 | Trinity College (Hartford, Conn.) - 1870 - 1008 σελίδες
...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 - 1872 - 382 σελίδες
...same kind. Let unity be added to both members of [1] ; then or, reducing, A + B = A' + B' \ B B' ' and dividing this by [1], A + B A' + B' A ~ A' ' [2]...members of [1], we should have found A — B A' — B' results which are briefly expressed by the theorem, if four quantities are in proportion, they are... | |
 | William Chauvenet - 1872 - 382 σελίδες
...unity from both members of [1], we should have found A — B A' — B' B A — B A B' A' — B' [3] results which are briefly expressed by the theorem,...quantities are in proportion, they are in proportion by division ; where the term division is employed to express the subtraction of consequent from antecedent... | |
 | Harvard University - 1874 - 668 σελίδες
...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 Chauvenet - 1875 - 466 σελίδες
...unity from both members of [1], we should have found A — B A' — B' B A — B B' A' — B' A' [3] results which are briefly expressed by the theorem, if four quantities are in proportion,they are in proportion by division; where the term division is employed to express the subtraction... | |
 | William Guy Peck - 1876 - 376 σελίδες
...inversion, a + b : a :: c + d : c, and a + b : b :: c + d : d, which was to be proved. PROPOSITION VI. THEOREM. If four quantities are in proportion, they are in proportion by division. Assume the proportion, a : b :: c : d, whence - = -, ... (1) subtracting each member of the... | |
 | William Chauvenet - 1877 - 396 σελίδες
...added to both members of [1] ; then •"• I -td*. .4 or, reducing, _ _1_ 1 B + B' A + B B A' + B' B' and dividing this by [1], A + BA + B' A A' [2]...members of [1], we should have found A — B A' — B' B A—B A B' A' — B' A' [3] results which are briefly expressed by the theorem, if four quantities... | |
 | William Henry Harrison Phillips - 1878 - 236 σελίδες
...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 —... | |
 | William Chauvenet - 1879 - 380 σελίδες
...of [1]; then or, reducing, A + B ^A' + B' \ B B' and dividing this by [1], [2] A + BA ' + B' A ~ A' results which are briefly expressed by the theorem,...members of [1], we should have found A — B A' — B' B B'. A — B A' — B' A A' [3] results which are briefly expressed by the theorem, if four quantities... | |
 | Henry Kiddle, Alexander Jacob Schem - 1881 - 378 σελίδες
...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... | |
| |
If four quantities are in proportion, they are in proportion by composition, ie 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. 
