Geometrical conic sections |
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Page 4
... example , it be required to increase the acute angle ACB subtended by AB the line of intersection to a right angle ; on AB de- scribe the semicircle AcB , and draw CD perpendicular to AB cutting the semicircle in c . A D B Then let the ...
... example , it be required to increase the acute angle ACB subtended by AB the line of intersection to a right angle ; on AB de- scribe the semicircle AcB , and draw CD perpendicular to AB cutting the semicircle in c . A D B Then let the ...
Page 6
... EXAMPLES . 1. If the inclination of two planes be the third of two right angles , and a line of 4 yards in one of the planes be inclined to the line of intersection at half the above angle , find the area of the square on the projected ...
... EXAMPLES . 1. If the inclination of two planes be the third of two right angles , and a line of 4 yards in one of the planes be inclined to the line of intersection at half the above angle , find the area of the square on the projected ...
Page 18
... EXAMPLES . 1. If an ellipse be projected on a plane intersecting its plane in BC , and having with its plane the maximum ratio of diminution AC : BC , it will project into a circle on BC as diameter . 2. If from any point P of an ...
... EXAMPLES . 1. If an ellipse be projected on a plane intersecting its plane in BC , and having with its plane the maximum ratio of diminution AC : BC , it will project into a circle on BC as diameter . 2. If from any point P of an ...
Page 19
... any parallelogram formed by tangents at the extremities of conjugate diameters coincide with conjugate diameters . 14. The angular points of these parallelograms lie on one 2--2 EXAMPLES . 19 Conjugate diameters Supplemental chords.
... any parallelogram formed by tangents at the extremities of conjugate diameters coincide with conjugate diameters . 14. The angular points of these parallelograms lie on one 2--2 EXAMPLES . 19 Conjugate diameters Supplemental chords.
Page 20
... - meter . 22. If from the extremity of each of any two semi - diameters ordinates be drawn to the other , the two triangles so formed will be equal in area . 23. Or if tangents be drawn from the extremity of 20 EXAMPLES .
... - meter . 22. If from the extremity of each of any two semi - diameters ordinates be drawn to the other , the two triangles so formed will be equal in area . 23. Or if tangents be drawn from the extremity of 20 EXAMPLES .
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Common terms and phrases
AC² Algebra ARITHMETIC asymptotes auxiliary circle axis major BC² BEGINNERS bisects the angle Cambridge CD² centre Chap Christ's College cloth Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo cutting plane directrix draw drawn parallel ELEMENTARY TREATISE ellipse English equal angles equally inclined Examination Papers Extra fcap extremities fcap focal chord foci focus GEOMETRY given Grammar Greek Hence intersect John's College Latin latus rectum line joining manual Mathematical meet the curve method Metric System middle point MIXED MATHEMATICS parabola parallelogram perpendicular point of contact produced meet Professor projection proposition prove quadrilateral rectangle rectangular hyperbola render revised right angles Schools Second Edition semi-diameters shew sphere straight line subtend tangent touch transverse axis triangles Trigonometry University of Cambridge vertex
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