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 vii
... Triangles , 80-83 Quadrantal Triangles , 84 Formulas for Oblique - angled Triangles ,. Solution of Oblique - angled Triangles , 85-92 92-104 MENSURATION . Mensuration Defined , 105 The Area of a Parallelogram , .. 106 The Area of a Triangle ...
... Triangles , 80-83 Quadrantal Triangles , 84 Formulas for Oblique - angled Triangles ,. Solution of Oblique - angled Triangles , 85-92 92-104 MENSURATION . Mensuration Defined , 105 The Area of a Parallelogram , .. 106 The Area of a Triangle ...
Page 16
... TRIANGLE is one which has no two of its 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 ...
... TRIANGLE is one which has no two of its 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 ...
Page 17
... triangle is obtuse , the triangle is said to be OBTUSE - ANGLED . If all of the angles are acute , the triangle is said to be ACUTE - ANGLED . 26. Quadrilaterals are classified with reference to the rel ative directions of their sides ...
... triangle is obtuse , the triangle is said to be OBTUSE - ANGLED . If all of the angles are acute , the triangle is said to be ACUTE - ANGLED . 26. Quadrilaterals are classified with reference to the rel ative directions of their sides ...
Page 25
... triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I. , D. 14 ) ; which was to be proved . PROPOSITION VI . THEOREM . If two triangles have two angles and the included side of the one equal to ...
... triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I. , D. 14 ) ; which was to be proved . PROPOSITION VI . THEOREM . If two triangles have two angles and the included side of the one equal to ...
Page 26
... triangles coincide throughout , therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . 1 PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle ...
... triangles coincide throughout , therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . 1 PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle ...
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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