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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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PR OF. 33.
De Sectionibus Conicis.
Docacur recta aA = - 1, _ C in ejuldem concinvatione) AII
d: Acg; ad rectam A EI ponaneur (ad opBoticas parteS) dux
rectae inricem parallelae; AS -L, _HB-- d. Talcem canca lIME
longicudinis AS, HB, uC EC AS a HB- 1d;) Sicq; angulus SAH
=aHB quisibec acucus, (modo major lic complemento ap-
euli inclinacionis in Hyperbola expolira.) Juncta vero aSpro-
ducacuE nE cum recta B H producta cocac in S; d juneta BA
producacurve occurrac ipsi aS in V; ue compleatur crianou-
lum VBS; quod eAo Triangulum ver. axem in COno contru-
endo.
Deinde rectis AH, BES, duo pIanA ItA CrIGANEUE, RE COM-
munis eorum sectio HO, Faciac ad rectam HB angulos rectos,
ad rectam rero AH angulum AHO agualem angulo inclina-
cionis in Hyperbola provotica.
Hoc enim ommino heri posse constre: Si enim recta quali-
bec HO perpendicalaricer intictens plano Trianguli VBS (2-
deog; angulos faciens verolq. OHA, OHB, rectos) circum-
volratur circa rectam BHS uc axem (invariaro anculo
OAB) donec ad sicum plani perveniac in Ha, Faciacq: in plano
crianguli anculum oHla acucum, qui minoc eric angulo incli-
nacionis in Hyp. rbola, CeAt enim, ex constructione, angulue
AHB istius inclinacionis complemento majori) neceste cR C
nim uc, in crensieu, aliguando fecerie angulum inclinationie.
anculo aqualem; (factus enim est cranticus ab anpulo recto,
adeoq; debico majori, vel lalcem aquali, ad angulum debito
MInOTEM;) adcoq; cunc tuerie in licu debito uc sic ducrum
Planorum provt reguiritur concurrencium communis lectio.
In plano rucem BOS sic posito scribi incelligatur circulus,
diamecrum habens BHS, qui sc batis conis aliiq; tuic paraI-
leli diamecros hrabenteo BDS, conum complentes, (per prop.
5.) qui plano AHO Ecctus exhibebic Ayperbolam (per PrOP.
7.) cujuo Ordinarim apelicaEx omnes (quarum HO cAuna)
ad diameerum AH aneulum Faciene equalem angulo inclin-
cionis ordinacim applicatarum in Experbola expoliea ad dia-
erum suam; sed e cildem lune respectire xquales (ue paccbit
ex demonstracione prop. 17, _ 30.) ideoqi lineuta linculis
congruune, adeoq; & Hyperbola expolica Hyperbolx scctione
conitactae. Quod crac taciendum. Adeoqi Hyperbola a nobis
detanica