 | Alexander Malcolm - 1718 - 396 σελίδες
...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 - 1730 - 702 σελίδες
...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 σελίδες
...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 - 1811 - 406 σελίδες
...± nm\. HA , both the same ratio. THEOREM LXXII. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent,...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, &c.... | |
 | Charles Hutton - 1812 - 620 σελίδες
...For = , both the same ratio. >«AA THEOREM LXXII. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent,...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- «B... | |
 | John Dougall - 1815 - 514 σελίδες
...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 - 1816 - 610 σελίδες
...--- = - , both the same ratio. fltA A THEOREM LXXH. If any Number of Quantities be Proportional, then any one of the Antecedents will be to 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 - 1822 - 616 σελίδες
...both the same ratio. OTB±mnA B±nA THEOREM LXXII. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent,...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 A For... | |
 | Etienne Bézout - 1824 - 238 σελίδες
...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... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 σελίδες
...;c',d, then will b ; a ; ; d ; c. 8. If a number of quantities be proportionals, the antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Thus, if a;6::c:rf::a::y::r:s, then will «:&::a+ctx+r;b + d+ y + s. 9. If four quantities be proportionals,... | |
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In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. 
