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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 311, page id 851387705:0331
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in A. Dico teclam A D diametrum este Parabolae in Cono cui Parabola pro.
Polita consruet. Quod Sic oltendo.
Super Friangulo V BDS, rectaque in illo AD, (quae estus ex constructione,
cruri VS parallela,) ad ansulos rectos crigatur Planum, D AO. Cum autem
tam plavum sic erectum, quam Batis Coni BOSD (ex constructione,) sint cri-
angulo VBS recta; eric eorum communis sectio DO, eidem Friangulo recta
sire perpendicularis (per TO CFF,) adeoque tam rectae AD quam (diametro ba-
lis Coni) BS perpendicularis (per 3 d IL;) ideoque (per 7 hujus) AO, sectio
in lupertieie Coni Plano sic crecto tacta, eric Parabola, ejusque AXIS AD.
Tum in AXC A D sumatur recta A P, rectae V x (hoc elt a X,) aequalis: du-
Etaque SDB, rectae SD B parallela; Cric (proxier similia triangula) PB aequa-
lis rectae B: Sed e SP (propier parallelas) aequalis rectae SD: Ideoque ordi-
nacim applicata PO (medlia proportionalis inter SP, PB, hoc est, InEEFSD, XB
aequalis elt rectae ncon (quae ipsis SD, B, media proporcionalis ct, ex con
Structione.)
Cum isITUIT TaM AP, aX, quam PO, nco, sint aquales rectae; acque angulus
comprehentus AP O, ansulo comprehento a xco, aequalis, (quoniam uterque re-
Etus;) puncta a, r, con punctis A, P, O, applicata ConsruenE; (rectae que AP, PO
rectis an Xc) Acque idem eodem modo probari potest de reliquis punctis. Pota
ixitur aco coni parabola AO consruit. Quod tieri polle probandum exat. Adeo.
que datam Parabolam dato Cono apcavimuS: Duod crat Faciendum.
Idem alytice sic poterit investicari. Proxolicum sc datam Parabolam a co (cu-
jus Axis a , Ordinatim applicata  co) daco Ciono V BOS acaptare. FF Suppo-
namus praestitum esse quod imperatur, (ique ea parabola COnO aptata AO, cujus
Axis AP =ax, eique ordinatim applicata PO = r co. Adeoque recta PO per-
pendicularis tam recta B PS bati Friansuli. per- Axem, aut ei parallela, (propter
Coni sectionem,) quam recta AP (pTOPter AXEM;) ideoque recta PO plano
APB (quod crianguli planum cAt) recta, (Der 4 C LF.) _ propterea tam planum
circuli BOP, quam Parabola AOP, (quorum communis lectio elt PO) cidem
Frianguli plano rectum eritu (Per LB C TT.) Atque hine quidem constat, Pri-
aneylum. per axem. Coni in quo quaerendus est Axis Parabola, illud este, quod Co-
ni bali rectum est; Acque intuper, Planum secans quod Parabolam efticit (adco-
que de Parabola planum) ilti Friangulo rectum tore. Ouxe est prima pars in-
quisicionis.
rabolae Axem AP in Priangulo per Ldem VBS jacere: Frit AP (prODEEE Pa
rabolam) alterutri Crurum, puta VS, Parallela. Ideoque (s per puncta A, P,
duci incelligantur in criansulo per Axem rectae AS, BPS, basi parallela,) PrO.
portionales erunt (propter similia criangula) VB. BS: : VA. AS = PS =
iem 15. 5B:: AP. PB3
r5
SXVA
D
Liem lpropter Conilectionem)
Scinde (reperto jam quodnam lE Lriangulum per Axem Coni in quo quaeren-
dus est Axis quaesitae Parabolae; es quam inclinationem habicurum est planum
Secans ad illud Friangulum: ut sicus Axis Parabolae in illo Friangulo reperiatur
sic progrediendum;) lupposito, ut prius, rem factam ese quae imperatur; et Pa