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. An Elementary Geometry - Page 30by William Frothingham Bradbury - 1872 - 110 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
...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
...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 a- * •••fg "g = bf Therefore ad + ag = be + bf... | |
| 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 + «B, &c.... | |
| 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. B -f- «B... | |
| 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... | |
| Sir John Leslie - Geometry - 1817 - 456 pages
...number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents **to the sum of all the consequents. Let A : B : : C : D : : E : F** : : G : H; then A : B : : A+C+E+G : B+D+F+H. Because A : B : : C : D, (V. 6.) AD = BC; and, since A... | |
| 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 A For... | |
| 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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