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

Table of figures

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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
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[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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[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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75363DE CIRCULI MAGNIT. INVENTA. goni A C D. Exceſſus igitur perimetrorum eſt H I; cujus
triens I K adjiciatur ipſi G I. Dico totâ G K majorem eſſe
circuli A B circumferentiam. Inſcribatur enim circulo tertium
polygonum æquilaterum A L E M C, quod ſit duplo nu-
mero laterum polygoni A E C B D F. Et ſuper lineis G H,
H I, I K, triangula conſtituantur quorum communis vertex
N, altitudo autem æqualis ſemidiametro circuli A B. Igi-
tur quoniam G H baſis æqualis eſt perimetro polygoni
A C D, erit triangulum G N H æquale polygono, cui bis
totidem ſunt latera, hoc eſt, polygono A E C B D F. Hoc
enim patet, ductis ex centro rectis O A & O E, quarum
hæc ſecet A C in P. Nam triangulum quidem A E O æ-
quale eſt triangulo baſin habenti A P & altitudinem radii
O E. Quanta autem pars eſt triangulum A E O polygo-
ni A E C B D F, eadem eſt recta A P perimetri A C D.
Itaque polygonum A E C B D F æquabitur triangulo cu-
jus baſis æqualis perimetro A C D, altitudo autem radio
E O: hoc eſt, triangulo G N H. Eâdem ratione, quo-
niam baſis G I eſt æqualis polygoni A E C B D F
perimetro, & altitudo trianguli G N I æqualis radio circu-
li, erit triangulum G N I æquale polygono A L E M C.
Itaque triangulum H N I æquale exceſſui polygoni
A L E M C ſupra polygonum A E C B D F. Trianguli
autem H N I ſubtriplum eſt ex conſtr triangulum I N K.
Ergo hoc æquale erit dicti exceſſus trienti. Quare totum tri-
angulum G N K minus erit circulo A B . Altitudo 11per 5. huj. trianguli æqualis eſt circuli ſemidiametro. Ergo evidens eſt
rectam G K totâ circuli circumferentiâ minorem eſſe. Quod
erat oſtendendum.
Hinc manifeſtum eſt, ſi à feſquitertio laterum polygoni
circulo inſcripti auferatur triens laterum polygoni alterius
inſcripti ſubduplo laterum numero, reliquum circumferen-
tiâ minus eſſe. Idem enim eſt, ſive perimetro majori adda-
tur {1/3} exceſſus quo ipſa ſuperat perimetrum minorem, ſive
addatur {1/3} perimetri majoris contraque auferatur {1/3} perimetri
minoris. Hinc autem fit ſeſquitertium majoris perimetri

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