THE MAGNITUDE OF THE MOON.

[1] Magnitudo quoque lunae minor fertur esse quam solis. Nam dum sol superior sit a luna, et tamen a nobis maior quam luna videtur, iam si prope nos accessisset, multo maior quam luna conspiceretur. Sicut autem sol fortior est terrae, ita terra fortior [est] lunae per aliquam quantitatem.

[1] The magnitude of the moon, too, is reported to be less than that of the sun. For while the sun is higher than the moon, and yet appears to us greater than the moon, then if it had come near to us, it would be seen much greater than the moon. But just as the sun is stronger than the earth, so the earth [is] stronger than the moon by some quantity.

XLIX. DE NATVRA SOLIS.

49. ON THE NATURE OF THE SUN.

[1] Sol dum igneus sit, prae nimio motu conversionis suae amplius incalescit. Cuius ignem dicunt philosophi aqua nutriri, et e contrario elemento virtutem luminis et caloris accipere. Vnde videmus eum saepius madidum atque rorantem.

[1] While the Sun is fiery, by reason of the excessive motion of its own revolution it grows more heated. Philosophers say that its fire is nourished by water, and that from the contrary element it receives the virtue of light and of heat. Whence we see it rather often moist and dewy.

L. DE CVRSV SOLIS.

50. ON THE COURSE OF THE SUN.

[1] Solem per se ipsum moveri, non cum mundo verti. Nam si fixus caelo maneret, omnes dies et noctes aequales existerent; sed quoniam alio loco cras occasurum, alio occidisse hesterno videmus, apparet eum per se ipsum moveri, non cum mundo verti. Spatiis enim inaequalibus orbes annuos conficit propter temporum mutationes.

[1] The sun moves by itself, not turned with the world. For if it remained fixed in the heaven, all days and nights would be equal; but since we see it about to set tomorrow in one place, and that yesterday it set in another, it is evident that it moves by itself, not turned with the world. For it completes its annual orbits in unequal spaces on account of the mutations of the seasons.

Oriens diem facit, occidens noctem inducit.

The Orient makes the day, the Occident brings in the night.

[2] Nam vadens longius ad meridiem hiemem facit, ut hibernis humoribus ac pruinis terra pinguescat. Accedens propius ad septentrionem aestatem reddit, ut fruges maturitate durentur, et quae sunt in humidis incocta, fervefacta mitescant.

[2] For, going farther toward the meridian (south), he makes winter, so that by wintry humors and hoarfrosts the earth may grow fat; drawing nearer to the septentrion (north), he renders summer, so that the crops are hardened by maturity, and those things which are unripe in humid places, once heated, grow mellow.

LI. DE EFFECTV SOLIS.

51. ON THE EFFECT OF THE SUN.

[1] Sol oriens diem facit, occidens noctem inducit; nam dies est sol super terras, nox est sol sub terras. Ex ipso enim sunt horae: ex ipso dies, cum ascenderit: ex ipso etiam nox, cum occiderit: ex ipso menses et anni numerantur; ex ipso vicissitudines temporum fiunt.

[1] The rising sun makes the day, the setting brings in the night; for day is the sun above the lands, night is the sun beneath the lands. For from it are the hours: from it the day, when it has ascended: from it also the night, when it has set: from it the months and years are numbered; from it the vicissitudes of the seasons come about.

[2] Quando autem per meridiem currit, vicinior terrae est; quando vero iuxta septentrionem, sublimis attollitur. [Cui ideo Deus diversa cursus instituit loca et tempora, ne, dum semper in isdem moraretur locis, cottidiano vapore eius consumeret; sed ut Clemens ait: 'Cursus diversos accipit, quibus aeris temperies pro ratione temporum dispensatur, et ordo vicissitudinum permutationumque servatur. Nam dum ad superiora conscenderit, ver temperat: ubi ad summum venerit, aestivos accendit calores: decedens rursus autumni temperiem reddit.

[2] But when it runs through the meridian, it is nearer to the earth; when indeed near the north, it is lifted on high. [To which end God established different places and times of its course, lest, while it always tarried in the same places, it should consume things with its daily vapor; but, as Clement says: 'It receives diverse courses, by which the temperateness of the air is dispensed according to the rationale of the times, and the order of vicissitudes and permutations is preserved. For when it has climbed to the higher regions, it tempers spring: when it has come to the highest, it kindles the summer heats: departing, it renders again the temperateness of autumn.

Vbi vero ad inferiorem redit circulum, ex glaciali conpage caeli rigorem nobis hiberni frigoris derelinquit.'] (sequitur figura circularis, quae in medio habet medium [est] mundi, circa autem stationes solis sic inscriptas: hic ortus solis in natale Domini; sexta hora diei; occasus in natale Domini; occasus in aequinoctio; occasus solis in natale Iohannis; semper media nox; ortus solis in natale Iohannis; hic ortus solis in aequinoctio.)

But when it returns to the lower circle, from the glacial compaction of the heaven it leaves to us the rigor of wintry cold.'] (there follows a circular figure, which in the middle has the center [it is] of the world, and around, the stations of the sun inscribed thus: here the sunrise on the Nativity of the Lord; the sixth hour of the day; sunset on the Nativity of the Lord; sunset at the equinox; the sunset of the sun on the Nativity of John; always midnight; the sunrise of the sun on the Nativity of John; here the sunrise at the equinox.)

LII. DE ITINERE SOLIS.

52. ON THE JOURNEY OF THE SUN.

[1] Sol oriens per meridiem iter habet. Qui postquam ad occasum venerit et Oceano se tinxerit, per incognitas sub terra vias vadit et rursus ad orientem recurrit.

[1] The sun, rising, has its journey through the meridian. Which, after it has come to its setting and has dipped itself in the Ocean, goes along unknown ways beneath the earth and returns again to the east.

LIII. DE LVMINE LVNAE.

53. ON THE LIGHT OF THE MOON.

[1] Lunam quidam philosophi dicunt proprium lumen habere, globique eius unam partem esse lucifluam, aliam vero obscuram, [ita: (sequitur figura)] et paulatim se vertendo diversas formas efficere.

[1] Some philosophers say the Moon has its proper light, and that of its globe one part is luciferous, while the other is obscure, [thus: (the figure follows)]; and by gradually turning itself it produces diverse forms.

[2] Alii e contra aiunt lunam non suum lumen habere, sed solis radiis inluminari. Vnde et eclipsim patitur, si inter ipsam et solem umbra terrae interveniat. [Sol enim illi loco superior est.

[2] Others, on the contrary, say that the moon does not have its own light, but is illuminated by the rays of the Sun. Whence also it suffers an eclipse, if the shadow of the earth intervenes between it and the Sun. [For the Sun is superior in that place.

Hinc evenit ut, quando sub illo est, parte superiore luceat, inferiore vero, quam habet ad terras, obscura sit.]

Hence it comes about that, when it is beneath him, it shines in its upper part, but the lower part, which it has toward the earth, is dark.]

LIV. DE FORMIS LVNAE.

54. ON THE FORMS OF THE MOON.

[1] Prima figura lunae bicornis est, ita (sequitur figura). Secunda sectilis [habet, ita] (seq. figura). Tertia dimidia [habet ita] (seq. figura). Quarta plena [ita] (seq.

[1] The first figure of the moon is bicorn, thus (the figure follows). The second, sectile, [has (it), thus] (fig. follows). The third, half, [has (it) thus] (fig. follows). The fourth, full, [thus] (fig.

figura). Quinta iterum dimidia [ex maiore] [ita] (seq. figura). Sexta iterum sectilis [ita] (seq. figura). Septima bicornis [ita] (seq.

figure). The fifth again is half [from the greater] [thus] (the following figure). The sixth again is sectile (crescent) [thus] (the following figure). The seventh is bicorn (two-horned) [thus] (seq.

figura).

figure).

[2] Septima autem semis et vicesima secunda semis in suo orbe mediae sunt (seq. figura). Ceterae [autem] pro portione sunt.

[2] The seventh-and-a-half and the twenty-second-and-a-half are in the middle in their own orb (see the figure). The others [however] are according to proportion.

LV. DE INTERLVNIO LVNAE.

55. ON THE INTERLUNIUM OF THE MOON.

[1] Interlunium lunae est tempus illud inter deficientem et nascentem lunam. Est autem trigesima dies, quo luna non lucet. Quae ideo tunc videri non potest, quia soli coniuncta obscuratur; sed eodem momento renascens paulatim ab eo recedendo videtur.

[1] The interlunar of the moon is that time between the deficient (waning) and the nascent moon. It is the thirtieth day, on which the moon does not shine. Which therefore cannot then be seen, because, conjoined to the sun, it is obscured; but at that same moment, being reborn, it is seen gradually as it recedes from it.

LVI. DE CVRSV LVNAE.

56. ON THE COURSE OF THE MOON.

[1] Luna amissi ac recepti luminis vicibus menstrua spatia moderat. Quae ideo obliquo incedit cursu et non recto, ut sol, scilicet ne incidat in centrum terrae et frequenter patiatur eclipsim.

[1] The Moon governs monthly intervals by the alternations of lost and regained light. Therefore it proceeds with an oblique course and not a straight one, like the Sun, namely lest it strike the earth’s center and suffer eclipse frequently.

[2] Vicinus est enim eius circulus terrae. Crescens autem orientem cornibus spectat, decrescens occidentem: merito, quia occasura et amissura est lumen.

[2] For its circle is near to the earth. When waxing, it looks toward the east with its horns, when waning, toward the west: rightly, because it is about to set and about to lose its light.

LVII. DE VICINITATE LVNAE AD TERRAS.

57. ON THE VICINITY OF THE MOON TO THE EARTH.

[1] Luna vicinior est terris quam sol. Inde et breviori orbe celerius peragit cursum suum. Nam iter, quod sol in diebus trecentis sexaginta quinque peragit, ista per triginta dies percurrit.

[1] The Moon is nearer to the earth than the Sun. Hence also, with a shorter orbit, she completes her course more swiftly. For the journey which the Sun completes in 365 days, this one runs through in 30 days.

Vnde et antiqui menses in luna, annos autem in solis cursum posuerunt.

Whence also the ancients set months by the Moon, but years by the Sun’s course.

LVIII. DE ECLIPSI SOLIS.

58. ON THE ECLIPSE OF THE SUN.

[1] Eclipsis solis est, quotiens luna trigesima ad eandem lineam, qua sol vehitur, pervenit, eique se obiiciens solem obscurat. Nam deficere nobis sol videtur, dum illi orbis lunae opponitur.

[1] An eclipse of the sun is, whenever the moon on the thirtieth [day] comes to the same line along which the sun is carried, and, by interposing itself to it, darkens the sun. For the sun seems to us to fail, while the orb of the moon is set opposite to it.

LIX. DE ECLIPSI LVNAE.

59. ON THE ECLIPSE OF THE MOON.

[1] Eclipsis lunae est, quotiens in umbram terrae luna incurrit. Non enim suum lumen habere, sed a sole inluminari putatur, unde et defectum patitur si inter ipsam et solem umbra terrae interveniat.

[1] An eclipse of the moon is whenever the moon runs into the earth’s shadow. For it is not thought to have its own light, but is thought to be illuminated by the sun, whence also it suffers a defect if the earth’s shadow intervenes between it and the sun.

[2] Patitur autem hoc quinta decima luna eo usque, quam diu centrum atque umbram obstantis terrae exeat videatque solem, vel a sole videatur.

[2] Moreover, it undergoes this on the fifteenth day of the moon, until such time as it goes out of the center and the umbra of the obstructing earth and sees the sun, or is seen by the sun.

LX. DE DIFFERENTIA STELLARVM, SIDERVM, ET ASTRORVM.

60. ON THE DIFFERENCE OF STARS, SIDEREAL BODIES, AND ASTRAL BODIES.

[1] Stellae et sidera et astra inter se differunt. Nam stella est quaelibet singularis. Sidera vero sunt stellis plurimis facta, ut Hyades, Pleiades.

[1] Stars and constellations and astral bodies differ among themselves. For a star is any single one. But constellations are made from very many stars, as the Hyades, the Pleiades.

Astra autem stellae grandes, ut Orion, Bootes. Sed haec nomina scriptores confundunt, et astra pro stellis et stellas pro sideribus ponunt.

Astra, however, are great stars, such as Orion, Boötes. But writers confuse these names, and put astra in place of stars and stars in place of constellations.

LXI. DE LVMINE STELLARVM.

61. ON THE LIGHT OF THE STARS.

[1] Stellas non habere proprium lumen, sed a sole inluminari dicuntur, sicut et luna.

[1] The stars are said not to have their own proper light, but to be illuminated by the sun, just as also the moon.

LXII. DE STELLARVM SITV.

62. ON THE POSITION OF THE STARS.

[1] Stellae inmobiles sunt et cum caelo fixae perpetuo motu feruntur, neque cadunt per diem, sed solis splendore obscurantur.

[1] The stars are immobile and fixed with the sky and are borne with perpetual motion, nor do they fall during the day, but are obscured by the sun’s splendor.

LXIII. DE STELLARVM CVRSV.

63. ON THE COURSE OF THE STARS.

[1] Sidera aut feruntur, aut moventur. Feruntur, quae caelo fixa sunt et cum caelo volvuntur. Moventur vero quaedam [sicut] planetae, id est erraticae, quae cursus suos vagos certa tamen definitione conficiunt.

[1] The stars are either borne along, or they move. Those are borne along which are fixed in the heaven and revolve with the heaven. But certain ones are moved, [as] the planets, that is, the erratic ones, which nevertheless complete their wandering courses by a certain fixed definition.

LXIV. DE VARIO CVRSV STELLARVM.

64. ON THE VARIED COURSE OF THE STARS.

[1] Stellae pro eo, quod per diversos orbes caelestium planetarum feruntur, quaedam celerius exortae serius occidunt: quaedam tardius exortae citius ad occasum perveniunt: aliae pariter oriuntur et non simul occidunt: omnes autem suo tempore ad cursum proprium revertuntur.

[1] The stars, because they are borne through the diverse orbs of the celestial planets, some, having risen more quickly, set later: some, having risen more slowly, come more quickly to setting: others rise together and do not set at the same time: but all return in their own time to their proper course.

LXV. DE STELLARVM INTERVALLIS.

65. ON THE INTERVALS OF THE STARS.

[1] Stellae inter se diversis intervaliis distant a terra, propterea dispari claritate magis minusve nostris oculis apparent. Nam multae maiores sunt his quas videmus conspicuas, sed longius positae parvae videntur a nobis.

[1] The stars, among themselves, are distant from the earth by diverse intervals; therefore they appear to our eyes with unequal brightness, more or less. For many are greater than those conspicuous ones which we see, but, placed farther away, they seem small to us.

LXVI. DE CIRCVLARI NVMERO STELLARVM.

66. ON THE CIRCULAR NUMBER OF THE STARS.

[1] Numerus circularis stellarum est, per quod cognosci dicitur in quanto tempore circulum suum unaquaeque stella percurrat, sive per longitudinem, sive per latitudinem.

[1] The circular number of the stars is that by which it is said to be known in how much time each star runs through its own circle, whether by longitude or by latitude.

[2] Nam Luna totannis fertur explere circulum suum, Mercurius annis XX, Lucifer annis IX, Sol annis XIX, Vesper [annis] XV, Phaethon annis XII, Saturnus [annis] XXX. Quibus peractis ad reversionem circuli sui isdem signis et partibus revertuntur.

[2] For Luna is said to complete her circle every year, Mercurius in 20 years, Lucifer in 9 years, Sol in 19 years, Vesper [in years] 15, Phaethon in 12 years, Saturnus [in years] 30. When these are completed, for the reversion of their circle they return to the same signs and parts.

[3] Quaedam sidera radiis solis praepedita anomala fiunt, aut retrograda, aut stationaria, iuxta quod et poeta meminit dicens (Lucan. 10,201):

[3] Certain stars, impeded by the rays of the sun, become anomalous, either retrograde or stationary, in accordance with which the poet also makes mention, saying (Lucan. 10,201):

Sol tempora dividit aevi:
mutat nocte diem, radiisque potentibus astra
ire vetat, cursusque vagos ratione moratur.

The Sun divides the times of the age:
he changes day with night, and with his powerful rays forbids
the stars to go, and by reason delays their wandering courses.

LXVII. DE STELLIS PLANETIS.

67. ON THE PLANETARY STARS.

[1] Quaedam stellae ideo planetae dicuntur, id est errantes, quia per totum mundum vario motu discurrunt. Vnde pro eo, quod errant, retrograda dicuntur, vel anomala efficiuntur, id est, quando particulas addunt et detrahunt. Ceterum quando tantum detrahunt, retrograda dicuntur; stationem autem faciunt, quando stant.

[1] Certain stars are for this reason called planets, that is, wanderers, because they run about through the whole world with a varied motion. Whence, because they wander, they are called retrograde, or are made anomalous, that is, when they add and subtract little particles. Moreover, when they only subtract, they are called retrograde; and they make a station when they stand.

LXVIII. DE PRAECEDENTIA ET ANTEGRADATIONE STELLARVM.

68. ON THE PRECEDENCE AND ANTEGRADATION OF THE STARS.

[1] Praecedentia vel antegradatio stellarum est, dum stella motum suum agere videtur, et aliquid praeter consuetudinem praecedit.

[1] Precedence or antegradation of the stars is, when a star seems to perform its motion, and it advances something beyond its customary course.

LXIX. DE REMOTIONE VEL RETROGRADATIONE STELLARVM.

69. ON THE REMOVAL OR RETROGRADATION OF THE STARS.

[1] Remotio vel retrogradatio stellarum est, in quo stella, dum motum suum agat, simul et retrorsum moveri videtur.

[1] Remotion or retrogradation of the stars is that in which a star, while it performs its own motion, at the same time seems to be moved backward.

LXX. DE STATV STELLARVM.

70. ON THE STATUS OF THE STARS.

[1] Status stellarum est, qua dum stella semper movetur, tamen in aliquibus locis stare videntur.

[1] The status of the stars is that in which, while a star is always moving, nevertheless in some places they seem to stand still.

LXXI. DE NOMINIBVS STELLARVM, QVIBVS EX CAVSIS NOMINA ACCEPERVNT.

71. ON THE NAMES OF THE STARS, BY WHAT CAUSES THEY RECEIVED NAMES.

[1] Sol appellatus eo quod solus appareat, obscuratis fulgore suo cunctis sideribus.

[1] The Sun is named thus because he alone appears, all the stars being obscured by his splendor.

[2] Luna dicta quasi Lucina, ablata media syllaba. De qua Vergilius (Ecl. 4,10):

[2] The Moon is called as if Lucina, with the middle syllable removed. About which Virgil (Ecl. 4,10):

Casta fave Lucina.

Chaste Lucina, be favorable.

Sumpsit autem nomen per derivationem a solis luce, eo quod ab eo lumen accipiat, acceptum reddat.

It has taken its name, moreover, by derivation from the light of the sun, because from it it receives the light, and renders back what it has received.

[3] Stellae dictae a stando, quia fixae stant semper in caelo nec cadunt. Nam quod videmus [e] caelo stellas quasi labi, non sunt stellae, sed igniculi ab aethere lapsi; qui fiunt, dum ventus altiora petens aethereum ignem secum trahit, qui tractu suo imitatur stellas cadentes. Nam stellae cadere non possunt: inmobiles enim, ut praedictum est, sunt, et cum caelo fixae feruntur.

[3] Stars are said to be named from standing, because, fixed, they always stand in the sky and do not fall. For what we see [from] the sky as stars, as if sliding, are not stars, but little fires fallen from the ether; which come about when a wind, seeking higher things, draws the aethereal fire along with it, which by its trail imitates falling stars. For stars cannot fall: motionless indeed, as has been said, they are, and, fixed with the sky, they are borne along.

[4] Sidera dicta, quod ea navigantes considerando dirigunt ad cursum consilium, ne fallacibus undis aut ventis alibi deducantur. Quaedam autem stellae idcirco signa dicuntur, quia ea nautae observant in gubernandis remigiis, contemplantes aciem fulgoremque eorum, quibus rebus status caeli futurus ostenditur.

[4] The sidereal bodies are so called, because sailors, by considering them, direct the counsel for their course, lest they be led elsewhere by deceitful waves or winds. But certain stars for this reason are called signs, because sailors observe them in governing the oar-crews, contemplating their keenness and their brilliance, by which things the future state of the sky is shown.

[5] Sed et omnes homines ea intendunt ad praevidendas aeris qualitates per aestatem et hiemem vernalemque temperiem. Ortu enim vel occasu suo certis stationibus temporum qualitatem significant.

[5] But also all men direct their attention to them to foresee the qualities of the air through summer and winter and the vernal tempering. For by their rising or their setting, at certain stations, they signify the quality of the seasons.

[6] Signorum primus Arcton, qui in axe fixus septem stellis in se revolutis rotatur. Nomen est Graecum, quod Latine dicitur ursa; quae quia in modum plaustri vertitur, nostri eam Septentrionem dixerunt.

[6] The first of the constellations is Arcton, which, fixed on the axis, is rotated, its seven stars revolving upon themselves. The name is Greek, which in Latin is said “bear”; and because it is turned in the manner of a wagon, our people have called it the Septentrion.

[7] Triones enim proprie sunt boves aratorii, dicti eo quod terram terant, quasi teriones. Septentriones autem non occidere axis vicinitas facit, quia in eo sunt.

[7] For triones are properly plow-oxen, so called because they thresh the earth, as if “teriones.” But it is the vicinity of the axis that makes the Septentriones not set, because they are in it.

[8] Arctophylax dictus, quod Arcton, id est Helicem Vrsam, sequitur. Eundem et Booten dixerunt, eo quod plaustro haeret: signum multis spectabile stellis, inter quas Arcturus est.

[8] Called Arctophylax, because he follows Arcton, that is Helice the Bear. The same one they also called Boötes, because he clings to the wagon: a constellation conspicuous with many stars, among which is Arcturus.

[9] Arcturus sidus est post caudam maioris ursae posita in signo Bootae. Vnde Arcturus dictus est, quasi ARKTOU OURA, quia Bootis praecordiis conlocata est. Oritur autem autumnali tempore.

[9] Arcturus is a star set after the tail of the greater Bear, positioned in the sign of Bootes. Whence it is called Arcturus, as if ARKTOU OURA, because it is located at the fore-chest of Bootes. It rises, moreover, at the autumnal time.

[10] Orion austro ante Tauri vestigia fulget, et dictus Orion ab urina, id est ab inundatione aquarum. Tempore enim hiemis obortus mare et terras aquis ac tempestatibus turbat.

[10] Orion, with the south wind, shines before the tracks of Taurus, and he is called Orion from urine, that is, from the inundation of waters. For at the time of winter, when he rises, he disturbs the sea and the lands with waters and storms.

[11] Hunc Latini Iugulam vocant, quod sit armatus, ut gladius, et stellarum luce terribilis atque clarissimus; in quo si haec fulgent omnia, serenitas portenditur, si obscuratur his acies, tempestas cernitur inminere.

[11] The Latins call this Iugula, because he is armed, as with a sword, and by the light of the stars he is most terrible and most brilliant; in which, if all these shine, serene weather is portended, but if the line is obscured among these, a tempest is discerned to be imminent.

[12] Hyades dictae APO TOU UEIN, id est a suco et pluviis. Nam pluviae Graece UETOS dicitur. Ortu quippe suo efficiunt pluvias.

[12] The Hyades are called APO TOU UEIN, that is, from moisture and rains. For rain in Greek is called UETOS. Indeed at their rising they effect rains.

Vnde et eas Latini suculas appellaverunt, quia, quando nascuntur, pluviarum signa monstrantur. De quibus Vergilius (Aen. 1,744):

Whence also the Latins appellated them little sows, because, when they rise, signs of rains are shown. About which Vergil (Aen. 1,744):

Arcturum pluviasque Hyadas.

Arcturus and the rainy Hyades.

Sunt autem septem in fronte Tauri, et oriuntur tempore vernali.

There are, moreover, seven in the forehead of Taurus, and they arise in vernal time.

[13] Pliades a pluralitate dictae, quia pluralitatem Gracci APO TOU PLEISTON appellant. Sunt enim stellae septem ante genua Tauri; ex quibus sex videntur, nam latet una. Has Latini Vergilias dicunt a temporis significatione, quod est ver, quando exoriuntur.

[13] The Pleiades are called from plurality, because the Greeks call plurality APO TOU PLEISTON. For there are seven stars before the knees of Taurus; of which six are seen, for one lies hidden. The Latins call these the Vergiliae from the signification of the season, which is spring, when they rise.

Nam occasu suo hiemem, ortu aestatem, primaeque navigationis tempus ostendunt.

For by their setting they show winter, by their rising summer, and the time of the first navigation.

[14] Canicula stella, quae et Sirius dicitur, aestivis mensibus in medio centro caeli est: et dum sol ad eam ascenderit, coniuncta cum sole duplicatur calor ipsius, et dissolvuntur corpora et vaporantur. Vnde et ex ipsa stella dies caniculares dicuntur, quando et molestae sunt purgationes.

[14] The Canicula star, which is also called Sirius, in the estival months is in the middle center of the sky; and when the sun has ascended to it, being conjoined with the sun its heat is doubled, and bodies are dissolved and vaporized. Whence also from that star the canicular days are so called, when purgations too are troublesome.

[15] Canis autem vocatur propter quod corpora morbo afficiat, vel propter flammae candorem, quod eiusmodi sit ut prae ceteris lucere videatur. Itaque quo magis eam cognoscerent, Sirion appellasse.

[15] But it is called Dog because it afflicts bodies with disease, or because of the flame’s white‑hot brightness, since it is of such a kind as to seem to shine before the rest. And so, that they might recognize it the more, they called it Sirion.

[16] Cometes stella est dicta eo quod comas luminis ex se fundat. Quod genus sideris quando apparuerit, aut pestilentiam, aut famem, aut bella significat.

[16] The comet is called a star because it pours forth from itself tresses of light. This kind of star, when it appears, signifies either pestilence, or famine, or wars.

[17] Cometae autem Latine crinitae appellantur, quia in modum crinium flammas spargunt; quas Stoici dicunt esse ultra triginta, quarum nomina et effectus quidam Astrologi scripserunt.

[17] Comets, however, are called crinite in Latin, because they scatter flames in the manner of hairs; of which the Stoics say there are more than thirty, whose names and effects certain Astrologers wrote.

[18] Lucifer dictus eo quod inter omnia sidera plus lucem ferat; est autem unus ex planetis. Hic proprie et iubar dicitur eo quod iubas lucis effundat, sed et splendor solis ac lunae et stellarum iubar vocatur, quod in modum iubae radii ipsorum extendantur.

[18] Lucifer is so called because among all the stars he bears more light; moreover, he is one of the planets. This is properly also called iubar because it pours forth manes of light; but the splendor of the sun and of the moon and of the stars is also called iubar, because their rays are stretched out in the manner of a mane.

[19] Vesperus stella [est] occidentalis, quam cognominatam perhibent ab Hespero Hispaniae rege. Est autem et ipsa ex quinque stellis planetis, noctem ducens et solem sequens. Fertur autem quod haec stella oriens luciferum, occidens vesperum facit.

[19] Vesperus is the occidental star, which they maintain to have been surnamed from Hesperus, king of Hispania. And it too is one of the five wandering stars (planets), leading the night and following the sun. Moreover it is reported that this star, when rising, makes Lucifer, and when setting, makes Vesper.

De qua Statius (Theb. 6,241):

About which Statius (Thebaid 6,241):

Et alterno dependitur unus in ortu.

And in alternate rising the one is suspended.

[20] Planetae stellae sunt quae non sunt fixae in caelo, ut reliquae, sed in aere feruntur. Dictae autem planetae APO TES PLANES, id est ab errore. Nam interdum in austrum, interdum in septentrionem, plerumque contra mundum, nonnumquam cum mundo feruntur.

[20] Planets are stars which are not fixed in the sky, like the rest, but are borne in the air. They are called planets APO TES PLANES, that is, from wandering. For sometimes toward the south, sometimes toward the north, for the most part against the world, and sometimes with the world, they are carried.

Quarum nomina Graeca sunt Phaethon, Phaenon, Pyrion, Hesperus, Stilbon.

Of which the Greek names are Phaethon, Phaenon, Pyrion, Hesperus, Stilbon.

[21] Has Romani nominibus deorum suorum, id est Iovis, Saturni, Martis, Veneris, atque Mercurii sacraverunt. Decepti enim et decipere volentes in eorum adulationem, qui sibi aliquid secundum amorem praestitissent, sidera ostendebant in caelo, dicentes quod Iovis esset illud sidus et illud Mercurii: et concepta est opinio vanitatis. Hanc opinionem erroris diabolus confirmavit, Christus evertit.

[21] The Romans consecrated them with the names of their own gods, that is, of Jupiter, Saturn, Mars, Venus, and Mercury. For, deceived and wishing to deceive, into the adulation of those who had granted them something according to love, they would point out the stars in the sky, saying that that star was Jupiter’s and that one Mercury’s; and an opinion of vanity was conceived. The devil confirmed this opinion of error; Christ overthrew it.

[22] Iam vero illa, quae ab ipsis gentilibus signa dicuntur, in quibus et animantium imago de stellis formatur, ut Arcton, [ut] Aries, Taurus, Libra et huiusmodi alia; hi, qui sidera perviderunt, in numerum stellarum speciem corporis superstitiosa vanitate permoti finxerunt, ex causis quibusdam deorum suorum et imagines et nomina conformantes.

[22] Indeed those things which are called signs by the gentiles themselves, in which even the image of living beings is formed from the stars—as Arcton, as Aries, Taurus, Libra, and others of this kind—those who scrutinized the stars, moved by superstitious vanity, fashioned a bodily form out of a number of stars, conforming both the images and the names for certain reasons having to do with their own gods.

[23] Nam Arietem primum signum, cui, ut Librae, mediam mundi lineam tradunt, propter Ammonem Iovem ideo vocaverunt, in cuius capite, qui simulacra faciunt, arietis cornua fingunt.

[23] For Aries, the first sign, to which, as to Libra, they assign the middle line of the world, they therefore named on account of Jupiter Ammon, on whose head those who make images fashion the horns of a ram.

[24] Quod signum gentiles ideo inter signa primum constituerunt, quia in Martio mense, qui est anni principium, solem in eo signo cursum suum agere dicunt. Sed et Taurum inter sidera conlocant, et ipsum in honorem Iovis, eo quod in bovem sit fabulose conversus, quando Europam transvexit.

[24] Which sign the Gentiles for that reason set as the first among the signs, because in the month of March, which is the beginning of the year, they say the sun makes its course in that sign. But they also place Taurus among the stars, and it too in honor of Jove, because he was fabulously transformed into a bull, when he carried Europa across.

[25] Castorem quoque et Pollucem post mortem inter notissima sidera constituere: quod signum Gemini dicunt.

[25] They also established Castor and Pollux, after death, among the most famous constellations: the sign which they call Gemini.

[26] Cancrum quoque inde dixerunt, eo quod cum ad id signum mense Iunio sol venerit, retrograditur in modum cancri, brevioresque dies facit. Hoc enim animal incertam habet primam partem, denique ad utramque partem gressum dirigit, ita ut prior pars sit posterior et posterior prior.

[26] They also thence named Cancer, because when the sun has come to that sign in the month of June, it goes retrograde in the manner of a crab, and makes the days shorter. For this animal has an uncertain foremost part; indeed it directs its stride to either side, such that the former part is the latter and the latter the former.

[27] Leonem in Graecia ingentem Hercules occidit, et propter virtutem suam hunc inter duodecim signa constituit. Hoc signum sol cum adtigerit, nimium calorem mundo reddit, et annuos flatus Etesias facit.

[27] In Greece Hercules slew a huge lion, and on account of his valor he established this one among the twelve signs. When the sun has touched this sign, it renders excessive heat to the world and produces the yearly Etesian winds.

[28] Virginis etiam signum idcirco intra astra conlocaverunt, propter quod isdem diebus, in quibus per eum sol decurrit, terra exusta solis ardore nihil pariat. Est enim hoc tempus canicularium dierum.

[28] They also placed the sign of the Virgin within the stars for this reason: because on the same days on which the sun runs through it, the earth, scorched by the ardor of the sun, bears nothing. For this is the time of the dog-days.

[29] Libram autem vocaverunt ab aequalitate mensis ipsius, quia VIII kal. Octobres sol per illud signum currens aequinoctium facit. Vnde et Lucanus (4,58):

[29] But they called it Libra from the equality of the month itself, because on the 8th day before the Kalends of October the sun, running through that sign, makes the equinox. Whence also Lucan (4,58):

Ad iustae pondera librae.

To the weights of the just balance.

[30] Scorpium quoque et Sagittarium propter fulgura mensis ipsius appellaverunt. Sagittarius vir equinis cruribus deformatus, cuius sagittam et arcum adiungunt, ut ex eo mensis ipsius fulmina demonstrarentur. Vnde et sagittarius est vocatus.

[30] They also named Scorpio and Sagittarius on account of the fulgurations of that month. Sagittarius is a man deformed with equine legs, to whom they adjoin the arrow and the bow, so that from this the lightnings of the month itself might be shown. Whence also he is called sagittarius.

[31] Capricorni figuram ideo inter sidera finxerunt, propter capr[e]am Iovis nutricem; cuius posteriorem partem corporis in effigiem piscis ideo formaverunt, ut pluvias eiusdem temporis designarent, quas solet idem mensis plerumque in extremis habere.

[31] They thus fashioned the figure of Capricorn among the stars on account of the she-goat, the nurse of Jove; whose posterior part of the body they formed into the effigy of a fish, in order to designate the rains of that same season, which the same month is accustomed for the most part to have toward the end.

[32] Porro Aquarium et Piscem ab imbribus temporum vocaverunt, quod hieme, quando in his signis sol vehitur, maiores pluviae profunduntur. Et miranda dementia gentilium, qui non solum pisces, sed etiam arietes et hircos et tauros, ursas et canes et cancros et scorpiones in caelum transtulerunt. Nam et aquilam et cignum propter Iovis fabulas inter caeli astra eius memoriae causa conlocaverunt.

[32] Furthermore, they named Aquarius and Pisces from the rains of the seasons, because in winter, when the sun is carried in these signs, greater rains are poured forth. And the madness of the gentiles is to be wondered at, who transferred not only fishes, but also rams and he-goats and bulls, bears and dogs and crabs and scorpions into heaven. For they even placed an eagle and a swan, on account of the fables of Jove, among the stars of the sky for the sake of his memory.

[33] Perseum quoque et uxorem eius Andromedam, posteaquam sunt mortui, in caelum receptos esse crediderunt; ita ut imagines eorum stellis designarent, eorumque appellare nominibus non erubescerent.

[33] Perseus too, and his wife Andromeda, after they had died, they believed to have been received into heaven; so that they might designate their images with stars, and did not blush to call them by their names.

[34] Aurigam etiam Ericthonium in caeli astra conlocaverunt, propter quod vidissent eum primum quadrigas iunxisse. Mirati sunt enim ingenium eius ad imitationem Solis accessisse, et propter hoc nomen eius post mortem inter sidera posuerunt.

[34] They also placed the Charioteer, Erichthonius, among the stars of heaven, because they had seen that he was the first to yoke a quadriga (four-horse chariot). For they marveled that his ingenuity had approached an imitation of the Sun, and on account of this they set his name among the stars after his death.

[35] Sic Callisto, Lycaonis regis filia, dum a Iove compressa et fabulose a Iunone in ursae fuisset speciem versa, quae Graece ARKTOS appellatur, post interfectionem ipsius nomen eius Iovis cum filio in stellis Septentrionalibus transtulit, eamque Arcton, filium autem eius Arctophylax appellavit.

[35] Thus Callisto, daughter of King Lycaon, while, having been embraced by Jove and, fabulously, by Juno had been turned into the appearance of a she-bear (which in Greek is called ARKTOS), after her killing Jove transferred her name together with her son into the Septentrional stars, and he called her Arcton, but her son Arctophylax.

[36] Sic Lyra pro Mercurio in caelum locata; sic Centaurus Chiron, propter quod nutrierit Aesculapium et Achillem, inter astra dinumeratus est.

[36] Thus the Lyre was placed into heaven for Mercury; thus the Centaur Chiron, because he had nurtured Aesculapius and Achilles, was enumerated among the stars.

[37] Sed quolibet modo superstitionis haec ab hominibus nuncupentur, sunt tamen sidera quae Deus in mundi principio condidit, ac certo motu distinguere tempora ordinavit.

[37] But in whatever mode of superstition these may be named by men, yet they are the stars which God created at the beginning of the world, and by a fixed motion ordained to distinguish the times.

[38] Horum igitur signorum observationes, vel geneses, vel cetera superstitiosa, quae se ad cognitionem siderum coniungunt, id est ad notitiam fatorum, et fidei nostrae sine dubitatione contraria sunt, sic ignorari debent a Christianis, ut nec scripta esse videantur.

[38] Therefore the observations of these signs, or the geneses, or the other superstitious things which couple themselves to the cognition of the stars, that is, to the knowledge of the fates, and are without doubt contrary to our faith, ought to be so ignored by Christians that they do not even seem to have been written.

[39] Sed nonnulli siderum pulcritudine et claritate perlecti in lapsus stellarum caecatis mentibus conruerunt, ita ut per subputationes noxias, quae mathesis dicitur, eventus rerum praescire posse conentur: quos non solum Christianae religionis doctores, sed etiam gentilium Plato, Aristoteles, atque alii rerum veritate conmoti concordi sententia damnaverunt, dicentes confusionem rerum potius de tali persuasione generari.

[39] But some, allured by the beauty and clarity of the stars, with minds blinded, have collapsed into errors concerning the stars, so that through harmful subcalculations, which is called mathesis (astrology), they attempt to foreknow the outcomes of things: whom not only the teachers of the Christian religion, but even the pagans Plato, Aristotle, and others, moved by the truth of things, condemned with concordant judgment, saying that rather a confusion of affairs is generated from such a persuasion.

[40] Nam sicut genus humanum ad varios actus nascendi necessitate premerentur, cur aut laudem mereantur boni aut mali legum percipiant ultionem? Et quamvis ipsi non fuerint caelesti sapientiae dediti, veritatis tamen testimonio errores eorum merito perculerunt.

[40] For if the human race were pressed by the necessity of being born to various acts, why should the good either merit praise or the evil receive the vengeance of the laws? And although they themselves were not devoted to celestial wisdom, yet by the testimony of truth they have deservedly smitten down their errors.

[41] Ordo autem iste septem saecularium disciplinarum ideo a Philosophis usque ad astra perductus est, scilicet ut animos saeculari sapientia implicatos a terrenis rebus abducerent, et in superna contemplatione conlocarent.

[41] But this order of the seven secular disciplines was for this reason conducted by the Philosophers even unto the stars, namely, that they might lead away minds entangled by secular wisdom from terrestrial things, and collocate them in supernal contemplation.