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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 - Geometry - 1876 - 446 pages
...this manner we form our idea of equality, •which is thus formally stated in the eighth axiom : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." Every specific definition is referred to this universal principle. With regard to a few more general...
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877 - 72 pages
...unequals the wholes are unequal. 5. If equals be taken from unequals 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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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877 - 58 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 cannot inclose a space. 11. All right angles are equal to one another. 1 2. If a straight...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...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...equal to one another. 9. The whole is greater than any of its parts. 10. The whole is equal to the sum of all its 'parts. * When this axiom is applied...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879 - 426 pages
...are double of the same thing are equal to one another. (7) Things that 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 cannot enclose a space, (n) All right angles are equal to one another. (12) If a straight...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 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 cannot enclose a space. 1t. All right angles are equal to one another. 12. If a straight...
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Scientific and practical geometry for self-instruction

Rolla Rouse - 1879 - 402 pages
...7. Things which are halves of the same are equal to one another (A = JB . C = £B .-. A = C). Axiom 8. Magnitudes which coincide with one another, that...exactly fill the same space, are equal to one another. (For example, squares with 1-inch sides.) Axiom 9. The whole is greater than its parts. (A > f A, Ac.)...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...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 one another. 11. Two straight lines which intersect each other cannot...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 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 cannot enclose a space. 11. All right angles are equal to one another. eJtV 12. If a...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1880 - 452 pages
...are halves of the same, or of equals, are equal to one another. 8. Magnitudes which coincide Avith one another, that is, which exactly fill the same...equal to one another. 9. The whole is greater than any of its parts. 10. The whole is equal to the sum of all its parts. 11. From one point to another...
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