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

[Item 1.]

[2.] Imprimatur,

[3.] LECTIONES _OPTICÆ & GEOMETRICÆ:_ In quibus PHÆNOMENωN OPTICORUM Genuinæ _Rationes_ inveſtigantur, ac exponuntur: ET _Generalia_ Curvarum Linearum _Symptomata declarantur_. Auctore Isaaco Barrow, Collegii _S S. Trinitatis_ in Academia _Cantab._ Præfecto, Et _SOCIETATIS REGIÆ_ Sodale.

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[4.] LONDINI, Typis _Guilielmi Godbid_, & proſtant venales apud _Robertum Scott_, in vico Little-Britain. 1674.

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[5.] SPECTATISSIMIS VIRIS Roberto Raworth & Thomæ Buck ARMIGERIS;

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[6.] Iſaac Barrow

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[7.] Epistola ad LECTOREM.

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[8.] Epiſtola; in qua Operis hujus Argumen-tum, & ſcopus brevitèr exponuntur.

[9.] Lect. I.

[10.] Lect. II.

[11.] Lect. III.

[12.] _Corol_. 1. Ang. _a_ BG. ang. _a_ BP > ang. δ BH. ang. δ BP. 2. Ang. _a_ BG. ang. PBG > ang. δ BH. PBH.

[13.] Lect. IV.

[14.] Lect.V.

[15.] Lect. VI.

[16.] Lect. VI I.

[17.] Lect. VIII.

[18.] Lect. IX.

[19.] Lect. X.

[20.] Lect. XIV.

[21.] Lect. XV.

[22.] APPENDICVLA.

[23.] Lect. XVI.

[24.] Lect. XVII.

[25.] Lect. XVIII.

[26.] ERRATA.

[27.] Benevolo Lectori.

[28.] Lectio I.

[29.] Lect. II.

[30.] Lect. III.

137119

AV. TV : : CV. CD; & conſequentes ſubduplandò, dividendó-
que AK. KV : : KV. KD : : KV. CK. vel AK. KH : : KH. CK;
hoc eſt HN (KX). NG : : KH. CK; quare CK x KX = KH
x NG. eſt autem XZq = CZq - CXq = XGq - CXq =
NGq + KHq - 2 NG x KH: - KXq - CKq + 2 CK
x KX = NGq + KHq - KXq - CKq. Sumatur K ζ = KX,
diſcurſúmque ſimilem adhibendo liquebit fore ξζ = XZ; & ideo
Dζ = CZ. unde Cζ - Dζ (DZ - CZ) = Cζ - CZ =
ξγ - XG = 2 KH = TV. quare manifeſtum eſt _cnrvas_ TZ,
Vζ eſſe _Hyperbolas,_ quarum axis TV, foci C,D.

IV. Tertiò demùm, ſit angulus CAE ſemirectus (vel CA =
11Fig. 192. CE) erit tum punctum Z ad parabolam; quæ itidem ita determina-
tur. Fiat angulus ACP ſemirectus, & ab ipſarum AE, CP in-
terſectione R ducatur RT ad CE parallela; erit T_Vertex_, atque C
_Focus Parabolæ._ id quod ex bene nota ſectionis hujus proprietate con-
ſtat; qua ſcilicet eſt TA = TR = TC (ob angulos TAR,
TCR ſemirectos) & AX = XG = CZ.

V. Manifeſtum eſt verò rectam AE ſectiones has ad E contingere.
quia nempe perpetuò major eſt CZ (vel XG) ordinatâ XZ; adeó-
que puncta G extra cuŕvas unaquæque jacent hoc eſt tota AG extra
illas cadit.

VI. Hiſce præſtratis: _Eſto Circulare ſpeculum_ MBND, cen-
22Fig. 193. trum habens C; cui exponatur recta quæpiam F α G; & huic per-
pendicularis ſit recta C α; quam ad parte@ averſas ſumpta CA, ad-
æquet. Sit etiam CE ad CA perpendicularis, ac æqualis qua-
dranti diametri BD; connexáque recta AE producatur utcunque.
ſumpto jam in recta F α G puncto quolibet F, connectatur FC, &
radiationis ab F in ipſa FC limes, ſeu _focus_, ſit Z; ac per Z du-
catur ZX ad AC perpendicularis, ipſi AE occurrens in H; dico
fore XH parem ipſi CZ.

Nam (è jam antè monſtratis) eſt FC. CZ : : FM. MZ (hoc eſt)
: : FC - CB. CB - CZ. hinc erit α C. CX (AC. CX) : :
FC - CB. CB - CZ. quare (ducendo in ſe extrema, ac media)
erit AC x CB - AC x CZ = CX x FC - CX x CB. hoc
eſt (ipſi CX x FC ſubſtituendo AC x CZ, propter α C. CX : :
FC. CZ) erit AC x CB - AC x CZ = AC x CZ - CX x
CB. tranſponendóque AC x CB + CX x CB = 2 AC x CZ.

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