Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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177450VERA CIRCULI. pezium L I K M eſſe medium arithmeticum inter prædicta re-
ctangula
, hoc eſt 49500000000000000000000000.
invenia-
tur
inter rectangula L N K M, Q I K M, medium geometri-
cum
28460498941515413987990042 quod erit pentagonum
ſpatio
hyperbolico L I K M regulariter circumſcriptum.
Sit-
que
ut trapezium LIKM unà cum dicto pentagono circumſcri-
pto
ad dictum pentagonum, ita duplum dicti pentagoni ad
hexagonum
ſpatio hyperbolico L I K M regulariter inſcriptum,
nempe
20779754131836628160009835;
quod hexagonum
erit
polygonum complicatum cum prædicto pentagono;
quæ
duo
rectilinea efficiant primos ſeriei terminos convergentes:
inter quæ ſit medium geometricum cujus quadrati duplum di-
vidatur
per idem medium geometricum unà cum majori ter-
mino
ſeu pentagono circumſcripto;
eruntque medium geo-
metricum
&
quotus, ſecundi terminiconvergentes: atque ita
continuetur
ſeries hæc convergens polygonorum complica-
torum
, donec medietas prima notarum eadem ſit in utroque
termino
convergente, nempe ad terminum vigeſimum;
po-
lygonum
enim circumſcriptum eſt 23025850929958961534-
173864
, &
inſcriptum 23025850929931203593181124: ad-
hibeatur
deinde approximatio in hujus 23 &
24 demonſtra-
ta
, &
invenientur termini intra quos conſiſtit vera ſpatii
hyperbolici
L I K M menſura, nempe 230258509299404562-
40178681
, minor ſpatio, &
23025850929940456240178704
eodem
major, &
ideo non latet ſpatii menſura, quam in-
venire
oportuit:
totam polygonorum ſeriem hic appono unà
cum
numero rectarum curvam hyperbolicam ſubtendentium
in
unoquoque polygono circumſcripto.

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