 | Euclid - 1845 - 218 pagina’s
...the magnitude A be to B, as C is to D, then also inversely B is to A, as D to C. Take of B and D, any equimultiples whatever E and F ; and of A and C, any...whatever G and H. First, let E be greater than G, then G • Hyp. is less than E : and because* A is to B as C is to D ; and of A and C, the first and third,... | |
 | Euclid, James Thomson - 1845 - 382 pagina’s
...A and C any like multiples G and H. First, let E be greater than G ; and, because A : B : : C : D, and of A and C, the first and third, G and H are like multiples ; and of B and D, the second and fourth, E and F are like multiples; and that G is less... | |
 | Euclides - 1846 - 292 pagina’s
...whatever, E, F, and of A, C, any equimultiples whatever G, H : Then, first, if E be greater than G, G is less than E : And because A is to B as C is to D, and of A and C, the first and third, G and H are equimultiples, and of B and D, the ^ ^ D i second... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pagina’s
...the magnitude A be to B, as C is to D, then also inversely B is to A, as D to C. Take of B and D, any equimultiples whatever E and F ; and of A and C, any...greater than G, then G is less than E : and because (Hyp.) A is to B as C is to D; and of A and C, the first and third, G and H are equimultiples ; and... | |
 | Euclides - 1853 - 176 pagina’s
...inversely b is to a as d to С. Take of b and d any equimultiples whatever e and f ; and of a and С any equimultiples whatever g and h. First, let e be...then g is less than e ', and because a is to b as С is to d, and of a and С, the first and third, g and h are equimultiples ; and of b and d, the second... | |
 | Euclides - 1855 - 270 pagina’s
...to D. Inversely (Def. 14), B is to A as D ig toC. GEH FTake of B and D any equimultiples whatever B and F; and of A and C any equimultiples whatever G and H. First, let E be greater than Q, then G is less than E. Because A is to B, as С is to D (ïïyp.), and of A and С, the first and... | |
 | Euclides - 1855 - 230 pagina’s
...DEMONSTRATION. Take E equal to A, and whatever multiple A or E is of B, make F the same multiple of D ; then, because A is to B as C is to D (a) ; and of B the second, and D the fourth, equimultiples have been taken, E and F ; therefore A is to E as C is... | |
 | Robert Potts - 1860 - 380 pagina’s
...Let A be to B, as C is to D. Then also inversely, B shall be to A, as D to (7. Take of B and D any equimultiples whatever E and F; and of A and C any equimultiples whatever CI and Jf. First, let E be greater than (?, then G is less than E: and because A is to B, as C is to... | |
 | Euclides - 1863 - 122 pagina’s
...proportionals when taken inverselg (B is to A as D is to C). A - B - C Q _ J£ __ _.___ JJ Take of B and D any equimultiples whatever E and F ; and of A and C any...First, let E be greater than G, then G is less than E. Because A is to B, as C is to D (Hgp ), and of A and C, the first and third, G and ] I are equimultiples... | |
 | Euclides - 1864 - 448 pagina’s
...to B, as C is to D. Then also inversely, B shall be to A, as D to C. AB C- D — Take of B and D any equimultiples whatever E and F; and of A and C any...less than E: and because A is to B, as C is to D, (hyp.) and of A and C, the first and third, G and H are equimultiples ; and of B and D, the second... | |
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Take of B and D any equimultiples whatever E and F; and of A and C any equimultiples whatever G and H. First, let E be greater than G, then G is less than E: and because A is to B, as C is to D, (hyp.) and of A and C... 
