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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
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Methode Tangentium
XB. it74. inquisitio in Methodum qua Cartesius
inversae exemplumsi invenit proprietates suarum ovalium
Adde alia de huc pertinenti desriptione
trochoidis curvae
h6. 2. Geom.
Esto Curva FC AEC, cujus duectrix AMdi
ordinata C M. perpendicularis CP. recta quaelibet
ex puncto determinato F ducta ad punctum
curvae quodlibet FC. et et ab atro puncto
veterminato ductur CG. Ex punctis FZ
Ex p. ducatur perpendicularis ad ratium FC
nem pe Pq. et alia ad GC. nemipe PN.
Ponatur jam evenire, ut PQ sit ad PN, ut  in data ratione D ad e.
de oproinde, ut a Corrtesio in dioptricis ostensum est, si AEC sit superficies
ex vitro, C radius; omnes radios, ex puncto F ad quodlibet pur
curvae punctum C. Cendentes, refractam iri ad G. positi ec d ad C
esse rationem quae refractiones metitur. Quaeritur jumq quaenam
sit curva hujus naturae. Cum Cartesio AM vocemus y: et
(FC vocemus X+ C + Z. 1
3A  b.
unde cF
FI
CnII pQ
unde G EK
ex esto AF⊓ f cm FM ySty
Fr N E H
Triangula rectangula sFQ et BC MF similia sunt
 + 2CZ+~
FDeCn
CF
jam F P f + v.
Cque
∞+20
GPH b = v.
fa
c9.
) nguy
5- fV
GPCM
cr
C9
FPCG
CF 2GPH C
CG1 b MG⊓ b - y
3) - 25 y + b - 2b0 (+ y
Ergo
F+ v, (Z +2CZ - 15y +c0
sue 2 +2cZ - 2+ y +c2
- 2b.. -f ~ Y
C2
vla
inde F YE B FDCM. item  angula F NG et CMG
PX+ 5P CCH.
FM H f eM 
cM sc
p2
e
2b..
c+Z, d, b - v
-f 2 H
e, f+ v
1. C
V - ipy (Y) A
52
Cp sive Z + 2CZ( y  2FY +C+
quius dudibus ponendo CPps. Quae posseri porro his duabus aqua
Jam _ Cn + MP Y
tionibus junctis etidi poterit y nempe ex priore ~ 
C+Z, d, b- v. +c 17+2
e, f+P,
AAb
+ 2
quo valore in posteriorem inserto aequatiorem, sita, incognitarum capitalium
rescubit restabit 7. ordinetur ergo aequatio secundum, Z, et cofer ubi
duae erunt incomihe incidentes (e v. et S. Quae invenitentur determinande
confhendo aequationem hanc cum isa productam (poest elisam y) cum aequatione
duarum radicm aequalium
22
= 209 + e2. atque ita invenietur V, quod
sufficit. Inventus valor ipsius V. inferatur in aequatione O. et habebitur aequatio
in qua sola ex incognitis restabilnt Z et V, nempe capitales  et habebitur
aequatio naturam explicans figurae quaesitae, unde et modus eam describendi
non difficulter habetur. Ex his apparet inquisitionem istam methodi
tangentium mocusa esse ex faclliniis redgatur cram ad aequationem
unius madgnitae capitalis lao methodum tangentum inversam
reducendae no duas
radies aequales determaxduabus
incidentibus. Epade suonethodo
existentibus incognitis
non dubites, quae a Cartesio umis sa sunt
 verae)
C +
d, b - v