 | Joseph Ray - Algebra - 1866 - 420 pages
...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... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...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 :... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...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 :... | |
 | Euclid - Geometry - 1872 - 284 pages
...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... | |
 | Euclides - 1874 - 342 pages
...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... | |
 | Horatio Nelson Robinson - Algebra - 1874 - 340 pages
...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,... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...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:... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...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... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...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... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...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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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. 
