 | Alexander Malcolm - 1718 - 396 páginas
...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 be as 3 to 8j... | |
 | John Dougall - 1810 - 554 páginas
...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... | |
 | Charles Hutton - 1811 - 406 páginas
...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.... | |
 | Charles Hutton - 1812 - 620 páginas
...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... | |
 | Charles Hutton - 1822 - 616 páginas
...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,... | |
 | Etienne Bézout - 1824 - 238 páginas
...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.... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 páginas
...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... | |
 | William Scott - 1844 - 568 páginas
...)q. a + c+e+g .. ._ a_a+c_a + c+e_ •'• b+d+f+h. . .~?~6~6+3~4+</+/~' ScWhence in every series of equal ratios the sum of all the antecedents is to the sum of all the consequents as one antecedent, a, is to its consequent A, or as a sum of antecedents, a+c, a+c+e, &c.,... | |
 | Nicholas Tillinghast - 1844 - 108 páginas
...10. Prop. 6. If several numbers are in proportion, any one antecedent will be to its consequent, as the sum of all the antecedents is to the sum of all the consequents. If 2:4::3:6::5:10: : 7 : 14, then is 2:4:: (2+3+5+7) : (4+6+10+14), or- 2 : 4 : : 17 :... | |
 | Anna Cabot Lowell - 1846 - 216 páginas
...This is called a continued proportion, being a series of equal ratios. In every continued proportion the sum of all the antecedents is to the sum of all the consequents as one antecedent is to its consequent. Therefore AB + BC + CD+DE + EA : ab+bc + cd -f-... | |
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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. 
