( 674 > 
rarores M, N~, 0 , P, &c. (^od facile confl:at cx con- 
tcmplatione Trianguli. Si itaque fuerinc M, N, 0, (jrc. 
M 
Numeri figurati cujufVis ordinis n, fumma Seriei — 
M 0 P ^ 
-I L — 4-— -\- &c. a^qualis eric Numeri binari- 
' 4 0 16 •* 1 
dignicati z\"~ \ Sic Series -7 + ^ -K = 
2 * " * = I, ut vulgQ notum ; Series — J- — 4. A 
-’p =: 1 ” ^ 1 ; Series*^ +‘^ + y "V ~ 
2 ’ “ ^ = 4, & fic porro. 
Scholium. Celeb. D, Jac. Bermnlli, iti TracSlatu fuo de 
Seriebus infinitis, folvic illud Problema. ‘‘ Invenire 
“ iummam Seriei infiniras: Fradionum quarum Denomi- 
“ natores crefcunc in Progreflione quacunque Geome- 
“ trica, Numeratores veto progrediuntur vel juxca Nu- 
meros naturales, i, 2, 3, 4, vel Trigonales i, 
** 3, 6 , ro, d'c. vel Pyramidales t, 4, lo, 20, 
aut jaxta-Quadratos i, 9, 16, ^c. aut Cubes r, 
“* 8, 27, 64, ^c» eorumve mulriplices.” Ipfius folu- 
tionem confula^ Ledor. Aliam vero, & quidem mub 
to generaliorem invenic D. N/V. ^illius Nepos, 
eamque ( poftquam ei hsec miferam, fed fine demon- 
ftrarione) mecum communiGare dignatus eft, in epiftola 
data i8° Septemhris 1715’, miris quidem invencis refer* 
tiflima, quaiibus me crebro dignatur vir Dodiftimus. 
De hoc vero Problemace fic fcribic. Pour la fbmme 
“ d’un nombre determine « de termes de la fuitte de 
“ voftre Theoreme 7. [ Ccrcllmum primum eft hujus 
Propoiltionis] j’ay trouve cette formule x 
m — 
m — I 
i_j_ d 
4_ 0^ Jes X-fiCtres B, <jre. marquenc 
ies 
