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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 236r, page id 00068196:0467
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Ergo NRp = da.
Eodem modo C pi
0. Julii 1027
y. tings gplX. sinu a. arcq
uadiatura quadratricis quariu sat vet suadu. vensa
Quadrans circuli CABC.
Regula
X
alversus A
Recta niS ita fertur descendem
celeritate proportiali illi qua fertur radius AF ciica centrum
intersectioneque regulae et padii formatur cycloides describitur.
quadratrio tet sore Motus autem talis esse debet
eo tempore quo radiu absolvit quadrantis arcum
etiam eat absolvat ser percurrat radium Ergo
erit. NR elementum motus regulae
CA rade
ad CE Barcum quadrantis 4
A ad FE ecu seu elementum motus adt. ut
et en
Tabebitur porro urea Et MCCqa M seu  (a)G-a
sydad
CEFI9
ut . seu M F,  a
ad Cpare  aq Api ct,
ESBta.
qu a Hased sufficit cobis
A vl MB vel Ap.
Quod sijam AP vel MM ducamus in N R habebitur Elementum Areae quadraticis
quare quaerendus valor quantitatis. AP. Est autem AP G_KNB simo
Ergo AP
1X
MD
Ergo pM in NR +
rNa in Xda
X  = a H XXa rd Paha KS situm qulti
a
1) pM. F t
ra da MRN. jam DEp dx. etud b mmangula
da.
qx MC
axp
EFd, EA L similia erit
da p FE
AEA. Ergo day rdx
li II AK
quo valore ipsius y da substituto in valore ct M Elementi quadralicis fier
id est si arcus EB, ducatur in DE productum dividatur, per AK habebtur vout cusN
+a
summa autem horum rectangulorum est areaspatii
habetatur Rectu  RNq
Ergo quaeritur
EGBE+ BEB
retet segmeire 
an-x
Tade p Ma AV M. Est autem adx  BGE B retorta Cyclordalis
ANY ninirum arcubus GE EBp a. sapplicatis ad DEF cx
VBEG BGB
ar-at
(+ retorc)
onaetort  XV ay sit jam curva B2B
Cpororatis ipsis retortis, seu A p
Ergo si sit curva BH talis ut fiatB EHBE spatiam
aequale vel proportionale perpetuo spatio VAMV.
 lunc ejus momentu ex AC, erit proportionale ipsi EG indE
incidit in c. quia
ullima relata aequali
1. quae per ndi
visa dat Y.
seu adx. Quiadatur quadratura omnim cyclordis portionum
dabitur utique et sact. Quadraturam earum portionum ita
segm. cyclo
Recorta Cycloidalis Vestic abimus: jungantur GB, EB. quia EGBEp,  2BGB
XY- ay. cum terari. C (ut alibi demonstravi) et EGBG + (BEB
natur arcu arius sinus y.
sinus compl. X. ipse
arcus a.
PBEG + segm
retort. Segmicire. si qu
H2BCB
segrd.
iins ud
cy eo
BGB
2. Retr
fiet: segm. cycl. 7 aequale Vrosine discrimine quod est
Erroi admorandum et ideo omne cycoidis segmentum obliquam
absolute quadra bile est. Et retorta EGB) semper aequalis
erit rectangulo AKE F Xy. Ergo (ade  xy sive
adx X dy + ydx. et adx du + Y dx. et sa dx +sa
so yt sco posito adtros
seu ed Z. eut cop,dFDA
drHx