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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)
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 Cuamorr Cetcididudis.
Cap. V
P ROP. XXVII.
A. B. Figura spHalIS (linea Spirali a principio Orta, et recta contermina,
terminata) est contermini Sectoris Priens: Toties repetitis omni-
busu quoties iterato describuntur.
Sumprisque anoulis AMI T, A M P, ec. arichmetice proportionalibus;
E Figura Spiralis primo conreniens ponatur F; eadem per duos con-
FInUata CFIE B; DEF FrCS, 27; Per quatuOr, 64; e sic deincCPS,
lecundum numeros cubos continue seguentes.
Pocaque fgura circulationis primae, est contermini circuli primi Fri-
ens; e, duarum circulationum (repetito quod in secunda iterato
describitur, quod ubique intelligendum est,) ejusdem Circuli primi
Octo trientes; Trium Circulationum, ejuldem Vixinti septem Tri-
ences, (seu corius Noncuplum;) Suacuor Circulationum, ejusdem
Sexaginta quatuor Frientes, et sic deinceps.
Ft, universaliter, (polico R procirculiprimi Radio; P, pro ejusdem
peripheria; ansulique circulationis quonsque libet continuatae pa-
tione ad quatuor rectos; vel correspondentis arcus circuli Primi, ad
inceoram ejus Peripheriam; ut à 2d P:) Fieurx Spirales sic
descriprae srepetitis toties omnibus quories deseribuntur) Magnitudo est
522
Adeoque, qua continuis Circulationum aneulis equalibus conveniunt
fourx Spirales, sunt ut numerorum cuborum continue sequentium
On 2, 8, 279649 T25, EC. differentia; 2, 7, 29, 37, 62, ec.
Et speciatim quod Circulatione Prima describitur, est contermini Cir-
culi primi Friens; quod secunda, ejusdem Primi Circuli Septem
trientes; quod Tertia, ejusdem Prientes Novendecim; quod Duar-
ta, ejuldem Frientes Frisinta septem; quod Oninra, ejusdem Iri-
entes nus et sexaginta. Fit sic deinceps.
Figurx Spiralis (a Principio orCX) quousque libet concinuatae, cories
repecitis omnibus quoties iterato describuntur: (positospro linu
recto anguli circulationis, ad Ractium R; ex pro sinu complemen-
ti; iploques, pro Semicirculis secundo, quarto, (exto, Octaro, Cx
cerisque in locis paribus, per contrarium signum semper expolito,
urpore ad concrarias diametri partes posito:) Momencum respectu
RECtR PMP, est a R = 65R =6av R - a P + 3ais  + a v; Cenrrique
22aR + Z25F = +2aVR 2a  +6a5R = 2~VR
Et quidem vel ad partes P. vel ad parres C, prouc sienum F, vet
Pravaluerie.
H. EiusquE MOmEnCUm respecta rectX F. MC,
v  + 32 P. = bas Re -3a v + asR. Cenerique eravicatis inde di-
Rtantia,
22VR1 = 6a 2 R3 - + 245P3 =6a 2 V R 2 + 2 a35 
vel ad partes P, rel ad parces F. prout sienum F, vel -, praeralue
2
2