Page:Euclid's Elements 1714 Barrow translation.djvu/19

Rh from citing the axiome, for brevity's ake altho' the force of the conequence depend thereon.

2. If to equal things you add equal things, the wholes hall be equal.

3. If from equal things you takeaway equal things, the things remaining will be equal.

4. If to unequal things you add equal things, the wholes will be unequal.

5. If from unequal things you take away equal things, the remainders will be unequal.

6. Things which are double to the ame third, or to equal things, are equal one to the other. Undertand the ame of triple, quadruple, &c.

7. Things which are half of one and the ame thing, or of things equal, are equal the one to the other. Conceive the ame of ubtriple, ubquadruple, &c.

8. Things which agree together, are equal one to the other.

The convere of this axiome is true in right lines and angles, but not in figures, unles they be like.

Moreover, magnitudes are aid to agree, when the parts of the one being applyed to the parts of the other, they fill up an equal or the ame place.

9. Every whole is greater than its part.

10. Two right lines cannot have one and the ame egment (or part) common to them both.

11. Two right lines meeting in the ame point, if they be both produced, they hall necearily cut one the other in that point.

12. All right angles are equal the one to the other.



13. If a right line BA falling on two right lines