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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
# Folio 15r, page id 00068021:0029
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Cuva HY parabola, axis AX. tangens TY. punctum quoddam fixum D, ex quo perpendicularis ad tngeatem
DE. orit ergo paralleta ipsi PY. quaeritur relatio inter DE et hY. Datur EF. dut DF, quam vocabimus d
et FA, quam volabimus f. Est  autem ex malura parabolae XP, a semilatus rectum et TAp AX BX.
et AFB X 2aX. Ergo TY, 4X + nax
 Ego GF B d srax. rum TG  AF suve X, demtis AF GF. Ego TGH X - f - d sraX
ran TE ⊓ TY. Ego TEp  4X + 2aX,X - f-  trax
TG TPrexia
2X + a
et EY TY= TE. 4X prax  X - f - d trax
2X + a
Sive EY, 14X + 2aY  X + a + f + srax
2X + a
quaritur relano
inter DE et EX
iam DGp   + d rax, sive DG ) S d ae +. L2 naX siv DG⊓) = Sa + raX
Et GE +, STG - TE. sine GEp X 2fX - ad xtrar, +f + ds scar +  ax-
hive
sire G2 1 Y7G - rY YG2
qu+ taxtar, sie GEp 2592) Curra, , +X 2a
sive GEp X -f -  srax
2X + a
 rax+ ae
2X + a
et DE X - f. d pax + D, scax tar, sic
27 ta
-d Tax (F4 X d= 3a
Frax + a
deut
Xa -fa - d sax + adX + ad (FraXFa)
xea+  (aX + a)
saxta
a 1Z. et quadranto, a de aX - 2de _ hax - 2dgathat + 2 X + 2eg a X + 9’ a 
Unde: nimanto. - 2a XZ - a Z2
+2e9
2a X + a
+2dg a
An teos. 2, +-f- 3 2 ns frarra pZ. Ergo 2 - f -  trar t
2x +a
EYA C
S4X +rax
q ua
2X + a san pi a Sraxta + Z Y
adeoque. Qu Prax +a = 33 S2aX+a +74
2a X + aV
ergo dividendo atobique per raX + a fier:
∞ac raxtae, - 2d7 Xa (2aX + a) + auZu X p7 a co2
(Xa - fa - dhac + 2d X + ad
- 2a X 7 - a Z + 2d ax + gr’a
V 4 209
+2de X
+ Fdg a
Aequationus 1: Z A X. f. d srax (raxta sa
 sixia
X - f - d L2aX,
X +a + f + d sraX, Dx
sic 1XISC cota - 8 sa  2X Z
N cor F2aX + aV
4X +2aX. Jam 2ar +4 2x
dat 4X + 2aX
vel 4X + 2aX C E  2a7 + a
sir e sine 
Six et quadrande: X et ordinandorosa X - cofra Y) codisZ V 2X
N +X 2
cosa X - cofsa d
sa
Ergo 2Xta a ria
ta
Sive suxp cota X -cofia Ea
+f.
Arz 8ed (2Xk, + f - x,  A
H.  . . . . . . a5 X +atf y + 2 fa 2X cd
xtars in
XZ
 - 2 Fixta + X 5, co sirra.  s 2X
5Z
sivi 
sa
llnve cotta X - costsa),  + f -XC + dn X (sa) rZ rdonaque ( +
= 178 1a).
Eror
sive xd 2ax + xda - 2 d xaxa + 2d Xata - 2 dXa2d X - 2dXa ad + a Z X - a  Y  seax
H
duuc:
12X + a 1
2X +a)
sa Y
R
x + a +f
Ho ) Unde reducendo patet X non assurgere
ultra quadratum. Cum antea semper
Ex hoc jam aequatione repertus valo ipsius X. insgratur in alqua ex aaequationibus, ad lubum assurgere videretur, quo specimine osamus
superioribus, et connescent X. sola restabunt incognitae Z et Cd.
tiones properandum
quo facto videndum est an aequatio inde atasit ejusmodi, ipsis, d. et f (: et inde pendente C) pro arbitrio explicatis,
ut de possit aequatio prodocta dividi per aliam ad Circulum, Z 1 2a=  + eaF. in qua rursus  arbitraria est.
ope intur trio arbitiariarum utique poaedaet dinsio, et ponde curva eaden certo caesu a circulo et a parubile probitutis vescribarem abeoi
habettem curvis crcularis et para boliae Aterm dincuso, vil quoratum circuli e Hypertilasimnt
X+a +f + 8 Trax
X
ax) sixa(six)
e vexta
Xb 1674 appendix phedia sina tis de trochonionus et relatione redurrarum adbrdinatus
G1
io
E
In
H