 | Euclides - 1816 - 588 sider
...unequals, the wholes are unequal V. If equals betaken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide... | |
 | John Playfair - 1819 - 354 sider
...equal to one another. VII. Things which are halves of the same thing, are equal to one another. VIII. Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. 3 X. All right angles are equal to one another. XI. " Two straight... | |
 | Dugald Stewart - 1821 - 348 sider
...w*£u'.Ç'*vrî «»' лллих» lea яллялмс tm : — thus translated by Dr. Simson ; " Magnituui's which coincide with one another, that is, which exactly...fill the same " space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; the... | |
 | Henry Aldrich - 1821 - 300 sider
...allowed as soon as perceived : such are axioms ; which neither require nor admit syllogistic proof: as, Things which are double of the same are equal to one another. In the secondary degree, it denotes the certainty of those relations which may be immediately deduced... | |
 | Euclid - 1822 - 222 sider
...taken from unequals, the remainders are unequal. 6. Things which are double of the 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 with one another, are equal to... | |
 | Peter Nicholson - 1823 - 210 sider
...taken from unequals, the remainders will be unequal. 6. Things which 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... | |
 | Peter Nicholson - 1825 - 1046 sider
...unequals, the wholes are unequal. 5. If equals be taken from unequal s, the remainders are unequal. 6. Things which are double of the same, are equal to...with one another, that is, which exactly fill the space, are equal to one another. 0. The whole is greater than its part. 10. Twfc«».^^^ lines cannot... | |
 | Euclides - 1826 - 226 sider
...unequals, the wholes are unequal. 5. If equals be taken from uncquals, the remainders are unequal. 6. Things which are double of the same, are equal to...are halves of the same, are equal to one another. 8. Things which mutually agree with one another, are equal to one another. 9. The whole is greater than... | |
 | Euclid - 1826 - 234 sider
...unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal to...are halves of the same, are equal to one another. 8. Things which mutually agree with one another, are equal to one another. 0. The whole is greater than... | |
 | George Lees - 1826 - 276 sider
...which are halves of the same thing, are equal to one another. VIII. — Magnitudes which coincide wiih one another, that is, which exactly fill the same space, are equal to one another. IX. — The whole is greater than its part, and equal to all its parts taken together. X. — All right... | |
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Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another. 
