Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα iii
... distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines M306198 of the figures are full lines , the lines employed QH453.
... distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines M306198 of the figures are full lines , the lines employed QH453.
Σελίδα 12
... fall on B ' , then if the side BA fall on B'A ' , the angle ABC equals the angle A'B'C ' ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A'B ' C " ; but if the side BA fall in the ...
... fall on B ' , then if the side BA fall on B'A ' , the angle ABC equals the angle A'B'C ' ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A'B ' C " ; but if the side BA fall in the ...
Σελίδα 17
... fall upon the point E , ( since OC = 0E by cons . ) . and But ( having their extremities in the same points ) . .. line CF : = line FE , ..CFFE = 2 C F , CO + OE 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance ...
... fall upon the point E , ( since OC = 0E by cons . ) . and But ( having their extremities in the same points ) . .. line CF : = line FE , ..CFFE = 2 C F , CO + OE 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance ...
Σελίδα 18
... being a rt . 4 ) . Point A will fall upon point 0 , ( FA FO , by hyp . ) . ... line CA = line CO , ( their extremities being the same points ) . $ 13 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 BOOK I. GEOMETRY . -
... being a rt . 4 ) . Point A will fall upon point 0 , ( FA FO , by hyp . ) . ... line CA = line CO , ( their extremities being the same points ) . $ 13 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 BOOK I. GEOMETRY . -
Σελίδα 21
... fall upon the point K ; otherwise one of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . $ 55 ..FE FK . Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the ...
... fall upon the point K ; otherwise one of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . $ 55 ..FE FK . Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the ...
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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