 | Peter Nicholson - 1825 - 1046 σελίδες
...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 σελίδες
...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 - 234 σελίδες
...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 - 608 σελίδες
...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... | |
 | George Bentham - 1827 - 304 σελίδες
...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 - 632 σελίδες
...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 Frederick Wright - 1827 - 344 σελίδες
...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 σελίδες
...: 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 - 138 σελίδες
...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 - 390 σελίδες
...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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Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term. 
