 If the first be the same multiple of the second which the third is of the fourth, and if of the first and third there be taken equimultiples, these shall be equimultiples, the one of the second, and the other of the fourth.  Manual of Euclid: Books IV, V, VI. - Page 38by Euclid - 1868Full view - About this book
 | Robert Simson - Trigonometry - 1806 - 546 pages
...same multiple of C, i that the whole of the last, viz. DL, is •ofF,' HCLF J D E-1K PROP. III. THEOR. IF the first be the same multiple of the second, which...first and third there be taken equimultiples, these shall be equimultiples, the one of the second, and the other of the fourth. < Let A the first, be the... | |
 | Euclid - Geometry - 1810 - 554 pages
...H D B— l' __ HCLF BookV. PROP. III. THEOR. IF the first be the same multiple of the second, whie" the third is of the fourth; and if of the first and third there be taken equimultiples, these shall be equimultiples, the one of the second, and the other of the fourth. Let A the first, be the... | |
 | John Mason Good - 1813 - 714 pages
...same multiple of the second, that the third together with the sixth is of the fourth. Prop. HI. Theor. If the first be the same multiple of the second, which the third is of the foartli; and if of the first and third there be taken equimultiples, these shall be equimultiples,... | |
 | Euclides - 1814 - 560 pages
...viz. DL, is of F.' HCLF CoR. ' From this it is plain, that, if any i/-. OF EUCLID. PROP. III. THEOR. If the first be the same multiple of the second, which the third is of the fourth ; and if of the tirst and third there be taken equimultiples, these shall be equimultiples, the one of the second,... | |
 | Euclides - 1816 - 588 pages
...the same multiple of C, that ' the whole of the last, viz, DL, is of F.' HCL d H PROP. III. THEOR. IF the first be the same multiple of the second, which...first and third there be taken equimultiples, these shall be equimultiples, the one of the second, and the other of the fourth. Let A the first, be the... | |
 | John Mason Good - 1819 - 800 pages
...with the sixth i- o[ the fourth. Piup. III. Theor. Il the fir«! be the »ame multiple of the «-cum!, which the third is of the fourth ; and if of the first and third l'iere he t.iken equimultiples, these shall be equimultiple«, the one of the second, and the other... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...multiple of C, that the ' whole of the last, viz. DL, is of F.' H Li PROP. III. THEOR. ' . x * * IP the first be the same multiple of the second, which...first and third there be taken equimultiples, these shall be equimultiples, the one of the second, and the other qf the fourth. Let A the first, be the... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...which GH the third, together with the sixth, is of the fourth D. If, therefore, the first, *c. &c. QED Let A the first, be the same multiple of В the second, that С the third U of D the fourth; and of A, C let the equimultiples EF, GH be taken : Then EF is the same multiple... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...multiple of C, that the whole of the last, viz. DL, is of F. B G E K I HCLF PROP. III. THEOR. If the Jirst be the same multiple of the second, "which the third is of the fourth; and if of the Jirst and third there be taken equimultiples ; these shall be equimultiples, the one of the second,... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...multiple of C, that the whole of the last, viz. DL, isofF.' H c LF PROPOSITION III. THEOREM. (476) If the first be the same multiple of the second, which...first and third there be taken equimultiples ; these shall be equimultiples, the one of the second, and the other of the fourth. EABGGI) Let A the first... | |
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