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

Table of figures

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[Figure 81]
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[Figure 82]
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[83] TAB. XLIV.Fig. 2.D H A B E F G
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[84] Fig. 1.E G N L O I Q P D K M H F A
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[85] Fig. 3.B E F A D G C
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[86] I. CasusFig. 4.Y Q R C A B M L I K V C O S X
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[87] II. CasusFig. 5.R C Y Q A B I L M K V O X S C
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[88] III. CasusFig. 6.Q C D Y K L I N M S V B X C A G O
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[89] Fig. 7.IV. CasusQ D C A B S L N X M I V Y K C G O
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[Figure 90]
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[91] Pag. 506.TAB. XLV.Fig. 1.C F D B
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[92] Fig. 2.C B A E F
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[93] Fig. 3.B b F f H c
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[94] Fig. 4.C D B A E F G H
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[95] Fig. 5.C b d D B E F G f g e
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[96] Fig. 6.B G A C D
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[Figure 97]
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[Figure 98]
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[Figure 99]
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[Figure 100]
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[Figure 101]
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[Figure 102]
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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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[Figure 109]
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[Figure 110]
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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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