## 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 24

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**chord**or subtense of an arc is the straight line FG , which joins its extremities . † 91. A segment of a circle is the portion comprehended be- tween an arc and its**chord**. 92. A sector is the part of a circle comprehended between an ... Page 25

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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 , ADAB ( 88 ) . 100 ... Page 26

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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 ... Page 27

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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 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