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 - Geometry - 438 pages
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ABCD base centre chord circle circumference common describe 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 greater half Hence inscribed intercepted Join Join AE less Let ABC let fall line joining lines be drawn lines drawn manner mean proportional meet opposite sides parallel parallel to BC 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
Page 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.
Page 317 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 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...
Page 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.
Page 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.
Page 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.
Page 289 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 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.
Page 88 - If from any point in the base of an isosceles triangle perpendiculars...