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1 84 GEOMETRY.
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PROBLEMS IN GEOMETRICAL DRAWING.
To divide a straight line into a
given number of equal parts. (See
Fig. 1).
Given line a b, which is to be
divided into a given number of equal
parts. Draw the line b c, of indefinite
length, and point off from b the re-
quired number of equal parts, as h.g,
1
t y
H
%
\y %
t ’ e
s&
, V F.G. 1
f, e, d, c’; join c’ and a, and draw the other lines parallel to c’ a.
To erect a perpendicular at a
given point on a straight line.
(See Fig. 2).
Given line a b, and the point
x. The required perpendicular
is xy.
Solution
:
With x as center and any
With 1 and 2 as
Fig. 2
’l * ’2
radius, as x 1, cut the line a b at 1 and 2
centers and with a radius somewhat greater than 1 to x, describe
arcs intersecting each other at y. Draw x y. This will be the
required perpendicular.
From a given point without a straight line to draw a per-
pendicular to the line. (See Fig. 3).
Given line a b and the point c.
The required perpendicular is x.
Solution:
^ With the point c as center and any
radius as c 1, strike the arc 1 to 2. With
1 and 2 as centers and any suitable
radius, describe arcs intersecting each
other at n, lay the straight edge through
points n and c and draw the perpendicular x.
To erect a perpendicular at the extremity of a straight line.
(See Fig. 4).
The required perpendicular is x.
Solution
:
From any point, as c, with radius
as a c, draw the circle. From point
of intersection, «, through center, c,
draw the diameter n fi. From the
points, through the point of intersec-
tion at ft,
draw the perpendicular x.
The correctness of this con-
struction is founded on the principle
that inside a half circle no other
V,
Given line a b.
Fig. a
S
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