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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 347, page id 851387705:0367
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 O N LC
P ROP. XL.
De Fyperbolis Asymptolis.
PEperbOla quotlibet ad candem diametrum (vecluS Cat pa-
R ECS) ita accommodatae, ut centrum idem hrabeant, atque ca(-
dem (ad communem diametrum) Ordinatim positas, rertices autem
(in eadem diametro) rarios quosti-
DCC, Puta A, an an (adeoque e V2-
rias diametros crantrer (as;) Si ea-
dem sic in omnibus ratio diametri
trancrersae ad luum respectire la-
cus rectum, (puta ratio t ad l in om-
nibus cadem,) casdem hrabebunt A-
EYIIPTOTASReCtAS, (Puta CM, Per
praeced.) Fruntque iplae ad invi-
cem Llyperbolae asymptotae: Nemve
ita ad inricem approxinquabume, ie earum distantia tandem eraclat
qualibet altignata minor, (quoniam carum qualibet ita prove ad re-
Cras Asymptotas accedit;) nec tamen invicem occurrent, (quoniam
Ordinatim applicatarum quadrata B == l minora crunt, caeteris
Paribuo, ubi s major et; adeoque HO major quam H o, acque lac
major quam IL c.)
Si vero non sic (in rariis ejusmodi Fyperbolis) ratio cadem:
Nec caldem habebunt A(ymptotas rectas; neque erunt ip (X ACympto-
Ex; Sed vel se mutuo sccabunt, (nempe E FIrperbola qua majorem
habet diametrum- tranlversam minorem habeat rationem F ad V;) vel
(si majorem habeat rationem e adt 1) debitam axpropinquationem non
alcingent. Prout ex praemistis non est diftieilé demonstratu.
Iis autem, quas diximus, Zyperbolis Nrmptotis, respondent Fyperbolae r0-
ridem ejuldem Coni planis parallelis secti; Oux quidem quo provius ad verri
cem Coni accedunt, eo ad Priangulum accedunt propius; donec tandem (in ivso
coni vertice,) cranescence diametro tranlverla, Lyperbola in Priangulum (vel
si placet, Feianguli crura) degenerer; cujus quidem Frianguli crura repraesen-
ranc binae Asymprota recta.
e at. ACl.
De Flyperbolae Diametris Conjuradis
E OPPOsitarum Eyperbola CtalCCIO. CTanIVeLIX A a Ordina-
cim ponatur rectâ per cenctunt o acetur illa Diameter con-
jurata: qua quidem rectas omns ametro A a pdrallelaS, oppostis
sectionibus terminatas, puca e Otariam sCcaBIE; quae propterCa
diametro dd ordinat a Tunt, quas Ordinatim transeribus 
cere licet.
lam