## 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 ... Page 25

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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 26

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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 35

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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 36

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**diameter**AD ; the angle BAD is a right angle ( 110 ) , and has for its measure 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 AMD ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence