## Elements of Geometry |

### From inside the book

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**centre**. The circle is the space terminated by this curved line * . 91. Every straight line CA , CE , CD ( fig . 46 ) , & c . drawn from the**centre**to the circumference is called a radius or semi- diameter , and every straight line , as ... Page 23

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**centre**, which is contrary to the definition of a circle . THEOREM . 99. Every chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the**centre**to the extremities of the chord AD ... Page 25

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**centre**, and the middle of the arc subtended by that chord . For this perpendicular is the same as that let fall from the**centre**upon the same chord , since they both pass through the middle of the chord ( 51 ) . THEOREM . 107. The ... Page 26

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**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 be made to pass through any three given points , which are not in the same straight line ; it remains ... Page 27

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**centre**, and of two unequal chords the less is at the greater distance from the**centre**. Demonstration 1. Let the chord AB = DE ( fig . 53 ) . Bisect Fig . 53 . these chords by the perpendicular CF , CG , and draw the radii CA , CD ...### 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