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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EPISTOL AE.
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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div713" type="section" level="3" n="37">
              <div xml:id="echoid-div717" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s4390" xml:space="preserve">
                    <pb o="369" rhead="EPISTOL AE." n="381" file="0381" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0381"/>
                  gentiæ gratia cogita ſilum illum (exempli adducti ab illis doctiſſimis viris) cui pon
                    <lb/>
                  dus appenſum eſt, æqualem eſſe axi orizontis, hoc eſt eius extremitatem immobi-
                    <lb/>
                  lem eſſe in primo mobili, & in ipſo zenit tui orizontis, </s>
                  <s xml:id="echoid-s4391" xml:space="preserve">tunc arcus motionis ipſius la
                    <lb/>
                  pidis per tantum interuallum, quantum eſt diameter terræ, inſenſibiliter differret à
                    <lb/>
                  linea recta, & cum lapis diſtans à centro mundi per ſemidiametrum terræ, iret re-
                    <lb/>
                    <reg norm="diretque" type="simple">diretq́;</reg>
                  , vt ſcis, ergo idem faceret ſi ſilum longius eſſet per dictum terræ ſemidia-
                    <lb/>
                  metrum, ita vt poſſetipſum centrum attingere, nam differentia illa ſemidiametri
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                  terræ, ferè nulla eſt reſpectu ſemidiametri ipſius primi mobilis.</s>
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            <div xml:id="echoid-div720" type="section" level="3" n="38">
              <div xml:id="echoid-div720" type="letter" level="4" n="1">
                <head xml:id="echoid-head546" xml:space="preserve">AN PENTAGONVS AB ALBERTO DVRERO
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                deſcriptus æquiangulus ſit.</head>
                <head xml:id="echoid-head547" style="it" xml:space="preserve">Conrado Neubart.</head>
                <p>
                  <s xml:id="echoid-s4392" xml:space="preserve">SI non credis Pentagonum ab Alberto Durero ſuper datam lineam deſi-
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                  gnatum, æquiangulum non eſſe. </s>
                  <s xml:id="echoid-s4393" xml:space="preserve">Fingamus hic ſubiectam ſiguram ſimi-
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                  lem ei quæ à Durero ponitur, in qua primò, ducta ſit linea
                    <var>.o.a.</var>
                  & habe
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                  bimus angulum
                    <var>.a.o.b.</var>
                  graduum .60. talium qualium duo recti fuerint gra
                    <num value="360">.
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                    360.</num>
                  vel .30. talium qualium duo recti fuerint .180. nam ex ſuppoſito, arcus
                    <var>.a.b.</var>
                  eſt
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                  ſexta pars totius circunferentiæ, angulus vero
                    <var>.b.o.d.</var>
                  rectus eſt, eo quod
                    <var>.b.o.q.</var>
                  rectus
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                  etiam ſit, </s>
                  <s xml:id="echoid-s4394" xml:space="preserve">quare angulus
                    <var>.d.o.a.</var>
                  reſiduus ex recto erit graduum .60. talium, ut rectus
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                  eſt .90. angulus verò
                    <var>.o.a.c.</var>
                  erit gra .15. eorundem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4395" xml:space="preserve">Ducatur deinde perpendicularis
                    <var>.a.e.</var>
                  ad
                    <var>.o.d.</var>
                  quæ vt ſinus anguli
                    <var>.a.o.e.</var>
                  erit par-
                    <lb/>
                  tium .86602. talium qualium
                    <var>.a.o.</var>
                  erit .100000. quæ quidem
                    <var>.o.a.</var>
                  vt chorda arcus
                    <var>.a.
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                    o.</var>
                  eſt partium .51762. talium qualium
                    <var>.a.d.</var>
                  vel
                    <var>.a.c.</var>
                  ſemidiameter eſt .100000.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4396" xml:space="preserve">Nam ſinus dimidij arcus
                    <var>.a.o.</var>
                  (exi
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                  ſtente
                    <var>.a.o.</var>
                  graduum .30.) eſt
                    <reg norm="partium" type="context">partiũ</reg>
                    <num value="25881">.
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                      <anchor type="figure" xlink:label="fig-0381-01a" xlink:href="fig-0381-01"/>
                    25881.</num>
                  ex quo
                    <var>.a.e.</var>
                  erit partium
                    <num value="44827">.
                      <lb/>
                    44827.</num>
                  talium qualium
                    <var>.a.d.</var>
                  erit
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                  100000. vnde angulus
                    <var>.a.d.o.</var>
                  cuius ſi
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                  nus eſt
                    <var>.a.e.</var>
                  erit graduum .26. min .38
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                  qui quidem angulus, ſumptus cum an
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                  gulo
                    <var>.a.o.d.</var>
                  erit gra .86. min .38. </s>
                  <s xml:id="echoid-s4397" xml:space="preserve">Dem
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                  pta denique hac ſumma ex duobus
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                  rectis gra .180. reliquum erit gra .93.
                    <lb/>
                  min .22. ideſt angulus
                    <var>.o.a.d.</var>
                  cui addi
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                  tus cum fuerit angulus
                    <var>.o.a.c.</var>
                  gra .15.
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                  talium, habebimus angulum
                    <var>.c.a.d.</var>
                    <lb/>
                  graduum .108. min .22. exuperantem
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                  verum angulum pentagoni per min
                    <num value="22">.
                      <lb/>
                    22.</num>
                  vel ſic, cum inuentus fuerit angu-
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                  lus
                    <var>.a.d.o.</var>
                  gra .26. min .38. ſi ex vno re
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                  cto demptus fuerit, relinquetur an-
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                  gulus
                    <var>.d.a.e.</var>
                  gra .63. min .22. qui qui-
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                  dem collectus cum fuer it cum angu-
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                  lo
                    <var>.e.a.o.</var>
                  reſiduo ex re cto dempto angulo
                    <var>.a.o.e.</var>
                  grad .60. qui
                    <var>.e.a.o.</var>
                  eſt grad .30. & </s>
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