 | 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... | |
 | 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 form one of... | |
 | 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 form one of... | |
 | 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 : d. By Art.... | |
 | 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 of ratio... | |
 | 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... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...i=^f+*) j c+d by a+b _L=J_ a+b c+d' This gives, <z+Z> : 6 : : c+d : d. ART. 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 second, as the difference... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...generally termed equality of ratios. It is almost self-evident. ART. JJ5O. — 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 offfie third... | |
 | 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.... | |
 | 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... | |
| |
If four quantities are in proportion, they will be in proportion by COMPOSITION... 
