 | James Ryan - Algebra - 1824 - 548 pages
...is to the first as^the fourth to the third. XV. Componendo, by composition, when it is inferred that the sum of the first and second is to the second as...the sum of the third and fourth is to the fourth. XVI. Dividendo, by division, when it is inferred that the excess of the first above the second is to... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...is to the first as the fourth to the third. XV. Componendo, by composition, when it is inferred that the sum of the first and second is to the second as...the sum of the third and fourth is to the fourth. XVI. Dividendo, by division, when it is inferred that the excess of the first above the second is to... | |
 | Enoch Lewis - Algebra - 1826 - 180 pages
...Keciprocally, if ad=bc, ,— ,=n. or -=-= — bd bd о а 63. When four quantities are proportionals, the sum of the first and second is to the second,...the sum of the third and fourth is to the fourth. c+d r Or, a+6:o :: c+d: d. If the word difference be substituted for sum, the proposition will still... | |
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...viz. : — If four magnitudes be proportional, the sum of the first and second will be to the first or second as the sum of the third and fourth is to the third or fourth. EE A ! BA ! B -D Let AE be to EB as CF is to FD ; then will AB be to BE, or AE, as... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 pages
...the extremes, and the terms of the other product the means. 3. If four quantities be proportionals, the sum of the first and second is to the second,...the sum of the third and fourth is to the fourth. Thus, if a;b; ;c'd, then will a+b:by.c+d;d. 4. If four quantities be proportionals, the difference... | |
 | John Playfair - Geometry - 1829 - 210 pages
...C : : B • D For AD = BC (26), .-. A : C : : B : D (33). ' 37. If four quantities be proportional, the sum of the first and second is to the second,...the sum of the third and fourth is to the fourth. A i^B* ::C +:1?' Den ^ comPosition) For *=-?, and * «J? - . A+g C + D B D' BD ' ' ' ^S~ " " D •>... | |
 | George Peacock - Algebra - 1830 - 732 pages
...shall Compo. be proportionals also componendo, that is, the sum of the nendo> first and second shall be to the second as the sum of the third and fourth is to the fourth. Let a : b :: c : d, then also a + b : b :: c + d : d. For if - = - , then also - + 1 = - -f 1, and, thereodba... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...tho third as the second to the fourth, ibid. ART. 172. In a series of four proportional right lines, the sum of the first and second is to the second as...the sum of the third and fourth is to the fourth, ibid. ART. 173. In a series of four proportional right lines, the difference between the first and... | |
 | Augustus De Morgan - Algebra - 1840 - 186 pages
...: T ac Let 7 = bd Then (114) 1+| = 1+| «+6 c+d or —7— = — - j~ bd or 0 + 6 : 6 :: c + d : d That is, the sum of the first and second is to the...the sum of the third and fourth is to the fourth. For brevity, we shall not state in words any more of these proportions, since, the pupil will easily... | |
 | Euclides - 1842 - 316 pages
...proportional, they will also be proportional by composition : that is, the sum of the first and second will be to the second, as the sum of the third and fourth is to the fourth. Let A : B : : c : D, then, by composition, A + B : B :: c + D : D. Let P measure both A and B, and let Q be the... | |
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