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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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2222LLDAUF
PRO P. XXIX.
Corollarium.
Tede intuper, Figura Sirales, quae prima, quae prima es secunda qua
prima, secunda C tertia, quae prima, secunda tertia e quarta, (es
sic deinceps) circulationibus describuntur, (puta MI A NI, AE AB NI.
NI ABCHC MI A BCDMC, C9c.) se habent ad invicem ut numerorum Arith-
metice proportionatium cubi 2, 8, 27, 64, 53c. sive in triplicata ratione recta-
rum D A MB, NC, AID, Cc.
Sune enim rectae M A, MB, MIC, MID, BC. ut F. 2 3 d dec. ( ut Paevins dictum
CAt,) ideoque circuli primus, secundus, CertiUS, gnartIS, _C. (his radiis deseripti)
Uc F, 4, 9, 26, eic. (nempe in duplicata ratione radiorum;) adeoque s Poa
circulus primus A = FC, crit secundus B = 4 C, TerTIUS C == OC, QuarEIS D =, 160
Sc. et propterea si lumatur primus semel, secundus bis, terrius ter, quartus qua-
ter, ECC. CFUINEF A = FC, 2B = 2X 4C =86, 3C = 3X9C ==276, 4D = 4 X16C
=64.6, ecc. adeoque ad inricem uc numeri cubici F, 8, 27, 64, dc. quapropier d
horum ErienteS 36, 5C, 376, 52C, _c. hoc est, (per prop. 25, 26.) figurae ipirales
MI AMI, M ABAI, M A BC M, M ABC DM, ec. lunc eriam incer se ut numext
cubici 1, 8, 27, 64, ec.
PROP. XXX.
Corollarium.
Snirersaliter, Fieut de Spirales (a Spiralis principio exorsae, c ea
dem vel simili linea dd ali terminatae) sunt ad invicem in criplicata
Cum enim (per constructionem linea spiralis) eadem suc ratio rectarum M L, in Ficyra
MF, qua eIL anSULOTUM PMT, PM F, (sumpra Anculi vOcC, e0 sensi quO Prop. 24
Supra pTOP. 5. uc d sectoris voce, eo sentu quo lupra Prop. 24.) Sectorum PMI,
PM P, ad inricem racio (quae componitur ex ratione ansulorum e duplicata
ratione radiorum,) est rectarum M L, M L, ad invicem, racio criplicata: FF
propterea eadem eru etiam ad invicem racio figurarum spiralium MI F M, M F M,
qua illorum Sectorum funt crientes. Per pr. 24.
Sic v. 8. Si recta M A (unius circulationis) dicatur Fr, e circulus eo ractio
descripius dicatur =c; tigura spiralis eodem cempore deleripta erit zC. Tgitur in
una circulatione cum semisse tier recta contermina FZr = 3r; circulus contermi-
nuS 3 X3 XC =26, qui ductus in 3 (numerum circulationum) FC 3 X 3 X Z XC
ejulque iriens 3c, est tigura spiralis quae et circularione inceora et insuper semillé
describicur. EF limilirer in quancacunque circulatione.
P RO P. ZZXI.
Corollarium.
ET vero ejusmodi feurae Spirales, ais spiratibus dissimilibus,  rectts
aequalibus terminentur: (puta s AB in una Spirali, tanta sit quatu
MIC in alia:) erunt ficurae illa splrans homolosis suis rectis (puta M A in
ratione rectarum conterminarum.
unam e M A in altera) reciproce proportionales.
Nam in prima exic Ligura M A BM (duabus circulationibus descripta) aequalis
Cumque lupponantur aequales cireus Dn pria e C’in secunda (propier aequales
radios,) erune tigura spirales M ABM prima, et M AB CM secunda, ad invi-
cem
HeH CHCMM sui B bis SumpE; FC in Lca HGura M A BCM (cribus cMeu
latiOnIbuS descripta) aequalIS FrienCI CC  C Tex CuMPEI (per pFOV. 29, 30.