Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
s
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<
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xml:space
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">Iiſdem ſtantibus, ſit curva AYI talis, ut ordinata FY ſit in-
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ter congruas FM, FZ proportione media; </
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<
s
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xml:space
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">erit _ſolidum_ ex ſpatio αδβ
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<
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xlink:label
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note-0284-01
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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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circa axem α β rotato factum æquale _ſolido_, quod à _ſpatio_ ADI circa
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axem AD converſo procreatur.</
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<
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<
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<
s
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echoid-s13977
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xml:space
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">Nam eſt MN. </
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<
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echoid-s13978
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<
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echoid-s13979
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xml:space
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">: PM. </
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<
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echoid-s13980
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xml:space
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">MF:</
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<
s
xml:id
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echoid-s13981
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xml:space
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">: PM x MF. </
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<
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echoid-s13982
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xml:space
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">MF q:</
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<
s
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echoid-s13983
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xml:space
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">:FZ x
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FM. </
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<
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">MFq. </
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<
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xml:space
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">unde MN x MFq = NR x FZ x FM; </
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<
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xml:space
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">hoc eſt
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μ ν x μ φ q = NR x FYq. </
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<
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xml:space
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">Unde liquet Propoſitum.</
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<
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xml:space
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<
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xml:space
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">Simili ratione colligetur, ſi FY ponatur inter FM, FZ _bime-_
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xml:space
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">Fig. 156,
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157.</
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_media_, fore _ſummam cuborum_ ex applicatis (quales μ φ) à curva α φ δ
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ad rectam α β, æqualem _ſummæ cuborum_ ex explicatis à curva AYI ad
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rectam AD. </
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<
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xml:space
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">paríque modo ſe res habebit quoad cæteras _poteſta-_
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_tes._</
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<
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">VI. </
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<
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">Porrò, ſtantibus reliquis, ſit curva VXO talis, ut EX ipſi MP
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æquetur; </
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">& </
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">curva πξψ talis, ut μ ξ æ quetur ipſi PF; </
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<
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">erit ſpatium
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">Fig. 156.</
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α π ψ β æqua le ſpatio DV OB.</
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<
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<
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<
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">PF; </
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<
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x MP. </
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<
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xml:space
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">hoc eſt μ ν x μ ξ = ES x EX. </
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<
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">vel rectang. </
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<
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</
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<
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_parameter_ R; </
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">erit curva VXO _byperbola_, cujus _centrum_ D, _Axis_ DV,
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cujuſque _parameter_ axi R æquatur (ſcilicet ob EXq = (PMq =
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PFq + FMq = {R q/4}+FMq = {R q/4}+ DEq = ) DVq+ DEq).
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</
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<
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">quoniam ſingulæ applicatæ
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μ ξ ipſi {R/2} æquantur. </
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">Conſtat itaque dato _ſpatio byperbolico_ DVOB
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curvam AMB dari; </
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<
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<
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ad rectam α β à curva π ξ ψ æquari rectangulis omnibus ex PE, EX
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ad rectam DB applicatis (ſeu computatis); </
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PFq x EX; </
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<
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<
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lis ipſi PQ, & </
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quari.</
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