Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

[31.] Lect. IV.

Page: 222 (29)

[32.] Lect. VII.

[33.] Lect. VIII.

[34.] Lect. IX.

[35.] Lect. X.

[36.] Exemp. I.

[37.] _Exemp_. II.

[38.] _Exemp_. III

[39.] Exemp. IV.

[40.] Eæemp. V.

[41.] Lect. XI.

[42.] APPENDICUL A.

[43.] Lect. XII.

[44.] APPENDICULA 1.

[45.] Præparatio Communis.

Page: 303 (110)

[46.] APPENDICULA 2.

Page: 308 (115)

[47.] Conicorum Superſicies dimetiendi Metbodus.

[48.] Exemplum.

[49.] Prop. 1.

[50.] Prop. 2.

[51.] Prop. 3.

[52.] Prop. 4.

[53.] APPENDICULA 3.

[54.] Problema I.

[55.] Exemp. I.

[56.] Exemp. II.

[57.] Probl. II.

[58.] Exemp. I.

[59.] _Exemp_. II.

[60.] _Probl_. III.

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APPENDICULA 1.

HIc demùm etſi præter inſtitutum ſit particularia nunc attingere;
qualibus ſanè, hæc generalia conſequentibus, admodum pro-
clive foret turgidum Volumen compingere (_amico tamen morem ge-_
_rens operâ_ dignum cenſenti) ſubtexam ad _Circuli Tangentes Secantéſq_;
ſpectantia nonnulla, pleraque de ſuprà poſitis emergentia.

Præparatio Communis.

11Fig. 166.

Eſto _cirtuli Quadrans_ ACB, quam tangant rectæ AH, BG; &
in productis HA, AC ſumantur AK, CE ſingulæ pares _radio_ CA;
& _aſymptotis_ AC, CZ per K deſcripta ſit _Hyperbola_ KZZ; _aſymp-_
_totis_ BC, BG per E _byperbola_ LEO. Sumatur etiam in arcu AB
22Fig. 167. _punctum arbitrarium_ M, per quod ducantur recta CMS (tangenti
AH occurrens in S) recta MT circulum tangens; recta MFZ ad
BC parallela, recta MPL ad AC parallela. Sit denuò recta α β æ-
qualis _arcui_ AB, & α μ arcui AM; & rectæ α γ, ξ μ π ψ rectæ α β
perpendiculares; quarum α γ = AC; μξ = AS; μψ = CS; μπ
= MP.

I. Recta CS æquatur rectæ FZ; adeoque _ſumma ſecantium ad_
_arcum_ AM pertinentium, & ad rectam AC applicatarum æquatur
_ſpatio byperbolico_ AF ZK.

Eſt enim CF. CA: : (CM. CS: :) CA. CS. adeòque CF
x CS = CAq. item CF x FZ = CA x AK = CAq. ergo CS = FZ.

II. _Spatium_ αμξ (hoc eſt _Smmma tangentium in arcu_ AM ad re-
33Fig. 167. ctam αμ applicatarum) æquatur _ſpatio byperbolico_ AFZK.

Patet ex hujuſce Lectionis 9.

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