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" AB; but things which are equal to the same are equal to one another... "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Page 12
by John Playfair - 1837 - 318 pages
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 534 pages
...AC is equal c to AB ; and becaufe the point B is the centre of the circle ACE, BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB; but things which are equal to the fame are equal to one another d ; therefore CA is equal to CB ; wherefore...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...is the centre of thec -i5ihDecirdc ACE, BC is equal to BA: But it has been proved that CAfin'tion' is equal to AB; therefore CA, CB are each 'of them equal tfo AB ; but things which are equal to the fame are equal to one another,1; therefore CA is equal to...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 374 pages
...AC is e- equal c to AB ; and becaufe the point B is the centre of the circle ACE, BC ;se^ual to BA . But it has been proved, that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; but things which are equal to the fame, are equal to one d tft Axi. another d ; therefore CA is equal...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...AC is equal ' to AB. and becaufe the point B is the center of the circle ACE, c. BC is equal to BA. but it has been proved that CA is equal to AB; therefore CA, CB are each of them equal to AB. but things which are equal to the fame are equal to one another d; therefore d. CA is equal to CB....
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...the centre of the c 15. Decircle ACL', BC is equal to BA: but it has been proved that CA finition. is equal to AB ; therefore CA, CB are each of them equal to AB ; but things which are equal to the same are equal to one Another d ; therefore CA is equal to CB ;...
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The Monthly Anthology, and Boston Review, Volume 5

David Phineas Adams, William Emerson, Samuel Cooper Thacher - 1808 - 708 pages
...confound our two articles. " In the Celtic" says he, " the article an signifies the and that." But as things, which are equal to the same, are equal to one another, it is easy to prove, since an means that, and //•.- means that, that an and the are in the English...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...because the point B is the centre' 15 Definio/' the circle ACE, BC is equal to BA : But it has been don proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB; but things, which are equal to the same are equal to one anotherj; therefore CA is equal ' itt.\xiom....
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The Scots Magazine and Edinburgh Literary Miscellany, Volume 76

English literature - 1814 - 1032 pages
...contrary, they are such 35, considered separately, do not afford room for a single inference. — That things which are equal to the same, are equal to one another, and that the whole is greater than its part, considered in themselves, are mere barren truisms. The...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 582 pages
...ACE, BC is equal to BA, by the \5th definition; therefore CA,.CB are each of them equal to AB ; but things which are equal to the same are equal to one another, by the 1st' axiom; wherefore CA and CB are equal to one another, being each equal to AB ; consequently...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...magnitudes, unto ratios, viz. that a magnitude cannot be both greater and less than another. That those things which are equal to the same are equal to one another, is a most.evident axiom when understood of magnitudes ; yet Euclid does not make use of it to infer,...
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