Frontinus: OPUSCULA RERUM RUSTICARUM

Principium artis mens<o>riae in agendi[s] positum est experimento. Exprimi enim locorum aut modi veritas sine rationa[bi]libus lineis non potest, quoniam omnium agrorum extremitas flexuosa et inaequali[s] cluditur finitione, quae propter angulorum dissimilium multitudinem numeris suis manentibus et cohiberi potest et extendi: nam sol<a> mobile[m] habent spatium et incertam iugerum enuntiationem. Sed ut omnibus extremitatibus species sua constet et intra clusi modus enuntietur, agrum quo usque loci positio permittet rectis lineis dimetiemur: ex quibus proximam quamque extremitat<iu>m obliquitatem per omnes angulos facta normatione conplectimur, et coher<cita>m mensuralibus <lineis> statutis certo pr<ae>cent<uria>to spatio simil<i> futurae tradimus formae: modum autem intra lineas clusum rectorum angulorum ratione subducimus.

The principle of the art of mensuration is placed in practice by experiment. For the truth of places or of form cannot be expressed without rational lines, since the extremity of all fields is closed by a winding and unequal termination, which, because of the multitude of dissimilar angles with their numbers remaining, can be both contained and extended: for only the movable have a space and an uncertain enunciation of their iugum (acreage). But so that to all extremities their species may be established and the mode enclosed within lines declared, we shall measure the field as far as the situation of the place permits with straight lines: from these we embrace each nearest obliquity of the extremities by making a norm at every angle, and the restrained form, with mensural having been set, we hand over to the future within a certain predetermined space of similar measure: but the mode closed within the lines we deduce by the reasoning of the right angles.

Subiectas deinde extremitatium partes, are<as> tangentium nostrarum postulationum, podismis suis ad<a>eramus, et adscriptis spatio suo finibus ipsam loci reddimus veritatem.

We then placed beneath the parts of the extremities the areas tangent to our postulations, we fitted them with their own podisms (paces/measures), and, with limits inscribed for their space, we restore the very truth of the place.

Haec ubique una ratione fieri multiplex locorum natura non patitur, oppositis ex alia parte montibus, alia flumine aut ripis aut quadam iacentis soli voragine, cum pluribus confragosorum locorum iniquitatibus, saepe et cultur<is>, propter quae maxime ad artis copia<m> est recurrendum. Debet enim <minima> quaeque pars agri in potestate esse mensoris et habit[ur]a rectorum angulorum ratione sua postulatione constringi. Itaque maxime providere debemus, quo usu ferramenti quidquid occurrerit transeamus; adhibere deinde metiundi diligentiam, qua[e] potius actus incess<us l>imitationis effectum laterum longitudine[s] aequ[e]et; ferramento primo ut<i> et omnia <momen>ta perpenso dirigere, <oculo> ex omnibus corniculis ex<t>ensa ponderibus et inter se conparata fila seu nervias ita perspicere, donec proxima[m> consumpto alterius visu sola<m intue>atur; tunc dictare moetas, et easdem transposito interim extrema meta ferramento reprehendere eodem momento quo tenebatur, et coeptum rigorem ad interversuram aut ad finem perducere.

The manifold nature of places does not permit all these things to be done everywhere by a single method; with mountains opposed on one side, on another a river or banks or a certain yawning hollow of lying ground, with many inequalities of broken-up places, and often cultivations, for which reasons one must chiefly have recourse to the store of the art. For every smallest <minima> part of a field ought to be under the control of the measurer and constrained by the requirement of the formerly occupied rectilinear angles according to their rule. Therefore we must especially provide by what use of the tool we shall traverse whatever may be met; then to apply the diligence of measuring, by which the rather act of the progress of limitation may be made equal in the lengths of the sides; with the first instrument to direct even all the moments weighed, to perceive with the <oculo> from all corners the extended weights and the compared threads or nerves between them so clearly, until by the consumed sight of one adjoining point the other alone is seen; then to mark the metae, and having meanwhile transposed those same extremes to seize them with the tool at the very moment they were held, and to carry the begun firmness to the turning or to the end.

Omnibus autem interversuris tetrantis locum perpendiculus ostendat.

But let the plumb-line show the perpendicular position for all the transverse offsets.

Cuiuscumque loci mensura agenda fuerit, eum circumire ante omnia oportet, et ad omnes angulos signa ponere, quae normaliter ex rigore cogantur; posito deinde et perpenso ferramento rigorem secundum <pro>ximo lateri dictare, et moet<i>s conlocatis respectis in alteram partem rigorem mittere, qui, cum ad extremum pervenerit, parallelon primi rigoris excipiat. Sed si in rigore dictando quaedam devitanda incurrunt, valles, loca confragosa, arbores quas propter moram aut fructum succidere non oportet, <item> aedificia, maceriae, petrae aut montes et his similia, haec qu<a>cumque ratione optime poterint mensuram accipere debebunt.

Whenever a mensura of any place must be made, it is necessary first to circumire it, and to set signs at all angles, which are normally to be driven out from the rigor; then, the ferramentum having been placed and considered, to dictate the rigor along the ximo side, and with the moets set and sighted to send the rigor into the other direction, which, when it has come to the extremity, will receive a parallel of the first rigor. But if in dictating the rigor certain things to be avoided are encountered — valles, rugged places, trees which on account of delay or fruit ought not to be cut down, buildings, walls, rocks or mountains and the like — these, by whatever method will best be able, ought to receive measurement.

Si fuerit ergo vallis quae conspectum agentis exsuperet, per ipsam moetis ad ferramentum adpositis erit descendendum. Cuius rigoris incessum ut s<es>contrario aequemus, adf[l]icta ante linea ad capitulum perticae aequaliter ad perpendiculum cultellare debemus, <tum ad> per<m>ensum rigorem extendere lineam, quam in cult[r>um loc<ata>m perpendiculus adsigna[n]t. Nam quotiens sine linea cultellamus, <cum> conspectum moetarum excedimus, et festinantes ex eo loco iterum rigorem conspicimus, tunc in illa perticarum quamvis exigua conversione non minus fit dis<p>endi quam si iacentia <se>quam<ur>.

If therefore there should be a valley which surpasses the sight of the surveyor, one must descend through it with the moetis set toward the ferramentum. In order that the progress of that rigour be made equal to the opposite, we must cut the line struck before at the head of the pole equally to the perpendicular, and then extend the line along the measured rigour, which the perpendiculars assign to the mark placed in the cult[r>um. For as often as we cut without a guiding line, when we pass beyond the sight of the moetae, and hastening from that place again behold the rigour, then in that however slight turning of the poles no less loss of alignment occurs than if they lay aside their positions.

Conpressiorem autem vallem et ultra quam pr<o>spici poterit evadendae difficultatis causa <l>ic<et> transire, in ulteriorem partem dictare moetas ne minus tres, quibus reprehensis transposito ferramento respicere priores oporteat, et perpenso coe<pt>um rigorem quo usque res exegerit perducere.

But if the valley is more compressed and stretches beyond what can be prospected — so that, for the sake of overcoming the difficulty, it is allowable to cross — then on the farther side one must set out moetas of no fewer than three, by which, when seized and the ferramentum transposed, one ought to look back to the earlier ones, and, having weighed it, carry the begun line as far as the matter requires.

Cultellandi ratio quae sit, saepe quaeritur, cu<m> pr<o>[p>ensi soli spatium consummamus, ut illam clivorum inaequalitatem planam esse cogamus, dum mensurae lateribus inseruimus; [cultellamus ergo agrum eminentiorem et ad planitia<e> redigimus aequalitatem]. Hanc nobis ipsa seminum natura monstravit: <n>o<n> enim illa soli inaequalitas re<cte> colligi poterit, nisi quod e terra quidquid nascitur in aere rectum ex[t]istit et illam terrae obliquitatem crescendo adterit, nec maiorem numerum occupat quam si ex plano nascatur.

The method of cultellandi — what it is — is often asked, when we consume only the space of the inclined soil, so that we force that inequality of the slopes to be level while we set our measures along the sides; therefore we cultellamus the more eminent field and reduce it to the equality of the plain. Nature of the seeds herself showed this to us: for that inequality of the soil cannot be rightly gathered up, unless whatever is born from the earth stands straight in the air and by growing wears down that obliquity of the ground, nor does it occupy a greater number than if it were born from a plane.

Quod si monti ordinat<a> semina nasc<ere>ntur omnia, secundum loci naturam me<ti>re<m>ur: cum non idem, hoc est totidem arborum ordines, capiat, quod pares ei[us] in campo limites, recte cultellabitur.

But if all the seeds were born ordered for the mountain,
we would measure according to the nature of the place: since it does not take the same, that is, as many orders of trees, which its equals in the field's bounds occupy, it will be rightly cut down/trimmed.