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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 181v, page id 00068195:0362
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Anquatio ad conicame generalis, prosito vertice. I
aloscis
axe  XE  XhZ, ter V ardinita A5 seu Z
fit 2. Y V + 70 = Z2. et pronatur
dp loco Ve. V1. seu v = b~ + py - 94, : 9
ponatr
et toco L AY seu Z = P5 - by, : 4
Erv - 25bE 127py
vo = - 2 7 b97. 27899) 1 = bEG + Z 1 yy + 27 bpEy +
27=
ppls =bgy 12b85y
Ex problemate Maximo in minimae pauloante
posito habemus cum ex M diccenda est ad conicam
inima vel maexima MY producatur MY in B, ut
distaclia ipsius M ab axe est MN, vocandaM,
et abserssa maxe, a vertice, YN, vocetur, n,
ibi curre occurrataxi.
= r+ fV. fit r + ∞6,:  - Ytr B +V +M: m
fit rM. + Y mv - tr  + (1P + 1) v  r+n =  e  rt t -5
fiec -rm - rmv + ey + fvy =0
rniv= - = mb. B- fal4.
tbesz - bx k 1
+eq- + et  = eli y
+
+rmq
12
Aequatio  a Addantur in unum aequationes 1. et 2. multiplicata altemtia per consantem
+3, vy = - f pe + fby +
tmultiplicata utraque pe constaltem, et summa eam
conferatur aequationi A ad Nirculu, multiplicataper constantem
+ ff =0
Quae aequalio ad circulum erat
= 29X - 2Cy + XX +gy
quando uni md maous determinandi locee ad interseotionem,
cirt figularum g. circuli  conice datae non
succedit, necsme.g. per norm ale sud rectas easdem
nec foicedet alis modo, utcunque mavietur modus cosrdina
interia jenus dat faciliorem constructionem quam alter
Oriia atce possunt esse parallela. et si coordi.
natie nen sint parallelae Axibus oppositis
g0. e circuleferent 6 puncto Y possunt dusi Y
emales ad rectas AB, AE, inter se non normales
et noestigari potest relatio inter ipsas YX,
rX H   d. Y XX = yy (b+ Y) y + 2Cy are  ex
si b+r = p q+r = K sit  G = 5 ea erX pqy +KXy = r9C + rex
et y = r rqc + YCX,: p9+ KX _ et yy = rrgqec + EYBCC X + rrCCXX,: Ya U P9 KX +KX
= EraX + YXX, : q et fit q rraha  ErrgqCCX D YIGCCXX
+2raepp X + 4rgqpk X + 2rgKKX
rquKX + r(CH.X
sint duae aequationes una ad Conicam, sexundum X et V E cajus latus  ransvertura  rectum dimidium r,
+rgqppXX
geeralis dutam
sit BV, Li BG, m; GV, n AB, d
Aequatio ad circulum, et  kxroo -igc rty= +H
quarum petollendo B, ut reliaquatur e, bebitura quatio quais i 1. p etc. Comotar anda datae
quad si succedit comparatio ut arbitrov habetur constructio. stibitrariae sunt m,n, a; f, g3i,
it duae aequationes una ad conicam px+b HBY bXX + exV+ (Cx  d AlCX +s = 0
oinduen identificationibus opus A
lastua ad circulm Xr +BBL. G X t ig gesta iX A k = 0 tollendo 1B sil bexx  ex B  hd A hoxt haf = 0
fit  = (h - b) XX +lhi - he) X  CB K - ) il 3. 7 ex + d 9) E X -hg = hi X - Ih K C
V
IX, X. XIy
B
=f
+X
pro e ponatur 4+X
in aequationibus 1 et 2
et buis
crtatien ae3 ditnbitarit mulliplica
erit
n
et a. si s
polamus
omissa a
 enbitum
eo
conserendae aegus. 6.