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

Page concordance

< >
Scan Original
281 88
282 89
283 90
284 91
285 92
286 93
287 94
288 95
289 96
290 97
291 98
292 99
293 100
294 101
295 102
296 103
297 104
298 105
299 106
300 107
301 108
302 109
303 110
304 111
305 112
306 113
307 114
308 115
309 116
310 117
< >
page |< < (95) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div399" type="section" level="1" n="42">
          <p>
            <s xml:id="echoid-s13094" xml:space="preserve">
              <pb o="95" file="0273" n="288" rhead=""/>
            ipſam AFB) ſit perpetuo TG major quàm SG; </s>
            <s xml:id="echoid-s13095" xml:space="preserve">dico nullam cur-
              <lb/>
            væ AFB partem intra ipſam AEB cadere.</s>
            <s xml:id="echoid-s13096" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13097" xml:space="preserve">Si fieri poteſt, cadat pars NFM; </s>
            <s xml:id="echoid-s13098" xml:space="preserve">ità ſcilicet ut curva AFB cur-
              <lb/>
            vam AEB interſecet punctis M, N; </s>
            <s xml:id="echoid-s13099" xml:space="preserve">his autem interjecta concipiatur
              <lb/>
            indeterminatè ordinata EFG; </s>
            <s xml:id="echoid-s13100" xml:space="preserve">ſint verò lineæ LXK, RYQ tales,
              <lb/>
            utductis rectis EO, FP ad ipſas ES, FT perpendicularibus, protra-
              <lb/>
            ctâque rectâ EG, ut hæc dictas lineas LK, QR ſecet punctis X, Y;
              <lb/>
            </s>
            <s xml:id="echoid-s13101" xml:space="preserve">ſit GX = GO, & </s>
            <s xml:id="echoid-s13102" xml:space="preserve">GY = GP. </s>
            <s xml:id="echoid-s13103" xml:space="preserve">Jam ex oſtenſis patet eſſe _ſpatium_
              <lb/>
            IHKL = {HMq - INq/2} = ſpat. </s>
            <s xml:id="echoid-s13104" xml:space="preserve">IHQR; </s>
            <s xml:id="echoid-s13105" xml:space="preserve">adeóq; </s>
            <s xml:id="echoid-s13106" xml:space="preserve">ſpat. </s>
            <s xml:id="echoid-s13107" xml:space="preserve">IHKL, IHQR
              <lb/>
            æquari. </s>
            <s xml:id="echoid-s13108" xml:space="preserve">Verùm ob GE. </s>
            <s xml:id="echoid-s13109" xml:space="preserve">GO (GX):</s>
            <s xml:id="echoid-s13110" xml:space="preserve">: SG; </s>
            <s xml:id="echoid-s13111" xml:space="preserve">GE. </s>
            <s xml:id="echoid-s13112" xml:space="preserve">&</s>
            <s xml:id="echoid-s13113" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13114" xml:space="preserve">SG. </s>
            <s xml:id="echoid-s13115" xml:space="preserve">GF &</s>
            <s xml:id="echoid-s13116" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13117" xml:space="preserve">TG. </s>
            <s xml:id="echoid-s13118" xml:space="preserve">GF:</s>
            <s xml:id="echoid-s13119" xml:space="preserve">:
              <lb/>
            GF. </s>
            <s xml:id="echoid-s13120" xml:space="preserve">GP (GY) &</s>
            <s xml:id="echoid-s13121" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13122" xml:space="preserve">GE. </s>
            <s xml:id="echoid-s13123" xml:space="preserve">GY; </s>
            <s xml:id="echoid-s13124" xml:space="preserve">eſt GX &</s>
            <s xml:id="echoid-s13125" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13126" xml:space="preserve">GY; </s>
            <s xml:id="echoid-s13127" xml:space="preserve">adeòque (cùm
              <lb/>
            hoc ubique ſimiliter contingat) ſpatium IHKL majus ſpatio IHQR; </s>
            <s xml:id="echoid-s13128" xml:space="preserve">
              <lb/>
            quod repugnat oſtenſo. </s>
            <s xml:id="echoid-s13129" xml:space="preserve">itaque liquet Propoſitum.</s>
            <s xml:id="echoid-s13130" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13131" xml:space="preserve">Hinc tota AFB extra totam AEB jacet, nec illa hane uſquam inter-
              <lb/>
            ſecat.</s>
            <s xml:id="echoid-s13132" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13133" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s13134" xml:space="preserve">Sit curva quæpiam BAE, cujus axis AD, & </s>
            <s xml:id="echoid-s13135" xml:space="preserve">ad hunc ordina-
              <lb/>
              <note position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">Fig. 135.</note>
            ta baſis ADE; </s>
            <s xml:id="echoid-s13136" xml:space="preserve">ſegmenti verò BAE centrum gravitatis ſit punctum
              <lb/>
            H, qer quod ducta ſit recta RS ad BE parallela Porrò per puncta
              <lb/>
            R, S tranſeat altera curva (vel linea quævis) MR ASN, habens iti-
              <lb/>
            dem axin AD, ac ita priorem curvam BAE ſecans, ut ejuſce pars
              <lb/>
            ſuperior RKAP Sintra curvam BAE cadat, inferiores verò reliquæ
              <lb/>
            partes RM, SN extra eandem; </s>
            <s xml:id="echoid-s13137" xml:space="preserve">erit ſegmenti MRASN centrum
              <lb/>
            gravitatis infra punctum H, verſus baſin MN.</s>
            <s xml:id="echoid-s13138" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13139" xml:space="preserve">Nam è ſegmento RIAO Sablatum RIAK + AOSP reſidu-
              <lb/>
            um BRKAPSE deprimet verſus baſin BE, puta ut jam ſit hujus
              <lb/>
            reſidui _Centrum gravitatis_ ad X; </s>
            <s xml:id="echoid-s13140" xml:space="preserve">tunc adjunctum BRM + ESN
              <lb/>
            adhuc totum MRKAPSN magis deprimet; </s>
            <s xml:id="echoid-s13141" xml:space="preserve">adeóque centrum ejus
              <lb/>
            infra X conſiſtet, velut ad Y. </s>
            <s xml:id="echoid-s13142" xml:space="preserve">itaque conſtat Propoſitum.</s>
            <s xml:id="echoid-s13143" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13144" xml:space="preserve">V. </s>
            <s xml:id="echoid-s13145" xml:space="preserve">_Circulum_ AFB, cujus _Centrum_ C, tangant duæ rectæ BT, E S
              <lb/>
              <note position="right" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">Fig. 136.</note>
            _Diametro_ CA occurrentes punctis T, S; </s>
            <s xml:id="echoid-s13146" xml:space="preserve">& </s>
            <s xml:id="echoid-s13147" xml:space="preserve">ad CA perpendiculares
              <lb/>
            ſint rectæ BD, EP; </s>
            <s xml:id="echoid-s13148" xml:space="preserve">ſit autem AD major quàm AP; </s>
            <s xml:id="echoid-s13149" xml:space="preserve">erit TD. </s>
            <s xml:id="echoid-s13150" xml:space="preserve">AD
              <lb/>
            &</s>
            <s xml:id="echoid-s13151" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13152" xml:space="preserve">SP. </s>
            <s xml:id="echoid-s13153" xml:space="preserve">AP.</s>
            <s xml:id="echoid-s13154" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13155" xml:space="preserve">Nam eſt CT. </s>
            <s xml:id="echoid-s13156" xml:space="preserve">CA:</s>
            <s xml:id="echoid-s13157" xml:space="preserve">: CA. </s>
            <s xml:id="echoid-s13158" xml:space="preserve">CD. </s>
            <s xml:id="echoid-s13159" xml:space="preserve">Ideoque CT - CA. </s>
            <s xml:id="echoid-s13160" xml:space="preserve">CA -
              <lb/>
            CD:</s>
            <s xml:id="echoid-s13161" xml:space="preserve">: CT. </s>
            <s xml:id="echoid-s13162" xml:space="preserve">CA; </s>
            <s xml:id="echoid-s13163" xml:space="preserve">hoc eſt TA. </s>
            <s xml:id="echoid-s13164" xml:space="preserve">AD:</s>
            <s xml:id="echoid-s13165" xml:space="preserve">: CT. </s>
            <s xml:id="echoid-s13166" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s13167" xml:space="preserve">Simili ratione conſtabit
              <lb/>
            eſſe SA. </s>
            <s xml:id="echoid-s13168" xml:space="preserve">AP:</s>
            <s xml:id="echoid-s13169" xml:space="preserve">: CS. </s>
            <s xml:id="echoid-s13170" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s13171" xml:space="preserve">Eſt autem CT. </s>
            <s xml:id="echoid-s13172" xml:space="preserve">CA &</s>
            <s xml:id="echoid-s13173" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13174" xml:space="preserve">CS. </s>
            <s xml:id="echoid-s13175" xml:space="preserve">CA.
              <lb/>
            </s>
            <s xml:id="echoid-s13176" xml:space="preserve">quare TA, AD &</s>
            <s xml:id="echoid-s13177" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13178" xml:space="preserve">SA. </s>
            <s xml:id="echoid-s13179" xml:space="preserve">AP. </s>
            <s xml:id="echoid-s13180" xml:space="preserve">vel componendo TD. </s>
            <s xml:id="echoid-s13181" xml:space="preserve">AD &</s>
            <s xml:id="echoid-s13182" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13183" xml:space="preserve">SP. </s>
            <s xml:id="echoid-s13184" xml:space="preserve">
              <lb/>
            AP.</s>
            <s xml:id="echoid-s13185" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum