DIAGONAL, 
a us then fuppofe, that i ie hoveonta this circle, we Divifion Bafe Perpendicular... 
mmence our operation at the horizontal diameter, and at e i 
the right hand, as at B in fig. 17. Plate : es aul th hie 5 se _ a 
Let us alfo fuppofe, that cs frame which carries the 
ftuff upon which the circle is to be defcribed, is moveable 
ae in a horizontal and vertical diretion, as in figs. 13,14, 
15. The calculation will then ftand as follows: 
13t — 7 2 as 17-9 
which compleats the circle. 
n the above calculation, the word rife is ufed when the 
rim of the wheel is to recede from the centre, and the word 
ft Quadrant. Jink, when it is to approach it. In the firft prea of the 
Divifion. Bafe. Perpendicular. oe ie polyee’s hat the a is aaa from ta i ag 
: ; the frame muft be move the horizontal wheel to- 
ift Angle Go° Rife 12 Sink 17.9 wards the right. Had the pate been ftationary, and 
2d a ‘9 — 364 os al the tracer required to move, the motion would, of courfe, 
Bd Be GZ have been inverted. The rifing-moation is, therefore, given 
eh ee OT 16.3 to the horizontal wheel, until the frame has come into con-. 
su oe 5 : = 7 ; — ie tat with the other end a “ canines. at the laft di- 
| — : mt ; vifion of the fecond quadra 
7th —— 45 =~ 127 = oa n the fame ea cee cael wheel mutt fink the frame 
8th ——- 39 — 40 — Eis3 to raife the tracer; and this is done during the firft qua- 
gth ——- 32 0 — 153 0 9-5 rant, when it has arri what may be ca he vertex 
roth 25 = 16.300 7.6 It then rifes for a whole femi-circle to the laft divifion of the 
vith ——- 18 RD 56 third quadrant, when in to compleat the circle 
a a A : a — : : The angles of all the quadrants are the fame, but alternately 
oT. _ i — inverted. Th plication to the dividing and cuttin 
2 2d Quadrant engine is taken on I. By fimilar means, a circl 
Divifion. afe Perpendicular of any radius or diameter may be defcribed, and confe- 
it Angle 4° Rife 17.9 te quently any arc or curve of a circle. The whole of eack - 
aa mo oy a 4 wheel, in the inftance given, muft be divided into 52 equal 
3d 7 ae a _ 7 6 parts, ‘both for the horizontal and vertical motion. It will 
4th of = 16.3 _ 6 feldom be neceffary to form curved lines, which are not .. 
sth 32 — 83 = 9.5 portions of circles, where mere ornament is to be con- 
Gth 39 — 140 _ - fulted ; but if it fhould, it is evident that the ellipfe, the 
sth 46 — i209 _ a parabola, and the hyperbola, may be _ . a feries o 
Sth slo «1103 a 14.0 triangles in the fame way as the circle els cut 
oth —— 58 _ 9.5 _ 15.3 accordingly, en ike any of thefe Sone figures, or 
ae A _ any oo of eit 
ate 7 _ iy —. Aik few ul o the atone this kind : baa 
pale "7 3.4 _ 17.9 ae to produce various s of figures, compofed o 
_ ’ » or curved lines, or of a combination of both, may - 
ee " ao a1? foes further to illuftrate the fubje&; and for thefe ah : 
3d Gesini. reader will be pleafed to confult Plate VII. 
Divifion. Bafe. Perpendicular. When fuch curves only as will produce a pleafing effec . 
rf Angle 86° Sink 1.2 Rife 17-9 o the eye are required, they may, almoft always, be ap- 
ad —- 79 3.4 17.7 ror very nearly to arcs of circles of various radii, as in 
34 0Cl 2 — 5.6 one 1761 the example, fg. 21. e three leaves of this flower confift 
4th o—— so 7.6 — 16.3 entirely of arcs of circles, the centres of whi € pointed 
Sth ——— 58 — 9.5 —_ 15.3 out by the s of reference; and the angles fubtending 
6th —— 51 — 11.3 he 14 the arcs are repre nted by dotted lines. Th dle leaf. 
sth ——~ 45 — 12.7 —_ 12.7 of the flower, it will appear, is formed by four circular 
8th —— .39 — 140 _ 11.3 ed the centres of which are refpectively at A, B, C, and 
oth —— 32 — 15,3 aan 9.5 ra. . fa vial ne yee ye elriel at H, | 
*xyoth -—— 2, mm 16. as ~.6 an orm the left hand leaf; and three curves 
tith —— 18 — a an £6 centered at G, E, and F, the right- -hand leaf; the. whole 
12th Ir o— 19.7 — 3.4 flower containing 12 curves. 
13th —— 4 17.9 os 1.2 It anh she a as to eee grees of . 
two wheels, adapted to form this wer, the means of re. 
_ 4th Quadrant, ; ducing it to the baile, and applying the cutter. 
Divifion. Bafe. . Perpendicular. Let the tracing of the lin : Ps commenced with the mid- 
if Angle 4° Sink aE 9 Sia 1 le leaf, beginning at 5. firft arc ii then be from 5 
2d II 7.9 4- to 4, the centre of which is iy mmon diagonal 
gd 18 ae — Ene) {cale of 400 parts to the inch, the Adige from A to 5, 
4th -—— 25 —— 16.3 —_ 7.6 meaf{ures about 334 of thefe parts, aud the diameter, o 
Sth -~——- 32 — 15.3 — 9-5 courfe, 668. his number, divided by 12.5, will reduce the 
6th -— 39 — 14.0 — 11.3 meafure to 32d parts, to adapt it for the en This wil 
7th —— 45 -—- 127 —_ 12.7 be. found to be 53-44, and the fraction may be ei fo 
Sth —— sr 103 — 14.0 that 53 willbe the meafure of the diameter of the a 
t —— 5 _ 9.5 — 1§.3 table II., the neareft approximation to this is 52, ir the Cire 
goth m= 65 — 7.6 — 16.3 eumference of the whole circle 165, The arc meafures 78°, 
amely, 
