Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 3
... extremities or limits . A Solid , as the term is used in Geometry , is a limited por- tion of space . After we acquire a clear notion of surfaces as boundaries of solids , we can easily conceive of surfaces apart from solids , and ...
... extremities or limits . A Solid , as the term is used in Geometry , is a limited por- tion of space . After we acquire a clear notion of surfaces as boundaries of solids , we can easily conceive of surfaces apart from solids , and ...
Σελίδα 5
... ( extremities ) of lines are points . The limits ( boundaries ) of surfaces are lines . The limits ( boundaries ) of solids are surfaces . 7. DEF . Extension is also called Magnitude . When reference is had to extent , lines , surfaces ...
... ( extremities ) of lines are points . The limits ( boundaries ) of surfaces are lines . The limits ( boundaries ) of solids are surfaces . 7. DEF . Extension is also called Magnitude . When reference is had to extent , lines , surfaces ...
Σελίδα 11
... extremities coincide . Two angles are equal , if they can be so placed that their vertices coincide in position and their sides in direction . In applying this test of equality , we assume that a line may be moved from one place to ...
... extremities coincide . Two angles are equal , if they can be so placed that their vertices coincide in position and their sides in direction . In applying this test of equality , we assume that a line may be moved from one place to ...
Σελίδα 17
... 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 between two points ) . Substitute and 2 CO for CO + OE , 2 CF for CFFE ; then we ...
... 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 between two points ) . Substitute and 2 CO for CO + OE , 2 CF for CFFE ; then we ...
Σελίδα 18
... ) . 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 . -
... ) . 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 . -
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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