Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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ſtantaneus, eò recurrendum ut per inſtantias nil aliud, quàm inde-
<
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finitas temporis particulas intelligamus; </
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<
s
xml:id
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echoid-s8514
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xml:space
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preserve
">quibus reſpondeant certo
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velocitatis gradu, alio atque alio, percurſa indefinitè minuta ſpatiola
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velocitatis gradibus adproportionata; </
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<
s
xml:id
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xml:space
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">tum autem repræſentando
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ſingulo cuipiam velocitatis gradui per tempuſculum aliquod retento,
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loco lineæ rectæ ſubſtituatur oportet exiguum rectangulum dicto tem-
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puſculo applicatum. </
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<
s
xml:id
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xml:space
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preserve
">Perinde fuerit, ac eodem recidet hoc an illo
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modo ſe res habeat, aſt ſimplicior & </
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<
s
xml:id
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xml:space
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">clarior videtur iſte modus, quem
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priùs expoſuimus, cui proinde poſthac inſiſtemus. </
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<
s
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echoid-s8518
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xml:space
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">Ut redeam, & </
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recolligam; </
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<
s
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echoid-s8520
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xml:space
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">ſicuti per omnia lineæ rectæ puncta traduci poſſunt pa-
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rallelæ rectæ, magnitudine pro lubitu pares, vel impares, è qui-
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bus aggregatis ſuperficiale planum exurgat, ità ad ſingula temporis
<
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inſtantia applicari poſſunt velocitatis gradus diverſi, pares vel impares,
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prout mobile per totam ſuam lationem vel eundem impetum retmere,
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vel aliquando varium adſciſſere ſupponatur, utcunque creſcendo vel
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decreſcendo. </
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<
s
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xml:space
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">Si velocitatem ſemper eandem conſervare dicatur, fa-
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cilè patet è dictis velocitatem aggregatam definito cuivis tempori con-
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venientem rectiſſimè per figuram parallelogrammam exprimi, qua-
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<
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">Fig. I.</
note
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lis eſt AZZE, in qua latus AE temporis deſiniti vicem obit, re-
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liquum AZ, eíque parallelæ rectæ omnes BZ, CZ, DZ, EZ
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velocitatis gradus ſingulos per ſingula temporis momenta penetrantes,
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in hoc ſcilicet caſu pares, exhibent. </
s
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<
s
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xml:space
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">Poſſunt etiam, ut dictum, pa-
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rallelogramma AZZB, AZZC, AZZD, AZZE ſpatia re-
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ſpectivis temporibus AB, AC, AD, AE decurſa appoſitè deſignare.
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</
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<
s
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xml:space
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">E qua conſideratione ſola, vel intuitu primo motûs hujuſmodi, quem
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æquabilem, & </
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<
s
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xml:space
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">uniformem vocitant, omnia ſymptomata deduci
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poſſunt. </
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<
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xml:space
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">Quales ſunt: </
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xml:space
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">quòd æquali perpetuò velocitate tranſmiſſa
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ſpatia ſeſe habent ut tempora: </
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xml:space
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">Quod æquali tempore peracta
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ſpatia ſeſe habent ut velocitates; </
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xml:space
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">& </
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<
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">viciſſim: </
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xml:space
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">Si ſpatia ſunt ut
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velocitates tempora fore æqualia; </
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<
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xml:space
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">ſi ut tempora, velocitates
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æquari. </
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<
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xml:space
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">Et ſi æqualia ſpatia fuerint, tempora velocitatibus propor-
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tione reciprocari; </
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<
s
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xml:space
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">contráque, ſi tempora velocitatibus proportione
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reciprocentur, ſpatia ſibimet exæquari. </
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<
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xml:space
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">Spatia denique quælibet
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compoſitam habere rationem è rationibus velocitatum & </
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<
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xml:space
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">temporum; </
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nec non, ſubducendo rationem temporum è ratione ſpatiorum reſiduam
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manere rationem velocitatum; </
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<
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xml:space
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">vel ſubducendo rationem velocitatum
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relinqui rationem temporum. </
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<
s
xml:id
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xml:space
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">Hæc enim parallelogrammorum inter
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ſe comparatorum aſſectiones ſunt (æquiangulorum intelligo paralle-
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logrammorum; </
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<
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xml:space
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">nam ubi repræſentativa, hæc parallelogramma con-
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feruntur inter ſe, æquiangula conſtituantur oportet; </
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<
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