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

Table of figures

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[61] Fig. 5.G L B H D O A E C K
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[62] Fig. 7.K F A C D B E H G
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[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
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[64] Fig. 3.G R D B H F E N A X C M P Q K
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[65] Fig. 2.K A F c S C L E B T G D R d
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[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
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[67] Fig. 5.B C R E G A F M Q D O
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[68] Fig. 6.B C H G E A M Q P K D
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[69] Fig. 7.B C E G A M P Q K H D
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[Figure 70]
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[71] Pag. 450.TAB.XLIII.Fig. 4.B A F R P C D E G H I K S L M N O
Page: 179
[72] Fig. 1.F G I K D L E S T O C N H M V R B Q P A
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[73] Fig. 2.F G I K D L E S T O C N V R B Q P A
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[74] Fig. 5.A C B D E
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[75] Fig. 3.A F G I K D L S T E O C N H M V R B Q P
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[Figure 76]
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[Figure 77]
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[Figure 78]
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[Figure 79]
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[Figure 80]
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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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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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