# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0401
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0401?run=74
# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 381, page id 851387705:0401
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=401
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000401.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 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.

PTOD XXXVIII. TNEENEEO
ad Tangentem angulos rectos,) FO, FO, _cc. quarum
minima dieatur Z; crunc illa ad inricem Der DFOD. 23
uc numeri quadraciei L, 4, 9, X6, ec. ec carum ditteren.
FIX UE L, 3, 5, 7, _c. numeri impares deinceps ab uni
tare; (gnarum ditterentiarum aximma Crit 2 n -- F.
Recta parallelarum illarum terminos (in linea Parabo-
lica conttItutos) connectentes, (quae crunt propterea
ipsi Parabola deinceps in(cripta,) CrunE ut V: a = L
V: a + O. V: a + 25. V: a + 49, ec. (quippe quarum
quadrata per 47 C c. aequantur quadraris cam particul.
rum an quam ditterenciarum inter proximas quasque pa
rallelas, hoc elt, numerorum imparium.) Ouxe quidem
rectae (Parabola inseripix) quo plures tuerine, co pro-
pius ad parabolica menturam acceder carum omnium ag.
Gresarum; ica tamen ue ex omnihus sic aggregata recta
tic ipla parabolica minor.
Sin velic aliquis rectam julta majorem (ut constet intra quos cancellos deter.
minare possie parabolica lonsicudinem;) neque difficilis erie haec inrectisatio,
tansencium ope perticienda.
Si vero curva AOO, non supponatur Parabola, sed Paraboloeides Cubicale,
Biguadraricale, _c. Idem proceltus erit, muratis mutandis, atque in Parabola.
Sumendae enim pro parallelarum differentiis, non 2, 3, 5, 7, ecc. ditterentia nu-
merorum Ouacracicorum; Sed F, 7, 19, 37, Sc. ditterentia numerorum cubico-
TUM; rel E, 25, 65, 275, ec. ditterentia numerorum Biguadratieorum; _c. Prout
Pacabolocideos cujusque nacura pottuler; adeoque inseripix erunt V: a f 1.
Y: a = 48, _c. vel V: a + T. V: a = 225, dec. et sic deinceps. Vt ex interius
tradendis pr. 45. Parebit.
Adem sere methodo; Invenietur recta Spirali senvina quam. proxi-
 me aequalis.
Si enim (per ea qux dicta TUNE prOP. 5.) lupponatur inleribi tisura Spirali
alia ex quodlibet sectoribus similibus contlara: Frume (propter Spiralem) tam
Fectorum arcus, quam horum finus sire recti sire verti, ut et radii, Arichmetice
proportionales. Radiorum autem concinuum aue
mencum dicacur a. Si isitur a lectoris cujulris ar
cus inicio ad ractium per iplius cerminum ductum
demicri supponatus perpendicularis, erit illa iltius
arcus sinus rectus, cujus quadratum simul cum qua-
draco linus rersi communi augmento a aucti, a
quabicur quadrato rectae Spirali in leripia: (Per 4
CF.) Sinus aurem verfus ilse dicatur 2, et tocius
circuli sui diameter d; erie isirur quadracum Linus
recti (ex ductu sinus versi v in diameeri residuum
a = v factum) va - 2; ec quadratum linus versi
communi augmento aucti (nempe v f à) crit
2 F 2Va f a; _ propterea quadratum inscripix (ex his contlatum) v d F 20a
a. Cum aurem (proprer aequales similium Sectorum angulos) eadem sic ubique
linus versi ad diametrum rario, elto ea quam habet F ad m (quae ratio major
minorre reputanda cric prour lingulorum sectorum ansuli majores minoresve tue
rInC:) Adeoque cum liE F. m:: V. d, erit d = Vm: et Proprerea quadrarum recta
Spirali inseripex v a F 2 va F a2 = vv m f 2 2 a + a. Denique, cum lint (.
milium illorum fectorum deinceps politorum arcus, adeoque e sinus versi, A.
richmetice proporcionales, (ab o inchoati,) dicancur illi 0, F, 2, 3, dC. Frunt
ergo inscripia illa V: Om L 0a + a. V: Em + 2 a + a V: a m f 4 a + à
I: 9m + 6a = a. V: 26 m. F 8 a + a2. e Sic deinceps. Ouo autem plures
Fupponantur eidem Rpurx Spirali sectores inseribi, eo proxius ad lineam Spiralem
accedet rectarum sic inseriptarum agoresatum: quod tamen rera Spirali perpetuo
MinuS CxiI.
Si aurem harum inseriptarum prima omittatur, et illius vice post ulciman sub.
IANSACUE