Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

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 ſubduplw [?] s ſpatii DKZP) & in CX capiatur C μ = PM; erit linea βμμ ipſius BMA involuta; vel ſpatium Cμβ ſpatii
ADB.)

66.1.

Fig. 192.

_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_.

_Coroll_. 1. Subnotari poteſt, ſi duæ ſiguræ ADB, ADG analogæ fu-
erint; & harum _involu [?] tæ_ ſint _Cμβ Cνγ_; & fuerit _Cμ. Cν_
: : DB. DG; erit reciprocè ang. _βCμ. β Cν: : DG_. DB.

66.1.

Fig. 193.

2. Illud etiam conversè valet.

3. Sin curvæ Cνγ, CS β ſuo modo analogæ fuerint, hoc eſt,
ſi utcunque à Cprojectâ rectâ C ν S, habeant Cν, CS ean-
dem perpetuò rationem, erunt hæ ſimilium linearum _invo-_
_lutæ_.

66.1.

Fig. 194.

67. _Probl_. X.

Dàta figurâ quâpiam β C φ rectis C β, C φ, & aliâ lineâ βφ
comprehensâ, eicompetentem _evolutam_ deſignare.

67.1.

Fig. 195.

_Centro_ Cutcunque deſcribatur _circularis arcus_ LE (cum rectis Cβ,
Cφ conſtituens ſectorem LCE) tum ductâ CK ad LC perpendicu-
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 eti [?] am PM = Cμ; erit ſpatium DBFA ipſins Cβφ _evolutum_.

67.1.

Fig. 196.

_Exemp_. Sit LZE arcus circuli centro C deſcripti, & βμ C ejuſmodi

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