Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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xml:space
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xml:space
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121.</
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AMO talis, ut in recta AV utcunque ſumptâ AP, quæ arcum BE
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adæquet, erectáque PM ad AV normali, ſit PM æqualis arcûs BE
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tangenti BG.</
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</
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<
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<
s
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xml:space
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">Sumpto arcu BF = AQ: </
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<
s
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xml:space
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">& </
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<
s
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xml:space
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">ductâ CFH; </
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<
s
xml:id
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xml:space
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">demiſſis EK, FL
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ad CB normalibus; </
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>
<
s
xml:id
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xml:space
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">nominentur CB = _r_. </
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<
s
xml:id
="
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xml:space
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">CK = _f_: </
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<
s
xml:id
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xml:space
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">KE = _g_.
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</
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<
s
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">Et quoniam eſt CE. </
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<
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xml:space
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<
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">vel CE. </
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<
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xml:space
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LK; </
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<
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">hoc eſt _r_. </
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<
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xml:space
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<
s
xml:id
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xml:space
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">: _e_. </
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<
s
xml:id
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xml:space
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">{_ge_/_r_} = LK; </
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<
s
xml:id
="
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xml:space
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">erit CL = _f_ + {_ge_.</
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<
s
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xml:space
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">/_r_} Et LF
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= √ _rr_ - _ff_ - {2 _fge_/_r_} = √ _gg_ - {2 _fge_.</
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<
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xml:space
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</
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<
s
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">Eſt autem CL. </
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">: (CB. </
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s
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<
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xml:space
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">hoc eſt,
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_f_ + {_ge_.</
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<
s
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xml:space
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">/_r_} √ _gg_ - {2 _fge_/_r_}:</
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<
s
xml:id
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xml:space
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">: _r_. </
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<
s
xml:id
="
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">_m_ - _a_. </
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<
s
xml:id
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xml:space
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">vel (quadrando) _ff_ +
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{2 _fge._</
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<
s
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xml:space
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">/_r_} _gg_ - {2 _fge_/_r_}:</
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<
s
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xml:space
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<
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">_mm_ - 2 _ma_. </
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<
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xml:space
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">Unde (dimiſſis quæ
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oportet) obtinetur æquatio, _rfma_ = _grre_ + _gmme_. </
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<
s
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ſubſtituendo, eſt _rfmm_ = _grrt_ + _gmmt_. </
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s
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xml:space
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">vel {_rfmm_/_grr_ + _gmm_} = _t_.
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<
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xml:space
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">ſeu (quoniam eſt _m_ = {_rg_/_f_}) erit _t_ = {_rr_/_rr_ + _mm_} _m_ = {CB_q_/CG_q_} BG =
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{CK_q_/CE_q_} BG.</
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<
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">Hæc ſufficere videntur huic methodo elucidandæ.</
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