## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

### From inside the book

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**bisect**a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal ...**bisected**by the straight line AF . Which was to be done . A B D PROP . X. PROB . To**bisect**a given finite OF ... Page 28

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**bisect**a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( 1. 1. ) upon it an equilateral triangle ABC , and**bisect**... Page 29

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**bisect**( 10. 1. ) FG in H , and D join CF , CH , CG ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the ... Page 31

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**Bisect**( 10. 1. ) AC in E , join BE and produce it to F , and make EF equal to BE ; join al- so FC , and produce AC to G. A E 4 Because AE is equal to EC , and BE ...**bisected**, it may be demonstrated that the OF GEOMETRY . BOOK I. 31. Page 32

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**bisected**, it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore