“DIAGONAL. 
the a hie aa! ufed; ‘ ‘ga, The leffer: ‘@iaineter has ©- < ~ 
“ihelination of the vebigkt diane. 
rder to this; nine t “ange have been 
- The 
is as follows 
Let ie al of the eeu: diameter 
An : the half of the leffer 
_ 
Se 
Triangle. Bafe. Perpendisilar. Hypoth, sere 
I +1437 2.80: 5 > 2.804 B79 7 
: 2 4875 2.65 2.693 8r 
3 | 69 2.55 2.64. 75 
4 * 92 2.3 ee “68 
‘6 Y612T25 nog - i 2g ° ">" 5B 
~ G 23.9096 +7 8a 208 9!) 5O 7s 
q 146625 9 2B? BH. 1.907 39 
8 1.523750 - pee 1.656° 25 
Q TOE Te 62g 7.598 9° 
Total hg ge 16. 00 - 5-°! 20.159 
Fig: ry*, Plate V.i3 a canes of an ellipfe of thefe pro. 
portions. 4 “Phe fcrleis five times the fize of that Seo 
upon; pe deny thefe Faken as 8th parts,’ ‘ iniftead of 32d 
parts.’ @A'B-istheleffer diameter or Ae ine; BC 
the greater: . seers ‘aiid the lines from At the ‘h 
‘thenufes: of ue ae one form the approximation e 
the el Hliptic-cu 
From. thefe vefalts it will appear, 
Oo» 
‘that the quarter of ie 
ts. But astherevare 
fettin' 
fac ant clelting each upon the pr abe pln. 
rf Side Angle with eae line 89° : 
ae do. “ - B75 at 
. 3d = do. =  - “ geo 
4th do. ” - = 83 
5th do. “ -- 80. 
6th. do. = = 74. 
ath do = = = 4 
P 
‘1 -and'n-are precifely the fame ; wae re 
8th’ Side Angle with bafe line 72° 
oth -d 
h ; - - - 70 
roth do- +- = - 65° 
11th - - - © 60 
ee ath dd eee OL 
© 73th dost eos 52 
i iqath do. ome 
1gthide® = soe AS 
6th — . - - 272 
i7th do - 8 30. 
18th do. - - - 25 
toth ° do. - - = 17. 
20th ie - “ - 9 
art 4 
Thus tie ccaloaletion would ee were the ellipfe placed 
upright, and the lefler diameter the fame with the bafe line. 
tas itis aflumed that the elli uft be inclined until 
the greater Ss will form an angle. of 65° with the bafe, 
the comple ies that angle, or 25°, muit be fubtraG&ed 
from each of the ngles. The 318th angle will then be 0° °3 
the igth, 8°, onde ‘ie bafe; the 2oth, 16°; and the 2ift, 21° 
The angles being thus found, the fir table will give the 
rules*for cutting as ufual. 
“he only other éxample relating to penmanthip, or the con- 
ftruGion of writing automata, which it appears neceflary or 
proper to trouble the readers: of this article with, is the letter 2 3. 
or the curvilinear part of this feems, in combination with the 
g, to form almoft every letter of the manufcript alphabet ; 
oft others will be.found very fimilar, and a 
seca ae of conftru€ting the reft will afterwards be in- - 
ha a great part of thefe oS much i is com- 
fimilar, and: therefore one calculation will anfwer for ie 
w ich © be 
mai 
rates are reCtilineat, The;fame is the cafe w 
ie letter :a, which is formed b sadine an 2 to the 
elliptival part, oro. The oblique lines, eee equal to the 
larger dicen of the ellipfe, are Ce expreffed by: 32. e 
dotted liries,. which bound and interfe&t the writing acrofs- 
the.plate, will ferve to thew. how ‘the centres of the circular 
ares*which form the curves have been yee -thefe lines are 
diftinguithed by the numbers 1, 2, 3 8. ¢ recti- 
inear oblique lines are eras a “ey ae ieee 2 and 
he ‘curves confit of t rcs; the » being a. 
femicircle of a {mall diameter, ie centre of Which is at of 
The dotted line, ¢ fi d, is - diameter, and. i is parallel to the 
leffer diameter of the ellipfe. The remaining curve, d e, ig. 
a {ma iE 
Grele, the centre of which isa 
hec 
fans may be diverfified to- canes extent, is the joint 
application of two. forces;. and it has been the obje& of 
thefe defcriptions to point out means. of oe this, wit 
great precifion. The addition of a thir » ating in: 
a line at right angles to this plates eden ie very oF 
