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... University Algebra - Page 263by Webster Wells - 1879 - 444 pagesFull view - About this book
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...remaining terms will be in proportion. PROPOSITION 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. Let A : B : : C : D : : E : F ; then will A:B::A+C + E:B + D + F. For, from the given proportion, we... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...remaining terms will be in proportion. PROPOSITION 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. Let A : B : : C : D : : E : F ; then will A:B::A + C + E:B + D + F. For, from the given proportion,... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...If there be a proportion, consisting of three or more equal ratios, then either antecedent will be to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Suppose a : Ь = с : d — e : f= g : h =, etc. Then by comparing the ratio, a : b, first with itself,... | |
| Benjamin Greenleaf - 1863 - 338 pages
...: : с : d. THEOREM X. 324 1 If any number of quantities are proportional, any antecedent is to ils consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b : : с : d : : e : f; then a : b : : a -|- с -f- e : b -f- d -J- f. For, by Theo. I., ,... | |
| Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...: B : : .£ : R. 2 2 7. By composition, implies that if any number of magnitudes are proportionals, the sum of all the antecedents is to the sum of all the consequents as . any one antecedent is to its consequent. Thus, If A : B : : C : D : : E : F, Then A+C+E : B+D+F... | |
| Benjamin Greenleaf - Algebra - 1864 - 336 pages
...^ = e-, , ce and -d=-f. Therefore, by Art. 38, Ax. 7, | — ^ or, a : b : : c : d. THEOREM X. 324 1 If any number of quantities are proportional, any...antecedents is to the sum of all the consequents. Let a : b : : c : d : : e : f; then a : b : : a-\-c-\-e : b -\-d-\- f. For, by Theo. I., od = bc, and... | |
| Benjamin Greenleaf - Algebra - 1864 - 420 pages
...d. _ae , ce .. ac For, - = -; , and - = — ; therefore r = -7 ; whence, a : i : : c : e?. 319. -Jf any number of quantities are proportional, any antecedent...antecedents is to the sum of all the consequents. If a : b : : c : d : : e :/, then a : b : : a-\-c-\-e : b-\-d-\-f. For, by Art. 311, ad = be, and af... | |
| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...tliere be a proportion, consisting of three or more equal ratios, then either antécédent will be to its consequent, as the sum of all the antecedents is to the sum of all the coimequmUs. Suppose a : b = с : d = e : _/°— g : h =, etc. Then by comparing the ratio, a : b,... | |
| Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...: Q. THEOREM VII. 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, C, D, E, etc., represent the several magnitudes which give the proportions A : B :: C : D... | |
| Paul Allen Towne - Algebra - 1865 - 314 pages
...mq = np; whence am X dy = bn X cp, or am : bn :: cp : dq. (14) PROP. IX. In a continued proportion, the sum of all the antecedents is to the sum of all the consequents as any one antecedent is to its consequent. (Vide § SS16, def. ,7.) For, since a : b : : c : d, we... | |
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