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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 Principles of psychology, Volum 2

Herbert Spencer - 1873
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — "Things which are equal to the same are equal to one another," can, by multiplied application, do more than establish the equality of some series of magnitudes. But...
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Journal of the Transactions of the Victoria Institute, Or ..., Volum 6

Victoria Institute (Great Britain) - 1873
...Here again the word is psyche, but containing all the attributes of kardia. The inference is obvious : things which are equal to the same are equal to one another. While we may freely admit that, in the terms of a language, this principle will not rigidly apply,...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...AB. [Def. 15.] And because the point B is the centre of the circle ACE, BC is equal to BA. [Def. 15.] But it has been proved that CA is equal to AB; therefore...equal to AB. But things which are equal to the same thing are equal to one another; [Ax. i.] therefore CA is equal to CB. Therefore CA, AB, BC are equal...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...because the point B is the centre of the circle ACE, BC is equal to BA ; (I. Def. 30.) therefore CA and CB are each of them equal to AB; but things which are equal to the same thing are equal to one another ; (Ax. 1.) therefore CA is equal to CB; and the three lines BA, AC,...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...circle ACE, , . 2. BC is equal to BA. But it has been proved that AC is equal to AB; therefore AC, BC are each of them equal to AB; but things which are equal to the same thing are equal to one another (Axiom 1) ; therefore 3. AC is equal to BC. Wherefore AB, BC, CA are...
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The philosophy of voice

Charles Lunn - 1874 - 72 sider
...living subject than are producible from the dead. Let us turn to the logical side of the question. Things which are equal to the same are equal to one another. Anatomy teaches us that there is no difference between the male and female larynx save in size, so...
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The Tanjore Mahratta Principality in Southern India: The Land of the Chola ...

William Hickey - 1874 - 225 sider
...laws, which they have been taught to believe sacred, and which alone they can possibly comprehend."1 ' Things which are equal to the same are equal to one another,' says Euclid. What applies to the part, will apply to the whole. A political agent, the only political...
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Aphorisms, maxims, &c., for learners, selected and arranged by R. Potts

Robert Potts - 1875 - 192 sider
...the evidence of the conclusion is manifest. — Dr. Whewell. 214. 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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Picture Logic: Or, The Grave Made Gay; an Attempt to Popularise the Science ...

Alfred Swinbourne - 1875 - 166 sider
...middle terms is called the minor premiss. The former always comes first. Unless the principle that " things which are equal to the same are equal to one another " were true, it would not follow that " Socrates " and " mortal," which are equal to the same (" man...
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Dedication and Inauguration of the Vanderbilt University: Nashville ...

Vanderbilt University - 1875 - 112 sider
...the same time be and not be; (2) that if equals be added to equals the wholes are equal; and (3) that things which are equal to the same are equal to one another. It so happens that each of these propositions which he has assumed to be true is, if true, much more...
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