## Elements of Geometry |

### From inside the book

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**chords**, of tangents , and of the measure of angles by the arcs of a circle . These two sections are followed by the resolution of certain problems relating to the construction of figures . The third section , entitled the proportions ... Page 22

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**chord**or subtense of an arc is the straight line FG , which joins its extremities ** . 93. A segment of a circle is the portion comprehended be- tween an arc and its**chord**. 94. A sector is the part of a circle comprehended between an ... Page 23

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**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 , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100 ... Page 24

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**chords**, and conversely , equal**chords**subtend equal arcs . Demonstration . The radius AC ( fig . 50 ) being equal to the radius EO , and the arc AMD equal to the arc ENG ; the**chord**AD will be equal to the**chord**EG . For , the diameter ... Page 25

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**chord**would diminish , and the reverse ; thus , the arc AKBD being greater than AKBH , the**chord**AD of the first is less than the**chord**AH of the second . THEOREM . 105. The radius CG ( fig . 51 ) , perpendicular to a**chord**AB , Fig ...### 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