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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; viz. the first six books, together with the eleventh ... - Side 262
av Euclides - 1834
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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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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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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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Lateinos; Lateinos; or, The only proper and appellative name of the man ...

Reginald Rabett - 1835 - 308 sider
...equal to 500, so must the former (as the representative of the latter,) be equal to 500 ; because ' things which are equal to the same are equal to one another.' But as the «ir«nj/*or or stenographical character q is a cypher, and no letter, or letters, of the...
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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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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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