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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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L
Arithometica Insinitorum.
PrOD. 32,33
qualiscrienei circuli Cui C ter Tumpei. (Per PrOD. 29, 30.)
cumq: Suxvonanens sequales circuli B in prima _ C in secun-
Sa (Propcer xquales radioe) crune Agura Epirales MABH
prima, _ NIABC. M Cccunda, ad invicem, ut 2 ad 3, DeMDEUC
circulus bis sumpcus 2d cundem vel aequalem cer sump
eum;) hoc ek, in reciproca ratione rectarum homologari
MA, MA. Nam MA in prima eA = recta MB, Ec MA in le-
conda 5 (aequalis rectxe) MC; luncisicur Ma in sccundas
ad Ma in prima, ut 3 2d 3, vel 5ad 2, vel 22d3 Idc09;
FIGUTa MABM in Spirali prima, ad AsuTAM MABCM in Spi
rali sccunda, uc recta M A in secunda ad rectam M A, iN
prima.
Acq; idem similicer octendetur, quaecunqi sic racio homolo
earum rectarum in dissimilibus Epiralibus.
PROP. XXXII. Corollarium.
autem ejusmodi fieurae spirales, lineis spirali-
bus dissimilibus, e rectis item inaequalibus termi-
nentur; erunt illa ad invicem in ratione qua com-
ponitur ex triplicata ratione rectarum terminantium,
ex reciproca ratione rectarum homolozarum.
DCquIeUE CX PFOD. 30, 31.
P R O P. XZXIIT. Corollarium.
Oero, Fieure spirales, quae circulationibus prima,
secunda tertia quarta, ec. describuntur, sunt
ad invicem, ut 1, 7, 19, 37, 61, 8 c. nempe ut
differentia numerorum cxbicorum, quorum latera sunt A-
rithmetice proportionalia.
NaMICDEEPP. 29.) quX prima, quae prima e CeCUMdB, qua
prima Eccunda e cercia, quae prima lecunila cerria _ quarca.
_c, deferituuneur: A PUMEUC 1,8, 27, 64, 125, EC. ergo, quae pri-
in1, qua Secunda, qu_ cercia, qua quarca, _c. describuncve
HINC CE 2, 8 -n 1.3 27 8, 64 = 27, 123 = 64 8 Ca HOC
cA