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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
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De Sectionibus Conicis.
PROP. 40.
ctum, (puta ratio + ad l in omnibus eadem) casdem
habebunt A(ympEOtaS recAS, (puta CMI, Per Prae-
ced.) Pruincgi ipse ad invicem syperbola Asymptotae.
lempeica ad invicem approxinquabune ut carum di-
llancia tandem cradat qualibet allignata minor, quo-
riam carum quaelibet ita prope ad rectas Alymptotas
accedic;) nec tamen invicem Occurrent, (quoniam
Oedinatim- applicatarum quadrata B2 = c = I ni
nora crunt, caeceris paribus, ubis major est; adc093
EsO major quam FIo, atq; haec major quam FIco.)
Si vero non sic (in variis ejulmodi Hyperbolis) ra
tio cadem: Nec ealdem habebunt alrmptotas re-
ctasi negi erunt ipse Asymptore; Ced vel se mutud
lecabune, (nempe Li Hyperbola que majorem habet
diametrumtran (verlam minorem habeat rationem t
ad 1;) vel (Amajorem habeat rationem 1. ad1) de
bicam appropinquationem non attinsent. ProuteZ
premistis non cs dithcile demonstratu.
Illis aurem, quas diximus, Fyperbolis Asumptoris, relpondent
Hlyperbola coridem ejuidem Coniplanis parallelis secti; Ju_
quidem quo propins ad vercicem Coni accedune, co ad Frian-
Sulumi accedune propiiis; donec tandem Cin iplo coni verti-
Ce,) eranelcente diameerotrantrerla, Hyperbola in Triangu
dum (. vel siplacet, Friansuli crura) degeneret; cujus quidem
Trianguli crura repralencant bina AIyPIOLA rect_.
PROP. ALL.
De Fyperbolae Dinmerris Conjueatis.
 Oppolitarum EIy perbolarum diametro trans-
verle Ra Ordinatim BOnatuE recta per Cen-
exum sCs, dicetur illa Diameter-conjucata:
GUX