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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 210r, page id 00067993:0421
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nica: Sciendum est, muleas series numero terminorum infinitas, esse in
summa gracitates Anicas. Exempli Facillimiloco sic series ab unicate de-
crelcens, progcestionis geometrica dupla, L,f. Z, f. 5 rt. 2o L5 L. For c
in intinicum; qua camen non Facic plus quam 1. Nam in adjecta
linea recta AB (FiC. 4.) qVX SICL, CTIE ACL, e residuum (CB) bise-
cando in D, habebis CD Z; de residuum (DB) bisecando in F, habebis
DE, 8; de residuum (F B) bisecando in F, habebis FF, 7G: d ita
concinuando sine finc, nunqram exredieris cerminum B. Idem in
Fractionibus numerorum fixuratorum scu crianoulo Fharmonico fcri,
a me alibi octentum est.
Mulca nocari possene circa hanc Oradraturam, sed quae nunc
PErseqri nOn VaCAL: hOC LaMeN PraeterirE NOn OpOrTCC, cerminos se
riei nostrae, 2, F, Z, 3 Z _c, esse proorestionis harmonica, sire in con-
tinua propoctione harmonica, uc experienei pacebic: Orin e per
Calcum, F,5, 5. 5, E7 dc, elt etiam series progrestionisharmonica;
e ∞  r9d est icidem series harmonice proporcionalium.
Ttag; cum Circulus (IcZ F. X F5F  L, _cc, 5 4 itr 15 od
Polteriorem seriem parciale à priori Cuberahendo; cric magnicudo
Circuli differentia duarum serierum progrectionis harmonica. FC
gronam groccungre cerminorum numero finitorum progrestionis
harmonicae Cumma, compendio aligro iniri porest, hinc approvin-
qraciones compendiolae, (Ei post Ludophinam illis esset opus) duci
Pollem.
Si quis in serie nostra cerminos signo n affectos collere volet,
is duos proximosi F, ilem (.Z i item 1( B  Y. dCrt +5 5 d
te 19, ee ita porro, in unum addendo, habebit seriem noram
pro maenicudine Circuli, nempe Z ( id eAt f. 5)  f (id est = Y
490(lC8 .) dec. itaquc:
Quadrato inseripeo existente. 
Eric Area Circuli 5F55l59Fr 95F325 ec.
Sune autem numeri 3. 35. 99. 195. 323 ec, excerpri per Caltum ex
Cerie numerorum gradratoru (4. 9. 16. 25 dcc.) unitace minuIOruM,
unde hc Ceries: 3, 8. 15, 24. 35. 45. 63. 80. 99, 120. 143, 168. 195. 224. 255.
288. 323, 360. 299 ec; ex cujus seriei numeris, quartus quisgre post
primum noster est. Inveni sutem (qrod memorabile est) leriei in-
tnica 5F5 F∞5 L25 F 55 L FL ZL05 F0c. summan esse J: quin
X lira-