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" A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater. "
The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ... - Page 25
by George Sturton Ward - 1862 - 79 pages
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

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...
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The Elements of Euclid, with many additional propositions, and explanatory ...

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,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

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...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

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,...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

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...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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,...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

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."...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

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...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

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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