 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
 | Euclides - 1834 - 518 pages
...multiple, &c. QED C1 H E II C LF EUCLID S ELEMENTS. PROPOSITION III. • 2. 5. H 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 - 1835 - 540 pages
...o/F.' Book V. PROP. III. THEOR. If the first of four magnitudes be the same multiple of the second, as the third is of the fourth ; and if of the first and third there be taken equimultiples, these will also be equimultiples, the one of the second, and the other of the fourth. Let A the first, be... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...; the whole of the first magnitudes is the same multiple of C, that the whole of the last is of F. IF the first be the same multiple of the second, which...fourth ; and if of the first and third there be taken like multiples, these will be like multiples of the second and fourth, each of each. Let A tin. first... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...of ' C, that the whole of the last, viz. DL, is 'ofF.' B— G D E— K— HC F F 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... | |
 | Euclides - Geometry - 1841 - 378 pages
...AH, is the same multiple of C, that the whole of the last, viz. DL, is of F. cl PROP. III. THEOR. r! 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 - 1845 - 218 pages
...the same multiple of C, that the whole of the last, viz. DL, is of F.' PROPOSITION III. THEOB. — 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, James Thomson - Geometry - 1845 - 382 pages
...first magnitudes is the same multiple of C, that the whole of the last is of F. PROP. III. THEOR. — If the first be the same multiple of the second, which...fourth ; and if of the first and third there be taken like multiples, these will be like multiples of the second and fourth, each of each. Let A the first... | |
 | Euclides - 1845 - 546 pages
...of C, that the whole of the last, viz. DL, is of F. B-! EK HCLF PROPOSITION III. THEOREM. Ifihefirst be the same multiple of the second, which the third...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... | |
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...Bame multiple of C and F. F Wherefore, if the first, &c. QED Recite (a) def. 1, 2, A of b 5. 3 Th. If the first be the same multiple of the second which...third is of the fourth ; and if of the first and third equimultiples be taken, these shall be equimultiples, one of the second the other of the fourth. Let... | |
 | Euclides - 1846 - 292 pages
...IV. THBOR. If the first of four magnitudes has the same ratio to the second which the i ' ird has to the fourth, and if of the first and third there be taken any equimultiples whatever, and also any whatever of the second and fourth, then the multiple of the... | |
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