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

Page concordance

< >
Scan Original
241 48
242 49
243 50
244 51
245 52
246 53
247 54
248 55
249 56
250 57
251 58
252 59
253 60
254 61
255 62
256 63
257 64
258 65
259 66
260 67
261 68
262 69
263 70
264 71
265 72
266 73
267 74
268 75
269 76
270 77
< >
page |< < (15) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div218" type="section" level="1" n="29">
          <p>
            <s xml:id="echoid-s8625" xml:space="preserve">
              <pb o="15" file="0193" n="208" rhead=""/>
            puncta quævis EE rectâ lineâ connectantur, iíſque reſpondentia
              <lb/>
            puncta BB rectâ quoque jungantur; </s>
            <s xml:id="echoid-s8626" xml:space="preserve">quoniam rectæ EB ſibimet
              <lb/>
            æquantur (etenim nil aliud ſunt, quam eadem ipſa linea diverſum
              <lb/>
              <note position="right" xlink:label="note-0193-01" xlink:href="note-0193-01a" xml:space="preserve">Fig. 5.</note>
            ſitum obtinens) ac parallelæ ſecundum _hypotbeſin_, erunt rectæ EE,
              <lb/>
            BB æquales ac parallelæ. </s>
            <s xml:id="echoid-s8627" xml:space="preserve">Unde patet curvas EE, BB adæquari ſi-
              <lb/>
            bimet, & </s>
            <s xml:id="echoid-s8628" xml:space="preserve">aſſimilari. </s>
            <s xml:id="echoid-s8629" xml:space="preserve">Adæquari quia ſubtenſæ omnes EE ſubtenſis BB
              <lb/>
            ſingillatim æquantur; </s>
            <s xml:id="echoid-s8630" xml:space="preserve">aſſimilari, quia rectæ AB cum ſubtenſis adja-
              <lb/>
            centibus reſpectivis EE, & </s>
            <s xml:id="echoid-s8631" xml:space="preserve">BB pares angulos conſtituunt, adeóque
              <lb/>
            rectæ ipſæ EE pares iis, quos rectæ BB; </s>
            <s xml:id="echoid-s8632" xml:space="preserve">ipſæ illæ cum ſeipſis, & </s>
            <s xml:id="echoid-s8633" xml:space="preserve">
              <lb/>
            hæ cum ſeipſis (nam in hujuſmodi proportionalitate partium, & </s>
            <s xml:id="echoid-s8634" xml:space="preserve">an-
              <lb/>
            gulorum æqualitate, ſicut alibi fortaſſe luculentiùs & </s>
            <s xml:id="echoid-s8635" xml:space="preserve">fuſiùs diſſere-
              <lb/>
            mus, omnis conſiſtit linearum, & </s>
            <s xml:id="echoid-s8636" xml:space="preserve">quarumcunque magnitudinum ſimi-
              <lb/>
            litudo.) </s>
            <s xml:id="echoid-s8637" xml:space="preserve">Quod ſi vice commutatâ linea curva BC fiat linea _Genetriæ
              <unsure/>
            ,_
              <lb/>
            & </s>
            <s xml:id="echoid-s8638" xml:space="preserve">recta BA _directrix_, hoc eſt ſi BC per BA ſibi parallela feratur,
              <lb/>
              <note position="right" xlink:label="note-0193-02" xlink:href="note-0193-02a" xml:space="preserve">Fig. 6.</note>
            producetur eadem ipſiſſima parallelogramma Superficies; </s>
            <s xml:id="echoid-s8639" xml:space="preserve">& </s>
            <s xml:id="echoid-s8640" xml:space="preserve">ſingula
              <lb/>
            rectæ BC puncta, veluti F, rectas lineas ad BA parallelas deſcri-
              <lb/>
            bent; </s>
            <s xml:id="echoid-s8641" xml:space="preserve">neque non interceptæ FF reſpectivis BB pares erunt; </s>
            <s xml:id="echoid-s8642" xml:space="preserve">quod
              <lb/>
            & </s>
            <s xml:id="echoid-s8643" xml:space="preserve">pari modo ex ſuppoſito perpetuo curvæ BC paralleliſmo facilè con-
              <lb/>
            ſectatur. </s>
            <s xml:id="echoid-s8644" xml:space="preserve">Sit denique curva quævis (vel è rectis angulos efficientibus
              <lb/>
            compoſita, quæ curvæ quoque nomen meritò ferat; </s>
            <s xml:id="echoid-s8645" xml:space="preserve">_Archimedes_
              <lb/>
            ſaltem è rectis compoſitas lineas, utì figurarum circulis inſcriptarum
              <lb/>
            aut adſcriptarum perimetros, {και} {πα}λῶν {γρ}αμμ@ν nomine complecti-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s8646" xml:space="preserve">ut & </s>
            <s xml:id="echoid-s8647" xml:space="preserve">viciſſim curvæ quævis lineæ cenſeri poſſunt è rectis, innu-
              <lb/>
            meris quidem illis indefinitè parvis, adjacentibus, & </s>
            <s xml:id="echoid-s8648" xml:space="preserve">deinceps ſe-
              <lb/>
            cum angulos efficientibus, conſlatæ) ſit, inquam, talis aliqua curva
              <lb/>
            BC, in plano quovis conſtituta, tum in alio plano, vel ſuper lineæ
              <lb/>
            BC planum ut libet elevata, recta AB ſibi continuò feratur parallela,
              <lb/>
            modo quo ſemel ac iterum oſtendimus; </s>
            <s xml:id="echoid-s8649" xml:space="preserve">deſcribetur hujuſmodi motu
              <lb/>
            _Superficies cylindrica_ (vel certè _priſmatica, ſi linea directrix è rectis_
              <lb/>
            ponatur compoſita) & </s>
            <s xml:id="echoid-s8650" xml:space="preserve">_cylindrica_ quidem ſtrictè dicta, ſi _directrix
              <unsure/>
            _
              <lb/>
            _fuerit linea circularis, aut elliptica_; </s>
            <s xml:id="echoid-s8651" xml:space="preserve">latiore verò ſenſu talis, ſi curva
              <lb/>
            fuerit alterius generis ut _parabolica_ puta, vel _hyperbolica_, vel alia
              <lb/>
            quæpiam. </s>
            <s xml:id="echoid-s8652" xml:space="preserve">In hoc autem motu lineæ quoque genetricis ſingula puncta
              <lb/>
            ſimiles & </s>
            <s xml:id="echoid-s8653" xml:space="preserve">æquales deſcribunt curvæ directrici lineas; </s>
            <s xml:id="echoid-s8654" xml:space="preserve">æquales
              <lb/>
            (ut in mox præcedente diſcurſu) quoniam EB pares ac paral-
              <lb/>
            lelæ ſunt; </s>
            <s xml:id="echoid-s8655" xml:space="preserve">adeóque EE, BB quoque pares, ac parallelæ
              <lb/>
            ſimiles; </s>
            <s xml:id="echoid-s8656" xml:space="preserve">*quoniam etiam anguli EEE, angulis BBB æquantur.
              <lb/>
            </s>
            <s xml:id="echoid-s8657" xml:space="preserve">
              <note position="right" xlink:label="note-0193-03" xlink:href="note-0193-03a" xml:space="preserve">10. XI
                <unsure/>
              . El
                <unsure/>
              @m.</note>
            Quinetiam reciprocè deſcribatur eadem Superficies ponendo curvam
              <lb/>
            BC perrectam AB parallelωs deportari. </s>
            <s xml:id="echoid-s8658" xml:space="preserve">Quomodò ſingula quoque
              <lb/>
            curvæ BC puncta rectas parallelas & </s>
            <s xml:id="echoid-s8659" xml:space="preserve">pares interceptis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum