 | George Albert Wentworth - 1877 - 416 páginas
...q/ or ai ~ а : fr i ~ b : : a : b. QED 272. DEF. Euclid's test of a proportion is as follows : — "The first of four magnitudes is said to have the...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; " If the multiple of the first be less than... | |
 | George Albert Wentworth - 1877 - 436 páginas
...third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; " If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth ; or,... | |
 | Samuel H. Winter - 1877 - 452 páginas
...into three, and also into five equal parts. 6. When is the first of four magnitudes said to have the the same ratio to the second which the third has to the fourth ? Prove that triangles which have the same altitude are to one another as their bases. Show also that... | |
 | Āryabhaṭa - 1878 - 100 páginas
...two magnitudes of the same kind to one another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fouitl', when any equimultiples whatsoever of the first and third i being taken, ai;d any equimultiples... | |
 | Robert Potts - 1879 - 668 páginas
...Eue. Vu., def. 20. Hence it follows that a, b, c, d are proportionals by Eue. V., def. 5, namely : — The first of four magnitudes is said to have the same...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that... | |
 | Robert Potts - 1879 - 672 páginas
...VII., def. 20. Hence it follows that a, b, c, d are proportionals by Eue. V., def. 5, ' namely : — | The first of four magnitudes is said to have the same...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that... | |
 | University of Oxford - 1879 - 414 páginas
...rectilineal figures. Explain homologous, alternando, ex sequali. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 7. In a right angled triangle, if a perpendicular be drawn from the right angle to the base, the... | |
 | Sandhurst roy. military coll - 1880 - 68 páginas
...triangle, pentagon, and hexagon. 7. Give Euclid's definition of ratio. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 8. The sides about the equal angles of equiangular triangles are proportional. If a straight line... | |
 | Isaac Todhunter - 1880 - 426 páginas
...together. [V. Definition 5. Wherefore, if any number &c. Q.EJ>. PROPOSITION 13. THEOREM. If the first have the same ratio to the second which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the si.cth, thefirst shall have to ths... | |
 | George Albert Wentworth - 1881 - 266 páginas
...a ± ? a : b ± ?-b : : a : b. Ч 1 QED 272. DEP. Euclid's test of a proportion is as follows : — "The first of four magnitudes is said to have the...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second, and fourth ; " If the multiple of the first be less than... | |
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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... 
