Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div237" type="section" level="1" n="106">
          <p>
            <s xml:id="echoid-s3722" xml:space="preserve">
              <pb o="98" file="128" n="128" rhead="GEOMETR. PRACT."/>
            nebitur altitudo A E, vel latus AD, in diſtantia ſecundum hunc numerum 500.
              <lb/>
            </s>
            <s xml:id="echoid-s3723" xml:space="preserve">quòd 1000. </s>
            <s xml:id="echoid-s3724" xml:space="preserve">diuiſa per 2. </s>
            <s xml:id="echoid-s3725" xml:space="preserve">dent Quotientem 500. </s>
            <s xml:id="echoid-s3726" xml:space="preserve">At vmbra verſa trium mille-
              <lb/>
            ſimarum dabunt Quotientem 333 {1/3}. </s>
            <s xml:id="echoid-s3727" xml:space="preserve">quià priori differt hoc numero, 166 {2/3}. </s>
            <s xml:id="echoid-s3728" xml:space="preserve">Ex
              <lb/>
            quo intelligi licet, quando vmbra verſa abſciſſa valde parua eſt, magnum poſ-
              <lb/>
            ſe errorem committi in diſtantia inueſtiganda. </s>
            <s xml:id="echoid-s3729" xml:space="preserve">Cum enim partes milleſimæ ſint
              <lb/>
            perexiguæ, facilè decipi poſſumus, vt nimirum putemus, ab ſciſſas eſſe tres mil-
              <lb/>
            leſimas, cum fortaſsis ſolum duæ abſciſſæ ſint: </s>
            <s xml:id="echoid-s3730" xml:space="preserve">ac proinde err or committi po-
              <lb/>
            terit 166 {2/3}. </s>
            <s xml:id="echoid-s3731" xml:space="preserve">altitudinem AE, vellaterum A D, qui error contemnendus non eſt. </s>
            <s xml:id="echoid-s3732" xml:space="preserve">
              <lb/>
            At quando partes vmbræ verſæ plures milleſimas continent, non tantus error
              <lb/>
            committitur, etiamſi vnam milleſimam pro altera accipiamus. </s>
            <s xml:id="echoid-s3733" xml:space="preserve">Nam ſi verbi
              <lb/>
            gratia putemus, ab ſciſſas eſſe partes {30/1000}. </s>
            <s xml:id="echoid-s3734" xml:space="preserve">ex vmbra verſa, cum verè abſciſſæ
              <lb/>
            ſint {31/1000}. </s>
            <s xml:id="echoid-s3735" xml:space="preserve">error fieri poterit ſolum in 1. </s>
            <s xml:id="echoid-s3736" xml:space="preserve">altitudine A E, vellatere A D, & </s>
            <s xml:id="echoid-s3737" xml:space="preserve">{7/93}. </s>
            <s xml:id="echoid-s3738" xml:space="preserve">
              <lb/>
            cum {30/1000}. </s>
            <s xml:id="echoid-s3739" xml:space="preserve">dent Quotientem 33 {1/3}. </s>
            <s xml:id="echoid-s3740" xml:space="preserve">at {31/1000}. </s>
            <s xml:id="echoid-s3741" xml:space="preserve">Quotientem offerant 32 {8/31}. </s>
            <s xml:id="echoid-s3742" xml:space="preserve">
              <lb/>
            Itaque magis probo, vt Quadratum in altiori loco ſtatuatur, quam in plano
              <lb/>
            Horizontis, quia ibi plures partes vmbræ verſę abſcinduntur, quam hic, vt con-
              <lb/>
            ſtat in diſtantiis æqualibus E F, D M. </s>
            <s xml:id="echoid-s3743" xml:space="preserve">Vides ergo magnam eſſe adhibendam
              <lb/>
            diligentiam, vt accuratè partes milleſimæ rep eriantur per ea, quæ lib. </s>
            <s xml:id="echoid-s3744" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3745" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s3746" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3747" xml:space="preserve">
              <lb/>
            Num. </s>
            <s xml:id="echoid-s3748" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3749" xml:space="preserve">ſcripſimus.</s>
            <s xml:id="echoid-s3750" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3751" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò, ſi quadratum conſtructum ſit ad certam aliquam menſuram, hoc
              <lb/>
            eſt, vt latus contineat vel 1. </s>
            <s xml:id="echoid-s3752" xml:space="preserve">paſſum, vel 1. </s>
            <s xml:id="echoid-s3753" xml:space="preserve">cubitũ, vel 2. </s>
            <s xml:id="echoid-s3754" xml:space="preserve">pedes, aut palmos, aut 3.
              <lb/>
            </s>
            <s xml:id="echoid-s3755" xml:space="preserve">aut 4. </s>
            <s xml:id="echoid-s3756" xml:space="preserve">&</s>
            <s xml:id="echoid-s3757" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3758" xml:space="preserve">res erit expeditiſsima, ſi ſemel tantum latus particularum 1000. </s>
            <s xml:id="echoid-s3759" xml:space="preserve">du-
              <lb/>
            catur in menſuras, quibus latus æquiualet. </s>
            <s xml:id="echoid-s3760" xml:space="preserve">Ita enim in longitudinibus ex-
              <lb/>
            quirendis, ſi quadratum ſupra planum, in quo eſt longitudo, ſtatuatur, (vt fit
              <lb/>
            in omnibus hypotenuſis, ſiue diſtantiis à loco menſoris vſque ad aliquod pun-
              <lb/>
            ctum menſore ſublimus, depreſsiuſue, quemadmo dum patuitin proxima figu-
              <lb/>
            ra, quando longitudo D M, inquiſita eſt, patebitque in ſcholio problematis 7. </s>
            <s xml:id="echoid-s3761" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s3762" xml:space="preserve">in ſcholio problem. </s>
            <s xml:id="echoid-s3763" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3764" xml:space="preserve">Item in problem. </s>
            <s xml:id="echoid-s3765" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3766" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3767" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3768" xml:space="preserve">& </s>
            <s xml:id="echoid-s3769" xml:space="preserve">in problem. </s>
            <s xml:id="echoid-s3770" xml:space="preserve">26. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">
              <lb/>
            Num. </s>
            <s xml:id="echoid-s3772" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3773" xml:space="preserve">& </s>
            <s xml:id="echoid-s3774" xml:space="preserve">in problem. </s>
            <s xml:id="echoid-s3775" xml:space="preserve">27. </s>
            <s xml:id="echoid-s3776" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3777" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3778" xml:space="preserve">nec non in problem. </s>
            <s xml:id="echoid-s3779" xml:space="preserve">37. </s>
            <s xml:id="echoid-s3780" xml:space="preserve">& </s>
            <s xml:id="echoid-s3781" xml:space="preserve">38. </s>
            <s xml:id="echoid-s3782" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3783" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3784" xml:space="preserve">& </s>
            <s xml:id="echoid-s3785" xml:space="preserve">
              <lb/>
            denique in problem. </s>
            <s xml:id="echoid-s3786" xml:space="preserve">43. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">& </s>
            <s xml:id="echoid-s3788" xml:space="preserve">44. </s>
            <s xml:id="echoid-s3789" xml:space="preserve">& </s>
            <s xml:id="echoid-s3790" xml:space="preserve">in aliis locis) diuidendus ſolum eſt numerus
              <lb/>
            productus per partes vmbræ verſæ (quæ ſemper abſcinditur) notatas. </s>
            <s xml:id="echoid-s3791" xml:space="preserve">Quo-
              <lb/>
            tiens enim dabit longitudinem quæſitám in data menſura. </s>
            <s xml:id="echoid-s3792" xml:space="preserve">Verbigratia, ſi in vno
              <lb/>
            latere comprehendantur 3. </s>
            <s xml:id="echoid-s3793" xml:space="preserve">pedes, multiplicabimus latus 1000. </s>
            <s xml:id="echoid-s3794" xml:space="preserve">per 3. </s>
            <s xml:id="echoid-s3795" xml:space="preserve">efficie-
              <lb/>
            muſque 3000. </s>
            <s xml:id="echoid-s3796" xml:space="preserve">Ita que ſi in inueſtiganda longitudine quapiam abſciſſæ ſint par-
              <lb/>
            tes 200. </s>
            <s xml:id="echoid-s3797" xml:space="preserve">ex vmbra verſa, partiemur 3000. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">per 200. </s>
            <s xml:id="echoid-s3799" xml:space="preserve">Nam Quotiens 15. </s>
            <s xml:id="echoid-s3800" xml:space="preserve">dabit 15. </s>
            <s xml:id="echoid-s3801" xml:space="preserve">
              <lb/>
            pedes pro quæſita longitudine. </s>
            <s xml:id="echoid-s3802" xml:space="preserve"> Nam cum in proxima figura ſit, vt
              <note symbol="a" position="left" xlink:label="note-128-01" xlink:href="note-128-01a" xml:space="preserve">4. ſexti.</note>
            verſa NB, 200. </s>
            <s xml:id="echoid-s3803" xml:space="preserve">ad latus BA, 1000. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">Italatus AD, 3. </s>
            <s xml:id="echoid-s3805" xml:space="preserve">pedum ad DM, multiplican-
              <lb/>
            dum eſt latus 1000. </s>
            <s xml:id="echoid-s3806" xml:space="preserve">per 3. </s>
            <s xml:id="echoid-s3807" xml:space="preserve">pedes, & </s>
            <s xml:id="echoid-s3808" xml:space="preserve">productus numerus 3000. </s>
            <s xml:id="echoid-s3809" xml:space="preserve">per 200. </s>
            <s xml:id="echoid-s3810" xml:space="preserve">diuiden-
              <lb/>
            dus. </s>
            <s xml:id="echoid-s3811" xml:space="preserve">Eademque decæteris ratio eſt. </s>
            <s xml:id="echoid-s3812" xml:space="preserve">Sic ſi latus contineret {1/2} cubiti, diuidendu@
              <lb/>
            eſſet numerus 500. </s>
            <s xml:id="echoid-s3813" xml:space="preserve">ex {1/2}. </s>
            <s xml:id="echoid-s3814" xml:space="preserve">in 1000. </s>
            <s xml:id="echoid-s3815" xml:space="preserve">procreatus per vmbram verſam. </s>
            <s xml:id="echoid-s3816" xml:space="preserve">Pari ratio-
              <lb/>
            ne ſi latus complecteretur 10. </s>
            <s xml:id="echoid-s3817" xml:space="preserve">palmos, diuidendus eſſet numerus 1000. </s>
            <s xml:id="echoid-s3818" xml:space="preserve">genitu@
              <lb/>
            ex 10. </s>
            <s xml:id="echoid-s3819" xml:space="preserve">in 1000. </s>
            <s xml:id="echoid-s3820" xml:space="preserve">per vmbram verſam: </s>
            <s xml:id="echoid-s3821" xml:space="preserve">vt in Quotiente prodeant palmi in longi-
              <lb/>
            @udine contenti, &</s>
            <s xml:id="echoid-s3822" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3823" xml:space="preserve">quod non indiligenter notandum eſt.</s>
            <s xml:id="echoid-s3824" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div244" type="section" level="1" n="107">
          <head xml:id="echoid-head110" xml:space="preserve">ALITER</head>
          <p>
            <s xml:id="echoid-s3825" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3826" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            diſtantia metienda magna eſt, & </s>
            <s xml:id="echoid-s3827" xml:space="preserve">adeſt bona planities campi,
              <lb/>
            vti poterimus Quadrato ſtabili commodiſsimè hoc modo. </s>
            <s xml:id="echoid-s3828" xml:space="preserve">Sit diſtantia </s>
          </p>
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