 | Euclid - 1868 - 138 pages
...equations together, we find a + 6 + c + &c. = m(œ+y+zt- &c.) QED PROPOSITION II.— THEOREM. If the first be the same multiple of the second that the third...the second that the sixth is of the fourth; then the first and fifth together shall be the same multiple of the second, that the third and sixth are of... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...omitted, and the numerator is said to be the ratio. Corollary 2. — If the first of four magnitudes be the same multiple of the second that the third is of the fourth, the ratio of the first magnitude to the second will be the same as the ratio of the third magnitude... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...the same multiple of B, that C, F together is of D. QED PROPOSITION III. (Eucl. v. 3.) If the first be the same multiple of the second that the third is of the fourth ; and if of the first and third there be taken equimultiples, these must be equimultiples, the one of the... | |
 | Euclides - 1874 - 342 pages
...demonstration holds in any number of magnitudes, which was here applied to two." QED PROPOSITION 2. —Theorem. If the first magnitude be the same multiple of the...of the second that the sixth is of the fourth; then shall the first together with the fifth be the same multiple of the second, that tIie tiiird together... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...demonstration holds in any number of magnitudes, which was here applied to two.' QEn PROPOSITION IL THEOREM. If the first magnitude be the same multiple of the...the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second, that the third together... | |
 | Euclid - 1876 - 240 pages
...second which the third is of the fourth, and if of the first and third there be taken equimultiples. If the first magnitude be the same multiple of the...multiple of the second that the sixth is of the fourth. CONSEf/UENCES. I The third is the same multiple f or submultiple of thefourth. These shall be equimultiples,... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pages
...A, B together is the same multiple of C, D together that PROPOSITION II. (Eucl. v. 2.) If (he first be the same multiple of the second that the third...multiple of the second that the sixth is of the fourth ; the first together with the fifth must be the same multiple of the second, that the third together... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...Of d PROPOSITION II. (Eucl. v. 2.) If Oie first be the same multiple of the second that the third it of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; the first together with the fifth must be the same multiple of the second, that the third together... | |
 | Euclides - 1878 - 398 pages
...together is the same multiple of C, D together that PROPOSITION II. (Eucl. T. 2.) If the first lie the same multiple of the second that the third is...multiple of the second that the sixth is of the fourth ; the first together with the fifth must be the same multiple of the second, that the third together... | |
 | University of Oxford - Greek language - 1879 - 414 pages
...figures. 2. About a given circle describe a triangle equiangular to a given triangle. 3. If the first be the same multiple of the second that the third is of the fourth, and if of the first and the third there be taken equimultiples, these shall be equimultiples, the one of... | |
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If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall... 
