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

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86371DE CIRCULI MAGNIT. INVENTA. jor quam 5176 {3/8}. cujus dupla F H major quam 10352 {3/4}. unde
G H major quam 352 {3/4}; & H I major quam 117 {7/12}. Tota igi-
tur F I major quam 10470 {1/3}. Arcus autem C D, ſextans pe-
ripheriæ, minor eſt quam 10472. Ergo deficiunt lineæ F I
partium earundem pauciores quam 1 {2/3}. Quæ non æquant {1/6000}
F I. Porro cum arcus quadrante major datus erit, dividen-
dus eſt in partes æquales 4 vel 6 vel plures, prout accura-
tiori dimenſione uti voluerimus; ſed numero pares: Earum-
que partium ſubtenſis ſimul ſumptis adjungendus eſt triens
exceſſus quo ipſæ ſuperant aggregatum earum quæ arcubus
duplis ſubtenduntur. Ita namque componetur longitudo ar-
cus totius. Vel hac etiam ratione eadem habebitur, ſi arcus
reliqui ad ſemicircumferentiam longitudo inveniatur aut ſu-
pra eandem exceſſus, aut reliqui ad circumferentiam totam,
ſi dodrante major fuerit datus; eaque longitudo adjungatur
vel auferatur à dimidiæ vel totius circumferentiæ longitudi-
ne, quam antea invenire docuimus.

Theor. X. Prop. XIII.

LAtus Polygoni æquilateri circulo inſcripti, pro-
portione medium eſt inter latus polygoni ſimi-
lis circumſcripti, & dimidium latus polygoni in-
ſcriptiſub duplo laterum numero.

IN circulo cujus centrum A, radius A B, ſit latus inſcri-
11TAB. XXXIX.
Fig. 4. pti polygoni æquilateri B C; & latus circumſcripti ſimilis
polygoni D E ipſi B C parallelum. Ergo producta A B trans-
ibit per D, & A C per E. Et ſi ducatur C F ipſi A B ad
angulos rectos, ea erit dimidium latus polygoni inſcripti ſub-
duplo numero laterum. Itaque oſtendendum eſt, B C me-
diam eſſe proportione inter E D & C F. Ducatur A G, quæ
dividat E D bifariam, itaque erit ipſa quoque circuli ſemi-
diameter & æqualis A B. Et quoniam eſt ut E D ad C B,
ſic D A ad A B, hoc eſt, D A ad A G; ſicut autem D

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Scan	Original
81
82	367
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89	374
90	375
91	376
92
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94
95	377
96	378
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99	381
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103	385
104	386
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