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18 EXPLANATION OF THE GEOMETRICAL FIGURES
FIGURE H.
To divide a given Circle into four equal Parts.
Draw a line through the centre C, and proceed as in Fig. I.
FIGURE III.
From a given point C, in a right Line, to erect a Perpendicular.
Set one point of the compasses in C, and, opening them at pleasure, set off the
distances A B, and proceed as in Fig. I.
FIGURE IV.
Upon a Point, situate at or near the end of a Line, to .erect a Perpendicular.
From the point B, on the line A B, extend the compasses, at pleasure, to the
centre C, from which describe a circle, and from the intersection in the line A B at
D, draw a line through C, which will cut the circumference at E, from which draw
a line to the point B.
FIGURE V.
Shews the manner of drawing parallel lines, which needs no explanation, and
may be drawn to any distance required.
FIGURE VI.
To form a Square from a given Line.
Erect a perpendicular (by the rule given in Fig. IV.) upon which and the base
line, set oif with the compasses the line proposed, and keeping the same distance*
draw the circular lines C D B, and A D B, from whose intersections at D draw the
lines D C and D A
FIGURE VII.
From two given Lines to form a Parallelogram, or long Square.
Draw the line C D at pleasure, upon which set off the longest given line A, erect
a perpendicular at E, upon which set off the given line B, mark off the line A
from F, and the line B from A, and draw the lines A G and G F.
FIGURE VIII.
From a given Line to form, an equilateral Triangle.
Take the length of the given line A B with the compasses, and from the points
A and B draw circular lines, from whose intersection draw A D and C B.
18 EXPLANATION OF THE GEOMETRICAL FIGURES
FIGURE H.
To divide a given Circle into four equal Parts.
Draw a line through the centre C, and proceed as in Fig. I.
FIGURE III.
From a given point C, in a right Line, to erect a Perpendicular.
Set one point of the compasses in C, and, opening them at pleasure, set off the
distances A B, and proceed as in Fig. I.
FIGURE IV.
Upon a Point, situate at or near the end of a Line, to .erect a Perpendicular.
From the point B, on the line A B, extend the compasses, at pleasure, to the
centre C, from which describe a circle, and from the intersection in the line A B at
D, draw a line through C, which will cut the circumference at E, from which draw
a line to the point B.
FIGURE V.
Shews the manner of drawing parallel lines, which needs no explanation, and
may be drawn to any distance required.
FIGURE VI.
To form a Square from a given Line.
Erect a perpendicular (by the rule given in Fig. IV.) upon which and the base
line, set oif with the compasses the line proposed, and keeping the same distance*
draw the circular lines C D B, and A D B, from whose intersections at D draw the
lines D C and D A
FIGURE VII.
From two given Lines to form a Parallelogram, or long Square.
Draw the line C D at pleasure, upon which set off the longest given line A, erect
a perpendicular at E, upon which set off the given line B, mark off the line A
from F, and the line B from A, and draw the lines A G and G F.
FIGURE VIII.
From a given Line to form, an equilateral Triangle.
Take the length of the given line A B with the compasses, and from the points
A and B draw circular lines, from whose intersection draw A D and C B.