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

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211481SUPER HUGENII EXCEPT. opera detur magis præciſa ex ultimis. At miror, cum Hu-
genius incidiſſet in meam Hyperbolæ approximationem, quod
eam non potuerit Circulo applicare; Nam in Hyperbola abſ-
que dubio 24 prop. approximationem ex ultimis ſimilibus
polygonis conſtruxit: Omnis enim ad Circulum approxi-
matio ex polygonis deducta, Hyperbolæ eſt etiam applica-
bilis, & vice verſa. Sed hoc non videtur animadvertiſſe Hu-
genius; alioqui in fine fuarum Animadverſionum non pro-
mitteret talem Hyperbolicam approximationem, de cujus
applicatione ad Circulum nihil dicit. Quæ autem illic affir-
mat (ſi de ſemet loquitur in plurali) tranſeant; ſi verò etiam
de me adeo fidenter ſibi perſuadeat, falli ipſum putem, cum
hæc eadem quadratura, de qua loquitur, antequam ab eo
videretur, ad laboris dimidium à me ſit reducta.
Ne autem Hugenii praxis geometrica minus peritis videa-
tur noſtram ſuperaſſe, ex noſtra approximatione, ab Hu-
genio rejecta, ſequentem praxin exhibebo.
In fig. Hugeniana ſit A C = A, A B C = B, ſitque
11TAB. XLIV.
fig. 3. A + B: B : : 2B: C; eritque {8C + 8B - A/15} major, quam
arcus A B C; differentia autem, in ſemi-circumferen-
tia minor erit quàm ipſius {1/3500}, in triente minor quam
ipſius {1/40000}, & in quadrante minor quam ipſius {1/300000}. Sed quo-
niam præcedens approximatio major eſt quàm arcus, aliam
addamus eodem minorem. Sit A: B: :B: D; {12 C + 4 B - D/15}
minor erit quam arcus A B C; differentia autem in ſemi-cir-
cumferentia minor erit quam ipſius {1/1000}, & in quadrante
minor quam ipſius {1/60000}, inter has approximationes ſit maxi-
ma, penultima ſex continuè Arithmeticè proportionalium,
quæ minor erit quàm arcus, differentia autem in ſemi-cir-
cumferentia minor erit quam ejuſdem {1/23000}, & in

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