 | Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 190 pages
...then the greatest and least of them together are greater than the sum of the other two. ENUNCIATION 2. If A, B, C, D are four magnitudes of the same kind, and if [A,B]^[C,D], then the sum of the greatest and least is greater than the sum of the other two. Suppose... | |
 | Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 165 pages
...[J3, sC], prove that sA=r£. Art. 83. PROPOSITION XXIL* (Euc. V. 16.) ENUNCIATION 1. If A, B, C, D be four magnitudes of the same kind, and if A : B = C: D, to prove that A : 0= B : D. ENUNCIATION 2. If A, B, C, D be four magnitudes of the same kind, and if... | |
 | Mathematics - 1913 - 692 pages
...: В = С : D. Prop. XXII. If A : C= X : Z, and if В : 0= Y : Z, then A +B:C=X+ Y :Z. Prop. XXIII. If A , B, C, D are four magnitudes of the same kind, it' A : В =• С : D, and if A be the greatest of the four magnitudes, then A + D> B + C. ART. 14.... | |
 | Cambridge Philosophical Society - Mathematics - 1927 - 1078 pages
...ratio and are not straightforward applications of the Fifth Definition. It is required to prove that if A, B, C, D are four magnitudes of the same kind, and if (A:B) = (C:D\ and if A > C, then (AC:BD) = (A :B). Using the simplified form of the Fifth Definition,... | |
 | Cambridge Philosophical Society - Mathematics - 1927 - 1058 pages
...ratio and are not straightforward applications of the Fifth Definition. It is required to prove that if A, B, C, D are four magnitudes of the same kind, and if (A :B) = (C: D), and if A > C, then (AC:BD) = (A :B). Using the simplified form of the Fifth Definition, it is enough... | |
 | Cambridge Philosophical Society - Philosophy - 1898 - 366 pages
...[C,A]-[C,B], then [A, O]-[B, C] (Prop. 3), .-. A=B (Prop. 5 (i)). PROPOSITION 6. (Euc. v. 16.) Art. 25. If A, B, C, D are four magnitudes of the same kind, and if [A, B]-[C, D], to prove that [A, C] - [B, D]. Take any multiples of A and C, say rA and sC. Then there... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1871 - 902 pages
...what circumstances a ratio is made greater or made less by adding the same quantity to both its terms. If a, b, c, d are four magnitudes of the same kind, prove that the ratio a + c : b + d is intermediate in magnitude to the two ratios a : b and c : d.... | |
 | Euclid - Euclid's Elements - 1908 - 196 pages
...A:rC=B:sC, prove that sA = rB. Art. 69. PROPOSITION XXIV. (Euc. V. 16.)* ENUNCIATION. If A, B, C, D be four magnitudes of the same kind, and if A : B = C: D, to prove that A : C = B : D. g Compare the ratio A : C with any rational fraction - . By Art. 48 it... | |
| |
It is required to prove that if A, B, C, D are four magnitudes of the same kind, and if (A :B) = (C: D), and if A > C, then (AC:BD) = (A :B). 