 Next, let there be four magnitudes A, B, C, D, and other four E, F, G, H, which, taken two and two in a cross order, have the same ratio, viz.: A...  Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ... - Page 44by Euclid, Lewis Carroll - 1874 - 62 pagesFull view - About this book
 | Robert Simson - Trigonometry - 1806 - 546 pages
...ex aquo per tur bate." M EF N First, Let there be three magnitudes A, B, C, and other three D, 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 is to C, as D to F. Take... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...nC, mD, nE, feF. Book V. Next, let there be four magnitudes, A, B, C, D, and other four, E, F, G, H, which, taken two and two, in a cross order, have the same ratio, A : B : : G : H, B : C : : F : G, and A, B, C, D, C : D : : E : F ; then A : D : : E : H. For, since... | |
 | Euclid - Geometry - 1810 - 554 pages
...or, " ex tequo perturbate." First, Let there be three magnitudes A, B, C, and other three D, L, F, which, taken two and two. in a cross order, have the same r do, rhat is, such that A is to B, as E to F; and as B is to C, so is D to E : A is to C, as D to... | |
 | John Mason Good - 1813 - 714 pages
...aequali,'' or " ex aequo." Prop. XXIII. Theor. If there be any number of mae -itudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to... | |
 | Euclides - 1816 - 588 pages
.... F HL K. M 2 HI Next, let there be four magnitudes A, B, C, D, and BouK V. other four £, F, G, H, which, taken two and two, in a cross order, have the same ratio, viz. A to B, as G to H ; B to C, as F to G ; and C to D, as E to F: A is to D, as E to H. Because A,... | |
 | John Playfair - 1819 - 354 pages
...: : E : F, then A : D : : E : H. For, since A, B, C are three magnitudes, and F, G, H other three, which taken two and two, in a cross order, have the same ratio, by the first case, A : C : : F : H. But C : D : : E : F, therefore, again, by the first case, A : D... | |
 | James Ryan - Algebra - 1824 - 550 pages
...magnitudes. QED 3«J PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio ; the 6rst shall have to the last of the first magnitudes the same ratio which the first of the others has... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...number of magnitudes. QED PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two in a cross order have the same ratio •; the 6rst shall have to the last of the first magnitudes the same ratio which the first of the others has... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...to F: A is to D. as E to H. Because А, В, С, яге three magnitudes, and F, G, H, other three, which, taken two and two in a cross order, have the same ratio ; by the first case, A is to C, as F to H: But с is to D, as E to F ; wheretbre again. by the first... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...<.] r tHyp. •11.5. tHyp. Next, let there be four magnitudes A, B, C, D, and other four E, F, G, H, which taken two and two in a cross order have the same ratio, viz. A to B, as G to H; B to C, as F to G ; and C to D, asEtoF: A shall be to D, as E to H. Because... | |
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