LIBER QUARTUS. I.
Quoniam in initio sphaerae circuli V quomodo efficerentur ostendimus, neque eos corpore siderum notauimus, et si duo nouissimi nihil ad solis cursum pertinent, hoc est arcticos et antarcticos, de mediis tribus dicemus. sed quoniam Aratus circulis IIII sphaeram plurimum ualere dicit, neque eorum aperte quemquam demonstrat, uoluntatem nostram apertius ostendemus. aestiuum circulum unum de quattuor esse dicimus, qui θερινὸς τροπικός uocatur, quo circulo aestatem confieri demonstrauimus; et si non nemo dubitat, quare non utrique circuli, hoc est aestiuus et hiemalis, uno nomine appellentur, ideo quod quem nos aestiuum diximus, nonnullis hiemalis fiat, et quo circulo hiemem effici diximus, eo circulo aliis aestas sit: qui si uoluerint intellegere id ad nostram collocationem mundi esse demonstratum, qui inter aestiuum circulum et arcticum sumus constituti, non ad illorum sphaeram, qui ab hiemali circulo antarcticum habitantes, nobis antipodes dicuntur, facilius ad nostram accesserint uoluntatem. si quis enim uoluerit eorum, quos antipodas diximus, quod inferiore a nobis circulo constituti uidentur, sphaeram facere, non inmerito nostrum hiemalem sibi aestiuum circulum finxerit; aut si quis scriptor eorum mentionem faciens, obscure uoluerit antipodas demonstrare et dixerit, quibus in Capricorno aestas summa, aut in Cancro hiems maxima fiat, non inperita ratione acutissime dixisse uidebitur. quodcumque enim nostris circulis contrarium dixerit, id illis erit rectum. sed ne longiore sermone praeter consuetudinem utamur, ad inceptum reuertamur.
Book 4. I. The circles of the sphere
Since at the beginning, in speaking of the sphere, we showed how the five circles are made, and have not marked them out with the bodies of the stars, and since the last two, that is the arctic and the antarctic, have nothing to do with the sun's course, we shall speak of the middle three. But since Aratus says that the sphere is chiefly effective by four circles, and does not clearly show any one of them, we shall make our intention plainer. We say that the summer circle is one of the four, which is called θερινὸς τροπικός ('summer tropic'), and by this circle we have shown that summer is brought about; and if someone doubts why the two circles, that is the summer and the winter, are not called by one name, because what we have called summer becomes winter for some, and the circle by which we said winter is produced is summer for others: if they are willing to understand that this was set out with reference to our own placing of the world, we who are situated between the summer circle and the arctic, and not to the sphere of those who, living from the winter circle toward the antarctic, are called our antipodes, they will more easily come to our view. For if one of those whom we have called antipodes, because they appear to be placed on a circle lower than ours, should wish to make a sphere, he would not unreasonably represent our winter circle as his summer circle; or if any writer, making mention of them, wished to indicate the antipodes obscurely and said that for those people the greatest summer occurs in Capricorn, or the greatest winter in Cancer, he will be seen to have spoken most acutely, with no unskilful reasoning. For whatever he says is opposite to our circles, that will be right for them. But lest we use a longer discourse than is our custom, let us return to what we began.
II. DE AESTIUO.
In aestiuo circulo, de quo primum dicere instituimus, haec signa siue partes eorum perspiciuntur: capita Geminorum, Aurigae genu utrumque sinistrumque Persei crus et humerus sinister. Andromeda autem a pectore et manu sinistra diuiditur, atque ita euenit, ut caput eius cum toto pectore et manu dextra uideatur esse inter aestiuum et aequinoctialem circulum, reliquum autem corpus inter aestiuum et arcticum finem. praeterea in eodem aestiuo circulo pedes equi Pegasi positi uidentur, et caput a reliquo corpore diuiditur Oloris et alae sinisterioris ut uolantis pars non magna. Ophiuchus humeris hunc circulum sustinere uidetur ex una parte, id est aequinoctiali, ex altera parte Hercules pari ratione. Uirgo prope hunc coniungens capite, inter hunc et aequinoctialem circulum collocata est, ut fulgens ad austrum. Leo a pectore ad lumbos diuiditur, ut caput eius et corporis superior a cruribus pars inter hunc et arcticum circulum uideatur, inferior autem pars inter aestiuum et aequinoctialem. Cancer autem sic diuiditur medius, ut inter oculos eius circulus traiectus uideatur.
II. On the summer circle
On the summer circle, of which we first undertook to speak, these signs, or parts of them, are seen: the heads of the Twins, both knees of the Charioteer, and the left leg and left shoulder of Perseus. Andromeda is divided by it at the breast and left hand, so that her head with the whole breast and the right hand is seen to be between the summer and the equinoctial circle, but the rest of the body between the summer and the arctic boundary. Besides, on the same summer circle the feet of the horse Pegasus are seen placed, and the head of the Swan is divided from the rest of the body, and a small part of its left wing, as of one flying. Ophiuchus is seen to support this circle with his shoulders on one side, that is on the equinoctial side, and on the other side Heracles likewise. The Virgin, joining this circle nearby with her head, is placed between it and the equinoctial circle, shining toward the south [?]. The Lion is divided from the breast to the loins, so that its head and the upper part of the body from the legs are seen between this circle and the arctic, but the lower part between the summer and the equinoctial. The Crab is divided in the middle in such a way that the circle appears to pass between its eyes.
In his signis et hoc, ut ante diximus, circulo cum uehitur sol, euenit ut nobis, qui hac inclinatione mundi utimur, sint diei de partibus VIII partes V, noctis autem tres; neque ita tamen ut ex horologiis, sed ex sphaerae ratione. cum enim sphaeram ita constitueris, ut circulus is, qui arcticus uocatur, semper appareat, antarcticus autem numquam exoriatur, atque ita sphaera constituta, si uoles circulum aestiuum diuidere in partes VIII, ex his inuenies partes V in sphaera apparere, tres autem infra tamquam sub terra esse.
While the sun is carried through these signs and on this circle, as we said before, it comes about that for us, who have this inclination of the world, of the 8 parts of the day 5 parts are the day, 3 the night; not however according to clocks but according to the principle of the sphere. For when you have set the sphere so that the circle called arctic always appears, but the antarctic never rises, and the sphere so set, if you wish to divide the summer circle into 8 parts, you will find 5 of these parts appearing in the sphere, but 3 below, as if beneath the earth.
At aliquis dixerit, cur sphaerae circulos diuidamus in partes VIII potius quam XII aut quot libuerit alias partes. hic non sphaeram, sed se fallere hac ratione inuenietur fere. si enim fecerit ex aestiuo circulo partes XII, ex his partes VII et dimidium partis apparere, IIII autem et dimidium sub terra inueniet esse. itaque euenit, ut cum ad VII partes addita dimidia sit, simili ratione ad partes IIII accedat pars dimidia, et fiant supra terram partes VII et dimidium partis, reliquum autem sub terra, quod sunt partes IIII et dimidium. igitur oportet intellegere, ut non inminutis partibus et dimidiis fiat, sed certis numeris conficiatur, ut euenit in partibus VIII. praeterea quoniam sphaera diuisa in partes XXX euenit, ut ab aestiuo circulo ad hiemalem sint partes VIII nimirum certe eos circulos diuidemus in partes VIII. praeterea quoniam ab aestiuo circulo ad aequinoctialem sunt partes IIII de XXX, et rursus ab aequinoctiali circulo ad hiemalem de partibus XXX partes IIII, et ita nihilominus aequinoctialis ipse per se circulus medius diuiditur, ut dimidia pars eius sit sub terra, de partibus VIII partes IIII, et totidem supra, et tota ratio ad octauam partem perueniat, non dubium est, quin recte diuidatur in partes VIII. praeterea cum sol per hos circulos currens iter annuum conficere uideatur, et ab omnium signorum octaua parte, ut posterius dicemus, incipiat exoriri, et ad aliud signum transire, neque ulla alia parte signi utatur, recto ipsi quoque circuli diuiduntur in partes VIII. praeterea cum VII sidera ad eundem statum reuertantur, ut quibusdam placuit, ut cuiusmodi dies hodiernus fuerit in solis aut lunae tempestate, eiusdem modi octauo anno sit futurus, uere sphaera quoque diuiditur in partes VIII. praeterea cum uideamus octauo quoque die eiusdem sideris horam primam, aut quamlibit denique esse, et cuius hodie fuerit hora prima, eiusdem octauam quoque futuram, uerissimum est ipsam quoque sphaeram mundi, unde horae sumuntur, diuidi in partes VIII. Sed ne reliqua praetermittamus in hoc occupati, ad propositum reuertamur.
But someone may say: why do we divide the circles of the sphere into 8 parts rather than 12, or any other number of parts that we please? In this reasoning he will most likely be found to be deceiving not the sphere but himself. For if he makes 12 parts from the summer circle, of these he will find 7 and a half parts appearing, and 4 and a half beneath the earth. And so it comes about that, when a half has been added to the 7 parts, a half part is added likewise to the 4 parts, and there are above the earth 7 parts and a half part, the rest beneath the earth, which are 4 and a half. So one must understand that it is not made with diminished parts and halves, but is completed with fixed numbers, as happens in 8 parts. Moreover, since the sphere divided into 30 parts has it that from the summer circle to the winter there are 8 parts, we shall surely divide those circles into 8 parts. Moreover, since from the summer circle to the equinoctial there are 4 parts of the 30, and again from the equinoctial circle to the winter 4 parts of the 30, and in the same way the equinoctial circle itself is divided in the middle of itself, so that half of it is under the earth, 4 parts of 8, and as many above, and the whole reckoning reaches an eighth part, there is no doubt that it is rightly divided into 8 parts. Moreover, since the sun, running through these circles, is seen to complete its annual journey, and begins to rise from the eighth part of all the signs, as we shall say later, and to pass to another sign, and uses no other part of a sign, rightly the circles themselves too are divided into 8 parts. Moreover, since 7 stars return to the same condition, as some have held, so that whatever kind of day today is in the season of the sun or moon, a day of the same kind will occur in the eighth year [?], truly the sphere too is divided into 8 parts. Moreover, since we see that on every eighth day the first hour of the same star, or any other hour whatever, occurs, and that of which today was the first hour, of the same the eighth too will be, it is most true that the sphere of the world itself, from which the hours are taken, is divided into 8 parts. But lest, being occupied with this, we pass over the rest, let us return to our theme.
III.
SECUNDUS ab aestiuo aequinoctialis est circulus, in quo haec signa et partes eorum perspici possunt. Aries totus omnibus pedibus innixus uidetur. hunc autem Aratus omnium siderum celerrimum esse demonstrat, etiam minore arcto, quae breui spatio uertitur, praestare. id quid uelit esse, sic poterimus uel facillime intellegere. cum sit enim maximus circulus aequinoctialis in sphaera, inque eo Aries ut adfixus uideatur, quomodocumque fuerint figurae corporum collocatae, ut ad eundum circulum perueniant, necesse est semel uerti sphaeram. quod cum fiat, et Aries in maximo circulo, et eodem tempore ad locum, quo reliqua sidera, perueniat, necesse est eum celerrimum dici. Sed nos ad circuli definitionem ueniemus et reliqua dicemus.
III. On the equinoctial circle
The second circle from the summer one is the equinoctial, on which these signs and parts of them can be seen. The Ram is seen resting wholly on all its feet. Aratus shows this to be the swiftest of all the stars, surpassing even the Lesser Bear, which turns in a short space. What he means by this we shall be able to understand most easily as follows. Since the equinoctial is the greatest circle in the sphere, and the Ram appears as if fixed on it, in whatever way the figures of the bodies have been placed, so as to reach the same circle, the sphere must turn once. When this happens, and the Ram, on the greatest circle, arrives at the same time at the place to which the other stars arrive, it must be called the swiftest. But we shall come to the definition of the circle and speak of the rest.
in eodem Tauri genua ut fixa perspiciuntur, et si nonnulli ita finxerunt, ut uno genu, hoc est dextro nixus, sinistro pede contingere uideatur, de hoc in medio relinquemus. sed in eodem circulo zona Orionis, ut ipso circulo praecinctus existimetur; Hydra flexu a capite primo, ut ceruicibus erectis Cancrum contingere uideatur, et ex inferiore corpore Hydrae Crater cum Coruo uelut fixus esse circulo conspicitur. item paucae stellae Chelarum eodem adiunguntur. Ophiuchi genua eodem circulo a reliquo corpore diuiduntur. Aquila sinisteriore penna paene coniungens figurata est, eodemque circulo caput Pegasi cum ceruicibus nititur. His corporibus signorum aequinoctialis circulus finitur. quo sol cum peruenit, bis uno anno conficit aequinoctium, hoc est in Ariete et Chelis. in hac enim parte sphaerae et uer et autumnus confici existimatur, ita ut uer sit in Ariete, autumnus in priore parte Scorpionis, quod signum nonnulli Libram dixerunt.
On the same circle the knees of the Bull are seen as if fixed, although some have figured it so that, resting on one knee, that is the right, it seems to touch with the left foot; about this we shall leave the question open. But on the same circle the belt of Orion, so that he is held to be girded by the circle itself; the Hydra, by a bend from the first head, so that, with neck erect, it seems to touch the Crab, and from the lower body of the Hydra the Cup with the Raven is seen as if fixed to the circle. Likewise a few stars of the Claws are joined to the same. The knees of Ophiuchus are divided from the rest of his body by the same circle. The Eagle is figured almost joining it with its left wing, and by the same circle the head of Pegasus with its neck is supported. By these bodies of the signs the equinoctial circle is bounded. When the sun reaches it, it makes the equinox twice in one year, that is in the Ram and in the Claws. For in this part of the sphere spring and autumn are held to be made, so that spring is in the Ram, autumn in the front part of the Scorpion, which sign some have called the Balance.
per hunc circulum transiens sol ab Ariete ad Chelas, efficit sex mensium diem his locis, qui intra arcticum uidentur orbem; noctem autem his, qui antarctico circulo sunt clausi: quare magis his locis nemo potest durare. et rursus ab autumno usque ad uer, hoc est a Chelis usque ad Arietem perueniens, efficit his locis sex mensibus perpetuis diem, in quibus ante noctem demonstrauimus; e contrario autem noctem his, qui boreo polo sunt proximi. sed de hoc ante diximus. neque enim mirum est hac collocatione sphaerae id euenire. erecto enim boreo polo neque umquam occidente euenit, ut corpora quoque, quae ei proxima sunt circulo, sero occidere uideantur. id ex hoc intellegere licebit: cum in his partibus sphaerae habitetur, quae pars est ab aestiuo circulo ad orbem, qui arcticos uocatur, et de arctico circulo, hoc est de duabus Ursis et Dracone, caput Draconis maxime niti ipso circulo uideatur, ita ut is qui Engonasin uocatur, inter aestiuum et arcticum collocatus, caput Draconis premere intellegatur: quicumque, ut ante diximus, ad ipsum caput Draconis habitant, ita longo die utuntur, ut ne tertia quidem horae pars in unaquaque nocte his obtingat. itaque Aratus ait: κείνῃ που κεφαλὴ τῇ νείσεται ἧχί περ ἄκραι μίσγονται δύσιές τε καὶ ἀντολαὶ ἀλλήλῃσι. idem Cicero dicit: quod caput hic paulum sese subitoque recondit, ortus ubi atque obitus parte admiscentur in una. de hoc Homerus quoque in Odyssea ita breuem noctem dicit esse, ut pastores cum alii exigant, alii reducant pecus, possit alius alium audire, cum unus propter noctem pecus reducat, alter propter lucem exigat. sed nos ad propositum reuertamur.
The sun, passing along this circle from the Ram to the Claws, makes a day of six months in those places that are seen to lie within the arctic orb; but night for those who are enclosed by the antarctic circle: so that no one can endure in those places all the more [?]. And again from autumn to spring, that is from the Claws reaching the Ram, it makes in those places in which we showed before that there was night a day of six unbroken months; but, on the contrary, night for those who are nearest the north pole. But of this we have spoken before. Nor is it surprising that this happens with this placing of the sphere. For, with the north pole raised and never setting, it happens that the bodies too which are nearest to it in the circle appear to set late. This can be understood from the following: when the parts of the sphere are inhabited which lie from the summer circle to the orb that is called arctic, and from the arctic circle, that is from the two Bears and the Dragon, the head of the Dragon is seen to rest most on the circle itself, so that the one called Engonasin, placed between the summer and the arctic, is understood to press down the Dragon's head: those who, as we said before, live at the very head of the Dragon, have so long a day that not even a third part of an hour falls to them in each night. And so Aratus says: κείνῃ που κεφαλὴ τῇ νείσεται ἧχί περ ἄκραι | μίσγονται δύσιές τε καὶ ἀντολαὶ ἀλλήλῃσι ('there, perhaps, the head goes down, where the extremities mingle, settings and risings with one another'). Cicero says the same: 'Because this head dips a little and suddenly hides, where risings and settings mingle in one part.' About this Homer too in the Odyssey says that the night is so short that, while some herdsmen are driving out their flocks and others bringing them back, one can hear another, when one brings back his flock because of the night, and the other drives his out because of the light. But let us return to our theme.
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