| Euclid - 1822 - عدد الصفحات: 222
...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 - 1825 - عدد الصفحات: 1046
...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 - عدد الصفحات: 226
...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 - عدد الصفحات: 234
...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 - 1827 - عدد الصفحات: 546
...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 - 1827 - عدد الصفحات: 304
...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 - عدد الصفحات: 632
...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... | |
| 1827 - عدد الصفحات: 608
...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 - عدد الصفحات: 344
...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 - عدد الصفحات: 364
...: 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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