PROPOSITION X. To finish a Circle begun, whofe Center is loft. Let ABC be the given Part of a Circle, whofe Center is to be found in order to finish it. PRACTICE. Place at Difcretion the three Points ABC in the Circum ference begun. From the Points A and B To draw a Circumference through three given Points. Let ABC be the three Points through which the Circumference of a Circle is to pafs. PRACTICE. From the given Points A, B, C, Describe the 3 Circles DEH, DEF, FGL. of an equal Circumference, and cutting each other at the Points D and E, F and G. Then draw the Right Lines DE, FG, Till they meet together at From this Point And the Space Describe the Circumference required. PROPOSITION XII. To draw an Oval upon a given Length. I. I ΙΑ Let AB be the Length upon which an Oval is to be formed. IN BOOK III. Of the Infcription of FIGURES. N Geometry a Figure is faid to be infcribed in another, when all the Angles of the Figure infcribed touch either the Angles, Sides, or Planes of the other Figure. To defcribe an Equilateral Triangle, an Hexagon or a Dodecagon, in a given Circle. Let ACD be the Circle in which an Equilateral Triangle, c. is to be defcribed, Mark the Semi-Diameter AB fix times round the given Circumference, For the DODECAGON. Divide the Arch of the Hexagon AC equally in two at O, AO will be a fingle Side of the Dodecagon required. PRO To draw an Oval upon two given Diameters. This Ruler being thus formed, place it in fuch a manner Exactly even with the Line AB, CD, N AB, O, CD. The Ruler being thus placed, keep ftrictly to the Directions here given with regard to its Pofition. Turn it round, and you will defcribe the Oval by the Extremity M. PROPOSITION XIV. To find the Center and the two Diameters of an Oval. Let ABCD be the Oval whofe Center and Diameters are to be found. PLMO Equally in two at Draw the Line Then divide it equally in two at E. The Point E will be the Center required, from which de fcribe at Discretion the Circle FGQ, Cutting the Oval at F and G From thefe Sections F and G Draw the Right Line FG Divide it equally in two at R Draw the great Diameter BD Through the Points ER Thus you have the Center, and the Diameter re quired. PROPOSITION XV. To conftruct a Rectilinear Figure upon a Right Line given of a determined Length, fimilar to a Rectilinear Figure given. Let AB be the Line upon which a Figure is to be formed like to the Figure CDEF. |