Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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pares ſubtenſis KD, MD, ND; </
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<
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">&</
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<
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">c. </
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<
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">erit ſpatium X _k d_ æquale ſpa-
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tio DKI.</
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<
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</
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<
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<
s
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echoid-s12989
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xml:space
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">Nam eſt KM. </
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<
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<
s
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echoid-s12991
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xml:space
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<
s
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echoid-s12992
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xml:space
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">KD; </
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<
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echoid-s12993
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xml:space
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">hoc eſt _km_. </
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<
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echoid-s12994
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xml:space
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<
s
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xml:space
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">: KI _kd_.
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</
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<
s
xml:id
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echoid-s12996
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xml:space
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">unde _km x k d_ = KP x KI. </
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<
s
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">Simiſique pacto, MN. </
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<
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<
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echoid-s12999
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xml:space
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<
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MD. </
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<
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">ſeu _mn_. </
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<
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<
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<
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xml:space
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">_md_. </
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<
s
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xml:space
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">unde _mnx_ = PQ x PZ. </
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<
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ac ità deinceps. </
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<
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xml:space
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">unde cònſtat Propoſitum.</
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<
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<
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xml:space
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">XXVI. </
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<
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">Sin porrò, perſiſtentibus reliquis, adſumptâ quâvis rectâ.
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</
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<
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xml:space
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">_kg_, completóque rectangulo X _kgb_, curva DZI talis intelligatur,
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ut ſit MD. </
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<
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xml:space
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">MS:</
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<
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xml:space
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">: _k g_. </
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<
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">PZ; </
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<
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xml:space
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">erit rectangulum X _k g b_ æquale ſpatio
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<
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xlink:label
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xml:space
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">Fig. 130.</
note
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DKI.</
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<
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</
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<
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<
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xml:space
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">Nam eſt rurſus KP. </
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<
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xml:space
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">KM:</
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<
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xml:space
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">: KD. </
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<
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="
echoid-s13020
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xml:space
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">KT:</
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<
s
xml:id
="
echoid-s13021
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xml:space
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">: _k g_. </
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<
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="
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xml:space
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">KI. </
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<
s
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xml:space
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">adeóque KP x
<
lb
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KI = (KM x _kg_ = ) _km_ x _kg_. </
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<
s
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xml:space
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">Similitérque PQ x PZ = _mn_ x
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_kg_. </
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<
s
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">ac ità ſemper. </
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<
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<
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<
s
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xml:space
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">Hinc noto ſpatio DKI cognoſcetur quantitas curvæ DOK.</
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<
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</
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<
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<
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">Hujuſmodi verò complura deprehendet quiſquis hanc _Mineram_ pe-
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nitiùs explorârit, ac excuſſerit. </
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<
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<
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cit</
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<
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<
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">Uſui fortè nonnunquam erit (mihi ſubinde fuit) & </
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<
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è præmiſſis deductum Theorema.</
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<
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</
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<
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">Fig. 131.</
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<
s
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">Sit curva quæpiam VEH (cujus axis VD, baſis DH) quam tangat ut-
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cunque recta ET; </
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">& </
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<
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<
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">tum altera ſta-
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tuatur curva GZZ talis, ut à puncto E ductâ EZ ad VD pa-
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rallelâ (quæ baſin DH in I, curvam GZZ in Z ſecet) adſumptâq;
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</
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<
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<
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DA. </
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<
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<
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<
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ductâque PQ ad DH parallelâ, erit _Rectangulum_ DPQI par _ſpa-_
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_tio_ DGZI).</
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<
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<
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<
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<
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<
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xlink:label
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nea KZL proprietate talis, ut ſumpto in AMB quocunque puncto
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M, & </
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<
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">ab eo ductis rectâ MP ad curvam AB perpendiculari (quæ
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axem AD ſecet in P) & </
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">rectà MG ad AD perpendiculari (quæ
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curvam KZL ſecet in Z) ſit conſtantèr GM. </
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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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">GZ; </
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<
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">erit _ſpatium_ ADKL æquale _ſemiſſi quadrati_ ex arcn AM.</
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<
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<
s
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">Hæcinquam, è præcedentibus haud magnâ o perâ colligantur, id
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verò ſufficiat admonitum; </
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<
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