| Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...will be in the ratio of 4 to 3; and if 8 be subtracted from each they will be in the ratio of 0 to 4. Prove that if four quantities are in proportion, they are in proportion by composition. 8. Find three numbers in geometrical progression such that their sum shall be 42, and the sum of the... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...dividing this by [1], A + B B' A' + B' A' '' [2] results which are briefly expressed by the theorem, if four quantities are in proportion, they are in proportion by composition; the term composition being employed to express the addition of antecedent and consequent in each ratio.... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...dividing this by [1], A + B A' + B' A ~ A' ' [2] results which are briefly expressed by the theorem, if four quantities are in proportion, they are in proportion by composition ; the term composition being employed to express the addition of antecedent and consequent in each... | |
| Harvard University - 1874 - 668 pages
...If two parallel lines are cut by a third straight line, the alternate interior angles are equal. 8. If four quantities are in proportion, they are in proportion by composition and division. 4. An inscribed angle is measured by one-half its intercepted arc. 5. A parallel to the base... | |
| William Guy Peck - Conic sections - 1876 - 412 pages
...alternation, a : b : : c : d, and a : b :: e : f, and consequently, c : d : : e : f. PROPOSITION V. THEOREM. If four quantities are in proportion, they are in proportion by composition. Assume the proportion, a : b : : c : d, whence - = - ; . . . (1) adding each member of the preceding... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...dividing this by the given equation, we have, ^JT- = - ~tD, or, A + B : A = C + D : C. .A. \_> Hence, if four quantities are in proportion, they are in proportion by composition. 9. Subtracting unity from both members of — = T~, we obtain, in like manner, AB CD BD , or, A —... | |
| Henry Kiddle, Alexander Jacob Schem - Education - 1881 - 378 pages
...transformation does not vitiate the proportion, is not brought to light at all. For example, suppose we are to prove that, If four quantities are in proportion, they are in proportion by composition, ie, if a : b : : a : d, then a : a-\-b : : a : c-{-d. The common method is to pass from the given proportion... | |
| Franklin Ibach - Geometry - 1882 - 208 pages
...d : c. Take the form — = — • о а Divide 1 by each member. Then 1-1, а с THEOREM VII. 162. If four quantities are in proportion, they are in proportion by composition. Let a : b :: с : d. To prove that a .\- b : b : : с -fd : d. Take the form .7- = -=-• о а To... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...have, AC -FT = -rr ; whence, B : A : : D : C ; b U which was to be proved. PROPOSITION VI. THEOREM. If four quantities are in proportion, they are in proportion by composition or division. Assume the proportion, RD A : B : : C : D ; whence, -v- = -.-' If we add 1 to each member,... | |
| Algebra - 1888 - 492 pages
...— - = 1 , a с a — b с — d or = — a с That is, a — b : a : : с — d : c. 373. IX. // four quantities are in proportion, they are in proportion by composition and division. Thus, if a : b : : с : d, then a + b : a — b : : с + d : c — d. a + b с + d By Prin.... | |
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