 | Euclides - 1877 - 58 pages
...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...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space. 11. All right... | |
 | Euclides - 1879 - 146 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 1t. All right... | |
 | Rolla Rouse - 1879 - 400 pages
...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 is...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.)... | |
 | Moffatt and Paige - 1879 - 428 pages
...are equal to one another. (7) Things that are halves of the same thing are equal to one another. (8) Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. (9) The whole is greater than its part. (10) Two straight lines cannot enclose a space, (n) All right... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...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,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right... | |
 | 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 space, are 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.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...are equal to one another. 7. Things which are halves of the same tiling are equal to one another. 8. Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right... | |
 | 1884 - 434 pages
...is no difference between m and «, or between iA and -jB in the cases instanced. Axiom VIII. : — " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This cannot be regarded as a distinct axiom, but as an application of Axiom I. ; for things which fill... | |
 | Euclides - 1884 - 182 pages
...space. 11. All right angles are equal to one another. The 8th axiom is often expressed thus : — " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." But the explanatory clause in italics cannot apply to angles and straight lines, which do not Jill... | |
 | Euclides - 1884 - 214 pages
...Therefore if two triangles &c. Axiom 10., Two straight lines cannot enclose a space. Q. !':. D. Axiom 8. Magnitudes which coincide with one another, that is which exactly fill the same space, are equal to one-another. PROPOSITION V. THEOREM. The angles at the base of an isosceles triangle are equal to one... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
