 | George Bentham - 1827 - 304 Seiten
...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 Frederick Wright - 1827 - 344 Seiten
...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 Seiten
...circle : 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... | |
 | Euclid, Robert Simson - 1829 - 548 Seiten
...circle ACE ; and from the point C, in which the circles cut one another, draw the straight lines (2. Post.) CA, CB to the points A, B ; ABC shall be an...which are equal to the same are equal to one another ; (1st Axiom.) therefore CA is equal to CB ; wherefore CA, AB, BC are equal to one another : and the... | |
 | John Playfair - 1829 - 210 Seiten
...Definition) ; and because the point B is the centre of the circle ACE, BC is equal to BA : therefore CA and CB are each of them equal to AB. But things which are equal to the same thing are equal to one another (1 Axiom); therefore CA is equal to CB; wherefore CA, AB, BC are equal... | |
 | Timothy Walker - 1829 - 138 Seiten
...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... | |
 | George Peacock - 1830 - 732 Seiten
...represented, or in terms of which they are expressed: without such a definition, the proposition that " things which are equal to the same are equal to one another," could no longer be considered as axiomatic, inasmuch as we should be at a loss for the principle or... | |
 | William Sewell - 1830 - 390 Seiten
...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... | |
 | Pierce Morton - 1830 - 584 Seiten
...the propositions of the following sections, and are therefore here premised : — • AXIOMS.* • 1. Things, which are equal to the same, are equal to one another. 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders... | |
 | Francis Bacon, Basil Montagu - 1831 - 478 Seiten
...similar to that of music termed the declining of a cadence. 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.... | |
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AB; but things which are equal to the same are equal to one another... 
