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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 64v, page id 00068255:0128
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IImo) e = O1
xtum = Oe xinn -∞D
fit xelle xrtam, xrim =  g2
ui aequando rrimum valorem cummedio sis F
2do) Hinc X = O =l = 0 tum = D- an q Hinc  C, D. Gset m et similiter
aquando ultimum valorem cum medio fit Z, D- O) pinmm. Unde sequitur tertia aequando primum
et  extremum valores inter se, sed sufficit nempe CD. Il=2D-n.  sufficit ergo duas
priores aequationes praestapi. ita ut C et  et D, prpractentur eadem modo et l atque n
itidem eodem modo; sed D et m, mediae quantitates a reliquis distiagventur
O = 12 Lvy + 113 IrZ + 123 fyZ + 100 p
P= 212 1yy +213Y07 +223Yy2 + 2009
F = 3I Woy + 313 YvZ + 323 VyZ + 300
9= 413. 523Z Nvy + Am2. sez y l02
Et eodem modo labebita
unm cujusque numeri pone
veluti
sessit F1Z.  id desopeetoggu2
123. S12. 323. 7e2 caeferis f125, 25 sus
2+ 33n = 1 
= l12 135
F112. SB = WX3(A1I. Sez = 51223 et ita porto SuE siiis. at . m. jujis a seinvilem agg 3 et  fieta Auferatur etiam aequ. 1. ab aq. 3 fit V13 sua ( m9 (71 Y51)S3 +(BHCE 11)313. 712
+ 12. S = 1ig1) +  = Co2sB et ita porro ctatt
1312. q = dutos = 3uem - 31 2s s +s 1r. 11 - 3 u1
L aequales fit . 100. 512p + 12 500t + lr13 Z= 0 100. 513p + 113 500F. + 11 23 y = 0 100. 523p. +. 123, 500F + l 213 V = 0
compendio scribamus uA P F 12L +137 =0 2ip + snt + 23V =0 et sip + 3it + 33y =0
Significant Sir I12 12313 S3
Ex duabus prioribus aequationibus inveniamus valores ipsarum p et t
FI1. 21 p) + 12. 21F + 1. 2Z =0 fit .t=
Es pari jure in notis dextris numerorum permutando L et 2 fif p = + 12. 23 Y,:
omissis intermi 100 et F
soo quia semperre
ouo sutlt intelligi
12. 23V: +12. 21
quibus valoribus substitutis in aequatione tertia 31p + 32t + 33y 20 fis -12. 23. 31V 4. 11. 23 32V + 12. 21 g9 20
413. 22.31Z = 13. 21. 322
em ipsorum 11, 12, etc. substituendo valores in aequationibus 1, 2, 3 hujus articuli
velu B: Suc3. Unde permutandu 1 et 5 sit 5e0F =  S12. 11h12 
13. 123137 nam ta t tr13, permn
nam l2g13 vel lau permutatis, 1 et S manent, sed S1223 vel similis) permutatis 1 et 5 mutatur in = 51223
+ si2. linvi:, Si quibus vatoribus substtutis
A3 523 11313 Z
=112. 513..... - 123- 512
+ 523121. y0 vel y = Sir D +515131Z, : Si2 231
(2) +712. 3129: .712 etce
et 72133V +713233Z 472313y= quam equationem conjungendo cum aeq. 6 articuli
et pcum Y, et t cum W, fit Bo Y= +343. 319
praecedentis  ut tollatur Y, fiet + Sirrl. 723123 D + 513221. 723123Z (+ Saur I. 70u3V
=GagEl. 71273 V - 52312(. 7132337 - 523121. 7131 231)
Unde quidem haberi posset v: Z, sed quia hoc non licet, neque enim eorum ratio debet esse data, alio qui
1VZ non foret irrationalis in indeterminatis, contra intentionem. ideo hanc aequationem oportet
(6to) 523,3t. 712293 - 51222l. 72413
1009- 100 P seu
pro quibus substituendo valores, ex aequationibus 4 et S articuli 6, et aeque 1. et 2 articulia 7, prodibit aequatio (M. 51, S1223. W SEC. SIB231 = u2 H 2h. 5+32(+13. 
adtem haber o deprassio. Ham mulliplicetur a q. 7 per aiti c. praced. per aiqu 4 aniculi Eum
8. 512. l1213. I122Z V = 523, lgg3. 71223 Z = 312. 3121B. Suues V. + 31. 32313. Si23 Z =)- 112. 1.213 fin2, Vel13. 12sis. In23Z + 3ahug siu, . 79tus. Sicese) et edem modys 123. 523. 51227. (2 131 9
ppermutando 12 et 23, fiet 122+ 522 um si i. ca. sed 52
32313, 51223. seu 123. 32313. 71223 + 523,12313.71223 -323.32313. 5123- 723. 32313. 51223
autem habena  prisstio. tam mullislictur aq.  pr ic. pacud. per aequaata
fid Erres He(7mo) Sc2I(si: 72233Ct1)
quam aequationem rursus divellendo in duas, ut destruantur V et Z ne determinetur v: Z, fiet ideo ut tollatur Y
 112. 1121Z. 71223 +512- 11213. 7.223 = 312. 31213. 51223 -712. 31213. 51223 60 seu 112 +512 ) 3icg. S1213
12
et) ut patet ex artic 3. seu 2009= 100 p + 700 W, ut patet ex artic. 6. itaque fit 500t + 300r= 100 p + 700W.
jam considerandum 500C esse 2009-300Y. seu
et et similiter ut tollatur
ope harum aequationum
pari jure destruendo irrationales in D, -O,  ex permutando initenles latd; cum 3167.
seu Si Sin3l. D + 51323I. Z
fietg (610)51213l, Jng.
in aq3 hujs articuli fis denique ex aeq. 3. explicatis 11, 12, ete fit +r23. 513. 12313Z + 11Z S12 ln13V 4. 112. 52(y = 9
Itaque tandem, = 4 123. 12313 2
F 11. 813 = S12131
6T jam in aequ’artii  destruamus irrationales ponendo coefficientes eorum nihilo
aant  in halor ipsis d, P.
= 11. 21 p) = 11. 22. + - 11. 23V
Bo  = a + . 123 Z
divellere in duas
ergo fit 123 +523
(5) in hoc aequatione primum destruamus omnes crrationales, faciendo coefficientes learum niilo aequeles e. peruntando 100p cum 300r
et compendii causa faciamqus
+112. 523,312.723 = 171223
+112. 523. 312. 723 = 711223
saudu s
51323. l = - 52313)
B - 12t  + 3
= Hll bitur ∞, D- 0, tantum pra 1 vet 5) et compendiose scribe