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" If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second will be to the first as the fourth to the third. "
Principles of Plane Geometry - Page 24
by James Wallace MacDonald - 1894 - 65 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 pages
...quantities N, M, Q, P, and thes« products being equal, N:M::Q:P(Prop.II.). PROPOSITION VI. THEOREM. ff four quantities are in proportion, they will be in proportion by composition, or division. D Let, as before, M, N, P, Q, be the numerical representatives of the four quantities,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1839 - 372 pages
...quantities N, M, Q, P, and these products being equal, N : M : : Q : P (Prop. II.). PROPO8ITION VI. THEOREM. If four quantities are in proportion, they will be in proportion by composition, or division. Let, as before, M, N, P, Q, be the numerical representatives of the four quantities, so...
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A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the ...

George Roberts Perkins - Algebra - 1842 - 370 pages
...inverting both terms c c< — =~Taa Therefore, by Art. 170, c : a : : c' : a'. (10) Which shows, that if four quantities are in proportion they will be in proportion by inversion. (173.) Quantities are in proportion by alternation, or alternately, when the antecedents...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...: c : : b : d. Illustration. 2 : 7 : : 6 : 21, and 2 : 6 : : 7 : 21. ART. 248.— PROPOSITION V.— If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second will be to the first as the fourth to the third. Let a : b : : c :...
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The Elements of Algebra: Designed for the Use of Common Schools, Also ...

George Roberts Perkins - Algebra - 1848 - 234 pages
...c~c" we have by inverting both terms Therefore, by Art. 137, с : a : : c' : a'. Which shows, that if four quantities are in proportion, they will be in proportion by inversion. (139.) Quantities are in proportion by alternation, or alternately, when the antecedents...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...27a : : 16+48 : 48, that is, 36 : 27 : : 64 : 48, in which the ratio is three fourths. THEOREM VIII. If four quantities are in proportion, they will be in proportion by division. Let us suppose that we have A : B : : C : D; we shall then have AxD=BxC. From each of these...
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An Elementary Treatise on Algebra: Designed as First Lessons in that Science

Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...two quantities is found by *'1' extracting the square root of their product. ui! l*5' PROPOSITION IV. If four quantities are in proportion, they will be in proportion ^ by INVERSION, that is, the second will be to the first, as the fourth to the third. Then, by the definition...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...the first, as the sum of the third and fourth is to the third. ART. 251. — PROPOSITION VIII. — If four quantities are in proportion, they will be in proportion by DIVISION; that is, the difference of the first and second, will be to the second, as the difference...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 408 pages
...divide both sides by b, £ =A ab That is (Art. 263), a : c : : b : d. ART. 271. PROPOSITION V. — If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second Witt be to the first, as the fourth to the third. Let n : li : : c...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...sum or difference of the antecedent and consequent is compared with either antecedent or consequent. If four quantities are in proportion, they will be in proportion by composition ; that is. if a : b : : с : d, then a ±b : a : : с ±d : c. COMPOSITION or EQUATIONS. The operation...
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