| Euclid - 1822 - 179 pages
...a circle may be described from any centre, /&, ff, at any distance from that centre. M o 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... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...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 - 226 pages
...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 - 236 pages
...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,... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...Euclid had given, has been deceived in applying what is manifest, when understood of magnitudes, unto **ratios, viz. that a magnitude cannot be both greater...those things which are equal to the same are equal** to'one another, is a most evident axiom when understood of magnitudes; yet Euclid does not make use... | |
| George Bentham - Logic - 1827 - 304 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... | |
| John Martin F. Wright - 1827 - 638 pages
...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... | |
| English literature - 1827 - 610 pages
...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 - 344 pages
...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... | |
| Leeds grammar sch - 1828 - 364 pages
...: 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... | |
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