128. To draw a triangle having its vertices on three given lines and its sides passing through three given points 129. Given two points A and B and a line L; given also two lines. Sm, Sn and a point 0; to find on L a point Q such that if 133. To determine the section of a cylinder by a given plane 134. To determine the sub-contrary section of an oblique cylinder 135. To determine the section of an oblique cylinder by any plane 136. To determine the sub-contrary section of an oblique cone. 137. To determine the section of an oblique cone by any plane To describe an epi-trochoid, the rolling and directing circles and 143. To describe a hypo-trochoid, the rolling and directing circles and the position of the tracing point being given 144. To describe the companion to the cycloid, the generating circle ib. ib. 150. Pole and two points on the curve being given ib. 167. To determine the point on a spherical mirror at which an CONSTRUCTIVE TREATISE ON PLANE CURVES. CHAPTER I. INTRODUCTORY. THE Instruments required for the accurate representation on paper of almost all known curves are few in number and of simple construction. For accurate work however it is essential they should be of good quality, and be kept in good order. A limited number of good instruments is in every way to be preferred to a larger number of inferior articles, and where economy is an object therefore, in preference to the usual large and small single jointed compasses found in cheap boxes of mathematical instruments the author strongly recommends the purchase of one medium size, double jointed pair of compasses with pen and pencil points, which can be used for both large and small circles if care be taken to adjust the legs so that the lower portions of both may be perpendicular to the paper. This is a sine quâ non for good work and it is of course impossible with the ordinary single jointed instruments. In addition to the above a pair of dividers, a drawing pen for inking in straight lines, a protractor which should also contain a diagonal scale of half-inches, a couple of set squares (45o and 60°), pencil and paper may be considered a complete equipment for the work of the following pages. More may be learnt as to the proper way of handling these tools by ten minutes' observation of a practised draughtsman than from pages of explanation, but failing the opportunity of this practical instruction, the following hints may be useful. |