Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

Page concordance

< >
Scan Original
361 345
362 346
363 347
364 348
365 349
366 350
367 351
368 352
369 353
370 354
371 355
372 356
373 357
374 358
375 359
376 360
377 361
378 362
379 363
380 364
381 365
382 366
383 367
384 368
385 369
386 370
387 371
388 372
389 373
390 374
< >
page |< < (346) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div1171" type="section" level="1" n="279">
          <pb o="346" file="0362" n="362" rhead="GNOMONICES"/>
        </div>
        <div xml:id="echoid-div1172" type="section" level="1" n="280">
          <head xml:id="echoid-head290" xml:space="preserve">PROBLEMA 17. PROPOSITIO 17.</head>
          <p>
            <s xml:id="echoid-s23073" xml:space="preserve">PARALLELOS Horizontis in eodem horologio declinante ab
              <lb/>
            Horizonte reponere.</s>
            <s xml:id="echoid-s23074" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s23075" xml:space="preserve">DESCRIBEMVS in hoc horologio parallelos Horizontis, vt in polari e
              <unsure/>
            oſdem deſignaui
              <lb/>
              <note position="left" xlink:label="note-0362-01" xlink:href="note-0362-01a" xml:space="preserve">Defcriptio pa-
                <lb/>
              rallel orum Ho
                <lb/>
              rizontis in eo-
                <lb/>
              dem horologio
                <lb/>
              declinante ab
                <lb/>
              Horizonte.</note>
            mus propoſ. </s>
            <s xml:id="echoid-s23076" xml:space="preserve">41. </s>
            <s xml:id="echoid-s23077" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s23078" xml:space="preserve">dummodo ea, quæ ſequuntur, diligenter obſeruentur. </s>
            <s xml:id="echoid-s23079" xml:space="preserve">In priori
              <lb/>
            modo circulus Analemmatis A B C, referet Verticalem propriè dictum, qui nimirum per ſtylum
              <lb/>
            tranſiens ad planum horologij rectus eſt, facitq́ue fectionem B D: </s>
            <s xml:id="echoid-s23080" xml:space="preserve">Paralleli autem Horizontis nõ
              <lb/>
              <note position="left" xlink:label="note-0362-02" xlink:href="note-0362-02a" xml:space="preserve">10</note>
            mutantur. </s>
            <s xml:id="echoid-s23081" xml:space="preserve">Rurſus pro axe E F, ducenda erit diameter, ſeu communis ſectio Verticalis, & </s>
            <s xml:id="echoid-s23082" xml:space="preserve">circuli
              <lb/>
            maximi, cui horologiũ æquidiſtat, ita vt tam arcus C E, quàm B F, æqualis ſit declinationi propo-
              <lb/>
              <figure xlink:label="fig-0362-01" xlink:href="fig-0362-01a" number="240">
                <image file="0362-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0362-01"/>
              </figure>
            ſitæ ab Horizonte. </s>
            <s xml:id="echoid-s23083" xml:space="preserve">Huicautẽ diametro ducẽda
              <lb/>
            eſt parallela R Q, pro magnitudine ſtyli I K, vel
              <lb/>
            A K, ita vt recta D I, rectam R Q, ad rectos a
              <unsure/>
            n-
              <lb/>
            gulos ſecans ſit ſtylo I K, æqualis. </s>
            <s xml:id="echoid-s23084" xml:space="preserve">Puncta deni-
              <lb/>
            que L, M, N, O, P, accepta ex T, puncto, vbi
              <lb/>
            Horizon B C, rectam R Q, ſecat, tran sferenda
              <lb/>
            erunt in rectam B D, ex D, puncto horizonta-
              <lb/>
            lis lineæ verſus B, in ſuperiori horologio: </s>
            <s xml:id="echoid-s23085" xml:space="preserve">In in-
              <lb/>
              <note position="left" xlink:label="note-0362-03" xlink:href="note-0362-03a" xml:space="preserve">20</note>
            feriori autem transferẽda erunt interualla S T,
              <lb/>
            & </s>
            <s xml:id="echoid-s23086" xml:space="preserve">alia, ſi qua fuerint, ex D, in eandem rectam
              <lb/>
            B D, ſed vltra D, productam. </s>
            <s xml:id="echoid-s23087" xml:space="preserve">Nam ſectiones
              <lb/>
            conicæ circa diametros L Q, M Q, N Q, &</s>
            <s xml:id="echoid-s23088" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s23089" xml:space="preserve">ſecundum doctrinam propoſ. </s>
            <s xml:id="echoid-s23090" xml:space="preserve">8. </s>
            <s xml:id="echoid-s23091" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s23092" xml:space="preserve">1. </s>
            <s xml:id="echoid-s23093" xml:space="preserve">deſcri-
              <lb/>
            ptæ, & </s>
            <s xml:id="echoid-s23094" xml:space="preserve">translatæ in horologium, ita vt diame-
              <lb/>
            tri earum rectæ B D, congruant, tranſeantq́ue
              <lb/>
            per puncta translata L, M, N, O, P, S, &</s>
            <s xml:id="echoid-s23095" xml:space="preserve">c. </s>
            <s xml:id="echoid-s23096" xml:space="preserve">& </s>
            <s xml:id="echoid-s23097" xml:space="preserve">
              <lb/>
            cornua earum à linea horizontali auertantur,
              <lb/>
            dabunt parallelos Horizontis.</s>
            <s xml:id="echoid-s23098" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s23099" xml:space="preserve">IN poſteriori autem modo recta A D, ſu-
              <lb/>
            menda eſt æqualis rectæ A B, quæ ex vertice ſtyli A, in figura præcedentis propoſ. </s>
            <s xml:id="echoid-s23100" xml:space="preserve">in Zenith B,
              <lb/>
            cadit, & </s>
            <s xml:id="echoid-s23101" xml:space="preserve">in rectam A B, transferenda ſunt interualla inter E, & </s>
            <s xml:id="echoid-s23102" xml:space="preserve">lineas Verticales in linea hori-
              <lb/>
            zontali, &</s>
            <s xml:id="echoid-s23103" xml:space="preserve">c. </s>
            <s xml:id="echoid-s23104" xml:space="preserve">Pro linea autem meridiana, quæ dat Verticalem grad. </s>
            <s xml:id="echoid-s23105" xml:space="preserve">90. </s>
            <s xml:id="echoid-s23106" xml:space="preserve">& </s>
            <s xml:id="echoid-s23107" xml:space="preserve">horizontalem lineã
              <lb/>
            non ſecat, ducenda eſt D F, ipſi A B, parallela, & </s>
            <s xml:id="echoid-s23108" xml:space="preserve">in alteram partem transferendæ lineæ, quæ ex
              <lb/>
            D, emiſ@æ rectam A B, ſecant, ſicut in lineis horarijs factum eſt in horizontali horologio. </s>
            <s xml:id="echoid-s23109" xml:space="preserve">Eſt
              <lb/>
            enim hic A D, tanquam axis; </s>
            <s xml:id="echoid-s23110" xml:space="preserve">A B, veluti radius Aequatoris, quanquam re uera radius ſit Horizon
              <lb/>
            tis; </s>
            <s xml:id="echoid-s23111" xml:space="preserve">rectæ ex A, ductæ ſunt inſtar radiorum ſignorum, &</s>
            <s xml:id="echoid-s23112" xml:space="preserve">c. </s>
            <s xml:id="echoid-s23113" xml:space="preserve">Demonſtratio huius operationis eadẽ
              <lb/>
            eſt, quæ in horizontali horologio, ſi recta A D, rectæ A B, axi Horizontis congruat, punctumq́ue
              <lb/>
            A, puncto A, & </s>
            <s xml:id="echoid-s23114" xml:space="preserve">punctum D, puncto B, & </s>
            <s xml:id="echoid-s23115" xml:space="preserve">circa illam figura A D F, in qua continentur radij paral
              <lb/>
              <note position="left" xlink:label="note-0362-05" xlink:href="note-0362-05a" xml:space="preserve">40</note>
            lelorum Horizontis, circumuertatur, quemadmodum in horologio horizontali figuram radio-
              <lb/>
            rum circa axem mundi moueri intelligimus, &</s>
            <s xml:id="echoid-s23116" xml:space="preserve">c. </s>
            <s xml:id="echoid-s23117" xml:space="preserve">Nam in hac ita ſe habent lineæ Verticales, vt
              <lb/>
            ibilineæ horariæ, ita vt punctum B, reſpondeat centro horologij, in quod axis A B, cadit, & </s>
            <s xml:id="echoid-s23118" xml:space="preserve">linea
              <lb/>
            horizontalis ſit veluti æquinoctialis linea, &</s>
            <s xml:id="echoid-s23119" xml:space="preserve">c. </s>
            <s xml:id="echoid-s23120" xml:space="preserve">Quapropter parallelos Horizontis in eodem horo
              <lb/>
            logio declinante ab Horizonte repoſnimus. </s>
            <s xml:id="echoid-s23121" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s23122" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1175" type="section" level="1" n="281">
          <head xml:id="echoid-head291" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s23123" xml:space="preserve">PER ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s23124" xml:space="preserve">2. </s>
            <s xml:id="echoid-s23125" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s23126" xml:space="preserve">ſcripſimus, non erit difficile iudicare, quinam paral
              <lb/>
              <note position="left" xlink:label="note-0362-06" xlink:href="note-0362-06a" xml:space="preserve">Qui paralleli
                <lb/>
              Horizontis in
                <lb/>
              horologio ſint
                <lb/>
              Hyperbolæ, Pa
                <lb/>
              rabolæ, aut El-
                <lb/>
              lipſes.</note>
              <note position="left" xlink:label="note-0362-07" xlink:href="note-0362-07a" xml:space="preserve">50</note>
            leli Horizontis in plano horologij ſint hyperbolę, & </s>
            <s xml:id="echoid-s23127" xml:space="preserve">qui parabolæ, aut Ellipſes. </s>
            <s xml:id="echoid-s23128" xml:space="preserve">Quando enim in figure,
              <lb/>
            in qua continentur radii parallelorum Horizontis, recta ex puncto D, egrediens, ſecans{q́ue} rectam A B,
              <lb/>
            in puncto, quod puncto A, eſt omnium propinquiſſimum, ſecat duos radios parallelorum oppoſitos ex A,
              <lb/>
            eductos, fient duæ hyperbolæ oppoſitæ, vt in exemplo nostro contingit in radijs parallelorum grad. </s>
            <s xml:id="echoid-s23129" xml:space="preserve">15.
              <lb/>
            </s>
            <s xml:id="echoid-s23130" xml:space="preserve">Si verò eadem recta ex puncto D, emiſſa æquidiſtet alicui radio ad ſiniſtram rectæ A B, poſito, erit pa-
              <lb/>
            rallelus radii oppoſiti Parabole. </s>
            <s xml:id="echoid-s23131" xml:space="preserve">Si denique recta eadem ex D, educta quempiam radiorum ad ſiniſtram
              <lb/>
            rectæ A B, neque ſecet, neque ei æquidiſtet, erit parallelus ex radio oppoſito deſcriptus, Ellipſis, vt ac-
              <lb/>
            cidit in propoſito exemplo in radiis parallelorum Horizontis grad. </s>
            <s xml:id="echoid-s23132" xml:space="preserve">30. </s>
            <s xml:id="echoid-s23133" xml:space="preserve">45. </s>
            <s xml:id="echoid-s23134" xml:space="preserve">60. </s>
            <s xml:id="echoid-s23135" xml:space="preserve">&</s>
            <s xml:id="echoid-s23136" xml:space="preserve">c. </s>
            <s xml:id="echoid-s23137" xml:space="preserve">Quæ omnia ibi-
              <lb/>
            dem demonſtrata ſunt.</s>
            <s xml:id="echoid-s23138" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum