Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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abjicienda) - 2 _rrma_ = - 4 _q_
<
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_e_ - 2 _qqma_ - 2 _qmme_. </
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<
s
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echoid-s12268
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xml:space
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">vel
<
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_rrma_ - qq_ma_ = 2 _q_
<
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>
_e_ + _qmme_; </
s
>
<
s
xml:id
="
echoid-s12269
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xml:space
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preserve
">vel denuò ſubſtituendo _m_
<
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pro _a_, & </
s
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<
s
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="
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xml:space
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">_t_ pro _e_, eſt _rrmm_ - _qqmm_ = 2 _q_
<
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style
="
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>
_t_ - _qmmt_; </
s
>
<
s
xml:id
="
echoid-s12271
"
xml:space
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preserve
">vel
<
lb
/>
{_rrmm_ - qq_mm_/2 q
<
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style
="
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">3</
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>
- q_mm_} = _t_ = PT.</
s
>
<
s
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echoid-s12272
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xml:space
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</
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</
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<
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<
head
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xml:space
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">_Exemp_. II.</
head
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<
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<
s
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echoid-s12273
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xml:space
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">Sit recta EA (poſitione ac magnitudine data) & </
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<
s
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echoid-s12274
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">curva EMO
<
lb
/>
proprietate talis, ut ab ea utcunque ductâ rectâ MP ad EA perpen-
<
lb
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<
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xlink:label
="
note-0260-01
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xlink:href
="
note-0260-01a
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xml:space
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">Fig. 117.</
note
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diculari _Summa Cuborum_ ex AP, & </
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<
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">MP æquetur _Cubo_ rectæ AE.</
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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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">Nominentur AE = _r_; </
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<
s
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xml:space
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">AP = _f_; </
s
>
<
s
xml:id
="
echoid-s12279
"
xml:space
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">unde AQ = _f_ + _e_; </
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>
<
s
xml:id
="
echoid-s12280
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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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">AQ
<
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cub. </
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>
<
s
xml:id
="
echoid-s12282
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xml:space
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">= _f_
<
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="
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">3</
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>
+ 3 _ffe_ + 3 _fee_ + _e_
<
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="
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">3</
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>
; </
s
>
<
s
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echoid-s12283
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xml:space
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preserve
">(ſeu abjectis ſuperfluis, ex præ-
<
lb
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ſcripto) = _f_
<
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style
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">3</
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>
+ 3 _ffe_. </
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>
<
s
xml:id
="
echoid-s12284
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xml:space
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">Item NQ cub. </
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<
s
xml:id
="
echoid-s12285
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xml:space
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">= cub. </
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<
s
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xml:space
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">_m_ - _a_ = _m_
<
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">3</
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>
-
<
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3 _mma_ + 3 _maa_ - _a_
<
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="
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">3</
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>
(hoc eſt) = _m_
<
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>
- 3 _mma_. </
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>
<
s
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xml:space
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">Quapropter
<
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eſt _f_
<
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="
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">3</
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>
+ 3 _ffe_ + _m_
<
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style
="
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">3</
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>
- 3 _mma_ = (AQ cub. </
s
>
<
s
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="
echoid-s12288
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xml:space
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">+ NQ cub. </
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>
<
s
xml:id
="
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xml:space
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">=
<
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AE cub. </
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>
<
s
xml:id
="
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xml:space
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">= ) _r_
<
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="
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>
. </
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<
s
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xml:space
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">abjectíſque datis, eſt 3 _ffe_ = 3 _mma_ = _o_.
<
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</
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<
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xml:space
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">ſeu, _ffe_ = _mma_; </
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<
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xml:space
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">ſubrogatíſque loco _a_, & </
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<
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">_e_ ipſis _m_, & </
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<
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xml:space
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">_t_, erit
<
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_fft_ = _m_
<
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; </
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<
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xml:space
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">ſeu _t_ = {_m_
<
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/_ff_}; </
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<
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xml:space
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">eſt ergò PT quarta proportionalis in ratio-
<
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ne AP ad PM continuata.</
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</
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<
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<
s
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">Similiter, Si fuerit APqq + MPqq = AEqq; </
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>
<
s
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">reperietur
<
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/>
fore PT = {_m_
<
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>
/_f_
<
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>
}; </
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<
s
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xml:space
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">vel PM quarta proportionalis in ratione AP ad
<
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PM; </
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<
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">ac ità porrò quod de _Cycloformibus_ iſtis lineis an obſervatu
<
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dignum ſit neſcio.</
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<
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</
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</
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<
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">_Exemp_. III</
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<
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<
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">Poſitione data ſit recta AZ, & </
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">AX magnitudine; </
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<
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">ſit etiam _curva_
<
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AMO talis, ut ductâ utcunque rectâ MP ad AZ normali, ſit AP
<
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<
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="
note-0260-02
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note-0260-02a
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">Fig. 118.
<
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_La Galande_</
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_cub._ </
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<
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">+ PM _cub_. </
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<
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">= AX x AP x PM.</
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<
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</
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<
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<
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">Dicantur AX = _b_; </
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<
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">& </
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<
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xml:id
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">AP = _f_; </
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<
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">ergò AQ = _f_ - _e_; </
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<
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xml:id
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">AQ
<
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_cub_. </
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>
<
s
xml:id
="
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xml:space
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">= _f_
<
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- 3 _ffe_; </
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<
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xml:space
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">& </
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<
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xml:id
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">QN _cub._ </
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>
<
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xml:id
="
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xml:space
="
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">= _m_
<
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="
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>
- 3 _mma_. </
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>
<
s
xml:id
="
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xml:space
="
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">& </
s
>
<
s
xml:id
="
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"
xml:space
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">AQ x
<
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/>
QN = _fm_ - _fa_ - _me_ + _ae_ = _fm_ - _fa_ - _me_; </
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>
<
s
xml:id
="
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"
xml:space
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">unde AX x
<
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/>
AQ x QN = _bfm_ - _bfa_ - _bme_; </
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>
<
s
xml:id
="
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xml:space
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">hinc æquatio _f_ - 3 _ffe_
<
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/>
+ _m_
<
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="
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">3</
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>
- 3 _mma_ = _bfm_ - _bfa_ - _bme_; </
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>
<
s
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">ſeu amoliendo </
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