# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/85138403X:0123
# Permalink to this reading: https://leibnizlegible.com/page/85138403X:0123?run=74
# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
# Folio 107, page id 85138403X:0123
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=85138403X&page=123
# Source image: https://digitale-sammlungen.gwlb.de/content/85138403X/jpgs/default/00000123.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.
# 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.

Et TINANOuOS.
angulo subdupla. Tocumque triangulum, tocius spacii Spiralis
duplum; sinempe incelligantur conroluriones interiores roties
reperi quocies noris circulacionibus iterato de scribuntur.
Nat revera; uri spiralis Archimedea, non aliud est quam Pa-
rabola conrolura; auc etiam Circulus vel Circuli Secto:, cOnvo-
lucum ParallelOBFAMUI, (quod PFOP. 26. Rrich. InFin. Olten
dimus:) Sicspiralis haec, Hg. 34, non aliud est quam iplim
M AS criangulum (f18. 35.) convolurum; contreetâ nempe in
vunctum recta S M, adeoque parallelogrammis (Ere inlcripus
sire circum scripris numero intimicis) in tocidem eriansula redlactis.
Nocundum aurem hic elt; Tum proprer radiorum M A, MI,
M 2, ∞c. (vel rectarum in criangulo his respondencium) con-
cinue proporcionalium procellum in intinicum, decrelcendo; tum
erium propier eundem ubique Tangeneis angulum cum recta cir-
cundueca factum, (unde, circuendo, ad punctum M medium,
nunquam Perveniri porerie;) Manifeltum elt, sSpiralem hancIn
crortum (non minus quim extrortum; esse incerminibilem. Ne-
que eni ab A per X2 3 e5c. quoccunque demum circulationi-
bus Peraetis, ad medium unqua perrenietur, magis quam, sumpris
A 2, X2, 2 3, Gc. ProporcionalibuS, extAULICEUE UnGUaI A S
recta. UE aucem hxe omnes in infinicum continuacae, siC A I 2 3
50. concinuata inerorsum in intinicum, aecuabie rectam AS
Ilabes itaque curvam interminabilem terminatae recta aegnalem.
Sed e Facendum erie, Tangencem spiralis hujus, non migis
duci posse Geonerrice, quam spiralis Archiiredex, (uC Qua ex
quadratura circuli dependeat, uc ec Spiralium omnium Tangen
TCs;) adeoque nec angulum A geonetrICO assiONaTI. LineA LA
menincerminabilis terminua recte equalis, non minus line hoc
altionabitur: Si nempe, sumaeur criongulum, non rectingulum,
UE AS V AO. 33. Sed crianoulo A SC simile; uC enim AC
2d AS, siC Omnes AC hoc est A M rectaad omnes AS rectas
drcubus aS numero infinicis in(cripEAE.
Flanc iptum curvam, alia occatione, concemplatus irem est
Wrennius noster. Nec eantum currae lonoirudinem, partiumene
iPlius, de magnicudinem adjacencis plani: Ced er, iplius ope, Li-
macum e Conchiliorum demunculos meritur. Exiltimac ucique.
masna veritmilicudine, domunculos hosce rion alios ene quam
Pyramides conrolutas; quarum Axis liC, istinsmodi Spiralis; non:
quidem