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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 131v, page id 00068200:0264
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 130r); this page is its left half.
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sed quia hic j ob nimiam compositionem deprimere difficcilefuerit ideo satur
erit alteram quoque deprimendi artem adhibere, quae saepe commodior ess per commines
mensuras numerorum.
Uet sunto tres numeri al. al- x
al -- 2
diftrantia ergo primi et secundi, item secundi et tertiu quadrati sunt. Piai et tarti sed ut
primi et tertis differentiae sint, quadrati, erit aequatio nl  X +Z   fac 
X + Z e s. pone  X  FB, et ZA C, fiat:  C 4 2eZ + Z, fier
X Z N X C  A F Summa primi et secundi al - X  +X d. Ergo  ar d 2x.
Sumtua
secundi et terti dZ . al - 2X - Z, sive (4). er
poncno 3 c (d) (+) 8 2dg + g. ponendo tam C BE A
st s. - 1, 29b ha, 9. = eAH 2d + g.
Ac. 15
fiet aequatio
summa primi et terrii erit;
d () (4 239 +9 + S S. h ri t ve (4)) 2dm + m
Ergo d 1 9 + f3 t = m
C+D m (F) 29
At idem d B
 E. -1
C1 X (+) 3
1g - g
(+) 2pC 2  in
Dividamus  + f qu
3.26. C+
41 Sd
afCF
Ss
(418
Noc divisionis artificium
etiam utile ad omnia
(+D in integris solvenda
 81 (
=m F Eip ntil suprest in
m g+ sh divisione
 et
.
ng.
do
+6625 d Habentur ergo m. et g. caeteris pro arbitrio sumtis. explicatoque (+) per +. Ergotd per-
62 512 Usus signorum ambignorum, ad efficiendum t evitentur ad ih omnia quantmmlitoet indetur
minata relinquenda; donec exprogressu appareat quae signa eligi satius sit.
quamadmodum ars it in promtu est efficiendi ut omnia solvantur in integrisrationaribus, ilem
integris, ita etiam effici potest, id omnia solvantur in quantitatibus veris; idque semper efficiendo
ut aequationes ferant, rationalitatis intyritatis, affirmationis characterem. Nam si quanitas
lt literae cujusdam valor habetur pure, si aequatio in interis; in tegrorum vator in integris; si
affirmativorum valor in pure affirmativis, tunc, aequationes praeparatae sunt, ut ferant characterem
et tunc, non aliter ipso in locum valores in locum quantitatum substitui possunt, si scilicet
valores sint imbuti charactere desiderato quantitatis. Ita effici potest, ut omnia solvantur in
numeris quadratis; in cubis; in Triangularibus in pyranadalibus; etc. in binariis ternariis;
in irrationalibus: in falsis; in datae cujusdam figurae numeris figuratis: et quod est difficillimum;
in minimis possibilibus; in maximis possibilibus:, in paribus; in imparibus; in numeris primis o in numeris primis
in numeris perfectiso in numeris pro
esto aequatio
: ab X c - df.
ut obiter dicam, omnia solvi in veris sic efficiemus
necesse est df esse Y) ct. Ergo. pro c pone df + gh. seu ab r gh.
Radedumus ad nostium exemplum. Yo f12  h 1  fiet M e 2g. 91 ,6 + 2 +
Erfo m 6+. ubi que
poncrdo, 3 A H _3 Ap 2
sine 62.6, + f2s +
furgri od
337  m sive
sut 64 +75  16 seni MF 503
enserto valore n, in aequatione ultima, tit: 
Si + a +1.
si   o addu m asit
 
I N s
seu  27g
2 F357 16
+ n9  g ng  S4 + 25, 1tet sive fiet
2 ponc jam n 18.
g. mo te ab g et fiet: sexit pl a lx
19  = P.
=1 
es
S 3  
+(+ e17 + ei pg. BB im  p g
Ergo Pd A48.
Ca = 1, eta
Concito i r  g. divisisque omnibus per g, quantum potest, fiet: Ego explicabitu () per-
osn 2 +f
(+)29(+) 2n
Ergo. (9)
inter se.
te oiu
ergo nH
einno
es 
357 0+
Est Ergo me