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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 352, page id 851387705:0372
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DE SECTTONEBUS PrOP.
Erit isitur (propier Paraboloeides cubicale Bex PrOP. 45.) P A. DA:: P aC.
DOc. hoc elt, d. d +5 Lg: : B3.  s=2,5 =DOc.
Irem (propter similia criangula) P. F. P a:: DC. DO. Hocest, 3d. P: : 3, d = 9.
3d
2p =DO. Ejusque cabus 27 ~ + 27 a 9 + dd9 = 4
(ict 1 27 43
=DOC
6=G
Ergo (utrinque diridendo per pe, ee mulciplicando per 27 43) erit 27 d2 L2789
FOdg2+93 = 2743 +27 d8 + 27 a29. RE (sublatis uerinque aequalibus)
9dg3=93 = 27 d8. Cujus quidem aequarionis radix q. si vel ope Coni lectionis
vel alio quoris modo reveriri pocerit, monttrabit quaelita puncta D, D, (alierum
quidem lupra punctum p. alterum intra;) adeoque propoliri vericatem. Incellise,
t binae radticesque (Tursum et deortum Tumendae) tuerine inricem aequales.
Analyli peracta, Demonstrationem Cynchericam sic liceret insticuere.
In Parabolocide cubicali Aa diametro A P, Paralle la ducatuK a N: per cujus
punctum quodvis (intra parabolocides) , ducatur recta r CF (diametro AP
OccurrenS in G) Parallela tangenti a F (quae eidem diametro occurric in F. ) Frit
an ejusdem Parabolocideos diameter, eique ordinatim polita n C.
Diametro A P ordinatim applicetur a P, eique parallela ducatur r p (cidem dia.
metro occurrens in p.) Fc lunco Cymbola P a = p. P A = d. FC = an
Tum sumancur in diametro, utrinque a puncto p, aequales rectae pD == p D =9.
utraque nempe tanta, quanca est radix hujus aequationis 9 d92 +93 = 27 d’ 8
(Nempe Lbinae radices oppotiea, tuerine aequales.) Et punctis D, D, ordinatim
ponantur rectae DO, DO, rectae in C occurrentes in O, O: qua cum parallela
sint rectae x D, Licur recta DD (ex constructione) bisecatur in P, crit ideo O0
(proprer parallelas) bisecta in n.
Supereltixitur ut ollendatur rectam DO (bilectam in ~) Papabo loeidi interi-
pram este, (’ut nempe ar recta bisecans sic diameter) hoc elt, puncta O, O, este in
Parabolocideos curra; nempe rectas D O, DO, (diametro A P ordinacim PoHtaS,
ex constructione,) ordinacim applicacis (ad eadem diameiri puncta) aequales elte,
adleoque in curra terminari. Quod sic octendi polse videatur;
DC = DC + pD = 3d +G
  34
ASIes
Tum (propier Paraboloeides, cubicale) ut PA, ad DA; Sic cubus re-
cta Pa puncto P ordinacim applicate, ad cubum ordinacim applicatae puncto D.
hocest a. a + 8 =9:: P3.  8, Z p  qui igimri cubus est ordinarim applicatae
Duncto D.
Sed et cancundem ett cubils tectae 150. Nam (propier Stilia crintibista ) PF
1.
a SCLF AICI
3a L g
Ysi
Pa:: DC. DO. hoc est 34. p: : 3 d =9-  5 9 B =D O.; Ejulque crtous
27d
4 pS L. Vel (prO. 949 L93 substimendo
erisit ~t
Eha S, quae per construtionem tulne aqalius) 32 a1. L. 2s d. 9 L 22 d. e pr, vet
l1337d21 8it
4+9 + 3 p = DOc. adeoque re
denique (abbreviando tractionem, per 27 d 2d =
Ex DO, DO, ordinatim applicarae sune punctis D, D, ad Patabolocieos curram
terminatae in O, O: et proxierea recta O Paraboloeidi inseripta est ad diame.
crum ax ordinacin. polita. Quod erat demonstrancum.
Fac aurem disquisitio, quanquam prima tronte speciosa videatur; non tamen
concludit: eo quod radix q ueriusque aequationis, lupponitur ejuldem magnicudi.
nis; quod rerera non concingit, ut ex Aequationis Cubica Resolucione pacebie
De qua plura diximus in Epiltola quae Fractatui meo conera Meibomir Dialorum
Dratisiur.) Et propterea ejusmodi Parallela Diametri in Parabolocide Cubicali
NOn REPCCIUNCT.
EIISEC
is
AROP.
esto aiie