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-div488" type="letter" level="4" n="3">
                <pb o="220" rhead="IO. BAPT. BENED." n="232" file="0232" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0232"/>
                <p>
                  <s xml:id="echoid-s2744" xml:space="preserve">Volo primum vt mediante
                    <reg norm="circunuolutione" type="context">circũuolutione</reg>
                  globi circa primos polos
                    <var>.f.g.</var>
                  & æqua
                    <lb/>
                  toris circa ſecundos
                    <var>.h.K.</var>
                  hoc eſt per longitudinem, & latitudinem, hi duo loci in
                    <lb/>
                  globo propoſiti ſub azimut
                    <var>.r.n.s.m.</var>
                  ſecundorum circulorum
                    <reg norm="ſitum" type="context">ſitũ</reg>
                  ſortiantur, qui azi-
                    <lb/>
                  mut orizontem in punctis
                    <var>.q.</var>
                  et
                    <var>.p.</var>
                  ſemper ad angulos rectos diſpeſcit
                    <reg norm="ibique" type="simple">ibiq;</reg>
                  globum
                    <lb/>
                  ita quieſcere vt circa polos
                    <var>.f.g.</var>
                  non voluatur, & æquatorem etiam ſic ſirmare, vt cir-
                    <lb/>
                  ca ſecundos polos
                    <var>.h.K.</var>
                  non vertatur faciamus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2745" xml:space="preserve">Quod cum factum fuerit, ſecundorum circulorum primus, qui eſt
                    <var>.n.i.m.</var>
                  deferens
                    <lb/>
                  azimut, circa tertios polos
                    <var>.i.</var>
                  & eius oppoſitum, eo uſque voluatur quouſque prior
                    <lb/>
                  globi locus, ideſt is a quo iter eſt incohandum per .90. gradus azimut diſtet ab ori-
                    <lb/>
                  zonte, ideſt ſub zenit orizontis
                    <var>.q.i.p.</var>
                  ſit poſitus, quemadmodum, exempli gratia, ſi
                    <lb/>
                  punctum
                    <var>.a.</var>
                  dicti primi loci globi rationem indueret, & borealius eſſet, mediante
                    <lb/>
                  circunuolutione circuli
                    <var>.n.i.m.</var>
                  circa dictos tertios polos æqualiter diſtans ab
                    <var>.q.</var>
                  et
                    <var>.p.</var>
                    <lb/>
                  ideſt per .90. gradus poneretur ſub
                    <var>.r</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s2746" xml:space="preserve">Conſideretur deinde vbi æquator
                    <var>.h.e.K.</var>
                  ſecundus circulus duorum primorum,
                    <lb/>
                  ab orizonte
                    <var>.q.i.p.</var>
                  ſecabitur, exempli gratia, in puncto
                    <var>.c.</var>
                  quartę orientalis ſepten-
                    <lb/>
                  trionalis eiuſdem orizontis. </s>
                  <s xml:id="echoid-s2747" xml:space="preserve">Videatur deinde quot nam gradibus conſtabit ar-
                    <lb/>
                  cus
                    <var>.i.c.</var>
                  & per totidem gradus conſtituatur extremitas ſeptentrionalis lineæ meridia-
                    <lb/>
                  nę pyxidis nauticę, diſtantis à cuſpide ſeptentrionali ipſius lanceolæ orientem ver-
                    <lb/>
                  ſus, mediante nauis circunuolutione. </s>
                  <s xml:id="echoid-s2748" xml:space="preserve">vnde ipſamet nauis in huiuſmodi ſitu azimut,
                    <lb/>
                  qui per duos hos loc
                    <unsure/>
                  os tranſit, dirigetur, eſſiciendo vt eius prora verſus
                    <reg norm="locum" type="context">locũ</reg>
                  ad
                    <reg norm="quem" type="context">quẽ</reg>
                    <lb/>
                  voluerimus tendere dirigatur. </s>
                  <s xml:id="echoid-s2749" xml:space="preserve">Cum verò vela ventis dabimus, tot milliarium
                    <lb/>
                  ſeu leucarum iter conficiemus, quot quarta pars vnius gradus requirit. </s>
                  <s xml:id="echoid-s2750" xml:space="preserve">& dum
                    <lb/>
                  hociter abſoluitur, ille qui pręeſt naui, defferentem azimut
                    <var>.n.i.m.</var>
                  circa ſuos polos
                    <var>.i.</var>
                    <lb/>
                  & eius oppoſitum, ſic circunuoluat, vt interſe ctio azimut
                    <var>.r.n.s.m.</var>
                  cum orizonte
                    <var>.q.i.
                      <lb/>
                    p.</var>
                  diſtet à prima ratione dictæ quartę partis vnius gradus, conſtituendo ſecundum lo
                    <lb/>
                  cum, proximiorem zenit, ratione dictæ quartæ partis gradus azimut. </s>
                  <s xml:id="echoid-s2751" xml:space="preserve">Hiſce ita pera
                    <lb/>
                  ctis, obſeruetur deinde vbiæquator
                    <var>.h.e.K.</var>
                  hac ſecunda vice interſecabit orizontem
                    <lb/>
                    <var>q.i.p.</var>
                  quod quidem interſectionis punctum ſemper appelletur
                    <var>.c.</var>
                  quod dico non am
                    <lb/>
                  plius in eadem diſtantia manſurum, ut prius à puncto
                    <var>.i.</var>
                  ſed aut longius diſtabit, aut
                    <lb/>
                  propius accedet, vt in præſenti exemplo. </s>
                  <s xml:id="echoid-s2752" xml:space="preserve">quemadmodum ex ſe manifeſtum eſt, cú
                    <lb/>
                  poli globi, ideſt ęquatoris ſint extra azimut, vt præſupponitur, quia loci ſunt in diuer
                    <lb/>
                  ſis meridianis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2753" xml:space="preserve">Pro huiuſmodi autem diſtantiæ ratione denuo dirigatur nauis prout æquator
                    <var>.h.
                      <lb/>
                    e.K.</var>
                  in orizonte
                    <var>.q.i.p.</var>
                  nobis oſtendet, atque hoc modo omnium iter quaſi breuiſſi-
                    <lb/>
                  mum fiet. </s>
                  <s xml:id="echoid-s2754" xml:space="preserve">dico autem, quaſi, quia omnibus modis neceſſariò conficitur iter contor-
                    <lb/>
                  tum & in formam ſerpigineæ lineæ. </s>
                  <s xml:id="echoid-s2755" xml:space="preserve">Applicantes deinde per vices extremitatem
                    <lb/>
                  quartæ appoſitæ (de qua ſuperius mentionem fecimus) ipſi zenit
                    <var>.r.</var>
                  efficientes ut per
                    <lb/>
                  ſitum poli globi pertranſeat, deueniemus in cognitionem altitudinis eiuſdem ab
                    <lb/>
                  orizonte, & per conſequens quantum itineris per latitudinem eiuſdem globi pere-
                    <lb/>
                  gerit. </s>
                  <s xml:id="echoid-s2756" xml:space="preserve">mediante deinde interſectione orizontis
                    <var>.q.i.p.</var>
                  cum æquatore, cognoſcemus
                    <lb/>
                    <reg norm="quantum" type="context">quãtum</reg>
                  itineris per longitudinem eiuſdem globi, in ipſo ęquatore fuerit peractum,.</s>
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