CHAP. XXXIX. (Book 39)
Of several Superficial Figures, and how they are to be measured. (Book 39)
TO speak of all sorts of Figures will be far beyond my intentions, there being so very many irregular Figures which have many un∣equal sides and angles; but they may all be brought into parts of some of the Figures following, and Measured like them; I shall shew you one Useful Prob. especially to make your Ovals by, whether they be made from two Centres, or four; and then I shall touch at some Su∣perficial Figures. (See Fig. 30.)
Suppose three pricks or points given (so they be not in a strait line) to find a Centre to bring them into a Circle. This may be done seve∣ral ways, viz. either by Circles, or by raising Perpendiculars; as if the points at A. B. C. were to be brought into a Circle: Draw a line from A. to B. and in the middle of that line raise a Perpendicular, as the line D. E. which you may soon do; for if you open your Com∣passes to any convenient distance, and set one point in B. draw the Arch 1. and 2. then setting one point in 4. draw 3. and 4. where these cross draw the line E. D. Do the same with the points B. C. and where the two Perpendicular lines meet is the Centre, as at F, &c. Superficial Figures that are irregular and right-lined, are such whose Sides or Angles are un-equal, of which some are triangles, or triangular Figures; and here Note, that there are five sorts of triangles, which are thus Named and known:
- 1. Isocheles hath two of the sides unequal.
- 2. Scalena hath the three sides unequal.
- 3. Orthygone hath one Right and two Acute Angles.
- 4. Ambligone hath one Obtuse and two Acute Angles.
- 5. Oxygone hath three Acute Angles, or Equilateral triangles.
(See Fig. 31.)
Every triangle is half of a square, whose Length and Breadth is equal to the Perpendicular, and Side cut by the Perpendicular; as is plain in the first Figure shewed by the pricked lines: therefore to Measure