| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...PROPOSITION XI. — - 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 514 pages
...proportion. PROPOSITION XI. — 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... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...PROPOSITION VUE. — If there be a proportion, consisting of three or more equal ratios, then either **antecedent will be to its consequent, as the sum of...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 - Geometry - 1863 - 504 pages
...proportion. PROPOSITION XI. — 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,... | |
| 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... | |
| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...VIII. — If 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,... | |
| Benjamin Greenleaf - Algebra - 1864 - 336 pages
...or, a : b : : c : d. THEOREM X. 324 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 : : e : f; then a : b : : a-\-c-\-e : b -\-d-\- f. For, by Theo. I., od = bc, and... | |
| Horatio Nelson Robinson - Conic sections - 1865 - 472 pages
...D : : P : 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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