Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div680" type="section" level="3" n="31">
              <div xml:id="echoid-div683" type="letter" level="4" n="2">
                <pb o="356" rhead="IO. BAPT. BENED." n="368" file="0368" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0368"/>
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              <div xml:id="echoid-div686" type="letter" level="4" n="3">
                <head xml:id="echoid-head522" style="it" xml:space="preserve">Duplex modus par allelam orizontalem alicui muro propoſito
                  <lb/>
                una tantummodo statione ducendi.</head>
                <head xml:id="echoid-head523" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4276" xml:space="preserve">DVcere parallelam orizontalem alicui muro recto propoſito vna tantummodò
                    <lb/>
                  ſtatione, non ſolum poſſibile eſt ſed etiam facile.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4277" xml:space="preserve">Sit exempli gratia murus rectus
                    <var>.a.d.</var>
                  ſitus verò
                    <var>.o.n</var>
                  . </s>
                  <s xml:id="echoid-s4278" xml:space="preserve">Si cupimus ducere
                    <var>.n.u.</var>
                    <lb/>
                  parallelam dicto muro, accipiatur quadratum geometricum, ſeu ſcala altimetra
                    <lb/>
                  vel aliquod ſimile inſtrumentum, quo mediante à ſitu
                    <var>.o.</var>
                  videbimus punctum
                    <var>.q.</var>
                    <lb/>
                  quod volueris ipſius muri,
                    <reg norm="dexteram" type="context">dexterã</reg>
                    <lb/>
                  verſus, inferius tamen. ipſo
                    <var>.o.</var>
                  vnde
                    <lb/>
                    <figure xlink:label="fig-0368-01" xlink:href="fig-0368-01a" number="406">
                      <image file="0368-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0368-01"/>
                    </figure>
                  formatum habebimus triangulum
                    <var>.
                      <lb/>
                    n.o.q</var>
                  . </s>
                  <s xml:id="echoid-s4279" xml:space="preserve">Quo facto ad partem
                    <reg norm="ſiniſtram" type="context">ſiniſtrã</reg>
                    <lb/>
                  cum eodem angulo
                    <var>.n.o.q.</var>
                  oporte-
                    <lb/>
                  bit nos inuenire punctum aliquod
                    <var>.
                      <lb/>
                    p.</var>
                  in dicta ſuperficie muri, </s>
                  <s xml:id="echoid-s4280" xml:space="preserve">& tunc
                    <lb/>
                  habebimus angulum
                    <var>.n.o.p.</var>
                  æqua-
                    <lb/>
                  lem angulo
                    <var>.n.o.q.</var>
                  vnde angulus
                    <var>.q.
                      <lb/>
                    n.p.</var>
                  nobis cognitus erit,
                    <reg norm="duoque" type="simple">duoq́;</reg>
                  late
                    <lb/>
                  ra
                    <var>.n.q.</var>
                  et
                    <var>.n.p.</var>
                  erunt inuicem æqua-
                    <lb/>
                  lia, ex .26. primi Euclid. cum angu-
                    <lb/>
                  li
                    <var>.q.o.n.</var>
                  et
                    <var>.q.n.o.</var>
                  ſint æquales angu
                    <lb/>
                  lis
                    <var>.p.o.n.</var>
                  et
                    <var>.p.n.o.</var>
                  & latus
                    <var>.o.n.</var>
                  com
                    <lb/>
                  mune, vnde angulus
                    <var>.q.n.g.</var>
                  extrinſe
                    <lb/>
                  cus trianguli
                    <var>.p.q.n.</var>
                    <reg norm="reſiduusque" type="simple">reſiduusq́;</reg>
                  ex
                    <lb/>
                  duobus rectis nobis cognitus erit,
                    <lb/>
                  etiam & eius medictas
                    <var>.q.n.u.</var>
                  æqua
                    <lb/>
                  lis angulo
                    <var>.p.q.n.</var>
                  eo quod ex .5. pri-
                    <lb/>
                  mi, anguli
                    <var>.q.p.</var>
                  ſunt inuicem æquales, & ex .32. eiuſdem, æquales ſunt extrinſeco
                    <var>.q.n.
                      <lb/>
                    g.</var>
                  & ex 27.
                    <var>n.u.</var>
                  erit parallela ipſi
                    <var>.q.p</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4281" xml:space="preserve">Aliter etiam poſſumus idem efficere, ſumendo duo illa puncta in ſuprem a linea
                    <lb/>
                  orizontali ipſius muri ad ſuperiorem partem aſpiciendo, quemadmodum ad infe-
                    <lb/>
                  riorem, quod vnum & idem erit, dummodò non aſpiciamus orizontaliter, eo quod
                    <lb/>
                  nos oportet ſuperficiem conicam producere, linea viſuali mediante. </s>
                  <s xml:id="echoid-s4282" xml:space="preserve">cognoſcere au­
                    <lb/>
                  tem angulum
                    <var>.q.n.p.</var>
                  facile erit, conſtituendo primò inſtrumentum in ſitu trianguli
                    <var>.
                      <lb/>
                    o.n.q.</var>
                    <reg norm="aſpiciendoque" type="simple">aſpiciendoq́;</reg>
                  punctum
                    <var>.c.</var>
                  in ſuperficie
                    <var>.n.q.o.</var>
                  & ſic in alia parte, exiſtente in-
                    <lb/>
                  ſtrumento in ſitu trianguli
                    <var>.o.p.n.</var>
                  aſpicere oportet punctum
                    <var>.e.</var>
                  proximum puncto
                    <var>.n.</var>
                    <lb/>
                  vbi poſſit metiri angulum
                    <var>.c.n.e</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4283" xml:space="preserve">Sed ſi ſitus puncti
                    <var>.n.</var>
                  talis eſſet, vt ab eo non poſſet aliquis murum videre ad re-
                    <lb/>
                  ctos angulos, aſpiceremus punctum
                    <var>.q.</var>
                  ſub orizontali ab oculis noſtris, in orizontali
                    <lb/>
                  tamen puncti
                    <var>.n.</var>
                  ita quod angulus
                    <var>.o.n.q.</var>
                  rectus exiſtat, quo facto obſeruando angu-
                    <lb/>
                  lum
                    <var>.n.o.q.</var>
                  eo mediante, medianteq́ue
                    <var>.n.o.</var>
                  cum angulo
                    <var>.o.n.q.</var>
                  cognoſcemus
                    <lb/>
                  quantitatem diſtantiæ
                    <var>.n.q.</var>
                  idem etiam faciendum eſt cum alio puncto
                    <var>.p.</var>
                  quod
                    <lb/>
                  volueris, & mediantibus duobus punctis inuicem proximis
                    <var>.c.e.</var>
                  cognoſcatur an- </s>
                </p>
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