Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

oſtenſis) curva OGO _Ellipſis_, quam recta GT tangit. ergò recta
GT curvam CGD quoque tanget.

33.1.

(_a_)_Hyp_.
(_b_) 24. lect.
VI.

XVI Sit curva quæpiam AFB (cujus axis AD, & ad hunc ap-
plicata DB) ſit etiam alia curva VGC ad iſtam ſic relata, ut a deſig-
nato quodam in axe AD puncto Z ad curvam AFB utcunque ductâ
rectâ ZF, & per F ductâ rectâ EFG ad DBC parallelâ, ſit EG
æqualis ipſi ZF; ſit autem PQ perpendicularis curvæ AFB; ſu-
matúruqe QR æqualis ipſi ZE; connexa recta GR ipſi curvæ VGC
perpendicularis erit.

33.1.

Fig. 90.

Nam ducatur FT ad ipſam FQ perpendicularis, ſeu curvam AFB
tangens; & concipiatur curva OGO talis, ut ductâ quâcunq; rectâ
HKO ad EFG parallelâ ( quæ rectas TE, TF, & curvam OGO
ſecet punctis H, K, O) connexâque ZK, ſit HO = ZK; tum du-
ctâ Z I, quoniam HK & gt; HI, erit ZK & gt; ZI, vel HO & gt; HL; quare curva OGO curvam VGC tangit. Eſt autem OGO (ex oſtenſis) _Hyperbola_, cui perpendicularis eſt recta GR; eadem
itaque GR curvæ VGC quoque perpendicularis erit: Quod E. D.

33.1.

(_a_)_Hyp_.
(_b_)25 Lect. VI

XVII. Sint recta DQ, duæque curvæ DRS, DYX ità relatæ,
ut ductâ utcunque rectâ REY ad poſitione datam DB parallelâ (quæ
dictas lineas ſecet, ut perſpicis) connexâque rectâ DY, ſit ſemper
RY. DY : : DY. EY; tangat autem recta RF curvam DRS ad R; oporter curvæ DYX tangentem ad Y rectam deſignare.

33.1.

Fig. 91.

Concipiatur linea DYO talis, ut ductâ utcunque GO ad DB pa-
rallelâ ( quæ lineas FR, FP, DYO ſecet punctis G, P, O) connexâ-
que DO ſit ſemper GO. DO_:_ : DO. PO; tanget curva DYO
curvam DYX ad Y; Nam ſecet recta GO curvas DRS, DYX
punctis S, X; & connectantur rectæ DG, DS, DX; patet (è cur-
varum natura) angulos XDP, DSP; nec non angulos ODP, DGP
æquari; quare cùm angulus DSP major ſit angulo DGP; erit an-
gulus XDP angulo ODP major, adeóque PX major erit quàm PO; hinc curva DYO curvam DYX tanget ad Y; eſt autem curva DYO
_hyperbolæ_ ſuperiùs determinata; hanc tangat YS; hæc igitur curvam DYX quoque tanget.

33.1.

(_a_) Y2 Lect.
VI.

_Not_. Si curva DRS ſit circulus, & angulus QDB rectus, erit cur-
va DYX _ciſſois_ vulgaris; hujus itaque ( cum innumeris aliis ſimiliter
genitis) tangens hîc deſinitur.

XVIII. Poſitione datæ ſint rectæ DB, BK; ſitque curva DYX

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer