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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 73, page id 85138403X:0089
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# Lines: 41 recognised, mean confidence 0.87
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DF
CacL
MI A B; Hac deinde BC ad BM uc R ad5, 8 ducatur C P ad
ansulos rectos secans C Veloidem in P, icem PF Bali Parallela se
cans Genitorem in P. Jungantur denique F.C. Dieo mixtilineum
A F. C esse ad Cemicirculum uE R ad S. Ducacus radius D FC; E
dCMIEEaEUE ED; _ junganeur F B.
Ouoniam seomenta a EP, A P F Pune limilia, erGO UEAECUS aC
ad e p, IE ArCUS A P ad P F; _ quonia aECUS A L. ductus in se-
miractium aequalis est sectori A F. D, ec semissiS basis D B sive sC-
miradius ductus in alticudinem F F xqualis est Triangulo D F B.
exBOUE A P ad F F, ita seSTOF A F D ad Triangulum D F B; 8
UE aEadE PIEA A F D, ad D E B: Ted uE 50 ad F F, ica TriaTOV
lum D E B ad Triangulum DF C (quia TUNE uE BaseS DB, DC:
exit igitur ex aquO UE a E ad E F, ita sectOF A F D, ad Prianou
LuI D P C, S converse limul _ inverse erit, ut a e PluS PF, ad
a C, IEa AF D pluS DE C, ad AF: D; Sed ac elt ad semiperi-
FheriaL a X B, UE sectOF A P D ad semicirculum A H B; eric ioi-
EAF Cx XQUO UE a EPIUS F F ad Pemiperi phCTIA, IEA A F: D pII S
DF. C ad semicirculum: Ped ex iis quae demonstrata sune de Cy-
cloide, quoniam P. P esad Balin BM, uc anguluS ABF ed F.
ctum, lire arcus a e ad semiperipneriam a n B qua quidem equ.
lis est ips BM; ergo a e plus P Laequalis est iph F P: est ergO uE
F P (vel BC) ad BM (SirC uE R ad S,) ita MirrilineU A FC
ad Temicirculu A K B. Guare PemicIECVIUS A R B per punctum
datum C. ita secatur a linea C. E uc pars lic ad torum in daca ra-
eione R ad S. Ouod erat Faciendum.
Scholia.
Duod si punctum C sic in ipla extremitate Diametri, puncta
C, B, B, coincident _ Balis B M aqualis est peripherix Geniro-
ris; Duare Crclois elt Primaria, ec ductis  P, PF codem moco
pertcitur Problema, Sc Facilius demonstratur.
Duod ( punctum C sIc exrra circulum productâ Diametro,
Crclois erit contracta, e Mixcilineum A L C, non Polum alI3-
nitur semicirculo minor in data racione, sed porest etiam major
esse vel aequalis.
Demonstratur d Keplero ex data sectione semicirculi a puncto
Diamecri, posse semiellipem quoque a puncto axiscrantrech in
data racione secari; sed idem eriam perticatur a puncto cujusvis
AX150
eida