Wherefore the points A, B, and C, have to one another like situation with the points E, F, and G, or are placed alike; which was to be proved. FIGURE _is quantity, determined by the situation or placing of all its extreme points_. Now I call those points extreme, which are contiguous to the place which is without the figure. In lines therefore and superficies, all points may be called extreme; but in solids only those which are in the superficies that includes them. _Like figures_ are those, whose extreme points in one of them are all placed like all the extreme points in the other; for such figures differ in nothing but magnitude. And like figures are _alike placed_, when in both of them the homologal strait lines, that is, the strait lines which connect the points which answer one another, are parallel, and have their proportional sides inclined the same way. And seeing every strait line is like every other strait line, and every plane like every other plane, when nothing but planeness is considered; if the lines, which include planes, or the superficies, which include solids, have their proportions known, it will not be hard to know whether any figure be like or unlike to another propounded figure. And thus much concerning the _first grounds of philosophy_. The next place belongs to _geometry_; in which the quantities of figures are sought out from the proportions of lines and angles. Wherefore it is necessary for him, that would study geometry, to know first what is the nature of quantity, proportion, angle and figure. Having therefore explained these in the three last chapters, I thought fit to add them to this part; and so pass to the next. ------------------------------------------------------------------------ [Illustration: _Vol. 1. Lat. & Eng._ C. XIV. _Fig. 1-10_ ] ------------------------------------------------------------------------ PART III PROPORTIONS OF MOTIONS AND MAGNITUDES. ------- CHAPTER XV. OF THE NATURE, PROPERTIES, AND DIVERS CONSIDERATIONS OF MOTION AND ENDEAVOUR. 1.. Repetition of some principles of the doctrine of motion formerly set down.—2. Other principles added to them.—3. Certain theorems concerning the nature of motion.—4. Divers considerations of motion.—5. The way by which the first endeavour of bodies moved tendeth.—6. In motion which is made by concourse, one of the movents ceasing, the endeavour is made by the way by which the rest tend.—7. All endeavour is propagated in infinitum.—8. How much greater the velocity or magnitude is of a movent, so much the greater is the efficacy thereof upon any other body in its way. [Sidenote: Repetition of some principles of the doctrine of motion formerly set down.]