 | Euclides - 1846 - 292 pages
...(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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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. Prop A. Book 5. 16. Componendo, by composition : When there are four proportionals, and it is inferred,... | |
 | Joseph Ray - Algebra - 1848 - 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. 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 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, hy composition ; when there are four proportionals, and it is inferred... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...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 - 228 pages
...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 - Geometry - 1853 - 176 pages
...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 - Mathematics - 1853 - 400 pages
...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 - Science - 1854 - 534 pages
...•=. 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 pages
...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... | |
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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. 
