 | Sir John Leslie - 1820 - 482 pàgines
...: A : : D : F. The principle of this and the preceding Proposition is named inverse, or pertwbate, equality. PROP. XIX. THEOR. If there be any number...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 - 1820 - 488 pàgines
...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 - 1821 - 648 pàgines
...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 - 1822 - 354 pàgines
...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 pàgines
...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 - 1823 - 210 pàgines
...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 - 1825 - 1046 pàgines
...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 - 1826 - 180 pàgines
...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. .-.... | |
 | George Lees - 1826 - 276 pàgines
...alternately, a+b : a — ,b::c+d: c — d. 117. WJien any number of quantities are proportionals, i as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let a : b : : c : d : : e :f, &c. Then shall a:b:: «+c+c+&c. : b+d+f+&c. For, since a : b : : c : d, ad... | |
 | John Radford Young - 1827 - 228 pàgines
...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... | |
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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. 
