| Euclides - 1826
...continually produced shall meet on that side where the angles are less than two right angles. AXIOMS. 1. **Things which are equal to the same are equal to one another.** 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...because the point B is the * 1-, Deficentre of the circle ACE, BC is equal to BA: but it has nitionbeen **proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB:** but things which are equal to the same thing are equal* to one another; therefore CA is equal to CB... | |
| John Martin Frederick Wright - 1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " **Things which are equal to the same, are equal to one another."** " Very good, Sir. What the second, and what the third?" "If equals be added to equals the sums are... | |
| John Scott, John Taylor - English literature - 1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous V " **Things which are equal to the same, are equal to one another."** " Very good, Sir. What the second, and what the thirdV " If equals be added to equals, the sums are... | |
| John Martin F. Wright - 1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " **Things which are equal to the same, are equal to one another."** " Very good, Sir. What the second, and what the third?" " If equals be added to equals the sums are... | |
| George Bentham - 1827 - 287 pages
...which a syllogistic conclusion can be founded ? Such may, perhaps, be found the four following : 1. **Things which are equal to the same, are equal to one another.** 2. When of two things, one only is equal to a third, and the other is not equal to that third, these... | |
| Leeds grammar sch - 1828
...: but Patience is equal to Poverty ; therefore Patience and Economy are each equal to Poverty ; but **things which are equal to the same are equal to one another;** therefore Patience and Economy are equal to one another ; wherefore the three, Patience, Economy, and... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...and are to geometry, what the foundations are to a building. Euclid's axioms are the following : I. **Things which are equal to the same are equal to one another.** 2k If equals be added to equals the wholes are equal. 3. If equals be taken from equals, the remainders... | |
| William Sewell - Classical education - 1830 - 371 pages
...experiment. A child never doubts that the fire which burnt him yesterday, will burn him to-day, or that two **things which are equal to the same, are equal to one another,** where he .has once seen the axiom illustrated by a single example—and hence one great advantage in... | |
| Pierce Morton - Geometry - 1830 - 272 pages
...the propositions of the following sections, and are therefore here premised : — • AXIOMS.* • 1. **Things, which are equal to the same, are equal to one another.** 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders... | |
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