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

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

Table of figures

[141] Fig. 22.* 19. Maii.

[142] Fig. 23.* 20. Maii.

[143] Fig. 24.* c a * 27. Maii.

[144] Fig. 25.c * 31. Maii. a *

[145] Fig. 26.* 13. Iun.

[146] Fig. 27.* 16. Ian. 1656.

[147] Fig. 28.* 19. Febr.

[148] Fig. 29.* 16. Mart.

[149] Fig. 30.* 30. Mart.

[150] Fig. 31.* 18. Apr.

[151] Fig. 32.* 17. Iun.

[152] Fig. 33.* 19. Oct.

[153] Fig. 34.* 21. Oct.

[154] Fig. 35.* 9. Nov.

[155] Fig. 36.* 27. Nov.

[156] Fig. 37.* 16. Dec.

[157] Fig. 38.* 18. Ian. 1657.

[158] Fig. 39.* 29. Mart.

[159] Fig. 40.* 30. Mart.

[160] Fig. 41.* 18. Maii.

[161] Fig. 42.* 19. Maii.

[162] Fig. 43.* 17. Dec.

[163] Fig. 44.* 18. Dec.

[164] Fig. 45.* 27. Dec.

[165] Fig. 46.* 11. Mart 1658.

[166] Fig. 47.* 16. Mart.

[167] Fig. 48.* 23. Mart.

[168] Fig. 49.* 3. Apr.

[169] Fig. 50.* 10. Nov.

[170] Fig. 51.* 16. Ian. 1659.

142415

VERA
CIRCULI ET HYPERBOLÆ
QUADRATURA.

Sit circuli, ellipſeos vel hyperbolæ ſegmentum B I P
11TAB. XLIII.
Fig. 1. 2. 3. cujus centrum A: compleatur triangulum A B P, &
ſegmentum in punctis, B, P, tangentes ducantur re-
ctæ B F, P F, ſe invicem ſecantes in puncto F; pro-
ducatur (ſi opus ſit) recta A F ſegmentum interſecans in
puncto I & rectam B P in puncto Q; deinde jungantur re-
ctæ B I, P I.

PROP. I. THEOREMA.

Dico trapezium B A P I eſſe medium propor-
tionale inter trapezium B A P F, &
triangulum B A P.

Quoniam recta A Q ducitur per F concurſum duarum re-
ctarum F B, F P, ſegmentum in punctis B, P, tan-
gentium; igitur recta A Q rectam B P contactuum
puncta jungentem bifariam ſecabit in puncto Q; & proinde
triangulum A B Q eſt æquale triangulo A Q P, & trian-
gnlum F B Q triangulo F Q P; & igitur triangulum A B F
æquale eſt triangulo A P F; eſt ergo triangulum A B F di-
midium trapezii A B F P: eodem modo probatur triangu-
lum A B I eſſe dimidium trapezii A B I P; & triangulum
A B Q eſt dimidium trianguli A B P: cumque triangula
A B F, A B I, A B Q, eandem habeant altitudinem, in-
ter ſe ſunt ut baſes, ſed eorum baſes nempe A F, A I, A Q,
ſunt continuè proportionales; & igitur ipſa quoque triangu-
la ſunt continuè proportionalia; & proinde eorum dupla ni-
mirum trapezia A B F P, A B I P, & triangulum A B P
ſunt continuè proportionalia in ratione A F ad A I, quod
demonſtrare oportuit.

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