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" AXIOMS. 1. Equimultiples of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes, of which the same or equal magnitudes are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same... "
The First Six Books of the Elements of Euclid: With Notes - Page 93
by Euclid - 1833 - 183 pages
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...BookV. Aiiomt. — I. Equimultiples of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes of which the same, or equal magnitudes, are equimultiples, are equal to one another. 4. That magnitude of which a multiple is greater than the same multiple uf...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...series as the first to the last in the other. Prop. 38. Axioms. See N. 1- Equi-multiples of the same or of equal magnitudes are equal-' 2. Those magnitudes...another, is greater than that other magnitude. PROP. I. THEOR. If there be given two equal magnitudes (BC and DE), as often as any third magnitude (A) is contained...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...page 167. AXIOMS. 1. " Equimultiples of the same, or of equal magnitudes, are equal to one another." 2. " Those magnitudes of which the same, or equal magnitudes, are equimultiples, are equal to one another." 3. " A multiple of a greater magnitude is greater than the same multiple...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...: : D r AXIOMS. 1. " Equimultiples of the same, or of equal magnitudes, are equal to one another." 2. " Those magnitudes of which the same, or equal magnitudes, are equimultiples, are equal to one another." 3. " A multiple of a greater magnitude is greater than the same multiple...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...(Eue. v. Ax. 1, 2, 3, 4.) 1. Equimultiples of the same or of equal magnitudes are equal to one another. 2. Those magnitudes of which the same, or equal magnitudes are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...of Book 5. AXIOMS. 1. EQUIMULTIPLES of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes of which the same, or equal magnitudes, are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...(Eue. v. Ax. l, 2, 3, 4.) J, Equimultiples of the same or of equal magnitudes are equal to one another. 2. Those magnitudes of which the same, or equal magnitudes are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...definition. AXIOMS. 1. Equimultiples of the same or of equal mag. nitudes, are equal to one another. 2. Those magnitudes of which the same or equal magnitudes, are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...and B by m. AXIOMS. 1. Equimultiples of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes of which the same, or equal magnitudes, are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...of Book 5. AXIOMS. 1. EQUIMULTIPLES of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes of which the same, or equal magnitudes, are equimultiples, are equal to one another. " 3. A multiple of a greater magnitude is greater than the same multiple...
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