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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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PFOp. XI. VI
HLC L S
e RO P. XL V1.
De recta Paraboloeides Cubicale contingente.
F Paraboloeides Cubicale A aq in puncto quoris an contineat re-
eta _ F, diametro P A OCCuTTenS in F, Stque cidem diametro
Ordinatim axplicata a P: erit recta A F (diamerri Continatio) du-
pla diaHCCI InTExCePIA P A: hOC ett, diameter continuata P F, tri-
bla diamerri P A.
pram, sumpeo ubivis (in eadtem diametro) vupeto D, cui ordinatim abplice.
tur DO, tangenci a F Occurrens in P: Punctum Y (prOpter tangenTEM) vel CxIE
idem cum puncto a (E nempe P, D, coincidanE; ) rel (si secuS) exit L exta
curram: e (prOPterCa) DF = DO (nempe aequales, si D, P, coincidant; rel
A secuS, D T lonsior erit.)
Ponamus autem (ob. commodiorem calculum) P a = p, P A = d, PF = f,
PD = a. Eric ergo (per det. praeccd.) PA. DA:: PaC. DOC. hoc est d. d = a
: P
P =DOC. liem (propiex similia criangula) PF. Pa:: DF. DF.
hoc cA f. P.: 5 = a. p = D T. Ejulque cubus 
DTC) = (DOC =
a
23s a +3sa La
P. Fr (urinque multiplicando per fod, et divi
dendo per p3) erit f3 d = 3 f d a  3fd a2 = da f. d =f a. Tum C alite
rendo utrinque f d, ec dividendo per L a d erit 3f L = 35 da + d a =f. De
nique, porendo puncta PD coincidere, (ut craneleat quancilas an adeoque et ips-
uo mulciplicia = 3F dan = d a 3) eric 3f d = f, hoc elt. 3a = f. Quod erot
demonstrandum.
F R OP. XLVII.
De Parabolocidis Cubicalis Diametris.
Nquirere, An in Paraboloeide Cubicali Diametri sine invicem pa
rallela: Er cujulris diametri Ordinatim applicata, sint rectae in
ipsus Vectiee conringenti parallotae.
Inquilucio sacile instimi pocerte ad imicacionem illius quae de Parabola achibe.
tur ad prop. 24. nili quod PF, quae iltic dicitur 2 a, hic dicenda est 3 d. Fam
nempe Anatycice sic inllicuamus. Supponamus scilicet rem ita este: Adeoque re-
etam l’a, quae paraboloeides Aa in puncto a continsat, diameno P’A producta
OcCuTrerE in F; eique parallelam OO Paraboloeidi inscriptam, quae (producta)
cidem diaerro supra verticem occurrat in C) (adeoque  intra verricem diaetro
Occurrat, cum tam. duarum D Ei, quam duarum DO, de quibus mox dicetur, al.
Eera eriu quantitas negatira, quod tamen calculum non curbabit; ) iplanique 00
rec
ipsi a ordinacim axplicata;) denique diametro AP ordinaciim applicari OD,
ODa P iplique Paralselam r P eidem diametro occurrere in P: quare e (prOPIeI
Paralletas) Pp = a 2 = F G; _ ProPterCa P F = P C: item (propter parallelas)
rectam DD. bilectam in p, SeutO bisecatur in 2. Ouarendum autem est, num-
cubi reperiri poltine puncta D, D; quae, quidem licubi inveniantur, conslabir pro.
Dolutum.
Sublticuris igitur idoneis lymboto = P. P A = d. (ideoguC, D Pa-
ced: PF = p G = 3 a.) PP = a n = F C = 8. (erBO p A = P A F Pp = 4 + 8.
PD = g. (adeoque D A = p A L pD = d + 5 Lg. _DC = p C + pD = 3d =9.
Fxit