Elements of Geometry |
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Page vi
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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 ...
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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