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
| Enoch Lewis - Algebra - 1826 - 180 pages
...quantities are 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, &c., then (art. 62.) ad=bc, of— be, ah=bg, &c., also ab=ba. .-. ab+ad+af+ah, &c. =ba+bc+be+bg,... | |
| George Lees - 1826 - 266 pages
...quantities are proportionals, i 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,** &c. Then shall a:b:: «+c+c+&c. : b+d+f+&c. For, since a : b : : c : d, ad = be, (No. 108.;) in like... | |
| John Darby (teacher of mathematics.) - 1829 - 214 pages
...Thus, if a', 6; ;c',d, then will b ; a ; ; d ; c. 8. If a number of quantities be proportionals, the **antecedent is to its consequent, as the sum of all...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,... | |
| John Playfair - Geometry - 1829 - 210 pages
...proportional, as one of the antecedents is to its consequent, so is the suril of all the antecedents **to the sum of all the consequents. Let A : B : : C : D : : E : F** : : G : H, &c. that is, let A : B : : C : D, and A : B : : E : F, &c. then A:B::AfC + K + G:B + D +... | |
| Charles Hutton - Mathematics - 1831 - 660 pages
...THEOREM LXXII. IP 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** : в : : m\ : тв : : ПА : им, &с. ; then will ... л : в : : A + я** + ЯА : в + MB + яв,... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...14, then 7 : 5 : : 14 : 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 : 34. Prop. 7.... | |
| William Scott - Algebra - 1844 - 568 pages
..... ._ 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., is to a... | |
| Admiralty - 1845 - 154 pages
...number of equal ratios, then will one antecedent be to its consequent, as the sum of all the antecedents **to the sum of all the consequents. Let a : b : : c : d : : e : f** ace that is, — =r— =— then will a : b : : a + c + e : b + d+f ab=ba •. ad— be af=be .-. ab... | |
| Charles William Hackley - Algebra - 1846 - 542 pages
...quantities, the first will have to the second the same ratio that t}ie sum of all the antecedents has **to the sum of all the consequents. Let a, b, c, d, e, f,** g, h be any number of proportional quantities, such that a:b::c:d::eif:igzhr Then a:l>::a+c+e+g:b+d+f+h.... | |
| Anna Cabot Lowell - Geometry - 1846 - 216 pages
...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- de-\-ea= AB... | |
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