 | Robert Simson - 1762 - 488 sider
...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 - 1775 - 534 sider
...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 - 1781 - 534 sider
...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 - 552 sider
...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 - 1795 - 462 sider
...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 - 1798 - 196 sider
...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 - 1799 - 374 sider
...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 - 1804 - 468 sider
...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 - 1806 - 320 sider
...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 - 1806 - 546 sider
...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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If there be any number of magnitudes, and as many others, which, taken two and two in 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 the last. NB This is usually... 
