| Euclides - 1842 - 320 pages
...less magnitude, or number, is said to be a part, or a submultiple, of a greater magnitude, or number, **when the less measures the greater, that is when the less is contained** in the greater a certain number of times exactly. IV. Equimultiples of magnitudes are such as contain... | |
| Euclides - 1845 - 546 pages
...circle by means of straight lines and circles, in those cases in which 2" + 1 is a prime number. BOOK V. **DEFINITIONS. I. A LESS magnitude is said to be a part...a certain number of times exactly in the greater.'** II. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less,... | |
| Euclid - Geometry - 1845 - 218 pages
...be inscribed in a given equilateral and equiangular quindecagon, and circumscribed about it. BOOK V. **DEFINITIONS. I. A LESS magnitude is said to be a part...certain number of times ' exactly in the greater.'** A greater magnitude is said to be a multiple of a less, when the greater is measured by the less ;... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...magnitude is said to measure a greater, or to be a measure, a part, or a submuUiple of the greater, **when the less is contained a certain number of times, exactly, in the greater** : and 2. The greater is said to be a multiple of the less.f 3. Magnitudes which can be compared in... | |
| Euclides - 1846 - 292 pages
...A'B'C' equilateral triangles inscribed in them, shew that AP'2 + BP- + CP'2 = A'P2 + B'P2 + CT2. BOOK V. **DEFINITIONS. i. A LESS magnitude is said to be a part...a certain number of times exactly in the greater.** II. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less,... | |
| John Playfair - Euclid's Elements - 1846 - 334 pages
...is the product of m into n ; and mnA is A mul' tiplied by the product of m into n. DEFINITIONS. 1. **A less magnitude is said to be a part of a greater...certain number of times, exactly, in the greater.** 2. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less,... | |
| Dennis M'Curdy - Geometry - 1846 - 166 pages
...; (d) p. 1, 4 ; (c) def. 36, I, and Note ; def. 1, 2, 3, 4, 5, of b. 1. BOOK FIFTH. Definitions. 1. **A less magnitude is said to be a part of a greater** one, when the less is a measure of the greater, or is contained a certain number of times in it. 2.... | |
| Euclid - 1848 - 52 pages
...straight line from the centre, that is, to the semidiameter of the circle. PROP. XVI. PROBLEM. BOOK V. **DEFINITIONS. I. A LESS magnitude is said to be a part...a certain number of times exactly in the greater.'** II. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less,... | |
| John Playfair - Euclid's Elements - 1849 - 332 pages
...is A mul" tiplied by the product of m into n. DEFINITIONS. 1. A less magnitude is said to be apart **of a greater magnitude, when the less measures the...certain number of times, exactly, in the greater.** 2. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less,... | |
| Euclides - 1853 - 176 pages
...square be inscribed in a circle, it shall be double the square of the radius of the circle. BOOK V. **DEFINITIONS. I. A LESS magnitude is said to be a part...a certain number of times exactly in the greater.** II. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less... | |
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