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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22
# Folio 2r, page id 00068235:0003
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si sit aequatio quaecunque: bb + lb _ aequ m compesita
ex numeris integris rationalibus positis  m. integris rationalibus
erit rationis ipsius incognitae b. ad unitatem quotiens primus h.
posito h esse numerum integum rationalem integrum proxime verum
qui sit sit nondum unitate minor ipso b. seu si ex m.
extrahas radiem affectam seanndum bb + t proxime veram
si sit aequatio: bb + Iba aequ m aa. et
sit b e a. et b aego h a +c posito h esse maximum
quotientem integrum rationalem b divisi per h. s
erit
Rh + lh  ppem. aequ. propem. m. seu radio extracta
 radix integra rationalis eextracta ex m, secundum hha th, omisso
affecta
proxicile
affectionem tih + Ch. jam in locum b substituendo. ha +c
fiet: cc +(2) h ac aequ. +th aa. Unde eodem modo ut aute fiet  quoliens e
frest
m a a
hh aa
22 + (2) h2 aqu. + lh -  + hh.
Jam C subtichi debet ab a seu fieri debet: ag _. Gptiet rla 3.  b) l 3.j.
seu e aequo seu fiet
cC + (2) fr 2 ce + (2) t C d aequ lh 228c + 2 d + dd
im
 cc-
hh
Eaego qud. posita ratione erit 2 aequ. + lh 22 - (2) t 2 aqu 1 properiod
vel pro 2. ponendo 3 firt: 33 +Cc) h 3 iequ +lh propemod.
jam a aequ 2c + d fiet.
iuo sub est parabo suu
cedtantim proxime
CC + (2) h = cC + (2)h cd aequ + lh 22 CC + Ih (2) 2cd + lh dd
- m
+ hh
 tih
seu ordinando secundum d. fiet.
+ th dd + lhC) 2 cd aequ +1
+hh
m
+tit
= (2) t2
+2) h.
.
=- 1h22
+m..
= th..
hh
Unde patet ultimum terminum hujus plane coincidere
cum similem esse aequationi praecedenti ordinatae secundum a
nam si 2f eum ponamus D. et ita inveniemus 2. fietu
d aequ. 0. seu aequatio dividi poterit per d. adeoque residuum foret
succurrit et eale erlificium sit aequalio lbb + lba aequ m aa
nullum
l bb  m b a + n aa equo ponatur b aequ 2a +c, fiet:
l 22 aa + 1(2) 2aC + lcc + n 2aa + mac + naa
sive  lcc + l(2)2 ac + 122aa nihil aliud requiritur
m.. + m2..
quam ut sit cga.
quod ita obtiner posse videtur fat  cum sit:
Lcc + 1() 2 ac aequae l2Ead ponendus jam C. p fingendo jam C pa deberet esse
+ m..
fiet l + l(2) 2 aequ. - l22
+m
amr.
cum vero C. sit Ba. debet 1 + l 2) esse p - 122
 m2
em ua pla n haluat s equata psuasse F. qaattetu debet
anterm ina ease raliralis quae roc prostet
et quia a qu.  aequ
+hh
ubi notandum Ih - m
Anh esse unitabe
minorem Naque potus
dividit, quam inultiplique
quia  non est revoera