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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 26
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si
inter logarithmum verum fractionis, et logarithmum
Quotiens est integer proxime minor fractione. Residuus et
integer proxime minor fractione in divisorem ductus sit et a dividendo
et productum a dividendo subtractum Axioma inter unitate majores
quorum numerorum major est si negarithmus unius numer logarithmo
alterius major est, etiam numerus ille hoc major est; et contra.
Hinc quotientis Logarithmus est Logarithmus Tabularis proxime minor
n integoru
in Tabula xumerorum at
Legaribhuno fractionis,sit enim alius major ipso, et minor Logaritimo
a
fractionis, etiam numerus ejus erit major lagurithmo quotients et
(perarioma
minor fractione, ergo dabitur numerus absolutus sed integer major
quotient et minor fractione, ergo propior fructioni quam est quotiens
contra definitionem (per definitionem numeri proprior propior fra
ctioni quam est quotiens, contra definitionem ovotientis. Ergo
pvotientis Logalithmus est Logarithmus Tabularis proxime
minor Logarithmo fractionis, Q. E. D.
fractionem
differentiam, inter seganitimum Quotient et Lanitemum
Lodartimum
sactionis vocemus E. et differentiam inter fortiente logarthmum
quotientes et fractionis vocemus 
f
differe differenbia inter cvotientem et fractionem est fractio
ex residuo per divisorem diviso, seu 4aequ. 4+ =. faequ. D
set
Ergo
p
qu
Y
() H =
faequ. 4 +
F aequ. 9+
utile erit hoc accommodare
(9)+
qV + 1
e
 (4) +  et rn
(9 +D
seu
(9) + (2) SB(9) +
(5)
dones tan
donec fiat _ TYD aequ0.
et demonstrari poteris reducendo ompes has
D tnctiones ab commanem denomipatolem
fo ultitiam q. mefiri f.
haer obiter. ubi nota si Y nunquam fiat 0. quod
sit in incommensurabilibus fore D et d incommensurabiles
seu F quantitatem irrationalem. Ubi consideratu dignissi
um videtur quaenam oriantur irrationales, prout ipsis
g. (4). (9). (qV) certas progressiones assignamus necesse
tamen observari, ut q semper sit major quam omnes 
6
 sequensa.
seu ita invenpi posse communem seu (1) aequ. d - n (∞ D - n 15 +
divisorem ipsis D et d.
el
et porro progrdiendo fiet. Seu (Y) oqu d= n 1 
d
integer
Fdabitur minor
fractione
cognrichmos