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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                <pb o="260" rhead="IO. BAPT. BENED." n="272" file="0272" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0272"/>
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              <div xml:id="echoid-div513" type="letter" level="4" n="2">
                <head xml:id="echoid-head388" style="it" xml:space="preserve">Deerroribus Ioannis Stadij.</head>
                <head xml:id="echoid-head389" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3263" xml:space="preserve">FIguram quam ponit Ioannes Stadius pag .147. in lib. ſuarum tabularum Prute-
                    <lb/>
                  nicarum, à Nicolao Copernico ſumpſit pag .64. à tergo in libr. reuolutionum
                    <lb/>
                  cœleſtium, ſed ipſe Stadius eam non intellexit, omitto, quod mutauerit characte-
                    <lb/>
                  res ipſius figurę, vt illa ſua videatur, quod nihil refert, alterat etiam
                    <reg norm="demonſtrationem" type="context">demonſtrationẽ</reg>
                  ,
                    <lb/>
                  ſed ipſum putare
                    <var>.i.K.</var>
                  perpendicularem à centro circuli ſemper dependere, eſt intol
                    <lb/>
                  lerabilis error; </s>
                  <s xml:id="echoid-s3264" xml:space="preserve">nec vnquam verificatur hoc, niſi quando punctum
                    <var>.K.</var>
                  interſectionis
                    <lb/>
                  diametrorum parallelorum, forte reperitur in axe mundi. </s>
                  <s xml:id="echoid-s3265" xml:space="preserve">Reliqua verò ſuæ demon
                    <lb/>
                  ſtrationis, ſi non intelligis, minimè miror, eo quod ipſemet Stadius ſeipſum confun
                    <lb/>
                  dit. </s>
                  <s xml:id="echoid-s3266" xml:space="preserve">Veram autem demonſtratio nem huiuſmodi figuræ in dicto libr. Copernici cla-
                    <lb/>
                  rè videbis. </s>
                  <s xml:id="echoid-s3267" xml:space="preserve">Quod verò diuersè cogitaui nunc acciptito.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3268" xml:space="preserve">Cum nobis cognita ſit maxima ecclipticæ declinatio, vt puta
                    <var>.a.c.</var>
                  ſi latitudo
                    <reg norm="etiam" type="context">etiã</reg>
                    <lb/>
                  ſtellæ nobis data fuerit, vt puta
                    <var>.c.e.</var>
                  cognitus nobis erit totalis arcus
                    <var>.a.e.</var>
                  & eius ſinus
                    <var>.
                      <lb/>
                    e.m.</var>
                  & quia notus etiam nobis eſt ſinus arcus
                    <var>.a.c.</var>
                  hoc eſt
                    <var>.c.n.</var>
                  & corda
                    <var>.e.f.</var>
                  medio eius
                    <lb/>
                  arcus
                    <var>.e.p.f.</var>
                  minoris media circunferentia, per duplum latitudinis datæ, vnde
                    <var>.e.l.</var>
                  eius
                    <lb/>
                  dimidium nobis cognitum erit, vel vt ſinus arcus
                    <var>.e.p.</var>
                  cognitus etiam nobis eſt ſinus
                    <var>.
                      <lb/>
                    q.g.</var>
                  declinationis
                    <var>.a.g.</var>
                  datæ, cui æqualis eſt
                    <var>.m.t.</var>
                  ex .34. primi Euclid. </s>
                  <s xml:id="echoid-s3269" xml:space="preserve">vnde
                    <var>.e.t.</var>
                  nobis
                    <lb/>
                  cognita remanet, cum verò duo trianguli
                    <var>.i.c.n.</var>
                  et
                    <var>.t.e.K.</var>
                    <reg norm="æquianguli" type="context">æquiãguli</reg>
                  ſint, propter duas
                    <lb/>
                  parallelas
                    <var>.e.m.</var>
                  et
                    <var>.n.c.</var>
                  ex .28. primi, & propter duas
                    <var>.a.b.</var>
                  et
                    <var>.g.h.</var>
                  & propter duas
                    <var>.c.d.</var>
                    <lb/>
                  et
                    <var>.e.f.</var>
                  eo quod ex communi ſcientia anguli
                    <var>.c.</var>
                  et
                    <var>.e.</var>
                  ſunt æquales, cum ex .29. dicti lib.
                    <lb/>
                    <reg norm="vnuſquiſque" type="simple">vnuſquiſq;</reg>
                  æqualis ſit angulo
                    <var>.m.ω.i.</var>
                  ita etiam infero de angulis
                    <var>.e.K.t.</var>
                  et
                    <var>.c.i.n.</var>
                    <reg norm="quorum" type="context">quorũ</reg>
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                  vnuſquiſque æqualis eſt angulo
                    <var>.ω.x.t.</var>
                  & ſic de alijs dico, co quod vnuſquiſque
                    <reg norm="eorum" type="context">eorũ</reg>
                    <lb/>
                  æqualis eſt angulo
                    <var>.m.</var>
                  vnde cum cognitum nobis ſit latus
                    <var>.n.c.</var>
                  et
                    <var>.c.i.</var>
                  et
                    <var>.t.e.</var>
                    <reg norm="notum" type="context">notũ</reg>
                  etiam
                    <lb/>
                  nobis erit
                    <var>.e.K.</var>
                  ex .19. ſeptimi, eo
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  ex .4. ſexti ſunt inuicem proportio-
                    <lb/>
                    <figure xlink:label="fig-0272-01" xlink:href="fig-0272-01a" number="300">
                      <image file="0272-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0272-01"/>
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                  nalia, detrahendo poſtea
                    <var>.e.K.</var>
                  ab
                    <var>.
                      <lb/>
                    e.l.</var>
                  cognito, vel ècontra, hoc ab il-
                    <lb/>
                  lo, nobis innoteſcet
                    <var>.K.l.</var>
                  ſinus longi
                    <lb/>
                  tudinis ſtellæ.</s>
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                <p>
                  <s xml:id="echoid-s3270" xml:space="preserve">Valde etiam miror id, quod di-
                    <lb/>
                  ctus Stadius pag .9. illius libr. ſcri-
                    <lb/>
                  bit, hoc eſt, Solem maiorem
                    <lb/>
                  eſſe Luna, ſolum .1644. vici-
                    <lb/>
                  bus, </s>
                  <s xml:id="echoid-s3271" xml:space="preserve">propterea
                    <reg norm="quod" type="simple">ꝙ</reg>
                  cum affirmet So-
                    <lb/>
                  lem maiorem eſſe terra (vt etiam
                    <lb/>
                  in Almageſto videre eſt) 166. vici
                    <lb/>
                  bus cum tribus quartis, terram ve-
                    <lb/>
                  ro maiorem Luna .39. vicibus cum
                    <lb/>
                  quarta parte, </s>
                  <s xml:id="echoid-s3272" xml:space="preserve">tunc Solem oporte-
                    <lb/>
                  ret maiorem eſſe Luna .6545. vici-
                    <lb/>
                  bus, & non .1644.</s>
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