## 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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**bisect**a given rectilineal angle , that is , to divide it into two equal angles . it . Let BAC be the given ...**bisected**by the straight line AF , which was to be done . PROP . X. PROB . B D E C To**bisect**a given finite straight ... Page 21

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**bisect**( 10. 1. ) FG A F in H , and join CF , CH , CG ; the straight line CH , drawn from the A H D G B given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two tri- angles ... Page 24

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**Bisect**( 10. 1. ) AC in BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G ...**bisected**, it may be demonstrat- ed that the angle BCG , that is , ( 15. 1. ) the angle ACD , is great- er than the ... Page 42

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**Bisect**( 10. 1. ) BC in E , join AE , and at the point E in the straight line EC make ( 23. 1. ) the angle CEF equal to D ; and through A draw ( 31. f . ) AG parallel to EC , and through C draw CG ( 31. 1. ) parallel to EF : there- fore ... Page 54

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**bisected**, and produced to any point ; the rectangle contained by the whole line thus pro- duced , and the part of it produced , together with the square of half the line**bisected**, is equal to the square of the straight line which 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