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Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Pągina 155
per Sir John Leslie - 1809 - 493 pągines
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## Elements of Algebra: For Colleges, Schools, and Private Students, Llibre 2

Joseph Ray - 1866 - 406 pągines
...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 : d. Then, (Art. 263), .... | = |; ac Inverting the fractions, . . j-=-^. That is, (Art. 263), . . 6 : a : : d...
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## Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - 1852 - 396 pągines
...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 (Art. 263), =- ; ac dividing 1 by each side, -=- ; oa ac a_c b dThat is, (Art. 263), b : a : : d :...
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## Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - 1866 - 240 pągines
...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 : d. This gives — = — . fa ao Inverting the fractions, we have -r— -~ 0 Cti That is, b : a : : d :...
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## Euclid's Elements of Geometry

Euclid - 1872 - 261 pągines
...becomes A to C as B to Do. 15. By Inversion, when it is inferred that if four magnitudes be proportional, the second is to the first as the fourth to the third ; as is demonstrated in Prop. 20, namely — A to B as CD to E, becomes B to A as E to CD. the fourth...
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## The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...Fifth Book. 14. Invertendo, by inversion ; when there are four proportionals, and it is inferred, that the second is to the first, as the fourth to the third. Prop. B. Book V. 15. Componendo, by composition ; when there are four proportionals, and it is inferred...
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## New Elementary Algebra

Horatio Nelson Robinson - 1874 - 312 pągines
...quantities be 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 = с : d Then by formula (A), - = - (i) а с Clearing of fractions, bo = ad (2) Hence by Prop. II,...
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## New University Algebra

Horatio Nelson Robinson - 1875 - 412 pągines
...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 : d ; fl f then by formula (A), - = -^ ; clearing of fractions, be = ad; hence by Prop. II., b : a = d:...
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## Elementary geometry of the right line and circle ...

William Alexander Willock - 1875 - 172 pągines
...second to the fourth. BY INVERSION. — When the first is to the second as the third to the fourth, the second is to the first as the fourth to the third. This is evident from the first test. For, since a submultiple of the first is contained in the second...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 pągines
...Fifth Book, XIV. Invertendo, by inversion ; when there are four proportionals, and it is inferred, that the second is to the first, as the fourth to the third. Prop. B. Book v. XV. Componendo, by composition ; when there are four proportionals, and it is inferred...
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## Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878 - 209 pągines
...is to the third as the second is to the fourth; that is, they are proportional by alternation. Also the second is to the first as the fourth to the third; that is, they are proportional by inversion. Tims if A : B = C : D, 6. By squaring, cubing, &c., and...
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