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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 214v, page id 00068200:0430
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similia his problemata alia formari possunt
multo cimplciora. sit quadrans ABC. quaeritur
segentum semisegmientum ADE ad quadrantem habens
rationem datam e _ b ad o. AB, Y
sit AE, AC, = AE: AC: : Z. N.: BAE: BAC-
jam BAC fi BAC b + pC. + =, Bd. DE 
BACH ACH _ AC. AEHZP. BAct e. BA 12C
BA
Ergo per 4. 5. 1. fiet: 2ZP pps bβ +  BD.X
Es. Z
F
e
eb + Bd, D52
D proponemus mroblema tale sato quadrante ABC.
puvenie. Aortionem ADEtalem, ut fiat, ut sit ad CFE
scunsegmentum ADE tale, ut sit ad sermisegmentum complementi
CFE, in ratione data
BCA, vd, 85
AdEL. CF Egil. m Adi +. pDDECAC + BDE:: AE. AC: Z. Y
aF
6c
et et
Am.  Sed notandum adhibendom
potlemata magis composita at destini possit quantitas cnrvitinea
magisque indefinita ut arbitraris explicatis destini queat
Quantitas curvilonea, et manebit silum aequato reflexa anguli
ad functiones
Ex hac methodo (vid prg. prared. sub fin. uidetur
demonstrari absoluta etiam specialis quadratinae impossibilitas
Nam ata alicujus sectoris quadratura semper reporiri potest
aliusus sector, cujus functionis relatio ad huj sctorem datas
exprimetur per potestatem, cujus exponens sit quantitas
irtrationalis. At eadem functionis relatio ad datas
habetur, algebraice. Habemus ergo duos ejus functionis exem
ili gratia chordae, valores, unum algebraicum,
alterum transcendentem. Sed cum ex. g. sit tran
chorda C. valor alyebraius sit Ix +a+YB+Xta
valor transcendens sit
il (2) aet Vhix + Y2) abax
posito Z. quantitatem esse datam quidem sied irrationalem.
aequantur ergo hiduo valores nd quae aequatio est aut
enuo
absurda sive determinans quantitates jam datas ac determimatus
 quod non est in potestate, aut est aequatio identica. Sed
identicam esse non posse sic constendo. Sint duae lineae curvae
nujus ordinata sit 1x + a rb +xta altenus sit vero
sit
Laxtsbaex + (2) ax- rbax patet enim non posse
ambas esse ad unam eandemque curvam seu non coincidere
inveniri posset algebur  indefinite idemque etiam numeris rollari potest. Quando
Ergo  Ergo si e secum  hae curvae secabunt tantum
certis in locis, adeoque determinabitur X. contra hypothesim
algebraicas
impossibilis est ergso Quadratura. Idem alun alticra emonstrari
potest. Nimorum quantitas analysica non analytice tracta
algebraica nanstendenter tractata, fit transcendens
ut ax + fbax transcendenteo tractata dat transcendente
harum autem duarum ranscendentium summa est transcendens.
quia nihal est in ipsis cur transcendentia trestinatur
videtur ego tande demonstrata impossibilitas quadraturae
ispeciatis. Quod antea non poteramus, quia ex aequationibus
hujusmodi non poteram facile tollere curvilineam quantitatem
oi, harte ioidtin  tnaper o plas aequatirs arpulare
ncam restante curvilinea semper
Ffingatur esse
Falioqui per lineam
curvam trans ententem
ptraeclari posset quod
per tinuscendentem