 | International Correspondence Schools - Building - 1906 - 634 pages
...denominators the consequents. The general truth was shown in that article, 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. AREAS OF POLYGONS 36. Definitions. — The area of a surface is the superficial space included within... | |
 | William James Milne - Algebra - 1906 - 444 pages
...ratio with the ratio a : b ; with the other ratios. PRINCIPLE 13. — 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. Thus, when a:6 = C:d = g: ft and so on, a + с + e + g + - : Ь + d +f+ Л + ••• : : a : Ь.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...±b:a = x±y: x; (2) a±b: b= x±y:y; (3) a ± b : x ± y = a : x, etc. NOTE II. In any proportion the sum of the antecedents is to the sum of the consequents as either antecedent is to its consequent. (Explain.) Also, in any proportion the difference of the antecedents... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Algebra - 1907 - 304 pages
...b, c, d, which are in proportion, are in proportion ; or — =—• XI. In a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its own consequent. If |=Л = ™ = *, (i) bdn у т : acmx УОЧ let - = r, - = r, - = r, - = r, (2)... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...(1) a ±b:a = x±y: x; (2) a±b:b = x±y:y; (3) a ± b: x± y = a: x, etc. NOTE II. In any proportion the sum of the antecedents is to the sum of the consequents as either antecedent is to its consequent. (Explain.) Also, in any proportion the difference of the antecedents... | |
 | Albert Harry Wheeler - Algebra - 1908 - 700 pages
...by the corresponding ratios obtained by applying (vii.) to (1). (ix.) In a seríes of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. That is, if a : Ъ — с : d = e : f — = m : n, then (a + с + e + + m) : (Ь + d + f + + n) = a... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...difference as the sum of the last two terms is to their difference. 334. 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. 336. A straight line parallel to the base of a triangle divides the other two sides proportionally.... | |
 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...Adding, а Whence, a + c + eH ---- =(b + d+/H ---- )r. And, a Or, That is : JTI a series o/ egwaZ ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. 382. Given a:b = b:c. Then a : c=a2 : b2. Proof: Since ^ = -, Ь с it follows that, ?x6=?x2b с b... | |
 | Michigan. Department of Public Instruction - Education - 1908 - 324 pages
...proportion by inversion, alternation, composition, and division; (b) that 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. 6. If y varies inversely as x, and y = 7 when x == 3; what is... | |
 | James William Nicholson - Algebra - 1909 - 332 pages
...respectively, an cn л/а л/с ... a" : b" = cn : d", Va : VB = л/с : Vd. 308. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents us any antecedent is to its consequent. i , а с е r/ Let l = d=fh Place each of these ratios equal... | |
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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. 
