## 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 26

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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 . Fig . 50 THEOREM . 103. In the same circle , or in equal circles , if the arc be less than half a circumference , the ... Page 27

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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 28

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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 29

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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 ...### 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