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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The first three books of Euclid's Elements of geometry, with theorems and ... - Σελίδα 5
των Euclides - 1849
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Alma Mater, Or, Seven Years at the University of Cambridge, Τόμος 1

John Martin Frederick Wright - 1827
...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...

Outline of a New System of Logic

George Bentham - 1827 - 298 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...

The London Magazine, Τόμος 17

1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous V " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the thirdV " If equals be added to equals, the sums are...

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...

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

Timothy Walker - 1829 - 129 σελίδες
...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 centre. The moderns, as Legendre, for example, are not thus scrupulous; but constantly suppose lines to be...

Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 σελίδες
...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 line which meets one of two parallel straight lines may oe produced till it meet...

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

William Sewell - 1830 - 371 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...

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

Pierce Morton - 1830 - 272 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...

A Treatise on Algebra

George Peacock - 1830 - 685 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...

The Works of Francis Bacon, Lord Chancellor of England, Τόμος 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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