Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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mæ VDq + EIq + FKq + GLq; </
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<
s
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xml:space
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">ergò ſumma IXq +
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KXq + LXq + HXq, ſubdupla eſt ſummæ VDq - EIq +
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FKq + GLq. </
s
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<
s
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xml:space
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">Vnde liquet Propoſitum.</
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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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ceu IX, inter congruas ordinatas IE, IZ bimedia *; </
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<
s
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xml:space
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">erit ſumma cubo-
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rum ex IX, KX, LX, &</
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<
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">c. </
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<
s
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">ſubtripla cuborum ex DV, IE, KF, &</
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<
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echoid-s12732
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">c. </
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<
s
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">Sin IX
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ſit trimed. </
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<
s
xml:id
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echoid-s12734
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xml:space
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">* erit IXqq + KXqq + LXqq, &</
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<
s
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echoid-s12735
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xml:space
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">c. </
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<
s
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xml:space
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">= {DVqq + IEqq + KFqq/4}
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&</
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<
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">c. </
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<
s
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">ac ità porrò quoad cæteras poteſtates. </
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<
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">* _Not._ </
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<
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pello, quæ duarum mediarum proportionalium prima; </
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<
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">trimediam,
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quæ trium prima eſt, &</
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<
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xml:space
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">c.</
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<
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</
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<
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<
s
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xml:space
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">Hæc ſimili ratione colliguntur, ac comprobantur. </
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<
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">piget χοχχὺζι
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ν.</
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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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ordinata BY ipſi BT, &</
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<
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">æquentur; </
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<
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">erit IZq + KZq + LZq,
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&</
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<
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xml:space
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">c. </
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<
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xml:space
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">(ſumma quadratorum ex ordinatis à curva DZO ad rectam DH)
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æqualis ſummæ VA x AE x AY + AB x BF x BY + BC x CG
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x CY, &</
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<
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">c. </
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<
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xml:space
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">(hoc eſt figuræ VDH in figuram VDQ ductæ).</
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<
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<
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<
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VA x AE x AYq + AB x BE x BYq + BC x CG x CYq,
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&</
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<
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<
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">_hoc eſt figuræ_ VDH _in figuræ_ VDQ _quadrata ductæ_). </
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<
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lis & </
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<
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<
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<
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Etiam ſi curvæ VH convexa rectæ VD obvertantur. </
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<
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DZO talis ſit, ut ductâ per quodvis in curva VH punctum E tangente
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ET, & </
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">EA ad HD parallelâ, ac EIZ ad VD parallelâ, ſit perpetim IZ =
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AT; </
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<
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<
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DHO circa axem VR converſo duplum erit ſolidi ex ſpatio VDH
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circa eundem axem VD rotato producti. </
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<
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convenient.</
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<
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<
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perpendicularis BD; </
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<
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">tum alia ſit linea KZL talis, ut ſumpto in cur-
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va AB utcunque puncto M; </
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<
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<
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<
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note
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AB tangente, rectâ MFZ ad DB parallelâ (quæ lineam KL ſecet
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in Z, rectam AD in F) datâque quâdam lineâ R; </
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