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

Table of figures

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        <div xml:id="echoid-div488" type="section" level="1" n="51">
          <head xml:id="echoid-head54" xml:space="preserve">Prop. 3.</head>
          <p>
            <s xml:id="echoid-s14769" xml:space="preserve">Datus ſit _Conus rectus_ ABC _p._ </s>
            <s xml:id="echoid-s14770" xml:space="preserve">Secetur à plano (puta _triangulo_
              <lb/>
              <note position="left" xlink:label="note-0298-01" xlink:href="note-0298-01a" xml:space="preserve">Fig. 178.</note>
            _qrt_) quod quidem planum ſecabit _axem coni_ in puncto _q_ ſupra _verti-_
              <lb/>
            _cem_ productum & </s>
            <s xml:id="echoid-s14771" xml:space="preserve">in communi interſectione cum _ſuperficie coni_ habe-
              <lb/>
            bit _lineam byperbolicam_ RS_t_ ducantur à vertice coni A rectæ A _r_, A _t_,
              <lb/>
            à puncto _q_ demittatur perpendiculum _q_ X lateri coni A _p_ producto & </s>
            <s xml:id="echoid-s14772" xml:space="preserve">à
              <lb/>
            puncto A perpendiculum AZplano _qrt._</s>
            <s xml:id="echoid-s14773" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14774" xml:space="preserve">Dico _ſuperficies contca_ terminata à _linca byperbolica, rst_ & </s>
            <s xml:id="echoid-s14775" xml:space="preserve">rectis
              <lb/>
            _r_ A, _t_ A, ita ſe habet ad _figuram byperbolicam cavam qrstq_ ut _perpen-_
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            _diculum_ AZad _perpendiculum q_ X.</s>
            <s xml:id="echoid-s14776" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14777" xml:space="preserve">Recta enim _qr_, circumlata, quieſcente termino _q_ per lineas _rst, t_ A, Ar
              <lb/>
            generat tres _ſuperficies_, nempe _byperbolicam cavam qr, st_, & </s>
            <s xml:id="echoid-s14778" xml:space="preserve">_duo tri-_
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            _angula qt_ A, _q_ A _r_, quæ unà cum _ſuperficie conica_ terminata à lineis
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            _rst, t_ A, A _r_, comprehendunt _Solidum qrs, t_ A _r._ </s>
            <s xml:id="echoid-s14779" xml:space="preserve">Hoc verò _ſolidum_
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            _œguale_ eſt _pyramidi_ cujus _altitudo_ eſt æqualis perpendiculo _q_ X, nam
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            infinitæ pyramides _q_ A _r_ V, _q_ AVV, exhauriunt ſolidum _qr_ S _t_ A _r._
              <lb/>
            </s>
            <s xml:id="echoid-s14780" xml:space="preserve">Si verò aliter contemplari volumus, hoc ſolidum _qrst_ A _r_ poteſt con-
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            ſideraritanquam _ſigura @onica_ A _r_ S _tqr_ habens pro _baſe figuram by-_
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            _perbolicam_ cavam _qr_ S _tq_, & </s>
            <s xml:id="echoid-s14781" xml:space="preserve">pro altitudine _perpendiculum_ AZ. </s>
            <s xml:id="echoid-s14782" xml:space="preserve">Ergò
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            reciprocando _baſes altitudinibus_, ut AZad q X, ita _ſuperficies, r_ S t A _r_
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            ad _figuram byperbolicam cavam qr_ S _tq._</s>
            <s xml:id="echoid-s14783" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div490" type="section" level="1" n="52">
          <head xml:id="echoid-head55" xml:space="preserve">Prop. 4.</head>
          <p>
            <s xml:id="echoid-s14784" xml:space="preserve">Datus ſit _Conus rectus_ AB _b g_ ſecetur à plano HFEGper axem
              <lb/>
            infra verticem, a puncto H ubi _planum_ fecat _axem coni_, demittatur HK
              <lb/>
              <note position="left" xlink:label="note-0298-02" xlink:href="note-0298-02a" xml:space="preserve">Fig. 179.</note>
            _perpendiculum_ lateri cuilibet coni & </s>
            <s xml:id="echoid-s14785" xml:space="preserve">à verticè A _perpendiculum_ ALpla-
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            no HFE G.</s>
            <s xml:id="echoid-s14786" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14787" xml:space="preserve">Dico, _Superſicies conica_ terminata a lineis FECGAAF ita ſe
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            habebit ad _planum_ HFEG ut _perpendiculum_ AL ad _perpendiculum_
              <lb/>
            H K.</s>
            <s xml:id="echoid-s14788" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14789" xml:space="preserve">Probatur eodem fere eodem fere argumento quo ſuperior.</s>
            <s xml:id="echoid-s14790" xml:space="preserve"/>
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