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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 11
av Euclid, Robert Simson - 1821 - 516 sider
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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
...: 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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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...POSTULATES. 1. LET it be !granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. That a circle may be described from any centre, at any distance from that centre. 4. That a straight...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 sider
...granted that a straight line may be drawn from any one point to any other point. 2. Let it be granted that a terminated straight line may be produced to any length in a straight line. i « f 3. Let it be granted that a circle may be described from any centre, at any distance from that...
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The London University Magazine, Volum 1

1829
...convenient to substitute for it. How do you reconcile the admission of Euclid's postulate, " that a straight line may be produced to any length in a straight line, 1 ' with the neces-, I. «*_ xy — x + y, II. 3x* — 2xy + y 3 — 4>x — 4y + 3 = 0. III. x>=xy...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...is evident, that, first, a straight line may be drawn from any one point to any other point ; 2ndly, a terminated straight line may be produced to any length in a straight line ; 3dly, from the greater of two straight lines, a part may be cut off equal to the less ; and 4thly,...
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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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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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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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to...centre, at any distance from that centre. Axioms. iTHINGS which are equal to the same thing are equal to one another. II. If equals be added to equals,...
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