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" Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. "
The Elements of Euclid [book 1] for beginners, by J. Lowres - Page 10
by Euclides - 1852
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...are equal to one another. VII. Things which are halves of the same, are equal to one another. VEIL Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot enclose a space. XI. All right...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 pages
...of the same, or of equals, 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. 1 0. Two right lines cannot enclose a space: 1 1 . All right angles are equal to one another. 12. If...
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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
...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...another. 9. The whole is greater than its part. 10. Two straight lines can not inclose a space. 12. If a straight line meet two straight lines, so as to make...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874 - 120 pages
...to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same are equal to...another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. Two straight...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal...another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space. 11. All right angles are equal to one another. • If a straight...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same are equal to...another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. C. Things which are double of the same are equal to one...another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight...
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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
...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...another. 9. The whole is greater than its part. 10. Two straight lines can not inclose a space. 12. If a straight line meet two straight lines, so as to make...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...which are halves of tho same, or of equals, are equal to one another. 8. Magnitudes which coincide, that is, which exactly fill the same space, are equal...another. 9. The whole is greater than its part. 10. The whole is equal to all its parts taken together. 11. All right angles are equal to one another....
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...unequals the wholes are unequal. 5. If equals be taken from uncquals the remainders are unequal. G. Things which are double of the same are equal to one...another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight...
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