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" Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another. "
Elements of geometry, based on Euclid, books i-iii - Page 9
by Edward Atkins - 1876 - 119 pages
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 pages
...equals he taken, the remainders are unequal. 6. Things which are douhle of the same, or of equals, are equal to one another. 7. Things which are halves of the same, or of equals, are equal to one another. 8. Magnitudes which coincide with one another are equal to...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1873 - 238 pages
...be taken from unequals the remainders will be unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1874 - 207 pages
...be taken from unequals the remainders will be unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...unequals, the wholes are unequal, V. If equals be taken from unequals, the remainders are unequal. VL Things which are double of the same, are equal to one another. VIL Things which are halves of the same, are equal to one another. vm. Magnitudes which coincide with...
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877 - 58 pages
...equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is which exactly...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...from unequals, the remain ders are unequal. 6. Things which are doubles of the same, or of equals, are equal to one another. 7. Things which are halves of the same, or of equals, are equal to one another. 8. Magnitudes which coincide with one another, that is, which...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 pages
...equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...subtracted from unequals, the remainders are unequal. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another are equal to one another. 9. The whole is greater than its part. 10. All right angles are equal to...
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Scientific and practical geometry for self-instruction

Rolla Rouse - 1879 - 402 pages
...If equals be taken from unequals, the remainders are unequal (B — A unequal to D — C). Axiom 6. Things which are double of the same are equal to one another (A — 2B . C = 2B .-. A = C). Axiom 7. Things which are halves of the same are equal to one another...
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First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880 - 152 pages
...one another. 6a. (Not given by Euclid, but assumed by him). Things which are doubles of equal things are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another are equal to one another....
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