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
231 211
232 212
233 213
234 214
235 215
236 216
237 217
238 218
239 219
240 220
241 221
242 222
243 223
244 224
245 225
246 226
247 227
248 228
249 229
250 230
251 231
252 232
253 235
254 236
255 237
256 238
257 239
258 240
259 241
260 242
< >
page |< < (219) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div749" type="section" level="1" n="180">
          <p style="it">
            <s xml:id="echoid-s14980" xml:space="preserve">
              <pb o="219" file="0239" n="239" rhead="LIBER SECVNDVS."/>
            ſim & </s>
            <s xml:id="echoid-s14981" xml:space="preserve">Horizon ad eadem rectus, ac proinde & </s>
            <s xml:id="echoid-s14982" xml:space="preserve">per polos eorundem horologiorum tranſibit, ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s14983" xml:space="preserve">13. </s>
            <s xml:id="echoid-s14984" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14985" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14986" xml:space="preserve">Theodoſii, & </s>
            <s xml:id="echoid-s14987" xml:space="preserve">ob id etiam per stylos eorundem, nempe per axem illorum. </s>
            <s xml:id="echoid-s14988" xml:space="preserve">Eundem autem Ho-
              <lb/>
            rizontem ad circulum quoque maximum per A E, ductum eſſe rectum, perſpicuum eſt; </s>
            <s xml:id="echoid-s14989" xml:space="preserve">propterea quòd
              <lb/>
            in illis horologiis dictus circulus vnus est ex Verticalibus, qui omnes recti ſunt ad Horizontem, & </s>
            <s xml:id="echoid-s14990" xml:space="preserve">viciſ-
              <lb/>
            ſim Horizon ad eoſdem rectus. </s>
            <s xml:id="echoid-s14991" xml:space="preserve">Hinc fit, rectas A G, C H, eſſe lineas horizontales in dictis horologiis. </s>
            <s xml:id="echoid-s14992" xml:space="preserve">
              <lb/>
            In reliquis antem horologijs ille circulus nullo modo eſſe poteſt Horizon; </s>
            <s xml:id="echoid-s14993" xml:space="preserve">quia Horizon ad eorum plana
              <lb/>
            rectus non est, cum huiuſmodi plana ad Horizontem ponantur eſſe inclinata: </s>
            <s xml:id="echoid-s14994" xml:space="preserve">quare neque rectę A G,
              <lb/>
            C H, horizontales erunt lineæ. </s>
            <s xml:id="echoid-s14995" xml:space="preserve">Sed in polari quidẽ horologio circulus ille erit Aequator, & </s>
            <s xml:id="echoid-s14996" xml:space="preserve">lineæ A G,
              <lb/>
            C H, æquinoctiales erunt: </s>
            <s xml:id="echoid-s14997" xml:space="preserve">In æquinoctiali vero horologio idem circulus erit horæ 6. </s>
            <s xml:id="echoid-s14998" xml:space="preserve">à meridie vel me-
              <lb/>
              <note position="left" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">10</note>
            dia nocte, & </s>
            <s xml:id="echoid-s14999" xml:space="preserve">lineæ A G, C H, horam 6. </s>
            <s xml:id="echoid-s15000" xml:space="preserve">à meridie, vel media nocte monstrabunt, vt patet poſitionem
              <lb/>
            horum circulorum diligenter contemplanti, & </s>
            <s xml:id="echoid-s15001" xml:space="preserve">ex ſequentibus planum fiet, ac manifeſtum. </s>
            <s xml:id="echoid-s15002" xml:space="preserve">In cæteris de-
              <lb/>
            nique horologiis dictus circulus erit alius, atque alius; </s>
            <s xml:id="echoid-s15003" xml:space="preserve">ſemper tamen rectæ A G, C H, parallelæ erunt
              <lb/>
            horizontali lineæ vtriuſque horologii. </s>
            <s xml:id="echoid-s15004" xml:space="preserve">Cum enim circulus hic maximus, de quo poſteriori loco diximus, re
              <lb/>
            ctus ſit ad priorem circulum maximum per rectas A E, C F, & </s>
            <s xml:id="echoid-s15005" xml:space="preserve">ſtylos A B, C D, ductum, hic autem ad
              <lb/>
            Horizontem rectus ſit poſitus, atque adeo & </s>
            <s xml:id="echoid-s15006" xml:space="preserve">Horizon viciſſim ad eundem rectus ſit, tranſibit tam Hori-
              <lb/>
            zon, quàm maximus ille circulus per rectas A G, C H, ductus, per polos huius circuli maximi per re-
              <lb/>
            ctas A E, C F, ducti, ex propoſ. </s>
            <s xml:id="echoid-s15007" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15008" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15009" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15010" xml:space="preserve">Theodoſii; </s>
            <s xml:id="echoid-s15011" xml:space="preserve">ac proinde axis eiuſdem huius circuli per rectas
              <lb/>
            A E, C F, ducti erit communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s15012" xml:space="preserve">alterius illius circuli maximi, qui per rectas A G,
              <lb/>
            C H, ducitur. </s>
            <s xml:id="echoid-s15013" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s15014" xml:space="preserve">circulus maximus, cui horologium æquidiſtat, per eoſdem polos circuli maximi per
              <lb/>
            rectas A E, C F, ducti tranſit. </s>
            <s xml:id="echoid-s15015" xml:space="preserve">(Quia enim circulus maximus per rectas A E, C F, & </s>
            <s xml:id="echoid-s15016" xml:space="preserve">ſtylos A B, C D,
              <lb/>
              <note position="left" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">20</note>
            ductus rectus eſt, per conſtructionem, ad planum horologij, hoc eſt, ad circulum, quem in ſphæra facit horo
              <lb/>
            logij planum, tranſibit idem per polos huius circuli in ſphęra procreati, per propoſ. </s>
            <s xml:id="echoid-s15017" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15018" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15019" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15020" xml:space="preserve">Theodoſii.
              <lb/>
            </s>
            <s xml:id="echoid-s15021" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s15022" xml:space="preserve">per polos circuli maximi, cui horologium ęquidiſtat, quòd circuli paralleli eoſdem habeant
              <lb/>
            polos, ex propoſ. </s>
            <s xml:id="echoid-s15023" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15024" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15025" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15026" xml:space="preserve">Thcodoſii. </s>
            <s xml:id="echoid-s15027" xml:space="preserve">Quare viciſſim circulus hic maximus, cui horologium æquidistat, per
              <lb/>
            polos illius, qui per rectas A E, C F, ducitur, tranſibit, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s15028" xml:space="preserve">15 lib. </s>
            <s xml:id="echoid-s15029" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15030" xml:space="preserve">Theodoſii.) </s>
            <s xml:id="echoid-s15031" xml:space="preserve">Habent
              <lb/>
            ergo Horizon, circulus maximus per rectas A G, C H, & </s>
            <s xml:id="echoid-s15032" xml:space="preserve">ſtylos A B, C D, ductus, & </s>
            <s xml:id="echoid-s15033" xml:space="preserve">circulus maxi-
              <lb/>
            mus, cui horologium æquidiſtat, eandem communem ſectionem, nempe axem circuli maximi per rectas
              <lb/>
            A E, C G, & </s>
            <s xml:id="echoid-s15034" xml:space="preserve">ſtylos A B, C D, ducti. </s>
            <s xml:id="echoid-s15035" xml:space="preserve">Quamobrem cum planum horologii huic poſtremo circulo æquidiſtet,
              <lb/>
            erunt per propoſ. </s>
            <s xml:id="echoid-s15036" xml:space="preserve">18. </s>
            <s xml:id="echoid-s15037" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s15038" xml:space="preserve">communes ſectiones aliorum, (nempe Horizontis, & </s>
            <s xml:id="echoid-s15039" xml:space="preserve">eius, qui per
              <lb/>
              <note position="left" xlink:label="note-0239-03" xlink:href="note-0239-03a" xml:space="preserve">30</note>
            rectas A G, C H, & </s>
            <s xml:id="echoid-s15040" xml:space="preserve">per ſtylos A B, C D, ducitur, & </s>
            <s xml:id="echoid-s15041" xml:space="preserve">plani horologii illos ſecantis) parallelę; </s>
            <s xml:id="echoid-s15042" xml:space="preserve">Ac pro-
              <lb/>
            inde cum ſectio, quam facit Horizon, ſit linea horizõtalis in horologio, ſectio autem alterius circuli maxi
              <lb/>
            mi ſit recta A G, in vno horologio, & </s>
            <s xml:id="echoid-s15043" xml:space="preserve">recta C H, in altero, parallelæ erunt rectæ A G, C H, horizontali
              <lb/>
            lineæ vtriuſque horologij.</s>
            <s xml:id="echoid-s15044" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15045" xml:space="preserve">IAM verò circulus aliquis maximus, ſiue horarius is ſit, ſiue alius quiſpiam, in horologio Auſtrali,
              <lb/>
            vel ſuperiori per centrum mundi, id eſt, per B, vel D, (duo enim hæc puncta vnum punctum conficiunt)
              <lb/>
            verticem ſtyli tranſiens faciat ſectionem E G, quę ſecet rectam A E, infra ſtylum in E, & </s>
            <s xml:id="echoid-s15046" xml:space="preserve">rectam A G,
              <lb/>
            ad dextram in G. </s>
            <s xml:id="echoid-s15047" xml:space="preserve">Secabit idem hic circulus in horologio boreali, vel inferiori, cum per ſtyli verticem
              <lb/>
            tranſeat, rectas C F, C H, in partibus oppoſitis, vt perſpicuum eſt, ſi planum horologij vtriuſque, & </s>
            <s xml:id="echoid-s15048" xml:space="preserve">pla-
              <lb/>
            num circuli ſectionem E G, facientis in proprijs poſitionibus conſiderentur; </s>
            <s xml:id="echoid-s15049" xml:space="preserve">ſecabit, inquam, rectam C F,
              <lb/>
            ſupra ſtylum, & </s>
            <s xml:id="echoid-s15050" xml:space="preserve">rectam C H, ad partem dextram. </s>
            <s xml:id="echoid-s15051" xml:space="preserve">Superior enim pars borealis horologij, vel inferioris,
              <lb/>
              <note position="left" xlink:label="note-0239-04" xlink:href="note-0239-04a" xml:space="preserve">40</note>
            parti inferiori Auſtralis, vel ſuperioris horologij opponitur, atque inferior ſuperiori, & </s>
            <s xml:id="echoid-s15052" xml:space="preserve">dextra dextræ,
              <lb/>
            ſiniſtra{q́ue} ſiniſtrę. </s>
            <s xml:id="echoid-s15053" xml:space="preserve">Appellamus autem partem dextram, ſiniſtramve, quæ nobis ad horologium conuerſis
              <lb/>
            ad dexteram eſt, vel ad ſiniſtram. </s>
            <s xml:id="echoid-s15054" xml:space="preserve">Vnde cum duo illa horologia ſe mutuo reſpiciant, reſpondebit dextra
              <lb/>
            pars vnius parti ſiniſtr æ alterius, & </s>
            <s xml:id="echoid-s15055" xml:space="preserve">contra; </s>
            <s xml:id="echoid-s15056" xml:space="preserve">dextra autem dextræ, & </s>
            <s xml:id="echoid-s15057" xml:space="preserve">ſiniſtra ſiniſtræ opponetur, cum
              <lb/>
            inter has partes medio loco ponatur ſtylus. </s>
            <s xml:id="echoid-s15058" xml:space="preserve">Sit ergo communis ſectio dicti circuli, & </s>
            <s xml:id="echoid-s15059" xml:space="preserve">plani horologij in
              <lb/>
            boreali horologio, ſeu inferiori, recta F H, ſecans C F, in F, ſupra ſtylum, & </s>
            <s xml:id="echoid-s15060" xml:space="preserve">C H, in H, ad partem eius
              <lb/>
            dextram. </s>
            <s xml:id="echoid-s15061" xml:space="preserve">Erunt autem ambæ ſectiones E G, F H, parallelæ, cum eas idem circulus in planis parallelis
              <lb/>
              <note position="right" xlink:label="note-0239-05" xlink:href="note-0239-05a" xml:space="preserve">16. vndec.</note>
            horologiorum efficiat. </s>
            <s xml:id="echoid-s15062" xml:space="preserve">Itaque quoniam rectæ A E, C F, parallelæ ſunt, vt demonſtratum eſt, erunt æqua-
              <lb/>
            les inter ſe anguli alterni in punctis E, & </s>
            <s xml:id="echoid-s15063" xml:space="preserve">F, rectarum E A, F C, facti à communi ſectione maximorum
              <lb/>
              <note position="right" xlink:label="note-0239-06" xlink:href="note-0239-06a" xml:space="preserve">29. primi.</note>
            circulorum ſectiones A E, C F, & </s>
            <s xml:id="echoid-s15064" xml:space="preserve">E G, C H, facientium, quæ quidem communis ſectio per puncta E, B,
              <lb/>
              <note position="left" xlink:label="note-0239-07" xlink:href="note-0239-07a" xml:space="preserve">50</note>
            D, F, tranſit, cum per hæc eadem ipſi circuli maximi tranſeant. </s>
            <s xml:id="echoid-s15065" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s15066" xml:space="preserve">anguli recti A, C, quos
              <lb/>
            ſtyli cum rectis A E, C F, per defin. </s>
            <s xml:id="echoid-s15067" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15068" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15069" xml:space="preserve">11. </s>
            <s xml:id="echoid-s15070" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s15071" xml:space="preserve">conſtituunt, æquales; </s>
            <s xml:id="echoid-s15072" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s15073" xml:space="preserve">ſtyli A B, C D, æquales,
              <lb/>
            qui æqualibus angulis E, F, ſubtenduntur in triangulis A B E, C D F, quorum baſes ſunt partes commu
              <lb/>
            nis ſectionis maximorum circulorum ſectiones A E, C F, & </s>
            <s xml:id="echoid-s15074" xml:space="preserve">E G, C H, in horologio vtroque facientium.
              <lb/>
            </s>
            <s xml:id="echoid-s15075" xml:space="preserve">Erunt igitur latera quoque A E, C F, æqualia. </s>
            <s xml:id="echoid-s15076" xml:space="preserve">Tantum ergo abest ſectio E G, in recta A E, à ſtylo
              <lb/>
              <note position="right" xlink:label="note-0239-08" xlink:href="note-0239-08a" xml:space="preserve">26. primi.</note>
            deorſum verſus, quantum ſectio F H, in recta C F, à ſtylo ſurſum verſus diſtat. </s>
            <s xml:id="echoid-s15077" xml:space="preserve">Rurſus quia rectæ E K,
              <lb/>
            E I, rectis F C, F H, parallelæ ſunt, vt ostendimus, erit angulus K E I, angulo C F H, æqualis. </s>
            <s xml:id="echoid-s15078" xml:space="preserve">Cum er-
              <lb/>
              <note position="right" xlink:label="note-0239-09" xlink:href="note-0239-09a" xml:space="preserve">10. vndec.</note>
            go angulo K E I, æqualis ſit angulus A E G, ad verticem, eruntin triangulis A E G, C F H, anguli ad
              <lb/>
              <note position="right" xlink:label="note-0239-10" xlink:href="note-0239-10a" xml:space="preserve">15. primi.</note>
            E, F, æquales. </s>
            <s xml:id="echoid-s15079" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s15080" xml:space="preserve">anguli E A G, F C H, æquales, vtpotè recti; </s>
            <s xml:id="echoid-s15081" xml:space="preserve">& </s>
            <s xml:id="echoid-s15082" xml:space="preserve">latera A E, C F, dictis
              <lb/>
            angulis adiacentia, oſtenſa ſunt æqualia. </s>
            <s xml:id="echoid-s15083" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s15084" xml:space="preserve">latera A G, C H, æqualia erunt. </s>
            <s xml:id="echoid-s15085" xml:space="preserve">Aequalibus ergo
              <lb/>
              <note position="right" xlink:label="note-0239-11" xlink:href="note-0239-11a" xml:space="preserve">26. primi.</note>
            ſpatijs abſunt rectæ E G, F H, in rectis A G, C H, à ſtylis dextram verſus. </s>
            <s xml:id="echoid-s15086" xml:space="preserve">Quòd ſi recta E G, ſecet </s>
          </p>
        </div>
      </text>
    </echo>
Impressum