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. The student's algebra - Page 14by John Darby (teacher of mathematics.) - 1829Full 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
...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... | |
| Isaac Dalby - Mathematics - 1806 - 526 pages
...— a : : d+ c -. d — c. (87.) 91. If there be any number of proportional quantities, Then either **antecedent, is to its consequent, as the sum of all the antecedents,** to the sum of all the consequents. Let a : b :: c : d : :f:g : Tiien a : b : : c : d, hence ad = be... | |
| 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
...THEOREM LXXII. 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 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
...THEOREM LXXII. 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 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... | |
| Charles Hutton - Mathematics - 1822 - 616 pages
...THEOREM LXXII. 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 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... | |
| Charles Hutton - Mathematics - 1831 - 632 pages
...THEOREM LXXII. 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, is to the sum of all the** conse^uents. Let A : в : : тл : тв : : пл : кн, &с. ; then will ... 'А : в : : А + "»•»•... | |
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