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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
# Folio 13r, page id 00068021:0025
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nova hic methodus
detegitur, qua diversar
de Trocholidibus, et Relationibus A eonctarum ad ordinatas
de ratione efficiendi ut dine cae
X67 1674  ipso Natalitiorum vigilus adem cuva sit trochor
figurarum quadraturae ad senvicem reducuntur, ope volutaitr Trodhverdio des plurium
clum
Ergo 
Data  Curva, et puncto quodam fixo extra curvam, unde perpendicularis
demittatur ad quamlibet curvae tangentem, investigare relationem inter
perpendicularem, et interceptam tangentis portionem inter t
demissam
perpendicularem et punctum contactus. Esto primum curva circuli
demissas
BL
crcumferentia.  si punctum fixum sit centrum, intercepta
tangentis portio erit infinite parva, et perpendicularis semper
eudem, nempe radius locus ergo est ad rectangulum.
set si vero punctum fixum verter A. quodlibet
incurva punctum L. Tangens axi occurrens LT.. SaH
AB. ordincita seu sinus rectus BC. constat esse AC AB
et esse quam appellemus X. Jam AL + V2a+.
FGN Nar
et AIL H 2a X. ergo CLp AL AC  2aX - X
ergo Ct A rax - X  BL. Hinc jam patet
relationem
figurum in qua ordinata ad reductam rationem
habent quam sinus versus ad rectum, esse Cyclocide
Nam c ut generaliter  in vig
curva
figura provolvenda AL, demissa ex puncto
quodam fixo, ut A, in iangentem LF, fit 
ordinata  in Trochocide et intervallum inter
demissam et punctum contactus seu LC, fit
reducta, quoniam LA in Trochocide semper
perpendicularis ad curvam. ut patet conferendo
figuram 2dam primae, ubi A L(L) provolvenda
curve L A vel (2) (A) perpendicu.
A(A) Trochocide
laris ad curvam Trochocidem AC vel
(A) (C)  ordnata ad planum volutionus
LC reducta sive intervallum inter
ordinatam et perpendicularem
in directrice sumtum.
Esto jam punctum describens, non
vertex circuli A, sed aliud quoddam
quodlibet D. A unde ad tangentem LT.
demissa perpendiculari DE, quaeratur rela tir
quae est inter DE et LE. Cum datum sit
punctum D datum erit ejus inservallum a dimuctio
AB, nempe (DF d dabitur et ejus intervallum a
vertice nempe recta AFHf In ipsa C LY
tangentem ducaptur AH. FG. AC pricme faci
Nam per DFG. habebitur et dE.  at FG. per AH.
AH autem cognita est, sunt Cum enim AC aequetur AB.
eunt tringula ACt. ducro enum radio ML patet
Triangula LBM TBL AC, H, esse similin,
adeoque AH esse ad _AC AB HX, ut B) A Ex Trar
ad radia. LM seu a, ergo AH p est ad BL phax
ergo AH
S AMBmnaX Eg TCB B
au
a
AH
ex
X +af.
ax
Jam ut BL ad BM ita TA ad AH
jam ran- X ABL BL 2AH, ax Ergo TA  ax
3
ec
a-X
∞x +f. Unde fiet
ax + a f + xY. Ergo B axtafe t (+) a
vrax- 
siar
divelis aegstis pesse qumio ess at  toM, ram indaera dicunctur probucta
neglici posset 1) hinc patet sempertos
ieo
TF
si Si
Ca -X
Scax- 
moctum D. esset in olametio producta