| Peter Nicholson - 1825 - 372 sider
...But it has been proved dial CA is equal to AB ; therefore CA, CB, are each of diem equal to AB ; but **things which are equal to the same are equal to one another** (1st Axiom.) tiierefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another j and the... | |
| 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... | |
| Euclid - 1826 - 180 sider
...but it has been shown that CA is equal to AB : therefore CA, св, are each of them equal to AB. And **things which are equal to the same are equal to one another.** Whence CA is equal to св ; wherefore the three, CA, AB, вс, are equal to one another ; and, consequently,... | |
| 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 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 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 - 298 sider
...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 - 1829 - 129 sider
...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 - 1830 - 371 sider
...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... | |
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