| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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 ;... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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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