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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 534, page id 851387705:0554
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DF C,Y CL OT D F.
IpH CO, _ SeBmentUM ExternuM UP Cst majus arCU OD; ergO XUD major est
ipsis c0, op limul Cumpris: ergo pX major est ip (a p 8: ergo cadic exera punctum
 Curra, ergo idem punctum ele intra ec extra curvam, quod ele ablurdum: eroo
non eltinera. Cadac jam intra curram versus verticem; et sic punctum aliquod
Y rectae cy inera Curram. Dueacur bali parallela y p’e, et producta secet Cyeloi.
dem in h. Ouoniam ergo ye clt aequalis ipsi t0, et hp plus areu po aequalis
ipli c0, e pe segmentum internum est minus arcu p’o; ergo hpe minor est ipsis
hip, Potimul sumpris, ergo minor est ipla c0, ergo cy major cM ipla ch. FrgO
punctum y est excra et inera curram, quod est ablurdum: ergo non elt intra. Si-
milicer demonttratur nullum punctum rectae XY esse inera curram, erso non se
cat curram in puncto t; erso ducta est cy tangens Crcloidem in dato punctoc;
quod erat Faciendum.
AAIANE c
eoduos Curvae linea Cycloidis primariae secundum methodum
Antiquorum demonstratus.
es Definitio.
Masnicudines in intinuu decrescentes sunc quarum non dacur minima.
 Problema.
In daco Semicireulo A DD subren tas quorcunque
A D in data ratione continua disponere. Sie Racio
AM ad AD. Ducacur cirentus AM M; tansenS
in A; 8 fiat ubique AD (Tubren sa majoris circuli)
aequalis ipsi A M (antecedenti Cubrenta minoris cir-
culi.) Dico iplas A. D esse in continua ratione ip.
tiuS AD ad AN. Junctis NNI, e DD, vel
MM, eDD, e sic utiris; quoniam M M, DD
Tunc parallelae, ob aequales in similibus scxmentis an.
sulos: ergo patet propolitum.
Scholium.
inTisdem potitis dico hanc subcenlarum rationem in intinitum continuari polte.
Nam S non posit, ergo datur minina subcensa, quo minor duei non pocest: lit
ea verbi gracia AD secans minorem circulum in M; e ducatur ut Prius AS
aquatiS ipEI AM: ergo AS ell minor minima, quod cst ablurdum; erso non
dacur minima, erso Falto subtensarum porest in intinitum concinuari.
Temma.
Sine tres circuli, tangences se invicem in puncto
A, quorum diamerri A F, A F, AC Tunc in conci-
nua proportione. Circulos aurem secet recta ANDC;
item recta Au S n, ita ut A d apcetur in medio cir-
culo aequalis ipsi A NI minimi Circuli. Per puncta
denique s et D medii circuli, ducatur tam SNO
diametro perpendicularis, quam D B ipA SN paral-
leia. Dico ip(aS NM, p. S ele aequales: item MD,
Sn: item DC, n B. Fungantur nCi; item MM: item
AF. Ouoniam AN M F. CA quadrilaterum circulo
inscriptum; erso ansulus externus sp. M aequalis est
oppotico incerno AP. M; sed anguli ANO, A F. M
ob similicudinem eriangulorum Tune aequales: ergo
anouli suM, SNM Tunc aequales: aequalia Tunt
exeo Priangula Ad P AV. M; e quoniam BD pa.
rallela
Fig. 15.