Elements of Geometry and Trigonometry |
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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 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 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 B E D ces . The area of OBC will be A F ...
... 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 B E D ces . The area of OBC will be A F ...
Page 125
... perimeters be to each other as any two homologous sides . For , any two homo- logous sides , as AB H B and FG , are like parts D of the perimeters to A which they belong : K hence ( B. II . , P. IX . ) , E the perimeters of the polygons ...
... perimeters be to each other as any two homologous sides . For , any two homo- logous sides , as AB H B and FG , are like parts D of the perimeters to A which they belong : K hence ( B. II . , P. IX . ) , E the perimeters of the polygons ...
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 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 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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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...