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
... Polygon is circumscribed about a circle , when all of its sides are tangent to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . Ө о POSTULATE . A circumference ...
... Polygon is circumscribed about a circle , when all of its sides are tangent to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches all of the sides of the polygon . Ө о POSTULATE . A circumference ...
Page 137
... polygon ; a circle may also be inscribed in it . ין 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 , C , describe the circum- ference ...
... polygon ; a circle may also be inscribed in it . ין 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 , C , describe the circum- ference ...
Page 138
... inscribed polygon . For , the sides are equal , because they are chords of equal arcs , and the angles are equal , because they are measured by halves of equal arcs . If the vertices A , B , C , & c . , of a regular inscribed polygon be ...
... inscribed polygon . For , the sides are equal , because they are chords of equal arcs , and the angles are equal , because they are measured by halves of equal arcs . If the vertices A , B , C , & c . , of a regular inscribed polygon be ...
Page 142
... inscribed pentagon . Scholium 1. If the arcs subtended by the sides of any regular inscribed polygon be bisected , and chords of the semi- arcs be drawn , the resulting figure will be a regular inscribed polygon of double the number of ...
... inscribed pentagon . Scholium 1. If the arcs subtended by the sides of any regular inscribed polygon be bisected , and chords of the semi- arcs be drawn , the resulting figure will be a regular inscribed polygon of double the number of ...
Page 143
... polygon which shall be similar to a given regular inscribed polygon . Let TNQ be a circle , O its centre , and ABCDEF a regular inscribed polygon . At the middle points T , N , P , & c . , of the arcs subtended by the sides of the inscribed ...
... polygon which shall be similar to a given regular inscribed polygon . Let TNQ be a circle , O its centre , and ABCDEF a regular inscribed polygon . At the middle points T , N , P , & c . , of the arcs subtended by the sides of the inscribed ...
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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