...alternately A : C :: B : D. PROP. IX. THEOR. The terms of an analogy are proportional by composition; or the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. Let A : B :: C : D; then by composition A+B : B :: C +D: D. Because A : B :: C: D, the...

...first above the second is to the first, as the excess of the third above the fourth to the fourth. 70. If four quantities be proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth to their difference. Let a : b :: c : d, then...

...ALTEUccd NDO, or PERMUTANDO. Euclid 1G, 5. 65. Jf four quantities be proportionals, the sum of the first d second is to the second, as the sum of the- third and fourth the fourth. Let a : b : : c : d, then will a+b :b:: c+d: d. Because — = b -, kt unity be added to...

...the third. Prop. 20. 16. By composition, when we infer that if there be four magnitudes proportional, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. Cor. Prop. 21. 17- By division, when we infer that if there be four magnitudes proportional,...

...and a±t : k ; : eid •. d. a ^ Hence, when four quantities are proportionals, the sum or difference of the first and second is to the second as the sum or difference of the third and fourth, is to the fourth. 479. In like manner, if a : b : : c : d ;...

...still be a true one. _ а с ас a^-bc^-d For T=-d-'- b^=^1' or —=Т' Or, a*rb : b : : c~rd : d. 64. If four quantities be proportionals, the sum of the first and second is to their difterence,.as the sum of the third and fourth is to their difference. * The terms are similarly...

...the third. Prop. 20. 16. By composition; when we infer that if there be four magnitudes proportional, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. Cor. prop. 21. 17. By division ; when we infer that if there be four magnitudes proportional,...

...the second, as the excess of the third above the fourth is to the fourth : and, (2.) by composition, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. If A : B : : C : D ; then, by division, A — B:B::C_D:D; and by composition, A + B...

...alternation, when the first is to the third as the second to the fourth ; (329.) By composition, when the sum of the first and second is to the second, as the sum of the third and fourth to the fourth ; (330.) By addition, when the first is to the sum of the first and second, as the third...

...&c. PROP. X. THEOR. (V. l8 and l7). — If four numbers be proportionals ; then, (l) by composition, the sum of the first and second is to the second, as the sum of the third and fourth to the fourth : and, (2) by division, the excess of the first above the second is to the second, as...