 | Robert Simson - Trigonometry - 1806 - 546 pages
...there be four magnitudes A, B, C, D, and other four E, F, G, H, which two and two have the same ratio, viz. as A is to B, so is E to F, and as B to C, so F to G ; and as C to D, so G to II : A shall be to D, as E to H. Because A, B, C are three... | |
 | Euclid - Geometry - 1810 - 554 pages
...E, F other three, v— v— -* which have the same ratio, taken two and two, but in a cross order, viz. as A is to B, so is E to F, and as B is to C, so is I) to E. If A be greater than C, D shall be greater than F ; and if equal, equal ; and if less, less.... | |
 | Euclides - 1816 - 588 pages
...be four magnitudes, A, B, C, D, and other four E, F, G, H, which, two and two, have the same ratio, viz. as A is to B, so is E to F; and as B to C, so F to G ; and as C to D, so G to H : A shall be to D, as E to H. Because A, B, C, are three... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...have the same- ratio, taken two and two, but in a cross order, viz. as A is to B, so is £ to f, ,.;.d as B is to C, so is D to E. If A be greater than C, D shall be greater than F; and if equal, equal; and if Less, less. Because A is greater than C, and B... | |
 | George Crabb - Industrial arts - 1823 - 704 pages
...of such magnitudes, taken two and two in cross order, is inferred : thus, supposing A to be to B as E to F ; and as B is to C so is D to E ; then A is to C as D to F. The principal writers on geometry, besides Euclid, are Archimides, Apollonius,... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...magnitudes, »iid D, E, F other three, which have the same ratio, taken two and two, but in a cross order, viz. as A is to B, so is E to F; and аз В is to C, so is D to E. If A be greater than C, D «hall be greater than F ; and if equal, equal... | |
 | Euclides - 1826 - 226 pages
...taken two and two have the same ratio, and let their proportion be perturbate ; viz. as A is to в so is E to F, and as B is to c so is D to E ; then if A be greater than c, D will also be greater than F ; if equal, equal; and if less, less.... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...E, F, which taken two and two in a cross order have the same ratio, that is, such that A is to B, as E to F ; and as B is to C, so is D to E : A shall be to C, as D to F. Take of A, B. D any equimultiples whatever G, H, K; and of C, E, F any... | |
 | Euclid, Robert Simson - Geometry - 1829 - 548 pages
...be four magnitudes, A, B, C, D, and other four, E, F, G, H, which, two and two, have the same ratio, viz. as A is to B, so is E to F, and 33 B to C, so F to G ; and as C to D, so G to H : A shall be to D, as E to H. Because A, B, C are three... | |
 | Euclides - 1834 - 518 pages
...and D, E, F other three, which have the same ratio, taken two and two, but in a cross order ; viz. us A is to B, so is E to F, and as B is to C, so is D to E : if A be greater than C, D shall be greater than 1" ; and if equal, equal ; and if less, less. Because A is greater than C, and... | |
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D, and other four E, F, G, H, which, two and two, have the same ratio, viz. as A is to B, so is E to F; and as B... 
