 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... | |
| |
