Questio de aqua et terra (30-39)

(30) [XIV]. Si ergo impossibile est aquam esse ecentricam, ut per primam figuram demonstratum est, et esse cum aliquo gibbo, ut per secundam est demonstratum; necesse est ipsam esse concentricam et coequam, hoc est equaliter in omni parte sue circumferentie distantem a centro mundi, ut de se patet. (30) If, then, it is impossible for water to be excentric, as was shown by the first figure, and also that it should have a hump, as is shown by the second, it must necessarily be concentric [with earth], and also symmetrical, that is equally distant from the centre of the universe at every point of its circumference, as is obvious.
(31) [XV]. Nunc arguo sic: Quicquid superheminet alicui parti circumferentie distantis equaliter a centro, est remotius ab ipso centro quam aliqua pars ipsius circumferentie: sed omnia littora, tam ipsius Amphitritis quam marium mediterraneorum, superheminent superficiei contingentis maris, ut patet ad oculum; ergo omnia littora sunt remotiora a centro mundi, cum centrum mundi sit centrum maris ut visum est, et superficies littorales sint partes totalis superficiei maris: et cum omne remotius a centro mundi sit altius, consequens est quod littora omnia sint superheminentia toti mari; et si littora, multo magis alie regiones terre, cum littora sint inferiores partes terre; et id flumina ad illa descendentia manifestant. (31) I now proceed to argue thus: Anything that is higher than any part of a circumference equidistant from its centre is remoter from that centre than any part of that circumference. But all the shores, both of Amphitrite herself and of the inland seas, are higher than the surface of the contiguous sea, as is plain to the eye; therefore all the shores are remoter from the centre of the universe, since the centre of the universe is also the centre of the sea, as we have seen; and the surfaces at the shores are parts of the total surface of the sea. And since everything remoter from the universe is loftier, it follows that all the shores are higher than all the sea; and if the shores, then much more the other regions of earth, since the shores are the lower portions of the land, as the rivers show by descending to them.
(32) Maior vero huius demonstrationis demonstratur in theorematibus geometricis; et demonstratio est ostensiva, licet vim suam habeat, ut in hiis que demonstrate sunt superius, per impossibile. (32) Now the major premise of this demonstration is demonstrated in geometrical theorems; and the demonstration is conclusive, although it derives its force (as in the case of our own proofs above) from a reductio ad impossibile.
(33) Et sic patet de secundo. (33) And so we have established the second point.
(34) [XVI]. Sed contra ea que sunt determinata, sic arguitur: Gravissimum corpus equaliter undique ac potissime petit centrum: terra est gravissimum corpus; ergo equaliter undique ac potissime petit centrum. Et ex hac conclusione sequitur, ut declarabo, quod terra equaliter in omni parte sue circumferentie distet a centro, per hoc quod dicitur 'equaliter'; et quod sit substans omnibus corporibus, per hoc quod dicitur 'potissime'; unde sequeretur, si aqua esset concentrica, ut dicitur, quod terra undique esset circumfusa et latens; cuius contrarium videmus. (34) But against the things now established it is argued thus: The heaviest body seeks the centre equally from every direction and with the greatest force. Earth is the heaviest body. Therefore it seeks the centre equally from every direction and with the greatest force. And from this conclusion follows, as I shall show, that the earth is equally distant from the centre at every point of its circumference (as is involved in the meaning of the word 'equally'), and that it is lower down than any other body (as is involved in the meaning of 'with the greatest force'); whence it would follow (if water were concentric, as declared) that the land would be submerged on every side, and would not appear; the contrary of which we see.
(35) Quod illa sequantur ex conclusione, sic declaro: Ponamus per contrarium sive oppositum consequentis illius quod est in omni parte equaliter distare, et dicamus quod non distet; et ponamus quod ex una parte superficies terre distet per viginti stadia, ex alia per decem: et sic unum emisperium eius erit maioris quantitatis quam alterum: nec refert utrum parum vel multum diversificentur in distantia, dummodo diversificentur. Cum ergo maioris quantitatis terre sit maior virtus ponderis, emisperium maius per virtutem sui ponderis prevalentem impellet emisperium minus, donec adequetur quantitas utriusque, per cuius adequationem adequetur pondus; et sic undique redibit ad distantiam quindecim stadiorum; sicut et videmus in appensione ac adequatione ponderum in bilancibus. (35) That these results follow from the conclusion I thus explain: Let us make an assumption contrary, or opposite, to this consequence (namely, that it is equidistant at every part), and let us say it is not equidistant. And let us suppose that at one point the surface of the earth is distant twenty stadia, and at another point ten, so that one of its hemispheres will exceed the other in quantity. Nor does it matter whether the difference in distance be little or much, so long as there is a difference. Since, then, there is more virtue of gravity in the greater quantity of earth, the greater hemisphere, by the superior virtue of its weight, will shove the lesser hemisphere until the quantity of each is equalised, by which equalising their weight will be equalised also; and thus the distance on either side will be reduced to fifteen stadia, as we see when we add weights to the balances to bring them to equality.
(36) Per quod patet quod impossibile est terram equaliter centrum petentem diversimode sive inequaliter in sua circumferentia distare ab eo. Ergo necessarium est oppositum suum quod est equaliter distare, cum distet; et sic declarata est consequentia, quantum ex parte eius quod est equaliter distare. (36) Whereby it is plainly impossible for earth, which equally seeks the centre, to be diversely or unequally distant from it in its circumference. Therefore the opposite of being unequally distant, namely, being equally distant, is necessary where there is any distance at all; and thus the sequence has been defended so far as refers to equi-distance.
(37) Quod etiam sequatur ipsam substare omnibus corporibus, quod sequi etiam ex conclusione dicebatur, sic declaro: Potissima virtus potissime attingit finem, nam per hoc potissima est, quod citissime ac facillime finem consequi potest: potissima virtus gravitatis est in corpore potissime petente centrum, quod quidem est terra; ergo ipsa potissime attingit finem gravitatis, qui est centrum mundi; ergo substabit omnibus corporibus, si potissime petit centrum; quod erat secundo declarandum. (37) That it also follows that it must be below all other bodies (which was likewise declared to follow from our conclusion), I thus maintain: The most potent virtue most potently attains the goal; for what makes it most potent is, that it can most swiftly and easily reach the goal. The most potent virtue of gravity is in the body which most potently seeks the centre; and that body is earth. Therefore earth most potently approaches the goal of gravity, which is the centre of the world. Therefore it will be below all the other bodies, seeing that it seeks the centre most potently; which was the second point to be elaborated.
(38) Sic igitur apparet esse impossibile quod aqua sit concentrica terre; quod est contra determinata. (38) Thus it appears that it is impossible for water to be concentric with earth, which is contrary to the conclusion we had reached.
(39) [XVII]. Sed ista ratio non videtur demonstrare, quia propositio maior principalis sillogismi non videtur habere necessitatem. Dicebatur enim 'gravissimum corpus equaliter undique ac potissime petit centrum'; quod non videtur esse necessarium; quia, licet terra sit gravissimum corpus comparatum ad alia corpora, comparatum tamen in se, secundum suas partes, potest esse gravissimum et non gravissimum, quia potest esse gravior terra ex una parte quam ex altera. (39) But this argument does not appear to be conclusive, because the major of the main syllogism does not itself appear to be necessarily true. For it was urged, 'that the heaviest body seeks the centre equally from every direction, and most potently,' which does not seem to be necessary; for though earth is the heaviest body compared to other bodies, yet compared to itself, to wit in its several parts, it may be both the heaviest and not the heaviest; for there may be heavier earth on the one side than on the other.