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

Page concordance

< >
Scan Original
81 63
82 64
83 65
84 66
85 67
86 68
87 69
88 70
89 71
90 72
91 73
92 74
93 75
94 76
95 77
96 78
97 79
98 80
99 81
100 82
101 83
102 84
103 85
104 86
105 87
106 88
107 89
108 90
109 91
110 92
< >
page |< < (65) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div99" type="section" level="1" n="18">
          <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>
          </p>
        </div>
      </text>
    </echo>
Impressum