Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s3828" xml:space="preserve">
              <pb o="99" file="129" n="129" rhead="LIBER TERTIVS."/>
            ta
              <unsure/>
            A E. </s>
            <s xml:id="echoid-s3829" xml:space="preserve">Erigatur quadratum ad Horizontem ad rectos angulos, circumduca-
              <lb/>
            turque, donec per eius planum oculus in A, conſtitutus ſignum E, perſpiciat,
              <lb/>
              <figure xlink:label="fig-129-01" xlink:href="fig-129-01a" number="56">
                <image file="129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/129-01"/>
              </figure>
            atque linea notetur AG. </s>
            <s xml:id="echoid-s3830" xml:space="preserve">Demiſſo deinde Qua-
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            dratovſquead Horizontis planum, ita vt latus
              <lb/>
            A B, recta tendat ad ſignum E, hoc eſt, à recta
              <lb/>
            notata A G, non recedat, protendatur linea re-
              <lb/>
            cta per latus A D, in qua accipiantur quotcun-
              <lb/>
            que partes lateri A D, æquales: </s>
            <s xml:id="echoid-s3831" xml:space="preserve">vel quotcun-
              <lb/>
            quealiæ menſuræ æquales, vt paſſus, vel cubiti,
              <lb/>
            vſque ad punctum a, in quo rurſus erigatur qua-
              <lb/>
            dratum, (In hoc ſecundo quadrato aſſcripſi-
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            mus Iiteras minuſculas, ne literæ vnius quadra-
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            ti cum literis alterius confundantur, quod in
              <lb/>
            ſequentibus etiam obſeruabimus.) </s>
            <s xml:id="echoid-s3832" xml:space="preserve">vertatur-
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            que, donec per eius planum idem ſignum E, ap-
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            pareat per rectam a H. </s>
            <s xml:id="echoid-s3833" xml:space="preserve">Poſt hæc quadratum
              <lb/>
            Horizonti incumbat, latuſque a d, rectæ A a
              <lb/>
            congruat, & </s>
            <s xml:id="echoid-s3834" xml:space="preserve">dioptra circumducatur, donec
              <lb/>
            eius linea fiduciæ rectæ a H, præcisè ſit ſuppoſita, notenturque partes milleſi-
              <lb/>
            mæin portione vmbræ verſæ b F, quam diligentiſsimè. </s>
            <s xml:id="echoid-s3835" xml:space="preserve">Abſcindetur autem ſem-
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            per vmbra verſa, propterea quod diſtantia AE, proponitur magna, ſaltem ma-
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            ior, quam A a: </s>
            <s xml:id="echoid-s3836" xml:space="preserve">alio quin menſurari poſſet ſine quadrato, quemadmodum & </s>
            <s xml:id="echoid-s3837" xml:space="preserve">
              <lb/>
            A a. </s>
            <s xml:id="echoid-s3838" xml:space="preserve">Quibus peractis, erunt triangula a b F, a A E, æquiangula, cum angulos
              <lb/>
              <note symbol="a" position="right" xlink:label="note-129-01" xlink:href="note-129-01a" xml:space="preserve">29. primi.</note>
            habeant rectos b, A, & </s>
            <s xml:id="echoid-s3839" xml:space="preserve">alternos æquales b a F, A E a. </s>
            <s xml:id="echoid-s3840" xml:space="preserve"> Si ergo fiat,</s>
          </p>
          <note symbol="b" position="right" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
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          Vt vmbra b F, # ad lat{us} b a, 1000, # Ita a A, nota # ad A E, diſtantiam,
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          </note>
          <p>
            <s xml:id="echoid-s3841" xml:space="preserve">inuenietur diſtantia A E, in partibus rectæ A a. </s>
            <s xml:id="echoid-s3842" xml:space="preserve">Vel ſi diuidatur latus b a, 1000.
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            </s>
            <s xml:id="echoid-s3843" xml:space="preserve">per partes milleſimas vmbræ B F, procreabitur numerus, ſecundum quem re-
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            cta A a, in diſtantia eadem A E, continetur: </s>
            <s xml:id="echoid-s3844" xml:space="preserve">poſita nimirum recta A a, vt 1. </s>
            <s xml:id="echoid-s3845" xml:space="preserve">vt
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            Num. </s>
            <s xml:id="echoid-s3846" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3847" xml:space="preserve">oſtendimus.</s>
            <s xml:id="echoid-s3848" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3849" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3850" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi ad manum non habeamus Quadratum, obtinebimus eandem
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            diſtantiam beneficio baculi, vel arundinis hoc artificio. </s>
            <s xml:id="echoid-s3851" xml:space="preserve">Figatur baculus, vel
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            arundo in G, ad rectos angulos plano Horizontis, quod per filum aliquod cum
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            perpendiculo facile fiet. </s>
            <s xml:id="echoid-s3852" xml:space="preserve">Deinderecede per quotlibet paſlus vſque ad A, ita vt
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            viſus per baculum incedens feratur in ſignũ E. </s>
            <s xml:id="echoid-s3853" xml:space="preserve">Poſt hæc ducatur linea A a, ad
              <lb/>
            AE, perpẽdicularis, in qua numera quotlibet etiam paſſus vſq; </s>
            <s xml:id="echoid-s3854" xml:space="preserve">ad a. </s>
            <s xml:id="echoid-s3855" xml:space="preserve">Ducta tan-
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            dem GI, ad A E, quoque perpendiculari, & </s>
            <s xml:id="echoid-s3856" xml:space="preserve">ipſi A a, æquali, figatur rurſum ba-
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            culus ad angulos rectos in tali puncto rectæ GI, nimirumin H, vt oculus iterum
              <lb/>
            ex a, per baculum in cedens feratur in ſignum E: </s>
            <s xml:id="echoid-s3857" xml:space="preserve">inquiranturque exquiſitiſsi-
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            me paſſus vna cum fragmentis vnius paſſus in H I, contenti. </s>
            <s xml:id="echoid-s3858" xml:space="preserve">His enim pera-
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            ctis, quo niam rurſus triangula H I a, a A E, æquiangula ſunt, ob angulos re-
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            ctos I, A, & </s>
            <s xml:id="echoid-s3859" xml:space="preserve">alternos æquales I a H, A E a, ſi fiat,</s>
          </p>
          <note symbol="c" position="right" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt H I, nota # ad I a, notam # Ita a A, nota # ad A E, diſtantiam ′
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          </note>
          <p>
            <s xml:id="echoid-s3860" xml:space="preserve">effi cietur nota diſtantia A E, in partibus rectarum G A, A a, a I. </s>
            <s xml:id="echoid-s3861" xml:space="preserve">Vel ſi diuidatur
              <lb/>
            a I, nota per IH, notam, reperiemus, quoties Aa, in diſtantia AE, contineatur, ſi
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            nimirum recta A a, ponatur vt 1.</s>
            <s xml:id="echoid-s3862" xml:space="preserve"/>
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