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

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75363DE CIRCULI MAGNIT. INVENTA. goni A C D. Exceſſus igitur perimetrorum eſt H I; cujus
triens I K adjiciatur ipſi G I.
Dico totâ G K majorem eſſe
circuli A B circumferentiam.
Inſcribatur enim circulo tertium
polygonum æquilaterum A L E M C, quod ſit duplo nu-
mero laterum polygoni A E C B D F.
Et ſuper lineis G H,
H I, I K, triangula conſtituantur quorum communis vertex
N, altitudo autem æqualis ſemidiametro circuli A B.
Igi-
tur quoniam G H baſis æqualis eſt perimetro polygoni
A C D, erit triangulum G N H æquale polygono, cui bis
totidem ſunt latera, hoc eſt, polygono A E C B D F.
Hoc
enim patet, ductis ex centro rectis O A &
O E, quarum
hæc ſecet A C in P.
Nam triangulum quidem A E O æ-
quale eſt triangulo baſin habenti A P &
altitudinem radii
O E.
Quanta autem pars eſt triangulum A E O polygo-
ni A E C B D F, eadem eſt recta A P perimetri A C D.
Itaque polygonum A E C B D F æquabitur triangulo cu-
jus baſis æqualis perimetro A C D, altitudo autem radio
E O:
hoc eſt, triangulo G N H. Eâdem ratione, quo-
niam baſis G I eſt æqualis polygoni A E C B D F
perimetro, &
altitudo trianguli G N I æqualis radio circu-
li, erit triangulum G N I æquale polygono A L E M C.

Itaque triangulum H N I æquale exceſſui polygoni
A L E M C ſupra polygonum A E C B D F.
Trianguli
autem H N I ſubtriplum eſt ex conſtr triangulum I N K.

Ergo hoc æquale erit dicti exceſſus trienti.
Quare totum tri-
angulum G N K minus erit circulo A B .
Altitudo 11per 5. huj. trianguli æqualis eſt circuli ſemidiametro. Ergo evidens eſt
rectam G K totâ circuli circumferentiâ minorem eſſe.
Quod
erat oſtendendum.
Hinc manifeſtum eſt, ſi à feſquitertio laterum polygoni
circulo inſcripti auferatur triens laterum polygoni alterius
inſcripti ſubduplo laterum numero, reliquum circumferen-
tiâ minus eſſe.
Idem enim eſt, ſive perimetro majori adda-
tur {1/3} exceſſus quo ipſa ſuperat perimetrum minorem, ſive
addatur {1/3} perimetri majoris contraque auferatur {1/3} perimetri
minoris.
Hinc autem fit ſeſquitertium majoris perimetri

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