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angle asymptotes axis base bisects the angle called centre chord coincides common conic conjugate constant construction corresponding course curve cutting describe describe a circle determined diameter difference direction directrix distance divided draw drawn ellipse equal evidently externally figure fixed foci focus follows formed four given circle given Fig given lines given point given tangent harmonic Hence hyperbola intersection known length line joining locus mean proportional meeting method obviously opposite sides pair parabola parallel pass pencil perpendicular plane point of contact polar position Prob PROBLEM produced Proof Prop radius range ratio respectively right angle segments shew shewn sides similar Similarly solutions square straight line Take taken tangent third touch triangle vertex vertices
Page 11 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 26 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 358 - TRIGONOMETRY. By Rev. JB LOCK, MA, Senior Fellow, Assistant Tutor and Lecturer in Mathematics, of Gonville -and Caius College, Cambridge ; late Assistant-Master at Eton. Globe 8vo.
Page 358 - AND BESSEL'S FUNCTIONS. Crown 8vo. WILSON (JM)— ELEMENTARY GEOMETRY. Books I. to V. Containing the Subjects of Euclid's first Six Books. Following the Syllabus of the Geometrical Association. By JM WILSON, MA, Head Master of Clifton College. New Edition. Extra fcap. 8vo. 4?.
Page 287 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 125 - The problem therefore is reduced to finding the centre of a circle to touch externally two given circles (DG, EG) and pass through a given point (Q), which is always possible since the circles must cut each other and Q lie outside both, ie the problem reduces to Prob. 32. [Draw a common tangent EDM to the two circles meeting fP in M.
Page 358 - SOLID GEOMETRY AND CONIC SECTIONS. With Appendices on Transversals and Harmonic Division. For the Use of Schools. By JM WILSON, MA New Edition. Extra fcap. 8vo. 3-r. 6d. WILSON— GRADUATED EXERCISES IN PLANE TRIGONOMETRY.
Page xi - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 30 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Page 97 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.