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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folio 19r, page id 00068033:0037
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Novembr. 1679.
imo pihit
hinc ductum
centala mpossibilitas quadraturae.
quae hic de Ayuibolae quadratum ea dempossumt applicari quadra
turam methodo mea
Sit aequatio
X
a p b. vel simalis
ajo si  X non sit quantitas rationalis
algebraicam
nec fore quantitatem analyticam. Nam
si sit irrationalis, substituatur ejus valor
alytica non est in exponente,
a
quas
unq
aequatio autem ljus exponens est irrationalis
alytica non est
numeri et sit b
sont a et b
Hinc si appareat
a et b tatem habere relationem, ut una
quomodocunque secundum exponentem rationalem in
se ducta non possit producere ulteram, tunc
quod statim apparet, tuto concludi potest
X non esse quantitatem unalyticam algebraicar
pono Cogarithinus. Inventio pendet
a resolutione exponentis aequationis in
qua incognita est in exponente. Et quadratur
Hyperbolae portionis hyperbolae pendet
a logarichmo et unius praeterea portionis
Hyperbolae Quadratura, exemplia gratia ejus
Lex
quinquelinei ACBDE
quadrilinci cujus altitudo
sit 1. et basis CB sit 2
cujus artam
cujus area n sibene memini est 
1
e
+L - 1 Ac. quae est ad aljam aream
quamcunque
ut
rithinum CB.
quaemaq
ACFGE. ut loganthmus CF ad loga
si jam figura coganthint
seu aescisra
cujus numeri sunt algebraici