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

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[51.] Prop. 3.
Page: 313 (120)
[52.] Prop. 4.
Page: 313 (120)
[53.] APPENDICULA 3.
Page: 314 (121)
[54.] Problema I.
Page: 314 (121)
[55.] Exemp. I.
Page: 314 (121)
[56.] Exemp. II.
Page: 315 (122)
[57.] Probl. II.
Page: 315 (122)
[58.] Exemp. I.
Page: 315 (122)
[59.] _Exemp_. II.
Page: 316 (123)
[60.] _Probl_. III.
Page: 316 (123)
[61.] _Probl_. IV.
Page: 317 (124)
[62.] _Probl_. V.
Page: 317 (124)
[63.] _Probl_. VI.
Page: 318 (125)
[64.] _Probl_. VII
Page: 318 (125)
[65.] _Probl_. VIII.
Page: 319 (126)
[66.] _Probl_. IX.
Page: 319 (126)
[67.] _Probl_. X.
Page: 320 (127)
[68.] _Corol. Theor_. I.
Page: 321 (128)
[69.] _Theor_. II.
Page: 321 (128)
[70.] _Theor_. III.
Page: 321 (128)
[71.] _Theor_. IV.
Page: 321 (128)
[72.] _Theor_. V.
Page: 322 (129)
[73.] _Theor_. VI.
Page: 323 (130)
[74.] _Theor_. VII.
Page: 323 (130)
[75.] Lect. XIII.
Page: 324 (131)
[76.] Æquationum Series prima.
Page: 324 (131)
[77.] _Notetur autem_,
Page: 325 (132)
[78.] Series ſecunda.
Page: 325 (132)
[79.] Not.
Page: 326 (133)
[80.] Series tertia.
Page: 326 (133)
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page |< < (127) of 393 > >|
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.)
_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-
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_.
_Probl_. X.
Dàta figurâ quâpiam β C φ rectis C β, C φ, & aliâ lineâ βφ
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_.
_Exemp_. Sit LZE arcus circuli centro C deſcripti, & βμ C ejuſmodi
55Fig. 197.

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