 | Bewick Bridge - Algebra - 1818 - 254 pages
...quantities, "•' a : b :• с : d : : e • /:: g. h &c. &c., then will the ßrst be •" to the second as the sum of all the antecedents to the sum of " all the consequents." And so on for any number of these proportions. Тн. 15. " If there be a set of quantities, a, b, c,... | |
 | Robert Patterson - Arithmetic - 1819 - 174 pages
...antecedents will = « — g, and the sum of all the consequents = s — I : but as one of the antecedents is to its consequent, so is the sum of all the antecedents, to the sum of all the consequents-)-. That is, / : IR : : s — g : * — /. Ilente - — Rg l- Theor. 1. And from the above r series it... | |
 | Sir John Leslie - Geometry, Plane - 1820 - 482 pages
...principle of this and the preceding Proposition is named inverse, or pertwbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the suin of all the antecedents to the snm of all the consequents. Let A : B : : C : D : : E : F : : G... | |
 | Sir John Leslie - Geometry, Modern - 1820 - 488 pages
...more generally expressed thus : A : B: AdbC=fcE=±=G : B=i=D=fc:F=±=H. Cor. 2. Hence, in a succession of proportionals, as one antecedent is to its consequent, so is the sum or difference of the several antecedents to the corresponding sum or difference of the consequents.... | |
 | Bewick Bridge - Algebra - 1821 - 648 pages
...proportional quantities, " a:b::c:d :: e :f :: g : h &c.&c., then will thejfrj/ be " to the second as the sum of all the antecedents to the sum of " all the consequents." And so on for any number of these proportions. TH. 15. " If there be a set of quantities, a, b, c,... | |
 | Thomas Keith - Arithmetic - 1822 - 354 pages
...A : A — B :: c : C — D. , IB. 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. Thus, if A : B :: C : D :: E : F :: G : H, &c. Then A : B :: A+C+E+G AA c EG . For, - = —=-=-=—,... | |
 | Euclid - 1822 - 222 pages
...magnitudes proportional (A ng. 23. to B as C to D) as one of the antecedents 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 Cto sum of B and D), For, if there be taken a and c equi-submultiples of (i)Pro;,.i2.... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...number of proportionals, of which all the ratios are equal, it will be, as the antecedent of any ratio is to its consequent, so is the sum of all the antecedents of the other ratios to the sum of all the consequents. For, let S = 5, $=;, }=l then will |= £-) =f... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...proportional quantities, a : b :: с : d :: e :/*:: g : h, &c. &c. then will the FIRST be to the SECOND as the SUM OF ALL THE ANTECEDENTS to the SUM OF ALL THE CONSEQUENTS. For since a : b :: с ": d, alternately, a : с :: Ь 'd. Hence (by THEOREM 7), a : a+c :: Ъ ;therefore,... | |
 | Enoch Lewis - Algebra - 1826 - 180 pages
...the former by the latter, = - r, or a+b : as-b : : c+d : c*rd. 65. When any number of quantities are proportionals, as one antecedent is to its consequent,...antecedents to the sum of all the consequents. Let a : b : : c :'d : : e :f : : g : h, &c., then (art. 62.) ad=bc, of— be, ah=bg, &c., also ab=ba. .-.... | |
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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. 
