Page:Euclid's Elements 1714 Barrow translation.djvu/20

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8
The firſt Book of

AD, CB, make the internal angles on the ſame ſide, BAD, ABC, leſs than two right angles, thoſe two right lines produced ſhall meet on that ſide, where the angles are leſs than two right angles.

14. Two right lines do not contain a ſpace.

15. If to equal things, you add things unequal, the exceſs of the wholes ſhall be equal to the exceſs of the additions.

16. If to unequal things equal be added, the exceſs of the wholes ſhall be equal to the exceſs of thoſe which were at firſt.

17. If from equal things, unequal things be taken away, the exceſs of the remainders ſhall be equal to the exceſs of the wholes.

18. If from things unequal, things equal be taken away, the exceſs of the remainders ſhall be equal to the exceſs of the wholes.

19. Every whole is equal to all its parts taken together.

20. If one whole be double to another, and that which is taken away from the firſt to that which is taken away from the ſecond, the remainder of the firſt ſhall be double to the remainder of the ſecond.

The Citations are to be underſtood in this manner; When you meet with two numbers, the firſt ſhews the Propoſition, the ſecond the Book; as by 4. 1. you are to underſtand the fourth Propoſition of the firſt Book; and ſo of the reſt. Moreover, ax. denotes Axiome, poſt. Poſtulate, def. Definition, ſch. ſcholium, cor. Corollary.