Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 73
... Chord of a circle is any straight line having its extremities in the circumference , as A B , Fig . 3 . Every chord subtends two arcs whose sum is the cir- cumference . Thus the chord AB , ( Fig . 3 ) , subtends the arc AMB and the arc ...
... Chord of a circle is any straight line having its extremities in the circumference , as A B , Fig . 3 . Every chord subtends two arcs whose sum is the cir- cumference . Thus the chord AB , ( Fig . 3 ) , subtends the arc AMB and the arc ...
Σελίδα 74
... chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as A DC , Fig . 1 ... chords of that circumference , as ZABC , Fig . 1 . A polygon is inscribed in a circle when its sides are chords of the ...
... chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as A DC , Fig . 1 ... chords of that circumference , as ZABC , Fig . 1 . A polygon is inscribed in a circle when its sides are chords of the ...
Σελίδα 75
... chord . Let A B be the diameter of the circle AMB , and AE any other chord . We are to prove AB > AE . M A E3 E B From C , the centre of the O , draw C E. But CE = CB , ( being radii of the same circle ) . AC + CEAE , ( the sum of two ...
... chord . Let A B be the diameter of the circle AMB , and AE any other chord . We are to prove AB > AE . M A E3 E B From C , the centre of the O , draw C E. But CE = CB , ( being radii of the same circle ) . AC + CEAE , ( the sum of two ...
Σελίδα 79
... chords . R B A R Pl BI In the equal circles ABP and A'B ' P ' let arc RS = arc R ' S ' . We are to prove chord RS chord R ' S ' . Draw the radii O R , OS , O ' R ' , and O ' S ' . In the AROS and R ' O'S ' OR = O ' R ' , § 176 ( being ...
... chords . R B A R Pl BI In the equal circles ABP and A'B ' P ' let arc RS = arc R ' S ' . We are to prove chord RS chord R ' S ' . Draw the radii O R , OS , O ' R ' , and O ' S ' . In the AROS and R ' O'S ' OR = O ' R ' , § 176 ( being ...
Σελίδα 80
... chords subtend equal arcs . R S B A R 22 BI P PI In the equal circles ABP and A'B ' P ' , let chord RS - chord R'S ' . We are to prove - arc RS : arc R ' S ' . Draw the radii O R , O S , O ' R ' , and O ' S ' . In the AROS and R ' O'S ...
... chords subtend equal arcs . R S B A R 22 BI P PI In the equal circles ABP and A'B ' P ' , let chord RS - chord R'S ' . We are to prove - arc RS : arc R ' S ' . Draw the radii O R , O S , O ' R ' , and O ' S ' . In the AROS and R ' O'S ...
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AABC ABCD altitude apothem arc A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide cone of revolution conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section S-ABC SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume