| (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. |
