# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0345
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0345?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 133, page id 824573315:0345
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=345
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000345.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.87
# 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.

PrOD. 166.
Arithmetica Insinitorum.
bel lX prOp. 138 nempe 1, 2, 6, 20, 70, _c. racio quam habet
unicas ad numerum corundem primo e secundo incermedi-
um, est ea quam habet Circulus ad guadrarum Diameeri: FF
Ellipss ad Parallelogrammum circumfcripeum. Ic deinceps
probabicur, ex prop. (c9.
DROD. CIXVI. Theoremao
Tleries infinica sequalium, Primanorum, Secun-
danorum, aut Tertianorum, _c. respective du-
catur in sciplam inverse politam; atq: cadem
etiam in sciplam directe politam: erit aggregatum
rectansulorumillorum, ad asgresarum horum; ut I
ad 1, 2969 20, 70, ec. numeros diagoniales Tabellae
PFOD. 132.
Nam silerier Aqualium in seiplam (sive directe sive inver-
Cc Poltam) respectire ducacur, tic leries AEgualium: cui con
venie ratio LadI.
Si autem Ceries Primanorum in sciplam dircece politam (10
malciplicetur; Fer Peries Sccundanorum; Si Peries Secundano-
rum sc ducacur, hec series ouarranorum; ( Peries Terrianorum.
hec leries Sexcancrum; et c. Per prop. 73. Ouibus conveniunt
rationes 3. 5. 3. 3. _c. Per PrOP. 44 vel 64.
Si aurem Series Primanorum respectire ducatur in sciplam
inverlam; (Duca Peries a b, c, _C. in Ceriem D = a, D= b.
D C, RC.) Iem Ccries Secundanorum in sciptam invertam,
(Duca Series a 2, b3 C2, _C. in Perie 9: D - a. d: D . b. d D  C_C.
vel D= = 2aD + a 2. D2 = 2bD +b2 V = = 2CD + c. _C.)
Icem Ccries Tercianorum in sciplem inversam; (pura leries a
b3,c3 _C. in Teriem C: D  a C: D  b. C: D  C. _C. ) EC HC
de reliquis; Raciones iplie ConvenicBe, 53 30, 1403 620, _C. PeK
ProD. 133, 134.
Racio igicur racionum harum sd rationes il-
la8, ea est quam habet + ac nymerOS L, 2, 6,
205 70, uc. nempe numeros diagoniales tabet.
2) + C.
D = C2
5. 36 6
IX PrOP. 132. (UF ex calculO PaTEL) Ouod eraE 3) 1to20
demonstrandum..
6630 (10
SCHOLo