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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

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...Q±w (Prop. II.). PROPOSITION X. THEOREM. ••• If any number of quantities are proportionals, any one antecedent will be to its consequent, as the sum of all the antecedents to the sum of the consequents. Let M : N : : P : Q : : R : S, &c. then will M : N : : M + P + R : N...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 pages
...N±»» : Q±ra (Prop. II.). PROPOSITION X. THEOREM. If any number of quantities are proportionals, any one antecedent will be to its consequent, as the sum of all the antecedent* to the sum of the consequents. Let M : N : : P ; Q : : R jj^ dcc^then will M : N : : M...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 384 pages
...N±m : Q±w (Prop. II.). PROPOSITION X. THEOREM. If any number of quantities are proportionals, anyone antecedent will be to its consequent, as the sum of all the antecedents to the sum of the consequents. Let M M M N N N N F : Q R fcclhen will : : M + P + lt : N + Q+S : :...

Elements of Arithmetic and Algebra: For the Use of the Royal Military College

William Scott - Algebra - 1844 - 568 pages
..... ._ a_a+c_a + c+e_ •'• b+d+f+h. . .~?~6~6+3~4+</+/~' ScWhence in every series of equal ratios the sum of all the antecedents is to the sum of all the consequents as one antecedent, a, is to its consequent A, or as a sum of antecedents, a+c, a+c+e, &c., is to a...

An Introduction to Geometry and the Science of Form: Prepared from the Most ...

Anna Cabot Lowell - Geometry - 1846 - 216 pages
...This is called a continued proportion, being a series of equal ratios. In every continued proportion the sum of all the antecedents is to the sum of all the consequents as one antecedent is to its consequent. Therefore AB + BC + CD+DE + EA : ab+bc + cd -f- de-\-ea= AB...

Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...— . mA. A THEOREM L. If any number of quantities be proportional, then 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 : : mA : mB : : wA : nB, &c. ; then will A : B : ; A + mA + nA : B + mB + nB, &c. B + mB...

Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...continued proportion, that is, any number of proportions having the same ratio, any one 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 : : m : n, &c. Then will a : b : : a+c+m : b+d+n ; Since a : 6 : : c : d, we have...

Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 324 pages
...a' : с : : a" : c" : : &.C., .'. PROPOSITION V. If any number of couplets have the same ratio: (41) The sum of all the antecedents is to the sum of all the consequents, as any one antecedent to its consequent. We should also have ± a =fc a ± a" ± ... : ± с ± c'...