Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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rectâ DB, ſit DB. </
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<
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<
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xml:space
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<
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xml:space
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<
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perpendicularis) tum per F, angulo BDHincluſa, tranſeat _hyperbola_
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FXX; </
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<
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">ſitque ſpatium BFXI (poſitâ nempe IX ad B
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F _parallelâ_)
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æquale duplo ſpatio ZDL; </
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<
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">ſit denuò DM = DG; </
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<
s
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">erit Min cur-
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va quæſita; </
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<
s
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xml:space
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">quam utique ſi tangat recta TM, erit TD. </
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<
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xml:space
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">DM:</
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<
s
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</
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<
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head
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">Sit rurſus ſpatium EDG (ut in præcedente) reperienda eſt curva
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AMB, ad quam ſi projiciatur recta DNM, & </
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<
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note
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dicularis, & </
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<
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<
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/DN}; </
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<
s
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xml:space
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">item acceptâ DB
<
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(cui perpendiculares DH, BF = {R
<
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/DBq}; </
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<
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">& </
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<
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">per F intra _aſymptotos_
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DB, DH deſcribatur _hyperboliformis_ ſecundi generis (in qua nempe
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ordinatæ, ceu BF, vel IX, ſint quartæ proportionales in ratione DB
<
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ad R, vel DG ad R) tum capiatur ſpatium BIXF æquale duplo
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ZDL; </
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<
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<
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gat MT, erit DT = DN.</
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<
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<
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">Fig. 189.</
note
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ductâ PM ad DB parallelâ datum ſit (ſeu expreſſum quomodocunque)
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ſpatium APM, oportet hinc ordinatam PM exhibere, vel expri-
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mere.</
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<
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">Acceptâ quâqiam R, ſit R x PZ = APM; </
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<
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AZZK; </
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<
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:</
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<
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<
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, ergo PZ = √
<
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{x
<
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style
="
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emph
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/r}; </
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<
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<
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/r}. </
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<
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:</
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<
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<
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<
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">unde AMB eſt _Parabola_, cujus _Pa-_
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rameter eſt {9/4} r.</
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