 | Dugald Stewart - 1847 - 666 sider
...force, either to Locke, to lieid, or to Campbell,) that furnishes, if I mistake not, the true too ; " Magnitudes which coincide with one another, that is which exactly fill the Fame space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the... | |
 | Euclides - 1848 - 52 sider
...unequals, the wholes are unequal. V. If equals be taken 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... | |
 | Euclid, Thomas Tate - 1849 - 120 sider
...unequals, the wholes are unequal. v. If equals be taken from unequala, th remainders are unequal. VI. Things which are double of the same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vm. Magnitudes which coincide with... | |
 | Henry Aldrich - 1850 - 406 sider
...operations, that they are often deemed intuitive ; and 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... | |
 | Euclides - 1852 - 152 sider
...wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. BOOK I. BOOK I. 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... | |
 | Euclides - 1853 - 176 sider
...unequals, the wholes are unequal. V. If equals be taken 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... | |
 | Euclid - 1853 - 176 sider
...wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Magnitudes which are double of the same are equal to one another. 7. Magnitudes which are halves of the same are equal to one another. SCHOLIUM. A similar extension may... | |
 | Euclides - 1853 - 146 sider
...unequals, the wholes are unequal. If equals be taken from unequals, the remainders are unequal. TI. Things which are double of the same, are equal to one another. TO. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide... | |
 | Dugald Stewart - 1854 - 452 sider
...place. Ka) TO. tf*(fii%i>rx !«•' aAXnX* tra £xx»x»« Irrl: — thus translated by Dr. Simson ; " Magnitudes which coincide with one another, that is,...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 ; —... | |
 | Thomas Lund - 1854 - 520 sider
...plain enough, for AB + CD = CD + DE = CE ; and AB taken from CE = CD. The same principle, viz. that ' magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another', leads to the conclusion that, in like manner areas and angles may be added, subtracted, multiplied,... | |
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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. 
