 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 páginas
...number of metres may make, a greater length can always be found containing an exact number of yards. 5. The first of four magnitudes is said to have the ' same ratio ' to the second that the third has to the fourth, when, any equimultiples whatever of the first and third being taken,... | |
 | Euclides, Micaiah John Muller Hill - 1900 - 165 páginas
...following manner : — The first of four magnitudes is said to have the same ratio to the second, as 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 being taken; if the multiple of the first be... | |
 | Euclid, Micaiah John Muller Hill - 1900 - 190 páginas
...Art. 67. Def. 13. EUCLID'S TEST FOR EQUAL RATIOS. Euclid states this Test in the following manner: — The first of four magnitudes is said to have the same ratio to the second, as the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
 | David Eugene Smith - 1900 - 340 páginas
...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 of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or,... | |
 | David Eugene Smith - 1902 - 418 páginas
...Teaching. One has but to read the Euclidean definition of equal ratios to be assured of this fact : " The first of four magnitudes is said to have the same...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that... | |
 | Joseph Battell - 1903 - 722 páginas
...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 páginas
...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 páginas
...geometrically as sound as Euclid's, and infinitely more natural. I need only quote it to enforce the point: " The first of four magnitudes is said to have the same...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 the... | |
 | ANZAAS (Association) - 1905 - 782 páginas
...geometrically as sound as Euclid's, and infinitely more natural. I need only quote it to enforce the point : " The first of four magnitudes is said to have the same...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 the... | |
 | Euclid - 1908 - 456 páginas
...unnecessary. Simson added, in place of Theon's corollary, the following : " Likewise, if the first has the same ratio to the second which the third has to the fourth, then also any equimultiples whatever of the first and third have the same ratio to the second and fourth... | |
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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... 
