Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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_ſpiralis_, ut pro arbitrio ductâ rectâ C μ Z habeat arcus EZ ad rectam
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C μ rationem aſſignatam (puta R ad S) Manifeſtum eſt lineam β YH
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eſſe rectam, quoniam EZ (KO). </
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<
s
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xml:space
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s
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<
s
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xml:space
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">: R. </
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<
s
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xml:space
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">S, perpetuò.
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</
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<
s
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xml:space
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<
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xlink:label
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note-0306-01
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xml:space
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">Fig. 198.</
note
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unde evoluta BMF ſit _Parabola_; </
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<
s
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xml:space
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">quoniam axis partes AP, AD ſe
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habent ut ſpatia KOY, KC β, hoc eſt ut quadrata ex ipſis OY, Cβ,
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vel ex ipſis PM, DB.</
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<
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n
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<
head
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xml:space
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">_Corol. Theor_. I.</
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<
s
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xml:space
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">Si ad figuram βCφ erigatur _cylindricus_ altitudinem habens æqua-
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lem peripheriæ integræ _circuli_, cujus radius CL; </
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>
<
s
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xml:space
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">erit iſte _cylindricus_
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æ
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qualis _ſolido_, quod procreatur è figurâ Cβ HK circa axem CK ro-
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tatâ.</
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<
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<
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<
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xml:space
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">_Theor_. II.</
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<
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<
s
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xml:space
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">Sit curva quæpiam AMB (cujus axis AD, baſis DB) & </
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<
s
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">curva
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<
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xml:space
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">Fig. 195.</
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AZL talis, ut liberè ductâ rectâ ZPM, ſit PZ = √ 2 APM; </
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<
s
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">ſit
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item alia curva OYY talis, ut ad hanc productâ rectâ ZPMY,
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adſumptâque rectâ R, ſit ZP q. </
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<
s
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">R q:</
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<
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<
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">PY; </
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<
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xml:space
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</
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<
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<
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xml:space
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<
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">& </
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<
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">per E intra angulum LDG deſcribatur _Hyper-_
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_bola_ EXX; </
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<
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">huic autem occurrat ducta recta ZHX ad AD parallela,
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erit ſpatium PDOY æquale _ſpatio Hyperbolico_ LHXE.</
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<
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xml:space
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">Hinc _ſumma_ omnium {PM/APM} = {2 LEXH/R q}.</
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<
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xml:space
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">Sit curva quæpiam AMB, cujus axis AD, baſis DB; </
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<
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<
s
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KZL talis, ut adſumptâ quâdam R, & </
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<
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">arbitrariè ductâ rectâ ZPM
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ad BD parallelâ, ſit √ APM. </
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<
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<
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<
s
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">erit ſpatium ADLK
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<
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æquale _rectangulo_ ex R in 2 √ ADB; </
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<
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√ 2 DA x arc. </
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<
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duæ lineæ EXK, GYL ità relatæ, ut in curva AMB ſumpto </
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