Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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mam illam & </
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<
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quidem circa reflectionem inquiſitionis conſectaria reſultabit hæc pro-
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poſitio, paſſim ab Opticis recepta:</
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<
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">II. </
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">_Radius inßidens, & </
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">reflexus ad ſpeculi, velopaci reflectentis_
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_ſuperficiem angulos conſtituunt aquales_. </
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<
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xml:space
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">Hujus effati declarationem
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ſic exequimur. </
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<
s
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">Parallelogramum rectangulum ABCD lucis repræ-
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ſentet radium obliquè plano ſpeculo EF incidentem. </
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<
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">(Recta ſcilicet
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EF ſit communis ſectio plani ad ſpeculum re@ i, in quo dictum Paral-
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lelogrammum exiſtit, & </
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<
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">in quo, ſecundum præmiſſa, reflectio per-
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agitur, cum plano ſpeculi.) </
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<
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">Cum itaque Parallelogrammi punctum B
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ſpeculo primùm impingens opaco acimpervio, recta progredi nequeat,
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conetur oportet (ut præſtruximus) retrò verſus A per ipſam rectam
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BA reſilire. </
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<
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">Cùm autem intereà rectæ BD ſupra ſpeculum eminen-
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tis alter terminus D, nullo præpeditus obſtaculo pari vehementiâ cur-
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ſum quoque ſuum adnitatur promovere per rectam CDH; </
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<
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">palam
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videtur utriuſque conatibus adverſis non aliter faciliùs aut propiùs ſa-
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tisfieri poſſe, quàm ſi utrumque circa punctum Z rectæ BD medium
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r@tationem concipiat. </
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">quàm minimum
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à recto quem affectent curſu deflectent; </
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<
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">ſiquidem rectæ BA, DC
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circulum B β D δ tangunt, centro Z per B & </
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autem hujuſmodi motum circularem obeundo punctum B deſcripſerit
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arcum B β, & </
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tinuerit ſitum β δ, etiam ipſum punctum D ſpeculo impinget ad δ;
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</
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ciſo curſu, molietur; </
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">nunc temporis ipſum punctum B ad β po-
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ſitum per arcum β D tendit; </
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<
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">quorum certè motuum adverſantium al-
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ter alterius effectum impediet; </
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<
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">itáque proximo ſaltem, quoad fieri
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poterit, utrumque progreſſus arripient; </
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">proximi vero ſunt qui per
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tangentes β α, δ κ; </
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">ſibi nihil repugnant, at potiùs omninò ſe-
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cum conſpirant; </
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<
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">itaque punctum B per rectam β κ, punctúmque D per
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rectam β κ procurrent, adeò ut totus radius ABDC jam acquirat
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ſitum α β δ κ; </
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">& </
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<
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">per hanc orbitam recta motum ſuum proſequatur. </
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Liquet autem angulos ABF, κ δE æquari. </
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ZB δ, Z δ B; </
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ABF, κ δ E pares erunt. </
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ABE, κ δ F æquari; </
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<
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">III. </
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">Ità de præmiſſis ſuppoſitionibus noſtris fundamentalem hanc
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Caεθptricæ legem ſeu regulani elicimus, quàm veriſimiliter aut </
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