Printed by J. Smith, Printer to the University; F. C. & J. RIVINGTON, LONDON. 1819 Erch Library Randi siland state college 3-1-1941 ADVERTISEMENT. (3-12-4i SL The following pages contain a collection of Problems, which are for the most part an easy application of the Elements of Euclid. They are arranged in what seemed to be the most natural order : The 1st section comprises such as contain the properties of straight lines and angles; the 2nd straight lines and circles: the 3rd straight lines and triangles ; and the 4th parallelograms, squares and polygons. The 5th section contains those which require lines to be drawn in certain directions, but which involve properties of rectangles or squares, or such others as were excluded from the three first. The 6th comprises those by which figures are described, and also inscribed in or circumscribed about each other. The 7th comprehends such as contain the properties of triangles described in or about circles; the 8th those which contain the squares or rectangles of lines connected with circles; and the 9th the construction of triangles. To these is added an Appendix, intended to contain so much of the Elements of Plane Trigonometry, as is necessary for understanding those parts of Natural Philosophy which are the common subjects of Lectures in the University. The Reader who wishes for farther information, From this performance the only credit expected is To the Syndics of the University Press, who from 1. From a given point to draw the shortest line possible to a 2. If a perpendicular be drawn bisecting a given straight line, any point in this perpendicular is at equal distances, and any point without the perpendicular is at unequal distances, from the extre- 3. Through a given point, to draw a straight line which shall make equal angles with two straight lines given in position. 4. From two given points, to draw two equal straight lines, which shall meet in the same point of a line given in position. 5. From two given points on the same side of a line given in position, to draw two lines which shall meet in that line, and make 6. From two given points on the same side of a line given in position, to draw two lines which shall meet in a point in this line, so that their sum shall be less than the sum of any two lines drawn from the same points and terminated at any other point in the same 7. Of all straight lines which can be drawn from a given point to an indefinite straight line, that which is nearer to the perpendi- cular is less than the more remote. And from the same point there cannot be drawn more than two straight lines equal to each other, viz. one on each side of the perpendicular. 8. Through a given point, to draw a straight line so that the parts of it intercepted between that point and perpendiculars drawn a |