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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 173r, page id 00068199:0345
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4 = 11. 2
1 2 12 = 1. 1.t. 3
Sit aequatio generalis
inter y et  L
c
l
finita vel infinita relationem exprimens
a ab aaab aaba abiaa 4ba
O= (0, 9 +025 4 03y ete) Z + (-10 + 11y +1y etc) Z + (204 2y ty  Z + (30r Hy Brgy CH) 
et sit Z = 101y + 102 yy + 103y + 104y2+ 105y etc. ponatur 10=1. flet
101 = 01
102 = 02 + 11. 101 +20, 101. 103 = 03+11. 102 +. 12. 101. +2. 20. 101. 102 + 2]. 1012+ 30 5013
04 = 04 + H. 103 + 12. 102 + 13. 101 +, 20. 101. 103 + 2B. 1022, f21(101. 102 + ax + 22. 101. 1014 3. 30. 101. 102
+ d 1027F+ 31. 1013 2 +40 10rt,   105 = 05+ 11. 104+ 12. 103+13. 102+14. 101 F 2, 20.101. 104 +
2. 20. 102,103 + 2120 10 +2. 21101. 103 + X. 21. 1 102. 102+2, 22. 101. 102. + 33a, ( 23. 101. 101 + 33no
+3. 30 101, 102 + 3.10 3. 30. 101. 103 + 35 10r o3 ∞3. 31. 1012. 102 + ( 32 ter 1 101 + 40. 101. 102
10b = osque +41. 101+ 50. 101
+ 20.103. 103, 106 = 06 4 11. 105 + 12. 102 + 13. 103+14. 102. +13. 101
a
F3. 101. 102 + 2. 29. 1324. 1012 +639, 105. 102. 103 + 30 102 +35, 31. 101102 + Por 103 331. 101. 103
F7. 32. 101. 102 + 33. 101 4540. 101. 102+448. 101. 103, + 4,41. 1013. 1024. 47, (0l 10 1017 1
+50.51012102 + 60 1016.
RRegulagereralis haec est
scribantur ordine literae qua numeri effi. aequalionis dutae , nci, et
ex qui in quovis membro ccurrunt non nisi semel, cum his conjungantur formae
ex literis equationis quaesitae ea lege ut notae dextrae omnium liteparum simul
sumtae equenturnum componant numerum aequalem notae dextrae ertis numt
cujus valor quanitur. forma autem ex  numeris posterioribus tot debet esse ingredi
ertium, quoc  sunt unitates in nota degtra simistra p numeni posterioris praefixi
enique numeri veri coefficientes sunt pameri transpositionum formae)
Exempli causa quaeritur valor 104 scribo  cum nota pref numerus minor
seu eat ex deuinor seu exe datu aequatione sinistram notam habens o, per
regulam nollam ascipttum habe at nundium majrem seu ex quae sita  aquaton
notae autem dexhae facere, debeant 4, non scribi potest nisi +og. sequantu
notae numeri minores notam smistram habentes  mempe 11, 12, etc. Et it indicat
ascribendum numerum unum majorem (ob notam in 1t sinistiam 1) eumque debere facere
is ergo a 3 nota dextra, isem eit cam 1 nota dextra in I1 componat 4 ergo non
pligerit quam 103, eti fit + 1. 103. Indescribo 12, cut pari jure ascubetur 102,
et fiel + 12. 102  item + 13, 101. jam pergo ad 20, ob 2. notam sinistram deberst
ascribi fonna duorum dimensionum, et ob notam sinistram o, ebent hujusforme notae dextiae
inadnere 4, et filt 20. 103. 183. cui praefigemus numerum verum 2, quia 101. 103
duas habet positiones 101. 103 et 103. 101, et fiet tandem + 2. 20. 101. 103. similiter
siel + 20. 102. 102 et e dende pergetur ad 21. Ergo forma secunda dimensionis
ex numens majoribus ascrbenda est ob 2 in 21; sed cujus notae dextiae componant 3 quia
Cin 21) +3 facil 4 numerum nolam dexlla in 104 cujus valor quaeritur Ergo
fiet 2. 21. 1018 102 nam 2 praefigitur b rationem dictam, 22 dabit 101. 101
seu fiet +22. 101. 101 30 dabitequirit formam 3 dimensionum, abi tres notae
dextrae conflant 4, et fit 1012. 102 ubi 1+ 1+ 2. faciunt 4 et ft praefigitur antem 3
quia (, 101. 102 tribus modis variari pt, adeoque stabil +3. 30. 10F. 102. et
31 requiret formula frium dimensionum uboe posit 3, quia e3=4 E 1 (in 31) +3 com
point 4, Ergo requiritur 101 adeoque fi T31. 10. denique 40 requi 32 patet scubi
omu et cujus notae faciant
4 Ergo non potest esse nisi  40. 104. sed hoc ultimu dinittitur, quia 104
ponamus
ni in aequatione data abessent omne termini, ubi y ducitur in e soliqus adeo
non dest ingredi in ipsius 104 vatorem 
addessent numeri minores 10, 20, 30, 40 esq cobi g0 posuimus = 1.
9
Ex literis aute
50101 104 = 2. 20.101103+
a
et ex y solis seu o1, o2, o3, etc extet soluin. 03 0
102 = 20. 10(V
fiet 101 = 01.
103 =20.  2. 20. 101.155
20. 1 102. 102 + 3. 3. 10(2. 102
+3. 30 10p, 103. + 4140 10r102
105 = 2. 10. 101. 104 + 2. 20. 102. 103 +3.30, 101. 102173
Et ita porro.