# A graduated course of elementary problems in Practical Plane Geometry, etc

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### Contents

 DEFINITIONS 1 PART II 19 PART III 39
 QUADRILATERALS 63 PART V 84 PART VI 99

### Popular passages

Page 3 - A circle is a plane figure bounded by a curved line called the circumference, every point of which is equally distant from a point within called the center, Fig.
Page 2 - Two straight lines are said to be parallel, when being situated in the same plane, they cannot meet, how far soever, either way, both of them be produced.
Page 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 38 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 3 - An angle in a segment is any angle contained by two straight lines drawn from any point in the arc of the segment, to the extremities of the straight line which is the base of the segment.
Page 17 - To divide a given line into two parts, such that the greater part shall be a mean proportional between the whole line and the other part. Let AB be the given line.
Page 13 - From a given point between two indefinite right lines given in position, to draw a line which shall be terminated by the given lines, and bisected in the given point.
Page 26 - Describe a circle which shall touch a given circle, and each of two given straight lines. 55. Two points are given, one in each of two given circles ; describe a circle passing through both points and touching one of the circles. 56. Describe a circle touching a straight line in a given point, and also touching a given circle. When the line cuts the given circle, shew that your construction will enable you to obtain six circles touching the given circle and the given line, but not necessarily in...
Page 43 - ... with each other, (2) with the opposite angles : shew that the two triangles so formed, are equilateral triangles. IV. 60. Describe a right-angled triangle upon a given base, having given also the perpendicular from the right angle upon the hypotenuse. , 61. Given one side of a right-angled triangle, and the difference between the hypotenuse and the sum of the other two sides, to construct the triangle. 62. Construct an isosceles right-angled triangle, having given (1) the sum of the hypotenuse...
Page 23 - In a given circle to inscribe a triangle similar to a given triangle. 92, Through a given point to draw to a given circle a secant such that the part within the circle may be equal to a given line. 93, With a given radius to draw a circumference, 1st. Through two given points. 2d. Through a given point and tangent to a given line. 3d. Through a given point and tangent to a given circumference. 4th. Tangent to two given straight lines. 5th. Tangent to a given straight line and to a given...