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" AB; but things which are equal to the same are equal to one another... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 7
av Euclides - 1853
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...AC is • is Defi. equal* to AB ; and because the point B is the centre of the uition. circle ACE, BC is equal to BA : but it has been proved that CA...equal to AB : but things which are equal to the same thing are ' 1 Axiom, equal* to one another; therefore CA is equal to CB ; wherefore CA, AB, BC are...
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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 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....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...AC is c 15. Defi- equal c to AB ; and because the point B is the centre of the nition. circle ACE, BC is equal to BA : But it has been proved that CA...things which are equal to the same are equal to one d 1st Axi- another d ; therefore CA is equal to CB ; wherefore CA, AB, om. BC are equal to one another;...
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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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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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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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The philosophy of morals

Alexander Smith (M.A.) - 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 First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...definition 30.) to AB; and because the point B is the centre of the circle ACE, BC is equal (I. def. 30.) to BA. But it has been proved that CA is equal to...AB: but things which are equal to the same are equal (I. axiom 1.) to one another ; therefore CA is equal to CB; wherefore CA, AB, BC are equal to one another;...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...Definition) to AB ; and because the point B is the centre of the cir-' cle ACE, BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now things which are equal to the same are equal to one another. (1. Axiom) ; therefore CA is equal...
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