Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
s
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<
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xml:space
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<
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<
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<
s
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xml:space
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">in tertio, ſi _n_
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&</
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<
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<
s
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xml:space
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">_cc_√{_cc_/3} - {_cc_/3} √ {_cc_/3} = {2/3}_cc_ √ {_cc_/3}; </
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<
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xml:space
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&</
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<
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<
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<
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; </
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<
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to ſi _n_
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&</
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<
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<
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xml:space
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">{_c_
<
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>
/4} - {_c_
<
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/16} = {3/16}_c_
<
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; </
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<
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">nulla radix habetur; </
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<
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caſibus recta EF curvas ſupergreditur; </
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<
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<
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<
s
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xml:space
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">Itidem in his omnibus maxima poſſibilis radix eſt AH = AC.</
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<
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<
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">6. </
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<
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xml:space
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">Curva CYH eſt _Circuli quadrans_, reliquæ AMH, ANH
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quodammodo κυχλο{ει}δ{ετ}ς.</
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<
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<
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">Ad ſextam ſeriem pertinentium curva HLL eſt _byperbola æqui_-
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_latera_, cujus axis AH; </
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<
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">reliquæ ſunt _Hyperboliformes_. </
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<
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xml:space
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<
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hanc ſeriem liquent cætera.</
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</
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<
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style
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<
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<
s
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xml:space
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">_a_ + _b_ + {_cc_/_a_} = _n_.</
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<
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</
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<
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<
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xml:space
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">_aa_ + _ba_ + _cc_ = _nn._</
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<
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</
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<
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<
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xml:space
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">_a_
<
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style
="
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">3</
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>
+ _baa_ + _cca_ = _n_
<
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>
.</
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<
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</
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<
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<
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xml:space
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<
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="
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+ _ba_
<
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+ _ccaa_ = _n_
<
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="
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>
, &</
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<
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.</
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</
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<
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<
s
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xml:space
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">In recta BAH indefinitè protensâ capiatur AB = _b_; </
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<
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">& </
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<
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">in AD
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<
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note
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ad BH perpendiculari ſit AC = _c_; </
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<
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<
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recti; </
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<
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">tum arbitrariè ductâ GY ad AH perpendiculari quæ ipſam
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BS ſecet in Y; </
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<
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<
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<
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xml:space
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">per K intra angulum
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DVS deſcribatur _hyperbola_ KKK; </
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<
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xml:space
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ANN tales, ut inter AG (vel GZ) & </
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<
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xml:space
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">GK ſit _media_ GL, _bime_-
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_dia_ GM, _trimedia_ GN; </
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<
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<
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xml:space
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+ _b_ + {_cc_/_a_}; </
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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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<
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xml:space
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+ _baa_
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+ _cca_; </
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<
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<
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+ _ba_
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+ _ccaa_.</
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<
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_centrum_ O, ipſam AB biſecans; </
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<
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<
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(ad AB perpendicularis, &)</
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<
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</
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<
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<
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<
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">AO, ejus axis eſt OI = √ AOq - ACq. </
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<
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verò curvæ AMM, ANN ſunt _hyperboliformes_.</
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