 | George Albert Wentworth - Geometry - 1899 - 500 pages
...+ d:c — d. QED PROPOSITION IX. THEOREM. _ 335. In a series of equal ratios, the sum of the ients is to the sum of the consequents as any antecedent is to its consequent. Let a:b = c:d = e:f = g:h. To prove that a + c + e + g : b + d + f + h = a : b. aceq Then a — br,- c... | |
 | James Morford Taylor - Algebra - 1900 - 504 pages
...Proof. By §§ 128 aud 186, from (1) we obtain (2). By §§ 221 and 225, from (1) we obtain (3). 331. In a series of equal ratios the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent. That is, if a:b = c:d=e:f=—, (1) then a + c + e + — :b + d... | |
 | George Edward Atwood - 1900 - 276 pages
...= e:f=g: h ba = ab bc = ad be = af bg = ah K)a NOTE. — Students should also be able to show that the sum of the antecedents is to the sum of the consequents as c : d, as « :/, and as g-.h. 435. The product of the corresponding terms of two or more proportions... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...Example: ci c e _ g — — — — — —. GLC* 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 b~d''f~h' « + c + e + g_e b+d+f+h~f a c e _ g To Prove Proof ? = 4 <2> § = ^ ( 3 ) 7=7 w 1=7 (5)... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...equal to each other. Example : acea 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. H=H- m To Prove «±i+£±4-«. Proof Add (6), (7), (8), and (9), and factor. /(a + c + e + g)=e(b... | |
 | William James Milne - Algebra - 1901 - 476 pages
...? 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 = с : d = e :/= g : h. It is to be proved that... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...two terms is to the second term as the difference of the last two terms is to the fourth term. 335. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 338. Like powers of the terms of a proportion are in proportion. 342. If a line is drawn through two... | |
 | George Albert Wentworth - Algebra - 1902 - 548 pages
...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, -... | |
 | George Albert Wentworth - Algebra - 1902 - 548 pages
...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 .:... | |
 | William James Milne - Algebra - 1902 - 620 pages
...? 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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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. 
