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... Bradbury's Elementary Algebra - Page 212by William Frothingham Bradbury - 1877 - 291 pagesFull view - About this book
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...remaining terms will be ill proportion. PROPOSITION XI. — THEOREM. 147. If any number of magnitudes **are proportional, any antecedent is to its consequent...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.... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...ma me nb ~- nd 1 or ma: nb :: me: nd. n 309. If any number of quantities are proportional, any one **antecedent is to its consequent as the sum of all...of all the consequents. Let a: b:: c : d :: e: f;** then, since a: b:: c: d, ad — be; A (1.) and, since a: b :: e: /, «/=fe; (2.) also ab ~ ba. (3.)... | |
| 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 :... | |
| Benjamin Greenleaf - 1869 - 516 pages
...remaining terms will be in proportion. PROPOSITTON XI. — THEOREM. 147. If any number of magnitudes **are proportional, any antecedent is to its consequent...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... | |
| Horatio Nelson Robinson - 1869 - 276 pages
...Q. THEOREM VII. X If any 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... | |
| William Frothingham Bradbury - Geometry - 1872 - 124 pages
...proportion. Let a : b = c : d that is 7=3 bd Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 **If any number of quantities are proportional, any...consequents. Let a : b = c : d = e :f Now ab = ab** (A) and by (12) ad=bc (B) and also af=."be (C) Adding (A), (B), (C) a (b -fd +/) = b (a + c -+- «)... | |
| William Frothingham Bradbury - Algebra - 1872 - 268 pages
...proportion. Let a : b = c : d ac 1.0. 7 = -, I d T-, a" c» Hence, = ie a" : bn = c" : ef THEOREM XII. 21 3. **If any number of quantities are proportional', any...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),... | |
| William Frothingham Bradbury - Geometry - 1872 - 262 pages
...proved. 23. If any number of quantities are proportional, any antecedent is to its consequent as tl;e **sum of all the antecedents is to the sum of all the...consequents. Let a : b = c : d=. e :f Now ab = ab** (A) and by (12) ad=bc (B) and also af=be (C) Adding (A), (B), (C) a (b + d +/) = b (a + c + e) Hence,... | |
| William Frothingham Bradbury - Geometry - 1873 - 132 pages
...= c : d that is i = ac od Hence -,- = -=a n c n 6 n rf" that is a" : 6" = c" : d n THEOREM IX. 23. **If any number of quantities are proportional, any...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... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...same in both, the remaining terms will be in proportion. THEOREM X. 115. If atiy number of magnitudes **are proportional, any antecedent is to its consequent...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... | |
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