295102
_Notandum_ eſt eſſe _p_ {2 _m_ - 2 _n_/ } = {ZD {_m_/ }/AD {2 _n_ - _m_/ }}.
&
_q_ {2 _m_ - 2 _n_/ } =
{ZG {_m_/ }/AG {2 _n_ - _m_/ }}. unde erit {ZD {_m_/ }/AD {2 _n_ - _m_/ }} & lt; {ZG {_m_/ }/AG {2 _n_ - _m_/ }}. quare {ZD {_m_/ }/AD {2 _n_ - _m_/ }} eſt mi-
11Fig. 149.nimum.
{ZG {_m_/ }/AG {2 _n_ - _m_/ }}. unde erit {ZD {_m_/ }/AD {2 _n_ - _m_/ }} & lt; {ZG {_m_/ }/AG {2 _n_ - _m_/ }}. quare {ZD {_m_/ }/AD {2 _n_ - _m_/ }} eſt mi-
11Fig. 149.nimum.
_Exemp_.
1.
Sit _n_ = 2;
&
_m_ = 3;
erit _p_2 = {ZD3/AD}.
= {BD6/AD4}.
&
_p_ = {BD3/ADq}. = {ZDq/BD}. Item AD = CA.
_p_ = {BD3/ADq}. = {ZDq/BD}. Item AD = CA.
2.
Sit _n_ = 3;
&
_m_ = 4;
erit _p_2 = {ZD4/AD2} vel p = {ZD2/AD}
= {BD4/AD3} = {ZD3/BD2}. Item AD = 2 CA.
= {BD4/AD3} = {ZD3/BD2}. Item AD = 2 CA.
3.
Sit _n_ = 5, &
_m_ = 8;
erit _p_ {6/ } = {ZD8/AD2}.
vel _p_3 = {ZD4/AD}
= {BD8/AD5} = {ZD5/BD2}. Item AD = {2/3} CA.
= {BD8/AD5} = {ZD5/BD2}. Item AD = {2/3} CA.
Quoniam in his _Cyclometriam_ attigi, quid ſi obiter eò ſpectantia
_Theoremata_, quæ ad manum, paucula ſubjunxero? præſternatur au-
22Fig. 150. tem autem hoc χαυολικὸν:
_Theoremata_, quæ ad manum, paucula ſubjunxero? præſternatur au-
22Fig. 150. tem autem hoc χαυολικὸν:
Sit curva quæpiam AGB, cujus axis AD, &
ad hunc ordinatæ
rectæ BD, GE; Habebit curva AB ad curvam AG majorem rati-
onem quàm recta BD ad rectam GE.
rectæ BD, GE; Habebit curva AB ad curvam AG majorem rati-
onem quàm recta BD ad rectam GE.
Nam ducatur recta GH ad AD parallela:
ſecentúrque recta B H
punctis Y, & recta GE punctis Z in particulas indefinitè multas; pér-
que puncta Y, Z ducantur rectæ YM, YN, ZO, ZP ad AD paral-
lelæ: curvam interſecantes punctis M, N, O, P; per quæ ducantur
rectæ MR, NS, OT, PV ad BD parallelæ. Eſtque angulus BM Y
(ut è ſuperius oſtenſis liquet) minor angulo NGS, unde MB. B Y
& gt; GN. NS. Similíque de cauſa eſt NM. MR & gt; GN. NS. 33Vid. _Append_.
Lect. XII. quare conjunctè eft BM + MN + NG. BY + MR + NS & gt;
GN. NS; hoc eſt arc. GB. BH & gt; GN. NS. rurſus (è diſcur-
ſu conſimili) ratio GN ad NS major eſt ſingulis rationibus OG ad
GZ, OP ad PT, & AP ad PV; idcircoq; junctè eſt GN. NS & gt;
arc. AG. GE. quapropter erit GB. BH & gt; AG. GE. permutan-
doque GB. AG & gt; BH. GE. quare componendo eſt AB. A G
& gt; BD. GE.
punctis Y, & recta GE punctis Z in particulas indefinitè multas; pér-
que puncta Y, Z ducantur rectæ YM, YN, ZO, ZP ad AD paral-
lelæ: curvam interſecantes punctis M, N, O, P; per quæ ducantur
rectæ MR, NS, OT, PV ad BD parallelæ. Eſtque angulus BM Y
(ut è ſuperius oſtenſis liquet) minor angulo NGS, unde MB. B Y
& gt; GN. NS. Similíque de cauſa eſt NM. MR & gt; GN. NS. 33Vid. _Append_.
Lect. XII. quare conjunctè eft BM + MN + NG. BY + MR + NS & gt;
GN. NS; hoc eſt arc. GB. BH & gt; GN. NS. rurſus (è diſcur-
ſu conſimili) ratio GN ad NS major eſt ſingulis rationibus OG ad
GZ, OP ad PT, & AP ad PV; idcircoq; junctè eſt GN. NS & gt;
arc. AG. GE. quapropter erit GB. BH & gt; AG. GE. permutan-
doque GB. AG & gt; BH. GE. quare componendo eſt AB. A G
& gt; BD. GE.