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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IO. BAPT. BENED.
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            <div xml:id="echoid-div690" type="section" level="3" n="32">
              <div xml:id="echoid-div695" type="letter" level="4" n="3">
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            <div xml:id="echoid-div698" type="section" level="3" n="33">
              <div xml:id="echoid-div698" type="letter" level="4" n="1">
                <head xml:id="echoid-head530" xml:space="preserve">NOTABILES ERRORES ORONTII
                  <lb/>
                & Tartaleæ.</head>
                <head xml:id="echoid-head531" style="it" xml:space="preserve">Cornelio Bitonto.</head>
                <p>
                  <s xml:id="echoid-s4314" xml:space="preserve">
                    <emph style="sc">PArvvs</emph>
                  error non fuit, vt putabat Orontius, quodanguli triangulorum
                    <lb/>
                  æquicrurium inuicem æqualium, baſibus oppoſiti, ijſdem baſibus propor
                    <lb/>
                  tionales eſſent, cuius opinionis cauſa fuit quod nunquam viderit vel me
                    <lb/>
                  minerit eius quod Ptolomeus ſcripſit lib. primo Almageſti, vbi de diſpro
                    <lb/>
                  portionalitate chordarum
                    <reg norm="arcuumque" type="simple">arcuumq́;</reg>
                  tractat, vel quod ſcribit Vitellio lib. primo pro
                    <lb/>
                  poſitione .35. ſeu lib. quarto, propoſitione .21. quod idem eſt. </s>
                  <s xml:id="echoid-s4315" xml:space="preserve">Sed nec ego tibi pro
                    <lb/>
                  ponam id quod ſcribit Nicolaus Tartalea diuiſioni .28. quinti capitis quartæ partis
                    <lb/>
                  ſuorum tractatuum, eo quod non exactè ſcientificè ſcripſerit, nec vniuerſaliter,
                    <reg norm="quan- uis" type="context">quã-
                      <lb/>
                    uis</reg>
                  talis propoſitio poſſit ſcientificè ſcribi, accipiendo
                    <var>.b.c.</var>
                  in eius figura, pro latere
                    <lb/>
                  octagoni, vnde angulus
                    <var>.a.e.b.</var>
                  duplum foret angulo
                    <var>.b.e.c.</var>
                  collocato poſtea
                    <var>.b.c.</var>
                  in
                    <lb/>
                  arcu
                    <var>.a.b.</var>
                  punctum
                    <var>.c.</var>
                  medium fuiſſet dicti arcus, et
                    <var>.e.c.</var>
                  diuideret
                    <var>.a.b.</var>
                  per æqualia,
                    <lb/>
                  ex quinta primi, nec non ad rectos ex .3. tertij, vnde ex .18. primi, clare vidiſſemus
                    <lb/>
                  non eſſe proportionem
                    <var>.a.b.</var>
                  ad
                    <var>.b.c.</var>
                  vt anguli ad angulum. </s>
                  <s xml:id="echoid-s4316" xml:space="preserve">Sed vniuerſaliori modo
                    <lb/>
                  poſſumus hoc ſpeculari. </s>
                  <s xml:id="echoid-s4317" xml:space="preserve">Nam manifeſtè ſcimus, eandem eſſe proportionem circun
                    <lb/>
                  ferentiæ ad diametrum in omnibus circulis tam maioribus, quam minoribus.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4318" xml:space="preserve">Sint igitur duo anguli
                    <var>.a.e.b.</var>
                  et
                    <var>.c.e.b.</var>
                  cuiuſuis amplitudinis, quorum latera
                    <var>.e.a</var>
                  :
                    <var>e.b</var>
                  :
                    <lb/>
                  et
                    <var>.e.c.</var>
                  ſint inuicem æqualia, protrahatur
                    <var>.b.a.</var>
                  et
                    <var>.b.c</var>
                  . </s>
                  <s xml:id="echoid-s4319" xml:space="preserve">Tunc dico maiorem proportio
                    <lb/>
                  nem eſſe anguli
                    <var>.a.e.b.</var>
                  ad angulum
                    <var>.b.e.c.</var>
                  quam
                    <var>.a.b.</var>
                  ad
                    <var>.c.b.</var>
                  ducatur enim
                    <var>.b.g.</var>
                  ita
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  faciat angulum
                    <var>.g.b.c.</var>
                  æqualem angulo
                    <var>.e.b.a.</var>
                  protracta poſtea
                    <var>.c.g.</var>
                  quæ idem faciat
                    <lb/>
                  in puncto
                    <var>.c.</var>
                  vnde
                    <var>.g.b.</var>
                  et
                    <var>.g.c.</var>
                  æquales inuicem erunt ex .6. primi, & quia angulus
                    <var>.a.</var>
                    <lb/>
                  æqualis eſt angulo
                    <var>e.b.a.</var>
                  ex quinta eiuſdem, ideo ex .32. dicti, et .4. ſexti, horum
                    <lb/>
                  duorum triangulorum latera, erunt inuicem proportionalia. </s>
                  <s xml:id="echoid-s4320" xml:space="preserve">Conſtituto deinde
                    <var>.g.</var>
                    <lb/>
                  centro, & ſecundum ſemidiametrum
                    <var>.g.b.</var>
                  vel
                    <var>.g.c.</var>
                  quod idem eſt, deſcripto circu-
                    <lb/>
                  lo
                    <var>.b.i.c.</var>
                  necnon circulo
                    <var>.b.c.a.</var>
                  circa centrum
                    <var>.e.</var>
                  ope ſemidiametri
                    <var>.e.b.</var>
                  et
                    <var>.e.a.</var>
                  vn
                    <lb/>
                  de iſte circulus eritillo maior, cum
                    <var>.e.b.</var>
                  maior ſit
                    <var>.g.b.</var>
                  ex .14. quinti. cum ex .14. tertij
                    <lb/>
                    <var>a.b.</var>
                  longior ſit
                    <var>.c.b.</var>
                  ſed ex vltima definitione tertij, arcus
                    <var>.b.i.c.</var>
                  et
                    <var>.b.c.a.</var>
                  erunt in-
                    <lb/>
                  uicem ſimiles, hoc eſt proportio totius cir-
                    <lb/>
                  cunferentiæ circuli
                    <var>.b.i.c.</var>
                  ad arcus
                    <var>.b.i.c.</var>
                  ea-
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0372-01a" xlink:href="fig-0372-01"/>
                  dem erit, quæ totius circunferentiæ circuli
                    <lb/>
                    <var>b.c.a.</var>
                  ad arcus
                    <var>.b.c.a.</var>
                  ſed proportio diame-
                    <lb/>
                  tri ad circunferentiam eſt vt diametri ad cir
                    <lb/>
                  cunferentiam, vt ſupra diximus; </s>
                  <s xml:id="echoid-s4321" xml:space="preserve">Quare ex
                    <lb/>
                  proportionum æqualitate, vt ſemidiametri
                    <lb/>
                  ad circunferentiam erit, vt ſemidiametri
                    <lb/>
                  ad circunferentiam, & per eandem propor
                    <lb/>
                  tionum ęqualitatem, proportio
                    <var>.e.b.</var>
                  ad
                    <reg norm="arcum" type="context">arcũ</reg>
                    <lb/>
                    <var>b.c.a.</var>
                  erit, vt
                    <var>.g.b.</var>
                  ad arcum
                    <var>.b.i.c.</var>
                  & per ean
                    <lb/>
                  dem æqualitatem, ita erit
                    <var>.a.b.</var>
                  chordæ ad ar
                    <lb/>
                  cum
                    <var>.b.c.a.</var>
                  vt
                    <var>.c.b.</var>
                  chordæ ad arcum
                    <var>.b.i.c.</var>
                    <lb/>
                  & permutando, ita erit chordæ
                    <var>.a.b.</var>
                  ad chor
                    <lb/>
                  dam
                    <var>.c.b.</var>
                  vt arcus
                    <var>.b.c.a.</var>
                  ad arcum
                    <var>.b.i.c.</var>
                  ſed
                    <lb/>
                  arcus
                    <var>.b.i.c.</var>
                  maior eſt arcu
                    <var>.b.d.c.</var>
                  ex commu­ </s>
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