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" 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. "
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 392 pages
...successively equal to each other. Example : BOOK III PROPOSITION X. THEOREM 443. In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let To Prove Proof bdfh b+d+f+hf lj (2i H ^3> a) From (1). 7=7 ^4) H (5) a/= be (6) ] cf=de (7) / = /...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...other. Example : - = - = — = -, etc. bdf ti PROPOSITION X. THEOREM 443. In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. (1) Let To Prove Proof bdfh o_-2_A+_fl! = ?. b+d+f+hf T = ~ (2) From (1). 5 = 7 (3) df - = - (4)...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...A'B' = BC : B'C' = CD : C'D', etc. 351 .-. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', 335 (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). That is, ' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the bases of a trapezoid...
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Elementary Algebra

John Henry Tanner - Algebra - 1904 - 396 pages
...first (or the second) as the sum of the third and fourth is to the third (or the fourth). PRINCIPLE 6. In a series of equal ratios the sum of the antecedents is to the sum of tl<e consequents as any antecedent is to its own consequent. Thus, if a : b = c : d = e :f=g : A= •••...
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Elementary Algebra

John Henry Tanner - Algebra - 1904 - 400 pages
...first (or the second) as the sum of the third and fourth is to the third (or the fourth}. PRINCIPLE 6. In a series of equal ratios the sum of the antecedents is to tlie sum of tJie consequents as any antecedent is to its own consequent. Thus, if a: b = c: d = e :f=g:...
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Essentials of Algebra: Complete Course (an Adequate Preparation for the ...

John Charles Stone, James Franklin Millis - Algebra - 1905 - 792 pages
...And O2 = c. 195. Hence, >=j/ac. Thus, in the proportion 9: 18=18: 36, we have 18=1/8 x 36. 205. In a, series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. ampx Suppose that _=_=.=_== onqy Ti a Let Ъ=г' mpx . . Then — =r. -=r. -—r, etc. Axiom 7. n...
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Elementary Algebra

Walter Randall Marsh - Algebra - 1905 - 462 pages
...(1) bd raising each member of (1) to the nth power, whether n is integral or fractional, 6"~d"' XI. In a series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. If a_c._m_x si*. , . a с mx /г,-. let - = r, - = r, - = r, -=r, (2) bdny clearing...
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Elementary Algebra

Walter Randall Marsh - Algebra - 1905 - 412 pages
...each member of (1) to the nth power, whether n is integral or fractional, an _ cn b'1 ~ cF XI. _Zn д series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. К а с т х ,л^ T=J=— = -•> t1) о dn у let f.* -,,_,, S.,, (2) о а...
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The Elements of Geometry

Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...is said to be derived from the given proportion by compositivn and division.) XI. 2. In any number of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent. Hyp. If a: 6 : : c : e : :/: g : : etc., Cone.: then a + c+/+ ...: b + e + g+ ... : : a: 6 : : c: e...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906 - 620 pages
...antecedents and the denominators the consequents. The general truth was shown in that article, that in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. AREAS OF POLYGONS 36. Definitions. — The area of a surface is the superficial space included within...
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