Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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27683 ctanea, _bfa_ - 3 _mma_ = 3 _ffe_ - _bme_; ſubſtituendóque _bfm_ -
3 _m_3 = 3 _fft_ - _bmt_; ſeu, {_bfm_ - 3 _m_3/3 _ff_ - _bm_} = _t_.

Exemp. IV.

Sit _Quadratrix_ CMV (ad circulum CEB pertinens cui centrum
A,) cujus axis VA; ordinatæ CA. MP ad VA perpendicula-
res.

Protractis rectis AME, ANF, ductíſque rectis EK, FL ad AB
11Fig. 119. perpendicularibus, dicantur arcus CB = _p_; radius AC = _r_; recta
AP = _f_; AM = _k_. Eſtque jam CA arc. CB: : NR. arc. FE.
hoc eſt, _r. p_: : _a_. {_pa_/_r_} = arc. FE. & AM. MP: : AE. EK; hoc
eſt, _k. m_: : _r_. {_rm_/_k_} = EK; item AE. EK: : arc. FE. LK. hoc
eſt, _r_. {_rm_: : _pa_/_kr_. } {_pma_/_rk_} = LK. Verùm AM. AE: : AP. AK;
hoc eſt _k_._ r_: : _f_. {_rf_/_k_} = AK. ergò {_rf_/_k_} - {_pma_/_rk_} = AL. Et{_rrff_/_kk_} -
{2 _fmpa_/_kk_} (abjectis ſuperfluis) = AL_q_; adeóque LF_q_ =
{_rrkk_ - _rrff_ + 2 _fmpa_/_kk_} = {_rrmm_ + 2 _fmpa_. /_kk_}

Eſt autem AQ_q_. QN_q_: : AL_q_. LF_q_; hoc eſt Q: _f_ - _e_.
Q: _m_ + _a_: : ALq. LFq. hoc eſt _ff_ - 2 _fe_. _mm_ + 2 _ma_: :
_rrff_ - 2 _fmpa_. _rrmm_ + 2 _fmpa_. Unde (ſublatis ex nor-
ma rejectaneis) emerget _æquatio_, _ffpa_ + _mmpa_ - _rrfa_ = _rrme_; ſeu
_kkpa_ - _rrfa_ = _rrme_; vel ſubſtituendo juxta _præſcriptum_; _kkpm_ - _rrfm_
= _rrmt_; vel {_kkp_/_rr_} - _f_ = _t_. Hinc colligitur eſſe rectam AT =
{_kk_/_rr_} _p_; hoc eſt (quoniam, ut notum eſt, AV = {_rr_/_p_}) erit AT =
{AMq/AV}; ſeu, AV. AM: : AM. AT.

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