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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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PROD. 7.
De Sectionibus conicis
parallelas, (roridem parallelis in Cono circulis, St C0-
Bi. sectioni communes,) Ordinatim-Subtensas (re Op-
dinatim inscriptas, appello: quae, cum sine circulo
rum diametris perpendiculares, (ut constructio postu-
lat,) ab ipsisbilccantur, 2dc0q; _ a C oni- sectionis
Diametro, (quae nempeper eadem bilectionum pun-
eta eran(IC;) Karunq: Cemisses, ut DO, diametro
Coni-sectionis Ordinatim- applicatae dicuntur; FunEg;
incer bina diametri circularis (cui perpendiculariter
anSICtunE) Scgmenta, BI, DS, medixe proportionales:
Exe quidem si diametro Conifectionis AD, ad an-
gulos rectos insittant, Diameter illa axis dici ColcE
(qui luis ordinarim-applicaris cst perpendicularis; )Tin
minus, Talcem Diameter, vel Diameter Obliqua vel
inclinata dici (olet.
TIc aurem Conusipse, sic _ Coni fectiones (Pa-
rabolam intellige _ Hyperbolam, nam de Klliph Pe-
cus clt,) Cimul cum Cono in intinitum continuandx
SUPBOnUREuT.
Ouod aucem Planum Coni. sectionem efficiens, si unam ex paralle-
Pis Coni cireulis secet secundum rectam OO, ipsius diametro BS per-
pendicularem, etiam relignos illi parallelos quos secet circulos secabit se-
eundum rectas quae ipsorum diameiris ipsi B S parallelis sent perpendicu-
Pores: Sic demonstrabitur. Cum circuli supponuntur parallelis
erunt e corum sectiones O0, O0, (eodem plano Factx) pa-
rallela, (Per 16CY1.) qua proprerea cum parallelis circulon
rum diamerris (BS, B S,) eoldem angulos Faciune, (per
IOCLF.) Donicur aurem, ansulos ad diametrorum parallela
rum unam rectos esse; ergo et ad omnes; Ouod erat demon
Atrandum.
Religua in Propolicione vel Definitiones Tune, vel ex propo-
Eicionis curriculo Talis Patent.
Monendum aurem eAt Parabolae, ElipsiS, _ Byperbolae appella
cionibus, apud Geometras, (qua igicur libertace e nos ali
quando uturi sumus,) nonnunquam curvas lineas in superticie
COnICa