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added base bisected centre chord circle circumference common completing the square construct describe describe a circle determine diameter difference distance divided double draw equal equation equiangular Eucl extracting the root extremities fall figure find the values formed former four gallons given angle given line given point given ratio greater half Hence inscribed intercepted Join less line joining lines be drawn lines drawn manner meet miles multiplying opposite side parallel parallelogram pass perpendicular produced progression quadrant quantity radius received rectangle rectangle contained remaining respectively right angles segments semicircle shillings sides similar sine straight line subtraction tang tangent third touch transposition triangle vertical angle whence whole yards
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 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 14 - 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.