| William Alexander Willock - Circle - 1875 - 196 pages
...OAv OB, be proportional, and the following statement hold good:— If there be four magnitudes, and **any equimultiples whatsoever of the first and third...equimultiples whatsoever of the second and fourth** being taken, if the equimultiples of the first and third together exceed, or are equal to, or are less... | |
| Euclid - 1876 - 240 pages
...Or, to bring it still nearer to the language of Euclid's definition: — The first of four magnitades **is said to have the same ratio to the second, which...equimultiples whatsoever of the first and third being taken,** the second is contained as often in the equimultiple of the first, as the fourth is contained in the... | |
| Robert Potts - Geometry - 1876 - 446 pages
...any integers, m,*l. mA. or m/ll : na, : : m/f, : na,. That i«, if the first of four magnitudes has **the same ratio to the second which the third has to the fourth** ; then any equimultiples whatever of the first and third shall have the game ratio to any equimultiples... | |
| 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... | |
| 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... | |
| 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...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 - 1882 - 442 pages
...- . Ч Then A ± P\ a : (l ± Л\ b : : a : 6, or a ±Pa : b ± ?-b : : a : b. Ч Ч QED 272. DEF. **Euclid's test of a proportion is as follows : —...second which the third has to the fourth, when any** equimultiplos whatsoever of the first and third being taken, and any equimultiples whatsoever of the... | |
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