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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 72, page id 85138403X:0080
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FVSooS Curva linea Cycloidis primariae secundum merhodu
Antignorum demonstratus.
Definirio.
Ronicudines  intinicum decrescentes sune quarum non da
Problema.
In dato Semicirculo ADD SubrenCaS quorcunque AD in daca
catione concinua disponere. Sic RatiO A M ad A D. DUCAEUE
CIrCUIUS AMM; tangens in A; _ Fat ubique AD (subrenta
majoris circuli) aequalis ipsi AM (ancecedenti subcensae minoris.
circuli.) Dico ipsas A D esse in continua ratione ipsiuS AD ad
e
AM. Junctis NN, _ DD, VeI NH, _D.D, e sic ubi-
vis; GuonIa MM, DD Cuntparallelae, ob aequales in similibus
segmentis AngulOS: ergO PATeE DEOPOTIEUM.
Scholium.
TiEdem posiris dico hranc subrensarum rationem in infinicun
concinuari posse. Nam E non possit, ergo dacur minima subren-
Ia, quo minor duci non potest: sIE ea verbI grALIa AD, seCANS
minorem circulum in Mu.
lis ip( ANI: ergo A s est minor minima, quod est absvr-
dum; ergo non dacur minima, eiso ratio subrentarum porest in
infInIEuM COnLInUALL.
Temma.
Sint eres circuli, tangentes se invicem in puncto A, quorum
diametri AF, A F, AC sunc in concinua proportione. Circulos
autem secet recta ANDC; item recta AuSK, ITA UC AS APTCTUE
in medio circulo aequalis ipsi A M minimi Circuli. Per puncta
deniquese D medii circuli. ducacue tam s NN O, diametro
perpendicularis, quam DB ipEI SN parallela. DicO ipIaS NM,
et s esse aequales: ILEM ND, SK: IFCM DC, n B. JUINSANEUEKC;
item ML: item MF. Duonia AuMF. est quadrilacerum cir-
culo inscripeum; ergo angulus externus suM aequalis est op.
POsicO incernO AFM; sed anguli ANO, AEM ob Cimilicudinem
eriangulorum sunE aequaLed: er50 anguli sp M, SLVM TUNE aqua-
lC5
F18. 15.
18.20.
lit hubltacndo