| (20) [XI]. Ad evidentiam igitur dicendorum, duo supponenda sunt: primum est quod aqua naturaliter movetur deorsum; secundum est quod aqua est labile corpus naturaliter, et non terminabile termino proprio. |
(20) To prove what we have to say, two points must be conceded: the first is that water naturally moves downward, and the second that water is naturally a fluid body and incapable of being bounded by a boundary intrinsic to itself. |
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| (21) Et si quis hec duo principia vel alterum ipsorum negaret, ad ipsum non esset determinatio, cum contra negantem principia alicuius scientie non sit disputandum in illa scientia, ut patet ex primo Physicorum; sunt etenim hec principia inventa sensu et inductione, quorum est talia invenire, ut patet ex primo Ad Nicomacum. |
(21) And if any one were to deny these two principles, or either of them, our proof would not appeal to him, since, if any one denies the principles of any science, there can be no discussion with him in that science, as is shown in the first Physicorum. For these principles are discovered by the senses and by induction, whose province it is to discover such, as is clear from the first ad Nichomachum. |
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| (22) [XII]. Ad destructionem igitur primi membri consequentis dico quod aquam esse ecentricam est impossibile. Quod sic demonstro: Si aqua esset ecentrica, tria impossibilia sequerentur; quorum primum est quod aqua esset naturaliter mobilis sursum et deorsum; secundum est quod aqua non moveretur deorsum per eandem lineam cum terra; tertium est quod gravitas equivoce predicaretur de ipsis; que omnia non tantum falsa sed impossibilia esse videntur.
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(22) For the refutation of the first member of the consequent, I say that it is impossible for water to be excentric; which I demonstrate thus: Were water excentric, three impossibilities would follow, the first of which is, that water would naturally move both up and down; the second is, that water would not drop along the same line as earth; the third is, that gravity would be predicated in a different sense of each of them. All which seem to be not only false but impossible. |
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| (23) Consequentia declaratur sic: Sit celum circumferentia in qua tres cruces, aqua in qua due, terra in qua una; et sit centrum celi et terre punctus in quo A, centrum vero aque ecentrice punctus in quo B; ut patet in figura signata. Dico ergo quod, si aqua erit in A et habeat transitum, quod naturaliter movebitur ad B, cum omne grave moveatur ad centrum proprie circumferentie naturaliter; et cum moveri ab A ad B sit moveri sursum, cum A sit simpliciter deorsum ad omnia, aqua movebitur naturaliter sursum; quod erat primum impossibile, quod sequi dicebatur. |
(23) The sequence is thus established. Let the circumference marked with three crosses be heaven, that marked with two crosses water, and that marked with one, earth. And let the centre of heaven and earth be the point marked A, and the centre of water, which is excentric, the point marked B, as shown in the marked figure. I say, then, that if there should be water at A having a free course, it would naturally move to B, since everything that has weight naturally moves to the centre of its proper circumference; and since moving from A to B is moving up (since A is absolutely down, with reference to everything), water will naturally move up, which was the first impossibility mentioned above. |
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| (24) Preterea sit gleba terre in Z, et ibidem sit quantitas aque, et absit omne prohibens: cum igitur, ut dictum est, omne grave moveatur ad centrum proprie circumferentie, terra movebitur per lineam rectam ad A, et aqua per lineam rectam ad B; sed hoc oportebit esse per lineas diversas, ut patet in figura signata; quod non solum est impossibile, sed rideret Aristotiles si audiret. Et hoc erat secundum, quod declarari debebatur. |
(24) Again, let there be a clod of earth at Z, and let there be a quantity of water at the same place, and let there be no obstacle. Then, since everything that has weight moves, as already declared, to the centre of its proper circumference, the earth will move along the straight line to A, and the water along the straight line to B; but this will of necessity be along different lines, as is clear from the marked figure; and not only is this impossible, but Aristotle would laugh to hear it; and this is the second point which had to be shown. |
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| (25) Tertium vero declaro sic: Grave et leve sunt passiones corporum simplicium, que moventur motu recto; et levia moventur sursum, gravia vero deorsum. Hoc enim intendo per grave et leve, quod sit mobile; sicut vult Phylosophus in Celo et Mundo. Si igitur aqua moveretur ad B, terra vero ad A, cum ambo sint corpora gravia, movebuntur ad diversa deorsum; quorum una ratio esse non potest, cum unum sit deorsum simpliciter, aliud vero secundum quid. Et cum diversitas in ratione finium arguat diversitatem in hiis que sunt propter illos, manifestum est quod diversa ratio gravitatis erit in aqua et in terra; et cum diversitas rationis cum identitate nominis equivocationem faciat, ut patet per Phylosophum in Antepredicamentis, sequitur quod gravitas equivoce predicetur de aqua et terra; quod erat tertium consequentie membrum declarandum. |
(25) The third I thus set forth: Heavy and light are affections of elementary bodies, which move in straight lines; and the light ones move up, but the heavy down. For what I mean by heavy and light is mobile, as the Philosopher in Caelo et Mundo has it. If, then; the water move to B and the earth to A, then, since they are both heavy bodies, they will move to different 'downs,' the meanings of which cannot be the same, since one is 'down' absolutely and the other relatively. And since difference of meaning in the ends argues difference in the things which conduce to them, it is manifest that the meaning of fluidity will be different in the case of water and of earth; and since difference of meaning with identity of name constitutes equivocality, as is clear from the Philosopher in Antepraedicamentis, it follows that gravity would be predicated in different senses of water and of earth, which was the third member of the sequence that we were to develop. |
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| (26) Sic igitur patet per veram demonstrationem hoc, quod aqua non est ecentrica; quod erat primum consequentis principalis consequentie quod destrui debebatur. |
(26) Wherefore it follows, from the true demonstration (derived from the character of the bodies concerned) whereby I have shown that this is not so, that water is not excentric; and this was the first [member] which we had to refute of the consequent of the main sequence. |
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| (27) [XIII]. Ad destructionem secundi membri consequentis principalis consequentie, dico quod aquam esse gibbosam est etiam impossibile. Quod sic demonstro: IMAGE Sit celum in quo quatuor cruces, aqua in quo tres, terra in quo due; et centrum terre et aque concentrice et celi sit D. Et presciatur hoc, quod aqua non potest esse concentrica terre, nisi terra sit in aliqua parte gibbosa supra centralem circumferentiam ut patet instructis in mathematicis, si in aliqua parte emergit a circumferentia aque. Et ideo gibbus aque sit in quo H, gibbus vero terre in quo G; deinde protrahatur linea una a D ad H, et una alia a D ad F. Manifestum est quod linea que est a D ad H est longior quam que est a D ad F, et per hoc summitas eius est altior summitate alterius; et cum utraque contingat in summitate sua superficiem aque, neque transcendat, patet quod aqua gibbi erit sursum per respectum ad superficiem ubi est F. Cum igitur non sit ibi prohibens si vera sunt que prius supposita erant, aqua gibbi dilabetur, donec coequetur ad D cum circumferentia centrali sive regulari; et sic impossibile erit permanere gibbum, vel esse; quod demonstrari debebat. |
(27) To refute the second member of the consequent of the main sequence, I say that it is also impossible for water to have a hump, which I thus demonstrate: Let heaven be the circumference marked with four crosses, water that to marked with three, and earth that marked with two; and let the centre of earth, of water (supposed concentric), and of heaven be D. And let us suppose it to be known that water cannot be concentric with earth unless earth have a hump somewhere, above its central circumference (as is clear to those who have studied mathematics), if indeed it emerges anywhere at all from the circumference of the water. So let the hump of water be at the place marked H, and the hump of the earth at the place marked G; then let a line be drawn from D to H, and another from D to F. It is clear that the line from D to H is longer than the line from D to F; and therefore its extremity is higher up than the extremity of the other; and since each touches the surface of the water at its extremity, but does not pass it, it is clear that the water of the hump will be 'up' with respect to the surface at which F is. Since, then, there is no obstacle, it follows from our axioms that the water of the hump will flow down until it is equidistant from D with the regular or central circumference; and thus it will be impossible for the hump to remain, or indeed to exist; which is what we were to show. |
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| (28) Et preter hanc potissimam demonstrationem, potest etiam probabiliter ostendi quod aqua non habeat gibbum extra circumferentiam regularem; quia quod potest fieri per unum, melius est quod fiat per unum quam per plura: sed totum suppositum potest fieri per solum gibbum terre, ut infra patebit; ergo non est gibbus in aqua; cum Deus et natura semper faciat et velit quod melius est, ut patet per Phylosophum primo De Celo et Mundo, et secundo De Generatione Animalium. |
(28) And besides this most cogent demonstration, it can also be shown by way of probability that water would not have a hump protruding from its regular circumference; for what can be done by one, is better done by one than by several; and the whole matter before us may be effected by a hump of earth alone, as will be seen below. Therefore there is no hump in the water, since God and nature ever doeth and willeth what is better, as is clear from the Philosopher, De Caelo et Mundo, and in the second De Generatione Animalium. |
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| (29) Sic igitur patet de primo sufficienter; videlicet quod impossibile est aquam in aliqua parte sue circumferentie esse altiorem, hoc est remotiorem ad centrum mundi, quam sit superficies huius terre habitabilis; quod erat primum in ordine dicendorum. |
(29) Thus we have sufficiently established the first point, namely, that it is impossible for water in any portion of its circumference to be loftier, that is remoter from the centre of the universe, than is the surface of this habitable earth, which was the first in order of the things we had to say. |
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