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" 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 30
by William Frothingham Bradbury - 1872 - 110 pages
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The Practical Analyst: Or, A Treatise on Algebra, Containing the Most Useful ...

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,...
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Elements of Arithmetic, Algebra, and Geometry

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...
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The student's algebra

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,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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 +...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

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,...
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Elements of Plane Geometry: For the Use of Schools

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....
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Elements of Arithmetic and Algebra: For the Use of the Royal Military College

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...
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The first principles of algebra, for the use of the boys of the Royal ...

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...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

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....
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An Introduction to Geometry and the Science of Form: Prepared from the Most ...

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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