| Robert Simson - Trigonometry - 1762 - 488 pages
...firft ; and therefore D is lefs than F. Therefore if there be three, &c. Q._E. D. PROP. XXII. THEOR, TF **there be any number of magnitudes, and as many others, which taken two and two in** order have the fame ratio ; the firft fhall have to the laft of the firft magnitudes the fame ratio... | |
| Robert Simson - Trigonometry - 1775 - 534 pages
...therefore D is lefs than F. Therefore, if there be three, &c. Q^ED A D B E PROP. XXII. THEO R.' TF **there be any number of magnitudes, and as many others, which taken two and two in** order have the fame ratio i the firft (hall have to the laft of the firft magnitudes the fame ratio... | |
| Robert Simson - Trigonometry - 1781 - 534 pages
...therefore D is lefs than F. Therefore if there be three, &c. OED C F A E Sec N. PROP. XXII. THEO R. **IF there be any number of magnitudes, and as many others, which taken two and two in** order have the fame ratio ; the firft mail have to the laft of the firft magnitudes the fame ratio... | |
| Euclid - 1781 - 550 pages
...firft ; and therefore D is lefs than F. Therefore, if there be three, &c. QJ£. D. PROP. XXII. THEO R. **IF there be any number of magnitudes, and as many others, which, taken two and two in** order have the fame ratio ; the firft fhall have to the laft of the firft magnitudes the fame ratio... | |
| Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...the demonftration extended to any number of magnitudes. Therefore, Scc. Q^ ED PROP. XXIII. THEO R. **IF there be any number of magnitudes, and as many others, which, taken two and two, in a** crofs order, have the fame ratio; the firft (hall have to the laft of the firft magnitudes the fame... | |
| Nicolas Vilant - Algebra - 1798 - 196 pages
...л . /Yj _ V -'HI ^n<^ ^° 4I>' v/batever be the number of magnitudes. PROPOSITION XXIIL— THEOREM. **If there be any number of magnitudes, and as many others, which taken two and two** inordinately, have the fame ratio ; then, by perturberate equality (Def. XX.), the firft mall have... | |
| Alexander Ingram - Trigonometry - 1799 - 374 pages
...as E to H ; and fo on, whatever be the number of magnitudes. Wherefore, &c. Q^ED PROP. XXIII. THEOR. **IF there be any number of magnitudes, and as many others, which, taken two and two, in a** crofs order, have the fame ratio ; the firll mail have to the laft of the firft magnitudes the fame... | |
| John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...therefore, by the firft cafe, fince C > A, F > D, that is, D < F. Therefore. . f RO P. ^XXII. THEO R. **IF there be any number of magnitudes, and as many others, which, taken two and two in** order, have the fame ratio ; the firft will have to the laft of the firft magnitudes, the fame ratio... | |
| John Playfair - Euclid's Elements - 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... | |
| 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... | |
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