| George Bentham - 1827 - 298 sider
...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
...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 - 516 sider
...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 - 186 sider
...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 - 129 sider
...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 - 272 sider
...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 - 685 sider
...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 - 371 sider
...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
...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 - 150 sider
...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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