Ir 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... The Elements of Plane and Solid Geometry - Page 161by Henry William Watson - 1871 - 285 pagesFull view - About this book
| 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 which the firft... | |
| Robert Simson - Trigonometry - 1775 - 534 pages
...Therefsre, i( there be any number, &c. Q^ED BC FG D. H. PROP. Book V. PROP. XXIII. THEO R. SeeK. TF 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 mall have to the laft of the firft magnitudes the fame... | |
| Euclid - 1781 - 552 pages
...of magnitudes. Theiefore, if there be any number, &c. Q^ED K a P IUO P. v. PROP. XXIII. THEO R. K. 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 mail have to the laft of the firft magnitudes the fame... | |
| Robert Simson - Trigonometry - 1781 - 534 pages
...if there be any number, &c. Q;_, ED • Book V. SeeN. a. if- Jkn ft 4ii. J. PROP. XXIII. THEO R. TF 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 lhall have to the laft of the firft magnitudes the fame... | |
| 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 which the firft... | |
| John Playfair - Mathematics - 1806 - 320 pages
...F>D, that is, D<F. Therefore, &c. QED But A : B : : : : D : E, and : E : De, and, PROP. XXII. THEOK. IF there be any number of magnitudes, and as many...and two in order, have the same ratio ; the first will have to the last of the first magnitudes the same ratio which the first of the others has to the... | |
| Robert Simson - Trigonometry - 1806 - 546 pages
...whatever be the number of magnitudes. Therefore, if there be any number, &c. 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 first shall have to the last of the first magnitudes the same... | |
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