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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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arithmetica insnitorum.
PROP. CLXXVI.
Lemma.
DEopolicum Atinquirere quam habeant rationem
numeri Pyramidales, ad lacus cuum.
Liceret _ hanc propolicionem pari procressu inrestigare, quo
in prop. 17 L ulis lum: (ob Cerraco incerim difcrimine quo dif-
Fere debica numeri pyramidalis dispolitio a dilpolicione nume.
i Triangularis:) quod qui rolec experiri porerit. Verum cum
non ila Facilo elsec lectori concipere debicum punctorum sicum
in poramide (uc quae non omnia lupponenda sune in eodem
plano) ee angulorum Colidorum ad ca puncta poticionem: (9-
eius ridecur illad hac quae sequitur mechodo praettare. (Oux
quidem, nisi mallem ucrumqu: modum octendisse, adhiberi pon
uillet eriam ad proD. 171.
F NumeruS egramidaliS RQUACUX AECTESATO nuMerOrUM
criangularium (uc pacec ex dictis ad prop. 230. _ 132.) nem-
De ab unicate ad numerum Priangularem sibi collaceralem in-
clutire. (hene _e numeri Priongulares tiune aggresarione La-
ceralium; e Lacerales, Monadicorum; uc de lriansulipreami-
dales, Pyramidalium; d sc deinceps.)
2. Ek aurem laceris l, numerus quilibet Trianeularis
2 DET PrOD. 171.
30 Ergo, Tumpeis lateribus 1, 2, 304,
C; rel (coru loc0) a, b, Codu dec; Cumma
horum a = + 2, B: FB, c 2 + c, d2 + d, _C.
eric duplum agcresaci Triangularium;
quorum numerus erie aequalis laceri maxi-
mi:) de hujus propcerea lemistis, crie nume-
aC
rus Pyramidalis, cujus lacus squatur lace. Num. Pyramid.
rimaximi Triangularium.
4. ER ixicur numerus Pyramida lis Cemistis agereBaciduarum
lerierum; cousq; ab unicate concinvacarum, donce numerus lon
corum ae querur laceri numeri Pyramidalis quaelici, quod lup.
Donacur l: Ouibus h praexonacur locus alcer 0 +O, CuE leri-
es incellixantur ab oinchoacx, sics harum nuerus lFT. PC
ucriusq.
PrOP 176
 +
+c