 If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.  A Text-book of Geometry - Σελίδα 130των George Albert Wentworth - 1888 - 386 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Adrien Marie Legendre - 1837 - 376 σελίδες
...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 - 1839 - 372 σελίδες
...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 - 1842 - 370 σελίδες
...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 - 1848 - 250 σελίδες
...: 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 - 1848 - 234 σελίδες
...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 - 1850 - 218 σελίδες
...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 - 1850 - 256 σελίδες
...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 - 1848 - 250 σελίδες
...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 - 1852 - 408 σελίδες
...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 - 1855 - 628 σελίδες
...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 of rinding... | |
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