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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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4C
Arithmetica infinitorum. PrOP. 178
Adcog, daro lacere ldabitur numeruo Priangularis isti l2-
ceri conveniens, Pacan =  + l.
EECONTA, Daco numero Priengulari, inveniecur ipsius
laCuS.
Nempe, retolvendo hanc A quationem 2n = 1 = + l, erie
:  + 2B. Z - b.
i
D R O D. CLRRIII.
Coroll.
P Hyperbola Diameter transversa set 2 ex Latus
rectum ?: sumptis diametris C. puncto applicationis
vertice interceptis) Ln 293,4,5,Oc. Ordinatim-
applicatarum quadrata erunt 1, 3, 6, 10, r5. ∞c. nempe
numeri triangulares, cnjus latera sunt 1, 2, 33435,  C.
Probatur per 17 vel 33 proD. C on. Sce. nos. Hyperbolam
iplam extribebir tipura prop. Ccg.
PROP. CIXXIV.
Corollarium.
C s pant ad eandem rectam AaO duo triancula
ata at B, aDB3 tq ut c ad V sic AD ad DB
aD ad DB; S sumantur agnales Aa = 1 = aD
DDSc. Rcctancula BDB, BDB,  c. erunt ad invi-
cem ut 1, 3, 6, 10,
_C. numeritrianeu
lares, quorum latera
sunt aD, aD. exc. M. -
diae vero proportiona.
les inter BD, DB; DB.
DB eC, sunt ordina-
tim. applicata in F-
perbola ADP: cujus
diameter transversa
Aa  latus rectum aB, vel ipsi agnale.
Pacet ex calculo. Nem rectangulorum BDB, primum crie
VEXZVE =1. Sccundum 2Y = +3V5 =3. Tercium 3 ~:
X4V.