PROBLEM XII.

To divide a given Triangle ABC, into two equal

parts.

B

C

A

D

Bifect one of the fides in D.

Draw a line from D, to the oppofite angle, which will divide the triangle into two equal parts.

PROBLEM XIII.

To defcribe a Square, upon a given line AB.

Raife a perpendicular, at one end of the given line.
Make the perpendicular B C, equal to A B.
With the radius AB, and C as a centre, describe an

arc.

With the fame radius, and A as a centre, defcribe another arc croffing the first in D.

Draw the lines DC, DA, which will complete the Square required.

PROBLEM XIV.

To defcribe a Rectangle, whofe length and breadth fhall be equal to two given lines, AB

Raise a perpendicular at one end of the longest line, as at B.

Make the perpendicular B D, equal to the shortest line C.

arc.

With the radius A B, and D as a centre, defcribe an

With the radius C, and A as a centre, defcribe another arc croffing the first in E.

Draw the lines DE and AE, which will complete the Rectangle required..

Draw

C

any chord A B, and bifect it' at right angles

with the perpendicular CD.

Bifect C D in E, which will be the centre of the circle required.

PROBLEM XVI:

Through three given points A, B and C, to deScribe the circumference of a Circle.

Draw two right lines A B and B C, joining the points A B and B C.

Bifect these two lines with two others drawn at right angles to them, and produce them till they meet in the point D.

With the radius D B, or DC, or D A, and D as a centre, describe a circle which will pafs through the points required.