# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/867984570:0663
# Permalink to this reading: https://leibnizlegible.com/page/867984570:0663?run=74
# Title: [Quo Continentur Claudii Ptolemaei, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunae, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Graece & Latine Edita, cum Notis ; Accedunt Epistolae nonnullae, rem Mathematicam spectantes; Et Opuscula quaedam Miscellanea] Quo Continentur Claudii Ptolemæi, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunæ, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Græce & Latine Edita, cum Notis ; Accedunt Epistolæ nonnullæ, rem Mathematicam spectantes; Et Opuscula quædam Miscellanea (shelfmark Leibn. Marg. 100:3)
# Folio 627, page id 867984570:0663
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=663
# Source image: https://digitale-sammlungen.gwlb.de/content/867984570/jpgs/default/00000663.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.80
# 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.

joris.
tet
ii 12
11
H
OL L F CTIO.
2
e FstO DF Ouadratrix, cujus vertex est V, existente A centro, _ A F semidiametro Cir
a
15 a 345 a
cl. Lit
25 a 169a
X
Fricque DB = a-
Ft aiea AVDB = a X
2025 a 803025 a l u. Onde vicillim, ex daco BB, vel V L, alt alla AVDB, ac.
24 X3
cuve YD, per resolucionem altectarum xequacionum crui porest x seu AB.
culi ad quem apcacur, et ansulo a L. ACc. Dm  A L DerPeHMLO quor B,
et acta Guacratricis Tangente DT occurrente axi ejus AV in Y: Dic AV = a, e AB = N;
= _C. FF arCUS VD = ∞ +
Da 225 a3 6625 a
it aa
604 X
Fc Sphaeroideos scgmencum C.D CF dictis quacuor planis comprehentum, erie
= 2 c X y
3a 
20 a
D. Fsto denique A F. B Sphaeroides, reroluctone FIlipleos A F. B cirea arem AB penica, et
secta planis quatuor, AB per axem cranscunte, DC parallelo AB, CD F. Perpendicularitet
a
Bilecante axem, _ F G Paralselo CF: Sirque recta C B == a, C. F. = e.
PF =
5
336644
20 c3
18CaA
406 a
336C a
40C aa
1600 4
=
576 a
Ovi numerales Coefticientes tupremorum cerminorum (2, = , =
563=3, dec. in
intinitum) producuntur mulciplicando primum coesticientem 2 concinud per cerminos hujus
progrestionis = LXF L X 3 3X5 5X7 7X 9
2X3 4X5 6X7 8X9 TONTZ
EC. Ft numerales coefticientes terminon
rum in unaquaque columna descendentium in intinirum, producuneur multiplicando conti.
Dud coesticientem supremi termini in prima columna, per eandem progrestionem; in secun.
da autem, per cerminos tujus = X L 3X3 5X5. 227, eec; in certia, per terminos. hujus
2X 3 4 X5 6X7 8Y9
2X3 445 6x 7 8X ec; in quarca, per terminos hujus
3XF 5X3 7X5 9X =
7X3 9X5
in guinta, per cerminos hujus ZL Z DX3 LFNS, ecc: et sic in intinicum.
2X 3 4X5  6X.
Ex eodem modo segmenta aliorum Colidorum delignari, de valores eorum aliquando commode
Der series quasdem numerales in intinitum produci pollunt.
FX his videre elt, quancum tines Analyseos per hujusmodi intinicas aequationes ampliantur:
Ouippe quae, earum beneticio, ad omnia pane dixerim Problemata (si Numeralia Diophanci de
limilia excipias) sese extendir.
Non camen omnino univertalis evadic, nisi per ulteriores quasdam meshodos eliciendi series
N M MIM 2
infinitas.
5
= _c.