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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xml:space
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<
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<
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xml:space
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">_ſummarectangulorum_ AZ x AE
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+ BZ x BF + CZ x CG, &</
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<
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xml:space
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">e. </
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<
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">æquatur _trienti cubi_ ex baſe
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<
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note-0264-01
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xml:space
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">Fig. 122.</
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DH.</
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<
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<
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<
s
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xml:space
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<
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xml:space
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<
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xml:space
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">: PD. </
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<
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<
s
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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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">erit HL x
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DHq = LG x PD x DH. </
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<
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">hoc eſt HL x HOq = DC x Dψ x
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DH. </
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<
s
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">Similíque diſcurſu, LK x LYq = CB x CZ x CG. </
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<
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xml:space
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">& </
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<
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">KI
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x KYq = BA x BZ x BF, &</
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<
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">c. </
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<
s
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xml:space
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">Verùm HL x HOq + LK x
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LYq + KI x KYq, &</
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<
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">c. </
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<
s
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">adæquant trientem cubi ex DH; </
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<
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">itaque
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liquet Propoſitum.</
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<
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</
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<
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<
s
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">III. </
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<
s
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xml:space
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">Simili ratione conſtabit ſummam AZ x AEq + BZ x BFq
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+ CZ x CGq, &</
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<
s
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<
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">æquari τῶ{DH_qq_;</
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<
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">/4} & </
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<
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">eſſe ſummam AZ x
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AE cub. </
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<
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<
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<
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">c. </
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<
s
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">= {DH {5/ }/5}; </
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<
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">ac
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eodem in continuum tenore.</
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</
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<
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<
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<
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">Exhinc conſectantur haud aſpernanda _Theoremata_: </
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<
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VDψφ ſpatium quodlibet, cujus axis VD, ut dictum, æquiſectus;
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</
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<
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ſi concipiantur ſingula ſpatia VAZφ, VBZφ, VCZφ, &</
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<
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<
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ſuas ordinatas AZ, BZ, CZ, &</
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<
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">c. </
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<
s
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">reſpectivè ſingulas duci, quæ pro-
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veniet ſumma adæquabitur ipſius ſpatii VDψφ ſemiquadrato.</
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<
s
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">Nam (utì priùs oſtenſum) figuræ VDψ φ adaptari poteſt ſpatium
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VDH; </
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<
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">tale nimirum ut ductà quâvis ad curvam VH perpendiculari,
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ceu EP, ſit AP ſibireſpondenti applicatæ AZ æqualis; </
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<
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ſpatium VAZ φ = {AE_q_/2}; </
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<
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">& </
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<
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<
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">/2} & </
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<
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&</
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<
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<
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x CZ, &</
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<
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<
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">æquabuntur omnibus {AE_q_ x AZ + BF_q_ x BZ + CG_q_ x CZ/2}
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hoc eſt τῶ {DH_qq_/4 x 2}; </
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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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<
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<
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<
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<
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gregatum æquale duabus tertiis radicis quadratæ facti ex ipſo ſpatio
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VDψφ cubato (τῶ {2/3} √ VDψφ {3/ })</
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<
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<
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">Nam adaptatâ curvâ VH, eſt √ VAZ φ = AE√ {1/2}; </
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<
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= BF √ {1/2}, & </
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<
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<
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