Problems and ExamplesDeighton, Bell and Company, 1862 - 141 pages |
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Page 59
... described , the one within , and the other about , the same circle ; what will be the number of sides when the space in- cluded between the two polygonal boundaries is of the interior polygon ? 9. Compare the areas of decagons inscribed ...
... described , the one within , and the other about , the same circle ; what will be the number of sides when the space in- cluded between the two polygonal boundaries is of the interior polygon ? 9. Compare the areas of decagons inscribed ...
Page 63
... described on its latus rectum as diameter ; if S be the focus of the parabola , SQ , SP make equal angles with the latus rectum . 4. If SPG be an equilateral triangle , SP is equal to the latus rectum . 5. If the ordinate at P bisects ...
... described on its latus rectum as diameter ; if S be the focus of the parabola , SQ , SP make equal angles with the latus rectum . 4. If SPG be an equilateral triangle , SP is equal to the latus rectum . 5. If the ordinate at P bisects ...
Page 65
... described on SP as diameter touches the tangent at the vertex . 23. The circle described on a focal chord as diameter touches the directrix . 24. From a point T two tangents TP , TQ are drawn to a parabola , shew that the angles PST ...
... described on SP as diameter touches the tangent at the vertex . 23. The circle described on a focal chord as diameter touches the directrix . 24. From a point T two tangents TP , TQ are drawn to a parabola , shew that the angles PST ...
Page 66
... the major axis of an ellipse , cut the circles described on SP , HP , as diameters in K , L respectively ; shew that KS , LH , BC , pro- duced , intersect in a point . 14. If from H a straight line be drawn parallel 66 CONIC SECTIONS.`
... the major axis of an ellipse , cut the circles described on SP , HP , as diameters in K , L respectively ; shew that KS , LH , BC , pro- duced , intersect in a point . 14. If from H a straight line be drawn parallel 66 CONIC SECTIONS.`
Page 67
... described , prove that the chord which passes through the focus and is parallel to either tangent is equal to the axis minor . 21. The circles described on SP , HP , as diameters , touch the auxiliary circle . 22. If the normal at P ...
... described , prove that the chord which passes through the focus and is parallel to either tangent is equal to the axis minor . 21. The circles described on SP , HP , as diameters , touch the auxiliary circle . 22. If the normal at P ...
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2nd Edition 3rd Edition 4th Edition acceleration tending arithmetical arithmetical mean arithmetical series bisected centre of gravity chord circle concave cone Conic Sections conjugate convex lens Crown 8vo cylinder determine diameter directrix distance drawn Elementary ellipse English equal equation extremity F. A. Paley Fcap feet Find the number find the value fluid focal length foci focus geometrical progression given point given weight harmonic mean horizontal inches incident inclined plane inscribed intersection Latin latus rectum locus luminous point middle point mirror Multiply parabola parallel particle describes passing perpendicular position Post 8vo pressure prism projected prove pully quantity radii radius ratio reflected refracting respectively shew sides sin² specific gravity sphere spherical square straight line string subtends surface tangent tower velocity vertex vertical
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