Hyginus: DE ASTRONOMIA LIBRI QVATTUOR

Etsi te studio grammaticae artis inductum, non solum versuum moderatione, quam pauci perviderunt, sed historiarum quoque varietate, qua scientia rerum perspicitur, praestare video, quae facilius etiam scriptis tuis perspici potest, desiderans potius scientem quam liberalem iudicem, tamen quo magis exercitatus et nonnullis etiam saepius in his rebus occupatus esse videor, ne nihil in adulescentia laborasse dicerer, et imperitorum iudicio desidiae subirem crimen, hoc velut rudimento scientiae nisus scripsi ad te, non ut imperito monstrans, sed ut scientissimum commonens.

Although I see that you, led by a zeal for the grammatical art, excel not only in the moderation of verses, which few have perceived, but also in the variety of histories, by which the science of things is discerned — a quality that can be seen even more plainly in your writings — desiring rather a judiciously learned than merely liberal judge, yet the more I seem to be exercised and even sometimes occupied in these matters, so that I might not be said to have labored in my youth for nothing and incur the charge of desidia in the judgment of the unskilled, I have written this effort to you as it were a rudiment of learning; not to show (it) to the unskilled, but to admonish the most learned.

Sphaerae figurationem circulorumque qui in ea sunt notationem, et quae ratio fuerit, ut non aequis partibus dividerentur; praeterea terrae marisque definitionem, et quae partes eius non habitentur, ut multis iustisque de causis hominibus carere videantur, ordine exposuimus. Rursusque redeuntes ad sphaeram, duo et XL signa nominatim pernumeravimus. Exinde uniuscuiusque signi historias causamque ad sidera perlationis ostendimus.

We have set forth in order the figure of the sphere and the notation of the circles that are in it, and the reason why they are not divided into equal parts; moreover the definition of land and sea, and which parts of them are uninhabited, so that for many and just causes they seem to lack men. Returning again to the sphere, we have counted by name 42 signs. Thence we showed the histories of each sign and the cause of their ascription to the stars.

Eodem loco nobis utile visum est persequi eorum corporum deformationes et in his numerum stellarum. Nec praetermisimus ostendere ad septem circulorum notationem, quo corpora aut partes corporum pervenirent et quemadmodum ab his dividerentur. Diximus etiam de aestivi circuli definitione, quaerentes, quare non idem hiemalis vocaretur, et quid eos fefellerit, qui ita senserint; et quid in ea parte sphaerae solis efficiat cursus.

In the same place it seemed useful to us to pursue the deformations of their bodies and, within these, the number of the stars. Nor did we omit to show the notation of the seven circles, to which bodies or parts of bodies they would extend and how they would be divided by them. We also spoke of the definition of the summer circle, asking why the winter one is not called the same, and what deceived those who have so judged; and what the course of the sun produces in that part of the sphere.

Praeterea, quare circulos in octo partes divideremus, ordine exposuimus. Scripsimus etiam, quo loco circulus aequinoctialis foret constitutus, et quid efficeret ad eum perveniens sol. In eiusdem circulis demonstratione ostendimus, quare Aries inter sidera celerrimus diceretur.

Furthermore, we expounded in order why we divide the circles into eight parts. We also wrote in what place the equinoctial circle is to be established, and what it brings about when the sun reaches it. In the demonstration of those same circles we showed why Aries was said to be the swiftest among the stars.

Pauca praeterea de hiemali circulo diximus. Exinde zodiacum circulum definivimus et eius effectus, et quare potius duodecim signa quam undecim numerarentur; quid etiam nobis de reliquis circulis videretur. His propositis rebus ad id loci venimus, ut exponeremus, utrum mundus ipse cum stellis verteretur, an mundo stante vagae stellae ferrentur; et quid de eo nobis et conpluribus viderentur, quaque ratione ipse mundus verteretur.

Few things moreover we have said about the winter circle. Thence we defined the zodiacal circle and its effects, and why twelve signs rather than eleven would be counted; and what also seemed to us about the remaining circles. With these matters proposed we came to that point of the discussion to set forth whether the world itself turns with the stars, or whether, the world standing still, the wandering stars are carried; and what on this point seemed to us and to many others, and by what reasoning the world itself would be turned.

Praeterea quare nonnulla signa celerius exorta serius occiderent, nonnulla etiam tardius ceteris exorta citius ad occasum pervenirent; quare etiam quae signa pariter oriantur, non simul occidant. Eodem loco diximus, quare non essent in sphaera superiora inferioribus hemicyclis aequalia, et quot modis stellas videre non possimus. Praeterea scripsimus in duodecim signorum ortu quae de reliquis corpora exoriri, et quae eodem tempore occidere viderentur.

Furthermore why certain signs, having risen more swiftly, set later; and why certain others, having risen later than the rest, would sooner arrive at setting; why also those signs which rise together do not set together. In the same place we explained why the upper spheres are not equal to the lower in their hemicycles, and in how many ways we cannot see the stars. Furthermore we wrote, in the rising of the twelve signs, which bodies would be seen to rise from the others, and which would be seen to set at the same time.

Deinde ordine perscripsimus, utrum sol cum mundo fixus verteretur, an ipse per se moveretur, et cum ipse per se moveatur et contra duodecim signorum ortus eat, quare videatur cum mundo exoriri et occidere. Deinde protinus de lunae cursu pauca proposuimus et utrum suo an alieno lumine uteretur; eclipsis solis et lunae quomodo fieret; quare luna per eundem circulum inter faciens, celerius sole currere videatur, et quid fefellerit eos qui ita senserint. Quinque stellae quantum habeant intervallum, et utrum quinque sint an septem, et utrum quinque certe errent, an omnes, et quinque quomodo currant.

Then in order we set forth whether the sun, fixed with the world, turned, or whether it moved of its own self; and since it moves of its own self and goes contrary to the rising of the twelve signs, why it appears to rise and set with the world. Then immediately we proposed a few matters about the course of the Moon, and whether it uses its own or a foreign light; how an eclipse of sun and moon is made; why the Moon, traversing the same circle, seems to run swifter than the sun, and what has deceived those who so judged. How much interval the five stars have, and whether there are five or seven, and whether five certainly wander, or all do, and how the five travel.

Diximus etiam, qua ratione priores astrologi non eodem tempore signa et reliquas stellas reverti dixerint, et quare Meton diligentissime observasse videatur, et quid reliquos fefellerit in eadem causa.

We also said by what rationale the earlier astrologers declared that the signs and the remaining stars do not return at the same time, and why Meton seems to have observed with the greatest diligence, and what has deceived the others in that same matter.

In his igitur tam multis et variis rebus non erit mirum aut pertimescendum, quod tantum numerum versuum scripsserimus; neque enim magnitudinem voluminis, sed rerum multitudinem peritos convenit spectare. Quod si longior in sermone visus fuero, non mea facunditate, sed rei necessitate factum existimato; nec si brevius aliquid dixero, minus idem valere confidito, quam si pluribus esset audiendum verbis. Etenim praeter nostram scriptionem sphaerae, quae fuerunt ab Arato obscurius dicta, persecuti planius ostendimus, ut penitus id quod coepimus exquisisse videremur.

Therefore in these so many and various matters it will not be strange or to be feared that we have written so great a number of verses; for one ought to regard not the bulk of the volume but the multitude of matters treated. And if I shall have seemed longer in speech, judge it not to be by my eloquence but by the necessity of the thing; nor if I shall have said something more briefly, trust that it has no less worth than if it had to be heard in more words. Moreover, besides our own writing, we have followed up and shown the sphere more plainly, which had been spoken more obscurely by Aratus, so that we might seem to have thoroughly examined that which we began.

Quod si vel optimis usus auctoribus effeci, ut neque brevius neque verius diceret quisquam, non inmerito fuerim laudari dignus a vobis, quae vel amplissima laus hominibus est doctis; si minus, non deprecamur in hac confusione nostram scientiam ponderari. Ideoque maioribus etiam niti laboribus cogitamus, in quibus et ipsi exerceamur et quibus volumus nos probare possimus. Etenim necessariis nostris hominibus scientissimis maximas res scripsimus; non levibus occupati rebus, populi captamus existimationem.

But if, even by using the best authors, I have achieved that no one should speak more briefly or more truly, I shall not undeservedly be worthy of praise from you, which is a very ample praise among learned men; if less, let our learning not be weighed in this confusion. Therefore we intend to strive in still greater labors, in which we ourselves may be exercised and by which we wish to be able to prove ourselves. For to meet our necessities and for the most learned men we have written the greatest matters; not being occupied with light affairs, we court the esteem of the people.

Sed ne diutius de eo, quod neglegimus, loquamur, ad propositum veniemus et initium rerum demonstrabimus.

But lest we speak any longer about that which we neglect, let us come to the purpose and demonstrate the beginning of things.

I. DE MUNDO. Mundus appellatur is qui constat ex sole et luna et terra et stellis omnibus.

CHAPTER 1. DE MUNDO. The world is called that which consists of the sun and the moon and the earth and all the stars.

DE SPHAERA. Sphaera est species quaedam in rotundo conformata, omnibus ex partibus aequalis apparens, unde reliqui circuli finiuntur. Huius autem neque exitus, neque initium potest definiri, ideo quod in rotundo omnes tractus et initia et exitus significare possunt.

ON THE SPHERE. The sphere is a certain species, conformed into a rotundity, appearing equal from all parts, whence the remaining circles are terminated. Of this, however, neither exit nor beginning can be defined, because in the round all tractus and initia and exitus can be signified.

II. DE CENTRO. Centron est cuius ab initio circumductio sphaerae terminatur, ac terrae positio constituta declaratur.

CHAPTER 2. ON THE CENTER. The Centron is that at whose beginning the circumduction of the sphere is terminated, and the position of the earth is constituted and declared.

III. DE DIMENSIONE. Dimensio, quae totius ostenditur sphaerae, est cum ex utrisque partibus eius ad extremam circumductionem rectae ut virgulae perducuntur; quae dimensio a compluribus axis est appellata. Huius autem cacumina, quibus maxime sphaera nititur, poli appellantur; quorum alter ad aquilonem spectans boreus, alter oppositus austro notius est dictus.

CHAPTER 3. ON DIMENSION. Dimension, which is shown of the whole sphere, is when from either of its parts straight lines, like little rods, are led out to the extreme circumference; this dimension has been called by many an axis. The summits of this, upon which the sphere most rests, are called poles; one of which, looking toward the north, is called boreal, the other, opposite, is more commonly called southern.

IV.Significationem quaedam in circumductione sphaerae circuli appellantur. E quibus paralleli dicuntur, qui ad eundem polum constituti finiuntur. Maximi autem sunt, qui eodem centro quo sphaera continentur.

4. Some significations in the circumduction of the sphere are called circles. Of these, those are called parallels which are terminated as set toward the same pole. But the greatest are those which are contained by the sphere with the same centre as the sphere.

Horizon appellatur is, qui terminat ea quae perspici aut non videri possunt. Hic autem incerta ratione definitur, quod modo polo subiectus et circulis his qui paralleli dicuntur, modo duobus extremis et aequalibus nixus, modo aliis partibus adiectus terrae, pervidetur ita, utcumque fuerit conlocata.

The horizon is called that which bounds those things that may be perceived or not be seen. But it is defined by uncertain reasoning, since it is sometimes regarded as subject to the pole and to those circles which are called parallels, sometimes seen as resting on two extremities and equal supports, sometimes as appended to other parts of the earth, and is thus apprehended however it may be placed.

V. POLUS is qui boreus appellatur, pervideri potest semper; notius autem ratione dissimili semper est a conspectu remotus. Naturalis autem mundi statio, quae physice dicitur, ea est in boreo polo finita. Ut omnia a dextris partibus exoriri, in sinistris occidere videantur.

V. POLE is who is called the Boreal Pole can always be perceived; yet the more known by a different rationale is always removed from sight. The natural station of the world, which is called the physical, is that fixed at the Boreal Pole. So that all things seem to rise on the right-hand parts and to set on the left.

Exortus enim est subita quaedam species obiecta nostro conspectui; occasus autem pari de causa, ut erepta ab oculis visa.

For an exortus is a certain sudden species placed before our conspect; an occasus, however, is for the same reason seen as snatched away from the eyes.

VI.In finitione mundi circulis sunt paralleli V, ini quibus tota ratio sphaerae consistit, praeter eum qui zodiacus appellatur; qui quod non, ut ceteri circuli, certa dimensione finitur, et inclinatior aliis videtur, loxos a Graecis est dictus. Quinque autem quos supra diximus, sic in sphaera metiuntur, initio sumpto a polo qui boreus appellatur, ad eum qui notius et antarcticus vocatur. In triginta partes unumquodque hemisphaerium dividitur, ita uti dimensio significare videatur in tota sphaera sexaginta partes factas.

6. In the bounding of the world there are five parallel circles, in which the whole order of the sphere consists, besides that which is called the zodiac; which, because it is not, like the other circles, terminated by a fixed measure, and seems more inclined than the others, is called loxos by the Greeks. The five, then, which we mentioned above, are measured on the sphere thus, the beginning taken from the pole called the boreal, to that which is called the notius and antarctic. Each hemisphere is divided into thirty parts, so that the dimension appears to signify sixty parts made in the whole sphere.

Deinde ab eodem principio boreo sex partibus ex utraque finitione sumptis, circulus dicitur, cuius centron ipse est polus finitus; qui circulus arcticus appellatur, quod intra eum Arctorum simulacra ut inclusa perspiciuntur; quae signa a nostris ursarum specie ficta, Septentriones appellantur. Ab hoc circulo de reliquis partibus quinque sumptis, eodem centro quo supra diximus, circulus ducitur, qui therinos tropikos appellatur, ideo quod sol cum ad eum circulum pervenit, aestatem efficit eis qui in aquilonis finibus sunt, hiemem autem eis, quos austri flatibus oppositos ante diximus. Praeterea, quod ultra eum circulum sol non transit, sed statim revertitur, tropikos est appellatus.

Then from the same northern principle, six parts being taken from each boundary, is said to be a circle whose center itself is the bounded pole; this circle is called the Arctic, because within it the likenesses of the Bears are seen as if enclosed; these signs, from our people’s invented kind of bears, are called the Septentriones. From this circle, five of the remaining parts being taken, and with the same center as we said above, a circle is drawn which is called the summer tropic (therinos tropikos), because when the sun reaches that circle it produces summer for those who are in the confines of the north, and winter for those whom we said before lie opposite in the blasts of the south. Moreover, because the sun does not pass beyond that circle but immediately turns back, it is named a tropic.

Ab hoc circuli significatione quattuor de reliquis partibus sumptis, ducitur circulus aequinoctialis, qui a Graecis isemerinos appellatur, ideo quod sol cum ad eum orbem pervenit, aequinoctium conficit.

From this signification of the circle, taking four of the remaining parts, is drawn the equinoctial circle, which the Greeks call isemerinos, because when the sun comes to that orb it effects the equinox.

Hoc circulo facto, dimidia sphaerae pars constituta perspicitur. E contrario item simili ratione a notio polo sex partibus sumptis, ut supra de boreo diximus, circulus ductus antartikos vocatur, quod contrarius est ei circulo, quem arcticon supra definivimus. Hac definitione sphaerae, centroque poli qui notius dicitur, V partibus sumptis, circulus cheimerinos tropikos instituitur, a nobis hiemalis, a nonnullis etiam brumalis appellatus, ideo quod sol cum ad eum circulum pervenit, hiemem efficit his qui ad aquilonem spectant; aestatem autem his qui in austri partibus domicilia constituerunt.

With this circle made, a part equal to half the sphere is seen to be constituted. Conversely likewise, by a similar method from the southern pole (notio polus) with six parts taken, as we above said of the north, a drawn circle is called antartikos, because it is contrary to that circle which we defined above as the arctic. With this definition of the sphere, and with the pole’s center which is called notius, with 5 parts taken, the circle cheimerinos tropikos is established, by us called the winter tropic, by some also brumalis; for when the sun comes to that circle it produces winter for those who face the north, but summer for those who have their dwellings fixed in the parts of the south.

Quanto enim abest longius ab illis qui in aquilonis habitant finibus, hoc hieme maiore conflictantur; aestate autem hi, quibus sol oppositus pervidetur. Itaque Aethiopes sub utroque orbe necessario fiunt. Ab hoc circulo ad aequinoctialem circulum reliquae fiunt partes quattuor, ita uti sol per octo partes sphaerae currere videatur.

For the farther any place is removed from those who dwell in the confines of the north, the more severely are they harassed by a greater winter; but in summer those for whom the sun is perceived as opposite. Therefore the Ethiopes necessarily exist under both hemispheres. From this circle to the equinoctial circle the remaining parts are four, so that the sun is seen to traverse eight parts of the sphere.

Zodiacus autem circulus sic vel optime definiri poterit, ut signis factis, sicut postea dicemus, ex ordine circulus perducatur. Qui autem lacteus vocatur, contrarius aequinoctiali, ibi oportet ut eum medium dividere et bis ad eum pervenire videatur, semel in eo loco ubi Aquila constituitur, iterum autem ad eius signi regionem, quod Procyon vocatur.

The zodiacal circle, however, can thus or best be defined: with signs made, as we shall say later, the circle is carried through in order. But that which is called the Milky, contrary to the equinoctial, there it must be that the sun divide it at the middle and seem to reach it twice, once in that place where the Eagle is placed, and again to the region of its sign, which is called Procyon.

Duodecim signorum partes sic dividuntur: quinque circulis, de quibus supra diximus, ita finiuntur, ut unusquisque eorum dividatur in partes duodecim, et ita ex eorum punctis lineae perducantur, quae circulos significent factos, in quibus duodecim signa describantur. Sed a nonnullis imperitioribus quaeritur, quare non aequis partibus circuli finiantur, hoc est, ut de triginta partibus quinae partes dividantur, et ita circuli pari ratione ducantur. Id facillime defendi posse confidimus.

The twelve parts of the signs are thus divided: they are bounded by five circles, of which we spoke above, so that each of them is divided into twelve parts, and thus from their points lines are drawn which indicate the circles made, within which the twelve signs are inscribed. But some unlearned persons ask why they are not bounded by equal parts of the circle, that is, so that out of thirty parts five parts are divided, and so the circles be drawn by the same proportion. We trust that this can be defended very easily.

Cum enim media sphaera divisa est, eius circuli nullus potest aequalis esse, qui quamvis proxime eum accedat, tamen minor esse videatur. Itaque qui primum sphaeram fecerunt, cum vellent omnium circulorum aequas rationes esse, pro rata parte voluerunt significare, ut quanto magis a polo discederetur, hoc minorem numerum partium sumerent in circulis metiendis, quo necesse his erat maiorem circulum definire. Quod etiam ex ipsa sphaera licet intellegere; quanto magis a polo discedes, hoc maiores circulos fieri necesse est, et hac re minorem numerum duci, ut pares eorum videantur effectus.

For when the middle sphere is divided, none of its circles can be equal; although one may come very near it, it will nevertheless seem smaller. Therefore those who first made the sphere, since they wished the ratios of all the circles to be equal, intended to signify this by proportional parts: that the more one receded from the pole, the fewer parts they would take in measuring the circles, because by this necessity they had to define a greater circle. And this may even be understood from the sphere itself: the more you depart from the pole, the greater the circles must become, and by this fact a smaller number is taken, so that the effects of them may appear equal.

Et si non in triginta partes unumquodque hemisphaerium dividatur, sed in alias quaslibet finitiones, tamen eo ratio pervenit eius, ac si triginta partes fecisset.

And if each hemisphere is not divided into thirty parts, but into any other divisions whatsoever, nevertheless its ratio comes to the same result as if it had been made into thirty parts.

VII.Zodiacus circulus tribus his subiectus, de quibus supra diximus, ex quadam parte contingit aestivum et hiemalem circulum, aequinoctialem autem medium dividit. Itaque sol per zodiacum circulum currens, neque extra eum transiens necessario etiam cum signis his, quibus innixus iter conficere videtur, pervenit ad eos quos supra diximus orbes et ita quattuor tempora definit.

7.The zodiacal circle, subject to those three mentioned above, from a certain part touches the summer and winter circles, and the equinoctial divides the middle. Thus the sun, running through the zodiacal circle, not passing outside it and necessarily with the signs by which, leaning on them, it seems to complete its journey, reaches those orbs which we named above and so determines the four seasons.

Nam ab Ariete incipiens ver ostendit; et Taurum et Geminos transiens, idem significat. Sed iam capitibus Geminorum circulum aestivum tangere videtur, et per Cancrum et Leonem transiens et Virginem, aestatem efficit. Et rursus a Virginis extrema parte transire ad aequinoctialem circulum perspicitur; in Libra autem aequinoctium conficit et autumnum significare incipit.

For beginning from Aries, spring manifests itself; and passing through Taurus and Gemini, it signifies the same. But now at the heads of Gemini the circle seems to touch the summer circle, and passing through Cancer and Leo and Virgo, it brings about summer. And again it is seen to pass from the extreme part of Virgo to the equinoctial circle; in Libra, however, it completes the equinox and begins to signify autumn.

Ab hoc signo transiens ad Scorpium et Sagittarium, deinde protinus incurrit in hiemalem circulum et Capricorno, Aquario, Piscibus hiemem transigit. Itaque ostenditur non per tres ipsos circulos currere, sed zodiacum transiens ad eos pervenire.

From this sign, passing on to Scorpio and Sagittarius, then immediately it runs into the winter circle and passes the winter in Capricorn, Aquarius, and Pisces. Thus it is shown not that it runs through the three circles themselves, but that, passing through the zodiac, it reaches them.

Sed quoniam de his rebus diximus, nunc terrae positionem definiemus, et mare quibus locis interfusum videatur, ordine exponemus.

But since we have spoken of these matters, now we will define the position of the land, and we will set forth in order in which places the sea is seen to be interposed.

VIII. DE TERRA. Terra mundi media regione collocata, omnibus partibus aequali dissidens intervallo, centron optinet sphaerae. Hanc mediam dividit axis in dimensione totius terrae.

CHAPTER 8. The earth, placed in the middle region of the world, lying at an equal interval from all parts, occupies the centrum of the sphere. The axis divides this middle in the dimension of the whole earth.

Oceanus autem e regione circumductionis sphaerae profusus, prope totius orbis alluit fines; itaque et signa occidentia in eum decidere existimantur. Sic igitur et terras contineri poterimus explanare. Nam quaecumque regio, quae inter arcticum et aestivum finem collocata est, ea dividitur trifarie; e quibus una pars Europa, altera Asia, tertia Africa vocatur.

Ocean, moreover, poured forth from the region of the sphere’s circumference, bathes the borders of nearly the whole orb; and so the western signs are thought to fall into it. Thus likewise we shall be able to explain how the lands are contained. For whatever region lies between the Arctic and the Aestival boundary, that region is divided threefold; of these one part is called Europe, another Asia, the third Africa.

Europam igitur ab Africa dividit mare ab extremis Oceani finibus et Herculis columnis. Asiam autem et Libyam cum Aegypto disterminat os Nili fluminis, quod Canopicon appellatur. Asiam ab Europa Tanais dividit, bifariam se coniciens in paludem quae Maeotis appellatur.

Europe therefore the sea divides from Africa, from the farthest bounds of the Ocean and the Pillars of Hercules. The mouth of the river Nile, which is called the Canopic, separates Asia and Libya with Egypt. Tanais divides Asia from Europe, casting itself in two into the marsh which is called Maeotis.

Hac igitur definitione facile pervidetur mare omnibus obiectum finibus terrae.

By this definition, then, it is easily perceived that the sea lies opposite all the bounds of the land.

Sed ne videatur nonnullis mirum, cum sphaera in sexaginta partes dividatur, ut ante diximus, quare definivimus ab aestivo circulo ad arcticum finem dumtaxat habitari, sic vel optime defendimus. Sol enim per mediam regionem sphaerae currens, nimium his locis efficit fervorem. Itaque quae finie est ab aestivo circulo ad hiemalem, ea terra a Graecis diakekaumene vocatur, quod neque fruges propter exustam terram nasci, neque homines propter nimium ardorem durare possunt.

But lest it seem strange to some, since the sphere is divided into sixty parts, as we said before, why we defined that it is inhabited only from the summer circle to the arctic end, thus we most aptly defend. For the sun, running through the middle region of the sphere, causes excessive fervor in those places. Therefore the land which lies from the summer circle to the winter circle is called by the Greeks diakekaumene, because neither crops, on account of the scorched earth, can be born, nor can men endure because of the excessive heat.

Extremae autem regiones sphaerae duorum circulorum, quorum alter boreus, alter notius vocatur, fine arctici circuli et eius qui antarcticos vocatur, non habitantur, ideo quod sol ab his circulis semper abest longe, ventique assiduos habent flatus. Quamvis enim sol perveniat ad aestivum circulum, tamen longe ab arctico videbitur fine. Id ita esse hinc quoque licet intellegere: cum enim sol pervenit ad eum circulum qui hiemalis vocatur, et efficiat nobis, qui prope eum sumus constituti, nimium frigus, quid arbitramur eis locis frigoris esse, qui longius etiam absunt a nobis?

The extreme regions of the sphere, of two circles, one called boreal, the other notial (southern), at the boundary of the arctic circle and of that which is called antarctic, are not inhabited, because the sun is always far absent from those circles, and the winds have continual blasts. For although the sun reaches the aestival (summer) circle, it will still seem far from the arctic boundary. This may also be understood from here: for when the sun reaches that circle which is called hiemal (winter), and produces for us, who are set near it, excessive cold, what do we suppose the cold to be in those places which are even farther removed from us?

Quod cum in hac parte sphaerae fiat, idem in altera parte definitum putavimus, ideo quod similes sunt eius effectus. Praeterea hinc quoque intellegimus illic maximum frigus et in aestivo circulo calorem esse, quod qua terra habitatur, eos tamen videmus, qui proxime sunt arcticum finem, uti bracis et eiusmodi vestimentis; qui autem proximi sunt aestivo circulo, eos Aethiopas et perusto corpore esse. Habitatur autem sic temperantissimo caelo, cum inter aestivum circulum et arcticum finem haec proveniat temperatio; quod ab arctico circulo frigus, ab aestivo fervor exortus in unum concurrens efficit mediam finem temperatam, quae habitari possit.

Since this occurs in this part of the sphere, we judged the same to be determined in the other part, for its effects are similar. Moreover from here we likewise understand that there is the greatest cold there and heat at the aestival circle, because of the land where it is inhabited; yet we see that those who are nearest the arctic limit wear braccae and garments of that sort; but those who are nearest the aestival circle are Ethiopes and of a sun‑scorched body. It is inhabited, however, under the most temperate sky, when between the aestival circle and the arctic limit this temperation arises; for cold, having risen from the arctic circle, and heat from the aestival circle, meeting together, make the middle boundary tempered, which can be inhabited.

Itaque cum sol ab eo loco discessit, hieme necessario conflictamur, quod ventum exorientem non reverberat sol. Quod cum veniat in hac definitione, illud quoque fieri posse videmus, ut hiemali circulo nobis ad antarcticum finem habitari possit, quod pares eodem proveniant casus. Certum quidem esse nemo contendit, neque pervenire eo potest quisquam propter interiectum terrae, quae propter ardorem non habitatur.

Therefore, when the sun has withdrawn from that place, we are necessarily afflicted by winter, because the sun does not warm the wind that rises. And when this happens in this region, we likewise see that it can also happen that toward the antarctic limit the winter circle might be habitable for us, since like occurrences arise there. Yet no one maintains that it is certain, nor can anyone reach it because of the intervening land, which, on account of its heat, is uninhabited.

Sed cum videmus hanc regionem sphaerae habitari, illam quoque in simili causa posse constitui suspicamur.

But since we see this region of the sphere to be inhabited, we suspect that that other likewise could be constituted for a similar cause.