Clavius, Christoph, Geometria practica

Table of handwritten notes

< >
[Handwritten note 19]
Page: 48
[Handwritten note 20]
Page: 48
[Handwritten note 15]
Page: 48
[Handwritten note 16]
Page: 48
[Handwritten note 17]
Page: 48
[Handwritten note 18]
Page: 48
[Handwritten note 19]
Page: 48
[Handwritten note 20]
Page: 48
[Handwritten note 15]
Page: 48
[Handwritten note 16]
Page: 48
[Handwritten note 17]
Page: 48
[Handwritten note 18]
Page: 48
[Handwritten note 19]
Page: 48
[Handwritten note 20]
Page: 48
[Handwritten note 15]
Page: 48
[Handwritten note 16]
Page: 48
[Handwritten note 17]
Page: 48
[Handwritten note 18]
Page: 48
[Handwritten note 19]
Page: 48
[Handwritten note 20]
Page: 48
[Handwritten note 21]
Page: 50
[Handwritten note 22]
Page: 50
[Handwritten note 23]
Page: 50
[Handwritten note 21]
Page: 50
[Handwritten note 22]
Page: 50
[Handwritten note 23]
Page: 50
[Handwritten note 21]
Page: 50
[Handwritten note 22]
Page: 50
[Handwritten note 23]
Page: 50
[Handwritten note 24]
Page: 69
< >
page |< < (12) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div17" type="section" level="1" n="17">
          <p>
            <s xml:id="echoid-s928" xml:space="preserve">
              <pb o="12" file="042" n="42" rhead="GEOMETR. PRACT."/>
            to, ſumendus eſtille ſinus totusin aliqua recta bis, ter, aut quater, &</s>
            <s xml:id="echoid-s929" xml:space="preserve">c. </s>
            <s xml:id="echoid-s930" xml:space="preserve">atque
              <lb/>
              <note position="left" xlink:label="note-042-01" xlink:href="note-042-01a" xml:space="preserve">ferrinequeat,
                <lb/>
              quid agen-
                <lb/>
              dum.</note>
            ita ex F, in G, transferendus. </s>
            <s xml:id="echoid-s931" xml:space="preserve">Nam ſi Tangentium quæſitarum, vel ſinuũ, aut
              <lb/>
            ſecantium reſpectu ſinus totius 100. </s>
            <s xml:id="echoid-s932" xml:space="preserve">capiantur ſemiſſes, vel tertiæ partes, aut
              <lb/>
            quartæ, &</s>
            <s xml:id="echoid-s933" xml:space="preserve">c. </s>
            <s xml:id="echoid-s934" xml:space="preserve">prout videlicet ſinus totus bis, ter, quateruè, &</s>
            <s xml:id="echoid-s935" xml:space="preserve">c. </s>
            <s xml:id="echoid-s936" xml:space="preserve">acceptus fuit,
              <lb/>
            habebũtur Tangẽtes quæſitæ, vel ſinus, aut ſecãtes. </s>
            <s xml:id="echoid-s937" xml:space="preserve">Vt ſi ſinus totus duplice-
              <lb/>
            tur, & </s>
            <s xml:id="echoid-s938" xml:space="preserve">poſito ſinu toto 100. </s>
            <s xml:id="echoid-s939" xml:space="preserve">Tangens verbigratia ſit 378. </s>
            <s xml:id="echoid-s940" xml:space="preserve">ſumenda eſt Tangẽs
              <lb/>
            189. </s>
            <s xml:id="echoid-s941" xml:space="preserve">&</s>
            <s xml:id="echoid-s942" xml:space="preserve">c. </s>
            <s xml:id="echoid-s943" xml:space="preserve">Sed commodiſsime res hæc peragetur, ſi ſinus totus, quiperpuſil-
              <lb/>
            lus eſt, decupletur. </s>
            <s xml:id="echoid-s944" xml:space="preserve">Ita enim poſito ſinu toto 100. </s>
            <s xml:id="echoid-s945" xml:space="preserve">ſi ex Tangente verbi gra-
              <lb/>
            tia propoſita (relicta prima figura ad dexteram) abijciatur vna figura ad de-
              <lb/>
            xteram, quæ eſt ſecunda in tota Tangente, habebitur decima eius pars. </s>
            <s xml:id="echoid-s946" xml:space="preserve">Ha-
              <lb/>
            benda tamen ſemper eſt ratio figuræ abiectæ, vt ſcilicet pro ea ſumatur 1. </s>
            <s xml:id="echoid-s947" xml:space="preserve">ſi
              <lb/>
            maior eſt quam 5. </s>
            <s xml:id="echoid-s948" xml:space="preserve">&</s>
            <s xml:id="echoid-s949" xml:space="preserve">c. </s>
            <s xml:id="echoid-s950" xml:space="preserve">Hacratione Tangente 2414. </s>
            <s xml:id="echoid-s951" xml:space="preserve">grad 67. </s>
            <s xml:id="echoid-s952" xml:space="preserve">min 30. </s>
            <s xml:id="echoid-s953" xml:space="preserve">propo-
              <lb/>
            ſita (relictis {4/1000}.) </s>
            <s xml:id="echoid-s954" xml:space="preserve">transferenda erit Tangens 24 paulo amplius, nimirum
              <lb/>
            pars decima Tangentis 241. </s>
            <s xml:id="echoid-s955" xml:space="preserve">reſpectu ſinus totius 100.</s>
            <s xml:id="echoid-s956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s957" xml:space="preserve">24. </s>
            <s xml:id="echoid-s958" xml:space="preserve">
              <emph style="sc">Sic</emph>
            etiam, quando Tangens aliqua ſinum totum ſuperat, ne coga-
              <lb/>
            mur primum ſinum totum aliquoties transferre, deinde vero reliquas partes,
              <lb/>
              <note position="left" xlink:label="note-042-02" xlink:href="note-042-02a" xml:space="preserve">Quando Tã-
                <lb/>
              gens ſuper{at}
                <lb/>
              ſinum totum,
                <lb/>
              quid agendũ,
                <lb/>
              vt per vnicã
                <lb/>
              tranſlationem
                <lb/>
              punctũ quæſi-
                <lb/>
              tum inuenia-
                <lb/>
              tur.</note>
            vel contra; </s>
            <s xml:id="echoid-s959" xml:space="preserve">ſed vt ſtatim punctum, quod quæritur, per vnam translationem
              <lb/>
            poſsimus inuenire, diuidenda eſt tota Tangens tabulæ ad finem nouæ deſcri-
              <lb/>
            ptionis Horologiorum poſitæ per 2. </s>
            <s xml:id="echoid-s960" xml:space="preserve">vel 3. </s>
            <s xml:id="echoid-s961" xml:space="preserve">vel per talem denique numerum,
              <lb/>
            vt producatur in Quotiente Tangens trium figurarum. </s>
            <s xml:id="echoid-s962" xml:space="preserve">Tunc enim abiecta
              <lb/>
            prima figura ad dexteram, reliqua Tangens transferenda eſt reſpectu ſinus
              <lb/>
            totius 100. </s>
            <s xml:id="echoid-s963" xml:space="preserve">multiplicatiper eundem numerum, per quem Tangẽs diuiſa fuit.
              <lb/>
            </s>
            <s xml:id="echoid-s964" xml:space="preserve">Vt Tangens hor. </s>
            <s xml:id="echoid-s965" xml:space="preserve">4. </s>
            <s xml:id="echoid-s966" xml:space="preserve">& </s>
            <s xml:id="echoid-s967" xml:space="preserve">8. </s>
            <s xml:id="echoid-s968" xml:space="preserve">reſpectu ſinus totius 1000. </s>
            <s xml:id="echoid-s969" xml:space="preserve">eſt 1732. </s>
            <s xml:id="echoid-s970" xml:space="preserve">quæ diuiſa per
              <lb/>
            2. </s>
            <s xml:id="echoid-s971" xml:space="preserve">facit 866. </s>
            <s xml:id="echoid-s972" xml:space="preserve">Ergo transferenda eſt Tangens 86. </s>
            <s xml:id="echoid-s973" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s974" xml:space="preserve">paulo amplius reſpectu ſi-
              <lb/>
            nus totius 100. </s>
            <s xml:id="echoid-s975" xml:space="preserve">duplicati. </s>
            <s xml:id="echoid-s976" xml:space="preserve">Item Tangens hor. </s>
            <s xml:id="echoid-s977" xml:space="preserve">5. </s>
            <s xml:id="echoid-s978" xml:space="preserve">& </s>
            <s xml:id="echoid-s979" xml:space="preserve">7. </s>
            <s xml:id="echoid-s980" xml:space="preserve">eſt 3732. </s>
            <s xml:id="echoid-s981" xml:space="preserve">quæ diuiſa per
              <lb/>
            quatuor ſacit 933. </s>
            <s xml:id="echoid-s982" xml:space="preserve">Ergo Tangens 93 {3/10}. </s>
            <s xml:id="echoid-s983" xml:space="preserve">transferenda eſt reſpectu ſinus totius
              <lb/>
            100. </s>
            <s xml:id="echoid-s984" xml:space="preserve">quadruplicati. </s>
            <s xml:id="echoid-s985" xml:space="preserve">Atqueita de cæteris.</s>
            <s xml:id="echoid-s986" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s987" xml:space="preserve">25. </s>
            <s xml:id="echoid-s988" xml:space="preserve">
              <emph style="sc">In</emph>
            hoc eodem denique inſtrumento facile duabus rectis tertiam pro-
              <lb/>
            portionalem, & </s>
            <s xml:id="echoid-s989" xml:space="preserve">tribus quartam adiungemus. </s>
            <s xml:id="echoid-s990" xml:space="preserve">Nam ſi, duabus propoſitis, pri-
              <lb/>
              <note position="left" xlink:label="note-042-03" xlink:href="note-042-03a" xml:space="preserve">Quo pacto
                <lb/>
              tertia, &
                <lb/>
              quarta pro-
                <lb/>
              portionalis
                <lb/>
              reperiatur.</note>
            mæinrecta A F, regulæ A B, æqualis capiatur: </s>
            <s xml:id="echoid-s991" xml:space="preserve">& </s>
            <s xml:id="echoid-s992" xml:space="preserve">ſecunda à fine huius, aperto
              <lb/>
            inſtrumento, per circinum transferatur in regulam A C, ad numerum ſimilem
              <lb/>
            illi, qui in extremo primæ in regula AB, appoſitus eſt (ita vt pedes circini ſta-
              <lb/>
            tuantur vel in ſimilibus partibus vtriuſque regulæ, vel in duobus punctis æ-
              <lb/>
            qualiter diſtantibus à ſimilibus partibus) eidemque ſecundæ in regula A B, æ-
              <lb/>
              <handwritten xlink:label="hd-042-1" xlink:href="hd-042-1a" number="11"/>
              <handwritten xlink:label="hd-042-1" xlink:href="hd-042-1a" number="12"/>
            qualis ſumatur, dabitinterualluminter finem huius ſecundæ, & </s>
            <s xml:id="echoid-s993" xml:space="preserve">numerumin
              <lb/>
            regula A C, ſimilemilli, qui prope finem ſecundæ ſcriptus eſt, tertiam propor-
              <lb/>
            tionalem; </s>
            <s xml:id="echoid-s994" xml:space="preserve">vt ex demonſtratis Num. </s>
            <s xml:id="echoid-s995" xml:space="preserve">2. </s>
            <s xml:id="echoid-s996" xml:space="preserve">conſtare poteſt.</s>
            <s xml:id="echoid-s997" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s998" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            ratione, ſi, tribus rectis propoſitis, prima & </s>
            <s xml:id="echoid-s999" xml:space="preserve">ſecunda in inſtru-
              <lb/>
            mentum transferantur, vt dictum eſt, tertiæ autem in regula A B, æqualis quo-
              <lb/>
              <handwritten xlink:label="hd-042-1" xlink:href="hd-042-1a" number="11"/>
              <handwritten xlink:label="hd-042-1" xlink:href="hd-042-1a" number="12"/>
            que capiatur, dabit interuallum inter finem tertiæ, & </s>
            <s xml:id="echoid-s1000" xml:space="preserve">numerum regulæ A C, ſi-
              <lb/>
            milem illi, qui ad extremum tertiæ in regula A B, notatus eſt, quartam propor-
              <lb/>
            tionalem.</s>
            <s xml:id="echoid-s1001" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1002" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi lineæ propoſitæ tam magnæ ſint, velaliqua illarum, vt in inſtru-
              <lb/>
            mentum tranſportari nequeant, ſumendæ erunt omnium ſemiſſes, vel tertiæ
              <lb/>
            partes, vel quartæ &</s>
            <s xml:id="echoid-s1003" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1004" xml:space="preserve">at que cum illis procedendum, vt dictum eſt. </s>
            <s xml:id="echoid-s1005" xml:space="preserve">Inuenta
              <lb/>
            enim duplicata, vel trip licata, vel quadruplicata, &</s>
            <s xml:id="echoid-s1006" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1007" xml:space="preserve">offeret tertiã aut quar-
              <lb/>
            tam proportionalem quæſitam.</s>
            <s xml:id="echoid-s1008" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum