## The Elements of 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 Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

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**ABC**shall be an equilateral**triangle**. A C E Because the point A is the ' centre of the circle 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 ... Page 15

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**triangle ABC**to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the R angle ABC to the angle DEF , and the angle ACB to DFE . B CE D F For , if the**triangle ABC**be ... Page 16

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**ABC**shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the ...**triangle**AFC to the**triangle**AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of ... Page 18

... triangle ACB ; produce AC , AD to E , F ; there- fore , because AC is equal ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ...

... triangle ACB ; produce AC , AD to E , F ; there- fore , because AC is equal ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ...

**triangle ABC**be applied to DEF , so that the point B be on E , and the B D G ... Page 19

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**triangles**that have their sides which are terminated in one extremity of the base ...**triangle**DEF ; then join AF ; the straight line AF bisects the angle BAC ...**ABC**, and bi- sect ( 9. 1. ) the angle ACB by the straight line CD . AB is ...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore