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

Table of handwritten notes

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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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