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-s1015" xml:space="preserve">
              <pb o="26" file="0044" n="44" rhead=""/>
            GP _a_, HP δ ità diſponantur, ut latera PG, PH ſibi congruant (un-
              <lb/>
            de major angulus GP _a_ minorem HP δ comprehendet) tum centro P
              <lb/>
            per δ deſcribatur circulus E δ F ipſas PG, P _a_ ſecans punctis F, E; </s>
            <s xml:id="echoid-s1016" xml:space="preserve">item
              <lb/>
            connexâ EH, centro H per δ tranſeat circulus HMN ipſas HP, HE
              <lb/>
            ſecans punctis N, M; </s>
            <s xml:id="echoid-s1017" xml:space="preserve">denuò connexa E δ cum PG conveniat in L.
              <lb/>
            </s>
            <s xml:id="echoid-s1018" xml:space="preserve">Eſtque jam ang. </s>
            <s xml:id="echoid-s1019" xml:space="preserve">_a_ P δ. </s>
            <s xml:id="echoid-s1020" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1021" xml:space="preserve">δ PH:</s>
            <s xml:id="echoid-s1022" xml:space="preserve">: ſector EP δ. </s>
            <s xml:id="echoid-s1023" xml:space="preserve">ſector δ PF &</s>
            <s xml:id="echoid-s1024" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1025" xml:space="preserve">
              <lb/>
            triang. </s>
            <s xml:id="echoid-s1026" xml:space="preserve">EP δ. </s>
            <s xml:id="echoid-s1027" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s1028" xml:space="preserve">δ PL:</s>
            <s xml:id="echoid-s1029" xml:space="preserve">: Eδ. </s>
            <s xml:id="echoid-s1030" xml:space="preserve">δ L :</s>
            <s xml:id="echoid-s1031" xml:space="preserve">: triang. </s>
            <s xml:id="echoid-s1032" xml:space="preserve">EH δ. </s>
            <s xml:id="echoid-s1033" xml:space="preserve">δ HL &</s>
            <s xml:id="echoid-s1034" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1035" xml:space="preserve">
              <lb/>
            ſector MH δ. </s>
            <s xml:id="echoid-s1036" xml:space="preserve">ſector δ HN :</s>
            <s xml:id="echoid-s1037" xml:space="preserve">: ang. </s>
            <s xml:id="echoid-s1038" xml:space="preserve">EH δ. </s>
            <s xml:id="echoid-s1039" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1040" xml:space="preserve">δ HP. </s>
            <s xml:id="echoid-s1041" xml:space="preserve">eſt igi-
              <lb/>
            tur ang. </s>
            <s xml:id="echoid-s1042" xml:space="preserve">_a_ P δ. </s>
            <s xml:id="echoid-s1043" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1044" xml:space="preserve">δ PH &</s>
            <s xml:id="echoid-s1045" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1046" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1047" xml:space="preserve">EH δ. </s>
            <s xml:id="echoid-s1048" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1049" xml:space="preserve">δ HP. </s>
            <s xml:id="echoid-s1050" xml:space="preserve">ergóque
              <lb/>
            compoſitè ang. </s>
            <s xml:id="echoid-s1051" xml:space="preserve">_a_ PG. </s>
            <s xml:id="echoid-s1052" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1053" xml:space="preserve">δ PH &</s>
            <s xml:id="echoid-s1054" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1055" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1056" xml:space="preserve">EHP. </s>
            <s xml:id="echoid-s1057" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1058" xml:space="preserve">δ HP. </s>
            <s xml:id="echoid-s1059" xml:space="preserve">per-
              <lb/>
            mutandóque ang. </s>
            <s xml:id="echoid-s1060" xml:space="preserve">_a_ PG. </s>
            <s xml:id="echoid-s1061" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1062" xml:space="preserve">EHP &</s>
            <s xml:id="echoid-s1063" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1064" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1065" xml:space="preserve">δ PH. </s>
            <s xml:id="echoid-s1066" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1067" xml:space="preserve">δ HP. </s>
            <s xml:id="echoid-s1068" xml:space="preserve">eſt
              <lb/>
            autem HP. </s>
            <s xml:id="echoid-s1069" xml:space="preserve">PE :</s>
            <s xml:id="echoid-s1070" xml:space="preserve">: HP. </s>
            <s xml:id="echoid-s1071" xml:space="preserve">P δ :</s>
            <s xml:id="echoid-s1072" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1073" xml:space="preserve">R :</s>
            <s xml:id="echoid-s1074" xml:space="preserve">: GP. </s>
            <s xml:id="echoid-s1075" xml:space="preserve">P _a_. </s>
            <s xml:id="echoid-s1076" xml:space="preserve">adeoque EH ad
              <lb/>
            _a_ G parallela; </s>
            <s xml:id="echoid-s1077" xml:space="preserve">vel ang. </s>
            <s xml:id="echoid-s1078" xml:space="preserve">EHP = ang. </s>
            <s xml:id="echoid-s1079" xml:space="preserve">_a_ GP. </s>
            <s xml:id="echoid-s1080" xml:space="preserve">ergò erit ang. </s>
            <s xml:id="echoid-s1081" xml:space="preserve">_a_ PG. </s>
            <s xml:id="echoid-s1082" xml:space="preserve">
              <lb/>
            ang. </s>
            <s xml:id="echoid-s1083" xml:space="preserve">_a_ GP &</s>
            <s xml:id="echoid-s1084" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1085" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1086" xml:space="preserve">δ PH. </s>
            <s xml:id="echoid-s1087" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1088" xml:space="preserve">δ HP. </s>
            <s xml:id="echoid-s1089" xml:space="preserve">hoc eſt ang. </s>
            <s xml:id="echoid-s1090" xml:space="preserve">_a_ BG, _a_ BP
              <lb/>
            &</s>
            <s xml:id="echoid-s1091" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1092" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1093" xml:space="preserve">δ BH. </s>
            <s xml:id="echoid-s1094" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1095" xml:space="preserve">δ BP. </s>
            <s xml:id="echoid-s1096" xml:space="preserve">vel componendo ang. </s>
            <s xml:id="echoid-s1097" xml:space="preserve">GBP. </s>
            <s xml:id="echoid-s1098" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1099" xml:space="preserve">_a_ BP
              <lb/>
            &</s>
            <s xml:id="echoid-s1100" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1101" xml:space="preserve">ang HBP. </s>
            <s xml:id="echoid-s1102" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s1103" xml:space="preserve">δ BP. </s>
            <s xml:id="echoid-s1104" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1105" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div32" type="section" level="1" n="12">
          <head xml:id="echoid-head15" xml:space="preserve">_Corol_. 1. Ang. _a_ BG. ang. _a_ BP &gt; ang. δ BH. ang. δ BP.
            <lb/>
          2. Ang. _a_ BG. ang. PBG &gt; ang. δ BH. PBH.</head>
          <p>
            <s xml:id="echoid-s1106" xml:space="preserve">Opportunum eſt hoc Theorema conciliandis cum experientia pro-
              <lb/>
            poſitis refractionum legibus. </s>
            <s xml:id="echoid-s1107" xml:space="preserve">Ut demirari ſubeat nuperrimum Opticæ
              <lb/>
            ſcriptorem, virum alioqui diffuſè doctum, hujuſmodi ratiocinio leges
              <lb/>
            iſtas impugnàſſe: </s>
            <s xml:id="echoid-s1108" xml:space="preserve">“In majoribus tamen angulis inclinationis (Ipſiſ-
              <lb/>
            "ſima ſunt ejus verba) falſum eſſe conſtat (principium nempe no-
              <lb/>
            "ſtrum;) </s>
            <s xml:id="echoid-s1109" xml:space="preserve">in his enim angulus refractionis major eſt ſubtriplo an-
              <lb/>
            "guli inclinationis; </s>
            <s xml:id="echoid-s1110" xml:space="preserve">quod mihi aliiſque ex luculentis experimentis
              <lb/>
            "compertum eſt. </s>
            <s xml:id="echoid-s1111" xml:space="preserve">Hæc, inquam, ille ταντοεπ@. </s>
            <s xml:id="echoid-s1112" xml:space="preserve">Quaſi verò dixiſſet;
              <lb/>
            </s>
            <s xml:id="echoid-s1113" xml:space="preserve">numeri 6 & </s>
            <s xml:id="echoid-s1114" xml:space="preserve">4 ſimul accepti non conficiunt 10, quia numerum effici-
              <lb/>
            unt majorem quam 8. </s>
            <s xml:id="echoid-s1115" xml:space="preserve">planè ſimilis eſt diſcurſus; </s>
            <s xml:id="echoid-s1116" xml:space="preserve">non ovum ovo ſi-
              <lb/>
            milius. </s>
            <s xml:id="echoid-s1117" xml:space="preserve">Nam in refractionibus ex. </s>
            <s xml:id="echoid-s1118" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1119" xml:space="preserve">ad vitrum factis ſi ponatur ad
              <lb/>
            quamvis inclinationem (puta graduum 15.) </s>
            <s xml:id="echoid-s1120" xml:space="preserve">quòd ſit angulus refra-
              <lb/>
            ctionis ſubtriplus anguli inclinationis (quem ille vocat, incidentiæ nos
              <lb/>
            angulum appellare ſolemus) neceſſariò, ſicuti modò demonſtratum
              <lb/>
            eſt, è principio noſtro conſequetur, quòd ad aliam quamcunque ma-
              <lb/>
            jorem inclinationem refractionis angulus major erit ſubtriplo anguli
              <lb/>
            inclinationis; </s>
            <s xml:id="echoid-s1121" xml:space="preserve">nominatim acceptâ graduum 30 inclinatione juxta di-
              <lb/>
            ctum principium inſtitutus calculus angulum præbebit reſractum
              <lb/>
            19.</s>
            <s xml:id="echoid-s1122" xml:space="preserve">24'; </s>
            <s xml:id="echoid-s1123" xml:space="preserve">angulúmque proinde refractionis 10. </s>
            <s xml:id="echoid-s1124" xml:space="preserve">36', qui 30 graduum
              <lb/>
            trientem exuperat. </s>
            <s xml:id="echoid-s1125" xml:space="preserve">Quare cùm Clariſſimus vir Hypotheſin hanc </s>
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    </echo>
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