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" If from a point without a circle there be drawn two straight lines, one of which is perpendicular to a diameter, and the other cuts the circle; the square of the perpendicular is equal to the rectangle contained by the whole cutting line and the part... "
Elements of the Conic Sections - Page 20
by Robert Simson - 1809 - 177 pages
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Elements of the Conic Sections

Robert Simson - Conic sections - 1817 - 298 pages
...straight lines ordinately applied to that BOOK i. diameter, touches the parabola. This is """"Y"*"'^ manifest from cor. 1. PROP. XII. THEOR. If from a...of the diameter and the latus rectum of the axis. »#*i* ,' (N. .B. An ah$cLssa is the segment interSn,niLj q,. f. ol MJW* °. v;I , ; t; centra betwixt...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...drawn two straight lines, one of which is perpendicular to a diameter, and the other cuts the circle; the square of the perpendicular is equal to the rectangle contained by the whole cutting line and the part without the circle, together with .the rectangle contained by the...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...drawn two straight lines, one of which is perpendicular to a diameter, and the other cuts the circle ; the square of the perpendicular is equal to the rectangle contained by the whole cutting line and the part without the circle, together with the rectangle contained by the...
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A Geometrical Treatise on the Conic Sections: With an Appendix, Containing ...

William Wallace - Conic sections - 1837 - 248 pages
...in a parabola a perpendicular be drawn to any diameter, and also, from the same point, an ordinate to that diameter ; the square of the perpendicular is equal to the rectangle contained by the absciss of the diameter and the parameter of the axis. Let P be a point in a parabola, DK any diameter,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...parts. 8. If a perpendicular be drawn from the right angle of a right-angled triangle to the hypotenuse, the square of the perpendicular is equal to the rectangle contained by the segments of the hypotenuse. 9. If the base of a triangle be bisected, the sum of the squares of...
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The Cone and Its Sections Treated Geometrically

S. A. Renshaw - Conic sections - 1875 - 222 pages
...point in a Parabola a perpendicular be drawn to any diameter, and also from the same point an ordinate to that diameter, the square of the perpendicular is equal to the rectangle contained by the absciss of the diameter and the parameter of the axis. •36. — If CD any diameter of a Parabola...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...drawn two straight lines, one of which is perpendicular to a diameter, and the other cuts the circle : the square of the perpendicular is equal to the rectangle contained by the whole cutting line, and the part without the circle, together with the rectangle contained by the...
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