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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 69r, page id 00068049:0137
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itaque superest, ut tribus sationalibus atamur
vlentis ipsis Z, 2,6, , fiat (a = n20 1G2 + 130 1h6 + 1230 146 + 10BV+ 10014
axtiam = AES ionobV X in ayaB + uro vuna +. 2. u7o uro  f. (7 12. 120 ug0  1G6 + 2. 1120. 130  26
1139. 1030V3 + 1130 10  an F 1135. 1. 31 aR
1230. 20 30 pV + 1eyo. 203) at 11 30 n. X aa
1000 a VB + 2. 100B 00IAV F 1001’aa
2, 1120. 1090aV + 2 . 1130, 101OV + 2. 122 IuaV
2. 1120, 1801 a_ 2. 1120. 1001a_ +2. 1230 1001 aa
sit jam exxtaum = quadato
ecitis o m et o faciam aun + aenn = 1) a 32e stit + 30 1o4, ne iti omnnia pro in eon eodem
cux fat l cra an Lhnot 4 2. 32o. 2 204 Ito  (ter 4) id
axxtana 
Ex a ilerficatis teruinis irrationalibus fit 3120. 2720= 1120. 1320
et
3t20 c =re 1020 AC  31B. 1. = 1120. 192)
 3ro - 12C. 122 3120. 10. 20 aq. 128, 1020 3125. 10.21 aequ. 1125. 10. 26
ex aeper aosit
1326, 30.20
1320.90. 21
3128. 11. 2 aequ. i12C
(47) 3320. 30. 20
3125.10.26 aequ. 3120. 1120. 10.16 se et ex 45per 4) sit 3125.10d aqu. 3125. 1120. 1221
1128. B20. 32
1126. 1320. 3028
3120. 1328. 30.26
( per 17  48 fit 3120+ 9d. 3120. 1129. 1025 -3120. 1328. 3076- 1125. 1320. 30. 26,: 10
3128 aq. 3128. 12d. p. 2 = 3125. 1320 3a21 - 1128. 1323. 3021, : 11. 2
(Sis 3t.
312d. 1920 3 2b
uquos duos valores ex eeyg.3.3
aequando inter se fiet:
(320. 123. 10r 10as) - 3,26. 193 18. 30. pudd = 12. 1910. 3o b. 2d ap. (3n t. 12B. 10. 1 1) - 31 5.128. toho 28 - 11o. 1926. 10.
et pari jure fere
4 fuit 3120 = 1120  209  30 - 10.31: , 1320 20 11. 38 931. Ergo 3128 = 1128
Ergo Ex aeg. 46, ope 53 et 54 fieret ainn-
nam etsi vellemus _3 H. 30 - 10. 31. facere ag. 0. ad hoc evitandum; tuns in inteterminatis
per aqu. 43. fiet 31263328= 1320.
6 et t in indeteatis coinciderent, quod _ freci, non debere pranovi. Ergo nec hic calculus succedit
5od. n
3101 a
ua vso 3iolae. 10
3302a 20 V
sd jam videm hoc con valoe issus axx+ann, qualis dicitur ex ag.6 non posse comparari quia in hoc quod ex  venctur 
occunrit v, nec vV sho, et licel tolli possit v, non tanen alterum
unum ad huc superest. sit aax = 1120 1k2 + 1320 162, ut aute
axX L ann Z 2 L210h + 2306, 21odF. +93 6
axxrann = 2o h + 2o 5, 41 dq ran ex6
 qua duae aequationes sunt efficienda ) sed praeterea opatet ut
Ziia nia Frustia sperabimus in
sit jam
+ 146. Sed nonquadrat Et revera
sehod
qaon fiun ib in simplaibus seu
ducentibe
quod igo  prodatii
coposit, debent pruducere quadratum, eprimus sit xd aequo a
sit p+d = quadrato a  e a Quod per se habetur, ex assunto valore , ipsius, ad
+ b X+C, H+1 a h+B
Hinc sam X + b et X+C debet uunumquodque aequari te multiplo conti per coem. sed pat, et
8.  +  16 non posse ( 1E+, 1 + vor posse aequari altiori quam est quadritum quin
id quadrptum est simplicissinum Em debet X -  X+d = quadrato a.. + 148
quodrato ergo si ergo xad simile C goto a 1+ S6 sed x +b debet esse simuile to
fecto ex consto in coem ergo Xrb simil est oto ab a S st ducto insimilesto asti+ +E
sed ita seriper non nisi non srafuinatis composita
162
et X+C similiter x+d -. vv + v. A6
X+b = ybo a lG+ 1d dust. in Da hoGC, et X +C allexi pto a 1t + 6, ducto in h+ HG6
occunl. Ergo faciemus X+d-  + 8 HZ, a A 
Quio si x habeat et dvisoram in constantem, ut si sit X+d = ov + b +tio: v+4 tai L enim
id saltem obtinebimus nesit nesit ne b, et c, solum quo discrimen faciunt in sola infimu rejiciantur
nad- xet mox emr api 13 sib:, i v coravs vraa X+ d == () Yt _ + 162:, v+ xia
et ob ita etam ad hic nova albiliara lubramum
X4 bE f4 +629q0vr q1a oy
et debet esse
t2 + 02 2 4 v. a 14 (7 roE+ rn,  2ooetioia + 2130, seu, 1  otu av + ua  + X. 200 + 2. 2a  G X
30. 20 30. 2
 avaia
2b0. 23. 404 2ba i.
sunt comparabitia t horum
Y L7 -82 - d 10 +4. 
15. 10. 200VV + 110. 10. 201 a b + 110. 14 201aa L 2no. 130. 20SV. A F ~ l10. 30 uB1 a ps
B∞. 30. 200 ∞Y 136. 30. 20l d v 135. 36. 201aa 110. 2130. 10 +HD. 230. 1a
calentem rollaa = 2. lr. 130. 20l, : , 110. 11 + 130. 31
3yoc a. 3ia monra
producta
110. 1X 200a V
16 quoad
d vi ton occurrit in ratonbus t
tem ad ratis aoles. At pia ibi ilum go ctat, hoculanm, s ab ds fiet
2IaL na_ et Esta
4a41 = 20104, 110. 1p + 130.31
el = 11. 20 + 30. 21 + 31. 20, C
duam comparationem) B(2(1
t asi  eta
fur pag.
bi it laculus desceritm
athoquia
a 2061 15. 10+13030 -20aa 1043
1 4B 40. 4) 4, 100. 11D. 1V+ 38. 30 - 20aa 10130, 201. 116. 11 +138. 31- 21a. 1F
110. 100+ 1do 1
omnis reducta est ad
od seli ad torjo.aa
1oCBS
. ao our ca
 et ror et ly hair
diod faegoHitio
ti aui doun ai
eoradi
(per 
at traracta
 accommodar
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10. 130 M. 31 = 23108) ol e)
ita
torci