Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

niam jam eſt KF & lt; NF; & KE * & gt; MF; perſpicuum eſt reſtare FE & lt; NM.

32.1.

* Per
Vi. 8 Lect.
Fig. 72.
(b) _Conſtr._

Ità quidem ab una rectæ BQ parte recta BR duci poteſt, quæ mi-
nores ipſis MN intercipiat; poteſt autem ab altera parte recta quoque duci, quæ minores intercipiat ipſis F E; unde totum liquet
Propoſitum.

XX. In recta DZ ſint tria puncta D, E, F; & in F ſit vertex an-
guli rectilinei BFC, cujus latera ſecet recta DBC; per E vero
ducta ſit recta EG; poteſt ab E recta duci (ceu EH) talis, ut à
puncto D projectâ utcunque rectâ DK ſit in hac à rectis EG, EH in-
tercepta minor à rectis FC, FB interceptâ.

32.1.

Fig. 73.

Ducantur ES ad FC, & ER ad FB parallelæ; & in primo caſu,
ubi punctum E puncto D vicinius eſt, (ob ſimilitudinem triangulorum
ENM, FKI) manifeſtum eſt fore MN & lt; IK; poteſt au- tem ab E duci recta (puta EH) talis, ut interceptæ PO minores ſint
interceptis MN; ergò liquet.

32.1.

(a) _19. bujus._

In altero caſu, ubi punctum F ipſi D propius, ſumatur SL æqualis
ipſi CB; & connectatur EL; Eſtque jam IK. MN : : FK. EN : :
DF. DE : : FC. ES : : BC. RS : : LS. RS & gt; QN. MN. quapropter eſt IK & gt; QN. poteſt autem ab E recta duci, ceu E H, ſic ut ab EG, EH interceptæ OP minores ſint interceptis
QN. quamobrem abundè conſtat Propoſitum.

32.1.

Fig. 74.
(_c_) _Conſtr_.
(_d_)6. Lect. VI.

XXI Curvam BA tangat recta BO in B; ſitque recta BO æ-
qualis curvæ B A; ſumpto tunc in curva puncto quopiam K conne-
ctatur recta KO; erit KO major arcu KA.

32.1.

Fig. 75.

Nam, quoniam recta minimum eſt inter bina puncta intervallum,
eſt BK + KO & gt; BO = BK + KA. ergò KA & gt; KO.

XXII. Hinc, utcunque ſumptis (ad eaſdem contactûs partes) duobus
punctis K, L, connexâque rectâ KL; erit KL + LO & gt; KA.

Nam, ſupra contactum verſus A, eſt KL + LO & gt; KO & gt; KA.

Infra verò, eſt KL + LB & gt; KB (ex hypotheſibus _Archime-_
_dæis_) adeóque KL + LO & gt; KA.

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