# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/85138403X:0086
# Permalink to this reading: https://leibnizlegible.com/page/85138403X:0086?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 78, page id 85138403X:0086
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=85138403X&page=86
# Source image: https://digitale-sammlungen.gwlb.de/content/85138403X/jpgs/default/00000086.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.89
# 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.

SCFOTD.
maliter rectae ma, e in prorime majorem m a rectae mu: du-
CaNCUE, Dn (Tubrenta genicoris) e M Z, Parallelae ipsI m’a
IteM AM, a Z, dS parallelae: quare a 2 cangit C veloidem in
an e Parallela e aequalis est ipsi mW. Qnonom igitur ip (x
i 2 (Guum (iMIE. aequales _ parallelae subrensiS genitOris) TunC (I-
nus angulorum suorum a mC ad Radium AD; e in Frian-
sulis rectangulis mu m, lacera mu linus corundem angulorum
2d Radiu M MS ergO eAt VE AD ad riII m, ica ma ad
m’u, vel a 2. Fcquoniam anguli a m C aequaliter sese ex-
cedune, ergo in Triangusis similibus AD n, ~’ I S, eA UE A D
ad An ica n a ad 25, e (quum An sic indetinite mini-
ma, e Propterea aequalis arcui An, live ipI mW) est uE
D ad mn, Ita M a ad aS; CTAE AULCM UE AD ad
M m, ita n a ad d Z3 quare est uE M a ad n d, IEa 2 Z
4d d5, Sed diferentia InFeF a M _ aM est ad a m data
quavis ratione minor, ergo a 2, dS lunt aequales, _ limul sumpEx
portioni currae a’a aequales. Fst ergo porrio aa duplum ipsius
mu: atque idem ubique demonttratur. Omnes igieur a a TuNE
duplae omnium m u. FE s abscindatur a verrice portio quaelibet
A a ea dupla eCL OMNIUM M u guX SIINE INEeF D EE M: Sed
omnes mu (quum ipsi mu sine Cines complementi, quorum
sinus recti une um) sunt aquales omnibus um: omnes aurem
i m (quum sint differentia ipCarum m a) Cune aequales maximae
m a hoc est ip(i AD. Frsosemicurva A a 8 dupla est diametri
A D. FE quoniam omnes um inter C _ mI, sunt aequales ma-
ximo siriui scilicet mlaIs ergo omnes mu inter C _E mI TunEX
quales linu complementi iplius mal. Ouare Porrio quaeliber
UE A Y (cujus normalis N Y est Imus rectus anguli Y N M ad
radium AD) dupla est sinus complementi AFI.
Curvis Cjeloidum Procractarum es Contractarum
assienantur semiellipses aequales.
N C. veloide contracta G0OM, demittantur ubigue 00 per
Lpendiculares in proxime majorem om, cui parallela ducatur
ay ex junctis00 inscribatur polrgonum. Ouoniam estuE AD
2IAO, ita ma ad a0,ec in Triangulis similibus ma65,
aOy, eltuem’aad aO, ica aS ad O1 y; ergo eAt uE AD
ad AO, iCa 
Sad Oli y, ec converse uc 2 A D, dd 2 AD + AO