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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 378, page id 851387705:0398
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A R PTEMETICA PFOP. XXXII.
cem, ut 2 ad 3, nempe ut circulus bis sumptus ad eundem vel aequalem ter sum-
Pcum;) hoc est, in reciproca ratione rectarum homolosarum M A, NI A. Nam
MA in prima Cst Z rectx MIB, e MA in Sccunda = (aequalis rectae) MC; Tunt
isicur M A in sccunda, ad MI A in prima, uC 3 ad Z, vel 3ad 3, vel 2 ad 3. Tdeo.
que Figura M A BM in Spirali prima, ad tiguram M ABCM in spirali sccundu,
uc recta M A in secunda ad rectam M A in prima.
Acque idem similicer oltendetur, quaecunque sit ratio homologarum rectarum in
distimilibus spiralibus.
PROP. XXXII
Corollarium.
CT autem ejusmodi fieurae Spirales, lineis Spiralibus dissimilibus, e rectis
item inaequalibus terminentur; erunt illae ad invicem in ratione quae com-
ponitur ex triplicata ratione rectarum terminantium, ed reciproca ratione re-
carum homolorarum.
Seguitur CX PFOP. 30, 3T.
eROP. AAACII
Corduurium.
quartan 6c. desrouut, sat ud norcemu ut 27 7, 29737, 649 66.
nempe ut differentia numerorum cubicorum, quorum latera sunt Arithmetice-
proportionalia.
Nam (Der pr. 29.) Guae pra, qua Pa e secunda, quae prima secunaa c
tertia, quae prima secunda tertia et quarta, ecc. describuntur: Tunt ut 2, 8, 27
64, +25, _c. ergo, quae prima, quae secunda, quae cerria, quae quarta, ec. deseri
DOrro, Fieura Spirales, quae bialindus prima secunda, tertia
buntur, Iut  L, 6 = 1, 27 -8, 64. = 2p 2
27, 61, dc. nempe ut ditterentix numerorim cubicorum continue proximorum:
5 = 64, _c. hoc est, UE Y
ATICLMCLICC PIDOIOnaleS: Nam X F 6 = 7. 7 F L um l9. 19 + 16- 31.
37 =24 = 0L. C.
Ouarum quidem disserentiarum exceltis, sire ditterentiarum differentix, sune
PROP.