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-s3922" xml:space="preserve">
              <pb o="65" file="0083" n="83" rhead=""/>
            nihilominùs gravatim admittuntur; </s>
            <s xml:id="echoid-s3923" xml:space="preserve">iſtâ tantummodò raptim inſinua-
              <lb/>
            tâ, ſubnectemus alìam ab illorum guſtu non abhorrentem; </s>
            <s xml:id="echoid-s3924" xml:space="preserve">illam
              <lb/>
            nempe (quando ſcilicet haud alia melior, ut varias pertentans analyſes,
              <lb/>
            & </s>
            <s xml:id="echoid-s3925" xml:space="preserve">hoc in alia complura _Problemata_ transformans exiſtimari poſſum,
              <lb/>
            facilè poſſit excogitari; </s>
            <s xml:id="echoid-s3926" xml:space="preserve">quum & </s>
            <s xml:id="echoid-s3927" xml:space="preserve">operæ meæ ſatìs alioquin exerci-
              <lb/>
            tatæ nonnunquam videatur parcendum) quam olim _Alhazenus Arabs_
              <lb/>
            ſcriptis commendavit; </s>
            <s xml:id="echoid-s3928" xml:space="preserve">ab horribili tamen illâ prolixitate ſimul ac
              <lb/>
            obſcuritate; </s>
            <s xml:id="echoid-s3929" xml:space="preserve">neque non ab incondita ſermonis barbarie nonnihil re-
              <lb/>
            purgatam. </s>
            <s xml:id="echoid-s3930" xml:space="preserve">quorſum hoc præmittimus _Lemmaticum Problema._</s>
            <s xml:id="echoid-s3931" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3932" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s3933" xml:space="preserve">Trianguli DPNangulus ad P rectus ſit; </s>
            <s xml:id="echoid-s3934" xml:space="preserve">& </s>
            <s xml:id="echoid-s3935" xml:space="preserve">in hujus uno cru-
              <lb/>
              <note position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">Fig. 91.</note>
            re PN adſignetur punctum F; </s>
            <s xml:id="echoid-s3936" xml:space="preserve">per F recta ducenda eſt, quæ reli-
              <lb/>
            quum latus DP (protractam nempe) ac hypotenuſam DN ità ſecet,
              <lb/>
            ut ab illis intercepta ad ſegmentum hypotenuſæ lateri primò contermi-
              <lb/>
            num datam obtineat proportionem R ad S.</s>
            <s xml:id="echoid-s3937" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3938" xml:space="preserve">Hoc ità peragatur licet. </s>
            <s xml:id="echoid-s3939" xml:space="preserve">Ducatur FH ad PD parallela. </s>
            <s xml:id="echoid-s3940" xml:space="preserve">& </s>
            <s xml:id="echoid-s3941" xml:space="preserve">Dia-
              <lb/>
            metro HN deſcribatur Circulus HFN(is nempe per F tranſibit, ob
              <lb/>
            angulum HFNrectum) tum connectatur DF; </s>
            <s xml:id="echoid-s3942" xml:space="preserve">& </s>
            <s xml:id="echoid-s3943" xml:space="preserve">fiat angulus
              <lb/>
            FHI = ang. </s>
            <s xml:id="echoid-s3944" xml:space="preserve">FD N. </s>
            <s xml:id="echoid-s3945" xml:space="preserve">ſit etiam R. </s>
            <s xml:id="echoid-s3946" xml:space="preserve">S:</s>
            <s xml:id="echoid-s3947" xml:space="preserve">: DF. </s>
            <s xml:id="echoid-s3948" xml:space="preserve">T & </s>
            <s xml:id="echoid-s3949" xml:space="preserve">a puncto I duca-
              <lb/>
            tur recta ILKdiametrum HN interſecans ad L, & </s>
            <s xml:id="echoid-s3950" xml:space="preserve">circulo occurrens
              <lb/>
            in K, ità quidem ut ſit intercepta LK = T (hoc autem quomodò
              <lb/>
            præſtetur in ſuperioribus oſtenſum) denuo per puncta KF trajiciatur
              <lb/>
            recta CF, ipſam DP ſecans in X. </s>
            <s xml:id="echoid-s3951" xml:space="preserve">Dico factum, vel ipſe CX.
              <lb/>
            </s>
            <s xml:id="echoid-s3952" xml:space="preserve">CN:</s>
            <s xml:id="echoid-s3953" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s3954" xml:space="preserve">S. </s>
            <s xml:id="echoid-s3955" xml:space="preserve">connectatur enim recta NK. </s>
            <s xml:id="echoid-s3956" xml:space="preserve">& </s>
            <s xml:id="echoid-s3957" xml:space="preserve">quoniam ang FK I
              <lb/>
              <note position="right" xlink:label="note-0083-02" xlink:href="note-0083-02a" xml:space="preserve">_Conſtr. &._</note>
            (vel FH I) = FDN, erit triangulum FDCſimile triangulo
              <lb/>
            LK C; </s>
            <s xml:id="echoid-s3958" xml:space="preserve">ac indè FD. </s>
            <s xml:id="echoid-s3959" xml:space="preserve">DC:</s>
            <s xml:id="echoid-s3960" xml:space="preserve">: KL. </s>
            <s xml:id="echoid-s3961" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s3962" xml:space="preserve">item ob ang. </s>
            <s xml:id="echoid-s3963" xml:space="preserve">FKN = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s3964" xml:space="preserve">FHN = ang. </s>
            <s xml:id="echoid-s3965" xml:space="preserve">XDC; </s>
            <s xml:id="echoid-s3966" xml:space="preserve">erunt triangula XDC, NKCſibi quoque
              <lb/>
            ſimilia, proindéque DC. </s>
            <s xml:id="echoid-s3967" xml:space="preserve">CX:</s>
            <s xml:id="echoid-s3968" xml:space="preserve">: CK. </s>
            <s xml:id="echoid-s3969" xml:space="preserve">CN. </s>
            <s xml:id="echoid-s3970" xml:space="preserve">quapropter erit ex
              <lb/>
            æquali FD. </s>
            <s xml:id="echoid-s3971" xml:space="preserve">CX :</s>
            <s xml:id="echoid-s3972" xml:space="preserve">: KL. </s>
            <s xml:id="echoid-s3973" xml:space="preserve">CN. </s>
            <s xml:id="echoid-s3974" xml:space="preserve">vel permutando FDCK:</s>
            <s xml:id="echoid-s3975" xml:space="preserve">: CX. </s>
            <s xml:id="echoid-s3976" xml:space="preserve">
              <lb/>
            C N; </s>
            <s xml:id="echoid-s3977" xml:space="preserve">hoc eſt FD. </s>
            <s xml:id="echoid-s3978" xml:space="preserve">T (vel R. </s>
            <s xml:id="echoid-s3979" xml:space="preserve">S):</s>
            <s xml:id="echoid-s3980" xml:space="preserve">: CX. </s>
            <s xml:id="echoid-s3981" xml:space="preserve">CN; </s>
            <s xml:id="echoid-s3982" xml:space="preserve">quod faciendum
              <lb/>
            erat.</s>
            <s xml:id="echoid-s3983" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3984" xml:space="preserve">Advertendum eſt autem, quod datum punctum F in recta PN
              <lb/>
            indefinitè protenſa variè ſtatui poteſt; </s>
            <s xml:id="echoid-s3985" xml:space="preserve">vel nimirum inter puncta P,
              <lb/>
            N; </s>
            <s xml:id="echoid-s3986" xml:space="preserve">vel extra illa partes ad alterutras item quòd in iſtorum caſuum
              <lb/>
            ſingulo quoque recta IK (conditione gaudens præſtitutâ) plurifa-
              <lb/>
            riàm duci poteſt; </s>
            <s xml:id="echoid-s3987" xml:space="preserve">ut antehac inculcatum; </s>
            <s xml:id="echoid-s3988" xml:space="preserve">unde plures emergent ſolu-
              <lb/>
            tiones. </s>
            <s xml:id="echoid-s3989" xml:space="preserve">at quoad omnes caſus perſimilis erit conſtructio, nec ferè di-
              <lb/>
            verſa demonſtratio. </s>
            <s xml:id="echoid-s3990" xml:space="preserve">quare cur plura?</s>
            <s xml:id="echoid-s3991" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3992" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s3993" xml:space="preserve">Proponatur jam circulus reflectens (is qui præ oculis, </s>
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