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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">Cum pridem ante plures annos illuſtris Viri, _Chriſtiani Hugenii,_
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_Cyclometrica_ luſtrarem, ac in eo verſatus adverterem ad id
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negotii duas præſertim ab ipſo methodos adhiberi; </
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<
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">quarum una _Cir-_
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_culi ſegmentum_ duobus parabolicis (uni inſcripto, alteri adſcripto)
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medium eſſe monſtrans, illius inde magnitudini limites præſcribit;
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</
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<
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">altera _Parabolici ſegmenti, & </
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<
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">Parallelogrammi_ æquè altorum cen-
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tris gravitatum medium interjacere centrum gravitatis circularis ſeg-
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menti oſtendens, alteros exindè limites, adſignat; </
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<
s
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">incidit mihi cogi-
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tatio poſſe loco parabolæ in prima methodo, nec non vice Parallelo-
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grammi in ſecunda, paraboliformium aliquam circulari ſegmento cir-
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cumſcriptibilem uſurpari, ſic ut res aliquanto propiùs attingatur; </
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<
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mox verum eſſe re perpensâ comperi; </
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<
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<
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pares methodos _Hyperbolici ſegmenti dimenſioni_ accommodari. </
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<
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rum demonſtratio (præ aliis fortaſſe, quæ excogitari poſſent) brevis
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& </
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<
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">clara cùm è ſuprà poſitis conſequatur aut pendeat, eam (alioquin
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opinor haud injucundam) hîc viſum eſt apponere.</
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<
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<
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nes è præmonſtratis haud difficilè variis modis colligantur; </
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<
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">Fig. 133.</
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_liformis_ BAE (cujus _Axis_ AD, _Baſis_ vel ordinata BDE, _Tan-_
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_gens_ BT; </
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<
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">_Gravitatis centrum_ K) exponens ſit {_n_/_m_}; </
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<
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">erit _Area_ BAE
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= {_m_/_n_ + _m_} AD x BE; </
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<
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axis AD, ordinata DB) ità ſe habentes, ut ductâ quâcunque rectâ
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EFG ad BD parallelâ, quæ lineas expoſitas punctis E, F, G ſecet, po-
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ſitóque quòd rectæ ES, FT tangant curvas, (illa curvam AEB, </
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