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 15
... perimeter of the polygon . The angles formed by the sides , are called angles of the polygon . 19. Polygons are ... perimeters in the same direction , the first side of the one is equal to the first side BOOK I. 15.
... perimeter of the polygon . The angles formed by the sides , are called angles of the polygon . 19. Polygons are ... perimeters in the same direction , the first side of the one is equal to the first side BOOK I. 15.
Page 100
... perimeter and the radius of the inscribed circle . For , let DEF be a circle inscribed in the triangle ABC . Draw OD , OE , and OF , to the points of contact , and OA , OB , and OC , to the verti- ces . The area of OBC will be equal to ...
... perimeter and the radius of the inscribed circle . For , let DEF be a circle inscribed in the triangle ABC . Draw OD , OE , and OF , to the points of contact , and OA , OB , and OC , to the verti- ces . The area of OBC will be equal to ...
Page 125
... perimeters be to each other as any two homologous sides . For , any two homo- logous sides , as AB and FG , are like parts of the perimeters to which they belong : B A E hence ( B. II . , P. IX . ) , the perimeters of the polygons are ...
... perimeters be to each other as any two homologous sides . For , any two homo- logous sides , as AB and FG , are like parts of the perimeters to which they belong : B A E hence ( B. II . , P. IX . ) , the perimeters of the polygons are ...
Page 126
... Perimeters of similar polygons are to each other as their homologous diagonals , or as any other homologous lines ; and the polygons are to each other as the squares of their homologous diagonals , or as the squares of any other ...
... Perimeters of similar polygons are to each other as their homologous diagonals , or as any other homologous lines ; and the polygons are to each other as the squares of their homologous diagonals , or as the squares of any other ...
Page 145
... perimeter and the apothem . For , draw lines from the centre to the vertices of the polygon . These lines will ... perimeter and the apothem ; which was to be proved . PROPOSITION IX . THEOREM . The perimeters of similar regular 10 BOOK ...
... perimeter and the apothem . For , draw lines from the centre to the vertices of the polygon . These lines will ... perimeter and the apothem ; which was to be proved . PROPOSITION IX . THEOREM . The perimeters of similar regular 10 BOOK ...
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Common terms and phrases
ABē ACē 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