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

174447ET HYPERBOLÆ QUADRATURA. convergente, nimirum uſque ad polygona laterum 16384;
inſcriptum enim eſt 3141592576586860 & circumſcriptum
3141592692091258; non conſideratur nota ultima, quoniam
in diviſionibus & radicum extractionibus ſemper à vera quan-
titate paululum aberramus, quod ultimam notam imperfectam
plerumque reddit. adhibeatur deinde approximatio in hujus
20 & 21 demonſtrata, & invenientur termini intra quos eſt vera
circuli menſura, poſito diametri quadrato 4000000000000000,
3141592653589789 minor circulo & 3141592653589792 eo-
dem major, & proinde non latet circuli menſura, quam
invenire oportuit. polygonorum ſeriem hic appono.

11
# Intra circulum # extra circulum
4 # 2000000000000000 # 4000000000000000
8 # 2828427124746190 # 3313708498984760
16 # 3061467458920718 # 3182597878074527
32 # 3121445152258051 # 3151724907429255
64 # 3136548490545938 # 3144118385245904
128 # 3140331156954752 # 3142223629942456
256 # 3141277250932772 # 3141750369168965
512 # 3141513801144299 # 3141632080703181
1024 # 3141572940367090 # 3141602510256808
2048 # 3141587725277158 # 3141595117749588
4096 # 3141591421543029 # 3141593269613390
8192 # 3141592345578073 # 3141592807595664
16384 # 3141592576586860 # 3141592692091258
### Circulus intra ſequentes terminos conſiſtit
# 3141592653589789 # 3141592653589792

@odem omnino modo reperitur rectilineum æquale cuicun-
que ſectori circulari vel elliptico ex cognito triangulo inſcri-
pro & trapezio circumſcripto.

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