Elements of Geometry and Trigonometry |
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Page 44
... chord EG . For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M D N BE K exactly ... chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is ...
... chord EG . For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M D N BE K exactly ... chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is ...
Page 45
... chord AD , of the first , is less than the chord AH of the second . PROPOSITION VI . THEOREM . The radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be a chord , and ...
... chord AD , of the first , is less than the chord AH of the second . PROPOSITION VI . THEOREM . The radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be a chord , and ...
Page 47
... chords , the less is at the greater distance from the centre . First . Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D A In the right angled triangles CAF , DCG , the ...
... chords , the less is at the greater distance from the centre . First . Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D A In the right angled triangles CAF , DCG , the ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex