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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 - Página 246
por Euclid - 1838 - 416 páginas
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 páginas
...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 páginas
...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, Volumen14

Francis Bacon, Basil Montagu - 1831 - 478 páginas
...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 páginas
...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 - 486 páginas
...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, Volumen7

1834 - 416 páginas
...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 ..., Volumen1

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 - 540 páginas
...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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The philosophy of morals

Alexander Smith (M.A.) - 1835 - 750 páginas
...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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...demonstrating 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 are equal. 3. If equals be taken from equals, the remainders...
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