Fig. VI. 
New Principles of Gardening. 
and acd are equal-fided, being Radius’s of equal Circles, and 
adcommon. Therefore the Angle ¢ da is equal to the Angle 
bda. QE. F. 
PIeesiLEM VI 
ROM a given Point (a or-h) to let fall or raife a Per- 
a pendicular (ah.) 
Definition I. Perpendiculum, or Perpendicular, (from the 
Latin, perpendo, to hang down,) is a ae Line falling upon 
a Right Line with equal Inclinations, (as 4aon 6c.) where the 
Angles on each Side (ba and hac) are equal to each other ; 
and therefore are called Right Angles. 
Practice. With any Interval make a¢ equal to 2d, and 
with the Diftance 4c on 6 deferibe the Arch ee, and on ¢ the 
Arch ff, croffing at 4, join 44, and twill be the Perpendicular 
required ; for 4d is equal to bc, and a6 to ac, and ha com- 
mon. Therefore the Angles at a are as and right-angled, 
bs 
and 2h perpendicular. Secondly, on 4, with any Interval, 
_ defcribe the Arch bc, join hc andhd; divide the Angle ch, 
Fig, VII. 
(by the preceding Problem,) and the Line 4a is the Perpendi- 
cular required: For the Angles at 2 may be proved to be Right 
Angles, as before. Therefore, 6c. VU. E.F. 
To let fall a Perpendicular from a Point, as at 4, over or 
near the End of a Line, draw a Right Line (¢#0) from the 
given Point (2) to any Part of the given Line, as to 0, which 
divide into two equal Parts at #, and on m defcribe the Semi- 
circle z/0, draw z/ the Perpendicular required. 0. E.F. 
To raife Perpendiculars at the End of a Right Line, take 
the following Ways, viz. 
firft, From a raife the Perpendicular @ ig 
Practice. With any Interval on @ defcribe an Arch, as 
(y¢d,)make_y¢ and ¢d each equal to ayd; and with the fame 
Openingon edefcribe the Arch 4d, and on dthe Arch c ¢, croffing 
the other in ff draw g @ through £ the Perpendicular required. 
Secondly, From & raifethe Perpendicular bp. 
‘ PRACTICE. 
