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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 165v, page id 00068198:0330
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xle. Epplicentur et fiat a Lt  +50.Z + 500a.
Assume _ = EIX +2a
4025+910 ap +quoaa
610r+601Z7600 a a
de uenauar sed contrecavi
et eo
3. in aeq. 1 substituatur valor ipsius X ex aeq. 2. contracta, et
et fiet 3) 11. 510 aD + 10. 601 az. aequentu. vatorestini ipsius Z ex aq9. 3 et 4
IIdocisto.
+ 2, 301. 510 aaZ
=11. 401. 510..
+20. 310. 601 ...
21. 510av +20. 601 aZ
=10,402. 601
01. 601 aa Z2
L20. 401. 601
+20. 300. 601 cZ
= 16. 408. 601.
or thaZhvav +30ona
non viden opus tot arbitrarus et possi  
et et aeq. 3 fint 302Z + 310a0 Fxo 
Cies + , 21. 310. 510 auve + 21. 32 510032 20302.601 a
-11. 410. 516....
10. 410.601.
+r. 300.510 eV
-11. 400. 510..
+21. 302.510 +20.302. 601 + 2. 310.510 8+20. 310 b01 +21. 301. 51
-11. 400. 510 10. 400. 00, -11. 402.510 = 10. 402. 601 = 11. 410. 5i0 =10, 40 6
Compendii causa fiat +21. 300. 510
Eit ex vq. G fier loa prndio
100. 700 200. 700 102. 702
00d. soda VB + 102. 702 4271
erit o ( = 000 710a
+000. 701 aaZV
+000. 810 ..
+1 av
202. 702 000. 710
+202. 702 a33
4 000. 801 aa22
+ 200. 700 aZ
haec formula comparetur
fit.D+ dCa o
+000. 701 aZ + 100. 700aa
D = Z 102.702 22 4000. 810 a2
P= 20270273 +000. 801a 27 +200. 700 aa Z
+ 3)
H02. 75 Z 4 9. 000. 102. 701. 70247 +2. 700. 102. 700. 702 a a 2Z
+2. 000. 10. 701. 700 a f. 100 1aa
210702 n. +1. 000. 000. 701.701 ... . .
-4. 00o 202 70r. 710- 4 000 000 . 710. 801 ... . .  4. ub. 20. 700. 710 e Z
nltisciat i... 102. 7or Z +Zol . Z + 102. 102. 7o2. 1o2 a   Z
formulae datae per 10
instituendae sunt aequationes iderte
dcatoria quatum
Ob teminum tinum 102. 702 Lap = 100. 700 a seu 8 700 = 102. 7or Lap. : 100 a
ob terminum penultimum 710 = 1000 (701 +910) : 2. 200 = (Ob secundum) 102 (701+81): 2. 202
unde fiet 100: 200 = 102: 202 seu 2021 = 102. 200 : 100
super est novissime aequatio ob ZZ, una ubi interpretando 700, et 710, fiet
. 102. 7027 ap(. + 000. 701 + 000. 810 , :, 2, 000. (100: 200) (701 +810) a = 8 07 11t
cor pocapo
S et hi valores inventi omnes id commudi habent quod sunt rationales quodsi pro allis compendio
assumtis
nec pasum contrahetur calculus sisat putosliceat ponere 701.  0 seu 401: 301 = 21: 11
ita manebit valor ipsius 700, et H et 202. et 71 = 100. 810: 2. 200
et 8D1 = 102. 702C + 2 Tap - m) +000. 818a, : 2. 0007 (100. 20) 810a
est autem 80l = 20. 301. 601 = 10. 401.601  et 401 = 301. 21 : 1. sot na 1d 11t 
et erit ocd. 801 = 301. 601, 20. 11 = 10. 21, : 11. ego sir 3. sublato 8D set
et
hiet 301 =  208, 102. 702 (2 lap - m) + 005. 810 a, : 2. ∞. H 601 (20. 11 - 10 21) 510 a
ila pro et 80I rem reduximus ad hi numerum initio assumtum 30(
Eodem modo ob  100. 700 a = 112. 702 lap fiet 21. 300.  32 ap + 21. 302 Lap
et ob . 7. 200. 710 = 100 _ 810 = 2200)
et ob 200 202 fiet
100 10g
30 - -
(tav. 300
11. 40H
es fiet odid
10 400 (601
ad 50 ea
 quat ( loot) sp- M)
quad M 4or.
Edo ter
c f. 66t. P 0407 (420 16) a
L. d. B. B01. C.10. 410) C- 21. 101
+20. 300
i  od
-1. 402..
21601 L0. 400
et
510 +240
quar (126. 1
S1B. 510. quadr (=il. 2) C lap - )
+601. 601 quad (t 10 410) a
+20. 310 +20. 11
510. 610, - 1. 410 ) - 21. 10
uibus quatuor novissimis aequationibus si addatur 401 301. 2
fint 401  ut 301 in aeq. 4 ha
itaque ex aeq9. 4 et G habemus 301 et 401
Ex aeq. 2 datur 4 per 400
Ex aq. 3 dt 2t  qr per 400
ec
Exags Ex aq. 2 latuo 48t per 40
(d .Cax) =, adx
itayu haum duarum aegq. ope
Gubetur 40d, et 302
Ex aeq. 1. Datur atoa t. god per . 300 d. 00) ilqe hatum
itaque ope G aoque valiorus auterm inverti isfel o 1 ipsim 410 et ipsolum 1302, 402 substituantur in aerp. 4 et 5
ita tundem, a habebimus absoluta valores ipsorum 410, 302, _02, 301, 401; remanentibus ad hac arbitraris
310, 300, 400, 10, e, 2012, 510,601.
=10.101. 001
et adhuc compendiosius
e00 ruativ + a  D +
in
dlar atax