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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 54r, page id 00068201:0107
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cD
DF V ax
CDwVaraz +b222
FFV ab , ax
ca 2ia 262- 2a262+6a24246222
Conferatur son
traluu XY - d by
62
ndeo
X Sa tbIE
unde β X 3+ allax- aex + ry
Yn
arer 1b222
a2b4222a26323 + c262 ∞4
aab2X2 = 2a 4b X 3 + a2c2 24
2b4
cognitur
y +X ( a
problema: Data basi Trianguli, pectangulo sub duobus
lateribus, et angulo a uno ad basin, reliqua invenire.
Esto DE basis = a. VEG
In Triangulo CDE esto data basis DE = a. angulus CDE, et
rectangulur CDX C CE. Dabitur ergo ed recta GE,. = b.
eritque Esto CF -X erit X = DF ideoque DF = ax : et
DF a et scit 6D = a X + bX sie X  aerbe et CD = X aut
EF L a = aX, ejus et EF = a = 2ax + a X = a b- 2abx + ax
et CE = a.b - 2a bX + ae X + b X et BE, C  X - rab X  s 
Ergo e CD CE = t arrat
61 Ergo X e l D
 Ergo conditio de rectangulo inepte adjicitro
ontra si ditio de rectangulo nepte adjicitu
rectangulum. Omisso ergo angulo, quaeramus
a seu CDB a
 ae
  1
E Ergo CE
eot
axti
ca
1 + 2b
14 X
est aequatio ad Paribolam seu  cLY
et cum proposita ad ciiculum ceo
habolae
+ b+ 4 X
diet agu
gulum
posito ram a = 1. fiet.
Erit ergo CDCGEB a X 
Ergo a X  y quae 
cvcu
o
ab
AEb
2ab
1b2X + bX L C.
4 -2
+ b3X
23 + H
=2 62
+b2
X : C-1 = 0.
sollatur secundus terminus, poneuto Zu f 2b +b3 Sublato secundo termino, patet problema esse planum
trage spt
n CF DsC
DZV a
C auterut by X, C b3 a X
la cont m
friore ad circulum
dat aequatioum
arbr-2a2ba tar
unius incognitae, renge X a a X quae est plana
fit ergo problema planum 
sBIBLIOTHBEA
RBCEA
X HANHOVENAie
arib2 vr
CF=X. XA = Y
CD= fa X +b X = 7 sa 2b
FE=a bX et F5 = a 6 bx eX
fiet Y+ X = a b-x + A
seu V +k. X + 24X - a = 0
locus est ciurculus
XC sa , 6. 2y = da
Ieu x = dab locus est Hyperbola
ratio
b2
v
B+
E
a
C= cognita
productum ex DCCE
a
CX b
DEVC
ab
dea
a
cEcd 1 at - 2a x+c
b2 - 2a2b∞ + c2X2
et ab  8 fiet C5  dL 2243Y
Cab
LaX a
2a 4bx3 -2 a2c2 X4
∞ dab4.
 b 2ex+X d
seue
=
vel Ce seb. 2 ex +X
o
 eb - 2 ex + X d
miletu
C
. 0v.
e + X ves +∞
2
e
Aitc