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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 310, page id 851387705:0330
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F
SECY 1ONIBUS
Conarum haec inrariata mase illa perpetuo rariatur, pront propius
aut remotius abest à L’alaoba rertice) duas alias jam olim (ubstitue-
runt Coni-sectionum Complatores; Ouarum altera est Diameter in-
tercepta AD, quae intra Lacabolam reperitur, eltque semper recta
DB (cujus vices supplet) proportionalis, (utraque nempe cadem ra-
tione simul et creseunt e decrescunt pro rario lieu puncti applicatio-
nis D.) Reliqua rete quod Latus rectum rocatur, (vel recta dia.
meter, vel recla suaea quam postunt orclinatim applicatae, rel etiam,
apud Midorsium, Parameter,) non ulpiam
vel in Conisectione, rel in ipIo COnO, TCa-
licer exsistit; Sed Cola imaginatione suppletur,
ut rices subeat rectae DS, vet AS: Ideoque
quantuplo major est vel minor AD quam
DB, tantuplo e contra minus vel majus sup-
Donitur Latus rectum, (PuTa L A,) quam
DS vel AS: Adeoque tribus DB, DS, D A,
vel DB, AS, D A, erit quarta reciproce.
proportionalis L A; ut aequalia sint rectan-
outa DA x AL, ipsis DB = DS, vel DB= AS
hoc eAt, quadratis DO. Vel, (substieutis ido-
neis (ymbolis, puta b = D B, 5 = AS, d = AD
1=E. A, p = DO,) erit ubiquue Muadarum sidinacim applicala in
Pac abo a p = (b5=) a1.
Fstore hoc quidem essentiale Parabolae symptoma, unde reliqua omnia depen-
dent e calculo deduei poltunt. Vc autem sectione Conitiat, omnino acciden-
carium est. Ideoque, genvino symptomate sic reperco, Conum dimittere licet:
adeoque ulteriorem in ipsius aftectiones inquititionem differemus donec ad ab.
Tolutam Parabolae tractationem (sine respectu ad Conum habito) perveniamus,
(quam PrOP. ZT. e sequentibus agcrediemur:) Interim similia Ellipseos ee FIy.
verbolae sennina sympiomata inguiremus, ult omnium tandem absoluram nacu-
ram seorlim perpendamus
Monendum tamen est de Latere Recto; non idem Latus Rectum omnibus ejuL
dem Parabola Diamerris convenire; (Ouod etiam de FIlipleos et Fyperbola
Lacere Recto poltea incellisendum exir:) Sed (uc habet quaelibet Parabola in-
tinicas numero Diametros, uc post dicetur, ita) quaelibet Diameter suas habet
ordinatim applieatas, Tuumque Lacus Rectum: Oux quidem linea imaginaria, cer-
ex tamen longicudinis, (quamiris vel ubiris alias setibi postit, vel etiam non
Teribi, sed sola imaginarione suppleri,) duei solet d Diametri Vertice ordinacim-
applicaris parallela.
Ouxe aurem de Parabola Larere recto dicta sunt, ea sere Lateribus rectis EI.
lipseos e Fyperbola intra accommodanda crunt.
Onod aurem supra polliciri sumus, ex abundanti, demonstrare; nempe, duam-
libet Parabolam cuitibet Ciono aptari posse; Cic Ostenditr.
Sit propotira Parabola (cujulcunque Coni) ac, cujus axis ax, ejusque pun-
Eto cuilibet r ordinatim applicata ra. (Ouod autem quaelibet Parabola Arem
habeat, e quomodo in dara Parabola reperiatur, post oltendecur; incerim illud
licebit, line riolata mechodo, quali concestum altumere, cum roca haec Demon-
stracio sic ex abundanci:) Dico Parabolam illam cuilibet Cono, Dura VBS,
aptari potte.
Secetur enim per axem Conus proposicus plano ad batin recto; (icque Frian-
sulum illa sectione lactum V BDS. In hujus alterutro crure puta VS, Suma
cux a vertice V_ aequalis ipti an diametro Parabola PrOPOTIX; ee incelligatur
recta duci x B parallela bati BS. Tum rectis xB, Xco Quaratur tertia provOr-
tionalis, cui aequalis lumatur (in bale Priansuli) secla SD; et, per punctum
D, ducacur recta D A, laceri VS paralleta, reliquoque eruri VB Occurrens
2