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 xml:id="echoid-s520" xml:space="preserve">
              <pb o="13" file="0031" n="31" rhead=""/>
            mam illam & </s>
            <s xml:id="echoid-s521" xml:space="preserve">completam, inveſtigabimus, ac exponemus; </s>
            <s xml:id="echoid-s522" xml:space="preserve">cujuſce
              <lb/>
            quidem circa reflectionem inquiſitionis conſectaria reſultabit hæc pro-
              <lb/>
            poſitio, paſſim ab Opticis recepta:</s>
            <s xml:id="echoid-s523" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s524" xml:space="preserve">II. </s>
            <s xml:id="echoid-s525" xml:space="preserve">5. </s>
            <s xml:id="echoid-s526" xml:space="preserve">_Radius inßidens, & </s>
            <s xml:id="echoid-s527" xml:space="preserve">reflexus ad ſpeculi, velopaci reflectentis_
              <lb/>
            _ſuperficiem angulos conſtituunt aquales_. </s>
            <s xml:id="echoid-s528" xml:space="preserve">Hujus effati declarationem
              <lb/>
            ſic exequimur. </s>
            <s xml:id="echoid-s529" xml:space="preserve">Parallelogramum rectangulum ABCD lucis repræ-
              <lb/>
            ſentet radium obliquè plano ſpeculo EF incidentem. </s>
            <s xml:id="echoid-s530" xml:space="preserve">(Recta ſcilicet
              <lb/>
            EF ſit communis ſectio plani ad ſpeculum re@ i, in quo dictum Paral-
              <lb/>
            lelogrammum exiſtit, & </s>
            <s xml:id="echoid-s531" xml:space="preserve">in quo, ſecundum præmiſſa, reflectio per-
              <lb/>
            agitur, cum plano ſpeculi.) </s>
            <s xml:id="echoid-s532" xml:space="preserve">Cum itaque Parallelogrammi punctum B
              <lb/>
            ſpeculo primùm impingens opaco acimpervio, recta progredi nequeat,
              <lb/>
            conetur oportet (ut præſtruximus) retrò verſus A per ipſam rectam
              <lb/>
            BA reſilire. </s>
            <s xml:id="echoid-s533" xml:space="preserve">Cùm autem intereà rectæ BD ſupra ſpeculum eminen-
              <lb/>
            tis alter terminus D, nullo præpeditus obſtaculo pari vehementiâ cur-
              <lb/>
            ſum quoque ſuum adnitatur promovere per rectam CDH; </s>
            <s xml:id="echoid-s534" xml:space="preserve">palam
              <lb/>
            videtur utriuſque conatibus adverſis non aliter faciliùs aut propiùs ſa-
              <lb/>
            tisfieri poſſe, quàm ſi utrumque circa punctum Z rectæ BD medium
              <lb/>
            r@tationem concipiat. </s>
            <s xml:id="echoid-s535" xml:space="preserve">Sic enim utrumque pariter & </s>
            <s xml:id="echoid-s536" xml:space="preserve">quàm minimum
              <lb/>
            à recto quem affectent curſu deflectent; </s>
            <s xml:id="echoid-s537" xml:space="preserve">ſiquidem rectæ BA, DC
              <lb/>
            circulum B β D δ tangunt, centro Z per B & </s>
            <s xml:id="echoid-s538" xml:space="preserve">D deſcriptum. </s>
            <s xml:id="echoid-s539" xml:space="preserve">Cùm
              <lb/>
            autem hujuſmodi motum circularem obeundo punctum B deſcripſerit
              <lb/>
            arcum B β, & </s>
            <s xml:id="echoid-s540" xml:space="preserve">punctum D arcum D δ, hoc eſt quando recta BD ob-
              <lb/>
            tinuerit ſitum β δ, etiam ipſum punctum D ſpeculo impinget ad δ;
              <lb/>
            </s>
            <s xml:id="echoid-s541" xml:space="preserve">reditúmque proinde per arcum δ D, ſcilicet ipſius quoque jam inter-
              <lb/>
            ciſo curſu, molietur; </s>
            <s xml:id="echoid-s542" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s543" xml:space="preserve">nunc temporis ipſum punctum B ad β po-
              <lb/>
            ſitum per arcum β D tendit; </s>
            <s xml:id="echoid-s544" xml:space="preserve">quorum certè motuum adverſantium al-
              <lb/>
            ter alterius effectum impediet; </s>
            <s xml:id="echoid-s545" xml:space="preserve">itáque proximo ſaltem, quoad fieri
              <lb/>
            poterit, utrumque progreſſus arripient; </s>
            <s xml:id="echoid-s546" xml:space="preserve">proximi vero ſunt qui per
              <lb/>
            tangentes β α, δ κ; </s>
            <s xml:id="echoid-s547" xml:space="preserve">qui & </s>
            <s xml:id="echoid-s548" xml:space="preserve">ſibi nihil repugnant, at potiùs omninò ſe-
              <lb/>
            cum conſpirant; </s>
            <s xml:id="echoid-s549" xml:space="preserve">itaque punctum B per rectam β κ, punctúmque D per
              <lb/>
            rectam β κ procurrent, adeò ut totus radius ABDC jam acquirat
              <lb/>
            ſitum α β δ κ; </s>
            <s xml:id="echoid-s550" xml:space="preserve">& </s>
            <s xml:id="echoid-s551" xml:space="preserve">per hanc orbitam recta motum ſuum proſequatur. </s>
            <s xml:id="echoid-s552" xml:space="preserve">
              <lb/>
            Liquet autem angulos ABF, κ δE æquari. </s>
            <s xml:id="echoid-s553" xml:space="preserve">Nam æquantur anguli
              <lb/>
            ZB δ, Z δ B; </s>
            <s xml:id="echoid-s554" xml:space="preserve">quapropter adjunctis hinc indè rectis ZBA, β δ κ toti
              <lb/>
            ABF, κ δ E pares erunt. </s>
            <s xml:id="echoid-s555" xml:space="preserve">Unde patet è duobus quoque rectis reſiduos
              <lb/>
              <note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">Fig. 5.</note>
            ABE, κ δ F æquari; </s>
            <s xml:id="echoid-s556" xml:space="preserve">quod propoſitum fuit oſtendere.</s>
            <s xml:id="echoid-s557" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s558" xml:space="preserve">III. </s>
            <s xml:id="echoid-s559" xml:space="preserve">Ità de præmiſſis ſuppoſitionibus noſtris fundamentalem hanc
              <lb/>
            Caεθptricæ legem ſeu regulani elicimus, quàm veriſimiliter aut </s>
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