 | 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... | |
 | Leeds grammar sch - 1828 - 364 σελίδες
...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 σελίδες
...BCD, AC is equal (15. Definition.) to AB ; and because the point B is the centre of the circle ACE, EC 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.) therefore CA is equal to CB ; wherefore CA, AB, BC are equal to one another : and the... | |
 | John Playfair - 1829 - 210 σελίδες
...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 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... | |
 | Pierce Morton - 1830 - 584 σελίδες
...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... | |
 | George Peacock - 1830 - 732 σελίδες
...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 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... | |
 | Francis Bacon, Basil Montagu - 1831 - 478 σελίδες
...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.... | |
 | Thomas Perronet Thompson - 1833 - 168 σελίδες
...But it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG. And things which are equal to the same, are* equal to one another ; therefore AL is equal to BC. Wherefore from the point A a straight line AL has been drawn, equal... | |
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AB; but things which are equal to the same are equal to one another... 
