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
... sides of the polygon . The broken line , made up of all the sides of the polygon , is called the perimeter of the polygon . The angles formed by the sides , are called angles of the polygon . 19. Polygons are classified according to the ...
... sides of the polygon . The broken line , made up of all the sides of the polygon , is called the perimeter of the polygon . The angles formed by the sides , are called angles of the polygon . 19. Polygons are classified according to the ...
Page 16
... sides equal . 2d . An ISOSCELES TRIANGLE is one which has two of its sides equal . When all of the sides are equal , the triangle is EQUILATERAL . 1 A When classified with reference to their angles , there are are two classes : right ...
... sides equal . 2d . An ISOSCELES TRIANGLE is one which has two of its sides equal . When all of the sides are equal , the triangle is EQUILATERAL . 1 A When classified with reference to their angles , there are are two classes : right ...
Page 17
... sides . There are then two classes : the first class embraces those which have no two sides par- allel ; the second class embraces those which have two sides parallel . Quadrilaterals of the first class , are called trapeziums ...
... sides . There are then two classes : the first class embraces those which have no two sides par- allel ; the second class embraces those which have two sides parallel . Quadrilaterals of the first class , are called trapeziums ...
Page 21
... side of one line , and on opposite sides of the other ; thus , ACE and ECB , or ACE and ACD , are adjacent angles . are A D B 2o . OPPOSITE , or VERTICAL ANGLES , are those which lie on opposite sides of both lines ; thus , ACE and DCB ...
... side of one line , and on opposite sides of the other ; thus , ACE and ECB , or ACE and ACD , are adjacent angles . are A D B 2o . OPPOSITE , or VERTICAL ANGLES , are those which lie on opposite sides of both lines ; thus , ACE and DCB ...
Page 25
... side EF : then AA CE will the triangles be equal in all their parts . For , let ABC be applied to DEF in such a manner that the angle B shall coincide with the angle E , the side BC taking the direction EF , and the side BA BOOK I. 25.
... side EF : then AA CE will the triangles be equal in all their parts . For , let ABC be applied to DEF in such a manner that the angle B shall coincide with the angle E , the side BC taking the direction EF , and the side BA BOOK I. 25.
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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