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Books Bücher 51 - 60 von 70 in Componendo, by composition ; when there are four proportionals, and it is inferred...
" 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 and Plane Trigonometry: With an Appendix, and Copious ... - Seite 137
von Sir John Leslie - 1817 - 432 Seiten
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Elements of Algebra: For Colleges, Schools, and Private Students, Bücher 2

Joseph Ray - 1866 - 406 Seiten
...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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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - 1866 - 240 Seiten
...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 Seiten
...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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New Elementary Algebra

Horatio Nelson Robinson - 1874 - 312 Seiten
...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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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 University Algebra

Horatio Nelson Robinson - 1875 - 412 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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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New Elementary Algebra: Containing the Rudiments of the Science for Schools ...

Horatio Nelson Robinson - 1879 - 324 Seiten
...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 = c : d. Then by formula (A), \ = § (1). oa Clearing of fractions, be = ad . . . (2). Hence by Prop. II., b : a...
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