Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page vii
... Diameter of a Circle , ... To find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 129 130 130 131 131 132 138 PAGE Area of the ...
... Diameter of a Circle , ... To find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 129 130 130 131 131 132 138 PAGE Area of the ...
Page 61
... DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any part of a circumference ...
... DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any part of a circumference ...
Page 62
... when its circumference touches each of the sides of the polygon . ооо о POSTULATE . A circumference can be described from any point as a rentre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
... when its circumference touches each of the sides of the polygon . ооо о POSTULATE . A circumference can be described from any point as a rentre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
Page 63
... diameter divides the circle , and also its circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . F E B For , let AFB be applied to ...
... diameter divides the circle , and also its circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . F E B For , let AFB be applied to ...
Page 64
... diameters AB D M N B E and EF . If the semicircle ADB be applied to the semi- circle EGF , it will coincide with it , and the semi - circum- ference ADB will coincide with the semi - circumference EGF . But the part AMD is equal to the ...
... diameters AB D M N B E and EF . If the semicircle ADB be applied to the semi- circle EGF , it will coincide with it , and the semi - circum- ference ADB will coincide with the semi - circumference EGF . But the part AMD is equal to the ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence