 | Euclid, Robert Simson - 1821 - 514 sider
...BCD, AC is equal (15. Definition.J to AB; and because the point B is the centre of the circle ACE, B^C is equal to BA: but it has been proved that CA is...which are equal to the same are equal to one another; (1st Axiom.J therefore CA is equal to CB; wherefore CA, AB, BC are equal to one another; and the triangle... | |
 | Henry Aldrich - 1821 - 300 sider
...reared, and as the final appeal in argument. They benr some slight analogy to the mathematical axioms, Things which are equal to the same are equal to one another ; and, Things of which one is equal and the other not equal to the same, are not equal to one another.... | |
 | Euclid - 1822 - 222 sider
...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 - 1046 sider
...is equal to BA : 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... | |
 | Euclid, John Playfair - 1826 - 326 sider
...(11. Definition) to AB; and beeause the point B is the eentre of the eirele ACE. BC is equal to AB : But it has been proved that CA is equal to AB; therefore CA, CB are eaeh of them equal to AB; now things whieh are equal to the same are equal to one another, (1. Axiom)... | |
 | Euclid - 1826 - 234 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,... | |
 | Euclides - 1826 - 226 sider
...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 - 1827 - 546 sider
...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...equal to AB: but things which are equal to the same thing are equal* to one another; therefore CA is equal to CB : wherefore CA, AB, BC are equal to one... | |
 | John Martin F. Wright - 1827 - 632 sider
...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 - 608 sider
...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... | |
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AB; but things which are equal to the same are equal to one another... 
