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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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ARITAME FICA
erop. XIII.
Nam v. 8. in prima, erie Epiralis MI A B (duabus circulationibus descripta)
aequalis Temith peripheriae Cux B, bis Cumpexe; e in secunda, Spiralis MI A BC (Eri-
bus circulationibus deseripta) aequalis lemilli sux peripherix C ter Ciimpex: Cum-
que Tupponantur aequales peripheriae B in prima, _C in sccunda, (propter X-
gnalesradios; crunt spirales MAB prima, _ MABC secunda, ad invicem UL 2 ad 3,
(nempe ur peripheria bis Cumpra, ad eandem vel aequalem tex lumpram;) hoc
C, in reciproca racione rectarum hOmOlOSATU MI A, M A. Nam recto M A in
Prima est = rectae MB, e recta M A in secunda est Z (ejuldem rel aqualis rectx)
MC: Tunc isitur M a in secunda ad M a in prima, uC5 2d Z, vel uc 3 ac 3, vel ut
2 ad 3. Ideoque Spiralis prioris legmencum MI AB, ad spiralis polterioris seg-
mentum MI A BC, uc recta M A in lecunda ad rectam MI A in priia.
Acque idem similirer oltendetur, quaecunque sic rario homologarum rectarum in
distimilibus spiralibus.
P R O P. XII
Corollarium.
d’aequales; et lta illa sprratun setrahio du olcem in ed ratione qua
componitur ex duplicata ratione reclarum conterminarum, e reciprocaratione
rectarum homolozarum.
Sequitur ex DFOD. FF, 12.
T autem ejusmodi Spiralium dissimilium rectae conterminae sint etiam in-
circumlocutione toties opus lit,) abulire ulum tuislé. Nempe, per Spiralem,
(quocies ea ad Peripheriam comparacur,) intellectum vellem Acerceatum omni-
PxOP. 5. CCC. BujuS, _ ArChImedeS a LFOP. 2F. _C. LII. SpIr. uh lumus.) ut 2d
SCHOLTV M
Notandum autem est, in propolicionibus praecedentibus, quae de Spirali aBunE
(quod _ I lecuturis aliquot tacturus Tum,) me Spiralis APDEIIAEIONCIM (NC LOHSd
um arcuum Sectorum similium, numero infinitorum, ex quibus constat fieura illa
ex infinitis numero sectoribus Spirali verae inscripta; (qua Scilicet e nos ad
Tumpra, perpecuorminus elt, e maxime gundem circa spiralis inicium. Ouamris
Deop. 5. innuimus eoiiod quidem Regresarum ipla linea Spirali proprio sensu
enim Scctorum illorum nmerO InTMIOrUM aBSTCSALCI SPILMa L ACa C
Spirali cerminata, (juxta methodum Indirilibitiim) agutase Ponatu, non tamen
ilud de omnium Arcubus cum ipta linea Spa CDCOPHIC dicta) comparatis oblI
nebil. Tancundem enim estet, acli quis, auli sumla numero parallelosram-
ma irtansulo inscripta, (aur ctiast erreumleripIa) Tor Transulo Bd a
oit Duca in criansulo volcols nON TaMeN le   CH.)
Atque hoc quidem co pollus admonendum duxn quoa os liblo
monvunquam speciora esutmoei veritimituucine in lab. t PrOCAreS esse. Cu
qualia videat, inde concluderer corum omnium latera rectae VS adjacentia (re.
etae V B paraltela) ip( VS simul aequalia este, vel quae rectae VB adjacent (ipsi
VS parallela) aequalia siniul CHIe TOE V B.  CC COHCIM-
autem