Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of Notes

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          <p>
            <s xml:id="echoid-s943" xml:space="preserve">
              <pb o="25" file="0043" n="43" rhead=""/>
            obliquiùs quàm DB.) </s>
            <s xml:id="echoid-s944" xml:space="preserve">Horum verò refracti ſint B _a_, Bδ; </s>
            <s xml:id="echoid-s945" xml:space="preserve">dico an-
              <lb/>
              <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">Fig. 21.</note>
            gulum β B _a_ majorem eſſe angulo HB δ. </s>
            <s xml:id="echoid-s946" xml:space="preserve">Nam ad BP in perpendicu-
              <lb/>
            lari liberè ſumptam diametrum conſtituatur ſemicirculus BGP; </s>
            <s xml:id="echoid-s947" xml:space="preserve">cui
              <lb/>
            occurrant ipſæ AB, DB protractæ ad G, H; </s>
            <s xml:id="echoid-s948" xml:space="preserve">nec non ipſæ B _a_, B δ
              <lb/>
            punctis _a_, δ. </s>
            <s xml:id="echoid-s949" xml:space="preserve">Fiat autem angulus GBK æqualis angulo HBδ, vel
              <lb/>
            arcus GK arcui Hδ; </s>
            <s xml:id="echoid-s950" xml:space="preserve">connectatur etiam rècta δ G, ſecans ipſam PK
              <lb/>
            in X; </s>
            <s xml:id="echoid-s951" xml:space="preserve">ducatnurque denuò ſubtenſæ G δ, H δ. </s>
            <s xml:id="echoid-s952" xml:space="preserve">Jam ob angulos PG δ,
              <lb/>
            PH δ pares (arcui quippe P δ inſiſtentes ambos) & </s>
            <s xml:id="echoid-s953" xml:space="preserve">angulos GPK,
              <lb/>
              <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">Fig. 22.</note>
            HP δ ex conſtructione quoque pares, erunt triangula GPX,
              <lb/>
            HP δ inter ſe ſimilia. </s>
            <s xml:id="echoid-s954" xml:space="preserve">Quapropter erit PG. </s>
            <s xml:id="echoid-s955" xml:space="preserve">PX :</s>
            <s xml:id="echoid-s956" xml:space="preserve">: PH. </s>
            <s xml:id="echoid-s957" xml:space="preserve">P δ. </s>
            <s xml:id="echoid-s958" xml:space="preserve">eſt
              <lb/>
            autem, è lege refractionum PH. </s>
            <s xml:id="echoid-s959" xml:space="preserve">P δ :</s>
            <s xml:id="echoid-s960" xml:space="preserve">: PG. </s>
            <s xml:id="echoid-s961" xml:space="preserve">P _a_. </s>
            <s xml:id="echoid-s962" xml:space="preserve">quare PG. </s>
            <s xml:id="echoid-s963" xml:space="preserve">PX :</s>
            <s xml:id="echoid-s964" xml:space="preserve">:
              <lb/>
            PG. </s>
            <s xml:id="echoid-s965" xml:space="preserve">P _a_: </s>
            <s xml:id="echoid-s966" xml:space="preserve">unde PX = P _a_. </s>
            <s xml:id="echoid-s967" xml:space="preserve">eſt autem PX minor quàm PK (quia
              <lb/>
            tota ſubtenſa G δ intra circulum jacet.) </s>
            <s xml:id="echoid-s968" xml:space="preserve">Quare P _a_ minor eſt quàm
              <lb/>
            PK; </s>
            <s xml:id="echoid-s969" xml:space="preserve">adeóque PK ſecabit angulum GP _a_. </s>
            <s xml:id="echoid-s970" xml:space="preserve">quamobrem arcùs G _a_ ma-
              <lb/>
            jor erit arcu GK, hoc eſt arcu H δ. </s>
            <s xml:id="echoid-s971" xml:space="preserve">& </s>
            <s xml:id="echoid-s972" xml:space="preserve">idcircò major erit angulus
              <lb/>
            GB _a_ angulo HB δ: </s>
            <s xml:id="echoid-s973" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s974" xml:space="preserve">E. </s>
            <s xml:id="echoid-s975" xml:space="preserve">D.</s>
            <s xml:id="echoid-s976" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s977" xml:space="preserve">Procedit hæc demonſtratio quoad caſum, ubi I &</s>
            <s xml:id="echoid-s978" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s979" xml:space="preserve">R (vel cùm ra-
              <lb/>
            dius è medio rariori denſius ingreditur) at exinde quoad alterum quo-
              <lb/>
            que caſum facilè deducitur concluſio. </s>
            <s xml:id="echoid-s980" xml:space="preserve">Nam ſi viciſſim _a_ B, δ B con-
              <lb/>
            cipiantur incidentes, erunt ipſæ BA, BD earum refractæ; </s>
            <s xml:id="echoid-s981" xml:space="preserve">ac etiam-
              <lb/>
            num anguli _a_ BG, δ BH erunt anguli refracti.</s>
            <s xml:id="echoid-s982" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s983" xml:space="preserve">Hujuſce Theorematis apud _Herigonium_ habetur alia demonſtra-
              <lb/>
              <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">_Diopt
                <unsure/>
              . Prop@.4_.</note>
            tio. </s>
            <s xml:id="echoid-s984" xml:space="preserve">Confer ſodes, & </s>
            <s xml:id="echoid-s985" xml:space="preserve">utramvis elige. </s>
            <s xml:id="echoid-s986" xml:space="preserve">No3 quam res obtulit
              <lb/>
            poſuimus.</s>
            <s xml:id="echoid-s987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s988" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s989" xml:space="preserve">In iſto refractionis caſu, quum I minor eſt quàm R, ſi anguli
              <lb/>
              <note position="right" xlink:label="note-0043-04" xlink:href="note-0043-04a" xml:space="preserve">Fig. 23.</note>
            incidentiæ, puta anguli DBQ, rectus ſinus PH, ad ſinum totum ſe
              <lb/>
            habeat ut I ad R; </s>
            <s xml:id="echoid-s990" xml:space="preserve">nullus incidente DB obliquior radius medium EF
              <lb/>
            refractus ingredietur, aut penetrabit.</s>
            <s xml:id="echoid-s991" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s992" xml:space="preserve">Nam penerret (ſi fieri poteſt) obliquioris alicujus ABG refractus
              <lb/>
            B _a_. </s>
            <s xml:id="echoid-s993" xml:space="preserve">Erit ergo PG. </s>
            <s xml:id="echoid-s994" xml:space="preserve">P _a_ :</s>
            <s xml:id="echoid-s995" xml:space="preserve">: (I. </s>
            <s xml:id="echoid-s996" xml:space="preserve">R :</s>
            <s xml:id="echoid-s997" xml:space="preserve">: ) *PH. </s>
            <s xml:id="echoid-s998" xml:space="preserve">PB. </s>
            <s xml:id="echoid-s999" xml:space="preserve">eſt autem PG
              <lb/>
              <note position="right" xlink:label="note-0043-05" xlink:href="note-0043-05a" xml:space="preserve">*_Hypotb_.</note>
            major quàm PH. </s>
            <s xml:id="echoid-s1000" xml:space="preserve">ergo P _a_ major erit quam PB. </s>
            <s xml:id="echoid-s1001" xml:space="preserve">quod planè
              <lb/>
            fieri nequit. </s>
            <s xml:id="echoid-s1002" xml:space="preserve">Ergò AB non refringetur in medium ipſi EF ſub-
              <lb/>
            jectum.</s>
            <s xml:id="echoid-s1003" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1004" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s1005" xml:space="preserve">Angulus incidentiæ major ad angulum ſuum refractum ma-
              <lb/>
            jorem habet rationem, quam angulus incidentiæ minor ad refra-
              <lb/>
            ctum fuum.</s>
            <s xml:id="echoid-s1006" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1007" xml:space="preserve">Erit ſcilicet (in figura numeri Sexti, cujus huc apparatus transfe-
              <lb/>
              <note position="right" xlink:label="note-0043-06" xlink:href="note-0043-06a" xml:space="preserve">Fig. 27, 22.</note>
            ratur) ang. </s>
            <s xml:id="echoid-s1008" xml:space="preserve">GBP. </s>
            <s xml:id="echoid-s1009" xml:space="preserve">_a_ BP. </s>
            <s xml:id="echoid-s1010" xml:space="preserve">&</s>
            <s xml:id="echoid-s1011" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1012" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1013" xml:space="preserve">HBP. </s>
            <s xml:id="echoid-s1014" xml:space="preserve">δ BP. </s>
            <s xml:id="echoid-s1015" xml:space="preserve">Nam </s>
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