 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...contradicts the hypothesis. PROPOSITION V. THEOREM. If any number of homogeneous magnitudes be proportional, as one antecedent is to its consequent, so is the sum of the antecedents to the sum of the consequents. First, let there be four magnitudes, or the proportion... | |
 | John Playfair - Geometry - 1829 - 210 pages
...division, conversion, and mixing. If several quantities be proportional, as one of the antecedents is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. If four quantities be proportional, and if the first and second be multiplied or divided by any quantity,... | |
 | John Radford Young - Algebra - 1832 - 408 pages
...uc eg/, &c. ' aei, &c. : bfk, &c. : : eg/, &c. : dhm, &c. THEOREM 7. In any number of equal ratios, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. A /7 f A Let the ratios be - = - = - = &c. : Put - = a ; then b = aa, ace a ' d = Cq,f= eq, &c. and,... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...magnitudes proportional (A to B as C to D), as one of the antecedents is to its consequent (A to B), so is the sum of all the antecedents to the sum of all the consequents (sum of A and C to sum of B andD.) For, if there be taken a and c equi-submultiples of A and C, the... | |
 | Mathematics - 1836 - 488 pages
...How — the ratio of lesser inequality ? If, in several couplets the ratios are equal, what ratio has the sum of all the antecedents to the sum of all the consequents ? How ¡я a ratio of greater inequality affected by adding the same quantity to both terms ? How —... | |
 | James Bryce - Algebra - 1837 - 322 pages
...: ôrta : : d : d±c, and b±a:b::d±c:d. 178. V. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let there be any number of proportionals, a:b::c:d::e:f; then ad=bc, and afz=be; also ab = ba; therefore,... | |
 | John Hind - Algebra - 1837 - 584 pages
...or, a(6 + d +/+ &c.) = b(a + c + e + &c.): , , aa + c + e + &c. whence, - = : b 6 + d+/+&c. that is, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. Similarly, if a : b = b : c = c : d = &c., we shall have aa + b + c + &c. 6 b + c + d + &c. ' (J f*... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...10). PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so is the sum of all the antecedents to that of the consequents. If A:B::C:D,andC:D::E:F;A:B:':A + C + E: B + D + F. nB + wD + «F ; and if... | |
 | Euclides - 1838 - 264 pages
...otherwise than proportional. PROP. V. THEOR. If any number of homogeneous magnitudes be proportional, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. First, let there be four magnitudes, A being one antecedent, B its consequent ; C the other antecedent,... | |
 | John Radford Young - 1839 - 332 pages
...&c. cgl, &c. ' aei, &c. : bfk, &c. : : cgl, &c. : dhm, &c. THEOREM 7. In any number of equal ratios, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. Т Ï /• • Let the ratios be - = - = - = &c. : Put - = a ; ace a then b — aq, d = cq, f= eq,... | |
| |
When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. 
