 | Bewick Bridge - Algebra - 1821 - 648 pages
...-;.•. a : c : b : d, and I : d :: a : c, 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 " be to the second... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...are equal, therefore we have ^+1=^+1, consequently AC B=D' A : B : : C : D. QED PROP XVIII. THEOR. If magnitudes taken separately 'be proportionals,...that is, if the first be to the second as the third is to fourth, the first and second together shall be to the second as the third and fourth together... | |
 | James Ryan - Algebra - 1824 - 550 pages
...have TJ+ 1 =T\+ *» consequently ACM « • g=D» that » A : B : : C : D. QED ff I'HOP XVIII. THEOR. If magnitudes taken separately be proportionals, they...that is, if the first be to the second as the third is to fourth, the first and second together shall be to the second as the third and fourth together... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...A is to В ал С it to D. Therefore, if the first be the same multiple, <Stc. QEO PROP. D. THEOR. If the first be to the second as the third to the fourth, and if the ßrst be a multiple, or part of the second ; the third is Ihr same multiple, or the tame... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...Therefore, &e. QED PROP. XVIII. THEOR. If magnitudes, taken separately, be proportionals, they will liiso be proportionals when taken jointly, that is, if the first be to the seeond as the third to the fourth, the first and seeond together will be to the seeond as the third... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...is to B, as C is to D. Therefore, if the first be the same multiple, &c. QED PROP. D. THEOR. See N. If the first be to the second as the third to the fourth, and if theJirst be a multiple, or a part of the second; the third is the same multiple, or the same... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...preceding case, B : A = D : C ; and therefore inversely, A : B = C : D. ABCD PROPOSITION D. THEOREM. (483) If the first be to the second as the third to the fourth, and if the first be a multiple or submultiple of the second ; the third is the same multiple or submultiple... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...M cS.def.5. PROP. XVIII. THEOR. If magnitudes, taken separately, be proportionals, Sec N. they will also be proportionals when taken jointly ; — that...third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth. Let AE, EB, CF, FD be proportionals... | |
 | Euclid - 1835 - 540 pages
...is to D. Therefore, " if the. first be the same multiple," &c. QED G- F D II AB CD PROP. D. THEOR. If the first be to the second as the third to the fourth, see N. and if the first be a multiple, or part of the second ; the third is the same multiple, or the... | |
 | 1841 - 488 pages
...send them to you for insertion in your valuable miscellany. Mathematical knowledge is Theorem. — If magnitudes, taken separately, be proportionals,...be to the second, as the third and fourth together, is to the fourth. I Let AC, B c, DF, and EF,.be proportionals ; That is, A c : B c : : DF : E F. It... | |
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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. 
