 | 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 reciprocals... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...proportional to b and d, the consequents of the given proportion. PROPOSITION IV. — If/our quantities be in proportion, they will be in proportion by INVERSION; that is, the second will be to tJieJirstt as the fourth to the third. Let a ; b = c : d ; then by formula (A), — = —... | |
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...have ac ac . ac . , 7 ,,,. — = — ,. le 7- = -,. whence o : a : : d : c. (11) be ad bd PROP. IV. If four quantities are in proportion, they will be in proportion by composition or division. For, since ' a : b : : c : d, we have ad = be. (2) Add or subtract bd according... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...This proposition is true, only when the four quantities are of the same kind. 271. 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 : d. Then, (Art. 263), .... | = |;... | |
 | Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...b : y Or, xy : a = a + Ъ : 1 Or, a : x = у : (a + 6) PROPOSITION IV. З66. If fyir quantities be in proportion, they will be in proportion by INVERSION ; that is, the second will be to theßrst, as the fourth to the third. Let a : 6 = с : d Then by formula (A) - = - « аc... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...Illustration, 3 : 5 : : 6 : 10. 3 : 5 : : 9 : 15. And 6 : 10 : : 9 : 15. 250. 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 second, as the sum of the third... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...Illustration, 3 . 5 : : 6 : 10. 3 : 5 : : 9 : 15. And 6 ; 10 : : 9 : 15. 2530. 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 second, as the sum of the third... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...from the 2nd, -=-. acae Hence, -=l ; which gives c : d : : e :f. ce ART. 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 second, as the sum of the third... | |
 | 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,... | |
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If four quantities are in proportion, they will be in proportion by inversion; that is, the second term will be to the first as the fourth to the third. 
