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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 17v, page id 00068255:0034
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sechemnea si sees ata habent columnam
Series summatrix non potest habere primam columnam unius periodi
nisi series summania habeat primam columnam ex aequalibus compositam
potentiae habent primat semper columnae periodum semper ex duobus
terminis compositam
Quadratorum seres habet primam corumnam l periodi binariae
secundam periodiq urtariae, seu aequalium, tertiam periodi quaternaciae
quartam periodi octonariae et ita porro.
in serie quadratorum qaevis terminos periodus composita est ex notis
r reciprocis. ita ut ultimae periodi a eaedem sint primis.
In seve triangularium una medietas est alteri quaevis perivous habet
unam medietatem alteri oppositam, quod etiam fit in quavis serie
progressionis Arithmetica
Si seriei summandae prima columna habeat periodum binariam, seriei
summatricis columnae habet periodum non plus quam quaternariam. Hoc ita
demonstravi sunto primae colomnae noseriei summandae nota abab, etc. dico prima
columnae serici ser summatricis peridum tole tghikeghik et
Hoc ita demonstro  erit a +g- 2ag = h l + h - 2ah = i, a +i - 2ai = K, b +H ebk
snam esto b + K - 2bk = l, dicu sert l = g. Nam
si in aeq. b +k - 2bK = l, seu in valore ipsius l substituatur pro K ipsius valor a+ 1 - 2ai et
dice sorehico fere b + R - 2bk = 9
pro i ipsius valor b+h - rat, et proh ipsius valor a +g- rage destructis omnibus siet l-q
ut comprobari sub firem staginae praecedentis. Unde patet hanc aequationem esse
vrtualiter identicam, seu ipsus g valorem per a et b, inveniri hinc non posse