 | William Alexander Willock - 1875 - 196 σελίδες
...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 σελίδες
...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 - 1876 - 446 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1879 - 414 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1881 - 236 σελίδες
...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 - 1882 - 442 σελίδες
...- . 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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The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when... 
