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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 42v, page id 00068000:0084
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supere
tu
sit (4) 2+ siet sf + 99 +2B) (2 (3.) F
Aalia Methodus ex natura numervum, solvatur plene
pars problematis
Cas invenre tres numeros ata ut ductum quorum libet sit summa
quadiatus, ita, ut Tabula ecrum condit condi possit
quae ab
solvatur deinde et plene _ altera pars problematis invenire
ries numeros, ita ut differentia duorum quorumlibet sit quadratus, ita ut etiam
Tibula condi possit
Hae rinae Tabulae irunt quasi duo loca
quoum in Geometria, quorum intersectio dabit quaesitum. E
inverta autem loge seu constructione Tabulae, apparebit, quando
concurrere possint
ax L ay = I ax + az - mn
ay +az= nn,
et fiet
ax = 1L - ay = inm = aZ et ay = l - mm taZ = nn - az, et fiet H- mn -nn -
Mm + nn - U1 = 2 a Z
U + nn -mm = 2ay
tmtum - un = 2ax
Timsus AX ay = pp ax - a Z= 79
2a
demm un= itaque satis faciunt tres quivis
quadrati, tales, ut duo quivis sint tertio
majores seu quadrata laterumcursos trinihiti
ay- az = rr, fint ax = ppt ay - 49AaZ 99 + aZ
jus a fit qu + az a pp = rrtaz fiet 9q = ep +YY
Ergo mane est fit non possunt eq hoc tres inveniri literae X, yiZ; sed assumta _ y pro artitnio et posits
imm son pp Rrnnum si quenn
cpptay et az = agApp- 49, prodibunt aequationes duae  em na ppL su him i
x =  +aZ sit az = ay rpp - 4q, sed rursus = _ ay- VV fit Pp + rY = 49
ax = eV ay epp et 2aZ = 2ay - XY; et 2 2ay = U +nn - nm
Utmm- m
t  op se U= untgue req
de Utnn- mn +ipp = Utmm- nn
seu a pp + nn =mm
res ergo ad has tres equationos reducta est
 PP + N = 99
mm+rr = U
Utnn-mm 2rr = mm +nn - U
seu u mm  mmtrr = U
a pp- gq i + ubi U et un occurrunt tantum semel
antpe
sp = 19- rr
Pem An Ipp = um pp +rr = 99
pp + nn = mm
sit m s s G iffgu sit a = = ff f0g et am = 259 fit al = f + 99
tursus) ap =  + dd q ee an = 2de am = d dd + ee = 2fg
stat d+-2ddee + f++ - 2ff99 = aagq, et pro g ponatur ddtee,. 2s
siet s 4 erddee +f p quod si praeterea Ydd ee aepur s ff- gg +f +gg possimus
t aequare ipsi 2de, habetetur aq =  dd te = am, sed non potest aquni
conicet, aqam si facimus +s 4 gg  59 +dd (ee - 2fg, h fieitaque = ffrgus, sed
haec rursus non licent d+  = 4ssu Eddee fit 4ffgg BddDC  f4+ g- 2ffg9 = A 194
sit f + gt + 21f99 = aaqqueet 4ddee quosi effet 2de (1 f+ gg et ag =
id siesset 2de = (+) Ss () gg et aq = 2f9, satisfieret etiam huic aequationi
q tantum opus est, ut simuls+ 2de = (+) B (4) 99 et dd + ee = 25g
fit dd+ ee t2de = + ff + 99 + 2f9 e = (+) sf (+) g9, : 2d, quo valore
substituto in altera aequatione fit dd + s4+ gt- 2559) = 2fg, seu fiet
4
+d
4
+g - 2558 = gddfg (A)B ()gg = dd Y 2d sist- Dd) solvasum
dglaraliter aff. dd= quadralo 
(H) 99 =
e hh sit  du Fd = fβ h= f9V, fiet 2ff. s + 2B+ BBH
( +) 2(fβ) (5_)) seu
(+) S (4)99 = 2ffa2(2) ( + 2
BB+VV seu βBB - 2β) = ff +  aq jou
sa
=que Be+ YY) Y au AN sin tou (8P. V). qull6+y)= al. et
a
fb.
et
lristererorisro
et f = β(+) P: 2(3+))
spus 4 qu (3(177