rcs are used. Draw the line
_a b_, the major axis, and at a right angle to it the line _c d_, the
minor axis of the figure. Now find the difference between the length of
half the two axes as shown below the figure, the length of line _f_
(from _g_ to _i_) representing half the length of the figure (as from
_a_ to _e_), and the length or radius from _g_ to _h_ equalling that
from _e_ to _d_; hence from _h_ to _i_ is the difference between half
the major and half the minor axis. With the radius (_h i_), mark from
_e_ as a centre the arcs _j k_, and join _j k_ by line _l_. Take half
the length of line _l_ and from _j_ as a centre mark a line on _a_ to
the arc _m_. Now the radius of _m_ from _e_ will be the radius of all
the centres from which to draw the figure; hence we may draw in the
circle _m_ and draw line _s_, cutting the circle. Then draw line _o_,
passing through _m_, and giving the centre _p_. From _p_ we draw the
line _q_, cutting the intersection of the circle with line _a_ and
giving the centre _r_. From _r_ we draw line _s_, meeting the circle and
the line _c, d_, giving us the centre _t_. From _t_ we draw line _u_,
passing through the centre _m_. These four lines _o_, _q_, _s_, _u_ are
prolonged past the centres, because they define what part of the curve
is to be drawn from each centre: thus from centre _m_ the curve from _v_
to _w_ is drawn, from centre _t_ the curve from _w_ to _x_ is drawn.
From centre _r_ the curve from _x_ to _y_ is drawn, and from centre _p_
the curve from _y_ to _v_ is drawn. It is to be noted, however, that
after the point _m_ is found, the remaining lines may be drawn very
quickly, because the line _o_ from _m_ to _p_ may be drawn with the
triangle of 45 degrees resting on the square blade. The triangle may be
turned over, set to point _p_ and line _q_ drawn, and by turning the
triangle again the line _s_ may be drawn from point _r_; finally the
triangle may be again turned over and line _u_ drawn, which renders the
drawing of the circle _m_ unnecessary.

To draw an elliptical figure whose proportion of width to breadth shall
remain the same, whatever the length of the major axis may be: Take any
square figure and bisect it by the line A in Figure 80. Draw, in each
half of the square, the diagonals E F, G H. From P as a centre with the
radius P R draw the arc S E R. With the same radius draw from O as a
centre the arc T D V. With radius L C draw arc R C V, and from K as a
centre dra