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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)
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DF CLCLOILL
RUTSUS QUOnIAM AM, AD, A C TUnE IN COnFINHA PPOPOEEIO-
ne; ereo C D (ancecedentis subren(a) aequalis est ipsi B C.
(consequentis) e Sic ubique. Ergo (eodem modo quo suDPA)
demonstratur, quod duplum summx ipsarum BC (hoc c.di-
plum subcensae AB1) minus summa lacerum BD, aqualis (IC M. -
Xia D C; ergo omnis Dolygoni circundari latera deticiune à
duplo subcenta ABI, defectu B C. Sed A P aequalis est ip( AC,
e B C ip CD. Ergo omnia Polrgoni circundati lacera super-
ant duplum Diamerri excesu DC.
Addatur demum defectus, _ excessus quibus, hinc inde poly-
oona difterunt à duplo diametri; ergo CM est urriusque difterer
tia; ex aequalis quidem ponitur iph Z. Ergo lemicirculo AD D
volvoonum serracum insertum est, se simile est circundatum,
hocmajus, illud minus duplo dimerri, utriusque aurem diffe-
rentia aequalis est datae magnicudini Z. Ouod erat Faciendum.
Scholium.
Dato circuli seomento quovis A s D, eodem prortus modo
polrsonum serracum inseritur e circundatur; e demonteratur
lacera inserti deficere a duplo balis Seomenti AD, defectu
D M; Lacera vero circundati excedere duplum ejusdem, exu
cessu D C utriusque rero differentiam esse C M; quae cum
minOr (IC quam C. M, minoc est qua Z.
Lemma.
Si d puncto quovis O in C ycloide primaria S PO A D; du-
cacur Tansens OV vertus Balin, icem bati parallelae NVOD.
_ VP C secances Genitorem in D, C, quibus A junOaEUF, e
ducatuE OF, Parallelaip( A C. DICO EANOenteM OV Ma-
iorem, iplam vero O F. minorem esse porrione Curra inter pa-
rallelaSInECTCCPEA OP.
DUCaEuE PYN ipE O F. parallelaicem, subcensa porrionis
PO. Guomiam angulus PF. O est obcusus (cum sic aequalis ipA
PC. A) ergo F O minor est recta PO, ergo mInO CTIaM
CurVa PO.
RUESUS quoniam P N parallela eA ipsI AC, ergO FAMBIE
Creloidem in puncto P, e quoniam angulus V P Y est obtu-
Tus, ergo YP minor est ipta TV, ergo OTV major estipsio
DE, LP, imul sumpris, ergomaior eAE POTLIOnC O L
Definitioo