| Adrien Marie Legendre - Geometry - 1837 - 376 pages
...quantities N, M, Q, P, and thes« products being equal, N:M::Q:P(Prop.II.). PROPOSITION VI. THEOREM. ff **four quantities are in proportion, they will be in proportion by composition,** or division. D Let, as before, M, N, P, Q, be the numerical representatives of the four quantities,... | |
| Adrien Marie Legendre - Geometry - 1839 - 372 pages
...quantities N, M, Q, P, and these products being equal, N : M : : Q : P (Prop. II.). PROPO8ITION VI. THEOREM. **If four quantities are in proportion, they will be in proportion by composition,** or division. Let, as before, M, N, P, Q, be the numerical representatives of the four quantities, so... | |
| George Roberts Perkins - Algebra - 1842 - 370 pages
...inverting both terms c c< — =~Taa Therefore, by Art. 170, c : a : : c' : a'. (10) Which shows, that **if four quantities are in proportion they will be in proportion by** inversion. (173.) Quantities are in proportion by alternation, or alternately, when the antecedents... | |
| Joseph Ray - Algebra - 1848 - 250 pages
...: c : : b : d. Illustration. 2 : 7 : : 6 : 21, and 2 : 6 : : 7 : 21. ART. 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 :... | |
| George Roberts Perkins - Algebra - 1848 - 234 pages
...c~c" we have by inverting both terms Therefore, by Art. 137, с : a : : c' : a'. Which shows, that **if four quantities are in proportion, they will be in proportion by** inversion. (139.) Quantities are in proportion by alternation, or alternately, when the antecedents... | |
| Charles Davies - Geometry - 1850 - 218 pages
...27a : : 16+48 : 48, that is, 36 : 27 : : 64 : 48, in which the ratio is three fourths. THEOREM VIII. **If four quantities are in proportion, they will be in proportion by** division. Let us suppose that we have A : B : : C : D; we shall then have AxD=BxC. From each of these... | |
| Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...two quantities is found by *'1' extracting the square root of their product. ui! l*5' PROPOSITION IV. **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. Then, by the definition... | |
| Joseph Ray - Algebra - 1848 - 250 pages
...the first, as the sum of the third and fourth is to the third. ART. 251. — 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 second, as the difference... | |
| Joseph Ray - Algebra - 1852 - 408 pages
...divide both sides by b, £ =A ab That is (Art. 263), a : c : : b : d. ART. 271. PROPOSITION V. — **If four quantities are in proportion, they will be in proportion by** INVERSION ; that is, the second Witt be to the first, as the fourth to the third. Let n : li : : c... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...sum or difference of the antecedent and consequent is compared with either antecedent or consequent. **If four quantities are in proportion, they will be in proportion by composition** ; that is. if a : b : : с : d, then a ±b : a : : с ±d : c. COMPOSITION or EQUATIONS. The operation... | |
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