 | Isaac Todhunter - 1870 - 818 pages
...or a + b : a — b :: c + d : c — d. 397. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of...the antecedents to the sum of all the consequents. Let a : b :: с : d :: e : f; then a : b :: a+c + e : For ad=bc, and o/= be, (Art. 386), also ab =... | |
 | Thomas Kimber - 1874 - 352 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 и terms of an arithmetic series of which the first term and... | |
 | 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... | |
 | 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... | |
 | J. G - 1878 - 408 pages
...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... | |
 | 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
...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 sum of...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... | |
 | Charles Scott Venable - 1881 - 380 pages
...b : a — b = c + d : c — d. THEOREM IX. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of...the antecedents to the sum of all the consequents. Let a : b = c : d = e : f ; then a: b = a + c + e: b + d + f. Because T = - , ad — be ; because 7... | |
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If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. 
