 | Euclides - 1846 - 292 Seiten
...(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 - 250 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 - 52 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, hy composition ; when there are four proportionals, and it is inferred... | |
 | Joseph Ray - 1848 - 250 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... | |
 | Royal Military Academy, Woolwich - 1853 - 400 Seiten
...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... | |
 | Euclides - 1853 - 176 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... | |
 | William Frederick Greenfield - 1853 - 228 Seiten
...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... | |
 | William Somerville Orr - 1854 - 534 Seiten
...•=. 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 - 218 Seiten
...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 - 230 Seiten
...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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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. 
