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 60
... circumscribed about a circle , when all of its sides are tangent o the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . о © о POSTULATE . A circumference can be ...
... circumscribed about a circle , when all of its sides are tangent o the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . о © о POSTULATE . A circumference can be ...
Page 89
... circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle , or it may lie without the given circle . 1o ...
... circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle , or it may lie without the given circle . 1o ...
Page 137
... circumscribed about any regular polygon ; a circle may also be inscribed in it . 1o . Let ABCF be a regular polygon : then can the circumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B ...
... circumscribed about any regular polygon ; a circle may also be inscribed in it . 1o . Let ABCF be a regular polygon : then can the circumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B ...
Page 138
... circumscribed and inscribed circles . 2. The ANGLE AT THE CENTRE , is the angle formed by drawing lines from the centre to the extremities of either side . The angle at the centre is equal to four right angles divided by the number of ...
... circumscribed and inscribed circles . 2. The ANGLE AT THE CENTRE , is the angle formed by drawing lines from the centre to the extremities of either side . The angle at the centre is equal to four right angles divided by the number of ...
Page 142
... . The area of any regular inscribed polygon 18 less than that of a regular inscribed pclygon of double the number of sides , because a part is less than the whole . PROPOSITION VII . PROBLEM . Tu circumscribe a polygon about 142 GEOMETRY .
... . The area of any regular inscribed polygon 18 less than that of a regular inscribed pclygon of double the number of sides , because a part is less than the whole . PROPOSITION VII . PROBLEM . Tu circumscribe a polygon about 142 GEOMETRY .
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence