 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...QKD PROPOSITION A. THEOREM. If the first of four magnitudes have the same ratio to the second that the third has to the fourth, then, if the first be greater than the second, the third shall also be greater than the fourth, and if equal equal, and if less less. Take... | |
 | Euclides - 1884 - 434 pages
...equimultiples of B and B + D + F; .-. A : B = A + O + E : B + D + FV Def. 5 PROPOSITION 13. THEOREM. If the first have to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth, the first shall also have... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...theorem : — " The product of a ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclides - 1885 - 340 pages
...: — •" The product of a ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | American Association for the Advancement of Science - American periodicals - 1898 - 620 pages
...diagonal of the parallelogram whose sides are the two quantities. The first, of four quantities is said to have to the second the same ratio which the third has to the fourth; when the first has in lewjth. to the second the same ratio which the third has in Irnyfh to the fourth,... | |
 | American Association for the Advancement of Science - Science - 1898 - 626 pages
...diagonal of the parallelogram whose sides are the two quantities. The first of four quantities is said to have to the second the same ratio which the third has to the fourth ; when the first has in lenijth to the second the same ratio which the third has in length to the fourth,... | |
 | Joseph Battell - Force and energy - 1903 - 722 pages
...: 2 : : 3 : 6, and 3 : 6>4 : 7 ; then 1 : 2^>4 : 7. "Self-evident. See Axiom 15. PROPOSITION XIV. ' If the first have to the second the same ratio which the third has to the fourth, and if the first is greater than the third, the second will be greater than the fourth ; if equal,... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...The same may be said of Simson's Prop. A to the effect that, " If the first of four magnitudes has to the second the same ratio which the third has to...the fourth : then, if the first be greater than the second, the third is also greater than the fourth ; and if equal, equal ; if less, less." This is needless... | |
 | Euclid - 452 pages
...The same may be said of Simson's Prop. A to the effect that, " If the first of four magnitudes has to the second the same ratio which the third has to...the fourth : then, if the first be greater than the second, the third is also greater than the fourth ; and if equal, equal ; if less, less." This is needless... | |
 | American Association for the Advancement of Science - Science - 1898 - 624 pages
...diagonal of the parallelogram whose sides are the two quantities. The first of four quantities is said to have to the second the same ratio which the third has to the fourth ; when the first has in length to the second the same ratio which the third has in lemjtli to the fourth,... | |
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THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the... 
