## Elements of Geometry |

### From inside the book

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**radius**or semi- 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 ... Page 24

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**radius**CD will fall upon the**radius**OG , and the point D upon G , therefore the arc AMD is equal to the arc ENG . THEOREM . 103. In the same circle , or in equal circles , if the arc be less than half a circumference , the greater arc ... Page 25

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**radius**CG ( fig . 51 ) , perpendicular to a chord AB , Fig . 51 . 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 ... Page 26

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**radius**OB , will pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any three given points , which are not in the same straight line ; it remains to show , that ... Page 27

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**radius**AC , is a tangent to the circumference . Demonstration . Since every oblique line CE is greater than the ...**radius**CA , and with respect to this new tangent the**radius**CA would be an oblique line , and the perpendicular let fall ...### 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