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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 15
# Folio 4r, page id 00068228:0007
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Ex his jam summa Tridivulsionum sic poterit
inveniri. Primum indagemus summam Bidivulsionum omnium Numetorum
a bidivellibili primo 2, usque ad datum f; Nempe datus f.
medictase
i prot Ehil ab f in proxime majorem  dimidio auferatur maximus integer contentu n du pune
roducte
psendodimidius proxinae majoris ipso f, residui dimidium erit, sea L, Sit H - mix. intes n r1) erit
in dimidio numero se
utrina inclusive: Hae slu octu  Pseudodimidium voco integrum maximum qui prodit
numctum aliquem inteorum dividendo per 2. et similiter Psendo frientem, si divisio fiat per 3
Mo letecte atentit  seu in i (h+ 1) contentus
quot sint Tridivulsiones, sumatur ejus, unitat psudotit
cest
nempe teg max integer in (h+ 1) qui vocetur f, et quaeratur
modo proxime summa omnium Bidivulsionum omnium numerorum
a primo bidivellibili usque ad finclusive, ea vocetur S.
A numero h detrahatur summa psendodimidii in hei et pse dotrientis in 
ex psendo dimidio in h+ 1, et psendotriente in h+2, residuum vocetur Q. = h  ntou in Z (ha ) -iteus in L, (12)
et pse dodimidius ipsuus set vocetur C
jam quia dividendo h per 6, quia  residums est vel
si Residuns estito vel 1 vel 2 vel 3 vel 4 vel 5
n  qui esactiae sit 0 vet 0 vel 0 vel.  vel ar vel 1
Et psndodimidius ipsius f+1, una cum d una cum β3 faciat R =  utcque inh ( (F1I+ B
Aio  summam Tridivulsionum Numeri h fore
dinid
4  S +LR Q  posito S = 4 , S. u - incy n (541) f= integ  (h1)
Comprobetur in exemplis
Si h erit 3
8
Q = h = integ. i (h +1) = integ. = (h+ 2)
C
16 2 et
R = intes. 4 (5+
= 0 vel 0 vel 0 vela vel at vela
6 0 et 1 vel 2 velue vela in
Hanc autem Methodum ex  praecedenti plagula derivare
e non facile est. Et  quidem est habsS habetur ejus pag. 3 signo N
quae est summa bidivulsionum totaliter utilium. Rursus sub finem
plagulae praecedentis dictum est ex sum quoad summandos multitudines
bidivulsionum partialiter utilium, es per earum summam fore
esse fieri si  dimidium ejus quod fit si samm namerus simmandarum
Multitudo  summandorum, quam voca rmus e multiplicetur perpri
summam primi et ultimi, quae est R. Et quidem de Qjam ex illicdictis
constat restat tantum investiganda  quantitas R. quocm
quae est ( intu. in fr (fr 1) + β seu inta n L (1X nbus in iliri)) + β.
posito β = = 2 int. in L (h+ D) + int. in L (h - intrin  (hr2)) _ + 2. infa in f(h +2)
reperi autem posito h = 6f vel 6f+1, vel 6f+2, vel 6f13, vel 0f14, vel 65+5, qui
unt omescasis estneque enim plures casus sunt possibiles) fare B ea
semper eoanescere f in valore ipsius B, cunque casu jno fore 6, 2do 0, ytio 0,
quarto ut, quiato F 1, Sexto -1.
Tridivulsiones
b