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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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DE SFCL IONIBUS LEP. XXXII
Data in Lllipse acuserro qualibet, diametrum conjueatum invenire. Vet ge-
neraliter,
Data inscripta qualibet, diametrum invenire cui illa ordinatim ponitur. Nempe
rectam quae datam inseripiam aliamque ipsi parallelam Bisecat: Vet ((i diameter
non sic) qua ipsius punctum medium, ec Fllioseos centrum conjungit.
Datae Fllipseos Axes invenire. Nempe delcribatur Peripheria Fllipsi concen-
trica, ipsamque saltem in binis punctis secans: Rectam enim bina puucta proxima
conjungencem quae bilecat diameter, est Axium alter; reliquusque elt huie con-
jugacus.
Noca lamen; In circule omnes Diametros Aes esse, ex quidem aequales; 
conjueatas ipsius diametros omnes esse conjueatos Aes. In aliis autem P. Iipsi-
bus quibusvis, non nisi duos Axes reperiri, eosque Conjueatos, se d  maequales:
 quidem conjue atarum diametrorum omnium maxime inaequales; quare  Dla
MCtFI EXtremX divi solent: Sicut e contra, DiametroS. Medias dicere licet, quae sunt
conjueatae aequales: Suntque inter extremas media proportionales
Datae F.lipseos ordinatim applicatas (positione) invenire, quae data EpuS Ma-
metro conveniunt. TRVeNEA nEMIDC DIAIELTO conjusaTa, quae huie aequidiltant
rectae lunt diametro darx Ordinatim. POTIX.
Fllipsin ad datam diametrum e datum latus rectum describere, quae adu
habeat inclinationis anculum. Nempe invencis (magnicudine) ad quocibet dia-
mecri puncta Ordinacim applicaris, (per PrOD. 28.) applicentur ad lua respectire
puncta in ansulo imperato: Per earum enim extrema puneta, curra aequabiliter
ducta, est FIIpLis. Vel etiam (qua eric in praxi commoda constructio) Descripio
Cireulo, cujus Diamerer sir aqualis diametro quae elt, in LPipsi, datae conjusata;
Acque inventis quodiber Ordinarim applicatis ad illam Circuli Diametrum, (hoc
elt quorliber Sinribus rectis:) Ila ipla, cum Diamerro data Ellipleos praescripcum
ansilum tacienres (sic dirisa uc diriditur illa Circuli Diamerer) sune ad relpectira
DIamCITI FIlipseoS puncta, Oranacim applicatae.
Acqui ego brericaris causa (praeseriim cum ex dietis Pacile deduci queant)
harum ectectionum demonstrationes, aliaque cam Problemaca quam Theoremaca
plurima Lubens omitto.
Bue (Sd
e RO P. XXXIII.
De Fyperbola absolute considerata.
Om sic in Hrperbola (ut ostendimus Prop. 20. inspecto Con0)
Ouadratum ordlinatim applicatae B = 1d F- d. Licebit hic
(ut Parabolam et FIipsm Tupra) Frperbolam eo charactere insigni-
tam, Cono eximere, atque absolute et universaliter contemplari, acsi
nullam ad Conum relationem haberet. 
Fyperbolam ixitur axpello cam (sive lineam curram in plano de-
scripeam; sive Reueam planam ejusmodi curra terminatam,) cujus
ordinacimm applicatarum lincularum quadrata requantur 289rcgatis bi-
norum rectansulorum; quorum quidem altera sunt incerceptis diame-
eris, altera earum quadracis, proportionalia. (Nempe h = l d + - d
Sunc enim rectanenta la, ipsis a diametris intercepris proportiona.
lia, proxter communem altitudinem I; rectansula vero= d’diame.
trorum interceptarum quacratis d sunt proporcionalia, propter can-
dem ubique rationem, puta L. l:: d. = d. Oerum vero rectanou
lorum majus sit, non retert; sed modo hoc, modo illud.)
Diametrum,