| Robert Potts - Geometry, Plane - 1860 - 380 pages
...holds in any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOREM. Jf **the first magnitude be the same multiple of the second...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... | |
| Eucleides - 1860 - 396 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...of the fourth, and the fifth the same multiple of** thesecond that the sixth is of the fourth. CONSEQUENCES. ^ The third is the same multiple or submultiple... | |
| Euclides - 1861 - 464 pages
...and у A = m E, B = n E, and C = p E ; .-. m E + n E + p E = (m + и + p) E. Pnоr. II. — TUEOK. **If the first magnitude be the same multiple of the second that the third is of the fourth, and** thefifth-thc same multiрle of the second that the sixth is of the fourth ; then shall the first. together... | |
| George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...then a + e + ff + k is the same multiple of b that с +f+ h + /is of d. PROPOSITION III. 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 any equimultiples ; these shall be equimultiples, the one... | |
| Euclides - 1864 - 448 pages
...demonstration holds in any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOREM. **If the first magnitude be the same multiple of the second that the third is of the fourth, and the** liflh the same multiple of the second that the sixth is of the fourth; then shall the jirst together... | |
| Euclides - 1865 - 402 pages
...them is of its part, the same multiple shall all the first magnitudes be of all the others ? Prop. 2. **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... | |
| Robert Potts - 1865 - 528 pages
...demonstration holds in any number of magnitudes, which was here applied to two.' QED PROPOSITION II. 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, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...that the whole of the last, namely. DL, is of/7. H J K HC JL F PROPOSITION 3. THEOREM. 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 equimtiltiples, the one... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...of C, that the whole of the last, namelv, H DL,isofF, G H J K PROPOSITION 3. THEOREM. 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... | |
| Robert Potts - 1868 - 434 pages
...demonstration holds m any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOREM. Jf **the first magnitude be the same multiple of the second...of the second that the sixth is of the fourth; then** shall Hie first together with the fifth be the same multiple of the second, that the third together... | |
| |