 | 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... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...multiple of the third is also equal to that of the fourth ; or, "If the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." PROPOSITION XIII. 273. If four quantities be proportional according... | |
 | Āryabhaṭa - 1878 - 100 pages
...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... | |
 | University of Oxford - Greek language - 1879 - 414 pages
...figures. 2. About a given circle describe a triangle equiangular to a given triangle. 3. 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 sixth, the first shall have to the... | |
 | Robert Potts - Algebra - 1879 - 672 pages
...multiple of the third is abo equal to that of the fourth ; or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. Conversely. If four magnitudes be proportional according to Eue. V.,... | |
 | Robert Potts - 1879 - 668 pages
...multiple of the third is also equal to that of the fourth ; or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. Conversely. If four magnitudes be proportional according to Eue. V.,... | |
 | 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... | |
 | Sandhurst roy. military coll - 1880 - 68 pages
...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... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...same kind, and so cannot have any ratio to each other. T. The Brst of four magnitudes is said to have the same ratio to the second, which the third has...of the first be less than that of the second, the mu'tiple of the third is also less than tlint of the fourth : or, if the multiple of the first be equal... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...multiple of the third is also equal to that of the fourth ; or, " If the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." PROPOSITION XIII. 273. If four quantities be proportional according... | |
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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... 
