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
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[45] Fig. 6.Y S H E K B C G F R A L D N P M Z X V T
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[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
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[49] Fig. 3.B Q N L M F G S H K A D C P
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[50] Fig. 4.B G R A C D E H F
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[51] Fig. 6.A C D M B
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[52] Fig. 5.A E N F B L D M C G H I K O
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[Figure 53]
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[Figure 54]
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[55] Pag. 398.TAB. XLI.Fig. 1.S T B R K H Q C N O M A E L D
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[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
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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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47338ΕΞΕΤΑΣΙΣ CYCLOM. tro Π P. Ducto deinde plano per A Π P, & alio huic pa-
rallelo D Φ S ſecundum lineam Φ S, erit jam pars ungulæ
hiſce duobus planis terminata, æqualis ſolido quod fit ex du-
ctu plani S Φ Π P in ſe ipſum; & pars ungulæ E D S Φ, æ-
qualis ei ſolido quod fit ex ductu plani E Φ S in ſe ipſum.
Quare nunc demonſtrandum erit duntaxat, partem E D S Φ
eſſe ad partem Φ A P ut 53 ad 203, Sit Φ N parallela E P,
& N C parallela Π A. Ergo quoniam ex proprietate Para-
boles, P N eſt {3/4} Π P, erit quoque P C {3/4} A P. Verùm &
S D æquatur {3/4} A P, quum ſit huic parallela , ſitque 1111. 16.
Elem. rabola E A F: Itaque junctâ C D, ea parallela & æqualis
erit lineis P S, N Φ. Ducatur ſecundùm D C planum
D B C parallelum baſi E Π F, fietque ſemiparabola B D C
æqualis & ſimilis ſemiparabolæ Π Φ N; & erit Φ B N di-
midius cylindrus parabolicus: D A C B verò dimidiata un-
gula. Hæc autem æquatur ſicut antea oſtendimus, duabus
quintis cylindri dimidiati, baſin habentis D B C & altitudi-
nem B A. Ergo quum ſemicylindrus Φ B N habeat altitu-
dinem B Π triplam ipſius B A, erit ungula dimid. D A C B
ad ſemicyl. Φ B N, ut 2 ad 15, hoc eſt, ut 8 ad 60.
Junctâ porro Φ Π, conſtat ſemiparabolam Π Φ N ad trian-
gulum Π Φ N eſſe ut 4 ad@ 3; ſed triangulus Π Φ N eſt ad
rectangulum Φ P ut 1 ad 6, (eſt enim baſis Π N tertia pars
ipſius N P) hoc eſt, ut 3 ad 18. Ergo ex æquo erit ſemi-
parab. Π Φ N ad rectang. Φ P ut 4 ad 18. Itaque & ſemi-
cylindrus Φ B N eſt ad parallelepipedum ejuſdem altitudinis
ſuper baſi Φ P, ut 4 ad 18. Dictiautem parallelepipedi di-
midium eſt priſma D N S; ergo ſemicylindrus Φ B N eſt ad
priſma D N S, ut 4 ad 9, hoc eſt, ut 60 ut 135. Qua-
lium igitur partium dimidiata ungula D A C B erat 8, ta-
lium ſemicylindrus parab. Φ B N erat 60, (ut ſuprà oſten-
ſum eſt) taliumque priſma D N S erit 135. Ac proinde ſo-
lidum A Π S D, quod ex iſtis tribus componitur, erit 203.
Eſt autem ungula dimidiata A D C B ad dimidiatam un-
gulam E A P Π, ut 1 ad 32, ſicut Cl. Vir. demonſtravit in
prop. 95. lib. 9. Ergo qualium partium ungula dimid.

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