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 16
... is one that has one right angle . The side opposite the right angle is called the hypothe- nuse . 2d . An OBLIQUE - ANGLED TRIANGLE is one whose angles are all oblique . If one angle of an oblique - angled triangle is 16 GEOMETRY .
... is one that has one right angle . The side opposite the right angle is called the hypothe- nuse . 2d . An OBLIQUE - ANGLED TRIANGLE is one whose angles are all oblique . If one angle of an oblique - angled triangle is 16 GEOMETRY .
Page 17
... opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2d . A ...
... opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2d . A ...
Page 21
... OPPOSITE , or VERTICAL ANGLES , are those which lie on opposite sides of both lines ; thus , ACE and DCB , or ACD and ECB , are opposite angles . From the proposition just demonstrated , the sum of any two adjacent angles is equal to ...
... OPPOSITE , or VERTICAL ANGLES , are those which lie on opposite sides of both lines ; thus , ACE and DCB , or ACD and ECB , are opposite angles . From the proposition just demonstrated , the sum of any two adjacent angles is equal to ...
Page 22
... opposite angle is also a right angle . B Cor . 2. If one line DE , is per- pendicular to another AB , then is the second line AB perpendicular to the first DE . For , the angles DCA and DCB are right angles , by definition ( D. 12 ) ...
... opposite angle is also a right angle . B Cor . 2. If one line DE , is per- pendicular to another AB , then is the second line AB perpendicular to the first DE . For , the angles DCA and DCB are right angles , by definition ( D. 12 ) ...
Page 30
... opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then the angle ...
... opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then the angle ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence