 | Euclides - 1860 - 288 pages
...the third, together with the fourth, is to the fourth. 24. By addition, when the first is to the sum of the first and second, as the third is to the sum of the third and fourth. 25. By division, when the excess of the first above the second, is to the... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...magnitudes be in proportion, they must be in proportion by COMPOSITION or DIVISION; that is, thefirstis to the sum or difference of the first and second,...to the sum or difference of the third and fourth. If a : Ъ = с : d, we are to prove that a : a±l = с : o±d. By formula U), - = -; (1) а с whence,... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...If four magnitudes be in proportion, they must be in proportion by COMPOSITION or DIVISION; that ù, the first is to the sum or difference of the first and second, as the third ù to the turn or difference of the third and fourth. If a : b = с : d, we are to prove that a : a±b... | |
 | Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...proportion, they must be in proportion by COMPOSITION or DIVISION ; that is, the first is to the sum of the first and second, as the third is to the sum of the third and fourth ; or, the first is to the difference between the first and second, as the third... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...proportional, etc. THEOREM VIII. If four magnitudes constitute a proportion, the first will be to the sum of the first and second as the third is to the sum of the third and fourth. By hypothesis, A : B : : C : D ; then we are to prove that A : A + B ; : C... | |
 | Euclid - Geometry - 1872 - 284 pages
...— A to B as C to D, becomes A — B to B as C — D to D. 18. By Conversion, when it is inferred, that if there be four magnitudes proportional, the...to the sum or difference of the third and fourth. See Props. 21 and 25, also Cor. 1, Prop. 25. Thus — A is to B as C is to D, becomes A to (A + B)... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...If four magnitudes le inproportion, they must le in proportion by COMPOSITION or DIVISION ; that is, the first is to the sum or difference -of the first and second, as the third ù to the sum or difference of the third and fourth. If a : Ъ = с : d, we aro to prove that a : а±Ъ... | |
 | Horatio Nelson Robinson - Algebra - 1874 - 340 pages
...proportion, they must be in proportion by COMPOSITION or DIVISION ; that is, the first is to the sum of the first and second, as the third is to the sum of the third and fourth ; or, the first is to the difference between the first and second, as the third... | |
 | Charles Scott Venable - 1881 - 380 pages
...or, by inversion, a : a + b = c : c + d a : a — b = c : c — d. That is, the first is to the sum of the first and second, as the third is to the sum of the third and fourth. Again, the first is to its excess above the second, as the third is to its... | |
 | International Correspondence Schools - 1914 - 880 pages
...stresses being 15,000 pounds per square *If four quantities are in proportion, the first is to the sum of the first and second as the third is to the sum of the third and fourth. Thus, in the proportion 3 : 5 = 7 : *, 3 :(3 + 5)=7 : (7+*.) From either proportion,... | |
| |
Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth. 
