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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 102r, page id 00068124:0203
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absolutum non successit
e a +X: A -. gyiaa quaritur Sydx. fiei a FX= y a + aa X  = XEyy
en v X= a aa:, ry-aa igitur gy- aa debet aequari quadrato- quadrato
Sit y= 10 + 110 + 12VV,:, 20 + 21V + 22VV. et f= O: D siet gu -aa = OO - aa DD, : 9D
aequetur OD- a4. DD, quadrato quad lalo, ita enim postea etiam ayu-aa facile aequabitur
quaduloqu glo quadrato tantum enim superert, ut D aquetur  quadrato, quod facile
P = 30 + 31V+ VP
30 = 1. 10. 10 + 2. 10. 11V + 2. 1012YV
+1. 11. 1.. + 2. 11. 12B3 + 1. 12, 12V
a qu. 2. 2 1. t2. 21. 2 F 1. 2. 2.
aa W= a, 1. 20. 20 + 2. 20. 2 v + 2. 20 22 
yta =menn yea = nnp
y = m nn -a = nnp  a. se fel
nn- 20 m- p
n + pp = quado et nm. pp = quadr
4 10) 36 + 4. 30. 31V + 6303 i vV +4. 30. 31V + 31 p
pro v poratur ex v et Y fit 4.31: 30 = 10. 11 + 20. 21,, 10. 10 + 20. 30 Ex v et B fit 2. 30: 31 = 11. 12 + 21. 22, :, 12. n + 22 22
unde ex 11 et 2 fit 4. 10. 10+20. 20, 12. 12 + 22. 22 = 11. 12 + 21. 22, 10. 11+ 20. 2)
tex v v fit 383 - 10. 10 + 20 20, 1 12 +Z  quod et prodit multiplicando V e in v, et v in P
B (13
30. 314 = Ex v in V fit A30 3 = 10. 11 + 20. 21, 11. 12 + 2121, : 4 Et rursus
Et ex 14 et 15 fit
per V fit 30t 31 = (2) ( n.n + 21 21 + 10. 12 +, 20. 22 : 36
(2) 1. 1 + 21. 21 + 2. 1012 + 2. 20. 22
N (16)
Ces 31.31:, 30. 30 = 11. 12. + 21.2,:, 10. 11 + 20. 21 rividtdo v ser r
H), 11. 12 +21. 22, :, 10. 11 + 20. 21 per 17
en e
312. 30 12. 12 + 2222, :, 10.10+ 20. 205
Unde ex 19 per 13 fit seu 12. 12 +22. 22, (2 ) 10. 11 +20. 21 = 10. 10 +20. 20, (2l11. 12+21. 2
B (20
enexcteus  10. 10 + 20. 20, 12. 12. +22 22, (2(10. M2O. 2) =410. 10 + 20 287 (2 ( 11 12 + 21. 22
unde per 13 fil 11. 12 + 21. 22, 10. 11+20. 21 10. 11+ 20.2) = 4. 10. 10+ 20. 20, (. 1. 12 + 1. 22
30 1010 + 102 51 = n. 12+ 22. 22
seu R (3) 1041 + 20. 21 = 4. 1. 12. +21. 22, 10. 10. + 20. 10y
35= 10r0+ 2O1OFB). ex net 15 fit Ex n est 30 = A: 2. 30. 31 c (per 13)  C:, 6. 3131 fit 3. 31. A = 3dC
 2. 38. 3  A +6. 3030. 31. 31 = 
2. 30. 313=B
1 3A
D
seu 31:30=
Ex 12 est 3l = B:, 2. 30. 31 = C: 6, 30. 30 seu 3. 30B = 31C seu 30: 3=  C:, 3B
Ex 11 et 15 fit 2. 31: 30A: D Ex R et 16 fil 2. 30. 31 = B.E 
23 et 2+ fit 4 = BA: DE seu 4DE= AB quod etiontiiberi potera
multi plicanda 1 per 12, et 15 per 16 Ex 20 et 23 fa CD = 6AA, et ex 21, 2  CE= obB
BE
hine sit CC = GAD
sufficiunt 25, 26, 27 nam hinc sequitur 2
Cc = 36DE  AB = +DE) His tribus aequationibus adde aeq. 13.
et ex et 11 et 12, 31. 310, 30. 31 = A: B
Ex 13 et 28 habentur 30 et 31. Et ex aeq. 25, 26,27 quaerenda sunt
10, 11, 12, 20, 21 22
solutio horum in Epistatis mers ad du. Baronem odenhus
Kebretupetac
exa rua
tantu ejus ope, ineniendo quis tunc
vulor y, habeatur y+b, et ytc
qorm  cois divisor, rclinquens
itas quotientes dabit P, ipsi
quolientes dabunt m, et n
ad eoque et habebitur m:n seu li
seo modus efficiendi, utrabio sit
quacratus, adeoque et ut  se
intota sit quadratus
diseoraso, quod fitri pe
ex _bW. Wib- aa
9+b- n t- man: aa
fiet fyg. bb= mn et
m= y= m- b = mun + aal
et  mui A cando per 3
sit nftco+ infal- a, aa
fit Maa-aab =mnntaob
seu m- 2aab
tiat A~ mfK . b9
N infal a
aabn
non
gab utt e mna
yy - bb = mm: pB
y = ma ba
ga= sk I
titns aa cug inh u influca, 
hh. aa = nsl3 1
D th anfia + 2C+ a
adfancot aal
hih - nesll- 25
maeum
ergopoet aa
Efla+a
Instat Ergo mu
Restat austat 2gah = 2fsiK + faK
Staa: na e
rahe 2Fb4 at. son t=
fit m. 1bppn
Bsbraa, un
mmetrame
sed h.   autento 2htt aem 2s imeraea ser.
app-ann
y-bb
aequand
seu 28= - 61
qoquaad
i   5
appr an
ap- ad
-2uslm rin
anumm
e
32= 1. 7to
16 422-
uet
Aaua
sit a
ga + 2 ahb
99c0co +2900 ak + antiti- a
nan sit 10 = + si, fia
ad lt inth  ragir in fKk = in flg - 29 3= mna + bp
sit v- CB KV+ B
sfkKCOCo +ZB alteco n haat
naeram portesale
102. 103