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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 341, page id 851387705:0361
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PFODZXXVI.
C O N IC F 5.
TuM (PEOPIeE Fangentem) DT q = DO4 C nempe aqualia, s DF
coincidant; vel, si secus, illud majus; ) hoc CA, f + a = 2f a
= 1d. + d. + a =2 a = 2 da pr. et (utrinque mulciplicando per L3
+d Y d
erie f27 a + 52 a + 7a a = d’a = 25+ da + 2f d a = f2 1d + f d +
c
= f7a =2fda. FF (deleris urinque f2 + d + f a2) erit t da  d a =2f1 da
+25d’ a = f a =f 2a = 25 da. Er (dividendo per = a) eric =1 d a = d a
 2f+a + 2fd2 = + f2. a + f27 + 2f2 d.
Denique, ponendo D H idem elle punctum, (ut cranescat quantitas a, adeo.
que de ipsius mulciplicia + da d2 a f2 a) erit 2 f1 d  2f d = f2 1 + 2f2 d.
Ec (diridendo per 2 f) + d = d2 = 3f+ L fa. (hoc cst, A AH a = D CHP;)
24 = 72. Hoc ests HC. H2:: H A. HF. Ouod
vel 3+ + d. 1 + d:: d. f -
erac inguirendum.
Duod Theorema sie inventum, hoc est; Si sit Ordinatim axplicata in
Erperbola ETan atque ab applicationis puncto FI continuetur diame-
TeF HI A ad P; sicque uc distantia puncti applicationis a Centro HIC,
ad aggresatum diametrorum trantrersa et interceptae HLa; sic dia.
meter intercepta IIA, ad eandem continuatam TTF: recta a F juncta
tErperbolam in puncto a continget.
Vel sic; S recta a F FEyperbolam contineat in termino ordinatim applicatae a;
erie, ue distantia puncti applicationis FY a centro FIC, ad ejusdem distantiam 
vertice remoriore FTa; sic diltantia a verrice propiori LIA, ad distanciam à puncto
concurtus tangentis e diametri TIF.
Demonstratio, Si sic opus, insticui poterit repetitis Analyseos restigiis.
Sed de patet, quod, cum sic HC. Fa:: H A. FIF. hoc cA HC. HC F C a::
AA. HIA f AF. eru (dividendo) HIC. Ca = C. A:: AA. AF. Adeoque SI fu-
macur (in diametro concinuaca) AF = FALAC, habetur punctum P. Sed
TTC
etiam, cum CIEFLC major quam C. A, (BAES L0EO) CxIL PFOPTerea FLA major quam
AF; hoc est, Diameter intercepta, major quam ipsius continuatio ad concursum
Pancentis; (contra quam in Fllipsi ubi minor elt, ee in Parabola, ubi aequalis;
uc oltendimus proP. 23, 830.)
liem, (ponendo C A = 31 = 5, e CH = C A F A H = 5 + d = c, 10
coque HA = 0 - 5, _ Ha = c + 5) erit HF -
_ CF = 0 -5 = =. HOC est CH. CA:: C. A. CF.
d2
aique hinc docemur, Rectam a F duvere quae Ly perbolam in dato puncto a
CA
concineat. Sumpia nempe C F = . , e quidem d C vertus A, si concactus
requiratur ad Hxperbolam Aa, vel (eadem ratione) a C. vertis a, Si ad Hyper.
bolam oppolicam.
Acque hinc seqVitE; Rectam contineentem LIy perbolae diametro citra centrum
occurrere: pata incra centrum e verricem: (nam quod ultra verricem Lic, patet
ex praecia
que _ ILA minor quam HF. Ouod autem sic citra centrum, patet etiam, quia,
ic dictum est, HIC. C A:: TTA. A F, adeoque HIC. HIA:: AC. AF. ac LSC ma-
jor est quam HI A, erBO A C major quam A F.)
Trem, Aquovis diametri puncto P, inter FEyperbolae verticem  centrum sum
pto, duei posse rectam Fa quae FEyperbolam contineat. Duo aucem punctum L
puncto C propius sic, eo remorius abest e punctum contactus a e punctum ap.
plicationis huic conveniens H. Ouia uc CiF. C A:: C A. C H.
Adeoque