...student. Л с The old mathematical term for this change is " composition." •* \** 338. Theorem. If a : b = с : d, then a - b : b = с — d : d. \ • >" The proof is left for the student. pS- , v-^V-x1 f' . ¿i 339. Theorem. If a : b = с : d,...

...PRINCIPLE 7. — If four numbers are in proportion, the. difference between the terms of the first ratio is to either term of the first ratio as the...proportion by Division. If a : b = с : d, then, a — b : Ь = с — d :d and a — 6 : a = с — d :c. Demonstrate Prin. 7, and give numerical illustrations....

...proportion, the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding...ratio ; that is, the numbers are in proportion by Composition. И а : b = с : d, then, a + b:b = c + d:d and a + b : a = с + d: c. Demonstrate Prin....

...proof is left for the student. The old mathematical term for this change is "inversion." 323. Theorem. If a : b = с : d, then a + b : b = с + d : d. The proof is left for the student. The old mathematical term for this change is " composition." 324....

...proportion, the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding...ratio ; that is, the numbers are in proportion by composition. For, given a:b = c:d, or а=«. bd Then, E+l=£+l, bd bd that is, a + b : b = с + d :...

...of the terms of the first ratio is to either term of the first ratio as the sum of the terms of tJie second ratio is to the corresponding term of the second ratio; that is, the numbers are in proportion by composition. For, given u:b = c:d, !=!• h (I Then, 2 + 1 = £ + 1, в а or bd that is, a + l> :...

...398. PRINCIPLE 7. — If four numbers are in proportion, the difference between the terms of the first ratio is to either term of the first ratio as the...that is, the numbers are in proportion by division. For, in the proof of Prin. 6, if 1 is subtracted instead of added, the following proportions are obtained...

...proportion, the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding...ratio ; that is, the numbers are in proportion by composition. For, given a : b - с : d, or a = «. bd Then, Ax. 1, a + i=2 + i, о а or а + b_с...

...taken by composition. „. а с Given - = -• 6 d Adding 1, £ + 1 = 5 + 1, о a a+6_c+d Т ~d~' 6. If a : b = с : d, then a — b :b = с — d: d. In this case the first proportion is said to be taken by diuision. Given l = c-. bd fit c Subtracting...

...PBINCIPLE 7. • — If four numbers are in proportion, the difference between the terms of the first ratio is to either term of the first ratio as the...second ratio; that is, the numbers are in proportion by división. For, in the proof of Prin. 6, if 1 is subtracted instead of added, the following proportions...