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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 90v, page id 00068124:0180
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Exemplum quadraturae specialis ubi
et de differentiali cycloidis, et de alia
eaqu algelinicais culva cujus fignia aequalis figmae cycloidis
Me ud
schiruhrusius ut suam demonstrationem
impossibilitalis quadraturae circuli et
Hyperbolae tueretur contra objectio.
nem meam asserit se posse demonstrare
1
quod non detur quadratura specialis
alicujus figurae linea algabraica terminata
nisi detur et generalis per quadratricem
algebraicam. Sed hoc praevideo falsum esse
Nam exempli causa
Ratio quia si series sit a. b. K. eit H Sutama
aabc et summse semmarum
a. a +b. 3a+2b+G unde y duet debet in hax
at
exemrplum afferam.
sit cycloeides linea AB
cujus ordinata EFB secans
seni circulum gereratorem 
AFC in F et diametrum
seuaxem cycloidis AG in E
GHCi
constat ductae AL, parullati
iEB, et BL Eylvidis tangente
et BH ad eam perpendicu-
cari sore aequales
et parallelas GF et HB
item AF et BL, AG et LH
ac denique AL et FB, quae aequalisarcin AF.
cumque eu ipsam EB secet in M. erit MB equ. EF
fachia jam producatur LB dum ipsi GC productae
occurratn T. erit HY: EF: AG: AE seu
producta AF usque ad GC cui occurrat in 5, erit G5aq.
ipsi HT (est autem Gd secans dinidir
as ata
dimidia ipsia EF secans dicidii arcus GF dimidrati
ent engo cuc loides aotem erit sigura quadratrx omnum
sigearuadsente
G5, sr tk, seu figura ejus differentialis, erit AE KA posito
AFK aequari ipsi G5 vel HF. nam dx: aB :d LH: HY.
porro si sit cuiulibe Trilinei gethogonii quadcandi altitudo X ut AE
ord nata u ut EK runctorainata figurae agebrnica cujus spatium triliaeo
quadratricis respondenti aequale est, (nempe AEPA aeq. AEBA)
ordinata E8 erit aqu.   y. n_ poscto h essi constantem AC
in tota curva Ay manestemed cursatuaternurum pronno trilinee AEDA
servit jam si AE sit eAG datur AEH. Ergo et AE _A. cumque
sit inen ADebyaira datur obi quadratum particularis
positoe
essevet
AE. seX