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

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[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.
[4.] LONDINI, Typis _Guilielmi Godbid_, & proſtant venales apud _Robertum Scott_, in vico Little-Britain. 1674.
[5.] SPECTATISSIMIS VIRIS Roberto Raworth & Thomæ Buck ARMIGERIS;
[6.] Iſaac Barrow
[7.] Epistola ad LECTOREM.
[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.
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Lect. VII.
ADhuc in _Veſtibulo_ hæremus; nec aliud quàm velitamus.
I. Sint duo quanta A, B; quorum majus A; adſumpto tertio quo-
piam X, erit A + X.
B + X & lt; A. B.
Nam ob X. A & lt; X. B; erit componendo X + A. A. & lt; X +
B.
B. vel permutando X + A. X + B & lt; A. B.
II. In linea YZ ſignentur tria puncta, L, M, N; & inter puncta
L, N ſumpto puncto quopiam E, alteróque G extra LN (verſus Z);
ſecetur EG in F, ut ſit GE. EF : : NL. LM; cadet punctum F ad
11Fig. 61. partes MZ:
Nam eſt N E. ME & gt; NL. ML : : GE. FE & gt; NE. PE. 22* I _hujus_. ergo FE & gt; ME.
III. Sint rectæ BA, DC parallelæ item rectæ BD, GP parallelæ;
pérque punctum B ducantur utcunque duæ rectæ BT, BS ipſam GP
33Fig. 62. ſecantes punctis L, K, dico fore D S.
DT : : KG. LG.
Nam eſt KG. LG = KG. GB + GB. LG = PK. PS +
PT.
PL = DB. DS + DT. DB = DT. DS.
IV. Eſto triangulum BDT, basíque DB parallelam quamvis PG
interſecent per B ductæ quæpiam duæ rectæ BS, BR punctis L, K;
dico fore LG x TD + KL x RD. KG x TD : : RD. SD.
Sumantur enim BM = GP, & BN = LP; & BO = KP;
44Fig. 63 unde conſtat junctas PM, PN, PO ipſis TB, SB, RB (reſpectivè)
parallelas eſſe.
Et quoniam eſt DM. PD : : DB. TD. erit DM x
TD = PD x Db.
Similiter eſt DN x SD = PD x DB. quare
DM x TD = DN x SD = DM x SD + MN x SD, tranſpo-
nendóque DM x TD - DM x SD = MN x SD.
Simili

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