## Elements of Geometry |

### From inside the book

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**bisect**each other . Demonstration . If we compare the triangle ADO with the triangle COB , we find the side AD = CB , and the angle ADO = CBO ( 67 ) : also the angle DAO OCB ; therefore these two triangles are equal ( 38 ) , and ... Page 23

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**bisects**the circle and its cir- Fig . 49 . cumference . Demonstration . If the figure AEB be applied to AFB , so that the base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there ... Page 25

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**bisects**this chord and the arc subtended by it AGB . Demonstration . Draw the radii CA , CB ; these radii are , with respect to the perpendicular CD , two equal oblique lines , there- fore they are equally distant from the perpendicular ... Page 26

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**bisect**these two straight lines by the perpendiculars DE , FG ; these perpendiculars will meet in a point 0 . For the lines DE , FG , will necessarily cut each other , if they are not parallel . Let us suppose that they are parallel ... Page 27

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**Bisect**Fig . 53 . these chords by the perpendicular CF , CG , and draw the radii CA , CD . The right - angled triangles CAF , DCG , have the hypothe- nuses CA , CD , equal ; moreover the side AF , the half of AB , is equal to the side ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence