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" If the first has to the second the same ratio which the third has to the fourth... "
Modern geometry [ed.] with an appendix by W.B. Jack - Side 241
av Richard Wormell - 1876
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 488 sider
...&c. Q^E. D* PROP. XIII. THE OR. IF the firft has to the fecond the fame ratio \irhich die srt **• third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the fixth; the firft fhall alfo have to the fecond a greater ratio than the fifth ha8 to the...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 534 sider
...number, &c. Q^ED I PROP. XIII. THEO R. F the firft has to the fecond the fame ratio which the See N. third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the fixth ; the firft fhall aJfo have to the fecond a greater ratio than the fifth has to the...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1781 - 534 sider
...any number, &c. Q._ ED PROP. Xlll. THEO R. IF the firft has to the fecond the fame ralio which SeeN> the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the fixth ; the firft fhall alfo have to the fecond a greater ratio than the fifth has to the...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 sider
...number, &c. Q^ED PROP. XIII. T fl EOR, IF the firft has to the fecond the fame ratio which the see N, third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the fixt,h ; the firft fhall allb have to the fecond a greater ratio than the fifth has to the...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 462 sider
...: : A4 C+E : B+D+F. There fore, &e. Q^ED PROP. XIII. PROB. IF the firft has to the fecond the fame ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the fixth; the firft fhall alfo have to the fecond a greater ratio than the fifth has to the...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 374 sider
...ED 1C a i. ll I D b5.Def.j. E PROP. XIII. THEOR. F the firft has to the fecond the fame ratio that the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the iixth ; the firll fhall alfo have to the fecond a greater ratio than the fifth has to the...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - 1804 - 468 sider
...B+D+F. Therefore, &c. Q^ED PROP. XIII. THEOR. IF the firft have to the fecond the fame ratio whicii the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the fixth : the firft has alfo to the fecond a greater ratio than the fifth has to the fixth....
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804 - 530 sider
...immber, &c; QJ2. D. tROP. Xlti. THE ORIF the firft has M the fecohd the fame ratid Vvhich the See N; third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the fixth ; the firft fliall alfo have to the fecond a greater ratio than the fifth has to the...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 sider
...has a greater ratio to the second, than the fifth has to the sixth. PROP. XIV. THEOR. SeeN. a 8. 5. IF the first has to the second the same ratio which the third has to the fourth; then, if the first be greater than the third, the second shall be greater than the fourth; and if equal,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 sider
...demonstration be extended to any number of magnitudes. Therefore, &c. QED PROP. XXIV. THEOR. IF the first have to the second the same ratio which the third has to the fourth, and the fifth to the second the same ratio which the sixth has to the fourth ; the first and fifth...
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