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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 - 1889 - 63 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...couplets may be made the consequents of the first, by alternation (P. III.). PROPOSITION V. THEOREM. If four quantities are in proportion, they will be in proportion by inversion. Assume the proportion, 7? D A : B : : C : D ; whence, -j- == -^ • .4 0 If we take the...
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Algebra: Adapted to the Course of Instruction Usually Pursued in the ...

Paul Allen Towne - Algebra - 1865 - 314 pages
...qua.nti.ties, the first two may be made the extremes, and the second two the means, of a proportion. PROP. II. If four quantities are in proportion, they will be in proportion by alternation. For, since a : b : : c : d, we have ad = be. (2) (Prop. 1.) Dividing both members of (2)...
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Elements of Algebra: For Colleges, Schools, and Private Students, Book 2

Joseph Ray - Algebra - 1866 - 420 pages
...: f. If 4 : 8 : : 10 : 20 and 4 : 8 : : 6 : 12; then, 10 : 20 : : 6 : 12. 273. Proposition VII. — If four quantities are in proportion, they will be in proportion by COMPOSITION ; that is, the sum of the first and second will be to the first or second, as the sum of the third...
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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 250 pages
...4: 10 8 5 10: 4 8 8 4: 10 5 8: 10: 4 6 4 5: 8 10 4 8: 5 10 10 5: 8 4 10 85 4 248. 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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Ray's Algebra, First Book: Primary Elements of Algebra, for Common ..., Book 1

Joseph Ray - Algebra - 1866 - 252 pages
...sades by T, — 5- = ,— , or — =-=-. o ao be ab That is, a : c : : b : d. 348. 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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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1852 - 422 pages
...proposition is true, only when tho four quantities are of the tame kind ART. 271. PROPOSITION V. — If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second wib be to the first, as the fourth to the third. Let a :b : :c :d Then...
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 264 pages
...ac l = d Adding 1 to each member, j -f- 1 = e- -\- '. ie a -\- b : b = c -\- d : d THEOREM VII. 208. If four quantities are in proportion, they will be in proportion by division. Let a : b — c : d M Subtracting 1 from each member, ? — 1 = - — 1 or a~ b = ~d b...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 284 pages
...between A and C; then we have, A : B :: B : C; whence (Th. I.), - S * = A X C, or, B = THEOREM IV. If four quantities are in proportion, they will be in proportion by alternation. Suppose A:B::C:D; from thia (Th. I.) we have, A X .D = B X C; dividing by D X C, we have,...
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Elements of Algebra: For Colleges, Schools and Private Students

Joseph Ray - Algebra - 1866 - 420 pages
...: 27 : 18. In a similar manner it may be shown that a+6 : a : : c+d : c. 274. 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 first or second, as the difference...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...have, AC M JJ ^f — ^ \ whence, JB : A : : D : C: which was to be proved. PROPOSITION VI. THEOREM. If four quantities are in proportion, they will be in. proportion by composition or division. Assume the proportion, A : B : : C : D ; whence, -j- = 7T • 7? 7) s*. \j If we add 1...
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