# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0387
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0387?run=74
# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 175, page id 824573315:0387
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=387
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000387.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.90
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

P. 1
Arithmetica insinitorum.
non possic, inveneus cR modus ejulinodi suppoliciciam divilio.
nem indicandi ad hanc Formam Z vel 1 =
In excractione Radicum; s proxonatur numerus resolven-
dus qui non sic Cui generis rere fguracus; verbi gracia, s quae
racur radix quadracica numeri 12; quoniam radix illa non po.
rcstullis numeris sire incegris sre Fractis exponi, ideo invenca
eA mectrodus ejulmodi R adicem suppoliciriam uccunq; indican
di ad hanc Formam, V. 12, vel 2 ~ 3.
Paricer, in Proxreltione Geomerrica, puta 3, 6, 12, _c. Si
guaeracur cerminus novus incer 3 _ b incerponendus, dicetur
ille 3 V2 vel ~ 18 vel V: 3.6: vel Force (quod cancundem ralec)
a: 2 n 9: quod idem elt acq; explicatius dicere, terminus mediu
inter 3 8 6 in proeressione 3, 6, 12, 8C. auc inter 2 89 in progressione
2, 9, 40:_C. Ica si incer 3, 6, incerponendi essene duo medii
Gcomecrici, essec eorum prior N c: 3 x 3X6: vel VC 54 vel po-
tias 3 VC2, (nempe 3 ducti in radicem cubicam communis ra-
tionis 2) et lic in caeceris.
Si aurem Propressio Geometrica, qux supponieur heri ex
concinua mulciplicarione primi cermini in numeros quocliber
inricem aequales, CpuTa 3,6, 22, 24, _C.) ex continua multi
plicacione 3 _ 2 H 2X 2_C.) non Cempee admictae cerminos
incermedios racionales: non mirandum cA B neqs illud concin
Bac in proprestione Facta ex termini primi concinua molciplica-
eione in quoclibet succedences numeros inaequales, sive crelcen.
ces sire decrelcentes; (Duca 1, 2, 6, 24, _C. ex continve mulei
mulciplicatis 1 X Z X Z X Z, _C.
63 10
63 A13 _C. ex concinue
Ouories aurem hoc concinvic, cum illud reris numeris detie
nari non possic (_ ne quidem Colis radicibus surdis) quaeren-
dus eric modus aliquis id iplum accunq; exprimendi. Si igitur uc
V: 3 X 6: Cignificac terminum medium inter 3 ∞ b inproeressione
Geomerrica aequabili 3, 6. 12, _C. (concinue mulciplicando z X 2
n 2_C.) ica nr: TIZ: sioniticec terminum medium nier F e Z
in proeressione Geomerrica decrescento F 2 2Z _C. (continue mul-
ciplicando r X Z de ZRC.) erit E = M: YIZ: PC prOPTerCA
circulus est ad quodrarum diametri, ut Z ad m: FY Z. Oux quidem
eric veca circuli quadracura in numeris, quacenus ipla numero
rum nacura paricur, explicaca.
Ec quidem, licuc in proxrestione Oeomeorica aquabilin 3, 22,