BOOK III.

Of the Infcription of FIGURES.

'N Geometry a Figure is faid to be infcribed in another, Ν 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, . is to be described,

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

PROPOSITION II.

To infcribe a Square and an Octagon in a given Circle. Let ABCD be the Circle in which a Square and an Octagon is to be infcribed.

PRACTICE.

For the SQUARE.

AB, CD

Cutting each other at Right Angles; that is, draw

Draw the two Diameters

the Right Line

Through the Center of the Circle

CD

Then from the Points or Extremities C and D

Subdivide each Quarter of the Circle in two, and you will

have the Octagon.

PROPOSITION.

To infcribe a Pentagon and a Decagon in a given Circle. Let ABCD be the given Circle.

For the DECAGON.

Subvide each fifth Part of the Circle equally in two.

PROPOSITION IV.

To infcribe an Heptagon in a given Circle.

Let ABC be the Circle in which an Heptagon is to be

infcribed.

will divide the Circumference of the Circle into feven equal

Parts, which gives the Heptagon required.

PROPOSITION V.

To infcribe a Nonagon in a given Circle.

Let BCD be the given Circle in which a Nonagon is to be infcribed.

Draw the Right Line

F

EG

AG

DH will be the ninth Part of the Circumference, which

therefore gives you the Nonagon required.

PRO