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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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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...to AB ; and because the point B is the centre of the circle ACE, BC is equal to BA ; but it has teen proved that CA is equal to AB ; therefore CA, CB, are each of them equal to AB ; therefore (Axiom I) CA is equal to CB ; wherefore CA, AB, BC, are equal to one another ; and the...
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Parochial lectures

William Josiah Irons - 1837
...proof. Our minds perceive all such truths by a direct glance. If any man should require proof that ' things which are equal to the same are equal to one another,' he would never get any such proof. If he should find by experience that it had been so, in a million...
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Remarks on Mathematical Or Demonstrative Reasoning

Edward Tagart - 1837 - 135 sider
...individual comprehended in it ; which is analogous to the axiom, or common notion of equality, that things which are equal to the same are equal to one another, or that the whole is made up of all the parts. A syllogism, to make a homely simile, is a kind of two-pronged...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...BCD, AC is equal (15. Definition.) to AB; and because the point B is the centre of the circle ACE, BC is equal to BA : but it has been proved that CA...which are equal to the same are equal to one another; (1st. Axiom.) therefore CA rs equal to CB ; wherefore CA, AB, BC are eqnal to one another ; and the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...the circle BCD, AC is equal* to AB; and because the point B is the cenfiu'uim" tre of ^e c'rcle 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 equal* to one another; A*'i'lm. therefore CA is equal toCB: wherefore CA, AB, BC are equal...
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Gradations in Algebra: In which the First Principles of Analysis are ...

Richard W. Green - 1839 - 148 sider
...dividing the 1st, x= — >£ Transposing and dividing the 2d, x= — —Jr. 5 Now, as it is evident that things which are equal to the same, are equal to one another ; one value of x is equal to the other value of x ; thus, ^. * 23— 3y _10+2y ~2~ ~~" ~5~ Destroying...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...AB; and because the point B is the Bullion. centre O f tn e c i rc i e ACE, BC is equal to BA: hut it has been proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB; but things * 1st which are equal to the same thing are equal* to one Axiom. anot her; therefore CA is equal to...
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The Works of Francis Bacon, Lord Chancellor of England, Volum 3

Francis Bacon - 1841
...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 Dublin Review, Volum 11

Nicholas Patrick Wiseman - 1841
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " things which are equal to the same are equal to one another." The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured...
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Works, Volum 3

Francis Bacon - 1841
...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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