 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 - Pagina 30door William Frothingham Bradbury - 1872 - 110 pagina’sVolledige weergave - Over dit boek
 | Alexander Malcolm - 1718 - 396 pagina’s
...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 pagina’s
...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 - 1806 - 526 pagina’s
...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 pagina’s
...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 pagina’s
...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 - 1812 - 620 pagina’s
...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 - 1815 - 514 pagina’s
...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 - 1817 - 456 pagina’s
...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 - 1822 - 616 pagina’s
...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 - 1824 - 238 pagina’s
...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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