| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...other lines is constant, wherever in the circumference the point be taken. BOOK V. DEFINITIONS. 1. **A LESS magnitude is said to be a part of a greater...a 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 - 1855 - 230 pages
...geometrically in a circle, when 2" + 1 is a prime number. THE ELEMENTS OF EUCLID. BOOK V. DEFINITIONS. 1. **A LESS magnitude is said to be a part of a greater...a certain number of times exactly in the greater.** In the four preceding books magnitudes have been compared simply as to their equality or inequality,... | |
| Euclides - 1855 - 262 pages
...or one of those parts, which is the side of the quindecagon required. BOOK V. DEFINITIONS. 1. A 1E8S **magnitude is said to be a part of a greater magnitude,...a certain number of times exactly in the greater.** The term part is here evidently understood in a restricted sense, andoae which Ħa commonly expressed... | |
| John Playfair - Euclid's Elements - 1856 - 346 pages
...is the product of m into n ; and mnA is A mul" tiplied by the product of m into n. DEFINITIONS. IA **less magnitude is said to be a part of a greater magnitude,...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,... | |
| Eucleides - 1860 - 396 pages
...geometrically ma circle, when 2" + 1 is a prime number. TIIE ELEMENTS OF EUCLID. BOOK V. DEFINITIONS. 1. **A LESS magnitude is said to be a part of a greater...a certain number of times exactly in the greater.** SCHOLIUM. In ordinary use the word " part " means " any portion whatever," but its geometrical sense... | |
| Euclides - 1860 - 288 pages
...squares on the sides of a hexagon and decagon, inscribed in the same circle. FIFTH BOOK. DEFINITIONS. 1. **A less magnitude is said to be a, part of a greater...a certain number of times exactly in the greater.** It is also called a measure, or submultiple of the greater. 2. A line, which is a measure of two or... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...the equilateral polygon has the greatest area. DEFINITIONS. I. A LESS magnitude is said to be apart **of a greater magnitude, when the less measures the...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,... | |
| Euclides - 1861 - 464 pages
...— variations are given in the notes, and if between brackets, or " " they are from the Greek text **of Euclid. DEFINITIONS. I. — A less magnitude is...a certain number of times exactly in the greater.** "A part is a magnitude of a magnitude,— the less of the greater, when it exactly measures the greater."... | |
| Euclides - 1863 - 122 pages
...pentagon, a circle may be inscribed in a given regular quindecagon, and circumscribed about it. BOOK V. **DEFINITIONS. I. A LESS magnitude is said to be a part of a greater magnitude, when the** lees measures the greater; that is, when the less is contained a certain number of times exactly iu... | |
| Euclides - 1864 - 448 pages
...equilateral polygon has the greatest area. BOOK V. DEFINITIONS. I. A LESS magnitude is said to he apart **of a greater magnitude, when the less measures the...a certain number of times exactly in the greater.'** II. A greater magnitude is said to he a multiple of a less, when the greater is measured by the less,... | |
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