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
Page: 130
[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
Page: 179
[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
Page: 179
[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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69 31[Figure 31]
CHRISTIANI HUGENII,
Const. f.
DE
CIRCULI MAGNITUDINE
INVENTA.
Theorema I. Propositio I.
SI Circuli portioni, ſemicirculo minori, trian-
gulum maximum inſcribatur, & portioni-
bus reliquis triangula ſimiliter inſcribantur,
erit triangulum primo deſcriptum duorum ſimul
quæ in portionibus reliquis deſcripta ſunt minus
quam quadruplum.
Eſto circuli portio A B C, ſemicirculo minor, cujus diameter
11TAB. XXXVI@
Fig. 1. B D; maximum autem inſcriptum ſit triangulum A B C,
hoc eſt, quod baſin & altitudinem habeat cum portione eandem.
Et reliquis duabus portionibus inſcribantur triangula item ma-
xima A E B, B F C. Dico triangulum A B C minus eſſe quam
quadruplum triangulorum A E B, B F C ſimul ſumpto-
rum. Jungatur enim E F, quæ ſecet diametrum portionis
in puncto G. Quoniam igitur arcus A B bifariam dividitur
in E puncto, erit utraque harum E A, E B, major dimi-
diâ A B. Quamobrem quadratum A B minus erit quam qua-
druplum quadrati E B vel E A. Sicut autem quadratum A B
ad quadr. E B, ita eſt D B ad B G longitudine; quia qua-
dratum quidem A B æquale eſt rectangulo quod à D B &
circuli totius diametro continetur, quadratum vero E B æ-
quale rectangulo ſub eadem diametro & recta B G. Minor
igitur eſt B D quam quadrupla B G. Sed & A C minor
eſt quam dupla E F, quoniam hæc ipſi A B æquatur. Er-
go patet triangulum A B C minus eſſe quam octuplum

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