Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved: To which is Added an Appendix Containing the Elements of Plane Trigonometry ...
J. Smith, 1821 - 438 σελίδες
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ABCD base centre chord circumference common describe a circle determine diameter difference distance divided double draw draw a line equal equiangular Eucl extremities figure formed given angle given circle given in position given line given point given ratio given square greater half Hence inscribed intercepted Join Join AE less Let ABC let fall line joining line required lines be drawn lines drawn manner mean proportional meet opposite side parallel parallel to AC parallelogram pass perpendicular point of intersection produced quadrant radius rectangle rectangle contained right angles right-angled triangle segments semicircle shewn similar square straight line tangent terminated trapezium triangle triangle ABC vertex whence
Σελίδα ix - 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.
Σελίδα 148 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other...
Σελίδα 202 - FC are equal to one another : wherefore the circle described from the centre F, at the distance of one of them, will pass through the extremities of the other two, and be described about the triangle ABC.
Σελίδα 113 - If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram. Ex. 2. The two triangles, formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides, are together half of the parallelogram.
Σελίδα 12 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Σελίδα 289 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Σελίδα 295 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.