Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 8
... common . Conversely Two straight lines lying in the same plane which do not meet have the same direction ; for if they had different directions they would meet , which is contrary to the hypothesis that they do not meet . Two straight ...
... common . Conversely Two straight lines lying in the same plane which do not meet have the same direction ; for if they had different directions they would meet , which is contrary to the hypothesis that they do not meet . Two straight ...
Σελίδα 9
... common vertex and a common side between them . Thus the angles CDE and CDF are adjacent angles . E D C B F 25. DEF . A Right Angle is an angle included between two straight lines which meet each other so that the two adjacent angles ...
... common vertex and a common side between them . Thus the angles CDE and CDF are adjacent angles . E D C B F 25. DEF . A Right Angle is an angle included between two straight lines which meet each other so that the two adjacent angles ...
Σελίδα 15
... common ≤ O C A. Then = LOCB LACP . In like manner we may prove = LACO Z PCB . Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four ...
... common ≤ O C A. Then = LOCB LACP . In like manner we may prove = LACO Z PCB . Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four ...
Σελίδα 16
... common ZOC A. Then = ZOCF ZOC B. .. C B and C F coincide , and cannot form two lines as rep- resented in the figure . .. A C and C B are in the same straight line . Q. E. D. PROPOSITION III . THEOREM . 52. A perpendicular measures the ...
... common ZOC A. Then = ZOCF ZOC B. .. C B and C F coincide , and cannot form two lines as rep- resented in the figure . .. A C and C B are in the same straight line . Q. E. D. PROPOSITION III . THEOREM . 52. A perpendicular measures the ...
Σελίδα 23
... common property . Thus , the perpendicular erected at the middle of a straight line is the locus of all points equally distant from the extremi- ties of that straight line . 60. SCHOLIUM . Since two points determine the position of a ...
... common property . Thus , the perpendicular erected at the middle of a straight line is the locus of all points equally distant from the extremi- ties of that straight line . 60. SCHOLIUM . Since two points determine the position of a ...
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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