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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 64v, page id 00068195:0128
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doctrina de Aipplicatis
ad Loca plana
rectam, et circulum:
Atrae nempe exhibentur:
aequationes generales.
tam ad circulum
is duorum si in Triangulo ABC. detur differentia lateris AC et AB, item
lateris AC et BC; deturque praeterea angulus aliquis ut c. invenire
Triangulum
quia datur angulus dabitur et ratio rectarum  BC. DC. Bd
sit AB aequ. X. BC aequ. y. AC aequ. 3. Differentia inter
AC et AB sit  a. firt 2- x aequ.a diff. inter quam ad
(3) Bd sit aequ.g-
sit AD aequ. e. DC aequ. f. fier et fae9. 3.
Ob rationes trium rectarum datas id est easdem cum rationibus rectarum
datarum l. m. n. faciemus. y: g: f:: l m: n.
e it tamen mint nn ego U. uti gg+fs aqu’yy
faeqo ny
denique quia AB Ft aequ AD F + B D 1. fiet _ Xx aequ. ec + gg.
ob 3 er 8 est C aequ. Z - n y. Ergo per 9 et 10. Xx aequ7Z + nagus -2n q1) + mmgy
Est autem Z aequ. a +X ex aequ. 1. f ex aequ. 11. et 12. fiet. 
(XX) aequ aa(t xx)t 2ax (t un y) + mmyy  - 2nay,
multiplicetur aequ. 15 per x+y. fiet: xx-yy ubx+by
(16
aequatio i3 multiplicetur per 2. eique addatur itus = -c7
0 aequ ina + 4 aX + 2yy - 2nay - 2 n Xy
16 fst 0 aequ. XX
summa
- b x - yy - by Xay +
+ax
1c y
 XX +2aa - 3ax + yy - n a y - 2 n Xy
0 aqu
Xago lvtDZt
yugo PVt9Z+
+ bx.
habita.
+ b y
+ c y
+y ZZ tay1
quae est ad circulum
redam
non obstante Xy.
Itaque aequatione 19 ad circulum, et 15 ad rectam, intersectione
rectae et circuli solutum erit problema
a XX ayy Xy
XA yy xg.
Ex xy ...
X..
yy eraequis
per 1 et 2. fiet: atx aequ. b4y seu X - v aequ. b. a
aequatio (18)
fres
AC et BC sit b. fiet Z- y aequ. b.
Ob analogiam 4 est g aequ mey
per 2 fiet
nic addatur
a XX + byy + cxy + dX Fey +f aequ. 0.
L xx + myy turu APX + 9y + Y aequ. 0.
1. . . . . . X .... X .... X .... X.
X +s X + FXXF Y aequ. 0
sit aequatio _Y + coco +Z 1pCo + 4 Y + 5C +6. aequ. 0. accommodam
ergo sr = s aqu. B3 paequ - , Erx dSaqu. E + 3+. kaego pp + dd
seu daequ = 1, + 3
on quia datur r S. aqu  ditmer faqu 1.
cd 1 S 22 7.
1) vabetur ergo constuctio quaesita
atbuc aeqe X
Jaqu aec
14y)
icc