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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)
# Folio 95, page id 824573315:0179
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PROP. 39.
De Sectionibus Comeis.
H, cui ordinarim. appliCetur HO recte CMR OCCUrEENS in MI.
Eric (propier similia eriansula) CN. NB:: CBI. TIH Adeo-
que CNg. NMg : : (1. I::) CH9- 12. HN9-- - c= -
Sed (propcer Hyperbolam) cric HOg-
lCvonendo
nempes = = 1, Id eoq; d - c = 5, _ dF 1 = c 8 5,) FF~O F)C
inuS CAquam AM9. e recta HO minor quam recta H M et
prOPterCa M eric exera Hy PerbOlam. Rccca igIIUE C H M
quancumris producta) Hyperbola nuIngua OcCLCIIC. OuOd
erat primo demonstrandum.
20. Cum (IC OM (=-HM - 1O)=
Tincq; 5, l,F, quencicares Aabiles, ac c variabilis, et quidem
TANEOmaION QuancO retocius ab eA DuNCtUI H a CCHETO C:
Differencia rectarum s
l hoc eR, recta
rUm HMI, HIO, PerPEEHO MINHIETUE pPOVE C, hoC CA, C H, a1-
SccuC. Nam in majoribus quadraris aqua le aUEMICHCUM (rC-
tenta figurae specie) minorem postulac laceris pruductionem
quam in quadraris minoribus, (Uc nOruI CA.) IdcOq; POVE
Longius abesta centro punctum H, adeogi ca maius cA, (rcli.
quis incerim immutaris) ica semper minuetur () M, disferencia
lacerum V
13 1
C2  5
l. Ec conlequencer distantia re.
Eta CMMT ab HyperBOIX CurVA AO, continne decrelcits
Ouod erar secundo demonttrandum.
30. Sit altignaca distancia qua libec quencumris exisua, puia
2a; Dico Hyperbolam AO rectamq; CM eo produci poste ur
earum distancia minor cracac quam cA asIBNACA 2a. SUIMIAEUT
enim linea recta aligianco minor, puca a cui xgualem esse vo-
lumus rectam OM; _ quaerendum sic punctum H (cui opdi-
macim ponenda sicHO) Ccu lonsicudo rectae C. H. Ouoniam
sicur suxponimus a = ON -- 1 =
cransvonendo)
12
 52
eite
t  a; e (acrinque