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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 133r, page id 00068194:0265
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earumque summis
Quoniam differentis uti possumus ad in-
finita mensuranda, ata ideo hujus
loci est, nonnihit de differenties ratiocinari.
Nimirum.
si fiant duo Rectangula alterum factum
ex ductu differentiae in nu Terminum
primum, alterum factum ex ductu
differentiae in Terminum secundum;
summa rectangulorum aequatur summa
Termi Rectangulo ex summa terminorum
in differentiam ducta, Et hoc quidem
per se patet. Sed pergamus:
Differentia inter eadem rectangula,
aequatur quadrato differentiae inter Terminos.
Hoc ita demonstratur.
a. a +b =) abtaa = ab. =aa.
Differentia inter eadem rectangu eorun-
dem rectangulorum summam, et eorundem
rectangulorum differentiam aequatur
rectangulo facto ex
Termino primo et differentia duplicata,
n ab + aa, + ab, = aa = ab + ab. = a 2b
Et contra si quadrato differentiae addas
Rectangulum fact um ex du plo differentiae
e termino primo, habebis summam
duorum rectangulorum
Data summa rectangulorum inveniam
2 a 2b + aa. terminoque primo, inve
nire differentiam et terminum alterum
vel nve dato quoli uno ex his tribus dato
invenire tertium, hoc nescio. an sit solubile
videamus. Secetur scilicet ista summa
rectangulorum  in ducaspartes, quarum
data
altera sit una sit quadratum termini
qui cum dato bis muetiplicatus faciat
alteram. Esto ergo summa data
C) quae ita secari jubetur, secta puletur
in partes duas, d. et c - d ea quibus
d.) ponatur, esse terminus pars una quae est quadratum
ergo ejus Rq d. d duplicata multiplicata per 
terminum datum b. bis faciet 2b RGd = C d
seu 2b = C) = d dseu 2b = c L.d ea, iba d F 
d
Nota, si partemrassumes summae rectangulorum
differ
seu d=
quadrati quantibet. Dividantu omnia per deifiet 1 = C-
atio ratio ad ipsam summam rectaneulorum
pecatan pa paes radum t
itep=
dd
(62 +82 =6+82
2 = 22
Aterunus datus b.