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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 4
# Folio 8r, page id 00068076:0015
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igo
AE
e
c. TBs
sit e
April1 6X6 invengre bixcerm figaror proportionalem, BoBu B. videtum
imcthodus Abselvendum
4
vaeritur modus lnvemendo puncta , sic ut
C C) sit ad ratio, C (C); B(B) sit datae
sit datae relationis ad AB. ponantur duae
 C(C): CH  in CH:  B(B) = c( B(B,
seus
u
rectae CB ex C(B) concurrere in F
C(C). CH) in CF. BF = CB. B(B) = dato per
BE AB. sit X AG sit 1 FG sit f.
TA= AC CC TAa AE i EC 7 A + AE +
CY = EC
quaeritur relatio inter AG et FG. Est autem seu quantur punctum
intersectionis rectarum CF et (F) F. quaeratur ergo relatio
cujusque puncti rectae CF ad rectam AF, quod pendet ex ratione
relatio
---
salicet CE. EB = FC; AG = AB C
(
~At
C: IB3. H
est  CB = (CE + AB -AE, et BF = FG+ AG= AB,
seu et CF = SCE + AB- AE, + PCS FG + AC = AB
Ergo denique ex 
L2
a 
FA+ AE + EC,: TA+ AB,, inYCE+ AB- AE, + VC FG + AG - AB, jid FG + AG AB.
-
si
L
CE ad EB. Est autem C F Quaeritur salicet t inter. AE et E
B CE: EB seu fF
sit AE C scilicet
Y
= VTA+ AE + EC: TH + AC AB
= dato ex AB. ubi TA, FG, AG sunt duplis simplices, AE, EC, AB sunt
duplices. addatur avinc Aequalio CE: AB- AE = FG: AG - AB cujus op e
tolli potert AB ex praecedente. fiet aequatio, qu cujus in qua ex duplicibus solae superea
AE et AB AE et CE.  simplices vero omnes TA, AG, FG
Haec aequatio
ita ordinetur, ut TA sit sola, et ejus quaerendo dffaequationem differentialem
(2) habebitur aequatio in qua atm habeb dAE: d. TE habebitur per AE CE,
AG et FG. sed ex aqu.  dAE: dCE etiam habetur (3) ex aeg. praecedenti (1) per
uod=
BBBeria per eam TA habetur et TA+ AE: CE(g. FaAE: dCE
ergo duos
ipsius d AE: dCE valores aequando exseqque 2 et 3) habetur aeq. (4.) libera a differentrali
in qua sola  sunt literae AE, CC, AG, FG. Quae aequatio in Trus divelli
potest cujus ope quam ope ex AE habeantuur EC, et AG et FG adeoque et AB et differentium
arcuum cc ad quadcandom figum ex pordinaliam applicatis ad AB, seriret mnddo dicto
hor ec
Euit