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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 32r, page id 00068196:0063
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CW)
Quia autem jam id agitur ut minima ducatur ad Conicam datam, ex puncto dato 5
occurrens Conicae (ad angulos rectos) in puncto quaesito 4. Ex puncto  in directriaem
GH agatur nornalis 587. Et ex in hanc Cx Y agutur normalis 13. Erit de d=
Y 3 est HZ H F ort β S7 sit B HZ sit Y. jam  YZ = _ ZH + H Z seu  Y+Z
et 53 = N 2 - YQ seu β = V. porro ex natura tangentium est YZ: ZN =  dv: d
fiet Y+Zi, B. v  dv: d3
a
per calculum differentiarum, fit amdrando + Z PPdZ + pZdv + 2YZd7 + 2 srdv =0
seu  25V1 pZ t a sec amt pZ+ 253:, am + pv + 27 =  flv: dy =  2) ) q: v. B
et fiet anY 1pX Z- an B - pB Z- 35BV
Sed quoniam video aequationem quam ducimus ex proprietate minimae
sci
ad tangentem, habere rectangulum ex incognitis, et aequatio localis
conicae, ad axem secundarium (regulariter) habet etiam rectangulum ex
incognitis. hinc componendo id rectangulum poter aequationes, poterit
tolli id rectangulum, et composita aequatio explicari potest, ut sit ad circulum
contenti etiam (opinor) esse poterimus ipsis  et W coordinatis, seu axettes. omissis hr et
g, adeoque f et K, Ponamus ergo ex puncto X ducendam esse minimam ad
dato
Conicam Y(V), et punctum quaesitum esse Y. Ex puncto NV agatur in axem secundarium
AG normalis NZ, quae est data, ut et AY, ob punctum e datum se sit β et
A2 sit Y jam Rurius ex Y agatur ro puncto quaesito acta putetur normalis Y3 in ipsam NY
jam YZ = AC + A7, erit YZ = +), et  N3 = Ne 2 - GY fet erit 5Z = β - W
porro ex natura tangentium est du: de = YZ: 3se, et fiet dW: d9= 11G:, β- W
Porro in aequatione dat simplice generali ad Conicam datam rg, nempe yy = 2t x+ FXY
pro X et y substituamus valores per 8 et 20, ex aeq9. 2 et 3, fiet
Uxi Ax = it  t 2tCW et bgu + Lb 99+ t c WoW
ec
+2t X = 2bb8 + 2tc W
o= h + GXK =
= y =
ee
ee
+ 2t be gW + F bb  L ce wW
ee
ce
éc
+2 be gW  ce 98 = bb 1010 
ee
compendio 2tbG+ 2tEW0 + 2B F A 8 + n WW0
e
e
(26)
0
(28.
fiet 2et t  de  A du + (dbe Wodg + + A9d +  1oduo = 0
ec
unde du: de = +b + Bbe W0  t 8FE + BbC g +  W= (per 25) +7,:, W -β
Et mulsiplicando
prcrucem
Et multiplicando
per crucem +
(2E
x b  du
+
B +ea + 0bc eu
ae
n + tc-G
at vequ
- 1b 20 - a gu 
+he + Dbc
sit 286 = n
XYU
Lbc + 2bC
E
ou lacaeue
qu 29 fiet
2
rec
 divindo per ole
Et ex aequ dividendo per B fiit Nequ issinimmd ut et b9, 2tero 1go + 18+   = 
et aequ. 29 diviam do per AB sit di vi dendo fit
+1
=d. et differentiando
27s
 Wu
(29s
gu. 199
a
Huic addatur aequ. 27. divisa per T: e, fit
evapescet W et fiet aequatio nova 32, quae ut
sit ad circulum portat facere n + A-
quae aequatio est impossibilis infil nisi
(32)
0=
 ibB ( N8 (+ MBM - GW + N98 -X Wu
-1 + C, seu
ra
A C GA id L- 1.
4 lite. (+
C
H-
A.
A- n
A B A
2tbg + utc 10 +gW +s  =n Wid
 seu 2MN = = BR- n
fiat X ∞ = 5 = n: sed H non potest esse = 0, quia foret B = 0 seu t -q
adorvinatas anguli obliqui deveniri sportet
30)
A. (t