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. Solid Geometry - Page 254by John H. Williams, Kenneth P. Williams - 1916 - 162 pagesFull view - About this book
| Trinity College (Hartford, Conn.) - 1870 - 1010 pages
...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
...antecedent into parts. The quotient of [2] divided by [3] is A + B A — B A' + B' A' — B''' that is, **if four quantities are in proportion, they are in proportion by composition** and division. 11. Definition. A continued proportion is a series of equal ratios, as A : B = A' : B'... | |
| William Chauvenet - Geometry - 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... | |
| William Guy Peck - Conic sections - 1876 - 394 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... | |
| Wm. H. H. 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 —... | |
| Webster Wells - Algebra - 1879 - 468 pages
...: d then, ad = b с Whence, b : a = d : c. 347. If four quantities are in proportion, they will be **in proportion by COMPOSITION ; that is, the sum of the first two terms** will be to the first term, as the sum of the last two terms is to the third term. Thus, if a : b =... | |
| Alexander Jacob Schem - Education - 1881 - 374 pages
...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... | |
| Webster Wells - Algebra - 1885 - 382 pages
...the third. Let a : b = с : d. Then, ad = be. Whence, b : a = d : c. 299. In any proportion the terms **are in proportion by Composition ; that is, the sum of the first two terms is to the** first term, as the sum of the last two terms is to the third ter.n. Let a : & = с : d. Then, ad =... | |
| |