Elements of Geometry and Trigonometry |
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Page 41
... chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord . 5. A sector is the part of the circle included ...
... chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord . 5. A sector is the part of the circle included ...
Page 42
... AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
... AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
Page 43
Adrien Marie Legendre Charles Davies. PROPOSITION II . THEOREM . Every chord is less than the diameter . Let AD be ... chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to ...
Adrien Marie Legendre Charles Davies. PROPOSITION II . THEOREM . Every chord is less than the diameter . Let AD be ... chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to ...
Page 44
... chord EG . For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied K N BE F exactly to ... 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 K N BE F exactly to ... 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 ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex