| Alexander Malcolm - Arithmetic - 1718 - 396 pages
...Extremes and 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 - 627 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... | |
| George Washington Hull - Geometry - 1807 - 408 pages
...Ax. 2 bn dq Whence am : bn = cp : dq. QED PROPOSITION XV. THEOREM. 133. In a series of equal ratios, **the sum of all the antecedents is to the sum of all the consequents** an any antecedent is to its consequent. Let a : b= c : d = e :/. Let r = the common ratio, Then r =... | |
| 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 all... | |
| Charles Hutton - Mathematics - 1811
...Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as **the Sum of all the 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 +... | |
| Charles Hutton - Mathematics - 1812
...Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as **the Sum of all the 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.... | |
| John Dougall - Encyclopedias and dictionaries - 1815 - 516 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 sum... | |
| Charles Hutton - Mathematics - 1822 - 618 pages
...Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as **the Sum of all the 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 - 219 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...consequents, as one antecedent is to its consequent.** From this principle we deduce the following example. EXAMPLE I. It is required to divide 120 into three... | |
| John Darby (teacher of mathematics.) - 1829 - 214 pages
...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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