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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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PROP. 36.
DeSectionibus Coneis.
quanticas a, adeoq: _ iphus mulciplicia idas 12 a, s: 4) eric
3fu T2fu- f 1+25 d. FCC dividendo per 2f) 1d t u = = 11 t) d:
(hoc CA D AHa =HC HF;) vel 21 F d 1+ d:: d. f -
Hoc eA HC. Ha:: HA. AF. Quod erat inquirendum.
eita do
Guod Theoremasic inventum, hoc est; Si Tc ordina-
cim applicata in Hrperbola H2, aeg ab applicationis
puncto H continuetur diameter H A ad F; CIc9; uE di-
ctancia puncti applicationis a C entro H C, ad argre0a-
tum diametrorum trantverse ec intercepie Ha;
sic diameter intercepta HI A, ad eandem concinuatam
HIF. recta eF juncta Hyperbolam in puncto a con-
tingct.
Vel sic; E recta aF Hyperbolum contingat in termino ordi-
nacim applicacae ai crit, ut dittancia puncti applicacionis HI
aceneroH C, ad ejuldem distanciam a vereice remociore H a;
Tic dittancia a verrice propiori H A, ad distanciam a puncto con-
curtus canpencis e diamecri H F.
Demonstracio, si lic opus, insticui poteric repecicis Analy(CoS
veltigiis.
Sed _ Patet, quod, cum (E HC. Ha:: HI H. HF. hoC CAHC.
ACtCa:: HA. HI + FIF, eric (diridendo) HC. Ca = CA::
HIR. AF. Adeoq; li Cumacur (in diametrO COnCINUatA) A F =
HA.AC
HC, habecur punCtUm F. Sed etiam, ciim sIC HC major
QuAmI CA, (DAPSEOTO) CFIE PEOPEerCA HA major qUAI A F;
hoc est. Diamerer intercepta, major quam ipsius continuaio ad Concur-
sum dancentis; C conera qam in F. Hipli abi minor est; et in l’a-
Tabola, ubi aequalis; uc oRendimes PeoV 23 20.)
lcem, (ponendo C1 = 2 -5, _ CH CA F AG- 5t d- c,
ideoq; HA = 5 - 5, _ Ha -c F5) cric HF -
=5, _ CF -c
EF.
iutu
HOc cA CH. C A: : C A.
la