 | George Albert Wentworth - Geometry - 1877 - 416 pages
...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...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... | |
 | Samuel H. Winter - 1877 - 452 pages
...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 pages
...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 pages
...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...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... | |
 | Robert Potts - Algebra - 1879 - 672 pages
...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...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... | |
 | University of Oxford - Greek language - 1879 - 414 pages
...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 pages
...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 - Euclid's Elements - 1880 - 426 pages
...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 pages
...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...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... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...they cannot be said to be of the same kind, and so cannot have any ratio to each other. T. The Brst of four magnitudes is said to have the same ratio...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 mu'tiple of the... | |
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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... 
