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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 48r, page id 00067993:0095
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simpas
cere ap
hanc esse arbitior: Emutam ent verticit sactionis conima ertam habentis
occurat tangens usit secter
ector
sertionit conae duabus rectis in centro Q
concurrentibus et curva adverticem  sectionis porremiente (sine axis extremam)
perveniente comprehensus. ex ltap at practortongens tungenti.
vertiuis AT, ocurrat tungum,  IFF  ipsam A7 vocems +
et rectangulum sub semilatere recto in semilatis transversum sit ec esr
verenque contnennt indivisibilium Mettodam ciseneratisime concextum s onitas; nit sector ciruli sperbola vel Ellipseos: per semilatus retite divisus
+3
dc siguo ambiguo  valente  in Hypertola
ex in liclipsi llude posito cirulo quadrato circum seripta 2.
erit circulus = L + t  ec. quae exmessio haud dabie
 omnium possibilium simplicissima
es  mapliucue ufficens omentem.
lludea duco harmoniam sequentem
 e Cm ett 1
1
aeas
Sc. aqur 2
 7u et Si 98 63 80 99 1neq
210 peud
Amote sc aequi 4
es Bara Bsila um 63 icdad 3
24
requa
dit
35
 son go cempto. AC: aqu. 4
48
Ca. Eudidibiv 39
481 in utum
.Se ) exprimuss cirenli
12
om nyplibo
U nosse ol in dum
ia
chete
Vicissim ex scriebus  regressonum pro Hyperbola hunc inveni
si sit numerus aliquis  simitate mindr)  M, ejusque logarithmus, hyperbolicuL
14 s si numerus sit 
erit M aequ. L =  +  )  7 279 
major unitate, ut 1+ n tonc pro eo niveutendo mihi etiam
 is e
prodiit regula quae  in Neuloni litera expressa est scilicet
voli
134 8c. Mut t_ Mato
hutem in proxi ad estrior tamen celerius appropinquat, ideo
diit n aequ. Let
ea sed semper efficio ut ea possim uti, etiam cum numerus n 1+ n
est majoo est unitate, nam sit nmerus idem sit numer
unde si
est logarithmus pro f  e 1+ n, et pro 1
1 n 
1+n major unitate, erit L miner unitate: fent ergo 1 n aequ. 
ac inventa m bebitur et n sit i+n q sine
I+n
ptro inventione lutetum sinvum exarcubus
non quidem in Nentim regulam Quod regressum ex arcubus altinet,
 in regulam
a
numerus quaesitus.
inaederam ego un segutat, quae es 
quae ex dato siu arcu sinum complementi exhibet
nempe sin compl. aequ.  1 a + a c. 5 sed iper tundem us postea
denum deprehendi e eqactusin denus er quoque deprehendi ex ea illam
1p,24
altram, quam colinius nobis inserat pro invevendo sinurecto
posse demonstrari, quod tribus verbis sic
qui est a - a3 + a5
fit: summa sinuum complementi adarcum, seu omnium a + a hc
13
indau smmmrim locsdebtas visistutm n + Ande
12,3,3
at sum summa sinuum complementi ad arcum, aquatur sinui recto
rec ducto in radium ut notum est Geometris, rad id est aequatur ipsi
H
gc
Ex dato arcu sile sine ul per priorem regulam ex dato arcu sin et radio sine
ulla puasus later aliorum nobitia haberi potest area segmenti
a
Ercularis qa est dupliati, quae est 
et mum ec
gradus colenlabiatur
em hibula
fig. fig. 2.
utra et ultra
 jam trieunid abtiine a me commu-
nicala amicis
cujus qurd ratum
lisristam AC
. 2.
131