320127
rallelâ, ſit rectangulum ex PM, PZ æquale quadrato ex CL (vel
PZ = {CL q/PM}). Sit tum arc. LX = {ſpat. DKZP/CL} (vel ſector
LCX ſubduplws ſpatii DKZP) & in CX capiatur C μ = PM;
erit linea βμμ ipſius BMA involuta; vel ſpatium Cμβ ſpatii
ADB.)
PZ = {CL q/PM}). Sit tum arc. LX = {ſpat. DKZP/CL} (vel ſector
LCX ſubduplws ſpatii DKZP) & in CX capiatur C μ = PM;
erit linea βμμ ipſius BMA involuta; vel ſpatium Cμβ ſpatii
ADB.)
_Exemp_.
Sit ADB circuli quadrans;
erit ergò (quod è præmonſtra-
tis conſtat) ſpat. DKZP (2 ſector LCX). ſect. BDM
: : CLq. DBq. unde arc. LX. arc. BM: : CL. DB.
quare ang. LCX = ang. BDM = ang. DMP. unde ang.
C μβ eſt rectus, adeóque linea βμ C eſt _ſemicirculus_.
tis conſtat) ſpat. DKZP (2 ſector LCX). ſect. BDM
: : CLq. DBq. unde arc. LX. arc. BM: : CL. DB.
quare ang. LCX = ang. BDM = ang. DMP. unde ang.
C μβ eſt rectus, adeóque linea βμ C eſt _ſemicirculus_.
_Coroll_.
1.
Subnotari poteſt, ſi duæ ſiguræ ADB, ADG analogæ fu-
11Fig. 193. erint; & harum _involutæ_ ſint _Cμβ Cνγ_; & fuerit _Cμ. Cν_
: : DB. DG; erit reciprocè ang. _βCμ. β Cν: : DG_.
DB.
11Fig. 193. erint; & harum _involutæ_ ſint _Cμβ Cνγ_; & fuerit _Cμ. Cν_
: : DB. DG; erit reciprocè ang. _βCμ. β Cν: : DG_.
DB.
2.
Illud etiam conversè valet.
3.
Sin curvæ Cνγ, CS β ſuo modo analogæ fuerint, hoc eſt,
22Fig. 194. ſi utcunque à Cprojectâ rectâ C ν S, habeant Cν, CS ean-
dem perpetuò rationem, erunt hæ ſimilium linearum _invo-_
_lutæ_.
22Fig. 194. ſi utcunque à Cprojectâ rectâ C ν S, habeant Cν, CS ean-
dem perpetuò rationem, erunt hæ ſimilium linearum _invo-_
_lutæ_.
_Probl_. X.
Dàta figurâ quâpiam β C φ rectis C β, C φ, &
aliâ lineâ βφ
33Fig. 195. comprehensâ, eicompetentem _evolutam_ deſignare.
33Fig. 195. comprehensâ, eicompetentem _evolutam_ deſignare.
_Centro_ Cutcunque deſcribatur _circularis arcus_ LE (cum rectis Cβ,
Cφ conſtituens ſectorem LCE) tum ductâ CK ad LC perpendicu-
44Fig. 196. lari, ſit curva β YH ità rectam CK reſpiciens, ut liberè projectâ rectà
CμZ, ſumptâque CO = arcLZ, ductâque OY ad CK perpen-
diculari, ſitOY = Cμ; porrò ad rectam DA ſic referatur curva
BMF, ut cùm ſit DP = {ſpat. C β YO/CL}; & PM ad DA perpendi-
cularis; ſit etiam PM = Cμ; erit ſpatium DBFA ipſins Cβφ _evolutum_.
Cφ conſtituens ſectorem LCE) tum ductâ CK ad LC perpendicu-
44Fig. 196. lari, ſit curva β YH ità rectam CK reſpiciens, ut liberè projectâ rectà
CμZ, ſumptâque CO = arcLZ, ductâque OY ad CK perpen-
diculari, ſitOY = Cμ; porrò ad rectam DA ſic referatur curva
BMF, ut cùm ſit DP = {ſpat. C β YO/CL}; & PM ad DA perpendi-
cularis; ſit etiam PM = Cμ; erit ſpatium DBFA ipſins Cβφ _evolutum_.
_Exemp_.
Sit LZE arcus circuli centro C deſcripti, &
βμ C ejuſmodi
55Fig. 197.
55Fig. 197.
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