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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 3r, page id 00068124:0005
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Segmentum obliquum cecloidis primariae, recta a vertice ad punctum mediae
aaltitudinis ducta, abscissum, aequatur semiquadrata radii circuli generatoris
 insimum
sit semicycloidalis linea AEH, cujus vertex A, punctum in basi GH, punctum
mediae altitudinis E,  situm in recta DE, basi  parallela, per lentrum D
Dcirculi 2circuli genexatoris ALGedecta, quae semicircumferentia  ABLG
circuli generatoris ducta, ipsam semicircumferentiam secante in L jungan
tur AL, AE, dico triangulum ADL aequari segmento AECA. Nam AL
c
AD BBA + ABLECA = ADECA = ADL + ALE + AECA
quadrans Retorta
circuli
cyclidat.
quae
sequ.
ADLF ADL
seu quadra-
toradii ut
jam olim
fuit ab
aliis demon
stratum vid.
Honor. F abr.
Trilin. Ci
cloidal.
de Linea simi-A Cerqu
um et Cycloide
prop.
Fit ergo
trianu
trianue
quod
aequ.
segment
quedranti
ADLBA
quio
cyltorde
basis trian-
uli LE aequ. arca
quadrantis
AB
ti-
itudo vero
Ae est radius
quadrans ADLBA + Ad L + ADL = ADL + quadrans ADL_A + AECA segm cycloid.
id est sublatis utrinque aequalibus
semiquadratum AD L = segment. cycloidat. AECA
quod erat dem.
Nam Trilineum cycloidale ADECA aequal qua est quadnani continet quadrautem
circuli, ADLBA, et retortam cycloidalem AB LE CA: Sed idem ADECA continet triangula ADL et
alliqu
ALE) ergo ADLBA + ABLECA aequ: ADL + ALE Sed dudum ab aliis demonstratum est (vid. p. Honorat
Fabriam r. de Linea sinuum et Cycloideliis tr. de Cycloide n. 76. Tretortam ABLECA aequalem esse quadrat radii
seu duplo triangulo ADL. et A)Cdgat triangulam ALEaequade est quadranti ADLBA, quia hujus trianguli
altitudo est rndicus AD, basis vero est LE) aequalis arcui quadrantali ABL ex natura cyclodis. fit ergo ADL BA cam
d aual re k. Lod
et segmen-
tum cycroidale
ArcA.
sit Ad L aequal AECA. Quod eradem. DEM.