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-div478" type="section" level="3" n="1">
              <div xml:id="echoid-div478" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s2575" xml:space="preserve">
                    <pb o="208" n="220" file="0220" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0220"/>
                  ad nos accedit: </s>
                  <s xml:id="echoid-s2576" xml:space="preserve">cum punctum Zodiaci, quod tropicum hyemalem Capricorni nobis
                    <lb/>
                  producit, reſpondeat puncto meridiani ſub terra, in quo Sol ſemel in die reperitur:
                    <lb/>
                  </s>
                  <s xml:id="echoid-s2577" xml:space="preserve">Quòd apertè norunt hi, qui ſub polo boreali conſtituti ſunt. </s>
                  <s xml:id="echoid-s2578" xml:space="preserve">
                    <reg norm="Atque" type="simple">Atq;</reg>
                  facilè diſcerne
                    <lb/>
                  re poſſumus, diem ſcilicet & annum, quaſi ſibi ad inuicem medio ſuarum partium
                    <lb/>
                  reſpondere; </s>
                  <s xml:id="echoid-s2579" xml:space="preserve">ſolſtitium inquam hyemale, mediæ nocti, æſtiuum meridiei, æquino-
                    <lb/>
                  ctium vernale ortui Solis, autumnale occaſui. </s>
                  <s xml:id="echoid-s2580" xml:space="preserve">Quam tamen ſimilitudinem, multò
                    <lb/>
                  quam nos manifeſtius deprehendunt, hi qui (ut diximus) ſub polo borcali verſantur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2581" xml:space="preserve">Quod ſi quis dubitet hac ratione correcto anno, quo nam pacto ad calculos coe-
                    <lb/>
                  leſtes motus medijs tabulis aſtronomicis hactenus in lucem æditis redigi poſſint, id
                    <lb/>
                  facilimum ſanè erit, exempli gratia; </s>
                  <s xml:id="echoid-s2582" xml:space="preserve">aliquis planetę ſitum, aut alicuius ſtellę fixæ, quo
                    <lb/>
                  cunque die menſis anni correcti inuenire cupit, detrahat ex huiuſmodi
                    <reg norm="tempore" type="context">tẽpore</reg>
                  dies
                    <num value="21">.
                      <lb/>
                    21.</num>
                  ab Aera Chriſti, cum reſiduo ſupputet ſtellam, cuius ſitum ſcire deſiderat; </s>
                  <s xml:id="echoid-s2583" xml:space="preserve">ſum-
                    <lb/>
                  pta quacunque tabula, ſupputatio erit exacta: </s>
                  <s xml:id="echoid-s2584" xml:space="preserve">Cuius ratio cuilibet manifeſta erit,
                    <lb/>
                  qui ſciet annum vt potè .1579. dierum .344. tantummodo conſtitutum fuiſſe. </s>
                  <s xml:id="echoid-s2585" xml:space="preserve">Nam
                    <lb/>
                  in ijſdem locis cœli prima die Ianuarij correcti, erunt ſtellæ quibus eſſe ſolebant .11
                    <lb/>
                  Decembris præcedentis anni ex ſupputatione tabularum: </s>
                  <s xml:id="echoid-s2586" xml:space="preserve">atque ita deinceps. </s>
                  <s xml:id="echoid-s2587" xml:space="preserve">Alia
                    <lb/>
                  præterea via idem perfici poſſet inuentione omnium motuum cęleſtium ipſo princi
                    <lb/>
                  pio anni .1580. correcti: </s>
                  <s xml:id="echoid-s2588" xml:space="preserve">hoc ſtatuto, vt hi motus radices eſſent Aeræ
                    <var>S.D.N.</var>
                  Grego
                    <lb/>
                  rij XIII. quod ſi alio
                    <reg norm="tempore" type="context">tẽpore</reg>
                  quiſpiam motus cęleſtes ad calculos redigere voluerit,
                    <lb/>
                  ſupputabit ab Aera huiuſmodi, quæ anno .1580. principium habuerit: </s>
                  <s xml:id="echoid-s2589" xml:space="preserve">Quæ vt nobi
                    <lb/>
                  lius nomen ſortiatur,
                    <reg norm="idque" type="simple">idq́;</reg>
                  merito ex nomine Gregorij. XIII. Pont. Max. appelletur;
                    <lb/>
                  </s>
                  <s xml:id="echoid-s2590" xml:space="preserve">exemplo antiquarum, quæ ex Principum nominibus ſunt appellate: </s>
                  <s xml:id="echoid-s2591" xml:space="preserve">vt tanto Pontifi
                    <lb/>
                  ci, cùm ex alijs multi, tum etiam ex hac non infima re, inter mortales immortale no
                    <lb/>
                  men comparetur. </s>
                  <s xml:id="echoid-s2592" xml:space="preserve">Ei verò ſummæ, quæ ex huiuſmodi Aera Gregoriana ex tabu-
                    <lb/>
                  lis colligetur, ipſiuſmet Aeræ radices addantur, vt exactus calculus habeatur. </s>
                  <s xml:id="echoid-s2593" xml:space="preserve">Et
                    <lb/>
                  hæc ſit primæ ſententiæ noſtræ explicatio.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2594" xml:space="preserve">Altera erit numerum dierum menſium anni alia ratione quam nunc ſe habeat, or
                    <lb/>
                  dinandum eſſe: </s>
                  <s xml:id="echoid-s2595" xml:space="preserve">nempe vt Ianuarius, Nouember
                    <reg norm="atque" type="simple">atq;</reg>
                  December dies .29. ſinguli con
                    <lb/>
                  tineant, Februarius, Martius, & October .30. </s>
                  <s xml:id="echoid-s2596" xml:space="preserve">Aprilis, Maius, Auguſtus, & September
                    <lb/>
                  dies .31. Iunius, ac Iulius .32. atque id hac potiſſimum de cauſa, vt Sol unum
                    <reg norm="quodque" type="simple">quodq́;</reg>
                    <lb/>
                  ſignum calendis menſrum ingredi poſſit. </s>
                  <s xml:id="echoid-s2597" xml:space="preserve">Nam detractis (ut dictum eſt) diebus .21.
                    <lb/>
                  & reuocato ingreſſu Solis in principium Capricorni ad principium Ianuarij, in quo
                    <lb/>
                  ſigno hac noſtra tempeſtate, Sol, dies propè .29. & quartam vnam verſatur: </s>
                  <s xml:id="echoid-s2598" xml:space="preserve">ſi Ianua
                    <lb/>
                  rius .29. dies continebit, exactis hiſce diebus, ingredietur Aquarium circa princi-
                    <lb/>
                  pium Februarii; </s>
                  <s xml:id="echoid-s2599" xml:space="preserve">hæret autem hoc noſtro ſæculo in Aquario Sol dies propè .29. cum
                    <lb/>
                  dimidio; </s>
                  <s xml:id="echoid-s2600" xml:space="preserve">quare ſi Februarius erit .30. dierum, elapſis ipſis diebus, Sol ingredietur pi-
                    <lb/>
                  ſces circa principium Martii: </s>
                  <s xml:id="echoid-s2601" xml:space="preserve">& ſic de cæteris.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2602" xml:space="preserve">Quamobrem ſi generali correctione annus emendandus erit, pulcherrimè acci-
                    <lb/>
                  det, ſi menſes anni cum duodecim partibus cœleſtibus, itineris annui Solis, concor-
                    <lb/>
                  dauerint; </s>
                  <s xml:id="echoid-s2603" xml:space="preserve">
                    <reg norm="eiſque" type="simple">eiſq́;</reg>
                  aptè reſponderint. </s>
                  <s xml:id="echoid-s2604" xml:space="preserve">Qua ex re, varię vtilitates promanabunt, pręſertim
                    <lb/>
                  Nautis, Agricolis, Medicis, & alijs qui vera principia, & interualla temporum per
                    <lb/>
                  ſpecta habebunt: </s>
                  <s xml:id="echoid-s2605" xml:space="preserve">terminos item & interualla incrementi & diminutionis dierum &
                    <lb/>
                  noctium, & eorundem æqualitatis. </s>
                  <s xml:id="echoid-s2606" xml:space="preserve">Exempli cauſa, ſcient omnes principium Ianua-
                    <lb/>
                  rij, eſſe non modo anni principium, verum etiam hyemis, eſſe minimam anni diem,
                    <lb/>
                  & eius noctem maximam; </s>
                  <s xml:id="echoid-s2607" xml:space="preserve">principium incrementi diei, & diminutionis noctis; </s>
                  <s xml:id="echoid-s2608" xml:space="preserve">atque
                    <lb/>
                  etiam omnia illa, quæ ex huiuſmodi conuerſione Solis ad nos dependent. </s>
                  <s xml:id="echoid-s2609" xml:space="preserve">Pariter
                    <lb/>
                  ſcient omnes primam diem Iulij, non tantum æqualiter annum diuidere, ſed prin­ </s>
                </p>
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