ine representing the centre of a cylinder is termed its
axis; thus, in Figure 53, dot _d_ represents the centre of the circle,
and line _b b_ the axial line of the cylinder.

To draw a circle that shall pass through any three given points: Let A B
and C in Figure 54 be the points through which the circumference of a
circle is to pass. Draw line D connecting A to C, and line E connecting
B to C. Bisect D in F and E in G. From F as a centre draw the semicircle
O, and from G as a centre draw the semicircle P; these two semicircles
meeting the two ends of the respective lines D E. From B as a centre
draw arc H, and from C the arc I, bisecting P in J. From A as a centre
draw arc K, and from C the arc L, bisecting the semicircle O in M. Draw
a line passing through M and F, and a line passing through J and Q, and
where these two lines intersect, as at Q, is the centre of a circle R
that will pass through all three of the points A B and C.

[Illustration: Fig. 54.]

[Illustration: Fig. 55.]

To find the centre from which an arc of a circle has been struck: Let A
A in Figure 55 be the arc whose centre is to be found. From the extreme
ends of the arc bisect it in B. From end A draw the arc C, and from B
the arc D. Then from the end A draw arc G, and from B the arc F. Draw
line H passing through the two points of intersections of arcs C D, and
line I passing through the two points of intersection of F G, and where
H and I meet, as at J, is the centre from which the arc was drawn.

A degree of a circle is the 1/360 part of its circumference. The whole
circumference is supposed to be divided into 360 equal divisions, which
are called the degrees of a circle; but, as one-half of the circle is
simply a repetition of the other half, it is not necessary for
mechanical purposes to deal with more than one-half, as is done in
Figure 56. As the whole circle contains 360 degrees, half of it will
contain one-half of that number, or 180; a quarter will contain 90, and
an eighth will contain 45 degrees. In the protractors (as the
instruments having the degrees of a circle marked on them are termed)
made for sale the edges of the half-circle are marked off into degrees
and half-degrees; but it is sufficient for the purpose of this
explanation to divide off one quarter by lines 10 degrees apart, and the
other by lines 5 degrees apart. The diameter of the circle obviously
makes no difference in the number of decrees contained in any portion of