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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 (shelfmarks Leibn. Marg. 84:1, Stück 2; Leibn. Marg. 84:1)
# Folio 107, page id 826605435:0127
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Et HINANOcIOS.
angulo subdupla. Tocumque triangulum, corius spacii Epirilis
duplum; finempe incelligantur convoluriones inceriores tocies
repeti quocies novis circulationibus icerato describuntur.
Nam revera; uti spiralis Archimedea, non aliud elt quam Pa-
rabola convoluea; auc etiam Circulus vel Circuli Cector, convo-
lucum Parallelogrammum, (quod prop. 26. Rrich. Intin. Ollen-
dimuIS:) Sic spiralis haec, Ag. 34, non aliud est quam iplum
M AS criangulum (Hig. 35.) convolucum; contrecta nempe in
punctum rectâ SM, adeoque parallelogrammis (live inscripeis
sire circum (cripeis numero infinicis) in coridem criangula redactis.
Nocandum aurem hic els Tum propter radiorum M A, MI,
M 2, 5c. (vel rectarum in criangulo his respondentium) con-
einue proportionalium processum in infinieum, decrescendo;eum
etiam propter eundem ubique Tangentis angulum cum recta cir-
cunducta factum, (unde, circuendo, ad punctum M medium,
nunquam pervenire poceries) Manifeltum elt, Spiralem hanc in-
ErOrTuM (NON MINUS QUAM CXETOTTU) esse incerminabilem. Ne-
que enim ab A PeC F 2 3 60. quorcunque demum circulacioni-
bus perectis, ad medium unqua perrenietur, magis quam, sumpris
A F, 12, 2 3, ∞c. ProPOrciOnalibUS, exHaUTICEUE UnQUaI A S
recta. Ie aurem hae omnes in intinicum concinuacxe, sic A L 23
cc. concinuaca incrorlum in intinicum, acuabie rectam AS.
Ilabes itaque curvam interminabilem terminata recta aequalem.
Sed e larendum erit, Tangentem spiralis hujus, non magis
duci posse Ceonerrice, quam spiralis Archimecex, (UE quXe ex
quadracura circuli dependeat, uc e Spiralium omnium Tangen
Tes;) adeoque nec angulum a geometrice actignari. Linea Fa-
menincerminabilis terminatxe rectae xegualis, non minus line hoc
allignabitur: Si nempe, sumaeur criangulum, non rectingulum,
UE AS V Fg. 33. Sed criangulo A SC simile; uc enim AC
ad AS, SiC AM ad Omnes AS restas arcubus A S nuMerO
intinicis inscrIDEAS.
Hane ipsam curvam, alia occasione, concemplatus irem es
VVrennius nolter. Nec tantum curra lonsicudinem, partiumque
ipsius, se magnicudinem adjaceneis plani: sed ec, iplius ope, Li-
macum e Conchiliorum demunculos mecitur. Exiltimac utique,
masna verilimilicudine, domunculos holce tion alios ese quam
Pyramides convoluras; qurum Axis lic, ictiusr odi Spiralis; non
quidem