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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 248r, page id 00067993:0497
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mute cum t deries L -  + L-  r + etc aufertur ab Hyp. 1. 2. . = ete. estabit 1. L.   2 + = =   += CsC. que diss. tubtr. G
decatero sunt B = bi + b = 1B e summa fiet C-  + C es inferantu at Up nnmentae cosdissocid. nov exbasi, quod = H. cridam. Eigo ista salies
Inventum est a me: si dato quodam segmento ciil, cujus arcus non sit quadrante.
major, Radius ponatur esse a, tangens semiarus b sinus versus vero
la a + h = b d d cstansiom, aqualem fore ipoi bc  ; seu
diffecutia epsi Residuo e post segmentum datum ex semirectangulo  tangents
Inde ante omnia consequentia ducitur ejusmodi; Posito Radio a, = 2, erit:
e
+ b
etc..
9 x per solestates
Hinc statim habetur Appropinquatio illa maeclara qualis Aactenus in Hyperbola tantum
extabat at in Circulo, undus cundis quantitatibus involuto, dessirata habebatur Modo
enim a sit major quam  b, posito a = L, erit b, = fractioni cuidam. At
fractiones quanto n ad majores assurgunt potestates, tanto sunt minores; adeo
sut ad uum si usum spectes, posteriores infinitae tuto negligi possint,  sumtis
tantum aliquot prioribus. plibus paior et eo pancioribus quo minor esse b quam a.
Et vero si B potest b fieri quantamvis minor quam a quia  seu mentum
in alia minora aequalia bisectione arcus resolvi potest. Ut autem exactitudo
tradminabilis appareat accipe specimen:
divisisque omnibus per b, ino ec
fiet et multipli calis se
X3 erc.
29. 2 - 36- 28- 30
Si a fit plusquam decuplo major s ipsa b ntfintunt quatuor seminis prioneb et.
19, 00o, 300, 000
bho Jam suta Unde videhi
apparere progressiones
sore summabiles modo termia:
pec spatio aliquo finito exhiu
veri possit, eluditur opera,
si tamen vocetur, b,- inde
sequetur summa haec:
b- 26 + 2b - 3
autem seriei cum sit pure geometrica haberi potest summa. erit enim summa harum
nos 514= 14, e 19 Y ut C
.F., ergo A- B, seu b b 3, b 2. b2. b1 - v et
10,000 1- 
erit b  = b1 jam b 1 - b = 1- 50000=
H1 109,000,004 4. 0 0 M  10009000000000
1000 1000000000
1000000000
10000-1
(10000)
10000 e +
100000 10000000
1010000
1000000000
(105000
897 1g
10umo exite  eitppe iollade otsi n temini sepuentes serici
10000000000 10000V0, 000,
propositae omissi sine fractionibus esse intellicantur, ac proinde sne pladatione majores
ponatur esse:
quam revera sunt; omnes tamen simul vix non dum ascendent ad
 sin Unde error ipsis omissis nondum erit seu unius deemillesimae.
q Uende et facile intelligi potest, quotoalii termini, adjici debeant, qualuor
assuntis prout salicet major exactiendo defideratur ut Astronomicis fieri solet.
Caelerum quotes Arcus seguinti dati est quarantem minr,
quod esi b intellgatur Numeysine limitare
infinitu figurae nostrae aeguile est.
pua lefo
t. b.5 = A. seu -
vicissin 4 b 2  b17+ b et, = B. et B ad b13, ut b 13 ad b12 - b 17.
ergo B = bB b.3
et ba - b3 _
10000
2 0  vel 1 +-
10o 48 18 4 a el
Ad G 16
eut finiti. d
edto adi certesimen
+ B1, b 19 & = b1 bch. b21
decrescens.
64 - 16 = 48; 125- 25 = 100  10,00 10000000 100000000
0- 4 - 4. 27 - 9 = 18
30 16
quia numen
 oa mamus
b = b1 + b19 etc = b13 be7 b2. otc id enim manifeste majus priore.  Huju
licet infinitae
(1 4 - 2- L 9- 3 - 5. 16- 4 - 12.) 1- b2
25 - 5 = 2 0
10, 20 12
termdnorum
fore v enita
semiarcus in sinum versum arcus  ductu facto, subtractum.
a -- 
1 -  +s
fore Serie in infinitum produ forectam
arcus integri  C tunc differentium inter
su prsequamum Jes
2s1a42
Ego: H.
si
a serslat.
Hyp cnidor enfntu stutua tost
et alue Hyp. mboupt: C
velue x L + F a + etc
udt eadem uto os
et d iplicaliva
89900)100 0 oua