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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 189v, page id 00067993:0380
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fier aequatio talis, 
in (3
BH m .
Qui hijus neae inquisitinis cexitus cum uti s 
ai 1p
TaTO omnium
, quo in quos tota Geometria incisdi, oper ae pretium cerit
applicare exemplo illustri marum Mediarum stroportionalium;
fateor suspicari me subesse errortems, sed cui in ipso calculo
deprehendam fullum superesse ut ex. lo quodam delut
lujide lydio comprobetur int refutetur. Si ae sunt
santo duae rectaa datae Cot inter quas nae quae runtur mediae
v. et X. sie d etduas dabebimus aequationet. by X go
=Cx 1Y
et (13) et Cx pp. i sse e unam ex altera fiet.
componendo be
Aep. (5)
1)
2 ..9nil , sice  +S
e
quae est ad circulum. Acplicando aequationem 12. per β.
et 19
per V. ac cmponendo fiet  y3 ia ta  denius multiplic
dco
cundo 13, per B. componendoque Eus tres aeydaationes, fiet:
utam
+7 X 487
1X 7bgen i a ctef 9
ee  ii
+ san b.
1
ficuado
l
( de sive  +
1V. B
X j+ Vad y   b X LVbLOB
2V+B
1+6 d 1el uytdaat 11.
2-ob ass
+3 aB
Aequaholi 16 gungatur Aep. 14
multiplicata. D. per poram arbitruriam, d, fiet: 
14
L in suc quidem casus
Sed ex his piii deprehando fontem moris ac dec indeo solis
compositionibu effici non posse; ut plus quam semel duo habe
duo iidem Termini habeantur puri. sim ohic quidem in aequa
tione tam dinsici ut ergo res succed  neresse est ab aequa
tione 14, alialu ac haberi diversos habentem Multiplicatores
Terminorum simcognitorum, eaque obt, nam hic quidem, quia b_ est
uantit
solu terminus; multiplicans X  et multiplicans y. et 1. sola multi-
plicans X vel it, hinc fieri non potest, ut quin dividendo semper redeatur
ad priora. Ut ergo ris succedat sumenda et a prr sunt duae aliae aequationes
duam incognitarum, quae ad us duas Medias proportionales reduci possunt
ipsis resolutis etiam methodo generalis patebit duarum mediarum proportio
nalium, ei Rutro darae ad (prutum non nisi ma us ndta fuid
obtinendo duas aeqationes ad parabolam,, quibus compositis fit. aigratio ad
circulum. Ex duas aleas adjicio at unam per nper Multiilicationem
Arbitrariarum, alteram per explicationem incognitae utramque hoc loco
expositam. Datis dnabus aequationibus quilocunque quadhaticis duarum
incognitarum verum est semper per solas composi ones nonnmntat
Incognita effici posse, ut habeatur quatio pps habens Terminos
peros, qualis est eratio, ad sarus iu vel efinus data noguni tadie
eadem vel
aecq.