| 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... | |
| 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 :... | |
| 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... | |
| 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,... | |
| 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... | |
| 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:... | |
| 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... | |
| 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... | |
| 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... | |
| 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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