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]

Table of contents

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[5.1.7.] SEPTIMVM. Euclidis uerò undecima propoſitio.
[5.1.8.] OCTAVVM. εuclidis uerò duodecima propoſitio.
[5.1.9.] NONVM. Euclidis uero tertiadecima propoſitio.
[5.1.10.] DECIMVM.
[5.1.11.] VNDECIMVM.
[5.1.12.] DVODECIMVM.
[Item 5.2.]
[5.2.1.] THEOR.I. II. ET III.
[5.2.2.] THEOREM. IIII.
[5.2.3.] THEOR.V. ET VI.
[5.2.4.] THEOR. VII. VIII. IX.X. XI. XII. XIII.
[5.2.5.] THEOREM. XIIII.
[5.2.6.] THEOR. XV.
[5.2.7.] THEOREM. XVI.
[5.2.8.] THEOR. XVII.
[5.2.9.] THEOREM. XVIII.
[5.2.10.] THEOREM. XIX.
[5.2.11.] THEOREM. XX.
[5.2.12.] THEOREM. XXI.
[5.2.13.] THEOREM. XXII. XXIII.
[6.] PHYSICA, ET MATHEMATICA RESPONSA. FO. BAPTISTAE BεNεDICTI PATRITII Veneti, Philoſophi Mathematici.
[Item 6.1.]
[Item 6.2.]
[Item 6.3.]
[Item 6.4.]
[Item 6.5.]
[Item 6.6.]
[Item 6.7.]
[Item 6.8.]
[Item 6.9.]
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                <p>
                  <s xml:id="echoid-s2513" xml:space="preserve">
                    <pb o="206" n="218" file="0218" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0218"/>
                  cùm tribus centeſimis
                    <reg norm="communibus" type="context">cõmunibus</reg>
                  , tres quartas diei partes plus æquo detraxerimus,
                    <lb/>
                  non enim centeſimo quoque anno, ſed centeſimo trigeſimo quarto, dictus dies de-
                    <lb/>
                  trahi debet, poſtquam tres integros dies, qui quadringentis detrahendi erant, tre-
                    <lb/>
                  centorum annorum ſpacio detraxerimus; </s>
                  <s xml:id="echoid-s2514" xml:space="preserve">ſitq́ue 134. penè tertia pars .400. quarto
                    <lb/>
                  annorum centenario, tres quartæ diei partes recuperabuntur; </s>
                  <s xml:id="echoid-s2515" xml:space="preserve">atque ita in fine qua-
                    <lb/>
                  dringentorum annorum omnia exactè ſuo loco reſtituta erunt. </s>
                  <s xml:id="echoid-s2516" xml:space="preserve">Idcirco dictus iam
                    <lb/>
                  quadringenteſimus annus intercalaris & non communis conſtituendus erit, non alia
                    <lb/>
                  de cauſa, quam vt biſſexti ordinem ſequamur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2517" xml:space="preserve">Is verò modus, qui à D. </s>
                  <s xml:id="echoid-s2518" xml:space="preserve">Lilio traditus eſt, de ratione inueniendi ſingulis menſibus
                    <lb/>
                  Nouilunij diem, interdum fallere nos poſſet vno die; </s>
                  <s xml:id="echoid-s2519" xml:space="preserve">prout Ianuario proximè
                    <lb/>
                  lapſo accidit; </s>
                  <s xml:id="echoid-s2520" xml:space="preserve">quo ex præſcripto modo nouilunij, dies nonus illius menſis eſſe debuiſ
                    <lb/>
                  ſet, qui fuit tamen dies ſeptimus, ſexta decima hora cum dimidia poſt meridiem. </s>
                  <s xml:id="echoid-s2521" xml:space="preserve">Ne
                    <lb/>
                  que etiam tutum eſt, via integrorum dierum, nulla habita horarum aut minutorum
                    <lb/>
                  ratione, nec minus ea, quæ à Pitato tradita eſt, mediorum ſeu æqualium
                    <reg norm="motuum" type="context">motuũ</reg>
                  pro
                    <lb/>
                  gredi: </s>
                  <s xml:id="echoid-s2522" xml:space="preserve">At cenſerem potius veros motus ſequendos eſſe ex calculis exactarum tabu-
                    <lb/>
                  larum, quales Prutenicas eſſe iudico; </s>
                  <s xml:id="echoid-s2523" xml:space="preserve">Et cum ſolius Paſchæ cauſa laboremus hac in
                    <lb/>
                  re, pleniluniorum verorum, in multos annos tabulas formarem, quæ æquinoctia ver
                    <lb/>
                  nalia ſequuntur, cum aſſignatione diei Paſchatis præcisè, prout fecit Pitatus; </s>
                  <s xml:id="echoid-s2524" xml:space="preserve">non
                    <lb/>
                  via tamen æqualium pleniluniorum ſed verorum. </s>
                  <s xml:id="echoid-s2525" xml:space="preserve">Porrò quod ad Paſchatis cele-
                    <lb/>
                  brationem attinet, rationi conſentaneum eſt, concilij Niceni decretum ea de re ſer
                    <lb/>
                  uari, prima ſcilicet dominica die poſt primum plenilunium, quod æquinoctium ver-
                    <lb/>
                  nale ſequitur; </s>
                  <s xml:id="echoid-s2526" xml:space="preserve">hoc tamen animaduerſo, ſi dictum plenilunium primum poſt æquino-
                    <lb/>
                  ctium contingens,
                    <reg norm="diem" type="context">diẽ</reg>
                  dominicum ſortiretur; </s>
                  <s xml:id="echoid-s2527" xml:space="preserve">nulla ratione tali die Paſcha celebran-
                    <lb/>
                  dum eſſe; </s>
                  <s xml:id="echoid-s2528" xml:space="preserve">verum ſubſequenti, ne cum Hębreis conſentiat Eccleſia Chriſti: </s>
                  <s xml:id="echoid-s2529" xml:space="preserve">quæ fuit
                    <lb/>
                  cauſa, vt in decreto concilij Niceni ſtatutum ſit, à quartadecima, in vigeſimam pri-
                    <lb/>
                  mam celebrari debere: </s>
                  <s xml:id="echoid-s2530" xml:space="preserve">Quod mihi Petrus Pitatus non animaduertiſſe videtur, cum
                    <lb/>
                  ex
                    <reg norm="eius" type="simple">eiꝰ</reg>
                    <reg norm="ſententia" type="context">ſentẽtia</reg>
                  in ſuis tabulis die Paſchate declarata, huiuſce anni Paſca
                    <reg norm="celebrandum" type="context">celebrandũ</reg>
                    <lb/>
                  fuerit .23. </s>
                  <s xml:id="echoid-s2531" xml:space="preserve">Martij, ipſomet de plenilunij non tantum æqualis, ſed veri.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2532" xml:space="preserve">Dies autem Paſchatum elapſorum, quos hactenus examinaui, reperi omnes con
                    <lb/>
                  cordare cum ea regula, quam nonnulli de die carnis priuij tradiderunt. </s>
                  <s xml:id="echoid-s2533" xml:space="preserve">nempe pri-
                    <lb/>
                  mum diem martis poſt nouilunium Februarij, carnis priuij diem eſſe; </s>
                  <s xml:id="echoid-s2534" xml:space="preserve">non autem
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                    <reg norm="sanctione" type="context">sãctione</reg>
                  Patrum concilij Niceni, qua ſtatuerunt à vigeſima prima Martii dirigen-
                    <lb/>
                  dum eſſe Paſchatis diem, vt potè qui ſibi perſuaſerunt, circa eum diem
                    <reg norm="æquinoctium" type="context">æquinoctiũ</reg>
                    <lb/>
                  perpetuò eſſe debere; </s>
                  <s xml:id="echoid-s2535" xml:space="preserve">prout tunc temporis erat. </s>
                  <s xml:id="echoid-s2536" xml:space="preserve">Non
                    <reg norm="itaque" type="simple">itaq;</reg>
                  error accidit, quod Pa
                    <lb/>
                  ſcha ex huiuſmodi ſuppoſitione concilij, poſt vigeſimam primam lunę celebretur,
                    <lb/>
                  cum ſeruata regula concilij non fuerit. </s>
                  <s xml:id="echoid-s2537" xml:space="preserve">Prout
                    <reg norm="manifeſtum" type="context">manifeſtũ</reg>
                  eſt de Paſchate anni .1566.
                    <lb/>
                  celebrato .14. </s>
                  <s xml:id="echoid-s2538" xml:space="preserve">Aprilis (quę fuit .24. lunę) quod .7. dicti menſis
                    <reg norm="celebrandum" type="context">celebrãdum</reg>
                  erat. </s>
                  <s xml:id="echoid-s2539" xml:space="preserve">Tum
                    <lb/>
                  anno .1569. 10. </s>
                  <s xml:id="echoid-s2540" xml:space="preserve">Aprilis ſolenne fuit Paſca, quod tertia eiuſdem eſſe debuerat. </s>
                  <s xml:id="echoid-s2541" xml:space="preserve">Anno
                    <lb/>
                  deinde 1572. 6. Aprilis, dies fuit Paſchatis, quæ .30. Martij futura erat, anno vero
                    <lb/>
                  1575. in tertiam Aprilis Paſcha incidit, caſurum in .27. Martii.</s>
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                <p>
                  <s xml:id="echoid-s2542" xml:space="preserve">Cum igirur (vt ex diplomate ad Celſit. tuam miſſo patet)
                    <var>S.D.N.</var>
                  mens ſit
                    <reg norm="atque" type="simple">atq;</reg>
                  vo
                    <lb/>
                  luntas, ut quiſque liberè in medium proferat quid hac dere ſentiat: </s>
                  <s xml:id="echoid-s2543" xml:space="preserve">quædam mihi
                    <lb/>
                  non omnino præmittenda occurrunt, quæ tantis cœptis non nihil adiumenti for-
                    <lb/>
                  taſſe adferre queant.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2544" xml:space="preserve">Atque illud in primis non tantum ut corrigatur Calendarium ob Paſcha cætera-
                    <lb/>
                  q́ue feſta mobilia ab illo manantia, vt decreto concilij Niceni ſancitum eſt, ſcilicet
                    <lb/>
                  vt ipſum Paſcha celebretur prima dominica poſt primum plenilunium, quod æqui- </s>
                </p>
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