if you add that part to it which was cut off from it at first, which was finite, the whole will be finite; and then it will be no longer or shorter than that Line which had nothing cut off from it, therefore equal to it; But this is finite, therefore the other is finite.  Therefore the Body in which such Lines are drawn is finite; And all Bodies in which such Lines may be drawn, are finite:  But such Lines may be drawn in all Bodies.  Therefore if we suppose an infinite Body, we suppose an Absurdity and Impossibility.

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[Illustration 6]

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Sec. 52b.  When by the singular strength of his Genius, (which he exerted in the finding out such a Demonstration) he had satisfied himself that the Body of Heaven was finite; he desired, in the next place, to know what Figure it was of, and how it was limited by the circumambient Superficies.  And first he observ’d the Sun, Moon and Stars, and saw that they all rose in the East, and set in the West; and those which went right over his Head describ’d a great Circle, but those at at greater distance from the Vertical Point, either Northward or Southward, describ’d a lesser Circle.  So that the least Circles which were describ’d by any of the Stars, were those two which went round the two Poles, the one North, the other South; the last of which is the Circle of Sohail or Canopus; the first, the Circle of those two Stars which are called in Arabick Alpherkadani.  Now because he liv’d under the Equinoctial Line, (as we shew’d before) all those Circles did cut the Horizon at right Angles, and both North and South were alike to him, and he could see both the Pole-Stars:  He observ’d, that if a Star arose at any time in a great Circle, and another Star at the same in a lesser Circle, yet nevertheless, as they rose together, so they set together:  and he observ’d it of all the Stars, and at all times.  From whence he concluded, that the Heaven was of a Spherical Figure; in which Opinion he was confirm’d, by observing the Return of the Sun, Moon and Stars to the East, after their Setting; and also, because they always appear’d to him of the same bigness, both when they rose, and when they were in the midst of Heaven, and at the time of their Setting; whereas, if their Motions had not been Circular, they must have been nearer to sight, at some times than others; and consequently their Dimensions would have appear’d proportionably greater or lesser; but since there was no such Appearance, he concluded that their Motions were Circular.  Then he consider’d the Motion of the Moon and the Planets from West to East, till at last he understood a great part of Astronomy.  Besides, he apprehended that their Motions were in different Spheres, all which were comprehended in another which was above them all, and which turn’d about all the rest in the space of a Day and a Night.  But it were too tedious to explain particularly how he advanc’d in this Science; besides, ’tis taught in other Books; and what we have already said, is as much as is requisite for our present purpose.