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" 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. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 256
av Euclid, Robert Simson - 1838 - 416 sider
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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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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. Lastly;...
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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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The Works of Francis Bacon, Lord Chancellor of England: A New Edition:

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. Lastly...
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The Quarterly Journal of Education, Volum 7

1834
...Proclus, had preceded him in this attempt : we give the demonstration by Apollonius of the axiom, that things which are equal to the same are equal to one another. He argues, that if A is equal to B, it occupies (may be made to occupy) the same place as B. And if...
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The Philosophy of Morals: An Investigation by a New and Extended ..., Volum 1

Alexander Smith - 1835
...of mathematical axioms. Take such instances as these, " all the parts are equal to the whole," — " things which are equal to the same are equal to one another." Why must we at once affirm that these propositions are true, and that the contrary of them cannot be...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...III. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders...
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