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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 312, page id 851387705:0332
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DE SECTIONTBUS
SP. PO. PB ::, hoc est.
RrSO PO9 =
VBKVSKNOC
TAXAP
XVA
P0
BSXAP
5
ProD L
 continue proportionales.
VBKYS = BS9. hOc elt, X09-
B59
VBKVS X V A X a r. e
BSgKE=  =VA. Ideoque proporrionalia BSq. VB, VS:: =
VA.
Elaberur eroo recta VA, adeoque Parabolae vertex A, in crure VB, unde ducta
AP cruri VS parallela, est diameter Paratolae quaelica.
Hoc est. Si Conus Propositus secetur plano per Avem, quod Basi Coni recrum
sit trianeulum faciente VBS: e fiat, ut BSq quadratum basis trianeuli, ad
VBKV S rectaneulum cruribus contentum; sic  (quadratum ordinarim.
sa
applicatae in Parabola provosita, per Axem divitum, hoc est) Farus rectum Pa-
rabolae propositae ai conveniens; ad VA distantiam vertieis Parabolae a vertice
Trianculi, in utrovis ipsius crure mensurandam; t denique a vertice A recta
ducatur AP opposito cruri parallela: eique Planum erisatur plano trianeuli VBS
rectum: Planum hoc in supersieie Cori fasiet Parabolam, cui Parabola proposita
coneruet.
Demonstratio, per rexetica Anatoseos vellieia facile insiruetur.
Pari tere methodo demonstrari poterit, Datam Fllipsin vel FErperbolam ( de
quibus postea dicendum exit,) non quidem Cons cuilibet, sed sattem Conis quosli-
bet specie differentibus, aptari posse. Cujus Propolitionis e Demonstrationem
et Vecerminationem lubens praetereo, partim ne cadio Cim, nec velim cironibus
ingenium suum exercendi antam praeripere, partim etiam quoniam illud insticuro
noltro non est necestarium.
P RO P. XII
De Ellipsi sectione Coni facta.
N ellipsi, Ouacrata ordinatum applicatarum aequalia sune differen-
ciis binorum rectangulorum; quorum quidem illa (majora) sunt
interceptis. Didmetris poporrionalia; haeC rerO (MinOTA) in CaruN.
dem cacione duplicatd.
Sunc enim Cuacrata DO aequalia Rectanoulis
BDX DS, (peT PrOP. 7.) Ducta vero recta SFF,
apsi A a parallela, e continuatis rectis BDS ad F;
erunt ubique rectae DS = DF = PS. Et Rectan-
suta BDX DS = BDKDF - BD X FS. SunE au-
tem (proprer aquales rectas DF) Rectansula BDX DF,
rectis BD provorcionalia, ideoque et rectis D A dia-
metris intercepris (propier similia criangula ADB.)
Rectansula vero BD X F S (quoniam tam BD quam
FS rectae Tunt rectis D A proporcionales) Tunt in
duplicata rarione diametrorum interceptarum D A.
Cum ixicur lic ubique DO9 = (BDF DS =) BD
XDF = BD XLS; constat propolic.
P ROP. ZIV.
De Clliptuco Lgramidoerde, e Converde, (seu Sphaeroeide) e Cuneo.
(UE PrOP. 5, 6. Formarimus Prramidem vel Conum, _ PrOP. 9
rim afracat I ellipsi Formetur Pyramidoeides ellipricum bieuspe
(hoc
Prramidocides Parabolicum,) ex omnibus quadratis DO ordina