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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 17r, page id 00068229:0033
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 18v); this page is its right half.
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cey. 1.
M H aml + 2C + lh. et mt - 1Em lu- 41
Ex priore fiet: m-aml (i at eth. et quadrando m - am,
Fiat expriore m  + L M g2 1. C quadrando M  gl M + is t m , 41+
-25 1. + dlo.
+ 52.
Ex aequatione posteriore fiat: M- 1tM L at 1
Expriorefiet m - aml  2l + lh. et quadrando: m - 8b m3 + 161 M pi 4l + 4lh+ lL V
= X collatisque duobus ippus mt valoribus, fiet: Dn + 151C ( + 4 17, , (2+ ah + BK + 8l m - 16Cm
C - amt + 4  pbl + th. Ergo f m F 2l B X modo qua dratum ab X, sit
majus quam 6.
jm  
 m + r  m+ 5, + m + +, m + co, dant
m+ + rm + rs m + rst m + rstco pa
+ rt
+ Yc0
+ s +
r0
Ponatur et ++sAco
item rsterscortcot sta po.
Ergor =s - + - c, quo valore in posteriore inserto,
fiet: - 5+ - 5d  +sco  - 5 0 - stco - 5C0
(- S+c0) - tc - +c0 (+ stco)
Et fiet ponendo rursus: 452 t + st + s + 5 +c0 + 5cd + trco + +co
Hoc duobus effici modis potest, tum ponendo duas radices simul, nihilo aequales tum
Quod malim ponendo ex ordinata aequatione inde extrahi posse radicem, vel
sallem affectam, id est conferende ipsam cum alia
nempe s
+co + +c0 H
+ e+ +S A 1c0 +a 0.
p. 3+ +e..
conferatuo cum 5 + b + Bs
et tc + V
et ordinando
+ + co
 + + C + cor sive F c0 + +c , yt + Va VF+ tors
2+ teo + co 7
(+YFO (+Ct)
+ + tco+ y +c 0. Jam faciamus:
 +4+ 2t c + 2t  a +co + cot +4  ho +32S to cC)
4t + 8 teo + 4co
4 +7 + 8 tCo + 4co
debet ergo ex 14 + 6+ co +1IF co + 3t Cd + co + extrahi posse radix.
sed haec prolipiora, et satius puto duas sumere radices aequales nihilo sive
tunc ex aequatione D (et (4   t a) (tCo+ 1 +(FC  0
0r. (43 - 13) (+ t c- 2t c) (= +c0) + t2 a (+ + cod
P 5- t.
+2a
Ergo in aequatio proposita fiet. Tantum
Quod ideo veri commodissimum, quia
pro Y substituatur  co et pro S substituatur
videtur ob exempli raritatem
Edus et quartus, fier:
jam ex aequatione proposita faliumus:
mt - 15  V m - ++ 0
Pit p  7 L3P- B i p - pB OP. 1BI. Ergo psu D (2 P. 512 . faciamus alidm. m  B
25.
 Unde m pi 4 X + 2l.
+ c..
licer aquationem pragositem epatarie in masi ctamus aliam. m -C 1
X 2 613
+ d
0.
m+.  (+ cot m  (+ cot  +fco
+ cot
=12n, mundo (, l9m - tet - 40
= cot)
= 41 go. Quam cumfacitia proposita posumus conferre siet Enebitur
+ +co)
valor tum ipsius h tum ipsius 9. Unde unam ex Tadicibus
possamus eligere, nempe sed non sufficit, quaeritur valor
is ex tadiabus, rensui ut lel c