PROPOSITION VI. To defcribe an Undecagon in a given Circle. Let AEF be the given Circle in which an Undecagon is to be infcribed. DO. The Length CO will be an exact Side of the Undecagon required. PROPOSITION VII. In a given Circle to infcribe whatever Polygon you please. Let BAC be a Circle in which you would infcribe an Heptagon. PRACTICE, Draw the Diameter Defcribe the Circle AB As if you would form Capable of containing 7 Times A Polygon like that which you are to in scribe in the given Circle AB B. 2. P. 5, upon the Line AB 6, 7, 8. Draw the Diameter Parallel to the Diameter ABC DE AB DAG, EBH DA, EB. ABC Draw the Right Lines Through the Extremities GH will divide the given Circle Into feven equal Parts. And thus of all other Polygons. PRO PROPOSITION VIII. To take a Portion from a given Circle, capable of containing an Angle, equal to a Rectilinear Angle given. Let ACE be the given Circle, from which a Portion is to be taken, capable of containing an Angle equal to the Angle D. PRACTICE. Draw the Semi-Diameter B. 1. P. 10. Draw the touching Line Make the Angle B. 1. P. 8. Equal to the given Angle AB AF FAC D All the Angles which fhall be formed And in the Portion Will be equal to the given Angle AC AEC D. And thus the Portion AEC, anfwers what was required. PROPOSITION IX. To inscribe a Triangle in a given Circle, equiangular to a Triangle given. Let ABC be the Circle in which a Triangle is to be inscribed like the Triangle DEF. Draw the Line BC. ABC is the Triangle required, like the given Triangle DEF. PROPOSITION X. To infcribe a Circle in a given Triangle. Let ABC be the Triangle in which a Circle is to be inscribed. PRA 1 PROPOSITION XI. To infcribe a Square in a given Triangle. Let ABC be the Triangle in which a Square is to be infcribed, PROPOSITION XII. To infcribe a Regular Pentagon in an Equilateral Triangle. Let ABC be the Triangle in which a Pentagon is to be infcribed, PRA PRACTICE. B. 1. P. 4. Bring down the Perpendicular ΑΙ From the Center A Describe the Arch BIM. PROPOSITION XIII. To infcribe an Equilateral Triangle in a Square. Let ABCD be the Square in which an Equilateral Triangle is to be formed. PROPOSITION XIV. To infcribe an Equilateral Triangle in a Pentagon. Let ABCDE be the Pentagon in which an Equilateral Triangle is to be inscribed. PRACTICE. Circumfcribe the Circle From the Point ABCDE. B. 2. P. 11. A And the Space of the Semi-Diameter AF. PROPOSITION XV. To infcribe a Square in a Pentagon. Let ABCDE be the Pentagon in which a Square is to be infcribed. |