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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 368, page id 851387705:0388
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AR IYHMEFICA
PrOP. 11.
Nam arcus conterminus spirali MI A, cA integra peripheria cireuli primi puncto
A deseripra. Ideoque _c. per PrOV. 5. quod crai demonstrandum.
P ROL. VIL.
Corollarium.
F Spiralis haec descripta circulationibus duabus, tribus, quatuor, 30.
interris; aequatur semissi peripheria circuli secundi, tertiiu quartiu Oc.
bisu ver, quater, 86. Sumptae.
Nam dum describicur Spiralis M AB (duabus circulationibus Facta,) Punctum
illud B, Peripheriam BB bis deseribir: S dum describitcur spiralis MI ABC, peri-
pheria C C ter describitur; ec peripheria DD quater, dum deseribitur spiralis
MABCD. Et sic deinccps, pro numero circulationum mulciplicanda cst peri-
pheria concermini circuli, e mulcipli semillis aequatur spirali incerea deseripra.
P ROP. VTIF
Corollarium.
T vero Spiralis haec ultra circulationem primam, sed non duabus inte-
Deris continuetur, aequabitur semissi tam peripheriae inteeri circuli con-
termini, quam ejusdem continuationis supra circulum interrum.
Nam incerea dum describitur (motu composico) Spiralis M A F, deseribetF
etiam (2 puncto P) arCuS P P F nempe tota peripheria P P cum adjuncto ad.
ditamenIO PY. ErGO EC. PET PTOP. 5. Quod exat demonstrandum.
eROP, TZ.
Corollarium.
T pariter, Si spiralis ea continuetur per circulationes duas, tres, qua
tuor, aut plures interras, cum additamento; aequabitur illa semissi con-
terminae peripisetiae intestu, oisque ver quibt iot suplus epta H ta
mero nempe interarum circulationum) cum semisse item additamenti.
mina inceora, aliue upet altestamentum: Hloc ets Coses P alelo CONTCKMI
nus continet tondem incegros circuli ambitus (quot lune intesrae circulationes)
cum addiramenio. Ideoque conttat propolirum, per prOP. 5.
Ouia nempe dum spiralis illa deseribitur, tories deseribitur peripheria conter-
EROL.