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 , 116 To find the length of an Arc , Arca of a Circle , Area of a Sector , ..... Area of a Segment , .... Area of a Circular Ring ,. 117 117 118 118 119 PAGE . Area of the Surface of a Prism , CONTENTS . vi.
... Diameter of a Circle , 116 To find the length of an Arc , Arca of a Circle , Area of a Sector , ..... Area of a Segment , .... Area of a Circular Ring ,. 117 117 118 118 119 PAGE . Area of the Surface of a Prism , CONTENTS . vi.
Page 59
... 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 60
... , when its circumference touches all of the sides of the polygon . Ө о POSTULATE . A circumference can be described from any point as a centre and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
... , when its circumference touches all of the sides of the polygon . Ө о POSTULATE . A circumference can be described from any point as a centre and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
Page 61
... 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 . A F 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 . A F B For , let AFB be applied to ...
Page 62
... diameters AB and EF If the semi - circle · ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB will coincide with the semi - circumference EGF . But the part AMD is equal to the part ENG ...
... diameters AB and EF If the semi - circle · ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB will coincide with the semi - circumference EGF . But the part AMD is equal to the part ENG ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence