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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 143v, page id 00068198:0286
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se fortasse obtinar quaesitum potest sine obliguitale sdinutaru. Generaliter in num cursa
B EB: BF = a: Y. fiet
EB = aEP- L pCP, is
Saatrr =s
_ BC = rEP = ACP, : 5. sit 18, DBC = EF Z BC
sit R ED = KR - K L et C p = CR = EL
fiet, EB = aKR - akL + YCR - rEL, :S BC = YKR - rK L - a CR + a EL,: 5
sit aequatio ad conicam 2a. AB + a AB = BC erit AB = EB AC seu EB - C = aEP+ r CP - e5, : 5
utfint et 2a B EP+ 24SCP + 4 aa EP + a rr Cp + a aY EP. CP
Fales -iaestp - raros . rrEI  E - rar Ep. cp S
EC
sit  A(A B), in circulo L() cujus radius tr sit  ah (B, - (DB) = (1) C sit  (BC: BC- B (B) L. BC. g
et (A) (B) = AB = AG seu AB- R et fit ad circulum aequatio G- ihk + 2h AB 
explicemus AB per a EP + rCP = e5,: S et BCper rP. al P3. 5
Ael
KK + 2KAB E
d
t2gBC
arhik = h HAess F E(seKaS EP + yht K) rS CP - aa Ep - rr Cp (= har Ep. CP
=KK S
g4
+29rS EP +29 a5 CP rri- aa p (+ rar sp. Ep.
+ 2a es EP + 2res Cp
AB2
c
-8C
jam aequatio data proe minima ad conicam ducenda s est ac + a AB + + BC - af AB. BC =0
hoc explitata dabit
+ac S tgcaSEP Facrs CP - afb ar EP + at b ar Cp + atb aa E P. CP
asess +HtSEP ( as CP
+ at best EP  atbesa (P
150
-a r Ep. Cp
=0
ponatur aequatio ad circulum muthiplicari per _ haec ad minimam multiplicari per m, at aequalio ad cirealur se
quae in unum additae dare debent aequationem ad conicam videamus an hoc liceat. Et primum 2
quo terminis fiet m. atb, ac - vY = a aY - 2aY
altiornibus
n(aa trI =
-m atbar _- n (aatr) = q aa = vr 
+ m atbar - n Caa + rr) = 4 rr - aa
duarum posteriorum ope tollando n fiet (2 aa = rr +  atb arm = q rr -aa - apb arm, seu fret carb
a -brr + aarm + abrm = arr - aab = aarm - abrm, seu m = arr - ab- a + b11:, aar tabr)
sed expriore aequatione fit m = aar = 2abY,:, aa - rY, a +b. ergo fiet 2aY, aaY- 2ubs = arr - aab - a +bYY, a a - WY
seu r4 - 6 aab rY + at
a +b
24b + aubeY - br4
+ aY
+ aabYY.
t 6aab N+ 3ba bb = 936 a bb - a = 364 b - 4 d arb  9 a bb - at at b
arb
A(a +b).
4arb
YY = (3a 3 aab taer 3bb - (a t bE
a+6
4a +
3aab + aa Y8bb - aa - 2ab
et debet esse 3b non minor quam a + b seu 2b major quam a 2b non minor quam a
a +b
seu
a +
aliter Y+ + 2aa rr + a = 2aa rr = Saab rr seu rYFaa = r Y raa. a +b + 6aa (atb)
quae limitatio diplicet
Et qude in Ellipsi semper latus tanversum ib
t
sed res at redit pro r absoluto ad
est autem in Ellipsi semper latus tronversum b, non minus latere recto. nam latus rectum
in parabisa latus
est ordinatim applicata id focos est in Hyp. parab. et Ellipsi
Ergo in Ellipsi cadit intra latitudinem Eblipseos, cum tamen ea sit longur qua ato2
in Parabola tatus hursversem est i
infiulum in Hyperbila vidiamus figuram adjunctam cum FNC) habenns constantem
et longitudo sit latus transversum.
simper differentian, latus rectum tansversum t sit socus FP2 + 2FVX VV) = (F)p
sd (F) P= F P+ S(V) et fret (Ep) + 2EV+ VV = (Fp) + VV)2 + 2FP. V(V)
seu fint
seu 4FV (+ VV) T. 4FV. VIV) = (V V) + EFP. VIV)
.Res igitur pro Hyperbola non est universalis sed
pro Elipse, et forte Hyperbola peculianter accummodabitar iad Ascymplotos
 -2a4)
+b
P = EFV: VV) +EFV
quia aequatio pro minina est ad Hypertactam
LM = 5 LN- f- y
LNqu + NC qu = LC qu
AM = g NC = x +g fietque ff tgy - 2fy + XX + 2xg + gg = th, quam differentiando
ABX BC,g gy = 2VX Hr. qux
fit Zydus - pSdy + (Xax + XgdX = fydy = fr dx + Y fxdx
ay: 1x = f-y :, X+9 Y+ 4X, :y fit se gy = X leex ZXX tre + g1
Msy +Rgy 1HXXX AM rX + Mgr debet esse m- n = (m + n) siu fiet
+ML gx
A, 1 - (n: m) =  + _ (r: 9) 4 (n: m )Y: 9)
seu sa - r: 4b , 1+ (1. 4) = n: m
si sit  m=q fiet 9 - r, :, 4+r = n: m sit ergo n = q- Y
=ngy. +nFXX + EurX
et m = quo fiet (9+r = 9tr) gy + (9+r + g- Y) Y: 4) XX
= ryy + 2rXX, habemus ergo aequationem ad circulum
mor coleli scubendum ernit ay. Ap. 1aji, 5. 7
vis
a fit ab -be - aemab
soa cu rati ma
.farit