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# 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 170, page id 824573315:0382
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.92
# 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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# After the first blank line: the recognised lines in reading order, one per line.

arithmetica Infinitorum.
PrOP. 190.
POEIS PrOCENUS demONSTRTUE Ex PrOD. praced.
Norandum aucem de hic numerum quemvis incermedium 28-
erceacum esse ex duobus alcero surtum oltero ad dexeram (non
proximis, sed post unum incermissum,) posiris.
Cajusq: Seriei CharacterEm (quacenUS Per, proP. 181 inno-
celcic,) libuic eciam adjunsere, quo melius perspiciat lcctor
quoulq; rem perduximus.
SCHOLTV M.
Acq; hactenus quidem rem perduxisse videamur Caris Felici.
cer. Verum hic candem heret aqua. Neqi enim video quo
pacto possim vel ouancicarem e reperire, vel characterem le-
xiei A. CCF Propterca, nec characteres lcrierum imparium
Penicus aslequi, licer eorum ad inricem raciones coenoleanturs
nec imparium serierum locosimpares, quamris d horum eci-
am cognoleantur quas habene ad invicem ratione s.) Ouan-
quam enim simameri lacerales sinc inceori, puta 1, 2, 3, 4, dC0
noca eric quancicas A, DUTa L, 23 3, 2̀, _c. non camen Facile
eA deprehendere quo pactohorum numerorum ad luos respe-
etire numeros lacerales racio possie una aligua aequacione ex-
plicari: unde e religuis laceribus (locorum imparium) 2,2:
E. RC accommodari possie sira quancicas A. onanquam enim hinc
Ipeo non exigua rila eA aftulsilse, lubricus camen quem pex ma-
nibushabemus Proceus cam hic quam superius non raro elap.
Cas, Ipem Fetellic. Ouem aucem ee hic comprimenci vulcum
octenderic, non cric Forcastis insracum appoluisse. NenPe-.--
PROP. CIXXXZ.
Theorema.
N Cerie quarta, (sive parium secunda,) cujus nu-
meri alterne Cumpri (in locis paribus) 13 2, 3, 4
5, EC. hunc continua mulciplicatione numero.
um scu racionum 1X Z a ZX 3 L Z, RC. CCH 2X4, EX 4 x 2
ci _, Cin locis imparibus,) 3,2. Z, Z, _c, ex mulciplicaris
2xZxZXZx3, _C: Si, propter incercalationem unius in
ingulis spaciis numeri, (uc ex locistam paribus quam
imparibus intermictis una Aat Peries,) quaelibet ratio-
num, in quas continue mulciplicatur terminus tam
Parium