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. Academic Algebra - Page 202by George Wentworth, David Eugene Smith - 1913 - 458 pagesFull view - About this book
| 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
...demonilrated is, 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
...§111 nq Multiplying, 2™ = ^. 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 - 406 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 : : OTA : »;B : : «A : »B, &c ; then will - — A : B : : A + '»A -f nA. : : B + mz +... | |
| Charles Hutton - Mathematics - 1812 - 620 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 : »>B : : "A : HB, Sec ; then will A : D : : A + ntA + «A : : B -f m& + na, See.... | |
| 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 sum... | |
| Charles Hutton - Mathematics - 1822 - 616 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 - 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 I.... | |
| John Darby (teacher of mathematics.) - 1829 - 212 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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