 | Mathematics - 1836 - 488 pages
...be taken from unequals, the remainders are unequal. 6. Things which are doubles 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... | |
 | Alexander Bryan Johnson - Language Arts & Disciplines - 1836 - 290 pages
...congruities and incongruities, must be interpreted by our sensible experience. They signify nothing more. Things which are double of the same are equal to one another. Why ? Because, to admit that A and B are severally double of C, is to admit that A is equal to B. But... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...from unequals, the remainders are unequal.f 6. Things which are doubles 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 exactly coincide with one another, are... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...be taken from unequals, the remainders are unequal. 6. Things which are doubles 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... | |
 | Euclides - 1838 - 264 pages
...remainders will be unequal. VI. Things which are double of the same, ate equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide, or which may be conceived to coincide with one another, that is, which... | |
 | Thomas Cogswell Upham - Intellect - 1839 - 476 pages
...one another ; If equals be added to equals, the wholes are equal ; The whole is greater than a part ; Things, which are double of the same, are equal to one another ; Things, which are halves of the same, are equal to one another ; Magnitudes, which coincide with... | |
 | Euclides - 1840 - 192 pages
...remains from the greater of the unequal magnitudes. 6. Things which are doubles 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 to say, which... | |
 | Euclides - Geometry - 1841 - 378 pages
...equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. 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... | |
 | Thomas Cogswell Upham - Intellect - 1841 - 474 pages
...one another ; If equals be added to equals, the 'wholes are equal; The whole is greater than a part; Things which are double of the same are equal to one another ; Things which are halves of the same are equal to one another ; Magnitudes which coincide with one... | |
 | Chambers W. and R., ltd - 1842 - 744 pages
...fact, merely what a logician would call the converse of it; for in the 8th axiom it is stated, that magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another ; and in this theorem, in order to prove them equal, it is proved that they coincide. The demonstration... | |
| |
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. 
