 | Dugald Stewart - 1847 - 666 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 146 σελίδες
...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... | |
 | Euclid - 1853 - 176 σελίδες
...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 - 176 σελίδες
...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... | |
 | Dugald Stewart - 1854 - 452 σελίδες
...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 σελίδες
...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. 
