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rectam AP ſecare ad T;
ut ipſius jam rectæ PT quantitatem exqui-
11Fig. 115. ram; curvæ arcum MN indefinitè parvum ſtatuo; tum duco rectas
NQ ad MP, & NR ad AP parallelas; nomino MP = _m_; PT
= _t_; MR = _a_; NR = _e_; reliquáſque rectas, ex ſpeciali curvæ
natura determinatas, utiles propoſito, nominibus deſigno; ipſas au-
tem MR, NR (& mediantibus illis ipſas MP, PT) per _æquationem_
è Calculo deprehenſam inter ſe comparo; regulas interim has obſer-
vans. 1. Inter computandum omnes abjicio terminos, in quibus
ipſarum _a_, vel _e_ poteſtas habetur, vel in quibus ipſæ ducuntur in ſe
(etenim iſti termini nihil valebunt).
11Fig. 115. ram; curvæ arcum MN indefinitè parvum ſtatuo; tum duco rectas
NQ ad MP, & NR ad AP parallelas; nomino MP = _m_; PT
= _t_; MR = _a_; NR = _e_; reliquáſque rectas, ex ſpeciali curvæ
natura determinatas, utiles propoſito, nominibus deſigno; ipſas au-
tem MR, NR (& mediantibus illis ipſas MP, PT) per _æquationem_
è Calculo deprehenſam inter ſe comparo; regulas interim has obſer-
vans. 1. Inter computandum omnes abjicio terminos, in quibus
ipſarum _a_, vel _e_ poteſtas habetur, vel in quibus ipſæ ducuntur in ſe
(etenim iſti termini nihil valebunt).
2.
Poſt _æquationem constitutam_, omnes abjicio terminos, literis
conftantes quantitates notas, ſeu determinatas deſignantibus; aut in
quibus non habentur _a_, vel _e_. (etenim illi termini ſemper, ad unam
æquationis partem adducti, nihilum adæquabunt).
conftantes quantitates notas, ſeu determinatas deſignantibus; aut in
quibus non habentur _a_, vel _e_. (etenim illi termini ſemper, ad unam
æquationis partem adducti, nihilum adæquabunt).
3.
Pro _a_ ipſam _m_;
(vel MP) pro _e_ ipſam _t_ (vel PT) ſubſtituo.
Hinc demùm ipſius PT quantitas dignoſcetur.
Hinc demùm ipſius PT quantitas dignoſcetur.
Quòd ſi calculum ingrediatur curvæ cujuſpiam indefinita particula;
ſubſtituatur ejus loco tangentis particula ritè ſumpta; vel ei quævis
(ob indefinitam curvæ parvitatem) æquipollens recta.
ſubſtituatur ejus loco tangentis particula ritè ſumpta; vel ei quævis
(ob indefinitam curvæ parvitatem) æquipollens recta.
Hæc autem è ſubnexis Exemplis clariùs eluceſcent.
Exemp. I.
Angulus ABH rectus ſit;
&
ſit curva AMO talis, ut per A du-
ctâ utcunque rectâ AK, quæ rectam BH ſecet in K, curvam AMO
22Fig. 116. in M, ſit ſemper ſubtenſa AM æqualis abſciſſæ BK; hujus curvæ ad
M tangens eſt deſignanda.
ctâ utcunque rectâ AK, quæ rectam BH ſecet in K, curvam AMO
22Fig. 116. in M, ſit ſemper ſubtenſa AM æqualis abſciſſæ BK; hujus curvæ ad
M tangens eſt deſignanda.
Fiant quæ ſuprà præſcripta ſunt, &
(ductâ ANL) nominetur
AB = _r_; & AP = _q_; unde AQ = _q_ - _e_; item QN = _m_ -
_a_. ergò eſt _qq_ + _ee_ - 2 _qe_ + _mm_ + _aa_ - 2 _ma_ = (AQq
+ QNq = ANq = ) BLq; hoc eſt (rejectis, uti monitum eſt,
rejiciendis) _qq_ - 2 _qe_ + _mm_ - 2 _ma_ = BLq. Porrò eſt
AQ. QN: : AB. BL; hoc eſt _q_ - _e. m_ - _a_: : _r._ BL =
{_rm_ - _ra_. /_q_ - _e_} quare {_rrmm_ + _rraa_ - 2 _rrma_/_qq_ + _ee_ - 2 _qe_. } = BLq; ſeu
(rejectis ſuperfluis) {_rrmm_ - 2 _rrma_/_qq_ - 2 _qe@_} = BLq = _qq_ - 2 _qe_ +
_mm_ - 2 _ma_. vel _rrmm_ - 2 _rrma_ = _q_4 - 2 _q_3_e_ + _qqmm_ - 2 _qqma_ - 2 _q_3_e_ +
4 _qqee_ - 2 _qmme_ + 4 _qmae_; hoc eſt (abjectis iis, quæ
AB = _r_; & AP = _q_; unde AQ = _q_ - _e_; item QN = _m_ -
_a_. ergò eſt _qq_ + _ee_ - 2 _qe_ + _mm_ + _aa_ - 2 _ma_ = (AQq
+ QNq = ANq = ) BLq; hoc eſt (rejectis, uti monitum eſt,
rejiciendis) _qq_ - 2 _qe_ + _mm_ - 2 _ma_ = BLq. Porrò eſt
AQ. QN: : AB. BL; hoc eſt _q_ - _e. m_ - _a_: : _r._ BL =
{_rm_ - _ra_. /_q_ - _e_} quare {_rrmm_ + _rraa_ - 2 _rrma_/_qq_ + _ee_ - 2 _qe_. } = BLq; ſeu
(rejectis ſuperfluis) {_rrmm_ - 2 _rrma_/_qq_ - 2 _qe@_} = BLq = _qq_ - 2 _qe_ +
_mm_ - 2 _ma_. vel _rrmm_ - 2 _rrma_ = _q_4 - 2 _q_3_e_ + _qqmm_ - 2 _qqma_ - 2 _q_3_e_ +
4 _qqee_ - 2 _qmme_ + 4 _qmae_; hoc eſt (abjectis iis, quæ
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