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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 161r, page id 00068200:0323
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Aequatio solida tata
y (V +am V + an V + ap 1 0. constimenda
ope sectionis onicae datae et Circuli. Sit sectionis Conica latus recduma transoersum 
AC Aequatio factitia ad conicam cendefinitam: + a X + b X +ca e Y + dy. -
adcirculum quaesitum: = X + eX + Da H y + Xy. Ergo per Aegu. ad circulum erit:
X , + eX + Da    Ay, substituatur hic valor ipsius X, in aequatione ad
1 Concam, fiet:
Ergo X
F2 C. X + a B + a y +a a y
+ b
1y 
4 41.
ca 
1dp + dy +a8
B ~ +d. 1= ca
 + e= ea sive per compendum
+ge + b
Xr
portnto + a. B - ca 14. Ent X B 1 V +  B y .
2 + β)
Quibus datoribus puris ipsarum X et X, in aequatione ad tirculum substitutis
firet: yt + 2a β y 1 d - ea apV-ba
s e..
+aja.
t
ta..
Quam aequationem factitiam incognitae unius conferendo cum data, fiet:
per Sem. 4.
Unc βpC 
Aee
seu eti + 48 + 24, sen B 4
 ad ami  Gpantem  _ 1) b hie ceda q  9  tob9
pateem. 2. 4 (β , L.
pertem  eda
VN. 14
X. 1 V
fietque 49 ad ql2c es 1
VL
Iqa bu cdei lim
u de A,-
d
12-am ex
H Lq
F it
Yq + Van
avr
+ n22 Est autem Et C- b ∞ - 2a
sii A lae qeaat go
= a 2d
+
er perte ) D L p Z 
 B pe Jam ostendum quomodo Aequatio + aX +6∞ ( C By+ dy.
revocetur ad sectionem Conicum datame  Epontequatioad Cnicam datam
S Inscriptum sit sectioni conicae rectanque illum comentricum, DEF. icentro B. axe
ACu cui parallela DE. constat esse
EL ad MHid latus rectum 24as
2a, ad transversum 24. poneum si scilice puncto incurva sumto H, inde demittalu
perpendicularis in DE, nempe HL. Appellemus AN  0 erit DE  29 + 20.
Et appellenus V. erit DE  24 + 2O + v, v, p 29V +2OV +V
sie At AHL  ML  EF B Z.. Ergo M HL B E + ZZB 4Z + ytet ) P + +Y
Ergo 2qV + 20v +V
1z+ yu  H  
sive
.Ergo 2aD + 10 aY + a v 7 8Z + Z
plicantem; = 2g. cur si componatur aequatio ad parabolam,  qv+ lypo  Ergo ponendo a + aaO p 5. fet 24 sV + a v p Q Z+ Z, et
explicando. V et Z. povendo  Vp 2 + 8 et Z, 3 + 6 fiet:
9 4
A1ex  a   v + 261
4+.. ad to s e d D
1 sa
 C = 48
per deq. 1. et 4, eut ber 4 2a G+ 2a + 2a 0
posita jar b i2a fiet EB = O
Ergo Spha 2a 
ce 
167 d-7
a 2
erunt aequationes collatitiae sequentes:
d uot  br12 a 8 + s
e 16
() Ca pyaq2 + S =6
(3) ad p 26 + P. Tumcas ( a ), rap fB 92- d 6 rd . P sed 
(4) S ei 2a 4 ad 
Erp et A d ra G  P F  Eypsea ap1a
ZN EF P Ergo  861 = d8 + 8  -d + 2d F- 70
Egoca  4qu + cat f f qu 42d7  Y) 175
Aequatio factitia ad Cirentum Racillime etiam
exhibetur: X + γ + ex +Ba - Ay. P ∞ -8+9
conferendi cum V  v p a W
ee
lol
erfier a H Egsia
V+ XY  + EX o Explicetur cor X + D, fiet:
l X 15. X. p70. conferendo fiet eHE. Ap, + ( = 2D. sive A B A + 2D.
unde 2) e, t d a 2D. Euo bapi. 18 =D. fcdte cyohateu cntes
bp 2a.
cr + at
er b
dn β4 + a X
Ego 71 a + a
On prsaga
2.  1 297 - a suc + 
4429 a
 a - a m
F9- 2a
llnde a
2a + 2405.
divisa s per ( pq + 20a
Ergo 29+20 L DE
29+ 202 a HI  H a