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-div726" type="section" level="3" n="40">
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                <pb o="374" rhead="IO. BAPT. BENED." n="386" file="0386" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0386"/>
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                  <s xml:id="echoid-s4426" xml:space="preserve">At poterit aliquis mihi obijcere quod cum
                    <var>.i.o.</var>
                  fuiſſet longior
                    <var>.i.e.</var>
                  per decem vi-
                    <lb/>
                  ces tantummodo, exiſtente oculo in
                    <var>.e.</var>
                  uel
                    <var>.c.</var>
                  per gradus .90. ab
                    <var>.a</var>
                  . </s>
                  <s xml:id="echoid-s4427" xml:space="preserve">tunc punctus
                    <var>.u.</var>
                  vel
                    <lb/>
                  n. ab ipſo oculo non videretur ob terræ globoſitatem. </s>
                  <s xml:id="echoid-s4428" xml:space="preserve">Imaginemur igitur à puncto
                    <lb/>
                  u. recta
                    <var>.u.b.</var>
                  tangens quartam
                    <var>.a.e.</var>
                  in puncto
                    <var>.b.</var>
                  vt in ſecunda figura videre eſt, in qua
                    <lb/>
                  ducantur
                    <var>.c.b</var>
                  :
                    <var>i.b</var>
                  : et
                    <var>.i.u.</var>
                  quæ
                    <var>.i.u.</var>
                  ſecabit arcum
                    <var>.c.</var>
                    <lb/>
                    <figure xlink:label="fig-0386-01" xlink:href="fig-0386-01a" number="427">
                      <image file="0386-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0386-01"/>
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                  b. in puncto
                    <var>.p.</var>
                  per æqualia et
                    <var>.c.b.</var>
                  ſimiliter in pun-
                    <lb/>
                  cto
                    <var>.y.</var>
                  quod nulli dubium eſt, cum
                    <var>.c.u.</var>
                  æqualis ſit
                    <var>.
                      <lb/>
                    u.b.</var>
                  ex .35. tertij Euclidis, </s>
                  <s xml:id="echoid-s4429" xml:space="preserve">unde ex octaua primi an-
                    <lb/>
                  gulus
                    <var>.c.i.u.</var>
                  æqualis erit angulo
                    <var>.u.i.b.</var>
                  & ideo arcus
                    <var>.
                      <lb/>
                    c.p.</var>
                  æquabitur arcui
                    <var>.p.b.</var>
                  ſed ex .4. primi
                    <var>.c.y.</var>
                  æqua
                    <lb/>
                  lis erit ipſi
                    <var>.y.b</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4430" xml:space="preserve">Nunc ſuppoſita
                    <var>.c.i.</var>
                  decima parte ipſius
                    <var>.c.u.</var>
                  nemi
                    <lb/>
                  ni dubium erit quod cum
                    <var>.u.i.</var>
                  ſubtendatur angulo
                    <lb/>
                  recto
                    <var>.u.c.i.</var>
                  (iam ſupra diximus angulum
                    <var>.c.</var>
                  ſenſibi-
                    <lb/>
                  liter minime differre à recto) ipſa vt ſinus totus erit
                    <lb/>
                  partium .100000. cuius quadratum cum diuiſum
                    <lb/>
                  fuerit in partes æquales centum &
                    <reg norm="vnam" type="context">vnã</reg>
                  , illarum vna
                    <lb/>
                  æqualis erit quadrto
                    <var>.c.i.</var>
                  reliquę vero quadrato ip-
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                  ſius
                    <var>.u.c.</var>
                  ex proportione duplicata quadratorum ad
                    <lb/>
                  eam quam continent eorum latera. </s>
                  <s xml:id="echoid-s4431" xml:space="preserve">Sed quadra-
                    <lb/>
                  tum ipſius
                    <var>.u.i.</var>
                  eſt partium .10000000000. </s>
                  <s xml:id="echoid-s4432" xml:space="preserve">quare
                    <lb/>
                  quadratum
                    <var>.c.i.</var>
                  erit .99009900. cuius radix
                    <var>.c.i.</var>
                    <lb/>
                  erit partium .9950. vnde quadratum ipſius
                    <var>.c.u.</var>
                  erit
                    <lb/>
                  partium .9900990100. cuius radix
                    <var>.u.c.</var>
                  erit
                    <reg norm="partium" type="context">partiũ</reg>
                    <lb/>
                  99500. vnde angulus
                    <var>.c.i.u.</var>
                  erit graduum .84. & mi
                    <lb/>
                  nu .17. & angulus
                    <var>.c.u.i.</var>
                  qui reſpondet ſinui
                    <var>.c.i.</var>
                  erit
                    <lb/>
                  gra .5. & min .43. cuius duplum, hoc eſt angulus
                    <var>.c.
                      <lb/>
                    u.b.</var>
                  erit grad .11. min .26. æqualis ferè angulo iam
                    <lb/>
                  ſupradicto. </s>
                  <s xml:id="echoid-s4433" xml:space="preserve">ſed
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                  ſinus anguli
                    <var>.c.i.y.</var>
                  erit ſimiliter
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                  partium .99500. talium vt
                    <var>.c.i.</var>
                  ſunt .100000. ſed vt
                    <lb/>
                    <var>c.i.</var>
                  eſt partium .9950. </s>
                  <s xml:id="echoid-s4434" xml:space="preserve">tunc
                    <var>.c.y.</var>
                  erit partium .9900
                    <lb/>
                  hoc eſt quaſi decima pars ipſius
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                  </s>
                  <s xml:id="echoid-s4435" xml:space="preserve">quare ſi ocu-
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                  lus in
                    <var>.e.</var>
                  non videbit punctum
                    <var>.u.</var>
                  hoc punctum be-
                    <lb/>
                  ne videbitur ab oculo in
                    <var>.b.</var>
                  abſque ſenſibili dimi-
                    <lb/>
                  nutione anguli in puncto
                    <var>.u.</var>
                  vt probauimus.</s>
                </p>
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            <div xml:id="echoid-div730" type="section" level="3" n="41">
              <div xml:id="echoid-div730" type="letter" level="4" n="1">
                <head xml:id="echoid-head554" xml:space="preserve">DE MAGNITVDINIBVS FIGVRARVM
                  <lb/>
                iſoperimetrarum.</head>
                <head xml:id="echoid-head555" style="it" xml:space="preserve">Domino Ioanni Mariæ Agatio.</head>
                <p>
                  <s xml:id="echoid-s4436" xml:space="preserve">
                    <emph style="sc">QVamvis</emph>
                  à Theone ſupra Ptolomei Almageſtum ſufficienter traditum
                    <lb/>
                  ſit de magnitudinibus figurarum iſopetimetrarum, nihilominus vt tibi
                    <lb/>
                  morem geram, ea nunc ſcribo, quæ mihi in mentem venerunt contra
                    <lb/>
                    <reg norm="Alexandrum" type="context">Alexãdrum</reg>
                  Piccolhomineum,
                    <reg norm="antequam" type="context">antequã</reg>
                  aliquid ipſius Theonis vidiſſem </s>
                </p>
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