 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...alternating the terms, as AB is to OP so is BC to PQ, so is CD to QE, etc. Wherefore as AB is to OP so is the sum of all the antecedents to the sum of all the consequents, that is, AJ3 is to OP as the perimeter of BE to the perimeter of PS (V. 8). PROP. XVIII.— PROBLEM.... | |
 | 1877 - 188 pages
...proportionals ? Prove that if any number of quantities be in continued proportion, as one of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. 9. Prove the rule for finding the sum to n terms of an arithmetic series of which the first term and... | |
 | J. G - 1878 - 408 pages
...a : b : c : d, to prove that ma±nb:pa±qb : : mc±nd :pc±qd. 7. 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 ail the consequents. 8. We will now exemplify a process somewhat different to the one usually employed... | |
 | London univ, exam. papers - 1878 - 164 pages
...proportionals? Prove that if any number of quantities be in continued proportion, as one of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. 9. Prove the rule for finding the sum to n terms of an arithmetic series of which the first term and... | |
 | Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...5+4+3, or 12 : 6 : : 36 : 18. the same ratio, then any one antecedent will be to its consequent OK the sum of all the antecedents to the sum of all the consequents. PROBLEMS IN PROPORTION. 1. Find a mean proportional between 72 and 18. Ans. 36. 2. What is a mean proportional... | |
 | Robert Potts - 1879 - 668 pages
...antecedent and consequent. 10. Prop. If any number of quantities are proportionals, at any antecedent i» to its consequent, so is the sum of all the antecedents to all the consequents. (Eue. VII. 12.) Suppose these quantities a, b, c, d, e, f to be proportionals... | |
 | R. M. Milburn - Mathematics - 1880 - 116 pages
...pa + qb pc+qd 48. If a :b :: c : d :: e :/&c. a : b :: a+c+e&c. : b+d+f&c. or - = ~ b + d+f&LC. ie as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. 49. Def. One quantity is said to vary directly as another when the two quantities depend upon each... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...CDE, CEF, CFG the consequents, and [v. xn.] any one of these equal ratios is equal to the ratio of the sum of all the antecedents to the sum of all the consequents ; therefore the triangle ABH : the triangle CDE : : the polygon ABHIJ : the polygon CDEFG. 3. The triangle... | |
 | Euclides - 1885 - 340 pages
...CDE, CEF, CFG the consequents, and [v. xn.] any one of these equal ratios is equal to the ratio of the sum of all the antecedents to the sum of all the consequents ; therefore the triangle ABH : the triangle CDE : : the polygon ABHIJ : the polygon CDEFG. 3. The triangle... | |
 | Euclid - Geometry - 1890 - 442 pages
...equal, all the magnitudes being of the same kind, as one of the antecedents is to its conseqzient, so is the sum of all the antecedents to the sum of all the consequents. (Addenda?) Let A, B, C, D, E, F be the terms of three ratios, such that A:B = C:D=E:F, where the magnitudes... | |
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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. 
