Elements of Geometry and TrigonometryA. S. Barnes and Company, 1838 - 269 σελίδες |
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Σελίδα 166
... cone ; the hypothenuse SB describes the convex surface of the cone . The point S is named the vertex of the cone , SA the axis or the altitude , and SB the side or the apothem . Every section HKFI , at right angles to the axis , is a ...
... cone ; the hypothenuse SB describes the convex surface of the cone . The point S is named the vertex of the cone , SA the axis or the altitude , and SB the side or the apothem . Every section HKFI , at right angles to the axis , is a ...
Σελίδα 167
... cone , any polygon ABCDE be inscribed , and from the vertices A , B , C , D , E , lines be drawn to S , the vertex of the cone , these lines may be regarded as the sides of a pyramid whose base is the polygon ABCDE and vertex S. The ...
... cone , any polygon ABCDE be inscribed , and from the vertices A , B , C , D , E , lines be drawn to S , the vertex of the cone , these lines may be regarded as the sides of a pyramid whose base is the polygon ABCDE and vertex S. The ...
Σελίδα 168
... form the bases of the zone or segment . Note . The Cylinder , the Cone , and the Sphere , are the three round bodies treated of in the Elements of Geometry . PROPOSITION I. THEOREM . The convex surface of a cylinder 168 GEOMETRY .
... form the bases of the zone or segment . Note . The Cylinder , the Cone , and the Sphere , are the three round bodies treated of in the Elements of Geometry . PROPOSITION I. THEOREM . The convex surface of a cylinder 168 GEOMETRY .
Σελίδα 171
... cone is equal to the circumference of its base , multiplied by half its side . Let the circle ABCD be the base of a cone , S the vertex , SO the altitude , and SA the side : then will its convex sur- face be equal to circ . OA × SA ...
... cone is equal to the circumference of its base , multiplied by half its side . Let the circle ABCD be the base of a cone , S the vertex , SO the altitude , and SA the side : then will its convex sur- face be equal to circ . OA × SA ...
Σελίδα 172
... cone . The con- vex surface of the frustum of the pyramid is equal to half the sum of the perimeters of its bases multiplied by the slant height fh ( Book VII . Prop . IV . Cor . ) . Odi I Let now the number of sides of the inscribed ...
... cone . The con- vex surface of the frustum of the pyramid is equal to half the sum of the perimeters of its bases multiplied by the slant height fh ( Book VII . Prop . IV . Cor . ) . Odi I Let now the number of sides of the inscribed ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Δημοφιλή αποσπάσματα
Σελίδα 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Σελίδα 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Σελίδα 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Σελίδα 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Σελίδα 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Σελίδα 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.