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# Title: LBr. 695 · Oldenburg
# Folio 46v, page id DE-611-HS-860722:0092
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 47r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
# Lines: 86 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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8. EH VDEi quad atria cusus verten. V,
exattente A centro circuli et AD Diametr
circuli ad quem aptatur, et angulo VAF recto.
demissoque ad AF. perpendiculo quouis D et
acla quadraticis tangente Dr occurrente ai
ejus in T: dic AV = a, et AB - r, eret que
BD = ∞ - XX
AVDB = ax
+ 604 2es
24
2 26
45 a 945 as c. Et V7- 3a
10 a3
+xc et area
+ 14 ∞
225a 6615 a rec: et arcus VD = X + 2X
= 2X7
Xa - 25
27aa 2025 at
893025 a6 + c. onde vicissim ex dato 8D, vel vr; aut area AVDB arcuvi
VD, per resoletionem assectarum aequationum orui potest X seu AB.
9 Esto denique AF: B sphaeroides, revolutione elliptees AEB circa aercemA
genita, et seita planis quatuor, AD per axemtrunteunte, D y parallelo
AB, CDe perpendiculariter bisecante auem, et krG parallelo Cc: sit que recta
CB =a. CE =C. CF = X et FG = y; et sphaeroideos segmentum corG dictis
quatuor planis conoprehensum erit.
+ 2 CX 15
CX3
3 aa
Eoa
exat
5CXG
576∞
E 3.
18Caa
40cat
5X7
336c ab
ac.
20c y5 - 3
tocdaa
160c at
V7 = 5X
33ocaa
dec.
576C7
ec
19 -_ec
Ubi numerales coefsicientes supremorum tern
rum (25, 20 15 570
in infinitum producuntur multoplicando primum coefficientem continuo per
52X7. 7X9
. -13, 3X5
4XS bX7 9XG 1OX UC. Et numena
rec, in tertia per torminos hujus 36. =X
4X5
6X7 ∞X9 UC, in quarta per terminos hujus =X1. 4X3.  9X5
erx 475 + 6X7 8c. et
in insinitum inquinta per terminos hujus 52,. 9X3. 11XE. dec et sic in
4X= 6X7
infinitum. et eodem modo segmenta aliorum soledorum delignari, et
valores eorum aliquando commode per serres quasdam numerales in infinit
produci possunt.
Ex his videre est quantum fines Analyseos per hujusmodi infinitas serins
aequationes ampliantur: puipste quae earum benesicie, ad omnia pene
dixerim, problemata (si numeralia diophanti et somilia eacipias s se entens
non vacat dicere; et neque alia quadam tradere quae circa reductionem
infinitarum serierum in finitas, osi rei natura tulerit, excogitavi nam
parcius scoito, quod hae speculationes due mini fassidie esse caperunt, aded
addam: quod postquam eroblema aliquod ad infinitam aquationem deduct,
non tamen omnino oniversalis ouadit, nisi per vlleriores quasd’an methodes
assectarumve pervenire: Sed quomodo in ittis casibus procedendum sit tam
ut ab eisdem Jampes quinque: fere annos abstinuerim. Onuum camen
possint inde varia approximationes inosum mechaniiae nullosere negotio
eliciendi serces infinitas, sunt enim quaedam Problemata inquibus non liceat
ad series enfinitas per divisionem vel exeractionem radicum simplicium
formari, quae per alias methodos quasitae, inulto labore temporis que
dispendio constare solent, cuypci nec coremplo este possunt soacracis
caessicientes terminorum in onaquaque columna descendentium in infinitum addenco aequationem 1. 112
4X5 6XY OXB
9X2
producuntur multiplicando continuo coefficientem supremi tormini irr,  e quod restat dividendo
columna per eandem progressionem, in secunda autem per terminos hujus
IXC 5X3, 5XF. 7X7
2X3
7X5