| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...couplets may be made the consequents of the first, by alternation (P. III.). PROPOSITION V. THEOREM. **If four quantities are in proportion, they will be in proportion by** inversion. Assume the proportion, 7? D A : B : : C : D ; whence, -j- == -^ • .4 0 If we take the... | |
| Paul Allen Towne - Algebra - 1865 - 314 pages
...qua.nti.ties, the first two may be made the extremes, and the second two the means, of a proportion. PROP. II. **If four quantities are in proportion, they will be in proportion by** alternation. For, since a : b : : c : d, we have ad = be. (2) (Prop. 1.) Dividing both members of (2)... | |
| Joseph Ray - Algebra - 1866 - 420 pages
...: f. If 4 : 8 : : 10 : 20 and 4 : 8 : : 6 : 12; then, 10 : 20 : : 6 : 12. 273. Proposition VII. — **If four quantities are in proportion, they will be in proportion by COMPOSITION** ; that is, the sum of the first and second will be to the first or second, as the sum of the third... | |
| Joseph Ray - Algebra - 1866 - 250 pages
...4: 10 8 5 10: 4 8 8 4: 10 5 8: 10: 4 6 4 5: 8 10 4 8: 5 10 10 5: 8 4 10 85 4 248. Proposition V. — **If four 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 :... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...sades by T, — 5- = ,— , or — =-=-. o ao be ab That is, a : c : : b : d. 348. Proposition V. — **If four 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 :... | |
| Joseph Ray - Algebra - 1852 - 422 pages
...proposition is true, only when tho four quantities are of the tame kind ART. 271. PROPOSITION V. — **If four 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... | |
| William Frothingham Bradbury - Algebra - 1868 - 264 pages
...ac l = d Adding 1 to each member, j -f- 1 = e- -\- '. ie a -\- b : b = c -\- d : d THEOREM VII. 208. **If four quantities are in proportion, they will be in proportion by** division. Let a : b — c : d M Subtracting 1 from each member, ? — 1 = - — 1 or a~ b = ° ~d b... | |
| Edward Brooks - Geometry - 1868 - 284 pages
...between A and C; then we have, A : B :: B : C; whence (Th. I.), - S * = A X C, or, B = THEOREM IV. **If four quantities are in proportion, they will be in proportion by** alternation. Suppose A:B::C:D; from thia (Th. I.) we have, A X .D = B X C; dividing by D X C, we have,... | |
| Joseph Ray - Algebra - 1866 - 420 pages
...: 27 : 18. In a similar manner it may be shown that a+6 : a : : c+d : c. 274. Proposition VIII. — **-If four quantities are in proportion, they will be in proportion by** DIVISION ; that is, the difference of the first and second will be to the first or second, as the difference... | |
| Charles Davies - Geometry - 1872 - 464 pages
...have, AC M JJ ^f — ^ \ whence, JB : A : : D : C: which was to be proved. PROPOSITION VI. THEOREM. **If four quantities are in proportion, they will be in. proportion by composition** or division. Assume the proportion, A : B : : C : D ; whence, -j- = 7T • 7? 7) s*. \j If we add 1... | |
| |