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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 164r, page id 00068200:0329
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facendo se 2a, universalitatis causa: altera ad iiculum: - X + eX +da B y + AY. umlfgni D ex X iB
ergo  ex aequatione ad Circulum 1  - X + eX + D a - A y. eumque valorem ipsius  inserendo in
aequatione ad conicam datam, fiet Y  + a X + 1a X +ca
Y(Aequationes nimorum sunt duae altera ad circulum, altera ad sectionem (onicam
 G
 Calculus qui hanc eyuntionem 2 pproduxit reperietur. datam. Aequatio ad sectionem comcam datam est: +a X + (1_) X, + ca Y + dV.
Ejusque valoris ipsius y ope eliminando y in aequatione ad circulum, fiet aequatio unius tantum
. X (. 10) X7. (.4) X  at N0
+342... a6. (raadis
+  
-0 de
Ponamus jam (n 1 o. ut calculum contrahamus
-0439
quae aequatio plane convenit cum
superiore, si modo quae illic est
quantitas  ponatur hicl e1
et ipsam e definita tβ pro
+ lX3 tam N + a nX + a p p70
aequationes collatitiae exurgent tales: conferendo cum X
B a B h per Term. 2. que ideque su  e  2 17 2a 4 3e -1
In Tern. 3. pro Ba, substituendo ejs valoem Lfar. et pro E ponendo d- A, fiet:
sie 4 + B F e p Y.
incognitae, multiplicatis scilicet omnibus per  et divisis per 
N4 +
B 1.
+ adat - ad p. L - d + 2d A - ua + am,  per Tern. 3t.
Et puo coa a, vel aos mate subsituendo cejus valorem, inventum per Term. 3t. fier
in Tem. 
1d  ada 4  ae c m .  e7 aen + la + 3- 28a + N 1 a - anl
Inde d. adt ad à r au+ l’a  = a m l
puri
Uide +
fiat  a
4. = e .. - Da
et5 r ~ X, yeX. . Y eX + X DpaX +  ar
18)
a .
p.
1a 2 
et fet
--
fiet:
27
san cunim..
Y  sive 2 her 1. 37
. tam sive A 1
at ta+ la- a m
27 87
27
2lt 1 la
y  29 27
1048
ata + 1a- a m
divisisque omnibus fict: 
per
Ultuu
2tt7 a
Halita jam Ea nlo negotio hatetur   aB. B) a p, perterninum quaitum, sive t BB  L
Atque ista quidem sucedunt in dubie, sed angunt tamen calculum fieri breviorem, si
sive e2  2n V P
detenta Y, ipsa X eliminetur. nmirum X C. V- AV + CX, +Da ex aeqratione ad
Circulumus substituatur ille valor in aequatione ad sonicam, fiet fZV 4G y +a eX + a da + GX + ca F y + dy
siet: X _ Y +23 =3
a ca
sive, ut isdem quibus ante terminis alamur, ne novo calculo opus
sit. Vy + BY + na
et contra
aerit eadem quae ante aequatio, nisi ubi illic A, c nunc substituatur e ibique nempe
+2c + b
in secunda linea, sualore  qui ante fuit A1) signa luntentur et in ulhina linea termini
medii, nempea e. signum mutetur in + caeteris manentibus: His positis
In omnibus que secundi termini salum dabitur  
Moinde licet ponere e, o Hini extra parabolam licebit ponere etam (  o habebiture
in parabola semper dabitur 2
aostructio omnium quae fingi possunt in hoc gerere elegantissima;t in
sarebola, quia Ed datur et e quoque, ideique relinquendo est B, ut sit quod ope tertus termini in
determinetur. In parabola ope semudi termni statum dabitur d. In parabola non licebit ponere e fi:
ut siti quod ope tertii terpuni veterminetur; quod si ergo nunc muversalittem quaerimu, relinquemus st
ubique, tollenus n ubque canescent 4 quanditates,. ide ponemus 4 e +bp. 2a quod in parabota statium constat
in alus ved cq bnini iuc opdti. Hae u pti d, nuta e, et G itae n tn feitu a ali potetmid o eest
pro t. et S. utile
in his lineis alias literas
assumi ne confunidantur
cum s imprimis paginae
prmae, et prus. post
hanc sequentis
N  a, seu quantilas
pro uitate assumta, in alion
calam quantitatem transum
tatur, utiliter; quia ita
ubique inferciri potest quantitas
data, et ipsa transimutatio
est faclis
ie