Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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rectam AP ſecare ad T; </
s
>
<
s
xml:id
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xml:space
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">ut ipſius jam rectæ PT quantitatem exqui-
<
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<
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note-0259-01
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xlink:href
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xml:space
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">Fig. 115.</
note
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ram; </
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<
s
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xml:space
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">curvæ arcum MN indefinitè parvum ſtatuo; </
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<
s
xml:id
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echoid-s12213
"
xml:space
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">tum duco rectas
<
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NQ ad MP, & </
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>
<
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xml:id
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echoid-s12214
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xml:space
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">NR ad AP parallelas; </
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>
<
s
xml:id
="
echoid-s12215
"
xml:space
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">nomino MP = _m_; </
s
>
<
s
xml:id
="
echoid-s12216
"
xml:space
="
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">PT
<
lb
/>
= _t_; </
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<
s
xml:id
="
echoid-s12217
"
xml:space
="
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">MR = _a_; </
s
>
<
s
xml:id
="
echoid-s12218
"
xml:space
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">NR = _e_; </
s
>
<
s
xml:id
="
echoid-s12219
"
xml:space
="
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">reliquáſque rectas, ex ſpeciali curvæ
<
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/>
natura determinatas, utiles propoſito, nominibus deſigno; </
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>
<
s
xml:id
="
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xml:space
="
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">ipſas au-
<
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tem MR, NR (& </
s
>
<
s
xml:id
="
echoid-s12221
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xml:space
="
preserve
">mediantibus illis ipſas MP, PT) per _æquationem_
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è Calculo deprehenſam inter ſe comparo; </
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<
s
xml:id
="
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xml:space
="
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">regulas interim has obſer-
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vans. </
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<
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">1. </
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<
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xml:space
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">Inter computandum omnes abjicio terminos, in quibus
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ipſarum _a_, vel _e_ poteſtas habetur, vel in quibus ipſæ ducuntur in ſe
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(etenim iſti termini nihil valebunt).</
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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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<
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xml:space
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">Poſt _æquationem constitutam_, omnes abjicio terminos, literis
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conftantes quantitates notas, ſeu determinatas deſignantibus; </
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<
s
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="
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xml:space
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">aut in
<
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quibus non habentur _a_, vel _e_. </
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>
<
s
xml:id
="
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xml:space
="
preserve
">(etenim illi termini ſemper, ad unam
<
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æquationis partem adducti, nihilum adæquabunt).</
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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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">3. </
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<
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xml:space
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">Pro _a_ ipſam _m_; </
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<
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xml:space
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">(vel MP) pro _e_ ipſam _t_ (vel PT) ſubſtituo.
<
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</
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<
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xml:space
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">Hinc demùm ipſius PT quantitas dignoſcetur.</
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</
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<
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<
s
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xml:space
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">Quòd ſi calculum ingrediatur curvæ cujuſpiam indefinita particula;
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</
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<
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xml:space
="
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">ſubſtituatur ejus loco tangentis particula ritè ſumpta; </
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>
<
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xml:id
="
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xml:space
="
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">vel ei quævis
<
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(ob indefinitam curvæ parvitatem) æquipollens recta.</
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>
<
s
xml:id
="
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xml:space
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"/>
</
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<
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<
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xml:space
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">Hæc autem è ſubnexis Exemplis clariùs eluceſcent.</
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<
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</
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</
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<
head
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">Exemp. I.</
head
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<
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">Angulus ABH rectus ſit; </
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<
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">& </
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<
s
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">ſit curva AMO talis, ut per A du-
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ctâ utcunque rectâ AK, quæ rectam BH ſecet in K, curvam AMO
<
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<
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xlink:label
="
note-0259-02
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xlink:href
="
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">Fig. 116.</
note
>
in M, ſit ſemper ſubtenſa AM æqualis abſciſſæ BK; </
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<
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M tangens eſt deſignanda.</
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</
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<
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">Fiant quæ ſuprà præſcripta ſunt, & </
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<
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xml:space
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">(ductâ ANL) nominetur
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AB = _r_; </
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<
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xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s12250
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xml:space
="
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">AP = _q_; </
s
>
<
s
xml:id
="
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xml:space
="
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">unde AQ = _q_ - _e_; </
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>
<
s
xml:id
="
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xml:space
="
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">item QN = _m_ -
<
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/>
_a_. </
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<
s
xml:id
="
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xml:space
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">ergò eſt _qq_ + _ee_ - 2 _qe_ + _mm_ + _aa_ - 2 _ma_ = (AQq
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+ QNq = ANq = ) BLq; </
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<
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xml:space
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">hoc eſt (rejectis, uti monitum eſt,
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rejiciendis) _qq_ - 2 _qe_ + _mm_ - 2 _ma_ = BLq. </
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<
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xml:space
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">Porrò eſt
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AQ. </
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<
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<
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<
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<
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<
s
xml:id
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xml:space
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">BL =
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{_rm_ - _ra_.</
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<
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xml:id
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xml:space
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">/_q_ - _e_} quare {_rrmm_ + _rraa_ - 2 _rrma_/_qq_ + _ee_ - 2 _qe_.</
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<
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xml:id
="
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xml:space
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<
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<
unsure
/>
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(rejectis ſuperfluis) {_rrmm_ - 2 _rrma_/_qq_ - 2 _qe@_} = BLq = _qq_ - 2 _qe_ +
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_mm_ - 2 _ma_. </
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<
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xml:id
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xml:space
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">vel _rrmm_ - 2 _rrma_ = _q_
<
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- 2 _q_
<
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>
_e_ + _qqmm_ - 2 _qqma_ - 2 _q_
<
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="
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>
_e_ +
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4 _qqee_ - 2 _qmme_ + 4 _qmae_; </
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<
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