 In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.  Elementary Algebra - Page 190by Herbert Ellsworth Slaught, Nels Johann Lennes - 1915 - 373 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1888 - 272 pages
....-, AB+ BC, etc. : A'B' + B'C', etc. =- AB : A'B', § 303 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent). NUMERICAL PROPERTIES OF FIGURES. PROPOSITION XV. THEOREM. 334. // in a right triangle a perpendicular... | |
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...= , and x = [P. I, Cor. 1] aa, L ' Therefore, x = d XVI. In any multiple proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Given a:b::c:d::c:f Given Г ( e :b::с :/:•ff :</ :h (A)) (B)î Prove, 1. aXe: ab bX f: d :cXg:... | |
 | David Martin Sensenig - Algebra - 1890 - 556 pages
...ab, , , — = -т ; whence а : с : : о : d. û Oí 449. In any multiple proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Given a :b : : с : d : : e :f : : g :h to prove e+g : b + d+f+h : : a : b Demonstration : Let т=г;-3-... | |
 | George Albert Wentworth - Algebra - 1891 - 380 pages
...= — * 0 be cd ab or - = _ cd .'. a : с = b : d. 317. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. •c, т a с à g For, 1f - = - = - = J-, bdfh r may be put for each of these ratios. Then |=r,.|=r,i... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...a proportion. SECTION IV.— CONTINUED PROPORTIONS. . PROP. XVI. In any proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. PROP. XVII. In any proportion, all the antecedents, or all the consequents, may be multiplied by any... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...297, 296, and 299. 303. If any number of magnitudes of the same kind form a proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Post. Let the quantities a, x, c, n, d, and r form a continued proportion, so that a:x::c:n::d:r. We... | |
 | George Albert Wentworth - Algebra - 1891 - 544 pages
...by $, ^ = ^7, с be cd 5=*. с d .-. a: c = b : d. 282. In a Series of Equal Batios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. •n •/. а с е ft For, if - = - = - = £, bdfh r may be put for each of these ratios. пи. а... | |
 | George Albert Wentworth - Algebra - 1891 - 380 pages
...с be cd ab or - = -. с d л a : с — b : d. L\. 317. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its 7 Ju_.'. r may be put for each of these ratios. mi „ Я „ С- -' * _ J <Г i aen - = r, - — r,... | |
 | Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...the theory of proportion, it is sometimes stated that : " In a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent." This is a true proposition applied to numbers, but is not true of geometrical magnitudes unless these... | |
 | George W. Lilley - Algebra - 1892 - 420 pages
...íSr;-7?H-í»HTherefore, a + c + e + g :l+d+f + h::a:b. Hence, XI. In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. a2 + Ь* а Ъ + b с EXAMPLE 1. .If ~ï~v~î~ = ~j,z 4. г > Prove that о as a mean proportional... | |
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