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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163436VERA CIRCULI jor eſt quam E, & ideo A B ſeu C C major eſt quam A E,
& igitur AE + CC minor eſt quam 2 CC: atque AC + E C
eſt ad 2 CC ut A + E ad 2 C, ſed A + E minor eſt quam
2 C; & ideo A C + E C minor eſt quam 2 CC; proinde
A C + E C + A E + CC minor eſt quam 4 CC; & igitur
C - A minor eſt quadruplo ipſius E - C, quod demon-
ſtrare oportuit.
PROP. XVI. THEOREMA.
SInt duo Polygona complicata A, B;
11
A # B
C # D
E # F
nempe A extra hyperbolæ ſecto-
rem & B intra: Continuetur ſeries con-
vergens horum polygonorum complica-
torum ſecundum noſtram methodum
ſubduplam deſcriptorum, ita ut polygona extra hyperbolem
ſint A, C, E, & c. & intra hyperbolem B, D, F & c; Dico A
+ E majorem eſſe quam 2 C. ex prædictis manifeſtæ ſunt ſe-
quentes duæ Analogiæ, prima quoniam A, C, B, ſunt con-
tinue proportionales; & ſecunda, quoniam C, D, B, ſunt
harmonicè proportionales; &
22
A - C:C - B::A:C
C - B:C - D::A + C:A
proinde exceſſus A ſupra C,
hoc eſt A - C, eſt ad ex ceſſum
C ſupra D ſeu C - D; In ratione
compoſita ex proportione A ad C & ex proportione A + C
ad A hoc eſt in ratione A + C ad C, at A + C eſt ma-
jor quam C & ideo exceſſus A ſupra C eſt major exceſſu C
ſupra D, eſt autem E major quam D; & proinde exceſſus A
ſupra C multo major eſt exceſſu C ſupra E; manifeſtum eſt
igitur A + E majorem eſſe quam 2 C, quod demonſtrare
oportuit.

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