 | Sandhurst roy. military coll - 1880 - 68 σελίδες
...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... | |
 | George Albert Wentworth - 1881 - 266 σελίδες
...DEP. Euclid's test of a proportion is as follows : — "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... | |
 | Euclides - 1881 - 236 σελίδες
...a greater ratio to the seccond, than the fifth lias to the sixth. PROP. XIV. THEOREM. If the first has the same ratio to the second which the third has to *>u. fourth ; and if the first be greater than the third, the second is greater than the fourth ; if... | |
 | James Hamblin Smith - 1883 - 466 σελίδες
...is given in Book v. Def. 5, where it stands thus : \ " 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... | |
 | Howard Candler - 1885 - 116 σελίδες
...proportionals if — = b а The geometrical definition is 2. 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 whatever being taken of the ist and 3rd, and any equimultiples whatever of... | |
 | David Eugene Smith - 1900 - 338 σελίδες
...definition of equal ratios to be assured of this fact : " 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... | |
 | Joseph Battell - 1903 - 722 σελίδες
...contains 2 three times; then 1 8 must contain 2, 3 X 3, or 9 times. See Axiom 6. PROPOSITION IV. ' If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiple whatever is taken of the first and third, and any whatever of the second and... | |
 | G. F. Burn - 1903 - 272 σελίδες
...proportion is the equality of two ratios. Four quantities are therefore in true proportion when the first has the same ratio to the second which the third has to the fourth ; thus, since 3 : 6 and 1 : 2 are equal ratios, we have a true proportion in 3 : 6 : : 1 : 2 (read... | |
 | Australasian Association for the Advancement of Science. Meeting - 1905 - 786 σελίδες
...natural. I need only quote it to enforce the point: " The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth when, if the first be divided into any number whatever of equal parts, and the third be divided into... | |
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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... 
