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-s1125" xml:space="preserve">
              <pb o="27" file="0045" n="45" rhead=""/>
            _Carteſio_ quidem primò repertam, ſed ab aliis pleriſque recentioribus
              <lb/>
            opticis _Merſenno. </s>
            <s xml:id="echoid-s1126" xml:space="preserve">Herigonio, Hobbio, Maignano_, quin & </s>
            <s xml:id="echoid-s1127" xml:space="preserve">ipſo ejus
              <lb/>
            conſodale doctiſſimo _Ricciolo_ ſuſceptam & </s>
            <s xml:id="echoid-s1128" xml:space="preserve">approbatam; </s>
            <s xml:id="echoid-s1129" xml:space="preserve">quam & </s>
            <s xml:id="echoid-s1130" xml:space="preserve">cer-
              <lb/>
            tè hujus Scientiæ non parùm intereſt veram deprehendi) labefactatum
              <lb/>
            iret; </s>
            <s xml:id="echoid-s1131" xml:space="preserve">eam potiùs imprudens experientiæ Suffragio communivit. </s>
            <s xml:id="echoid-s1132" xml:space="preserve">Qui-
              <lb/>
            nimò ſi quid inſit huic principio vitii, illud potiùs erit, quod in maxi-
              <lb/>
            mis inclinationibus refractionis angulos exhibet apparentibus ali-
              <lb/>
            quantillo majores; </s>
            <s xml:id="echoid-s1133" xml:space="preserve">quæ tamen diſcrepantia num ipſius legis hujus, an
              <lb/>
            experimentorum defectui, vel accidentariis quíbuſdam intervenienti-
              <lb/>
            bus cauſis adſcribi debeat, haud facilè pronunciaverim. </s>
            <s xml:id="echoid-s1134" xml:space="preserve">Nec enim
              <lb/>
            fortaſſis cognata reflectionis lex, a nemine non admiſſa, experimen-
              <lb/>
            tis omnibus præciſè reſponderet. </s>
            <s xml:id="echoid-s1135" xml:space="preserve">Nobis ſuſficiet quòd in reliquis in-
              <lb/>
            clinationibus, mediis præſertim, dicta lex experientiæ, quam præfe-
              <lb/>
            runt authores, perquam conſentanea reperitur; </s>
            <s xml:id="echoid-s1136" xml:space="preserve">addo, quòd ab ea de-
              <lb/>
            ductæ concluſiones cum experientia mirè conſpirant; </s>
            <s xml:id="echoid-s1137" xml:space="preserve">nec ab ea quòd
              <lb/>
            animadvertere potuerim, unquam diſcordant. </s>
            <s xml:id="echoid-s1138" xml:space="preserve">Eam proinde (cùm alia
              <lb/>
            probabilis haud ſuppetat, Geometricis, ratiociniis præſternenda) non
              <lb/>
            verebimur ubivis ut ratam ſumere, ac adhibere; </s>
            <s xml:id="echoid-s1139" xml:space="preserve">ſatis certi (apud nos
              <lb/>
            ſaltem) in elicitis ab ea concluſionibus haud omnino quicquam nota-
              <lb/>
            bilis erroris emerſurum.</s>
            <s xml:id="echoid-s1140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1141" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s1142" xml:space="preserve">Obiter hîc & </s>
            <s xml:id="echoid-s1143" xml:space="preserve">παρεπβαπκ\~ες problemation quoddam interſeram
              <lb/>
              <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">Fig 21.</note>
            (quia Schema num. </s>
            <s xml:id="echoid-s1144" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1145" xml:space="preserve">ſuperius ei gratis inſerviet, ejuſque conſtructio
              <lb/>
            è ſuperiore conſtructione derivatur.) </s>
            <s xml:id="echoid-s1146" xml:space="preserve">Per datum in refringente pun-
              <lb/>
            ctum (B) incidentem ducere, cui datus conveniat angulus refractionis.
              <lb/>
            </s>
            <s xml:id="echoid-s1147" xml:space="preserve">Ducatur BP refringenti perpendicularis (hanc autem duci poſſe ſup-
              <lb/>
            ponimus, aut poſtulamus) & </s>
            <s xml:id="echoid-s1148" xml:space="preserve">ad diametrum BP conſtruatur ſemicir-
              <lb/>
            culus; </s>
            <s xml:id="echoid-s1149" xml:space="preserve">& </s>
            <s xml:id="echoid-s1150" xml:space="preserve">ſit utcunque PG. </s>
            <s xml:id="echoid-s1151" xml:space="preserve">P _a_ :</s>
            <s xml:id="echoid-s1152" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1153" xml:space="preserve">R (pro PG verò præſtat ipſam
              <lb/>
            diametrum PB accipere) ſumatúrque Arcus GK ſubtendens angulum
              <lb/>
            parem dato. </s>
            <s xml:id="echoid-s1154" xml:space="preserve">Fiat autem PX = P _a_. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">& </s>
            <s xml:id="echoid-s1156" xml:space="preserve">per G, X ducta recta circulo
              <lb/>
            occurrat in δ. </s>
            <s xml:id="echoid-s1157" xml:space="preserve">demum accipiatur Arcus δ H = GK, erit ductæ BH
              <lb/>
            refractus B δ (uti præcedentem diſcurſum invertendo non difficilè col-
              <lb/>
            ligitur) adeóque liquet factum eſſe quod erat propoſitum. </s>
            <s xml:id="echoid-s1158" xml:space="preserve">Hoc præter
              <lb/>
            ordinem; </s>
            <s xml:id="echoid-s1159" xml:space="preserve">ergo perfunctoriè.</s>
            <s xml:id="echoid-s1160" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1161" xml:space="preserve">X. </s>
            <s xml:id="echoid-s1162" xml:space="preserve">Cujuſcunque generis lineæ RBS incidat radius MNO ad N,
              <lb/>
              <note position="right" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">Fig. 24, 25.</note>
            ſitque dictæ lineæ perpendicularis recta NC; </s>
            <s xml:id="echoid-s1163" xml:space="preserve">& </s>
            <s xml:id="echoid-s1164" xml:space="preserve">in hac utcunque
              <lb/>
            ſumpto puncto C, per hoc tranſeat incidenti parallela CB; </s>
            <s xml:id="echoid-s1165" xml:space="preserve">quâcum
              <lb/>
            conveniat ipſius MO inflexus GNK; </s>
            <s xml:id="echoid-s1166" xml:space="preserve">erit in reflectione KN = KC;
              <lb/>
            </s>
            <s xml:id="echoid-s1167" xml:space="preserve">in refractione verò KN. </s>
            <s xml:id="echoid-s1168" xml:space="preserve">KC :</s>
            <s xml:id="echoid-s1169" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1170" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1171" xml:space="preserve">(vel item, ſi in ipſo </s>
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