| 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...which, taken two 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... | |
| 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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