N ; and if equal, equal ; and if less, less : but if G be greater than L, it has been shown that L HC K E M F N H is greater than M ; and if equal, equal; and if less, less: therefore, if G be greater than L, K is greater than N ; and if equal, equal... The First Six Books of the Elements of Euclid, with a Commentary and ... - Page 107by Euclid, Dionysius Lardner - 1828 - 324 pagesFull view - About this book
| Robert Simson - Trigonometry - 1762 - 488 pages
...V^"\°OM ; and if equal, equal ; and if lefs, lefs". Again, becaufe C is to a. 5. Def. 3. D, as E is to F, **and H, K are taken equimultiples of C, E ; and M,'...K is greater than N ; and if equal, equal; and if** lefs, lefs. but if G be greater than L, it has ACE BDF L M- Nbeen fhewn that H is greater than M ;... | |
| Robert Simson - Trigonometry - 1775 - 534 pages
...lefs, lefs '. Again, bei 5- def. 5. caufe C is to I), as E is to F, and H, K are takf n equimultiple* **of C, E; and M, N of D, F ; if H be greater than M,...K is greater than N ; and if equal equal ; and if** lefs, lefs : But, if G GHI A.- — CE te greater than L, it has been fhewn, thatH is greater than M;... | |
| Euclid - 1781 - 552 pages
...lefs, lefs'. Again, bo • 5. &(• S. caufe C. is to D, as E is to F, and H, K are taken equimultiple* **of C, E ; and M, N, of D. F; if H be greater than...K is greater than N; and if equal, equal ; and if** lels, lefs : But, if G GH A. • c ~ B D. be greater than L, it has been fhpwn that H is greater than... | |
| Robert Simson - Trigonometry - 1804 - 530 pages
...eater than "v M; and if equal, equal; and if lefs, lefs •. Again, becaufe C is to D, as E is to F, **and H, K are taken equimultiples of C, E; and M, N...K is greater than N ; and if equal, equal } and if** lefs, lefs. but' if G be greater than L, it has GH KAC EBD FL M- N. been fhewn that H is greater than... | |
| Robert Simson - Trigonometry - 1806 - 546 pages
...M, N, which have the same ratio taken two and two in a cross order; if G "be greater than L, d21. 5. **K is greater than N; and if equal, equal; and if less,** lessd; and G, K are any equimultiples whatever of A, D ; and L, N any whatever of C, F ; as, therefore,... | |
| Euclid - Geometry - 1810 - 554 pages
...M; and if equal, equal; and if less, less ». Again, because a 5. del. o. C is to D, as E is to F, **and H, K are taken equimultiples of C, E: and M, N, of D, F: if H be greater than M, K is greater** ili. ii N; and if equal, equal; and if less, less: but if G be G HA CBD FLM Ngreater than L, it has... | |
| Euclides - 1814 - 560 pages
...S of C, E; and M, N, of D, F; v ^ v ~"' less, less3. Again, because C is to D, as E is to F, and H, **if H be greater than M, K is greater than N; and if...if less, less: But if G be greater than L. it has** G II KA f > t?B I> lfM— N been shown that H is greater than M; and if equal, equal; and if less,... | |
| Euclides - 1816 - 588 pages
...that H is greater than M ; and if equal, equal ; and if less, less; therefore if G be greater than L, **K is greater than N ; and if equal, equal ; and if less, less** : And G, K are any equimultiples whatever of A, E ; and L, N any whatever of B, F : Therefore, as A... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 pages
...G, K, M, and other three H, L, N, which, two and two, have the same ratio: if G be greater than M, H **is greater than N; and if equal, equal; and if less, less** (20. 5.); and G, H are any equimultiples whatever of A, D, and M, N are any equimultiples whatever... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...K, M, N, which have the same ratio, taken two ant) two, in a cross order : if G be greater than L, **K is greater than N ; and if equal, equal ; and if less,** K'ss : (21. 5.) and G, K are any equimultiples whatever of A, D ; and L, N any whatever of C, F ; as,... | |
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