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 ABC circles cut circumference completing the square construct the triangle cosecant cosine describe a circle divided equation equiangular Eucl extracting the root extremities find the values given angle given circle given in position given line given point given ratio given square given straight line given triangle inscribed intercepted isosceles triangle Join AE Join BD least common multiple Let ABC let fall line given line joining lines be drawn lines drawn mean proportional meeting opposite sides parallel to AC parallelogram pendicular perpendicular point of intersection produced quadrant radius rectangle contained right angles right-angled triangle segments semicircle shewn sine squares of AC tang tangent touches the circle transposition trapezium triangle ABC triangle required vertex vertical angle whence
Page iii - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Page xiii - 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 321 - 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 152 - 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 206 - 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 117 - 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 20 - 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 293 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 299 - 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.