 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...equal to one another. 8. Magnitudes which coincide with one another — that is, which fill exactly the same space — are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose space. 11. All right angles are equal to one another. 12. If a straight... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...are double of the same thing are equal to one another. 7. Things which are halves of the same tiling 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. 12. If a straight... | |
 | 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... | |
 | Mathematics - 1885 - 150 pages
...is no difference between in and «, or between JA 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 bo regarded as a distinct axiom, but as an application of Axiom I. ; for things which fill... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...unequals, the Remainders are unequai. 6. Things which are Double of the same are Equal to one another. '}. Things which are Halves 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... | |
 | Euclid - Geometry - 1892 - 460 pages
...things, are equal to one another. 7. Things which are halves of the same thing, or of equal things, are equal to one another. 9.* The whole is greater than its part. * To preserve the classification of general and geometrical axioms, we have placed Euclid's ninth axiom... | |
 | Elias Loomis - Geometry - 1895 - 450 pages
...equals, are equal to one another. 8. Magnitudes which coincide with one another, that is, which .xactly 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. 11. From one point to another... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...things, are equal to one another. . 7. Things which are halves of the same thing, or of equal things, are equal to one another. 9.* The whole is greater than its part. * To preserve the classification of general and geometrical axioms, we have placed Euclid's ninth axiom... | |
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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. 
