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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 375, page id 851387705:0395
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XC
XIV.
LNFTNLTORC
ROP. XX
Corollarium.
Tem, Fieura DIZM, quae Spirali NLZ (a principio Spiralis NI exorsa)
PMT; ut + ad 3.
ed recta MIT contermina continetur: est ad Sectorem correspondentem
Nam (utdlixitulis adt LTOD. 5.) conitare supponimus Figuram illam e LML Cx
intinicis Sectoribus similibus, quorum radii sunc Arichmetice proportionales, adeo.
que Sectores ipsi in duplicata ratione Arichmetice proportionalium (quippe Luo-
rum lacerum;) Sectorem autem PM P ex cocidem Sectoribus maximo aequali-
bus: Frirque propterea Figura illa ad hanc, UE F ad 3. per PFOD. 2F
Sectoris autem nomine hric appello etiam Sectorum quortibet agpresatum, licet
semi circulum (auequidem circulum incesrum) aequer rel etiam superet; (SICut
et de Anguli appellatione supra monvimus, ad PrOB. 5. )
SMisI.
ROP. XXV.
on sler eC Corollarium.
 P DEOPIEECA FieuraMIF A quae Spiralis circulatione prima describi-
tur, aequatur trienti circuli primi AA.
Nam correspondens sector conterminus est ipse circulus inceger A A, circuli
primi radio M A eodem cemipore deleriputo.
R O P.
Corollarium.
deinceps: (qualibet parte totres repetita, quolies circulando describitur:)
aequatur trienti circuli secundi, tertii, quarti, 836. bis, ter, quater, edc. (junta
numerum circulationum) sumpti.
Nam dum describicur Spicalis M A B (duabus eirculacionibus tacta) d puncto
mobili ab M ad B (in recta circumducta M B) promoro; et simul tigura plana
2 recta (hic continue crescente) circumducta: Fodem tempore describitur (2
recta cola
a toca M B circumducta) circulus secundus bIS. Adeoque quot partibus con
cinve crescencibus (in ratione duplicata Arichimetiee PropoonatuM) cousat
bis deseriprus. Ouare ligura sic deleripca Spirali adjacens, eric ad circulum con-
tur, erit 3d circulum cerrium res sumprum, uT X ad 3. Ft quae describitur circu-
lationibus
A: vero fieura describitur interre  baltaibus prima C secron.
da: prima secunda e tertia; prima, secunda, tertia,  quarta: (8 sic
terminum B BBe LpC  L all 3. PeT pFOD. 24.
Et paricet ligura Spiralis, qua circulatios prima, secunda de terria describi-