‘ :.l( '
: : ) V
scale, with less accuracy, by applying the gairien-square (h ) ; o'8^M ^10 ^
of a rope or line united at the extremity, and divided in the proportions of 6, 8, and 10 (c).
The 6 is to be placed as the perpendicular
of a right-angled triangle, the 'Y- ^ ^
8 as the base, and the 10 as the hypothenuse;
or, three rods of similar
proportions, or divided into feet, and
the proper numbers taken, may be
used for this purpose. Switzer informs
ns this was the mode in which
all right-angled figures in gardens,
and all other works, were set out in
his time.
2348. T o divide an angle, a line
united at the extremities, and divided
into four equal parts (d), may readily . , n
be so applied to any angle as to divide it e q u a lly ; or the same thing may be done by
a portion of line bisected, and its extremities applied at equal distances from the
angle (e). A lino divided into three equal parts readily forms an e q u ilate ra l trian g le
^"^2349. T o describe a n o v a l w ith in a given length, the length may be divided into three
equal parts; then let the two inner points so found be the centres of tivo circles which
shall form the ends of the oval, and the sides may be fonned by segments whose centres
ai-e the intersecting points of the circles ( fig . 691. a). The same oval may be formed
by dividing the given line into four parts; forming the ends by segments of whicli the
two outermost points arc the centres, and the sides b y segments proceeding from a
line passing at right angles thi-ough the centre of the given line (Jig . 691. o).
2350 T h e gardener’s oval, or one in which both diameters are given, is thus formed.
Bisect the long diameter by the transverse one, itself thus bisected by the othcn
half the transverse diameter into three parts. Take one of these parts, and set it ott
fi-om both extremities of the long diameter. Fix there two pms or stakes, and hx a
third stake one part from the end of the transverse diameter; donble a line and put it
round these stakes, of such a length that when stretched, it may touch the extremities ot
one of the diameters. Then, with a pin in this extremity, move it completely round,
and so strike out the oval (Jig . 691. c .J The long and short diameters are more easily
divided arithmetically ; thus, supposing the given length
of the oval be 90 ft. and its width 60 ft.; then the
third part of half of the width is 10 ft., and this ffis-.
tance set back from the extremities of the diameters gives
the situation of the stakes at once.
2351. A s p ira l line, or volute, may be sometimes re- ¿j
quired in gardening, for laying out labjTinths or curious
partei-res. The width or diameter of the spiral being
given (Jig . 692. i, h ), bisect it, and divide each half into
as many parts as the spiral is to form revolutions (Jig.
692. g to h ). Then, from the centre draw all the halves
of the spirals which are on one side of the diameter line
(be, de, fg , k i ) ; and from the point where the first semi-
spiral intersects the diameter hne (b ), as a centre, draw
all the others /i^).
2352. U n itin g three p oints in a curved line. A very
useful problem, both in laying down plans on paper and
ti-ansfen-ing them to gardening, is that which teaches
how, fr o m any three p oints (fig . 693. a, b, c), not in a
sh'aig ht line, to fin d the centre o f a circle whose c irc um fe rence
s h a ll pass through them. Imagine the tliree points connected
by two straight lines ; bisect these lines by others
(a and e), perpendicular to them, and where these intersect (at g) will be found tbe
centre of the circle whose circumference sliall pass tlirough the three points.
2353. T he method o f laying out pohjgons on even ground, or any geometrical figure,
will be perfectly simple to such as can perform the problems on paper ; all the difference
on the ground is, that the line is used instead of the compasses, with or without the
assistance of the square and aritlimctical calculation.
2354. L a y in g out the ground-lines o f gardens, p a rte rres, or any large figures on plane
surfaces, is merely a mixed application of geometrical problems. It is only necessary to
premise, that a straight line is found by placing
rods upright, so that they may range one behind
the other at convenient distances, and so accurately
adjusted, that the one next the eye may
conceal all the rest. A plan of a garden, &c.,
(fig . 694. a ) being given, with a scale and
north and south line attached, first find its
extreme dimensions, and supposing you have
space sufficient for laying it out, find the central
lines (fig . 695. a a ,b h), and lay them down first,
distinguishing them by row’s of stakes; then
from these set off the lines of the central plot,
if any, the walks, alleys, walls, &c., distinguishing
them by strong stakes, whicli may remain
till the ground is put into proper fonn.
2355. I n laying o u t polygonal gardens, ov plots, or ponds (fig . 694. b), when the dimensions
are too great for inscribing a circle of the full size with a line, the obvious mode
is to foi-m a small circle in the centre, and mai-k the figui-e on its circimiference; then
from the point where the sides intersect, radii can be extended as far as required, and the
length of one being found, the rest can be adjusted accordingly, and the plot thus laid
out of the required size (Jig . 696.).
695
-1 7 ....... ........ ..................J A 696
T T - . . , ; _ r é T l t a
•-Jré-Jré-J,
"•JJ
7
T
£ .1.4 ]. J— I------ U
i t a
.-•t=-..... ......‘r.
.. K \
fft r S Y f r ri i ;
kH r T , . / Y : 4
lIirlkT,'.?...'..".....'.
I a
r: r. .~.. ......t r /
2356. In tric a te and fa n c ifu l fig u re s o f p a rte rre s are most corteetly transferred to
ground, as they are copied on paper, by covering the figure to be copied with squares
(fig . 697. a ) foi-med by temporary lines intersecting each other at equal distances and at
right angles, and by fiacing on the ground similar squares, but much larger, according
to the scale (Jig . 697. b ). Sometimes the figure is drawn on paper m black, and the
U u
I?
M ■ t l
r i
iil
ta ré f il
!