 | Alexander Malcolm - Arithmetic - 1718 - 396 pages
...middle Terms are the fame. Propofoion 4th, IF four (or more) Numbers arc in Geometrical Proportion; the Sum of all the Antecedents is to the Sum of all the Confequents, in the fame Rath, as any one of thefe Antecedents is to its Confequent. Example, If it... | |
 | Alexander Malcolm - Algebra - 1730 - 702 pages
...that b— a :/— a: : л : t — l::b: s — a. Thus; Of any Number of lîmilar and equal Ratios, the Sum of all the Antecedents is to the Sum of all the Confequents as any one of the Antecedents to its Confequent (by Thetr. IV. Ceroll. y: Bot in cafe of... | |
 | John Dougall - 1810 - 554 pages
...which each partner has contributed. From the nature of proportionals it follows that of any series, the sum of all the antecedents is to the sum of all the consequents, as each antecedent is to its consequent : that is, that the sum of all the shares is to the sum of... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...antecedents ; then will A : B ± «A : : m-\ : tnz ± nm\. HA , both the same ratio. THEOREM LXXII. If any Number of Quantities be Proportional, then...Antecedents is to the Sum of all the Consequents. LET A : B : : OTA : »;B : : «A : »B, &c ; then will - — A : B : : A + '»A -f nA. : : B + mz + «B,... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...± HA : : »IA : IWB ± HTOA. IMB ± nm\ B ± «A For = , both the same ratio. >«AA THEOREM LXXII. If any Number of Quantities be Proportional, then...Antecedents is to the Sum of all the Consequents. LET A : B : : MA : »>B : : "A : HB, Sec ; then will A : D : : A + ntA + «A : : B -f m& + na, See. B -f-... | |
 | John Dougall - Encyclopedias and dictionaries - 1815 - 514 pages
...contributed to that,stock. From the nature of proportional quantities it follows that in any number the smh of all the antecedents is to the sum of all the consequents, as each antecedent is to its consequent : or in other words that the sum of all the shares is to the... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...n\ : : OTA = m& ± nmA. ma ± run*. B ± n\ For --- = - , both the same ratio. fltA A THEOREM LXXH. If any Number of Quantities be Proportional, then...its Consequent, as the Sum of all the Antecedents h to the Sum of all the Consequents. LET A : B : : 7BA ' WB : : JJA : «B, &C ; thenwill - --- A k... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...mA : mB ± rim A. ms ± nmA i: + . \ For — — - = - , both the same ratio. THEOREM LXXH. • lf any Number of Quantities be Proportional, then any...Antecedents is to the Sum of all the Consequents. LET A : B : : MA : mB : : KA : T1B, die. ; then will -- — — A : B : : A + mA + 1iA : : B + mB + T1B,... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...t ± nA : : mA : ms ± nmA. «ri AA For -- = - , both the same ratio. OTB±mnA B±nA THEOREM LXXII. If any Number of Quantities be Proportional, then...Antecedents is to the Sum of all the Consequents. LET A : B : : mA : mB : : nA : UB, &c ; then will ---- A : B ;; A-{-n»Af-ftA ;; B+ms-4-nB, &c. A+»nA+nA... | |
 | Etienne Bézout - Mathematics - 1824 - 238 pages
...purpose is founded upon the principle established in article (186), that if many equal ratios are given, the sum of all the antecedents is to the sum of all the consequents, as one antecedent is to its consequent. From this principle we deduce the following example. EXAMPLE... | |
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If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I. 
