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In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Elements of Plane Geometry: For the Use of Schools - Page 54
by Nicholas Tillinghast - 1844 - 96 pages

## Elements of Geometry and Trigonometry: With Practical Applications

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...

## Elements of Plane and Spherical Trigonometry: With Practical Applications

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...

## New University Algebra: A Theoretical and Practical Treatise, Containing ...

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,...

## Elements of Geometry: With Practical Applications to Mensuration

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,...

## New Elementary Algebra: in which the First Principles of Analysis are ...

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., ,...

## Primary Elements of Plane and Solid Geometry: For Schools and Academies

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...

## New University Algebra: A Theoretical and Practical Treatise, Containing ...

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,...

## New Elementary Algebra: In which the First Principles of Analysis are ...

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...