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

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          <p>
            <s xml:id="echoid-s1171" xml:space="preserve">
              <pb o="28" file="0046" n="46" rhead=""/>
            ſumatur utcunque punctum K; </s>
            <s xml:id="echoid-s1172" xml:space="preserve">& </s>
            <s xml:id="echoid-s1173" xml:space="preserve">ab eo ducta KL ad perpendicularem
              <lb/>
            CN parallela cum incidente conveniet ad L, erit illic KN = NL; </s>
            <s xml:id="echoid-s1174" xml:space="preserve">& </s>
            <s xml:id="echoid-s1175" xml:space="preserve">
              <lb/>
            hìc KN. </s>
            <s xml:id="echoid-s1176" xml:space="preserve">NL :</s>
            <s xml:id="echoid-s1177" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1178" xml:space="preserve">R.)</s>
            <s xml:id="echoid-s1179" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1180" xml:space="preserve">Nam 1. </s>
            <s xml:id="echoid-s1181" xml:space="preserve">in reflectione; </s>
            <s xml:id="echoid-s1182" xml:space="preserve">quoniam ang. </s>
            <s xml:id="echoid-s1183" xml:space="preserve">ONC = KNC (ex lege
              <lb/>
              <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">Fig. 24, 25.</note>
            reflectionis.) </s>
            <s xml:id="echoid-s1184" xml:space="preserve">Etang. </s>
            <s xml:id="echoid-s1185" xml:space="preserve">ONC = KCN (ex Hypotheſi quòd ON,
              <lb/>
            CB parallelæ ſunt ) erit ang. </s>
            <s xml:id="echoid-s1186" xml:space="preserve">KCN = ang. </s>
            <s xml:id="echoid-s1187" xml:space="preserve">KNC. </s>
            <s xml:id="echoid-s1188" xml:space="preserve">adeóque KN
              <lb/>
            = KC = NL: </s>
            <s xml:id="echoid-s1189" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s1190" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1192" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1193" xml:space="preserve">2 In refractione; </s>
            <s xml:id="echoid-s1194" xml:space="preserve">ducantur CE ad NO, & </s>
            <s xml:id="echoid-s1195" xml:space="preserve">CF ad NK perpen-
              <lb/>
            diculares (unde liquet puncta E, F exiſtere in circulo ſuper diametrum
              <lb/>
            CN deſcripto) quare, connexâ EF; </s>
            <s xml:id="echoid-s1196" xml:space="preserve">erunt anguli CEF = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s1197" xml:space="preserve">FNC (eidem inſiſtentes peripheriæ FC) æquales. </s>
            <s xml:id="echoid-s1198" xml:space="preserve">Item propterea
              <lb/>
            eſt ang. </s>
            <s xml:id="echoid-s1199" xml:space="preserve">ECF = ang. </s>
            <s xml:id="echoid-s1200" xml:space="preserve">FNE = ang. </s>
            <s xml:id="echoid-s1201" xml:space="preserve">NKC. </s>
            <s xml:id="echoid-s1202" xml:space="preserve">quare triangula ECF,
              <lb/>
            NKC ſunt æquiangula ſibi mutuo; </s>
            <s xml:id="echoid-s1203" xml:space="preserve">quamobrem eſt CE. </s>
            <s xml:id="echoid-s1204" xml:space="preserve">CF:</s>
            <s xml:id="echoid-s1205" xml:space="preserve">:
              <lb/>
            KN. </s>
            <s xml:id="echoid-s1206" xml:space="preserve">KC. </s>
            <s xml:id="echoid-s1207" xml:space="preserve">atqui (juxta legem refractionis) eſt CE. </s>
            <s xml:id="echoid-s1208" xml:space="preserve">CF:</s>
            <s xml:id="echoid-s1209" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1211" xml:space="preserve">
              <lb/>
            qua propter erit, KN .</s>
            <s xml:id="echoid-s1212" xml:space="preserve">. KC :</s>
            <s xml:id="echoid-s1213" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1214" xml:space="preserve">R : </s>
            <s xml:id="echoid-s1215" xml:space="preserve">vel KN. </s>
            <s xml:id="echoid-s1216" xml:space="preserve">NL :</s>
            <s xml:id="echoid-s1217" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1218" xml:space="preserve">R: </s>
            <s xml:id="echoid-s1219" xml:space="preserve">
              <lb/>
            Q. </s>
            <s xml:id="echoid-s1220" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1221" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1222" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1223" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s1224" xml:space="preserve">Quod ſi per N ducatur tangens UT; </s>
            <s xml:id="echoid-s1225" xml:space="preserve">erit (in reflectione) eti-
              <lb/>
            am KT = KN; </s>
            <s xml:id="echoid-s1226" xml:space="preserve">& </s>
            <s xml:id="echoid-s1227" xml:space="preserve">NT angulum MNK biſecabit. </s>
            <s xml:id="echoid-s1228" xml:space="preserve">In refracti-
              <lb/>
            one verò erit KT ad KN, ut co-ſinus anguli refracti, ad coſinum an-
              <lb/>
            guli incidentiæ. </s>
            <s xml:id="echoid-s1229" xml:space="preserve">Quæ ſaltem ad noto, ceu Lemmatica.</s>
            <s xml:id="echoid-s1230" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1231" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">Exhis facilè deducantur Conicarum Sectionum circa radiorum
              <lb/>
            inflectionem ſatis jam pervulgatæ proprietates; </s>
            <s xml:id="echoid-s1233" xml:space="preserve">at quæ fortaſsè per
              <lb/>
            nimias ambages.</s>
            <s xml:id="echoid-s1234" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1235" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1236" xml:space="preserve">Demonſtratæ proſtant. </s>
            <s xml:id="echoid-s1237" xml:space="preserve">Ut in parabola (puta RBS, cujus axis
              <lb/>
            BC) incidat MNO axi BC parallelus; </s>
            <s xml:id="echoid-s1238" xml:space="preserve">ejuſque reflexus ſit NK;
              <lb/>
            </s>
            <s xml:id="echoid-s1239" xml:space="preserve">crit igitur (ex oſtenſis) KN = KC. </s>
            <s xml:id="echoid-s1240" xml:space="preserve">at ſi punctum K ponatur umbi-
              <lb/>
            licus parabolæ; </s>
            <s xml:id="echoid-s1241" xml:space="preserve">erit etiam indè (juxta notiſſimam hujuſce curvæ pro-
              <lb/>
            prietatem) KN = KC. </s>
            <s xml:id="echoid-s1242" xml:space="preserve">quare paralleli radii reflexus neceſſariò
              <lb/>
            per umbilicum tranſibit; </s>
            <s xml:id="echoid-s1243" xml:space="preserve">qui proptereà non immeritò quoque _focus_
              <lb/>
            appèllatur.</s>
            <s xml:id="echoid-s1244" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1245" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">Item _in ellipſe_, cujus axis BD, foci H, K, ſi ad quodvis curvæ
              <lb/>
              <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">Fig. 26.</note>
            punctum N à focis ducantur rectæ HN, KN; </s>
            <s xml:id="echoid-s1247" xml:space="preserve">ſatis celebre eſt, quòd
              <lb/>
            perpendicularis CN angulum HNK biſecabit. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">Unde NH. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">NK:</s>
            <s xml:id="echoid-s1250" xml:space="preserve">:
              <lb/>
            HC. </s>
            <s xml:id="echoid-s1251" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s1252" xml:space="preserve">& </s>
            <s xml:id="echoid-s1253" xml:space="preserve">componendo NH + NK. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">NK :</s>
            <s xml:id="echoid-s1255" xml:space="preserve">: HK. </s>
            <s xml:id="echoid-s1256" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s1257" xml:space="preserve">vel BD.
              <lb/>
            </s>
            <s xml:id="echoid-s1258" xml:space="preserve">NK :</s>
            <s xml:id="echoid-s1259" xml:space="preserve">: HK. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s1261" xml:space="preserve">vel permutando BD. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">HK :</s>
            <s xml:id="echoid-s1263" xml:space="preserve">: NK. </s>
            <s xml:id="echoid-s1264" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s1265" xml:space="preserve">quare
              <lb/>
            ſi talis@fuerit ellipſis, ut ſit BD. </s>
            <s xml:id="echoid-s1266" xml:space="preserve">HK :</s>
            <s xml:id="echoid-s1267" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1268" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1269" xml:space="preserve">etiam erit NK. </s>
            <s xml:id="echoid-s1270" xml:space="preserve">CK:</s>
            <s xml:id="echoid-s1271" xml:space="preserve">:
              <lb/>
            I. </s>
            <s xml:id="echoid-s1272" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1273" xml:space="preserve">verum ſi incidens MN ad BD parallelus refringatur in NK; </s>
            <s xml:id="echoid-s1274" xml:space="preserve">
              <lb/>
            erit (juxta mox oſtenſa) etiam NK. </s>
            <s xml:id="echoid-s1275" xml:space="preserve">CK:</s>
            <s xml:id="echoid-s1276" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1277" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1278" xml:space="preserve">patet itaque quòd
              <lb/>
            ipſius MN refractus per focum K tranſibit, Quid plura?</s>
            <s xml:id="echoid-s1279" xml:space="preserve"/>
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