Clavius, Christoph, Geometria practica

Table of contents

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[131.] PROBLEMA XIV.
[132.] PROBLEMA XV.
[133.] PROBLEMA XVI.
[134.] PROBLEMA XVII.
[135.] PROBLEMA XVIII.
[136.] PROBLEMA XIX.
[137.] PROBLEMA XX.
[138.] PROBLEMA XXI.
[139.] PROBLEMA XXII.
[140.] PROBLEMA XXIII.
[141.] PROBLEMA XXIV.
[142.] PROBLEMA XXV.
[143.] SCHOLIVM.
[144.] PROBLEMA XXVI.
[145.] PROBLEMA XXVII.
[146.] PROBLEMA XXVIII.
[147.] PROBLEMA XXIX.
[148.] PROBLEMA XXX.
[149.] PROBLEMA XXXI.
[150.] PROBLEMA XXXII.
[151.] PROBLEMA XXXIII.
[152.] PROBLEMA XXXIV.
[153.] PROBLEMA XXXV.
[154.] PROBLEMA XXXVI.
[155.] PROBLEMA XXXVII.
[156.] PROBLEMA XXXVIII.
[157.] PROBLEMA XXXIX.
[158.] ALITER.
[159.] ALITER.
[160.] PROBLEMA XL.
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            <s xml:id="echoid-s4272" xml:space="preserve">
              <pb o="110" file="140" n="140" rhead="GEOMETR. PRACT."/>
            vicies ſumpta eidem FG, æqualis. </s>
            <s xml:id="echoid-s4273" xml:space="preserve">Igitur 128. </s>
            <s xml:id="echoid-s4274" xml:space="preserve">paſſus, vna cum a F, octies ſumpta
              <lb/>
            æquiualent ipſi a F, vicies ſumptæ. </s>
            <s xml:id="echoid-s4275" xml:space="preserve">Si ergo vtrobique auferatur a F, octies ſum-
              <lb/>
            pta, reliqui erunt 128. </s>
            <s xml:id="echoid-s4276" xml:space="preserve">paſſus æquales ipſi a F, duodecies ſumptæ. </s>
            <s xml:id="echoid-s4277" xml:space="preserve">Quare ſi 128.
              <lb/>
            </s>
            <s xml:id="echoid-s4278" xml:space="preserve">diuiduntur per 12. </s>
            <s xml:id="echoid-s4279" xml:space="preserve">prodibunt 10 {2/3}. </s>
            <s xml:id="echoid-s4280" xml:space="preserve">paſſus pro recta, a F, cum hic Quotiens in
              <lb/>
            12. </s>
            <s xml:id="echoid-s4281" xml:space="preserve">ductus producat 128. </s>
            <s xml:id="echoid-s4282" xml:space="preserve">Cumigitur a F, contineatur vicies in F G: </s>
            <s xml:id="echoid-s4283" xml:space="preserve">ſi a F, 10 {2/3}. </s>
            <s xml:id="echoid-s4284" xml:space="preserve">
              <lb/>
            paſſuum ducatur in 20. </s>
            <s xml:id="echoid-s4285" xml:space="preserve">pro creabitur altitudo F G, 213 {1/3}. </s>
            <s xml:id="echoid-s4286" xml:space="preserve">paſſuum. </s>
            <s xml:id="echoid-s4287" xml:space="preserve">Vides ergo
              <lb/>
            minorem Quotientem 8. </s>
            <s xml:id="echoid-s4288" xml:space="preserve">in differentiam ſtationum paſſuum 16. </s>
            <s xml:id="echoid-s4289" xml:space="preserve">ductam eſſe, vt
              <lb/>
            gignerentur 128. </s>
            <s xml:id="echoid-s4290" xml:space="preserve">& </s>
            <s xml:id="echoid-s4291" xml:space="preserve">hunc numerum diuiſum eſſe per 12. </s>
            <s xml:id="echoid-s4292" xml:space="preserve">differentiam Quotien-
              <lb/>
            tum, vt pro dirent paſſus 10 {2/3}. </s>
            <s xml:id="echoid-s4293" xml:space="preserve">pro recta a F: </s>
            <s xml:id="echoid-s4294" xml:space="preserve">ac tandem hunc Quotientem 10 {2/3}. </s>
            <s xml:id="echoid-s4295" xml:space="preserve">
              <lb/>
            ductum eſſe in 20. </s>
            <s xml:id="echoid-s4296" xml:space="preserve">Quotientem maiorem, vt produceretur altitudo F G, paſ-
              <lb/>
            ſuum 213 {1/3}. </s>
            <s xml:id="echoid-s4297" xml:space="preserve">vt in regula pręcepimus. </s>
            <s xml:id="echoid-s4298" xml:space="preserve">Quam altitudinem etiam reperies per præ-
              <lb/>
            cedentem viam, ſi nimirum fiat, vt 75. </s>
            <s xml:id="echoid-s4299" xml:space="preserve">differentia vmbrarum rectarum, ad diffe-
              <lb/>
            rentiam ſtationum, nimirum ad 16. </s>
            <s xml:id="echoid-s4300" xml:space="preserve">paſſus. </s>
            <s xml:id="echoid-s4301" xml:space="preserve">ita quadrati latus 1000. </s>
            <s xml:id="echoid-s4302" xml:space="preserve">ad aliud. </s>
            <s xml:id="echoid-s4303" xml:space="preserve">
              <lb/>
            Nam 16. </s>
            <s xml:id="echoid-s4304" xml:space="preserve">ducta in 1000. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">& </s>
            <s xml:id="echoid-s4306" xml:space="preserve">productus numerus 16000. </s>
            <s xml:id="echoid-s4307" xml:space="preserve">diuiſus per 75. </s>
            <s xml:id="echoid-s4308" xml:space="preserve">facit Quo-
              <lb/>
            tientem 213 {1/3}. </s>
            <s xml:id="echoid-s4309" xml:space="preserve">veluti prius.</s>
            <s xml:id="echoid-s4310" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4311" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4312" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            in remotiore ſtatione inter-
              <lb/>
              <figure xlink:label="fig-140-01" xlink:href="fig-140-01a" number="67">
                <image file="140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/140-01"/>
              </figure>
            ſecetur vmbra verſa in E, & </s>
            <s xml:id="echoid-s4313" xml:space="preserve">in propinquiore
              <lb/>
            vmbra recta in H, vt in 3. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">figura problem. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4316" xml:space="preserve">Re-
              <lb/>
            ducta vmbra verſa adrectam, vt in Quadrati
              <lb/>
            conſtructione Num. </s>
            <s xml:id="echoid-s4317" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4318" xml:space="preserve">principio huius lib. </s>
            <s xml:id="echoid-s4319" xml:space="preserve">ſcri-
              <lb/>
            pſimus: </s>
            <s xml:id="echoid-s4320" xml:space="preserve">ſi fiat, vt IN, differentia vmbrarum re-
              <lb/>
            ctarum ad A a, differentiam ſtationum, ita A B,
              <lb/>
            latus Quadrati 1000. </s>
            <s xml:id="echoid-s4321" xml:space="preserve">ad aliud, procreabitur al-
              <lb/>
            titudo F G, quemadmodum Num. </s>
            <s xml:id="echoid-s4322" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4323" xml:space="preserve">oſten-
              <lb/>
            dimus.</s>
            <s xml:id="echoid-s4324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4325" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4326" xml:space="preserve">
              <emph style="sc">Si</emph>
            fortè in vna ſtatione tranſiret linea fiduciæ, aut filum perpendiculi per
              <lb/>
            punctum C, aſſumendum eſſet in primo caſu latus C D, vmbrę verſę in duo-
              <lb/>
            bus autem aliis caſibus latus BC, vmbrę rectæ.</s>
            <s xml:id="echoid-s4327" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div278" type="section" level="1" n="120">
          <head xml:id="echoid-head123" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s4328" xml:space="preserve">Sine reductione vmbrę verſę ad rectam ita agendum erit. </s>
            <s xml:id="echoid-s4329" xml:space="preserve">Numerus, qui fit
              <lb/>
            ex vmbra verſa D E, in vmbram rectam b H, auferatur ex 1000000. </s>
            <s xml:id="echoid-s4330" xml:space="preserve">quadrato
              <lb/>
            lateris 1000@ reſi duumque ſit P. </s>
            <s xml:id="echoid-s4331" xml:space="preserve">Item ex vmbra verſa DE, in latus 1000. </s>
            <s xml:id="echoid-s4332" xml:space="preserve">fiat Q.
              <lb/>
            </s>
            <s xml:id="echoid-s4333" xml:space="preserve"> Et quoniam ob triangulorum ſimilitudinem eſt, vt BN, ad BA, ita AF, ad F G:</s>
            <s xml:id="echoid-s4334" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-140-01" xlink:href="note-140-01a" xml:space="preserve">4. ſexti.</note>
            Etpermutando, vt BN, ad AF, ita BA, ad FG. </s>
            <s xml:id="echoid-s4335" xml:space="preserve">Sed vt BN, vmbra recta maior ad
              <lb/>
            A F, diſtantiam, ita eſt I N, differentia vmbrarum rectarum ad A a, differentiam
              <lb/>
            ſtationum, vt Num. </s>
            <s xml:id="echoid-s4336" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4337" xml:space="preserve">in problem. </s>
            <s xml:id="echoid-s4338" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4339" xml:space="preserve">dictum eſt. </s>
            <s xml:id="echoid-s4340" xml:space="preserve">Igitur erit quoque IN, ad Aa,
              <lb/>
            ſicuti AB, ad FG: </s>
            <s xml:id="echoid-s4341" xml:space="preserve">Et permutando IN, ad AB, vt Aa, ad FG. </s>
            <s xml:id="echoid-s4342" xml:space="preserve">Dico iam ita eſſe
              <lb/>
            P, ad Q, vt IN, ad AB. </s>
            <s xml:id="echoid-s4343" xml:space="preserve"> Quoniam enim eſt, vt DE, ad AD, ita AB, vel AD,
              <note symbol="b" position="left" xlink:label="note-140-02" xlink:href="note-140-02a" xml:space="preserve">4. ſexti.</note>
            BN:</s>
            <s xml:id="echoid-s4344" xml:space="preserve"> erit rectangulum ſub DE, BN, ęquale quadrato numero 1000000. </s>
            <s xml:id="echoid-s4345" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-140-03" xlink:href="note-140-03a" xml:space="preserve">17. ſexti.</note>
            AB, 1000. </s>
            <s xml:id="echoid-s4346" xml:space="preserve"> Eſt autemrectangulum ſub DE, BN, æquale rectangulis ſub DE,
              <note symbol="d" position="left" xlink:label="note-140-04" xlink:href="note-140-04a" xml:space="preserve">1. ſecundi.</note>
            BI, & </s>
            <s xml:id="echoid-s4347" xml:space="preserve">ſub DE, IN. </s>
            <s xml:id="echoid-s4348" xml:space="preserve">Igitur ſi productum ex vmbra verſa DE, in B I, hoc eſt, in
              <lb/>
            vmbram rectamb H, dematur ex rectangulo ſub DE, BN, hoc eſt, ex quadrato
              <lb/>
            1000000. </s>
            <s xml:id="echoid-s4349" xml:space="preserve">remanebit rectangulum ſub DE, IN. </s>
            <s xml:id="echoid-s4350" xml:space="preserve">Ac propterea P, fiet ex DE, in
              <lb/>
            IN. </s>
            <s xml:id="echoid-s4351" xml:space="preserve">Fit autem Q, ex eadem vmbra verſa DE, in latus AB, 1000. </s>
            <s xml:id="echoid-s4352" xml:space="preserve">Igitur cum DE,
              <lb/>
            multiplicans IN, & </s>
            <s xml:id="echoid-s4353" xml:space="preserve">AB; </s>
            <s xml:id="echoid-s4354" xml:space="preserve">producat P, Q, erit P, ad Q, ſicut IN, ad AB; </s>
            <s xml:id="echoid-s4355" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-140-05" xlink:href="note-140-05a" xml:space="preserve">17. ſexti.@</note>
            eſt, ſicut Aa, ad FG. </s>
            <s xml:id="echoid-s4356" xml:space="preserve">Quocirca ſi fiat.</s>
            <s xml:id="echoid-s4357" xml:space="preserve"/>
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