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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 SECTIOHEBUS PTOP. LLLLVII.
Adeoque si supponamus punctum Fipsi C coincidere, nt distantia C F = 0 nulla
Lic; exir proprerea CH intinita; HIoc et, punctum HI,, (adeoque ee punctum e)
supponendum est intinire distare, adeoque rel nusquam ret non nili i Hlyper-
bola actu infinita reperiri.
Cumque punctum Ci indifterenter se habeat ad ucramque Flyperbolarum oppo.
litarum, ea quae supponitur Continsens per centrum ducenda, vertus utramris
partem producatur, intinira erit, adeoque Fyperbolarum illarum neutri occurret.
Oux propterea ssimptoca, dici Coler, ue post dicetur.
Alia quae adjunsi posteus corollaria lubens omitio.
P R OP. ZXXVII.
De Fyperbolae Diametris.
I per Frperbolae Centrum C, punctumque in curra quodlibet ou
 tranleat C a recta; erit illa ejuldem Eyperbola diameter, rerti
cem habens an acque ordinatim applicatas rectae e FFyperbolam in a
contingenci parallela5.
T ibet hanc proposicionem (uE priuS 24, 8 3F.) Analyrice examinare, de
inde ee Synchetice demonstrare.
Supponamus isicur rem esse ut perhibetur, adeoque inscripram quamlibet OO
cansenri a Li parallelamt a recta Ca (per centrum ee contactum transcunte)
vilectam in n. Sintque rectae OD, OD, a FI, diametro HI a ordinatim applicata,
et propierea inricem parallela; quibus etiam parallela ducatur nh eidem dia
mecro in h OccurrenS; quae propierea (propies parallelas) bilecabit, (ut OO in n,
Lic) DD in h. Denique recta OO, (producta li Opus) diamerro FIA OCCUErAE
in G: Occurturam enim omnino ese patet, quoniam a L ipti parallela cidem dia-
metro occurrit, per praeced.
Supponemus etiam impraelentiarum, occursus punctum C contingere supra ver-
ricem A, exira Fyperbolam. Si aurem secus contingat, (uti tieri potelt, si in-
Teripta OO remorius a tangente sumatur, ita uc diametrum cranseat,) non tamen
Teries operationis variabitur aliter quam vel mutanda aliquando ligna  , vel
quancirarem aliquando nesatire incerpietandam tore, adeoque ex parte suppoli.
tioni concracia, incelliseneam.
Dicantur aucem (ob commodiorem caleulum) Ia = B, F A = du A a = 1.
HIa (= +
=3320
2 (= 21 +4) = C, HD = 9, an = 5, aC = 0, nC. (= 0 +5)
Tum (per praeced.) HC. Ha:: HI A. HF. hoc est c. 2. : 4.  = =HF. Et
(proprer parallelas, et simulia vrianeuta) C.a. an: : C H. HIh. Hoc cst 0. 8:: c.
 =HM. Et Ca. Cn: : HXa. Rn:: HIF. hC. hoc Cst, 5. 7: : b. = = hn. : 2~, 3d 2
= hG. ideoque DC (= nO FHD) =
do +g. Icem na C = AH + HH)
= a + =, et ha (= 1 + a + =) = = + . ideoque D A = a. + 
D2 = 2 f -= = g. EF rectangulum DA X D
F849 =20869 +0836 +0d d6 + sec
vel
0ut2
(vet 
540.
2
Deinde