Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 15
... right angle . 16. Two straight lines are parallel , when they lie in the same plane and can- not meet , how far ... six sides , a hexagon ; one of seven sides , a hepta- gon ; one of eight sides , an octagon ; one of ten sides , a ...
... right angle . 16. Two straight lines are parallel , when they lie in the same plane and can- not meet , how far ... six sides , a hexagon ; one of seven sides , a hepta- gon ; one of eight sides , an octagon ; one of ten sides , a ...
Page 46
... six right angles : hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right angles , or to g of one right angle . Cor . 3. The sum of the interior angles of a hexagon is equal to eight right angles ...
... six right angles : hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right angles , or to g of one right angle . Cor . 3. The sum of the interior angles of a hexagon is equal to eight right angles ...
Page 140
From the Works of A. M. Legendre Adrien Marie Legendre. two - thirds of a right angle . The three angles of the ... six times as a chord ; then will ABCDEF be the hexagon required ( P. IV . ) . Cor . 1. If the alternate vertices of ...
From the Works of A. M. Legendre Adrien Marie Legendre. two - thirds of a right angle . The three angles of the ... six times as a chord ; then will ABCDEF be the hexagon required ( P. IV . ) . Cor . 1. If the alternate vertices of ...
Page 250
... six right angles , and greater than two right angles . Let ABC be a spherical triangle , and DEF its polar triangle then will the sum of the angles A , B , and C , be less than six right angles and greater than two . For , any angle ...
... six right angles , and greater than two right angles . Let ABC be a spherical triangle , and DEF its polar triangle then will the sum of the angles A , B , and C , be less than six right angles and greater than two . For , any angle ...
Page 257
... six triangles exceeds the hemis phere , or four times T , by twice the triangle ABC . Wa shall therefore have , 2 ... right polyedral angle ; and if placed at the centre of a sphere , its faces will inter- cept a tri - rectangular triangle .
... six triangles exceeds the hemis phere , or four times T , by twice the triangle ABC . Wa shall therefore have , 2 ... right polyedral angle ; and if placed at the centre of a sphere , its faces will inter- cept a tri - rectangular triangle .
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following