 Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...  An Elementary Geometry and Trigonometry - Page 30by William Frothingham Bradbury - 1872 - 238 pagesFull view - About this book
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let A : B : : C : D : : E : F ; then will A:B::A+C + E:B + D+F. For, from the given proportion, we have AXD = BXC, and AXF = BX E.... | |
 | William Frothingham Bradbury - Algebra - 1868 - 264 pages
...XII. 213. If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b=; c : d = e if Now ab = ab (1) and by Theorem I. ad = bc (2) and also a/=6« (3) Adding (1), (2), (3), g(b+.d+f)... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...proportional, any one of the antecedents will be to its consequent as the sum of all thf tnlfcedents is to the sum of all the consequents. Let A, B, C, D, 13, etc., represent the several magm tudes whi ih give the proportions A : B :: C : J) A : B :: E :... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...number of magnitudes are proportional, any one of the antecedents will be to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let A, B, (7, D, E, etc., represent the several magnitudes which give the proportions To which we may annex the... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. feet A:B::C:D::E:F; then will A:B::A + C + E:B + D + F. For, from the given proportion, we have AXD... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...— -In any number of proportions having the same ratio, any antecedent is to its consequent as the sum. of all the antecedents is to the sum of all the contequents. Let ...... a : 6 : : c : d : : m : n, etc. Then, ..... a : b : : a+c+m : 6+d+n. Since... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the...(B) and also af=."be (C) Adding (A), (B), (C) a (b -fd +/) = b (a + c -+- «) Hence, by (14) a :b=a-\-c-\-e:b-\-d-\-f THEOREM X. 21. If there are two... | |
 | William Frothingham Bradbury - Algebra - 1872 - 268 pages
...XII. 21 3. If any number of quantities are proportional', any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a:b = c:d = e:f Now ab — ab (1) and by Theorem I. ad = bc (2) and also af=be (3) Adding (1), (2),... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...THEOREM X. 115. If atiy number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let A : B : : C : D : : E : F; then will A:B::A+C+E:B\-D + F. For, from the given proportion, we have AXD = BXC, and AXF = BX E. By... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...THEOREM IX. 23. If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a :b = e : d=.e :f Now ab = ab (A) and by (12) ad —be (B) and also af=be (C) Adding (A), (B), (C) a (b... | |
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