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.

26976 ſit ſemper HK = HT; tum curvam TKF tangat recta FS in F; 1117. Lect.
VIII. hæc curvam AIF quoque continget.

Eſt enim GK = GH + HK = GH + HT GA = GI. 2222. Lect.
VII. quare punctum K extra curvam AIF jacet; adeóque recta FS cur-
vam AIF continget.

IV. Quòd ſi recta EF ad arcum AE eandem aliquamcunque ſtatu-
atur habere proportionem, tangens ejus facilè determinatur ex hac, &
octava octavæ Lectionis.

V. Sint recta AP, duæque _curvæ_ AEG, AFI, ità ad ſe relatæ
33Fig. 106. ut ductâ utcunque rectâ DEF (quæ rectam AP, curvas AEG,
AFI punctis D, E, F, ſecet) ſit ſemper recta DT æqualis arcui AE;
tangat autem recta ET curvam AEG ad E; ſumatúrque ET par
arcui EA; & ſit TR ad BA parallela; connectatur denuò recta RF;
hæc curvam AFI tanget.

Concipiatur enim curva LFL talis; ut ductâ quâcunque rectâ PL
4422. Lect.
VII. ad AB parallelâ (quæ curvam AEG in G, rectam TE in H, cur-
5526. Lect.
VI. vam LFL in L ſecet) ſit perpetuò recta PL æqualis ipſis TH, HG
ſimul; eſt itaque PL & gt; arc. AEG * = PI. Unde curva 66Hyp. curvam AFI tangit. Item recta IK æquatur rectæ TH; 773 Lect.
VIII. adeóque curva LFL rectam RFK tangit; quare curvam 882. Lect.
VIII. tanget recta.

VI. Etiam ſi rectæ DE ad arcus AE quamlibet ſemper eandem ra-
tionem habeant, recta RF nihilominus curvam AFI tanget, ut
ex hac, & ſexta octavæ Lectionis facilè patet.

VII. Sit punctum D; duæque curvæ AGE, DIF itâ verſus ſe
99Fig. 107. relatæ ſint, ut à puncto D projectâ quâvis rectâ DFE, ſit perpetuò
recta DF æqualis arcui AE; tangat autem recta ET curvam AGE
ad E; deſignanda jam eſt recta, quæ curvam DIF tangat (ad F).

Sumatur ET par _arcui_ FS; concipiatúrque _carva_ DKK talis, ut
à D projectâ utcunque rectâ DH (quæ curvam DKK in K, rectam
101016. Lect.
VIII. TE in H ſecet) ſit perpetuò DK = TH; tum curvam DKK tangat recta FS ad F; hæc curvam DIF quoque tanget.

Intelligatur enim _curva_ LFL talis, ut à D projectâ quapiam rectâ
111122. Lect.
VII. DH (quæ rectam TE ſecet in H, curvam LFL in L) ſit ſemper
1212Hyp. DL = TH + HG; eſt itaque DL & gt; are. AG = 13134. Lect.
VIII. itaque curvæ DIF, LFL ſeſe contingent, item curvæ

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