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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 367, page id 851387705:0387
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Crop.
TFINTTORU
(Per Spiralem, trie intellico, non iptam Curram Archimedeam, led, Neree
tum Arcuum Sectorum similium numero infinitorum, Spirali Archimedeae con-
tinue inscriptorum, Fieuram complentium; F.c Sic deinceps, quocies de ipsa linea
aGItuT. Ouories autem de Figura Spirali adjacente agitur; perinde est sive ve-
ram curram Archimedeam incellisas, sive hanc quam Spuriam dicimus.
Ecto enim Linea Spiralis (una circulatione facta) MITA, Principium Spiralis M
(quod idem esto eE Centrum ArcuS Peripheria, quem Correspondentem voco
Principium circlilarionis recta M A, qua aquabili moru circumducta (manente
Buncto M) supponicur puncto suo A Periphieriam deseribere AO A (qui Circum
lus primus rel pocius Cireuli primi P eripheriam diei vel solet vel commode porett,)
dum intu Puu aliquod (in eadem recta circumducta) moveri supponitur
Caequabili IECM MOLI) ab M ad A, mou suO lineam Spiralem MI F A deleribens:
Adeoquo recta quaelibet MT (a principio spiralis M, ad spiralem ubiris ducta
eric ad rectam M A, ur peripheria arcus A O (eodem retpOE detCripEIS) ad pC
ripheriam EOtam AO A, vel ut anoulus AMI F ad quatuor rectos: AdCoque ee
rectae MP, MI P, arcubus AO, AO proportionales CrUnE; ut Patet.
Tum, ductis quorlibet rectis M F pI T, _c. angulos COntinUOS A NT Y
TM T, dc. aquales inricem facientibus (adeoque Arichmetice proportionalibus,)
Supponamus (super illis angulis) similes Sectores cocidem (Caltem uno minus,
quid in spacio primo sector inseribi non poteric) figurae M TM (spirali vera
M L ee recta TMI comprehena) inscribi. Sectores illi omnes constiment Aou
ram (ex similibus sectoribus compoticam,) ipta figura MTM (cui inseribitur
minorem: Dilferencia rero perpeco minuetur prour sectores illi (cidem M TM
figura inscripei) plures Fuerines (uc Patet,) adeo ue, si fectores illi TupPOnantIE
numero intinici, tigura sic inseripra ipEi M FMI fISUTA CONSTUCL, (per ca quae
univerlaliter monumus ad prOP. 2. Con. Sect.) et propterca sectorum illorum
omnium arcus ipsi Epirali (Spurix) MI P COnGTUCNE.
Sunc aurem illi similium sectorum arcus (sicut eorum radii) Arichmetice pro-
porrionales, nempe ut 0, T, 2, ecc. angulus aurem cujustibet sectoris elt ea pars
anguli TOcUS AM F quae sectorum sire spaciorum numero cognominis est: 2.
eoque si sectores supponantur numero intinici, erit angulus cujustibet L (varS
intinicesima, seu intinite parra) anguli corius AMT, ita nempe uc omnes timul
XGVENEUT tOt AMT. (Liceat aurem mihi, narazensins Cortan, Anguli nomine
appellare ansulorum eriam aggresatum, quamvis torcalle duos rectos Vet aquet
rel etiam Cuperet.)
Spiralis isitur nostra M P constare supponitur ex infiniris sectorum arcrbus
Arichmetice proxorcionalibus, (subrensis S anguli AMT,) quorum minimi ra-
dius elt0, seu punctum, (nullius magnicudinis,) maximi vero recta M T.
Correspondens aurem arcus concerminus PP, ex coridem constat sectorum ac-
CubUS MAXIIO aQualibUS, Ut PateL.
Ergo aggregatum illorum (hoc est linea spiralis nostra N F) ad aGoreBaLI
horum (hoc cAt accum conterminum PF) cAF uC L adt 2. PeF PFOD. 2.
PRO P. VI.
Corollarium.
E ProPterea, Linea Sp (nostra) M A una ciroulatione salti
aequatur semissi peripheriae circuli primin A A.
Nam