| Euclides - 1846
...(S. 16) : 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** (S. B) : xv. Componendo, by composition ; when there are four proportionals, and it is inferred that... | |
| Joseph Ray - 1848 - 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.** By Art. 244, ad=bc. Dividing both sides by 6, ~T=CDividing both sides by d, i=jThat is, b : a : : d... | |
| Euclides - 1848
...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, hy composition ; when there are four proportionals, and it is inferred... | |
| Joseph Ray - 1848 - 240 Seiten
...quantities are in proportion, they will be in proportion by INVERSION ; that is, the second m1l be **to the first as the fourth to the third. Let a : b** : : e : d. By Art. 244, ad=bc. Dividing both sides by b, -r=cft fDividing both sides by d, T— 3That... | |
| William Frederick Greenfield - 1853
...dcca a X t, — = — , >•*• c : a :: -d : b. ba Cor. 1. Hence, if four numbers are proportional, **the second is to the first as the fourth to the third.** For if a : b :: c : d, a X rf= b X c ; .-. from the Prop, b : a : : d : c. Cor. 2. Also, in the same... | |
| Euclides - 1853 - 147 Seiten
...5th 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 5. XV. Componenda, by composition ; when there are four proportionals, and it is inferred... | |
| Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - 1853
...5th 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... | |
| William Somerville Orr - 1854
...•=. Í . 3. If four quantities are proportional they are proportional when taken inversely, that is, **the second is to the first as the fourth to the third** : thus, ifa:6::c:d, then Ь : a ; : 4 : e ; because from ,- = -j we get, by taking the reciprocals,... | |
| John Radford Young - 1855
...2. If four quantities are in proportion, they are also in proportion when taken inversely; that is, **the second is to the first as the fourth to the third. Let a '. b '.: c '. d,** that is, T=- : then, since the reciprocals of two oa equal quantities must be equal, -=- .'. b : a... | |
| Euclides - 1855
...this book. 15. 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.** Proposition B, book 5. 16. Componendo, by composition ; when there are four proportionals, and it is... | |
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