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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 140v, page id 00068200:0282
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et ita potygonum hor determinari potest per puncta: potest
laberum posygoni longitudo sumi quaecunque semper
aequalis, sed anguli determinabuntur per hanc imposlamige
debet esse
AE+ E, 2B3B
E F A 2E2F. 2F2d  1Fid
1D3B p 2D2E
poratur ZB33B longitudine data, erit punctum r5
datu, et punctum 2F.
datur et recta 2B.D, et 2B-d
qu
Ergo intersectione circulorum centro 2B radio 2B. D
et centro 2F radio Fd desculplorom habetur 2d
punctum datur ergo et angulus, 1d2B2D.
at is aequalis angulo (2B) 1B2B seu 2Ep.E, 3B
datur ergo angulus 1B2B3B. seu datur in triangulo
esoscele + D2B 1D daties curibus 1D2B vel 2D2B
datur ratio baseos 1D 1D ad ipsa
investiganda inde sublensa plurium simul, ut B a D
porendo seuper  1B2B. 2B3B. 3B4B aequales; et
1838. 2134B. et certa ratione crescentes
et B4B, 2B5B iteum certa ratione crescentes
et 1B5B. 2B6B Elerum certa ratione, ex his dimetur
quomodo crescant, 1B2B. 1B3B. 1B4B. 1B5B relatione ad
arcus quibus sunt subtensae
positoque curvam; B 2B 3B moveri super recta LM et puncto
ddescribere trochoidem, pater hujus trochoidis ra ab. d.D
descriptae perpendicatures esse ipsas dB et q et ad invenientum
purvani 1B2B3B res redit ad hoec duo problemata ex datis
perpendicularibus DB invenire curvam ad2d. et rursus ex
in quo resolvendo hic credo nursu opus quadratura aliqua vel
summatione, quia ipsae perpendiculares summandae) e
inenta curva Trochoide 1d2D anvenire ejus generatricem 1B. BB
x
sed quia haec omnia invenire, adt huc nimis difficile
licebit aliud quid comminisci. curva 1B2B3B sit
immobilis circa eam mo et evolvatur filo silo BFN
alligato, ita ut ut 1B. F et 1B. N sit eadem, recta sciliat
data) extremo fili fixo N. describatur curva evolutione
generata 1N2N3N. sed in filo B N semper sumatur
BF aequalis datae. debet autem cuiva B2B3B
esse talis, ut F cadat semper in eeandem servet
distantiam a puncto dato D. seu ut F semper cadat
in circumferentiam circuli centro D. radio
et BF
et descripti
descripti. problema etium ita concipi potest, quaeritur
curva 1N2 N3N talis, ut si ducatur ad eam perpendicularis
ad partes concavas producatur NB donec occurrat, circulo uF 2FI
scentro d descripto et inde a puncto concursus occursus in ea producta
jumatur recta FB magni tudinis datae, sit punctum B.
punctum curvae cuius evolutione ipsa 1V2N, N addita
describitur. Ijam aliunde haberi potest
data
cmon entum genernttes ex duca eritatine descupta, nam pran
1E 2E
iF 2F