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

Table of figures

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[41] Fig. 2.D B G H C E F
Page: 93
[42] Fig. 4.E C G A F B D
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[43] Fig. 3.E C D F G H I
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[44] Fig. 5.B F R C P L M O
Page: 93
[45] Fig. 6.Y S H E K B C G F R A L D N P M Z X V T
Page: 93
[46] Fig. 7.G F D M L E A K C B H
Page: 93
[47] Pag. 386.TAB. XL.Fig. 2.K B H F G E A I D L C
Page: 106
[48] Fig. 1.L K E D H C A G B
Page: 106
[49] Fig. 3.B Q N L M F G S H K A D C P
Page: 106
[50] Fig. 4.B G R A C D E H F
Page: 106
[51] Fig. 6.A C D M B
Page: 106
[52] Fig. 5.A E N F B L D M C G H I K O
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[Figure 53]
Page: 108
[Figure 54]
Page: 109
[55] Pag. 398.TAB. XLI.Fig. 1.S T B R K H Q C N O M A E L D
Page: 121
[56] Fig. 2.D E F B G H C A
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[57] Fig. 3.F D E G A B C
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[58] Fig. 4.G N B H D K A E C F
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[59] Fig. 8K A F c C E B h H G D d
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[60] Fig. 6.C E D A F B R Q
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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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16316THEOR. DE QUADRAT. minor erit dato ſpatio; ſit ea parallelogrammum B F, & di-
vidatur baſis A C in partes æquales ipſi D F, punctis
G, H, K & c. atque inde ducantur ad ſectionem rectæ
G L, H M, K N & c. diametro B D parallelæ, & perfi-
ciantur parallelogramma D O, G P, H Q, K R & c. Di-
co figuram ex omnibus iſtis parallelogrammis compoſitam
(quæ impoſterum ordinatè circumſcripta vocabitur) ſupera-
re portionem A B C minori quàm datum ſit ſpatio.
Jungantur enim A N, N M, M L, L B, B S, & c.
eritque hac ratione inſcripta quoque portioni figura quædam
rectilinea; majorque erit exceſſus figuræ circumſcriptæ quæ
ex parallelogrammis compoſita eſt, ſuper inſcriptam, quàm
ſupra portionem A B C. Exceſſus autem circumſcriptæ ſuper
inſcriptam ex triangulis conſtat, quorum quæ ſunt ab una
diametri parte, ut A R N, N Q M, M P L, L O B,
æquantur dimidio parallelogrammi O D vel B F, quia ſin-
gulorum baſes baſi D F æquales ſunt, & omnium ſimul al-
titudo, parallelogrammi B F altitudini. Eâdem ratione trian-
gula qu& ſunt ab altera diametri parte, æquantur dimidio
parallelogrammi B F: Ergo omnia ſimul triangula ſive di-
ctus exceſſus æqualis eſt parallelogrammo B F, eóque mi-
nor ſpatio dato. Sed eodem exceſſu adhuc minor erat ex-
ceſſus figuræ circumſcriptæ ſupra portionem A B C: igitur
hic exceſſus dato ſpatio multo minor eſt. Et apparet fieri
poſſe quod proponebatur.
Theorema II.
DAtâ portione hyperboles, vel ellipſis vel circuli
portione, dimidiâ ellipſi dimidiove circulo non
majore, & dato triangulo qui baſin habeat baſi por-
tionis æqualem; poteſt utrique figura circumſcribi ex
parallelogrammis quorum ſit omnium eadem latitu-
do, ita ut uterque ſimulexceſſus quo figuræ circum-
ſcriptæ portionem & triangulum ſuperant, ſit minor
ſpatio quovis dato.

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