Elements of Plane and Solid GeometryGinn, Heath, 1877 - 398 σελίδες |
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Σελίδα viii
... SPHERE . SECTIONS AND TANGENTS • DISTANCES ON THE SURFACE OF THE SPHERE SPHERICAL ANGLES . • SPHERICAL POLYGONS AND PYRAMIDS . 349 356 363 365 COMPARISON AND MEASUREMENT OF SPHERICAL SURFACES 383 • VOLUME OF THE SPHERE 396 ELEMENTS OF ...
... SPHERE . SECTIONS AND TANGENTS • DISTANCES ON THE SURFACE OF THE SPHERE SPHERICAL ANGLES . • SPHERICAL POLYGONS AND PYRAMIDS . 349 356 363 365 COMPARISON AND MEASUREMENT OF SPHERICAL SURFACES 383 • VOLUME OF THE SPHERE 396 ELEMENTS OF ...
Σελίδα 348
... be that of a cone of revo- lution , and R and r be the radii of its bases , we have B and b = r2 , and √BXb = Rr . .. V = } π H ( R2 + y2 + R r ) . П = TR2 , BOOK VIII . THE SPHERE . ON SECTIONS AND TANGENTS 348 BOOK VII . GEOMETRY . -
... be that of a cone of revo- lution , and R and r be the radii of its bases , we have B and b = r2 , and √BXb = Rr . .. V = } π H ( R2 + y2 + R r ) . П = TR2 , BOOK VIII . THE SPHERE . ON SECTIONS AND TANGENTS 348 BOOK VII . GEOMETRY . -
Σελίδα 350
George Albert Wentworth. PROPOSITION I. THEOREM . 678. Every section of a sphere made by a plane is a circle . A Let the section ABC be a plane section of a sphere whose centre is 0 . We are to prove section ABC a circle . From the ...
George Albert Wentworth. PROPOSITION I. THEOREM . 678. Every section of a sphere made by a plane is a circle . A Let the section ABC be a plane section of a sphere whose centre is 0 . We are to prove section ABC a circle . From the ...
Σελίδα 351
... sphere is a section of the sphere made by a plane not passing through the centre . 683. DEF . An Axis of a circle of a sphere is the diameter of the sphere perpendicular to the circle ; and the extremities of the axis are the Poles of ...
... sphere is a section of the sphere made by a plane not passing through the centre . 683. DEF . An Axis of a circle of a sphere is the diameter of the sphere perpendicular to the circle ; and the extremities of the axis are the Poles of ...
Σελίδα 353
... sphere . It is required to find its diameter . From any point P of the given surface , with any opening of the ... sphere . For , if we bisect the sphere through P and B , and in the section draw the diameter P P and chord BP ' , the ...
... sphere . It is required to find its diameter . From any point P of the given surface , with any opening of the ... sphere . For , if we bisect the sphere through P and B , and in the section draw the diameter P P and chord BP ' , the ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC ABCD altitude apothem arcs A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 188 - Two triangles having 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.
Σελίδα 347 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 134 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 221 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Σελίδα 217 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Σελίδα 44 - Two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other. In the triangles ABC and A'B'C', let AB be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'.
Σελίδα 186 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 346 - A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases, of the frustum. For, let ABCDE-F be a frustum of any pyramid S-ABCDE. Let S'-A'B'C' be a triangular pyramid, having the same altitude as the pyramid S-ABCDE, and a base A'B'C' equivalent to the base ABCDE, and in the same plane with it.
Σελίδα 95 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.