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

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[161] Fig. 42.* 19. Maii.
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[162] Fig. 43.* 17. Dec.
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[163] Fig. 44.* 18. Dec.
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[164] Fig. 45.* 27. Dec.
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[165] Fig. 46.* 11. Mart 1658.
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[166] Fig. 47.* 16. Mart.
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[167] Fig. 48.* 23. Mart.
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[168] Fig. 49.* 3. Apr.
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[169] Fig. 50.* 10. Nov.
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[170] Fig. 51.* 16. Ian. 1659.
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[171] Fig. 52.12. Febr. *
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[172] Fig. 53.* 24. Febr.
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[173] Fig. 54.25. Febr. *
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[174] Fig. 55.14. Mart. *
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[175] Fig. 56.16. Mart. *
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[176] Fig. 57.* 21. Mart.
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[177] Fig. 58.* 22. Mart.
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[178] Fig. 59.26. Mart. *
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[179] Pag. 574.TAB. XLIX.Fig. 2.
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[180] Fig. 1.C K O B H N G M S * F D A L E
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[181] Fig. 3.E C D A * B
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[182] Fig. 4.P Q O N M L * C R
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[183] Fig. 5.C * V S X T Y
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[184] Fig. 6.
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[185] Fig. 7.
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[186] Pag. 580.TAB. L.Fig. 2.R ♈ L D I T A N ♋ H G E P F K C Q O B M S
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[187] Fig. 3.
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[188] Fig. 4.N Q F C P L E A M H O D f
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[189] Fig. 1.B A
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[Figure 190]
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72360CHRISTIANI HUGENII
Theor. IV. Prop. IV.
Omnis circuli portio, ſemicirculo minor, minor
eſt duabus tertiis trianguli eandem cum ipſa
baſin babentis, & latera portionem contingentia.
Eſto circuli portio, ſemicirculo minor, A B C, & contin-
11TAB. XXXVIII.
Fig. 4. gant ipſam ad terminos baſis rectæ A D, C D, quæ con-
veniant in puncto D. Dico Portionem A B C minorem eſſe
duabus tertiis trianguli A D C. Ducatur enim E F quæ por-
tionem contingat in vertice B, & inſcribatur ipſi triangu-
lum maximum A B C. Quum igitur triangulum E D F ma-
jus ſit dimidio trianguli A B C , manifeſtum eſt ab 22per. 2. huj. partem abſcindi poſſe, ita ut reliquum tamen majus ſit di-
midio dicti A B C trianguli. Sit igitur hoc pacto abſciſſum
triangulum E D G. Et ducantur porro rectæ H I, K L,
quæ portiones reliquas A M B, B N C in verticibus ſuis
contingant, ipſiſque portionibus triangula maxima inſcri-
bantur. Idemque prorſus circa reliquas portiones fieri intel-
ligatur, donec tandem portiones reſiduæ ſimul minores ſint
quam duplum trianguli E D G. Erit igitur inſcripta portio-
ni figura quædam rectilinea, atque alia circumſcripta. Et
quoniam triangulum E G F majus eſt dimidio trianguli
A B C; & rurſus triangula H E I, K F L, majora quam
dimidia triangulorum A M B, B N C; idque eadem ſem-
per ratione in reliquis locum habet, ut triangula ſuper por-
tionum verticibus conſtituta, eorum quæ intra portiones i-
pſas deſcripta ſunt, majora ſint quam ſubdupla: apparet tri-
angula omnia extra portionem poſita etiam abſque triangu-
lo E G D majora ſimul eſſe quam dimidia triangulorum o-
mnium intra portionem deſcriptorum. Atqui ſegmentorum in
portione reliquorum triangulum quoque E G D majus eſt
quam ſubduplum. Ergo triangulum E D F ſimul cum reli-
quis triangulis, quæ ſunt extra portionem, majus erit dimi-
dio portionis totius A B C. Quare multo magis ſpatium

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