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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 25v, page id 00068197:0050
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po aequ. 7. compendro scrilatur W11DD + 144 4Q + 1+ D Q + 112D8 + 113DC) + 12380 2 0
2u DD + 244 4 8 f etc
Collamus utrobique 8Q, et videamus an simul tolli possiti sC, ita enim residuum poterit dividi per D et habebitur valor ipsum
q integer simplex. Ex 9 fint - 8 = 111DD + 114 D_ + etc.: 144 = (ex 10) = +211∞) + 21434 + etc. ,: 244
et faciendo 1230244 = (12) = 223. 144, evanescet C in reducta eq. 1, et fiet divisione institula per D
- 144211. = 144. 214.  144. 212 8 = 44213
prodit f (ff + (b- at). (- c) h (99 + 1b - 0)h), = 99 (39H (b - 9) h). (b -a) h (ff + b - a 2), seu fFCb -c) = 9g(b - a)
22g hx- f = he 144
(5 Compendio b a sit = e bac sit = K gg f +(b - a) A =  sund gg Ib C) H = trq fit 144 +h et 24+ ft q
114 = 2hemm 214 = -2hkmn 123 = fstip 22 = gglq
11I = 211 = mmun +13= -ffum 112 = -5fnn
tg nm gnn
gg = f(H: e) 99 + b- c) h = HfF K (s Fhe): C et Z = K hf: C. Ergo 244 = hhKKS: e
223ifKktip: ee
23 = - ffmmK: C
212 = -ffnnK: C
Kk- eC = (b6) + cc - 2bc ( bb) = aa + 2ba = breviter) t(5 h)
mmnn 1 V: C) D Ac = 2lmn tetikK F 8
+Tlikmn litie
seu mranntz D + 2h mHKe (C- f) 
Hun trhk(K: e) 
tinhurp..
1C 244- 144 = hh (Kk - eC): C
-frum tihk flk: C)
+tctipe Aun)  + HmmK (C - K) O
et quia s) divisum per ek dat = (C + K) quod compendis do cabumus
=pd + H Yspe C
 2tenin F
Ammk ltiq
etk = b- a + b- c2 2b- a -c = 5
+snC.. qui vator substituendis est in aquatione 9 explicata,
mmun DD + hhop q 2 - 2 hema D Z - fnn D  - ffmm DC + Htip 40 (0
set ptke A DD (= AKKC fFmmu +) DQ (-aL K eff mnty DO + 4h kK exumun ZC
+smeddDD =2mndkff
+KKF DG
tfm 0
- 2Fmnnsfdk _.. + 2VKK fEmmnn.. 18,
TeKoni DD (F AKK esfmmi). (+ AkK effmun) u
si jam in aju e8 liceret  esea ut canes
co stegentio 18 per compendium exet scibum  
cam autem in rem fiet 2 tif Kffmmun (FF + 2he) = 0 seu f + che X 0 seuf = 2h (a- b)
Ergo ex aequ 15. 4g. 19 pe 14 per iy fiet 7h (a - l) (b C)  9gtb. a) seu 9g  h (C - b)
qui consensu valsuum f et g, spem facit ob concinnitatem
lmteemmim
AKKemnnn
auemmun
EKKemmun
H + 2he = hp+ pC
Non autum licuiset in hoc calculo facene idie Y =0 in aeq. 17 vel. tollere seunt BR et D C intaeqius vat Z ita eantu nan
in q licuisset ope  et 10 simul, vel ope 7 ut 8 simul tollere et8 et O. sed vaus fuisse
jam instituimus paus prima, et reperimus ducere cio non permissa, aut certe nomfaciti pirmit ergo peculi calculor quem
aequatio 1B compendio ila exprimatur i _ L 20.
2000C +020DD +(C02 EQ HLIDOD + 1,OIDG HO1∞
t sit 000D = 210( + 201G + 200h. Eoque vadore substitut
prodibit aequatio canonica pro datis. 4. 1200 1D29. 1002 + Vd tet H2110. 2101. 2011 = _ 2110.1002 + 2101. 1020 + 2011.120
fMnn 2101 = 2KKfmnRLN, ubi hN - f+ :tie
et 2011 = -2rdkffmmn quos valores substituendo in aequatione canonica, fiet
YK fErCE hh= ArrSSKKfLMENEKKfEMurhH = ArrSdHKF m ntt Hk fEnt, ama ktismu rtikfhi, atif nuretlinmntlia
dividatur hac aequatio per rrt F 2m BnS. prodit f hhA + 2rhICDS 5 = Y5554 + T8SF4 + AhtNNCM, et pro h substituendo valorem, fit
fahit  +2Y8 f F 4rsshess = (2r58f 4 (atit o ft stst + atihs hhee + ahtia heff, et dividendo per 4he, fit
r6Sff = s eA F hhs f. Est autem thx = 4KHC + rds - +etd ego (rss  = 4Ht  + rodhe - aCKShe. + 2t t e rdd p. t et S
quae aequatio dividi potest per e. in reliquo pro tr subsituatur valor A+he, fiat 0 = 4hHHt _SSt5 + tr ode - 4hR KS + AKKIF - 4KSf
de 2K - d = 2b- 2C - C: k = 2b - 2C - b + a - b+ C = a -c. 4HK +d AHS Haec aequatio dividi potest per 4Fk + 58 - 4kd
 seu per qu (a-c), et fit ff +he = 0. quod sper paginam primam) non licet
 sufficere, ut t, 2, +  t C, D, e sint intigria simplices, sed , 
) et F modo ss sic explicatur, ut utruque in iis coefficientes psirs d
illud adhuc considerandum superest,
sed sufficere ut Q, et qui ab eo pendent 7 s sint rationales
coincidunt nemp ud sit quia gnes erit gg ss, et hil quia jaca hebet esse hHt he = tit
si sit  = f et n -0 fieri potest ut coincidant
si esset b f( + he = 0, fieiet munus- 2hemnt +homn6 + henne
ggt hki -o fieiet mmn) - 2hk mu + htinmo + hk nn 8 X
et tollendo VB sit  E t h (C- K),  - nn Z = nn O + n C = 0 sed ita sit mmnns
+ 11344 D8  
13. 244.
4 172
Generalissima ratio sine omni suppositione soret, ut terenus , ft  per aeq. 9 et 10. fuit 4= 22F 
(144. 214 = 114. 244) 5
Videamus an liceat s+ h(b. a) QG  (Hi +b- a) h) t Hm BD + fpht ED aequade quadrato, ita enim ceque s fiet extrahita
icu licet sit 178 + m O4 + a ODABCFD. siat Z- YC +5Q + LS, sist lde+ lsier LitB +. 1150gt 2LHtOGlst ED +mOEm CD1YE fiat m-Alrs n=- Elet. 
et o= - 4 l5t. et res succedit, hine autem quaerendae Y, S, t, quae hateri possint fit ns = - m: gl rE = - n: 4, st = - p: AC irgu t - n - n: aEr = p: _ 4(5
Erus n5 =rp, seu S = rp. H. sed runus f= -m: AY, fiet rep aL al rrp = nm. seu ry= -va ma: 41p Et eodem modo B -- Ip: alm et HL - - np. 4m
juniiam vioeorem nonsumdere, seu ad CC; F, inio jurendeo rem non
a qu(C + +4) a fri sic disse tutam inter duo quadrata, nn frpomia, in quibus quadeato nominum
posse contnere tres  biniones sed tantum duas ita hic opyseset tollere coe, quid esset recidenem priora. Sed si ope duar aegu.) et 8 vola
et fiit mndt bib. a) (70+sC _tD) = il. r.
procedere seu non posse
Ed ita duae prodeunt aequatione in quibus C) C D inteo sela servant
Sit _ 140bI9 L 2P L 1301 3ZF 1X2075V + 1202 y) 2 + 1211y v Et 1121 9 1Z
aliquet ex dinionibus, lv.g. 1Q notent talis haber aequalio, quae sic fiat extraribiis
+112yVIZ + 1022 vrZ Z. 20 fiat v = 17 FukB,: ~ 2= 2oy + 2h, : on hablnu 9t, 93, 37, 5,3) attoque 414. quique, sed literassoturo 4
dais geneitatem inde cam determinatur atius quod non est licilum