SAW the acym regular polygon may be divided saxaria Pangles. For what polygon are

Show the be sure of all the angles of a polygon ang the sides either in magnitude ng as their number remains the

lar polygon of any num

cth cha d®lar polygon of double the

rue de mas by which the area of any phae my dearestat mé an equivalent rectangle.

義

we amie palygons are equal to

one be equal to the corre

gons be constructed such

de a dezas the corresponding side with the areas of the two

& garden, which is

Mages become exactly four A is present shape, how would you may at the boundary?

1 Can a dre de nabədid shall have its circumference ezzely equal to the circmferences of two ser given arces mien nogether? If so, shew how it may be done.

If the area of one circle be vise times that of another, what is the ratio of their diameters ?

(18) Describe a circle whose circumference shall be <za.) twice the circumference of a given circle.

(19) Describe a circle whose areu shall be exactly ..e area of a given circle.

Shew that the areas of circles are to one ansquares inscribed in them.

ew that all regular polygons of the same cessarily similar.

(22) The corresponding sides of two similar polygons are in the ratio of a side of a square to its diagonal; find the ratio of the areas of the polygons.

(23) If in any circle four radii be drawn at right angles to one another, and with each of these four radii as diameters circles be described within the former, shew that the areas of the four circles are together equal to that of the original circle.

(24) From a given polygon cut off a similar polygon whose area shall be one-fourth of the original one.

(25) Shew how the square may be found which is equal to any given polygon.

END OF PART I.

ELEMENTS

OF

GEOMETRY AND MENSURATION.