Constructive Geometry of Plane Curves: With Numerous Examples
Macmillan and Company, 1885 - Conic sections - 374 pages
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Common terms and phrases
angle asymptotes axis base bisects the angle called centre circle coincides cone conic conjugate diameters constant construction corresponding course curve cutting describe determined diameter direction directrix distance divided draw drawn ellipse equal evidently extremities figure Find fixed foci focus focus F follows formed four given Fig given lines given point given tangent harmonic Hence intersection involution known length locus major axis mean proportional meeting method opposite sides pair parabola parallel pass pencil perpendicular plane point of contact polar pole position Prob PROBLEM produced Proof Prop radius range ratio reduces respectively right angle second focus segments shew shewn sides similar Similarly solutions straight line Take taken tangent touch triangle vertex vertices
Page 28 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 28 - 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 303 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 32 - 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 99 - 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.
Page 13 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 40 - Upon a given straight line to describe a segment of a circle which shall contain a given angle. Let AB be the given straight line.