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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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...equilateral and equiangular quindecagon, and circumscribed about it. THE ELEMENTS OF EUCLID. BOOK V. DEFINITIONS. I. A LESS magnitude is said to be a part of a greater magni- Book V. tude, when the less measures the greater; that is, 'when vv"-'' ' the less is contained...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...circle, when the extremities of it are in the circumference of the circle. BOOK v. — 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,...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...circle, its opposite sides are together equal to half its perimeter. 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 sul/multiple of the greater. 2. A line, which is a measure of two or...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...mn 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,...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...magnitude is said to measure a greater, or to be a measure, a part, or a submulliple 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.* 3. Magnitudes which can be compared in...
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The Elements of Euclid

Euclid - Geometry - 1838 - 470 pages
...quindecagon, and circumscribed about it. • See Note, THE ELEMENTS OF EUCLID. BOOK V. DEFINITIONS. A LESS magnitude is said to be a part of a greater...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 Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...APPENDIX D. [95] BOOK V. DEFINITIONS. 1. A less magnitude is said to be a PART (that is, an aliquot part) of a greater magnitude, when the less measures...contained a certain number of times exactly in the greater ; and in this case the less is said to be a SUBMULTIPLE of the greater). 2. A greater magnitude is...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...l4+l. So also may regular polygons of 257 and 65537 sides. M 2 126 THE ELEMENTS OF EUCLID. BOOK V. DEFINITIONS. * I. A LESS magnitude is said to be 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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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Ratio and proportion - 1841 - 140 pages
...November, 1840. BOOK V. DEFINITIONS. I. A LESS magnitude is said to be an aliquot part or submultiple of a greater magnitude, when the less measures the...a certain number of times exactly in the greater. Thus, if be contained in S nnnnn three times ехас11y> the former is said to be a submultiple...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 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 o a less, when the greater is measured by the less,...
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