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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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DE
C2C 10LD
lum ateinsie, e angulum incernum polygoni circundati ad ver
cicem habet.
Problema.
Polrgonum Serrarum semicirculo dato inserere, cujus summa
lacerum lie duplo diamerri minor; aeque aliud circundare cujus
Tumma lacerum sic duxlo diameeri major; ita camen ur urrius
que lumnae differeneia sit dacae cuicunque mognicudini aequalis.
Sic Pemicirculus dacusi A DD, cujus diAMEEeF SIE AD;
mienicudo daca X. Dacaigitur media proxorrionalium AD.
FIAHE A M, AD, A C concinue proxorcioniles, ita uc diste-
TENEIA EXErCMATuM N C, aequalis lic ip(i X. Disponantur autem
subcensae A D ubique in daca ratione AD ad AM, _E COntI-
nuetur ratio in infinitum. Productis deinde (ubFen(IS, per Unu-
quodque D ducancur parallelae NDB, ad P orimam uETIn-
que liibrentam. Patec ex iis quae dicta sunc, Polygonum semicie-
culo intertum esse. Aeque aliud circundatum. Dico aurem insu-
pec lacera Inserei simul sumpea (Ecilicer omnes in inFniEUM DN)
deticere à duxlo diamerri defectu D M; Latera vero circun-
daci (Scilicer omnes in insinitum BD) excedere duplum dia-
metri, excessu D C: differentiam denique lacerum utriusque
polysoni aequalem esse dacae magnicudint R.
Diamerris A M _ AC, ducantur circuli tangentes eriam
In A _ secontes Tubcentas in M e C ubique. Ouoniam ergo
subrensae AD dispOnUnEuE in daca PatiOne AD ad A M; ereo
AM Canrecedentis Tuhren(a) aqualis est (consequenti) A V.
ergo M N (anrecedentis) aequalis est ipsi D M
EIS) _ Sc ubique: ergo differentIA ipTaTUM DM, W N (ejus-
dem subrentae) aqualis et differentix ipTarUI D M, D M(an-
recedentis ex consequentis:) Ip(X rerO D M cum SinE magnitU-
dines in infinicum decrescences differentiarum summam aqua-
lem habene maximae DM; ergo summa omnium D M minus
MN (ejusdem Subren (X,) aGUaEUF MaXIMA D M. Sed quoniam
DM minuS M NI, aequalis est duplo DM minuS DN _ CC
ubique; ec quoniam summa omniur. DM, cum sinc differentie
subrensarum in infinirum decresceneium, RQUaEUE MAXIINX A 1)
(Tcilicer diameEFO:) EFBO dUPIUM SIMAIMA IDTAFUI D M (hoC est
duplum diamerri) minus cumma L acerum DN, aequalis est ips
DN. Ereo omnium polygoni Inserri Lacera deticiune a duplo
diamerri defectu D M
RurTU