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

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[Figure 101]
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[103] Pag. 520.TAB. XLVI.Fig. 1.D C E A X F K V O I L T α M N
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[104] Fig. 3.Δ A Φ G F N E M I D H L B C K O P Q Σ R T V X Y Z S Γ Δ Θ @
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[105] Fig. 5.C B A D E
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[106] Fig. 4.H C L E B A D F K G
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[107] Fig. 6.L G C F M A H B E I D K
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[108] Fig. 2.G C H B A Y L X P K V Q I O S R F D E N
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[113] Pag. 542.Fig. 1.♃
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[114] Fig. 2.♃
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[115] Fig. 3.♂
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[116] Fig. 5.25 Mart. 1655. * a b *
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[117] Fig. 7.26 Mart. * a b *
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[118] Fig. 4.
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[119] Fig. 6.
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[120] Pag. 550.TAB. XLV III.Fig. 1.* a * b 27. Mart. 1655.
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[121] Fig. 2.a * 3. Apr.
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[122] Fig. 3.* a c * 9. Apr.
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[123] Fig. 4.* a * c 10. Apr.
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[130] Fig. 11.* 21. Apr.
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175448VERA CIRCULI.
PROP. XXX. PROBLEMA.
Ex dato ſinu invenire arcum.
Sit arcus circuli A E deſcriptus ex centro B. hujus arcus da-
11TAB. XLIII.
fig. 5. tur radius nempe A B & ſinus nempe A D: oportet in-
venire quam proportionem habetipſe arcusad integram circuli
circunferentiam. ſit arcus chorda A E & ejus ſemiſſis tan-
gens A C vel C E. ex quadrato radii A B auferatur quadra-
tum ſinus A D & relinquetur quadratum ſinus complementi
B D, datur igitur B D; & ideo datur area trianguli rectanguli
A B D; datur quoque area trianguli A B E nempe rectangu-
lum ſinus dati A D in ſemiſſem radii B E. deinde fiat ut ſumma
triangulorum A B D, A B E, ad triangulum A B E ita duplum
trianguli A B E ad trapezium A B E C, ut conſtat ex hujus
5. & ex dato triangulo inſcripto A B E & trapezio circum-
ſcripto A B E C, inveniatur per præcedentem ſector ipſe
A B E, qui ad circulum integrum datum quæſitam habet pro-
portionem arcus A E ad totam circumferentiam, quam inve-
nire oportuit.
PROP. XXXI. PROBLEMA.
Ex dato arcu invenire ſinum.
Ex dato arcu manifeſtum eſt dari ſectoris aream; hoc igitur
22TAB. XLIII.
fig. 5. ſectore dato conſideretur ex quot notis arithmeticis con-
ſtet ſinus totus: deinde ſumatur ſectoris dati talis pars ali-
quota nempe ſector A B E, ut trianguli inſcripti A B E &
trapezii circumſcripti A B E C toties multiplicia, quoties ſe-
ctor datus multiplex eſt ſectoris A B E, concordent in totno-
tis arithmeticis quot continet radix quadrata ſinus totius; hoc
enim facile fieri poteſt ex ſpeculatione tabellæ hujus 29: non
enim requiritur in hoc praxis præciſa, nam nihil refertetiam-
ſi in magnis radiis diſcrepantia ſit notarum aliquot.

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