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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 2
# Folio 2r, page id 00068204:0003
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fatur
Sntabr. Oetob. (2A 1676 La Maller
G
Dutent
Quanta cum voluptate legi Epistolas Sarissimorum virorum
D. Leibnilii d D. Sschurnhausii, vix dixerim. Perelegans sane
est Leibnitii methodus perveniendi ad series convergentes, i satis
osten disset ingenium authoris et si nitie aliud scripsisset. Sed
quae alibiper epistolam sparguneur suo nominé dignissima,
efficiunt etiam ut ab eo speremus maxima. Diversitas modorum
quibus eodem tenditur, eo magis placuit, quod mitri traes
methodi per veniendi ad ejusmodi serces innotuerant, ad eo ut
novam nobis communicandami vix expectarem. Vnam emers prius
descripsi; jam addo aleam, illam scilicet qu’a primum incidi
in has series: nam incidi in eus antequam Scirem divisiones
et extractiones nadicum quibus jam utor. et hujus explicatione
pandendum est fundamentum Theorematis subinitio epistolae prioris
positi quod D. Leibnilius à me desiderat.
Sub initio Sudiorum meorum Mathematicorum, ubi incideram
in opera celeberrimi Wallisii nostri, considerando serres quarum intur
calatione ipse exhibet aream crculi et hyperbolae, utpote quod
in serce curvarum, quarum basio sive axis communis sit X et
ordinatim applicatae. 1 - XeX 12. 1 = ∞ X 12. 1= X ∞ 12. 1.  X X 18. 1. Xat
1= XX Z. dil, si areae alternarum quae sunt X.  Z X
X 3 +  X5.  BX +7 X 7  de interpolan
posent haberemus areas in termediarum, quarum prima 1-
est circulus: ad has in terpolandas notabam quod in omnibus primu
terminus esset X, quod qs se cundi termini & X. X. 2 X. 3. B
essent in arith melrea progressione; et proirde quod duo primi
termini Serierum intercalandarum decdrent esse +X LX3.
(. - 22
XC adrehguas intercalandas considraban
quod denominatores 1. 13. 5. 7 C erant in arithmetica progresione
adeoqs sola numeratorum coefficientes numetales estabant investigand
dae autem in alternis datis areis erant figurae. potestalum:
numeri 11, nempeharum 11]. 11]1. 112 313 15]
1. den 1, 1. Aersio 1, 2, 1, quarto 1, 3, 3, 1. quinto 1, H, 6, 4, 1. dC.
Guaerebam itag. quomodo in tris Seriebus ex dalis, duabus prine
figuris reliquae derivari possent, et inveni, que d positae secunda
figura M, reliquae producerentur per continuam multiplicationem
Terminorum hujuo Serrei, M  M 1 ( M 2 X M  M A de
13
Si
C. G. Sit M = 9, et erit 1 m 1, hoc est 6 fertius terminus, de
67 m a hoc est, 4 quartus, et AY M 3 hoc est, gcuntus, &
Yn A hoc est, O Scaetus, quo Series inhoe casu terminatur. hanc
regulam itaq’applicui, ad series interserendao, et cum pro cireulo
secunduo derminuo ettet , posii ma et prodierunt termint
XXNV 13
si
Vir dignisme
Copied Nov.
. 1676.