## The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |

### From inside the book

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**EUCLID**VIZ . THE FIRST SIX BOOKS , TOGETHER WITH THE ELEVENTH AND TWELFTH . The Errors , by which THEON , or others , have long ago vitiated these Books , are corrected , And fome of**EUCLID'S**Demonftrations are reftored . ALSO THE BOOK ... Page 5

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**Euclid's**name , are very different and contrary to one another . Peter Ramus afcribes the Propofitions , as well as their Demonftra- tions , to Theon ; others think the Propofitions to be**Euclid's**, but that the Demonftrations are ... Page 6

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**Euclid's**accuracy , and which plainly thew , that his Elements have been much corrupted by unskil- ful Geometers ; and , though these are not fo grofs as the o- thers now mentioned , they ought by no means to remain un- corrected . Upon ... Page 31

... the two fides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the bafe CB is greater than the bafe EF ; the angle BAC is likewife greater than the angle EDF . For 4 Book I. a 4. I. b 24. I. For OF

... the two fides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the bafe CB is greater than the bafe EF ; the angle BAC is likewife greater than the angle EDF . For 4 Book I. a 4. I. b 24. I. For OF

**EUCLID**. 31. Page 34

Together with the Eleventh and Twelfth

Together with the Eleventh and Twelfth

**Euclid**. Book I. a 16. I. PROP . XXVII . THEOR . IF a ftraight line falling upon two other ftraight line : makes the alternate angles equal to one another , these two straight lines fhall be parallel ...### Other editions - View all

### Common terms and phrases

alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore

### Popular passages

Page 472 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.

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Page 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

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Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

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Page 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.