07 Dec




















from the points in No. 2 into the HP, and their intersection by those drawn through C, 2, B, 4, D, No. 1, will give points through which the ellipse No. 4 which is the plan of the circular plate is to be drawn. It is here seen that the form assumed by a circular plate or a circle entirely depends upon the direction in which itr is viewed, alternating, as it may be made to do, from that of being a true circle or any form of ellipse to that of a perfectly straight line. The student will note what may appear to be a discrepancy in the lettering of the last-obtained projection of the original object, No. 1, but he will find that it is correct when he remembers that the view of it given in No. 2 is that of No. 1 looked at in the direction of the arrow -jc t and therefore turned through an angle of 90. If a disc, 96 FIRST PRINCIPLES OF similar in size and similarly figured, be cut out in card and laid upon No. 1 with a pin through the centres, it will be found, on turning the card disc through an angle of 90, that all the points on it will have shifted through that angle, bringing A and B where C and D now are, thus showing the projection No. 4 to be correct. 44. Before leaving this part of our subject, as elliptical figures will be very frequently required, we here give a simple method of drawing such a figure, which is sufficiently near the true form for all the practical purposes of the draughtsman, and which obviates the necessity of finding all the points in the curve. Premising that the student understands that an ellipse differs from the circle in having its diameters of unequal length, and that the sum of the distance of any point in its curved-bounding line, from two fixed points called its

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