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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 328v, page id 00068194:0658
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Solvere hoc problema a me diu
quaesitum inveniendi summam proscessio
nis (Zeometricae seu reassumtae, idem
est quod invenire progressionem Har
monicam datis ejus differentiis, diffe
rentiarum qu rationibus:
Xc. at
e = a +
=ea +2b,
GBe: 4
4
1
Xa 1
a13+b
a= R +a a+b, +b
= a+b4b
D+1((2)
Brevius ita concipet: quadratum differentiae diffe-
vertiarum dividatur, per differentiam minorem
producto a; quotienti addatur differentia diffe
rentiarum. d triplicata et differentia minor
triplicata. Summa est Terminus Major
au +9a + 12b.
proportionis Harmo.
nica
a dissra pna  ada. Ratio earum a
terminus primus qu progcessionis hannonicae
quaesitus 2. Ergo tertius est Za. Ergo
secundus est za 
Ergo Ergo segindus erit 2Z- a. et
tertius Z- a + b. at idem tertius est
Za. Ergo Pa = Z- a - b.
quaerendum est aliquid aequale ipsi Z.
2B = 2 4 +. Ergo
a. - 2 - ab - bb
arta a
2b = 24- e- ba
22+ a 2b+ da + ba = Za.
aa + ba = ea - Zb.
Dividantur omnia per a. fiet
A + b = X
jam Zb e = Z. a - b perpra
Ergo.
a+ b = Z 7 2. acb, seu
 2absi a + b = 2+ a+ b-7. En aequa.
imnia Exergo inventam havem.
datis differentis invenire
ei terminos progrestionis par-
tionem nugatoriam, et
a + ba = 2a - Z b. i
Poidantur aa +ba. in duas partes
t
2- a + b, + b, = 7 b e (Erraveram
ante, quod non expresa +B in aequatione
ratimm attram differentiam praecedento
sequente majorem) multiplicenti omnia per atb
monicae proportionis num qu ati. fet  Atb, + bg a + b = 2b. Et
 n minon diph addatur differentia ejus
a majore. Summa multiplicetur per ratioem
quolitam unitatem auctum quotiente
dio
producto ex divisione differentiae interdisse
rentias per differentiam minorem, productum
terminus quae sitae profressionim maximus
quo dato racipui duo facile inveniunt
2 atibatibm a + b b =
2
La+1. =2
a2-- 42 4a + a,, + 27 a + b, + b = Z+Z
2- a +brC + 4 1att a 1 a+b+C. - X
2 termins g.
B, 1b, =