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     <author>Barocius, Franciscus</author>
     <title>Heronis mechanici liber</title>
     <date>1572</date>
     <place>Venice</place>
     <translator></translator>
     <lang>la</lang>
     <cvs_file>baroc_heron_052_la_1572.xml</cvs_file>
     <locator>052.xml</locator>
</info>


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<s><emph type="center"></emph>HERONIS <lb></lb>MECHANICI <lb></lb>LIBER<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>DE MACHINIS <lb></lb>BELLICIS, <lb></lb>NECNON LIBER DE GEODAESIA<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>A&#039; FRANCISCO BAROCIO Patritio Veneto latinitate <lb></lb>donati, multis mendis expurgati, &amp; fi<lb></lb>guris, ac ſcholijs illuſtrati.<emph.end type="center"></emph.end></s></p><figure id="id.052.01.001.1.jpg" xlink:href="052/01/001/1.jpg"></figure><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>VENETIIS, <lb></lb>Apud Franciſcum Franciſcium Senenſem. </s>
<s>1572.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p>
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<s><emph type="center"></emph>ILLVSTRISSIMO<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>ET EXCELLENTISSIMO<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>D. D. VINCENTIO<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>GONZAGAE, MANTVAE<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>PRINCIPI.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Franciſcus Franciſcius Senenſis. </s>
<s>S. D.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s>H<emph type="italics"></emph>E<emph.end type="italics"></emph.end>RONEM <emph type="italics"></emph>de machinis bellicis <lb></lb>vetuſtißimum, &amp; celeberrimum <lb></lb>Auctorem nuper græco latinum <lb></lb>fecit nobilis, &amp; tum vtriuſque <lb></lb>linguæ, tum Mathematicæ ſcien<lb></lb>tiæ eruditißimus vir patritius <lb></lb>Venetus Franciſcus Barocius. </s>
<s><lb></lb>Hunc ego quum ad communem vſum ſtudioſorum <lb></lb>meis typis diligenter imprimendum curauerim, at<lb></lb>que impreſſum edere conſtituerim, veritus ſi ſine po<lb></lb>tentis alicuius tuto, fideli〈qué〉 patrocinio abiret in vul<lb></lb>gus, ne ſitu, &amp; ſqualore obſitus, vt qui nunc primum <lb></lb>in lucem prodeat, vix agnoſceretur, in tuam maxi<lb></lb>me clientelam tradere uolui: cuius nomine, ac ſplen<lb></lb>dore non dubito, quin illuſtrior multo futurus ſit, &amp; <lb></lb>carior. </s>
<s>Neque vero ſuccurrebat quiſquam cuius fi<lb></lb>dei melius <expan abbr="cõmittere">committere</expan> poſſe confiderem. </s>
<s>tecum enim<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/004.jpg"></pb><emph type="italics"></emph>iſtud ætatis conferre quem audeam? </s>
<s>qui tam illuſtri <lb></lb>Auguſto〈qué〉 genere editus, ſingularis &amp; ſanctitatis, <lb></lb>&amp; ſapientiæ, parentibus genitus, cum inſigni corpo<lb></lb>ris venuſtate, &amp; gratia, tum animi indole, &amp; inge<lb></lb>nij diuina felicitate præditus eo fato natus videris, <lb></lb>vt ad longe ampliorem, quam in quo nunc es Man<lb></lb>tuæ, ac Montisferrati, principatum eueharis; præ<lb></lb>ſertim quum ijs moribus, ijs〈qué〉 diſciplinis ornere, quæ <lb></lb>vel infimum hominem ad altißimum gradum facil<lb></lb>lime tollant. </s>
<s>quippe qui nondum exacto anno decimo <lb></lb>ætatis tuæ in ſtudijs litterarum græcarum, &amp; latina<lb></lb>rum admirabiles progreſſus feceris, hiſtorias rerum <lb></lb>geſtarum, &amp; poetarum volumina euoluas, &amp; incre<lb></lb>dibili facilitate ediſcas, <expan abbr="Arithmeticẽ">Arithmeticem</expan>, <expan abbr="Geometriã〈qué〉">Geometriam〈qué〉</expan>, <lb></lb>&amp; Euclidis elementa it a tractes, it a explices, it a de<lb></lb>monſtres, vt nihil videaris habere facilius; at que ijs <lb></lb>artibus ad rei militaris ſcientiam tibi <expan abbr="viã">viam</expan> munias, <lb></lb>&amp; proſpero curſu contendas qua in re non <expan abbr="parũ">parum</expan> opi<lb></lb>nor adiuuabit <expan abbr="inſtrumẽtorum">inſtrumentorum</expan> bellicorum, cognitio, <lb></lb>&amp; apparatus, quem ex Herone conſequeris. </s>
<s>Tibi igi<lb></lb>tur Illuſtriß. </s>
<s>&amp; Excellentiß. </s>
<s>Princeps Heronem <expan abbr="meũ">meum</expan> <lb></lb>dedico, &amp; in <expan abbr="tuã">tuam</expan> <expan abbr="clientelã">clientelam</expan> trado: ei〈qué〉 gratulor, quod <lb></lb>tecum propemodum natus tuis auſpicijs editus, <expan abbr="te-cũ">te<lb></lb>cum</expan> vna coaleſcet, &amp; creſcet. </s>
<s>Tu pro tua benignitate <lb></lb>munus <expan abbr="libẽter">libenter</expan> accipe, &amp; me <expan abbr="tuorũ">tuorum</expan> numero adſcribe.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/005.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>BREVIS AD LECTOREM<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>PRAEFATIO.<emph.end type="center"></emph.end></s></p><figure id="id.052.01.005.1.jpg" xlink:href="052/01/005/1.jpg"></figure><p type="main">
<s><emph type="italics"></emph>HERONIS vocati Mechanici, propterea quod <lb></lb>in conſcribendis Mechanicis præualuit, volu<lb></lb>men de Machinis Bellicis, ac de Geodęſia: <lb></lb>quod hucuſque lacerum, &amp; fragmentatum in <lb></lb>tenebris latitabat: à nobis denique reſtaura<lb></lb>tum, &amp; in latinum ſermonem conuerſum, <expan abbr="ſcho-lijsq́ue">ſcho<lb></lb>lijsque</expan> dilucidatum: libentißimè tibi ſtudioſe <lb></lb>lector propter maximam eius vtilitatem perle<lb></lb>gendum eſſe non dubito. </s>
<s>Quantam enim vtili<lb></lb>tatem ad obſidendas, <expan abbr="expugnandasq́ue">expugnandasque</expan> ciuitates <lb></lb>antiquis tormenta reperta nondum habenti<lb></lb>bus præſens de Machinis bellicis doctrina præbuerit; ex ijs, quæ tot gra<lb></lb>uißimi Autores, <expan abbr="doctißimiq́ue">doctißimique</expan> viri de hac materia diligentißimè conſcri<lb></lb>pſere: cuique perſpicuum eſſe poteſt. </s>
<s>Præterea verò maxima eius vtilitas <lb></lb>est ad ſtruendos, <expan abbr="præparandosq́ue">præparandosque</expan> pontes artificioſos, quibus exercitus <lb></lb>flumina, <expan abbr="foſſasq́ue">foſſasque</expan> traijciant: necnon ſcalas maximo cum artificio conſtru<lb></lb>ctas, ac portatiles, ad inſcendendum muros. </s>
<s>Amplius autem ex hac <lb></lb>ſcientia pulcherrima eliciuntur præcepta, quippe quæ ad multiformium <lb></lb>Parmarum, &amp; omnis generis Clypeorum, necnon Balliſtarum, <expan abbr="Catapulta-rumq́ue">Catapulta<lb></lb>rumque</expan> conſtructionem, ac demum ad ciuitatum obſidionem, ab <expan abbr="obſidione-q́ue">obſidione<lb></lb>que</expan> defenſionem ſpectant. </s>
<s>Quinetiam Machinarum bellicarum in hoc li<lb></lb>bro deſcriptarum cognitio magnopere nos iuuat ad intelligenda multa pri<lb></lb>ſcorum Hiſtoricorum cum Græcorum, tum Latinorum loca: quæ hucuſque <lb></lb>obſcurißima, &amp; quaſi imperceptibilia viſa ſunt ijs, qui nullam iſtarum Ma<lb></lb>chinarum agnitionem habuerunt. </s>
<s>Atque hæc est vtilitas libri Heronis de <lb></lb>Machinis bellicis. </s>
<s>Verùm libellus quoque de Geodæſia maximam nobis <lb></lb>vtilitatem affert. </s>
<s>cùm præſertim ad hanc etiam noſtram ætatem eius do<lb></lb>ctrina valde neceſſaria ſit ad menſurandum à longe radijs viſualibus, <expan abbr="in-strumentoq́ue">in<lb></lb>strumentoque</expan> Dioptrico murorum altitudines, ac longitudines: necnon <lb></lb>foſſarum, ac fluuiorum latitudines, &amp; profunditates: atque etiam ad ſu<lb></lb>ſcipiendum ſitus varios castrorum expugnandæ ciuitatis, vt contraria Ca-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/006.jpg"></pb><emph type="italics"></emph>stra extra ciuitatem ipſam oppugnandi gratia rite fabricari poßint: atque <lb></lb>rurſus in vniuerſum ad menſurandam quamcumque diſtantiam, ſiue longi<lb></lb>tudinem, &amp; quamlibet cùm ſuperficialem, tum corpoream aream: ac de<lb></lb>nique multas aſtrologicas obſeruationes in corporibus cœlestibus, <expan abbr="eorum-q́ue">eorum<lb></lb>que</expan> motibus peragendas. </s>
<s>His it a que de vtilitate præſentis voluminis bre<lb></lb>uiter adnotatis, antequam ad Heronis lectionem accedas amice lector non<lb></lb>nullorum te commonefaciendum eſſe cenſeo. </s>
<s>Quòd ſcilicet græcum Hero<lb></lb>nis exemplar, quod in latinum ſermonem conuertimus, illud est quod Bo<lb></lb>noniæ in Bibliotheca S. </s>
<s>Saluatoris reperitur. </s>
<s>Nullum autem aliud græ<lb></lb>cum exemplar vidimus: ſed poſtquam illud à nobis latinitate donatum fuit, <lb></lb>ostendit nobis Magnificus D. </s>
<s>Bernardinus Lauredanus in Bibliotheca Di<lb></lb>ui Marci Venetiarum quandam etiam aliam tralationem operis de Ma<lb></lb>chinis bellicis à quod am Ioanne Sophiano factam, quam Cardinali Beſſa<lb></lb>rioni ſua quadam epistola cum dedicaſſet aſſerit ſe neſcire cuius Autoris <lb></lb>illud opus ſit, quandoquidem titulo carebat. </s>
<s>verùm iam dicta tralatio à <lb></lb>noſtra longe diuerſa est propter multos defectus, <expan abbr="locosq́ue">locosque</expan> deprauatos, <lb></lb>atque mendoſos exemplaris gręci, quod ipſe habuerat. </s>
<s>in ipſa verò So<lb></lb>phiani tralatione non eſt ſecundum opus de Geodęſia, ſed primum tantùm <lb></lb>de Machinis bellicis. </s>
<s>Postremò animaduertas velim quòd in vnoquoque <lb></lb>meorum ſcholiorum nomen meum aſcriptum reperies, exceptis illis in ſcho<lb></lb>lijs, quę mea non ſunt, ſed ab antiquo manuſcripto gręco libro tralata. </s>
<s><lb></lb>hoc autem hac ratione factum eſt, vt mea ſcholia ab alienis ſecernantur.<emph.end type="italics"></emph.end></s></p>
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<s>TABELLE WAR HIER</s></p>
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<s><emph type="center"></emph>PROEMIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s>QVAECVNQVE quidem obſidionalium <lb></lb>Machinarum difficiles, atque incompre<lb></lb>henſibiles eſſe videntur, hoc eis natura <lb></lb>comparatum eſt, aut propter earum de<lb></lb>ſcriptionis varietatem, ac difficilem co<lb></lb>gnitionem, aut propterea quòd earum <lb></lb>conſiderationes captu difficiles, atque <lb></lb>(vt ita potius dicam) multis incompre<lb></lb>henſibiles ſunt: forſan autem ignoran<lb></lb>tia ſola comprehenſæ, ita vt ne quidem ab ipſa figurarum po<lb></lb>ſitione dilluciditatem, ac facilem apprehenſionem poſſideant: <lb></lb>quippe cùm non omnibus promptæ, <expan abbr="cognitæq́ue">cognitæque</expan> ſint, neque <lb></lb>etiam ad conſtructionem, &amp; fabricationem expeditæ: ſolis ve<lb></lb>rò ipſismet <expan abbr="inuẽtoribus">inuentoribus</expan>, &amp; ſcriptoribus Mechanicis ad earum </s></p><p type="main">
<s><arrow.to.target n="note1"></arrow.to.target><lb></lb>explanationem, <expan abbr="dillucidationemq́ue">dillucidationemque</expan> indigentes. </s>
<s>quemadmo<lb></lb>dum eæ, quæ ab Apollodoro ad Adrianum Imperatorem ob<lb></lb>ſidionales machinæ conſtructæ fuerunt: &amp; ea quæ ab Athe<lb></lb>næo ad Marcellum ex Angiſiſtrati, &amp; aliorum ſapientum com<lb></lb>poſitionibus ad obſidionem expoſita ſunt commentaria: nec <lb></lb>non quæ à Bitone ad Attalum de conſtructione bellicorum <lb></lb>inſtrumentorum ex diuerſis antiquioribus Mechanicis colle<lb></lb>cta fuere iaculatoria: pręterea quæ ad obſidionem contra mo<lb></lb>liuntur tum cuſtodientia, tum etiam hominum conſeruationi <lb></lb>deſſeruientia, ac demum ad ianuarum conſtitutionem <expan abbr="expu-gnationemq́">expu<lb></lb>gnationemque</expan>; varia præcepta. </s>
<s>Hæc quùm in præſentia multis <lb></lb>inſolita penitus, <expan abbr="cognituq́ue">cognituque</expan> difficilia propter præteritam cur<lb></lb>riculo temporis obliuionem, quin etiam ſcientiarum nomina <lb></lb>communibus ſermonibus inuſitata ſint: non vtique iuxta ve-<pb xlink:href="052/01/010.jpg"></pb>terem ab ipſis uiris conſtructam, uniuerſalem, <expan abbr="artificioſam-q́ue">artificioſam<lb></lb>que</expan> orationem in præſenti libro in ordinem redigere conſen<lb></lb>taneum eſſe duximus. </s>
<s>ne dum ea, quæ in ipſis apparet obſcu<lb></lb>ritas animum ad ſe ipſam retrahit, circa etiam dillucidorum <lb></lb>cognitionem <expan abbr="quiſpiã">quiſpiam</expan> defatigetur. </s>
<s>Sola uero ea, quæ ab Apol<lb></lb>lodoro tradita fuerant, quippe quæ finem uerſus declaraui<lb></lb>mus, culturis, <expan abbr="conſequentibusq́ue">conſequentibusque</expan> enthymematibus conclu<lb></lb>ſimus. </s>
<s>cùm nos etiam quam plurima conſona adinueneri<lb></lb>mus, &amp; appoſuerimus. </s>
<s>quæcunque autem à reliquis ſparſim <lb></lb>collegimus cognitu, ad <expan abbr="ueramq́ne">ueramque</expan> intelligentiam captu faci<lb></lb>lia, communis <expan abbr="ſentẽtiæ">ſententiæ</expan> pronuntiata ſecundum Anthemium <lb></lb>exiſtentia, <expan abbr="quæq́ue">quæque</expan> ſolo problemate, ac ſola configuratione <lb></lb>percipi poſſunt, cùm nulla doctrina, uel interpretatione indi<lb></lb>geant: dictionum proprietate, <expan abbr="ſermonisq́ue">ſermonisque</expan> ſimplicitate à no<lb></lb>bis ipſa quoque in maiorem facilitatem tranſmutata, ita ut <lb></lb>à quibuſcunque fabricari, conſtruique facilè poſſint: ijs, quę <lb></lb>ab Apollodoro inuenta fuerant cùm contexerimus, <expan abbr="atq;">atque</expan> vnà <lb></lb>cum figuris exactè deſignauerimus, in ordinem redegimus. </s>
<s><lb></lb>quandoquidem cognouimus quòd ſola etiam configuratio <lb></lb>bene deſignata poteſt id, quod circa conſtructionem <expan abbr="obſcurũ">obſcurum</expan> <arrow.to.target n="note2"></arrow.to.target><lb></lb>eſt, &amp; inexplicabile, perſpicuum efficere. </s>
<s>Verumenimuero <lb></lb>ad obſidionem quidem Machinis, ac varijs, <expan abbr="diuerſarumq́ue">diuerſarumque</expan> <lb></lb>figurarum Teſtudinibus opus eſt. </s>
<s>verbi gratia foſſorijs, ag<lb></lb>geribus, arietes geſtantibus, præcurſorijs, ac demum ijs, quę <lb></lb>nunc ex inſertione adinuentæ ſunt leuiſſimis parmis: ad ea <lb></lb>uerò, quæ deuoluuntur pondera, cuneatim conſtipatis cu<lb></lb>ſtodientibus Machinis: Teſtudinibus cratibus uimineis con<lb></lb>textis: necnon ligneis tribulis quinque cubitorum menſura <lb></lb>præditis: Arietibus tum compoſitis, tum etiam unico ligno <lb></lb>conſtantibus: turribus ligneis ferri idoneis, <expan abbr="paratuq́ue">paratuque</expan> fa<lb></lb>cilibus; Scalis tum compoſitis cùm leuiſſimis: id genus formis <lb></lb>uarijs. </s>
<s>Rurſus hæc omnia nobis neceſſaria ſunt. </s>
<s>nempe prę<lb></lb>munitio adarcendum cùm ea, quæ in ſublimi inferuntur pon<lb></lb>dera, cùm ea, quæ à tormentis ad iaculandum ignem factis, <lb></lb>accenduntur: ſpectator ad inſpiciendum ea, quæ intra ciui<lb></lb>tatem ſunt: variæ murorum diuerſorum perforationes: ſcalę <lb></lb>nauticæ ad cuiuſcunque generis foſſas tranſeundas peruiæ:
<pb xlink:href="052/01/011.jpg"></pb>Machinæ, quæ ſine ſcalis muros inſcendunt: obſidionales <lb></lb>Machinæ ad obſidendum maritimas ciuitates, quippe quæ <lb></lb>collabi minimè poſſint: ac denique copioſæ multarum turba<lb></lb>rum ordinatim per flumina traiectiones. </s>
<s>Hæc omnia porrò <lb></lb>iuxta príſcorum Architectorum doctrinam conſtruenda ſunt <lb></lb>paratu facilia quo ad materiam, uaria quo ad figuras, paruiſ<lb></lb>ſima quo ad menſuras, leuia quo ad pondera, quippe quæ à <lb></lb>quibuſcunque Artificibus citò fieri poſſint, erectu facilia, in<lb></lb>ſidiatu difficilia, tranſlatu facilia, ſtabilia, fractu difficilia, ac <lb></lb>tandem eiuſmodi ſint, ut quatenus neceſſitas poſtulauerit fa<lb></lb>cilè componi, <expan abbr="facileq́ue">facileque</expan> diſſolui poſſint. </s>
<s>Hæc autem omnia <lb></lb>quandoquidem militarem ſcientiam quo ad obſidionem faci<lb></lb>lè inſtituunt, in præſenti libello quo ad conſtructionem, &amp; <lb></lb>vſum pertinent deinceps progredientes ordinatim <expan abbr="perſcribẽdo">perſcriben<lb></lb>do</expan> <arrow.to.target n="note3"></arrow.to.target> expoſuimus. </s>
<s>At ſiquis fortaſſe dictionum ad unguem ex<lb></lb>plorator compoſitionem Atticam, uel orationis grauitatem, <lb></lb>&amp; pulchritudinem, atque concentum, necnon figurarum ac <lb></lb>numeri uenuſtatem perſcrutans, deruditate, ac negligentia <lb></lb>nos reprehendat: Antiquos ſapientes audiat dicentes, quòd <lb></lb>cùm omnis de obſidione ſermo facilis, crebris eiuſdem ora<lb></lb>tionis repetitionibus, ac reſumptionibus, &amp; conſequentibus <lb></lb>enthymematibus ad cogitationum, <expan abbr="operationumq́ue">operationumque</expan> perce<lb></lb><arrow.to.target n="note4"></arrow.to.target>ptionem, fiat: à Dialecticis utique præceptis, aut horum <expan abbr="cõuerſis">con<lb></lb>uerſis</expan> alienus exiſtit. </s>
<s>Sciat autem quòd magnus etiam Ploti<lb></lb>nus (ut ait ſapientiſſimus Porphyrius) nec literas pulchrè for <lb></lb>mans, neque ſyllabas perſpicuè diuidens, <expan abbr="nullamq́ue">nullamque</expan> rectè <lb></lb>ſcribendi artis curam gerens: ſed ſolùm menti, <expan abbr="rebusq́ue">rebusque</expan> ip<lb></lb>ſis incumbens, ſcribebat. </s>
<s>nam ea, quæ ſunt tripliciter ſubſi<lb></lb>ſtere ſtatuebat, cùm in uocibus, tum animi conceptibus, tum <lb></lb>demum rebus: atque eum quidem, qui circa uoces errat, <expan abbr="nõ">non</expan> <lb></lb>eſſe impugnandum, quoniam mentis conceptum, aut rem <lb></lb>ipſam nullo pacto lædit: eum uerò, qui circa mentis <expan abbr="cõceptus">conceptus</expan> <lb></lb>peccat, amarè redarguendum, quia de vocibus ignoranter <lb></lb>loquitur: multò magis autem eum, qui circa res ipſas obcęca<lb></lb>tur, condemnandum, propterea quòd ſtolidus, ac falſus de<lb></lb>ſcriptor exiſtit, cùm in eam, quæ ſecundum diſpoſitionem <lb></lb>eſt ignorantiam incidat. </s>
<s>quippe quam duplicem Plato uo-<pb xlink:href="052/01/012.jpg"></pb>cat, eò quòd noſcit quidem quòd ſcit, neſcit <expan abbr="autemq̨">autemque</expan> igno<lb></lb>rat. </s>
<s>At Caliſthenes etiam Hiſtoriographus ſic inquit. </s>
<s>Opor<lb></lb>tet eum, qui aliquid ſcribere tentat, à perſona non aberrare, <lb></lb>ſed &amp; ſibi &amp; rebus ipſis proprios doctrinæ ſermones propo<lb></lb>nere. </s>
<s>Hoc enim pacto quiſpiam de rebus utiliter uerba face<lb></lb>ret aut ex diſcipulis Philolai, &amp; Ariſtotelis, &amp; Iſocratis, &amp; <lb></lb>Ariſtophanis, &amp; Apollonij, &amp; ijs, qui ſimilia illis conſcripſe<lb></lb>re. </s>
<s>nam iunioribus quidem addiſcere cupientibus haud inu<lb></lb>tilia hæc ad habendam elementarem quandam inſtitutionem <lb></lb>uidebuntur: ijs uerò, qui uolunt tandem aliquid agere lon<lb></lb>gè prorſus, &amp; ab operatrice contemplatione aliena erunt. </s>
<s>Vn<arrow.to.target n="note5"></arrow.to.target><lb></lb>de Heron quoque Mathematicus animaduertens <expan abbr="Delphicũ">Delphicum</expan> <lb></lb>illud præceptum, quod nos admonet tempore parcè uti, <lb></lb>&amp; quòd menſuras temporis oportet agnoſcere, <expan abbr="tãquam">tanquam</expan> eius, <lb></lb>quod <expan abbr="intẽpeſtiuum">intempeſtiuum</expan> exiſtit: maximam, <expan abbr="ualdeq́ue">ualdeque</expan> neceſſariam <lb></lb>conuerſationis in philoſophia partem, quæ etiam ad hanc uſ<lb></lb>que noſtram ætatem quæritur, circa imperturbationes conſi<lb></lb>ſtere cenſebat, &amp; nunquam per ſermones finem habituram. </s>
<s><lb></lb>At Mechanica doctrina, quæ operationibus in ſermones <expan abbr="trãſiit">tran<lb></lb>ſiit</expan>, omnes homines edocuit ſcire tranquillam ducere <expan abbr="uitã">uitam</expan>, <lb></lb>una ipſius parte, quæ circa artem iaculorum effectricem uer<lb></lb>ſari dicitur. </s>
<s>Quapropter ut neque in pacifico ſtatu, <expan abbr="neq;">neque</expan> in<lb></lb>ſtante bello, uel in quocunque tempore ac ſtatu inimicorum; <lb></lb>uel hoſtium ingreſſibus perturbemur: unà cum ijs, quæ in <lb></lb>obſidionibus, &amp; exercitibus componuntur ualde nutrienti<lb></lb><arrow.to.target n="note6"></arrow.to.target><lb></lb>bus, frugalibus Epimenideis uocatis medicamentis: necnon <lb></lb>paruiſſimis cibis, gulæ gratis, <expan abbr="ſitimq́ue">ſitimque</expan> prohibentibus, de ia<lb></lb>culatorijs etiam inſtrumentis prouidentiam habemus. </s>
<s>Rur<lb></lb>ſus quoniam ij, qui res ad obſidionem uniuerſales ſciunt, re<lb></lb>ctè etiam oppoſitas norunt: oppoſitorum autem una eſt ſcien<lb></lb>tia: ij ergo, qui per Mechanicam, &amp; præparatricem artem, &amp; <lb></lb>frugalem diuturnum cibum, &amp; quamlibet communem in bo<lb></lb>na diſpoſitione diætam obſidionem conſtituere, aut diſſol<lb></lb>uere poſſunt, ſemper in tranquillitate degent. </s>
<s>Non ab re <lb></lb>igitur ad eos, qui de ciuitatibus ſcribunt, &amp; in non neceſſariis <lb></lb>ſermonibus tempus abſumunt floridè loquentes, uanis ora<lb></lb>tionibus res inanimatas exprimentes, &amp; animalia laudantes,
<pb xlink:href="052/01/013.jpg"></pb>uel uitùperantes, haud inordinationem per enphaſin <expan abbr="eorũ">eorum</expan> <lb></lb>multiiugæ diſciplinæ quiſpiam dixiſſe uidebitur. </s>
<s>Nos autem <lb></lb>Græcorum philoſophis non aſſimilabimur, apud quos de <lb></lb>paruis ac inutilibus rebus multi graues ſermones impendun<lb></lb>tur. </s>
<s>nos etenim de maximis, <expan abbr="uitæq́ue">uitæque</expan> utiliſſimis rebus mini<lb></lb>ma, <expan abbr="ſimpliciaq́ue">ſimpliciaque</expan> (ut ab omnibus facilè memoriæ commen<lb></lb>dari poſſint) præcipere conſueuimus. </s></p><p type="margin">
<s><margin.target id="note1"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note2"></margin.target>b.</s></p><p type="margin">
<s><margin.target id="note3"></margin.target>c.</s></p><p type="margin">
<s><margin.target id="note4"></margin.target>d.</s></p><p type="margin">
<s><margin.target id="note5"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note6"></margin.target>f</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>OBſidionales Machinas ab Apollodoro ad Adrianum Impera<lb></lb><arrow.to.target n="note7"></arrow.to.target><lb></lb>torem conſtructas: necnon ea, quæ ab Athenæo ad Marcelli <lb></lb>de obſidione ſcripta ſunt: ac demum ea, quæ à Bitone ad Atta<lb></lb>lum regem de conſtructione bellicorum inſtrumentorum tradita fueri <lb></lb>iaculatoria commentaria, quorum Heron hìc meminit, poſt præſens <lb></lb>eius opus nos edituri ſumus: vt quæ ab illis antiquioribus autoribus <lb></lb>Heron excerpſerit, atque ampliauerit, quæ〈qué〉 deſuo addiderit facilè <lb></lb>quiſque videre poßit.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note8"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note7"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note8"></margin.target>b</s></p><p type="main">
<s><emph type="italics"></emph>Proponit cuncta ea, de quibus in præſenti libro per tractaturus est <lb></lb>quemadmodum proprijs in locis nobis perſpicuum erit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note9"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note9"></margin.target>c</s></p><p type="main">
<s><emph type="italics"></emph>Digreditur ſe excuſans de inornato ſermone, quo in bellicarum ma<lb></lb>chinarum deſcriptione coactè uſus eſt: oſtendens teſtimonijs antiquo<lb></lb>rum grauißimorum virorum elegantem ſermonem præſenti negoti <lb></lb>minimè conuenire.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note10"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note10"></margin.target>d</s></p><p type="main">
<s><emph type="italics"></emph>Verbis illis [aut horum conuerſis] intelligit Autor præcepta Rhet<lb></lb>rica. </s>
<s>nam (ut oſtendit Ariſtoteles in principio primi libri Rhetorico <lb></lb>rum) Rhetorica eſt Dialecticæ conuerſa. </s>
<s>quapropter præcepta quoque <lb></lb>Rhetorica præceptis dialecticis conuerſa ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note11"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note11"></margin.target>e</s></p><p type="main">
<s><emph type="italics"></emph>Heron Mathematicus, de quo præſens alius Heron hìc mentionen <lb></lb>facit, eſt ille Heron Alexandrinus Philoſophus, ac Mathematicus ce<lb></lb>leberrimus, qui ſcripſit quatuor libros de aquaticis horologys, duos de <lb></lb>ſpiritalibus. </s>
<s>&amp; unum de ijs, quæ perſe mouentur. </s>
<s>quippe qui Deo an<lb></lb>nuente iamiam à nobis edentur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note12"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note12"></margin.target>f</s></p><p type="main">
<s><emph type="italics"></emph>Epimenideum eſt quoddam medicamentum valde nutriens, ſitim <lb></lb>prohibens, quo ueſcebantur cùm ij, qui ciuitates obſidebant, tum ij qui <lb></lb>in ciuitatibus obſidebantur. </s>
<s>Epimenideum autem dictam eſt ab Epi<lb></lb>menidea Scylla in eius compoſitionem ingrediente de qua herba uide <emph.end type="italics"></emph.end>
<pb xlink:href="052/01/014.jpg"></pb><emph type="italics"></emph>Theophraſtum lib. </s>
<s>7. capit. </s>
<s>11. Hiſtor. </s>
<s>Plant. </s>
<s>componebatur autem ab <lb></lb>antiquis hoc modo.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Decocta Sylla, &amp; aqua abluta, &amp; exſiccata, ac demum paruißimas <lb></lb>in partes diſſecta. </s>
<s>&amp; poſthæc in ipſa ſeſamo admiſto quintæ partis, pa<lb></lb>paueris autem quintedecimæ, atque hiſce omnibus in ipſo mele tan<lb></lb>quam optimo, maſſam〈qué〉 agente mitigatis, totum diuidendum eſt uelu<lb></lb>ti in maximas oliuas. </s>
<s>&amp; harum unam quidem circa horam <expan abbr="ſecũdam">ſecundam</expan>, <lb></lb><expan abbr="unã">unam</expan> uerò circa <expan abbr="horã">horam</expan> <expan abbr="decimã">decimam</expan> <expan abbr="abſumẽtes">abſumentes</expan>: <expan abbr="nullũ">nullum</expan> à fame <expan abbr="malũ">malum</expan> patientur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Alia eiuſdem Pharmaci compoſitio, quæ fit hoc modo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>SVſcipientes ſeſami Attici ſemiſextarium, &amp; melis  ſemiſexta<lb></lb>rium, &amp; olei Cotilem, &amp; Chœnicem amigdalarum dulcium decor<lb></lb>ticatarum exſiccando ſeſamum, &amp; amigdalas molere &amp; uibrare opor<lb></lb>tet: deinde Scyllas <expan abbr="circũcirca">circumcirca</expan> <expan abbr="decorticãdo">decorticando</expan>, et radices, ac folia <expan abbr="abſcindẽdo">abſcinden<lb></lb>do</expan>, &amp; in paruas partes <expan abbr="diſſeccãdo">diſſeccando</expan> <expan abbr="ponẽtes">ponentes</expan> in mortario <expan abbr="cõtundere">contundere</expan> opus <lb></lb>eſt donec maximè leuigentur poſthæc verò <expan abbr="cõtuſarum">contuſarum</expan> Syllarum equa<lb></lb>lem meli partem æquabiliter vnà cum oleo ſubigere, atque in ollam in <lb></lb>fundendo &amp; ſuper carbones imponendo coquere oportet. </s>
<s>Cùm autem <lb></lb>inceperint calefieri, ſeſamum &amp; amigdalas interponendo ſimul ligno <lb></lb>hinc inde permouenda ſunt, donec omnia imponantur. </s>
<s>Cùm verò val<lb></lb>de ſolidum corpus factum fuerit, ipſum accipientes in paruas buccel<lb></lb>las circiter diuidere operæ pretium eſt. </s>
<s>atque vnam mane, unam〈qué〉 ve<lb></lb>ſperi quiſpiam abſumens, nutrimentum ſufficiens habet. </s>
<s>Hoc autem <lb></lb>Pharmacum apud exercitus etiam optimum eſt dulce enim exiſtit, &amp; <lb></lb>ſaturitatem inuehens, &amp; ſitim non inducit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Duplicem hanc præſentis Pharmaci compoſitionem ita deſcriptam <lb></lb>in quodam antiquo ſcholio in librum Heronis inuenimus; &amp; quoniam <lb></lb>ipſe Heron eius mentionem habuit: <expan abbr="nõ">non</expan> abrefactum iri exiſtimauimus, <lb></lb>vt illud qualecumque ſit de verbo ad uerbum in latinum ſermonem <lb></lb>conuerſum hìc apponeremus. </s>
<s>quippe quod an <expan abbr="bonũ">bonum</expan>, an malum ſit, per<lb></lb>ſpicacißimis Medicis iudicandum relinquimus. </s>
<s>Hanc <expan abbr="eandẽ">eandem</expan> verò du<lb></lb>plicem huiuſce Pharmaci compoſitionem vide etiam apud Philonem <lb></lb>Athenienſem in quinto libro ſuæ de re bellica tractationis, ubi ipſe <lb></lb>multa etiam alia Pharmaca ad hanc rem ſpectantia ponit. </s>
<s>ex quo loco <lb></lb>Heron quoque haſce duas Epimenidei Pharmaci compoſitiones ex<lb></lb>cerpſiſſe videtur.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/015.jpg"></pb><p type="main">
<s><emph type="center"></emph>DE CIVITATVM OBSIDIONE<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>TVM IN ALTIS COLLIBVS, <lb></lb>TVM INPLANO IACENTIVM:<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>ET DE MACHINIS ATQVE INSTRVMENTIS <lb></lb>huic obſidioni neceſſarijs. </s>
<s>Caput primum.<emph.end type="center"></emph.end></s></p><p type="main">
<s>PRINCIPEM rei militaris peritiſſimum, à <lb></lb>ſuperna prouidentia in pietate conſer<lb></lb>uatum: iuſſui, ac ſententiæ, <expan abbr="bonoq́ue">bonoque</expan> con<lb></lb>ſilio eorum, qui ſumma in autoritate, <lb></lb><expan abbr="poteſtateq́ue">poteſtateque</expan> conſtituti ſunt religioſiſſi<lb></lb>morum obſequentem: necnon hoſtes, &amp; <lb></lb>apoſtatas obſeſſurum: ciuitatum ſitus ac<lb></lb>curratè peragrando priùs obſeruare, <expan abbr="atq;">atque</expan> <lb></lb>ante omnia proprij populi cuſtodiam ab <lb></lb><expan abbr="oĩ">omni</expan> periculo immunem faciendo obſidionis <expan abbr="initiũ">initium</expan> ſumere opor<lb></lb>tet ad alios quidem locos caſtris pugnaturum ſe indicando, ut <lb></lb>illic inimici decepti præparentur, atque ad alios machinas ad<lb></lb>ducendo: ipſam verò irruptionem ad imbeciliores murorum <lb></lb>partes per uiciſſitudinem, <expan abbr="continuationemq́ue">continuationemque</expan> militarium or<lb></lb>dinum faciendo: multò cum ſtrepitu eos, qui intra ciuitatem <lb></lb>ſunt, huc illuc diſcerpendo: &amp; tubas noctu ad tutiores partes <lb></lb>ſonando, ut quamplurimi <expan abbr="putãtes">putantes</expan> haſce expugnari ab eis, quæ <lb></lb>inter turres ſunt ſpatijs vnà cum alijs effugiant. </s>
<s>At ſi in altis <lb></lb>quidem collibus, aut imperuijs præcipitijs ciuitates Sitæ fue<lb></lb>rint, ea, quæ deſuper à contrarijs deuoluuntur pondera ſum<lb></lb>ma cum obſeruatione euitanda ſunt. </s>
<s>vt lapides rotundi, colum <lb></lb>næ, rotæ, uerticuli, currus quatuor rotarum ponderibus one<lb></lb>rati, uaſa textilia uaria calculorum, aut terræ madefactæ plena, <lb></lb>cuiuſmodi ſunt ea, quæ ex aſſeribus circulariter compoſita, <expan abbr="li-gaminibusq́ue">li<lb></lb>gaminibusque</expan> extrinſecus <expan abbr="circumquaq;">circumquaque</expan> percincta ſunt, quip<lb></lb>pe quæ ad ſuſcipiendum uinum, &amp; oleum, &amp; quemcunque li<lb></lb>quorem fiunt: &amp; quotcunque alia ad defenſionem à contrariis <lb></lb>excogitari contingit. </s>
<s>Aduerſus hæc autem repugnantes muri<arrow.to.target n="note13"></arrow.to.target><lb></lb>ces ligneos conſtruere oportet <expan abbr="quinq;">quinque</expan> cubitorum Labdareos
<pb xlink:href="052/01/016.jpg"></pb>à quibuſdam vocatos, quorum vnumquodque crus gyrum <lb></lb>quaſi duorum pedum habeat, ne frangantur, uel <expan abbr="diſrũpantur">diſrumpantur</expan>: <lb></lb>ſed reſiſtant ponderibus, quæ deorſum feruntur. </s>
<s>Sufficientes <lb></lb>autem multitudine ipſi conſtruendi ſunt, ut triplicata, aut <expan abbr="etiã">etiam</expan> <lb></lb>quadruplicata horum poſitio fiat. </s>
<s>ita enim <expan abbr="locorũ">locorum</expan> partes aſcen<lb></lb>ſu difficiles, &amp; arduas circummuniendo fieri poteſt ut (excepta <lb></lb>ſagitta) ſine periculo aſcendatur. </s>
<s>nam lapidum <expan abbr="vehemẽs">vehemens</expan> deor<lb></lb>ſum latio in muricum conuerſione offendens, quieſcet. </s>
<s>Poſſu<lb></lb>mus autem alio quoque modo læſionem ex ijs, quæ deorſum <lb></lb>feruntur prouenientem euitare. </s>
<s>ab ipſo enim <expan abbr="mõtis">montis</expan> pede deor<lb></lb>ſum incipientes laterales foſſas fodere, &amp; ad quaſdam <expan abbr="murorũ">murorum</expan> <lb></lb>partes proſpicere, atque aſcendere opus eſt. </s>
<s>quæ quidem foſſæ <lb></lb>profunditatem quinque pedum circiter habeant, necnon mu<lb></lb>rum unum erectum ab eadem foſſa ad partes ſiniſtras exiſten<lb></lb>tem, ad quem deferantur pondera, quæ deuoluuntur: quique <lb></lb>propugnaculum, &amp; ſcutum aſcendentium fiat. </s>
<s>Locus autem <lb></lb>præeffoſſus, ſic ab effodientibus muniendus eſt. </s>
<s>Ligna quaſi <lb></lb>ſex cubitorum, uel nuper acuta, uel in parte inferiori acuta fa<lb></lb>cientes <expan abbr="tãquam">tanquam</expan> palos ad murum ab aggeſta terra ad partes ſi<lb></lb>niſtras iam erectum tractum ad reſiſtendum infigere oportet. </s>
<s><lb></lb>quippe quæ obliquentur uerſus deorſum ferentem collis decli<lb></lb>nationem. </s>
<s>necnon tabulæ ſuper ipſis extrinſecùs apponendæ, <lb></lb>&amp; arborum rami complectentes circumligandi ſunt, ac <expan abbr="demũ">demum</expan> <lb></lb>omnem effoſſam materiam illuc proiiciendo uiæ rectæ ad te<lb></lb>ſtudinum aſcenſionem æquandæ ſunt. </s>
<s>eas autem, quæ addu<lb></lb>cunt teſtudines roſtratas iuxta <expan abbr="faciẽ">faciem</expan>, hoc eſt cuncatas, ex trian<lb></lb>gularibus, aut quinquangularibus baſibus conſtitutas: in acu<lb></lb>tum in anteriori parte angulum terminantes: ab inferiori verò <lb></lb>latitudine ad altitudinem eleuatas: &amp; uſque ad verticalem dor<lb></lb>ſum in acutum procedentes: nauium terram verſus reſpicien<lb></lb>tium proris anteriùs aſſimilatas fieri oportet. </s>
<s>paruas pręterea, <lb></lb>&amp; quam plures ipſas eſſe opus eſt, vt citò <expan abbr="facileq́ue">facileque</expan> conſtrui, à <lb></lb><expan abbr="paucisq́ue">paucisque</expan> viris abſque labore ferri poſſint: leuia ligna pedalia <lb></lb>circa baſim habentes, &amp; loco rotarum clauos ferreos, vt dum <lb></lb>in terra ponuntur ipſi affingantur, &amp; ab impetu non <expan abbr="diſtrahã-tur">diſtrahan<lb></lb>tur</expan>: necnon obliquum lignum earum vnaquæque iuxta fron<lb></lb>tem habere debet (quemadmodum in temonibus currus ha-<pb xlink:href="052/01/017.jpg"></pb>bent) vt eam ad imas partes ſubuertentem retineat, atque <lb></lb>ſuffulciat, &amp; præſertim cùm eam ſurſum ferrentes defatigati <lb></lb>fuerint, ac paululum quieſcere debuerint. </s>
<s>Eueniet itaque <lb></lb>aut foſſæ laterali exiſtenti incidentia <expan abbr="põdera">pondera</expan> perperam prę<lb></lb>teruehi: aut obliquos palos lateralem ſitum habentes in cu<lb></lb>tientia, percuti: aut in roſtris machinum offendentia in alte<lb></lb>ram partem præterire, intermedium uerò locum liberari. </s>
<s><lb></lb>Melius autem eſt teſtudines etiam cratis vimineis contextas <lb></lb>leuiores iam dictis roſtratis, &amp; conformes exiſtentes addu<lb></lb>cere. </s>
<s>quippe quæ ex inſertione ſalignarum virgarum recèns <lb></lb>inciſarum, aut ex myrica, uel Tilia conſtruuntur, acutæ ipſæ <lb></lb>quoque iuxta faciem vſque ad verticalem dorſum exiſten<lb></lb>tes. </s>
<s>eas verò, quæ parmæ vocantur, leuiſſimas exiſtentes, ex <lb></lb>contextu ipſas quoque vinealium uitium, vel nuper cæſa<lb></lb>rum virgarum in figura conuerſionali quam celerrimè fa<lb></lb>ctas non eſt opus ad decliues, ac præcipites locos afferre. </s>
<s>ne <lb></lb>fortè ferentibus pernitiem inferant, quandoquidem <expan abbr="immẽ-ſis">immen<lb></lb>ſis</expan> ponderibus reſiſtere nequeunt. </s>
<s>ipſis autem potiùs uten<lb></lb>dum eſt cùm in planis, <expan abbr="enodisq́">enodisque</expan>; locis ciuitates ſitæ fuerint. </s>
<s><lb></lb>tunc enim eis vti commodè poſſumus. </s>
<s>Verùm populus, qui <lb></lb>ad caſtrorum pugnam aſcendit, ad latitudines roſtratarum <lb></lb>machinarum cuſtoditus, uel poſt teſtudines, &amp; teſtudinibus <lb></lb><arrow.to.target n="note14"></arrow.to.target><lb></lb>vineis vocatis coopertus ſequetur, propter ſagittas, <expan abbr="funda-rumq́ue">funda<lb></lb>rumque</expan> iactationes. </s>
<s>At ligna teſtudinis, quæ milites ferunt <lb></lb>huiuſcemodi ſunt. </s>
<s>erecta ſcilicet in altitudinem, inæqualia, <lb></lb>ſingula craſſitiem circumquaque circiter duodecim digito<lb></lb>rum habentia, iuxta verò quinque pedes ad altera latera in<lb></lb>directum connexa, vt ipſum quinque pedum ad ſe inuicem <lb></lb>interuallum ſeruetur. </s>
<s>atque eorum altiora quidem ſupra vi<lb></lb>ri ſtaturam vnam, &amp; dimidiam: depreſſiora verò, ſupra <expan abbr="virũ">virum</expan> <lb></lb>ſint: deſuper autem cooperta propter inęqualitatem ſurſum <lb></lb>currentibus aſſimilantur. </s>
<s>ſpatium verò, quod eſt à vertice <lb></lb>roſtratæ machinæ vſque ad cooperta inæqualia ligna in fi<lb></lb>gura ſimul intus apparebit. </s>
<s>Rurſus ligna, quæ à militibus fe<lb></lb>runtur, inferiùs ueluti cuſpides habeant, vt terræ affixa, por<lb></lb>tantes refocillent. </s>
<s>coria verò carnoſa, craſſa, uel cilicina ex<lb></lb>teriùs iuxta faciem <expan abbr="ſuſpẽduntur">ſuſpenduntur</expan>. </s>
<s>in ipſis autem inæqualibus
<pb xlink:href="052/01/018.jpg"></pb>lignis còria duplicata ſuperponantur, non extenſa ad eno<lb></lb>dam, &amp; æqualem ſuperficiem, ſed paululum <expan abbr="cõtracta">contracta</expan>, in <expan abbr="ip-ſisq́ue">ip<lb></lb>ſisque</expan> lignis inæqualibus depreſſa: vt in horum tumiditate <lb></lb>incidentes ſagittæ, debiles in percutiendo, <expan abbr="remiſſæq́ue">remiſſæque</expan> ſint; <lb></lb>qui verò introrſum cooperiuntur, à læſione immunes per<lb></lb><arrow.to.target n="note15"></arrow.to.target>maneant. </s>
<s>Verumtamen ſi in planis, <expan abbr="enodisq́ue">enodisque</expan> locis ciuita<lb></lb>tes ſitæ ſint, operæ pretium eſt aggeres teſtudines rotis ſur<lb></lb>repentes, atque in anteriori parte munitas adducere, ne ij, <lb></lb>qui foſſas aggerant à <expan abbr="cõtrarijs">contrarijs</expan> feriantur: aut iam dictas Par<lb></lb>mas vti leuiſsimas, atque vtiles ad aggerandas foſſas, <expan abbr="necnõ">necnon</expan> <lb></lb>locos aquoſos, ac madidos replendos, &amp; cuiuſcunque gene<lb></lb>ris ſciſſuras mœnijs proximas æquandas: vt machinarum <lb></lb>adductionem peruiam, ab <expan abbr="omniq́ue">omnique</expan> periculo vacuam facia<lb></lb>mus. </s>
<s>Opus eſt autem nos accuratè proſpicientes in ueſtigare <lb></lb>eas, quæ in foſſis ipſis apparent complanatæ traiectiones, <lb></lb>propter fictiles tegulas, quæ ſæpenumero ſubter à contra<lb></lb>riis abſconduntur: vt cælis quidem via meatu facilis, peri<lb></lb>culoque carens appareat, ipſa verò, quæ adducuntur inſtru<lb></lb>menta cùm admodum grauiſſima ſint, in ipſa porrò ſubie<lb></lb>ctarum tegularum fractione, <expan abbr="progreſsioneq́ue">progreſsioneque</expan> ſubeant, <expan abbr="atq;">atque</expan> <lb></lb>dirumpantur. </s>
<s>Quapropter oportet nos cum haſtis acuta ſpi<lb></lb>cula, fortiaque habentibus, aut quibuſdam idoneis terebris <lb></lb><arrow.to.target n="note16"></arrow.to.target><lb></lb>periculum facere: aduerſus verò ferreos murices ab inimi<lb></lb>cis diſſeminatos, terræ admiſtos, atque latentes lignea ſup<lb></lb>poſitoria ad pedes ſub ſoleis ſupponentes innocuè permea<lb></lb>re: ſeu georgicis pectinibus (quos cùm ſint dentibus prædi<lb></lb>ti, Raſtros etiam quidam appellant) eos repurgare: ac de<lb></lb>nique circa eas, quæ in foueis ponuntur ianuas periculum <lb></lb>priùs facientes ligonibus effodire. </s>
<s>Operæpretium eſt autem <lb></lb>eos etiam, qui ſub terra prope murum aguntur cuniculos, <lb></lb>occultos, <expan abbr="profundosq́ue">profundosque</expan> iuxta fundamenta, &amp; non in terræ <lb></lb>faciem fieri: ne cùm hoc hoſtes deprehenderint, intus è di<lb></lb>uerſo fodiant, <expan abbr="murumq́ue">murumque</expan> ipſum cùm contra perforauerint, <lb></lb>eos, qui cuniculum agunt, fumo, &amp; aqua perimant. </s>
<s>Verùm <lb></lb>cuncta ea, quæ iam deſcripta ſunt, vnà cum figuris ordina<lb></lb>tim ſubiiciuntur. </s></p>
<pb xlink:href="052/01/019.jpg"></pb><p type="margin">
<s><margin.target id="note13"></margin.target>a.</s></p><p type="margin">
<s><margin.target id="note14"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note15"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note16"></margin.target>d</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note17"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note17"></margin.target>a</s></p><p type="main">
<s><emph type="italics"></emph>LAbdareos hoc eſt ſimiles literæ labda Grecæ, quæ huiuſce <lb></lb>figuræ eſt. <foreign lang="grc">λ.</foreign> &amp; quoniam vnuſquiſque ipſorum ligneorum <lb></lb>Muricum duas in ſe labdas oſtendit, non immeritò labda<lb></lb>rei vocabantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note18"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note18"></margin.target>b</s></p><p type="main">
<s><emph type="italics"></emph>Teſtudines illas, quæ vineæ dicuntur non deſcripſit autor, quem<lb></lb>admodum eas, quæ roſtratæ: eas, quæ cratibus vimineis contextæ <lb></lb>ſunt: &amp; eas, quę Parmę nuncupantur. </s>
<s>Sunt autem teſtudines vineę <lb></lb>ex lignis compactae, latę pedibus octo, altę ſeptem, longę ſedecim, du<lb></lb>plici ligno tectę, cratibus contextæ, latera vimine ſepta habentes <lb></lb>(ne ſaxorum, ac telorum impetu perfringantur) crudis, ac recen<lb></lb>tibus corijs extrinſecùs cooperta. </s>
<s>quas ideo <expan abbr="nõ">non</expan> deſcripſit autor, quia <lb></lb>teſtudinibus quæ ſunt vimine is cratibus contextæ ſimiles ſunt. </s></p><p type="main"><s><expan abbr="quẽ-admodum">quem-<lb></lb>admodum</expan> etiam Aggeres non deſcripſit quoniam exceptis rotis a <lb></lb> roſtratis nil differunt. <emph type="italics"></emph><arrow.to.target n="note20"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note19"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note20"></margin.target>d</s></p><p type="main">
<s><emph type="italics"></emph>Tria Muricum genera ſunt, quibus in militia priſci bellatores <lb></lb><expan abbr="vtebãtur">vtebantur</expan>: nempe lignei labdarei, &amp; ferrei ſuper terram diſſemina<lb></lb>ti, quorum autor in præſenti capite mentionem facit: ac demum fer<lb></lb>rei ignem artificioſum ferentes, qui mucronibus ſuis vbicunque <lb></lb>iactati fuerint affiguntur, &amp; flamma, quam geſtant, locum cui affi<lb></lb>xi ſunt, comburunt. </s>
<s>de quibus etiam ignem ferentibus muricibus <lb></lb>autor inferiùs in capite. </s>
<s>14. verba facturus eſt. </s>
<s>Ex his autem tribus <lb></lb>muricum generibus duo postrema, præſertim〈qué〉 tertium vſque in <lb></lb>hodiernum diem in vſu maximè ſunt.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/020.jpg"></pb><figure id="id.052.01.020.1.jpg" xlink:href="052/01/020/1.jpg"></figure><p type="caption">
<s>CIVITAS IN ALTO COLLE IACENS</s></p>
<pb xlink:href="052/01/021.jpg"></pb><figure id="id.052.01.021.1.jpg" xlink:href="052/01/021/1.jpg"></figure><p type="caption">
<s>CIVITAS IN PLANO SITA</s></p>
<pb xlink:href="052/01/022.jpg"></pb><p type="main">
<s><emph type="center"></emph>DE SCALIS CORIACEIS, ET RETICV<lb></lb>LATIS CAPVT SECVNDVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s>VERVM enimuero ciuitates ipſas nullo negotio <lb></lb>expugnare uolentem iuxta Philonis <expan abbr="Atheniẽ-ſis">Athenien<lb></lb>ſis</expan> ſententiam, oportet vindemia mirum in mo<lb></lb>dum exiſtente, vel dum extra ciuitatem cele<lb></lb>britas agitur, numeroſam aggreſſionem facere: <lb></lb>tunc etenim cum quamplurimos foris in ſuas manus ventu<lb></lb>ros, quos lædere facilè poteſt, uel ipſi ſubiectos, ac denique <lb></lb>ciuitatem ipſam à reliquis habitatoribus propter amoris er<lb></lb>ga ipſos affectum, <expan abbr="cognationemq́">cognationemque</expan>; ſibi deditam habere ne<lb></lb>ceſſe eſt. </s>
<s>Si uerò furtim nocte ciuitatem capere volumus, ci<lb></lb>uibus aduentum noſtrum ignorantibus, <expan abbr="minimeq́ue">minimeque</expan> <expan abbr="ſperã-tibus">ſperan<lb></lb>tibus</expan>, hyeme præueniente, quando frigoris cauſa horum <lb></lb>maior pars in domos contrahitur, ad <expan abbr="bellumq́ue">bellumque</expan> parati mi<lb></lb>nimè ſunt: aut quando celebratiſſimum feſtum in ciuitate <lb></lb>peragitur, &amp; populus in ſacrificio ludis vacat, vel ob ebrie<lb></lb>tatem ſomnolentus exiſtit: ſcalas coriaceas cùm fecerimus, <lb></lb>muro eas applicabimus. </s>
<s>quæ quidem quemadmodum vt res <lb></lb>conſuuntur, &amp; vnctione obturandi gratia circa conſutiones <lb></lb>replentur ita ut non euaporent. </s>
<s>ſi namque inflentur, <expan abbr="ſpiri-tuq́ue">ſpiri<lb></lb>tuque</expan> impleantur, eo quòd euaporare non poſſunt, erigi <lb></lb>eas à ſpiritu neceſſum eſt, ad <expan abbr="aſcenſionemq́ue">aſcenſionemque</expan> nobis ſuffi<lb></lb>ciunt. </s>
<s>Quòd ſi altior ſcalis ipſis coriaceis murus exiſtat, <lb></lb>alijs ipſæ ſtupeis ſcalis ante ſubijciuntur. </s>
<s>quippe quæ con<lb></lb>ſtruuntur dum textura, &amp; conſutione colligantur, reticula<lb></lb>tæ exiſtentes, eorum inſtar, quæ verricula dicuntur. </s>
<s>ad ea<lb></lb>rum autem extremitates hami adiiciuntur, vt ab ipſis iam <lb></lb>ſubiectis coriaceis ſcalis iniecti, murorum pinnas <expan abbr="apprehẽ-dant">apprehen<lb></lb>dant</expan>, atque ita ſuper murum aſcenſionem uolentibus vnà <lb></lb>diſponant. </s>
<s>ipſæ verò ſcalarum figuræ ſubſcriptæ ſunt. </s></p>
<pb xlink:href="052/01/023.jpg"></pb><figure id="id.052.01.023.1.jpg" xlink:href="052/01/023/1.jpg"></figure><p type="caption">
<s>Scala coriacea inflata</s></p><p type="main">
<s><emph type="center"></emph>De Teſtudinibus foſſoriis. </s>
<s>Caput Tertium.<emph.end type="center"></emph.end></s></p><p type="main">
<s>AT cùm eæ, quæ ſuperius dictæ ſunt roſtratæ <lb></lb>Machinæ, vnà cum Teſtudinibus vineis voca<lb></lb>tis prope murum aduenerint, varias tunc Te<lb></lb>ſtudines adducere oportet: alias quidem ad fo<lb></lb>diendum murum, alias verò ad <expan abbr="oppugnãdum">oppugnandum</expan> <lb></lb>Arietibus. </s>
<s>ad fodiendum igitur eas, quæ foſſoriæ nuncu<lb></lb>pantur. </s>
<s>has autem vel dupliciter fluentes eſſe neceſſe eſt, &amp; <lb></lb>in faciem coopertas adduci, <expan abbr="muroq́ue">muroque</expan> appropinquari: vel <lb></lb>vnicam habentes alam, retro quidem decliues, in faciem <lb></lb>verò quadrangulas, à <expan abbr="lateribusq́">lateribusque</expan>; trapezio ſimiles, aut trian<lb></lb>gulas, quippe quæ hoc modo conſtruantur. </s>
<s>Ligna <expan abbr="ſuſcipiẽ-tes">ſuſcipien<lb></lb>tes</expan> tria, vel quatuor, quandoque autem &amp; quinque (vt ſpiſ<lb></lb>ſius, <expan abbr="ſolidiusq́ue">ſolidiusque</expan> fiat opus) longitudinem habentia non mi-<pb xlink:href="052/01/024.jpg"></pb>norem pedum decem, craſſitiem verò quaſi vnius pedis, ſi<lb></lb>militer autem &amp; latitudinem: hæc in ſuperiori parte obli<lb></lb>què ad vnguis ſimilitudinem abſcindere opus eſt. </s>
<s>vt dum à <lb></lb>rotatis axibus adducuntur, à <expan abbr="rectisq́ue">rectisque</expan> lignis intrinſecùs ſu<lb></lb>ſtinentur, muro applicentur. </s>
<s>erigatur autem ad murum li<lb></lb>gnea columna baſin inferiùs habens, quæ &amp; ſuperiacentia <lb></lb>ligna, &amp; ſuffulcientia erecta ſuſtineat: vt ea, quæ deſuper <lb></lb>deferuntur tecto minimè nocentia, retrorſum elabantur. </s>
<s>ip<lb></lb>ſa verò erecta ligna, &amp; vnguis inſtar abſciſſa, ſpicula ferrea <lb></lb>retrorſum habeant, vt terræ affigantur, &amp; non diſtrahan<lb></lb>tur. </s>
<s>ad latera autem ſuſpendantur coria tegentia, ſeu bacu<lb></lb>li, ſiue ea, quæ ex virgis, vel palmarum ramis contexta <lb></lb>ſunt: propter ſagittas, quæ hinc inde perferuntur: idem <lb></lb>verò anteriores etiam in partes fiat. </s>
<s>at cùm muro appropin<lb></lb>quauerint, extendantur ſuperiores in partes ea, quæ in an<lb></lb>teriores ſunt. </s>
<s>Verùm in unaquaque Teſtudine viri duo ab<lb></lb>ſcondendi ſunt, erecti ſtantes, <expan abbr="murumq́ue">murumque</expan> fodientes, ad craſ<lb></lb>ſitiem quidem plus dimidio: ſecundum verò latitudinem, <lb></lb>quanta eſt etiam ipſius Teſtudinis latitudo: in altitudinem <lb></lb>autem, à tribus pedibus ſupra terram fodere incipientes: <lb></lb>vt ea, quæ ab ipſa fodina deſcendunt, verſus relictum infe<lb></lb>riùs locum incidant. </s>
<s>in ſuperiorem autem partem tantum <lb></lb>fodiendum eſt, quantum fodientes ſine impedimento po<lb></lb>terint. </s>
<s>propiùs autem quàm viginti pedibus ab inuicem <lb></lb>Teſtudines diſtent, vt &amp; plures ſint, &amp; multum in muro lo<lb></lb>cum ipſi fodientes operentur. </s>
<s>necnon paruæ ſint, vt celeri<lb></lb>ter, ac facilè deducantur: atque ea, quæ à muro ab aduer<lb></lb>ſariis iaciuntur, haud directè ad ſcopum, <expan abbr="perſpicienterq́ue">perſpicienterque</expan> <lb></lb>ad latera Teſtudinum magnam ab inuicem diſtantiam ha<lb></lb>bentium ferantur. </s></p>
<pb xlink:href="052/01/025.jpg"></pb><figure id="id.052.01.025.1.jpg" xlink:href="052/01/025/1.jpg"></figure><p type="caption">
<s>Fossoriæ testudines baſis muro applicata </s></p><p type="main">
<s><emph type="center"></emph>De fodinarum ſuſtentatione, &amp; combuſtione. </s>
<s>Cap. </s>
<s>IIII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>CVm <expan abbr="aũt">aut</expan> murus à facie introrſum ad <expan abbr="craſſitiẽ">craſſitiem</expan> per <lb></lb>foratus fuerit, <expan abbr="totq́ue">totque</expan> ſeparationes ſecundum <lb></lb>latitudinem ſuſceperit, quot etiam teſtudines <lb></lb>ſunt: atque iam dicti duo viri à ſe inuicem con<lb></lb>uerſi intus abſque impedimento in ipſis ſepa<lb></lb>rationibus fodiant: non amplius indigent Teſtudine, cùm <lb></lb>ad laterales fodiant partes, ab <expan abbr="ipſaq́ue">ipſaque</expan> muri craſſitie intus <lb></lb>conſeruentur. </s>
<s>At ne fodientibus murus coincidat, ſuſtente<lb></lb>tur intus, <expan abbr="fulciaturq́ue">fulciaturque</expan> <expan abbr="ſuſtẽraculis">ſuſtentaculis</expan> ſubtilibus  potius, ac fre<lb></lb>quentibus, quàm craſſis, &amp; raris tabula ſupra, <expan abbr="infraq́ue">infraque</expan> poſi<lb></lb>ta, ne dum terram verſus ſub relaxantur ſuſtentacula, male <lb></lb>ſuſtineant. </s>
<s>cùm verò fodina completa, <expan abbr="ſuſtentataq́ue">ſuſtentataque</expan> fuerit: <lb></lb>intercapedo epiſtyliorum repleatur materijs facilè combu<lb></lb>ſtibilibus, verbi gratia virgultis, lignis ſiccis, tædis ſciſſis, &amp;
<pb xlink:href="052/01/026.jpg"></pb>alijs huiuſcemodi, quæ ad combuſtionem idonea ſunt: ac <lb></lb>demum accendatur. </s>
<s>quòd ſi locus aliquis extinguatur, ijs, <lb></lb>quæ ad iaculandum ignem fiunt tormentis, ſubaccendatur. </s>
<s><lb></lb>habeat autem &amp; raſuras lignorum ſiccas circumſperſas vnà <lb></lb>cum liquida pice, ſiue oleo perunctas. </s>
<s>ac denique combuſtis <lb></lb>ſuſtentaculis, murus corruet. </s></p><figure id="id.052.01.026.1.jpg" xlink:href="052/01/026/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>De Teſtudinum conſolidatione. </s>
<s>Cap. </s>
<s>V.<emph.end type="center"></emph.end></s></p><p type="main">
<s>IPSIS autem harum Teſtudinum erectis lignis <lb></lb>claui <expan abbr="latũ">latum</expan> caput habentes, altitudinis verò digi<lb></lb>torum octo, ſeu ſurculi ex ferro facti ſuper infi<lb></lb>gantur vſque ad quatuor digitos, reliquos ve<lb></lb>rò quatuor ſupereminentes habeant. </s>
<s>locum <lb></lb>autem, qui intermedius eſt creta opima, &amp; glutinoſa cum <lb></lb>pilis ſuinis, vel hircinis ſubacta illinere, <expan abbr="replereq́ue">replereque</expan> oportet, <lb></lb>ne diſrumpantur, neque diſcindantur. </s>
<s>nam tum propter
<pb xlink:href="052/01/027.jpg"></pb>clauorum frequentiam, tum etiam propter capitum eorum <lb></lb>latitudinem confirmabitur. </s>
<s>à lateribus autem panni lacera<lb></lb>ti, ſeu coria ſuſpendantur: vt neque ſabulum calidum, ne<lb></lb>que pix, neque reſina decocta, neque oleum (quod infun<lb></lb>ditur, tanquam id, quod natura citiùs caleſcit, <expan abbr="tardiusq́ue">tardiusque</expan> <lb></lb>frigeſcit) ijs, qui intus operantur inſtillent. </s>
<s>nam inſtar ignis <lb></lb>hominum carnes conſumunt. </s>
<s>Cùm itaque ſic Teſtudines <lb></lb>conficiantur, conſeruabuntur ita vt ab ijs, quæ deſuper deij<lb></lb>ciuntur ignem ferentibus, <expan abbr="accenſisq́ue">accenſisque</expan> flammis minimè <expan abbr="cõ-buri">com<lb></lb>buri</expan>: neque ij, qui infunduntur calefacti liquores intus pe<lb></lb>netrare poſſint. </s>
<s>Similiter <expan abbr="aũt">aut</expan> &amp; Parmæ, <expan abbr="Teſtudinesq́ue">Teſtudinesque</expan> crati<lb></lb>bus vimineis <expan abbr="cõtextæ">contextæ</expan> ad texturas operiantur coriis madidis <lb></lb>bouum recèns occiſorum, <expan abbr="tanquã">tanquam</expan> iis, quæ igni reſiſtere poſ<lb></lb>ſunt. </s>
<s>ipſæ verò Teſtudines procul ab inſtrumentis lapides <lb></lb>iacientibus, <expan abbr="ſagittasq́ue">ſagittasque</expan> mittentibus linantur. </s>
<s>cùm autem <lb></lb>condenſatæ, rotiſque ſurrepentes contextæ fuerint, muris <lb></lb>adducantur. </s>
<s><expan abbr="figuraq́ue">figuraque</expan> ſubiecta eſt. </s></p><p type="caption">
<s>Teſtudinis foſsoriae baſisillita cr<gap></gap>ta </s></p><figure id="id.052.01.027.1.jpg" xlink:href="052/01/027/1.jpg"></figure><p type="caption">
<s>Teſtudo foſsoría <lb></lb>completa at〈que〉 <lb></lb>munita</s></p><figure id="id.052.01.027.2.jpg" xlink:href="052/01/027/2.jpg"></figure><p type="main">
<s><emph type="center"></emph>De murorum lapideorum per vrnam combuſtione. </s>
<s>Cap. </s>
<s>VI.<emph.end type="center"></emph.end></s></p><p type="main">
<s>QVidam verò iuxta lapideos muros ligna (vt <lb></lb>mos erat) inferiori parti contigua ad <expan abbr="accendẽ-dos">accenden<lb></lb>dos</expan>, <expan abbr="confringendosq́ue">confringendosque</expan> lapides circumpone<lb></lb>bant. </s>
<s>Verùm hæc operatio difficilis vſu, &amp; <expan abbr="quãdo">quan<lb></lb>do</expan>  que fallax exiſtit: quoniam tum aqua deſu<lb></lb>per infuſa ignem extinguit: <expan abbr="tũ">tum</expan> debilior ad latus ipſius ignis
<pb xlink:href="052/01/028.jpg"></pb>latio fit, tanquam ea, quæ natura ſurſum tendit, ad <expan abbr="actionẽ-q́ue">actionen<lb></lb>que</expan> potentior eſt: tum demum in ipſo flammæ impetu, qui <lb></lb>introrſum operantur, ſub teſtudine eſſe minimè poterunt, <lb></lb>quandoquidem ſimul comburentur. </s>
<s>Fiunt itaque fictiles <lb></lb>vrnæ laminis ferreis exteriori parte colligatæ, <expan abbr="minutisq́ue">minutisque</expan> <lb></lb>carbonibus implentur: ab extrinſeca verò laminæ facie fun<lb></lb>dum verſus forantur, &amp; aperiuntur vſque vnius digiti fora<lb></lb>men, <expan abbr="ferreumq́ue">ferreumque</expan> tubulum inde ſuſcipiunt, cui tubus alius <lb></lb>follem habens adiungitur. </s>
<s>Cùm autem ignem carbones ſu<lb></lb>ſceperint, dum ſufflantur, ſimilem flammæ perficiunt com<lb></lb>buſtionem. </s>
<s>quippe quæ lapidem penetrat, atque confringit, <lb></lb>aceto, vel vrina, vel alio quopiam acrium ſuperinfuſo. </s>
<s><expan abbr="eſtq́">eſtque</expan>; <lb></lb>figura qualis ſubſcribitur. </s>
<s>hoc autem plumbarij frequenter <lb></lb>vtuntur. </s></p><figure id="id.052.01.028.1.jpg" xlink:href="052/01/028/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>De murorum lateritiorum per terebras perforationibus. </s>
<s><lb></lb>Caput ſeptimum.<emph.end type="center"></emph.end></s></p><p type="main">
<s>SI lateritios muros cito deſtruere voluerimus, <lb></lb>frequentiſſimas in ipſis perforationes terebris <lb></lb>faciemus, cooperti ſub teſtudinibus deſuper <lb></lb>illitis, aut Parmis, quæ tecta tutiſſima habeant, <lb></lb><expan abbr="ſintq́ue">ſintque</expan> corijs bouum recèns occiſorum circa <lb></lb>texturas opertæ: cùm propter pondera, quæ aduerſus eas <lb></lb>mittuntur, tum propter calefactos, qui infunduntur liquo<lb></lb>res. </s>
<s>Terebræ verò fabrilibus inſtrumentis ſimiles ſint. </s>
<s>Ve-<pb xlink:href="052/01/029.jpg"></pb>ctis enim ferreus fit longitudinis pedum ad minus quinque<lb></lb>vnius digiti diametrum habens, &amp; craſſitudinem circum, <lb></lb>quaque fermè quatuor digitorum: laminam ſimiliter <expan abbr="ferreã">ferream</expan> <lb></lb>in anteriori extremitate affixam latitudinis pedum duode<lb></lb>cim, &amp; altitudinis octo, quæ circa medium in anteriori par<lb></lb>te coarctetur, iuxta figuram cuiuſdam olitorii inſtrumenti, <lb></lb>quod à Græcis Platilyſgium vocatur: ad alteram autem re<lb></lb>trorſum exiſtentem extremitatem ligneum, torno factum, <lb></lb>atque in medio arctum ſuſcipit Cylindrum. </s>
<s>quippe qui à <lb></lb>quodam arcuato inſtrumento fabrili (quod Græci aridha <lb></lb><expan abbr="vocãt">vocant</expan>) vertatur, atque circa poſterioris partis medium emi<lb></lb>nentiam <expan abbr="quãdam">quandam</expan> habeat, quæ capitis formam referat, <expan abbr="quæ-q́ue">quæ<lb></lb>que</expan> ingrediatur, atque circumuoluatur eò in vaſe (quod <lb></lb>Pyelis, ideſt vrna dicitur, ſiue capitulum quoddam exiſtit) <lb></lb>regula quadam terræ impoſita capitulum ipſum adducente, <lb></lb>atque eum, qui perforatur locum ſemper conſequente. </s>
<s>cir<lb></lb>cumuoluetur autem ad eandem operationem Cylindrus <lb></lb>vnà cum terebra manibus etiam motus, ſi paruas regulas <lb></lb>iuxta medium ſuſceperit fuſi putealis inſtar in crucis <expan abbr="modũ">modum</expan> <lb></lb>traiectas, quas nonnulli ex ipſa figura Aſtericos, nempe ſtel<lb></lb>lulas nuncupant. </s>
<s>Verùm eas, quæ in muro fiunt perforatio<lb></lb>nes, tranſuerſas, ac ſurſum tendentes fieri oportet: tanquam <lb></lb>eas, quæ ad interiorem partem altiores eſſe debent. </s>
<s>cùm vt <lb></lb>ea, quæ ex latere à terebris circumraduntur facilè deorſum <lb></lb>tendentia fiant: tum ut lamina in extremitate uectis affixa <lb></lb>bene ad <expan abbr="operationẽ">operationem</expan> ſuſtentetur, dum à regula terræ tranſ<lb></lb>uerſa impoſita, <expan abbr="ipſiq́ue">ipſique</expan> renitente fulcitur: tum demum ut ea, <lb></lb>quæ à terebris fit ſurſum tendens perforatio non ſolam mu<lb></lb>ri ſubmiſſionem, uerùm etiam declinantem ad extrinſecùs <lb></lb>deorſum lationem faciat, <expan abbr="multaq́ue">multaque</expan> repente circa murum <lb></lb>collapſio fiat. </s>
<s>atque declinationis figura talis eſt. </s></p>
<pb xlink:href="052/01/030.jpg"></pb><figure id="id.052.01.030.1.jpg" xlink:href="052/01/030/1.jpg"></figure><p type="caption">
<s>Pvelis, siue <lb></lb>Capitulum</s></p><p type="main">
<s>Foretur autem exæquali murus in eadem recta linea diſtan<lb></lb>tibus abinuicem foraminibus pede, &amp; quarta pedis parte, <lb></lb>hoc eſt viginti digitis, ſiue dodrante, <expan abbr="duobusq́ue">duobusque</expan> Palmis. </s>
<s><lb></lb>Dodrans enim duodecim, palmus verò quatuor digito<lb></lb>rum eſt. </s>
<s>ipſas autem perforationes nos à tribus ferè pedibus <lb></lb>ſurſum à terra initium ſumentes facere oportet, quemad<lb></lb>modum etiam lapideis in muris iam diximus, vt quæ à fora<lb></lb>minibus deſcendit materia in ommiſſum inferius locum in<lb></lb>cidat. </s></p>
<pb xlink:href="052/01/031.jpg"></pb><p type="main">
<s><emph type="center"></emph>De murorum lateritiorum combuſtione. </s>
<s>Cap. </s>
<s>VIII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>CVm autem ordinatim ipſius muri frontes per<lb></lb>forati fuerint, replentur foramina ab extrinſe<lb></lb>ca facie ad interiores partes non iuxta totam <lb></lb>craſſitiem, ſed iuxta pedem tantùm lignis ſic<lb></lb>cis, ſciſſis, non quadrangulis (quòd ſecundum <lb></lb>latitudinem ſibiinuicem congruant) verùm quaſi rotundis <lb></lb>veluti palis craſſitiem habentibus baſim verſus ad plus <expan abbr="triũ">trium</expan> <lb></lb>digitorum, ad uerticem autem anguſtioribus ad ſuſtentan<lb></lb>dum murum operationis tempore. </s>
<s>&amp; ſi contingit tædæ pali <lb></lb>ſint: ſin minùs, ligna ſicca pice, vel ſulphure trito vnà cum <lb></lb>liquida pice, ſiue oleo peruncta, vbi ignis <expan abbr="penetrãs">penetrans</expan>, <expan abbr="ſurſum-q́ue">ſurſum<lb></lb>que</expan> conuerſus accendatur, <expan abbr="haudq́ue">haudque</expan> à denſitate ſuffocatus <lb></lb>extinguatur. </s>
<s>Cùm autem cuncta foramina repleta fuerint <lb></lb>ad pedem vſque ſecundum profunditatem quemadmodum <lb></lb>dictum eſt, rurſus in eadem recta linea iuxta medium inter<lb></lb>iecta interualla ordinatim exæquali verſus priora forentur: <lb></lb>ipſa verò poſtrema foramina ad vtramque partem obli<lb></lb>quentur, vt ad priora poſteriorum conforatio perueniat. </s>
<s>at<lb></lb>que hæc etiam raſuris, vel fruſtis ligneis, aut ijs, quæ runci<lb></lb>na in leuigatione tabularum abraduntur, ſiccis, ac facilè <expan abbr="cõ-buſtibilibus">con<lb></lb>buſtibilibus</expan> virgultis, ſiue lignorum fragmentis implean<lb></lb>tur: in quibus ignis operans, celerem efficit combuſtionem. </s>
<s><lb></lb>Conſultò itaque pali ſuperficiem æqualem, non habent, ſed <lb></lb>maiores inferiùs ſunt: vt ignem retinere, <expan abbr="ſpiranteq́ue">ſpiranteque</expan> vento <lb></lb>accendi poſſint. </s>
<s>Quòd ſi <expan abbr="vẽtorum">ventorum</expan> tranquillitas in operatio<lb></lb>nis tempore, ſeu loco eſſet: calami introrſum omnino confo<lb></lb>rati commiſceantur (quales ij ſunt, quos ipſi venatores <expan abbr="auiũ">auium</expan> <lb></lb>habere ſolent) quippe qui follibus fabrilibus <expan abbr="ſufflẽtur">ſufflentur</expan>. </s>
<s>nam <lb></lb>ad quemlibet quiſpiam voluerit locum folles ipſi transfe<lb></lb>runtur, <expan abbr="ignemq́ue">ignemque</expan> accendunt, cùm ferreum tubulum ante <lb></lb>ignem habeant. </s>
<s>ac demum figura ſubijcitur. </s></p>
<pb xlink:href="052/01/032.jpg"></pb><figure id="id.052.01.032.1.jpg" xlink:href="052/01/032/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>De Teſtudinibus Arietem geſtantibus. </s>
<s>Cap. </s>
<s>IX.<emph.end type="center"></emph.end></s></p><p type="main">
<s>IPSA perforatione, ſuſtentatione, &amp; combu<lb></lb>ſtione peracta, ſi murus indeclinabilis perman<lb></lb>ſerit, <expan abbr="intrepidusq́ue">intrepidusque</expan> ſteterit: ad craſſum lateri<lb></lb>tij parietis opificium Arietibus oppugnare ne<lb></lb>ceſſe eſt. </s>
<s>licet enim languida, &amp; debilis Arietis <lb></lb>ad laterem percuſſio fiat, fodiens potius propter fungoſita<lb></lb>tem, ac mollitiem: quàm vibrans, &amp; rumpens propter duri<lb></lb>tiem, atque reſiſtentiam vt in lapidibus: attamen cùm per <lb></lb>eam, quæ deorſum facta eſt operationem debilitatus prope <lb></lb>baſim murus ſit, aduerſus continuos Arietum preſſus reſi<lb></lb>ſtere minimè poterit: ſed dum violentia percutitur, perfora<arrow.to.target n="note21"></arrow.to.target><lb></lb>tione declinationem ſuſcipiet. </s>
<s>Veruntamen adaptationes, <lb></lb>&amp; colligationes Arietum, qui ſecundum longitudinem co<arrow.to.target n="note22"></arrow.to.target><lb></lb>aptantur: <expan abbr="necnõ">necnon</expan> eas, quæ circa membra ipſorum, &amp; eas, quæ <lb></lb><arrow.to.target n="note23"></arrow.to.target><lb></lb>in monoxylis iuxta diſtantiam conuenientes, &amp; in Teſtudi<lb></lb>nibus Arietes geſtantibus, ac Turribus, atque duplicatis <lb></lb>ſcalis appenſiones, atque etiam eas, quæ per ipſos Arietes <lb></lb>iuxta murum affabrè factæ ſcalæ nauticæ fiunt: ad congruen<lb></lb>tem deinceps vnicuique operationem in præſenti tractatio<lb></lb>ne ſubtiliter dilucidando expoſuimus. </s>
<s>Si citiùs cum Arieti<lb></lb>bus muros vel portas rumpere, <expan abbr="perfringereq́">perfringereque</expan>; voluerimus: <lb></lb>faciemus Teſtudines Arietes geſtantes, quatuor rotarum, <lb></lb>altas, quæ ſuperiùs catenas, vel funes iuxta craſſitiem robu-<pb xlink:href="052/01/033.jpg"></pb>ſtos arietem ſuſtollentes, ac <expan abbr="ſuſtinẽtes">ſuſtinentes</expan> habeant. </s>
<s>quùm enim <lb></lb>ab altiori loco aries ſuſtentetur, plus retrorſum interualli <lb></lb>ad motum ſuſcipit: &amp; quùm à longè cum impetu feratur, &amp; <lb></lb>incutiatur, maiorem aquirit vim: &amp; offendendo muro oc<lb></lb>currens, violentam, <expan abbr="fortemq́ue">fortemque</expan> perficit percuſſionem. </s>
<s>Sit au<arrow.to.target n="note24"></arrow.to.target><lb></lb>tem iuxta formam alta Teſtudo ipſa, &amp; non admodum ma<lb></lb>gna, vt ad motum deductu facilis ſit: altitudinem latitudi<lb></lb>nis duplam habens, <expan abbr="lõgitudinem">longitudinem</expan> verò altitudini æqualem, <lb></lb>vel parùm ea minorem: vt roſtrum acutum habeat, <expan abbr="oblon-gaq́ue">oblon<lb></lb>gaque</expan> ſit: atque vt ea, quæ in ipſam incidunt pondera cùm <arrow.to.target n="note25"></arrow.to.target><lb></lb>obliquentur, deorſum hinc inde decurrant. </s>
<s>Conſtruitur au<arrow.to.target n="note26"></arrow.to.target><lb></lb>tem hoc modo. </s>
<s>Iuga duo, atque duo ponuntur, quorum <lb></lb>ſingula ſint longitudinis pedum vigintiquatuor, <expan abbr="diſtentq́ue">diſtentque</expan> <lb></lb>ab <expan abbr="inuicẽ">inuicem</expan> pedibus ad minùs duodecim. <expan abbr="atq̨">atque</expan> in ipſis inſerun<lb></lb>tur ligna <expan abbr="digitorũ">digitorum</expan> octo iuxta <expan abbr="craſſitudinẽ">craſſitudinem</expan>, pedalis latitudi<lb></lb>nis, vigintiquatuor ad minùs <expan abbr="pedũ">pedum</expan> iuxta altitudinem, quæ <lb></lb>ſunt octo numero, ſcilicet quatuor, &amp; quatuor in <expan abbr="vtriſq;">vtriſque</expan> la<lb></lb>teralibus partibus aſtantia: annuentia verò ſuperiùs, iuxta <lb></lb>verticem inuicem copulantur: amplectentia lignum, quod <lb></lb>Teſtudinis dorſum eſt, longius ea, quæ circa iuga eſt longi<lb></lb>tudine, &amp; <expan abbr="aliquãtulum">aliquantulum</expan> excedens anteriùs propter eas, quas <lb></lb>progrediendo dicemus cauſas. </s>
<s>iuxta medium autem ligno<lb></lb>rum erectorum aſtantium eius parti ad quam volumus Te<lb></lb>ſtudinem ipſam annuere, alia iuga clauis affigantur: atque <lb></lb>ab interna parte ſuſtentacula ſupponantur, à quibus iuga <lb></lb>interna, <expan abbr="dorſumq́ue">dorſumque</expan> ſuſtineatur, ac fulciatur. </s>
<s>iuxta verò ex<lb></lb>trinſecam ſuperficiem tabulis <expan abbr="digitorũ">digitorum</expan> quatuor ſecundum <lb></lb>craſſitiem ipſa erecta aſtantia ligna muniantur. </s>
<s>atque hoc <lb></lb>modo figura perficitur. </s>
<s>ab ipſo autem internorum iugorum <lb></lb><expan abbr="pauimẽto">pauimento</expan> externa iuga lignis erectis, in decliuibus, ad per<lb></lb>pendiculum exiſtentibus <expan abbr="ſuſtentẽtur"> ſuſtententur</expan> </s>
<s>ipſum verò vacuum, <lb></lb>quod eſt circa inferiora iuga, hoc eſt <expan abbr="interuallù">interuallum</expan> rotas qua<lb></lb>tuor totam, quæ circa Teſtudinem eſt congeriem ſuſtinen<lb></lb>tes, <expan abbr="geſtantesq́ue">geſtantesque</expan> habeat. </s>
<s>ne autem inferiora iuga aperian<lb></lb><arrow.to.target n="note27"></arrow.to.target><lb></lb>tur, quædam ligna tranſuerſa (quæ Græci peritomidas di<lb></lb>cunt) ſuſcipiant, que non ſine ſectione fiunt, ſed ea, quæ cla<lb></lb>uis ſit cheloniorum fixione retinent: inſtar quorundam
<pb xlink:href="052/01/034.jpg"></pb>pugillorum circumſectorum, ac hemiſphęriorum inſculpto<lb></lb>rum ſimilium iis, qui in portarum cardinibus ponuntur. </s>
<s><lb></lb>quæ quidem ligna ipſius acutum habentis dorſum Te<lb></lb>ſtudinis baſes erunt. </s>
<s>Fit autem quandoque obtuſius, ac de<lb></lb>preſſius Teſtudinis tectum, quippe cùm in ſemiaſtantibus <lb></lb>partibus lignorum ſuper iuga erectorum conſiſtentium ſu<arrow.to.target n="note28"></arrow.to.target><lb></lb>periùs adiecta fuerint ea ligna, quæ græcè ſyngiptæ, hoc eſt <lb></lb>ſimul incuruantia vocantur: <expan abbr="ſupremumq́ue">ſupremumque</expan> pinnaculi dor<lb></lb>ſum comprehenderint: quando videlicet aries longiſſimus <lb></lb>fuerit, <expan abbr="Teſtudoq́ue">Teſtudoque</expan> à muro longè diſtiterit. </s>
<s>nam ſi fortaſſe <lb></lb>minor iuxta longitudinem Aries, <expan abbr="Teſtudoq́ue">Teſtudoque</expan> propè mu<lb></lb>rum ſit: aduerſum ea, quæ præcipitantur, in <expan abbr="ipſamq́ue">ipſamque</expan> inci<lb></lb>dunt pondera reſiſtere nequaquam poterit, propter ipſius <lb></lb>tecti depreſſionem. </s>
<s>ſed cùm ruptionem, ſeu fractionem in <lb></lb>coniunctionum commiſſuris ſuſceperit: periculoſa tum ſi<lb></lb>biipſi, <expan abbr="tũ">tum</expan> ariete oppugnantibus fiet. </s>
<s>Dorſum verò à iam di<arrow.to.target n="note29"></arrow.to.target><lb></lb>ctis erectis monoxylis ſupernè comprehenſum, anteriùs in <lb></lb>muri faciem præponere oportet. </s>
<s>vt in ipſo fulcimentum ſit, <lb></lb>&amp; ea, quæ aduerſus arietem mittuntur recipiat. </s>
<s>ſi enim ma<lb></lb>ximi lapides, qui à muro deorſum feruntur: &amp; tranſuerſa li<lb></lb>gna, quæ ex æquali æqueponderando, &amp; æquilibrando de<lb></lb>ſcendunt, detectum fortè arietem inuenerint, qui aduerſus <lb></lb>murum cum impetu fertur: aut aries ipſe deorſum <expan abbr="annuẽs">annuens</expan>, <lb></lb>diſrumpetur: aut eum mouentes abiiciet, atque interimet. </s>
<s><lb></lb>Talis quidem eſt anterior Teſtudo, quæ etiam arietis ſu<lb></lb>ſtentacula ſecundum diſtantiam habet: ſecunda verò de<lb></lb>preſſior quoad altitudinem, &amp; minor: atque aliæ duæ re<lb></lb>trorſum adhuc minores. </s>
<s>ad ipſius enim aditus tutelam ne<lb></lb>ceſſariæ ſunt. </s>
<s>Plures autem &amp; minores ipſas (queadmodum <lb></lb>iam diximus) eſſe decet, vt abſque labore adducantur, ex <lb></lb><expan abbr="paruisq́ue">paruisque</expan> lignis componantur: non autem unam maxi<lb></lb>mam, eò quòd ex magnis, <expan abbr="inuentuq́ue">inuentuque</expan> difficilibus lignis <lb></lb>fiat: necnon tardè, <expan abbr="magnoq́ue">magnoque</expan> cum labore deducatur. </s>
<s>Ve<lb></lb>rùm ordinatim ipſæ figuræ ſubiiciuntur. </s></p>
<pb xlink:href="052/01/035.jpg"></pb><p type="margin">
<s><margin.target id="note21"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note22"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note23"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note24"></margin.target><emph type="italics"></emph>Teſtudi<lb></lb>nis Arie<lb></lb><expan abbr="tẽ">tem</expan> geſtan<lb></lb>tis deſcri<lb></lb>ptio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note25"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note26"></margin.target><emph type="italics"></emph>Eiuſdem <lb></lb>conſtru<lb></lb>ctio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note27"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note28"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note29"></margin.target>g</s></p><figure id="id.052.01.035.1.jpg" xlink:href="052/01/035/1.jpg"></figure>
<pb xlink:href="052/01/036.jpg"></pb><p type="main">
<s>Sciendum autem eſt, quòd cùm Aries ab anteriori, <expan abbr="maioriq́ue">maiorique</expan> <lb></lb>Testudine ſuſtentetur: magis in muri faciem eleuatur, re<lb></lb>trorſum verò deprimitur. </s>
<s>atque id non abrefactum eſt. </s>
<s>cùm <lb></lb>etenim ſurſum tendens moueatur, fortiſſimam ad ſuperio<lb></lb>res murorum partes: deorſum verò ſe inclinans, imbecilli<lb></lb>mam, &amp; languidam, quandoque autem fallacem quoque <lb></lb>percuſſionem ipſam efficit. </s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>QVoniam nonnulla in hoc capite obſcura mihi videntur, ea <lb></lb>dilucidanda, declaranda〈qué〉 eſſe cenſeo, vt ab omnibus faci<lb></lb>lè percipi poßint. </s>
<s>Cùm itaque præſens caput cum ſuperio<lb></lb>ribus Autor continuaſſet, dixiſſet〈qué〉 quòd murorum perforatione, <lb></lb>ſuſtentatione, &amp; combuſtione peractis de quibus ſuperiùs pertra<lb></lb>ctauit: ſi murus adhuc indeclinabilis permanſerit, intrepidus〈qué〉 <lb></lb>ſteterit: arietibus ipſis ad partes craßiores parietis oppugnan<lb></lb>dum eſt: quoniam in hoc capite non declarat omnia ea, quæ ad <lb></lb>Arietem ipſam ſpectant: idcirco ait ſe in ſequentibus huius tra<lb></lb>ctationis partibus ea ſubtiliter dilucidando expoſuiſſe. </s>
<s>Verùm ea, <lb></lb><arrow.to.target n="note30"></arrow.to.target><lb></lb>quæ ad Arietem pertinent hæc ſunt. </s>
<s>nempe adaptationes, &amp; colli<lb></lb>gationes Arietum: necnon earum appenſiones. </s>
<s>quæ ſcilicet appen<lb></lb>ſione; variæ ſunt ſecundum varios neceßitatis vſus. </s>
<s>quandoque <lb></lb>enim Arietes ipſi circa ſua membra appenduntur, aliquando in <lb></lb>Monoxylis, aliàs in Teſtudinibus, interdum alijs in machinis, quæ <lb></lb>turres vocantur, nonnunquam in duplicatis ſcalis, de quibus om<lb></lb>nibus appenſionibus: necnon de nauticis ſcalis, quæ per ipſos Arie<lb></lb>tes ad aſcendendum murum fiunt, in ſequentibus ordinatim iux<lb></lb>ta conuenientem unicuique vſum, &amp; operationem pertractaturus <lb></lb><arrow.to.target n="note31"></arrow.to.target><lb></lb>eſt. </s>
<s>Membra autem Arietis hìc intelligenda ſunt ea ligna, in qui<lb></lb>bus Aries appenditur, quæ tamquam eius crura ſunt, vt in ſequen<lb></lb>tis capitis figura nobis manifeſtum erit.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note32"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note30"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note31"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note32"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quid verò ſibi velit Autor verbo illo Monoxylis declarandum <lb></lb>eſt, quoniam diuerſimodè vocabulum hoc ab Autore in præſenti ca<lb></lb>pite accipitur. </s>
<s>Quare ſciendum eſt, quòd propriè Monoxyla ſunt <lb></lb>nauigia, ſiue lyntres ex vnico ligno excauatæ, quibus Aegyptij per<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/037.jpg"></pb><emph type="italics"></emph>ſtagna, &amp; Nili innundationes vtebantur, Autore Strabone lib. </s>
<s>3. <lb></lb>&amp; Plinio lib. </s>
<s>6. cap. </s>
<s>23. &amp; quoniam inferiùs de quibuſdam naui<lb></lb>gijs Arietes geſtantibus, quibus maritimæ ciuitates expugnaban<lb></lb>tur, ſermonem habiturus est: propterea de illis Monoxylis hìc in<lb></lb>telligit, cùm ait ſe in præſenti tractatione eas Arietum appenſio<lb></lb>nes, quæ in Monoxylis iuxta diſtantiam (ſcilicet tum ipſorum in<lb></lb>ter ſe nauigiorum, tum lignorum in ipſis nauigijs Arietem ſuſti<lb></lb>nentium) conuenientes fiunt, ſubtiliter dilucidando expoſuiſſe. </s>
<s><lb></lb>paulo inferiùs autem in alia quoque ſignificatione dictionem hanc <lb></lb>ab Autore acceptam reperiemus, vt mox ſuo loco declarabimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note33"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note33"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Iuga hìc intelligenda ſunt ligna duo inſtar iugi bouini coniun<lb></lb>cta, quæ vnà cum alijs duobus eodem modo coniunctis baſim Te<lb></lb>ſtudinis conſtituunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note34"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note34"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Peritomidæ ſunt ea ligna tranſuerſa, à quibus iuga ipſa reti<lb></lb>nentur ne aperiantur, ſed eandem ſemper adinuicem diſtantiam <lb></lb>obtineant. </s>
<s>quæ porrò ligna ait eſſe diſſecanda inſtar quorumdam <lb></lb>pugillorum iuga ipſa apprehendentium, ſcilicet in anterioribus, <lb></lb>extremis〈qué〉 ipſorum tranſuerſorum lignorum partibus: in eorum<lb></lb>dem verò lateralibus faciebus, instar cheloniorum conſimilium <lb></lb>ijs, in quibus portarum cardines euoluuntur. </s>
<s>quemadmodum in <lb></lb>huiuſce capitis figuris perſpicere licet, quas nos exquiſitè deſigna<lb></lb>ri curauimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note35"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note35"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Syngyptæ ſunt ligna curua, cuiuſmodi ſunt ea, ex quibus <expan abbr="nauiũ">nauium</expan> <lb></lb>carina conſtruitur. </s>
<s>ex huiuſmodi autem lignis conſtruitur etiam <lb></lb>dorſum Teſtudinum cùm depreßiores eas facere volumus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note36"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note36"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Monoxyla hìc intelligenda ſunt ea ſuſtentacula, quæ ſuperiùs <lb></lb>adſecunda iuga poni dixit. </s>
<s>Hæc itaque in præſenti capite decla<lb></lb>ratione quadam indigere nobis viſa ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>De quibuſdam, quæ in omnibus Teſtudinibus obſeruan<lb></lb>da ſunt. </s>
<s>Cap. </s>
<s>X.<emph.end type="center"></emph.end></s></p><p type="main">
<s>IN omnibus <expan abbr="aũt">aut</expan> Teſtudinibus claui <expan abbr="latũ">latum</expan> caput <lb></lb><expan abbr="habẽtes">habentes</expan> (<expan abbr="quẽadmodũ">quemadmodum</expan> <expan abbr="iã">iam</expan> <expan abbr="dictũ">dictum</expan> eſt) ad tecti late<lb></lb>ra, <expan abbr="partesq́">partesque</expan>; <expan abbr="deorsũ">deorsum</expan> <expan abbr="tẽdẽtes">tendentes</expan>, <expan abbr="vſq;">vſque</expan> ad <expan abbr="eorũ">eorum</expan> <expan abbr="dimi-diũ">dimi<lb></lb>dium</expan> ſuper <expan abbr="infigãtur">infigantur</expan>: ea verò <expan abbr="clauorũ">clauorum</expan> pars, quæ <lb></lb>in medio erecta interiacet, creta opima, &amp; glu<pb xlink:href="052/01/038.jpg"></pb>tinoſa, cum pilis ſubacta, atque indiuiſa conſeruata replea<lb></lb>tur. </s>
<s>ad ipſas autem rotas Teſtudinem ſuſtinentes in inferio<lb></lb>ra iuga cuneos, permagnos ex vtriſque partibus exceden<lb></lb>tes ſupponere oportet, vt altitudinis magnitudinem ſuſti<lb></lb>neant. </s>
<s>Soli enim rotarum claui, &amp; præſertim quoniam, per <lb></lb>ſingula iuga inſtar axium pertranſientes, breues ſunt: Te<lb></lb>ſtudinem ſuſtinere <expan abbr="nõ">non</expan> poterunt: neque tutè ipſam ſtantem <lb></lb>habebimus ad eam, quę fieri debet Arietis motionem. </s>
<s>Sup<lb></lb>ponuntur autem inferiùs cunei non ſolùm, vt altitudinis <lb></lb>pondus ſuſtineant, verumetiam vt inſtabilem rotarum mo<lb></lb>tionem impediant. </s>
<s>cùm autem Teſtitudinem mouere vo<lb></lb>luerimus, cuneos ſubtus poſitos ſublaxabimus. </s>
<s>At ſcien<lb></lb>dum eſt, quòd lapidei muri citiùs quàm lateritij incutiun<lb></lb>tur, atque rumpuntur. </s>
<s>nam propter fungoſitatem, ac moli<lb></lb>tiem ipſius lateris ea, quæ ab Ariete fit percuſſio, debilis, &amp; <lb></lb>languida eſt, excauans potius, ac fodiens laterem, quàm <lb></lb>rumpens, atque perfringens. </s>
<s>lapis verò aduerſus ferri du<lb></lb>ritiem reſiſtens, vehementem percuſſionem ſuſcipit, atque <lb></lb>ita concutitur. </s></p><p type="main">
<s><emph type="center"></emph>De Ariete, &amp; Arietaria Machina ſecundùm Byzantium <lb></lb>principem. </s>
<s>Cap. </s>
<s>XI.<emph.end type="center"></emph.end></s></p><p type="main">
<s>VErùm principis Byzantij familiares Arietem <lb></lb>cubitorum centum &amp; viginti iuxta longitudi<lb></lb>nem faciebant. </s>
<s>ab ipſius autem calce iuxta <lb></lb>craſſitiem quidem, pedalem: in latitudinem <lb></lb>verò, palmorum quinque: in anteriori autem <lb></lb>parte coarctabant ipſum in pedalem latitudinem, &amp; trium </s></p><p type="main">
<s><arrow.to.target n="note37"></arrow.to.target><lb></lb>palmorum craſſitiem: Helicas ferreas quatuor, quæ ſe ſe in <lb></lb>longitudinem vſque ad decem cubitos extendant, in ante<lb></lb>riori parte clauis affigentes: <expan abbr="totumq́ue">totumque</expan> Arietem tribus fu<lb></lb>nibus octo iuxta craſſitudinem circumquaque digitorum <lb></lb>exiſtentibus ſuccingentes: ac loris eum circulariter ligan<lb></lb>tes, iuxta medium tribus quidem interuallis, quatuor verò <lb></lb>ſuſtentaculis conſtringebant. </s><s>funes verò, qui ab aliis cana<lb></lb>binis funibus ab Arietaria Machina pendentibus Arietem
<pb xlink:href="052/01/039.jpg"></pb>ipſum ſuſtinent, atque inferunt: à ferreis contextis catenis <lb></lb>initia ſumebant. </s>
<s>At ſcalam etiam nauticam faciebant aſſe<lb></lb>re in Arietis elatione anteriùs clauis affixo, <expan abbr="habenteq́ue">habenteque</expan> re<lb></lb>te contextum iuxta craſſitiem ſufficiens, &amp; iuxta diſtantiam <lb></lb>quatuor, vel etiam plurium digitorum foramina habens, vt <lb></lb>facilè ſupra murum aſcendatur. </s>
<s><expan abbr="appendebãt">appendebant</expan> autem ipſum, <lb></lb>&amp; mouebant in Teſtudine rotis octo prædita. </s>
<s>quippe quæ <lb></lb>iuxta quidem infernam pauimenti longitudinem, quadra<lb></lb>gintaduo: iuxta verò latitudinem, vigintiocto cubitos ha<arrow.to.target n="note38"></arrow.to.target><lb></lb>beat. </s>
<s>ipſa præterea quatuor crura, quæ in pauimento ad al<lb></lb>titudinem iuxta angulos affiguntur, ex duobus ſimul iun<lb></lb>ctis lignis ſingula faciebant, longitudinem habentia ſingu<lb></lb>la cubitorum vigintiquatuor, &amp; craſſitiem palmorum quin<lb></lb>que: iuxta verò latitudinem vnius cubiti exiſtentia. </s>
<s>In ſu<arrow.to.target n="note39"></arrow.to.target><lb></lb>periori autem Arietariæ Machinæ parte Thoracium tan<lb></lb>quam ſepimentum ſtruebant, vt in eo tutè ſtare poſſent ſpe<lb></lb>ctantes ea, quę aduerſus Arietem ab aduerſarijs mittuntur. <arrow.to.target n="note40"></arrow.to.target><lb></lb>Huiuſcemodi autem Arietem ſexies mouebant deſtruen<lb></lb>tes à ſeptuaginta cubitis altitudinis, <expan abbr="rurſusq́ue">rurſusque</expan> ad latera ad <lb></lb>ſeptuaginta cubitos peruertentes. </s>
<s>à centum autem viris <lb></lb>allatus mouebatur. </s>
<s>totum verò, quod mouebatur pondus <lb></lb>talentorum ferè quadrigentorum erat. </s>
<s>ac demum figura <lb></lb>ſubijcitur. </s></p>
<pb xlink:href="052/01/040.jpg"></pb><p type="margin">
<s><margin.target id="note37"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note38"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note39"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note40"></margin.target>d</s></p><figure id="id.052.01.040.1.jpg" xlink:href="052/01/040/1.jpg"></figure>
<pb xlink:href="052/01/041.jpg"></pb><p type="main">
<s>Sciendum autem eſt <expan abbr="q̨">quod</expan> Arietum alij quidem à virorum <lb></lb>multitudine reguntur, iuxta quorundam antiquorum me<lb></lb>chanicorum opinionem: alij verò à contranitentibus lignis <lb></lb>diſtenduntur: <expan abbr="alijq́">alijque</expan> demum ſuper cylindros propelluntur: <lb></lb>poſſunt autem quandoque etiam funibus circumuolutis <lb></lb>adductionem, &amp; reuerſionem facientes, percuſſionem effi<lb></lb>cere. </s>
<s>verùm ad artificem ſpectat iuxta magnitudines Arie<lb></lb>tum decentem quoque operationis vſum, ac motionem ex<lb></lb>cogitare. </s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note41"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note41"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>HElicas hìc intelligit mucrones illos, quos debet habere fer<lb></lb>rum in extremitate Arietis affixum tanquam eius ca<lb></lb>put, quod ſit cornibus præditum: quibus murus ipſe rum<lb></lb>pitur. </s>
<s>Helicas autem ipſos vocauit ad ſimilitudinem pampino<lb></lb>rum vitis, qui à Græcis Helices nuncupantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note42"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note42"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Crura Arietis hìc appellat ea ligna, quæ ſuperius membra vo<lb></lb>cauit, quæ in figura huius capitis manifeſta ſunt, quemadmo<lb></lb>dum in ſuperiori capite adnotauimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note43"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note43"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Thoracium propriè eſt ſumitas mali nauis, vbi ſpectatores <lb></lb>ſtant<emph.end type="italics"></emph.end> <foreign lang="grc">ἀπὸ τοῡ θεωρε̄ιν</foreign> <emph type="italics"></emph>quaſi<emph.end type="italics"></emph.end> <foreign lang="grc">θεωράκιον</foreign>: <emph type="italics"></emph>ſeu vas quoddam è lignis <lb></lb>conſtructum, &amp; ſumitati mali nauis affixum, in quo ſpectatores <lb></lb>ipſi commodè, tute〈qué〉 stare poßint. </s>
<s>ad eius autem ſimilitudinem hìc <lb></lb>thoracium appellat paruam illam machinullam, quam in altiori <lb></lb>parte Arietariæ machinæ conſtruebant, vt in ea ſpectatores ſine <lb></lb>offenſione ſtantes cernerent ea, quæ ab aduerſarijs ad perfringen<lb></lb>dum Arietem demittuntur: darent〈qué〉 ſignum ijs, qui <expan abbr="Arietẽ">Arietem</expan> mo<lb></lb>uent, ne tunc ipſum propellant, ſed retro trahant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note44"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note44"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Sexies hìc intellige ſex motibus iuxta ſex recti motus inter<lb></lb>ualla factis. </s>
<s>nam arietem ipſum regentes, ſex motibus eum mo<lb></lb>uebant, ſcilicet antè, retro, dextrorſum; ſiniſtrorſum, ſurſum, at<lb></lb>que deorſum: ne ſemper eodem in loco murus incaſſum percute<lb></lb>retur, ſed diuerſis in locis percuſſus citius deſtrueretur. </s>
<s>quem<lb></lb>admodum declarat Athenæus in primo libro ſuæ de rebus bellicis <lb></lb>tractationis.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/042.jpg"></pb><p type="main">
<s><emph type="center"></emph>De conſtructione ſcalarum, quæ ſpectatores vocantur. </s>
<s><lb></lb>Cap. </s>
<s>XII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>SI murorum craſſitiem agnoſcere, &amp; aduerſo<lb></lb>rum operationes, ac multitudinem ex aduer<lb></lb>ſo perſpicere: necnon eas, quæ intra murum <lb></lb>circa ciuitatem tum diurnę, tum nocturnę <expan abbr="fiũt">fiunt</expan> <lb></lb>actiones, <expan abbr="inſidiarumq́ue">inſidiarumque</expan> ſtructiones obſerua<lb></lb>re voluerimus: ſpectatorem huiuſcemodi conſtruemus. </s>
<s><lb></lb>Duo ligna quadrangula parte altera latiora ſuſcipientes, <lb></lb>latitudinem habentia <expan abbr="vnumquodq;">vnumquodque</expan> duodecim digitorum, <lb></lb>craſſitudinem verò vnumquodque octo, erecta conſtitue<lb></lb>mus. </s>
<s>quorum alterum quidem ſit inter duo ad verticem ia<lb></lb>centia, itidem iuxta craſſitiem parte altera latiora ipſa quo<lb></lb>que exiſtentia, abinuicem verò diſtantia quantum iuxta la<lb></lb>titudinem ipſum erectum lignum diſtare poteſt. </s>
<s>Similiter <lb></lb>autem alterum quoque ad alia duo cùm æqualia, tum ſimi<arrow.to.target n="note45"></arrow.to.target><lb></lb>lia, <expan abbr="ſimiliterq́ue">ſimiliterque</expan> iacentia ponatur. </s>
<s>ex aduerſo autem duo<lb></lb>rum duplorum lignorum iuxta medium aliud lignum ter<lb></lb>ram verſus ponatur, quippè quod ipſis duplis iacentibus <lb></lb>opponatur, <expan abbr="atq;">atque</expan> coniungatur iuxta duo erecta conſiſtentia. <lb></lb><arrow.to.target n="note46"></arrow.to.target><lb></lb>ac <expan abbr="demũ">demum</expan> baſis ipſa configuretur inſtar græcæ litteræ H ſolu<lb></lb>tæ habentis latera duplicibus lineis conſtantia. </s>
<s>ab extremis <lb></lb>vero duorum duplorum iacentium quatuor aſſiſtere facie<lb></lb>mus ligna, quorum vtique bina <expan abbr="vnicuiq;">vnicuique</expan> ſurſum reſiſtant, <lb></lb><expan abbr="ipſaq́ue">ipſaque</expan> erecta conſiſtentia ſuffulciant. </s>
<s>hæc autem erecta <lb></lb>ſuſcipiant iuxta medium alia duo ligna, quorum vnum<lb></lb>quodque ſit latitudinis digitorum octo: iuxta verò craſſi<lb></lb>tiem vnumquodque ſex: <expan abbr="diſtentq́ue">diſtentque</expan> abinuicem ad minus <lb></lb>tribus pedibus. </s>
<s>hæcautem quatuor indirectum adinuicem <lb></lb>forentur, <expan abbr="clauisq́ue">clauisque</expan> ſimul transfigantur: erecta quidem, <lb></lb>iuxta duas tertias eorum partes ſurſum: interpoſita verò <lb></lb>iuxta ſextam eorum partem deorſum. </s>
<s>deſcendant autem <lb></lb>ab erectis, <expan abbr="rurſusq́">rurſusque</expan>; aſcendant dum à clauo  volubiliter fe<lb></lb>runtur. </s>
<s>Rurſus autem hæc quoque iuxta duas eorum ter<lb></lb>tias partes, necnon iuxta reliquam ſextam partem à clauo <lb></lb>forentur. </s>
<s>Verùm in præſentia duas tertias, totius longitu-<pb xlink:href="052/01/043.jpg"></pb>dinis intellige, ſpatium illud, quod eſt iuxta duas ſextas par<lb></lb>tes, quippe quæ <expan abbr="tertiã">tertiam</expan> totius longitudinis partem efficiunt. </s>
<s><lb></lb>Hæc <expan abbr="itaq;">itaque</expan> deſcendentia ligna iuxta medium ſcalam leuem <lb></lb>clauis transfixam ſuſcipiant, cuius vtique claui ad iam di<lb></lb>cta foramina ſint affixi. </s>
<s>At crura ſcalam ipſam conſtituen<lb></lb>tia ſint quoad latitudinem digitorum ad minus ſex: quo ve<lb></lb>rò ad craſſitudinem, quatuor. </s>
<s>Ab inferiori autem clauo, <lb></lb>qui per ligna erecta ſtantia tranſit, ad eleuatam ſurſum ſex<lb></lb>tam <expan abbr="deſcendẽtium">deſcendentium</expan> lignorum partem capiſtrum apponatur <lb></lb>baſem quandam, vel funium connexionem comprehen<lb></lb>dens, vel ad annulos ferreos propter attractionem pene<lb></lb>trans. </s>
<s>Lignum autem eſt circumflexum, ac flexile longitu<lb></lb>dinis circiter octo pedum, vt ſufficienter attrahere, <expan abbr="defer-req́ue">defer<lb></lb>reque</expan> per medium erectorum lignorum eleuatum ſurſum <lb></lb>ſextam partem: totam verò inclinatam partem vnà cum ip<lb></lb>ſa ſcala ſublimem in altitudinem eleuare poſſit. </s>
<s>Eueniet <lb></lb><expan abbr="itaq;">itaque</expan> vt dum hæc pars à capiſtro ad inferiora trahitur, à reli<lb></lb>qua parte explorator in altitudinem miruminmodum eri<lb></lb>gatur, <expan abbr="ſcalaq́ue">ſcalaque</expan> erecta permaneat, eò quòd duobus clauis <lb></lb>connexa fuit. </s>
<s>Verùm oportet inferiorem partem, quæ à <lb></lb>capiſtro retinetur ſi fieri poteſt in ſtabilitate permanere. </s>
<s>ſin <lb></lb>minùs: à tranſuerſalibus <expan abbr="penetrãtibuslignis">penetrantibus lignis</expan>, aut verticulis <lb></lb>iuxta iuncturas clauſam in ipſo ſtabilitatis tempore intre<lb></lb>pidam ſtare. </s>
<s>Præterea ſciendum eſt, quòd ſupereminens <lb></lb>tertia erectorum lignorum pars ad eorum, quæ inclinantur <lb></lb>ſecuritatem erigitur: ſuperior autem ſexta eorum, quæ in<lb></lb><arrow.to.target n="note47"></arrow.to.target><lb></lb>clinantur, ſiue quarta interiecti inter ipſa ſpatij pars (vt ſu<lb></lb>perius manifeſtum fuit) ad ſuſtentandam leuem ſcalam du<lb></lb>pliciter ſurſum clauis transfixam: infima verò ſexta eorum <lb></lb>pars propter capiſtri ad ipſam impetum in ea, quæ fit vehe<lb></lb>mentia, deorſum trahet. </s>
<s>ſimul autem ipſa quoque reliquæ <lb></lb><arrow.to.target n="note48"></arrow.to.target><lb></lb>quintuplæ partis, <expan abbr="ſcalæq́ue">ſcalæque</expan> ſurſum latio deprehenſa eſt. </s>
<s>Sit <lb></lb>autem ex ſuppoſitione altitudo erectorum ſtantium ligno<lb></lb>rum, vſque ad duas eorum tertias partes, quanta eſt altitu<lb></lb><arrow.to.target n="note49"></arrow.to.target><lb></lb>do tertiæ muri partis. </s>
<s>&amp; ab ipſo loco, vſque ad duas tertias <lb></lb>eorum, quæ inclinantur lignorum partes, ſiue ad primum <lb></lb>coniunctionis ſcalæ clauum, quantum eſt muri dimidium:
<pb xlink:href="052/01/044.jpg"></pb>necnon ſcala ipſa, quantum idem dimidium. </s>
<s>Quæ igitur <lb></lb>ex hiſce tribus componitur altitudo, tertia parte ſuper mu<lb></lb>rum exploratorem ſuſtollet. atq; hoc perſpicuum eſt. </s>
<s>Cùm <lb></lb>enim altitudo muri palmorum, vel pedum, vel cubitorum, <lb></lb>vel quarundam aliarum menſurarum ſexaginta ſuppoſita <lb></lb>ſit: ligna, quæ ad baſim erecta ſtant ſingula menſurarum tri<lb></lb>ginta ſint: ad altitudinem autem viginti menſurarum, cla<lb></lb>uum ſuſcipiant. </s>
<s>duæ ſiquidem tertiæ partes viginti menſu<lb></lb>ræ triginta menſurarum ſunt. </s>
<s>at ligna, quæ ab erectis de<lb></lb>ſcendunt lignis, ſingula quadraginta <expan abbr="quinq;">quinque</expan> menſurarum <lb></lb>quoad longitudinem fiant, à iam dicto verò clauo ad pri<lb></lb>mam ſcalæ coniunctionem triginta <expan abbr="mẽſuræ">menſuræ</expan> intercipiantur. </s>
<s><lb></lb>hæ autem, duæ tertiæ ipſarum quadragintaquinque ſunt, <lb></lb><arrow.to.target n="note50"></arrow.to.target><lb></lb>quemadmodum ſuperius iam oſtenſum eſt. </s>
<s>ſit autem ipſa <lb></lb>quoque ſcala ab ea coniunctione ad reliquàm eius altitudi<lb></lb>nem aliarum triginta menſurarum. </s>
<s>Quæ igitur ex hiſce tri<lb></lb>bus altitudinibus iuxta numerum colligitur altitudo men<lb></lb>ſuras octoginta complet. </s>
<s>hæ autem, ipſas ſexaginta tertia <lb></lb>parte ſuperant. </s>
<s>tertia namque pars viginti menſuræ ſexa<lb></lb>ginta menſurarum ſunt. </s>
<s>Verùm in ſuprema ſcalæ parte te<lb></lb>gumentum quoque fiat ex corio craſſo, atque robuſto, in<lb></lb>ſtar clypei circumflexi: aut dorſum acutum circa medium <lb></lb>habens, <expan abbr="necnõ">necnon</expan> declinationem ad latera ſufficientem ad ex<lb></lb>ploratorem à ſagitta, ſeu funda præſeruandum. </s>
<s><expan abbr="Nõ">non</expan> parum <lb></lb>autem auxilium præſtabunt etiam funes ſubtiles, robuſti, <lb></lb>ſuperioris leuis ſcalæ cruribus circumalligati, &amp; ad clauo<lb></lb>rum vſque coniunctionem extenſi. </s>
<s>ne altitudinis porrectio, <lb></lb>vel contingens lapides iacientis percuſſio fractionem, con<lb></lb>uulſionemùe in lignis efficiat, <expan abbr="exploratoremq́ue">exploratoremque</expan> perimat. </s>
<s><lb></lb>Ad ipſius autem ſpectatoris erectam, atque indecliuem ſta<lb></lb>bilitatem maximè conferunt etiam quatuor funes erecto<lb></lb>rum ſtantium lignorum extremis alligati, atque extenſi: ſi <lb></lb>è contrariò ſibi inuicem ferreis, aut ligneis palis terræ pro<lb></lb>cul affixis alligati fuerint. </s>
<s>ne opus propter altitudinem in <lb></lb>extremis ponderoſum exiſtens corruat. </s>
<s>atque figuræ tum <lb></lb>iacens, tum erecta ſubiectæ ſunt. </s></p>
<pb xlink:href="052/01/045.jpg"></pb><p type="margin">
<s><margin.target id="note45"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note46"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note47"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note48"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note49"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note50"></margin.target>f</s></p><figure id="id.052.01.045.1.jpg" xlink:href="052/01/045/1.jpg"></figure><p type="main">
<s>Fit autem ſimpliciter eiuſdem ſpectatoris baſis ex tribus <lb></lb>ſolis lignis iuxta latitudinem terra poſitis, duobus quidem <lb></lb><expan abbr="trãſuerſalibus">tranſuerſalibus</expan> abinuicem diſtantibus, &amp; alio iuxta medium <lb></lb>è <expan abbr="cõtrariò">contrariò</expan> coaptato, quemadmodum græca littera H ſoluta <lb></lb>ex duplicibus lineis configurata. </s>
<s>at ſuper ipſis tranſuerſis à <lb></lb><arrow.to.target n="note51"></arrow.to.target><lb></lb>quadam lingula iuxta medium erecta ligna conſtituuntur: <lb></lb>ab extremis verò, quatuor illa, quæ ipſis reſiſtunt. </s></p>
<pb xlink:href="052/01/046.jpg"></pb><p type="margin">
<s><margin.target id="note51"></margin.target>g</s></p><figure id="id.052.01.046.1.jpg" xlink:href="052/01/046/1.jpg"></figure><p type="main">
<s>Fit <expan abbr="etiã">etiam</expan> aliter ex tribus lignis in terra iacentibus, à ſe <expan abbr="inuicẽ">inui<lb></lb>cem</expan> autem <expan abbr="parũ">parum</expan> diſtantibus quatenus iuxta latitudinem ere<lb></lb>cta ligna ſuſcipere poſſint. </s>
<s>hiſce autem iacentibus ſupernè <lb></lb>reſectis: atque alio tum æquali, tum ſimili, tum etiam ſimi<lb></lb>liter infernè reſecto ipſis erecta iuxta latitudinem infigun<lb></lb>tur: ab extremis autem iacentium reſiſtentia duo ad latitu<lb></lb>dines erectorum: ac demum duo ab obliquo ad craſſitudi<lb></lb><arrow.to.target n="note52"></arrow.to.target><lb></lb>nes obliquè. </s>
<s>Verùm neutra iſtarum tuttiſſima eſt quemad<lb></lb>modum ea, quæ priùs enarrata fuit. </s>
<s>Interuallum verò, quo <lb></lb>ligna cùm tranſuerſalia poſita, tum erecta à ſe inuicem di<lb></lb>ſtant artifex determinabit, ad altitudinis compoſitionem <lb></lb><expan abbr="commenſurationemq́">commenſurationemque</expan>; reſpiciens. </s>
<s>ſimiliter autem magnitu<lb></lb>dines etiam lignorum tum baſis, tum altitudinis ad tria in<lb></lb><arrow.to.target n="note53"></arrow.to.target><lb></lb>terualla ſecundum proportionem augebit, <expan abbr="atq;">atque</expan> imminuet. </s></p><p type="margin">
<s><margin.target id="note52"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note53"></margin.target>i</s></p><figure id="id.052.01.046.2.jpg" xlink:href="052/01/046/2.jpg"></figure>
<pb xlink:href="052/01/047.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>COnſtructio baſis ſcalæ prioris, quam Autor in principio <lb></lb>præſentis capitis tradidit primùm à figura, quæ in vetere <lb></lb>exemplari erat, hoc diſcrepat: quòd ſcilicet <expan abbr="vnumquodq;">vnumquodque</expan> <lb></lb>duorum erectè stantium lignorum inter alia duo ligna in terra <lb></lb>aduerticem, ideſt ſe ſe interſecando iacentia docet Autor eſſe po<lb></lb>nendum: in figura verò, eorum vtrumque in altero iam dictorum <lb></lb>duorum in terra proſtratorum lignorum infixum eſt. </s>
<s>Deinde mu<lb></lb>tila, atque imperfecta eiuſdem primæ baſis conſtructio apud Au<lb></lb>torem eſſe mihi videtur. </s>
<s>Cùm enim vſque ad illa verba [ſimili<lb></lb>ter〈qué〉 iacentia ponatur.] nondum totam ipſam primam baſim con<lb></lb>ſtruxerit: ad conſtructionem baſis ſecundæ figuræ tranſire vide<lb></lb>tur illis verbis [ex aduerſo autem duorum duplorum] id enim, <lb></lb>quod his verbis præcipit in primæ figuræ baſi nequaquam fieri <lb></lb>poteſt, cùm duo in terra iacentia ligna ſe ſe interſecent, vt cuili<lb></lb>bet manifeſtum eſt. </s>
<s>Aut itaque poſt illa verba [ſimiliter〈qué〉 iacen<lb></lb>tia ponatur.] nonnulla deſiderantur, quibus conſtructio, quæ vi<lb></lb>detur eſſe ipſius baſis ſecundæ figuræ, continuetur, fiat〈qué〉 vna &amp; <lb></lb>eadem cum ſuperiori baſis primæ figuræ conſtructione, quod fieri <lb></lb>nequit (vt iam diximus) propter duorum in terra proſtratorum <lb></lb>lignorum mutuam interſectionem: aut quædam eodem in loco de<lb></lb>ſunt, quibus conſtructio primæ baſis perficiatur, &amp; ab ipſius ſe<lb></lb>cundæ baſis conſtructione diſtinguatur, <expan abbr="atq;">atque</expan> hoc modo tota ſecun<lb></lb>dæ baſis conſtructio ſuperuacanea erit. </s>
<s>quando quidem inferiùs <lb></lb>etiam in fine huiuſce capitis <expan abbr="eandẽmet">eandemmet</expan> conſtructionem Autor tra<lb></lb>dit. </s>
<s>Verùm quid de hac re ſentiendum ſit ijs, qui perfectius habent <lb></lb>exemplar iudicandum relinquo, mihi verò ſatis ſit huiuſce loci <lb></lb>imperfectionem animaduertiſſe.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note54"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note54"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ex aduerſo autem duorum duplorum lignorum] Dupla ligna <lb></lb>in toto præſenti capite vocat Autor illa duo, quæ in terra prostra<lb></lb>ta iacent, &amp; veluti <expan abbr="fundamentũ">fundamentum</expan>, ac <expan abbr="pauimentũ">pauimentum</expan> ipſius baſis ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note55"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note55"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[inſtar Græcæ litteræ<emph.end type="italics"></emph.end> H <emph type="italics"></emph>ſolutæ] Græca littera, vocata Ita, du<lb></lb>pliciter aſcriptoribus figuratur: vno quidem modo ſic<emph.end type="italics"></emph.end> H, <emph type="italics"></emph>quæ ſolu<lb></lb>ta dicitur quoniam ex partibus ſuis ſolutis trina calami motione <lb></lb>fit: alio verò modo ſic n, quæ ligata nuncupatur, quia cunctis ſuis<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/048.jpg"></pb><emph type="italics"></emph>partibus colligatis vnico calami continuo motu perficitur. </s>
<s>ipſi igi<lb></lb>tur ſolute hoc modo<emph.end type="italics"></emph.end> ||=|| <emph type="italics"></emph>duplicibus lineis factæ ſecundam ſca<lb></lb>læ baſim Autor aßimilari dixit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note56"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note56"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[vt ſuperiùs manifeſtum fuit] ſcilicet ex conſtructione ipſius <lb></lb>machinæ.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note57"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note57"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Animaduertendum quòd cùm ea ſcalæ pars, quæ est à prima <lb></lb>eius coniunctione, vſque ad ipſius ſummitatem, triginta menſu<lb></lb>rarum iuxta longitudinem ab Autore ſupponatur: dubio procul <lb></lb>pars eius inferior ſub clauis exiſtens, quinta iam dictæ longitu<lb></lb>dinis pars ſupponi videtur. </s>
<s>Quare cùm ait [reliquæ quintuplæ <lb></lb>partis] de ea ſcalæ parte intelligendum eſt, quæ à tam dictis cla<lb></lb>uis ad totius ſcalæ ſummitatem vſque porrigitur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note58"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note58"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[&amp; ab ipſo loco] hoc eſt ab ea parte, vbi iam dictæ duę tertiæ li<lb></lb>gnorum erectorum partes terminantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note59"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note59"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quemadmodum ſuperiùs iam oſtenſum eſt] videlicet vt ex <lb></lb>priori machinæ conſtructione patuit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note60"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note60"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[lingula] hìc intelligenda eſt pars quædam erectorum ligno<lb></lb>rum inferior, ſubtilior, &amp; quadrangula, qua tanquam cardine <lb></lb>quodam ipſa erecta ligna in proſtratorum in terra duorum ligno<lb></lb>rum quadrangulis foraminibus infiguntur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note61"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note61"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[priùs enarrata] ſcilicet prima baſis, quam ab Autoris con<lb></lb>ſtructione aliquantulum diſcrepantem eſſe oſtendimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note62"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note62"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ad tria interualla] videlicet ad trinæ dimenſionis interualla, <lb></lb>nempe longitudinem, latitudinem, atque craßitiem.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Hæc ad præſentis capitis dilucidationem animaduerſione, ex<lb></lb>plicatione〈qué〉 digna mihi viſa ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>De conſtructione Turrium ſecundum Polyidis Thetali <lb></lb>diſcipulos. </s>
<s>Cap. </s>
<s>XIII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>DIades quidem &amp; Charias Polyjdis Thetali di<lb></lb>ſcipuli, qui vnà cum Alexandro Macedone in <lb></lb>militiam profecti ſunt mechanici primi cùm <arrow.to.target n="note63"></arrow.to.target><lb></lb>terebras, tum ſcalas nauticas, tum etiam eas, <lb></lb>quæ rotis feruntur turres ligneas adinuene<lb></lb>runt. </s>
<s>atque minores quidem earum ſexaginta cubitorum <arrow.to.target n="note64"></arrow.to.target><lb></lb>quoad altitudinem faciebant: baſim autem quadrabant,
<pb xlink:href="052/01/049.jpg"></pb>vnumquodque latus, tum longitudinis, tum latitudinis de<lb></lb>cem &amp; ſeptem cubitorum ponentes: decem tectis præditas <lb></lb>ipſas facientes: in ſupremo vero tecto cumulum æquiqua<lb></lb>drangulum intercludentes, ſecundum proportionem quin<lb></lb>tæ partis baſis areæ, ſeu ſpatij, quòd à quatuor lateribus <arrow.to.target n="note65"></arrow.to.target><expan abbr="circumquaq;">cir<lb></lb>cumquaque</expan> terminatur, quemadmodum conſequenter per<lb></lb>ſpicuum erit. </s>
<s>maiores autem, <expan abbr="harumq́">harumque</expan>; ſeſquialteras, quin<lb></lb>decim tectis conſtructas faciebant: altitudinis verò cubito<lb></lb>rum nonaginta: necnon duplas, viginti tectis conſtantes, <lb></lb>quo ad altitudinem verò, centum &amp; viginti. </s>
<s>Rurſus autem <lb></lb>vnumquodque latus baſis duplarum turrium vigintiqua<lb></lb>tuor ferè cubitorum. </s>
<s>&amp; maiores, atque minores ſecundùm <lb></lb>proportionem conſtruebant ad tres dimenſiones ligna au<lb></lb>gentes vel minuentes, nempe iuxta longitudinem, &amp; latitu<lb></lb>dinem, atque craſſitiem. </s>
<s>Similiter autem tectorum quoque <lb></lb>diuiſiones iuxta altitudinis commenſurationem partieban<lb></lb>tur. </s>
<s>ſex quidem, &amp; quandoque octo rotis præditas ſecun<lb></lb>dum magnitudinis tumorem ipſas faciebant: in omnibus <lb></lb>ſemper quintam baſis partem ſurſum ponebant. </s></p><p type="margin">
<s><margin.target id="note63"></margin.target>a. </s>
<s>b</s></p><p type="margin">
<s><margin.target id="note64"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note65"></margin.target>d</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note66"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note66"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>TErebras hìc intelligit eas, quas deſcripſit ſuperiùs in Ca<lb></lb>pite ſeptimo.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note67"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note67"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Scalas nauticas vocat omnes ſcalas ex funibus factas, <lb></lb>quarum multis in locis huius operis mentio fit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note68"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note68"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quadrare baſim nil aliud hoc in loco eſt, niſi quodlibet laterum <lb></lb>eius in quotlibet partes ſecare, at que numerum ipſarum <expan abbr="partiũ">partium</expan> in <lb></lb>ſeipſum multiplicare, vt area quadrata ipſius baſis producatur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note69"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note69"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[conſequenter] ſcilicet inferiùs in ſequenti capite.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Animaduerſione verò dignum eſt, quòd in tradenda præſenti <lb></lb>machinarum obſidionalium, quæ turres vocantur, conſtructione <lb></lb>iuxta Polyidis Thetali diſcipulos, ſcilicet Diadem, &amp; Chariam <lb></lb>antiquos mechanicos: non declarauit perfectè Autor omnes ipſa<lb></lb>rum turrium menſuras, ſed quaſdam duntaxat breuißimè teti<lb></lb>git: reſeruans ſibi eas declarandas inferiùs in ſequenti capite,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/050.jpg"></pb><emph type="italics"></emph>poſtquam turrium ipſarum conſtructionem ſecundum Apollodori <lb></lb>doctrinam priùs tradiderit. </s>
<s>Quapropter non ab re factum iri <lb></lb>exiſtimo, ſi quædam nos hoc in loco ad earum menſurarum decla<lb></lb>rationem, perfectam〈qué〉 cognitionem adnotabimus. </s>
<s>Cùm itaque <lb></lb>minoris turris altitudinem quidem 60 cubitorum, baſis autem <lb></lb>eius vnumquodque latus tetragonicum, hoc est radicem quadra<lb></lb>tam 17 fuiſſe dixerit: area quadrata ipſius baſis 280 dubio pro<lb></lb>cul erit: latus autem cubicum areæ cubicæ inter baſim, &amp; primum <lb></lb>tectum interiectæ erit ſimiliter 17: ipſa demum area cubica 4913. <lb></lb>cùm verò decimum, ſiue ſupremum ipſius quadrangulum te<lb></lb>ctum quintam partem areæ iam dictæ baſis fuiſſe aſſeruerit: erit <lb></lb>ipſa quidem pars quinta 57 3/4 ferè. </s>
<s>huius autem numeri latus <lb></lb>tetragonicum, nempe radix ipſius 57 3/4 ferè erit latus vniuſcu<lb></lb>iuſque laterum iam dicti quadrangularis ſupremi tecti: quæ ra<lb></lb>dix tanquam latus cubicum ſi multiplicet ipſam 57 3/4 ferè qua<lb></lb>dratam aream, producetur area cubica, quæ inter culmen &amp; pro<lb></lb>ximum culminis tectum intercipitur. </s>
<s>Datis itaque menſuris ba<lb></lb>ſis, &amp; culminis harum minorum turrium, data〈qué〉 tota earum alti<lb></lb>tudine: nemini dubium quòd peritus Arithmeticæ, Geometriæ〈qué〉 <lb></lb>artifex eodem modo inueniet <expan abbr="etiã">etiam</expan> reliquorum octo tectorum men<lb></lb>ſuras: videlicet quadratas eorum areas, arearum〈qué〉 tetragonica <lb></lb>latera: necnon latera cubica, &amp; areas cubicas inter ipſa tecta in<lb></lb>teriectas, ab ipſis〈qué〉 tectis, &amp; à quatuor ipſius turris faciebus com<lb></lb>prehenſas. </s>
<s>Præterea quoniam maiores etiam turres tecta quinde<lb></lb>cim habentes ſeſquialteras priorum ipſos Polyidis diſcipulos con<lb></lb>ſtruxiſſe ait, quarum longitudo erat 90 cubitorum: ſi harum quo<lb></lb>que reliquas menſuras inuenire voluerimus, habentes iam baſim <lb></lb>ſeſquialteram prioris baſis, procedemus ſicut in minoribus. </s>
<s>At <lb></lb>quoniam duplas etiam priorum minorum, tectis vigiti præditas, <lb></lb>altitudinem autem 120 cubitorum habentes ait conſtructas fuiſ<lb></lb>ſe: non immerite latus tetragonicum baſis earum 24 ferè cubito<lb></lb>rum eſſe dixit. </s>
<s>cùm enim minorum, ſcilicet ſubduplarum baſis ſit, <lb></lb>vt iam oſtendimus, 289: duplæ eius erit 578. verùm area, quæ ex <lb></lb>24 tetragonico latere producitur, eſt 576. quare latus tetragoni<lb></lb>cum ipſius baſis iam dictarum duplarum turrium (vt rectè in<lb></lb>quit Autor) 24 ferè cubitorum erit. </s>
<s>culmen autem earundem<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/051.jpg"></pb><emph type="italics"></emph>erit 115 1/2 ferè. </s>
<s>ſimiliter autem reliquorum <expan abbr="etiã">etiam</expan> quo ad areas, <lb></lb>&amp; latera tectorum omnes menſuræ reperientur tum in ſeſquial<lb></lb>teris, tum in duplis turribus, quemadmodum in earum ſubſeſqui<lb></lb>alteris, ſubduplis〈qué〉 diximus. </s>
<s>Verùmenimuero tria nobis adno<lb></lb>tanda ſunt, primum quòd turres ſeſquialteræ, vel duplæ aliarum <lb></lb>turrium eſſe dicuntur non ſolùm iuxta earum altitudinem, &amp; <lb></lb>iuxta tectorum numerum: verumetiam iuxta areas baſium &amp; <lb></lb>culminum, &amp; reliquorum tectorum omnes menſuras: necnon <lb></lb>iuxta rotarum numerum, &amp; magnitudinem. </s>
<s>Quemadmodum <lb></lb>enim ſe habet 120 cubitorum altitudo ad 60 cubitorum altitudi<lb></lb>nem, &amp; 20 ad 10 tecta: ita ſe habet etiam 578 area baſis ad <lb></lb>289 baſis aream: necnon 115 1/2 ferè area culminis ad 57 3/4 <lb></lb>ferè culminis aream. </s>
<s>Secundò adnotandum quòd augendo, vel <lb></lb>minuendo turrium altitudinem, omnes etiam earum partes pro<lb></lb>portionaliter nobis augendæ ſunt: nempe areæ quadratæ, |&amp; cu<lb></lb>bicæ: latera quadrata, &amp; cubica tum baſium, tum culminum, <lb></lb>tum etiam reliquorum tectorum, &amp; ſpatiorum inter ipſa interie<lb></lb>ctorum: necnon lignorum omnium longitudo, latitudo, atque craſ<lb></lb>ſities quod Autor in fine huius capitis breuiter tetigit. </s>
<s>Tertiò <lb></lb>adnotandum, quòd reliquorum tectorum inter baſim, &amp; culmen <lb></lb>iacentium diuiſiones proportionaliter iuxta altitudinis commen<lb></lb>ſurationem fieri debent: maiores quidem, quæ baſi: minores ve<lb></lb>rò, quæ culmini propinquiores futuræ ſunt. </s>
<s>quod etiam Autor <lb></lb>illis verbis [ſimiliter autem tectorum quoque diuiſiones iuxta al<lb></lb>titudinis commenſurationem partiebantur.] breuißimè innuiſſe <lb></lb>videtur. </s>
<s>Hæc autem in præſentia paucula de menſuris harum <lb></lb>turrium ad dilucidationem huiuſce capitis breuiter nobis dicta <lb></lb>ſint. </s>
<s>in ſequenti verò capite poſtquam turrium conſtructionem <lb></lb>iuxtæ doctrinam Apollodori tradiderit Autor, exquiſitam de iam <lb></lb>dictis omnibus turrium menſuris doctrinam nobis traditurus eſt.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/052.jpg"></pb><p type="main">
<s><emph type="center"></emph>De conſtructione turrium ſecundum Apollodorum. </s>
<s><lb></lb>Cap. </s>
<s>XIIII.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note70"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note70"></margin.target>a</s></p><p type="main">
<s>AT Apollodorus grauiorem pedes verſus tur<lb></lb>rem conſtruens, ſub ſeſquialteram ipſorum <lb></lb>ſexaginta cubitorum, &amp; quatuor rotis prædi<lb></lb>tam ipſam declarat, pedum quoad altitudi<lb></lb>nem ſexaginta oſtendens. </s>
<s>vnde ipſe quoque <lb></lb>vnumquodque circa baſim latus pedum ſedecim iuxta lon<lb></lb>gitudinem faciebat, vltra pedalem in extremitatibus pro<lb></lb>minentiam: quoad latitudinem, vnius pedis, &amp; digitorum <lb></lb>quatuor: iuxta verò craſſitiem, duodecim digitorum: in<lb></lb>feriora iuga dupla faciens, vbi rotæ quidem in medio, ligna <lb></lb>verò medio aſtantia in ipſis prominentijs imponi debent. </s>
<s><lb></lb>Hæc bina, atque bina iuga ſecundum craſſitiem ponebat, <lb></lb>&amp; inter ipſa ad ſingula digitorum duodecim interceptum <lb></lb>locum, ſiue etiam maiorem in latitudines diſtinguens: ere<lb></lb>cta in extremis medio aſtantia ligna infigit, ad <expan abbr="pauimẽtum">pauimentum</expan> <lb></lb>vſque deſcendentia, quippe quæ turris crura quidam no<lb></lb>minarunt, pedum ſedecim quoad altitudinem ſingula exi<lb></lb>ſtentia: quo vero ad latitudinem, pedis, vnius, &amp; quatuor <lb></lb>digitorum: quoad craſſitudinem autem ſingula digitorum <lb></lb>duodecim. </s>
<s>Hæc ad ea, quæ dupla iacent paruis regulis, <lb></lb><expan abbr="tranſuerſisq́ue">tranſuerſisque</expan> lignis (quæ à Græcis Peritomidæ vocan<arrow.to.target n="note71"></arrow.to.target><lb></lb>tur) necnon chelonijs, ſiue hemiſpherijs circa medium in<lb></lb>ſculptis, &amp; tanquam pugillis quibuſdam diſſectis ſimilibus <lb></lb>ijs, qui in <expan abbr="portarũ">portarum</expan> cardinibus ponuntur, circa clauorum fi<lb></lb>xionem firmantur, vt erecta permaneant. </s>
<s>Hiſe erectis cru<lb></lb>ribus medio ſtantibus à duplis iacentibus ad oppoſita du<lb></lb>pla, alia ligna æqualia exiſtentia quoad longitudinem tan<lb></lb>quam contraria iuga ponebat, æquiquadrangulum turris <lb></lb>fundamentum figurans, ſeu baſim ex æquali circumquaque <lb></lb>terminans, vt iam dicta quatuor medio ſtantia ligna æqua<lb></lb>liter à ſeinuicem vndequaque diſtent. </s>
<s>in vnoquoque au<lb></lb>tem ipſorum quatuor, duo adhærere faciebat ligna, quæ <lb></lb>erant octo numero, æqualis tum latitudinis, tum craſſitudi<lb></lb>nis cum prioribus, altitudinis ſingula pedum nouem: ſtan-<pb xlink:href="052/01/053.jpg"></pb>tia verò, atque adhærentia, ad vtraſque medio ſtantium par<lb></lb>tes ad dupla iacentia, quæ etiam tutò clauis affixa ſint cùm <lb></lb>ad iuga, tum ad medio ſtantia. </s>
<s>atque hoc modo tria conſti<lb></lb>tuebat in ordine, vno ex rectis ſtantibus lignis iuxta me<lb></lb>dium ſupereminente. </s>
<s>hæc autem octo ligna, adhærentia <lb></lb>vocentur. </s>
<s>Et quoniam ipſa adhærentia, &amp; medio ſtantia <lb></lb>ligna propter latitudinis magnitudinem inuentu difficilia <lb></lb>ſunt, neceſſe eſt ipſum Diadem, &amp; Chariam ſequi: atque <lb></lb>æquiquadrangula digitorum ſingula duodecim deorſum <lb></lb>ipſa crura facere: ſurſum autem minora: præcipuè verò ea, <lb></lb>quæ adhærent, <expan abbr="maximeq́ue">maximeque</expan> ad huiuſcemodi turris conſtru<lb></lb>ctionem commenſurabilia exiſtunt. </s>
<s>Rurſus autem ad ipſa <lb></lb>deſuper iam dictus Apollodorus ſimiliter inferiora, &amp; ad<lb></lb><arrow.to.target n="note72"></arrow.to.target><lb></lb>hærentia iuga minora longitudine ponebat, <expan abbr="vſq;">vſque</expan> ad vnum <lb></lb>pedem: ac demum vſque ad ſupremum tectum iuxta lon<lb></lb>gitudinem, &amp; latitudinem ex vnoquoque eorum, quæ po<lb></lb>nuntur, pedem vnum auferebat: vt collectionem ſurſum <lb></lb>turris ſuſcipiat: ne <expan abbr="põderoſa">ponderoſa</expan> in extremis fiens, circumruat: <lb></lb>ſed tutam ex inferiori ſedis latitudine ſtabilitatem habeat. </s>
<s><lb></lb>Verùm ipſorum tectorum alia quidem circumalta ſint, alia <lb></lb>verò eiuſmodi, quòd circumquaque circumcurri poſſint: <lb></lb>habentia latitudinem circiter trium pedum. </s>
<s>perutilia nam<lb></lb>que ſunt ad euitanda incendia. </s>
<s>At iuxta ſpatium illud, quo <lb></lb>diſtant ad latitudines inferiora iuga, quæ ad iam dictos di<lb></lb>gitorum duodecim, vel etiam maiores interceptos locos <lb></lb>medio ſtantia ligna ſuſcipiunt, artifici commoſtrans præci<lb></lb>pit quatuor imponere rotas, validis axibus ſimul <expan abbr="trãsfixas">transfixas</expan>, <lb></lb><arrow.to.target n="note73"></arrow.to.target><lb></lb>&amp; laminis ferreis ad frigus curſis, colligatas: dimetientem, <lb></lb>ſiue altitudinem pedum circiter quatuor cum dimidio ha<lb></lb>bentes: <expan abbr="quandoq;">quandoque</expan> autem eaſdem rotas breuibus etiam fer<lb></lb>reis axibus ſimul transfigi, propter ſuperimpoſitum pon<lb></lb>dus, &amp; magnitudinis molem: atque duas quidem earum ad <lb></lb>ſingula <expan abbr="tãtùm">tantùm</expan> duo ligna firmari, reliquas vero duas ad ea, <lb></lb>quæ è contrario oppoſita ſunt: ſuſtolentes quidem à terra, <lb></lb><expan abbr="ſuſtinentesq́ue">ſuſtinentesque</expan> dupla ligna, vt magna cum volubilitate, <expan abbr="fa-cilitateq́ue">fa<lb></lb>cilitateque</expan> rotę vertantur, ac totam turris congeriem com<lb></lb>moueant. </s>
<s>Sic igitur conſtructione conſtituta, prima medio
<pb xlink:href="052/01/054.jpg"></pb>ſtantia ligna tertia eorum longitudinis parte ſuper tecto ſu<lb></lb>periori eminentia reperientur. </s>
<s>Quamobrem adhærentia <lb></lb>medio ſtans lignum excedenti. </s>
<s>ad ſuperiora iuga rurſus <lb></lb>ponebat: atque ad ipſum medio ſtans lignum, aliud ab <lb></lb>adhærentibus comprehenſum. </s>
<s>&amp; ſic iuxta omne tectum <lb></lb>quadripertitò contexens, turrem ſtabiliuit. </s>
<s>&amp; primum <lb></lb>quidem medio ſtans lignum hiſce adhærentibus æquale mi<lb></lb>nimè faciebat, ne coniunctiones eorum propè ſeinuicem <lb></lb>ſint: ſed omnis <expan abbr="cõmiſſura">commiſſura</expan> reſpectu alterius ex aduerſo per<lb></lb>mutatim, <expan abbr="diſiunctimq́ue">diſiunctimque</expan> variet: &amp; adhærentium lignorum <lb></lb><arrow.to.target n="note74"></arrow.to.target><lb></lb>coarctatione, <expan abbr="vnioneq́ue">vnioneque</expan> robur ſuſcipiat. </s>
<s>Præterea ſcalas <lb></lb>alterum ipſius turris latus ab altero per diagonium (vel vt <lb></lb>ita dicam) diametraliter ſeparantes ad adherentia iuga pro<lb></lb>pter aſcenſum ponebat. </s>
<s>turrem autem funibus etiam deſu<lb></lb>per iuxta angulos alligatis, &amp; extra per medium attractis <lb></lb>ſtabiliebat: latiorem in figura baſim turri præſtans <expan abbr="tanquã">tanquam</expan> <lb></lb>ſedem, circumalligatis palis clauos habentibus, aut ferreis <lb></lb>clauis, &amp; annulis lateralibus ad extenſionem infixis: non <lb></lb>parum auxilium propter funium tenſionem ad ſuſtentatio<lb></lb>nem turri præbens. </s>
<s>Hoc modo ex paucis, <expan abbr="paruisq́ue">paruisque</expan> lignis <lb></lb>magnam turris machinam conſtruebat, quæ æqualem <lb></lb>cum muro altitudinem habebat: neque tectorum diuiſio<lb></lb>nes, vel altitudines exprimens, neque ſuperioris collectio<lb></lb>nis quintam partem declarans. </s>
<s>Verùmenimuero ſi quis <lb></lb><arrow.to.target n="note75"></arrow.to.target><lb></lb>dubitans quærat hoc: ex inferiori baſi per ſuppoſitum in <lb></lb>vnoquoque latere numerum id ſuſcipiet. </s>
<s>cùm enim latus <lb></lb>pedum datum ſit ſedecim, multiplicatum autem in alterum <lb></lb>æqualis cum ipſo longitudinis, faciat totam aream, ſiue in<lb></lb>ternum quadrialteri ſpatium pedum <expan abbr="ducẽtorum">ducentorum</expan> quinqua<lb></lb>ginta ſex: atque etiam horum quinta pars pedum quinqua<lb></lb>ginta &amp; vnius, &amp; quintæ partis pedis ſit: quæro quis nume<lb></lb>rus in ſeipſum, vel in alium æqualis cum ipſo longitudinis <lb></lb>multiplicatus hunc efficit? </s>
<s>&amp; inuenio ſeptenarium, &amp; ſex<lb></lb>tam partem proximè. </s>
<s>nam ſeptenarius in ſeptenarium mul<lb></lb>tiplicatus, quadraginta nouem: &amp; ſeptenarius in ſextam <lb></lb><arrow.to.target n="note76"></arrow.to.target><lb></lb>partem, hoc eſt in decem minuta multiplicatus, minuta pri<lb></lb>ma ſeptuaginta efficit. </s>
<s>rurſus autem denarius in ſeptena-<pb xlink:href="052/01/055.jpg"></pb>rium, ſeptuaginta efficit. </s>
<s>&amp; ex collectis centum &amp; quadra<lb></lb>ginta minutis primis ipſa quidem <expan abbr="centũ">centum</expan> &amp; viginti in pedes <lb></lb><arrow.to.target n="note77"></arrow.to.target><lb></lb>duos, reliqua verò in partem <expan abbr="computãda">computanda</expan> ſunt. </s>
<s>Quare iuga, <lb></lb>quæ ad ſupremi tecti collectionem ponuntur, ſingula <expan abbr="pedũ">pedum</expan> <lb></lb><arrow.to.target n="note78"></arrow.to.target><lb></lb>ſeptem, &amp; ſextæ partis iuxta longitudinem fiant. </s>
<s>At ea <lb></lb>quoque nouem tecta, quæ ad altitudinem ab inferiori baſi <lb></lb>ponuntur in ipſa longitudinis, &amp; latitudinis ſuper adiectio<lb></lb>ne iuxta quadrialteri circumterminationem ſingula pedem <lb></lb>auferentia ex ipſis ſedecim, ſeptem proximè relinquunt. </s>
<s><lb></lb>eadem autem via in ſuprema turris collectione, &amp; in tertia, <lb></lb><arrow.to.target n="note79"></arrow.to.target><lb></lb>&amp; in quarta, &amp; qualibet parte ſemper quærentibus ſit. </s>
<s>Ip<lb></lb>ſas verò tectorum diuiſiones, &amp; ad altitudinem exaltatio<lb></lb>nes Diades quidem, &amp; Charias iuxta cubita numerantes, <lb></lb>primum, quod ab inferiori baſi fit tectum <expan abbr="cubitorũ">cubitorum</expan> quo ad <lb></lb>altitudinem ſeptem ponebant, &amp; digitorum duodecim: ſu<lb></lb>periora <expan abbr="autẽ">autem</expan> <expan abbr="quinq;">quinque</expan> tecta, ſingula <expan abbr="cubitorũ">cubitorum</expan> <expan abbr="quinq;">quinque</expan> tantùm: <lb></lb>reliqua verò, ſingula quatuor, &amp; tertię partis. </s>
<s>necnon craſſi<lb></lb>tiem pauimenti tectorum, &amp; inferiorem fundamenti craſſi<lb></lb>tudinem, unà cum ſuperiori pinnaculo altitudini <expan abbr="cõnume-rabant">connume<lb></lb>rabant</expan>. </s>
<s>ſimiliter autem in minori <expan abbr="quoq;">quoque</expan> turre diuiſio tecto<lb></lb><arrow.to.target n="note80"></arrow.to.target><lb></lb>rum eandem rationem ad altitudinem ſuſcipiebat. </s>
<s>Verùm <lb></lb>iam dictus Apollodorus iuxta pedes enumerans turrim <lb></lb>adhærentia prima, quæ à baſi eriguntur, pedum <expan abbr="nouẽ">nouem</expan> in al<lb></lb>titudinem facit. </s>
<s>&amp; ſi æqualis quidem altitudinis omnia ad<lb></lb>hærentia eſſe vult, ſex tectis præditam turrem ipſam, &amp; pe<lb></lb>dum ſex tantùm ſuper adiectione eſſe declarat: vigeſimam<lb></lb>tertiam verò partem proximè areæ baſis ſurſum colligere, <lb></lb>ſingula decem pedum ſuperiora quoque iuga ponens: ſi au <lb></lb>tem quintam baſis <expan abbr="partẽ">partem</expan> in turri ſex tectis prædita ſurſum <lb></lb>colligit, vnius cum dimidio pedis tectorum ſuper adiectio<lb></lb>nem quadripertitò euenire: ſi autem decem quoque tectis <lb></lb>præditam, ſingulam pedis vnius ſuper adiectionem (vt <expan abbr="iã">iam</expan> <lb></lb>dictum eſt) &amp; quintam baſis partem ſurſum intercipere: ita <lb></lb>vt ſuperiora quoque iuga ſingula pedum ſeptem, &amp; ſextæ <lb></lb>partis fiant: atque in ipſa quidem turri decem tectis prædi<lb></lb>ta inferiora adhærentia ſingula pedum nouem fieri: ipſa ve<lb></lb>rò, quæ in ſuperioribus quatuor tectis ſunt, ſingula pedum
<pb xlink:href="052/01/056.jpg"></pb>ſex tantùm: ipſa demum, quæ in quatuor reliquis adhuc ſu<lb></lb><arrow.to.target n="note81"></arrow.to.target><lb></lb>periora ſunt, ſingula quinque, &amp; partis. </s>
<s>Hoc itaque pacto <lb></lb>non ſolùm ea, quæ iuxta numerum diſcrepant turrium te<lb></lb>cta ad ſexaginta pedum altitudinem cùm æqualis, tum in<lb></lb>æqualis altitudinis exiſtentia reperientur: verùm etiam eæ, <lb></lb>quæ ex vtriſque iuxta cubitos, &amp; pedes <expan abbr="conſtruũtur">conſtruuntur</expan>, ac iux<lb></lb>ta magnitudinem diſcrepant turres commenſurabiles ad ſe <lb></lb>ſe inuicem ſecundum proportionem oſtendentur. </s>
<s>Si enim <lb></lb>cubitus vigintiquatuor ſecundum longitudinem eſt digito<lb></lb>rum, pede ſedecim exiſtente, habet autem ipſe vigintiqua<lb></lb>tuor numerus numerum ſedecim, &amp; eius dimidium: ſeſqui<lb></lb>alter ipſius eſt, ſubſequialter verò ad cubitum pes. </s>
<s>Quare <expan abbr="tũ">tum</expan> <lb></lb>ipſi ſexaginta cubiti altitudinis, tum ipſi ſeptemdecim lon<lb></lb>gitudinis baſis eandem proportionem ad pedes habebunt: <lb></lb>eodem modo autem eam etiam, quæ in rationibus eſt con<lb></lb>uenientiam: quoniam <expan abbr="vtriq;">vtrique</expan> communi menſura menſuran<lb></lb>tur. </s>
<s>nam triginta numerus ter quidem menſurat ipſum no<lb></lb>naginta numerum, bis verò ipſum ſedecim. </s>
<s>&amp; quemadmo<lb></lb>dum ſe habet nonaginta numerus ad ſexaginta numerum, <lb></lb>ita vigintiquatuor ad ſedecim. </s>
<s>&amp; ſicut ſe habet vigintiqua<lb></lb>tuor ad ſedecim, ſic etiam rotæ ad ſe inuicem tum iuxta nu<lb></lb>merum, tum etiam iuxta magnitudinem: necnon baſis ad <lb></lb>baſim ſicut etiam tria ad duo. </s>
<s>Oſtenſæ ſunt igitur ipſæ quo<lb></lb>que menſurantes turres ad ſe inuicem eandem, <expan abbr="quã">quam</expan> cæ quę <lb></lb>menſurantur iuxta proportionem habere rationem. </s>
<s>Quam<lb></lb>obrem non ſolùm iuxta commenſurationem, verùm etiam <lb></lb>iuxta conuenientiam turrium ferri idonearum conſtructio<lb></lb>nes Diodorus, <expan abbr="necnõ">necnon</expan> Diades, &amp; Charias <expan abbr="faciẽtes">facientes</expan> reperiun<lb></lb>tur. </s>
<s>Atque manifeſtum eſt quòd Antiqui Mechanici, <expan abbr="erru-ditiſſimiq́ue">erru<lb></lb>ditiſſimique</expan> Architecti ſcientificè, &amp; non <expan abbr="abſq;">abſque</expan> ratione Ma<lb></lb><arrow.to.target n="note82"></arrow.to.target><lb></lb>chinarum conſtructiones faciebant. </s>
<s>Turre ſic quoad con<lb></lb>ſtructionem, completa, ſi non enodus <expan abbr="complanatusq́ue">complanatusque</expan> ad <lb></lb>baſim ſubiectus locus ſit, ſed ſurſum ferens exiſtat: faciemus <lb></lb>ſuppoſitorium prope turris baſim contexione, quæ turris <lb></lb>contexioni ſimilis ſit, &amp; ſuper terræ in æqualitatem adue<lb></lb>niat, <expan abbr="locumq́ue">locumque</expan> inferiùs ſubiectum amplificet: vt in con<lb></lb>greſſu, ac turbatione certaminis indecliuis quoad ſtatio-
<pb xlink:href="052/01/057.jpg"></pb>nem turris conſeruetur. </s>
<s>Cuſtodietur autem ne combura<lb></lb>tur ab ijs, qui mittuntur ignem ferentibus muricibus, &amp; <lb></lb>accenſis flammis: ſi tabulæ in ipſa clauis <expan abbr="affigãtur">affigantur</expan> præcipuè <lb></lb>quidem palmeæ, vel eæ, quæ ex fortibus lignis fiunt. </s>
<s>exce<lb></lb>ptis cedrinis, &amp; pineis, <expan abbr="atq;">atque</expan> alneis, propter earum <expan abbr="feruidã">feruidam</expan>, <lb></lb>facilè combuſtibilem, <expan abbr="friabilemq;">friabilemque</expan> naturam. </s>
<s>appendantur au<lb></lb>tem &amp; coria turri in iam dictis in conſtructione circumala<lb></lb>tis, <expan abbr="circumcurſatisq́">circumcurſatisque</expan>; tectis, non adhærentia tabulis, ſed <expan abbr="ali-quantulũ">ali<lb></lb>quantulum</expan> extrinſecùs diſtantia. </s>
<s>cùm propter ea, quæ ad <expan abbr="iaculandũ">iacu<lb></lb>landum</expan> ignem fiunt tormenta: tum <expan abbr="quoniã">quoniam</expan> lapides <expan abbr="iacientiũ">iacientium</expan> <lb></lb>percuſſiones imbecilles ad ipſa, <expan abbr="languidæq́ue">languidæque</expan> in ipſa iactus <lb></lb>irruptione ad mole fiunt. </s>
<s>Affigatur <expan abbr="aũt">aut</expan> clauis etiam turris <lb></lb>deſuper quemadmodum in teſtudinibus <expan abbr="quoq;">quoque</expan> dictum eſt, <lb></lb>&amp; creta opima, &amp; glutinoſa locus intermedius repleatur. </s>
<s>ad <lb></lb>eas verò turris partes, quæ <expan abbr="tormẽtis">tormentis</expan> ad iaculandum ignem <lb></lb>factis proponuntur, loco tuborum aquam mittentium, in<lb></lb>teſtina bouum præparata veluti ſale condita aquam effun<lb></lb>dentia apponantur. </s>
<s>hiſce inteſtinis vtres aqua pleni ſuppo<lb></lb>nuntur, qui extricti, atque ſuppreſſi ſurſum aquam ferunt. </s>
<s><lb></lb>Quòd ſi <expan abbr="etiã">etiam</expan> turris pinnaculum aliqua in parte inacceſſibi<lb></lb>le <expan abbr="cõburatur">comburatur</expan>, non ſit <expan abbr="aũt">aut</expan> <expan abbr="inſtrumentũ">inſtrumentum</expan>, quod tubus vocatur: <lb></lb>calami per totam <expan abbr="internã">internam</expan> partem perforati, cuiuſmodi ſunt <lb></lb>ij, quos venatores habent ad ſein uicem coniunguntur, <expan abbr="atq;">atque</expan> <lb></lb><expan abbr="vbicumq;">vbicumque</expan> opus fuerit aquam emittunt. </s>
<s>vtres enim quemad<lb></lb>modum etiam in inteſtinis ſupponuntur ferentes ipſam per <lb></lb>calamos in eum, qui comburitur locum. </s>
<s>Non paruam <expan abbr="autẽ">autem</expan> <lb></lb>vtilitatem turri præbebunt etiam inuolucra extrinſecùs ap<lb></lb>penſa, paleis aceto madefactis plena: ſiue retia repleta humi<lb></lb>dis muſcis, vel ea algę ſpecie, quę thalaſſopraſon, hoc eſt ma<lb></lb>rinum porrum vocatur: tamquam ea, quæ <expan abbr="nõ">non</expan> ſolùm incen<lb></lb>dijs, quæ à tormentis ignem iaculantibus fiunt, oppugna<lb></lb>re, verùm etiam lapides iacientium percuſſionibus reſiſte<lb></lb>re poſſunt. </s>
<s>&amp; ſciendum eſt quòd omnes, quæ ex ignem fe<lb></lb>rentibus, <expan abbr="accenſisq́ue">accenſisque</expan> flammis * * * * </s></p><p type="margin">
<s><margin.target id="note71"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note72"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note73"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note74"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note75"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note76"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note77"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note78"></margin.target>i</s></p><p type="margin">
<s><margin.target id="note79"></margin.target>k</s></p><p type="margin">
<s><margin.target id="note80"></margin.target>l</s></p><p type="margin">
<s><margin.target id="note81"></margin.target>m</s></p><p type="margin">
<s><margin.target id="note82"></margin.target>n</s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Finis huius Capitis deſideratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p>
<pb xlink:href="052/01/058.jpg"></pb><figure id="id.052.01.058.1.jpg" xlink:href="052/01/058/1.jpg"></figure>
<pb xlink:href="052/01/059.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>MVlta ſunt in hoc capite, quæ niſi adnotentur, <expan abbr="declaren-turq́ue">declaren<lb></lb>turque</expan>, omnium huius operis capitum præſens obſcurißi<lb></lb>mum reddent. </s>
<s>in primis itaque adnotabimus quòd par<arrow.to.target n="note83"></arrow.to.target><lb></lb>ticula illa [grauiorem] in textu græco legitur<emph.end type="italics"></emph.end> <foreign lang="grc">σεμνότερον</foreign>, <emph type="italics"></emph>quæ in <lb></lb>præſenti loco nil aliud ſignificare poteſt niſi grauiorem, aut ma<lb></lb>gnificientiorem, quorum neutrum eſt ad propoſitum Autoris. </s>
<s>Cùm <lb></lb>enim turris, quam ſecundum Apollodori doctrinam in principio <lb></lb>huius capitis Autor conſtruit, debeat eſſe ſubſeſquialtera eius tur<lb></lb>ris, quam in præcedenti capite <expan abbr="minorẽ">minorem</expan> <expan abbr="oĩum">omnium</expan> eſſe dixit, nempe ſexa<lb></lb>ginta cubitorum altitudinem habentis: nemo eſt, qui non videat <lb></lb>quòd hæc Apollodori turris leuior, minus〈qué〉 ampla, &amp; magnifica <lb></lb>erit quàm iam dicta minor diſcipulorum Polyidis Thetali turris. </s>
<s><lb></lb>Quamobrem<emph.end type="italics"></emph.end> <foreign lang="grc">λεπτότερον</foreign>, <emph type="italics"></emph>hoc eſt leuiorem potiùs quàm<emph.end type="italics"></emph.end> <foreign lang="grc">σεμνότε<lb></lb>ρον</foreign>, <emph type="italics"></emph>ſcilicet grauiorem legendum eſſe nobis videtur. </s>
<s>minor enim <lb></lb>in ratione ſeſquialtera eſt hac turris quàm illa. </s>
<s>quippe cùm hu<lb></lb>ius quidem omnes menſuræ pedes, illius verò cubiti ſint: cubitus <lb></lb>autem (vt ipſemet Autor in præſenti capite declarat) ad pedem <lb></lb>ſeſquialteram habeat rationem: quandoquidem pes ſedecim, cu<lb></lb>bitus vigintiquatuor digitis conſtat. </s>
<s>vndè ſanè volens Apollodo<lb></lb>rus ipſius turris, quæ ſexaginta cubitorum altitudinem habebat, <lb></lb>ſubſeſquialteram turrem tanquam leuiorem conſtruere, non im<lb></lb>merito ſexaginta pedum altitudinis eam fecit, quatuor〈qué〉 ipſi ro<lb></lb>tas tantùm, &amp; non ſex quemadmodum eius ſeſquialteræ, ſuppo<lb></lb>ſuit. </s>
<s>Quoniam autem dubitabat ne propter eius leuitatem corrue<lb></lb>ret, funibus (vt docet Autor in hoc capite) ad palos, ſiue clauos <lb></lb>ferreos in terram affixos circumalligatis, <expan abbr="beneq́ue">beneque</expan> extenſis eam <lb></lb>ſtabiliebat.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note84"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note83"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note84"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quæ nam ſint Peritomidæ in cap 9. declarauimus. </s>
<s>Chelonium <lb></lb>autem eſt propriè Teſtudinis animalis tegumentum, ad cuius ſi<lb></lb>militudinem vocat Avtor tum in hoc, tum in nono capite lignum <lb></lb>quoddam inſculptum, quod inſculptura ſua retinendi alia ligna, <lb></lb>conſtringendi〈qué〉 vim habens, <expan abbr="nõ">non</expan> ſecus quam chelonium concauita<lb></lb>te ſua teſtudinem ipſam intra ſe comprehendit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note85"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note85"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Adhærentia iuga, quæ græcè<emph.end type="italics"></emph.end> <foreign lang="grc">ἐπιζυγίδαι</foreign> <emph type="italics"></emph>dicuntur, ea ſunt,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/060.jpg"></pb><emph type="italics"></emph>quæ ſuperiùs<emph.end type="italics"></emph.end> <foreign lang="grc">ἀντιζυγίδας</foreign>, <emph type="italics"></emph>ideſt contraria iuga vocauit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note86"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note86"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Particula illa, quam nos vertimus [ad frigus curſis] in græco <lb></lb>exemplari legitur<emph.end type="italics"></emph.end> [<foreign lang="grc">ψυχρηλάτοις</foreign>] <emph type="italics"></emph>quæ nil aliud ſonat, quam ad <lb></lb>frigus curſis ſed videtur non eſſe ad propoſitum. </s>
<s>ideo dubitandum <lb></lb>eſt an fortaſſe dictio hæc deprauatè legatur. </s>
<s>potiùs enim legen<lb></lb>dum eſſet [clauis <expan abbr="circũaſſixis]">circumaffixis]</expan> <expan abbr="quoniã">quoniam</expan> laminæ, quibus rotæ cingun<lb></lb>tur, clauis circumaffigi debent.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note87"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note87"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Animaduerſione dignum eſt, quòd tota quidem huiuſce turris <lb></lb>conſtructio nimis obſcurè ab Autore tradita cuilibet eſſe videbi<lb></lb>tur niſi figuram præ oculis habeat, quæ maximum legentibus <lb></lb>præbebit auxilium ad ipſius Autoris verba rectè percipienda. </s>
<s>ipſæ <lb></lb>verò ſcalæ, quæ ab Autore intra turrem ſituantur, perperam in <lb></lb>ipſa figura plana repræſentari nobis poſſunt in eo ſitu, quo Autor <lb></lb>eas deſcribit. </s>
<s>idcirco ad perfectam earum intelligentiam imagi<lb></lb>natione ſupplendum est.<emph.end type="italics"></emph.end></s></p><p type="main">
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<s><margin.target id="note88"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[quærat hoc] ſcilicet tectorum diuiſiones, vel altitudines: &amp; <lb></lb>ſuperioris collectionis quintam partem. </s>
<s>hoc eſt quibus nam men<lb></lb>ſuris tectorum diuiſiones, vel eorum altitudines, nempe ab vno <lb></lb>tecto ad aliud diſtantiæ fiant: necnon quomodo ſuperioris colle<lb></lb>ctionis, ſiue vltimi tecti quadrata area fiat quinta pars quadra<lb></lb>tæ areæ baſis. </s>
<s>cùm enim Apollodorus hæc minimè declaraſſet, vo<lb></lb>lens Autor ea declarare, ait, quòd, ſiquis dubitans quærat hoc: ex <lb></lb>inferiori baſi per ſuppoſitum in <expan abbr="vnoquoq;">vnoquoque</expan> latere numerum id ſu<lb></lb>ſcipiet. </s>
<s>videlicet ex ipſius inferioris baſis area quadrata auxilio <lb></lb>numeri in vnoquoque ipſius baſis latere ſuppoſiti colliget id, quod <lb></lb>quærit. </s>
<s>exempli gratia, quoniam vnumquodque baſis latus ab <lb></lb>Apollodoro 16 pedum iuxta longitudinem <expan abbr="ſuppoſitũ">ſuppoſitum</expan> fuit, erit area <lb></lb>quadrata ab ipſis lateribus comprehenſa 256: huius autem quin<lb></lb>ta pars, hoc eſt area quadrata ſuperioris collectionis, ſiue poſtre<lb></lb>mi tecti erit 51 1/5: huius verò areæ latus tetragonicum 7 1/6 pro<lb></lb>ximè. </s>
<s>quandoquidem 7 1/6 multiplicatus per 7 1/6 efficit 51 1/3 <lb></lb>&amp; (1/36), qui ab ipſo 51 1/5 parum diſcrepat. </s>
<s>atque hoc modo ex in<lb></lb>feriori baſi per ſuppoſitum in vnoquoque litere numerum nempe <lb></lb>16, inuenimus quintam partem areæ quadratæ ipſius baſis, quæ <lb></lb>quadrata poſtremi tecti area futura eſt: necnon eius tetragonica <lb></lb>latera. </s>
<s>quibus ita revertis, reliquorum etiam tectorum diuiſio-<emph.end type="italics"></emph.end><pb xlink:href="052/01/061.jpg"></pb><emph type="italics"></emph>nes, vel altitudines (vt mox ſubiunget Autor) inueniemus.<emph.end type="italics"></emph.end></s></p><p type="main">
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<s><margin.target id="note89"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[in ſextam partem, hoc eſt in decem minuta] in multiplican<lb></lb>do 7 1/6 in ſeipſum vtitur Autor multiplicatione <expan abbr="Aſtronomorũ">Aſtronomorum</expan>; <lb></lb>qui non more minutiarum, ſ. </s>
<s>per reductionem integrorum in mi<lb></lb>nutias, ſed per minuta prima, ſecunda, &amp; tertia, numeros inte<lb></lb>gros cum fractis, in numeros integros cum fractis, necnon fractos <lb></lb>adinuicem multiplicant. </s>
<s>idcirco pedem in 60 prima minuta par<lb></lb>tiens Autor, 120 minuta prima in duos pedes, reliqua verò<emph.end type="italics"></emph.end> 20 <emph type="italics"></emph>in </s></p><p type="main">
<s><arrow.to.target n="note90"></arrow.to.target><lb></lb>partem, ſcilicet tertiam diſtribuit.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note91"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note90"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note91"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[At ea quoque nouem tecta &amp;c.] in hac parte declarat Au<lb></lb>tor quo nam pacto reliquorum etiam nouem tectorum diuiſiones, <lb></lb>ſiue altitudines in iam dicta Apollodori turri decem tectis prædita <lb></lb>ſuſcipiendæ ſint. </s>
<s>Ait igitur quòd reliqua nouem tecta, quæ ab in<lb></lb>feriori baſi in altitudinem eleuantur, ſingula iuxta longitudinem, <lb></lb>&amp; latitudinem quadratæ eorum areæ pedem vnum ex iam dictis <lb></lb>ſedecim ipſius baſis pedibus auferre debent. </s>
<s>quamobrem vnum<lb></lb>quodque laterum ſecundi tecti, quindecim pedum: tertij, qua<lb></lb>tuordecim: quarti, tredecim: quinti, duodecim: ſexti, vndecim: <lb></lb>ſeptimi, decem: octaui, nouem: noni, octo: decimi〈qué〉, ſeptem pedum <lb></lb>erit. </s>
<s>attamen cùm vltimi tecti area quadrata quinta pars areæ <lb></lb>quadratæ ipſius baſis eſſe debeat, quam 51. 1/5, eius〈qué〉 latus <expan abbr="tetra-gonicũ">tetra<lb></lb>gonicum</expan> 7 1/6 eſſe iam oſtendimus: non immerito reliqua nouem te<lb></lb>cta ſingula pedem auferentia ex ipſis ſedecim, ſeptem proximè <lb></lb>relinquere dixit. </s>
<s>quandoquidem reuera 7 1/6 proximè relinque<lb></lb>re debent. </s>
<s>quod eſt quintæ ipſius 256 partis latus tetragoni<lb></lb>cum, vt modò declarauimus. </s>
<s>vndè profecto ſingula poſtremi te<lb></lb>cti latera minus quàm vnum pedem ex ipſis ſedecim auferre ne<lb></lb>ceſſariò debent, nempe 5/6 vnius pedis. </s>
<s>Non eſt autem prætereun<lb></lb>dum quòd huius quidem turris altitudo 115 pedum eſſe colligitur: <lb></lb>vniuſcuiuſque verò eius tectorum area quadrata ex vnoquoque <lb></lb>laterum numero in ſeipſum multiplicato producitur: eorumdem <lb></lb>autem area cubica ex multiplicatione vniuſcuiuſque laterum in <lb></lb>ſuam quadratam aream gignitur.<emph.end type="italics"></emph.end></s></p><p type="main">
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<s><emph type="italics"></emph>[ipſas verò tectorum diuiſiones &amp;c.] Hac in parte videtur <lb></lb>Autor explicare tectorum diuiſiones aliter factas fuiſſe à Diade,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/062.jpg"></pb><emph type="italics"></emph>&amp; Charia Polyidis Thetali diſcipulis, quorum in præcedenti ca<lb></lb>pite mentionem fecit. </s>
<s>Verùm ea, quæ in præſentia de tectorum di<lb></lb>uiſionibus ab Autore dicuntur, non in turribus, quas in pręceden<lb></lb>ti capite iuxta Diadis, &amp; Chariæ doctrinam conſtruxit: ſed in <lb></lb>quadam alia turri intelligenda ſunt: cuius tota quidem altitudo <lb></lb>ſit cubitorum 49 2/3 1/2, hoc eſt cubitorum 49 &amp; digitorum<emph.end type="italics"></emph.end> 20, <emph type="italics"></emph>ſiue <lb></lb>cubitorum 49 &amp; pedis vnius &amp; quartæ partis pedis: latus verò <lb></lb>primi tecti, ideſt ipſius baſis 7 1/2: vnumquodque autem laterum <lb></lb>ſecundi, tertij, quarti, quinti, &amp; ſexti tecti, quinque: vnum<lb></lb>quodque demum reliquorum quatuor tectorum latus, 4 1/3: ex qui<lb></lb>bus porrò cunctis altitudinibus totius turris altitudo cubitorum <lb></lb>49 2/3 1/2 colligitur. </s>
<s><expan abbr="Animaduertẽdum">Animaduertendum</expan> autem eſt quòd in hac tur<lb></lb>re quadrata area poſtremi tecti non erit quinta pars areæ qua<lb></lb>dratæ ipſius baſis. </s>
<s>quoniam area quadrata ſuę baſis erit 51 1/3 &amp; <lb></lb>(1/36), ſiue 51 &amp; (13/36), cuius quidem pars quinta eſt cubitorum 10 &amp; <lb></lb>digitorum 6 2/5 ſerè: quadrata verò area poſtremi tecti eſt 18 7/9 <lb></lb>cùm à radice 4 1/3 producatur. </s>
<s>Adnotauit inſuper Autor, quòd <lb></lb>ipſas tectorum omnium craßitudines altitudini connumerabant, <lb></lb>hoc eſt in tota turris altitudine computabant: &amp; quòd ſi minor <lb></lb>etiam turris ipſa fuiſſet, diuiſionem tectorum iuxta eandem ra<lb></lb>tionem reſpectu totius altitudinis faciebant.<emph.end type="italics"></emph.end></s></p><p type="main">
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<s><margin.target id="note93"></margin.target><emph type="italics"></emph>l<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Verum iam dictus Apollodorus &amp;c.] in hac parte propoſitum <lb></lb>Autoris eſt declarare iuxta doctrinam Apollodori menſuras eo<lb></lb>rum lignorum, quę ſuperiùs adhærentia nuncupari dixit. </s>
<s>Ait <lb></lb>igitur quòd Apollodorus pedibus <expan abbr="menſurãs">menſurans</expan> turrim, adhærentia pri<lb></lb>ma, quæ statim à baſi eriguntur pedum nouem iuxta altitudinem <lb></lb>fecit. </s>
<s>Præterea inquit quòd ſi idem Apollodorus omnia adhæ<lb></lb>rentia, ſcilicet in omnibus tectis adhærentia ligna, ęqualis qui<lb></lb>dem altitudinis eſſe vult: tunc ſex tectis pręditam eſſe turrem ip<lb></lb>ſam declarat, <expan abbr="necnõ">necnon</expan> ſuperadiectionem pedum ſex tantùm eſſe. </s>
<s>vo<lb></lb>cat autem Autor hìc ſuperadiectionem (quemadmodum etiam ſu<lb></lb>periùs id, quod vnius tecti laterum numerus addit ſuper alterius <lb></lb>tecti laterum numerum, vt ſuperiùs vidimus. </s>
<s>uerbi gratia 16 <lb></lb>ſuper 15, &amp; 15 ſuper 14, &amp; ſic in reliquis. </s>
<s>ſi enim turris ſex te-<emph.end type="italics"></emph.end><pb xlink:href="052/01/063.jpg"></pb><emph type="italics"></emph>ctis prædita eſt, quorum vnumquodque pedem vnum ſuper aliud <lb></lb>addit, dubio procul ipſa ſuper. </s>
<s>diectio ſex pedum erit. </s>
<s>atque huc<lb></lb>uſque verba Autoris clara, vera〈qué〉 ſunt. </s>
<s>quæ verò mox ſubiungit <lb></lb>incipientia ab illis verbis [vigeſimamtertiam verò partem] &amp; fi<lb></lb>nientia incluſiuè in illis [quadripertitò euenire] prorſus falſa <lb></lb>mihi videntur. </s>
<s>nam in turre quidem ab Autore ſuperiùs iuxta <lb></lb>mentem Apollodori deſcripta vera nequaquam eſſe poſſunt. </s>
<s>quan<lb></lb>doquidem in ipſa, hoc eſt vſque ad ipſius ſex tecta (cùm ſex tectis <lb></lb>præditam eam ſupponat) vigeſimatertia pars proximè areæ baſis <lb></lb>ſurſum minimè colligitur: neque etiam ſingula decem pedum ſu<lb></lb>periora iuga poſita ſunt, imo vndecim: niſi baſis non connumere<lb></lb>tur. </s>
<s>quouiſmodo autem fiat, nullo pacto vigeſimatertia pars pro<lb></lb>ximè areæ baſis ſurſum colligetur. </s>
<s>Potiùs autem hæc duo, quæ ab <lb></lb>Autore dicuntur, vera eſſent in quadam turri, cuius area qui<lb></lb>dem ipſius baſis eſſet 2300 pedum, area verò ſupremi tecti 100. <lb></lb>tunc etenim area quadrata ſupremi tecti ſurſum a lateribus col<lb></lb>lecta reuera vigeſimatertia pars areæ baſis eſſet: &amp; ſuperiora iu<lb></lb>ga nempe latera tecti ſupremi iam dictam vigeſimamtertiam par<lb></lb>tem comprehendentia ſingula decem pedum eſſent: latera verò <lb></lb>areæ ipſius baſis ſingula pedum 48 proximè. </s>
<s>at hucuſque nullam <lb></lb>talis turris mentionem Autor fecit, ſed videtur de iam deſcripta <lb></lb>ſuperiùs Apollodori turre ſtatim hæc ſubiunxiſſe, quippe quæ nul<lb></lb>lo pacto in ea quidem accommodari poſſunt. </s>
<s>Quod autem poſt <lb></lb>hæc ſubdit, quòd ſcilicet ſi quintam baſis partem Apollodorus in <lb></lb>turri ſex tectis prædita ſurſum colligit, vnius cum dimidio pedis <lb></lb>tectorum ſuperadiectionem quadripertitò euenire declarat: om<lb></lb>nino falſum eſſe videtur, &amp; ijs, quæ dicit Autor minimè quadrat. <lb></lb>ſi enim vnumquodque ſex laterum (vt ait Autor) ex ipſo pedum <lb></lb>ſedecim latere pedem vnum cum dimidio auferat, ita vt ſuperad<lb></lb>iectio ſit pedis unius cum dimidio: nemo eſt, qui non fateatur quòd <lb></lb>ſecundum latus 14 1/2, tertium 13, quartum 11 1/2, <expan abbr="quintũ">quintum</expan> 10, ſex<lb></lb>tum〈qué〉 <expan abbr="demũ">demum</expan> 8 1/2 erit. </s>
<s>At 8 1/2 latus in ſeipſum <expan abbr="multiplicatũ">multiplicatum</expan> pro<lb></lb>ducit aream quadratam 78 1/9, quæ non eſt quinta pars areæ <lb></lb>quadratæ 256 ipſius baſis. </s>
<s>Quòd ſi quis dicat <expan abbr="ſuperadiectionẽ">ſuperadiectionem</expan> <lb></lb>ipſam deſuper incipiendo à ſupremo turris tecto faciendam eſſe, <lb></lb>atque turrem ſex tectis prædictam in ſuperiori turris decem te-<emph.end type="italics"></emph.end><pb xlink:href="052/01/064.jpg"></pb><emph type="italics"></emph>ctis præditæ parte ſuſcipi, ac baſim eius non connumerari: ita vt <lb></lb>cùm ſupremum tectum ſit 7 1/6, eius proximum nempe ſecun<lb></lb>dum deſcendendo latus ſit 8 2/3, tertium 10 1/6, <expan abbr="quartũ">quartum</expan> 11 2/3, <lb></lb>quintum 13 1/6, ſextum 14 2/3, huius〈qué〉 demum proximum, ui<lb></lb>delicet ſeptimum, ſeu baſis ipſa non connumerata in numero ſex <lb></lb>tectorum 16 1/6: erit quadrata quidem area ipſius 16 1/6 lateris <lb></lb>(261 23/36), cuius non eſt quinta pars 51 1/5 &amp; (1/36) area, quæ à 7 1/6 <lb></lb>producitur. </s>
<s>proximior enim quinta eius pars eſt 52 1/5. niſi for <lb></lb>taſſe dicat aliquis ipſam unius cum dimidio ſuperadiectionem <lb></lb>non eſſe faciendam in baſi, ſed in ſex <expan abbr="tantũmodo">tantummodo</expan> tectis. </s>
<s>tunc enim <lb></lb>area baſis erit ſicut à principio 256, cuius quinta pars eſt 51 1/5, <lb></lb>cuius quintæ partis latus tetragonicum est 7 1/6 proximè. </s>
<s>Verùm <lb></lb>ſi uerba autoris ſic intelligenda ſunt, uerum erit quod ait, ſcili<lb></lb>cet quòd ſi quintam baſis partem in turri ſex tectis prædita ſur<lb></lb>ſum colligit Apollodorus, unius cum dimidio pedis tectorum ſu<lb></lb>peradiectionem quadripertitò euenire declarat. </s>
<s>Sed reuera tur<lb></lb>ris hæc non erit ſex tectis prædita, ſed ſeptem computando baſim <lb></lb>pro uno tecto, ut in omnibus turribus autorem ſeciſſe uidimus. </s>
<s><lb></lb>particula uerò illa [quadripertitò] ſic intelligenda eſt. </s>
<s>quòd ſci<lb></lb>licet quadrifariam iuxta quatuor laterum numeros ſuperadie<lb></lb>ctio facienda ſit. </s>
<s>Quamuis autem hoc ultimum ab autore dictum <lb></lb>ſic intelligendo turrem ingeniosè uerum oſtendi potest, illa duo ta<lb></lb>men ab eo ſuperiùs dicta nullo modo in ſe ueritatem contine<lb></lb>re poſſunt: niſi in ea, quàm diximus turre, cuius autor nullam <lb></lb>mentionem ſecit. </s>
<s>Quapropter ego potius crediderim ante illa <lb></lb>uerba [uigeſimam tertiam uerò partem] nonnulla intextu deſide <lb></lb>rari. </s>
<s>Quę cùm ita dixerit autor ſequitur propoſitum ſuum his <lb></lb>verbis [ſi autem decem tectis pręditam &amp;c.] ubi primùm repe<lb></lb>tit ea, quæ ſuperiùs de turri decem tectis prædita ab Apollodoro <lb></lb>conſtructa dixerat: quòd ſcilicet Apollodorus declarat ſingu<lb></lb>lam pedis unius ſuperadiectionem euenire, &amp; quintam baſis par<lb></lb>tem ſurſum ab ipſo intercipi, ita ut ſuperiora iuga ſingula pedum <lb></lb>ſeptem &amp; ſextæ partis fiant: Deinde declarat in hac turri, ſci-<emph.end type="italics"></emph.end><pb xlink:href="052/01/065.jpg"></pb><emph type="italics"></emph>licet decem tectis prædita menſuras adhærentium lignorum ab <lb></lb>Apollodoro traditas, dicens quòd Apollodorus inferiora adhæren<lb></lb>tia ſingula pedum nouem fieri declarat: ipſa verò, quæ in ſupe<lb></lb>rioribus quatuor tectis ſunt, ſingula pedum ſex tantum: ipſa de<lb></lb>mum, quæ in quatuor reliquis (cùm adhærentia ligna ſint nouem <lb></lb>ordinum) adhuc ſuperiora ſunt, ſingula quinque, &amp; partis. </s>
<s>quæ <lb></lb>quidem pars, quæ nam ſit tertia ſcilicet, an quarta, vel quinta, <lb></lb>vel quæuis alia, neſcitur, cùm Autor eam minimè poſuerit, aut <lb></lb>fortaſſe in textu deficiat.<emph.end type="italics"></emph.end></s></p><p type="main">
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<s><margin.target id="note94"></margin.target><emph type="italics"></emph>m<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Hoc itaque pacto &amp;c.] in præſenti parte primùm epilogat Au<lb></lb>tor breuiter ea, quæ de tectorum diuiſionibus, ſiue altitudinibus <lb></lb>edocuit: deinde declarat turres ex tectis cùm æqualis, tum inæ<lb></lb>qualis altitudinis iuxta cubitos ac pedes conſtructas adinuicem <lb></lb>proportionales, &amp; commenſurabiles eſſe. </s>
<s>Epilogans igitur inquit. <lb></lb>[Hoc itaque pacto] ſcilicet quemadmodum iam docuimus [non <lb></lb>ſolùm ea, quæ iuxta numerum diſcrepant turrium tecta] hoc est, <lb></lb>quæ modo ſex, modo decem numero ſunt in turribus ſcilicet, quæ <lb></lb>quandoque ſex, quandoque decem tectis præditæ ſupponuntur. <lb></lb>[ad ſexaginta pedum altitudinem] videlicet in turri ipſius Apol<lb></lb>lodori, quam ſexaginta pedum altitudinis conſtruxit, vt in prin<lb></lb>cipio præſentis capitis Autor declarauit. [cùm æqualis] nempe in <lb></lb>turri ſex tectis prædita, in qua omnia adhærentia ligna, quibus <lb></lb>tectorum altitudo diſtinguitur, ſingula pedum nouem ab Apollo<lb></lb>doro ponuntur. [tum inæqualis altitudinis] vt puta in turri de<lb></lb>cem tectis prædita, in qua (vt paulò ſuperiùs dictum eſt) infe<lb></lb>riora quidem adhærentia, pedum nouem: ſuperiora autem qua<lb></lb>tuor, pedum ſex: reliqua verò quatuor adhuc ſuperiora, quinque, <lb></lb>&amp; partis ab Apollodoro poſita ſunt. [exiſtentia reperientur.] hoc <lb></lb>est ita vt iam diximus ſe ſe habere inuenientur. </s>
<s>quæ quidem cùm <lb></lb>ſic epilogauerit, ſubiungit. [verumetiam eæ, quæ ex vtriſque] ſci<lb></lb>licet tum æqualis, tum inæqualis altitudinis tectis [iuxta cubi<lb></lb>tos] quales ſunt Diadis, &amp; Chariæ [&amp; pedes conſtruuntur,] qua<lb></lb>les Apollodori ſunt. [ac iuxta magnitudinem diſcrepant turres] <lb></lb>quandoquidem iuxta cubitos conſtructæ iuxta pedes conſtructis <lb></lb>maiores ſunt, vt nobis perſpicuum erit. [commenſurabiles ad ſe <lb></lb>ſe inuicem ſecundum proportionem ostendentur] hoc eſt commu<lb></lb>nibus menſuris proportionaliter menſurari demonstrabuntur. </s>
<s>ve-<emph.end type="italics"></emph.end><pb xlink:href="052/01/066.jpg"></pb><emph type="italics"></emph>rùm vt id, quod ait Autor clarum fiat, ſint exempli gratia duæ <lb></lb>Diadis, &amp; Charię turres iuxta cubitos ab eis conſtructæ, qua<lb></lb>rum altera quidem nonaginta, altera verò ſexaginta cubitorum <lb></lb>altitudinem habebant. </s>
<s><expan abbr="hç">haec</expan> igitur adinuicem <expan abbr="cõmenſurabiles">commenſurabiles</expan> ſunt. </s>
<s><lb></lb>quoniam non ſolùm communi menſura, nempe cubito menſuran<lb></lb>tur, verumetiam à triginta cubitibus tamquam vna communi <lb></lb>earum menſura ſuſceptis altera quidem ter, altera verò bis men<lb></lb>ſuratur. </s>
<s>Rurſus autem adinuicem in ratione ſeſquialtera ſunt, <lb></lb>cùm nonaginta altitudo, ſexaginta altitudinem ſemel, ac eius di<lb></lb>midiam partem contineat. </s>
<s>Similiter ſint aliæ duæ turres iuxta pe<lb></lb>des ſecundum Apollodorum conſtructæ, quarum altera quidem <lb></lb>nonaginta, altera verò ſexaginta pedum altitudine prædita ſit. </s>
<s><lb></lb>hæ itaque turres eodem modo, quo duæ priores, tum commenſura<lb></lb>biles, tum adinuicem in ratione ſeſquialtera ſunt. </s>
<s>Præterea verò <lb></lb>ſi quatuor iſtæ turres adinuicem comparentur, duæ quidem prio<lb></lb>res duabus poſterioribus, tum commenſurabiles, tum in ratione <lb></lb>ſeſquialtera reperientur. </s>
<s>commenſurabiles enim ſunt, quoniam <lb></lb>octo digiti cubitum quidem ter, pedem verò bis menſurant: cùm <lb></lb>pes 16, cubitus 24 digitis conſtet: vndè etiam cubitus ad pedem <lb></lb>ſeſquialter eſt. </s>
<s>in ratione verò ſeſquialtera ſunt, quandoquidem <lb></lb>altitudo nonaginta cubitorum altitudinis nonaginta pedum, ſimi<lb></lb>liter〈qué〉 altitudo ſexaginta cubitorum altitudinis ſexaginta <expan abbr="pe-dũ">pe<lb></lb>dum</expan>, necnon <expan abbr="ſeptẽdecim">ſeptendecim</expan> cubitorum longitudo baſis <expan abbr="ſeptẽdecim">ſeptendecim</expan> pe<lb></lb>dum longitudinis baſis ſeſquialtera eſt. </s>
<s>quemadmodum enim ſe <lb></lb>habet cubitus ad pedem, ita etiam 90, vel 60, vel 17, vel quot<lb></lb>cumque cubiti ad 90, vel 60, vel 17, vel quotcumque pedes ſe ſe <lb></lb>habebunt. </s>
<s>Non ſolùm autem iuxta altitudines, &amp; baſium longi<lb></lb>tudines: verumetiam iuxta reliquas omnes earum partes iam di<lb></lb>ctæ quatuor turres, tum <expan abbr="cõmenſurabilitatem">commenſurabilitatem</expan>, tum eam rationum <lb></lb>poßident conuententiam, quæ proportio dicitur. </s>
<s>atque propterea <lb></lb>ſubiunxit Autor, [&amp; ſicut ſe habent 24 ad 16, ſic etiam rotæ ad <lb></lb>ſeinuicem tum iuxta numerum, tum etiam iuxta magnitudinem: <lb></lb>necnon baſis ad baſim ſicuti etiam tria ad duo.] hoc eſt ipſe quoque <lb></lb>turrium rationem adinuicem ſeſquialteram habentium rotæ in <lb></lb>ratione ſeſquialtera eſſe debent [tum iuxta numerum] vt ſcilicet <lb></lb>rotæ ſeſquialteræ turris, ſex numero: ſub ſeſquialteræ verò, qua<lb></lb>tuor ſint, [tum etiam iuxta magnitudinem] vt nempe rotæ ſeſ-<emph.end type="italics"></emph.end><pb xlink:href="052/01/067.jpg"></pb><emph type="italics"></emph>quialteræ turris rotis ſubſeſquialteræ maiores in ratione ſeſqui<lb></lb>altera ſint, quemadmodum 24 ad 16. Similiter autem &amp; baſis <lb></lb>ſeſquialteræ turris ad baſim ſubſeſquialteræ ſicut tria ad duo ra<lb></lb>tionem ſeſquialteram habere debet. </s>
<s>Quæ quidem concludens <lb></lb>Autor ait, [oſtenſæ ſunt igitur ipſæ quoque menſurantes turres,] <lb></lb>nempe ſubſeſquialteræ, ſiue iuxta pedes conſtructę [ad ſeinui<lb></lb>cem eam, quam eæ, quæ menſurantur] hoc eſt ſeſquialteræ, ſiue <lb></lb>iuxta cubitos fabricatæ [iuxta proportionem] ideſt rationum ſi<lb></lb>militudinem, atque conuenientiam, ſiue proportionaliter [habere <lb></lb>rationem] vtpotè videlicet ſeſquialteram. </s>
<s>vocat autem ſubſeſ<lb></lb>quialteras quidem menſurantes, ſeſquialteras verò menſuratas <lb></lb>hac ratione: quia ſcilicet ſeſquialteræ ab earum ſubſeſquialte<lb></lb>ris, videlicet ab earum dimidijs partibus ter menſurantur. </s>
<s>po<lb></lb>ſtea verò concludens Autor cuncta ea, quæ in hac vltima capitis <lb></lb>parte de commenſurabilitate, proportione〈qué〉 turrium ab eo dicta <lb></lb>ſunt ait, quòd non ſolùm iuxta commenſurationem, verumetiam <lb></lb>iuxta conuenientiam, ſcilicet rationum, ſeu proportionem ipſam, <lb></lb>turrium ferri idonearum conſtructiones. </s>
<s>Diodorus, necnon Dia<lb></lb>des, &amp; Charias fecerunt. </s>
<s>vbi quærendum eſt quiſnam ſuerit iſte <lb></lb>Diodorus, cuius nullibi niſi hoc in loco mentionem Autor fecit: an <lb></lb>potiùs Apollodorus legendum ſit, cuius potißimùm doctrina de <lb></lb>conſtructione turrium in toto præſenti capite traditur. </s>
<s>Poſthæc <lb></lb>demum ex ijs, quæ hucuſque dicta ſunt <expan abbr="corollariũ">corollarium</expan> quoddam Au<lb></lb>tor excerpſit dicens manifeſtum eſſe [quòd Antiqui Mechanici] <lb></lb>ſcilicet profeſſores eius Mathematicæ ſcientiæ partis, quę Me<lb></lb>chanica nuncupatur [eruditißimi〈qué〉 architecti] hoc eſt ipſi machi<lb></lb>narum bellicarum artifices iam dictę Mechanicæ ſcientiæ peri<lb></lb>tißimi, vel ab alijs eiuſdem ſcientiæ peritißimis coadiuuati [ſcien <lb></lb>tificè] hoc eſt cum debitis proportionibus, ac menſuris ab ipſa ſcien<lb></lb>tia traditis [&amp; non abſque ratione] nempe fortuitò [<expan abbr="Machinarũ">Machinarum</expan>] </s></p><p type="main">
<s><arrow.to.target n="note95"></arrow.to.target><lb></lb>vtique bellicarum [conſtructiones faciebant. [Turre ſic quoad <lb></lb>conſtructionem conſtructa] in hac poſtrema præſentis capitis par<lb></lb>te de quibuſdam ad ipſarum turrium confirmationem, deffenſio<lb></lb>nem〈que〉 pręuidendis, ac præparandis ſermonem habet Autor, cu<lb></lb>ius verba perſpicua ſunt. </s>
<s>finis autem huiuſce capitis, &amp; princi<lb></lb>pium ſequentis, ac fortaſſe quoddam aliud integrum caput de<lb></lb>ſiderantur in omnibus quæ vidimus græcis exemplaribus, ve-<emph.end type="italics"></emph.end><pb xlink:href="052/01/068.jpg"></pb><emph type="italics"></emph>rùm hæc à nobis pro dilucidatione præſentis capitis omnium quæ <lb></lb>in toto præſenti opere continentur tum longißimi, tum obſcurißi<lb></lb>mi dicta ſint.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note95"></margin.target>n</s></p><p type="main">
<s><emph type="center"></emph>De ſcalis Arietem geſtantibus. </s>
<s>Cap. </s>
<s>XV.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Principium huius Capitis deſideratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s>* * * partes Arietem ſuſtentatum ferri. </s>
<s>à tertio uerò <lb></lb>gradu ſuperioris ſcalæ ad alterius tertium, &amp; æqualis altitu<lb></lb>dinis exiſtentem tabulis, uel uirgis textis teguntur: utriſque <lb></lb>autem creta ſuperillitis, aut corijs bouum recens occiſo<lb></lb>rum coopertis, tum propter tormenta ignem iaculantia, <lb></lb>tum propter lapidum iactus. </s>
<s>at paulò infra tertium <expan abbr="gradũ">gradum</expan> <lb></lb>poſt octo decim, aut <expan abbr="ẽt">etiam</expan> uiginti pedes, contingentes gradus <lb></lb>aliud tectum ſuſcipiunt, non ad totam graduum latitudi<lb></lb>nem. </s>
<s>locus enim ad aſcenſum pertinens abſque tecto relin<lb></lb>quetur. </s>
<s>Oportet <expan abbr="aũt">aut</expan> eos, <expan abbr="q̨">quod</expan> ad <expan abbr="ſcalarũ">ſcalarum</expan> crura imponuntur cla<lb></lb>uos, multùm ad latera foras prodire: ut latiùs ſcalarum ſpa<lb></lb>tium tegatur. </s>
<s>nam Aries ibi maximè aget, à ſupremo te<lb></lb><arrow.to.target n="note96"></arrow.to.target><lb></lb>cto pendens duobus ſuſtentaculis æqualis ferè altitudinis, <lb></lb>ut qui Arietem pellunt ſuper pauimento ſpatii tabulis co<lb></lb>operti ſtantes, ad ſuperiores murorum partes Ariete oppu<lb></lb>gnent. </s>
<s>nam omne erectum, &amp; excedens tanquam liberum, <lb></lb><expan abbr="haudq́ue">haudque</expan> coniunctum facilè frangi, <expan abbr="deſtruiq́ue">deſtruique</expan> poteſt. </s>
<s>cu<lb></lb>iuſmodi ſunt murorum pinnæ, <expan abbr="turriumq́ue">turriumque</expan> propugnacu<lb></lb>la, ac demum quæcunque non adinuicem continuata ſu<lb></lb>ſtentantur. </s>
<s>atque per ipſum Arietem quadrangulum exi<lb></lb>ſtentem ad murum peruenire facilè poterint, non aliter <lb></lb>quam ij, qui per eas, quæ in turribus iam dictæ ſunt ad la<lb></lb>tera circumſeptiones, perueniunt. </s>
<s>nam huiuſcemodi ſcalæ <lb></lb>non circumflectuntur ad crura <expan abbr="circũuerſæ">circumuerſæ</expan>, ſed ſemper ere<lb></lb>ctæ, <expan abbr="eademq́ue">eademque</expan> ad ſeinuicem interualla conſeruantes per<arrow.to.target n="note97"></arrow.to.target><lb></lb>manent. </s>
<s>&amp; deſcriptio propoſita eſt. </s></p>
<pb xlink:href="052/01/069.jpg"></pb><p type="margin">
<s><margin.target id="note96"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note97"></margin.target>b</s></p><figure id="id.052.01.069.1.jpg" xlink:href="052/01/069/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>MAchinæ ex ſcalis conſtructæ, arietem〈qué〉 geſtantis, de qua <lb></lb>loquitur Autor in hoc capite, constructione caremus, quo<lb></lb>niam in ea parte, quæ in principio capitis huius deſidera<lb></lb>tur ea tradi debebat. </s>
<s>habemus <expan abbr="aũt">aut</expan> <expan abbr="eã">eam</expan> ab Apollodoro traditam in <lb></lb>libro ſuo de machinis obſidionalibus, quam hìc poſuiſſemus ſi fi<lb></lb>guræ ab Autore propoſitæ correſponderet. </s>
<s>cùm <expan abbr="autẽ">autem</expan> ei minimè cor<lb></lb>reſpondeat, ſed ab ea longè diuerſa ſit, pluribus〈qué〉 figuris indigeat,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/070.jpg"></pb><emph type="italics"></emph>noluimus eam hìc interſerere, ne Autoris <expan abbr="ordinẽ">ordinem</expan> peruerteremus. </s>
<s><lb></lb>verùm ipſa etiam ædetur cùm à nobis iam dictus Apolloderi li<lb></lb>ber vnà cum Athænei, Cteſibij, Bitonis, diuerſorum〈qué〉 aliorum au<lb></lb>torum opera varia de re bellica è græco ſermone in latinum iam <lb></lb>conuerſa impreſſoribus excudenda tradentur.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note98"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note98"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ferè] particulam hanc appoſuit Autor, vt nobis oſtenderet, <lb></lb>quòd illa duo ſuſtentacula, quibus aries ipſa pendet, inæqualis al<lb></lb>titudinis eſſe debent; ita ſcilicet quòd anterius ſuſtentaculum po<lb></lb>ſteriore breuius aliquantulum ſit, vt aries ad ſuperiores muro<lb></lb>rum partes tendat, maiorem〈qué〉 percußionem efficiat: quemadmo<lb></lb>dum ſuperiùs in <expan abbr="teſtudinũ">teſtudinum</expan> arietem <expan abbr="geſtantiũ">geſtantium</expan> conſtructione docuit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note99"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note99"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Dubitandum an præſens figura in fine huius capitis ab Autore <lb></lb>poſita fuerit, quoniam in fine omnium huius operis capitum vſus <lb></lb>eſt Autor his verbis [&amp; figura ſubiecta eſt.] vel [ſubſcripta eſt] <lb></lb>vel [huiuſcemodi eſt] hìc autem ait [propoſita eſt] quod indicat <lb></lb>figuram hanc ante hunc locum ab Autore ſuiſſe collocatam: for<lb></lb>ſan in ijs, quæ inter finem præcedentis, &amp; initium præſentis ca<lb></lb>pitis deſunt. </s>
<s>nos verò cùm hoc in loco eam apud græcum exem<lb></lb>plar inuenimus, hìc etiam ponendam eſſe voluimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Alia ſcalarum deſcriptio duos Arietes geſtantium. </s>
<s><lb></lb>Cap. </s>
<s>XVI.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note100"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note100"></margin.target>a</s></p><p type="main">
<s>RVrſus alium ordinem, <expan abbr="ſitumq́ue">ſitumque</expan> ſcalæ ſuſci<lb></lb>piunt, eum ſcilicet, qui verſus murum adue<lb></lb>niat, æqualis exiſtens, &amp; parallelus, aut ſecun<lb></lb>dum faciem erectus: &amp; ipſos quidem gradus <lb></lb>iuxta muri faciem, <expan abbr="retroq́ue">retroque</expan> reſpicientes ha<lb></lb>bent: ipſa verò à ſeinuicem tum ſurſum, tum deorſum in<lb></lb>terualla, non quemadmodum primæ inæqualia habent, ſed <lb></lb>ex æquali idem interuallum conſeruant. </s>
<s>At tecta eadem, <lb></lb>quæ priores habent: variant <expan abbr="autẽ">autem</expan> iuxta hoc. </s>
<s>nam vice vnius <lb></lb>arietis, qui inter priores duas ſcalas fertur, duo extrinſecùs <lb></lb>ad crurium latera poſiti feruntur. </s>
<s>Hi autem arietes cùm ali<lb></lb>quid peregerint ſiue commouentes, ſiue rumpentes aliquid <lb></lb>eorum, quæ in muri faciem præponuntur: eos funes, qui ex <lb></lb>poſterioribus ſunt relaxabant, &amp; ſimul duæ ſcalæ muro ap-<pb xlink:href="052/01/071.jpg"></pb>portantur. </s>
<s>verùm anterior quidem <expan abbr="earũ">earum</expan> penes gradus ſuos <lb></lb>muro appropinquat: altera verò diſtat ab ipſa, quantùm <lb></lb>etiam id, quod eſt inter eas adinuicem interuallum iuxta <lb></lb><expan abbr="connexionẽ">connexionem</expan> remouetur. </s>
<s>ac <expan abbr="demũ">demum</expan> ea, quæ deſuper eſt ſcala<lb></lb>rum connexio, tamquam pauimentum tabulis proſtratis <lb></lb>facta, &amp; circumquaque cooperta, efficax ad murum ſcanſo<lb></lb>rium fit. </s>
<s><expan abbr="figuraq́ue">figuraque</expan> ipſa ſubijcitur. </s></p><figure id="id.052.01.071.1.jpg" xlink:href="052/01/071/1.jpg"></figure>
<pb xlink:href="052/01/072.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note101"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note101"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>VErbæ illa [eũ ſcilicet, qui verſus murum adueniat, æqua<lb></lb>lis exiſtens, &amp; parallelus, aut ſecundum faciem erectus] <lb></lb>aliquantulum obſcura ſunt ſi ordini, ſitui〈qué〉 applicentur, <lb></lb>vt verborum ſeries exigit. </s>
<s>durum eſt enim dicere quòd ordo, ſi<lb></lb>tus〈qué〉 ſcalarum talis ſit, qui verſus murum adueniat, æqualis <lb></lb>exiſtens, &amp; parallelus, ac ſecundum faciem erectus. </s>
<s>cùm enim <lb></lb>ordo, ac ſitus corporis accidentia ſint: nec ad murum aduenire, <lb></lb>neque prorſus moueri niſi vnà cum aliquo corpore poſſunt. </s>
<s>præte<lb></lb>rea cùm æquale, parallelum, &amp; erectum eſſe magnitudinis paſ<lb></lb>ſiones ſint: ſitus autem, ac ordo ſub prædicamento quantitatis <lb></lb>cadere minime queant, nulli dubium quòd iam dictæ paßiones de <lb></lb>his prædicari non poſſunt. </s>
<s>Quapropter paßiones iſtæ ſcalis ipſis <lb></lb>applicandæ ſunt. </s>
<s>ita vt eorum verborum ſententia ſit huiuſmodi. </s>
<s><lb></lb>quòd ſcilicet talem ordinem, ſitum〈qué〉 ſcale ſuſcipiunt: qui eas ad <lb></lb>murum aduenire, æquales muri altitudini exiſtere, &amp; parallelas <lb></lb>tum muro, tum <expan abbr="ſibiinuicẽ">ſibiinuicem</expan>, aut ſecundum faciem erectas eſſe faciat.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Alia ſcalarum deſcriptio vnicum arietem, ſed in deſtruen<lb></lb>do vehementiorem geſtantium. </s>
<s>Cap. </s>
<s>XVII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>QVùm in hac poſitione, tum in prima (excepta <lb></lb>iam dicta ſecunda, quæ ſitu, ac ordine paral<lb></lb>lela ad murum eſt) eorum, qui arietibus addi<lb></lb>cati ſunt illi, qui ſuper <expan abbr="pauimẽto">pauimento</expan> ſtant, &amp; arie<lb></lb>te ſurſum oppugnant turbantur, ac propu<lb></lb>gnantes hoſtes extimeſcunt. </s>
<s>verùm duos de<lb></lb>ſuper eminentes gradus in eo, cui ſit arietis motu, corijs <lb></lb>circum operientes, propugnaculum, &amp; cuſtodiam <expan abbr="tãquam">tanquam</expan> <lb></lb>muri pinnas ſibi ipſis præbebunt. </s>
<s>Non paruam autem vti<lb></lb>litatem ad indubitatum auxilium, ac ſeruitium duplæ ſca<lb></lb>læ præſtabunt, ſi in vnaquaque compoſitarum ab æqualis <lb></lb>altitudinis clauo ad alterius ex aduersò æqualis altitudinis <lb></lb>clauum, ſiue in eiuſdem ordinis gradum <expan abbr="vniuſcuiuſq;">vniuſcuiuſque</expan> ſe<lb></lb>cundum eandem menſuram ab eodemmet alterius gradu
<pb xlink:href="052/01/073.jpg"></pb>ligna parte altera latiora indirectum accommodabimus: <lb></lb>ad ea, quæ ad latera extra excedunt clauium extrema, pe<lb></lb>netrantia: &amp; immutabiles conſeruantia eos interceptos lo<lb></lb>cos, qui ab ipſis inuicem ſcalis ad crura diſtant, quique nec </s></p><p type="main">
<s><arrow.to.target n="note102"></arrow.to.target><lb></lb>adaperiri in ipſo lationis motu poſſunt, neque tota machi<lb></lb>na claudi. </s>
<s>At ne ligna ipſa diſrumpantur, neque decidant <arrow.to.target n="note103"></arrow.to.target><lb></lb>à loco, quem poſſident: chelonaria impoſita ſuper ſcala<lb></lb>rum cruribus, clauis affigantur, quemadodum iam dicta <lb></lb>inſculpta hemiſphæria, ſiue pugilli iuxta medium circum<lb></lb>ſecti ad aſtringendum, &amp; continendum ligna, quæ clauis <lb></lb><expan abbr="trãsfixa">transfixa</expan> ſunt. </s>
<s>verùm aries quam iuxta medium ſcalę ferunt, <lb></lb>ex vtriſque lateribus iuxta anterius extremum ſuſcipiat <lb></lb>duas tabellas quadrangulas tamquam maxillas erectas ad <lb></lb>altitudinem, ſuper arietem vſque ad cubitum eminentes, <lb></lb>in ipſa verò clauorum affixione, atque inferiùs propter ex<lb></lb>tenſionis <expan abbr="vehementiã">vehementiam</expan> confirmatas. </s>
<s>Hæ <expan abbr="itaq;">itaque</expan> indirectum ex <lb></lb>aduerſo ſibiinuicem circa medium forentur, atque ad ex<lb></lb>trinſecas foraminum partes coronæ ſolidæ tamquam anuli <arrow.to.target n="note104"></arrow.to.target><lb></lb>clauis affigantur, quæ modiolos vocatos iuxta medium ſu<lb></lb>ſcipiant, quoad figuras fictilibus tubeculis ſimiles, ex ære <lb></lb>interiùs tornatiles, vel ex fortibus lignis factos, ferreis ex<lb></lb>trinſecùs laminis alligatos, ampliores baſes circa poſitio<lb></lb>nem habentes, ac demum iuxta circum uolutionem ab anu<lb></lb>lis, qui clauis affixi ſint, impeditos ne ab ipſis foraminum lo<lb></lb>cis excidant. </s>
<s>ipſæ verò modiolorum buculæ repercutian<lb></lb>tur, <expan abbr="ſuſcipiantq́ue">ſuſcipiantque</expan> paruas regulas quadrangulas penetran<arrow.to.target n="note105"></arrow.to.target><lb></lb>tes tamquam periſtomidas verſus bucularum extrema ex<lb></lb>cedentes. </s>
<s>ad quas neruis humerarijs, ſiue dorſalibus om<lb></lb>nium animalium (exceptis porcorum) per medium modio<lb></lb>lorum tranſeuntibus, in ipſa circum uolutionis vehemen<lb></lb>tia propter fortitudinem eos circumuolui oportet: aut eis <lb></lb>robuſtioribus chordis, quæ ex ſericis textis fiunt, vel ex li<arrow.to.target n="note106"></arrow.to.target><lb></lb>no netilibus, iuxta medium ſuſcipientibus lignum longum <lb></lb><expan abbr="interpoſitũ">interpoſitum</expan>, in figura reflexi angonis, è contrario retrorſus <lb></lb>conuerſum, &amp; iuncturam retinens: quales ſunt ij, qui lapi<arrow.to.target n="note107"></arrow.to.target><lb></lb>des iaciunt monangones, quos nonnulli fundas appellant. </s>
<s><lb></lb>vectem autem ferreum anulari radice præditum ad iam di-
<pb xlink:href="052/01/074.jpg"></pb>ctas periſtomidas interpoſitum violentam circumuolutio<lb></lb>nem in ipſis modiolis agere, <expan abbr="fortemq́ue">fortemque</expan> violentiam perfice<lb></lb>re opus eſt. </s>
<s>aries verò, quæ à ſcalis pellitur, &amp; muro affer<lb></lb>tur, inijciet ijs, qui murum cuſtodiunt demiſſum monan<lb></lb>gonem, &amp; multam aſſiſtentium expugnationem faciet. </s>
<s>at<lb></lb>que figura deſcripta eſt. </s></p><p type="margin">
<s><margin.target id="note102"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note103"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note104"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note105"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note106"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note107"></margin.target>f</s></p><figure id="id.052.01.074.1.jpg" xlink:href="052/01/074/1.jpg"></figure>
<pb xlink:href="052/01/075.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note108"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note108"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[tota machina claudi] ſic in græco codice legitur. </s>
<s>ſed meliùs <lb></lb>eſſet legere [totam machinam claudere.]<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note109"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note109"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[chelonaria hìc intelligenda ſunt parua chelonia, quæ quidem <lb></lb>cuiuſmodi ſint in præcedenti capite declarauimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note110"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note110"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Modiolus, qui græcè<emph.end type="italics"></emph.end> <foreign lang="grc">χοινικὶς</foreign> <emph type="italics"></emph>dicitur, eſt rotæ pars axim cir<lb></lb>cumambiens, cui affixi ſunt radij.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note111"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note111"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Ea ligna, quæ ſuperiùs in nono, ac præcedenti capite perito<lb></lb>midas Autor vocauit, nunc periſtomidas non immerito nuncupat: <lb></lb>quandoquidem circa ſtomium, hoc eſt buculam ipſorum modio<lb></lb>lorar: ponenda ſunt. </s>
<s>verùm peritomidæ quoque dicuntur<emph.end type="italics"></emph.end> <foreign lang="grc">ἀπὸ <lb></lb>τοῡ περιτέμνειν</foreign>, <emph type="italics"></emph>hoc eſt circumincidere, quoniam circuminciſa, <lb></lb>inſculpta〈qué〉 circumquaque iam dicta ligna ſunt, quemadmodum <lb></lb>in duobus ſuperioribus locis declarauimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note112"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note112"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Angon eſt quædam ſpecies arcus reflexi, qui cum chordam <lb></lb>non habet, è contrario retrorſum conuertitur. </s>
<s>cuiuſmodi arcus ij <lb></lb>ſunt, quibus nunc græci, turcæ〈qué〉 ſagittarij vtuntur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note113"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note113"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Monangon eſt quoddam iaculatorium inſtrumentum balliſtæ <lb></lb>ſimile, cuius exquiſitam conſtructionem Athenæus quidem tra<lb></lb>dit: Auior verò breuiter in ſequenti capite mentionem facturus <lb></lb>eſt. </s>
<s>hoc autem inſtrumentum quidam (vt ait Autor) antiquorum <lb></lb>Mechanicorum fundam etiam appellarunt: licet funda propriè <lb></lb>ſit inſtrumentum ex lino factum, quo longè lapides iactantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>De quibuſdam iaculatorijs inſtrumentis breuis <lb></lb>enarratio. </s>
<s>Cap. </s>
<s>XVIII.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note114"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note114"></margin.target>a</s></p><p type="main">
<s>IPſa verò monangonis conſtructio ad catapul<lb></lb>ticam etiam contemplationem volentes inſti<arrow.to.target n="note115"></arrow.to.target><lb></lb>tuet. </s>
<s>quandoquidem ad longiùs iaculandum <lb></lb>tum rectè extenſis, tum reflexis: ſiue tum la<lb></lb>pides iacientibus, tum ſagittas celeriter iacu<lb></lb>lantibus inſtrumentis multùm confert. </s>
<s>nam ipſa modiolo<lb></lb>rum appoſitio parte altera oblongius per chordam inſtru<lb></lb>mentum: &amp; circa vehementiam, fortiorem emiſſionem effi<pb xlink:href="052/01/076.jpg"></pb>cit. </s>
<s>quantùm enim chorda iuxta longitudinem ad augetur, <lb></lb>tantùm ſagittæ quoque emiſſio extendi innata eſt: chorda <lb></lb>ipſius arcus omnia peragente, <expan abbr="ipſiùsq́ue">ipſiùsque</expan> emiſſionis violen<lb></lb>tiam ſuſtinente. </s>
<s>quamobrem huius contexionem ex robu<lb></lb>ſtioribus, &amp; quamplurimùm exercitatis neruis animalis <lb></lb>fieri dicunt. </s>
<s>verbi gratia Cerui quidem, ex ijs, qui in cruri<lb></lb>bus, pedibusq̀ue: Tauri verò, ex ijs, qui in humero ſunt. <arrow.to.target n="note116"></arrow.to.target><lb></lb>atque ipſas quidem erectè extenſorum chordas rotundas <lb></lb>quoad contexionem eſſe, vt inter ſagittarum forficulas in<lb></lb>cidant: ipſas vero reflexorum, latas zonarum inſtar, anſas <lb></lb>ex earum extremis habentes, ad quas angones ipſi ingre<lb></lb>diuntur. </s>
<s>vt lapis à medietate chordæ ſecundum <expan abbr="latitudinẽ">latitudinem</expan> <lb></lb>percuſſus, benè emittatur, non excidens verſus extrema. </s>
<s><lb></lb>Ipſam autem, quæ in angonibus eſt chordam ex commis <lb></lb>etiam muliebribus texi dicunt. </s>
<s>ſubtiles enim exiſtentes, <arrow.to.target n="note117"></arrow.to.target><lb></lb>atque longæ, <expan abbr="multoq́ue">multoque</expan> oleo educatæ: cùm contextæ fue<lb></lb>rint, multum roborem ſuſcipiunt: ita vt ab ipſa, quæ ner<lb></lb>uis fit fortitudine non diſcrepent. </s>
<s>Verumtamen de his <expan abbr="nũc">nunc</expan> <arrow.to.target n="note118"></arrow.to.target><lb></lb>ſatis. </s>
<s><expan abbr="nã">nam</expan> in iaculorum effectrice tractatione ſubtiliter curio<lb></lb>ſioribus ad conſtructionem non ſolùm hæc, verumetiam <lb></lb>foraminum in inſtrumentis dimetientes, necnon ij, qui in <lb></lb>triplicata ratione dimetientium in baſibus exiſtentium ſi<lb></lb>miles, adinuicem oſtenduntur cylindri, ac demum diuul<lb></lb>gata cubi duplatio: quibus iaculorum magnitudines iuxta <lb></lb>magnitudines contingentium inſtrumentorum duplæ, vel <lb></lb>etiam triplæ cùm fiant, ad eaſdem longitudines emittun<lb></lb>tur: mathematicè ibi, ac inſtrumentaliter cuncta ab Ale<arrow.to.target n="note119"></arrow.to.target><lb></lb>xandrino Herone per demonſtrationem enarrata ſunt. </s></p><p type="margin">
<s><margin.target id="note115"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note116"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note117"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note118"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note119"></margin.target>f</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note120"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note120"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>QVis nam ſit Angon, &amp; Monangon ſuperiùs quidem dixi<lb></lb>mus: nunc verò ſciendum eſt quòd catapulta eſt quædam <lb></lb>machina bellica, qua tela, aut ſaxa excuti ſolent. </s>
<s>hæc <lb></lb>autem machina (vt docet Athenæus) varijs modis conſtruitur, <lb></lb>eius〈qué〉 multæ ſunt ſpecies, de quibus pertractans ſcientia cata-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/077.jpg"></pb><emph type="italics"></emph>pultica vocatur. </s>
<s>Verùm animaduertendum eſt quòd<emph.end type="italics"></emph.end> <foreign lang="grc">βελοποιϊκὴ</foreign>, <lb></lb><emph type="italics"></emph>ideſt iaculatoria, ſeu<emph.end type="italics"></emph.end> <foreign lang="grc">βελοποιία</foreign>, <emph type="italics"></emph>hoc eſt iaculorum effectrix ſcien<lb></lb>tia differt à catapultica tamquam genus à ſpecie. </s>
<s>nam ipſa qui<lb></lb>dem iaculatoria docet cuncta ea inſtrumenta conficere, quæ ſagit<lb></lb>tas, tela, ſaxa, &amp; cuiuſcumque generis iacula longiùs excutiunt: <lb></lb>catapultica verò ea tantum iaculatoria conſtruit inſtrumenta, <lb></lb>quæ proprio nomine catapultæ dicuntur. </s>
<s>Quoniam autem Mo<lb></lb>nangon quoad eius conſtructionem catapultæ ſimilis eſt, idcirco <lb></lb>dixit Autor, quòd Monangonis conſtructio ad <expan abbr="catapulticã">catapulticam</expan> etiam <lb></lb>contemplationem volentes inſtituet. </s>
<s>cuius equidem rei rationem </s></p><p type="main">
<s><arrow.to.target n="note121"></arrow.to.target><lb></lb>reddens ait [quandoquidem ad longiùs iaculandum, tum rectè <lb></lb>extenſis, tum reflexis: ſiue tum lapides iacientibus, tum ſagittas <lb></lb>celeriter iaculantibus inſtrumentis multùm confert.] hoc eſt Mo<lb></lb>nangonis conſtructio ad catapulticam contemplationem volentes <lb></lb>inſtituet, hac ſcilicet ratione, quoniam multùm ipſa Monangonis <lb></lb>conſtructio nobis confert ad longiùs <expan abbr="iaculandũ">iaculandum</expan> inſtrumentis tum <lb></lb>rectè extenſis, tum reflexis: ſiue tum lapides iacientibus, tum ſa<lb></lb>gittas celeriter iaculantibus. </s>
<s>vt verò perſpicuum fiat quænam ſint <lb></lb>ista inſtrumenta rectè extenſa, &amp; reflexa: ſiue lapides iactantia, <lb></lb>&amp; ſagittas celeriter mittentia, de quibus Autor in præſentia lo<lb></lb>quitur : ſciendum est quòd multa, varia〈qué〉 ſunt inſtrumenta ia<lb></lb>culatoria, de quibus ipſa<emph.end type="italics"></emph.end> <foreign lang="grc">βελοποιία</foreign>, <emph type="italics"></emph>ideſt iaculorum effectrix <lb></lb>ſcientia pertractat: vt Angones, Monangones, catapultæ, Balli<lb></lb>ſtæ, &amp; alia id genus. </s>
<s>quorum inſtrumentorum alia ſunt rectè ex<lb></lb>tenſa iuxta eorum chordas, quæ quidem à græcis Euthitona, hoc <lb></lb>eſt rectè extenſa, ſiue rectè extenſas eorum chordas habentia: alia <lb></lb>verò iuxta eorum chordas reflexa, quæ ab eiſdem Palintona, hoc <lb></lb>est reflexa, ſeu reflexas eorum chordas habentia nominantur. </s>
<s>ho<lb></lb>rum autem reflexa quidem lapides longiùs iactandi, rectè exten<lb></lb>ſa verò ſagittas, tela, &amp; cuiuſcumque generis iacula celeriter <arrow.to.target n="note122"></arrow.to.target><lb></lb>iaculandi vim habent. </s>
<s>Quapropter paulò inferiùs in præſenti <lb></lb>capite ait Autor quòd rectè extenſorum inſtrumentorum chordæ <lb></lb>rotundæ contexendæ ſunt, vt inter <expan abbr="ſagittarũ">ſagittarum</expan> forficulas incidant: <lb></lb>ipſæ verò reflexorum chordæ latæ Zonarum hoc est faſciarum, vel <lb></lb>cingulorum inſtar eſſe debent, vt lapis à medietate chordæ ſecun<lb></lb>dum latitudinem percuſſus, benè emittatur, non excidens verſus <lb></lb>extrema. </s>
<s>ait præterea quòd anſas etiam ex earum extremis,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/078.jpg"></pb><emph type="italics"></emph>ſcilicet reflexis, confectas habere debent, vt ad eas ingrediantur <lb></lb>Angones ipſi, videlicet arcus, quos ſuperiùs declarauimus, quip<lb></lb>pe qui in fronte iſtorum reflexorum inſtrumentorum coaptantur.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note123"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note121"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note122"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note123"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[multo oleo educatæ] commas muliebres multo oleo nutritas <lb></lb>eſſe ait, quoniam græcis mulieribus mos est commas ſuas oleo co<lb></lb>tidie perungere, tum vt creſcant, <expan abbr="tũ">tum</expan> vt robustiores conſeruentur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note124"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note124"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[in iaculorum effectrice tractatione] hæc est<emph.end type="italics"></emph.end> <foreign lang="grc">βελοποιϊκὴ</foreign>, <emph type="italics"></emph>ſeu<emph.end type="italics"></emph.end><lb></lb><foreign lang="grc">βελοποιία</foreign> <emph type="italics"></emph>ab Athenæo, &amp; Bitone, &amp; Alexandrino Herone, <lb></lb>alijs〈qué〉 antiquioribus Mechanicis tradita: in qua quidem non ſo<lb></lb>lùm hæc, quæ ad <expan abbr="iaculatoriorũ">iaculatoriorum</expan> inſtrumentorum conſtructionem <lb></lb>ſpectant (de quibus Autor etiam in præſenti capite ſermonem ha<lb></lb>buit) ſubtiliter curioſioribus demonſtrantur: verùm etiam fora<lb></lb>minum in inſtrumentis ipſis exiſtentium dimetientes, ac reliqua <lb></lb>omnia, quæ in fine huius capitis breuiter Autor tetigit, mathema<lb></lb>ticè, ac inſtrumentaliter ab Alexandrino Herone per demonſtra<lb></lb>tionem enarrata ſunt. </s>
<s>Cæterùm vt ea, quæ in fine præſentis ca<lb></lb>pitis Autor recenſet, dilucidiora nobis reddantur, ignorandum <lb></lb>non eſt quòd (quemadmodum Athenæus in primo, &amp; ſecundo <lb></lb>libro de machinis bellicis docet) ipſi Mechanici maxima cum pro<lb></lb>portione tum inſtrumenta iaculatoria, tum etiam tela, ac iacula <lb></lb>ipſa conſtruebant. </s>
<s>nam ſecundum locorum diſtantias, ad quas <lb></lb>iacula mittenda erant, instrumenta ipſa modo maiora, modo mi<lb></lb>nora proportionaliter faciebant. </s>
<s>alterum quidem eorum alterius <lb></lb>iuxta omnes ſuas partes duplum, aut triplum, vel quotuplum li<lb></lb>buerit conſtruentes, ad mittenda longiùs duplo, vel triplo, vel quo<lb></lb>uis alio ſpatio iacula ipſa. </s>
<s>non ſolùm autem inſtrumenta iam di<lb></lb>cta ſecundum proportionem, quam habent adinuicem augebant, <lb></lb>ac minuebant: verùm etiam iacula ipſa, tela, ac ſaxa ſuis inſtru<lb></lb>mentis proportione quoad eorum longitudinem, craßitiem, ac pon<lb></lb>deroſitatem correſpondentia ponebant. </s>
<s>Vnde etiam ipſa iacula ean<lb></lb>dem inter ſe rationem, quam eorum inſtrumenta ſeruabant: tum <lb></lb>quoad eorum magnitudinem, ac pondus, tum etiam quoad lon<lb></lb>gitudines ſpatiorum, quas ab inſtrumentis emiſſa percurrere de<lb></lb>bebant. </s>
<s>Has autem cùm inſtrumentorum, &amp; eorum partium, tum <lb></lb>iaculorum proportiones duabus potißimùm geometricis propo<lb></lb>ſitionibus vtentes inueniebant. </s>
<s>quarum altera quidem eſt Theo<lb></lb>rema duodecimum libri duodecimi Elementorum Euclidis, in quo<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/079.jpg"></pb><emph type="italics"></emph>demonſtratur quòd ſimiles coni, &amp; cylindri in triplicata ſunt ad<lb></lb>inuicem ratione dimetientium in ſuis baſibus exiſtentium. </s>
<s>alte<lb></lb>ra verò propoſitio eſt illud diuulgatißimum, ad cubique duplatio<lb></lb>nem neceſſarium problema, quòd inter duas datas rectas lineas <lb></lb>alias duas medias proportionales inuenire docet. </s>
<s>quippe quod ab <lb></lb>antiquis <expan abbr="nõ">non</expan> ſcientificè, ſed cum inſtrumentis demonſtratum fuit. </s>
<s><lb></lb>His enim duabus propoſitionibus foraminum, per quæ tum chor<lb></lb>dæ, tum iacula in inſtrumentis pertranſeunt: necnon ſagittarum, <lb></lb>ac iaculorum, rotundarum〈qué〉 chordarum cylindricam formam ha<lb></lb>bentium dimetientes in quauis ratione peritißimi Mechanici re<lb></lb>periebant. </s>
<s>His itaque declaratis ea, quæ in præſentia breuiter <lb></lb>Autor enucleat, perſpicua nobis erunt. </s>
<s>ait enim quòd in ipſa ia<lb></lb>culorum effectrice tractatione non ſolùm hæc, ſcilicet quæ ipſe de <lb></lb>iaculatoriorum inſtrumentorum conſtructione in præſenti capite <lb></lb>breuiter enarrauit: ſubtiliter ijs, qui ad conſtructionem curioſio<lb></lb>res ſunt, per demonſtrationem enarrata fuere: verùmetiam fo<lb></lb>raminum in ipſis inſtrumentis exiſtentium dimetientes: necnon ij <lb></lb>ſimiles cylindri, qui in triplicata adinuicem dimetientium in ſuis <lb></lb>baſibus exiſtentium in ratione eſſe oſtenduntur: ac demum diuul<lb></lb>gata cubi duplatio: quibus ſcilicet duabus propoſitionibus, ia<lb></lb>culorum magnitudines, iuxta magnitudines contingentium, hoc <lb></lb>eſt quorumcumque inſtrumentorum, duplæ, vel etiam triplæ, vi<lb></lb>delicet adinuicem, cùm fiant, ad eaſdem, nempe duplas, vel tri<lb></lb>plas, longitudines, idest locorum diſtantias emittuntur: cuncta <lb></lb>in quam hæc mathematicè, ac inſtrumentaliter, nempe tum ma<lb></lb>thematicis ſcientificis propoſitionibus, qualis eſt iam dicta duode<lb></lb>cima duodecimi Euclidis Elementorum, tum inſtrumentalibus, <lb></lb>qualis eſt diuulgata cubi duplatio, quam inſtrumentorum admi<lb></lb>niculo priſci geometræ faciebant: ab Alexandrino Herone per <lb></lb>demonſtrationem enarrata ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note125"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note125"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Præterea hìc adnotandum eſt quòd Heron qui ſcripſit hunc de <lb></lb>machinis bellicis librum, quem nunc præmanibus habemus, non <lb></lb>eſt Heron Alexandrinus, qui ſcripſit librum<emph.end type="italics"></emph.end> <foreign lang="grc">περὶ βελοπιίας</foreign>,<lb></lb><emph type="italics"></emph>ideſt de iaculorum effectrice tractatione, libros quatuor de aqua<lb></lb>ticis horologijs, libros duos deſpiritalibus, librum<emph.end type="italics"></emph.end> <foreign lang="grc">περὶ ἀυτο<lb></lb>ματικω̄ν ποιϊτικω̄ν</foreign>, <emph type="italics"></emph>hoc eſt de ijs, quæ per ſe fieri, moueri〈qué〉 inna<lb></lb>ta ſunt, librum de Mechanicis, librum de re ruſtica, libros de<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/080.jpg"></pb><emph type="italics"></emph>Geometria. </s>
<s>quandoquidem Alexandrinus Heron longè anterior <lb></lb>fuit hoc Herone, qui præſentem librum compoſuit. </s>
<s>Quare non ſo<lb></lb>lùm hoc in loco, verúm etiam inferiùs præſens Heron illius anti<lb></lb>quioris Heronis Alexandrini mentionem facit. </s>
<s>Hoc autem ad<lb></lb>notandum eſſe duximus, ne quiſpiam in eundem cum Conrado <lb></lb>Geſnero in ſua Bibliotheca, &amp; cum Conrado Lycoſthene in eiuſ<lb></lb>dem Bibliothecæ epitome, incidat errorem: qui de vnico tantùm <lb></lb>Alexandrino ſcilicet Herone mentionem fecerunt, aſſerentes <lb></lb>eundem Heronem Alexandrinum, qui iam dicta ſuperiùs opera <lb></lb>ſcripſit, præſentem etiam de machinis bellicis librum ſcripſiſſe. </s>
<s><lb></lb>quem dicunt Bononiiæ in Bibliotheca Sancti Saluatoris græcum <lb></lb>vnà cum figuris eleganter deſcriptum extare. </s>
<s>quod quam ſit à <lb></lb>veritate alienum, præſens locus declarat. </s>
<s>Hęc autem ad præſen<lb></lb>tis etiam capitis dilucidationem breuiter à nobis dicta ſint.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>De ſcala rotis ſurrepente, <expan abbr="pontemq́ue">pontemque</expan> ferente. </s>
<s><lb></lb>Cap. </s>
<s>XIX.<emph.end type="center"></emph.end></s></p><p type="main">
<s>FIt etiam alia iuxta formam ſcala rotis ſurre<lb></lb>pens, ex lignis cùm fortibus, tum leuibus ipſa <lb></lb>quoque conſtructa. </s>
<s>ad quam alia pontis inſtar <lb></lb>iuxta medium ſurſum interpoſita, per dime<lb></lb>tientem cylindrica &amp; polyta ex torno facta <lb></lb>ea, quæ cruribus copulantur extrema poſſidentem conne<lb></lb>ctitur. </s>
<s>vt ſolubiliter verſus alteram deorſum lata reclinetur, <lb></lb><expan abbr="rurſusq́ue">rurſusque</expan> ad ipſam ſurſum erectè feratur, dum à funibus <lb></lb>retrorſum retinetur, ac torcularibus ijs, quæ multùm con<lb></lb>torta dicuntur, ſiue trochleis volubilibus violentam vim <lb></lb>in remiſſione, <expan abbr="intenſioneq́ue">intenſioneque</expan> funium ipſa rotularum adhe<lb></lb>rentium appoſitione innaſci facientibus commenſurabili<lb></lb>ter præbetur, atque attrahitur. </s>
<s>impedimenta verò ſurſum <lb></lb>in ea, quæ ſtat erecta, fiant: vel prominentiæ quædam reci<lb></lb>pientes eam, quæ erigitur ſcalam dum retrorſum conuer<lb></lb>titur. </s>
<s>ne raptim ſuper alterius verticem eleuata, caſum in<lb></lb>operantibus potiùs ſit minatura. </s>
<s>At ſi quidem ſimplicibus <lb></lb>lignis conſtans fuerit ſcala, quæ deorſum erecta ſtare de<lb></lb>bet: gradus habeat ſingulos ſingulis alternatim prætermiſ<pb xlink:href="052/01/081.jpg"></pb>ſis excedentes crura, &amp; in exceſſu foratos, vt per foramina <lb></lb>funis robuſtus extenſus pertranſiens infrangibilem ipſam </s></p><p type="main">
<s><arrow.to.target n="note126"></arrow.to.target><lb></lb>ſeruet: ſi verò compoſita fuerit, iam dictarum ſcalarum con<lb></lb>ſtructionem ſuſcipiat. </s>
<s>Ipſa autem quæ ſurſum eleuanda eſt, <lb></lb>iuxta totam eius longitudinem tabulis proſternatur, &amp; fu<lb></lb>nibus circundata confirmetur, <expan abbr="indubitataq́ue">indubitataque</expan> ſuper mu<lb></lb>rum traiectio fiat. </s>
<s>cùm enim ipſa ſuper alteram eleuata, <expan abbr="ere-cteq́ue">ere<lb></lb>cteque</expan> portata fuerit: ambæ muro ſimul afferuntur. </s>
<s>atque <lb></lb>ea quidem, quæ deorſum erecta ſtat, <expan abbr="gradusq́ue">gradusque</expan> ad aſcen<lb></lb>ſum habet, à muro diſtet quantum amuſſi quadam, ac men<lb></lb>ſura funibus relaxatis ipſius proſtratæ extremum deſcen<lb></lb>dens muro applicetur, <expan abbr="volentibusq́ue">volentibusque</expan> ſit aditus. </s>
<s>Latitudo <lb></lb>autem tum ſcalæ, tum pontis ſufficiens fiat, ita vt ordina<lb></lb>tim quinque, ſeu quatuor, vel ad minus tres viri feriatim <lb></lb>aſcendant ſuper ponte pertranſeuntes: adhoc vt vnanimi<lb></lb>ter ſuper murum propugnantibus ex aduerſo repugnent. </s>
<s><lb></lb>Circumſeptiones verò ex corijs ad vtraſque partes tum ſca<lb></lb>læ, tum pontis fiant, propter ſagittas, quæ à lateribus effe<lb></lb>runtur. </s>
<s>Operæpretium eſt autem ſcalam deorſum ſtantem <lb></lb>palis infixis ſtabiliri, <expan abbr="funibusq́ue">funibusque</expan> extenſis confirmari, nec<lb></lb>non altiorem muro reperiri tribus ad minus pedibus: vt <lb></lb>ea, quæ à muro deſupter veniunt, ad altum peruenire, <expan abbr="cæ-demq́ue">cæ<lb></lb>demque</expan> in aſcendentibus agere nequeant. </s>
<s>Verùm ponte <lb></lb>decliui ſupra murum exiſtente, promptiores, <expan abbr="audacioreſ-q́ue">audacioreſ<lb></lb>que</expan> milites ad deſcenſum erunt. </s>
<s>ſi verò depreſſior muro <lb></lb>ſcala fuerit, hiſce contraria euenient, <expan abbr="figuræq́ue">figuræque</expan> ipſæ ſubie<lb></lb>ctæ ſunt. </s></p>
<pb xlink:href="052/01/082.jpg"></pb><p type="margin">
<s><margin.target id="note126"></margin.target>a</s></p><figure id="id.052.01.082.1.jpg" xlink:href="052/01/082/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note127"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note127"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[iam dictarum ſcalarum conſtructionem] conſtructio compoſita<lb></lb>rum ſcalarum, de qua hìc loquitur Autor, ſuperiùs in quartide<lb></lb>cimi capitis initio deſideratur. </s>
<s>apud Apollodorum autem eam <lb></lb>habemus.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/083.jpg"></pb><p type="main">
<s><emph type="center"></emph>De aggere teſtudine pontem ferente. </s>
<s>Cap. </s>
<s>XX.<emph.end type="center"></emph.end></s></p><p type="main">
<s>Flet autem vtilis pons ſola quoque iam dicta <lb></lb>traiectio, quando ſcilicet foſſas latas, aut pro<lb></lb>fundas, <expan abbr="aquarumq́ue">aquarumque</expan> plenas aggerare <expan abbr="nõ">non</expan> poſ<lb></lb>ſumus: ſi longitudine commenſurabilis ad foſ<arrow.to.target n="note128"></arrow.to.target><lb></lb>ſarum latitudines fiat, atque vt iam didicimus <lb></lb>ſolubiliter connexa fuerit, ante aggerem teſtudinem ere<lb></lb>ctè ſtans, à funibus retrorſum attracta, ac tradita, vel à iam <lb></lb>dictis ſuperiùs multùm contortis torcularibus: quando vi<lb></lb>delicet magnitudo, ac onus ponderis ipſius traiectionis tan<lb></lb>tæ molis fuerit. </s>
<s>cùm enim à teſtudine geſtata fuerit, <expan abbr="ante-rioriq́ue">ante<lb></lb>riorique</expan> foſſæ labro ſuperuenerit: funes retrorſum relaxan<lb></lb>tur, <expan abbr="extremumq́ue">extremumque</expan> deſcendens, ſuper oppoſito labro poni<lb></lb>tur, <expan abbr="viaq́ue">viaque</expan> tuta fit volentibus promptè cum parmis creta, <lb></lb>aut cinere ſanguini admiſto circa contexiones illitis, corijſ<lb></lb>que bouum recèns occiſorum coopertis pertransire: tum <lb></lb>propter <expan abbr="tormẽta">tormenta</expan> ignem iaculantia, tum etiam propter eos, <lb></lb>qui infunduntur feruidos liquores. </s>
<s>&amp; quemadmodum in <lb></lb>foſſorijs teſtudinibus iam oſtenſum eſt, ita etiam parma<lb></lb>rum abinuicem diſtantiam viginti pedibus minorem fieri: <lb></lb>necnon à tribus pedibus ſupra terram incipiendo eam, <lb></lb>quæ ad murum fit fodinam agere oportet. </s>
<s>&amp; figura ſubie<lb></lb>cta eſt. </s></p>
<pb xlink:href="052/01/084.jpg"></pb><p type="margin">
<s><margin.target id="note128"></margin.target>a</s></p><figure id="id.052.01.084.1.jpg" xlink:href="052/01/084/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note129"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note129"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſi longitudine commenſurabilis ad foſſarum latitudines fiat] <lb></lb>commenſurabilitas in præſentia non eodem modo, quo docet Eu<lb></lb>clides in definitionibus decimi libri Elementorum accipienda eſt: <lb></lb>quòd ſcilicet pontis longitudo, &amp; foſſarum latitudines tamquam <lb></lb>recta lineæ ſuſceptæ longitudine commenſurabiles fiant, hoc eſt <lb></lb>communi menſura quoad earum longitudinem menſurentur. </s>
<s>nam <lb></lb>fieri poteſt, vt tam dictæ rectæ lineæ iuxta doctrinam Euclidis lon<lb></lb>gitudine commenſurabiles ſint, ipſius tamen pontis longitudo qua<lb></lb>cumque foſſarum latitudine minor existat: ac propterea cùm ipſe <lb></lb>pons à teſtudine geſtatus anteriori foſſæ labro ſuperuenerit, fu<lb></lb>nibus retrorſum relaxatis, extrema〈qué〉 pontis parte deſcendente, <lb></lb>ſuper oppoſito foſſa labro minimè ponatur, ſed intra foſſam inci<lb></lb>dat: quod vtique præter Autoris intentionem erit. </s>
<s>Quamobrem <lb></lb>verba hac [ſi longitudine commenſurabilis ad foſſarum latitudi<lb></lb>nes fiat] ſic intelligenda ſunt: quòd ſcilicet pons ipſe iuxta ſui <lb></lb>longitudinem à quacumque foſſarum latitudine pluribus vici<lb></lb>bus. </s>
<s>aut ſaltem ſemel commenſuretur. </s>
<s>Cùm enim foſſarum lati<pb xlink:href="052/01/085.jpg"></pb>tudines eiuſdem ciuitatis variæ poßint eſſe, neceſſe eſt vt iam di<lb></lb>cti pontis longitudo maximam foſſarum latitudinem aliquantu<lb></lb>lum excedat: ita vt ſaltem ſemel quidem ab ipſa, pluries autem <lb></lb>à minoribus etiam commenſuretur: vndè ſanè commenſurabili<lb></lb>tas in præſenti loco pro ſimplici lineæ rectæ maioris à minoribus <lb></lb>rectis lineis commenſuratione ſuſcipienda est, non quidem quòd <lb></lb>ab eis ita menſuretur, vt toties ipſæ ſuſceptæ ſeu repetita hanc in<lb></lb>tegram conſtituant: ſed quòd hæc cùm illis maior ſit eas in ſe <lb></lb>comprehendat, quamuis <expan abbr="etiã">etiam</expan> illis longitudine incommenſurabilis <lb></lb>eſſet. </s>
<s>quemadmodum etiam dimetiens quadrati cùm costa maior <lb></lb>ſit eam in ſe continet, longitudine tamen adinuicem incommen<lb></lb>ſurabiles ſunt, vt in eodem decimo Euclidis libro docetur. </s>
<s>fortaſ<lb></lb>ſe namque poſſet euenire quòd longitudo pontis ipſius ad aliquam <lb></lb>foſſarum latitudinem, vel vna foſſarum latitudo ad aliam earun<lb></lb>dem foſſarum latitudinem, eam haberet rationem, quam habet <lb></lb>dimetiens quadrati ad eius coſtam. </s>
<s>hoc autem adnotatu dignum <lb></lb>cenſuimus, nequis credat Autorem huiuſce rei nos aſtringere, vt <lb></lb>nempe longitudinem ipſius pontis foſſarum latitudinibus commen<lb></lb>ſurabilem longitudine faciamus: quod nimirum in quibuſdam <lb></lb>ciuitatum foßis nequaquam fieri poſſet.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>De aggere teſtudine ratem habente ſecundum Philo<lb></lb>nem Bizantium. </s>
<s>Cap. </s>
<s>XXI.<emph.end type="center"></emph.end></s></p><p type="main">
<s>PHilon autem Bizantius prope huiuſcemodi <lb></lb>foſſas teſtudines aggeres ponens, iuxta ipſas <lb></lb>rates connectit, &amp; ad quamcumque muti par<lb></lb>tem voluerit milites adducit, ferreos palos af<lb></lb>figentes. </s>
<s>quippe qui obdurati, acutique facti, <lb></lb>ad murorum cùm lapideorum, tum lateritiorum commiſ<lb></lb>ſuras, <expan abbr="compaginesq́ue">compaginesque</expan> penetrant, ferreis malleis ab aſcen<lb></lb>dentibus percuſſi. </s>
<s>atque hamis inſuperfactis, qui in extre<lb></lb>mitatibus funium exiſtentes vnà cum retibus ad mari pin<lb></lb>nas inijciuntur: ita vt militibus potiſſimum aſſuetis haud <lb></lb>difficilis ſit <expan abbr="aſcẽſus">aſcenſus</expan>. </s>
<s>tali <expan abbr="nãq;">namque</expan> methodo vtentes Aegyptij <expan abbr="nõ">non</expan> <lb></lb>paratas, ac <expan abbr="nõ">non</expan> fortes, &amp; quoad altitudinem humiles ciuita<lb></lb>tes facilè obſidere conſueuerunt. </s>
<s><expan abbr="figuraq́">figuraque</expan>; ipſa ſubiecta eſt. </s></p>
<pb xlink:href="052/01/086.jpg"></pb><figure id="id.052.01.086.1.jpg" xlink:href="052/01/086/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>De quibuſdam animaduerſionibus ad omnes ſcalas, &amp; <lb></lb>pontes pertinentibus. </s>
<s>Cap. </s>
<s>XXII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>OPeræpretium eſt autem in omnibus ſcalis, &amp; <lb></lb>eis, quæ ad murum fiunt aſcenſionibus, ſiue <lb></lb>pontibus animaduertere ea, quæ ex lino præ<lb></lb>parantur craſſa verricula. </s>
<s>nam iniecta, <expan abbr="colle-ctimq́ue">colle<lb></lb>ctimque</expan> rurſus retracta aſcendentes, vel in<lb></lb>gredientes viuos venantur, <expan abbr="inimicisq́ue">inimicisque</expan> captiuos præſen<arrow.to.target n="note130"></arrow.to.target><lb></lb>tant. </s>
<s>Verum in ipſis quidem ſcalis inoffenſum aſcenſum <lb></lb>conſeruauimus, quemadmodum in trabibus in anchoræ <lb></lb>modum incuruatis  deſcendentium ponderum ſuperiùs <lb></lb>ſtruendo determinauimus. </s>
<s>Ad ipſos autem pontes duo <lb></lb>anteriùs ligua erigenda ſunt, ſolubiliter deorſum conne<lb></lb>xa, aduerſus quidem inimicorum faciem facilè inciden<arrow.to.target n="note131"></arrow.to.target><lb></lb>tia, <expan abbr="retrorſumq́ue">retrorſumque</expan> reſiſtentia, ſuperiùs verò ad unguem ab<lb></lb>ſciſſa, ad verticem coeuntia, atque ad acutum angulum ac<lb></lb>commodata, triangulam figuram vnà cum baſi perficien<lb></lb>tia, <expan abbr="necnõ">necnon</expan> clauos ferreos à lateribus ſuſcipientia, vt iniecta <lb></lb>verricula illius implicentur, non amplius ad contrariam
<pb xlink:href="052/01/087.jpg"></pb>attractionem, <expan abbr="collectionemq́ue">collectionemque</expan> reuertentia. </s>
<s>Cæterùm qui <lb></lb>mutum inſcendere debent aduerſus inimicorum <expan abbr="faciẽ">faciem</expan> hæc <lb></lb>inijcientes ad ingreſſum illæſi conſeruabuntur. </s>
<s>At ſi non<lb></lb>nulli eorum, qui ſuper ponte ſtant cum conuertibilibus <arrow.to.target n="note132"></arrow.to.target><lb></lb>manuarijs ignem iaculantibus tormentis aduerſus hoſtium <lb></lb>faciem igne infeſtauerint: eos, qui muro præaſſiſtunt tan<lb></lb>to terrore afficient, vt pugnæ aggreſſionem, ac ignis impe<lb></lb>tum minimè ſuſtinentes, celeriter locum ſubterfugiant. </s>
<s>&amp; <lb></lb>figura deſcripta eſt. </s></p><p type="margin">
<s><margin.target id="note130"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note131"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note132"></margin.target>c</s></p><figure id="id.052.01.087.1.jpg" xlink:href="052/01/087/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note133"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note133"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>HAec quæ in præſentia dicit Autor ſe ſuperiùs determi<lb></lb>naſſe, fortaſſe ex ijs ſunt, quæ in principio quintidecimi <lb></lb>capitis deſiderantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note134"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note134"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ad vnguem] ideſt obliquè ad unguis ſimilitudinem, quemad<lb></lb>modum etiam ſuperiùs in capite tertio dixit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note135"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note135"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[manuarijs] hoc eſt inſtrumentis, quæ manu teneri, vibrari〈qué〉 <lb></lb>poſſunt. </s>
<s>enchiridium enim (vt in græco textu legitur) eſt omne <lb></lb>inſtrumentum, quod manu tenetur.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/088.jpg"></pb><p type="main">
<s><emph type="center"></emph>De curru ſeu teſtudine quatuor rotis ſurrepente, <expan abbr="canalem-q́ue">canalem<lb></lb>que</expan> murum inſcendentem ferente. </s>
<s>Cap. </s>
<s>XXIII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>VErumenimuero fieri poteſt, vt etiam abſque <lb></lb>ſcalis ſupra murum aſcendatur, quemadmo<lb></lb>dum Aſcræus Cteſibius Heronis Alexandri<lb></lb>ni magiſter in ſuis commentarijs declarauit, <arrow.to.target n="note136"></arrow.to.target><lb></lb>per huiuſcemodi <expan abbr="machinã">machinam</expan>, ſicut inquit Athe<lb></lb>næus, quòd ſcilicet currum rotis quatuor præditum, vnde<lb></lb>quaque circumtectum exiſtentem, ſeu teſtudinem arietem <lb></lb>geſtantem conſtruere oportet. </s>
<s>&amp; ad vtramque harum dua<lb></lb>rum machinum iuxta medium duo ligna erecta ſtantia ſunt <lb></lb>affigenda, &amp; aliud tranſuerſum altera parte latius deſuper <lb></lb>ad ipſa interiacens iuxta latitudinem ſuperimponendum <lb></lb>eſt. </s>
<s>quippe quod abſciſiones rotundas habeat ex vtriſque <lb></lb>partibus, <expan abbr="ſuſcipiatq́ue">ſuſcipiatque</expan> veluti canalem quendam ſuperiacen<lb></lb>tem tubo ſimilem, <expan abbr="arcuatisq́ue">arcuatisque</expan> lignis conſtructum, à late<lb></lb>ribus autem clauis affixum, ac tabulis exteriùs clauis affi<lb></lb>xis ſuperalligatum, aut ſolis corijs craſſis, ac robuſtis tam<lb></lb>quam leuioribus circumopertum: ita vt armati viri erecti <lb></lb>ingredientis, &amp; modò quidem progredientis, modò verò <lb></lb>regredientis capax ſit. </s>
<s>quo facto canalis ſurſum eleuandus <lb></lb>eſt, ac transferendus in quacumque parte quiſpiam volue<lb></lb>rit. </s>
<s>cuius vna parte verſus pauimentum declinante, reliqua <lb></lb>in altum eleuabitur: eo quòd ſuper ipſas ſuperiacentis li<lb></lb>gni abſciſiones ferreis catenis ad eius vtrumque latus at<lb></lb>tracta circumuertitur. </s>
<s>dum autem canalis ipſe ſublimis fer<lb></lb>tur, cùm os eius prope <expan abbr="murũ">murum</expan> aduenerit: adducta rotis qua<lb></lb>tuor prædita teſtudine, ſeu curru: is, qui intus eſt eam, quæ <lb></lb>anteriùs eſt ianuam adaperire, <expan abbr="murumq́ue">murumque</expan> armatus inſcen<lb></lb>dere debet. </s>
<s>ſimile verò faciundum eſt à pluribus etiam, qui <lb></lb>per eandem canalis baſim intus progrediuntur. </s>
<s>At canalis <lb></lb>ipſe, qui iuxta tabulas clauis affixas eſt roborem ſuſcipiens <lb></lb>robuſtis funibus vndequaque ſubcingitur, necnon corijs, <lb></lb>ac madidis pellibus concinnatur, vt à tormentis ignem fer<lb></lb>rentibus illæſus ſeruetur. </s>
<s>Verumtamen huiuſce problema<lb></lb>tis menſuras quoad conſtructionem <expan abbr="Cteſibiũ">Cteſibium</expan> minimè com<pb xlink:href="052/01/089.jpg"></pb>poſuiſſe: ſed commentarium ſolum veluti mathematicis <lb></lb>gerentibus architectis hæc imponentem inuenimus. </s>
<s>ad eos <lb></lb>enim ſpectat inſtrumentorum commenſurabilitatem tranſ<lb></lb>formare, ad <expan abbr="conuenientemq́ue">conuenientemque</expan> loci vſum transferre. </s>
<s>Nos <lb></lb>autem exercitationis gratia ijs, qui inſtituuntur ad præſen<lb></lb>tis problematis conſtructionem huiuſcemodi commenſu<lb></lb>rabilitatem expoſuimus. </s>
<s>Fiat itaque pauimentum ſuperia<lb></lb>cens in curru, ſiue teſtudine quatuor, vel ſex rotis prædita <lb></lb>quoad longitudinem quidem cubitorum quindecim: quo<lb></lb>ad latitudinem verò, decem. </s>
<s>rotarum autem dimetientes <lb></lb>cubitorum duorum cum dimidio fiant. </s>
<s>ligna verò duo ere<lb></lb>cta ſtantia fiant cubitorum viginti. </s>
<s>lignum autem tranſuer<lb></lb>ſum, quod inter ipſa mouetur vnà cum ſuperpoſito canali <lb></lb>cubitorum quoad longitudinem triginta, latitudinem ha<lb></lb>bens iuxta baſim pedis vnius cum dimidio, craſſitiem verò <lb></lb>vnius dodrantis. </s>
<s>vt quam rationem habet longitudo paui<lb></lb>menti ad latitudinem, eandem etiam habeat quod moue<lb></lb>tur tranſuerſum lignum ad ligna erecta ſtantia. </s>
<s>&amp; <expan abbr="quã">quam</expan> rur<lb></lb>ſus habet rationem ipſum, quod mouetur tranſuerſum li<lb></lb>gnum ad pauimenti longitudinem, eandem etiam ligna <arrow.to.target n="note137"></arrow.to.target><lb></lb>erecta ſtantia ad eandem latitudinem rationem habeat. </s>
<s><expan abbr="nã">nam</expan> <lb></lb>ſicut quindecim ad decem, ſic triginta ad viginti: &amp; ſicuti <lb></lb>triginta ad quindecim, ita viginti ad decem. </s>
<s>ſeſquialter au<lb></lb>tem eſt numerus quindecim numeri denarij, quando qui<lb></lb>dem denarium, ac dimidium eius in ſe continet. </s>
<s>ſeſquialter <lb></lb>igitur eſt etiam ipſe triginta numerus ipſius viginti nume<lb></lb>ri. </s>
<s>rurſus autem ipſe triginta ipſius quindecim duplus eſt, <arrow.to.target n="note138"></arrow.to.target><lb></lb>duplus ergo ipſe viginti ipſius denarij. </s>
<s>ſimiliter autem la<lb></lb>titudo <expan abbr="quoq;">quoque</expan> ipſius baſis ad eius craſſitudinem dupla erit. <arrow.to.target n="note139"></arrow.to.target><lb></lb>Verùm ipſæ quoque rotarum dimetientes commenſurabi<lb></lb>les iuxta commenſurationem, &amp; conuenientes in ratione <lb></lb>oſtendentur. </s>
<s>etenim duo cum dimidio cubiti ipſius dime<lb></lb>tientis ſexies quidem ipſum quindecim numerum metiun<lb></lb>tur, quater vero denarium, &amp; duodecies quidem ipſum tri<lb></lb>ginta, octies verò ipſum viginti. </s>
<s>atque veluti ſe habet ſena<lb></lb>rius ad quaternarium, ita ipſe triginta ad ipſum viginti, &amp; <lb></lb>quindecim ad decem: &amp; quemadmodum numerus quin<pb xlink:href="052/01/090.jpg"></pb>decim ad ſenarium, eodem modo denarius ad quaterna<lb></lb>rium. </s>
<s>ſeſquialter <expan abbr="autẽ">autem</expan> eſt ſenarius quaternarij, habet enim <lb></lb>ipſum, &amp; eius dimidium: ſeſquialter igitur eſt ipſe etiam <lb></lb>quindecim ipſius denarij. </s>
<s>at ipſe quindecim ſenarij duplus <lb></lb>ſeſquialter exiſtit, duplus ſeſquialter ergo denarius etiam <lb></lb>quaternarij erit. </s>
<s>Quapropter ipſa quoque dimetientis ro<arrow.to.target n="note140"></arrow.to.target><lb></lb>tarum commenſuratio conueniens ad magnitudinis con<lb></lb>ſtructionem reperitur. </s>
<s>quandoquidem eandem ipſa cum <arrow.to.target n="note141"></arrow.to.target><lb></lb>ijs, quæ menſurantur rationem ſecundum proportionem <lb></lb>ſeruat. </s>
<s>figura autem ſubſcripta eſt. </s></p><p type="margin">
<s><margin.target id="note136"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note137"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note138"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note139"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note140"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note141"></margin.target>f</s></p><figure id="id.052.01.090.1.jpg" xlink:href="052/01/090/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note142"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note142"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>CTeſibius patria Aſcræus Heronis Alexandrini præceptor <lb></lb>ſcripſit commentaria de rebus bellicis, necnon<emph.end type="italics"></emph.end> <foreign lang="grc">βελοπιϊκὰ</foreign><lb></lb><emph type="italics"></emph>nempe iaculatoria, quæ in Athenei volumine inſerta ha<lb></lb>bentur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note143"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note143"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ad eandem latitudinem] hoc eſt <expan abbr="eiuſdẽ">eiuſdem</expan> pauimenti <expan abbr="latitudinẽ">latitudinem</expan>.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note144"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note144"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſimiliter latitudo quoque ipſius baſis] nempe latitudo baſis<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/091.jpg"></pb><emph type="italics"></emph>ipſius canalis. [ad eius craßitiem dupla erit] cùm enim iam di<lb></lb>cta latitudo pedis vnius cum dimidio, hoc eſt digitorum viginti<lb></lb>quatuor, craßities verò vnius dodrantis, ideſt duodecim digito<lb></lb>rum ab Autore ſuppoſitæ ſint: dubio procul duplam adinuicem ra<lb></lb>tionem habebunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note145"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note145"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[verùm ipſæ quoque rotarum &amp;c.] quæ in hac vltima capitis <lb></lb>parte de dimetientium rotarum commenſurabilitate, &amp; quoad <lb></lb>rationem conuenientia reſpectu aliarum huius machinæ menſu<lb></lb>rarum declarat Autor: ex ijs, quæ nos in ſcholio quintidecimi <lb></lb>capitis de commenſurabilitate, proportione〈qué〉 turrium diximus, <lb></lb>perſpicua cuilibet erunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note146"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note146"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[conueniens] ſcilicet in ratione.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note147"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note147"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[cum ijs, quæ menſurantur] videlicet reliquarum machinæ <lb></lb>partium quoad longitudinem, &amp; latitudinem, atque craßitiem <lb></lb>menſuris, quippe quæ ab ipſis rotarum dimetientibus menſu<lb></lb>rantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Alia ſuperius iam deſcripti canalis exquiſitior de<lb></lb>ſcriptio. </s>
<s>Cap. </s>
<s>XXIIII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>IDem autem canalis efficatior ad obſidionem <lb></lb>fiet, ſi maior iuxta magnitudinem in anteriori <lb></lb>bucula fuerit, &amp; à duobus oſtiolis exitum ha<lb></lb>buerit: ita vt etiam duos armatos uiros mu<lb></lb>rum unà inſcenſuros uiciſſim adinuicem ſtan<lb></lb>tes ſuſcipiat. </s>
<s>eiuſdem autem buculæ oſtia extrinſecùs hor<lb></lb>ribilia apparenti ſculptura, <expan abbr="uerſicoloriq́ue">uerſicolorique</expan> pictura in ante<lb></lb>riori canalis parte fiant: draconis, aut leonis ignem ferens <lb></lb>caput ad terrorem, ac metum hoſtium adueniens offeren<lb></lb>tia. </s>
<s>vt etiam ante ingreſſionem terrore affecti muro aſſiſten<lb></lb>tes à murorum ſpatijs inter turres exiſtentibus effugiant. </s>
<s><lb></lb>At ſciendum eſt quòd ſi indirectum quidem æqualis alti<lb></lb>tudinis canalis ſuper erectis lignis interiacens muro adue<lb></lb>niat, indirectum quoque baſim oſtendet: ſi autem muro ſu<lb></lb>perior quoad ſitum reperiatur, paulò ante deductus, ac de<lb></lb>clinans, actionem perficiet: ſi uerò muro depreſſior quoad <lb></lb>altitudinem fortaſſe ſit, productus adhuc anteriùs, atque
<pb xlink:href="052/01/092.jpg"></pb>erectus adductus ex minori, <expan abbr="poſterioriq́ue">poſteriorique</expan> parte à catena <lb></lb>ſubtractus, ad <expan abbr="ſupernaq́ue">ſupernaque</expan> tendens paulò ſuper murum pro<lb></lb>minens, ipſum quoque ad maiorem altitudinem aſcendere <lb></lb>volentibus vſum complebit. </s>
<s>atque figura ſubſcripta eſt. </s></p><figure id="id.052.01.092.1.jpg" xlink:href="052/01/092/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>De machinis maritimas ciuitates deuaſtantibus. </s>
<s><lb></lb>Cap. </s>
<s>XXV.<emph.end type="center"></emph.end></s></p><p type="main">
<s>EAs, quæ ex nauigijs aguntur machinas inquit <arrow.to.target n="note148"></arrow.to.target><lb></lb>Athenæus, quas nonnulli Sambucas appel<lb></lb>lant ex metaphora muſicorum inſtrumento<lb></lb>rum figuratas, ſimiles quoad arcuatam con<lb></lb>ſtructionem iam dicto canali exiſtentes, nil in <lb></lb>ſe ſcriptu dignum habere, eo quòd omnibus cognitu faci<lb></lb>les, <expan abbr="manifeſtæq́ue">manifeſtæque</expan> ſint: potius autem eo quòd nec etiam ſe<lb></lb>pius ipſæ fiant, vel irrationabiliter, ac incommenſurabili<lb></lb>ter conſtructæ ſint. </s>
<s>etenim qui in obſidione circa Chium <lb></lb>vrbem facta coniecturando à ſcopo aberrarunt, <expan abbr="altioresq́">altioresque</expan>; <lb></lb>turribus Sambucas adduxerunt: eos, qui in ipſas aſcende<lb></lb>runt ab igne enecari fecere. </s>
<s>quippe cùm ab altitudine tur<lb></lb>res inſcendere minimè potuiſſent. </s>
<s>vt deprimerentur verò <lb></lb><expan abbr="nequaquã">nequaquam</expan> fieri poterat, quin nauigia ſubuerterentur one<lb></lb>re, quod ſuperimpoſitum eſt extra ponderante geſtato. <arrow.to.target n="note149"></arrow.to.target><lb></lb>quapropter hortatur non eſſe ignaros opticæ tractationis <lb></lb>eos, qui huiuſcemodi machinis vti debent. </s>
<s>&amp; quòd ſi qui-<pb xlink:href="052/01/093.jpg"></pb>dam architectorum maritimam ciuitatem aſſequi decreue<lb></lb>rint, duo nauigia tamquam ad iugum iungendo ſuper ipſis <lb></lb>ad altitudinem machinam ponunt, atque in maris tran<lb></lb>quillitatibus muris ipſam adducere conſueuere. </s>
<s>verùm ſi <lb></lb>à contrario vento nauigia aggreſſa fuerint, &amp; vnda fracta <lb></lb>ad ipſa ſubrepat: obruit, &amp; circumactu euertit concutien<lb></lb>do machinam, quæ in nauigijs firmata fuerat. </s>
<s>nauigia nam<lb></lb>que non eundem, ac ſimilem ſemper motum efficiunt: ſed <lb></lb>alterum quidem eorum in undæ culmine quandoque, al<lb></lb>terum verò in depreſſione exiſtit. </s>
<s>vndè cùm diſcerpantur, <lb></lb>franguntur machinæ ab ipſa per ſe inſidiante machinatio<lb></lb>ne concuſſæ: hoſtes autem audacia potiùs, <expan abbr="fiduciaq́ue">fiduciaque</expan> affi<lb></lb>ciunt. </s>
<s>At quoniam anima humana quadam, qua perſe <lb></lb>mouetur excitatione prædita eſt, non ſolùm quæ bene ab <lb></lb>alijs inuenta ſunt nos agnoſcere, verùmetiam aliquid eo<lb></lb>rum, quæ ad vtilitatem ſpectant adinuenire oportet. </s>
<s>qua<lb></lb>propter ad ſuffulciendam machinam ipſam conati ſumus, <lb></lb>adinuenientes hoc, quòd vtique iuxta medium connexio<arrow.to.target n="note150"></arrow.to.target><lb></lb>nis duorum nauigiorum coaptetur illud, quod pithicium <lb></lb>dicitur. </s>
<s>quippe quod pondus quoddam quoad magnitu<arrow.to.target n="note151"></arrow.to.target><lb></lb>dinem quidem figuræ ſimile, pendulum inferiùs, ac pon<lb></lb>deroſum propter æquilibrium eſt. </s>
<s>vt marina fluctuatione <lb></lb>vndequaque mouente, <expan abbr="quatienteq́ue">quatienteque</expan> nauigia, machina <lb></lb>ipſa erecta, ac indeclinabilis conſeruetur. </s>
<s>aduerſus autem <lb></lb>ventos, atque ad habendum in conſtructione in promptu <lb></lb>ea, quæ ad obſidionem pertinent præſidia: paruæ machi<lb></lb><arrow.to.target n="note152"></arrow.to.target>næ (quæ a græcis Elepolis, hoc eſt vrbium deuaſtatrices <lb></lb><arrow.to.target n="note153"></arrow.to.target>dicuntur) præſtruendæ ſunt, tamquam thoracia quædam <lb></lb>turribus ſimilia, vel aſcenſoria, iuxta altitudinem com<lb></lb>menſurabilia, <expan abbr="promptaq́ue">promptaque</expan> exiſtentia. </s>
<s>vt cùm nauigia pro<lb></lb>pe murum aduenerint, tunc funibus, aut iam dictis mul<lb></lb>tùm contortis torcularibus huiuſcemodi machinæ, ſupra <lb></lb>murum aditum præparantes, erigantur. </s>
<s>efficax autem ad <lb></lb>huiuſcemodi vſum iam dictus etiam canalis oſtendetur ſi <lb></lb>magnitudine commenſurabilis exiſtens ad coniuncta na<lb></lb>uigia in lignis erectè ſtabilitis ſurſum feratur tranſmotus <arrow.to.target n="note154"></arrow.to.target><lb></lb>(vt iam oſtenſum eſt) aut ſuper charcheſio vocato, potens
<pb xlink:href="052/01/094.jpg"></pb><arrow.to.target n="note155"></arrow.to.target>ſuper ipſo ſex motus facere, quemadmodum etiam inſtru<lb></lb><arrow.to.target n="note156"></arrow.to.target>menta, quæ grues, ſiue ciconiæ dicuntur: aut etiam ſuper <lb></lb><arrow.to.target n="note157"></arrow.to.target>circumcurrente clauiculo, quod ſuper circumuoluto cau<lb></lb><arrow.to.target n="note158"></arrow.to.target>le impoſitum ſit, qui ſanè caulis operario circumuolutio<lb></lb><arrow.to.target n="note159"></arrow.to.target>nem ad altum, ad <expan abbr="imumq́ue">imumque</expan> faciat. </s>
<s>ſic itaque Damis etiam <lb></lb>Colophonius ſuper caulibus Sambucas ponebat, quemad<lb></lb>modum mechanicus Biton in ſuis commentarijs obſiden<lb></lb>di arte tradit. </s>
<s>iam dictæ verò quinque configuratæ machi<lb></lb>næ expoſitæ ſunt. </s></p>
<pb xlink:href="052/01/095.jpg"></pb><p type="margin">
<s><margin.target id="note148"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note149"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note150"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note151"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note152"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note153"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note154"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note155"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note156"></margin.target>i</s></p><p type="margin">
<s><margin.target id="note157"></margin.target>k</s></p><p type="margin">
<s><margin.target id="note158"></margin.target>l</s></p><p type="margin">
<s><margin.target id="note159"></margin.target>m</s></p><figure id="id.052.01.095.1.jpg" xlink:href="052/01/095/1.jpg"></figure>
<pb xlink:href="052/01/096.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note160"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note160"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>SAmbuca eſt quoddam muſicum inſtrumentum triangula<lb></lb>rem formam habens ex inæqualibus tum longitudine, tum <lb></lb>craßitie neruis effectum, vt Porphyrius ſcribit. </s>
<s>præ<lb></lb>terea instrumentum est obſidionale oppugnandis vrbibus ido<lb></lb>neum apud Polybium. </s>
<s>in præſentia verò machina bellica eſt ma<lb></lb>ritimarum ciuitatum deuaſtatrix, quam Autor diligenter de<lb></lb>ſcribit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note161"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note161"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[quapropter hortatur] ipſe ſcilicet Athenæus [non eſſe igna<lb></lb>ros opticæ tractationis] optica tractatio non eſt hìc accipienda <lb></lb>pro ſcientia optica, ſeu perſpectiua, quæ viſus paßiones demon<lb></lb>ſtrat, ab Euclide, Sereno, Vitellione alijs〈qué〉 autoribus tradita: ſed <lb></lb>pro illa ſcientiæ mathematicæ parte Geodæſia dicta, quæ viſu, ſiue <lb></lb>radio viſuali coadiuuantibus varijs inſtrumentis <expan abbr="tũ">tum</expan> longitudines <lb></lb>altitudinum, planitierum, ac profunditatum: tum longitudi<lb></lb>nes, &amp; latitudines ſimul ſuperficierum: tum etiam longitudines, <lb></lb>latitudines, craßitudines〈qué〉 ſimul corporum metiri docet. </s>
<s>quam <lb></lb>porrò ſcientiam multi quidem cùm antiqui, tum recentiores au<lb></lb>tores locupletißimè tradidere: Autor verò in fine præſentis ope<lb></lb>ris, quatenus rei bellicæ neceſſariam ſubiunxit. </s>
<s>Qui enim ci<lb></lb>uitates expugnaturi ſunt, prius earum ſitus, ambitus, mœnium <lb></lb>altitudines, foſſarum latitudines, ac profunditates à longe iam <lb></lb>dictæ ſcientiæ præceptis, ac regulis ſcire debent: vt machinas <lb></lb>antiquorum more, vel terrea caſtra iuxta recentiorum vſum ad <lb></lb>earum expugnationem proportionaliter, <expan abbr="commenſurabiliterq́ue">commenſurabiliterque</expan> <lb></lb>præſtruere poßint. </s>
<s>Quamobrem non immerito Athenæus hor<lb></lb>tatur non eſſe ignaros iam dictæ opticæ tractationis eos, qui huiu<lb></lb>ſcemodi machinis bellicis, quales Autor in hoc opere deſcribit, vti <lb></lb>debent. </s>
<s>ne idem inconueniens eis accidat, quod Chium ciuitatem <lb></lb>temere obſidentibus eueniſſe Autor inquit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note162"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note162"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Pithicium eſt quoddam pondus ſaxeum, aut ferreum, vel <lb></lb>plumbeum, cuius formam Author declarat.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note163"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note163"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ figuræ ] hoc eſt formæ, quam habet tota machina, de qua <lb></lb>hìc agitur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note164"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note164"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Elepolis est quædam machina bellica ciuitatum deuaſtatrix,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/097.jpg"></pb><emph type="italics"></emph>quam Athenæus ex Apollodori doctrina conſtruere diligentiſ<lb></lb>ſimè docet. </s>
<s>hæc autem tum magna, tum parua fit, vt neceßitas, <lb></lb>vſus〈qué〉 poſtulat.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note165"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note165"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quid nam ſit thoracium ſuperiùs in vndecimo capite decla<lb></lb>rauimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note166"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note166"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Charcheſium eſt quoddam poculi genus, necnon ſummitas <lb></lb>mali, vel antenæ nauis.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note167"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note167"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſex motus] ſcilicet dextrorſum, ſiniſtrorſum, ante, retro, <lb></lb>ſurſum, atque deorſum.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note168"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note168"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Grues, ſiue ciconiæ græcè<emph.end type="italics"></emph.end> <foreign lang="grc">γέρανοι</foreign>, <emph type="italics"></emph>ſeu<emph.end type="italics"></emph.end> <foreign lang="grc">κηλόνια</foreign>, <emph type="italics"></emph>ſunt inſtru<lb></lb>menta, quibus aqua è puteis hauritur, ſubleuandis etiam pon<lb></lb>deribus apta.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note169"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note169"></margin.target>k</s></p><p type="main">
<s><emph type="italics"></emph>Caulis hìc intelligendus eſt fuſtis, ſiue fuſus ſpiricis, aut he<lb></lb>lici ſimilibus ſcalptura factis circumuolutionibus præditus. </s>
<s>cu<lb></lb>iuſmodi ſunt ij, quibus in torcularibus etiam vtimur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note170"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note170"></margin.target><emph type="italics"></emph>l<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Operario] videlicet inſtrumento illo, quod eleuandi trahen<lb></lb>di〈qué〉 pondera vim habet, atque Italica lingua Argana vocatur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note171"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note171"></margin.target><emph type="italics"></emph>m<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Damis colophonius antiquus fuit ſcriptor, cuius nullum vi<lb></lb>dimus volumen. </s>
<s>Bitonis autem commentarij de conſtructione bel<lb></lb>licorum inſtrumentorum extant inter Athenai libros inſerti.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>De Rate fluuio, ſiue foſſæ aqua plenæ imponenda. </s>
<s><lb></lb>Cap. </s>
<s>XXVI.<emph.end type="center"></emph.end></s></p><p type="main">
<s>FIat Ratis longitudinem habens paulò maio<lb></lb>rem latitudine fluuij, cui pons imponendus <lb></lb>eſt: <expan abbr="inſternaturq́ue">inſternaturque</expan> tabulis clauis ligneis affi<lb></lb>xis ne iuxta varios fluuialis vndæ motus amo<lb></lb>ueatur, <expan abbr="diuulſaq́ue">diuulſaque</expan> decidat. </s>
<s>Et maior qui<lb></lb>dem pars lignorum ipſius ratis funibus alligatis, &amp; ligneis <lb></lb>clauis raris affixis ſtabiliatùr. </s>
<s>tota verò ratis longitudo, quę <lb></lb>ante inimicorum faciem ventura eſt, vnà cum duobus <lb></lb><expan abbr="vtrobiq;">vtrobique</expan> exiſtentibus lateribus, propugnaculum ligneum, <lb></lb>cardinibus volubile. </s>
<s>altitudinis pedum duodecim habeat. </s>
<s><lb></lb>Fit autem per affixionem erectorum ſtantium lignorum, ro<lb></lb>tunda foramina inferiùs ſuſcipientium, <expan abbr="politisq́ue">politisque</expan> clauis <lb></lb>connexorum ad laterales tabulas extrinſecùs confixas, qui<pb xlink:href="052/01/098.jpg"></pb>bus porrò clauis extractis propugnaculum etiam vnà co<lb></lb>incidit. </s>
<s>Appendantur autem &amp; coria, ſiue panni laceres <lb></lb>in ipſis tabulis extrinſecè parum excedentia. </s>
<s>necnon ſcalæ <lb></lb>intus apponantur, ſuperna quidem crura ad erecta ligna <lb></lb>clauis affixa habentes, ipſis <expan abbr="etiã">etiam</expan> erectis lignis ſupernè per<lb></lb>foratis exiſtentibus: inferna verò in pauimento funibus <lb></lb>alligata. </s>
<s>vt ſcalis erectis ex aduerſo ſtantibus occurrens <lb></lb>propugnaculum erectum permaneat. </s>
<s>Sic igitur qui ſuper <lb></lb>ſcalis ſtant ante inimicorum faciem altiores exiſtentes, <expan abbr="an-terioresq́ue">an<lb></lb>terioresque</expan> turres in eorum cuſtodiam, ac tutellam ex pro<lb></lb>pugnaculo habentes, promptè in aduerſum oppugnabunt. </s>
<s><lb></lb>Non vniatur autem totum quod erectum ſtat propugnacu<lb></lb>lum, ſed ad quaſdam partes haud colligatum ſit. </s>
<s>vt ſi ſecun<lb></lb>dùm aggreſſionem neceſſe fuerit, altera quidem eius pars <lb></lb>ſtet, altera verò decidat. </s>
<s>quòd ſi fuerit opus vt totum quo<lb></lb>que decidat, ſcalas omnes oppugnantes, ſuper <expan abbr="propugna-culoq́ue">propugna<lb></lb>culoque</expan> reſiſtentes ſoluendo, ex inferioribus cruribus ſub<lb></lb>trahemus, ſuper pauimento eas reponentes. </s>
<s>Hanc autem <lb></lb>ratem palis terræ procul infixis per funes retinendo firma<lb></lb>bimus. </s>
<s>atque à ripa nobis proxima vnum eius extremum <lb></lb>paululum tradentes expellemus, cuneo, qui deſuper ipſam <lb></lb>retinet abſoluto. </s>
<s>atque hoc modo ratis ipſa inſtar ianuæ ſe <lb></lb>adaperiens, exercitu plena exiſtens ab aquæ decurſu pau<lb></lb>latim protrahitur, ac denique vnum eius extremum ad flu<lb></lb>minis ripam hoſtibus proximam aduenit. </s>
<s>At quoniam lon<lb></lb>gior fluminis latitudine ſuppoſita fuit, non poteſt ab vnda <lb></lb>ad defluxum iterum conuerti. </s>
<s>intra propugnaculum verò <lb></lb>in pauimento relicta ſunt foramina quaſdam ad partes, ac <lb></lb>ad terram vſque peruenientia, ad quæ lignei pali acuratè <lb></lb>figuntur, <expan abbr="ipſaq́ue">ipſaque</expan> ratis latenter alligatur. </s>
<s>ac demum figu<lb></lb>ra talis eſt. </s></p>
<pb xlink:href="052/01/099.jpg"></pb><figure id="id.052.01.099.1.jpg" xlink:href="052/01/099/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>De quibuſdam ſuperioris machinæ additamentis, eiuſque <lb></lb>motu, &amp; vſu. </s>
<s>Cap. </s>
<s>XXVII.<emph.end type="center"></emph.end></s></p><p type="main">
<s>OVum autem vnum ratis extremum ad contra<lb></lb>riam fluminis ripam aduenerit, atque ex inte<lb></lb>riore propugnaculi parte in terra firmatum <lb></lb>fuerit, vt iam dictum eſt: tunc ab extremitate <lb></lb>alterum quoque extremum abſoluitur, <expan abbr="ite-rumq́ue">ite<lb></lb>rumque</expan> ipſius vndæ decurſus tranſuerſam ipſam impedit, <lb></lb>atque ad alterum fluminis litus totam ſecundùm longitu<lb></lb>dinem coaptatam apponit. </s>
<s>multitudine collecta, <expan abbr="prompta-q́ue">prompta<lb></lb>que</expan> ad pugnæ contrariam aciem exiſtente. </s>
<s>qui verò ſuper <lb></lb>ſcalas aſcenderunt tamquam ſuper muro ſtantes, audacter <lb></lb>in aduersùm certabunt. </s>
<s>Cùm autem perterrens à propu<lb></lb>gnaculo congreſſus hoſtes auerterit, inferiora ſcalarum li<lb></lb>gna ſoluuntur, <expan abbr="totusq́ue">totusque</expan> propugnaculi paries pedetentim <lb></lb>obliquatur, ſubtractis ſcilicet ſcalis, ac ſuper pauimentum <lb></lb>incidentibus. </s>
<s><expan abbr="totumq́ue">totumque</expan> interiectum ſpatium, via inciden<lb></lb>tis propugnaculi fit, ac demum hoc pacto continua traie<pb xlink:href="052/01/100.jpg"></pb>ctio erit. </s>
<s>Foretur autem latenter infernè quoque propu<lb></lb>gnaculum in lateralibus tabulis iuxta faciem affixis, ita vt <lb></lb>ab inferiori etiam parte ad hoſtes iacula, <expan abbr="ſagittæq́ue">ſagittæque</expan> diri<lb></lb>gantur: occultis autem certantibus exiſtentibus, duplici <lb></lb>ſerie iuxta faciem certent: ad ſolam verò ſupernam hoſtes <lb></lb>reſpiciant, atque repugnent. </s>
<s>Expoſuimus itaque quonam <lb></lb>pacto figura rectè deſcribitur, vt cùm ſcalarum poſitio, tum <lb></lb>propugnaculi ſitus perſpicuus fiat. </s>
<s>ipſi autem rati dum ex <lb></lb>proxima nobis ripa ſoluitur, ac tamquam ianua adaperi<lb></lb>tur, in fluuialis vndæ defluxu auxiliari oportet, ne raptim <lb></lb>ad reliquam fluminis ripam verſus hoſtes exiſtentem ad<lb></lb>ueniat. </s>
<s>quapropter à proxima nobis ripa retinendo fræ<lb></lb>nanda, <expan abbr="coercendaq́ue">coercendaque</expan> eſt: funium vero traditio paulatine <lb></lb>facienda: vt leniter, <expan abbr="ſenſimq́ue">ſenſimque</expan> progrediens, alteram flu<lb></lb>minis ripam ab omni periculo immunis occupet. </s>
<s>atque fi<lb></lb>gura ſubijcitur. </s></p>
<pb xlink:href="052/01/101.jpg"></pb><figure id="id.052.01.101.1.jpg" xlink:href="052/01/101/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>Operis concluſio.<emph.end type="center"></emph.end></s></p><p type="main">
<s>HAs igitur obſidionales machinas, quæ à nobis <lb></lb>quoad deſcriptionem, <expan abbr="configurationemq́ue">configurationemque</expan> </s></p><p type="main">
<s><arrow.to.target n="note172"></arrow.to.target><lb></lb>per electionem iam conſtructæ ſunt, ipſi exer<lb></lb>cituum præſides cum ratione, <expan abbr="aſſiduaq́ue">aſſiduaque</expan> me<lb></lb>ditatione accuratè conficientes: diuinam vbi<lb></lb>que locorum vltionem illuceſcere facientes: iuſtitia, ac pie<lb></lb>tate ornati: &amp; forti manu, atque mutua opera, <expan abbr="bellicaq́ue">bellicaque</expan> <lb></lb>ſocietate Dei cultorum, <expan abbr="Chriſtiq́ue">Chriſtique</expan> amatorum Romano<pb xlink:href="052/01/102.jpg"></pb>rum Imperatorum conualeſcentes, ac præſidijs cuſtoditi: <lb></lb>facilè ipſius potiſſimùm Agar ciuitates capient, nullum ip<lb></lb>ſi in commodum à deſtruentibus diuinum cultum inimicis <arrow.to.target n="note173"></arrow.to.target><lb></lb>patientes. </s></p><p type="margin">
<s><margin.target id="note172"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note173"></margin.target>b</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note174"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note174"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>PEr electionem non ab re dixit, quoniam non omnes obſi<lb></lb>dionales machinas ab antiquioribus autoribus traditas <lb></lb>ipſe deſcripſit: ſed eas <expan abbr="tantũ">tantum</expan>, quas eligere ſibi viſum fuit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note175"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note175"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Chriſti〈qué〉 amatorum] hoc eſt Chriſtianorum Romanorum Im<lb></lb>peratorum Chriſti fidem contra Gentiles defendentium. </s>
<s>vndè ad<lb></lb>notandum est quod Autor noſter poſt Chriſti aduentum floruit, vt <lb></lb>in fine ſequentis ſui operis perſpicuum nobis erit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Operis de machinis bellicis finis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p>
<pb xlink:href="052/01/103.jpg"></pb><figure id="id.052.01.103.1.jpg" xlink:href="052/01/103/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>HERONIS MECHANICI <lb></lb>LIBER DE GEODAESIA. <lb></lb>PROEMIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s>QVONIAM autem non licet obſidere <lb></lb>volentibus à longe murorum altitu<lb></lb>dines, ac ſpatiorum interualla, nec<lb></lb>non fluuiorum latitudines in menſu<lb></lb>ratione ſupputare: ſed exercitatos li<arrow.to.target n="note176"></arrow.to.target><lb></lb>nearum peritia, <expan abbr="Dioptricæq́ue">Dioptricæque</expan> facul<lb></lb>tatis cognitione conſiderationem fa<lb></lb>cere: ad hoc vt Elepolis æqualem <lb></lb>cum muris ſtaturam habentes, <expan abbr="com-menſurabilesq́ue">com<lb></lb>menſurabilesque</expan> pontes ratibus ad <lb></lb>fluuiorum latitudines inducantur: vt tamquam in ponte, <lb></lb>vel traiectione innocuè exercitus ordinatim pertranſigat: <lb></lb>quandoquidem multi ſæpe maiores, vel minores quàm de<lb></lb>cebat machinas cùm conſtruxiſſent, <expan abbr="atq;">atque</expan> attuliſſent (quem<arrow.to.target n="note177"></arrow.to.target><lb></lb>admodum etiam in præcedenti opere claruit) eos, qui in <lb></lb>ipſis propugnaturi ſunt, à contrarijs enecari fecerunt: ſen<lb></lb>ſu temerario, <expan abbr="coniecturaq́ue">coniecturaque</expan> perſuaſi: propterea decreui<arrow.to.target n="note178"></arrow.to.target><lb></lb>mus ipſam Dioptriæ cum ratione vim, ac eam ipſius par<lb></lb>tem, quæ multis in rebus vitam humanam maximè iuuat: <lb></lb>ex antiquioribus, <expan abbr="eruditiſſimisq́ue">eruditiſſimisque</expan> ſimpliciora colligentes, <arrow.to.target n="note179"></arrow.to.target><lb></lb>nudis linearibus indaginibus explicare, in <expan abbr="paucisq́ue">paucisque</expan> dia<lb></lb>grammatibus demonſtrationes facere, quonam pacto ex<arrow.to.target n="note180"></arrow.to.target><lb></lb>tra iaculum hoſtium ſtantes, altitudines, ac longitudines, <lb></lb><expan abbr="interualaq́">interualaque</expan>; reuera ſine mendacio connumerare valeamus.
<pb xlink:href="052/01/104.jpg"></pb>Hæc autem conſideratio <expan abbr="nõ">non</expan> ſolùm ad militarem ſcientiam <lb></lb>addiſcendi cupidos inſtituet, verùmetiam ad aquæ dedu<lb></lb>ctiones, ac murorum conſtructiones, &amp; lacuum circumſcri<arrow.to.target n="note181"></arrow.to.target><lb></lb>ptiones vtiliſſima: necnon ad Geodæſiam, <expan abbr="cœleſtiumq́ue">cœleſtiumque</expan> <lb></lb>contemplationem non parum conferens apparebit. </s>
<s>Atque <lb></lb>operæpretium eſt nos prolixitatem, ac multiloquium effu<lb></lb>gientes, id quidem, quod obſcurum, ac inexplicabile circa <lb></lb>dictiones priſcorum ſcientia præditorum eſt, ſecernere, at<lb></lb>que in rudius tranſmutare: eam verò, quæ circa demon<lb></lb>ſtrationes mathematicè dicta eſt orationum compendio ca<lb></lb>ptu <expan abbr="faciliũ">facilium</expan> dilatationem aggredi: ac tandem id, quod eius, <lb></lb>quæ circa mentis conceptus verſatur contemplationis al<lb></lb>tum eſt, ad humile, <expan abbr="magisq́ue">magisque</expan> ſenſuale deferre: conſpicuam <lb></lb>ipſam tractationem facientes viris, qui facilè inſidiari vo<lb></lb>lunt, &amp; quibuſcumque alijs, qui forſan hanc ſtudio proſe<lb></lb>quuntur, præcipuè verò ijs, qui quomodocumque Geo<lb></lb>metriam obſeruant. </s></p><p type="margin">
<s><margin.target id="note176"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note177"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note178"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note179"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note180"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note181"></margin.target>f</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note182"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note182"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>DIoptrica facultas (vt docet Proculus in 14. cap. </s>
<s>primi li<lb></lb>bri ſuorum commentariorum in primum Euclides Ele<lb></lb>mentorum) dicitur illa pars Aſtrologiæ, quæ ſolis, ac <lb></lb>lunæ cæterarum〈qué〉 ſtellarum diſtantias dioptricis inſtrumentis di<lb></lb>gnoſcit. </s>
<s>Dioptrica verò inſtrumenta ſunt ea, in quibus exiſtunt <lb></lb>duo parua foramina, per quæ radij viſuales oculorum noſtrorum <lb></lb>tranſeunt dum aliquod interuallum metiri volumus. </s>
<s>quoniam <lb></lb>autem huiuſcemodi inſtrumentis Geodæſia ſcientiæ mathematicæ <lb></lb>pars operatur, idcirco dioptricam facultatem hìc eam Autor vo<lb></lb>cat. </s>
<s>quam in 25 capite præcedentis operis opticam etiam nuncu<lb></lb>pauit, quemadmodum ibi iam adnotauimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note183"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note183"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[in præcedenti opere claruit] ſcilicet in principio vigeſimi<lb></lb>quinti capitis vbi loquebatur de ijs, qui temere <expan abbr="Chiũ">Chium</expan> obſidebant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note184"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note184"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Dioptriam hìc appellat eam, quam ſuperius dioptricam fa<lb></lb>cultatem vocauit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note185"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note185"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Diagramma propriè hìc accipiendum eſt pro figura lineis, ac<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/105.jpg"></pb><emph type="italics"></emph>elementis deſignata: cuiuſmodi ſunt figuræ, in quibus geometræ <lb></lb>propoſitiones ſuas demonſtrant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note186"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note186"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[extra iaculum hoſtium ſtantes] hoc eſt extra terminum illum <lb></lb>ſtantes, ad quem hoſtium iacula peruenire poſſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note187"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note187"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[necnon ad Geodæſiam, cœleſtium〈qué〉 contemplationem] Quæ<lb></lb>nam ſit Geodæſia ſcientia nos quidem in præcedentis operis 25 <lb></lb>capite diximus, Proclus autem in tam dicto loco declarat. </s>
<s>Cœle<lb></lb>ſtium vero contemplationem hic intelligit Autor cam, quam mo<lb></lb>dò diximus dioptricam Aſtrologiæ partem. </s>
<s>Hæc ad faciliorem hu<lb></lb>iuſce proemij perceptionem adnotanda eſſe duximus. </s>
<s>verùm ani<lb></lb>maduertendum eſt, quòd hoc in loco magna præſentis operis ha<lb></lb>betur imperfectio. </s>
<s>quandoquidem ſequentis propoſitionis prin<lb></lb>cipium deſideratur, necnon inter proemium, ipſam〈qué〉 propoſitio<lb></lb>nem quædam altæ propoſitiones deſunt, vt ex ſine iam dictæ ſe<lb></lb>quentis propoſitionis, ex alijs〈qué〉 ſequentibus propoſitionibus pa<lb></lb>tet. </s>
<s>fortaſſe verò proemium etiam hoc prolixius ab Autore com<lb></lb>poſitum ſuit, eius〈qué〉 ſinis deſideratur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Propoſitio earum, quæ extant prima, cuius principium <lb></lb>deſideratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s>* * * &amp; cd baſim. </s>
<s>ſimiliter autem ipſum etiam li<lb></lb>neæ ab ad lineam bd. </s>
<s>atque rurſus in qua ratione eſt ip<lb></lb>ſa bd ad vtramlibet ipſarum dc, dg, in eadem eſt ipſa <lb></lb><expan abbr="quoq;">quoque</expan> ab ad vtramlibet ipſarum hg, ec altitudinem. </s>
<s>opor<lb></lb>tet autem vt palus, qui perpendiculariter ante ſtat ad ma<lb></lb>iores altitudines, &amp; aquarum deductionem iuxta h ſignum <lb></lb>ad clauum quaedam ſuſpenſam ſuſcipiat dioptram, quæ <arrow.to.target n="note188"></arrow.to.target><lb></lb>etiam lychnia vocatur. </s>
<s>cùm autem ipſas dc, dg minoris <lb></lb>trianguli baſes verſus nos exiſtentes meritus fuero, <expan abbr="ipſasq́">ipſasque</expan>; <lb></lb>iuxta longitudinem inuenero: ipſas etiam ce, gh cogni<lb></lb>tas habebo, tamquam cas, quæ ipſius dioptræ, ac pali alti<lb></lb>tudines vniunt. </s>
<s>&amp; ſi baſim altitudinis decuplam inuenero, <lb></lb>decuplam totam etiam db ipſius ab enuntiabo. </s>
<s>poſſum <arrow.to.target n="note189"></arrow.to.target><lb></lb>autem totam quoque db reperire quemadmodum in lon<lb></lb>gitudine, ac latitudine didicimus. </s>
<s>&amp; cùm ipſam <expan abbr="paſiuũ">paſſuum</expan> 120 <lb></lb>reperiero, ipſam etiam ab 12 affirmabo. </s>
<s>quæ quidem ea
<pb xlink:href="052/01/106.jpg"></pb>eſt muri altitudo, quæ in extremo propugnaculi quæritur, <lb></lb>tam quam ipſius à portarum pauimento ſuppoſiti b ſigni <arrow.to.target n="note190"></arrow.to.target><lb></lb>ad id, quod ad quandam quadrigalis curriculi partem ſi<arrow.to.target n="note191"></arrow.to.target><lb></lb>gnatum eſt a ſignum. </s>
<s>De partibus autem, ac particulis ſuf<lb></lb>ficienter quærentibus per arithmeticos methodos ſuperiùs <lb></lb>diſſeruimus. </s></p><p type="margin">
<s><margin.target id="note188"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note189"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note190"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note191"></margin.target>d</s></p><figure id="id.052.01.106.1.jpg" xlink:href="052/01/106/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>NIſi materia hæc. </s>
<s>de qua in præſenti opuſculo agit Autor, <lb></lb>à multis cùm antiquis, tùm recentioribus autoribus locu<lb></lb>pletißimè tradita fuiſſet: plena huius, ſequentium〈qué〉 pro<lb></lb>poſitionum componeremus commentaria, vt geometricas earum <lb></lb>demonſtrationes iuxta Euclidis doctrinam rudioribus faciliores, <lb></lb>dilucidiores〈qué〉 redderemus. </s>
<s>quoniam autem ab alijs ſufficienter <lb></lb>hanc materiam traditam habemus, nos iam inceptum ordinem <lb></lb>noſtrum ſequentes ea duntaxat breuibus ſcholijs exponemus, quæ <lb></lb>penitus obſcura nobis eſſe videbuntur.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note192"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note192"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Dioptram, hoc eſt inſtrumentum dioptricum lychniam etiam <lb></lb>antiqui vocabant, ab ipſis lucernæ ſimilitudine: quippe cùm in <lb></lb>menſurando tamquam lucerna libere pendeat, duobus〈qué〉 forami<lb></lb>nibus lucem oculis noſtris offerat.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note193"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note193"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[quemadmodum in longitudine, ac latitudine didicimus] nem<lb></lb>pe in propoſitionibus ijs, in quibus longitudinem, ac latitudinem <lb></lb>interuallorum ipſe metiri docuit, quę inter proemium, <expan abbr="præſentem-q́ue">præſentem<lb></lb>que</expan> mutilam propoſitionem deſiderantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note194"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note194"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quadrigale, ſiue quadrigarium curriculum eſt ſpatium ſuper <lb></lb>muros ciuitatum, ſuper quod quadrigæ circumcurrunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note195"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note195"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[De partibus autem, ac particulis] hoc eſt minutis, ſecun<lb></lb>dis, tertijs, cæteris〈qué〉 minoribus partium minutijs ait ſe ſuperiùs <lb></lb>ſufficienter per arithmeticos methodos diſſeruiſſe. </s>
<s>vndè manife-<emph.end type="italics"></emph.end><pb xlink:href="052/01/107.jpg"></pb><emph type="italics"></emph>ſtum nobis eſt multa inter proemium, præſentem〈qué〉 principio ca<lb></lb>rentem propoſitionem deſiderari. </s>
<s>cùm enim menſurandi facul<lb></lb>tatem Autor pertractaturus eſſet, quę ſine ſupputatione integro<lb></lb>rum, fractorum〈qué〉 numerorum tradi non poterat: neceſſarium ei <lb></lb>fuerat de arte ſupputandi, tum integros, tum fractos numeros per <lb></lb>minuta, ſecunda, tertia, cætera〈qué〉 hiſce adhuc minora more græ<lb></lb>corum Aſtronomorum priùs ſermonem habuiſſe.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Secunda.<emph.end type="center"></emph.end></s></p><p type="main">
<s>OStendemus autem quonam pacto etiam duo<arrow.to.target n="note196"></arrow.to.target><lb></lb>bus ſignis longe à nobis datis, <expan abbr="atq;">atque</expan> viſis: quod <arrow.to.target n="note197"></arrow.to.target><lb></lb>inter ea iuxta circinum interiacet interuallum <lb></lb>capere poſſimus, non appropinquantes datis <lb></lb>ſignis. </s>
<s>Sint ſigna viſa ab, quæ in ipſa cancel<arrow.to.target n="note198"></arrow.to.target><arrow.to.target n="note199"></arrow.to.target><lb></lb>lorum diſtantia obſeruentur. </s>
<s>ipſum quidem a in tertio, ip<arrow.to.target n="note200"></arrow.to.target><lb></lb>ſum vero b in nono. </s>
<s>firmans itaque dioptram in ſuperna <lb></lb>orbita verſus tertium ſignum, atque ad ſitum plani dato<arrow.to.target n="note201"></arrow.to.target><lb></lb>rum ſignorum tympanum conſtituens: duas rectas lineas <arrow.to.target n="note202"></arrow.to.target><lb></lb>per foramina regulæ diduco: ad tertium quidem ipſam ca, <lb></lb>ad nonum verò ipſam cb. </s>
<s>atque harum vnam regula me<arrow.to.target n="note203"></arrow.to.target><lb></lb>tior, vel <expan abbr="quẽamodum">quemamodum</expan> etiam ſuperiùs oſtenſum eſt. </s>
<s>&amp; ſi for<lb></lb>taſſe paſſuum octoginta eam inuenero, ſeco ipſam iuxta <lb></lb>quam cumque partem voluero. </s>
<s>ſit ſectio iuxta decimam par<lb></lb>tem earum, quæ verſus orbitam ſunt rectarum linearum, ad <lb></lb>paſſus octo, iuxta d ſignum. </s>
<s>&amp; cùm dioptram ad ipſum <expan abbr="traſpoſuero">traſ<lb></lb>poſuero</expan>, ipſam de <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan> per <expan abbr="regulã">regulam</expan> diduco, quæ ſimi<lb></lb>liter ipſam cb iuxta <expan abbr="decimã">decimam</expan> partem ad e ſignum ſecet. </s>
<s>Erit <lb></lb>igitur ipſa <expan abbr="quoq;">quoque</expan> de decima pars ipſius ab diſtantiæ. </s>
<s><expan abbr="quẽ-admodum">quem<arrow.to.target n="note204"></arrow.to.target><lb></lb>admodum</expan> enim ipſa ac ad ipſam cd, &amp; ipſa bc ad ipſam <lb></lb>ce, ita etiam ipſa ab ad ipſam de erit at veluti etiam ipſa d <lb></lb>e ad ipſam ec, ſic ipſa quoque ab ad ipſam bc. </s>
<s>cùm autem <lb></lb>ipſam etiam ed verſus nos exiſtentem menſurauero, &amp; paſ<lb></lb>ſuum quatuor eam cognitam inuenero: ipſam quoque ab <lb></lb>tamquam decuplam quadraginta paſſuum exiſtentem ha<lb></lb>bebo. </s>
<s>Quapropter quod quæritur inter ab ſigna interia<arrow.to.target n="note205"></arrow.to.target><lb></lb>cens interuallum quadraginta paſſuum repertum eſt. </s></p>
<pb xlink:href="052/01/108.jpg"></pb><p type="margin">
<s><margin.target id="note196"></margin.target><emph type="italics"></emph>Propoſi<lb></lb>tio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note197"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note198"></margin.target><emph type="italics"></emph>Conſtru<lb></lb>ctio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note199"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note200"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note201"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note202"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note203"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note204"></margin.target><emph type="italics"></emph>Demon<lb></lb>ſtratio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note205"></margin.target><emph type="italics"></emph><expan abbr="Cõcluſio">Concluſio</expan>.<emph.end type="italics"></emph.end></s></p><figure id="id.052.01.108.1.jpg" xlink:href="052/01/108/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note206"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note206"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[iuxta circinum] ideſt iuxta quandam circini aperturam.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note207"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note207"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ipſum quidem a in tertio, ipſum verò b in nono] intelligen<lb></lb>dum eſt cancello.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note208"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note208"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[in ſuperna orbita] duæ ſunt in Dioptra, ſiue dioptrico inſtru<lb></lb>mento partes, quarum altera quidem vocatur orbita ſuperna, <lb></lb>altera verò orbita inferna. </s>
<s>hæ autem ſunt duæ ſemicircumferen<lb></lb>tiæ, ſuperna ſcilicet, ac inferna: in quibus etiam in Aſtrolabij <lb></lb>dorſo ſunt duæ illæ vnius rectæ lineæ partes, quarum ſuperna qui<lb></lb>dem vocatur linea medij cœli, ſiue mediæ diei: inferna verò, linea <lb></lb>mediæ noctis, ſiue angulus terræ.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/109.jpg"></pb><p type="main">
<s><arrow.to.target n="note209"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note209"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Tympana ſunt rotulæ in Aſtrolabij matre contentæ, in quibus <lb></lb>diuerſorum climatum tabulæ deſignantur. </s>
<s>in pręſentia uerò tym<lb></lb>panum accipiendum eſt pro plana ſuperficie ipſius dioptræ, ſeu <lb></lb>dioptrici inſtrumenti, quo Autor utitur. </s>
<s>quod autem ait [ad ſi<lb></lb>tum plani datorum ſignorum] ſic intelligendum eſt. </s>
<s>quòd ſcilicet <lb></lb>tympanum ipſum ita ſituetur, vt in eodem plano tympanum, ocu<lb></lb>lus, menſurantis, data〈qué〉 ſigna ſint.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note210"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note210"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Regulæ] hoc eſt alidadæ, ſeu voluellæ, in qua duæ pinnulæ <lb></lb>paruis foraminibus præditæ ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note211"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note211"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſuperiùs oſtenſum eſt] videlicet in propoſitionibus ijs, quæ <lb></lb>deſiderantur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Tertia.<emph.end type="center"></emph.end></s></p><p type="main">
<s>ALiter etiam interuallum inter data duo ſigna <arrow.to.target n="note212"></arrow.to.target><lb></lb>interiacens percipi poteſt iuxta diagramma, <lb></lb>quod nunc exponitur. </s>
<s>Intelligatur per ſup<lb></lb>poſitionem ipſum quidem a ſignum, quod <arrow.to.target n="note213"></arrow.to.target><lb></lb>iuxta latitudinem hippici ad ſiniſtram fundæ <lb></lb>partem obſeruetur: ipſum verò b ad dexteram. </s>
<s>Statuo igi<arrow.to.target n="note214"></arrow.to.target><arrow.to.target n="note215"></arrow.to.target><lb></lb>tur ad eum, qui inacceſſibilis vocatur dioptram parum di<lb></lb>ſtantem à ſuperna è contrario iacente orbita, vt ad c <expan abbr="ſignũ">ſignum</expan>. </s>
<s><lb></lb>ita vt viſus ad rectam datorum ſignorum inſpectionem ne<lb></lb>quaquam impediatur. </s>
<s>cùm autem tympanum ad ſitum pla<lb></lb>ni baſis fundæ conſtituero, diduco duas rectas lineas per <lb></lb>regulam ad ſiniſtrum quidem terminum ipſam ca: ad dex<lb></lb>trum verò ipſam cb. </s>
<s>atque harum vnam (vt iam dictum <lb></lb>eſt) cùm partitus fuero, &amp; fortaſſe paſſuum 126 inuenero: <arrow.to.target n="note216"></arrow.to.target><lb></lb>ad alterum regulæ radium me confero. </s>
<s>atque immobilibus <lb></lb>cunctis, quæ in dioptra ſunt permanentibus, ſuper tympa<lb></lb>num oculos paululum attollo: &amp; in ipſa bc recta linea, vt <lb></lb>puta ad eius decimamoctauam partem ad ſiniſtras ipſius <lb></lb>inacceſſibilis partes iuxta ſeptem paſſus ſignum d perci<lb></lb>pio: ſimiliter autem ad dexteras etiam partes in ipſa ac re<lb></lb>cta linea, ſignum e: <expan abbr="ipſamq́ue">ipſamque</expan> ed connecto. </s>
<s>Et quoniam <arrow.to.target n="note217"></arrow.to.target><lb></lb>ipſa ec ipſius ca, &amp; ipſa dc ipſius cb decimaoctaua <lb></lb>pars eſt: ipſius quoque de interuallum ad ipſius ab in<pb xlink:href="052/01/110.jpg"></pb>teruallum decimaoctaua pars erit. </s>
<s>quemadmodum enim <lb></lb>minora latera duorum, quæ è contrario aduerticem figu<lb></lb>rantur <expan abbr="triangulorũ">triangulorum</expan> ad maiora ſe ſe <expan abbr="habẽt">habent</expan>: ita <expan abbr="etiã">etiam</expan> baſis trian<lb></lb>guli minoris, ad maioris baſem ſe habebit. </s>
<s>cùm <expan abbr="autẽ">autem</expan> ipſam <lb></lb>de minoris trianguli baſim <expan abbr="tãquã">tamquam</expan> apud nos <expan abbr="exiſtentẽ">exiſtentem</expan> men lb/&gt;ſurauero, ac fortaſſe paſſuum duorum cum dimidio ipſam <lb></lb>inuenero: ipſa <expan abbr="quoq;">quoque</expan> ab <expan abbr="tãquam">tanquam</expan> octodecupla exiſtens mi<arrow.to.target n="note218"></arrow.to.target><lb></lb>hi cognita erit. </s>
<s>Quamobrem rurſus ipſum inter ab ſigna <lb></lb>interiacens <expan abbr="interuallũ">interuallum</expan> iuxta extremitatem latitudinis hip<lb></lb>pici ad baſim fundæ paſſuum 45 repertum eſt. </s></p><p type="margin">
<s><margin.target id="note212"></margin.target><emph type="italics"></emph>Propoſi<lb></lb>tio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note213"></margin.target>a b</s></p><p type="margin">
<s><margin.target id="note214"></margin.target><emph type="italics"></emph>Conſtru<lb></lb>ctio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note215"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note216"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note217"></margin.target><emph type="italics"></emph>Demon<lb></lb>stratio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note218"></margin.target><emph type="italics"></emph><expan abbr="Cõcluſio">Concluſio</expan>.<emph.end type="italics"></emph.end></s></p><figure id="id.052.01.110.1.jpg" xlink:href="052/01/110/1.jpg"></figure>
<pb xlink:href="052/01/111.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note219"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note219"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>HIppicum est equitatus menſura quatuor cubitos conti<lb></lb>nens, quod etiam pro quocumque ſtadiorum quatuor in<lb></lb>teruallo ſuſcipitur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note220"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note220"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[fundæ] hoc eſt Monangonis inſtrumenti iaculatorij, quod in <lb></lb>17 capite præcedentis operis fundam etiam à nonnullis appellari <lb></lb>dixit. </s>
<s>de hac etenim funda hìc intelligenda ſunt ea, quæ ab Au<lb></lb>tore dicuntur: non autem de funda ex lino facta.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note221"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note221"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ad eum, qui inacceßibilis vocatur] hoc eſt verſus eum, ſcilicet <lb></lb>locum, quem peragrare nobis minimè licet propter varia impe<lb></lb>dimenta, qui à geometris inacceßibilis nuncupatur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note222"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note222"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[radium] hoc eſt pinnulæ foramen, per quod viſualis radius <lb></lb>tranſit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Quarta.<emph.end type="center"></emph.end></s></p><p type="main">
<s>FIeri autem poteſt, vt <expan abbr="nõ">non</expan> ſolùm interiacens in<arrow.to.target n="note223"></arrow.to.target><lb></lb>ter data duo ſigna interuallum ſuſcipiamus, <lb></lb>verùmetiam vt rectæ lineæ ſigna connectentis <lb></lb>ſitum reperiamus, alicui datorum ſignorum <lb></lb>non approximantes. </s>
<s>Sint ſigna quæ videntur <arrow.to.target n="note224"></arrow.to.target><arrow.to.target n="note225"></arrow.to.target><lb></lb>ab, ipſum quidem a ad vnum ex ſeptem Euripi ſegmentis <arrow.to.target n="note226"></arrow.to.target><lb></lb>in pectorum baſi obſeruatum: ipſum vero b ad id, quod in <arrow.to.target n="note227"></arrow.to.target><lb></lb>regali ſede eſt pauimentum, aut in vna earum, quæ vtro<arrow.to.target n="note228"></arrow.to.target><lb></lb>bique in curſoribus iuxta gymnicos agones inſtructiones <lb></lb>appellantur. </s>
<s>cùm ita que dioptram ad infernæ orbitæ è con<lb></lb>trario circumductionem è regione ſigni b ad c ſignum con<lb></lb>ſtituero, per regulam diſpicio, donec in recta linea iam di<lb></lb>ctum a ſignum ab extremitate conſpexero. </s>
<s>&amp; cùm ad la<lb></lb>tus dioptræ, quod in orbita eſt, me contulerim, ſuper tym<lb></lb>panum paululum oculos attollo, &amp; rectam diduco lineam <arrow.to.target n="note229"></arrow.to.target><lb></lb>ex oppoſito ſcalæ graduum ipſam cd tamquam ad paui<lb></lb>mentum ante ſtantium pectorum iuxta d ſignum reſpicien<lb></lb>tem, ad rectos exiſtentem angulos ipſi ac rectæ lineæ in <lb></lb>recto angulo, qui ad c ſignum eſt. </s>
<s>atque dioptram in ipſa
<pb xlink:href="052/01/112.jpg"></pb>cd recta linea deduco, donec in recta linea b ſignum aſpi<arrow.to.target n="note230"></arrow.to.target><lb></lb>ciam. </s>
<s>ſituetur dioptra ad e ſignum. </s>
<s>Ipſa igitur be ipſi qui<lb></lb>dem cd ad rectos eſt angulos, ipſi verò ac parallela. </s>
<s>poſ<lb></lb>ſum autem id, quod à ſigno c ad ſignum a, &amp; quod à ſigno <lb></lb>e ad ſignum b eſt interuallum capere, quemadmodum ſæ<lb></lb>pe triangularem figuram faciens ſuppoſui. </s>
<s>&amp; ſi æqualem <lb></lb>quidem ipſam ca ipſi eb inuenero, æquale ipſum quoque <lb></lb>ce interuallum ipſi ab enuntiabo: ſi verò vnam ipſarum <lb></lb>altera maiorem, exceſſum à maiore aufero, deinde mino<lb></lb>rem connecto. </s>
<s>verbi gratia ſi ipſam ce rectam latitudinis <lb></lb>lineam paſſuum duodecim inuenero, ipſam verò ca 90, &amp; <lb></lb>81 ipſam eb: excedentes paſſus nouem à ſigno c ad <expan abbr="ſignũ">ſignum</expan> <lb></lb>f aufero, deinde minorem ipſa fe connecto æquale, &amp; pa<lb></lb>rallela iuxta ſitum ipſi ab exiſtente. </s>
<s>nam ſi æqualis qui<lb></lb>dem eſſet ac ipſi be, duodecim <expan abbr="vtiq;">vtique</expan> paſſuum ipſum quo<lb></lb>que lineæ ab, quemadmodum ipſum lineæ ce interual<lb></lb>lum eſſet. </s>
<s>at quoniam excedens ipſa ca ipſam eb nouem <lb></lb>paſſibus reperta eſt, hos ipſa fe reſecat, &amp; angulum rectum <lb></lb>ad c ſignum exiſtentem ſubtendit. </s>
<s>eſt autem ipſa quoque <lb></lb>ce baſis paſſuum duodecim: quare quindecim ipſa fe erit, <arrow.to.target n="note231"></arrow.to.target><lb></lb>tamquam ea, quæ ſecundum potentiam duobus circa re<lb></lb>ctum angulum iacentibus lateribus adæquatur. </s>
<s>eorundem <lb></lb>igitur paſſuum erit ipſum etiam, quod ab a ſigno ad b ſi<arrow.to.target n="note232"></arrow.to.target><lb></lb>gnum eſt interuallum. </s>
<s>Quare non ſolùm interiacens inter <lb></lb>ab ſigna interuallum iuxta magnitudinem repertum eſt, <lb></lb>verùm etiam ſitus rectæ lineæ ſigna connectentis: quemad<lb></lb>modum propoſitum etiam diagramma ſuppoſuit. </s></p>
<pb xlink:href="052/01/113.jpg"></pb><p type="margin">
<s><margin.target id="note223"></margin.target><emph type="italics"></emph>Propoſi<lb></lb>tio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note224"></margin.target><emph type="italics"></emph>Constru<lb></lb>ctio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note225"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note226"></margin.target>b. </s>
<s>c</s></p><p type="margin">
<s><margin.target id="note227"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note228"></margin.target>e.f. </s>
<s>g</s></p><p type="margin">
<s><margin.target id="note229"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note230"></margin.target><emph type="italics"></emph>Demon<lb></lb>ſtratio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note231"></margin.target>i</s></p><p type="margin">
<s><margin.target id="note232"></margin.target><emph type="italics"></emph><expan abbr="Cõcluſio">Concluſio</expan>.<emph.end type="italics"></emph.end></s></p><figure id="id.052.01.113.1.jpg" xlink:href="052/01/113/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>QVibuſdam antiquioribus, <expan abbr="obſcurioribusq́ue">obſcurioribusque</expan> vocabulis in <lb></lb>principio præſentis propoſitionis vſus eſt Autor, quæ niſi <lb></lb>declarentur, fortaſſe minis obſcura legentibus videbun<lb></lb>tur: ſunt autem hæc.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note233"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note233"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Euripus Autore Mela eſt fretum, ſeu mare anguſtum inter <lb></lb>Aulidem Bœotiæ portum, &amp; Euboeam inſulam ſitum, quod vi<lb></lb>gintiquatuor horarum ſpatio ſepties recurrit eo impetu, vt naui<lb></lb>gia repugnantibus etiam ventis plena ſecum rapiat: vndè ſe<lb></lb>ptem agit in recurſibus ipſis in terra ſegmenta ſinuum inſtar.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note234"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note234"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[pectorum] græcè<emph.end type="italics"></emph.end> <foreign lang="grc">στηθέων</foreign> <emph type="italics"></emph>legitur, quod nil aliud latinè ſonat, <lb></lb>quàm pectorum, quemadmodum ego conuerti, vt ſim ſidus inter<emph.end type="italics"></emph.end><pb xlink:href="052/01/114.jpg"></pb><emph type="italics"></emph>pres. </s>
<s>verùm metaphoricè hoc ab Autore dictum eſſe mihi videtur. </s>
<s><lb></lb>quandoquidem in præſentia vocabulum<emph.end type="italics"></emph.end> <foreign lang="grc">στήθος</foreign>, <emph type="italics"></emph>quod propriè pe<lb></lb>ctus ſignificat, pro dictione<emph.end type="italics"></emph.end> <foreign lang="grc">κόλλοψ</foreign>, <emph type="italics"></emph>ſiue<emph.end type="italics"></emph.end> <foreign lang="grc">κόλπος</foreign>, <emph type="italics"></emph>hoc eſt ſinus <lb></lb>accipiendum eſt. </s>
<s>nam quemadmodum ſinus vocatur litus curuum <lb></lb>duobus quaſi brachijs longiùs in mare procurrentibus incluſum <lb></lb>per tranſlationem deſumptam à curuitate illa, quæ eſt intra pe<lb></lb>ctoris, brachiorum〈qué〉 complexum: ita etiam hoc in loco Autor pe<lb></lb>ctus pro ſinu maris conuerſa metaphora ſuſcepit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note235"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note235"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Baſim pectorum vocat intimam ſinuum partem.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note236"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note236"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ad id, quod in regali ſede eſt pauimentum] hoc eſt ad ipſius <lb></lb>regalis ſedis, nempe pallatij baſim, ac fundamentum.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note237"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note237"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Curſores in præſentia pro locis, ſiue interuallis accepit, vbi in <lb></lb>ludis publicis curſatur, qui proprio nomine curricula dicuntur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note238"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note238"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Gymnici Agones ſunt loci, in quibus Scenica, Muſica, Dioniſia<lb></lb>ca, bellica, alia〈qué〉 varia ſpectacula, necnon certamina exerceban<lb></lb>tur: quorum quatuor præcipui in Græcia fuere, ſcilicet Nemæus, <lb></lb>Pythius, Iſthmius, ac Olimpius.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note239"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note239"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[inſtructiones] ideſt apparatus gradibus conſtructi, cuiuſmo<lb></lb>di ſunt Theatra, Amphitheatra, Arenæ, Palestræ, aliæ〈qué〉 id genus <lb></lb>machinæ.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>His ita declaratis quod ait Autor nobis perſpicuum erit. </s>
<s>nam <lb></lb>excogitans ipſe ſe prope quandam eſſe maritimam, opulentam〈qué〉 <lb></lb>ciuitatem in Euripi litore poſitam, cuius ſitus à longe ſibi capien<lb></lb>dus ſit: ait duo ſigna per dioptram obſeruanda eſſe, quorum al<lb></lb>terum quidem ſit ad vnum ex ſeptem Euripi ſegmentis in baſi <lb></lb>pectorum ipſorum ſegmentorum: reliquum verò, ad <expan abbr="pauimentũ">pauimentum</expan>, <lb></lb>quod in regali ſede eſt, aut ad pauimentum, quod in vna earum <lb></lb>machinarum eſt, quæ vtrobique in curſoribus iuxta gymnicos <lb></lb>Agones inſtructiones appellantur. </s>
<s>talis itaque ſit ordo, ſenſus〈qué〉 <lb></lb>præſentium obſcurorum Autoris verborum. </s>
<s>Animaduertendum <lb></lb>autem eſt quòd tam in hac, quàm in præcedentibus, ac ſequen<lb></lb>tibus huius operis propoſitionibus dioptram modò pro toto dioptri<lb></lb>co inſtrumento, modò pro voluella, aut ea <expan abbr="inſtrumẽti">inſtrumenti</expan> parte, in qua <lb></lb>duo, per quæ inſpicimus parua foramina ſunt, Autor accipere <lb></lb>videtur. </s>
<s>quod diſtinguendum prudenti legentium iuditio relin<lb></lb>quimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note240"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note240"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſcalæ graduum] hoc est ſcalæ altimetrs in ipſo dioptrico in-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/115.jpg"></pb><emph type="italics"></emph>ſtrumento deſignatæ, in qua gradus vmbræ rectæ, &amp; vmbræ ver<lb></lb>ſæ in ſuis partibus, ac particulis diuiſi ſunt, quemadmodum <lb></lb>etiam in dorſo Aſtrolabij.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note241"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note241"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſecundum potentiam] potentia rectarum linearum nil aliud <lb></lb>est niſi quadratum ab ipſis deſcriptum, , vt ex decimo libro Ele<lb></lb>mentorum Euclidis patet. </s>
<s>quoniam autem in omni rectangulo <lb></lb>triangulo quadratum à latere rectum angulum ſubtendente de<lb></lb>ſcriptum æquale est ijs, quæ à reliquis lateribus <expan abbr="deſcribũtur">deſcribuntur</expan> qua<lb></lb>dratis, vt Euclides in penultima propoſitione primi Elementorum <lb></lb>demonſtrat: idcirco inquit Autor quòd ipſa fe rectum angulum <lb></lb>ſubtendens recta linea quindecim paſſuum erit, quandoquidem <lb></lb>ſecundum potentiam duobus circa rectum angulum iacentibus <lb></lb>lateribus adæquatur, hoc eſt quadratum eius quadratis eorum <lb></lb>duorum laterum æquale exiſtit. </s>
<s>cùm enim alterum quidem ipſo<lb></lb>rum duorum laterum nouem, alterum verò duodecim paſſuum <lb></lb>ſuppoſita ſint: quadratum alterius quidem 81, reliqui vero 144 <lb></lb>erit, quæ ſimuliuncta 225 efficiunt, totidem igitur quadratum <lb></lb>etiam a latere ef deſcriptum continet. </s>
<s>quare latus ef 15 paſ<lb></lb>ſuum erit. </s>
<s>Hæc autem pro dilucidatione huiuſce propoſitionis bre<lb></lb>uiter adnotata ſint.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Quinta.<emph.end type="center"></emph.end></s></p><p type="main">
<s>AT ipſam quidem rectarum linearum menſu<lb></lb>rationem hoc modo cognitam habebimus. </s>
<s>ip<lb></lb>ſa verò, quæ tum à rectilineis, tum à curuili<lb></lb>neis figuris continentur plana ſpatia hoc pa<arrow.to.target n="note242"></arrow.to.target><lb></lb>cto menſurabuntur. </s>
<s>in quadrangulis quidem <lb></lb>tum æquilateris, tum altera parte longioribus oportet lon<lb></lb>gitudinis latus in latitudinis latus multiplicare, vel etiam <arrow.to.target n="note243"></arrow.to.target><lb></lb>è conuersò: &amp; eum, qui ex duobus ipſis lateribus fit <expan abbr="planũ">planum</expan> <arrow.to.target n="note244"></arrow.to.target><lb></lb>numerum, figuræ aream, ſiue ſpatium, quod à quatuor la<lb></lb>teribus circum qua que terminatur, enuntiare. </s>
<s>quemadmo<lb></lb>dum in iamdicto diagrammate oſtendetur. </s>
<s>Quum enim la<lb></lb>tus ac paſſuum ſit nonaginta, duodecim verò latus ce: ſi <lb></lb>in ſeinuicem multiplicentur 1080 faciunt, quod eſt totum <arrow.to.target n="note245"></arrow.to.target><lb></lb>alterapartelongioris ſpatium. </s>
<s>idem autem modus in æqui-<pb xlink:href="052/01/116.jpg"></pb><arrow.to.target n="note246"></arrow.to.target><lb></lb>lateris etiam quadrangulis fiat. </s>
<s>Quaſi ſimilem autem, ac <lb></lb>euidentem menſurationem habebunt ipſa etiam quadran<lb></lb>gula, quæ Rhombi vocantur: tamquam ij, qui ex quadran<lb></lb>gulorum æquilaterorum, <expan abbr="quemadmodũ">quemadmodum</expan> etiam ipſæ Rhom <lb></lb>boides figuræ ex ipſarum alterapartelongiorum <expan abbr="figurarũ">figurarum</expan> <lb></lb>diſtortione fiunt. </s>
<s>etenim latera terminata, vnamque dia<arrow.to.target n="note247"></arrow.to.target><lb></lb>goniorum datam habent. </s>
<s>nam Rhombus quidem, ex duo<lb></lb>bus æquicruribus: Rhomboides verò, ex duobus acutan<lb></lb>gulis, vel obtuſangulis triangulis componitur. </s>
<s>vt in dia<lb></lb>grammate quiſque perſpicere poteſt ipſum quadrangulum <lb></lb>ab af, fe, eb, &amp; ab lateribus <expan abbr="cõtentum">contentum</expan>, ex ipſius altera<lb></lb>partelongioris diſtortione in Rhomboides <expan abbr="trãsfiguratum">transfiguratum</expan>: <lb></lb>&amp; ab ipſa quidem fb diagonio in duo acutangula, ab ipſa <arrow.to.target n="note248"></arrow.to.target><lb></lb>vero ae in duo obtuſangula triangula diuiſum. </s>
<s>At ipſa <lb></lb>triangulorum ſpatia à dimidio quadrangulorum, quæ ex ip <lb></lb>ſis deſcribuntur, ſupputare oportet. </s>
<s>quandoquidem omne <lb></lb>etiam quadrangulum à diagonio in duo triangula ſecatur, <lb></lb>quinquangulum verò in tria, ſexangulum in quatuor, &amp; ſic <lb></lb>deinceps diuiſiones fiant. </s>
<s>&amp; ſi area quidem quadranguli <lb></lb>1000 reperta fuerit, 500 trianguli area erit. </s>
<s>verùm quòd <arrow.to.target n="note249"></arrow.to.target><lb></lb>omne triangulum, quod tum intelligentia, tum ſenſu per<lb></lb>cipitur tres angulos duobus rectis æquales habet, hìc mani <lb></lb>feſtum eſt. </s>
<s>ſi enim omne quadrangulum quatuor rectis æ<lb></lb>quales ſuos angulos habet, à diagonio verò in duo diſtin<lb></lb>guitur triangula, atque in ſex angulos, alios quidem rectos, <lb></lb>alios verò ſecundum magis &amp; minus acutiores, <expan abbr="obtuſioreſ-q́ue">obtuſioreſ<lb></lb>que</expan> euadentes: hi autem ſex in omni quadrangulo quatuor <lb></lb>rectis æquales ſunt: vtrumque igitur duorum, quæ diſtin<lb></lb>guuntur triangulorum tres angulos duobus rectis æquales <lb></lb>habebit: vndè etiam omne, quod tum ſenſu, tum phanta<arrow.to.target n="note250"></arrow.to.target><lb></lb>ſia percipi poteſt. </s>
<s>De menſuratione verò earum, quæ Tra<lb></lb>peziæ, &amp; trapezoideæ vocantur tamquam ab angulorum <lb></lb>æqualitate ordinatarum: <expan abbr="cæterarumq́ue">cæterarumque</expan> cùm ordinatarum, <lb></lb>tum inordinatarum figurarum Archimedes, &amp; Heron in <arrow.to.target n="note251"></arrow.to.target><lb></lb>vniuerſali tractatione eruditioribus demonſtrarunt. </s>
<s>nos <lb></lb>autem eos, qui ad Mathematicas diſciplinas inſtituuntur <lb></lb>excitare volentes, metricas commentationes floribus col-
<pb xlink:href="052/01/117.jpg"></pb>lectis compoſuimus, anſas ſuppoſitionis propter prompti<lb></lb>tudinem præbentes, &amp; quod ſane iuxta prouerbium dici<lb></lb>tur, in latere <expan abbr="figulinã">figulinam</expan> <expan abbr="artẽ">artem</expan> ipſos addiſcere iam ſuppoſuimus. </s></p><p type="margin">
<s><margin.target id="note242"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note243"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note244"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note245"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note246"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note247"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note248"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note249"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note250"></margin.target>i</s></p><p type="margin">
<s><margin.target id="note251"></margin.target>k</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note252"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note252"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>QVamuis quadrangulum ſit nomen genericum omnes figu<lb></lb>ras angulis quatuor præditas in ſe continens, quadran<lb></lb>gulum tamen per excellentiam à Geometris vocatur <lb></lb>illa quadrilatera, quadrangula〈qué〉 figura, quæ æquilatera, necnon <lb></lb>rectangula eſt. </s>
<s>vt docet Proclus in 18 commentario libri ſecundi <lb></lb>in primum librum Elementorum Euclidis. </s>
<s>Autor autem in præ<lb></lb>ſentia nomen hoc neque pro genere omnium quadrangularum fi<lb></lb>gurarum, neque pro iam dicta ſpecie ſuſcepit, quæ per excellen<lb></lb>tiam quadrangulum dicitur: ſed pro quadrangulo rectangulo, <lb></lb>cuius duæ ſunt ſpecies, altera quidem iam dictum æquilaterum <lb></lb>&amp; rectangulum, quod à Græcis<emph.end type="italics"></emph.end> <foreign lang="grc">τετράγωνον</foreign>, <emph type="italics"></emph>hoc est quadrangu<lb></lb>lum per excellentiam, à latinis quadratum appellatur: altera ve<lb></lb>rò rectangulum &amp; non æquilaterum, quod alterapartelongius <lb></lb>nuncupatur. </s>
<s>in his enim duobus tantùm quadrangulis verum eſt <lb></lb>quod ait Autor, nempe quòd ex multiplicatione longitudinis in la<lb></lb>titudinem eorum area producitur. </s>
<s>in alijs autem quadrangulis, <lb></lb>quæ rectangula non ſunt, hoc verum eſſe minimè poteſt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note253"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note253"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Planus numerus (vt docet Euclides in 16 definitione libri ſe<lb></lb>ptimi Elementorum) eſt, qui ex duorum numerorum in ſe ſe in<lb></lb>uicem multiplicatione producitur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note254"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note254"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Area figuræ in Geometria (vt ipſemet Autor in præſentia <lb></lb>declarat) eſt ſpatium, quòd à lateribus ipſius figuræ circumqua<lb></lb>que terminatur, ſi figura plura habuerit latera: ſi verò ab vnica <lb></lb>linea fuerit comprehenſa, vt circulus, eius area ſpatium illud eſt, <lb></lb>quod à circumferentia continetur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note255"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note255"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[in æquilateris etiam quadrangulis] hoc eſt in quadratis.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note256"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note256"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quaſi ſimilem menſurationem habere dicit Rhombos, &amp; Rhom<lb></lb>boides quadrangulas figuras iam dictæ menſurationi quadrati, <lb></lb>&amp; alterapartelongioris: quoniam non per multiplicationem qui<lb></lb>dem eorum longitudinis in latitudinem quemadmodum iam di-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/118.jpg"></pb><emph type="italics"></emph>cta duo rectangula quadrangula <expan abbr="menſurãtur">menſurantur</expan>. </s>
<s>ſed Rhombus qui<lb></lb>dem per multiplicationem vnius ſuarum diagoniorum in dimi<lb></lb>dium alterius earundem diagoniorum (quæ quidem menſurandi <lb></lb>regula Rhombo, &amp; quadrato communis eſt) Rhomboides verò per <lb></lb>inuentionem areæ alterius duorum, in quibus à diagonio diuidi<lb></lb>tur triangulorum, eiuſdem〈qué〉 areæ duplicationem: vt apud Auto<lb></lb>res materiam hanc diligenter pertractantes videre licet. </s>
<s>quod <lb></lb>etiam Autor innuens in præſentia dixit [etenim latera termina<lb></lb>ta, vnam〈qué〉 diagonium datam habent] hoc eſt latera terminata, <lb></lb>ideo〈qué〉 nobis cognita: vnam〈qué〉 diagonium datam, ſcilicet ex late<lb></lb>ribus repertam habent. </s>
<s>Cum enim latera terminata ſint, ea men<lb></lb>ſurare poſſumus: ex ipſorum autem longitudine reperta, diago<lb></lb>niorum etiam longitudo data, ideſt cognita nobis erit. </s>
<s>Diagonius <lb></lb>autem dicitur illa recta linea, quæ in figuris angularibus ab vno <lb></lb>earum angulo ad alterum earum angulum ex oppoſito iacentem <lb></lb>ducta figuram per medium diuidit. </s>
<s>quæ etiam diameter, ſiue di<lb></lb>metiens communiter appellatur. </s>
<s>nam Dimetiens quidem commu<lb></lb>ni nomine dicitur omnis recta linea figuram aliquam ſiue <expan abbr="planā">planam</expan>, <lb></lb>ſiue ſolidam per medium diuidens: Diagonius verò propriè in an<lb></lb>gularibus figuris: quemadmodum etiam dimetiens quidem pro<lb></lb>priè in circulo, Axis vero in ſolidis figuris dicitur. </s>
<s>vt docet Pro<lb></lb>clus in 14 commentario ſecundi libri in primum Elementorum <lb></lb>Euclidis. </s>
<s>Non immerito autem dixit Autor, quaſi ſimilem eſſe <lb></lb>menſurationem Rhombi, ac Rhomboidis menſurationi quadrati, <lb></lb>&amp; alterapartelongioris: quoniam omnes iſtæ menſurationes per <lb></lb>multiplicationem fiunt, ſed diuerſimode. </s>
<s>nempe rectangulorum <lb></lb>quidem, per multiplicationem lateris longitudinis in latus latitu<lb></lb>dinis eorum: non rectangulorum verò, per multiplicationem dia<lb></lb>gonij vnius in dimidium alterius diagonij, vt in Rhombo: vel per <lb></lb>duplicationem vnius <expan abbr="eorũ">eorum</expan>, in quibus a diagonio diuiſum eſt trian<lb></lb>gulorum, vt in Rhomboide, quæ porrò duplicatio nil aliud quàm <lb></lb>multipticatio per binarium eſt. </s>
<s>Hanc autem menſurationum iſta<lb></lb>rum ſimilitudinem ait Autor ex ea prouenire ſimilitudine, quam <lb></lb>Rhombus cum quadrato, &amp; Romboides cum alterapartelongiore <lb></lb>habet quandoquidem Rhombus quidem ex quadrati, Rhomboides <lb></lb>verò ex alterapartelongioris distortione fiunt. </s>
<s>vt ipſe quoque <lb></lb>Proclus in ſuperiùs dicto 18 commentario declarauit. </s>
<s>Poteſt au-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/119.jpg"></pb><emph type="italics"></emph>tem Rhombus, ac Rhomboides quaſi ſimilem, ac cuidentem (vt <lb></lb>ait Autor) menſurationem habere, menſurationi ſcilicet qua<lb></lb>drati, &amp; altera parte longioris, hoc etiam modo. </s>
<s>quòd nempe ſu<lb></lb>per vno Rhombi, vel Rhomboidis latere, &amp; in eiſdem Parallelis <lb></lb>eorum lateribus, altero videlicet producto, alterapartelongius <lb></lb>conſtituatur, quod per 35 propoſitionem primi Elementorum Eu<lb></lb>clidis æquale ipſis erit. </s>
<s>huius enim alterapartelongioris area (vt <lb></lb>docet Autor) menſurata, Rhombi quoque, ſeu Rhomboidis eius <lb></lb>æqualis aream habebimus. </s>
<s>atque hæc etiam Rhombi, <expan abbr="Rhomboidiſ-q́ue">Rhomboidiſ<lb></lb>que</expan> menſuratio quadrati, &amp; altera parte longioris menſurationi <lb></lb>quaſi ſimilis, ac euidens erit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note257"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note257"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Animaduertendum autem eſt, quòd cùm dicit Autor <expan abbr="rhombũ">rhombum</expan> <lb></lb>quidem ex duobus æquicruribus, rhomboides uerò ex duobus acu<lb></lb>tangulis, vel obtuſangulis triangulis componi: non eſt hoc ita in<lb></lb>telligendum quòd non poßit etiam rhombus quidem ex duobus æ<lb></lb>quilateris, rhomboides verò ex duobus rectangulis componi trian<lb></lb>gulis quandoquidem quadratum quidem, &amp; alterapartelongius <arrow.to.target n="note258"></arrow.to.target><lb></lb>cùm rectangula ſint, ex duobus rectangulis triangulis alterum <lb></lb>quidem æquicruribus, alterum verò ſcalenis ſemper componun<lb></lb>tur, in quæ etiam diſſoluuntur: Rhombus verò ex duobus æquila<lb></lb>teris acutangulis, vel æquicruribus tum acutangulis, tum obtu<lb></lb>ſangulis, ſed numquam ex rectangulis, vel ſcalenis: Rhomboides <lb></lb>autem, ſemper ex ſcalenis tum acutangulis, tum obtuſangulis, <lb></lb>tum etiam rectangulis. </s>
<s>Quòd enim rhombus ex æquilateris etiam <lb></lb>triangulis componi poßit manifestum nobis erit, ſi in eadem recta <lb></lb>linea duo æquilatera triangula alterum quidem ſurſum, alterum <lb></lb>verò deorſum conſtituantur, quippe quæ dubio procul rhombum <lb></lb>efficient. </s>
<s>quòd autem rhomboides ex duobus etiam rectangulis <lb></lb>triangulis componatur perſpicuum nobis erit ſi dato ſcaleno re<lb></lb>ctangulo triangulo ab eius angulo recto recta linea parallela, &amp; <lb></lb>æqualis eius lateri rectum angulum ſubtendenti ad eas partes <lb></lb>ducatur, in quibus eſt angulus eius minimus, &amp; cum iam dicto la<lb></lb>tere per aliam rectam lineam coniungatur. </s>
<s>ſic enim ex duobus <lb></lb>rectangulis triangulis rhomboides componetur. </s>
<s>vt ijs, qui ali<lb></lb>quantulum in Geometria verſati ſunt, ignotum non eſt. </s>
<s>Verùm <arrow.to.target n="note259"></arrow.to.target><lb></lb>prætereundum etiam non eſſe exiſtimo quòd illud quod ait Autor, <lb></lb>quòd ſcilicet in præcedenti diagrammate rhomboides a b e f, ab<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/120.jpg"></pb><emph type="italics"></emph>ipſa fb diagonio in duo acutangula triangula diuiditur, omnino <lb></lb>falſum eſt. </s>
<s>ſi enim hoc verum eſſet, ſequeretur per penultimam <lb></lb>propoſitionem ſecundi libri Elementorum Euclidis quòd quadra<lb></lb>tum lateris af eſſet minus quadratis ipſarum ab &amp; bf ſimul <lb></lb>iunctis: ſimiliter〈qué〉 quadratum ipſius be minus eſſet quadratis <lb></lb>ipſarum ef, fb ſimul iunctis, quod falſum eſt. </s>
<s>quoniam qua<lb></lb>dratum quidem tum ipſius af, tum ipſius be, 6561: quadratum <lb></lb>autem ipſius ab, necnon ipſius fe, 225: quadratum verò ipſius <lb></lb>fb, 5328 vt patet per penultimam primi libri Elementorum Eu<lb></lb>clidis, ducta ſcilicet perpendiculari à ſigno f ad ipſam be. </s>
<s>quare <lb></lb>quadratum 6561 quadratis 5328, &amp; 225 ſimul iunctis, hoc eſt <lb></lb>ipſis 5553 minus eſſe non potest. </s>
<s>patet igitur falſitas eius quòd <lb></lb>dicit Autor. </s>
<s>fortaſſe autem hæc ab Autore in pręſentia non ita di<lb></lb>ligenter quemadmodum à Geometris conſiderata ſunt.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note260"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note258"></margin.target>Regula <lb></lb>generalis</s></p><p type="margin">
<s><margin.target id="note259"></margin.target><expan abbr="No&#039;ãdũ">Notandum</expan>.</s></p><p type="margin">
<s><margin.target id="note260"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Præterea verò adnotandum eſt quòd illud, quod ait Autor [at <lb></lb>ipſa triangulorum ſpatia à dimidio quadrangulorum, quæ ex ipſis <lb></lb>deſcribuntur, ſupputare oportet.] ſic intelligendum eſt. </s>
<s>quòd ſci<lb></lb>licet dato <expan abbr="quocumq;">quocumque</expan> triangule, cuius aream menſurare debemus, <lb></lb>quadrangulum ex ipſo deſcribendum eſt, hoc eſt ab vno eius angu<lb></lb>lorum vni eius laterum parallela &amp; æqualis recta linea producen<lb></lb>da est, parallelogramum〈qué〉 complendum: cuius area modis qui<lb></lb>bus ſuperiùs diximus reperienda, <expan abbr="eiusq́ue">eiusque</expan> dimidium quantitas <lb></lb>areæ trianguli propoſiti affirmanda eſt. </s>
<s>quoniam omne parallelo<lb></lb>grammum ſuper eadem baſi, &amp; in eiſdem parallelis cum triangu<lb></lb>lo exiſtens, duplum ipſius trianguli eſt, vt Euclides in 41 propoſi<lb></lb>tione primi Elementorum demonſtrauit. </s>
<s>&amp; hoc quidem est, quod <lb></lb>ait Autor, quod ſcilicet ipſa triangulorum ſpatia à dimidio qua<lb></lb>drangulorum, quæ ex ipſis deſcribuntur ſupputare oportet. </s>
<s>atque <lb></lb>hoc pacto triangulorum omnium areas facilè menſurare poſſu<lb></lb>mus. </s>
<s>quamuis etiam multis alijs pulcherrimis regulis menſurari <lb></lb>poßint, quas multi alij Autores diligentißimi tradidere.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note261"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note261"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[omne triangulum, quod tum intelligentia, tum ſenſu percipi<lb></lb>tur] De duplici triangulo ſermonem hic habet Autor, altero qui<lb></lb>dem, quod intelligentia percipitur, hoc eſt in phantaſia tamquam <lb></lb>in materia intelligibili mathematicis formis ſubiecta impreſſum <lb></lb>à cognitatione intelligitur: altero verò, quod ſenſu deprehenditur, <lb></lb>hoc eſt in aliqua ſenſibili materia cernitur. </s>
<s>de hoc auiem ſenſibili<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/121.jpg"></pb><emph type="italics"></emph>triangulo præſens de menſuratione tractatio, ſiue Geodæſia ipſa <lb></lb>pertractat. </s>
<s>quare paulò inferiùs per inductionem concludens Au<lb></lb>tor inquit [vndè etiam omne, quod tum phantaſia, tum ſenſu per<lb></lb>cipi poteſt] ſcilicet triangulum, tres angulos duobus rectis æqua<lb></lb>les habet.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note262"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note262"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quænam ſint Trapeziæ, &amp; Trapezoideæ figuræ, earum〈qué〉 ſpe<lb></lb>cies elegantißimè docet Proclus in commentario 18 ſecundi libri <lb></lb>in primum librum Elementorum Euclidis. </s>
<s>quas quidem ordina<lb></lb>tas eſſe dicit Autor ab angulorum æqualitate, quoniam quidam in <lb></lb>eis anguli ſibiinuicem æquales extant: ad differentiam aliarum <lb></lb>figurarum inordinatarum nullos angulos æquales habentium. </s>
<s><lb></lb>Harum autem omnium cùm ordinatarum, tum inordinatarum <lb></lb>figurarum nullam tradidit Autor menſurationem, duabus de cau<lb></lb>ſis. </s>
<s>primò quoniam (vt ait ipſe) Archimedes, &amp; Heron, ſcilicet <lb></lb>Alexandrinus eam eruditioribus demonſtrarunt in vniuerſali <lb></lb>tractatione. </s>
<s>hoc eſt in quadam tractatione, quæ non de menſura<lb></lb>tione linearum, ſuperficierum, &amp; corporum ſenſibilium ad rem mi <lb></lb>litarem ſpectante tractat: ſed in vniuerſum de <expan abbr="mẽſuratione">menſuratione</expan> linea<lb></lb>rum, ſuperficierum, &amp; corporum intelligibilium quatenus lineæ, <lb></lb>ſuperficies, &amp; corpora ſunt. </s>
<s>hæc autem Archimedis, &amp; Heronis <lb></lb>vniuerſalis de menſuratione tractatio deſideratur. </s>
<s>ſecundò quo<lb></lb>niam omnes Trapeziæ, &amp; Trapezoideæ, necnon cæteræ tum ordi<lb></lb>natæ, tum inordinatæ rectilineæ figuræ in triangula reſſolui, per <lb></lb>ipſa〈qué〉, (ſicut ipſe docuit) menſurari poſſunt. </s>
<s>cùm enim propoſitum <lb></lb>Autoris in hoc opere ſit menſurationem linearum ſuperficierum, <lb></lb>&amp; corporum ſenſibilium docere, quatenus rei militari neceſſaria <lb></lb>eſt: noluit amplam, ac perfectam menſurandi doctrinam (quem<lb></lb>admodum alij Autores fecerunt) tradere: ſed (vt ipſe ait) flo<lb></lb>ſculis collectis haſce metricas, hoc est aliquam menſurandi doctri<lb></lb>nam continentes commentationes compoſuit: anſas ſuppoſitionis, <lb></lb>ideſt ſubiectæ, de qua nunc agit, materiæ, præbens, ſcilicet ijs, qui <lb></lb>vt obſidionis gratia prompti ſint in capiendis menſurando ciuita<lb></lb>tum ſitibus ad mathematicas diſciplinas inſtituuntur. </s>
<s>ac demum <lb></lb>quodam antiquo pulcherrimo〈qué〉 prouerbio inquit ſe ſuppoſuiſſe ip<lb></lb>ſos in latere figulinam artem addiſcere, hoc eſt in rerum bellica<lb></lb>rum vſu menſurandi facultatem aquirere, eius instar, qui <expan abbr="figu-linã">figu<lb></lb>linam</expan> artem in latere conficiendo addiſcit. </s>
<s>cùm enim aliquam ſcien<emph.end type="italics"></emph.end><pb xlink:href="052/01/122.jpg"></pb><emph type="italics"></emph>tiam addiſcimus in eo humanæ vitæ vſu, cui vtilis, ac neceſſaria <lb></lb>eſt: tunc in latere figulinam artem addiſcere iuxta iam dictum <lb></lb>antiquum prouerbium dicimur. </s>
<s>Verùm ſi de quadrilaterorum <lb></lb>ſpatiorum menſuratione perfectam hìc doctrinam tradere velle<lb></lb>mus. </s>
<s>plura nobis eſſent dicenda: quoniam autem ab alijs autoribus <lb></lb>materia hæc diligentißimè pertracta fuit, &amp; præſertim à Sauaſ<lb></lb>ſorda hebreo doctißimo viro, in libro de dimenſionibus arearum: <lb></lb>&amp; ab Erſemide in libro de dimenſionibus, quos nos iam reſtaura<lb></lb>uimus, &amp; impreſſoribus excudendos annuente Deo tradituri ſu<lb></lb>mus: necnon à nobis in quodam noſtro de hac re opuſculo, quod <lb></lb>etiam ædituri ſumus: idcirco paucula hæc pro dilucidatione præ<lb></lb>ſentis propoſitionis breuiter à nobis adnotata ſufficiant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>SCHOLIVM ANTIQVVM<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>INCERTI AVTORIS IN PRAESENTEM<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>quintam propoſitionem à Franciſco Batocio è græco <lb></lb>in latinum ſermonem conuerſum.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note263"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note263"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>NAm ea, quæ ad menſurationem, ac figurationem à longe <lb></lb>incertæ magnitudinis ſuper terra iacent ſpatia, milita<lb></lb>rem ſcientiam cùm ad obſidionem, tum ad pugnæ reſiſten<lb></lb>tiam ordinatim inſtituere conſueuere. </s>
<s>etenim qui exercitui præ<lb></lb>eſt ad quadratorum, ſiue alterapartelongiorum ſpatiorum ma<lb></lb>gnitudines reſpiciens, quot milites iuxta pedeſtrem ordinem tum <lb></lb>velites, tum cetratos, vel tum haſtatos, tum iaculatores iuxta <arrow.to.target n="note264"></arrow.to.target><lb></lb>phalangarchiam ſuſcipient: necnon rhomboidum ad turmæ ordi<lb></lb>nes quot milites ſimul eorum, qui tamquam ad iugum ſecundum <lb></lb>longitudinem coniunguntur, quos græci<emph.end type="italics"></emph.end> <foreign lang="grc">ζυγοιώτας</foreign>, <emph type="italics"></emph>&amp; qui in ſe<lb></lb>rie ſecundum craßitiem collocantur, quos græci<emph.end type="italics"></emph.end> <foreign lang="grc">στοιχοιώτας</foreign> <emph type="italics"></emph><expan abbr="vo-cãt">vo<lb></lb>cant</expan>, ex impari numero: ſiue<emph.end type="italics"></emph.end> <foreign lang="grc">ζυγοιώτας</foreign> <emph type="italics"></emph><expan abbr="quidẽ">quidem</expan> &amp; <expan abbr="nõ">non</expan><emph.end type="italics"></emph.end> <foreign lang="grc">στοιχοιώτας</foreign>, <lb></lb><emph type="italics"></emph>velè contra, expari: &amp; quonam pacto à medio iugo lateralibus cu <arrow.to.target n="note265"></arrow.to.target><lb></lb>ſtodibus in duo diſſectis embola, ſiue ſphinoideas à tergo figuras <arrow.to.target n="note266"></arrow.to.target><lb></lb>nominatas iuxta turmarium, iuxta verò ductorem extrema par<lb></lb>tis, ſiue ſiniſtri cornu, vel caudæ exercitus<emph.end type="italics"></emph.end> <foreign lang="grc">οὐραγόν</foreign> <emph type="italics"></emph>à græcis di<lb></lb>ctum, retrorſum: &amp; quomodo oporteat phalangem ad locorum ſi<lb></lb>tus iuxta dextrum, ac ſiniſtrum cornu in decurias diſtinguere,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/123.jpg"></pb><emph type="italics"></emph>contrariæ progreßionis, ſeu alterius cornu hoſtium circumuentio<lb></lb>nis gratia. </s>
<s>&amp; quoniam iuxta craßitudinem agmen ſingulum octo <lb></lb>vel duodecim virorum propter bipertitam diuiſionem ſecundum <lb></lb>quoſdam ordinatur: plurium verò <expan abbr="quandoq;">quandoque</expan>, ac pauciorum iux<lb></lb>ta parem numerum, qui iuxta ipſam pedeſtrium, &amp; equeſtrium <arrow.to.target n="note267"></arrow.to.target><lb></lb>multitudinem ad unitatem vſque diuiditur. </s>
<s>ſit igitur agmen, to<lb></lb>ta verò phalanx ſedecim milium trecentorum octogintaquatuor. </s>
<s><lb></lb>quare 1024 ſunt qui à tergo phalangis deſignati existunt mani<lb></lb>pulares. </s>
<s>manifeſtum eſt autem quòd ordinati quidem, ſeu veró <lb></lb>gratia à cubitis quatuor diſtantes, 4096 iuxta confinium habe<lb></lb>bunt, cùm ſtadia <expan abbr="decẽ">decem</expan>, &amp; cubiti 96 ſint: contracti verò vt à duo<lb></lb>bus cubitis, ſtadia quinque, &amp; cubiti 48: ſecundùm autem cubi<lb></lb>tum vnum conglutinati, duo cum dimidio, &amp; cubiti vigintiqua<arrow.to.target n="note268"></arrow.to.target><lb></lb>tuor. </s>
<s>stadio quidem centum paſſuum, paſſu cubitorum quatuor, <lb></lb>&amp; cubito dodrantium duorum, digitorum autem <expan abbr="etiã">etiam</expan> vigintiqua<lb></lb>tuor exiſtente. </s>
<s>Hæc ſcientes exercituum ductores, ipſos verò lo<lb></lb>corum ſitus iuxta figuram, ac magnitudinem eligentes à longe: <lb></lb>ordinatè, ac ſine periculo itinera facient, tum in obſidionibus, tum <lb></lb>in reſiſtentijs contrarios deuincentes.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note264"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note265"></margin.target>c d</s></p><p type="margin">
<s><margin.target id="note266"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note267"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note268"></margin.target>g</s></p><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>SVperius antiquum incerti Autoris ſcholium in libri mar<lb></lb>gine ſcriptum inuenimus, fortaſſe autem ipſiuſmet Hero<lb></lb>nis eſt cùm propter phraſis ſimilitudinem, tum propter do<lb></lb>ctrinam in eo contentam. </s>
<s>multa enim hoc in ſcholio magna cum <lb></lb>breuitate, non parua〈qué〉 obſcuritate tanguntur, quæ ex ipſius ſcien<lb></lb>tiæ militaris viſceribus excerpta fuerunt: vt ijs perſpicuum eſt, <lb></lb>qui in ipſa militari doctrina diu verſati ſunt. </s>
<s>nos autem ne præ<lb></lb>ter inſtitutum in præſentia nimis prolixo ſermone vtamur, pau<lb></lb>cula quædam ad iam dicti ſcholij faciliorem intelligentiam breui<lb></lb>ter explicabimus. </s>
<s>ſunt autem hæc.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note269"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note269"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Nam ea, quæ ad menſurationem &amp;c.] Propoſitio hæc licet qua<lb></lb>dam verborum obſcuritate propoſita ſit, ſic tamen intelligenda <lb></lb>eſt. </s>
<s>quòd ſcilicet camporum, locorum, ſituum〈qué〉 ſpatia incertæ ma<lb></lb>gnitudinis, quæ ſuper terra circumcirca ciuitatem obſidendam<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/124.jpg"></pb><emph type="italics"></emph>iacent, ad menſurationem, ac figurationem à longe, ideſt apta na<lb></lb>ta vt à longe menſurentur, atque figurentur, nempe vt geometri<lb></lb>cis regulis, ac inſtrumentis menſurerentur quanta ſint, ad figu<lb></lb>ras〈qué〉 geometricas reducantur: hæc (inquam) menſuranda, fi<lb></lb>guranda〈qué〉 ſpatia militarem ſcientiam cùm ad obſidionem, tum ad <lb></lb>pugnæ reſiſtentiam ordinatim inſtituere conſueuere. </s>
<s>quoniam ſci<lb></lb>licet abſque iam dictorum ſpatiorum menſuratione, ac figuratio<lb></lb>ne militaris ſcientia neque obſidionem, neque pugnæ reſiſtentiam <lb></lb>ordinatim edocere poteſt. </s>
<s>talis eſt hæc propoſitio, quæ in toto præ<lb></lb>ſenti ſcholio rationibus confirmatur. </s>
<s>cùm oſtendatur quòd ſine <lb></lb>quadratorum, alterapartelongiorum, rhomborum, <expan abbr="atq;">atque</expan> rhomboi<lb></lb>dorum figuratione, ac menſuratione qui exercitui præeſt quanti<lb></lb>tatem diuerſorum cùm pedeſtrium tum equeſtrium militum, quæ <lb></lb>in iam dictis quadrangulis ſpatijs collocanda eſt, multa〈qué〉 alia hìc <lb></lb>breuiter enucleata militaris ſcientiæ neceſſaria ſcire minimè po<lb></lb>teſt. </s>
<s>Hæc eſt totius præſentis antiqui ſcholij ſententia, quod quàm <lb></lb>neceſſaria militari ſcientiæ ſuperior quinta propoſitio ſit, nobis <lb></lb>oſtendit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note270"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note270"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Phalangarchia eſt acies quadrata continens armatos milites <lb></lb>4096. ex quatuor autem phalangarchijs vna phalanx componi<lb></lb>tur continens armatos milites 16384.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note271"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note271"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[lateralibus cuſtodibus] hoc eſt eius phalangis, quæ plagia vo<lb></lb>catur, latera cuſtodientibus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note272"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note272"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Embolum eſt dimidium rhombi militibus pleni.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note273"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note273"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Sphinoides eſt rhomboides figura exercitus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note274"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note274"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſit igitur agmen, &amp;c.] in hac potißimùm ſcholij parte demon<lb></lb>ſtratur quàm neceſſaria ſit cognitio menſurationis, ac figurationis <lb></lb>quadratorum et, qui exercitus ordinaturus eſt. </s>
<s>Ponitur enim pha<lb></lb>lanx 16384 militum ex quatuor phalangarchijs conſtans, <expan abbr="quarũ">quarum</expan> <lb></lb>quodlibet latus 1024 milites continet. </s>
<s>ſi igitur quatuor cubitis à <lb></lb>ſeinuicem ipſi 1024 milites diſtiterint, dubio procul 4096 cubito<lb></lb>rum quoad longitudinem eorum confinium erit. </s>
<s>hoc est decem ſta<lb></lb>diorum, &amp; 96 cubitorum. </s>
<s>ſiquidem quodlibet ſtadium 400 cubi<lb></lb>tos in ſe continet. </s>
<s>ſi verò milites ipſi ita contrahantur vt duobus <lb></lb>cubitis abinuicem diſtent, stadia quinque &amp; cubiti 48 eorum con<lb></lb>finium erit. </s>
<s>ſi autem ſecundùm cubitum vnum conglutinentur, <lb></lb>ſtadia duo cum dimidio, &amp; cubitos 24 eorum confinium contine-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/125.jpg"></pb><emph type="italics"></emph>bit. </s>
<s>Confinium autem hìc pro longitudine totius lateris ipſius pha<lb></lb>langarchiæ ſuſcipitur. </s>
<s>vndè adnotandum eſt quòd numerus mi<lb></lb>litum phalangarchiæ numquam variat, quandoquidem ſemper <lb></lb>est 4096. &amp; hic eſt numerus <expan abbr="militũ">militum</expan> quatuor quadrati latera com<lb></lb>pletium. </s>
<s>numerus verò confinij quandoque idem eſt cum phalan<lb></lb>garchiæ numero, quandoque ab eo diſcrepat. </s>
<s>ſi enim quatuor cu<lb></lb>bitis milites inuicem diſtiterint, idem erit numerus confinij cum <lb></lb>phalangarchiæ numero: ſi verò duobus, vel vnico tantùm, aut <lb></lb>etiam pluribus quàm quatuor diſtiterint cubitis, tunc numerus <lb></lb>confinij à phalangarchiæ numero differt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note275"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note275"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[stadio quidem centum paſſuum &amp;c.] Quoniam hic geometri<lb></lb>carum menſurarum ſit mentio, adnotandum eſſe cenſeo, quòd di<lb></lb>gitus eſt omnium geometricarum menſurarum minima, <expan abbr="quẽ">quem</expan> qua<lb></lb>tuor grana hordei <expan abbr="ſecundã">ſecundam</expan> latitudinem contiguè poſita conficiunt. </s>
<s><lb></lb>vncia verò habet tres digitos: palmus, quatuor; dichas, duos pal<lb></lb>mos: ſpithame, ſiue dodrans, tres palmos: pes, quatuor palmos: <lb></lb>ſeſquipes, ſiue cubitus, ſexpalmos: gradus pedes duos. </s>
<s>paſſus, <expan abbr="aũt">aut</expan> <lb></lb>duplex eſt, alter ſimplex, alter Geometricus: ſimplex quidem ha<lb></lb>bet duos pedes cum dimidio, Geometricus verò dupliciter etiam <lb></lb>ab autoribus acceptus eſſe videtur: à gracis enim ſex pedes, à la<lb></lb>tinis verò quinque tantùm continere dicitur. </s>
<s>pertica duos habet <lb></lb>pedes. </s>
<s>ſtadium ſecundùm Græcos centum, ſecundùm latinos 125 <lb></lb>paßibus conſtat. </s>
<s>leuca 1500 paſſus continet. </s>
<s>milliarius italicus <lb></lb>1000 paſſus habet. </s>
<s>vnde iuxta Græcos quidem ſtadium decima, <lb></lb>iuxta Latinos autem octaua milliarii pars eſt. </s>
<s>Quibus ſic adnota<lb></lb>tis manifeſtum eſt quòd digiti duodecim dodrantem <expan abbr="vnũ">vnum</expan>, duo do<lb></lb>drantes vnum cubitum, quatuor cubiti ſecundùm Græcos, vel tres <lb></lb>&amp; pars tertia ſecundum Latinos, paſſum vnum: centum paſſus <lb></lb>ſecundùm Græcos, vel 125 ſecundum Latinos vnum ſtadium: octo <lb></lb>ſtadij ſecundùm Græcos, aut decem ſecundum Latinos vnum mil<lb></lb>liarium efficiunt. </s>
<s>Quare perſpicuum eſt iuxta Græcos quod in <lb></lb>ſcholio dicitur, nempe quòd ſtadium quidem 100 paſſuum exiſtit, <lb></lb>paſſus cubitorum quatuor, &amp; cubitus dodrantium duorum, vel <lb></lb>etiam 24 digitorum. </s>
<s>Hæc quoque pro dilucidatione præſentis an<lb></lb>tiqui ſcholij breuiter à nobis enucleata ſint.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/126.jpg"></pb><p type="main">
<s><emph type="center"></emph>Propoſitio Sexta.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note276"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note276"></margin.target>a</s></p><p type="main">
<s>CIrculi autem dimetientem, &amp; eum, qui ad ip<arrow.to.target n="note277"></arrow.to.target><lb></lb>ſam fit ambitum, ac totum ſpatium cum dio<lb></lb>ptra reperiemus in circuli centro ſtantes, cir<lb></lb>cumferentiæ non appropinquantes. </s>
<s>Sit igitur <arrow.to.target n="note278"></arrow.to.target><lb></lb>circuli centrum a, in quo dioptram ſtatuo, &amp; <lb></lb>cùm conſtituero tympanum, quod in ipſa eſt, ad ſitum pla<lb></lb>ni, ſuper quo is, qui ex dioptria circulus deſcribendus eſt: <lb></lb>ſuſcipio ſignum per foramina regulæ in directum ipſum b, <lb></lb>&amp; ab eodem ſigno circulariter tympanum vnà cum regula <arrow.to.target n="note279"></arrow.to.target><lb></lb>circumduco per incumbentem modio modiolum, aut per <arrow.to.target n="note280"></arrow.to.target><lb></lb>caulem in dioptra forſan exiſtente: donec rurſus in eodem <lb></lb>ſigno ſecundùm datum planum circumductio fiat, à quo <lb></lb>etiam moueri cęperat. </s>
<s>in hac autem circulari circumuolu<lb></lb>tione ſi<lb></lb><arrow.to.target n="fig1"></arrow.to.target><lb></lb>gna quę<lb></lb>dam <expan abbr="cir-culũ">cir<lb></lb>culum</expan> <expan abbr="cir-cumter-minãtia">cir<lb></lb>cumter<lb></lb>minantia</expan> <lb></lb>ad ſaxa, <lb></lb>vel arbu<lb></lb>ſta, vel <lb></lb><expan abbr="quoſdã">quoſdam</expan> <lb></lb>alios fa<lb></lb>cilè ex<lb></lb>plorabi<lb></lb>les ſco<lb></lb>pos aſpi<lb></lb>cientur. </s>
<s><lb></lb>qualia <lb></lb>ſunt bc <lb></lb>defgi <lb></lb>klmnx <lb></lb>op. </s>
<s><expan abbr="atq;">atque</expan> <lb></lb>hæc in ipſa circuli circumterminatione cùm annotauero,
<pb xlink:href="052/01/127.jpg"></pb>illud, quod ab a ſigno ad b ſignum, ſiue id, quod à centro <lb></lb>ad circumferentiam eſt interuallum metior, <expan abbr="quemadmodũ">quemadmodum</expan> <lb></lb>in longitudine, <expan abbr="latitudinemq́ue">latitudinemque</expan> didicimus. </s>
<s>&amp; cùm ipſum <arrow.to.target n="note281"></arrow.to.target><lb></lb>paſſuum fortaſſe 105 inuenero, totam etiam circuli dime<arrow.to.target n="note282"></arrow.to.target><lb></lb>tientem 210 habeo, tamquam eius, quæ ex centro, duplam. </s>
<s><lb></lb>quoniam autem omnis dimetientis triplusſeſquiſeptimus <lb></lb>eſt ipſe ambitus, manifeſtus eſt, 660 ipſe quoque exiſtens, <lb></lb>tamquam is, qui ipſum 210 numerum ter, eiuſque partem <arrow.to.target n="note283"></arrow.to.target><lb></lb>ſeptimam habet. </s>
<s>verùm quoniam rurſus quod ex dimetien<lb></lb>te &amp; quarta ambitus parte, æquum eſt areæ circuli, vt Ar<arrow.to.target n="note284"></arrow.to.target><lb></lb>chimedes in quit. </s>
<s>quòd omnis circulus æqualis eſt triangu<lb></lb>lo rectangulo, cuius quæ ex centro, æqualis eſt vni eorum, <lb></lb>quæ circa rectum angulum ſunt laterum, ambitus verò ba<arrow.to.target n="note285"></arrow.to.target><lb></lb>ſi: quod autem à dimetiente, <expan abbr="totoq́ue">totoque</expan> ambitu, quadruplum <lb></lb>circuli eſt. </s>
<s>ſi ita que ipſi dimetientis paſſus 210 ad ipſos 165 <lb></lb>quartæ partis ipſius ambitus multiplicentur, 34650 fient, <arrow.to.target n="note286"></arrow.to.target><lb></lb>quæ circuli area eſt. </s>
<s><expan abbr="nã">nam</expan> ſi 200 in 100 <expan abbr="multiplicẽtur">multiplicentur</expan>, 20000 <lb></lb>efficiunt: ſi verò in 60, 12000: &amp; in quinque, 1000: ac rur<lb></lb>ſus 10 in 100, 1000: in 60 verò, 600: necnon in quinque, <lb></lb>50. Quapropter reperta eſt quæ quidem ex centro circuli <arrow.to.target n="note287"></arrow.to.target><lb></lb>105: dimetiens autem, 210: &amp; ambitus 660: area verò, <lb></lb>ſiue totum ſpatium à dimetiente &amp; quarta ambitus parte <lb></lb>factum, paſſuum 34650. Faciliùs autem abſque etiam <lb></lb>dioptra circuli tum dimetientem, tum ambitum, tum etiam <lb></lb>ſpatium agnoſcemus à fune quodam iuxta longitudinem <arrow.to.target n="note288"></arrow.to.target><arrow.to.target n="note289"></arrow.to.target><lb></lb>dato. </s>
<s>Sit itaque datus funis <expan abbr="paſſuũ">paſſuum</expan> iuxta longitudinem 35, <lb></lb>aut quantùm quiſque propria ſponte deſiderat. </s>
<s>atque ad <lb></lb>vnum quidem extremum annulum ferreum cum clauo ha<lb></lb>beat, quippe qui clauus centri loco terræ affigatur, vt per <lb></lb>alterum extremum circularis <expan abbr="circũſcriptio">circunſcriptio</expan> ordinatim per<lb></lb>ficiatur: donec à quo cœperat ſigno in eodem rurſus funis <arrow.to.target n="note290"></arrow.to.target><lb></lb>extenſa circumducatur. </s>
<s>Quare ea, quæ in principio, &amp; à <arrow.to.target n="note291"></arrow.to.target><lb></lb>principio, &amp; ad principium triadicè in circuli circumſcri<lb></lb>ptione perſpicietur. </s>
<s>in principio quidem, ipſum centrum, <lb></lb>circa quod funis extremum ſuper clauo per annulum cir<arrow.to.target n="note292"></arrow.to.target><lb></lb>cumagitur: à principio verò, alterum funis <expan abbr="extremũ">extremum</expan>, quod <lb></lb>circa eam, quæ ad principium ſecundùm æqualem diſtan<pb xlink:href="052/01/128.jpg"></pb>tiam circulariter ad ipſa bcdefgh ſigna circumuertitur. <arrow.to.target n="note293"></arrow.to.target><lb></lb>Sic igitur circulo patefacto, reperietur quidem eius dime<lb></lb>tiens paſ<arrow.to.target n="fig2"></arrow.to.target><lb></lb>ſuum 70, <lb></lb><expan abbr="tãquam">tanquam</expan> <lb></lb>dupla e<lb></lb>ius, quæ <lb></lb>à centro: <lb></lb>ipſius <expan abbr="au-tẽ">au<lb></lb>tem</expan> dime<lb></lb>tientis tri<lb></lb>plus ſeſ<lb></lb>quiſepti<lb></lb>mus am<lb></lb>bitus, paſ <lb></lb><expan abbr="ſuũ">ſuum</expan> 220 <lb></lb>exiſtens: <lb></lb>necnon <lb></lb>quod à <lb></lb>dimetien<lb></lb>te &amp; quar<lb></lb>ta ambi<lb></lb>tus parte, 3850, quæ circuli area eſt. </s>
<s>nam 70 paſſus dime<lb></lb>tientis in ipſos 50 paſſus quartæ partis ipſius ambitus <lb></lb>multiplicati, 3500 faciunt: &amp; in ipſos quinque, 350. Quam<lb></lb>obrem à dato fune paſſuum 35 reperta eſt ipſa quidem cir<lb></lb>culi dimetiens paſſuum 70, 220 autem ambitus, &amp; 3850 <lb></lb>ſpatium, quod comprehenditur. </s></p><p type="margin">
<s><margin.target id="note277"></margin.target><emph type="italics"></emph>Propoſi<lb></lb>tio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note278"></margin.target><emph type="italics"></emph>Constru<lb></lb>ctio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note279"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note280"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note281"></margin.target><emph type="italics"></emph>Demon<lb></lb>ſtratio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note282"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note283"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note284"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note285"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note286"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note287"></margin.target><emph type="italics"></emph><expan abbr="Cõcluſio">Concluſio</expan>.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note288"></margin.target><emph type="italics"></emph>Aliter <lb></lb><expan abbr="eadẽ">eadem</expan> pro <lb></lb>poſitio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note289"></margin.target>i</s></p><p type="margin">
<s><margin.target id="note290"></margin.target>k</s></p><p type="margin">
<s><margin.target id="note291"></margin.target><emph type="italics"></emph>Pulchræ <lb></lb><expan abbr="cõſidera-tio">conſidera<lb></lb>tio</expan>.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note292"></margin.target><emph type="italics"></emph>[eam] ſ. </s>
<s><lb></lb>circumſe<lb></lb>rentiam.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note293"></margin.target><emph type="italics"></emph>Demon<lb></lb>ſtratio.<emph.end type="italics"></emph.end></s></p><figure id="id.052.01.128.1.jpg" xlink:href="052/01/128/1.jpg"></figure><figure id="id.052.01.128.2.jpg" xlink:href="052/01/128/2.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note294"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note294"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>AMbitus figuræ in Geometria eſt linea ex omnibus ipſius fi<lb></lb>guræ lateribus compoſita, ſi latera habuerit: ſi verò ab <lb></lb>vnico termino fuerit contenta veluti circulus, terminus <lb></lb>ille, ambitus vocatur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note295"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note295"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Modius qui gręcè<emph.end type="italics"></emph.end> <foreign lang="grc">τόρμος</foreign> <emph type="italics"></emph>dicitur, est illa pars rotæ, quæ eſt ſi-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/129.jpg"></pb><emph type="italics"></emph>milis vaſi, quod modius dicitur, in qua voluitur Axis. </s>
<s>Modiolus <lb></lb>verò (vt etiam in ſuperiori opere declarauimus) eſt paruus mo<lb></lb>dius ipſi modio ſuperimpoſitus, in quo radij rotæ affiguntur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note296"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note296"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[per caulem in dioptra forſan exiſtentem] regula, quæ in dio<lb></lb>ptra ſiue dioptrico inſtrumento circumuoluitur, duplici modo po<lb></lb>teſt in inſtrumento accommodari: aut ita vt per ſuperpoſitum mo<lb></lb>dio modiolum, aut ſic vt per caulem ſibi affixum circumuertatur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note297"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note297"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[eius, quæ ex centro] ideſt ſemidimetientis. </s>
<s>nam græci ſæpe <lb></lb>ſemidimetientem, lineam quæ ex centro vocant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note298"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note298"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[quod ex dimetiente, &amp; quarta ambitus parte] ſcilicet fit pa<lb></lb>rallelogrammum rectangulum ſpatium.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note299"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note299"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Archimedes demonſtrat ea, quæ hìc dicit Autor, in libro de <lb></lb>circuli dimenſione, in quo doctrinam hanc diligentißimè tradidit. </s>
<s><lb></lb>quàm etiam à Sauaſſorda, &amp; Erſemeide locupletißimè pertracta<lb></lb>tam habemus. </s>
<s>verùm adnotandum eſt, quòd non eſt ambitus cir<lb></lb>culi ad dimetientem triplusſeſquiſeptimus (vt ait Autor) ſed mi<lb></lb>nor quam triplusſeſquiſeptimus, &amp; maior quàm triplusſuper<lb></lb>deciespartiensſeptuageſimasprimas, vt Archimedes in tertia <lb></lb>propoſitione iam dicti libri de circuli dimenſione demonſtrauit. </s>
<s><lb></lb>quoniam autem hæc paruißima differentia quaſi inſenſibilem er<lb></lb>rorem in dimenſionibus efficere potest, idcirco viri hac in ſcientia <lb></lb>peritißimi ambitum circuli triplamſeſquiſeptimam rationem ad <lb></lb>dimetientem habere ſuppoſuerunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note300"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note300"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[quod autem à dimetiente, toto〈qué〉 ambitu] ſcilicet fit paralle<lb></lb>logrammum rectangulum ſpatium.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note301"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note301"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[nam ſi 200 in 100 multiplicentur, &amp;c.] Multiplicationem nu<lb></lb>meri 210 per numerum 165, quæ à recentioribus Arithmeticis <lb></lb>practicis hoc modo fit:<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Multiplicatio ſecundum recentiores Arithmeticos<emph.end type="center"></emph.end></s></p><p type="table">
<s>TABELLE WAR HIER</s></p>
<pb xlink:href="052/01/130.jpg"></pb><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>alio vetuſtiori quodam pacto facit Autor, ſic.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Multiplicatio ſecundum Autorem.<emph.end type="center"></emph.end></s></p><p type="table">
<s>TABELLE WAR HIER</s></p><p type="main">
<s><emph type="italics"></emph>[dato] ſcilicet nobis cognito.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note302"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note302"></margin.target>k</s></p><p type="main">
<s><emph type="italics"></emph>[Quare ea, quæ in principio, &amp; à principio, &amp; ad principium] <lb></lb>ſubintelligitur exornatio [triadicè in circuli <expan abbr="circũſcriptione">circumſcriptione</expan> per<lb></lb>ſpicietur.] hoc eſt in circumſcribendo circulo illa trina, ſiue tria<lb></lb>dica <expan abbr="rerũ">rerum</expan> omnium exornatio, quam Platonici græcè<emph.end type="italics"></emph.end> <foreign lang="grc">διακόσμησιν</foreign><lb></lb><emph type="italics"></emph>vocant, ea ſcilicet, quæ in principio, à principio, &amp; ad principium <lb></lb>eſt, triadicè perſpicietur. </s>
<s>nempe centro, lineis ex centro, &amp; cir<lb></lb>cumferentia, ſiue ambitu. </s>
<s>nam <expan abbr="centrũ">centrum</expan> quidem eſſentiam in prin<lb></lb>cipio exiſtentem, linea ex centro eſſentiam à principio promanan<lb></lb>tem, circumferentia〈qué〉 eſſentiam ad principium reuertentem ex<lb></lb>primunt. </s>
<s>quippe quæ tria oſtendunt nobis triadicam in vnico cir<lb></lb>culo rerum omnium exornationem, necnon Dei Optimi Maximi <lb></lb>triadicam in vnum eſſentiam: ad cuius <expan abbr="vtiq;">vtique</expan> ſimilitudinem men<lb></lb>tem etiam noſtra triadicam, ac vnam ipſe creauit. </s>
<s><expan abbr="quemadmodũ">quemadmodum</expan> <lb></lb>enim in Deo ſic <expan abbr="etiã">etiam</expan> in mente noſtra tria hæc <expan abbr="vnũ">vnum</expan> ſunt, intelligens, <lb></lb>intellectio, &amp; res intellecta. </s>
<s>idcirco mens etiam noſtra immorta<lb></lb>lis, trina, &amp; vna ad ſui opificis æterni, trini, &amp; vni imaginem, ac <lb></lb>ſimilitudinem creata fuit. </s>
<s>Hanc itaque Trinitatis, ac vnitatis <lb></lb>ſimul altißimam, vix〈qué〉 perceptibilem, ac explicabilem materiam <lb></lb>Autor in circuli deſcriptione tetigit: quam profecto ſi ad plenum <lb></lb>declarare nunc vellemus, ab inſtituto noſtro longè aberraremus. </s>
<s><lb></lb>idcirco eos, qui hanc pulcherrimam conſiderationem perfectè gu<lb></lb>ſtare cupiunt, ad Platonem ipſum, &amp; Proclum eius expoſitorem,<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/131.jpg"></pb><emph type="italics"></emph>cæteros〈qué〉 Platonicos, necnon ad eundem Proclum in 13 commen<lb></lb>tario ſecundi libri in primum librum Elementorum Euclidis re<lb></lb>mittimus. </s>
<s>Hæc autem pro dilucidatione huiuſce propoſitionis di<lb></lb>cta ſint.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Septima.<emph.end type="center"></emph.end></s></p><p type="main">
<s>SOlidæ verò figuræ non quemadmodum iam <lb></lb>dictæ planæ iuxta duas tantummodo, ſed ne<lb></lb>ceſſariò iuxta tres dimenſiones conſiderabun<lb></lb>tur. </s>
<s>quandoquidem omne corpus triplici di<lb></lb>menſione diſtat longitudinem habens, &amp; lati<lb></lb>tudinem, <expan abbr="atq;">atque</expan> craſſitudinem, idem autem ac ſi dicamus pro<lb></lb>funditatem, aut altitudinem. </s>
<s>nam eum, qui ex longitudi<lb></lb>ne, ac latitudine fit planum numerum, in tertiam altitudi<lb></lb>nis dimenſionem multiplicantes, ſolidas figuras ſupputare <lb></lb>nos oportet. </s>
<s>Ac primùm quidem in cubica figura menſu<lb></lb>ratio fiat. </s>
<s>Cubus enim eſt figura ſolida à ſex quadrangu<lb></lb>lis æqualibus comprehenſa, quę in latera <expan abbr="quidẽ">quidem</expan> duodecim, <arrow.to.target n="note303"></arrow.to.target><lb></lb>angulos autem rectos octo, &amp; plana ſex in tribus dimenſio<arrow.to.target n="note304"></arrow.to.target><lb></lb>nibus ſecundùm æqualitatem conſideratur. </s>
<s>vndè <expan abbr="etiã">etiam</expan> har<lb></lb>monicas in conſonantia, <expan abbr="diuinasq́ue">diuinasque</expan> rationes in huiuſcemo<lb></lb>di figura Pythagorei oſtendunt, harmoniam ipſum cubum <lb></lb>nominantes. </s>
<s>verùm ipſa figuræ ſoliditas ita reperietur. </s>
<s>Si <lb></lb>enim baſis cubi 28 vnitatum iuxta longitudinem fuerit, ea<lb></lb>rundem iuxta latitudinem <arrow.to.target n="fig3"></arrow.to.target><lb></lb>etiam erit, necnon iuxta al<lb></lb>titudinem ſimiliter. </s>
<s>ipſas au<lb></lb>tem longitudinis 28 in eaſ<lb></lb>dem latitudinis multiplican<lb></lb>tes, ipſum baſis planum vni<lb></lb>tatum 784 habebimus: <expan abbr="atq;">atque</expan> <lb></lb>hoc rurſus in ipſas altitudi<lb></lb>nis 28 multiplicantes, colli<lb></lb>gimus vnitates 21952, quas <lb></lb>vtique cubi ſoliditatem eſſe <arrow.to.target n="note305"></arrow.to.target><lb></lb>pronuntiabimus. </s>
<s>Si autem in eodem cubo <expan abbr="cylindrũ">cylindrum</expan> ęquè<pb xlink:href="052/01/132.jpg"></pb><arrow.to.target n="note306"></arrow.to.target><lb></lb>altum excogitauerimus inſcribi, qui etiam ſphæram in me<lb></lb>dio circumambiat, ita vt ſphæra ſecundum maximum ip<lb></lb>ſius ſphæræ circulum cylindri ſuperficiem tangat: oſten de<lb></lb>tur cubi baſis ad cylindri baſem rationem habere eam, <expan abbr="quã">quam</expan> <arrow.to.target n="note307"></arrow.to.target><lb></lb>in minimis, <expan abbr="primisq́ue">primisque</expan> numeris ipſe 14 numerus ad ipſum <lb></lb>11 numerum habet. </s>
<s>Similiter autem ipſa quoque ſex cubi <lb></lb>plana ad cylindri ſuperficiem vnà cum duabus baſibus ſe ſe <lb></lb>habebunt: necnon quatuor, ſine baſibus: &amp; ſolidum ad <expan abbr="ſo-lidũ">ſo<lb></lb>lidum</expan> ſe habebit. </s>
<s>at ipſa cylindri ſuperficies ſine baſibus qui<lb></lb>dem æqualis eſt ſuperficiei ſphæræ, quæ ab ipſo circumam<lb></lb>bitur: vnà verò cum baſibus, ſeſquialter ipſius ſphæræ cy<lb></lb>lindrus tum iuxta ſuperficiem, tum iuxta ſoliditatem inue<lb></lb>nietur. </s>
<s>Verùm ipſa cylindri baſis agnoſcetur ex dimetien<lb></lb>te, &amp; quarta ambitus parte, quemadmodum ſuperiùs iam <lb></lb>dictum fuit. </s>
<s>cùm enim ipſa dimetiens 28 data ſit, 88 am<lb></lb>bitus erit, triplusſeſquiſeptimus exiſtens. </s>
<s>atque pars eius <lb></lb>quarta 22. ipſæ igitur 28 ſi in ipſas 22 vnitates multiplicen<lb></lb>tur, aream baſis 616 faciunt. </s>
<s>eſt autem baſis etiam cubi 784. <lb></lb>baſis ergo cubi ad baſim cylindri ſic ſe habet, quemadmo<lb></lb>dum in minimis, <expan abbr="primisq́ue">primisque</expan> (vti iam diximus) numeris ipſe <lb></lb>14 ad ipſum 11. nam ipſe 784 numerus ipſum 616 nume<arrow.to.target n="note308"></arrow.to.target><lb></lb>rum, <expan abbr="eiusq́ue">eiusque</expan> partem quartam 154, necnon partem quadra<lb></lb>geſimamquartam, quæ eſt 14, habet. </s>
<s>Hoc itaque pacto ipſæ <lb></lb>etiam quatuor ſuperficies, quæ ab ipſius cubi baſi ſurrexe<lb></lb>runt ad cylindricam ſuperficiem ſe ſe habebunt: ac rurſus <lb></lb>ſex cubi plana ad cylindri ſuperficiem, <expan abbr="baſiumq́ue">baſiumque</expan> plana: <lb></lb>necnon ſolidum ad ſolidum. </s>
<s>nam ſi ipſa cubicæ baſis qua<lb></lb>tuor latera in ipſas 28 altitudinis vnitates multiplicentur, <lb></lb>3136 fiunt: necnon ſi ipſæ 88 vnitates ambitus cylindricæ <lb></lb>baſis in eaſdem 28 altitudinis, 2464 efficiunt, in <expan abbr="eademq́ue">eademque</expan> <lb></lb>ratione ſunt. </s>
<s>eodem modo ſex <expan abbr="quoq;">quoque</expan> plana cubi, quæ 4704 <lb></lb>fiunt, ad ipſam cylindri ſuperficiem vnà cum baſibus in in<lb></lb>ferna, <expan abbr="ſupernaq́ue">ſupernaque</expan> ſede exiſtentibus, earum 3696, quæ col<lb></lb>liguntur, vnitatum. </s>
<s>ſimiliter autem ipſa etiam cubi ſolidi<lb></lb>tas, quæ ab ipſius baſis plano ipſarum 784 vnitatum, in ip<lb></lb>ſas altitudinis 28 vnitates multiplicato, 21952 reperitur, ad <lb></lb>cylindri ſoliditatem, quæ ab ipſis 616 ipſius baſis vnitati-<pb xlink:href="052/01/133.jpg"></pb>bus in eaſdem 28 altitudinis vnitates multiplicatis, 17248 <lb></lb>fit. </s>
<s>ita vt in eadem ratione vndequaque cubus circa eum, <lb></lb>qui in ipſo inſcribitur æquè altum cylindrum perſpiciatur. </s>
<s><lb></lb>Verùmenimuero quòd cylindrus ſeſquialter ſit ſphæræ, <lb></lb>quæ in ipſo inſcribitur, ſic oſtendemus. </s>
<s>cùm enim cylindri <lb></lb>ſuperficies vnà cum baſium planis 3696 exiſtat, 17248 ve<lb></lb>rò ſoliditas: oſtendetur etiam ſphæræ ſuperficies, quæ ex <lb></lb>ipſis 88 ipſius ambitus maximi circuli in ipſa exiſtentis, &amp; <lb></lb>ex ipſis 28 ipſius Axis altitudinis vnitatibus fit, 2464: ſoli<lb></lb>ditas autem ipſius ſphæræ, quæ ab area maximi circuli ip<lb></lb>ſarum 616 in duas tertias ipſius Axis, ſiue in 18 2/3 multi<lb></lb>plicata fit, 11498 2/3. atque ſuperficies ad ſuperficiem, &amp; ſo<lb></lb>lidum ad ſolidum (vt iam dictum eſt) in ratione ſeſquialte<lb></lb>ra ſunt. </s>
<s>quare ſphæra duæ tertiæ partes circumambientis ip<lb></lb>ſam æquè alti cylindri reperta eſt. </s>
<s>Omnis autem ſphærica <lb></lb>ſuperficies areæ quidem ſui maximi circuli quadrupla eſt. </s>
<s><lb></lb>ipſius verò circuli ambitum tot vicibus continet, quot <expan abbr="etiã">etiam</expan> <lb></lb>axis in ipſa exiſtens iuxta longitudinem vnitates in ſe com<lb></lb>prehendit. </s>
<s>nam ipſæ 2464 numerus quadruplus quidem <lb></lb>eſt ipſius 616: vigincuplus octuplus verò ipſius 88. Eſt au<lb></lb>tem omnis etiam ſphæra quadrupla coni baſim quidem ha<lb></lb>bentis maximum ſpheræ circulum, altitudinem verò ęqua<lb></lb>lem ei, quæ ex centro ſphæræ. </s>
<s>etenim conicæ baſis ambitus <lb></lb>88 exiſtens, ſi in axis dimidium, vt à centro ad altitudinem, <lb></lb>14, multiplicetur, 1232 efficiunt. </s>
<s>necnon ipſæ areæ baſis <arrow.to.target n="note309"></arrow.to.target><lb></lb>616 vnitates, in eaſdem 14 axis dimidiæ partis, 8624. </s>
<s>Quám<lb></lb>obrem hemiſphærium cùm iuxta ſuperficiem, tum iuxta ſo<lb></lb>liditatem duobus conis æquale repertum eſt: ſphaera verò, <arrow.to.target n="note310"></arrow.to.target><lb></lb>quatuor. </s>
<s>Conus autem eſt figura ſolida à circulari baſi ad <lb></lb>vnum ſublime ſignum contracta. </s>
<s>ſecundùm verò <expan abbr="Euclidẽ">Euclidem</expan>: <lb></lb>cùm altero rectanguli trianguli latere eorum, quæ circa re<lb></lb>ctum ſunt angulum quieſcente circumuolutum <expan abbr="triãgulum">triangulum</expan> <lb></lb>in eundem rurſus locum reſtitutum fuerit, vndè moueri cę<lb></lb>perat, circumſcripta figura conus vocatur. </s>
<s><expan abbr="atq;">atque</expan> ſi quieſcens <lb></lb>recta linea æqualis ſit reliquæ, quæ circumrectum angulum <lb></lb>conuertitur, rectangulus erit conis: ſin minor obtuſangu-<pb xlink:href="052/01/134.jpg"></pb>lus: ſi uerò maior, acutangulus. </s>
<s>axis <expan abbr="autẽ">autem</expan> coni eſt quieſcens <lb></lb>illa recta linea, circumquam triangulum uertitur: baſis ue<arrow.to.target n="note311"></arrow.to.target><lb></lb>rò, circulus, qui à circumducta linea recta deſcribitur. </s>
<s>Re<lb></lb>peritur autem omnis etiam cylindrus triplus coni eandem <lb></lb>cum ipſo baſim, &amp; æqualem <expan abbr="altitudinẽ">altitudinem</expan> habentis. </s>
<s>cùm enim <lb></lb>cylindri ſuperficies 2464 ſit, ſoliditas uero 17248: ipſa <expan abbr="au-tẽ">au<lb></lb>tem</expan> coni ſuperficies ex eodem 88 unitatum ambitu, &amp; tertia <lb></lb><expan abbr="unitatũ">unitatum</expan> 9 1/3 axis parte, 821 1/3 ſit, ex ipſis uerò 616 areæ <lb></lb>baſis unitatibus in eandem tertiam axis partem multiplica<lb></lb>tis 5749 1/3 ſoliditas reperiatur, in triplaque ratione adin<lb></lb>uicem ſint: tertia pars igitur æquè alti cylindri conus de<arrow.to.target n="note312"></arrow.to.target><lb></lb>monſtratus eſt. </s>
<s>Quinetiam priſma <expan abbr="parallelepipedũ">parallelepipedum</expan> exiſtens <lb></lb>pyramidis eandem cum ipſo baſem, &amp; æqualem <expan abbr="altitudinẽ">altitudinem</expan> <arrow.to.target n="note313"></arrow.to.target><lb></lb>habentis triplum inuenitur. </s>
<s>Atque centrum grauitatis cy<lb></lb>lindri eſt in bipertita ſectione ipſius axis. </s>
<s>ſimiliter autem in <lb></lb>priſmate <expan abbr="ẽt">etiam</expan> erit. </s>
<s>ipſum uerò <expan abbr="conicentrũ">conicentrum</expan> grauitatis eſt in axe <lb></lb>ita diuiſo, ut ſegmentum uerſus <expan abbr="uerticẽ">uerticem</expan> exiſtens reliqui tri<lb></lb>plum ſit. </s>
<s>eadem igitur ipſius axis diuiſo in pyramide quo<lb></lb>que fiat. </s>
<s>Pyramis autem eſt figura ſolida, quæ planis conti<lb></lb>netur ab ipſius baſis plano ad vnum ſignum collecta: aut à <lb></lb>baſi triangula, vel quadrangula, vel multangula ad vnum <lb></lb>ſublime ſignum contracta. </s>
<s>Priſma verò eſt figura ſolida, <lb></lb>quæ planis comprehenditur, quorum duo nempe ex ad<lb></lb>uerſo iacentia cùm æqualia, tum ſimilia, tum etiam paral<lb></lb>lela ſunt: reliqua verò parallelogramma. </s></p>
<pb xlink:href="052/01/135.jpg"></pb><p type="margin">
<s><margin.target id="note303"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note304"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note305"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note306"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note307"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note308"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note309"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note310"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note311"></margin.target>i</s></p><p type="margin">
<s><margin.target id="note312"></margin.target>k</s></p><p type="margin">
<s><margin.target id="note313"></margin.target>l</s></p><figure id="id.052.01.135.1.jpg" xlink:href="052/01/135/1.jpg"></figure><p type="caption">
<s>Cylindrus in cubo in<lb></lb>ſcriptus ſphæram am<lb></lb>biens conum in hemi<lb></lb>ſphærio habentem. </s>
<s>&amp; <lb></lb>conus in eadem cum <lb></lb>cylindro baſi, &amp; alti<lb></lb>tudine tacens.</s></p><figure id="id.052.01.135.2.jpg" xlink:href="052/01/135/2.jpg"></figure><p type="caption">
<s>Nota quòd in infe<lb></lb>riori diagramma<lb></lb>te .m. </s>
<s>quidem mul<lb></lb>tiplicationem, .p. </s>
<s><lb></lb>verò partitionem <lb></lb>ſignificat.</s></p><p type="main">
<s><emph type="center"></emph>Diagramma cunctas, de quibus Autor in hac propoſitione loquitur cor<lb></lb>porum, <expan abbr="eorumq́ue">eorumque</expan> partium quantitates oſtendens.<emph.end type="center"></emph.end></s></p><p type="table">
<s>TABELLE WAR HIER</s></p><p type="table">
<s>TABELLE WAR HIER</s></p><p type="table">
<s>TABELLE WAR HIER</s></p><p type="table">
<s>TABELLE WAR HIER</s></p>
<pb xlink:href="052/01/136.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note314"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note314"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[angulos autem rectos octo] Quemadmodum angulus planus <lb></lb>triplex eſt, rectus ſcilicet, acutus, ac obtuſus: ita etiam angu<lb></lb>lus ſolidus (cùm ex planis conſtituatur angulis) triplex erit, <lb></lb>nempe rectus, qui ex rectis: acutus, qui ex acutis: obtuſus, qui <lb></lb>ex obtuſis planis angulis conſtat. </s>
<s>quamobrem angulos rectos octo <lb></lb>in præſentia ſolidos, non <expan abbr="autẽ">autem</expan> planos eſſe intelligere debemus. </s>
<s>quan<lb></lb>doquidem 24 rectos angulos planos quilibet cubus habet.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note315"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note315"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quonam pacto diuinas rationes in cubo iuxta rectitudinem, <lb></lb>æqualitatem, ac trinam dimenſionem Pythagorei oſtendant, lon<lb></lb>gum eſſet in præſentia declarare: quomodo verò harmonicas in <lb></lb>conſonantia exiſtentes rationes, in cubo indicent, cùm ipſum <lb></lb>harmoniam nuncupent, paucis explicabo. </s>
<s>Cùm itaque cubus late<lb></lb>ribus duodecim, angulis octo, planis〈qué〉 ſex conſtet, dubio procul om<lb></lb>nes quinque præcipuæ conſonantiarum harmonicæ rationes in hi<lb></lb>ſce tribus numeris. </s>
<s>6.8.12. reperiuntur. </s>
<s>nam 8 quidem ad 6 ſeſ<lb></lb>quitertiam habet rationem, in qua Diateſſaron conſonantia eſt: <lb></lb>12 verò ad 8 ſeſquialteram, in qua Diapente: 12 autem ad 6 du<lb></lb>plam, in qua Diapaſſon: 12 rurſus ad exceſſum, quo duo denarius <lb></lb>octonarium ſuperat, nempe ad 4, triplam, in qua Diapaſſon cum <lb></lb>diapente: S demum ad exceſſum, quo ſenarium octonarius exce<lb></lb>dit, ſcilicet ad 2, quadruplam, in qua Biſdiapaſſon. </s>
<s>Quapropter <lb></lb>cùm harmonicæ conſonantiarum rationes in cubo ſint, non imme<lb></lb>rito Pythagorei harmoniam ipſum nominarunt. </s>
<s>Hæc autem obiter <lb></lb>à nobis dicta sint, quoniam non ſunt præſentis contemplationis.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note316"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note316"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Cylindrus, ſphæra, &amp; conus, ac cætera ſolida, <expan abbr="eorumq́ue">eorumque</expan> par<lb></lb>tes ab Euclide in definitionibus vndecimi libri Elementorum dili<lb></lb>gentißimè definiuntur. </s>
<s>quorum ſanè corporum aream, ſeu capaci<lb></lb>tatem Autor ſolidum, ſiue ſoliditatem appellat.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note317"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note317"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[æquè altum] hoc eſt cuius altitudo ſit æqualis altitudini cubi.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note318"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note318"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[in minimis, primis〈qué〉 numeris &amp;c.] Dupliciter numeri pri<lb></lb>mi dicuntur, aut per ſe, aut adinuicem conſiderati. </s>
<s>&amp; qui nam <lb></lb>ſint numeri primi per ſe conſiderati docet Euclides in undecima <lb></lb>definitione ſeptimi libri Elementorum: qui verò ſint primi adin-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/137.jpg"></pb><emph type="italics"></emph>uicem, in duodecima definitione eiuſdem. </s>
<s>hìc autem non de pri<lb></lb>mis per ſe, ſed de primis adinuicem conſideratis Autor loquitur. </s>
<s><lb></lb>quippe qui etiam minimi ſemper ſunt omnium eandem cum eis <lb></lb>rationem habentium, ut idem Euclides in 23 propoſitione eiuſdem <lb></lb>ſeptimi demonſtrat. </s>
<s>Quomodo autem datis quotcumque numeris <lb></lb>minini omnium eandem cum eis rationem habentium reperian<lb></lb>tur demonſtrat Euclides in 35 propoſitione libri eiuſdem.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note319"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note319"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Adnotandum quòd melius eſt dicere, quòd 784 ad 616 ha<lb></lb>bet rationem ſupertripartientem vndecimas, ſiue ſupertriunde<lb></lb>cimas ſicut 14 ad 11: quàm dicere quòd continet cum, ac eius par <lb></lb>tem quartam, &amp; quadrageſimam quartam. </s><s>nam quemadmo<lb></lb>dum 14 continet 11 &amp; eius (3/11), ſic <expan abbr="ẽt">etiam</expan> 784 continet 616 &amp; eius <lb></lb>(3/11): quæ ſunt 168, exceſſus videlicet, quo ipſe 784 ipſum 616 ſu<lb></lb>perat. </s>
<s>ter enim 56, 168: &amp; undecies 56, 616 faciunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Præterea notandum quòd illud, quod ait Autor [quamobrem <arrow.to.target n="note320"></arrow.to.target><lb></lb>hemiſphærium cùm iuxta ſuperficiem, tum iuxta ſoliditatem <lb></lb>duobus conis æquale repertum eſt: ſphæra verò, quatuor.] falſum <lb></lb>eſt in ea parte [cùm iuxta ſuperficiem] quandoquidem ſuperfi<lb></lb>cies hemiſphærij, quæ eſt 1232, non eſt (ut ait Autor) æqualis <lb></lb>duplo ſuperficiei coni in hemiſphærio inſcripti, quod eſt 821 1/3, ſed <lb></lb>ſeſquialtera ipſius eſt. </s>
<s>quamobrem nec etiam tota ſphærica ſuper<lb></lb>ficies, quæ eſt 2464 ad totam iam dicti in hemiſphærio conſtituti co<lb></lb>ni ſuperficiem 410 2/3 exiſt entem quadrupla (quemadmodum ait <lb></lb>Autor) ſed reuera ſexcupla quidem erit. </s>
<s>Cùm enim cylindri ſu<lb></lb>perficies, quæ ſuperficiei ſphæræ in ipſo inſcriptæ æqualis oſtenſa <lb></lb>eſt, tripla ſuperficiei coni eandem cum ipſo baſim, &amp; æqualem alti<lb></lb>tudinem <expan abbr="habẽtis">habentis</expan> demonſtrata ſit, qui conus duplus eſt per 14 pro<lb></lb>poſitionem duodecimi elementorum coni in hemiſphærio inſcripti: <lb></lb>nemini dubium quòd ſphæræ ſuperficies ad inſcripti in hemiſphæ<lb></lb>rio coni ſuperficiem ſexculpam rationem habebit. </s>
<s>non eſt igitur <lb></lb>uerum quod ait Autor, quòd ſcilicet hemiſpærium iuxta ſuperfi<lb></lb>ciem duobus, ſphæra uerò quatuor conis <expan abbr="eorũ">eorum</expan>, qui in hemiſphærio <lb></lb>inſcribuntur, ęqualis reperta ſit, ſed iuxta ſoliditatem dumtaxat <lb></lb>hoc verum. </s>
<s>Soliditas et enim ſphæræ, quæ eſt 11498 2/3 ſoliditatis <lb></lb>iam dicti coni in hemiſphærio constituti, quæ eſt 2874 2/3, qua-<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/138.jpg"></pb><emph type="italics"></emph>drupla dubio procul existit. </s>
<s>aut ergo textus corruptè legitur, aut <lb></lb>bonus dormitauit Homerus.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note321"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note320"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note321"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Hìc dupliciter conum Autor definit, primò definitioue forma<lb></lb>li, deinde Euclidis definitione, quæ ab efficienti cauſa deſumitur. </s>
<s><lb></lb>Apollonius autem Pergæus aliter, &amp; exquiſitiùs conum, eius〈qué〉 <lb></lb>partes, ac ſpecies definiuit in definitionibus primi libri conicorum, <lb></lb>vt nos alibi ſatis ſuper〈qué〉 declarauimus.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note322"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note322"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Reperitur autem &amp;c.] hanc propoſitionem demonſtrauit Eu<lb></lb>clides in decimo theoremate duodecimi libri Elementorum.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note323"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note323"></margin.target>k</s></p><p type="main">
<s><emph type="italics"></emph>Quinetiam Priſma &amp;c.] hæc propoſitio eſt corollarium ſepti<lb></lb>mæ propoſitionis iam dicti duodecimi, quod demonſtrauit Campa<lb></lb>nus in ſuis additionibus ſuper octauam propoſitionem eiuſdem li<lb></lb>bri. </s>
<s>verùm quid nam ſit Priſma, atque pyramis in fine propoſitio<lb></lb>nis declarat Autor iuxta <expan abbr="doctrinã">doctrinam</expan> duodecimæ, &amp; tertiædecimæ <lb></lb>definitionis vndecimi <expan abbr="Elementorũ">Elementorum</expan> Euclidis. </s>
<s><expan abbr="Parallelepipedũ">Parallelepipedum</expan> <expan abbr="aũt">aut</expan> <lb></lb>eſt figura ſolida parallelis planis <expan abbr="cõtenta">contenta</expan>, quæ priſmatis ſpecies eſt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note324"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note324"></margin.target><emph type="italics"></emph>l<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Centrum grauitatis duplex eſt, alterum planorum, alte<lb></lb>rum ſolidorum. </s>
<s>quidnam ſit autem centrum grauitatis plano<lb></lb>rum patet ex Archimedis libro de centris grauitatis plano<lb></lb>rum, in quo de iam dictis centris exactißimam doctrinam tradi<lb></lb>dit. </s>
<s>quid ſit verò centrum grauitatis ſolidorum elegantißimè de<lb></lb>clarauit Federicus Commandinus Mathematicarum eruditißi<lb></lb>mus in prima definitione ſui opuſculi de centro grauitatis ſolido<lb></lb>rum, in quo doctrinam hanc hactenus in tenebris latentem doctiſ<lb></lb>ſimè dilucidauit. </s>
<s>hæc autem, quæ hìc ab Autore de centris gra<lb></lb>uitatis cylindri, priſmatis, coni, &amp; pyramidis dicuntur ipſe Com<lb></lb>mandinus in octaua, &amp; vigeſimaſecunda propoſitionibus iam di<lb></lb>cti ſui opuſculi diligentißimè demonſtrauit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Verumtamen animaduerſione dignum eſt, quòd poſtquam ex <lb></lb>cubi lateribus ſuperficies, &amp; aream ſolidam eius inuenire docuit: <lb></lb>comparans eum cum alijs corporibus, <expan abbr="eorũ">eorum</expan> <expan abbr="ẽt">et</expan> ſuperficies, ac ſolidi<lb></lb>tates reperire docet. </s>
<s>vndè ſeptem pulcherrimas Geometricas pro<lb></lb>poſitiones, ac vnum corollarium proponit, eas〈qué〉 demonſtrationi<lb></lb>bus Arithmeticis demonſtrat. </s>
<s>ſunt autem hæ, quæ ordinatim ſe<lb></lb>quuntur, quemadmodum etiam ab Autore proponuntur.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/139.jpg"></pb><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Propoſitio prima.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Omnis cubi baſis ad cylindri in ipſo inſcripti baſim, &amp; ſex eiuſ<lb></lb>dem cubi plana ad eiuſdem cylindri ſuperficiem vnà cum dua<lb></lb>bus cylindri baſibus, necnon quatuor cubi plana ad eandem cylin<lb></lb>dri ſuperficiem ſine duabus cylindri baſibus, ac demum cubi ſoli<lb></lb>ditas ad cylindri ſoliditatem rationem eam, quam numerus 14 ad <lb></lb>11 numerum habent.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Secunda.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Omnis cylindri ſuperficies ſine baſibus ſuperficiei ſphæræ in ip<lb></lb>ſo inſcriptæ æqualis eſt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Tertia.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Omnis cylindrus ſphæræ in ipſo inſcriptæ <expan abbr="tũ">tum</expan> iuxta ſuperficiem <lb></lb>vnà cum baſibus, tum iuxta ſoliditatem ſeſquialter eſt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Vnde conſtat quòd omnis ſphæra tum iuxta ſuperficiem, tum <lb></lb>iuxta ſoliditatem duætertiæ partes est circumambientis ipſam <lb></lb>æquè alti cylindri.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Quarta.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Omnis ſphærica ſuperficies areæ quidem ſui maximi circuli <lb></lb>quadrupla eſt: iam dicti verò circuli ambitum tot vicibus conti<lb></lb>net, quot in eius axe iuxta longitudinem vnitates ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Quinta.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Omnis ſphæra iuxta ſoliditatem eſt quadrupla coni baſim qui<lb></lb>dem habentis maximum ipſius ſphæræ circulum, altitudinem verò <lb></lb>æqualem dimidio axis eiuſdem ſphæræ: dupla autem coni baſim <lb></lb>quidem habentis maximum ipſius ſphæræ circulum, altitudinem <lb></lb>verò totum eiuſdem ſphæræ axem.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Sexta.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Omnis cylindrus triplus eſt coni eandem <expan abbr="cũ">cum</expan> ipſo baſim, &amp; æqua<lb></lb>lem altitudinem habentis tum iuxta ſuperficiem ſine baſibus, tum <lb></lb>iuxta ſoliditatem.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>Septima.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Omne priſma parallelepipedum pyramidis eandem cum ipſo ba<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/140.jpg"></pb><emph type="italics"></emph>ſem, &amp; æqualem altitudinem habentis triplum exiſtit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quarum quidem propoſitionum geometricę demonſtrationes <lb></lb>partim apud Euclidem iam dictis in locis, partim apud Archi<lb></lb>medem in ſuis de ſphæra, &amp; cylindro libris habentur. </s>
<s>Arithmè<lb></lb>ticæ verò earundem demonſtrationes ab Autore breuiter enarra<lb></lb>tæ, in figura, ac diagrammate in fine præſentis ſeptimæ propoſi<lb></lb>tionis à nobis appoſitis à quouis explicari facilè poſſunt. </s>
<s><expan abbr="Hęc">Haec</expan> <expan abbr="etiã">etiam</expan> <lb></lb>pro dilucidatione propoſitionis huiuſce dicenda nobis erant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Octaua.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note325"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note325"></margin.target><emph type="italics"></emph>Propoſi<lb></lb>tio.<emph.end type="italics"></emph.end></s></p><p type="main">
<s>OPus itaque ſit in parallelogrammo, &amp; altera <lb></lb>parte longiori ædificio, vel humoris recepta<arrow.to.target n="note326"></arrow.to.target><lb></lb>culo ſimilis figuræ, vt in Aetia ciſterna ſolidi<lb></lb>tatis menſurationem manifeſtare: faciliùs au<lb></lb>tem in piſcina propter dimenſionum circa ba<lb></lb>ſim exiſtentium æqualitatem lateritia figura ipſa exiſtente. </s>
<s><lb></lb>Later autem eſt figura ſolida à ſex planis <expan abbr="cõtenta">contenta</expan> æqualem <lb></lb>baſis longitudinem, ac latitudinem habens, minorem verò <lb></lb>altitudinem. </s>
<s>ſi enim æqualis iuxta altitudinem etiam exi<lb></lb>ſteret, cubus quidem eſſet: ſi autem maior, trabs figurare<lb></lb>tur. </s>
<s>Trabs enim eſt, quæ altitudinem longitudine baſis ac <arrow.to.target n="note327"></arrow.to.target><lb></lb>latitudine <expan abbr="maiorẽ">maiorem</expan> habet. </s>
<s>Supponatur igitur baſis ipſius pi<lb></lb>ſcinæ, ſeu ciſternæ iuxta longitudinem paſſuum 70, latitu<lb></lb>dinem ſimiliter eandem habens, &amp; altitudinem <expan abbr="paſſuũ">paſſuum</expan> 12. <arrow.to.target n="note328"></arrow.to.target><lb></lb>Quæro igitur inuenire quot paſſuum eſt ciſternæ ſoliditas, <lb></lb>&amp; quot amphoras humoris capere poteſt. </s>
<s>Multiplicans ip<arrow.to.target n="note329"></arrow.to.target><lb></lb>ſos 70 longitudinis in eoſdem latitudinis paſſus, habeo pla<lb></lb>num iuxta baſim exiſtens paſſuum 4900. </s><s>hos itaque rurſus <lb></lb>in ipſos altitudinis, 12 paſſus multiplico, <expan abbr="fiuntq́ue">fiuntque</expan> 58800. <arrow.to.target n="note330"></arrow.to.target><lb></lb>At quoniam ea, quæ longitudine quaprupla ſunt, potentia <lb></lb>ſexdecupla exiſtunt, ſoliditate verò ſexagincuplaquadru<arrow.to.target n="note331"></arrow.to.target><lb></lb>pla: paſſus autem eſt digitorum 96, cubitus verò 24: qua<lb></lb>druplus ergo paſſus ipſius cubiti iuxta longitudinem eſt: <lb></lb>&amp; baſis longitudo cubitorum 280 exiſtit. </s>
<s>ex his autem in<lb></lb>uenietur <expan abbr="planũ">planum</expan> 78400. etenim 16 in 4900 faciunt 78400. <lb></lb>ex his autem rurſus ſoliditas fit 3763200. ita enim 64 in
<pb xlink:href="052/01/141.jpg"></pb><arrow.to.target n="note332"></arrow.to.target><lb></lb>58800 faciunt. </s><s>At quoniam rurſum ea, quæ longitudine <lb></lb>ſexcupla ſunt, potentia trigincuplaſexcupla oſtenduntur, <lb></lb>ſoliditate verò ducentuplaſexdecupla erunt. </s><s>eſt enim pes <lb></lb>16 quoad longitudinem digitorum ſexta paſſus pars exi<lb></lb>ſtens. </s>
<s>vndè rurſus longitudo iuxta baſim iacens, <expan abbr="pedũ">pedum</expan> 420 <lb></lb>fit: planum vero, 176400: <expan abbr="totaq́">totaque</expan>; ſoliditas <expan abbr="pedũ">pedum</expan> 12700800. <lb></lb><expan abbr="nã">nam</expan> 36 in 4900 faciunt 176400, &amp; 216 in 58800, 12700800. <lb></lb>Et quoniam ſolidus pes, qui ſecundum Mechanicorum <arrow.to.target n="note333"></arrow.to.target><lb></lb><expan abbr="conſtitutionẽ">conſtitutionem</expan> ab ipſis 16 longitudinis digitis cubatur, 4096 <arrow.to.target n="note334"></arrow.to.target><lb></lb>reperitur. </s>
<s>ipſi autem 16 digiti per ſe ſe quatuor aquæ vn<lb></lb>cias ferè ſuſcipiunt, digiti verò 51 1/5 ipſam duodecim vn<arrow.to.target n="note335"></arrow.to.target><lb></lb>ciarum italicarum libram continebunt: ipſi autem 256 ip<lb></lb>ſius plani digiti, libras quinque: necnon ipſius ſoliditatis di<lb></lb>giti 4096, libras 80. Reperitur itaque ſolidus pes humoris <arrow.to.target n="note336"></arrow.to.target><lb></lb>capax quoad menſuram amphoræ librarum italicarum 80. <arrow.to.target n="note337"></arrow.to.target><lb></lb>Quamobrem quot pedum ſolidorum ipſum humoris rece<lb></lb>ptaculum computatum eſt, tot etiam amphorarum humo<lb></lb>ris eſt capax. </s>
<s>Similiter autem ad quamlibet <expan abbr="etiã">etiam</expan> profundi<lb></lb>tatis partem ſignum adnotantes, aquæ molem connumera<lb></lb>bimus. </s>
<s>Cylindri verò figura <expan abbr="exiſtẽte">exiſtente</expan>, circuli aream (vt iam <lb></lb>diximus) accipere oportet: &amp; eos, qui iuxta ipſam baſim re<lb></lb>periuntur pedes in altitudinem multiplicare: eum autem, <lb></lb>qui fit numerum, in ipſo quidem humoris receptaculo, de <lb></lb>ipſa aquæ mole pronuntiare: in ſimilis autem figuræ ædifi<lb></lb>cio ſine ſuperimpoſito tecto triticum, &amp; hordeum, &amp; legu<lb></lb>mina, ac demum quotcumque ex diſretæ quantitatis for<arrow.to.target n="note338"></arrow.to.target><lb></lb>mis iuxta medimnos, &amp; modios, ac ſemodios, <expan abbr="ſimplicioreſ-q́ue">ſimplicioreſ<lb></lb>que</expan> menſuras conſiderantur, ad pondus, &amp; magnitudinem <lb></lb>ex eo, qui conſtruitur ſolido pede, reſpicientes ſupputare. </s></p>
<pb xlink:href="052/01/142.jpg"></pb><p type="margin">
<s><margin.target id="note326"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note327"></margin.target><emph type="italics"></emph>Expoſi<lb></lb>tio et <expan abbr="cõ-ſtructio">con<lb></lb>ſtructio</expan>.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note328"></margin.target><emph type="italics"></emph>Determi<lb></lb>natio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note329"></margin.target><emph type="italics"></emph>Demon<lb></lb>ſtratio.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note330"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note331"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note332"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note333"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note334"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note335"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note336"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note337"></margin.target><emph type="italics"></emph><expan abbr="Cõcluſio">Concluſio</expan>.<emph.end type="italics"></emph.end></s></p><p type="margin">
<s><margin.target id="note338"></margin.target>k.i</s></p><p type="caption">
<s>Ciſterna ſeu piſcina lateris figuram habens.<lb></lb><arrow.to.target n="fig4"></arrow.to.target></s></p><figure id="id.052.01.142.1.jpg" xlink:href="052/01/142/1.jpg"></figure><p type="table">
<s>TABELLE WAR HIER</s></p>
<pb xlink:href="052/01/143.jpg"></pb><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note339"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note339"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Aetia] hoc eſt Aegyptiaca, iuxta formam ſcilicet Aegy<lb></lb>ptiacarum ciſternarum fabricata. </s>
<s>nam Aetia dicta est Aegyptus <lb></lb>à quodam Indo Aeto, vt Stefanus adnotauit. </s>
<s>Melior autem lectio <lb></lb>eſt Y etia, hoc eſt pluuioſa.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note340"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note340"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ea, quæ longitudine quadrupla &amp;c.] ipſæ ſcilicet rectæ lineæ, <lb></lb>quæ longitudine <expan abbr="quadruplã">quadruplam </expan>inter ſe rationem habent: potentia, <lb></lb>videlicet iuxta earum quadrata, ſexdecuplam rationem ſeruant: <lb></lb>ſoliditate verò, nempe iuxta ſolida ex ipſis producta, ſexdecuplam <lb></lb>rationem ſortitæ ſunt. </s>
<s>Hæc autem regula vera, &amp; vniuerſalis <lb></lb>eſt, <expan abbr="demonſtrariq́ue">demonſtrarique</expan> geometricè poteſt per quintam definitionem <lb></lb>ſexti, &amp; ſecundam partem vigeſimæ propoſitionis eiuſdem, &amp; de<lb></lb>cimam definitionem quinti Elementorum Euclidis.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note341"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note341"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[paſſus autem eſt digitorum 96 &amp;c.] paſſum hìc non ſimpli<lb></lb>cem, ſed geometricum intelligere debemus, quem ſex pedes iuxta <lb></lb>græcorum ſententiam continere ſuperiùs diximus. </s>
<s>cùm autem <lb></lb>pes quidem quatuor palmis, palmus verò quatuor digitis conſtet: <lb></lb>nemo eſt, qui non fateatur iam dictum paſſum 96 digitis comple<lb></lb>ri. </s>
<s>Similiter etiam cubitus cùm ſex palmos contineat, dubio pro<lb></lb>cul 24 digitis conſtat. </s>
<s>vndè etiam paſſus ipſe cubiti iuxta longi<lb></lb>tudinem quadruplus eſt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note342"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note342"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ea, quæ longitudine ſexcupla ſunt &amp;c.] Hæc etiam regula <lb></lb>vera &amp; vniuerſalis eſt, iam dictis〈qué〉 geometricis rationibus demon <lb></lb>ſtrari poteſt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note343"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note343"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[cubare] græcè<emph.end type="italics"></emph.end> <foreign lang="grc">κυβίζειν</foreign>, <emph type="italics"></emph>verbum hoc licet apud latinos alias <lb></lb>habeat ſignificationes, tamen apud Mathematicos nil aliud ſigni<lb></lb>ficat, niſi numerum cubum ex aliquo numero producere, vel figu<lb></lb>ram cubicam ex aliqua recta linea deſignare. </s>
<s>Adnotandum au<lb></lb>tem eſt quòd omnes menſuræ geometricæ tripliciter conſiderari <lb></lb>poſſunt, vel quatenus linearum longitudinem, vel quatenus ſu<lb></lb>perficierum aream, vel quatenus corporum ſoliditatem <expan abbr="menſurãt">menſurant</expan>. </s>
<s><lb></lb>Quapropter cuiuſcumque generis menſura geometrica tum li<lb></lb>nearis vel recta, vel circularis, vel ex hiſce miſta: tum ſuperfi<lb></lb>cialis vel plana, vel ſphærica, vel miſta: tum etiam ſolida vel hu<lb></lb>ius, vel illius formæ iuxta corporum diuerſitatem appellari poteſt.<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/144.jpg"></pb><emph type="italics"></emph>atque talis eſt ſolidus pes, de quo Autor in præſentia loquitur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note344"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note344"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[quatuor aquæ vncias ferè] vnciam hìc non pro geometrica <lb></lb>illa menſura ſuſcipienda eſt, quam tribus conſtare digitis ſupe<lb></lb>riùs diximus: ſed pro duodecima ipſius aßis, ſiue libræ parte. </s>
<s>quo<lb></lb>niam autem quælibet humoris libra 51 1/5 digitis conſtat, non im<lb></lb>merito quatuor ferè vncias aquæ (ſicut ait Autor) ipſi 16 digiti <lb></lb>habent. </s>
<s>cùm enim quatuor vnciæ ſint tertia libræ pars, libra ve<lb></lb>rò 51 1/5 digitis conſtet, dubio procul digiti 17 &amp; tertia pars vnius <lb></lb>quintæ digiti partis vncias quatuor <expan abbr="continẽt">continent</expan>. </s>
<s>quare 16 digiti fe<lb></lb>rè quatuor vncias habent, vt Autor inquit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[italicarum] cùm italorum libræ à libris græcorum iuxta quan<arrow.to.target n="note345"></arrow.to.target><lb></lb>titatem diſcrepent, non immerito vnciæ quoque diuerſæ ſunt. </s>
<s>quo<lb></lb>niam autem italica libra eſt digitorum 51 1/5, idcirco vnciarum, <lb></lb>ac librarum italicarum Autor dixit.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note346"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note345"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note346"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Amphora eſt Autore Budeo menſura congios quidem octo, ſex<lb></lb>tarios verò 48 continens. </s>
<s>ſextarius enim eſt ſexta congij pars. </s>
<s>hìc <lb></lb>autem Amphoram Autor pro vaſe fictili libras 80 italicas humo<lb></lb>ris, ſiue pedem vnum ſolidum recipiente ſuſcipere videtur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note347"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note347"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Medimnus est menſura <expan abbr="capiẽs">capiens</expan> quinos modios ſecundùm ſicu<lb></lb>lam menſuram, vel ſenos ſecundùm Atticam, aut Romanam teſte <lb></lb>Budeo libro quinto de Aſſe.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note348"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note348"></margin.target>k</s></p><p type="main">
<s><emph type="italics"></emph>Simpliciores menſuras hìc intelligere debemus modij partes ſe <lb></lb>modio minores, ex quibus modius componitur, &amp; in quas reſſolui<lb></lb>tur. </s>
<s>Hæc autem pro præſentis etiam propoſitionis intelligentia <lb></lb>breuiter à nobis dicta ſufficiant. </s>
<s>nam ex figura, &amp; diagramma<lb></lb>te, quod in eius calce appoſuimus, clara ſunt ea, quæ ab Autore <lb></lb>demonſtrationibus Arithmeticis oſtenduntur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Nona.<emph.end type="center"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note349"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note349"></margin.target>a</s></p><p type="main">
<s>COgnoſcemus autem fontis quoque defluxum <lb></lb>ſecundum Heronem, quantuſcumque ſit. </s>
<s>ve<lb></lb>rùm ſcire quidem oportet quòd non ſemper <lb></lb>eadem ſcaturigo permanet. </s>
<s><expan abbr="nã">nam</expan> imbribus qui<lb></lb>dem exiſtentibus intenditur, eò quod in api<lb></lb>cibus montium aqua ſuperabundans, violentiùs eliditur:
<pb xlink:href="052/01/145.jpg"></pb>ſiccitatibus autem exiſtentibus deficit. </s>
<s>At fontes illi, qui <lb></lb>ſuapte natura ſcaturiendi vim habent, non multam ſcaturi<lb></lb>ginem ſortitæ ſunt. </s>
<s>Operæpretium eſt igitur totam fontis <lb></lb>aquam circumambientes, vt nuſquam defluat: tubum <expan abbr="plumbeũ">plum<lb></lb>beum</expan> quadrangulum facere, qui defluxu iuxta receptionem <lb></lb>multò maior exiſtat. </s>
<s><expan abbr="ipſumq́ue">ipſumque</expan> vni loco ſic adaptare, vt per <lb></lb>ipſum fontis aqua defluat. </s>
<s>Opus eſt autem tubum ipſum <lb></lb>ad depreſſiorem fontis locum iacere, vt facilem defluxum <lb></lb>habeat. </s>
<s>ipſum autem depreſſiorem locum per dioptram <lb></lb>agnoſcemus. </s>
<s>ipſa verò defluens aqua, in bucula tubi iuxta <arrow.to.target n="note350"></arrow.to.target><lb></lb>altitudinem manifeſta fiet. </s>
<s>Sit itaque iuxta altitudinem di<lb></lb>gitorum trium, habeat autem &amp; latitudinem ipſa bucula di<lb></lb>gitorum ſex. </s>
<s>at digiti tres in ſex digitos multiplicati, 18 fa<lb></lb>ciunt. </s>
<s>ipſam ergo fontis ſcaturiginem 18 <expan abbr="digitorũ">digitorum</expan> eſſe pro<lb></lb>nuntiabimus. </s>
<s>Verùmenimuero ſciendum eſt, quòd non ſuf<lb></lb>ficit ad agnoſcendum quantam fons exhibet aquam, ipſius <lb></lb>defluxus molem inuenire: ſed ipſa quoque velocitas repe<lb></lb>rienda eſt. </s>
<s>nam velociori defluxu quidem exiſtente, plus <lb></lb>aquæ præbetur: tardiori verò, minus. </s>
<s>Quare ſub fontis de<lb></lb>fluxum foſſam effodientes obſeruare oportet ex ſolari ho<lb></lb>rologio, quanta per vnamquamque horam aqua in foſſa <lb></lb>defluit: &amp; ſic aquam, quæ per totam diem exhibetur, con<lb></lb>ſiderare quanta iuxta molem ſit. </s>
<s>Quamobrem non ſolùm <lb></lb>defluxus molem, verùmetiam velocitatem obſeruare ne<lb></lb>ceſſum eſt. </s>
<s>nam per horarium tempus diurnam etiam aquæ <lb></lb>contributionem explo<arrow.to.target n="fig5"></arrow.to.target><lb></lb>ratam habebimus, ſi <lb></lb>enim omne <foreign lang="grc">νυχθήμερον</foreign><arrow.to.target n="note351"></arrow.to.target><lb></lb>hoc eſt diei ſimul &amp; no<lb></lb>ctis ſpatium æquino<arrow.to.target n="note352"></arrow.to.target><lb></lb>ctialium <expan abbr="tẽporũ">temporum</expan> 360, <lb></lb>horarum verò 24 eſt: <lb></lb>quęlibet hora quinde<lb></lb>cim æquinoctialia tem <lb></lb>pora continebit: plu<lb></lb>ra verò quandoque, <expan abbr="paucioraq́ue">paucioraque</expan> ſuppeditatio ipſa. </s>
<s>quo<lb></lb>niam hyeme quidem exiſtente maior defluxus fit, æſtate
<pb xlink:href="052/01/146.jpg"></pb>verò, minor. </s>
<s>Si igitur in qualibet hora aquam in foſſa de<arrow.to.target n="note353"></arrow.to.target><lb></lb>fluentem 20 fortaſſe cadorum eſſe perceperimus, quadri<lb></lb>gentorum ergo &amp; octoginta fontis exhibitionem per diem, <lb></lb><expan abbr="noctemq́ue">noctemque</expan> pronuntiabimus. </s></p><p type="margin">
<s><margin.target id="note350"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note351"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note352"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note353"></margin.target>e</s></p><figure id="id.052.01.146.1.jpg" xlink:href="052/01/146/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end><lb></lb><arrow.to.target n="note354"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note354"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>QViſnam fuerit Heron, cuius hìc, &amp; multis alijs in locis <lb></lb>Autor noſter mentionem facit, in ſuperioribus ſatis ſu<lb></lb>per〈qué〉 diximus. </s>
<s>fontium autem defluxum menſurare do<lb></lb>cuit ille Alexandrinus Heron in libris quatuor, quos de aquati<lb></lb>cis horologijs ſcripſit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note355"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note355"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſit it aque] ſcilicet ipſa aqua, quæ in tubo eſt dum fluit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note356"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note356"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Dies hìc intelligendus eſt artificialis, videlicet ab ortu ſolis ad <lb></lb>occaſum vſque.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note357"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note357"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Aequinoctialia tempora vocat Autor ipſas 360 particulas <lb></lb>æquinoctialis circuli cæleſtis, quas Aſtrologi latini gradus ap<lb></lb>pellant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note358"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note358"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Cadus eſt vinarium vas congios decem, vel (vt <expan abbr="quidã">quidam</expan> volunt) <lb></lb>duodecim continens. </s>
<s>Hæc paucula pro huiuſce dilucidæ per ſe pro<lb></lb>poſitionis faciliori perceptione dicta ſint.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph>Propoſitio Decima, &amp; vltima.<emph.end type="center"></emph.end></s></p><p type="main">
<s>QVandoquidem igitur promiſſos ſuperiùs dio<lb></lb>ptricos vſus enarrauimus, propter commo<lb></lb>dum huiuſcemodi dioptræ vſum ad <expan abbr="cœleſtiũ">cœleſtium</expan> <lb></lb>etiam contemplationem eleuari poterimus: <lb></lb>cùm ſolis, tum lunę magnitudinem ipſa diſcer<lb></lb>nentes: necnon ſtellarum abinuicem diſtantias tum <expan abbr="fixarũ">fixarum</expan> <lb></lb>ad fixas ac errantes, tum errantium ad errantes &amp; fixas per<lb></lb>ſpicere. </s>
<s>nam ex ea, quæ in tympano facta eſt ipſorum 360 <lb></lb>graduum, &amp; iacentium inter ipſos minutorum deſcriptio</s></p><p type="main">
<s><arrow.to.target n="note359"></arrow.to.target><lb></lb>ne: magnitudines, quæ quæruntur ſimul aſpicere valebi<lb></lb>mus. </s>
<s>Quùm itaque diſtantiam inter duas ſtellas exiſtentem <lb></lb>obſeruare voluerimus, quot partium exiſtat: tympani par<pb xlink:href="052/01/147.jpg"></pb>tem verſus nos iacentem inclinabimus, ad altum alteram <lb></lb>attollentes, donec vtique per idem planum ambarum ſtel<lb></lb>larum ſitus conſpexerimus: atque cunctis, quæ in dioptra <lb></lb>ſunt, immobilibus permanentibus regulam ſuper tympano <lb></lb>circumuoluemus donec vnam ſtellarum per duo foramina <lb></lb>diſpiciamus: &amp; cùm gradum, ſeu minutum adnotaueri<lb></lb>mus, in eo loco, vbi graduum index exiſtit: regulam ſtatim <lb></lb>circumuertemus, <expan abbr="quouſq;">quouſque</expan> per duo foramina reliquam quo<lb></lb>que perſpiciamus: <expan abbr="gradumq́ue">gradumque</expan> demum illum, qui iuxta gra<lb></lb>duum indicem iacet cùm ſimiliter adnotauerimus, &amp; gra<arrow.to.target n="note360"></arrow.to.target><lb></lb>dus inter iam dicta duo ſigna iacentes ſuper tympano nu<lb></lb>merauerimus, ipſas ſtellarum abinuicem diſtantias enun<lb></lb>tiabimus. </s>
<s>cùm autem ad aliquem Zodiaci locum vnam ſtel<arrow.to.target n="note361"></arrow.to.target><lb></lb>larum diſpexerimus, ſi quidem iuxta longitudinem ad an<lb></lb>tecedentia, vt ab oriente ad occidentem: ad partes dexte<lb></lb>ras regulam in tympano exiſtentem circumagentes, hanc <lb></lb>diſpicimus: ſi verò ad conſequentia, vt ab occidente ad <lb></lb>cœli medium, ſiue ad horoſcopum: ad partes ſiniſtras. </s>
<s>An<lb></lb>tecedentia autem ſigna vocantur, quę ſunt ab Ariete ad Pi<lb></lb>ſces, Aquarium, Sagittarium, &amp; cætera: conſequentia verò, <lb></lb>quæ ſunt ab Ariete ad Taurum, Geminos, Cancrum, &amp; re<lb></lb>liqua. </s>
<s>&amp; ſi quidem ſecundùm Zodiaci longitudinem diſtan<lb></lb>tiam conſideramus haud fortuitò diſpiciemus: ſed ſuper li<lb></lb>nea meridiana parallelam dioptram conſtituentes. </s>
<s>ſi verò <arrow.to.target n="note362"></arrow.to.target><lb></lb>ſecundùm latitudinem quæſtionem facimus, vt à Borea ad <lb></lb>Auſtrum, aut è contrario: ſuper linea æquinoctiali. </s>
<s>Hæ au<lb></lb>tem lineæ in admiratione digno regali verſus Auſtrum cu<lb></lb>biculo ijs, qui de hoc curant, à nobis inſcriptæ, ſuper viri<lb></lb>dibus iacent. </s>
<s>harum autem inuentionem in poſitione ſola<arrow.to.target n="note363"></arrow.to.target><lb></lb>rium horologiorum conſcripſimus. </s>
<s>Cùm igitur ſuper cir<lb></lb>culo hemiſphærium ſuper terram exiſtens definiente ad <lb></lb>ortus ipſos, vel occaſus cùm tropica, tum æquinoctialia, <arrow.to.target n="note364"></arrow.to.target><lb></lb>tum etiam ea, quæ inter hæc menſtrua ſunt ſigna ſuſcipere <lb></lb>voluerimus: ad lineam meridianam dioptram parallelam <lb></lb>ſtatuentes, regulam ipſam dirigimus: &amp; per duo foramina <lb></lb>ad ortum, &amp; occaſum indirectùm diſpicientes, hæc in no<lb></lb>ſtro orizonte obſeruabimus: vbi Sol cùm in primum Arie
<pb xlink:href="052/01/148.jpg"></pb>tis, vel Libræ gradum aduenerit, tum vernalia, tum autum<arrow.to.target n="note365"></arrow.to.target><lb></lb>nalia facit æquinoctia. </s>
<s>&amp; quoniam parallelum orizonti <lb></lb>tympanum apponitur, cùm à ſitu indicis regulæ ad partes <lb></lb>boreales gradus 32 numerauerimus, ad <expan abbr="ipſosq́ue">ipſosque</expan> regulam <lb></lb>direxerimus: æſtiua tropica ſigna ſuſcipiemus. </s>
<s>ibi enim Sol <lb></lb>in primum Cancri gradum veniens æſtiuas efficit conuer<lb></lb>ſiones. </s>
<s>quæ verò in medio interiacent menſtrua ſigna ab <lb></lb>æquinoctiali per 16, &amp; 28 gradus accipiemus. </s>
<s>&amp; è contra<arrow.to.target n="note366"></arrow.to.target><lb></lb>rio ab æquinoctiali ad partes auſtrales eoſdem gradus nu<lb></lb>merantes, ad <expan abbr="ipſosq́ue">ipſosque</expan> regulam deducentes: cùm hyema<lb></lb>lia tropica, tum medio interiacentia menſtrua ſigna conſpi<lb></lb>cere poterimus. </s>
<s>At quoniam per 180 ſemicirculi gradus <lb></lb>ſigna ſecundùm dimetientem oppoſita ſuper orizontem <lb></lb>oriuntur, &amp; occidunt: Cancro ſiquidem oriente, Capri<lb></lb>cornus occidit: Aquario verò occidente, oritur Leo: volui <lb></lb>obſeruare quot gradibus diſtet in <expan abbr="antecedẽtibus">antecedentibus</expan> ſignorum <arrow.to.target n="note367"></arrow.to.target><lb></lb>lucida Hyadum ſtella (quæ etiam Lambauras, hoc eſt fax <lb></lb>ardens dicitur) ab ea, quæ in corde Leonis eſt, vocatur au<lb></lb>tem Baſiliſcus: <expan abbr="atq;">atque</expan> circa ſecundam horam nocturnam cùm <lb></lb>orientem verſus diſpexerim, ac <expan abbr="tãquam">tanquam</expan> manifeſtam cam, <lb></lb>quæ in corde Leonis eſt ſtellam acceperim: adnotaui gra<lb></lb>dum in tympano, iuxta quem regulæ index extitit: &amp; cùm <lb></lb>ad antecedentia regulam conuerterim, diſpexi in Tauro ip <lb></lb>ſam <expan abbr="Lambaurã">Lambauram</expan>, hoc eſt facem <expan abbr="ardentẽ">ardentem</expan>, cùm <expan abbr="gradũ">gradum</expan>, qui apud <lb></lb>ipſam eſt ſimiliter adnotarim. </s>
<s>&amp; <expan abbr="cũ">cum</expan> in tympano gradus in<lb></lb>ter ſigna <expan abbr="iacẽtes">iacentes</expan> enumerauerim, eos 80 ferè inueni. </s>
<s>quot <expan abbr="ẽt">etiam</expan> <arrow.to.target n="note368"></arrow.to.target><lb></lb>ſunt ij, quibus ambæ ſtelle abinuicem diſtant. </s>
<s>nam ipſe <lb></lb>Baſiliſcus unà cum additamento motus eorum, quæ ab <lb></lb>ætate Ptolem˛i ſunt temporum, gradus 10 1/2 in Leone <expan abbr="nũc">nunc</expan> <lb></lb>poſſidens reperitur: Et lucida Hyadum in Tauro, 20 <arrow.to.target n="note369"></arrow.to.target><lb></lb>2/3. </s><s>Cùm autem ipſos 10 1/2 gradus leonis in antecedentia <lb></lb>tum Cancri, tum Geminorum ſingula 30, &amp; in 9 1/3 Tau<lb></lb>ri connumerauerim, eoſdem 80 ferè gradus inueni: </s><s>Simili<lb></lb>ter autem in conſequentia quoque, vt à Tauro ad <expan abbr="Leonẽ">Leonem</expan>. </s>
<s><lb></lb>Rurſus autem circa mediam noctem cùm ab ea, quæ in cor <lb></lb>de Leonis eſt ſtella ad conſequentia Arcturum, qui Boo-<pb xlink:href="052/01/149.jpg"></pb><arrow.to.target n="note370"></arrow.to.target><lb></lb>tes etiam uocatur, in libra, borealiorem autem æquino<lb></lb>ctiali gradus 31 exiſtentem diſpexerim: adnotaui, <expan abbr="reperi-q́ue">reperi<lb></lb>que</expan> in medio gradus 54 ferè, quot ſunt ij, quibus etiam <lb></lb>Arcturus ad conſequentia à Baſiliſco diſtat. </s>
<s>Arcturus enim <lb></lb>hac noſtra <expan abbr="tẽpeſtate">tempeſtate</expan> unà cum iam dicto motus additamen<lb></lb>to quintum Libræ gradum obtinet. </s>
<s><expan abbr="Suntq́ue">Suntque</expan> Leonis qui<lb></lb>dem ad conſequentia 19 1/2, virginis 30, &amp; quinque Li<lb></lb>bræ, quot etiam in tympano ferre connumerati fuere. </s>
<s><lb></lb>Idem itaque modus in reliquis etiam fixis ſtellis primæ, <arrow.to.target n="note371"></arrow.to.target><lb></lb><expan abbr="ſecundæq́ue">ſecundæque</expan> magnitudinis exiſtentibus, ac in quinque pla<lb></lb>netis ſemper fiat. </s>
<s>Lunæ verò diſtantiam non ſolùm ad pla<arrow.to.target n="note372"></arrow.to.target><lb></lb>netas, &amp; eas fixarum, quæ manifeſtæ, <expan abbr="ſimilemq́ue">ſimilemque</expan> ad ipſam <lb></lb>Lunam, vel contrariam temperiem adeptæ ſunt, obſeruare <lb></lb>oportet: verùmetiam ad eas, quæ nebuloſæ dicuntur con<arrow.to.target n="note373"></arrow.to.target><lb></lb>ſtellationes, verbi gratia ad Præſepium, vel <expan abbr="Crinẽ">Crinem</expan>, aut eas, <arrow.to.target n="note374"></arrow.to.target><lb></lb>quæ in bipertita ſectione Tauri Pleiades vocantur, aut eas, <arrow.to.target n="note375"></arrow.to.target><lb></lb>quæ in cornibus propter ipſius Y elementi figuram Hya<lb></lb>das, &amp; pluuiarum, ac imbrium effectrices. </s>
<s>Præſertim autem <arrow.to.target n="note376"></arrow.to.target><lb></lb>obſeruanda eſt luna circum quas etiam ſtellas ad ſolem <arrow.to.target n="note377"></arrow.to.target><lb></lb>aſpectus ſeptem facit: ſi hiſce proxima eſt, aut graduatim <lb></lb>ad ipſam ſtellæ figurantur, aut coniunctores aſpectus ad <lb></lb>ſolem efficiunt. </s>
<s>Hæc igitur qui circa dioptriam, &amp; Phæno<lb></lb>mena conſiderarunt, <expan abbr="ſitusq́ue">ſitusque</expan> ſyderum ex prompta regula <lb></lb>ſuſcipiunt: non ſolùm ſtellarum diſtantias enuntiabunt, <lb></lb>verùmetiam auræ conſtitutiones, &amp; inæquabilitates, nec<lb></lb>non intemperies, ac temperies per eas, quæ fiunt quotan<lb></lb>nis ſtellarum ſignificationes, intelligentes præſagient. </s></p>
<pb xlink:href="052/01/150.jpg"></pb><p type="margin">
<s><margin.target id="note359"></margin.target>a</s></p><p type="margin">
<s><margin.target id="note360"></margin.target>b</s></p><p type="margin">
<s><margin.target id="note361"></margin.target>c</s></p><p type="margin">
<s><margin.target id="note362"></margin.target>d</s></p><p type="margin">
<s><margin.target id="note363"></margin.target>e</s></p><p type="margin">
<s><margin.target id="note364"></margin.target>f</s></p><p type="margin">
<s><margin.target id="note365"></margin.target>g</s></p><p type="margin">
<s><margin.target id="note366"></margin.target>h</s></p><p type="margin">
<s><margin.target id="note367"></margin.target>i</s></p><p type="margin">
<s><margin.target id="note368"></margin.target>k</s></p><p type="margin">
<s><margin.target id="note369"></margin.target>l</s></p><p type="margin">
<s><margin.target id="note370"></margin.target>m</s></p><p type="margin">
<s><margin.target id="note371"></margin.target>n</s></p><p type="margin">
<s><margin.target id="note372"></margin.target>o</s></p><p type="margin">
<s><margin.target id="note373"></margin.target>p. </s>
<s>q</s></p><p type="margin">
<s><margin.target id="note374"></margin.target>r</s></p><p type="margin">
<s><margin.target id="note375"></margin.target>s</s></p><p type="margin">
<s><margin.target id="note376"></margin.target>t</s></p><p type="margin">
<s><margin.target id="note377"></margin.target>u</s></p><figure id="id.052.01.150.1.jpg" xlink:href="052/01/150/1.jpg"></figure><p type="main">
<s><emph type="center"></emph>FRANCISCI BAROCII <lb></lb>SCHOLIVM.<emph.end type="center"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>MVlta nobis eſſent hoc in loco dicenda pro perfecta præſen<lb></lb>tis propoſitionis intelligentia ſi plenos à principio commen<lb></lb>tarios inſtituiſſemus. </s>
<s>Verùm cùm institutum noſtrum fue<lb></lb>rit breuißima quoad fieri potuit ſcholia locos obſcuros dilucidan<lb></lb>tia componere, iam inceptum ordinem ſequentes, nonnulla dum<lb></lb>taxat obſcurior a verba declarabimus. </s>
<s>hoc priùs adnotantes, quòd <lb></lb>propoſitum Autoris in hac propoſitione eſt oſtendere quomodo per<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/151.jpg"></pb><emph type="italics"></emph>dioptram, ſiue dioptricum inſtrumentum cœleſtes quoque diſtan<lb></lb>tias metiri poſſumus. </s>
<s>in quo quidem oſtendendo tali procedit or<lb></lb>dine. </s>
<s>primùm demonſtrat <expan abbr="quonã">quonam</expan> pacto diſtantia inter duas quaſ<lb></lb>libet stellas per dioptram obſeruatur. </s>
<s>Secundò demonſtrat quo<lb></lb>modo duo æquinoctialia, &amp; duo tropica, &amp; quæ inter hæc ſunt men<lb></lb>ſtrua puncta, tum orientalia, tum occidentalia in Orizonte noſtro <lb></lb>per eandem dioptram obſeruari poſſunt. </s>
<s>Tertiò cauſa exempli de<lb></lb>monſtrat quomodo diſtantia inter quaſdam ſtellas fixas per dio<lb></lb>ptram reperiri poteſt. </s>
<s>Dioptram autem hìc, &amp; in ſuperioribus pro<lb></lb>poſitionibus intelligere debemus fuiſſe quoddam antiquum inſtru<lb></lb>mentum ab aſtrolabij dorſo parum dißimile, aptum ad menſuran<lb></lb>das <expan abbr="quaſcumq;">quaſcumque</expan> diſtantias. </s>
<s>cuius figuram qualem in veteri exem<lb></lb>plari inuenimus, talem in fine huius propoſitionis appoſuimus. </s>
<s><lb></lb>commodiùs autem, ac faciliùs iam dictæ diſtantiæ capiuntur, mul<lb></lb>ta〈qué〉 alia Geometrica, &amp; Aſtrologica problemata fiunt per dorſum <lb></lb>aſtrolabij. </s>
<s>vt multi Autores locupletißimè docuere.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note378"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note378"></margin.target><emph type="italics"></emph>a<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[magnitudines, quæ quæruntur] ſcilicet stellarum ſoliditates, <lb></lb>atque diſ antias.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note379"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note379"></margin.target><emph type="italics"></emph>b<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Signa hìc pro punctis, ſiue gradibus, &amp; inferiùs modò pro pun<lb></lb>ctis, ſine gradibus, modò pro ſignis Zodiaci ſuſcipienda ſunt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note380"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note380"></margin.target><emph type="italics"></emph>c<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Antecedentia vocat Autor ſigna Zodiaci, quæ contra ſucceſ<lb></lb>ſionem ipſorum ſignorum: conſequentia verò, quæ ſecundum ſuc<lb></lb>ceßionem eorumdem ſequuntur, vt ipſemet exempto declarauit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note381"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note381"></margin.target><emph type="italics"></emph>d<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quænam ſint iſtæ duæ lineæ, ſcilicet meridiana, &amp; æquinoctia<lb></lb>lis Aſtrologi, Coſmographi, &amp; Horologiographi paßim ſatis ſuper〈qué〉 <lb></lb>declarant. </s>
<s>Sunt enim (vt breuiter dicam) duo maximi terreſtris <lb></lb>globi circuli, qui ſe ſe ad angulos rectos ſphærales interſecant, al<lb></lb>ter quidem ſub cœleſti meridiano in terra iacens, alter verò ſub <lb></lb>eo cœleſti circulo, qui per æquinoctialia puncta, &amp; Zenith habitan<lb></lb>tium tranſit. </s>
<s>quas vtique duas lineas Autor in quodam admiran<lb></lb>do regalis palatij verſus auſtrum exiſtente cubiculo ſuper qua<lb></lb>dam virids ſuperficie ad eorum commoditatem, qui de hac re ſoli<lb></lb>citi ſunt, ſe deſignaſſe inquit. </s>
<s>harum autem duarum linearum <lb></lb>inuentionem, quam multi doctißimi viri diuerſis pulcherrimis re<lb></lb>gulis tradidere, ipſe etiam Autor in libro de ſolarium <expan abbr="horologiorũ">horologiorum</expan> <lb></lb>poſitione (qui adhuc deſideratur) ſe conſcripſiſſe ait.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note382"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note382"></margin.target><emph type="italics"></emph>e<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[circulo hemiſphærium ſuper terram existens definiente] hoc<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/152.jpg"></pb><emph type="italics"></emph>eſt Orizonte, quippe qui noſtrum ſupernum hemiſphærium ab in<lb></lb>ferno noſtrorum antipodum hemiſphærio ſeparat, atque diſtinguit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note383"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note383"></margin.target><emph type="italics"></emph>f<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Quænam ſint intelligenda ſigna tropica, æquinoctialia, &amp; in<lb></lb>ter hæc iacentia menſtrua, paucis abſoluam. </s>
<s>Duo itaque ſunt æqui<lb></lb>noctialia ſigna ſiue puncta, ſcilicet primus gradus Arietis, &amp; pri<lb></lb>mus gradus libræ, in quibus cùm Sol fuerit, vernale, &amp; autum<lb></lb>nale æquinoctium facit. </s>
<s>Duo præterea ſunt tropica, ſiue ſolſtitialia <lb></lb>puncta, videlicet principium Cancri, &amp; principium Capricorni, <lb></lb>in quibus cùm Sol fuerit, æſtiuale, hyemale〈qué〉 ſolſtitium efficit. </s>
<s>vo<lb></lb>cantur autem tropica<emph.end type="italics"></emph.end> <foreign lang="grc">ἀπὸ τη̄ς τροπη̄ς</foreign>, <emph type="italics"></emph>hoc eſt à conuerſione, quo<lb></lb>niam cùm in eis Sol fuerit, incipit ſe conuertere à parte boreali <lb></lb>ad auſtralem, aut ab auſtrali ad borealem. </s>
<s>inter hæc verò quatuor <lb></lb>iam dicta puncta reliqui omnes 356 Zodiaci gradus ſunt, in quo<lb></lb>rum vnoquoque cùm Sol cotidie moueatur cauſat ipſas 178 ſpi<lb></lb>ras, quæ inter æquinoctialem, ac tropicos ab aſtrologis fieri exco<lb></lb>gitantur. </s>
<s>ex his itaque 356 Zodiaci punctis omnia principia ſiue <lb></lb>primi gradus ſignorum menstrua puncta nuncupantur, quoniam <lb></lb>ſpatio menſis vnius ab uno eorum ad aliud Sol migrat. </s>
<s>Quare per<lb></lb>ſpicuum nobis eſt quænam ſint puncta ſiue ſigna æquinoctialia, <lb></lb>tropica, &amp; inter hæc media iacentia menſtrua. </s>
<s>Adnotatu verò <lb></lb>dignum eſt <expan abbr="q̨">quae</expan> <expan abbr="oĩa">omnia</expan> hæc ſigna tripliciter conſiderantur, nempe aut in <lb></lb>Zodiaco, aut in Meridiano, aut in Orizonte: necnon in vnoquoque <lb></lb>etiam iſtorum circulorum dupliciter in Zodiaco quidem aut inſi<lb></lb>gnis borealibus, vbi Sol exiſtens dies noctibus longiores: aut in au<lb></lb>ſtralibus, vbi dies breuiores quàm noctes nobis efficit. </s>
<s>in Meri<lb></lb>diano verò, aut in ſuperno hemiſphærio, vbi noſtrum meridiem: <lb></lb>aut in inferno, vbi noſtram mediam noctem agit. </s>
<s>in orizonte de<lb></lb>mum, aut in oriente, vbi ſui ortus: aut in occidente vbi eiuſdem <lb></lb>occaſus varietatem cotidiè nobis indicat. </s>
<s>hæc igitur quæ in ori<lb></lb>zonte conſiderantur orientalia, &amp; occidentalia cùm æquinoctia<lb></lb>lia, tum tropica, tum inter hæc iacentia menſtrua ſigna, ſiue pun<lb></lb>cta ſunt, quæ per dioptram in orizonte noſtro reperire nos Au<lb></lb>tor docet.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note384"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note384"></margin.target><emph type="italics"></emph>g<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[&amp; quoniam parallelum orizonti &amp;c.] hæc Autoris demonſtra<lb></lb>tio in inſtrumento dioptrico, ſiue in ſphæra materiali clara eſt. </s>
<s><lb></lb>Animaduertendum autem eſt quòd ea, quæ dicit Autor ibi [gra<lb></lb>dus 32 numerauerimus &amp;c.] vera non ſunt apud omnes mundi<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/153.jpg"></pb><emph type="italics"></emph>habitantes, ſed apud eos tantùm, qui habent polum arcticum, ſeu <lb></lb>borealem eleuatum 35 gradibus. </s>
<s>vndè manifeſtum nobis eſt Au<lb></lb>torem noſtrum in aliqua regionum iam dictum polum ſupra ori<lb></lb>zontem 35 gradibus altum habentium fuiſſe dum præſens opus <lb></lb>componebat. </s>
<s>Adnotandum præterea quòd illud [16, &amp; 28 gra<lb></lb>dus accipiemus] non ita intelligendum eſt, quòd ſcilicet per ho<lb></lb>ſce tantùm duos graduum numeros ipſa interiacentia men<lb></lb>ſtrua ſigna ſuſcipienda ſunt: ſed per omnes etiam reliquos, qui <lb></lb>ab vnitate vſque ad 32 ſunt. </s>
<s>hoſce verò duos Autor exempli gra<lb></lb>tia fortuitò ſuſcepit, tamquam eos, quorum vterque ab ipſo 32 <lb></lb>numero comprehenditur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note385"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note385"></margin.target><emph type="italics"></emph>h<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[eoſdem gradus] ſcilicet 32, &amp; eos qui à 32 continentur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note386"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note386"></margin.target><emph type="italics"></emph>i<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Hyadum stellam lucidam ſiue Lambauram hìc intelligere de<lb></lb>bemus eam stellam fixam primæ magnitudinis, quæ oculus Tauri <lb></lb>vocatur. </s>
<s>Animaduertendum eſt autem quòd hæc ſtella non eſt ex <lb></lb>eis ſtellis inter cornua Tauri iacentibus, quæ Hyades vocantur, <lb></lb>vt videtur velle hìc Autor: illæ enim ſunt quintæ magnitudinis, <lb></lb>vt ex Hyginio, Ptolemæo〈qué〉 patet.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note387"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note387"></margin.target><emph type="italics"></emph>k<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[Nam ipſe Baſiliſcus &amp;c.] illius ſtellæ fixæ, quæ cor Leonis <lb></lb>vocatur in octauæ ſphæræ Zodiaco exiſtentis ſitus in Zodiaco de<lb></lb>cimæ ſphæræ non fuit idem tempore, quo ſcripſit Autor hoc opus, <lb></lb>qui fuerat etiam Ptolemæi temporibus: ſed orientalior propter <lb></lb>motum proprium nonæ ſphæræ. </s>
<s>idcirco ait Autor quòd ipſe Baſi<lb></lb>liſcus, ſcilicet octauæ ſphæræ vnà cum additamento motus eorum, <lb></lb>quæ ab ætate Ptolemæi ſunt temporum, gradus 10 1/2 in Leone vi<lb></lb>delicet decimæ ſphæræ, nunc, ſcilicet Autoris temporibus, poßi<lb></lb>dens reperitur. </s>
<s>ſic autem intelligendum <expan abbr="etiã">etiam</expan> eſt quod ait [&amp; luci<lb></lb>da Hyadum in Tauro 20 2/3]<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note388"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note388"></margin.target><emph type="italics"></emph>l<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[cùm autem ipſos 10 1/2 gradus &amp;c.] verba hæc ſic intelli<lb></lb>genda ſunt. </s>
<s>quòd ſcilicet ipſos 10 1/2 gradus Leonis decimæ ſphæ<lb></lb>ræ vnà cum antecedentibus 30 cancri, &amp; 30 Geminorum, &amp; 9 1/3 <lb></lb>Tauri gradibus in vnum coaceruando: 80 ferè graduum diſtan<lb></lb>tiam inter iam dictas duas stellas fixas reperiſſe ait. </s>
<s>eadem au<lb></lb>tem eſt diſtantia in conſequentia quoque ſigna, à Tauro ad Leo<lb></lb>nem. </s>
<s>nempe ſià Tauri 20 1/3 gradibus enumerationem facere<emph.end type="italics"></emph.end>
<pb xlink:href="052/01/154.jpg"></pb><emph type="italics"></emph>cæperimus, vſque ad 10 1/2 Leonis gradus progredientes.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note389"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note389"></margin.target><emph type="italics"></emph>m<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[borealiorem autem æquinoctiali gradus 31 exiſtentem] Ad<lb></lb>notandum hìc eſt, quòd quamuis paulò poſt dicat Arcturum tem<lb></lb>pore ſuo quintum Libræ gradum in decima ſphæra occupare, po<lb></lb>teſt attamen etiam 31 gradibus ab æquinoctiali diſtare, ſi ſigna li<lb></lb>bræ in decimæ ſphæræ Zodiaco ſuſcipiantur hìc ſecundum <expan abbr="tertiã">tertiam</expan> <lb></lb>ſignorum ſignificationem declaratam à Ioanne de Sacroboſco in <lb></lb>ſecundo capitulo ſphæræ. </s>
<s>Adnotandum præterea quòd ex hiſce <lb></lb>iam dictarum stellarum fixarum ſitibus ſic tempore Autoris exi<lb></lb>ſtentibus quilibet aſtrologicarum tabularum peritus ſupputando <lb></lb>in cognitionem venire poterit æui, quo noſter Autor præſentem li<lb></lb>brum conſcripſit. </s>
<s>floruit enim poſt Chriſti aduentum. </s>
<s>quandoqui<lb></lb>dem tempore quo Chriſtus redemptor noſter ortus eſt, reperiebatur <lb></lb>ſecundum Ptolem˛i obſeruationem principium Arietis octauæ, &amp; <lb></lb>nonæ, &amp; decimæ ſphæræ ſimul iuncta. </s>
<s>vndè etiam principium Tau<lb></lb>ri octauæ ſphæræ vnà cum principio Tauri decimę coniunctum <lb></lb>erat. </s>
<s>tempore verò Autoris initium Tauri octauæ ſphæræ erat in <lb></lb>gradu 20 1/3 Tauri decimæ ſphæræ.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note390"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note390"></margin.target><emph type="italics"></emph>n<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[in quinque planetis] dixit, quoniam inter ſolem, &amp; cætera ſi<lb></lb>dera diſtantias per dioptram obſeruare die non poſſumus cùm ſtel<lb></lb>læ ſole ſuper noſtrum orizontem exiſtente non luceant. </s>
<s>de luna <lb></lb>verò mox ſubiungit.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note391"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note391"></margin.target><emph type="italics"></emph>o<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Stellarum fixarum aliæ manifestæ, aliæ nebuloſæ ſunt: aliæ ean<lb></lb>dem cum planetis, aliæ contrariam cis naturam, temperiem〈qué〉 ha<lb></lb>bent, vt ab Aſtrologis declaratur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note392"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note392"></margin.target><emph type="italics"></emph>p<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph><expan abbr="Præſepiũ">Præſepium</expan> eſt <expan abbr="quędã">quędam</expan> nubiloſa conſtellatio in ſigno Cancri <expan abbr="exiſtẽs">exiſtens</expan>.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note393"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note393"></margin.target><emph type="italics"></emph>q<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Crinis autem, ſcilicet Berenices, ſimiliter alia conſtellatio eſt <lb></lb>in Leone iacens.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note394"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note394"></margin.target><emph type="italics"></emph>r<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Pleiades verò eſt conſtellatio exiſtens in bipertita ſectione Tau<lb></lb>ri, in qua ſi Taurus iuxta latitudinem ſecandus ſit, bifariam ſe<lb></lb>cabitur.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note395"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note395"></margin.target><emph type="italics"></emph>ſ<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>Hyades <expan abbr="aũt">aut</expan> eſt alia ſtellarum <expan abbr="fixarũ">fixarum</expan> conſtellatio in faciem Tau<lb></lb>ri inter eius cornua exiſtens, quam Autor ab ipſius y elementi fi<lb></lb>gura ſic dictam eſſe vult, quamuis etiam alijs de cauſis ita dica<lb></lb>tur, vt apud Autores materiam hanc pertractantes legitur.<emph.end type="italics"></emph.end></s></p>
<pb xlink:href="052/01/155.jpg"></pb><p type="main">
<s><arrow.to.target n="note396"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note396"></margin.target><emph type="italics"></emph>t<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ad ſolem aſpectus ſeptem] ſeptem aſpectus lunæ ad ſolem <lb></lb>ſunt ij, qui in quolibet menſe lunari fiunt: ſcilicet duo trini, duo <lb></lb>quadrati, duo ſextiles, &amp; vnica oppoſitio. </s>
<s>Coniunctionem enim <lb></lb>lunæ cum ſole non connumerauit, quoniam cùm inuiſibilis nobis <lb></lb>tunc luna ſit, per dioptram à nobis obſeruari minimè poteſt.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><arrow.to.target n="note397"></arrow.to.target></s></p><p type="margin">
<s><margin.target id="note397"></margin.target><emph type="italics"></emph>u<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="italics"></emph>[ſi hiſce proxima eſt &amp;c.] Hoc est tria hæc de Luna reſpectu <lb></lb>earum ſtellarum fixarum, circum quas iam dictos ſeptem ad ſo<lb></lb>lem aſpectus facit, per dioptram obſeruanda ſunt: nempe ſi ſtel<lb></lb>lis ipſis proxima eſt, videlicet ſi in eodem cœli loco cum ipſis exi<lb></lb>ſtat: aut ſi graduatim ad ipſam ſtellæ figurantur, ideſt ſi per gra<lb></lb>dus aliquot ab ipſa Luna diſtantes ipſę ſtellæ in aſpectu quodam <lb></lb>figurantur: aut ſi coniunctores aſpectus ad ſolem efficiunt, hoc eſt <lb></lb>ſi ipſæ ſtellæ in coniunctione cum ſole ſunt. </s>
<s>Verùm hęc etiam pro <lb></lb>præſentis vltimæ, ac pulcherrima, <expan abbr="doctrinaq́ue">doctrinaque</expan> aſtrologica plenę <lb></lb>propoſitionis dilucidationem dicta ſufficiant.<emph.end type="italics"></emph.end></s></p><p type="main">
<s><emph type="center"></emph><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p>

			</chap>
		</body>
		<back></back>
	</text>
</archimedes>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Wed, 29 Nov 2017 16:55:37 +0100
parents	22d6a63640c6
children