I. DE MUNDO.
Mundus appellatur is qui constat ex sole et luna et terra et stellis omnibus.
I. On the World
'World' (mundus) is the name for that which consists of sun and moon and 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. A sphere is a kind of shape formed in the round, appearing equal on all sides, from which the other circles are bounded. Of this neither end nor beginning can be fixed, because in a round all paths can mark both beginnings and ends.
II. DE CENTRO.
Centron est cuius ab initio circumductio sphaerae terminatur, ac terrae positio constituta declaratur.
II. On the Centre
The centre (centron) is that from which, at the outset, the circuit of the sphere is bounded, and by which the position of the earth is established and made plain.
III. DE DIMENSIONE.
Dimensio, quae totius ostenditur sphaerae, est cum ex utrisque partibus eius ad extremam circumductionem rectae ut uirgulae 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.
III. On the Dimension
The dimension that is shown for the whole sphere is when straight lines, like rods, are drawn from both its sides to the outermost circuit; this dimension has been called by very many the axis. Its tips, on which the sphere chiefly rests, are called poles; of these one, looking toward the north, is called boreus, the opposite one, toward the south, notius.
IV.
SIGNIFICATIONES 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.
IV. Circles and the Horizon
Certain marks on the circuit of the sphere are called circles. Of these, those are called parallels which are drawn about the same pole; the greatest are those that are contained with the same centre as the sphere.
Horizon appellatur is, qui terminat ea quae perspici aut non uideri 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, peruidetur ita, utcumque fuerit sphaera conlocata.
The horizon is the name for that which bounds what can and cannot be seen. This is defined on no fixed principle, since it is perceived now resting on the pole and on the circles called parallels, now supported by the two extreme and equal [circles] [?], now attached to other parts of the earth, according to how the sphere happens to be placed.
V.
POLUS is qui boreus appellatur, peruideri 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 uideantur. exortus enim est subita quaedam species obiecta nostro conspectui; occasus autem pari de causa, ut erepta ab oculis uisa.
V. The Poles; Rising and Setting
The pole called boreus can always be seen; the notius, on a different principle, is always removed from sight. The natural station of the world, which is called 'physical', is fixed at the boreal pole, so that everything appears to rise on the right-hand side and to set on the left. For a rising is a sudden appearance presented to our sight; a setting, for the same reason, is something seen snatched away from the eyes.
VI.
In finitione mundi circuli sunt paralleli V, in quibus tota ratio sphaerae consistit, praeter eum qui zodiacus appellatur; qui quod non, ut ceteri circuli, certa dimensione finitur, et inclinatior aliis uidetur, λοξός a Graecis est dictus.
VI. The Five Circles and the Zodiac
In the definition of the world there are five parallel circles, on which the whole system of the sphere rests, apart from the one called the zodiac; because this one is not bounded by a fixed measure like the other circles, and appears more inclined than the others, it is called by the Greeks λοξός ('oblique').
quinque autem quos supra diximus, sic in sphaera metiuntur, initio sumpto a polo qui boreus appellatur, ad eum qui notius et antarcticus uocatur. in triginta partes unumquodque hemisphaerium diuiditur, ita uti dimensio significare uideatur in tota sphaera sexaginta partes factas. deinde ab eodem principio boreo sex partibus ex utraque finitione sumptis, circulus ducitur, cuius centron ipse est polus finitus; qui circulus arcticos appellatur, quod intra eum Arctorum simulacra ut inclusa perspiciuntur; quae signa a nostris ursarum specie ficta, Septentriones appellantur.
The five that we mentioned above are measured on the sphere as follows, starting from the pole called boreus and going to the one called notius and antarcticus. Each hemisphere is divided into thirty parts, so that the dimension is seen to signify sixty parts made in the whole sphere. Then, from the same boreal starting point, six parts being taken from either bound [?], a circle is drawn whose centre is the pole itself, the bounded one; this circle is called arcticos, because within it the figures of the Bears are seen as though enclosed; these signs, made by our people in the likeness of she-bears, are called the Septentriones.
ab hoc circulo de reliquis partibus quinque sumptis, eodem centro quo supra diximus, circulus ducitur, qui θερινὸς τροπικός appellatur, ideo quod sol cum ad eum circulum peruenit, 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 reuertitur, τροπικός est appellatus, ab hoc circuli significatione quattuor de reliquis partibus sumptis, ducitur circulus aequinoctialis, qui a Graecis ἰσημερινός appellatur, ideo quod sol cum ad eum orbem peruenit, aequinoctium conficit.
From this circle, five of the remaining parts being taken, with the same centre as we said above, a circle is drawn that is called θερινὸς τροπικός ('summer tropic'), because the sun, when it reaches that circle, brings summer to those who are in the northern regions, but winter to those whom we said earlier lie exposed to the blasts of the south wind. Further, because the sun does not pass beyond that circle but turns back at once, it is called τροπικός ('of turning'). From this marking of the circle, four of the remaining parts being taken, the equinoctial circle is drawn, which is called by the Greeks ἰσημερινός, because the sun, when it reaches that orbit, produces 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 ἀνταρκτικός uocatur, quod contrarius est ei circulo, quem arcticon supra definiuimus. hac definitione sphaerae, centroque poli qui notius dicitur, V partibus sumptis, circulus χειμερινὸς τροπικός instituitur, a nobis hiemalis, a nonnullis etiam brumalis appellatus, ideo quod sol cum ad eum circulum peruenit, hiemem efficit his qui ad aquilonem spectant; aestatem autem his qui in austri partibus domicilia constituerunt. quanto enim abest longius ab illis qui in aquilonis habitant finibus, hoc hieme maiore conflictantur; aestate autem hi, quibus sol appositus peruidetur. 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 uideatur.
When this circle has been made, half of the sphere is seen to be marked out. In the opposite direction likewise, on a like principle, six parts being taken from the southern pole, as we said above of the boreal one, the circle drawn is called ἀνταρκτικός ('anti-arctic'), because it is opposed to the circle that we defined above as the arctic. With this marking out of the sphere, and with the pole called notius as centre, five parts being taken, a circle is set up called χειμερινὸς τροπικός ('winter tropic'), by us 'hiemalis', by some also 'brumalis', because the sun, when it reaches that circle, brings winter to those who look toward the north, but summer to those who have made their homes in the southern parts. For the farther one is from those who live in the northern regions, the heavier the winter with which they are struggling; and in summer, those to whom the sun is seen close at hand. And so the Ethiopians necessarily come to lie beneath either orbit. From this circle to the equinoctial circle four parts remain, so that the sun is seen to run through eight parts of the sphere.
Zodiacus autem circulus sic uel optime definiri poterit, ut signis factis, sicut postea dicemus, ex ordine circulus perducatur, qui autem lacteus uocatur, contrarius aequinoctiali, ibi oportet ut eum medium diuidere et bis ad eum peruenire uideatur, semel in eo loco ubi Aquila constituitur, iterum autem ad eius signi regionem, quod Procyon uocatur.
The zodiac circle can best be defined thus: that, signs having been made, as we shall say later, the circle is drawn through in order. The one called the Milky Way, opposite to the equinoctial, ought to divide the latter in the middle and to be seen to meet it twice, once at the place where the Eagle is stationed, and again at the region of the sign called Procyon [?].
Duodecim signorum partes sic diuiduntur: Quinque circuli, de quibus supra diximus, ita finiuntur, ut unusquisque eorum diuidatur 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 diuidantur, et ita circuli pari ratione ducantur. id facillime defendi posse confidimus. cum enim media sphaera diuisa est, eius circuli nullus potest aequalis esse, qui quamuis proxime eum accedat, tamen minor esse uideatur. itaque qui primum sphaeram fecerunt, cum uellent omnium circulorum aequas rationes esse, pro rata parte uoluerunt 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 uideantur effectus. et si non in triginta partes unumquodque hemisphaerium diuidatur, sed in alias quaslibet finitiones, tamen eo ratio peruenit eius, ac si triginta partes fecisset
The parts of the twelve signs are divided as follows: the five circles of which we spoke above are bounded so that each of them is divided into twelve parts, and from their points lines are drawn which mark the circles made, on which the twelve signs are described. But some rather unskilled persons ask why the circles are not bounded in equal parts, that is, why of thirty parts five-part portions are not divided, and the circles drawn on the same principle. We trust this can very easily be answered. For when the sphere has been divided in the middle, none of its circles can be equal [to that one], since even the one that comes nearest to it will still appear smaller. So the first makers of the sphere, wanting all the circles to have equal proportions, chose to indicate them by proportional part: that the farther one withdrew from the pole, the smaller the number of parts they took in measuring the circles, since for these they had to mark out the larger circle [?]. This can also be understood from the sphere itself: the farther you withdraw from the pole, the larger the circles must be, and for this reason a smaller number must be drawn, so that their effects appear equal. And even if each hemisphere were not divided into thirty parts, but into any other divisions whatever, the reasoning would still arrive at the same result as if it had made thirty parts.
VII.
Zodiacus circulus tribus his subiectus, de quibus supra diximus, ex quadam parte contingit aestiuum et hiemalem circulum, aequinoctialem autem medium diuidit. itaque sol per zodiacum circulum currens, neque extra eum transiens necessario etiam cum signis his, quibus innixus iter conficere uidetur, peruenit ad eos quos supra diximus orbes et ita quattuor tempora definit. nam ab Ariete incipiens uer ostendit; et Taurum et Geminos transiens, idem significat. sed iam capitibus Geminorum circulum aestiuum tangere uidetur, et per Cancrum et Leonem transiens et Uirginem, aestatem efficit. et rursus a Uirginis extrema parte transire ad aequinoctialem circulum perspicitur; in Libra autem aequinoctium conficit et autumnum significare incipit. 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 peruenire.
VII. The Zodiac and the Seasons
The zodiac circle, lying under these three of which we spoke above, touches the summer and the winter circle in one part, and divides the equinoctial in the middle. And so the sun, running through the zodiac circle and not passing outside it, necessarily comes also, with the signs on which it is seen to make its journey, to the orbits we spoke of, and so fixes the four seasons. For beginning from the Ram it shows spring; and passing through the Bull and the Twins it signifies the same. But already at the heads of the Twins it is seen to touch the summer circle, and passing through the Crab and the Lion and the Virgin it makes summer. And again, from the last part of the Virgin it is seen to pass to the equinoctial circle; in the Balance (Libra) it makes the equinox and begins to signify autumn. From this sign, passing to the Scorpion and the Archer, it runs straight into the winter circle and spends the winter in Capricorn, Aquarius and the Fishes. So it is shown that it does not run along the three circles themselves, but, passing through the zodiac, comes to them.
Sed quoniam de his rebus diximus, nunc terrae positionem definiemus, et mare quibus locis interfusum uideatur, ordine exponemus.
But since we have spoken of these matters, we shall now define the position of the earth, and set out in order in what places the sea is seen to lie between.
VIII. DE TERRA.
Terra mundi media regione collocata, omnibus partibus aequali dissidens interuallo, centron optinet sphaerae. hanc mediam diuidit axis in dimensione totius terrae. 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 aestiuum finem collocata est, ea diuiditur trifarie; e quibus una pars Europa, altera Asia, tertia Africa uocatur. Europam igitur ab Africa diuidit 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 diuidit, bifariam se coniciens in paludem quae Maeotis appellatur. hac igitur definitione facile peruidetur mare omnibus obiectum finibus terrae.
VIII. On the Earth
The earth, set in the middle region of the world, standing equally distant on all sides, holds the centre of the sphere. The axis divides it in the middle, in the dimension of the whole earth. Ocean, poured forth along the circuit of the sphere, washes almost the bounds of the whole orb; and so the setting signs are thought to fall into it. In this way, then, we shall be able to explain how the lands are contained. For whatever region lies between the arctic and the summer boundary is divided three ways; of these one part is called Europe, another Asia, the third Africa. Europe, then, is divided from Africa by the sea, from the farthest bounds of Ocean and the Pillars of Heracles. Asia and Libya with Egypt are separated by the mouth of the Nile that is called the Canopic. Asia is divided from Europe by the Tanais, which, splitting in two, throws itself into the marsh called the Maeotis. By this definition, then, it is easily seen that the sea lies against all the bounds of the earth.
Sed ne uideatur nonnullis mirum, cum sphaera in sexaginta partes diuidatur, ut ante diximus, quare definiuimus ab aestiuo circulo ad arcticum finem dumtaxat habitari, sic uel optime defendimus sol enim per mediam regionem sphaerae currens, nimium his locis efficit feruorem. itaque quae finis est ab aestiuo circulo ad hiemalem, ea terra a Graecis διακεκαυμένη uocatur, 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 have defined only the region from the summer circle to the arctic boundary as inhabited, we defend this best as follows: the sun, running through the middle region of the sphere, produces excessive heat in these places. And so the tract from the summer circle to the winter circle is called by the Greeks διακεκαυμένη ('burnt up'), because neither can crops grow, the ground being scorched, nor can men endure, because of the excessive burning.
extremae autem regiones sphaerae duorum circulorum, quorum alter boreus, alter notius uocatur, fine arctici circuli et eius qui antarcticos uocatur, non habitantur, ideo quod sol ab his circulis semper abest longe, uentique assiduos habent flatus. quamuis enim sol perueniat ad aestiuum circulum, tamen longe ab arctico uidebitur fine.
But the outermost regions of the sphere, of the two circles of which one is called boreus, the other notius, at the boundary of the arctic circle and of the one called antarcticus, are not inhabited, because the sun is always far from these circles, and the winds blow there continually. For although the sun reaches the summer circle, it will still be seen to be far from the arctic boundary.
id ita esse hinc quoque licet intellegere: Cum enim sol peruenit ad eum circulum qui hiemalis uocatur, et efficiat nobis, qui prope eum sumus constituti, nimium frigus, quid arbitramur eis locis frigoris esse, qui longius etiam absunt a nobis? quod cum in hac parte sphaerae fiat, idem in altera parte definitum putauimus, ideo quod similes sunt eius effectus. praeterea hinc quoque intellegimus illic maximum frigus et in aestiuo circulo calorem esse, quod qua terra habitatur, eos tamen uidemus, qui proxime sunt arcticum finem, uti bracis et eiusmodi uestimenta; qui autem proximi sunt aestiuo circulo, eos Aethiopas et perusto corpore esse. habitatur autem sic temperatissimo caelo, cum inter aestiuum circulum et arcticum finem haec proueniat temperatio; quod ab arctico circulo frigus, ab aestiuo feruor exortus in unum concurrens efficit mediam finem temperatam, quae habitari possit.
That this is so can be understood from this too: when the sun reaches the circle that is called the winter circle, and produces excessive cold for us, who are placed near it, what do we suppose is the cold in those places that are still farther from us? Since this happens in this part of the sphere, we thought the same defined in the other part, because its effects are similar. Besides, from this too we understand that there is the greatest cold there, and heat at the summer circle [?]: on the land that is inhabited we see, nevertheless, that those who are nearest the arctic boundary wear trousers (bracae) and clothing of that kind, while those who are nearest the summer circle are Ethiopians, with scorched bodies. It is inhabited, then, under a most temperate sky, since this temperateness arises between the summer circle and the arctic boundary; because the cold from the arctic circle and the heat arising from the summer circle, meeting in one, make the middle boundary temperate, so that it can be inhabited.
itaque cum sol ab eo loco discessit, hieme necessario conflictamur, quod uentum exorientem non reuerberat sol. quod cum ueniat in hac definitione, illud quoque fieri posse uidemus, ut hiemali circulo nobis ad antarcticum finem habitari possit, quod pares eodem proueniant casus, certum quidem esse nemo contendit, neque peruenire eo potest quisquam propter interiectum terrae, quae propter ardorem non habitatur. sed cum uidemus hanc regionem sphaerae habitari, illam quoque in simili causa posse constitui suspicamur.
And so, when the sun has departed from that place, we are necessarily afflicted by winter, because the sun does not beat back the wind that arises. Since this comes about in this definition, we see that this too can happen: that between the winter circle and the antarctic boundary there may be habitation as for us [?], because like events occur there; no one maintains that this is certain, nor can anyone reach there on account of the intervening land, which is not inhabited because of the heat. But when we see that this region of the sphere is inhabited, we suspect that that one too can be established on a like ground.
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