Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/183

 are alo known; and therefore, for brevity's ake, I omit any farther demontration of them.

To tranform figures into other figures of the ame kind. Pl. 10. Fig. 5.

Suppoe that any figure figure, HGI is to be tranformed. Draw, at pleaure, two parallel lines AO, BL, cutting any third line AB given by psition, in A and B, and from any point G of the figure, draw out any right line GD, parallel to OA, till it meet the right line AB. Then from any given point O in the line OA, draw to the point D the right line OD, meeting BL in d, and from the point of concoure raie the right line dg containing any given angle with the right line BL, and having uch ratio to Od, as DG has to OD; and g will be the point in the new figure hgi, correponding to the point G. And in like manner the everal points of the firt figure will give as many correpondent points of the new figure. If we therefore conceive the point G to be carried along by a continual motion through all the points of the firt figure, the point g will be likewie carried along by a continual motion through all the points of the new figure, and decribe the ame. For ditinction's ake, let us call DG the firt ordinate, dg the new ordinate, AD the firt abcia, ad the new abcia; O the pole, OD the abcinding radius, OA the firt ordinate radius, and Oa (by which the parallelogram