 | Mathematics - 1836 - 488 pages
...magnitudes, taken separately, be proportionals, they will also be proportionals when taken joint, ly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second as the third and fourth together to the fourth. XIX. If a whole magnitude be... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...separately, be proportionals, they will also be proportionals when taken jointly, that is, if the f-rst be to the second as the third to the fourth, the first and second together will be to the second as the third and fourth together to the fourth. If A : B : : C : D, then, by... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...preceding case, B : A : : D : C ; and inversely (VB) A : B : : C : D. If, therefore, &c. PROP. D. THEOR. IF the first be to the second as the third to the fourth, and if the first be a multiple, or a part of the second ; the third is the same multiple, or part of... | |
 | Euclid - Geometry - 1838 - 470 pages
...to B, as C is to D. Therefore, if the first be the same multiple, &c. Q,. ED ABCD PROP. D. THEOR. Ir the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second ; the third is the same multiple, or the same... | |
 | Bewick Bridge - Algebra - 1839 - 280 pages
...or cit cd ab T, J -=-?; s-. a : c :: b : d. cd TH. 5. " If there be six proportional quantities, and the first be to the second as the third to the fourth ; and the third to the fourth as the fifth to the sixth ; then will the first be to the second as the... | |
 | Euclides - 1840 - 192 pages
...equal parts or submultiples of their consequents, the four terms are proportional. PROP. C. THEOR. If the first be to the second as the third to the fourth, and if the first be a multiple or a part of the second, the third is the same multiple or the same... | |
 | John D. Williams - Algebra - 1840 - 634 pages
...=-7, or -==- ; .-. a : с : : b : d. cd cd cd Тн. 5. If there be six proportional quantities, and the first be to the second as the third to the fourth, and the third to the fourth as the fifth to the sixth, then will the first be to the second as the... | |
 | John D. Williams - Algebra - 1840 - 216 pages
...—7=—, or -=- ; .-. a I c '. '. b : d. cd cd cd TH. 5. If there be six proportional quantities, and the first be to the second as the third to the fourth, and the third to the fourth as the fifth to the sixth, then will the first be to the second as the... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...A :: D : С, then, by " componendo," we infer that В + A : A f. D + С : С. . PROP. XVIII. THEO. If magnitudes, taken separately, be proportionals,...that is, if the first be to the second as the third is to the fourth, the first and second together shall be to the second as the third and fourth together... | |
 | Euclides - Geometry - 1841 - 378 pages
...multiple, &c. QED 'Hyp. * Cor. 4. 5. * A. 5. * Const. See the figure at the top of this PROP. D. THEOR. If the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same... | |
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Ij the first be to the second as the third to the fourth, and if the first be a multiple, or a part of the second ; the third is the same multiple, or the same part of the fourth. 
