| 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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