g ~ New Principles of Gardening. 
each other, and the Rhombus xeda equal to the Rhombus 
ec. Therefore the Lines xe, ec, da, dh, hc, and oa, 
are equal to one another. And as ’tis plain, that 0@ is a mean 
Proportional between 4a and ¢ a, fo likewife is « @ (equal to 
0a) a mean Proportional between 4a and ca; for twill be, 
as ba to ax, fo ax to ca; and being compounded, as 4a 
more ax, (that is, 4x,) tox 2 more ac, (that is; xc or 4a,) 
fo likewife is ba to hc; therefore 4x is divided in ¢ and 4; fo 
that the whole Line 4x, a Part 44, and the remaining Part 
hc, likewife x4, a Part xc, and the remaining Part x a, 
are continual Proportionals. Therefore fa (that is, 40) 
is the greater Segment of the Right Line 4x, divided in ex- 
tream and mean Proportion. Q, E. D. 
N. B. Thofe Segments may alfo be found as follows: 
Continue x4 to &, making 4 & equal to bv; on 4, with 
the Interval &v, defcribe the Arch v ao, which will cut 4x 
in 2; fo will 4a be the greater Segment. F, 
PROBLEM XIiil. 
Fig. XIV, O jind the Center of an Arch (or Circle) given ( ghi) 
or to deftribe a Circle, whofe Circumference {hall pafs 
through three Points given. 
PRACTICE. Join any two, as 4g and 42, bife& each by 
Perpendiculars, crofling in ”, which is the Center; for each 
Perpendicular is a Diameter, and confequently the Center muft 
be where they interfec&. 
PROBLEM XIV. 
Fig. XV. O draw a Tangent (nh) from a Point given (h) 
DeriniT10n. A Tangent (comes from the Latin Word Tango, 
to touch) is a perpendicular Right Line without a Circle falling 
upon the End of the Diameter, as 74. 
_Practics. Draw a Right Line from 4 to the Center 4, 
bifect 44 in 7, and thereon deferibe the Semicircle kunh, cut- 
ting 
