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

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24956
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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