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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 540, page id 851387705:0560
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E CY CL OFD F.
ver accidens, ex eo quoreatum axes applicentur ejusmodi Curra, quae ex natura
Tua lic Enthysini patiens; quod de nulla Curra, hactenus nota (ne quidem altumpta
Circuli Ouadratura) prius demonstratum fuit, quam cso haec de Cycloide Prima-
ria amicis communicareram; nis quod TIIustris Juvenis Cnliclmus Nelius, Cur-
vam quandam ita construendam uc sic P ucty sini capax, summa cum laude inrene.
De problemate Fepteriano per Creloidem solvendo.
Dseru Replecus, et Cauu phylicis, planetas ita Perri cirea solem in Orbica
La Alliprica, ut relocitas plasserxe sic ubique distantixe ejuldem a Sole reciproce
proportionalis; unde sequenem Hlypochelin ingeniole commentus elt. Sccat sci-
licet aream F. Iip(eos Planetaria lineis a Sole ductis in infinica Friangula MixtilI.
nea aequalia; unde HE ut Curra FMip Leos diricatur in porriones inaquales, mino-
res quidem circa Aphelium, majores circa Perihelium: per has aurem portiones
ponit Planetam aequalibus temporibus terri. Ouare ex Medio motu Anomaliam
conquatam ut indasaret, secanda est semiesliplis per Pocum in data rarione; vel
(quod perinde ese ab eodem demonstratur) Sccundus est Semicireulus per quod-
vis punctum Diametri in data ratione. Mirum estquantum in hoc problemate
Tudaverit Kexlerus, Orbitas Suas - - -- volvens nitendo neque proficit Bilum.
Fandem antielus, Geomerrarum opem implOraE; INCCTIM VeTILIS nE PTOPTeE aE-
cuum ee Linuum crepoverciar inreniacur Problema inexplicabile. Ouod nihilominus
ope Cycloicis procracla nos olim sic extibuimus.
Problema.
oriculum per datum punctum Diametur lit
data ratione secare.
T SemicireuluS ARB, cujus Centrum D. Punctum dacum C. Ratio dala L ale
DS. Fiane DC, DB, DB concinue proportionales; e cetto D delexibalue au B
cui aequalis ponacur recta BM; data aurem baH BM, et Genitore A K b, deleri-
vatur Temicy lois Prorracta M A B; Rat deinde BC ad BM uE R ad S, et ducacur
CP ad angulos rectos secans Cxeloidem in P, item P F Basi parallela secans Creni-
rorem in L. Jungantur denique L. C. Dico mixcilineum A F. Ci elle ad lemicireu
lum uE R adt S. Ducalut LaatuIS D F. C, e demittatuEL P; et jungantur F. B.
Moat esCa a 28, H C.L I tmissia, ersO UIareUS a. c dE8, IIa aFCUS
AF. ad F. F; ec quoniam arcus A F. ductus in semiradium aequalis elc lectori A L. D,
_ semiltis balis BD sive semiradius ductus in alcicudinem L. P aequalis ett Prian-
outoDE B: ergO UE A F, ad E F ita sector AF. D ad Friansulum DL B; d ut
ac ad ED ita A F D, ad DE B: sed ut E∞ ad F. F, ita Friangulum DE B ad Fpi.
angulum DE C (quia Tunt ut Bates DB, DC:) erit igitur ex aequo ut ac ad R. F,
ita sector AF D, ad Friangulum D F C, et converse simul et inverte crit, ut aE
pluS E F, ad acg ita AF, D pluS DF. C, ad A F. D; Sed ac est ad semiperipheriam
anB, ut sector AF. D ad Pemicirentum A RB; eris igituT ex aequo ut ac pIuS
E. F ad semiperipheriam, ita A E D pluS DEC. ad femietreulum: Sed ex iis qux
demonstrata