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 49
... figure is a parallelogram ; which was to be proved . Cor . If two points be taken at equal distances from a given straight line , and on the same side of it , the straight . line joining them will be parallel to the given line ...
... figure is a parallelogram ; which was to be proved . Cor . If two points be taken at equal distances from a given straight line , and on the same side of it , the straight . line joining them will be parallel to the given line ...
Page 59
... figure , bounded by a curved line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir cumference . 2. A RADIUS is a straight line drawn from the centre to any point of ...
... figure , bounded by a curved line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir cumference . 2. A RADIUS is a straight line drawn from the centre to any point of ...
Page 89
... figure is a parallelogram ( D. 28 ) ; it is also formed with the given sides and given angle . PROBLEM XIII . To find the centre of a given circumference . Take any three points A , B , and C , on the circumference or arc , and join ...
... figure is a parallelogram ( D. 28 ) ; it is also formed with the given sides and given angle . PROBLEM XIII . To find the centre of a given circumference . Take any three points A , B , and C , on the circumference or arc , and join ...
Page 93
... distance is measured , is called the vertex of the triangle , and the opposite side , is called the base of the triangle . 5. The ALTITUDE OF A PARALLELOGRAM , is the perpen BOOK IV Proportions of Figures-Measurement of Areas,
... distance is measured , is called the vertex of the triangle , and the opposite side , is called the base of the triangle . 5. The ALTITUDE OF A PARALLELOGRAM , is the perpen BOOK IV Proportions of Figures-Measurement of Areas,
Page 103
... figure ABILKE is equal to the sum of the squares described on AB and BC . The part CBIG is equal to the rect- angle of AB and BC ; the part DGLK is also equal to the rect- angle of AB and BC . If from the whole figure ABILKE ...
... figure ABILKE is equal to the sum of the squares described on AB and BC . The part CBIG is equal to the rect- angle of AB and BC ; the part DGLK is also equal to the rect- angle of AB and BC . If from the whole figure ABILKE ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence