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

Table of contents

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[171.] Propositio VIII. Nunc verò ponamus tres eſſe colluſores, quorum pri-mo ut & ſecundo unus luſus deficiat, ſed tertio duo luſus.
Page: 500 (734)
[172.] Propositio IX.
Page: 501 (357)
[173.] Tabula pro 3 colluſoribus.
Page: 502 (736)
[174.] Propositio X. Invenire, quot vicibus ſuſcipere quis poſſit, ut unâ teſſerâ 6 puncta jaciat.
Page: 504 (738)
[175.] Propositio XI. Invenire, quot vicibus ſuſcipere quis poſſit, ut dua-bus teſſeris 12 puncta jaciat.
Page: 505 (739)
[176.] Propositio XII. Invenire quot teſſeris ſuſcipere quis poſſit, ut primâ vice duos ſenarios jaciat.
Page: 506 (740)
[177.] Propositio XIII.
Page: 507 (741)
[178.] Propositio XIV.
Page: 508 (742)
[179.] Coronidis loco ſubjungantur ſequentia Problemata. Problema I.
Page: 509 (743)
[180.] Problema II.
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[181.] Problema III.
Page: 509 (743)
[182.] Problema IV.
Page: 510 (744)
[183.] Problema V.
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[184.] FINIS.
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[185.] CHRISTIANI HUGENII NOVUS CYCLUS HARMONICUS.
Page: 511
[186.] CHRISTIANI HUGENII NOVUS CYCLUS HARMONICUS. Litteræ D. Hugenii de Cyclo Harmonico.
Page: 513 (747)
[187.] Tabulæ Explicatio.
Page: 519 (753)
[188.] FINIS.
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[189.] CHRISTIANI HUGENII VARIA DE OPTICA.
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[190.] CHRISTIANI HUGENII VARIA DE OPTICA. I. Excerpta ex literis Dni Hugenii, Academiæ Regiæ Scientiarum Socii, ad Autorem Diarii Eruditoruns de Catoptrico conſpicillo Dni Newtoni.
Page: 523 (757)
[191.] II. CONSTRUCTIO PROBLEMATIS OPTICI. Propoſitio 39 Libri v. Alhazeni, & 22 lib. VI. Vitellionis.
Page: 525 (759)
[192.] III. ALITER. Dato Speculo Cavo aut Convexo, itemque Oculo & Puncto Rei viſæ, invenire Punctum Reflexionis.
Page: 526 (760)
[193.] IV. COMPENDIUM.
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[194.] V. ALIA SOLUTIO.
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[195.] VI. Excerpta ex litteris Dni. Hugenii Acad. Reg. ſcient. Socii, ad auctorem Diarii Paris. de novo Mi-croſcopio ex Hollandia allato.
Page: 530 (764)
[196.] FINIS.
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[197.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA.
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[198.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA. Excerpta ex literis Dni Hugenii, Academiæ regiæ ſcien-tiarum Socii, ad Auctorem Diarii Eruditorum, de Phænomenis aquæ aëre purgatæ.
Page: 535 (769)
[199.] EXPERIMENTUMI. Aqua, ſublatâ aëris preſſione, hæret in tubo.
Page: 536 (770)
[200.] EXPERIMENTUM II. Notabile quid in deſcenſu aquæ aëre purgatæ.
Page: 537 (771)
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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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