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 62
... when its circumference touches each of the sides of the polygon . ооо о POSTULATE . A circumference can be described from any point as a rentre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
... when its circumference touches each of the sides of the polygon . ооо о POSTULATE . A circumference can be described from any point as a rentre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
Page 68
... described from O as a centre , with a radius equal to the distance from O to A , it will pass through A , B , and C. Again , O is the only point which is equally distant from A , B , and C : for , DE contains all of the points which are ...
... described from O as a centre , with a radius equal to the distance from O to A , it will pass through A , B , and C. Again , O is the only point which is equally distant from A , B , and C : for , DE contains all of the points which are ...
Page 79
... described from the vertex of any angle , as a centre , and with a fixed radius , the arc intercepted between the sides of the angle may be taken as the measure of the angle . In Geometry , the right angle , which is measured by a ...
... described from the vertex of any angle , as a centre , and with a fixed radius , the arc intercepted between the sides of the angle may be taken as the measure of the angle . In Geometry , the right angle , which is measured by a ...
Page 98
... described on the linear unit as a side . PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes : then the ...
... described on the linear unit as a side . PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes : then the ...
Page 105
... described on the sum of two lines is equal to the sum of the squares described on the lines , increased by twice the rectangle of the lines . AC Let AB and BC be two lines , and BOOK IV . 105.
... described on the sum of two lines is equal to the sum of the squares described on the lines , increased by twice the rectangle of the lines . AC Let AB and BC be two lines , and BOOK IV . 105.
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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