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-div483" type="letter" level="4" n="1">
                <pb o="216" rhead="IO. BABPT. BENED." n="228" file="0228" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0228"/>
                <p>
                  <s xml:id="echoid-s2700" xml:space="preserve">Superius poſitæ meæ demonſtrationis ope, deuenimus in cognitionem magnitu
                    <lb/>
                  dinis arcus
                    <var>.n.q.</var>
                  cognoſcimus etiam angulum
                    <var>.n.q.t.</var>
                  vnde nobis
                    <reg norm="manifeſtum" type="context">manifeſtũ</reg>
                  eſſet quo
                    <lb/>
                  vento oporteret iter facere. cum à puncto
                    <var>.q.</var>
                  nauis aliqua diſceſſura eſſet, in eodem
                    <lb/>
                  azimut propoſito. </s>
                  <s xml:id="echoid-s2701" xml:space="preserve">Idem etiam dico de puncto
                    <var>.u.</var>
                  cum cogniti eſſent arcus
                    <var>.n.u.</var>
                  et
                    <var>.n.
                      <lb/>
                    r.</var>
                  vt ſupponitur, ſimul cum angulo
                    <var>.r.n.u.</var>
                  vnde cognitus eſſet nobis angulus
                    <var>.n.u.r.</var>
                  ex
                    <lb/>
                  11. primi lib. Copernici, ex quo ventus nobis cognitus foret.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2702" xml:space="preserve">Modus autem quem idem Medina cap .9. lib. tertij ad cognoſcendam diſtantiam
                    <lb/>
                  vnius meridiani ab alio præſcribit, in genere eſt falſus, etiam ſi is ab antiquis eum de
                    <lb/>
                  ſumat, qui, hic non viderunt quam magna inter meridianos differentia ſit interuallo
                    <lb/>
                  rum eorum quæ ſunt vicina polis & eorum quæ ſunt circa æquatorem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2703" xml:space="preserve">Falſus eſt etiam modus ab eo traditus ad cognoſcendos gradus longitudinis per
                    <lb/>
                  medium itineris cogniti in quouis parallelo extra æquatorem facti, & hoc cap .14. li
                    <lb/>
                  bri tertij eiuſdem, & primo cap. lib. 4.
                    <reg norm="continetur" type="context">cõtinetur</reg>
                  , vbi .17. leucas cum dimidia cuilibet
                    <lb/>
                  gradui tam paralleli quàm meridiani aſſignat.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2704" xml:space="preserve">Falſum eſt etiam quod ab eo aſſeritur, Solem, cum reperiretur in æquatore, circa
                    <lb/>
                  eos qui ſub ipſo æquatore habitant, vnius diei
                    <reg norm="noctisque" type="simple">noctisq́;</reg>
                  ſpatio per omnes uentos cir-
                    <lb/>
                  cunuolui. </s>
                  <s xml:id="echoid-s2705" xml:space="preserve">quia illis æquator idem eſt cum verticali, qui duos tantum rhumbos pro-
                    <lb/>
                  ducit, ideſt orientis, & occidentis: </s>
                  <s xml:id="echoid-s2706" xml:space="preserve">hic verò error, in ſecundo cap. lib. 6. habetur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2707" xml:space="preserve">Falſum eſt etiam quod profert Solem ijs qui habitant ſphæram obliquam, qua-
                    <lb/>
                  libet hora tertia, regulariter ab vno rhumbo ad alium ex præcipuis ideſt ab vno azi
                    <lb/>
                  mut ad alium progredi, quemadmodum eadem cap .2. lib. 6. et .7. cap. ſeptimi libr.
                    <lb/>
                  ſcribit. </s>
                  <s xml:id="echoid-s2708" xml:space="preserve">Huius autem rei falſitas ita facile depræhendetur, ponamus hemiſphęrium
                    <lb/>
                  orientale, verbi gratia, cuius meridianus ſit
                    <var>.p.z.b.</var>
                  æquator
                    <reg norm="autem" type="wordlist">aũt</reg>
                    <var>.e.m.</var>
                  vnus verò paral
                    <lb/>
                  lelorum ſeptentrionalium ſit
                    <var>.c.a.</var>
                  in quo Solem exiſtere ponamus, orizon autem ſit
                    <var>.
                      <lb/>
                    b.m.</var>
                  zenit vero
                    <var>.z.</var>
                  polus arcticus
                    <var>.p.</var>
                  ſit poſtea azimut
                    <var>.z.q.</var>
                  à meridiano diſtans per gra
                    <lb/>
                  dus .45. qui quidem azimut in hoc hemiſphęrio erit rhumbus illius venti, quem uul-
                    <lb/>
                  go Itali Sirocum dicunt, et
                    <var>.z.m.</var>
                  ſit azimut verticalis qui in hoc hemiſphærio erit
                    <reg norm="ron" type="context">rõ</reg>
                    <lb/>
                  bus venti orientalis, ita
                    <reg norm="quod" type="simple">ꝙ</reg>
                  ſecundum Medinam à rhumbo
                    <var>.z.m.</var>
                  ad
                    <var>.z.q</var>
                  . </s>
                  <s xml:id="echoid-s2709" xml:space="preserve">Solabſoluet
                    <lb/>
                  ſpatium
                    <reg norm="temporis" type="context">tẽporis</reg>
                  trium horarum, & aliud
                    <lb/>
                  æquale temporis ſpatium abſoluet à
                    <reg norm="rhum" type="context">rhũ</reg>
                    <lb/>
                    <figure xlink:label="fig-0228-01" xlink:href="fig-0228-01a" number="281">
                      <image file="0228-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0228-01"/>
                    </figure>
                  bo
                    <var>.z.q.</var>
                  ad
                    <var>.z.b.</var>
                  ex ipſo Medina, vnde ar-
                    <lb/>
                  cus
                    <var>.a.o.</var>
                  paralleli eſſet graduum .45. &
                    <lb/>
                  item arcus
                    <var>.o.c</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s2710" xml:space="preserve">Ponamus
                    <reg norm="nunc" type="context">nũc</reg>
                  Solem reperiri in ęqua
                    <lb/>
                  tore, vbi per ipſum Medinam arcus
                    <var>.u.m.</var>
                    <lb/>
                  ſimiliter eſſet graduum .45. & ſic
                    <var>.u.e</var>
                  : pro
                    <lb/>
                  tracto ergo arcu
                    <var>.p.o.f.</var>
                  palam erit ar-
                    <lb/>
                  cum
                    <var>.f.e.</var>
                  fore graduum .45. ſed cum
                    <lb/>
                  arcus
                    <var>.e.u.</var>
                  ſit graduum .45. ex ſuppoſito
                    <lb/>
                  ipſius Medinæ, ſequeretur arcum
                    <var>.e.f.</var>
                    <lb/>
                  æqualem eſſe arcui
                    <var>.e.u.</var>
                  pars igitur æqua
                    <lb/>
                  lis erit ſuo toto.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2711" xml:space="preserve">Id etiam quod Petrus Nonius pagina
                    <lb/>
                  124. et .125. lib. de arte nauigandi con-
                    <lb/>
                  tra nautas de diſtantijs Solis à meridiano ſcribit, hanc opinionem Petrià Medina &
                    <lb/>
                  corum qui idem ei perſuaſerunt falſam eſſe demonſtrat.</s>
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