Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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. XII.</
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<
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xml:space
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">IN ſuſcepto negotio progredimur; </
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<
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xml:space
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">quod ut (quatenus licet) decurte-
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xml:space
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">_Praparati@_
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_Communis_.</
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mus, verbíſque parcamus; </
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<
s
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xml:space
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">obſervetur, in ſequentibus ubique _line-_
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_am_ AB _curvam_ eſſe (quales tractamus) quampiam; </
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<
s
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echoid-s13933
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xml:space
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">cujus _Axis_ AD;
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</
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<
s
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xml:space
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">huic applicatas omnes rectas BD, CA, MF, NG perpendiculares; </
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<
s
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& </
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<
s
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echoid-s13936
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">ME, NS, CB parallelas eſſe; </
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<
s
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xml:space
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">_punctum_ M liberè ſumi; </
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<
s
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">_arcum_
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MN indefinitè parvum eſſe; </
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<
s
xml:id
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xml:space
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">rectam α β curvæ VB, α μ curvæ AM,
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μ ν _arcui_ MN æquales eſſe; </
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<
s
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xml:space
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">ad rectam α β applicatas ei perpendicu-
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lares eſſe. </
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<
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">His præſtratis,</
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<
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">I. </
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<
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">Sit MP curvæ AB perpendicularis; </
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<
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xml:space
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">& </
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<
s
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xml:space
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">lineæ KZ L, α φ δta-
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<
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xlink:label
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note-0283-02
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xlink:href
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xml:space
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">Fig. 156,
<
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157.</
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les, ut FZ ipſi MP, & </
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<
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">μ φ ipſi M Fæquentur; </
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<
s
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xml:space
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">erît _ſpatium_ α β δ ipſi
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AD LK æquale.</
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<
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<
s
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xml:space
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">Nam _Triangula_ MRN, PFM ſimilia ſunt, adeoque MN. </
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<
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">NR
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:</
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<
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">: PM. </
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<
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">MF. </
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<
s
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xml:space
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">unde MN x MF = NR x PM, hoc eſt (ſubſtitutis
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æqualibus) μ ν x μ φ = FG x FZ; </
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<
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<
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">μ θ = rectang. </
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<
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</
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<
s
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xml:space
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">ſpatium verò α β δ minimè differt ab indeſinitè multis rectangulis,
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qualia μθ & </
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<
s
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xml:space
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">ſpatium AD LK totidem rectangulis, qualia FH, æ-
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quivalet. </
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<
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">unde liquet Propoſitum.</
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<
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<
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<
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">II. </
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<
s
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">Hinc, ſi curva AMB circa axem AD rotetur, habebit ſe _pro._
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</
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<
s
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">_ducta ſuperficies_ ad _ſpatium_ AD LK, ut _Circumferentia circuli Ad ra-_
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">Fig. 156.</
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_dium_; </
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<
s
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">unde noto ſpatio AD LK cognoſcetur dicta _ſuperficies._ </
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<
s
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ſequentiæ rationem jam anteà pridem aſſignavimus.</
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<
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">III. </
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">Exhinc _Spbæræ, Spbæroidis_ utriuſque, _Conidúmque ſuperficies_
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_dimenſionem_ accipiunt; </
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<
s
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xml:space
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">nam ſi AD ſit conicæ ſectionis, à qua iſtæ
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figuræ oriuntur, axis; </
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<
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">linea KZL ſemper aliqua conicarum exiſtet,
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haud difficili negotio determinabilis. </
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<
s
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">Hoc ſuggero tantùm, quoniam
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nunc evulgatum habet ur.</
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