Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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xml:space
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xml:space
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">1. </
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<
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xml:space
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">Si in AD (ad ipſam AB perpendiculari) deſumatur AE = _n_;
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xml:space
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">Fig. 208.</
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& </
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<
s
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xml:space
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">ducatur EF ad AB parallela, hujuſce cum lineis expoſitis interſe-
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ctiones exhibebunt radices _a_ reſpectivè.</
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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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">2. </
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<
s
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xml:space
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">Cum ad haſce curvas ordinatæ ſemper terminatæ ſint, & </
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<
s
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xml:space
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">inter
<
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ipſas maxima quædam detur, hujus _ſeriei æquationes_, pro modulo aſ-
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ſignatæ AE (vel _n_) ſubinde duas radices veras habent (cùm utique
<
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fuerit AE curvæ maximâ ordinatâ minor reſpectivè, hoc eſt cùm EF
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curvæ bis occurrerit) nonnunquam duntaxat unam (cum AE nempe
<
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maximam adæquet, adeóque EF curvam contingat) aliquando nullam
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(cum ſcilicet AE maximam excedat, adeoque nec EF curvæ unquam
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occurrat).</
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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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">3. </
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<
s
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xml:space
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">In ſecundo gradu ſi AO = OB, & </
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>
<
s
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xml:space
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">ordinetur OT, erit OT
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maxima; </
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<
s
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xml:space
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">(adeóque radicum una major quàm {AB/2}, altera minor) in
<
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tertio, ſi AP = 2 PB, & </
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<
s
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xml:space
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">ordinetur PV, erit PV maxima (unde
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radicum una major erit quàm {1/3} AB, altera minor) demùm in quar-
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to gradu ſi AQ = 3 QB, & </
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>
<
s
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="
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xml:space
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preserve
">ordinetur QX, erit QX _maxima_
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(& </
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>
<
s
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xml:space
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">hinc una radicum ſemper major, quàm {1/4} AB, & </
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<
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xml:space
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">altera minor).</
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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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">4. </
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<
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xml:space
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">Hinc conſectatur, ſi fuerit, in ſecundo gradu n &</
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<
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">gt; </
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<
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">{_b_/2}; </
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<
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xml:space
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">in tertio
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_n_
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&</
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<
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">gt;</
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<
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xml:space
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">{4_b_
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/9} - {8_b_
<
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">3</
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>
/27
<
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} = {4 _b_
<
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/27}; </
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>
<
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="
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xml:space
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">in quarto _n_
<
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style
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&</
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<
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">gt;</
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>
<
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xml:space
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">{27/64}_b_
<
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style
="
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- {81/256}_b_
<
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">4</
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=
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{27_b_
<
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="
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/256}; </
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<
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">nullam dari radicem.</
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</
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<
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<
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xml:space
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">5. </
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<
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xml:space
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">Omnium radicum _maxima_ eſt ipſa AB, vel _b_.</
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<
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">6. </
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<
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">Omnium curvarum communis _interſectio_ (ſeu _nodus_) eſt pun-
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ctum T; </
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">& </
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<
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">ſi fuerit _n_ = {_b_/2}; </
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<
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">ſemper AO (vel {_b_/2}) eſt una radix.</
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<
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">7. </
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<
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xml:space
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">Curva ALB eſt _Circulus_, reliquæ AMB, ANB eum quo-
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dammodo referunt.</
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1. # 2. # 3.
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_a_ + _b_ = _n_ \\ _a_ + _b_ = {_nn_/_a_} \\ _a_ + _b_ = {_n_
<
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/_aa_} \\ _a_ + _b_ = {_n_4
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/_a_
<
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} # _a_ - _b_ = _n_. \\ _a_ - _b_ = {_nn_/_a_} \\ _a_ - _b_ = {_n_
<
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/_aa_} \\ _a_ - _b_ = {_n_
<
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/_a_
<
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3} # {_b_ - _a_ = _n_. \\ _b_ - _a_ = {_nn_/_a_} \\ _b_ - _a_ = {_n_
<
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/aa} \\ _b_ - _a_ = {_n_
<
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/_a_
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}
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