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# 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 71, page id 85138403X:0079
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# Lines: 41 recognised, mean confidence 0.89
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DF CTet
ergo complementum anguli u po sciliceer p m, est minus com-
plemento anguli mop, scilicet anguloom P; ergo in criangulo
FPm lacus Fm, estminus lacere r D. Sed u F, FO aequales esse jam
demonCEEANEuT, ergOu P major elc ipta O, _ OM MajoF arcu
Op: exgo W P elEMLIOE AICU OP.
Dico poltremo seomencum incernum D e ese minuS arcU OP.
Ouoniam enim anguli roc, reo lune aequales, ergo minor est
angulus poC angulo peo, ergo in eriangulo DOC lacus D CMI-
nus eltlatere PO; reEtA aurem P O minOr elt AFCU P O; C19O
De minor eltareu P0. Similiter demonstratur de a e.
Problema.
Ad datum punctum c in Crcloide st a d Tangentem ducere.
Ducacur co basi parallela, e per punctumo Genicoris duco-
cur Tubrenta aou, cui par allela ducacur XCY, dico rectam Xy
cangere in puncto c. Nam Sinon LanSAE, ergo sCCAF IN C, erSO CA
dic inera curvam aue versus basim, auc vertus verricem.
Cadac primo si Reri possic versus Balim ex sic punctum aliquod
ZIMETA CurVaM: e ducacur ba(I ParaIlela X uP, _ producta sC-
CeE CurVaM In S, e producarur subrenta ad u. Ouoni-
am ergo alibi demonstratur e primis Cycloidis proprie-
earibus esse quod Parallela basi incer Cyeloidem et Genirorem
cerminatx, sinc arcubus Cenitoris ad verricem abscissis aequales:
ereo sp est aequalis arcui pO P 2, _ F O arcui OPA, CrGO CO
plus arcu op aequalis eA iph g P: Ped x u aequalis est ipsiCO, _
segmentum externum up eA majus arcu op; eroox up majoe
eit iplS C0, OpEmul Cumpris: ergo p x major eAt ipld P 8.
ereo cadic exera punctum s currae, ergo idem punctum est intra _
exera curram, quod est absurdum: ergo non est inrra. Cadat jam
inera curram versus verricem; ex sic punctum aliquod y rectx
CY intra curram. Ducatur baliparallela y Ne, ee producta secet
Creloidem in h. Quoniam ergo ve est aequalis ipsi C0, _c h D
Plus arcuplo equalis ipsi c0, et pe segmentum internum est
minus arcu No; ergoh De minor es ipsis h B, B0 simul sumpris.
ergo minor est ipta F0 ergo e y major eh ipsa ch. Frgo punctum
V est exera e inera curvam quod est absurdum: ergo non estintra.
Similirer demonstracur nullum punctum rectae X y ese inErA CUr-
vam, ergo non secar curram in punctoc; ereo ducta eAtcy can
sens Creloidem in dato puncto c; quod erar Faciendum.
Evdvoud5
Fig. 24