 | Isaac Sharpless - Geometry - 1879 - 282 pages
...subtracted from unequals, the remainders are unequal. 7. Things which 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... | |
 | 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...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... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...unequal. Things which are double of the same are equal to one another. Things which are halves of the same are 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.... | |
 | T S. Taylor - 1880 - 152 pages
...are doubles of equal things 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 are equal to one another. 8a, (Not given by Euclid, but assumed by him). Lines and angles which are... | |
 | 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...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... | |
 | Euclides - 1884 - 214 pages
...another, and likewise those which are terminated at the other extremity equal to one another. Axiom 8. Magnitudes which coincide with one another, that is which exactly fill the same space, are equal to one another. NB Angles are said to coincide when the angular points have the... | |
 | 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, which exactly fill the same space, are equal to one another." This cannot be regarded as a distinct axiom, but as an application... | |
 | 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, which exactly fill the same space, are equal to one another." But the explanatory clause in italics cannot apply to angles... | |
 | 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, which exactly fill the same space, are equal to one another." This cannot bo regarded as a distinct axiom, but as an application... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 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...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... | |
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Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
