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gles may be placed around one point to touch

it.

90. Can you divide a circle into six equal sectors?

A sector that contains a sixth part of a circle is called a sextant.

91. Make a sextant, and write upon it its

name.

92. Construct an equilateral triangle, and write in each angle the number of degrees it contains.

93. Can you place a circle in a semi-circle? 94. Can you place a hexagon in a circle? divide a circle into eight equal

95. Can you

sectors?

A sector that contains the eighth part of a circle is called an octant.

96. Make an octant, and in it write its name, and underneath state the number of degrees that the angle of an octant contains.

97. Make a regular octagon in a circle.
That point in a square which is equally dis-

tant from the sides of that square, and also equally distant from the angular points of that square, is called the centre of that square?

98. Draw a line an inch and a half long, and erect a square upon it, and find the centre of it.

99. Can you place a circle in a square?

100. Place three circles so that the circumference of each may rest upon the centres of the other two, and find the centre of the curvilinear figure, which is common to all three circles.

That point in an equilateral triangle which is equally distant from each side of the triangle, and equally distant from each of the angular points of the triangle, is called the centre of the triangle.

101. Can you make an equilateral triangle whose sides shall be two inches, and find the centre of it?

102. Can you place a circle in an equilateral triangle?

103. Can you divide an equilateral triangle into six parts that shall be equal and similar?

104. Can you divide an equilateral triangle into three equal and similar parts?

105. What is the greatest number of angles that can be made with four lines?

106. Make a hexagon, and place a trigon on the outside of each of its boundaries, and say what the figure reminds you of.

107. Can you, any more ways than one, divide a hexagon into two figures that shall be equal to each other, and similar to each other?

108. Can you divide a circle into three equal sectors?

109. Can you fit an equilateral triangle in a circle?

110. Draw two lines cutting each other, and show what is meant when it is said that those angles which are vertically opposite are equal to one another.

111. Can you place two squares so that one angle of one square may vertically touch one angle of the other square?

112. Can you place two hexagons so that

one angle of one hexagon may touch vertically. one angle of the other?

113. Can you place two octagons so that one angle of one octagon may touch vertically one angle of the other?

You have divided a line into two equal parts.

114. Can you divide a line into four equal parts?

115. Make a scale of inches, and with its assistance make a rectangle whose length shall be 3 and breadth 2 inches.

116. Draw a line, and on it, side by side, construct two right-angled triangles that shall be exactly alike, and whose corresponding sides shall face the same way.

When a line meets a circle in such a direction as just to touch it, and yet on being produced goes by it without entering it, such line is called a tangent to the circle.

117. Describe a circle, and draw a tangent

to it.

The tangent to a circle, at a particular point

in the circumference of that circle, is at right angles to a radius drawn to that point. And as every point in the circumference of a circle may have a radius drawn to it, so every point in the circumference of a circle may have a tangent drawn from it.

118. Can you draw a tangent to a circle that shall touch the circumference in a point given?

119. Given a circle, and a tangent to that circle; it is required to find the point in the circumference to which it is a tangent.

120. Given a line, and a point in that line; it is required to find the centre of a circle, having a diameter of one inch, the circumference of which shall touch that line at that point.

121. Show by a figure how many equilateral triangles may be placed around one equilateral triangle to touch it.

122. Divide a square into four equal and similar figures several ways, and give the name to each variety.

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