## Elements of Geometry |

### From inside the book

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**diameter**, and every straight line , as AB , which passes through the centre and is terminated each way by the circumference , is called a**diameter**. By the definition of a circle the radii are all equal , and all the**diameters**also are ... Page 23

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**diameter**AB ( fig . 49 ) 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 ... Page 24

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**diameter**AB being equal to the**diameter**EF , the semicircle AMDB may be applied exactly to the semicircle ENGF , and then the curved line AMDB will coincide entirely with the curved line ENGF ; but the portion AMD being sup- posed equal ... Page 33

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**diameter**AE , and the radii CB , CD . The angle BCE , being the exterior angle of the triangle ABC , is equal to the sum of the two opposite interior angles , CAB , ABC . But , the triangle BAC being isosceles , the angle CAB = ABC ... Page 34

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**diameter**AD ; the angle BAD is a right angle ( 110 ) , and has for its meas- ure the half of the semicircumference AMD ; the angle DAC has for its measure the half of DC ; therefore BAD + DAC , or BAC , has for its measure the half of ...### 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