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AB; but things which are equal to the same are equal to one another...
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 7
av Euclides - 1853
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## Outline of a New System of Logic

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...
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## The Leodiensian; or Leeds grammar school magazine

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...
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## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

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...
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## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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...
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## Elements of Geometry: With Practical Applications, for the Use of Schools

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...
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## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

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...
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## A Treatise on Algebra

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...
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## An Essay on the Cultivation of the Intellect by the Study of Dead Languages

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...
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## The Works of Francis Bacon, Lord Chancellor of England, Volum 14

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....
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## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

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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