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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. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 17
por International Correspondence Schools - 1906
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A College Algebra

George Albert Wentworth - 1902 - 530 páginas
...this in any particular case, it will be found sufficient to substitute ra for b and re for d. 245. In a series of equal ratios, the sum of the antecedents...the sum of the consequents as any antecedent is to ifs consequent. we may put r fur each of these ratios. ,,., « xeg I hen, . . = r, — = r, = r, -...
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A College Algebra

George Albert Wentworth - 1902 - 530 páginas
...particular case, it will be found sufficient to substitute ra for b and re for d. 245. In a serie» of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent. For,« 6 dfh we may put r for each of these ratios. H а-* г- И.-. a = br, c = dr, e=fr, g = kr .:...
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Advanced Algebra for Colleges and Schools

William James Milne - 1902 - 608 páginas
...? with the ratio of any antecedent to its consequent ? PRINCIPLE 13. — In any multiple proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Principle 13 may be established as follows : Let a:b = c:d = e:f=g:h. It is to be proved that a + c...
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High School Algebra

Middlesex Alfred Bailey - 1902 - 297 páginas
...division.) (By composition.) a + b c + d PROPOSITION LXXXIV. THEOREM In a series of equal ratios, the sinn of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a:b = c:d — e:f To prove that a + с + e:b + d +/: : a : 6 a6 = 6a (The product of two quantities...
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Shorter Course in Algebra

George Albert Wentworth - 1902 - 282 páginas
...Division. а — с : с : : Ь — d: d. 295. In a series of equal ratios, the sum of the antecedente is to the sum of the consequents as any antecedent is to us consequent. H-;-f r may be pat for each of these ratios. i---S--7"-i--- .-. a =- br, с=- dr, e...
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School Algebra

John Marvin Colaw - 1903 - 432 páginas
...solving equations in the fractional form, as will he seen in the solution of Ex. 4, Art. 408. 408. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. •Ei •£ « I' e for, if - = = = •••, b 'I- j we may put each of these equal ratios equal...
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Elements of Plane and Solid Geometry

Alan Sanders - 1903 - 384 páginas
...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 - 1904 - 473 páginas
...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 - 1904 - 364 páginas
...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 - 1904 - 364 páginas
...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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