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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. 9. The whole is greater than its part. 10. Two straight lines cannot enclose... "
Elements of Geometry: With Practical Applications, for the Use of Schools - Page xiv
by Timothy Walker - 1829 - 129 pages
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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...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 the two interior...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873 - 182 pages
...: — 8. Magnitudes which coincide, or which exactly fill the same space, are equal to each other. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to each other.) Further Explanation of Terms, &c. The...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. THINGS which are equal to the same thing are equal...cannot inclose a space. 11. All right angles are equal to one another. • If a straight line meets two straight lines, so as to make the two interior angles...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874 - 120 pages
...line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. Things which are equal to the same thing are equal...greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. Two straight lines which cut one...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...distance from that centre. Axioms. 1. Things which are equal to the same thing are equal to one another. 3. If equals be taken from equals the remainders are...cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight lines, so as to make the two interior angles...
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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...cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight lines, so as to make the two interior angles...
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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...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 the two interior...
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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...cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight lines, so as to make the two interior angles...
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