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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 168r, page id 00067993:0337
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A. B, C. D.
ab. c. d.
Datis quatuor punctis in una recta positis,
invenire aliud punctum, in quo linea
illis quatuor punctis datis concurrentes AE
omnes
BE. CE. DE. angulos faciant aequales AEB.
BEC. CED., quando id fieri potest.
Non potest autem punctum E determinari
nisi distantia ejus a dato quodam in linea
puncto determinari, cui scilicet imminet per-
pendiculariter, vel data simpliciter distantia
ejus a duobus determinatis in linea punctis;
vel data perpendiculari a linea educta in
quam cadit, et distantia seu loco in per-
perpendicular per distantiam ab alio
quodam in linea puncto definitam etli AF
AE, esse alti-
supponamus ergo lineam
tudinem Trianguli d AED. cuju basis AD.
esse esse (3) et latus unum, et lineam
rectam EF. altitudinem Tri angulii AED.
cujus batis AD. nobis esse cognitas, id est earum AB b
loco literas supponamus, atque ita aequationem
quaeremgus. Quare recta AB. vocetur )
recta BC vocetur (_) recta  CD
vocetur (d) recta AE vocetur (a)
et recta FE vocetur (P)
Hinc literae reliquarum linearum  EB. EC.
EC non habent opus peculiari suppositione
sed ex praecedentibus, determinantur
Nam ante omnia determinanda est recta AF
inele
Ea subtrahatur quadratum EF. a quadrato
AE, nempe (aa). refidui Radix qu. a- e,
est. AF.
quodsi recta AF a recta Ad subtrahatur
fiet: B +c +d = R4 a = e. A esse
est enim F cadere in lineam AD si suppo.
namus line Dunctum F. cadere ln
lineam AF. Sed quia hoc semper necesse
non est. Ideo mutandus est problematis
tractandi modus, et vel sptudi sunt
Casus diversi vel si una analysi omnes com–
plecti volumque necesse est quam libet darum
linearum AE BE. CE. DE Supponi eb
alia in de pendentem
a0ou
00oudoi estvoox.
AE a. B AE. a
EF
D. EF. C2
+d
AD. Btct
AF. R9 a= C
FD. b+c+ d - B9a- C
AC. B+C.