Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 244
... that of Q ' . Q. E. D. 415. COROLLARY . The circumference of a circle is less than the perimeter of any other plane figure of equal area . ON SYMMETRY . SUPPLEMENTARY . 416. Two points are Symmetrical 244 GEOMETRY . BOOK V.
... that of Q ' . Q. E. D. 415. COROLLARY . The circumference of a circle is less than the perimeter of any other plane figure of equal area . ON SYMMETRY . SUPPLEMENTARY . 416. Two points are Symmetrical 244 GEOMETRY . BOOK V.
Σελίδα 245
... symmetrical with re- P spect to a centre , if the centre bisect the straight line terminated by these points . Thus , P , P are symmetrical with respect to C , if C bisect the straight line PP ' . PI 419. The distance of either of the ...
... symmetrical with re- P spect to a centre , if the centre bisect the straight line terminated by these points . Thus , P , P are symmetrical with respect to C , if C bisect the straight line PP ' . PI 419. The distance of either of the ...
Σελίδα 246
... symmetrical point in the other . A B N A B ' B C X X M B Α ' A ' Fig . 1 . Fig . 2 . 1 / Fig . 3 . Thus , the lines A B and A ' B ' are symmetrical with respect to the centre C ( Fig . 1 ) , to the axis XX ' ( Fig . 2 ) , to the plane ...
... symmetrical point in the other . A B N A B ' B C X X M B Α ' A ' Fig . 1 . Fig . 2 . 1 / Fig . 3 . Thus , the lines A B and A ' B ' are symmetrical with respect to the centre C ( Fig . 1 ) , to the axis XX ' ( Fig . 2 ) , to the plane ...
Σελίδα 247
... symmetrical figure , either when it can be divided by an axis , or plane , into two figures symmetrical with respect to that axis or plane ; or , when it has a centre such that every straight line drawn through it cuts the perimeter of ...
... symmetrical figure , either when it can be divided by an axis , or plane , into two figures symmetrical with respect to that axis or plane ; or , when it has a centre such that every straight line drawn through it cuts the perimeter of ...
Σελίδα 248
... symmetrical point of H. But H is any point in AB ; .. every point in AB has its symmetrical point in A'B ' . .. A B and A ' B ' are symmetrical with respect to C as a centre of symmetry . Q. E. D. 426. COROLLARY . If the extremities of ...
... symmetrical point of H. But H is any point in AB ; .. every point in AB has its symmetrical point in A'B ' . .. A B and A ' B ' are symmetrical with respect to C as a centre of symmetry . Q. E. D. 426. COROLLARY . If the extremities of ...
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AABC ABCD altitude apothem arc A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide cone of revolution 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 pass perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section S-ABC 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