## Elements of Geometry |

### From inside the book

Results 6-10 of 82

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**Hence**the greatest straight line that can be inscribed in a circle is equal to its diameter . THEOREM . 101. A straight line cannot meet the circumference of a circle in more than two points . Demonstration . If it could meet it in ... Page 24

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**hence**the angle ACD = EOG . Now , if the semicircle ADB be placed upon EGF , because the angle ACD = EOG , it is evident , that the radius CD will fall upon the radius OG , and the point D upon G , therefore the arc AMD is equal to the ... Page 26

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**hence**the three distances OA , OB , OC , are equal ; therefore the circumference , described from the centre O with the radius OB , will pass through the three points A , B , C. It is thus proved , that the circumference of a circle may ... Page 29

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**Hence**, if two circles touch each other , either internally or externally , the centres and the point of contact are in the same straight line . 118. Scholium . All the circles , which have their centres in the straight line CD and ... Page 32

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**hence**two sectors ACB , ACD , taken in the same circle or in equal circles , are to each other , as the arcs AB , AD , the bases of these sectors . It will be perceived therefore , that the arcs of a circle , which are used as a measure ...### 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