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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 160, page id 824573315:0372
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160
Arithmetica infinitorum.
acq; hic quidem modus omnium optime convenicproD. 3
26, ubi hguram Sxirali adjacencem cum Parabolica compara
mus. Nam C, in Agura Exirali, ductis quoclibet rectis MI an
sulos taciencibus concinuos invicem equales, s in singulis (p2-
cies lectores inCcribi lupponantur, crunc eorum arcuS, Ut 0, 1,
2, 3, dC; In circum Ccribi, uc 2, 2, 5, 4, ec; s vero ita abCcribi
uc sectorum arcus a Exirali bi-
SCCeNTUT, erunEUL Z, 123 26,
32, _C, Vel UE 1, 3,5,7, _C.
(nempe ut differentia nume
rorum quadraticorum:) adc0qi
Aarcusilli (sive numero inf
nicisire tinici, quamris ibidem
de intinicis cancummodo verba
Factaline, adcoq: tranc curios-
earem illic omictendam duxe.
rim,) Cuxponantur in rectum
excendi sc invicem concinuari.
ve tranc cocidem Cegmenta dia-
amecri parabolae (continue potita;) unde cradane diametriin-
TCFCCPEX L, 4,9, 16, _C. (nam 2 + 3 = 4, 2 + 3+5 = 9.
BC;) quibus conreniane ordinacim. applicacxe (quippe in diau
metrorum ratione subduplicata) quae erune ad invicem, uC L,
2,3,4, _c, hoc eA uc ipsa rectae NI T, MT, Qc, intixura (pirali
vera per similium sectorum terminos cranlcuntes.
Acq; hoc vacto comparare licer, non modo fisuram ex lecto-
ribusnumero infinicis (quod nos illic Fecimes) sed eriam ex nu-
meroEnitis conslacam, spirali adjacencem, cum fioura ex Foci-
dem parallelogrammis adjacence parabole. Ouod quidem (B-
nenora tiguca) lacis incellisi poreric. Si illi sectorum arcus po-
naNEUE + 4, 3a,5a, _C; radii vero (ip(S proporcionalCs) 2r, Gr, IOr,
Rc; erunt lectores Lar, 9 ar, 25 ar, C. (nempe Pemisses paralle-
locrammorii radiis ee arcubus respectiris concentaru.) Sumpris
icem in parabola diametro continuis legmentis I a, 3 435 a, Rc.
adcog: diamerris intercepris L a, 4 a, (= 1 a F 3 a,) 9 a ( = 44
+5 a) _C, e ordinacim applicaris quae illis diamerris conreni-
ane Cindiamerrorum racione lubduplicaca) 2r, 4r, 6r, Ec.
(quae Spacia ab seindane non a que alta, sed quorum alcirudi-
nes sine arichmerice proportionales, ut 2, 303, _C. UE PaLCL)
parallelogramma lpaciis iILISINCCTIPTA CTUNE. LAXOF, 3aX2Y,
P1Op. 182