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


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<pb xlink:href="052/01/001.jpg"/><p type="main">
<s><emph type="center"/>HERONIS <lb/>MECHANICI <lb/>LIBER<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>DE MACHINIS <lb/>BELLICIS, <lb/>NECNON LIBER DE GEODAESIA<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>A' FRANCISCO BAROCIO Patritio Veneto latinitate <lb/>donati, multis mendis expurgati, &amp; fi&shy;<lb/>guris, ac &longs;cholijs illu&longs;trati.<emph.end type="center"/></s></p><figure id="id.052.01.001.1.jpg" xlink:href="052/01/001/1.jpg"/><p type="main">
<s><emph type="center"/><emph type="italics"/>VENETIIS, <lb/>Apud Franci&longs;cum Franci&longs;cium Senen&longs;em. </s>
<s>1572.<emph.end type="italics"/><emph.end type="center"/></s></p>
<pb xlink:href="052/01/002.jpg"/>
<pb xlink:href="052/01/003.jpg"/><p type="main">
<s><emph type="center"/>ILLVSTRISSIMO<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>ET EXCELLENTISSIMO<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>D. D. VINCENTIO<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>GONZAGAE, MANTVAE<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>PRINCIPI.<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Franci&longs;cus Franci&longs;cius Senen&longs;is. </s>
<s>S. D.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s>H<emph type="italics"/>E<emph.end type="italics"/>RONEM <emph type="italics"/>de machinis bellicis <lb/>vetu&longs;ti&szlig;imum, &amp; celeberrimum <lb/>Auctorem nuper gr&aelig;co latinum <lb/>fecit nobilis, &amp; tum vtriu&longs;que <lb/>lingu&aelig;, tum Mathematic&aelig; &longs;cien<lb/>ti&aelig; eruditi&szlig;imus vir patritius <lb/>Venetus Franci&longs;cus Barocius. </s>
<s><lb/>Hunc ego quum ad communem v&longs;um &longs;tudio&longs;orum <lb/>meis typis diligenter imprimendum curauerim, at&shy;<lb/>que impre&longs;&longs;um edere con&longs;tituerim, veritus &longs;i &longs;ine po&shy;<lb/>tentis alicuius tuto, fideli&queacute; patrocinio abiret in vul<lb/>gus, ne &longs;itu, &amp; &longs;qualore ob&longs;itus, vt qui nunc primum <lb/>in lucem prodeat, vix agno&longs;ceretur, in tuam maxi&shy;<lb/>me clientelam tradere uolui: cuius nomine, ac &longs;plen&shy;<lb/>dore non dubito, quin illu&longs;trior multo futurus &longs;it, &amp; <lb/>carior. </s>
<s>Neque vero &longs;uccurrebat qui&longs;quam cuius fi&shy;<lb/>dei melius <expan abbr="c&otilde;mittere">committere</expan> po&longs;&longs;e confiderem. </s>
<s>tecum enim<emph.end type="italics"/>
<pb xlink:href="052/01/004.jpg"/><emph type="italics"/>i&longs;tud &aelig;tatis conferre quem audeam? </s>
<s>qui tam illu&longs;tri <lb/>Augu&longs;to&queacute; genere editus, &longs;ingularis &amp; &longs;anctitatis, <lb/>&amp; &longs;apienti&aelig;, parentibus genitus, cum in&longs;igni corpo&shy;<lb/>ris venu&longs;tate, &amp; gratia, tum animi indole, &amp; inge&shy;<lb/>nij diuina felicitate pr&aelig;ditus eo fato natus videris, <lb/>vt ad longe ampliorem, quam in quo nunc es Man<lb/>tu&aelig;, ac Montisferrati, principatum eueharis; pr&aelig;&shy;<lb/>&longs;ertim quum ijs moribus, ijs&queacute; di&longs;ciplinis ornere, qu&aelig; <lb/>vel infimum hominem ad alti&szlig;imum gradum facil&shy;<lb/>lime tollant. </s>
<s>quippe qui nondum exacto anno decimo <lb/>&aelig;tatis tu&aelig; in &longs;tudijs litterarum gr&aelig;carum, &amp; latina&shy;<lb/>rum admirabiles progre&longs;&longs;us feceris, hi&longs;torias rerum <lb/>ge&longs;tarum, &amp; poetarum volumina euoluas, &amp; incre<lb/>dibili facilitate edi&longs;cas, <expan abbr="Arithmetic&etilde;">Arithmeticem</expan>, <expan abbr="Geometri&atilde;&queacute;">Geometriam&queacute;</expan>, <lb/>&amp; Euclidis elementa it a tractes, it a explices, it a de&shy;<lb/>mon&longs;tres, vt nihil videaris habere facilius; at que ijs <lb/>artibus ad rei militaris &longs;cientiam tibi <expan abbr="vi&atilde;">viam</expan> munias, <lb/>&amp; pro&longs;pero cur&longs;u contendas qua in re non <expan abbr="par&utilde;">parum</expan> opi&shy;<lb/>nor adiuuabit <expan abbr="in&longs;trum&etilde;torum">in&longs;trumentorum</expan> bellicorum, cognitio, <lb/>&amp; apparatus, quem ex Herone con&longs;equeris. </s>
<s>Tibi igi<lb/>tur Illu&longs;tri&szlig;. </s>
<s>&amp; Excellenti&szlig;. </s>
<s>Princeps Heronem <expan abbr="me&utilde;">meum</expan> <lb/>dedico, &amp; in <expan abbr="tu&atilde;">tuam</expan> <expan abbr="clientel&atilde;">clientelam</expan> trado: ei&queacute; gratulor, quod <lb/>tecum propemodum natus tuis au&longs;picijs editus, <expan abbr="te-c&utilde;">te&shy;<lb/>cum</expan> vna coale&longs;cet, &amp; cre&longs;cet. </s>
<s>Tu pro tua benignitate <lb/>munus <expan abbr="lib&etilde;ter">libenter</expan> accipe, &amp; me <expan abbr="tuor&utilde;">tuorum</expan> numero ad&longs;cribe.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/005.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>BREVIS AD LECTOREM<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>PRAEFATIO.<emph.end type="center"/></s></p><figure id="id.052.01.005.1.jpg" xlink:href="052/01/005/1.jpg"/><p type="main">
<s><emph type="italics"/>HERONIS vocati Mechanici, propterea quod <lb/>in con&longs;cribendis Mechanicis pr&aelig;ualuit, volu&shy;<lb/>men de Machinis Bellicis, ac de Geod&ecedil;&longs;ia: <lb/>quod hucu&longs;que lacerum, &amp; fragmentatum in <lb/>tenebris latitabat: &agrave; nobis denique re&longs;taura&shy;<lb/>tum, &amp; in latinum &longs;ermonem conuer&longs;um, <expan abbr="&longs;cho-lijs&qacute;ue">&longs;cho&shy;<lb/>lijsque</expan> dilucidatum: libenti&szlig;im&egrave; tibi &longs;tudio&longs;e <lb/>lector propter maximam eius vtilitatem perle&shy;<lb/>gendum e&longs;&longs;e non dubito. </s>
<s>Quantam enim vtili&shy;<lb/>tatem ad ob&longs;idendas, <expan abbr="expugnandas&qacute;ue">expugnandasque</expan> ciuitates <lb/>antiquis tormenta reperta nondum habenti&shy;<lb/>bus pr&aelig;&longs;ens de Machinis bellicis doctrina pr&aelig;buerit; ex ijs, qu&aelig; tot gra&shy;<lb/>ui&szlig;imi Autores, <expan abbr="docti&szlig;imi&qacute;ue">docti&szlig;imique</expan> viri de hac materia diligenti&szlig;im&egrave; con&longs;cri&shy;<lb/>p&longs;ere: cuique per&longs;picuum e&longs;&longs;e pote&longs;t. </s>
<s>Pr&aelig;terea ver&ograve; maxima eius vtilitas <lb/>est ad &longs;truendos, <expan abbr="pr&aelig;parandos&qacute;ue">pr&aelig;parandosque</expan> pontes artificio&longs;os, quibus exercitus <lb/>flumina, <expan abbr="fo&longs;&longs;as&qacute;ue">fo&longs;&longs;asque</expan> traijciant: necnon &longs;calas maximo cum artificio con&longs;tru&shy;<lb/>ctas, ac portatiles, ad in&longs;cendendum muros. </s>
<s>Amplius autem ex hac <lb/>&longs;cientia pulcherrima eliciuntur pr&aelig;cepta, quippe qu&aelig; ad multiformium <lb/>Parmarum, &amp; omnis generis Clypeorum, necnon Balli&longs;tarum, <expan abbr="Catapulta-rum&qacute;ue">Catapulta&shy;<lb/>rumque</expan> con&longs;tructionem, ac demum ad ciuitatum ob&longs;idionem, ab <expan abbr="ob&longs;idione-&qacute;ue">ob&longs;idione&shy;<lb/>que</expan> defen&longs;ionem &longs;pectant. </s>
<s>Quinetiam Machinarum bellicarum in hoc li&shy;<lb/>bro de&longs;criptarum cognitio magnopere nos iuuat ad intelligenda multa pri&shy;<lb/>&longs;corum Hi&longs;toricorum cum Gr&aelig;corum, tum Latinorum loca: qu&aelig; hucu&longs;que <lb/>ob&longs;curi&szlig;ima, &amp; qua&longs;i imperceptibilia vi&longs;a &longs;unt ijs, qui nullam i&longs;tarum Ma&shy;<lb/>chinarum agnitionem habuerunt. </s>
<s>Atque h&aelig;c est vtilitas libri Heronis de <lb/>Machinis bellicis. </s>
<s>Ver&ugrave;m libellus quoque de Geod&aelig;&longs;ia maximam nobis <lb/>vtilitatem affert. </s>
<s>c&ugrave;m pr&aelig;&longs;ertim ad hanc etiam no&longs;tram &aelig;tatem eius do&shy;<lb/>ctrina valde nece&longs;&longs;aria &longs;it ad men&longs;urandum &agrave; longe radijs vi&longs;ualibus, <expan abbr="in-strumento&qacute;ue">in&shy;<lb/>strumentoque</expan> Dioptrico murorum altitudines, ac longitudines: necnon <lb/>fo&longs;&longs;arum, ac fluuiorum latitudines, &amp; profunditates: atque etiam ad &longs;u&shy;<lb/>&longs;cipiendum &longs;itus varios castrorum expugnand&aelig; ciuitatis, vt contraria Ca-<emph.end type="italics"/>
<pb xlink:href="052/01/006.jpg"/><emph type="italics"/>stra extra ciuitatem ip&longs;am oppugnandi gratia rite fabricari po&szlig;int: atque <lb/>rur&longs;us in vniuer&longs;um ad men&longs;urandam quamcumque di&longs;tantiam, &longs;iue longi&shy;<lb/>tudinem, &amp; quamlibet c&ugrave;m &longs;uperficialem, tum corpoream aream: ac de&shy;<lb/>nique multas a&longs;trologicas ob&longs;eruationes in corporibus c&oelig;lestibus, <expan abbr="eorum-&qacute;ue">eorum&shy;<lb/>que</expan> motibus peragendas. </s>
<s>His it a que de vtilitate pr&aelig;&longs;entis voluminis bre&shy;<lb/>uiter adnotatis, antequam ad Heronis lectionem accedas amice lector non&shy;<lb/>nullorum te commonefaciendum e&longs;&longs;e cen&longs;eo. </s>
<s>Qu&ograve;d &longs;cilicet gr&aelig;cum Hero&shy;<lb/>nis exemplar, quod in latinum &longs;ermonem conuertimus, illud est quod Bo&shy;<lb/>noni&aelig; in Bibliotheca S. </s>
<s>Saluatoris reperitur. </s>
<s>Nullum autem aliud gr&aelig;&shy;<lb/>cum exemplar vidimus: &longs;ed po&longs;tquam illud &agrave; nobis latinitate donatum fuit, <lb/>ostendit nobis Magnificus D. </s>
<s>Bernardinus Lauredanus in Bibliotheca Di&shy;<lb/>ui Marci Venetiarum quandam etiam aliam tralationem operis de Ma&shy;<lb/>chinis bellicis &agrave; quod am Ioanne Sophiano factam, quam Cardinali Be&longs;&longs;a&shy;<lb/>rioni &longs;ua quadam epistola cum dedica&longs;&longs;et a&longs;&longs;erit &longs;e ne&longs;cire cuius Autoris <lb/>illud opus &longs;it, quandoquidem titulo carebat. </s>
<s>ver&ugrave;m iam dicta tralatio &agrave; <lb/>no&longs;tra longe diuer&longs;a est propter multos defectus, <expan abbr="locos&qacute;ue">locosque</expan> deprauatos, <lb/>atque mendo&longs;os exemplaris gr&ecedil;ci, quod ip&longs;e habuerat. </s>
<s>in ip&longs;a ver&ograve; So&shy;<lb/>phiani tralatione non e&longs;t &longs;ecundum opus de Geod&ecedil;&longs;ia, &longs;ed primum tant&ugrave;m <lb/>de Machinis bellicis. </s>
<s>Postrem&ograve; animaduertas velim qu&ograve;d in vnoquoque <lb/>meorum &longs;choliorum nomen meum a&longs;criptum reperies, exceptis illis in &longs;cho&shy;<lb/>lijs, qu&ecedil; mea non &longs;unt, &longs;ed ab antiquo manu&longs;cripto gr&ecedil;co libro tralata. </s>
<s><lb/>hoc autem hac ratione factum e&longs;t, vt mea &longs;cholia ab alienis &longs;ecernantur.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/007.jpg"/><p type="table">
<s>TABELLE WAR HIER</s></p>
<pb xlink:href="052/01/008.jpg"/>
<pb xlink:href="052/01/009.jpg"/><figure id="id.052.01.009.1.jpg" xlink:href="052/01/009/1.jpg"/><p type="main">
<s><emph type="center"/>PROEMIVM.<emph.end type="center"/></s></p><p type="main">
<s>QVAECVNQVE quidem ob&longs;idionalium <lb/>Machinarum difficiles, atque incompre<lb/>hen&longs;ibiles e&longs;&longs;e videntur, hoc eis natura <lb/>comparatum e&longs;t, aut propter earum de&shy;<lb/>&longs;criptionis varietatem, ac difficilem co&shy;<lb/>gnitionem, aut propterea qu&ograve;d earum <lb/>con&longs;iderationes captu difficiles, atque <lb/>(vt ita potius dicam) multis incompre&shy;<lb/>hen&longs;ibiles &longs;unt: for&longs;an autem ignoran&shy;<lb/>tia &longs;ola comprehen&longs;&aelig;, ita vt ne quidem ab ip&longs;a figurarum po&shy;<lb/>&longs;itione dilluciditatem, ac facilem apprehen&longs;ionem po&longs;&longs;ideant: <lb/>quippe c&ugrave;m non omnibus prompt&aelig;, <expan abbr="cognit&aelig;&qacute;ue">cognit&aelig;que</expan> &longs;int, neque <lb/>etiam ad con&longs;tructionem, &amp; fabricationem expedit&aelig;: &longs;olis ve<lb/>r&ograve; ip&longs;ismet <expan abbr="inu&etilde;toribus">inuentoribus</expan>, &amp; &longs;criptoribus Mechanicis ad earum </s></p><p type="main">
<s><arrow.to.target n="note1"/><lb/>explanationem, <expan abbr="dillucidationem&qacute;ue">dillucidationemque</expan> indigentes. </s>
<s>quemadmo<lb/>dum e&aelig;, qu&aelig; ab Apollodoro ad Adrianum Imperatorem ob&shy;<lb/>&longs;idionales machin&aelig; con&longs;truct&aelig; fuerunt: &amp; ea qu&aelig; ab Athe&shy;<lb/>n&aelig;o ad Marcellum ex Angi&longs;i&longs;trati, &amp; aliorum &longs;apientum com<lb/>po&longs;itionibus ad ob&longs;idionem expo&longs;ita &longs;unt commentaria: nec <lb/>non qu&aelig; &agrave; Bitone ad Attalum de con&longs;tructione bellicorum <lb/>in&longs;trumentorum ex diuer&longs;is antiquioribus Mechanicis colle&shy;<lb/>cta fuere iaculatoria: pr&ecedil;terea qu&aelig; ad ob&longs;idionem contra mo<lb/>liuntur tum cu&longs;todientia, tum etiam hominum con&longs;eruationi <lb/>de&longs;&longs;eruientia, ac demum ad ianuarum con&longs;titutionem <expan abbr="expu-gnationem&qacute;">expu&shy;<lb/>gnationemque</expan>; varia pr&aelig;cepta. </s>
<s>H&aelig;c qu&ugrave;m in pr&aelig;&longs;entia multis <lb/>in&longs;olita penitus, <expan abbr="cognitu&qacute;ue">cognituque</expan> difficilia propter pr&aelig;teritam cur&shy;<lb/>riculo temporis obliuionem, quin etiam &longs;cientiarum nomina <lb/>communibus &longs;ermonibus inu&longs;itata &longs;int: non vtique iuxta ve-<pb xlink:href="052/01/010.jpg"/>terem ab ip&longs;is uiris con&longs;tructam, uniuer&longs;alem, <expan abbr="artificio&longs;am-&qacute;ue">artificio&longs;am&shy;<lb/>que</expan> orationem in pr&aelig;&longs;enti libro in ordinem redigere con&longs;en<lb/>taneum e&longs;&longs;e duximus. </s>
<s>ne dum ea, qu&aelig; in ip&longs;is apparet ob&longs;cu<lb/>ritas animum ad &longs;e ip&longs;am retrahit, circa etiam dillucidorum <lb/>cognitionem <expan abbr="qui&longs;pi&atilde;">qui&longs;piam</expan> defatigetur. </s>
<s>Sola uero ea, qu&aelig; ab Apol<lb/>lodoro tradita fuerant, quippe qu&aelig; finem uer&longs;us declaraui&shy;<lb/>mus, culturis, <expan abbr="con&longs;equentibus&qacute;ue">con&longs;equentibusque</expan> enthymematibus conclu<lb/>&longs;imus. </s>
<s>c&ugrave;m nos etiam quam plurima con&longs;ona adinueneri&shy;<lb/>mus, &amp; appo&longs;uerimus. </s>
<s>qu&aelig;cunque autem &agrave; reliquis &longs;par&longs;im <lb/>collegimus cognitu, ad <expan abbr="ueram&qacute;ne">ueramque</expan> intelligentiam captu faci&shy;<lb/>lia, communis <expan abbr="&longs;ent&etilde;ti&aelig;">&longs;ententi&aelig;</expan> pronuntiata &longs;ecundum Anthemium <lb/>exi&longs;tentia, <expan abbr="qu&aelig;&qacute;ue">qu&aelig;que</expan> &longs;olo problemate, ac &longs;ola configuratione <lb/>percipi po&longs;&longs;unt, c&ugrave;m nulla doctrina, uel interpretatione indi<lb/>geant: dictionum proprietate, <expan abbr="&longs;ermonis&qacute;ue">&longs;ermonisque</expan> &longs;implicitate &agrave; no<lb/>bis ip&longs;a quoque in maiorem facilitatem tran&longs;mutata, ita ut <lb/>&agrave; quibu&longs;cunque fabricari, con&longs;truique facil&egrave; po&longs;&longs;int: ijs, qu&ecedil; <lb/>ab Apollodoro inuenta fuerant c&ugrave;m contexerimus, <expan abbr="atq;">atque</expan> vn&agrave; <lb/>cum figuris exact&egrave; de&longs;ignauerimus, in ordinem redegimus. </s>
<s><lb/>quandoquidem cognouimus qu&ograve;d &longs;ola etiam configuratio <lb/>bene de&longs;ignata pote&longs;t id, quod circa con&longs;tructionem <expan abbr="ob&longs;cur&utilde;">ob&longs;curum</expan> <arrow.to.target n="note2"/><lb/>e&longs;t, &amp; inexplicabile, per&longs;picuum efficere. </s>
<s>Verumenimuero <lb/>ad ob&longs;idionem quidem Machinis, ac varijs, <expan abbr="diuer&longs;arum&qacute;ue">diuer&longs;arumque</expan> <lb/>figurarum Te&longs;tudinibus opus e&longs;t. </s>
<s>verbi gratia fo&longs;&longs;orijs, ag&shy;<lb/>geribus, arietes ge&longs;tantibus, pr&aelig;cur&longs;orijs, ac demum ijs, qu&ecedil; <lb/>nunc ex in&longs;ertione adinuent&aelig; &longs;unt leui&longs;&longs;imis parmis: ad ea <lb/>uer&ograve;, qu&aelig; deuoluuntur pondera, cuneatim con&longs;tipatis cu&shy;<lb/>&longs;todientibus Machinis: Te&longs;tudinibus cratibus uimineis con<lb/>textis: necnon ligneis tribulis quinque cubitorum men&longs;ura <lb/>pr&aelig;ditis: Arietibus tum compo&longs;itis, tum etiam unico ligno <lb/>con&longs;tantibus: turribus ligneis ferri idoneis, <expan abbr="paratu&qacute;ue">paratuque</expan> fa&shy;<lb/>cilibus; Scalis tum compo&longs;itis c&ugrave;m leui&longs;&longs;imis: id genus formis <lb/>uarijs. </s>
<s>Rur&longs;us h&aelig;c omnia nobis nece&longs;&longs;aria &longs;unt. </s>
<s>nempe pr&ecedil;&shy;<lb/>munitio adarcendum c&ugrave;m ea, qu&aelig; in &longs;ublimi inferuntur pon<lb/>dera, c&ugrave;m ea, qu&aelig; &agrave; tormentis ad iaculandum ignem factis, <lb/>accenduntur: &longs;pectator ad in&longs;piciendum ea, qu&aelig; intra ciui&shy;<lb/>tatem &longs;unt: vari&aelig; murorum diuer&longs;orum perforationes: &longs;cal&ecedil; <lb/>nautic&aelig; ad cuiu&longs;cunque generis fo&longs;&longs;as tran&longs;eundas perui&aelig;:
<pb xlink:href="052/01/011.jpg"/>Machin&aelig;, qu&aelig; &longs;ine &longs;calis muros in&longs;cendunt: ob&longs;idionales <lb/>Machin&aelig; ad ob&longs;idendum maritimas ciuitates, quippe qu&aelig; <lb/>collabi minim&egrave; po&longs;&longs;int: ac denique copio&longs;&aelig; multarum turba<lb/>rum ordinatim per flumina traiectiones. </s>
<s>H&aelig;c omnia porr&ograve; <lb/>iuxta pr&iacute;&longs;corum Architectorum doctrinam con&longs;truenda &longs;unt <lb/>paratu facilia quo ad materiam, uaria quo ad figuras, parui&longs;&shy;<lb/>&longs;ima quo ad men&longs;uras, leuia quo ad pondera, quippe qu&aelig; &agrave; <lb/>quibu&longs;cunque Artificibus cit&ograve; fieri po&longs;&longs;int, erectu facilia, in&shy;<lb/>&longs;idiatu difficilia, tran&longs;latu facilia, &longs;tabilia, fractu difficilia, ac <lb/>tandem eiu&longs;modi &longs;int, ut quatenus nece&longs;&longs;itas po&longs;tulauerit fa&shy;<lb/>cil&egrave; componi, <expan abbr="facile&qacute;ue">facileque</expan> di&longs;&longs;olui po&longs;&longs;int. </s>
<s>H&aelig;c autem omnia <lb/>quandoquidem militarem &longs;cientiam quo ad ob&longs;idionem faci<lb/>l&egrave; in&longs;tituunt, in pr&aelig;&longs;enti libello quo ad con&longs;tructionem, &amp; <lb/>v&longs;um pertinent deinceps progredientes ordinatim <expan abbr="per&longs;crib&etilde;do">per&longs;criben<lb/>do</expan> <arrow.to.target n="note3"/> expo&longs;uimus. </s>
<s>At &longs;iquis forta&longs;&longs;e dictionum ad unguem ex&shy;<lb/>plorator compo&longs;itionem Atticam, uel orationis grauitatem, <lb/>&amp; pulchritudinem, atque concentum, necnon figurarum ac <lb/>numeri uenu&longs;tatem per&longs;crutans, deruditate, ac negligentia <lb/>nos reprehendat: Antiquos &longs;apientes audiat dicentes, qu&ograve;d <lb/>c&ugrave;m omnis de ob&longs;idione &longs;ermo facilis, crebris eiu&longs;dem ora&shy;<lb/>tionis repetitionibus, ac re&longs;umptionibus, &amp; con&longs;equentibus <lb/>enthymematibus ad cogitationum, <expan abbr="operationum&qacute;ue">operationumque</expan> perce&shy;<lb/><arrow.to.target n="note4"/>ptionem, fiat: &agrave; Dialecticis utique pr&aelig;ceptis, aut horum <expan abbr="c&otilde;uer&longs;is">con<lb/>uer&longs;is</expan> alienus exi&longs;tit. </s>
<s>Sciat autem qu&ograve;d magnus etiam Ploti&shy;<lb/>nus (ut ait &longs;apienti&longs;&longs;imus Porphyrius) nec literas pulchr&egrave; for <lb/>mans, neque &longs;yllabas per&longs;picu&egrave; diuidens, <expan abbr="nullam&qacute;ue">nullamque</expan> rect&egrave; <lb/>&longs;cribendi artis curam gerens: &longs;ed &longs;ol&ugrave;m menti, <expan abbr="rebus&qacute;ue">rebusque</expan> ip&shy;<lb/>&longs;is incumbens, &longs;cribebat. </s>
<s>nam ea, qu&aelig; &longs;unt tripliciter &longs;ub&longs;i&shy;<lb/>&longs;tere &longs;tatuebat, c&ugrave;m in uocibus, tum animi conceptibus, tum <lb/>demum rebus: atque eum quidem, qui circa uoces errat, <expan abbr="n&otilde;">non</expan> <lb/>e&longs;&longs;e impugnandum, quoniam mentis conceptum, aut rem <lb/>ip&longs;am nullo pacto l&aelig;dit: eum uer&ograve;, qui circa mentis <expan abbr="c&otilde;ceptus">conceptus</expan> <lb/>peccat, amar&egrave; redarguendum, quia de vocibus ignoranter <lb/>loquitur: mult&ograve; magis autem eum, qui circa res ip&longs;as obc&ecedil;ca&shy;<lb/>tur, condemnandum, propterea qu&ograve;d &longs;tolidus, ac fal&longs;us de&shy;<lb/>&longs;criptor exi&longs;tit, c&ugrave;m in eam, qu&aelig; &longs;ecundum di&longs;po&longs;itionem <lb/>e&longs;t ignorantiam incidat. </s>
<s>quippe quam duplicem Plato uo-<pb xlink:href="052/01/012.jpg"/>cat, e&ograve; qu&ograve;d no&longs;cit quidem qu&ograve;d &longs;cit, ne&longs;cit <expan abbr="autem&qtail;">autemque</expan> igno&shy;<lb/>rat. </s>
<s>At Cali&longs;thenes etiam Hi&longs;toriographus &longs;ic inquit. </s>
<s>Opor<lb/>tet eum, qui aliquid &longs;cribere tentat, &agrave; per&longs;ona non aberrare, <lb/>&longs;ed &amp; &longs;ibi &amp; rebus ip&longs;is proprios doctrin&aelig; &longs;ermones propo&shy;<lb/>nere. </s>
<s>Hoc enim pacto qui&longs;piam de rebus utiliter uerba face&shy;<lb/>ret aut ex di&longs;cipulis Philolai, &amp; Ari&longs;totelis, &amp; I&longs;ocratis, &amp; <lb/>Ari&longs;tophanis, &amp; Apollonij, &amp; ijs, qui &longs;imilia illis con&longs;crip&longs;e&shy;<lb/>re. </s>
<s>nam iunioribus quidem addi&longs;cere cupientibus haud inu&shy;<lb/>tilia h&aelig;c ad habendam elementarem quandam in&longs;titutionem <lb/>uidebuntur: ijs uer&ograve;, qui uolunt tandem aliquid agere lon&shy;<lb/>g&egrave; pror&longs;us, &amp; ab operatrice contemplatione aliena erunt. </s>
<s>Vn<arrow.to.target n="note5"/><lb/>de Heron quoque Mathematicus animaduertens <expan abbr="Delphic&utilde;">Delphicum</expan> <lb/>illud pr&aelig;ceptum, quod nos admonet tempore parc&egrave; uti, <lb/>&amp; qu&ograve;d men&longs;uras temporis oportet agno&longs;cere, <expan abbr="t&atilde;quam">tanquam</expan> eius, <lb/>quod <expan abbr="int&etilde;pe&longs;tiuum">intempe&longs;tiuum</expan> exi&longs;tit: maximam, <expan abbr="ualde&qacute;ue">ualdeque</expan> nece&longs;&longs;ariam <lb/>conuer&longs;ationis in philo&longs;ophia partem, qu&aelig; etiam ad hanc u&longs;&shy;<lb/>que no&longs;tram &aelig;tatem qu&aelig;ritur, circa imperturbationes con&longs;i<lb/>&longs;tere cen&longs;ebat, &amp; nunquam per &longs;ermones finem habituram. </s>
<s><lb/>At Mechanica doctrina, qu&aelig; operationibus in &longs;ermones <expan abbr="tr&atilde;&longs;iit">tran<lb/>&longs;iit</expan>, omnes homines edocuit &longs;cire tranquillam ducere <expan abbr="uit&atilde;">uitam</expan>, <lb/>una ip&longs;ius parte, qu&aelig; circa artem iaculorum effectricem uer&shy;<lb/>&longs;ari dicitur. </s>
<s>Quapropter ut neque in pacifico &longs;tatu, <expan abbr="neq;">neque</expan> in&shy;<lb/>&longs;tante bello, uel in quocunque tempore ac &longs;tatu inimicorum; <lb/>uel ho&longs;tium ingre&longs;&longs;ibus perturbemur: un&agrave; cum ijs, qu&aelig; in <lb/>ob&longs;idionibus, &amp; exercitibus componuntur ualde nutrienti&shy;<lb/><arrow.to.target n="note6"/><lb/>bus, frugalibus Epimenideis uocatis medicamentis: necnon <lb/>parui&longs;&longs;imis cibis, gul&aelig; gratis, <expan abbr="&longs;itim&qacute;ue">&longs;itimque</expan> prohibentibus, de ia&shy;<lb/>culatorijs etiam in&longs;trumentis prouidentiam habemus. </s>
<s>Rur&shy;<lb/>&longs;us quoniam ij, qui res ad ob&longs;idionem uniuer&longs;ales &longs;ciunt, re&shy;<lb/>ct&egrave; etiam oppo&longs;itas norunt: oppo&longs;itorum autem una e&longs;t &longs;cien<lb/>tia: ij ergo, qui per Mechanicam, &amp; pr&aelig;paratricem artem, &amp; <lb/>frugalem diuturnum cibum, &amp; quamlibet communem in bo<lb/>na di&longs;po&longs;itione di&aelig;tam ob&longs;idionem con&longs;tituere, aut di&longs;&longs;ol&shy;<lb/>uere po&longs;&longs;unt, &longs;emper in tranquillitate degent. </s>
<s>Non ab re <lb/>igitur ad eos, qui de ciuitatibus &longs;cribunt, &amp; in non nece&longs;&longs;ariis <lb/>&longs;ermonibus tempus ab&longs;umunt florid&egrave; loquentes, uanis ora&shy;<lb/>tionibus res inanimatas exprimentes, &amp; animalia laudantes,
<pb xlink:href="052/01/013.jpg"/>uel uit&ugrave;perantes, haud inordinationem per enpha&longs;in <expan abbr="eor&utilde;">eorum</expan> <lb/>multiiug&aelig; di&longs;ciplin&aelig; qui&longs;piam dixi&longs;&longs;e uidebitur. </s>
<s>Nos autem <lb/>Gr&aelig;corum philo&longs;ophis non a&longs;&longs;imilabimur, apud quos de <lb/>paruis ac inutilibus rebus multi graues &longs;ermones impendun<lb/>tur. </s>
<s>nos etenim de maximis, <expan abbr="uit&aelig;&qacute;ue">uit&aelig;que</expan> utili&longs;&longs;imis rebus mini&shy;<lb/>ma, <expan abbr="&longs;implicia&qacute;ue">&longs;impliciaque</expan> (ut ab omnibus facil&egrave; memori&aelig; commen&shy;<lb/>dari po&longs;&longs;int) pr&aelig;cipere con&longs;ueuimus. </s></p><p type="margin">
<s><margin.target id="note1"/>a</s></p><p type="margin">
<s><margin.target id="note2"/>b.</s></p><p type="margin">
<s><margin.target id="note3"/>c.</s></p><p type="margin">
<s><margin.target id="note4"/>d.</s></p><p type="margin">
<s><margin.target id="note5"/>e</s></p><p type="margin">
<s><margin.target id="note6"/>f</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>OB&longs;idionales Machinas ab Apollodoro ad Adrianum Impera&shy;<lb/><arrow.to.target n="note7"/><lb/>torem con&longs;tructas: necnon ea, qu&aelig; ab Athen&aelig;o ad Marcelli <lb/>de ob&longs;idione &longs;cripta &longs;unt: ac demum ea, qu&aelig; &agrave; Bitone ad Atta&shy;<lb/>lum regem de con&longs;tructione bellicorum in&longs;trumentorum tradita fueri <lb/>iaculatoria commentaria, quorum Heron h&igrave;c meminit, po&longs;t pr&aelig;&longs;ens <lb/>eius opus nos edituri &longs;umus: vt qu&aelig; ab illis antiquioribus autoribus <lb/>Heron excerp&longs;erit, atque ampliauerit, qu&aelig;&queacute; de&longs;uo addiderit facil&egrave; <lb/>qui&longs;que videre po&szlig;it.<emph.end type="italics"/><lb/><arrow.to.target n="note8"/></s></p><p type="margin">
<s><margin.target id="note7"/>a</s></p><p type="margin">
<s><margin.target id="note8"/>b</s></p><p type="main">
<s><emph type="italics"/>Proponit cuncta ea, de quibus in pr&aelig;&longs;enti libro per tractaturus est <lb/>quemadmodum proprijs in locis nobis per&longs;picuum erit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note9"/></s></p><p type="margin">
<s><margin.target id="note9"/>c</s></p><p type="main">
<s><emph type="italics"/>Digreditur &longs;e excu&longs;ans de inornato &longs;ermone, quo in bellicarum ma<lb/>chinarum de&longs;criptione coact&egrave; u&longs;us e&longs;t: o&longs;tendens te&longs;timonijs antiquo<lb/>rum graui&szlig;imorum virorum elegantem &longs;ermonem pr&aelig;&longs;enti negoti <lb/>minim&egrave; conuenire.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note10"/></s></p><p type="margin">
<s><margin.target id="note10"/>d</s></p><p type="main">
<s><emph type="italics"/>Verbis illis [aut horum conuer&longs;is] intelligit Autor pr&aelig;cepta Rhet<lb/>rica. </s>
<s>nam (ut o&longs;tendit Ari&longs;toteles in principio primi libri Rhetorico <lb/>rum) Rhetorica e&longs;t Dialectic&aelig; conuer&longs;a. </s>
<s>quapropter pr&aelig;cepta quoque <lb/>Rhetorica pr&aelig;ceptis dialecticis conuer&longs;a &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note11"/></s></p><p type="margin">
<s><margin.target id="note11"/>e</s></p><p type="main">
<s><emph type="italics"/>Heron Mathematicus, de quo pr&aelig;&longs;ens alius Heron h&igrave;c mentionen <lb/>facit, e&longs;t ille Heron Alexandrinus Philo&longs;ophus, ac Mathematicus ce<lb/>leberrimus, qui &longs;crip&longs;it quatuor libros de aquaticis horologys, duos de <lb/>&longs;piritalibus. </s>
<s>&amp; unum de ijs, qu&aelig; per&longs;e mouentur. </s>
<s>quippe qui Deo an<lb/>nuente iamiam &agrave; nobis edentur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note12"/></s></p><p type="margin">
<s><margin.target id="note12"/>f</s></p><p type="main">
<s><emph type="italics"/>Epimenideum e&longs;t quoddam medicamentum valde nutriens, &longs;itim <lb/>prohibens, quo ue&longs;cebantur c&ugrave;m ij, qui ciuitates ob&longs;idebant, tum ij qui <lb/>in ciuitatibus ob&longs;idebantur. </s>
<s>Epimenideum autem dictam e&longs;t ab Epi<lb/>menidea Scylla in eius compo&longs;itionem ingrediente de qua herba uide <emph.end type="italics"/>
<pb xlink:href="052/01/014.jpg"/><emph type="italics"/>Theophra&longs;tum lib. </s>
<s>7. capit. </s>
<s>11. Hi&longs;tor. </s>
<s>Plant. </s>
<s>componebatur autem ab <lb/>antiquis hoc modo.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Decocta Sylla, &amp; aqua abluta, &amp; ex&longs;iccata, ac demum parui&szlig;imas <lb/>in partes di&longs;&longs;ecta. </s>
<s>&amp; po&longs;th&aelig;c in ip&longs;a &longs;e&longs;amo admi&longs;to quint&aelig; partis, pa&shy;<lb/>paueris autem quintedecim&aelig;, atque hi&longs;ce omnibus in ip&longs;o mele tan&shy;<lb/>quam optimo, ma&longs;&longs;am&queacute; agente mitigatis, totum diuidendum e&longs;t uelu&shy;<lb/>ti in maximas oliuas. </s>
<s>&amp; harum unam quidem circa horam <expan abbr="&longs;ec&utilde;dam">&longs;ecundam</expan>, <lb/><expan abbr="un&atilde;">unam</expan> uer&ograve; circa <expan abbr="hor&atilde;">horam</expan> <expan abbr="decim&atilde;">decimam</expan> <expan abbr="ab&longs;um&etilde;tes">ab&longs;umentes</expan>: <expan abbr="null&utilde;">nullum</expan> &agrave; fame <expan abbr="mal&utilde;">malum</expan> patientur.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Alia eiu&longs;dem Pharmaci compo&longs;itio, qu&aelig; fit hoc modo.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>SV&longs;cipientes &longs;e&longs;ami Attici &longs;emi&longs;extarium, &amp; melis  &longs;emi&longs;exta&shy;<lb/>rium, &amp; olei Cotilem, &amp; Ch&oelig;nicem amigdalarum dulcium decor&shy;<lb/>ticatarum ex&longs;iccando &longs;e&longs;amum, &amp; amigdalas molere &amp; uibrare opor<lb/>tet: deinde Scyllas <expan abbr="circ&utilde;circa">circumcirca</expan> <expan abbr="decortic&atilde;do">decorticando</expan>, et radices, ac folia <expan abbr="ab&longs;cind&etilde;do">ab&longs;cinden<lb/>do</expan>, &amp; in paruas partes <expan abbr="di&longs;&longs;ecc&atilde;do">di&longs;&longs;eccando</expan> <expan abbr="pon&etilde;tes">ponentes</expan> in mortario <expan abbr="c&otilde;tundere">contundere</expan> opus <lb/>e&longs;t donec maxim&egrave; leuigentur po&longs;th&aelig;c ver&ograve; <expan abbr="c&otilde;tu&longs;arum">contu&longs;arum</expan> Syllarum equa<lb/>lem meli partem &aelig;quabiliter vn&agrave; cum oleo &longs;ubigere, atque in ollam in <lb/>fundendo &amp; &longs;uper carbones imponendo coquere oportet. </s>
<s>C&ugrave;m autem <lb/>inceperint calefieri, &longs;e&longs;amum &amp; amigdalas interponendo &longs;imul ligno <lb/>hinc inde permouenda &longs;unt, donec omnia imponantur. </s>
<s>C&ugrave;m ver&ograve; val&shy;<lb/>de &longs;olidum corpus factum fuerit, ip&longs;um accipientes in paruas buccel&shy;<lb/>las circiter diuidere oper&aelig; pretium e&longs;t. </s>
<s>atque vnam mane, unam&queacute; ve&shy;<lb/>&longs;peri qui&longs;piam ab&longs;umens, nutrimentum &longs;ufficiens habet. </s>
<s>Hoc autem <lb/>Pharmacum apud exercitus etiam optimum e&longs;t dulce enim exi&longs;tit, &amp; <lb/>&longs;aturitatem inuehens, &amp; &longs;itim non inducit.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Duplicem hanc pr&aelig;&longs;entis Pharmaci compo&longs;itionem ita de&longs;criptam <lb/>in quodam antiquo &longs;cholio in librum Heronis inuenimus; &amp; quoniam <lb/>ip&longs;e Heron eius mentionem habuit: <expan abbr="n&otilde;">non</expan> abrefactum iri exi&longs;timauimus, <lb/>vt illud qualecumque &longs;it de verbo ad uerbum in latinum &longs;ermonem <lb/>conuer&longs;um h&igrave;c apponeremus. </s>
<s>quippe quod an <expan abbr="bon&utilde;">bonum</expan>, an malum &longs;it, per&shy;<lb/>&longs;picaci&szlig;imis Medicis iudicandum relinquimus. </s>
<s>Hanc <expan abbr="eand&etilde;">eandem</expan> ver&ograve; du&shy;<lb/>plicem huiu&longs;ce Pharmaci compo&longs;itionem vide etiam apud Philonem <lb/>Athenien&longs;em in quinto libro &longs;u&aelig; de re bellica tractationis, ubi ip&longs;e <lb/>multa etiam alia Pharmaca ad hanc rem &longs;pectantia ponit. </s>
<s>ex quo loco <lb/>Heron quoque ha&longs;ce duas Epimenidei Pharmaci compo&longs;itiones ex&shy;<lb/>cerp&longs;i&longs;&longs;e videtur.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/015.jpg"/><p type="main">
<s><emph type="center"/>DE CIVITATVM OBSIDIONE<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>TVM IN ALTIS COLLIBVS, <lb/>TVM INPLANO IACENTIVM:<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>ET DE MACHINIS ATQVE INSTRVMENTIS <lb/>huic ob&longs;idioni nece&longs;&longs;arijs. </s>
<s>Caput primum.<emph.end type="center"/></s></p><p type="main">
<s>PRINCIPEM rei militaris periti&longs;&longs;imum, &agrave; <lb/>&longs;uperna prouidentia in pietate con&longs;er&shy;<lb/>uatum: iu&longs;&longs;ui, ac &longs;ententi&aelig;, <expan abbr="bono&qacute;ue">bonoque</expan> con&shy;<lb/>&longs;ilio eorum, qui &longs;umma in autoritate, <lb/><expan abbr="pote&longs;tate&qacute;ue">pote&longs;tateque</expan> con&longs;tituti &longs;unt religio&longs;i&longs;&longs;i&shy;<lb/>morum ob&longs;equentem: necnon ho&longs;tes, &amp; <lb/>apo&longs;tatas ob&longs;e&longs;&longs;urum: ciuitatum &longs;itus ac&shy;<lb/>currat&egrave; peragrando pri&ugrave;s ob&longs;eruare, <expan abbr="atq;">atque</expan> <lb/>ante omnia proprij populi cu&longs;todiam ab <lb/><expan abbr="o&itilde;">omni</expan> periculo immunem faciendo ob&longs;idionis <expan abbr="initi&utilde;">initium</expan> &longs;umere opor<lb/>tet ad alios quidem locos ca&longs;tris pugnaturum &longs;e indicando, ut <lb/>illic inimici decepti pr&aelig;parentur, atque ad alios machinas ad&shy;<lb/>ducendo: ip&longs;am ver&ograve; irruptionem ad imbeciliores murorum <lb/>partes per uici&longs;&longs;itudinem, <expan abbr="continuationem&qacute;ue">continuationemque</expan> militarium or&shy;<lb/>dinum faciendo: mult&ograve; cum &longs;trepitu eos, qui intra ciuitatem <lb/>&longs;unt, huc illuc di&longs;cerpendo: &amp; tubas noctu ad tutiores partes <lb/>&longs;onando, ut quamplurimi <expan abbr="put&atilde;tes">putantes</expan> ha&longs;ce expugnari ab eis, qu&aelig; <lb/>inter turres &longs;unt &longs;patijs vn&agrave; cum alijs effugiant. </s>
<s>At &longs;i in altis <lb/>quidem collibus, aut imperuijs pr&aelig;cipitijs ciuitates Sit&aelig; fue&shy;<lb/>rint, ea, qu&aelig; de&longs;uper &agrave; contrarijs deuoluuntur pondera &longs;um&shy;<lb/>ma cum ob&longs;eruatione euitanda &longs;unt. </s>
<s>vt lapides rotundi, colum <lb/>n&aelig;, rot&aelig;, uerticuli, currus quatuor rotarum ponderibus one&shy;<lb/>rati, ua&longs;a textilia uaria calculorum, aut terr&aelig; madefact&aelig; plena, <lb/>cuiu&longs;modi &longs;unt ea, qu&aelig; ex a&longs;&longs;eribus circulariter compo&longs;ita, <expan abbr="li-gaminibus&qacute;ue">li&shy;<lb/>gaminibusque</expan> extrin&longs;ecus <expan abbr="circumquaq;">circumquaque</expan> percincta &longs;unt, quip&shy;<lb/>pe qu&aelig; ad &longs;u&longs;cipiendum uinum, &amp; oleum, &amp; quemcunque li&shy;<lb/>quorem fiunt: &amp; quotcunque alia ad defen&longs;ionem &agrave; contrariis <lb/>excogitari contingit. </s>
<s>Aduer&longs;us h&aelig;c autem repugnantes muri&shy;<arrow.to.target n="note13"/><lb/>ces ligneos con&longs;truere oportet <expan abbr="quinq;">quinque</expan> cubitorum Labdareos
<pb xlink:href="052/01/016.jpg"/>&agrave; quibu&longs;dam vocatos, quorum vnumquodque crus gyrum <lb/>qua&longs;i duorum pedum habeat, ne frangantur, uel <expan abbr="di&longs;r&utilde;pantur">di&longs;rumpantur</expan>: <lb/>&longs;ed re&longs;i&longs;tant ponderibus, qu&aelig; deor&longs;um feruntur. </s>
<s>Sufficientes <lb/>autem multitudine ip&longs;i con&longs;truendi &longs;unt, ut triplicata, aut <expan abbr="eti&atilde;">etiam</expan> <lb/>quadruplicata horum po&longs;itio fiat. </s>
<s>ita enim <expan abbr="locor&utilde;">locorum</expan> partes a&longs;cen<lb/>&longs;u difficiles, &amp; arduas circummuniendo fieri pote&longs;t ut (excepta <lb/>&longs;agitta) &longs;ine periculo a&longs;cendatur. </s>
<s>nam lapidum <expan abbr="vehem&etilde;s">vehemens</expan> deor&shy;<lb/>&longs;um latio in muricum conuer&longs;ione offendens, quie&longs;cet. </s>
<s>Po&longs;&longs;u&shy;<lb/>mus autem alio quoque modo l&aelig;&longs;ionem ex ijs, qu&aelig; deor&longs;um <lb/>feruntur prouenientem euitare. </s>
<s>ab ip&longs;o enim <expan abbr="m&otilde;tis">montis</expan> pede deor<lb/>&longs;um incipientes laterales fo&longs;&longs;as fodere, &amp; ad qua&longs;dam <expan abbr="muror&utilde;">murorum</expan> <lb/>partes pro&longs;picere, atque a&longs;cendere opus e&longs;t. </s>
<s>qu&aelig; quidem fo&longs;&longs;&aelig; <lb/>profunditatem quinque pedum circiter habeant, necnon mu&shy;<lb/>rum unum erectum ab eadem fo&longs;&longs;a ad partes &longs;ini&longs;tras exi&longs;ten&shy;<lb/>tem, ad quem deferantur pondera, qu&aelig; deuoluuntur: quique <lb/>propugnaculum, &amp; &longs;cutum a&longs;cendentium fiat. </s>
<s>Locus autem <lb/>pr&aelig;effo&longs;&longs;us, &longs;ic ab effodientibus muniendus e&longs;t. </s>
<s>Ligna qua&longs;i <lb/>&longs;ex cubitorum, uel nuper acuta, uel in parte inferiori acuta fa&shy;<lb/>cientes <expan abbr="t&atilde;quam">tanquam</expan> palos ad murum ab agge&longs;ta terra ad partes &longs;i&shy;<lb/>ni&longs;tras iam erectum tractum ad re&longs;i&longs;tendum infigere oportet. </s>
<s><lb/>quippe qu&aelig; obliquentur uer&longs;us deor&longs;um ferentem collis decli<lb/>nationem. </s>
<s>necnon tabul&aelig; &longs;uper ip&longs;is extrin&longs;ec&ugrave;s apponend&aelig;, <lb/>&amp; arborum rami complectentes circumligandi &longs;unt, ac <expan abbr="dem&utilde;">demum</expan> <lb/>omnem effo&longs;&longs;am materiam illuc proiiciendo ui&aelig; rect&aelig; ad te&shy;<lb/>&longs;tudinum a&longs;cen&longs;ionem &aelig;quand&aelig; &longs;unt. </s>
<s>eas autem, qu&aelig; addu&shy;<lb/>cunt te&longs;tudines ro&longs;tratas iuxta <expan abbr="faci&etilde;">faciem</expan>, hoc e&longs;t cuncatas, ex trian&shy;<lb/>gularibus, aut quinquangularibus ba&longs;ibus con&longs;titutas: in acu&shy;<lb/>tum in anteriori parte angulum terminantes: ab inferiori ver&ograve; <lb/>latitudine ad altitudinem eleuatas: &amp; u&longs;que ad verticalem dor<lb/>&longs;um in acutum procedentes: nauium terram ver&longs;us re&longs;picien&shy;<lb/>tium proris anteri&ugrave;s a&longs;&longs;imilatas fieri oportet. </s>
<s>paruas pr&ecedil;terea, <lb/>&amp; quam plures ip&longs;as e&longs;&longs;e opus e&longs;t, vt cit&ograve; <expan abbr="facile&qacute;ue">facileque</expan> con&longs;trui, &agrave; <lb/><expan abbr="paucis&qacute;ue">paucisque</expan> viris ab&longs;que labore ferri po&longs;&longs;int: leuia ligna pedalia <lb/>circa ba&longs;im habentes, &amp; loco rotarum clauos ferreos, vt dum <lb/>in terra ponuntur ip&longs;i affingantur, &amp; ab impetu non <expan abbr="di&longs;trah&atilde;-tur">di&longs;trahan&shy;<lb/>tur</expan>: necnon obliquum lignum earum vnaqu&aelig;que iuxta fron&shy;<lb/>tem habere debet (quemadmodum in temonibus currus ha-<pb xlink:href="052/01/017.jpg"/>bent) vt eam ad imas partes &longs;ubuertentem retineat, atque <lb/>&longs;uffulciat, &amp; pr&aelig;&longs;ertim c&ugrave;m eam &longs;ur&longs;um ferrentes defatigati <lb/>fuerint, ac paululum quie&longs;cere debuerint. </s>
<s>Eueniet itaque <lb/>aut fo&longs;&longs;&aelig; laterali exi&longs;tenti incidentia <expan abbr="p&otilde;dera">pondera</expan> perperam pr&ecedil;&shy;<lb/>teruehi: aut obliquos palos lateralem &longs;itum habentes in cu&shy;<lb/>tientia, percuti: aut in ro&longs;tris machinum offendentia in alte&shy;<lb/>ram partem pr&aelig;terire, intermedium uer&ograve; locum liberari. </s>
<s><lb/>Melius autem e&longs;t te&longs;tudines etiam cratis vimineis contextas <lb/>leuiores iam dictis ro&longs;tratis, &amp; conformes exi&longs;tentes addu&shy;<lb/>cere. </s>
<s>quippe qu&aelig; ex in&longs;ertione &longs;alignarum virgarum rec&egrave;ns <lb/>inci&longs;arum, aut ex myrica, uel Tilia con&longs;truuntur, acut&aelig; ip&longs;&aelig; <lb/>quoque iuxta faciem v&longs;que ad verticalem dor&longs;um exi&longs;ten&shy;<lb/>tes. </s>
<s>eas ver&ograve;, qu&aelig; parm&aelig; vocantur, leui&longs;&longs;imas exi&longs;tentes, ex <lb/>contextu ip&longs;as quoque vinealium uitium, vel nuper c&aelig;&longs;a&shy;<lb/>rum virgarum in figura conuer&longs;ionali quam celerrim&egrave; fa&shy;<lb/>ctas non e&longs;t opus ad decliues, ac pr&aelig;cipites locos afferre. </s>
<s>ne <lb/>fort&egrave; ferentibus pernitiem inferant, quandoquidem <expan abbr="imm&etilde;-&longs;is">immen&shy;<lb/>&longs;is</expan> ponderibus re&longs;i&longs;tere nequeunt. </s>
<s>ip&longs;is autem poti&ugrave;s uten&shy;<lb/>dum e&longs;t c&ugrave;m in planis, <expan abbr="enodis&qacute;">enodisque</expan>; locis ciuitates &longs;it&aelig; fuerint. </s>
<s><lb/>tunc enim eis vti commod&egrave; po&longs;&longs;umus. </s>
<s>Ver&ugrave;m populus, qui <lb/>ad ca&longs;trorum pugnam a&longs;cendit, ad latitudines ro&longs;tratarum <lb/>machinarum cu&longs;toditus, uel po&longs;t te&longs;tudines, &amp; te&longs;tudinibus <lb/><arrow.to.target n="note14"/><lb/>vineis vocatis coopertus &longs;equetur, propter &longs;agittas, <expan abbr="funda-rum&qacute;ue">funda&shy;<lb/>rumque</expan> iactationes. </s>
<s>At ligna te&longs;tudinis, qu&aelig; milites ferunt <lb/>huiu&longs;cemodi &longs;unt. </s>
<s>erecta &longs;cilicet in altitudinem, in&aelig;qualia, <lb/>&longs;ingula cra&longs;&longs;itiem circumquaque circiter duodecim digito&shy;<lb/>rum habentia, iuxta ver&ograve; quinque pedes ad altera latera in&shy;<lb/>directum connexa, vt ip&longs;um quinque pedum ad &longs;e inuicem <lb/>interuallum &longs;eruetur. </s>
<s>atque eorum altiora quidem &longs;upra vi&shy;<lb/>ri &longs;taturam vnam, &amp; dimidiam: depre&longs;&longs;iora ver&ograve;, &longs;upra <expan abbr="vir&utilde;">virum</expan> <lb/>&longs;int: de&longs;uper autem cooperta propter in&ecedil;qualitatem &longs;ur&longs;um <lb/>currentibus a&longs;&longs;imilantur. </s>
<s>&longs;patium ver&ograve;, quod e&longs;t &agrave; vertice <lb/>ro&longs;trat&aelig; machin&aelig; v&longs;que ad cooperta in&aelig;qualia ligna in fi&shy;<lb/>gura &longs;imul intus apparebit. </s>
<s>Rur&longs;us ligna, qu&aelig; &agrave; militibus fe<lb/>runtur, inferi&ugrave;s ueluti cu&longs;pides habeant, vt terr&aelig; affixa, por&shy;<lb/>tantes refocillent. </s>
<s>coria ver&ograve; carno&longs;a, cra&longs;&longs;a, uel cilicina ex&shy;<lb/>teri&ugrave;s iuxta faciem <expan abbr="&longs;u&longs;p&etilde;duntur">&longs;u&longs;penduntur</expan>. </s>
<s>in ip&longs;is autem in&aelig;qualibus
<pb xlink:href="052/01/018.jpg"/>lignis c&ograve;ria duplicata &longs;uperponantur, non exten&longs;a ad eno&shy;<lb/>dam, &amp; &aelig;qualem &longs;uperficiem, &longs;ed paululum <expan abbr="c&otilde;tracta">contracta</expan>, in <expan abbr="ip-&longs;is&qacute;ue">ip&shy;<lb/>&longs;isque</expan> lignis in&aelig;qualibus depre&longs;&longs;a: vt in horum tumiditate <lb/>incidentes &longs;agitt&aelig;, debiles in percutiendo, <expan abbr="remi&longs;&longs;&aelig;&qacute;ue">remi&longs;&longs;&aelig;que</expan> &longs;int; <lb/>qui ver&ograve; intror&longs;um cooperiuntur, &agrave; l&aelig;&longs;ione immunes per&shy;<lb/><arrow.to.target n="note15"/>maneant. </s>
<s>Verumtamen &longs;i in planis, <expan abbr="enodis&qacute;ue">enodisque</expan> locis ciuita&shy;<lb/>tes &longs;it&aelig; &longs;int, oper&aelig; pretium e&longs;t aggeres te&longs;tudines rotis &longs;ur&shy;<lb/>repentes, atque in anteriori parte munitas adducere, ne ij, <lb/>qui fo&longs;&longs;as aggerant &agrave; <expan abbr="c&otilde;trarijs">contrarijs</expan> feriantur: aut iam dictas Par&shy;<lb/>mas vti leui&longs;simas, atque vtiles ad aggerandas fo&longs;&longs;as, <expan abbr="necn&otilde;">necnon</expan> <lb/>locos aquo&longs;os, ac madidos replendos, &amp; cuiu&longs;cunque gene&shy;<lb/>ris &longs;ci&longs;&longs;uras m&oelig;nijs proximas &aelig;quandas: vt machinarum <lb/>adductionem peruiam, ab <expan abbr="omni&qacute;ue">omnique</expan> periculo vacuam facia&shy;<lb/>mus. </s>
<s>Opus e&longs;t autem nos accurat&egrave; pro&longs;picientes in ue&longs;tigare <lb/>eas, qu&aelig; in fo&longs;&longs;is ip&longs;is apparent complanat&aelig; traiectiones, <lb/>propter fictiles tegulas, qu&aelig; &longs;&aelig;penumero &longs;ubter &agrave; contra&shy;<lb/>riis ab&longs;conduntur: vt c&aelig;lis quidem via meatu facilis, peri&shy;<lb/>culoque carens appareat, ip&longs;a ver&ograve;, qu&aelig; adducuntur in&longs;tru&shy;<lb/>menta c&ugrave;m admodum graui&longs;&longs;ima &longs;int, in ip&longs;a porr&ograve; &longs;ubie&shy;<lb/>ctarum tegularum fractione, <expan abbr="progre&longs;sione&qacute;ue">progre&longs;sioneque</expan> &longs;ubeant, <expan abbr="atq;">atque</expan> <lb/>dirumpantur. </s>
<s>Quapropter oportet nos cum ha&longs;tis acuta &longs;pi<lb/>cula, fortiaque habentibus, aut quibu&longs;dam idoneis terebris <lb/><arrow.to.target n="note16"/><lb/>periculum facere: aduer&longs;us ver&ograve; ferreos murices ab inimi&shy;<lb/>cis di&longs;&longs;eminatos, terr&aelig; admi&longs;tos, atque latentes lignea &longs;up&shy;<lb/>po&longs;itoria ad pedes &longs;ub &longs;oleis &longs;upponentes innocu&egrave; permea&shy;<lb/>re: &longs;eu georgicis pectinibus (quos c&ugrave;m &longs;int dentibus pr&aelig;di&shy;<lb/>ti, Ra&longs;tros etiam quidam appellant) eos repurgare: ac de&shy;<lb/>nique circa eas, qu&aelig; in foueis ponuntur ianuas periculum <lb/>pri&ugrave;s facientes ligonibus effodire. </s>
<s>Oper&aelig;pretium e&longs;t autem <lb/>eos etiam, qui &longs;ub terra prope murum aguntur cuniculos, <lb/>occultos, <expan abbr="profundos&qacute;ue">profundosque</expan> iuxta fundamenta, &amp; non in terr&aelig; <lb/>faciem fieri: ne c&ugrave;m hoc ho&longs;tes deprehenderint, intus &egrave; di&shy;<lb/>uer&longs;o fodiant, <expan abbr="murum&qacute;ue">murumque</expan> ip&longs;um c&ugrave;m contra perforauerint, <lb/>eos, qui cuniculum agunt, fumo, &amp; aqua perimant. </s>
<s>Ver&ugrave;m <lb/>cuncta ea, qu&aelig; iam de&longs;cripta &longs;unt, vn&agrave; cum figuris ordina&shy;<lb/>tim &longs;ubiiciuntur. </s></p>
<pb xlink:href="052/01/019.jpg"/><p type="margin">
<s><margin.target id="note13"/>a.</s></p><p type="margin">
<s><margin.target id="note14"/>b</s></p><p type="margin">
<s><margin.target id="note15"/>c</s></p><p type="margin">
<s><margin.target id="note16"/>d</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note17"/></s></p><p type="margin">
<s><margin.target id="note17"/>a</s></p><p type="main">
<s><emph type="italics"/>LAbdareos hoc e&longs;t &longs;imiles liter&aelig; labda Grec&aelig;, qu&aelig; huiu&longs;ce <lb/>figur&aelig; e&longs;t. <foreign lang="greek">l.</foreign> &amp; quoniam vnu&longs;qui&longs;que ip&longs;orum ligneorum <lb/>Muricum duas in &longs;e labdas o&longs;tendit, non immerit&ograve; labda&shy;<lb/>rei vocabantur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note18"/></s></p><p type="margin">
<s><margin.target id="note18"/>b</s></p><p type="main">
<s><emph type="italics"/>Te&longs;tudines illas, qu&aelig; vine&aelig; dicuntur non de&longs;crip&longs;it autor, quem&shy;<lb/>admodum eas, qu&aelig; ro&longs;trat&aelig;: eas, qu&aelig; cratibus vimineis context&aelig; <lb/>&longs;unt: &amp; eas, qu&ecedil; Parm&ecedil; nuncupantur. </s>
<s>Sunt autem te&longs;tudines vine&ecedil; <lb/>ex lignis compactae, lat&ecedil; pedibus octo, alt&ecedil; &longs;eptem, long&ecedil; &longs;edecim, du&shy;<lb/>plici ligno tect&ecedil;, cratibus context&aelig;, latera vimine &longs;epta habentes <lb/>(ne &longs;axorum, ac telorum impetu perfringantur) crudis, ac recen&shy;<lb/>tibus corijs extrin&longs;ec&ugrave;s cooperta. </s>
<s>quas ideo <expan abbr="n&otilde;">non</expan> de&longs;crip&longs;it autor, quia <lb/>te&longs;tudinibus qu&aelig; &longs;unt vimine is cratibus context&aelig; &longs;imiles &longs;unt. </s></p><p type="main"><s><expan abbr="qu&etilde;-admodum">quem-<lb/>admodum</expan> etiam Aggeres non de&longs;crip&longs;it quoniam exceptis rotis a <lb/> ro&longs;tratis nil differunt. <emph type="italics"/><arrow.to.target n="note20"/></s></p><p type="margin">
<s><margin.target id="note19"/>c</s></p><p type="margin">
<s><margin.target id="note20"/>d</s></p><p type="main">
<s><emph type="italics"/>Tria Muricum genera &longs;unt, quibus in militia pri&longs;ci bellatores <lb/><expan abbr="vteb&atilde;tur">vtebantur</expan>: nempe lignei labdarei, &amp; ferrei &longs;uper terram di&longs;&longs;emina&shy;<lb/>ti, quorum autor in pr&aelig;&longs;enti capite mentionem facit: ac demum fer<lb/>rei ignem artificio&longs;um ferentes, qui mucronibus &longs;uis vbicunque <lb/>iactati fuerint affiguntur, &amp; flamma, quam ge&longs;tant, locum cui affi&shy;<lb/>xi &longs;unt, comburunt. </s>
<s>de quibus etiam ignem ferentibus muricibus <lb/>autor inferi&ugrave;s in capite. </s>
<s>14. verba facturus e&longs;t. </s>
<s>Ex his autem tribus <lb/>muricum generibus duo postrema, pr&aelig;&longs;ertim&queacute; tertium v&longs;que in <lb/>hodiernum diem in v&longs;u maxim&egrave; &longs;unt.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/020.jpg"/><figure id="id.052.01.020.1.jpg" xlink:href="052/01/020/1.jpg"/><p type="caption">
<s>CIVITAS IN ALTO COLLE IACENS</s></p>
<pb xlink:href="052/01/021.jpg"/><figure id="id.052.01.021.1.jpg" xlink:href="052/01/021/1.jpg"/><p type="caption">
<s>CIVITAS IN PLANO SITA</s></p>
<pb xlink:href="052/01/022.jpg"/><p type="main">
<s><emph type="center"/>DE SCALIS CORIACEIS, ET RETICV&shy;<lb/>LATIS CAPVT SECVNDVM.<emph.end type="center"/></s></p><p type="main">
<s>VERVM enimuero ciuitates ip&longs;as nullo negotio <lb/>expugnare uolentem iuxta Philonis <expan abbr="Atheni&etilde;-&longs;is">Athenien&shy;<lb/>&longs;is</expan> &longs;ententiam, oportet vindemia mirum in mo&shy;<lb/>dum exi&longs;tente, vel dum extra ciuitatem cele&shy;<lb/>britas agitur, numero&longs;am aggre&longs;&longs;ionem facere: <lb/>tunc etenim cum quamplurimos foris in &longs;uas manus ventu<lb/>ros, quos l&aelig;dere facil&egrave; pote&longs;t, uel ip&longs;i &longs;ubiectos, ac denique <lb/>ciuitatem ip&longs;am &agrave; reliquis habitatoribus propter amoris er&shy;<lb/>ga ip&longs;os affectum, <expan abbr="cognationem&qacute;">cognationemque</expan>; &longs;ibi deditam habere ne&shy;<lb/>ce&longs;&longs;e e&longs;t. </s>
<s>Si uer&ograve; furtim nocte ciuitatem capere volumus, ci&shy;<lb/>uibus aduentum no&longs;trum ignorantibus, <expan abbr="minime&qacute;ue">minimeque</expan> <expan abbr="&longs;per&atilde;-tibus">&longs;peran&shy;<lb/>tibus</expan>, hyeme pr&aelig;ueniente, quando frigoris cau&longs;a horum <lb/>maior pars in domos contrahitur, ad <expan abbr="bellum&qacute;ue">bellumque</expan> parati mi&shy;<lb/>nim&egrave; &longs;unt: aut quando celebrati&longs;&longs;imum fe&longs;tum in ciuitate <lb/>peragitur, &amp; populus in &longs;acrificio ludis vacat, vel ob ebrie&shy;<lb/>tatem &longs;omnolentus exi&longs;tit: &longs;calas coriaceas c&ugrave;m fecerimus, <lb/>muro eas applicabimus. </s>
<s>qu&aelig; quidem quemadmodum vt res <lb/>con&longs;uuntur, &amp; vnctione obturandi gratia circa con&longs;utiones <lb/>replentur ita ut non euaporent. </s>
<s>&longs;i namque inflentur, <expan abbr="&longs;piri-tu&qacute;ue">&longs;piri&shy;<lb/>tuque</expan> impleantur, eo qu&ograve;d euaporare non po&longs;&longs;unt, erigi <lb/>eas &agrave; &longs;piritu nece&longs;&longs;um e&longs;t, ad <expan abbr="a&longs;cen&longs;ionem&qacute;ue">a&longs;cen&longs;ionemque</expan> nobis &longs;uffi&shy;<lb/>ciunt. </s>
<s>Qu&ograve;d &longs;i altior &longs;calis ip&longs;is coriaceis murus exi&longs;tat, <lb/>alijs ip&longs;&aelig; &longs;tupeis &longs;calis ante &longs;ubijciuntur. </s>
<s>quippe qu&aelig; con&shy;<lb/>&longs;truuntur dum textura, &amp; con&longs;utione colligantur, reticula&shy;<lb/>t&aelig; exi&longs;tentes, eorum in&longs;tar, qu&aelig; verricula dicuntur. </s>
<s>ad ea&shy;<lb/>rum autem extremitates hami adiiciuntur, vt ab ip&longs;is iam <lb/>&longs;ubiectis coriaceis &longs;calis iniecti, murorum pinnas <expan abbr="appreh&etilde;-dant">apprehen&shy;<lb/>dant</expan>, atque ita &longs;uper murum a&longs;cen&longs;ionem uolentibus vn&agrave; <lb/>di&longs;ponant. </s>
<s>ip&longs;&aelig; ver&ograve; &longs;calarum figur&aelig; &longs;ub&longs;cript&aelig; &longs;unt. </s></p>
<pb xlink:href="052/01/023.jpg"/><figure id="id.052.01.023.1.jpg" xlink:href="052/01/023/1.jpg"/><p type="caption">
<s>Scala coriacea inflata</s></p><p type="main">
<s><emph type="center"/>De Te&longs;tudinibus fo&longs;&longs;oriis. </s>
<s>Caput Tertium.<emph.end type="center"/></s></p><p type="main">
<s>AT c&ugrave;m e&aelig;, qu&aelig; &longs;uperius dict&aelig; &longs;unt ro&longs;trat&aelig; <lb/>Machin&aelig;, vn&agrave; cum Te&longs;tudinibus vineis voca&shy;<lb/>tis prope murum aduenerint, varias tunc Te&shy;<lb/>&longs;tudines adducere oportet: alias quidem ad fo&shy;<lb/>diendum murum, alias ver&ograve; ad <expan abbr="oppugn&atilde;dum">oppugnandum</expan> <lb/>Arietibus. </s>
<s>ad fodiendum igitur eas, qu&aelig; fo&longs;&longs;ori&aelig; nuncu&shy;<lb/>pantur. </s>
<s>has autem vel dupliciter fluentes e&longs;&longs;e nece&longs;&longs;e e&longs;t, &amp; <lb/>in faciem coopertas adduci, <expan abbr="muro&qacute;ue">muroque</expan> appropinquari: vel <lb/>vnicam habentes alam, retro quidem decliues, in faciem <lb/>ver&ograve; quadrangulas, &agrave; <expan abbr="lateribus&qacute;">lateribusque</expan>; trapezio &longs;imiles, aut trian&shy;<lb/>gulas, quippe qu&aelig; hoc modo con&longs;truantur. </s>
<s>Ligna <expan abbr="&longs;u&longs;cipi&etilde;-tes">&longs;u&longs;cipien&shy;<lb/>tes</expan> tria, vel quatuor, quandoque autem &amp; quinque (vt &longs;pi&longs;&shy;<lb/>&longs;ius, <expan abbr="&longs;olidius&qacute;ue">&longs;olidiusque</expan> fiat opus) longitudinem habentia non mi-<pb xlink:href="052/01/024.jpg"/>norem pedum decem, cra&longs;&longs;itiem ver&ograve; qua&longs;i vnius pedis, &longs;i&shy;<lb/>militer autem &amp; latitudinem: h&aelig;c in &longs;uperiori parte obli&shy;<lb/>qu&egrave; ad vnguis &longs;imilitudinem ab&longs;cindere opus e&longs;t. </s>
<s>vt dum &agrave; <lb/>rotatis axibus adducuntur, &agrave; <expan abbr="rectis&qacute;ue">rectisque</expan> lignis intrin&longs;ec&ugrave;s &longs;u&shy;<lb/>&longs;tinentur, muro applicentur. </s>
<s>erigatur autem ad murum li&shy;<lb/>gnea columna ba&longs;in inferi&ugrave;s habens, qu&aelig; &amp; &longs;uperiacentia <lb/>ligna, &amp; &longs;uffulcientia erecta &longs;u&longs;tineat: vt ea, qu&aelig; de&longs;uper <lb/>deferuntur tecto minim&egrave; nocentia, retror&longs;um elabantur. </s>
<s>ip&shy;<lb/>&longs;a ver&ograve; erecta ligna, &amp; vnguis in&longs;tar ab&longs;ci&longs;&longs;a, &longs;picula ferrea <lb/>retror&longs;um habeant, vt terr&aelig; affigantur, &amp; non di&longs;trahan&shy;<lb/>tur. </s>
<s>ad latera autem &longs;u&longs;pendantur coria tegentia, &longs;eu bacu&shy;<lb/>li, &longs;iue ea, qu&aelig; ex virgis, vel palmarum ramis contexta <lb/>&longs;unt: propter &longs;agittas, qu&aelig; hinc inde perferuntur: idem <lb/>ver&ograve; anteriores etiam in partes fiat. </s>
<s>at c&ugrave;m muro appropin&shy;<lb/>quauerint, extendantur &longs;uperiores in partes ea, qu&aelig; in an&shy;<lb/>teriores &longs;unt. </s>
<s>Ver&ugrave;m in unaquaque Te&longs;tudine viri duo ab&shy;<lb/>&longs;condendi &longs;unt, erecti &longs;tantes, <expan abbr="murum&qacute;ue">murumque</expan> fodientes, ad cra&longs;&shy;<lb/>&longs;itiem quidem plus dimidio: &longs;ecundum ver&ograve; latitudinem, <lb/>quanta e&longs;t etiam ip&longs;ius Te&longs;tudinis latitudo: in altitudinem <lb/>autem, &agrave; tribus pedibus &longs;upra terram fodere incipientes: <lb/>vt ea, qu&aelig; ab ip&longs;a fodina de&longs;cendunt, ver&longs;us relictum infe&shy;<lb/>ri&ugrave;s locum incidant. </s>
<s>in &longs;uperiorem autem partem tantum <lb/>fodiendum e&longs;t, quantum fodientes &longs;ine impedimento po&shy;<lb/>terint. </s>
<s>propi&ugrave;s autem qu&agrave;m viginti pedibus ab inuicem <lb/>Te&longs;tudines di&longs;tent, vt &amp; plures &longs;int, &amp; multum in muro lo&shy;<lb/>cum ip&longs;i fodientes operentur. </s>
<s>necnon paru&aelig; &longs;int, vt celeri&shy;<lb/>ter, ac facil&egrave; deducantur: atque ea, qu&aelig; &agrave; muro ab aduer&shy;<lb/>&longs;ariis iaciuntur, haud direct&egrave; ad &longs;copum, <expan abbr="per&longs;picienter&qacute;ue">per&longs;picienterque</expan> <lb/>ad latera Te&longs;tudinum magnam ab inuicem di&longs;tantiam ha&shy;<lb/>bentium ferantur. </s></p>
<pb xlink:href="052/01/025.jpg"/><figure id="id.052.01.025.1.jpg" xlink:href="052/01/025/1.jpg"/><p type="caption">
<s>Fossori&aelig; testudines ba&longs;is muro applicata </s></p><p type="main">
<s><emph type="center"/>De fodinarum &longs;u&longs;tentatione, &amp; combu&longs;tione. </s>
<s>Cap. </s>
<s>IIII.<emph.end type="center"/></s></p><p type="main">
<s>CVm <expan abbr="a&utilde;t">aut</expan> murus &agrave; facie intror&longs;um ad <expan abbr="cra&longs;&longs;iti&etilde;">cra&longs;&longs;itiem</expan> per <lb/>foratus fuerit, <expan abbr="tot&qacute;ue">totque</expan> &longs;eparationes &longs;ecundum <lb/>latitudinem &longs;u&longs;ceperit, quot etiam te&longs;tudines <lb/>&longs;unt: atque iam dicti duo viri &agrave; &longs;e inuicem con&shy;<lb/>uer&longs;i intus ab&longs;que impedimento in ip&longs;is &longs;epa&shy;<lb/>rationibus fodiant: non amplius indigent Te&longs;tudine, c&ugrave;m <lb/>ad laterales fodiant partes, ab <expan abbr="ip&longs;a&qacute;ue">ip&longs;aque</expan> muri cra&longs;&longs;itie intus <lb/>con&longs;eruentur. </s>
<s>At ne fodientibus murus coincidat, &longs;u&longs;tente&shy;<lb/>tur intus, <expan abbr="fulciatur&qacute;ue">fulciaturque</expan> <expan abbr="&longs;u&longs;t&etilde;raculis">&longs;u&longs;tentaculis</expan> &longs;ubtilibus  potius, ac fre&shy;<lb/>quentibus, qu&agrave;m cra&longs;&longs;is, &amp; raris tabula &longs;upra, <expan abbr="infra&qacute;ue">infraque</expan> po&longs;i&shy;<lb/>ta, ne dum terram ver&longs;us &longs;ub relaxantur &longs;u&longs;tentacula, male <lb/>&longs;u&longs;tineant. </s>
<s>c&ugrave;m ver&ograve; fodina completa, <expan abbr="&longs;u&longs;tentata&qacute;ue">&longs;u&longs;tentataque</expan> fuerit: <lb/>intercapedo epi&longs;tyliorum repleatur materijs facil&egrave; combu&shy;<lb/>&longs;tibilibus, verbi gratia virgultis, lignis &longs;iccis, t&aelig;dis &longs;ci&longs;&longs;is, &amp;
<pb xlink:href="052/01/026.jpg"/>alijs huiu&longs;cemodi, qu&aelig; ad combu&longs;tionem idonea &longs;unt: ac <lb/>demum accendatur. </s>
<s>qu&ograve;d &longs;i locus aliquis extinguatur, ijs, <lb/>qu&aelig; ad iaculandum ignem fiunt tormentis, &longs;ubaccendatur. </s>
<s><lb/>habeat autem &amp; ra&longs;uras lignorum &longs;iccas circum&longs;per&longs;as vn&agrave; <lb/>cum liquida pice, &longs;iue oleo perunctas. </s>
<s>ac denique combu&longs;tis <lb/>&longs;u&longs;tentaculis, murus corruet. </s></p><figure id="id.052.01.026.1.jpg" xlink:href="052/01/026/1.jpg"/><p type="main">
<s><emph type="center"/>De Te&longs;tudinum con&longs;olidatione. </s>
<s>Cap. </s>
<s>V.<emph.end type="center"/></s></p><p type="main">
<s>IPSIS autem harum Te&longs;tudinum erectis lignis <lb/>claui <expan abbr="lat&utilde;">latum</expan> caput habentes, altitudinis ver&ograve; digi<lb/>torum octo, &longs;eu &longs;urculi ex ferro facti &longs;uper infi<lb/>gantur v&longs;que ad quatuor digitos, reliquos ve<lb/>r&ograve; quatuor &longs;upereminentes habeant. </s>
<s>locum <lb/>autem, qui intermedius e&longs;t creta opima, &amp; glutino&longs;a cum <lb/>pilis &longs;uinis, vel hircinis &longs;ubacta illinere, <expan abbr="replere&qacute;ue">replereque</expan> oportet, <lb/>ne di&longs;rumpantur, neque di&longs;cindantur. </s>
<s>nam tum propter
<pb xlink:href="052/01/027.jpg"/>clauorum frequentiam, tum etiam propter capitum eorum <lb/>latitudinem confirmabitur. </s>
<s>&agrave; lateribus autem panni lacera&shy;<lb/>ti, &longs;eu coria &longs;u&longs;pendantur: vt neque &longs;abulum calidum, ne&shy;<lb/>que pix, neque re&longs;ina decocta, neque oleum (quod infun&shy;<lb/>ditur, tanquam id, quod natura citi&ugrave;s cale&longs;cit, <expan abbr="tardius&qacute;ue">tardiusque</expan> <lb/>frige&longs;cit) ijs, qui intus operantur in&longs;tillent. </s>
<s>nam in&longs;tar ignis <lb/>hominum carnes con&longs;umunt. </s>
<s>C&ugrave;m itaque &longs;ic Te&longs;tudines <lb/>conficiantur, con&longs;eruabuntur ita vt ab ijs, qu&aelig; de&longs;uper deij&shy;<lb/>ciuntur ignem ferentibus, <expan abbr="accen&longs;is&qacute;ue">accen&longs;isque</expan> flammis minim&egrave; <expan abbr="c&otilde;-buri">com&shy;<lb/>buri</expan>: neque ij, qui infunduntur calefacti liquores intus pe&shy;<lb/>netrare po&longs;&longs;int. </s>
<s>Similiter <expan abbr="a&utilde;t">aut</expan> &amp; Parm&aelig;, <expan abbr="Te&longs;tudines&qacute;ue">Te&longs;tudinesque</expan> crati<lb/>bus vimineis <expan abbr="c&otilde;text&aelig;">context&aelig;</expan> ad texturas operiantur coriis madidis <lb/>bouum rec&egrave;ns occi&longs;orum, <expan abbr="tanqu&atilde;">tanquam</expan> iis, qu&aelig; igni re&longs;i&longs;tere po&longs;&shy;<lb/>&longs;unt. </s>
<s>ip&longs;&aelig; ver&ograve; Te&longs;tudines procul ab in&longs;trumentis lapides <lb/>iacientibus, <expan abbr="&longs;agittas&qacute;ue">&longs;agittasque</expan> mittentibus linantur. </s>
<s>c&ugrave;m autem <lb/>conden&longs;at&aelig;, roti&longs;que &longs;urrepentes context&aelig; fuerint, muris <lb/>adducantur. </s>
<s><expan abbr="figura&qacute;ue">figuraque</expan> &longs;ubiecta e&longs;t. </s></p><p type="caption">
<s>Te&longs;tudinis fo&longs;soriae ba&longs;isillita cr<gap/>ta </s></p><figure id="id.052.01.027.1.jpg" xlink:href="052/01/027/1.jpg"/><p type="caption">
<s>Te&longs;tudo fo&longs;sor&iacute;a <lb/>completa at&que; <lb/>munita</s></p><figure id="id.052.01.027.2.jpg" xlink:href="052/01/027/2.jpg"/><p type="main">
<s><emph type="center"/>De murorum lapideorum per vrnam combu&longs;tione. </s>
<s>Cap. </s>
<s>VI.<emph.end type="center"/></s></p><p type="main">
<s>QVidam ver&ograve; iuxta lapideos muros ligna (vt <lb/>mos erat) inferiori parti contigua ad <expan abbr="accend&etilde;-dos">accenden&shy;<lb/>dos</expan>, <expan abbr="confringendos&qacute;ue">confringendosque</expan> lapides circumpone&shy;<lb/>bant. </s>
<s>Ver&ugrave;m h&aelig;c operatio difficilis v&longs;u, &amp; <expan abbr="qu&atilde;do">quan<lb/>do</expan>  que fallax exi&longs;tit: quoniam tum aqua de&longs;u&shy;<lb/>per infu&longs;a ignem extinguit: <expan abbr="t&utilde;">tum</expan> debilior ad latus ip&longs;ius ignis
<pb xlink:href="052/01/028.jpg"/>latio fit, tanquam ea, qu&aelig; natura &longs;ur&longs;um tendit, ad <expan abbr="action&etilde;-&qacute;ue">actionen&shy;<lb/>que</expan> potentior e&longs;t: tum demum in ip&longs;o flamm&aelig; impetu, qui <lb/>intror&longs;um operantur, &longs;ub te&longs;tudine e&longs;&longs;e minim&egrave; poterunt, <lb/>quandoquidem &longs;imul comburentur. </s>
<s>Fiunt itaque fictiles <lb/>vrn&aelig; laminis ferreis exteriori parte colligat&aelig;, <expan abbr="minutis&qacute;ue">minutisque</expan> <lb/>carbonibus implentur: ab extrin&longs;eca ver&ograve; lamin&aelig; facie fun&shy;<lb/>dum ver&longs;us forantur, &amp; aperiuntur v&longs;que vnius digiti fora&shy;<lb/>men, <expan abbr="ferreum&qacute;ue">ferreumque</expan> tubulum inde &longs;u&longs;cipiunt, cui tubus alius <lb/>follem habens adiungitur. </s>
<s>C&ugrave;m autem ignem carbones &longs;u&shy;<lb/>&longs;ceperint, dum &longs;ufflantur, &longs;imilem flamm&aelig; perficiunt com&shy;<lb/>bu&longs;tionem. </s>
<s>quippe qu&aelig; lapidem penetrat, atque confringit, <lb/>aceto, vel vrina, vel alio quopiam acrium &longs;uperinfu&longs;o. </s>
<s><expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; <lb/>figura qualis &longs;ub&longs;cribitur. </s>
<s>hoc autem plumbarij frequenter <lb/>vtuntur. </s></p><figure id="id.052.01.028.1.jpg" xlink:href="052/01/028/1.jpg"/><p type="main">
<s><emph type="center"/>De murorum lateritiorum per terebras perforationibus. </s>
<s><lb/>Caput &longs;eptimum.<emph.end type="center"/></s></p><p type="main">
<s>SI lateritios muros cito de&longs;truere voluerimus, <lb/>frequenti&longs;&longs;imas in ip&longs;is perforationes terebris <lb/>faciemus, cooperti &longs;ub te&longs;tudinibus de&longs;uper <lb/>illitis, aut Parmis, qu&aelig; tecta tuti&longs;&longs;ima habeant, <lb/><expan abbr="&longs;int&qacute;ue">&longs;intque</expan> corijs bouum rec&egrave;ns occi&longs;orum circa <lb/>texturas opert&aelig;: c&ugrave;m propter pondera, qu&aelig; aduer&longs;us eas <lb/>mittuntur, tum propter calefactos, qui infunduntur liquo&shy;<lb/>res. </s>
<s>Terebr&aelig; ver&ograve; fabrilibus in&longs;trumentis &longs;imiles &longs;int. </s>
<s>Ve-<pb xlink:href="052/01/029.jpg"/>ctis enim ferreus fit longitudinis pedum ad minus quinque&shy;<lb/>vnius digiti diametrum habens, &amp; cra&longs;&longs;itudinem circum, <lb/>quaque ferm&egrave; quatuor digitorum: laminam &longs;imiliter <expan abbr="ferre&atilde;">ferream</expan> <lb/>in anteriori extremitate affixam latitudinis pedum duode&shy;<lb/>cim, &amp; altitudinis octo, qu&aelig; circa medium in anteriori par&shy;<lb/>te coarctetur, iuxta figuram cuiu&longs;dam olitorii in&longs;trumenti, <lb/>quod &agrave; Gr&aelig;cis Platily&longs;gium vocatur: ad alteram autem re&shy;<lb/>tror&longs;um exi&longs;tentem extremitatem ligneum, torno factum, <lb/>atque in medio arctum &longs;u&longs;cipit Cylindrum. </s>
<s>quippe qui &agrave; <lb/>quodam arcuato in&longs;trumento fabrili (quod Gr&aelig;ci aridha <lb/><expan abbr="voc&atilde;t">vocant</expan>) vertatur, atque circa po&longs;terioris partis medium emi&shy;<lb/>nentiam <expan abbr="qu&atilde;dam">quandam</expan> habeat, qu&aelig; capitis formam referat, <expan abbr="qu&aelig;-&qacute;ue">qu&aelig;&shy;<lb/>que</expan> ingrediatur, atque circumuoluatur e&ograve; in va&longs;e (quod <lb/>Pyelis, ide&longs;t vrna dicitur, &longs;iue capitulum quoddam exi&longs;tit) <lb/>regula quadam terr&aelig; impo&longs;ita capitulum ip&longs;um adducente, <lb/>atque eum, qui perforatur locum &longs;emper con&longs;equente. </s>
<s>cir&shy;<lb/>cumuoluetur autem ad eandem operationem Cylindrus <lb/>vn&agrave; cum terebra manibus etiam motus, &longs;i paruas regulas <lb/>iuxta medium &longs;u&longs;ceperit fu&longs;i putealis in&longs;tar in crucis <expan abbr="mod&utilde;">modum</expan> <lb/>traiectas, quas nonnulli ex ip&longs;a figura A&longs;tericos, nempe &longs;tel&shy;<lb/>lulas nuncupant. </s>
<s>Ver&ugrave;m eas, qu&aelig; in muro fiunt perforatio&shy;<lb/>nes, tran&longs;uer&longs;as, ac &longs;ur&longs;um tendentes fieri oportet: tanquam <lb/>eas, qu&aelig; ad interiorem partem altiores e&longs;&longs;e debent. </s>
<s>c&ugrave;m vt <lb/>ea, qu&aelig; ex latere &agrave; terebris circumraduntur facil&egrave; deor&longs;um <lb/>tendentia fiant: tum ut lamina in extremitate uectis affixa <lb/>bene ad <expan abbr="operation&etilde;">operationem</expan> &longs;u&longs;tentetur, dum &agrave; regula terr&aelig; tran&longs;&shy;<lb/>uer&longs;a impo&longs;ita, <expan abbr="ip&longs;i&qacute;ue">ip&longs;ique</expan> renitente fulcitur: tum demum ut ea, <lb/>qu&aelig; &agrave; terebris fit &longs;ur&longs;um tendens perforatio non &longs;olam mu&shy;<lb/>ri &longs;ubmi&longs;&longs;ionem, uer&ugrave;m etiam declinantem ad extrin&longs;ec&ugrave;s <lb/>deor&longs;um lationem faciat, <expan abbr="multa&qacute;ue">multaque</expan> repente circa murum <lb/>collap&longs;io fiat. </s>
<s>atque declinationis figura talis e&longs;t. </s></p>
<pb xlink:href="052/01/030.jpg"/><figure id="id.052.01.030.1.jpg" xlink:href="052/01/030/1.jpg"/><p type="caption">
<s>Pvelis, siue <lb/>Capitulum</s></p><p type="main">
<s>Foretur autem ex&aelig;quali murus in eadem recta linea di&longs;tan<lb/>tibus abinuicem foraminibus pede, &amp; quarta pedis parte, <lb/>hoc e&longs;t viginti digitis, &longs;iue dodrante, <expan abbr="duobus&qacute;ue">duobusque</expan> Palmis. </s>
<s><lb/>Dodrans enim duodecim, palmus ver&ograve; quatuor digito&shy;<lb/>rum e&longs;t. </s>
<s>ip&longs;as autem perforationes nos &agrave; tribus fer&egrave; pedibus <lb/>&longs;ur&longs;um &agrave; terra initium &longs;umentes facere oportet, quemad&shy;<lb/>modum etiam lapideis in muris iam diximus, vt qu&aelig; &agrave; fora&shy;<lb/>minibus de&longs;cendit materia in ommi&longs;&longs;um inferius locum in&shy;<lb/>cidat. </s></p>
<pb xlink:href="052/01/031.jpg"/><p type="main">
<s><emph type="center"/>De murorum lateritiorum combu&longs;tione. </s>
<s>Cap. </s>
<s>VIII.<emph.end type="center"/></s></p><p type="main">
<s>CVm autem ordinatim ip&longs;ius muri frontes per&shy;<lb/>forati fuerint, replentur foramina ab extrin&longs;e&shy;<lb/>ca facie ad interiores partes non iuxta totam <lb/>cra&longs;&longs;itiem, &longs;ed iuxta pedem tant&ugrave;m lignis &longs;ic&shy;<lb/>cis, &longs;ci&longs;&longs;is, non quadrangulis (qu&ograve;d &longs;ecundum <lb/>latitudinem &longs;ibiinuicem congruant) ver&ugrave;m qua&longs;i rotundis <lb/>veluti palis cra&longs;&longs;itiem habentibus ba&longs;im ver&longs;us ad plus <expan abbr="tri&utilde;">trium</expan> <lb/>digitorum, ad uerticem autem angu&longs;tioribus ad &longs;u&longs;tentan&shy;<lb/>dum murum operationis tempore. </s>
<s>&amp; &longs;i contingit t&aelig;d&aelig; pali <lb/>&longs;int: &longs;in min&ugrave;s, ligna &longs;icca pice, vel &longs;ulphure trito vn&agrave; cum <lb/>liquida pice, &longs;iue oleo peruncta, vbi ignis <expan abbr="penetr&atilde;s">penetrans</expan>, <expan abbr="&longs;ur&longs;um-&qacute;ue">&longs;ur&longs;um&shy;<lb/>que</expan> conuer&longs;us accendatur, <expan abbr="haud&qacute;ue">haudque</expan> &agrave; den&longs;itate &longs;uffocatus <lb/>extinguatur. </s>
<s>C&ugrave;m autem cuncta foramina repleta fuerint <lb/>ad pedem v&longs;que &longs;ecundum profunditatem quemadmodum <lb/>dictum e&longs;t, rur&longs;us in eadem recta linea iuxta medium inter&shy;<lb/>iecta interualla ordinatim ex&aelig;quali ver&longs;us priora forentur: <lb/>ip&longs;a ver&ograve; po&longs;trema foramina ad vtramque partem obli&shy;<lb/>quentur, vt ad priora po&longs;teriorum conforatio perueniat. </s>
<s>at&shy;<lb/>que h&aelig;c etiam ra&longs;uris, vel fru&longs;tis ligneis, aut ijs, qu&aelig; runci&shy;<lb/>na in leuigatione tabularum abraduntur, &longs;iccis, ac facil&egrave; <expan abbr="c&otilde;-bu&longs;tibilibus">con&shy;<lb/>bu&longs;tibilibus</expan> virgultis, &longs;iue lignorum fragmentis implean&shy;<lb/>tur: in quibus ignis operans, celerem efficit combu&longs;tionem. </s>
<s><lb/>Con&longs;ult&ograve; itaque pali &longs;uperficiem &aelig;qualem, non habent, &longs;ed <lb/>maiores inferi&ugrave;s &longs;unt: vt ignem retinere, <expan abbr="&longs;pirante&qacute;ue">&longs;piranteque</expan> vento <lb/>accendi po&longs;&longs;int. </s>
<s>Qu&ograve;d &longs;i <expan abbr="v&etilde;torum">ventorum</expan> tranquillitas in operatio&shy;<lb/>nis tempore, &longs;eu loco e&longs;&longs;et: calami intror&longs;um omnino confo&shy;<lb/>rati commi&longs;ceantur (quales ij &longs;unt, quos ip&longs;i venatores <expan abbr="aui&utilde;">auium</expan> <lb/>habere &longs;olent) quippe qui follibus fabrilibus <expan abbr="&longs;uffl&etilde;tur">&longs;ufflentur</expan>. </s>
<s>nam <lb/>ad quemlibet qui&longs;piam voluerit locum folles ip&longs;i transfe&shy;<lb/>runtur, <expan abbr="ignem&qacute;ue">ignemque</expan> accendunt, c&ugrave;m ferreum tubulum ante <lb/>ignem habeant. </s>
<s>ac demum figura &longs;ubijcitur. </s></p>
<pb xlink:href="052/01/032.jpg"/><figure id="id.052.01.032.1.jpg" xlink:href="052/01/032/1.jpg"/><p type="main">
<s><emph type="center"/>De Te&longs;tudinibus Arietem ge&longs;tantibus. </s>
<s>Cap. </s>
<s>IX.<emph.end type="center"/></s></p><p type="main">
<s>IPSA perforatione, &longs;u&longs;tentatione, &amp; combu&shy;<lb/>&longs;tione peracta, &longs;i murus indeclinabilis perman&shy;<lb/>&longs;erit, <expan abbr="intrepidus&qacute;ue">intrepidusque</expan> &longs;teterit: ad cra&longs;&longs;um lateri&shy;<lb/>tij parietis opificium Arietibus oppugnare ne&shy;<lb/>ce&longs;&longs;e e&longs;t. </s>
<s>licet enim languida, &amp; debilis Arietis <lb/>ad laterem percu&longs;&longs;io fiat, fodiens potius propter fungo&longs;ita&shy;<lb/>tem, ac mollitiem: qu&agrave;m vibrans, &amp; rumpens propter duri&shy;<lb/>tiem, atque re&longs;i&longs;tentiam vt in lapidibus: attamen c&ugrave;m per <lb/>eam, qu&aelig; deor&longs;um facta e&longs;t operationem debilitatus prope <lb/>ba&longs;im murus &longs;it, aduer&longs;us continuos Arietum pre&longs;&longs;us re&longs;i&shy;<lb/>&longs;tere minim&egrave; poterit: &longs;ed dum violentia percutitur, perfora&shy;<arrow.to.target n="note21"/><lb/>tione declinationem &longs;u&longs;cipiet. </s>
<s>Veruntamen adaptationes, <lb/>&amp; colligationes Arietum, qui &longs;ecundum longitudinem co&shy;<arrow.to.target n="note22"/><lb/>aptantur: <expan abbr="necn&otilde;">necnon</expan> eas, qu&aelig; circa membra ip&longs;orum, &amp; eas, qu&aelig; <lb/><arrow.to.target n="note23"/><lb/>in monoxylis iuxta di&longs;tantiam conuenientes, &amp; in Te&longs;tudi&shy;<lb/>nibus Arietes ge&longs;tantibus, ac Turribus, atque duplicatis <lb/>&longs;calis appen&longs;iones, atque etiam eas, qu&aelig; per ip&longs;os Arietes <lb/>iuxta murum affabr&egrave; fact&aelig; &longs;cal&aelig; nautic&aelig; fiunt: ad congruen<lb/>tem deinceps vnicuique operationem in pr&aelig;&longs;enti tractatio&shy;<lb/>ne &longs;ubtiliter dilucidando expo&longs;uimus. </s>
<s>Si citi&ugrave;s cum Arieti&shy;<lb/>bus muros vel portas rumpere, <expan abbr="perfringere&qacute;">perfringereque</expan>; voluerimus: <lb/>faciemus Te&longs;tudines Arietes ge&longs;tantes, quatuor rotarum, <lb/>altas, qu&aelig; &longs;uperi&ugrave;s catenas, vel funes iuxta cra&longs;&longs;itiem robu-<pb xlink:href="052/01/033.jpg"/>&longs;tos arietem &longs;u&longs;tollentes, ac <expan abbr="&longs;u&longs;tin&etilde;tes">&longs;u&longs;tinentes</expan> habeant. </s>
<s>qu&ugrave;m enim <lb/>ab altiori loco aries &longs;u&longs;tentetur, plus retror&longs;um interualli <lb/>ad motum &longs;u&longs;cipit: &amp; qu&ugrave;m &agrave; long&egrave; cum impetu feratur, &amp; <lb/>incutiatur, maiorem aquirit vim: &amp; offendendo muro oc&shy;<lb/>currens, violentam, <expan abbr="fortem&qacute;ue">fortemque</expan> perficit percu&longs;&longs;ionem. </s>
<s>Sit au<arrow.to.target n="note24"/><lb/>tem iuxta formam alta Te&longs;tudo ip&longs;a, &amp; non admodum ma&shy;<lb/>gna, vt ad motum deductu facilis &longs;it: altitudinem latitudi&shy;<lb/>nis duplam habens, <expan abbr="l&otilde;gitudinem">longitudinem</expan> ver&ograve; altitudini &aelig;qualem, <lb/>vel par&ugrave;m ea minorem: vt ro&longs;trum acutum habeat, <expan abbr="oblon-ga&qacute;ue">oblon&shy;<lb/>gaque</expan> &longs;it: atque vt ea, qu&aelig; in ip&longs;am incidunt pondera c&ugrave;m <arrow.to.target n="note25"/><lb/>obliquentur, deor&longs;um hinc inde decurrant. </s>
<s>Con&longs;truitur au<arrow.to.target n="note26"/><lb/>tem hoc modo. </s>
<s>Iuga duo, atque duo ponuntur, quorum <lb/>&longs;ingula &longs;int longitudinis pedum vigintiquatuor, <expan abbr="di&longs;tent&qacute;ue">di&longs;tentque</expan> <lb/>ab <expan abbr="inuic&etilde;">inuicem</expan> pedibus ad min&ugrave;s duodecim. <expan abbr="at&qtail;">atque</expan> in ip&longs;is in&longs;erun<lb/>tur ligna <expan abbr="digitor&utilde;">digitorum</expan> octo iuxta <expan abbr="cra&longs;&longs;itudin&etilde;">cra&longs;&longs;itudinem</expan>, pedalis latitudi&shy;<lb/>nis, vigintiquatuor ad min&ugrave;s <expan abbr="ped&utilde;">pedum</expan> iuxta altitudinem, qu&aelig; <lb/>&longs;unt octo numero, &longs;cilicet quatuor, &amp; quatuor in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> la&shy;<lb/>teralibus partibus a&longs;tantia: annuentia ver&ograve; &longs;uperi&ugrave;s, iuxta <lb/>verticem inuicem copulantur: amplectentia lignum, quod <lb/>Te&longs;tudinis dor&longs;um e&longs;t, longius ea, qu&aelig; circa iuga e&longs;t longi&shy;<lb/>tudine, &amp; <expan abbr="aliqu&atilde;tulum">aliquantulum</expan> excedens anteri&ugrave;s propter eas, quas <lb/>progrediendo dicemus cau&longs;as. </s>
<s>iuxta medium autem ligno&shy;<lb/>rum erectorum a&longs;tantium eius parti ad quam volumus Te&shy;<lb/>&longs;tudinem ip&longs;am annuere, alia iuga clauis affigantur: atque <lb/>ab interna parte &longs;u&longs;tentacula &longs;upponantur, &agrave; quibus iuga <lb/>interna, <expan abbr="dor&longs;um&qacute;ue">dor&longs;umque</expan> &longs;u&longs;tineatur, ac fulciatur. </s>
<s>iuxta ver&ograve; ex&shy;<lb/>trin&longs;ecam &longs;uperficiem tabulis <expan abbr="digitor&utilde;">digitorum</expan> quatuor &longs;ecundum <lb/>cra&longs;&longs;itiem ip&longs;a erecta a&longs;tantia ligna muniantur. </s>
<s>atque hoc <lb/>modo figura perficitur. </s>
<s>ab ip&longs;o autem internorum iugorum <lb/><expan abbr="pauim&etilde;to">pauimento</expan> externa iuga lignis erectis, in decliuibus, ad per&shy;<lb/>pendiculum exi&longs;tentibus <expan abbr="&longs;u&longs;tent&etilde;tur"> &longs;u&longs;tententur</expan> </s>
<s>ip&longs;um ver&ograve; vacuum, <lb/>quod e&longs;t circa inferiora iuga, hoc e&longs;t <expan abbr="interuall&ugrave;">interuallum</expan> rotas qua&shy;<lb/>tuor totam, qu&aelig; circa Te&longs;tudinem e&longs;t congeriem &longs;u&longs;tinen&shy;<lb/>tes, <expan abbr="ge&longs;tantes&qacute;ue">ge&longs;tantesque</expan> habeat. </s>
<s>ne autem inferiora iuga aperian&shy;<lb/><arrow.to.target n="note27"/><lb/>tur, qu&aelig;dam ligna tran&longs;uer&longs;a (qu&aelig; Gr&aelig;ci peritomidas di&shy;<lb/>cunt) &longs;u&longs;cipiant, que non &longs;ine &longs;ectione fiunt, &longs;ed ea, qu&aelig; cla&shy;<lb/>uis &longs;it cheloniorum fixione retinent: in&longs;tar quorundam
<pb xlink:href="052/01/034.jpg"/>pugillorum circum&longs;ectorum, ac hemi&longs;ph&ecedil;riorum in&longs;culpto&shy;<lb/>rum &longs;imilium iis, qui in portarum cardinibus ponuntur. </s>
<s><lb/>qu&aelig; quidem ligna ip&longs;ius acutum habentis dor&longs;um Te&shy;<lb/>&longs;tudinis ba&longs;es erunt. </s>
<s>Fit autem quandoque obtu&longs;ius, ac de&shy;<lb/>pre&longs;&longs;ius Te&longs;tudinis tectum, quippe c&ugrave;m in &longs;emia&longs;tantibus <lb/>partibus lignorum &longs;uper iuga erectorum con&longs;i&longs;tentium &longs;u&shy;<arrow.to.target n="note28"/><lb/>peri&ugrave;s adiecta fuerint ea ligna, qu&aelig; gr&aelig;c&egrave; &longs;yngipt&aelig;, hoc e&longs;t <lb/>&longs;imul incuruantia vocantur: <expan abbr="&longs;upremum&qacute;ue">&longs;upremumque</expan> pinnaculi dor&shy;<lb/>&longs;um comprehenderint: quando videlicet aries longi&longs;&longs;imus <lb/>fuerit, <expan abbr="Te&longs;tudo&qacute;ue">Te&longs;tudoque</expan> &agrave; muro long&egrave; di&longs;titerit. </s>
<s>nam &longs;i forta&longs;&longs;e <lb/>minor iuxta longitudinem Aries, <expan abbr="Te&longs;tudo&qacute;ue">Te&longs;tudoque</expan> prop&egrave; mu&shy;<lb/>rum &longs;it: aduer&longs;um ea, qu&aelig; pr&aelig;cipitantur, in <expan abbr="ip&longs;am&qacute;ue">ip&longs;amque</expan> inci&shy;<lb/>dunt pondera re&longs;i&longs;tere nequaquam poterit, propter ip&longs;ius <lb/>tecti depre&longs;&longs;ionem. </s>
<s>&longs;ed c&ugrave;m ruptionem, &longs;eu fractionem in <lb/>coniunctionum commi&longs;&longs;uris &longs;u&longs;ceperit: periculo&longs;a tum &longs;i&shy;<lb/>biip&longs;i, <expan abbr="t&utilde;">tum</expan> ariete oppugnantibus fiet. </s>
<s>Dor&longs;um ver&ograve; &agrave; iam di&shy;<arrow.to.target n="note29"/><lb/>ctis erectis monoxylis &longs;upern&egrave; comprehen&longs;um, anteri&ugrave;s in <lb/>muri faciem pr&aelig;ponere oportet. </s>
<s>vt in ip&longs;o fulcimentum &longs;it, <lb/>&amp; ea, qu&aelig; aduer&longs;us arietem mittuntur recipiat. </s>
<s>&longs;i enim ma&shy;<lb/>ximi lapides, qui &agrave; muro deor&longs;um feruntur: &amp; tran&longs;uer&longs;a li&shy;<lb/>gna, qu&aelig; ex &aelig;quali &aelig;queponderando, &amp; &aelig;quilibrando de&shy;<lb/>&longs;cendunt, detectum fort&egrave; arietem inuenerint, qui aduer&longs;us <lb/>murum cum impetu fertur: aut aries ip&longs;e deor&longs;um <expan abbr="annu&etilde;s">annuens</expan>, <lb/>di&longs;rumpetur: aut eum mouentes abiiciet, atque interimet. </s>
<s><lb/>Talis quidem e&longs;t anterior Te&longs;tudo, qu&aelig; etiam arietis &longs;u&shy;<lb/>&longs;tentacula &longs;ecundum di&longs;tantiam habet: &longs;ecunda ver&ograve; de&shy;<lb/>pre&longs;&longs;ior quoad altitudinem, &amp; minor: atque ali&aelig; du&aelig; re&shy;<lb/>tror&longs;um adhuc minores. </s>
<s>ad ip&longs;ius enim aditus tutelam ne&shy;<lb/>ce&longs;&longs;ari&aelig; &longs;unt. </s>
<s>Plures autem &amp; minores ip&longs;as (queadmodum <lb/>iam diximus) e&longs;&longs;e decet, vt ab&longs;que labore adducantur, ex <lb/><expan abbr="paruis&qacute;ue">paruisque</expan> lignis componantur: non autem unam maxi&shy;<lb/>mam, e&ograve; qu&ograve;d ex magnis, <expan abbr="inuentu&qacute;ue">inuentuque</expan> difficilibus lignis <lb/>fiat: necnon tard&egrave;, <expan abbr="magno&qacute;ue">magnoque</expan> cum labore deducatur. </s>
<s>Ve&shy;<lb/>r&ugrave;m ordinatim ip&longs;&aelig; figur&aelig; &longs;ubiiciuntur. </s></p>
<pb xlink:href="052/01/035.jpg"/><p type="margin">
<s><margin.target id="note21"/>a</s></p><p type="margin">
<s><margin.target id="note22"/>b</s></p><p type="margin">
<s><margin.target id="note23"/>c</s></p><p type="margin">
<s><margin.target id="note24"/><emph type="italics"/>Te&longs;tudi&shy;<lb/>nis Arie<lb/><expan abbr="t&etilde;">tem</expan> ge&longs;tan<lb/>tis de&longs;cri<lb/>ptio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note25"/>d</s></p><p type="margin">
<s><margin.target id="note26"/><emph type="italics"/>Eiu&longs;dem <lb/>con&longs;tru&shy;<lb/>ctio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note27"/>e</s></p><p type="margin">
<s><margin.target id="note28"/>f</s></p><p type="margin">
<s><margin.target id="note29"/>g</s></p><figure id="id.052.01.035.1.jpg" xlink:href="052/01/035/1.jpg"/>
<pb xlink:href="052/01/036.jpg"/><p type="main">
<s>Sciendum autem e&longs;t, qu&ograve;d c&ugrave;m Aries ab anteriori, <expan abbr="maiori&qacute;ue">maiorique</expan> <lb/>Testudine &longs;u&longs;tentetur: magis in muri faciem eleuatur, re&shy;<lb/>tror&longs;um ver&ograve; deprimitur. </s>
<s>atque id non abrefactum e&longs;t. </s>
<s>c&ugrave;m <lb/>etenim &longs;ur&longs;um tendens moueatur, forti&longs;&longs;imam ad &longs;uperio&shy;<lb/>res murorum partes: deor&longs;um ver&ograve; &longs;e inclinans, imbecilli&shy;<lb/>mam, &amp; languidam, quandoque autem fallacem quoque <lb/>percu&longs;&longs;ionem ip&longs;am efficit. </s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>QVoniam nonnulla in hoc capite ob&longs;cura mihi videntur, ea <lb/>dilucidanda, declaranda&queacute; e&longs;&longs;e cen&longs;eo, vt ab omnibus faci&shy;<lb/>l&egrave; percipi po&szlig;int. </s>
<s>C&ugrave;m itaque pr&aelig;&longs;ens caput cum &longs;uperio&shy;<lb/>ribus Autor continua&longs;&longs;et, dixi&longs;&longs;et&queacute; qu&ograve;d murorum perforatione, <lb/>&longs;u&longs;tentatione, &amp; combu&longs;tione peractis de quibus &longs;uperi&ugrave;s pertra&shy;<lb/>ctauit: &longs;i murus adhuc indeclinabilis perman&longs;erit, intrepidus&queacute; <lb/>&longs;teterit: arietibus ip&longs;is ad partes cra&szlig;iores parietis oppugnan&shy;<lb/>dum e&longs;t: quoniam in hoc capite non declarat omnia ea, qu&aelig; ad <lb/>Arietem ip&longs;am &longs;pectant: idcirco ait &longs;e in &longs;equentibus huius tra&shy;<lb/>ctationis partibus ea &longs;ubtiliter dilucidando expo&longs;ui&longs;&longs;e. </s>
<s>Ver&ugrave;m ea, <lb/><arrow.to.target n="note30"/><lb/>qu&aelig; ad Arietem pertinent h&aelig;c &longs;unt. </s>
<s>nempe adaptationes, &amp; colli&shy;<lb/>gationes Arietum: necnon earum appen&longs;iones. </s>
<s>qu&aelig; &longs;cilicet appen&shy;<lb/>&longs;ione; vari&aelig; &longs;unt &longs;ecundum varios nece&szlig;itatis v&longs;us. </s>
<s>quandoque <lb/>enim Arietes ip&longs;i circa &longs;ua membra appenduntur, aliquando in <lb/>Monoxylis, ali&agrave;s in Te&longs;tudinibus, interdum alijs in machinis, qu&aelig; <lb/>turres vocantur, nonnunquam in duplicatis &longs;calis, de quibus om&shy;<lb/>nibus appen&longs;ionibus: necnon de nauticis &longs;calis, qu&aelig; per ip&longs;os Arie&shy;<lb/>tes ad a&longs;cendendum murum fiunt, in &longs;equentibus ordinatim iux&shy;<lb/>ta conuenientem unicuique v&longs;um, &amp; operationem pertractaturus <lb/><arrow.to.target n="note31"/><lb/>e&longs;t. </s>
<s>Membra autem Arietis h&igrave;c intelligenda &longs;unt ea ligna, in qui&shy;<lb/>bus Aries appenditur, qu&aelig; tamquam eius crura &longs;unt, vt in &longs;equen<lb/>tis capitis figura nobis manife&longs;tum erit.<emph.end type="italics"/><lb/><arrow.to.target n="note32"/></s></p><p type="margin">
<s><margin.target id="note30"/>a</s></p><p type="margin">
<s><margin.target id="note31"/>b</s></p><p type="margin">
<s><margin.target id="note32"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Quid ver&ograve; &longs;ibi velit Autor verbo illo Monoxylis declarandum <lb/>e&longs;t, quoniam diuer&longs;imod&egrave; vocabulum hoc ab Autore in pr&aelig;&longs;enti ca&shy;<lb/>pite accipitur. </s>
<s>Quare &longs;ciendum e&longs;t, qu&ograve;d propri&egrave; Monoxyla &longs;unt <lb/>nauigia, &longs;iue lyntres ex vnico ligno excauat&aelig;, quibus Aegyptij per<emph.end type="italics"/>
<pb xlink:href="052/01/037.jpg"/><emph type="italics"/>&longs;tagna, &amp; Nili innundationes vtebantur, Autore Strabone lib. </s>
<s>3. <lb/>&amp; Plinio lib. </s>
<s>6. cap. </s>
<s>23. &amp; quoniam inferi&ugrave;s de quibu&longs;dam naui&shy;<lb/>gijs Arietes ge&longs;tantibus, quibus maritim&aelig; ciuitates expugnaban&shy;<lb/>tur, &longs;ermonem habiturus est: propterea de illis Monoxylis h&igrave;c in&shy;<lb/>telligit, c&ugrave;m ait &longs;e in pr&aelig;&longs;enti tractatione eas Arietum appen&longs;io&shy;<lb/>nes, qu&aelig; in Monoxylis iuxta di&longs;tantiam (&longs;cilicet tum ip&longs;orum in&shy;<lb/>ter &longs;e nauigiorum, tum lignorum in ip&longs;is nauigijs Arietem &longs;u&longs;ti&shy;<lb/>nentium) conuenientes fiunt, &longs;ubtiliter dilucidando expo&longs;ui&longs;&longs;e. </s>
<s><lb/>paulo inferi&ugrave;s autem in alia quoque &longs;ignificatione dictionem hanc <lb/>ab Autore acceptam reperiemus, vt mox &longs;uo loco declarabimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note33"/></s></p><p type="margin">
<s><margin.target id="note33"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Iuga h&igrave;c intelligenda &longs;unt ligna duo in&longs;tar iugi bouini coniun&shy;<lb/>cta, qu&aelig; vn&agrave; cum alijs duobus eodem modo coniunctis ba&longs;im Te&shy;<lb/>&longs;tudinis con&longs;tituunt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note34"/></s></p><p type="margin">
<s><margin.target id="note34"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Peritomid&aelig; &longs;unt ea ligna tran&longs;uer&longs;a, &agrave; quibus iuga ip&longs;a reti&shy;<lb/>nentur ne aperiantur, &longs;ed eandem &longs;emper adinuicem di&longs;tantiam <lb/>obtineant. </s>
<s>qu&aelig; porr&ograve; ligna ait e&longs;&longs;e di&longs;&longs;ecanda in&longs;tar quorumdam <lb/>pugillorum iuga ip&longs;a apprehendentium, &longs;cilicet in anterioribus, <lb/>extremis&queacute; ip&longs;orum tran&longs;uer&longs;orum lignorum partibus: in eorum&shy;<lb/>dem ver&ograve; lateralibus faciebus, instar cheloniorum con&longs;imilium <lb/>ijs, in quibus portarum cardines euoluuntur. </s>
<s>quemadmodum in <lb/>huiu&longs;ce capitis figuris per&longs;picere licet, quas nos exqui&longs;it&egrave; de&longs;igna&shy;<lb/>ri curauimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note35"/></s></p><p type="margin">
<s><margin.target id="note35"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Syngypt&aelig; &longs;unt ligna curua, cuiu&longs;modi &longs;unt ea, ex quibus <expan abbr="naui&utilde;">nauium</expan> <lb/>carina con&longs;truitur. </s>
<s>ex huiu&longs;modi autem lignis con&longs;truitur etiam <lb/>dor&longs;um Te&longs;tudinum c&ugrave;m depre&szlig;iores eas facere volumus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note36"/></s></p><p type="margin">
<s><margin.target id="note36"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Monoxyla h&igrave;c intelligenda &longs;unt ea &longs;u&longs;tentacula, qu&aelig; &longs;uperi&ugrave;s <lb/>ad&longs;ecunda iuga poni dixit. </s>
<s>H&aelig;c itaque in pr&aelig;&longs;enti capite decla&shy;<lb/>ratione quadam indigere nobis vi&longs;a &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>De quibu&longs;dam, qu&aelig; in omnibus Te&longs;tudinibus ob&longs;eruan&shy;<lb/>da &longs;unt. </s>
<s>Cap. </s>
<s>X.<emph.end type="center"/></s></p><p type="main">
<s>IN omnibus <expan abbr="a&utilde;t">aut</expan> Te&longs;tudinibus claui <expan abbr="lat&utilde;">latum</expan> caput <lb/><expan abbr="hab&etilde;tes">habentes</expan> (<expan abbr="qu&etilde;admod&utilde;">quemadmodum</expan> <expan abbr="i&atilde;">iam</expan> <expan abbr="dict&utilde;">dictum</expan> e&longs;t) ad tecti late&shy;<lb/>ra, <expan abbr="partes&qacute;">partesque</expan>; <expan abbr="deors&utilde;">deorsum</expan> <expan abbr="t&etilde;d&etilde;tes">tendentes</expan>, <expan abbr="v&longs;q;">v&longs;que</expan> ad <expan abbr="eor&utilde;">eorum</expan> <expan abbr="dimi-di&utilde;">dimi&shy;<lb/>dium</expan> &longs;uper <expan abbr="infig&atilde;tur">infigantur</expan>: ea ver&ograve; <expan abbr="clauor&utilde;">clauorum</expan> pars, qu&aelig; <lb/>in medio erecta interiacet, creta opima, &amp; glu&shy;<pb xlink:href="052/01/038.jpg"/>tino&longs;a, cum pilis &longs;ubacta, atque indiui&longs;a con&longs;eruata replea&shy;<lb/>tur. </s>
<s>ad ip&longs;as autem rotas Te&longs;tudinem &longs;u&longs;tinentes in inferio&shy;<lb/>ra iuga cuneos, permagnos ex vtri&longs;que partibus exceden&shy;<lb/>tes &longs;upponere oportet, vt altitudinis magnitudinem &longs;u&longs;ti&shy;<lb/>neant. </s>
<s>Soli enim rotarum claui, &amp; pr&aelig;&longs;ertim quoniam, per <lb/>&longs;ingula iuga in&longs;tar axium pertran&longs;ientes, breues &longs;unt: Te&shy;<lb/>&longs;tudinem &longs;u&longs;tinere <expan abbr="n&otilde;">non</expan> poterunt: neque tut&egrave; ip&longs;am &longs;tantem <lb/>habebimus ad eam, qu&ecedil; fieri debet Arietis motionem. </s>
<s>Sup&shy;<lb/>ponuntur autem inferi&ugrave;s cunei non &longs;ol&ugrave;m, vt altitudinis <lb/>pondus &longs;u&longs;tineant, verumetiam vt in&longs;tabilem rotarum mo&shy;<lb/>tionem impediant. </s>
<s>c&ugrave;m autem Te&longs;titudinem mouere vo&shy;<lb/>luerimus, cuneos &longs;ubtus po&longs;itos &longs;ublaxabimus. </s>
<s>At &longs;cien&shy;<lb/>dum e&longs;t, qu&ograve;d lapidei muri citi&ugrave;s qu&agrave;m lateritij incutiun&shy;<lb/>tur, atque rumpuntur. </s>
<s>nam propter fungo&longs;itatem, ac moli&shy;<lb/>tiem ip&longs;ius lateris ea, qu&aelig; ab Ariete fit percu&longs;&longs;io, debilis, &amp; <lb/>languida e&longs;t, excauans potius, ac fodiens laterem, qu&agrave;m <lb/>rumpens, atque perfringens. </s>
<s>lapis ver&ograve; aduer&longs;us ferri du&shy;<lb/>ritiem re&longs;i&longs;tens, vehementem percu&longs;&longs;ionem &longs;u&longs;cipit, atque <lb/>ita concutitur. </s></p><p type="main">
<s><emph type="center"/>De Ariete, &amp; Arietaria Machina &longs;ecund&ugrave;m Byzantium <lb/>principem. </s>
<s>Cap. </s>
<s>XI.<emph.end type="center"/></s></p><p type="main">
<s>VEr&ugrave;m principis Byzantij familiares Arietem <lb/>cubitorum centum &amp; viginti iuxta longitudi&shy;<lb/>nem faciebant. </s>
<s>ab ip&longs;ius autem calce iuxta <lb/>cra&longs;&longs;itiem quidem, pedalem: in latitudinem <lb/>ver&ograve;, palmorum quinque: in anteriori autem <lb/>parte coarctabant ip&longs;um in pedalem latitudinem, &amp; trium </s></p><p type="main">
<s><arrow.to.target n="note37"/><lb/>palmorum cra&longs;&longs;itiem: Helicas ferreas quatuor, qu&aelig; &longs;e &longs;e in <lb/>longitudinem v&longs;que ad decem cubitos extendant, in ante&shy;<lb/>riori parte clauis affigentes: <expan abbr="totum&qacute;ue">totumque</expan> Arietem tribus fu&shy;<lb/>nibus octo iuxta cra&longs;&longs;itudinem circumquaque digitorum <lb/>exi&longs;tentibus &longs;uccingentes: ac loris eum circulariter ligan&shy;<lb/>tes, iuxta medium tribus quidem interuallis, quatuor ver&ograve; <lb/>&longs;u&longs;tentaculis con&longs;tringebant. </s><s>funes ver&ograve;, qui ab aliis cana&shy;<lb/>binis funibus ab Arietaria Machina pendentibus Arietem
<pb xlink:href="052/01/039.jpg"/>ip&longs;um &longs;u&longs;tinent, atque inferunt: &agrave; ferreis contextis catenis <lb/>initia &longs;umebant. </s>
<s>At &longs;calam etiam nauticam faciebant a&longs;&longs;e&shy;<lb/>re in Arietis elatione anteri&ugrave;s clauis affixo, <expan abbr="habente&qacute;ue">habenteque</expan> re&shy;<lb/>te contextum iuxta cra&longs;&longs;itiem &longs;ufficiens, &amp; iuxta di&longs;tantiam <lb/>quatuor, vel etiam plurium digitorum foramina habens, vt <lb/>facil&egrave; &longs;upra murum a&longs;cendatur. </s>
<s><expan abbr="appendeb&atilde;t">appendebant</expan> autem ip&longs;um, <lb/>&amp; mouebant in Te&longs;tudine rotis octo pr&aelig;dita. </s>
<s>quippe qu&aelig; <lb/>iuxta quidem infernam pauimenti longitudinem, quadra&shy;<lb/>gintaduo: iuxta ver&ograve; latitudinem, vigintiocto cubitos ha&shy;<arrow.to.target n="note38"/><lb/>beat. </s>
<s>ip&longs;a pr&aelig;terea quatuor crura, qu&aelig; in pauimento ad al&shy;<lb/>titudinem iuxta angulos affiguntur, ex duobus &longs;imul iun&shy;<lb/>ctis lignis &longs;ingula faciebant, longitudinem habentia &longs;ingu&shy;<lb/>la cubitorum vigintiquatuor, &amp; cra&longs;&longs;itiem palmorum quin&shy;<lb/>que: iuxta ver&ograve; latitudinem vnius cubiti exi&longs;tentia. </s>
<s>In &longs;u&shy;<arrow.to.target n="note39"/><lb/>periori autem Arietari&aelig; Machin&aelig; parte Thoracium tan&shy;<lb/>quam &longs;epimentum &longs;truebant, vt in eo tut&egrave; &longs;tare po&longs;&longs;ent &longs;pe&shy;<lb/>ctantes ea, qu&ecedil; aduer&longs;us Arietem ab aduer&longs;arijs mittuntur. <arrow.to.target n="note40"/><lb/>Huiu&longs;cemodi autem Arietem &longs;exies mouebant de&longs;truen&shy;<lb/>tes &agrave; &longs;eptuaginta cubitis altitudinis, <expan abbr="rur&longs;us&qacute;ue">rur&longs;usque</expan> ad latera ad <lb/>&longs;eptuaginta cubitos peruertentes. </s>
<s>&agrave; centum autem viris <lb/>allatus mouebatur. </s>
<s>totum ver&ograve;, quod mouebatur pondus <lb/>talentorum fer&egrave; quadrigentorum erat. </s>
<s>ac demum figura <lb/>&longs;ubijcitur. </s></p>
<pb xlink:href="052/01/040.jpg"/><p type="margin">
<s><margin.target id="note37"/>a</s></p><p type="margin">
<s><margin.target id="note38"/>b</s></p><p type="margin">
<s><margin.target id="note39"/>c</s></p><p type="margin">
<s><margin.target id="note40"/>d</s></p><figure id="id.052.01.040.1.jpg" xlink:href="052/01/040/1.jpg"/>
<pb xlink:href="052/01/041.jpg"/><p type="main">
<s>Sciendum autem e&longs;t <expan abbr="&qtail;">quod</expan> Arietum alij quidem &agrave; virorum <lb/>multitudine reguntur, iuxta quorundam antiquorum me&shy;<lb/>chanicorum opinionem: alij ver&ograve; &agrave; contranitentibus lignis <lb/>di&longs;tenduntur: <expan abbr="alij&qacute;">alijque</expan> demum &longs;uper cylindros propelluntur: <lb/>po&longs;&longs;unt autem quandoque etiam funibus circumuolutis <lb/>adductionem, &amp; reuer&longs;ionem facientes, percu&longs;&longs;ionem effi&shy;<lb/>cere. </s>
<s>ver&ugrave;m ad artificem &longs;pectat iuxta magnitudines Arie&shy;<lb/>tum decentem quoque operationis v&longs;um, ac motionem ex&shy;<lb/>cogitare. </s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note41"/></s></p><p type="margin">
<s><margin.target id="note41"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>HElicas h&igrave;c intelligit mucrones illos, quos debet habere fer&shy;<lb/>rum in extremitate Arietis affixum tanquam eius ca&shy;<lb/>put, quod &longs;it cornibus pr&aelig;ditum: quibus murus ip&longs;e rum&shy;<lb/>pitur. </s>
<s>Helicas autem ip&longs;os vocauit ad &longs;imilitudinem pampino&shy;<lb/>rum vitis, qui &agrave; Gr&aelig;cis Helices nuncupantur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note42"/></s></p><p type="margin">
<s><margin.target id="note42"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Crura Arietis h&igrave;c appellat ea ligna, qu&aelig; &longs;uperius membra vo&shy;<lb/>cauit, qu&aelig; in figura huius capitis manife&longs;ta &longs;unt, quemadmo&shy;<lb/>dum in &longs;uperiori capite adnotauimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note43"/></s></p><p type="margin">
<s><margin.target id="note43"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Thoracium propri&egrave; e&longs;t &longs;umitas mali nauis, vbi &longs;pectatores <lb/>&longs;tant<emph.end type="italics"/> <foreign lang="greek">a)po\ tou_ qewre_in</foreign> <emph type="italics"/>qua&longs;i<emph.end type="italics"/> <foreign lang="greek">qewra/kion</foreign>: <emph type="italics"/>&longs;eu vas quoddam &egrave; lignis <lb/>con&longs;tructum, &amp; &longs;umitati mali nauis affixum, in quo &longs;pectatores <lb/>ip&longs;i commod&egrave;, tute&queacute; stare po&szlig;int. </s>
<s>ad eius autem &longs;imilitudinem h&igrave;c <lb/>thoracium appellat paruam illam machinullam, quam in altiori <lb/>parte Arietari&aelig; machin&aelig; con&longs;truebant, vt in ea &longs;pectatores &longs;ine <lb/>offen&longs;ione &longs;tantes cernerent ea, qu&aelig; ab aduer&longs;arijs ad perfringen&shy;<lb/>dum Arietem demittuntur: darent&queacute; &longs;ignum ijs, qui <expan abbr="Ariet&etilde;">Arietem</expan> mo&shy;<lb/>uent, ne tunc ip&longs;um propellant, &longs;ed retro trahant.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note44"/></s></p><p type="margin">
<s><margin.target id="note44"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Sexies h&igrave;c intellige &longs;ex motibus iuxta &longs;ex recti motus inter&shy;<lb/>ualla factis. </s>
<s>nam arietem ip&longs;um regentes, &longs;ex motibus eum mo&shy;<lb/>uebant, &longs;cilicet ant&egrave;, retro, dextror&longs;um; &longs;ini&longs;tror&longs;um, &longs;ur&longs;um, at&shy;<lb/>que deor&longs;um: ne &longs;emper eodem in loco murus inca&longs;&longs;um percute&shy;<lb/>retur, &longs;ed diuer&longs;is in locis percu&longs;&longs;us citius de&longs;trueretur. </s>
<s>quem&shy;<lb/>admodum declarat Athen&aelig;us in primo libro &longs;u&aelig; de rebus bellicis <lb/>tractationis.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/042.jpg"/><p type="main">
<s><emph type="center"/>De con&longs;tructione &longs;calarum, qu&aelig; &longs;pectatores vocantur. </s>
<s><lb/>Cap. </s>
<s>XII.<emph.end type="center"/></s></p><p type="main">
<s>SI murorum cra&longs;&longs;itiem agno&longs;cere, &amp; aduer&longs;o&shy;<lb/>rum operationes, ac multitudinem ex aduer&shy;<lb/>&longs;o per&longs;picere: necnon eas, qu&aelig; intra murum <lb/>circa ciuitatem tum diurn&ecedil;, tum nocturn&ecedil; <expan abbr="fi&utilde;t">fiunt</expan> <lb/>actiones, <expan abbr="in&longs;idiarum&qacute;ue">in&longs;idiarumque</expan> &longs;tructiones ob&longs;erua&shy;<lb/>re voluerimus: &longs;pectatorem huiu&longs;cemodi con&longs;truemus. </s>
<s><lb/>Duo ligna quadrangula parte altera latiora &longs;u&longs;cipientes, <lb/>latitudinem habentia <expan abbr="vnumquodq;">vnumquodque</expan> duodecim digitorum, <lb/>cra&longs;&longs;itudinem ver&ograve; vnumquodque octo, erecta con&longs;titue&shy;<lb/>mus. </s>
<s>quorum alterum quidem &longs;it inter duo ad verticem ia&shy;<lb/>centia, itidem iuxta cra&longs;&longs;itiem parte altera latiora ip&longs;a quo&shy;<lb/>que exi&longs;tentia, abinuicem ver&ograve; di&longs;tantia quantum iuxta la&shy;<lb/>titudinem ip&longs;um erectum lignum di&longs;tare pote&longs;t. </s>
<s>Similiter <lb/>autem alterum quoque ad alia duo c&ugrave;m &aelig;qualia, tum &longs;imi&shy;<arrow.to.target n="note45"/><lb/>lia, <expan abbr="&longs;imiliter&qacute;ue">&longs;imiliterque</expan> iacentia ponatur. </s>
<s>ex aduer&longs;o autem duo&shy;<lb/>rum duplorum lignorum iuxta medium aliud lignum ter&shy;<lb/>ram ver&longs;us ponatur, quipp&egrave; quod ip&longs;is duplis iacentibus <lb/>opponatur, <expan abbr="atq;">atque</expan> coniungatur iuxta duo erecta con&longs;i&longs;tentia. <lb/><arrow.to.target n="note46"/><lb/>ac <expan abbr="dem&utilde;">demum</expan> ba&longs;is ip&longs;a configuretur in&longs;tar gr&aelig;c&aelig; litter&aelig; H &longs;olu&shy;<lb/>t&aelig; habentis latera duplicibus lineis con&longs;tantia. </s>
<s>ab extremis <lb/>vero duorum duplorum iacentium quatuor a&longs;&longs;i&longs;tere facie&shy;<lb/>mus ligna, quorum vtique bina <expan abbr="vnicuiq;">vnicuique</expan> &longs;ur&longs;um re&longs;i&longs;tant, <lb/><expan abbr="ip&longs;a&qacute;ue">ip&longs;aque</expan> erecta con&longs;i&longs;tentia &longs;uffulciant. </s>
<s>h&aelig;c autem erecta <lb/>&longs;u&longs;cipiant iuxta medium alia duo ligna, quorum vnum&shy;<lb/>quodque &longs;it latitudinis digitorum octo: iuxta ver&ograve; cra&longs;&longs;i&shy;<lb/>tiem vnumquodque &longs;ex: <expan abbr="di&longs;tent&qacute;ue">di&longs;tentque</expan> abinuicem ad minus <lb/>tribus pedibus. </s>
<s>h&aelig;cautem quatuor indirectum adinuicem <lb/>forentur, <expan abbr="clauis&qacute;ue">clauisque</expan> &longs;imul transfigantur: erecta quidem, <lb/>iuxta duas tertias eorum partes &longs;ur&longs;um: interpo&longs;ita ver&ograve; <lb/>iuxta &longs;extam eorum partem deor&longs;um. </s>
<s>de&longs;cendant autem <lb/>ab erectis, <expan abbr="rur&longs;us&qacute;">rur&longs;usque</expan>; a&longs;cendant dum &agrave; clauo  volubiliter fe<lb/>runtur. </s>
<s>Rur&longs;us autem h&aelig;c quoque iuxta duas eorum ter&shy;<lb/>tias partes, necnon iuxta reliquam &longs;extam partem &agrave; clauo <lb/>forentur. </s>
<s>Ver&ugrave;m in pr&aelig;&longs;entia duas tertias, totius longitu-<pb xlink:href="052/01/043.jpg"/>dinis intellige, &longs;patium illud, quod e&longs;t iuxta duas &longs;extas par&shy;<lb/>tes, quippe qu&aelig; <expan abbr="terti&atilde;">tertiam</expan> totius longitudinis partem efficiunt. </s>
<s><lb/>H&aelig;c <expan abbr="itaq;">itaque</expan> de&longs;cendentia ligna iuxta medium &longs;calam leuem <lb/>clauis transfixam &longs;u&longs;cipiant, cuius vtique claui ad iam di&shy;<lb/>cta foramina &longs;int affixi. </s>
<s>At crura &longs;calam ip&longs;am con&longs;tituen&shy;<lb/>tia &longs;int quoad latitudinem digitorum ad minus &longs;ex: quo ve&shy;<lb/>r&ograve; ad cra&longs;&longs;itudinem, quatuor. </s>
<s>Ab inferiori autem clauo, <lb/>qui per ligna erecta &longs;tantia tran&longs;it, ad eleuatam &longs;ur&longs;um &longs;ex&shy;<lb/>tam <expan abbr="de&longs;cend&etilde;tium">de&longs;cendentium</expan> lignorum partem capi&longs;trum apponatur <lb/>ba&longs;em quandam, vel funium connexionem comprehen&shy;<lb/>dens, vel ad annulos ferreos propter attractionem pene&shy;<lb/>trans. </s>
<s>Lignum autem e&longs;t circumflexum, ac flexile longitu&shy;<lb/>dinis circiter octo pedum, vt &longs;ufficienter attrahere, <expan abbr="defer-re&qacute;ue">defer&shy;<lb/>reque</expan> per medium erectorum lignorum eleuatum &longs;ur&longs;um <lb/>&longs;extam partem: totam ver&ograve; inclinatam partem vn&agrave; cum ip&shy;<lb/>&longs;a &longs;cala &longs;ublimem in altitudinem eleuare po&longs;&longs;it. </s>
<s>Eueniet <lb/><expan abbr="itaq;">itaque</expan> vt dum h&aelig;c pars &agrave; capi&longs;tro ad inferiora trahitur, &agrave; reli<lb/>qua parte explorator in altitudinem miruminmodum eri&shy;<lb/>gatur, <expan abbr="&longs;cala&qacute;ue">&longs;calaque</expan> erecta permaneat, e&ograve; qu&ograve;d duobus clauis <lb/>connexa fuit. </s>
<s>Ver&ugrave;m oportet inferiorem partem, qu&aelig; &agrave; <lb/>capi&longs;tro retinetur &longs;i fieri pote&longs;t in &longs;tabilitate permanere. </s>
<s>&longs;in <lb/>min&ugrave;s: &agrave; tran&longs;uer&longs;alibus <expan abbr="penetr&atilde;tibuslignis">penetrantibus lignis</expan>, aut verticulis <lb/>iuxta iuncturas clau&longs;am in ip&longs;o &longs;tabilitatis tempore intre&shy;<lb/>pidam &longs;tare. </s>
<s>Pr&aelig;terea &longs;ciendum e&longs;t, qu&ograve;d &longs;upereminens <lb/>tertia erectorum lignorum pars ad eorum, qu&aelig; inclinantur <lb/>&longs;ecuritatem erigitur: &longs;uperior autem &longs;exta eorum, qu&aelig; in&shy;<lb/><arrow.to.target n="note47"/><lb/>clinantur, &longs;iue quarta interiecti inter ip&longs;a &longs;patij pars (vt &longs;u&shy;<lb/>perius manife&longs;tum fuit) ad &longs;u&longs;tentandam leuem &longs;calam du&shy;<lb/>pliciter &longs;ur&longs;um clauis transfixam: infima ver&ograve; &longs;exta eorum <lb/>pars propter capi&longs;tri ad ip&longs;am impetum in ea, qu&aelig; fit vehe&shy;<lb/>mentia, deor&longs;um trahet. </s>
<s>&longs;imul autem ip&longs;a quoque reliqu&aelig; <lb/><arrow.to.target n="note48"/><lb/>quintupl&aelig; partis, <expan abbr="&longs;cal&aelig;&qacute;ue">&longs;cal&aelig;que</expan> &longs;ur&longs;um latio deprehen&longs;a e&longs;t. </s>
<s>Sit <lb/>autem ex &longs;uppo&longs;itione altitudo erectorum &longs;tantium ligno&shy;<lb/>rum, v&longs;que ad duas eorum tertias partes, quanta e&longs;t altitu&shy;<lb/><arrow.to.target n="note49"/><lb/>do terti&aelig; muri partis. </s>
<s>&amp; ab ip&longs;o loco, v&longs;que ad duas tertias <lb/>eorum, qu&aelig; inclinantur lignorum partes, &longs;iue ad primum <lb/>coniunctionis &longs;cal&aelig; clauum, quantum e&longs;t muri dimidium:
<pb xlink:href="052/01/044.jpg"/>necnon &longs;cala ip&longs;a, quantum idem dimidium. </s>
<s>Qu&aelig; igitur <lb/>ex hi&longs;ce tribus componitur altitudo, tertia parte &longs;uper mu&shy;<lb/>rum exploratorem &longs;u&longs;tollet. atq; hoc per&longs;picuum e&longs;t. </s>
<s>C&ugrave;m <lb/>enim altitudo muri palmorum, vel pedum, vel cubitorum, <lb/>vel quarundam aliarum men&longs;urarum &longs;exaginta &longs;uppo&longs;ita <lb/>&longs;it: ligna, qu&aelig; ad ba&longs;im erecta &longs;tant &longs;ingula men&longs;urarum tri&shy;<lb/>ginta &longs;int: ad altitudinem autem viginti men&longs;urarum, cla&shy;<lb/>uum &longs;u&longs;cipiant. </s>
<s>du&aelig; &longs;iquidem terti&aelig; partes viginti men&longs;u&shy;<lb/>r&aelig; triginta men&longs;urarum &longs;unt. </s>
<s>at ligna, qu&aelig; ab erectis de&shy;<lb/>&longs;cendunt lignis, &longs;ingula quadraginta <expan abbr="quinq;">quinque</expan> men&longs;urarum <lb/>quoad longitudinem fiant, &agrave; iam dicto ver&ograve; clauo ad pri&shy;<lb/>mam &longs;cal&aelig; coniunctionem triginta <expan abbr="m&etilde;&longs;ur&aelig;">men&longs;ur&aelig;</expan> intercipiantur. </s>
<s><lb/>h&aelig; autem, du&aelig; terti&aelig; ip&longs;arum quadragintaquinque &longs;unt, <lb/><arrow.to.target n="note50"/><lb/>quemadmodum &longs;uperius iam o&longs;ten&longs;um e&longs;t. </s>
<s>&longs;it autem ip&longs;a <lb/>quoque &longs;cala ab ea coniunctione ad reliqu&agrave;m eius altitudi&shy;<lb/>nem aliarum triginta men&longs;urarum. </s>
<s>Qu&aelig; igitur ex hi&longs;ce tri&shy;<lb/>bus altitudinibus iuxta numerum colligitur altitudo men&shy;<lb/>&longs;uras octoginta complet. </s>
<s>h&aelig; autem, ip&longs;as &longs;exaginta tertia <lb/>parte &longs;uperant. </s>
<s>tertia namque pars viginti men&longs;ur&aelig; &longs;exa&shy;<lb/>ginta men&longs;urarum &longs;unt. </s>
<s>Ver&ugrave;m in &longs;uprema &longs;cal&aelig; parte te&shy;<lb/>gumentum quoque fiat ex corio cra&longs;&longs;o, atque robu&longs;to, in&shy;<lb/>&longs;tar clypei circumflexi: aut dor&longs;um acutum circa medium <lb/>habens, <expan abbr="necn&otilde;">necnon</expan> declinationem ad latera &longs;ufficientem ad ex&shy;<lb/>ploratorem &agrave; &longs;agitta, &longs;eu funda pr&aelig;&longs;eruandum. </s>
<s><expan abbr="N&otilde;">non</expan> parum <lb/>autem auxilium pr&aelig;&longs;tabunt etiam funes &longs;ubtiles, robu&longs;ti, <lb/>&longs;uperioris leuis &longs;cal&aelig; cruribus circumalligati, &amp; ad clauo&shy;<lb/>rum v&longs;que coniunctionem exten&longs;i. </s>
<s>ne altitudinis porrectio, <lb/>vel contingens lapides iacientis percu&longs;&longs;io fractionem, con&shy;<lb/>uul&longs;ionem&ugrave;e in lignis efficiat, <expan abbr="exploratorem&qacute;ue">exploratoremque</expan> perimat. </s>
<s><lb/>Ad ip&longs;ius autem &longs;pectatoris erectam, atque indecliuem &longs;ta&shy;<lb/>bilitatem maxim&egrave; conferunt etiam quatuor funes erecto&shy;<lb/>rum &longs;tantium lignorum extremis alligati, atque exten&longs;i: &longs;i <lb/>&egrave; contrari&ograve; &longs;ibi inuicem ferreis, aut ligneis palis terr&aelig; pro&shy;<lb/>cul affixis alligati fuerint. </s>
<s>ne opus propter altitudinem in <lb/>extremis pondero&longs;um exi&longs;tens corruat. </s>
<s>atque figur&aelig; tum <lb/>iacens, tum erecta &longs;ubiect&aelig; &longs;unt. </s></p>
<pb xlink:href="052/01/045.jpg"/><p type="margin">
<s><margin.target id="note45"/>a</s></p><p type="margin">
<s><margin.target id="note46"/>b</s></p><p type="margin">
<s><margin.target id="note47"/>c</s></p><p type="margin">
<s><margin.target id="note48"/>d</s></p><p type="margin">
<s><margin.target id="note49"/>e</s></p><p type="margin">
<s><margin.target id="note50"/>f</s></p><figure id="id.052.01.045.1.jpg" xlink:href="052/01/045/1.jpg"/><p type="main">
<s>Fit autem &longs;impliciter eiu&longs;dem &longs;pectatoris ba&longs;is ex tribus <lb/>&longs;olis lignis iuxta latitudinem terra po&longs;itis, duobus quidem <lb/><expan abbr="tr&atilde;&longs;uer&longs;alibus">tran&longs;uer&longs;alibus</expan> abinuicem di&longs;tantibus, &amp; alio iuxta medium <lb/>&egrave; <expan abbr="c&otilde;trari&ograve;">contrari&ograve;</expan> coaptato, quemadmodum gr&aelig;ca littera H &longs;oluta <lb/>ex duplicibus lineis configurata. </s>
<s>at &longs;uper ip&longs;is tran&longs;uer&longs;is &agrave; <lb/><arrow.to.target n="note51"/><lb/>quadam lingula iuxta medium erecta ligna con&longs;tituuntur: <lb/>ab extremis ver&ograve;, quatuor illa, qu&aelig; ip&longs;is re&longs;i&longs;tunt. </s></p>
<pb xlink:href="052/01/046.jpg"/><p type="margin">
<s><margin.target id="note51"/>g</s></p><figure id="id.052.01.046.1.jpg" xlink:href="052/01/046/1.jpg"/><p type="main">
<s>Fit <expan abbr="eti&atilde;">etiam</expan> aliter ex tribus lignis in terra iacentibus, &agrave; &longs;e <expan abbr="inuic&etilde;">inui<lb/>cem</expan> autem <expan abbr="par&utilde;">parum</expan> di&longs;tantibus quatenus iuxta latitudinem ere&shy;<lb/>cta ligna &longs;u&longs;cipere po&longs;&longs;int. </s>
<s>hi&longs;ce autem iacentibus &longs;upern&egrave; <lb/>re&longs;ectis: atque alio tum &aelig;quali, tum &longs;imili, tum etiam &longs;imi&shy;<lb/>liter infern&egrave; re&longs;ecto ip&longs;is erecta iuxta latitudinem infigun&shy;<lb/>tur: ab extremis autem iacentium re&longs;i&longs;tentia duo ad latitu&shy;<lb/>dines erectorum: ac demum duo ab obliquo ad cra&longs;&longs;itudi&shy;<lb/><arrow.to.target n="note52"/><lb/>nes obliqu&egrave;. </s>
<s>Ver&ugrave;m neutra i&longs;tarum tutti&longs;&longs;ima e&longs;t quemad&shy;<lb/>modum ea, qu&aelig; pri&ugrave;s enarrata fuit. </s>
<s>Interuallum ver&ograve;, quo <lb/>ligna c&ugrave;m tran&longs;uer&longs;alia po&longs;ita, tum erecta &agrave; &longs;e inuicem di&shy;<lb/>&longs;tant artifex determinabit, ad altitudinis compo&longs;itionem <lb/><expan abbr="commen&longs;urationem&qacute;">commen&longs;urationemque</expan>; re&longs;piciens. </s>
<s>&longs;imiliter autem magnitu&shy;<lb/>dines etiam lignorum tum ba&longs;is, tum altitudinis ad tria in&shy;<lb/><arrow.to.target n="note53"/><lb/>terualla &longs;ecundum proportionem augebit, <expan abbr="atq;">atque</expan> imminuet. </s></p><p type="margin">
<s><margin.target id="note52"/>h</s></p><p type="margin">
<s><margin.target id="note53"/>i</s></p><figure id="id.052.01.046.2.jpg" xlink:href="052/01/046/2.jpg"/>
<pb xlink:href="052/01/047.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>COn&longs;tructio ba&longs;is &longs;cal&aelig; prioris, quam Autor in principio <lb/>pr&aelig;&longs;entis capitis tradidit prim&ugrave;m &agrave; figura, qu&aelig; in vetere <lb/>exemplari erat, hoc di&longs;crepat: qu&ograve;d &longs;cilicet <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>duorum erect&egrave; stantium lignorum inter alia duo ligna in terra <lb/>aduerticem, ide&longs;t &longs;e &longs;e inter&longs;ecando iacentia docet Autor e&longs;&longs;e po&shy;<lb/>nendum: in figura ver&ograve;, eorum vtrumque in altero iam dictorum <lb/>duorum in terra pro&longs;tratorum lignorum infixum e&longs;t. </s>
<s>Deinde mu&shy;<lb/>tila, atque imperfecta eiu&longs;dem prim&aelig; ba&longs;is con&longs;tructio apud Au&shy;<lb/>torem e&longs;&longs;e mihi videtur. </s>
<s>C&ugrave;m enim v&longs;que ad illa verba [&longs;imili&shy;<lb/>ter&queacute; iacentia ponatur.] nondum totam ip&longs;am primam ba&longs;im con&shy;<lb/>&longs;truxerit: ad con&longs;tructionem ba&longs;is &longs;ecund&aelig; figur&aelig; tran&longs;ire vide&shy;<lb/>tur illis verbis [ex aduer&longs;o autem duorum duplorum] id enim, <lb/>quod his verbis pr&aelig;cipit in prim&aelig; figur&aelig; ba&longs;i nequaquam fieri <lb/>pote&longs;t, c&ugrave;m duo in terra iacentia ligna &longs;e &longs;e inter&longs;ecent, vt cuili&shy;<lb/>bet manife&longs;tum e&longs;t. </s>
<s>Aut itaque po&longs;t illa verba [&longs;imiliter&queacute; iacen&shy;<lb/>tia ponatur.] nonnulla de&longs;iderantur, quibus con&longs;tructio, qu&aelig; vi&shy;<lb/>detur e&longs;&longs;e ip&longs;ius ba&longs;is &longs;ecund&aelig; figur&aelig;, continuetur, fiat&queacute; vna &amp; <lb/>eadem cum &longs;uperiori ba&longs;is prim&aelig; figur&aelig; con&longs;tructione, quod fieri <lb/>nequit (vt iam diximus) propter duorum in terra pro&longs;tratorum <lb/>lignorum mutuam inter&longs;ectionem: aut qu&aelig;dam eodem in loco de&shy;<lb/>&longs;unt, quibus con&longs;tructio prim&aelig; ba&longs;is perficiatur, &amp; ab ip&longs;ius &longs;e&shy;<lb/>cund&aelig; ba&longs;is con&longs;tructione di&longs;tinguatur, <expan abbr="atq;">atque</expan> hoc modo tota &longs;ecun&shy;<lb/>d&aelig; ba&longs;is con&longs;tructio &longs;uperuacanea erit. </s>
<s>quando quidem inferi&ugrave;s <lb/>etiam in fine huiu&longs;ce capitis <expan abbr="eand&etilde;met">eandemmet</expan> con&longs;tructionem Autor tra&shy;<lb/>dit. </s>
<s>Ver&ugrave;m quid de hac re &longs;entiendum &longs;it ijs, qui perfectius habent <lb/>exemplar iudicandum relinquo, mihi ver&ograve; &longs;atis &longs;it huiu&longs;ce loci <lb/>imperfectionem animaduerti&longs;&longs;e.<emph.end type="italics"/><lb/><arrow.to.target n="note54"/></s></p><p type="margin">
<s><margin.target id="note54"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ex aduer&longs;o autem duorum duplorum lignorum] Dupla ligna <lb/>in toto pr&aelig;&longs;enti capite vocat Autor illa duo, qu&aelig; in terra prostra&shy;<lb/>ta iacent, &amp; veluti <expan abbr="fundament&utilde;">fundamentum</expan>, ac <expan abbr="pauiment&utilde;">pauimentum</expan> ip&longs;ius ba&longs;is &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note55"/></s></p><p type="margin">
<s><margin.target id="note55"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in&longs;tar Gr&aelig;c&aelig; litter&aelig;<emph.end type="italics"/> H <emph type="italics"/>&longs;olut&aelig;] Gr&aelig;ca littera, vocata Ita, du&shy;<lb/>pliciter a&longs;criptoribus figuratur: vno quidem modo &longs;ic<emph.end type="italics"/> H, <emph type="italics"/>qu&aelig; &longs;olu&shy;<lb/>ta dicitur quoniam ex partibus &longs;uis &longs;olutis trina calami motione <lb/>fit: alio ver&ograve; modo &longs;ic n, qu&aelig; ligata nuncupatur, quia cunctis &longs;uis<emph.end type="italics"/>
<pb xlink:href="052/01/048.jpg"/><emph type="italics"/>partibus colligatis vnico calami continuo motu perficitur. </s>
<s>ip&longs;i igi&shy;<lb/>tur &longs;olute hoc modo<emph.end type="italics"/> &verbar;&verbar;=&verbar;&verbar; <emph type="italics"/>duplicibus lineis fact&aelig; &longs;ecundam &longs;ca&shy;<lb/>l&aelig; ba&longs;im Autor a&szlig;imilari dixit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note56"/></s></p><p type="margin">
<s><margin.target id="note56"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[vt &longs;uperi&ugrave;s manife&longs;tum fuit] &longs;cilicet ex con&longs;tructione ip&longs;ius <lb/>machin&aelig;.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note57"/></s></p><p type="margin">
<s><margin.target id="note57"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Animaduertendum qu&ograve;d c&ugrave;m ea &longs;cal&aelig; pars, qu&aelig; est &agrave; prima <lb/>eius coniunctione, v&longs;que ad ip&longs;ius &longs;ummitatem, triginta men&longs;u&shy;<lb/>rarum iuxta longitudinem ab Autore &longs;upponatur: dubio procul <lb/>pars eius inferior &longs;ub clauis exi&longs;tens, quinta iam dict&aelig; longitu&shy;<lb/>dinis pars &longs;upponi videtur. </s>
<s>Quare c&ugrave;m ait [reliqu&aelig; quintupl&aelig; <lb/>partis] de ea &longs;cal&aelig; parte intelligendum e&longs;t, qu&aelig; &agrave; tam dictis cla&shy;<lb/>uis ad totius &longs;cal&aelig; &longs;ummitatem v&longs;que porrigitur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note58"/></s></p><p type="margin">
<s><margin.target id="note58"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&amp; ab ip&longs;o loco] hoc e&longs;t ab ea parte, vbi iam dict&aelig; du&ecedil; terti&aelig; li&shy;<lb/>gnorum erectorum partes terminantur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note59"/></s></p><p type="margin">
<s><margin.target id="note59"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Quemadmodum &longs;uperi&ugrave;s iam o&longs;ten&longs;um e&longs;t] videlicet vt ex <lb/>priori machin&aelig; con&longs;tructione patuit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note60"/></s></p><p type="margin">
<s><margin.target id="note60"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[lingula] h&igrave;c intelligenda e&longs;t pars qu&aelig;dam erectorum ligno&shy;<lb/>rum inferior, &longs;ubtilior, &amp; quadrangula, qua tanquam cardine <lb/>quodam ip&longs;a erecta ligna in pro&longs;tratorum in terra duorum ligno&shy;<lb/>rum quadrangulis foraminibus infiguntur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note61"/></s></p><p type="margin">
<s><margin.target id="note61"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[pri&ugrave;s enarrata] &longs;cilicet prima ba&longs;is, quam ab Autoris con&shy;<lb/>&longs;tructione aliquantulum di&longs;crepantem e&longs;&longs;e o&longs;tendimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note62"/></s></p><p type="margin">
<s><margin.target id="note62"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ad tria interualla] videlicet ad trin&aelig; dimen&longs;ionis interualla, <lb/>nempe longitudinem, latitudinem, atque cra&szlig;itiem.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>H&aelig;c ad pr&aelig;&longs;entis capitis dilucidationem animaduer&longs;ione, ex&shy;<lb/>plicatione&queacute; digna mihi vi&longs;a &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>De con&longs;tructione Turrium &longs;ecundum Polyidis Thetali <lb/>di&longs;cipulos. </s>
<s>Cap. </s>
<s>XIII.<emph.end type="center"/></s></p><p type="main">
<s>DIades quidem &amp; Charias Polyjdis Thetali di&shy;<lb/>&longs;cipuli, qui vn&agrave; cum Alexandro Macedone in <lb/>militiam profecti &longs;unt mechanici primi c&ugrave;m <arrow.to.target n="note63"/><lb/>terebras, tum &longs;calas nauticas, tum etiam eas, <lb/>qu&aelig; rotis feruntur turres ligneas adinuene&shy;<lb/>runt. </s>
<s>atque minores quidem earum &longs;exaginta cubitorum <arrow.to.target n="note64"/><lb/>quoad altitudinem faciebant: ba&longs;im autem quadrabant,
<pb xlink:href="052/01/049.jpg"/>vnumquodque latus, tum longitudinis, tum latitudinis de&shy;<lb/>cem &amp; &longs;eptem cubitorum ponentes: decem tectis pr&aelig;ditas <lb/>ip&longs;as facientes: in &longs;upremo vero tecto cumulum &aelig;quiqua&shy;<lb/>drangulum intercludentes, &longs;ecundum proportionem quin&shy;<lb/>t&aelig; partis ba&longs;is are&aelig;, &longs;eu &longs;patij, qu&ograve;d &agrave; quatuor lateribus <arrow.to.target n="note65"/><expan abbr="circumquaq;">cir<lb/>cumquaque</expan> terminatur, quemadmodum con&longs;equenter per&shy;<lb/>&longs;picuum erit. </s>
<s>maiores autem, <expan abbr="harum&qacute;">harumque</expan>; &longs;e&longs;quialteras, quin&shy;<lb/>decim tectis con&longs;tructas faciebant: altitudinis ver&ograve; cubito&shy;<lb/>rum nonaginta: necnon duplas, viginti tectis con&longs;tantes, <lb/>quo ad altitudinem ver&ograve;, centum &amp; viginti. </s>
<s>Rur&longs;us autem <lb/>vnumquodque latus ba&longs;is duplarum turrium vigintiqua&shy;<lb/>tuor fer&egrave; cubitorum. </s>
<s>&amp; maiores, atque minores &longs;ecund&ugrave;m <lb/>proportionem con&longs;truebant ad tres dimen&longs;iones ligna au&shy;<lb/>gentes vel minuentes, nempe iuxta longitudinem, &amp; latitu&shy;<lb/>dinem, atque cra&longs;&longs;itiem. </s>
<s>Similiter autem tectorum quoque <lb/>diui&longs;iones iuxta altitudinis commen&longs;urationem partieban&shy;<lb/>tur. </s>
<s>&longs;ex quidem, &amp; quandoque octo rotis pr&aelig;ditas &longs;ecun&shy;<lb/>dum magnitudinis tumorem ip&longs;as faciebant: in omnibus <lb/>&longs;emper quintam ba&longs;is partem &longs;ur&longs;um ponebant. </s></p><p type="margin">
<s><margin.target id="note63"/>a. </s>
<s>b</s></p><p type="margin">
<s><margin.target id="note64"/>c</s></p><p type="margin">
<s><margin.target id="note65"/>d</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note66"/></s></p><p type="margin">
<s><margin.target id="note66"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>TErebras h&igrave;c intelligit eas, quas de&longs;crip&longs;it &longs;uperi&ugrave;s in Ca&shy;<lb/>pite &longs;eptimo.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note67"/></s></p><p type="margin">
<s><margin.target id="note67"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Scalas nauticas vocat omnes &longs;calas ex funibus factas, <lb/>quarum multis in locis huius operis mentio fit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note68"/></s></p><p type="margin">
<s><margin.target id="note68"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Quadrare ba&longs;im nil aliud hoc in loco e&longs;t, ni&longs;i quodlibet laterum <lb/>eius in quotlibet partes &longs;ecare, at que numerum ip&longs;arum <expan abbr="parti&utilde;">partium</expan> in <lb/>&longs;eip&longs;um multiplicare, vt area quadrata ip&longs;ius ba&longs;is producatur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note69"/></s></p><p type="margin">
<s><margin.target id="note69"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[con&longs;equenter] &longs;cilicet inferi&ugrave;s in &longs;equenti capite.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Animaduer&longs;ione ver&ograve; dignum e&longs;t, qu&ograve;d in tradenda pr&aelig;&longs;enti <lb/>machinarum ob&longs;idionalium, qu&aelig; turres vocantur, con&longs;tructione <lb/>iuxta Polyidis Thetali di&longs;cipulos, &longs;cilicet Diadem, &amp; Chariam <lb/>antiquos mechanicos: non declarauit perfect&egrave; Autor omnes ip&longs;a&shy;<lb/>rum turrium men&longs;uras, &longs;ed qua&longs;dam duntaxat breui&szlig;im&egrave; teti&shy;<lb/>git: re&longs;eruans &longs;ibi eas declarandas inferi&ugrave;s in &longs;equenti capite,<emph.end type="italics"/>
<pb xlink:href="052/01/050.jpg"/><emph type="italics"/>po&longs;tquam turrium ip&longs;arum con&longs;tructionem &longs;ecundum Apollodori <lb/>doctrinam pri&ugrave;s tradiderit. </s>
<s>Quapropter non ab re factum iri <lb/>exi&longs;timo, &longs;i qu&aelig;dam nos hoc in loco ad earum men&longs;urarum decla&shy;<lb/>rationem, perfectam&queacute; cognitionem adnotabimus. </s>
<s>C&ugrave;m itaque <lb/>minoris turris altitudinem quidem 60 cubitorum, ba&longs;is autem <lb/>eius vnumquodque latus tetragonicum, hoc est radicem quadra&shy;<lb/>tam 17 fui&longs;&longs;e dixerit: area quadrata ip&longs;ius ba&longs;is 280 dubio pro&shy;<lb/>cul erit: latus autem cubicum are&aelig; cubic&aelig; inter ba&longs;im, &amp; primum <lb/>tectum interiect&aelig; erit &longs;imiliter 17: ip&longs;a demum area cubica 4913. <lb/>c&ugrave;m ver&ograve; decimum, &longs;iue &longs;upremum ip&longs;ius quadrangulum te&shy;<lb/>ctum quintam partem are&aelig; iam dict&aelig; ba&longs;is fui&longs;&longs;e a&longs;&longs;eruerit: erit <lb/>ip&longs;a quidem pars quinta 57 3/4 fer&egrave;. </s>
<s>huius autem numeri latus <lb/>tetragonicum, nempe radix ip&longs;ius 57 3/4 fer&egrave; erit latus vniu&longs;cu&shy;<lb/>iu&longs;que laterum iam dicti quadrangularis &longs;upremi tecti: qu&aelig; ra&shy;<lb/>dix tanquam latus cubicum &longs;i multiplicet ip&longs;am 57 3/4 fer&egrave; qua&shy;<lb/>dratam aream, producetur area cubica, qu&aelig; inter culmen &amp; pro&shy;<lb/>ximum culminis tectum intercipitur. </s>
<s>Datis itaque men&longs;uris ba&shy;<lb/>&longs;is, &amp; culminis harum minorum turrium, data&queacute; tota earum alti&shy;<lb/>tudine: nemini dubium qu&ograve;d peritus Arithmetic&aelig;, Geometri&aelig;&queacute; <lb/>artifex eodem modo inueniet <expan abbr="eti&atilde;">etiam</expan> reliquorum octo tectorum men&shy;<lb/>&longs;uras: videlicet quadratas eorum areas, arearum&queacute; tetragonica <lb/>latera: necnon latera cubica, &amp; areas cubicas inter ip&longs;a tecta in&shy;<lb/>teriectas, ab ip&longs;is&queacute; tectis, &amp; &agrave; quatuor ip&longs;ius turris faciebus com&shy;<lb/>prehen&longs;as. </s>
<s>Pr&aelig;terea quoniam maiores etiam turres tecta quinde&shy;<lb/>cim habentes &longs;e&longs;quialteras priorum ip&longs;os Polyidis di&longs;cipulos con&shy;<lb/>&longs;truxi&longs;&longs;e ait, quarum longitudo erat 90 cubitorum: &longs;i harum quo&shy;<lb/>que reliquas men&longs;uras inuenire voluerimus, habentes iam ba&longs;im <lb/>&longs;e&longs;quialteram prioris ba&longs;is, procedemus &longs;icut in minoribus. </s>
<s>At <lb/>quoniam duplas etiam priorum minorum, tectis vigiti pr&aelig;ditas, <lb/>altitudinem autem 120 cubitorum habentes ait con&longs;tructas fui&longs;&shy;<lb/>&longs;e: non immerite latus tetragonicum ba&longs;is earum 24 fer&egrave; cubito&shy;<lb/>rum e&longs;&longs;e dixit. </s>
<s>c&ugrave;m enim minorum, &longs;cilicet &longs;ubduplarum ba&longs;is &longs;it, <lb/>vt iam o&longs;tendimus, 289: dupl&aelig; eius erit 578. ver&ugrave;m area, qu&aelig; ex <lb/>24 tetragonico latere producitur, e&longs;t 576. quare latus tetragoni&shy;<lb/>cum ip&longs;ius ba&longs;is iam dictarum duplarum turrium (vt rect&egrave; in&shy;<lb/>quit Autor) 24 fer&egrave; cubitorum erit. </s>
<s>culmen autem earundem<emph.end type="italics"/>
<pb xlink:href="052/01/051.jpg"/><emph type="italics"/>erit 115 1/2 fer&egrave;. </s>
<s>&longs;imiliter autem reliquorum <expan abbr="eti&atilde;">etiam</expan> quo ad areas, <lb/>&amp; latera tectorum omnes men&longs;ur&aelig; reperientur tum in &longs;e&longs;quial&shy;<lb/>teris, tum in duplis turribus, quemadmodum in earum &longs;ub&longs;e&longs;qui&shy;<lb/>alteris, &longs;ubduplis&queacute; diximus. </s>
<s>Ver&ugrave;menimuero tria nobis adno&shy;<lb/>tanda &longs;unt, primum qu&ograve;d turres &longs;e&longs;quialter&aelig;, vel dupl&aelig; aliarum <lb/>turrium e&longs;&longs;e dicuntur non &longs;ol&ugrave;m iuxta earum altitudinem, &amp; <lb/>iuxta tectorum numerum: verumetiam iuxta areas ba&longs;ium &amp; <lb/>culminum, &amp; reliquorum tectorum omnes men&longs;uras: necnon <lb/>iuxta rotarum numerum, &amp; magnitudinem. </s>
<s>Quemadmodum <lb/>enim &longs;e habet 120 cubitorum altitudo ad 60 cubitorum altitudi&shy;<lb/>nem, &amp; 20 ad 10 tecta: ita &longs;e habet etiam 578 area ba&longs;is ad <lb/>289 ba&longs;is aream: necnon 115 1/2 fer&egrave; area culminis ad 57 3/4 <lb/>fer&egrave; culminis aream. </s>
<s>Secund&ograve; adnotandum qu&ograve;d augendo, vel <lb/>minuendo turrium altitudinem, omnes etiam earum partes pro&shy;<lb/>portionaliter nobis augend&aelig; &longs;unt: nempe are&aelig; quadrat&aelig;, &verbar;&amp; cu&shy;<lb/>bic&aelig;: latera quadrata, &amp; cubica tum ba&longs;ium, tum culminum, <lb/>tum etiam reliquorum tectorum, &amp; &longs;patiorum inter ip&longs;a interie&shy;<lb/>ctorum: necnon lignorum omnium longitudo, latitudo, atque cra&longs;&shy;<lb/>&longs;ities quod Autor in fine huius capitis breuiter tetigit. </s>
<s>Terti&ograve; <lb/>adnotandum, qu&ograve;d reliquorum tectorum inter ba&longs;im, &amp; culmen <lb/>iacentium diui&longs;iones proportionaliter iuxta altitudinis commen&shy;<lb/>&longs;urationem fieri debent: maiores quidem, qu&aelig; ba&longs;i: minores ve&shy;<lb/>r&ograve;, qu&aelig; culmini propinquiores futur&aelig; &longs;unt. </s>
<s>quod etiam Autor <lb/>illis verbis [&longs;imiliter autem tectorum quoque diui&longs;iones iuxta al&shy;<lb/>titudinis commen&longs;urationem partiebantur.] breui&szlig;im&egrave; innui&longs;&longs;e <lb/>videtur. </s>
<s>H&aelig;c autem in pr&aelig;&longs;entia paucula de men&longs;uris harum <lb/>turrium ad dilucidationem huiu&longs;ce capitis breuiter nobis dicta <lb/>&longs;int. </s>
<s>in &longs;equenti ver&ograve; capite po&longs;tquam turrium con&longs;tructionem <lb/>iuxt&aelig; doctrinam Apollodori tradiderit Autor, exqui&longs;itam de iam <lb/>dictis omnibus turrium men&longs;uris doctrinam nobis traditurus e&longs;t.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/052.jpg"/><p type="main">
<s><emph type="center"/>De con&longs;tructione turrium &longs;ecundum Apollodorum. </s>
<s><lb/>Cap. </s>
<s>XIIII.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note70"/></s></p><p type="margin">
<s><margin.target id="note70"/>a</s></p><p type="main">
<s>AT Apollodorus grauiorem pedes ver&longs;us tur&shy;<lb/>rem con&longs;truens, &longs;ub &longs;e&longs;quialteram ip&longs;orum <lb/>&longs;exaginta cubitorum, &amp; quatuor rotis pr&aelig;di&shy;<lb/>tam ip&longs;am declarat, pedum quoad altitudi&shy;<lb/>nem &longs;exaginta o&longs;tendens. </s>
<s>vnde ip&longs;e quoque <lb/>vnumquodque circa ba&longs;im latus pedum &longs;edecim iuxta lon&shy;<lb/>gitudinem faciebat, vltra pedalem in extremitatibus pro&shy;<lb/>minentiam: quoad latitudinem, vnius pedis, &amp; digitorum <lb/>quatuor: iuxta ver&ograve; cra&longs;&longs;itiem, duodecim digitorum: in&shy;<lb/>feriora iuga dupla faciens, vbi rot&aelig; quidem in medio, ligna <lb/>ver&ograve; medio a&longs;tantia in ip&longs;is prominentijs imponi debent. </s>
<s><lb/>H&aelig;c bina, atque bina iuga &longs;ecundum cra&longs;&longs;itiem ponebat, <lb/>&amp; inter ip&longs;a ad &longs;ingula digitorum duodecim interceptum <lb/>locum, &longs;iue etiam maiorem in latitudines di&longs;tinguens: ere&shy;<lb/>cta in extremis medio a&longs;tantia ligna infigit, ad <expan abbr="pauim&etilde;tum">pauimentum</expan> <lb/>v&longs;que de&longs;cendentia, quippe qu&aelig; turris crura quidam no&shy;<lb/>minarunt, pedum &longs;edecim quoad altitudinem &longs;ingula exi&shy;<lb/>&longs;tentia: quo vero ad latitudinem, pedis, vnius, &amp; quatuor <lb/>digitorum: quoad cra&longs;&longs;itudinem autem &longs;ingula digitorum <lb/>duodecim. </s>
<s>H&aelig;c ad ea, qu&aelig; dupla iacent paruis regulis, <lb/><expan abbr="tran&longs;uer&longs;is&qacute;ue">tran&longs;uer&longs;isque</expan> lignis (qu&aelig; &agrave; Gr&aelig;cis Peritomid&aelig; vocan&shy;<arrow.to.target n="note71"/><lb/>tur) necnon chelonijs, &longs;iue hemi&longs;pherijs circa medium in&shy;<lb/>&longs;culptis, &amp; tanquam pugillis quibu&longs;dam di&longs;&longs;ectis &longs;imilibus <lb/>ijs, qui in <expan abbr="portar&utilde;">portarum</expan> cardinibus ponuntur, circa clauorum fi&shy;<lb/>xionem firmantur, vt erecta permaneant. </s>
<s>Hi&longs;e erectis cru&shy;<lb/>ribus medio &longs;tantibus &agrave; duplis iacentibus ad oppo&longs;ita du&shy;<lb/>pla, alia ligna &aelig;qualia exi&longs;tentia quoad longitudinem tan&shy;<lb/>quam contraria iuga ponebat, &aelig;quiquadrangulum turris <lb/>fundamentum figurans, &longs;eu ba&longs;im ex &aelig;quali circumquaque <lb/>terminans, vt iam dicta quatuor medio &longs;tantia ligna &aelig;qua&shy;<lb/>liter &agrave; &longs;einuicem vndequaque di&longs;tent. </s>
<s>in vnoquoque au&shy;<lb/>tem ip&longs;orum quatuor, duo adh&aelig;rere faciebat ligna, qu&aelig; <lb/>erant octo numero, &aelig;qualis tum latitudinis, tum cra&longs;&longs;itudi&shy;<lb/>nis cum prioribus, altitudinis &longs;ingula pedum nouem: &longs;tan-<pb xlink:href="052/01/053.jpg"/>tia ver&ograve;, atque adh&aelig;rentia, ad vtra&longs;que medio &longs;tantium par<lb/>tes ad dupla iacentia, qu&aelig; etiam tut&ograve; clauis affixa &longs;int c&ugrave;m <lb/>ad iuga, tum ad medio &longs;tantia. </s>
<s>atque hoc modo tria con&longs;ti&shy;<lb/>tuebat in ordine, vno ex rectis &longs;tantibus lignis iuxta me&shy;<lb/>dium &longs;upereminente. </s>
<s>h&aelig;c autem octo ligna, adh&aelig;rentia <lb/>vocentur. </s>
<s>Et quoniam ip&longs;a adh&aelig;rentia, &amp; medio &longs;tantia <lb/>ligna propter latitudinis magnitudinem inuentu difficilia <lb/>&longs;unt, nece&longs;&longs;e e&longs;t ip&longs;um Diadem, &amp; Chariam &longs;equi: atque <lb/>&aelig;quiquadrangula digitorum &longs;ingula duodecim deor&longs;um <lb/>ip&longs;a crura facere: &longs;ur&longs;um autem minora: pr&aelig;cipu&egrave; ver&ograve; ea, <lb/>qu&aelig; adh&aelig;rent, <expan abbr="maxime&qacute;ue">maximeque</expan> ad huiu&longs;cemodi turris con&longs;tru&shy;<lb/>ctionem commen&longs;urabilia exi&longs;tunt. </s>
<s>Rur&longs;us autem ad ip&longs;a <lb/>de&longs;uper iam dictus Apollodorus &longs;imiliter inferiora, &amp; ad&shy;<lb/><arrow.to.target n="note72"/><lb/>h&aelig;rentia iuga minora longitudine ponebat, <expan abbr="v&longs;q;">v&longs;que</expan> ad vnum <lb/>pedem: ac demum v&longs;que ad &longs;upremum tectum iuxta lon&shy;<lb/>gitudinem, &amp; latitudinem ex vnoquoque eorum, qu&aelig; po&shy;<lb/>nuntur, pedem vnum auferebat: vt collectionem &longs;ur&longs;um <lb/>turris &longs;u&longs;cipiat: ne <expan abbr="p&otilde;dero&longs;a">pondero&longs;a</expan> in extremis fiens, circumruat: <lb/>&longs;ed tutam ex inferiori &longs;edis latitudine &longs;tabilitatem habeat. </s>
<s><lb/>Ver&ugrave;m ip&longs;orum tectorum alia quidem circumalta &longs;int, alia <lb/>ver&ograve; eiu&longs;modi, qu&ograve;d circumquaque circumcurri po&longs;&longs;int: <lb/>habentia latitudinem circiter trium pedum. </s>
<s>perutilia nam&shy;<lb/>que &longs;unt ad euitanda incendia. </s>
<s>At iuxta &longs;patium illud, quo <lb/>di&longs;tant ad latitudines inferiora iuga, qu&aelig; ad iam dictos di&shy;<lb/>gitorum duodecim, vel etiam maiores interceptos locos <lb/>medio &longs;tantia ligna &longs;u&longs;cipiunt, artifici commo&longs;trans pr&aelig;ci&shy;<lb/>pit quatuor imponere rotas, validis axibus &longs;imul <expan abbr="tr&atilde;sfixas">transfixas</expan>, <lb/><arrow.to.target n="note73"/><lb/>&amp; laminis ferreis ad frigus cur&longs;is, colligatas: dimetientem, <lb/>&longs;iue altitudinem pedum circiter quatuor cum dimidio ha&shy;<lb/>bentes: <expan abbr="quandoq;">quandoque</expan> autem ea&longs;dem rotas breuibus etiam fer&shy;<lb/>reis axibus &longs;imul transfigi, propter &longs;uperimpo&longs;itum pon&shy;<lb/>dus, &amp; magnitudinis molem: atque duas quidem earum ad <lb/>&longs;ingula <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> duo ligna firmari, reliquas vero duas ad ea, <lb/>qu&aelig; &egrave; contrario oppo&longs;ita &longs;unt: &longs;u&longs;tolentes quidem &agrave; terra, <lb/><expan abbr="&longs;u&longs;tinentes&qacute;ue">&longs;u&longs;tinentesque</expan> dupla ligna, vt magna cum volubilitate, <expan abbr="fa-cilitate&qacute;ue">fa&shy;<lb/>cilitateque</expan> rot&ecedil; vertantur, ac totam turris congeriem com&shy;<lb/>moueant. </s>
<s>Sic igitur con&longs;tructione con&longs;tituta, prima medio
<pb xlink:href="052/01/054.jpg"/>&longs;tantia ligna tertia eorum longitudinis parte &longs;uper tecto &longs;u<lb/>periori eminentia reperientur. </s>
<s>Quamobrem adh&aelig;rentia <lb/>medio &longs;tans lignum excedenti. </s>
<s>ad &longs;uperiora iuga rur&longs;us <lb/>ponebat: atque ad ip&longs;um medio &longs;tans lignum, aliud ab <lb/>adh&aelig;rentibus comprehen&longs;um. </s>
<s>&amp; &longs;ic iuxta omne tectum <lb/>quadripertit&ograve; contexens, turrem &longs;tabiliuit. </s>
<s>&amp; primum <lb/>quidem medio &longs;tans lignum hi&longs;ce adh&aelig;rentibus &aelig;quale mi<lb/>nim&egrave; faciebat, ne coniunctiones eorum prop&egrave; &longs;einuicem <lb/>&longs;int: &longs;ed omnis <expan abbr="c&otilde;mi&longs;&longs;ura">commi&longs;&longs;ura</expan> re&longs;pectu alterius ex aduer&longs;o per&shy;<lb/>mutatim, <expan abbr="di&longs;iunctim&qacute;ue">di&longs;iunctimque</expan> variet: &amp; adh&aelig;rentium lignorum <lb/><arrow.to.target n="note74"/><lb/>coarctatione, <expan abbr="vnione&qacute;ue">vnioneque</expan> robur &longs;u&longs;cipiat. </s>
<s>Pr&aelig;terea &longs;calas <lb/>alterum ip&longs;ius turris latus ab altero per diagonium (vel vt <lb/>ita dicam) diametraliter &longs;eparantes ad adherentia iuga pro&shy;<lb/>pter a&longs;cen&longs;um ponebat. </s>
<s>turrem autem funibus etiam de&longs;u<lb/>per iuxta angulos alligatis, &amp; extra per medium attractis <lb/>&longs;tabiliebat: latiorem in figura ba&longs;im turri pr&aelig;&longs;tans <expan abbr="tanqu&atilde;">tanquam</expan> <lb/>&longs;edem, circumalligatis palis clauos habentibus, aut ferreis <lb/>clauis, &amp; annulis lateralibus ad exten&longs;ionem infixis: non <lb/>parum auxilium propter funium ten&longs;ionem ad &longs;u&longs;tentatio&shy;<lb/>nem turri pr&aelig;bens. </s>
<s>Hoc modo ex paucis, <expan abbr="paruis&qacute;ue">paruisque</expan> lignis <lb/>magnam turris machinam con&longs;truebat, qu&aelig; &aelig;qualem <lb/>cum muro altitudinem habebat: neque tectorum diui&longs;io&shy;<lb/>nes, vel altitudines exprimens, neque &longs;uperioris collectio&shy;<lb/>nis quintam partem declarans. </s>
<s>Ver&ugrave;menimuero &longs;i quis <lb/><arrow.to.target n="note75"/><lb/>dubitans qu&aelig;rat hoc: ex inferiori ba&longs;i per &longs;uppo&longs;itum in <lb/>vnoquoque latere numerum id &longs;u&longs;cipiet. </s>
<s>c&ugrave;m enim latus <lb/>pedum datum &longs;it &longs;edecim, multiplicatum autem in alterum <lb/>&aelig;qualis cum ip&longs;o longitudinis, faciat totam aream, &longs;iue in&shy;<lb/>ternum quadrialteri &longs;patium pedum <expan abbr="duc&etilde;torum">ducentorum</expan> quinqua&shy;<lb/>ginta &longs;ex: atque etiam horum quinta pars pedum quinqua&shy;<lb/>ginta &amp; vnius, &amp; quint&aelig; partis pedis &longs;it: qu&aelig;ro quis nume&shy;<lb/>rus in &longs;eip&longs;um, vel in alium &aelig;qualis cum ip&longs;o longitudinis <lb/>multiplicatus hunc efficit? </s>
<s>&amp; inuenio &longs;eptenarium, &amp; &longs;ex&shy;<lb/>tam partem proxim&egrave;. </s>
<s>nam &longs;eptenarius in &longs;eptenarium mul<lb/>tiplicatus, quadraginta nouem: &amp; &longs;eptenarius in &longs;extam <lb/><arrow.to.target n="note76"/><lb/>partem, hoc e&longs;t in decem minuta multiplicatus, minuta pri&shy;<lb/>ma &longs;eptuaginta efficit. </s>
<s>rur&longs;us autem denarius in &longs;eptena-<pb xlink:href="052/01/055.jpg"/>rium, &longs;eptuaginta efficit. </s>
<s>&amp; ex collectis centum &amp; quadra&shy;<lb/>ginta minutis primis ip&longs;a quidem <expan abbr="cent&utilde;">centum</expan> &amp; viginti in pedes <lb/><arrow.to.target n="note77"/><lb/>duos, reliqua ver&ograve; in partem <expan abbr="comput&atilde;da">computanda</expan> &longs;unt. </s>
<s>Quare iuga, <lb/>qu&aelig; ad &longs;upremi tecti collectionem ponuntur, &longs;ingula <expan abbr="ped&utilde;">pedum</expan> <lb/><arrow.to.target n="note78"/><lb/>&longs;eptem, &amp; &longs;ext&aelig; partis iuxta longitudinem fiant. </s>
<s>At ea <lb/>quoque nouem tecta, qu&aelig; ad altitudinem ab inferiori ba&longs;i <lb/>ponuntur in ip&longs;a longitudinis, &amp; latitudinis &longs;uper adiectio&shy;<lb/>ne iuxta quadrialteri circumterminationem &longs;ingula pedem <lb/>auferentia ex ip&longs;is &longs;edecim, &longs;eptem proxim&egrave; relinquunt. </s>
<s><lb/>eadem autem via in &longs;uprema turris collectione, &amp; in tertia, <lb/><arrow.to.target n="note79"/><lb/>&amp; in quarta, &amp; qualibet parte &longs;emper qu&aelig;rentibus &longs;it. </s>
<s>Ip&shy;<lb/>&longs;as ver&ograve; tectorum diui&longs;iones, &amp; ad altitudinem exaltatio&shy;<lb/>nes Diades quidem, &amp; Charias iuxta cubita numerantes, <lb/>primum, quod ab inferiori ba&longs;i fit tectum <expan abbr="cubitor&utilde;">cubitorum</expan> quo ad <lb/>altitudinem &longs;eptem ponebant, &amp; digitorum duodecim: &longs;u&shy;<lb/>periora <expan abbr="aut&etilde;">autem</expan> <expan abbr="quinq;">quinque</expan> tecta, &longs;ingula <expan abbr="cubitor&utilde;">cubitorum</expan> <expan abbr="quinq;">quinque</expan> tant&ugrave;m: <lb/>reliqua ver&ograve;, &longs;ingula quatuor, &amp; terti&ecedil; partis. </s>
<s>necnon cra&longs;&longs;i&shy;<lb/>tiem pauimenti tectorum, &amp; inferiorem fundamenti cra&longs;&longs;i&shy;<lb/>tudinem, un&agrave; cum &longs;uperiori pinnaculo altitudini <expan abbr="c&otilde;nume-rabant">connume&shy;<lb/>rabant</expan>. </s>
<s>&longs;imiliter autem in minori <expan abbr="quoq;">quoque</expan> turre diui&longs;io tecto&shy;<lb/><arrow.to.target n="note80"/><lb/>rum eandem rationem ad altitudinem &longs;u&longs;cipiebat. </s>
<s>Ver&ugrave;m <lb/>iam dictus Apollodorus iuxta pedes enumerans turrim <lb/>adh&aelig;rentia prima, qu&aelig; &agrave; ba&longs;i eriguntur, pedum <expan abbr="nou&etilde;">nouem</expan> in al&shy;<lb/>titudinem facit. </s>
<s>&amp; &longs;i &aelig;qualis quidem altitudinis omnia ad&shy;<lb/>h&aelig;rentia e&longs;&longs;e vult, &longs;ex tectis pr&aelig;ditam turrem ip&longs;am, &amp; pe&shy;<lb/>dum &longs;ex tant&ugrave;m &longs;uper adiectione e&longs;&longs;e declarat: vige&longs;imam&shy;<lb/>tertiam ver&ograve; partem proxim&egrave; are&aelig; ba&longs;is &longs;ur&longs;um colligere, <lb/>&longs;ingula decem pedum &longs;uperiora quoque iuga ponens: &longs;i au <lb/>tem quintam ba&longs;is <expan abbr="part&etilde;">partem</expan> in turri &longs;ex tectis pr&aelig;dita &longs;ur&longs;um <lb/>colligit, vnius cum dimidio pedis tectorum &longs;uper adiectio&shy;<lb/>nem quadripertit&ograve; euenire: &longs;i autem decem quoque tectis <lb/>pr&aelig;ditam, &longs;ingulam pedis vnius &longs;uper adiectionem (vt <expan abbr="i&atilde;">iam</expan> <lb/>dictum e&longs;t) &amp; quintam ba&longs;is partem &longs;ur&longs;um intercipere: ita <lb/>vt &longs;uperiora quoque iuga &longs;ingula pedum &longs;eptem, &amp; &longs;ext&aelig; <lb/>partis fiant: atque in ip&longs;a quidem turri decem tectis pr&aelig;di&shy;<lb/>ta inferiora adh&aelig;rentia &longs;ingula pedum nouem fieri: ip&longs;a ve&shy;<lb/>r&ograve;, qu&aelig; in &longs;uperioribus quatuor tectis &longs;unt, &longs;ingula pedum
<pb xlink:href="052/01/056.jpg"/>&longs;ex tant&ugrave;m: ip&longs;a demum, qu&aelig; in quatuor reliquis adhuc &longs;u&shy;<lb/><arrow.to.target n="note81"/><lb/>periora &longs;unt, &longs;ingula quinque, &amp; partis. </s>
<s>Hoc itaque pacto <lb/>non &longs;ol&ugrave;m ea, qu&aelig; iuxta numerum di&longs;crepant turrium te&shy;<lb/>cta ad &longs;exaginta pedum altitudinem c&ugrave;m &aelig;qualis, tum in&shy;<lb/>&aelig;qualis altitudinis exi&longs;tentia reperientur: ver&ugrave;m etiam e&aelig;, <lb/>qu&aelig; ex vtri&longs;que iuxta cubitos, &amp; pedes <expan abbr="con&longs;tru&utilde;tur">con&longs;truuntur</expan>, ac iux&shy;<lb/>ta magnitudinem di&longs;crepant turres commen&longs;urabiles ad &longs;e <lb/>&longs;e inuicem &longs;ecundum proportionem o&longs;tendentur. </s>
<s>Si enim <lb/>cubitus vigintiquatuor &longs;ecundum longitudinem e&longs;t digito&shy;<lb/>rum, pede &longs;edecim exi&longs;tente, habet autem ip&longs;e vigintiqua&shy;<lb/>tuor numerus numerum &longs;edecim, &amp; eius dimidium: &longs;e&longs;qui&shy;<lb/>alter ip&longs;ius e&longs;t, &longs;ub&longs;equialter ver&ograve; ad cubitum pes. </s>
<s>Quare <expan abbr="t&utilde;">tum</expan> <lb/>ip&longs;i &longs;exaginta cubiti altitudinis, tum ip&longs;i &longs;eptemdecim lon&shy;<lb/>gitudinis ba&longs;is eandem proportionem ad pedes habebunt: <lb/>eodem modo autem eam etiam, qu&aelig; in rationibus e&longs;t con&shy;<lb/>uenientiam: quoniam <expan abbr="vtriq;">vtrique</expan> communi men&longs;ura men&longs;uran&shy;<lb/>tur. </s>
<s>nam triginta numerus ter quidem men&longs;urat ip&longs;um no&shy;<lb/>naginta numerum, bis ver&ograve; ip&longs;um &longs;edecim. </s>
<s>&amp; quemadmo&shy;<lb/>dum &longs;e habet nonaginta numerus ad &longs;exaginta numerum, <lb/>ita vigintiquatuor ad &longs;edecim. </s>
<s>&amp; &longs;icut &longs;e habet vigintiqua&shy;<lb/>tuor ad &longs;edecim, &longs;ic etiam rot&aelig; ad &longs;e inuicem tum iuxta nu&shy;<lb/>merum, tum etiam iuxta magnitudinem: necnon ba&longs;is ad <lb/>ba&longs;im &longs;icut etiam tria ad duo. </s>
<s>O&longs;ten&longs;&aelig; &longs;unt igitur ip&longs;&aelig; quo&shy;<lb/>que men&longs;urantes turres ad &longs;e inuicem eandem, <expan abbr="qu&atilde;">quam</expan> c&aelig; qu&ecedil; <lb/>men&longs;urantur iuxta proportionem habere rationem. </s>
<s>Quam<lb/>obrem non &longs;ol&ugrave;m iuxta commen&longs;urationem, ver&ugrave;m etiam <lb/>iuxta conuenientiam turrium ferri idonearum con&longs;tructio&shy;<lb/>nes Diodorus, <expan abbr="necn&otilde;">necnon</expan> Diades, &amp; Charias <expan abbr="faci&etilde;tes">facientes</expan> reperiun&shy;<lb/>tur. </s>
<s>Atque manife&longs;tum e&longs;t qu&ograve;d Antiqui Mechanici, <expan abbr="erru-diti&longs;&longs;imi&qacute;ue">erru&shy;<lb/>diti&longs;&longs;imique</expan> Architecti &longs;cientific&egrave;, &amp; non <expan abbr="ab&longs;q;">ab&longs;que</expan> ratione Ma&shy;<lb/><arrow.to.target n="note82"/><lb/>chinarum con&longs;tructiones faciebant. </s>
<s>Turre &longs;ic quoad con&shy;<lb/>&longs;tructionem, completa, &longs;i non enodus <expan abbr="complanatus&qacute;ue">complanatusque</expan> ad <lb/>ba&longs;im &longs;ubiectus locus &longs;it, &longs;ed &longs;ur&longs;um ferens exi&longs;tat: faciemus <lb/>&longs;uppo&longs;itorium prope turris ba&longs;im contexione, qu&aelig; turris <lb/>contexioni &longs;imilis &longs;it, &amp; &longs;uper terr&aelig; in &aelig;qualitatem adue&shy;<lb/>niat, <expan abbr="locum&qacute;ue">locumque</expan> inferi&ugrave;s &longs;ubiectum amplificet: vt in con&shy;<lb/>gre&longs;&longs;u, ac turbatione certaminis indecliuis quoad &longs;tatio-
<pb xlink:href="052/01/057.jpg"/>nem turris con&longs;eruetur. </s>
<s>Cu&longs;todietur autem ne combura&shy;<lb/>tur ab ijs, qui mittuntur ignem ferentibus muricibus, &amp; <lb/>accen&longs;is flammis: &longs;i tabul&aelig; in ip&longs;a clauis <expan abbr="affig&atilde;tur">affigantur</expan> pr&aelig;cipu&egrave; <lb/>quidem palme&aelig;, vel e&aelig;, qu&aelig; ex fortibus lignis fiunt. </s>
<s>exce&shy;<lb/>ptis cedrinis, &amp; pineis, <expan abbr="atq;">atque</expan> alneis, propter earum <expan abbr="feruid&atilde;">feruidam</expan>, <lb/>facil&egrave; combu&longs;tibilem, <expan abbr="friabilemq;">friabilemque</expan> naturam. </s>
<s>appendantur au<lb/>tem &amp; coria turri in iam dictis in con&longs;tructione circumala&shy;<lb/>tis, <expan abbr="circumcur&longs;atis&qacute;">circumcur&longs;atisque</expan>; tectis, non adh&aelig;rentia tabulis, &longs;ed <expan abbr="ali-quantul&utilde;">ali&shy;<lb/>quantulum</expan> extrin&longs;ec&ugrave;s di&longs;tantia. </s>
<s>c&ugrave;m propter ea, qu&aelig; ad <expan abbr="iaculand&utilde;">iacu<lb/>landum</expan> ignem fiunt tormenta: tum <expan abbr="quoni&atilde;">quoniam</expan> lapides <expan abbr="iacienti&utilde;">iacientium</expan> <lb/>percu&longs;&longs;iones imbecilles ad ip&longs;a, <expan abbr="languid&aelig;&qacute;ue">languid&aelig;que</expan> in ip&longs;a iactus <lb/>irruptione ad mole fiunt. </s>
<s>Affigatur <expan abbr="a&utilde;t">aut</expan> clauis etiam turris <lb/>de&longs;uper quemadmodum in te&longs;tudinibus <expan abbr="quoq;">quoque</expan> dictum e&longs;t, <lb/>&amp; creta opima, &amp; glutino&longs;a locus intermedius repleatur. </s>
<s>ad <lb/>eas ver&ograve; turris partes, qu&aelig; <expan abbr="torm&etilde;tis">tormentis</expan> ad iaculandum ignem <lb/>factis proponuntur, loco tuborum aquam mittentium, in&shy;<lb/>te&longs;tina bouum pr&aelig;parata veluti &longs;ale condita aquam effun&shy;<lb/>dentia apponantur. </s>
<s>hi&longs;ce inte&longs;tinis vtres aqua pleni &longs;uppo&shy;<lb/>nuntur, qui extricti, atque &longs;uppre&longs;&longs;i &longs;ur&longs;um aquam ferunt. </s>
<s><lb/>Qu&ograve;d &longs;i <expan abbr="eti&atilde;">etiam</expan> turris pinnaculum aliqua in parte inacce&longs;&longs;ibi&shy;<lb/>le <expan abbr="c&otilde;buratur">comburatur</expan>, non &longs;it <expan abbr="a&utilde;t">aut</expan> <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan>, quod tubus vocatur: <lb/>calami per totam <expan abbr="intern&atilde;">internam</expan> partem perforati, cuiu&longs;modi &longs;unt <lb/>ij, quos venatores habent ad &longs;ein uicem coniunguntur, <expan abbr="atq;">atque</expan> <lb/><expan abbr="vbicumq;">vbicumque</expan> opus fuerit aquam emittunt. </s>
<s>vtres enim quemad&shy;<lb/>modum etiam in inte&longs;tinis &longs;upponuntur ferentes ip&longs;am per <lb/>calamos in eum, qui comburitur locum. </s>
<s>Non paruam <expan abbr="aut&etilde;">autem</expan> <lb/>vtilitatem turri pr&aelig;bebunt etiam inuolucra extrin&longs;ec&ugrave;s ap<lb/>pen&longs;a, paleis aceto madefactis plena: &longs;iue retia repleta humi<lb/>dis mu&longs;cis, vel ea alg&ecedil; &longs;pecie, qu&ecedil; thala&longs;&longs;opra&longs;on, hoc e&longs;t ma<lb/>rinum porrum vocatur: tamquam ea, qu&aelig; <expan abbr="n&otilde;">non</expan> &longs;ol&ugrave;m incen&shy;<lb/>dijs, qu&aelig; &agrave; tormentis ignem iaculantibus fiunt, oppugna&shy;<lb/>re, ver&ugrave;m etiam lapides iacientium percu&longs;&longs;ionibus re&longs;i&longs;te&shy;<lb/>re po&longs;&longs;unt. </s>
<s>&amp; &longs;ciendum e&longs;t qu&ograve;d omnes, qu&aelig; ex ignem fe&shy;<lb/>rentibus, <expan abbr="accen&longs;is&qacute;ue">accen&longs;isque</expan> flammis * * * * </s></p><p type="margin">
<s><margin.target id="note71"/>b</s></p><p type="margin">
<s><margin.target id="note72"/>c</s></p><p type="margin">
<s><margin.target id="note73"/>d</s></p><p type="margin">
<s><margin.target id="note74"/>e</s></p><p type="margin">
<s><margin.target id="note75"/>f</s></p><p type="margin">
<s><margin.target id="note76"/>g</s></p><p type="margin">
<s><margin.target id="note77"/>h</s></p><p type="margin">
<s><margin.target id="note78"/>i</s></p><p type="margin">
<s><margin.target id="note79"/>k</s></p><p type="margin">
<s><margin.target id="note80"/>l</s></p><p type="margin">
<s><margin.target id="note81"/>m</s></p><p type="margin">
<s><margin.target id="note82"/>n</s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Finis huius Capitis de&longs;ideratur.<emph.end type="italics"/><emph.end type="center"/></s></p>
<pb xlink:href="052/01/058.jpg"/><figure id="id.052.01.058.1.jpg" xlink:href="052/01/058/1.jpg"/>
<pb xlink:href="052/01/059.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>MVlta &longs;unt in hoc capite, qu&aelig; ni&longs;i adnotentur, <expan abbr="declaren-tur&qacute;ue">declaren&shy;<lb/>turque</expan>, omnium huius operis capitum pr&aelig;&longs;ens ob&longs;curi&szlig;i&shy;<lb/>mum reddent. </s>
<s>in primis itaque adnotabimus qu&ograve;d par&shy;<arrow.to.target n="note83"/><lb/>ticula illa [grauiorem] in textu gr&aelig;co legitur<emph.end type="italics"/> <foreign lang="greek">semno/teron</foreign>, <emph type="italics"/>qu&aelig; in <lb/>pr&aelig;&longs;enti loco nil aliud &longs;ignificare pote&longs;t ni&longs;i grauiorem, aut ma&shy;<lb/>gnificientiorem, quorum neutrum e&longs;t ad propo&longs;itum Autoris. </s>
<s>C&ugrave;m <lb/>enim turris, quam &longs;ecundum Apollodori doctrinam in principio <lb/>huius capitis Autor con&longs;truit, debeat e&longs;&longs;e &longs;ub&longs;e&longs;quialtera eius tur&shy;<lb/>ris, quam in pr&aelig;cedenti capite <expan abbr="minor&etilde;">minorem</expan> <expan abbr="o&itilde;um">omnium</expan> e&longs;&longs;e dixit, nempe &longs;exa&shy;<lb/>ginta cubitorum altitudinem habentis: nemo e&longs;t, qui non videat <lb/>qu&ograve;d h&aelig;c Apollodori turris leuior, minus&queacute; ampla, &amp; magnifica <lb/>erit qu&agrave;m iam dicta minor di&longs;cipulorum Polyidis Thetali turris. </s>
<s><lb/>Quamobrem<emph.end type="italics"/> <foreign lang="greek">lepto/teron</foreign>, <emph type="italics"/>hoc e&longs;t leuiorem poti&ugrave;s qu&agrave;m<emph.end type="italics"/> <foreign lang="greek">semno/te&shy;<lb/>ron</foreign>, <emph type="italics"/>&longs;cilicet grauiorem legendum e&longs;&longs;e nobis videtur. </s>
<s>minor enim <lb/>in ratione &longs;e&longs;quialtera e&longs;t hac turris qu&agrave;m illa. </s>
<s>quippe c&ugrave;m hu&shy;<lb/>ius quidem omnes men&longs;ur&aelig; pedes, illius ver&ograve; cubiti &longs;int: cubitus <lb/>autem (vt ip&longs;emet Autor in pr&aelig;&longs;enti capite declarat) ad pedem <lb/>&longs;e&longs;quialteram habeat rationem: quandoquidem pes &longs;edecim, cu&shy;<lb/>bitus vigintiquatuor digitis con&longs;tat. </s>
<s>vnd&egrave; &longs;an&egrave; volens Apollodo&shy;<lb/>rus ip&longs;ius turris, qu&aelig; &longs;exaginta cubitorum altitudinem habebat, <lb/>&longs;ub&longs;e&longs;quialteram turrem tanquam leuiorem con&longs;truere, non im&shy;<lb/>merito &longs;exaginta pedum altitudinis eam fecit, quatuor&queacute; ip&longs;i ro&shy;<lb/>tas tant&ugrave;m, &amp; non &longs;ex quemadmodum eius &longs;e&longs;quialter&aelig;, &longs;uppo&shy;<lb/>&longs;uit. </s>
<s>Quoniam autem dubitabat ne propter eius leuitatem corrue&shy;<lb/>ret, funibus (vt docet Autor in hoc capite) ad palos, &longs;iue clauos <lb/>ferreos in terram affixos circumalligatis, <expan abbr="bene&qacute;ue">beneque</expan> exten&longs;is eam <lb/>&longs;tabiliebat.<emph.end type="italics"/><lb/><arrow.to.target n="note84"/></s></p><p type="margin">
<s><margin.target id="note83"/>a</s></p><p type="margin">
<s><margin.target id="note84"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Qu&aelig; nam &longs;int Peritomid&aelig; in cap 9. declarauimus. </s>
<s>Chelonium <lb/>autem e&longs;t propri&egrave; Te&longs;tudinis animalis tegumentum, ad cuius &longs;i&shy;<lb/>militudinem vocat Avtor tum in hoc, tum in nono capite lignum <lb/>quoddam in&longs;culptum, quod in&longs;culptura &longs;ua retinendi alia ligna, <lb/>con&longs;tringendi&queacute; vim habens, <expan abbr="n&otilde;">non</expan> &longs;ecus quam chelonium concauita&shy;<lb/>te &longs;ua te&longs;tudinem ip&longs;am intra &longs;e comprehendit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note85"/></s></p><p type="margin">
<s><margin.target id="note85"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Adh&aelig;rentia iuga, qu&aelig; gr&aelig;c&egrave;<emph.end type="italics"/> <foreign lang="greek">e)pizugi/dai</foreign> <emph type="italics"/>dicuntur, ea &longs;unt,<emph.end type="italics"/>
<pb xlink:href="052/01/060.jpg"/><emph type="italics"/>qu&aelig; &longs;uperi&ugrave;s<emph.end type="italics"/> <foreign lang="greek">a)ntizugi/das</foreign>, <emph type="italics"/>ide&longs;t contraria iuga vocauit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note86"/></s></p><p type="margin">
<s><margin.target id="note86"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Particula illa, quam nos vertimus [ad frigus cur&longs;is] in gr&aelig;co <lb/>exemplari legitur<emph.end type="italics"/> [<foreign lang="greek">yuxrhla/tois</foreign>] <emph type="italics"/>qu&aelig; nil aliud &longs;onat, quam ad <lb/>frigus cur&longs;is &longs;ed videtur non e&longs;&longs;e ad propo&longs;itum. </s>
<s>ideo dubitandum <lb/>e&longs;t an forta&longs;&longs;e dictio h&aelig;c deprauat&egrave; legatur. </s>
<s>poti&ugrave;s enim legen&shy;<lb/>dum e&longs;&longs;et [clauis <expan abbr="circ&utilde;a&longs;&longs;ixis]">circumaffixis]</expan> <expan abbr="quoni&atilde;">quoniam</expan> lamin&aelig;, quibus rot&aelig; cingun&shy;<lb/>tur, clauis circumaffigi debent.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note87"/></s></p><p type="margin">
<s><margin.target id="note87"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Animaduer&longs;ione dignum e&longs;t, qu&ograve;d tota quidem huiu&longs;ce turris <lb/>con&longs;tructio nimis ob&longs;cur&egrave; ab Autore tradita cuilibet e&longs;&longs;e videbi&shy;<lb/>tur ni&longs;i figuram pr&aelig; oculis habeat, qu&aelig; maximum legentibus <lb/>pr&aelig;bebit auxilium ad ip&longs;ius Autoris verba rect&egrave; percipienda. </s>
<s>ip&longs;&aelig; <lb/>ver&ograve; &longs;cal&aelig;, qu&aelig; ab Autore intra turrem &longs;ituantur, perperam in <lb/>ip&longs;a figura plana repr&aelig;&longs;entari nobis po&longs;&longs;unt in eo &longs;itu, quo Autor <lb/>eas de&longs;cribit. </s>
<s>idcirco ad perfectam earum intelligentiam imagi&shy;<lb/>natione &longs;upplendum est.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note88"/></s></p><p type="margin">
<s><margin.target id="note88"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[qu&aelig;rat hoc] &longs;cilicet tectorum diui&longs;iones, vel altitudines: &amp; <lb/>&longs;uperioris collectionis quintam partem. </s>
<s>hoc e&longs;t quibus nam men&shy;<lb/>&longs;uris tectorum diui&longs;iones, vel eorum altitudines, nempe ab vno <lb/>tecto ad aliud di&longs;tanti&aelig; fiant: necnon quomodo &longs;uperioris colle&shy;<lb/>ctionis, &longs;iue vltimi tecti quadrata area fiat quinta pars quadra&shy;<lb/>t&aelig; are&aelig; ba&longs;is. </s>
<s>c&ugrave;m enim Apollodorus h&aelig;c minim&egrave; declara&longs;&longs;et, vo&shy;<lb/>lens Autor ea declarare, ait, qu&ograve;d, &longs;iquis dubitans qu&aelig;rat hoc: ex <lb/>inferiori ba&longs;i per &longs;uppo&longs;itum in <expan abbr="vnoquoq;">vnoquoque</expan> latere numerum id &longs;u&shy;<lb/>&longs;cipiet. </s>
<s>videlicet ex ip&longs;ius inferioris ba&longs;is area quadrata auxilio <lb/>numeri in vnoquoque ip&longs;ius ba&longs;is latere &longs;uppo&longs;iti colliget id, quod <lb/>qu&aelig;rit. </s>
<s>exempli gratia, quoniam vnumquodque ba&longs;is latus ab <lb/>Apollodoro 16 pedum iuxta longitudinem <expan abbr="&longs;uppo&longs;it&utilde;">&longs;uppo&longs;itum</expan> fuit, erit area <lb/>quadrata ab ip&longs;is lateribus comprehen&longs;a 256: huius autem quin&shy;<lb/>ta pars, hoc e&longs;t area quadrata &longs;uperioris collectionis, &longs;iue po&longs;tre&shy;<lb/>mi tecti erit 51 1/5: huius ver&ograve; are&aelig; latus tetragonicum 7 1/6 pro&shy;<lb/>xim&egrave;. </s>
<s>quandoquidem 7 1/6 multiplicatus per 7 1/6 efficit 51 1/3 <lb/>&amp; (1/36), qui ab ip&longs;o 51 1/5 parum di&longs;crepat. </s>
<s>atque hoc modo ex in&shy;<lb/>feriori ba&longs;i per &longs;uppo&longs;itum in vnoquoque litere numerum nempe <lb/>16, inuenimus quintam partem are&aelig; quadrat&aelig; ip&longs;ius ba&longs;is, qu&aelig; <lb/>quadrata po&longs;tremi tecti area futura e&longs;t: necnon eius tetragonica <lb/>latera. </s>
<s>quibus ita revertis, reliquorum etiam tectorum diui&longs;io-<emph.end type="italics"/><pb xlink:href="052/01/061.jpg"/><emph type="italics"/>nes, vel altitudines (vt mox &longs;ubiunget Autor) inueniemus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note89"/></s></p><p type="margin">
<s><margin.target id="note89"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in &longs;extam partem, hoc e&longs;t in decem minuta] in multiplican&shy;<lb/>do 7 1/6 in &longs;eip&longs;um vtitur Autor multiplicatione <expan abbr="A&longs;tronomor&utilde;">A&longs;tronomorum</expan>; <lb/>qui non more minutiarum, &longs;. </s>
<s>per reductionem integrorum in mi&shy;<lb/>nutias, &longs;ed per minuta prima, &longs;ecunda, &amp; tertia, numeros inte&shy;<lb/>gros cum fractis, in numeros integros cum fractis, necnon fractos <lb/>adinuicem multiplicant. </s>
<s>idcirco pedem in 60 prima minuta par&shy;<lb/>tiens Autor, 120 minuta prima in duos pedes, reliqua ver&ograve;<emph.end type="italics"/> 20 <emph type="italics"/>in </s></p><p type="main">
<s><arrow.to.target n="note90"/><lb/>partem, &longs;cilicet tertiam di&longs;tribuit.<emph.end type="italics"/><lb/><arrow.to.target n="note91"/></s></p><p type="margin">
<s><margin.target id="note90"/>h</s></p><p type="margin">
<s><margin.target id="note91"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[At ea quoque nouem tecta &amp;c.] in hac parte declarat Au&shy;<lb/>tor quo nam pacto reliquorum etiam nouem tectorum diui&longs;iones, <lb/>&longs;iue altitudines in iam dicta Apollodori turri decem tectis pr&aelig;dita <lb/>&longs;u&longs;cipiend&aelig; &longs;int. </s>
<s>Ait igitur qu&ograve;d reliqua nouem tecta, qu&aelig; ab in&shy;<lb/>feriori ba&longs;i in altitudinem eleuantur, &longs;ingula iuxta longitudinem, <lb/>&amp; latitudinem quadrat&aelig; eorum are&aelig; pedem vnum ex iam dictis <lb/>&longs;edecim ip&longs;ius ba&longs;is pedibus auferre debent. </s>
<s>quamobrem vnum&shy;<lb/>quodque laterum &longs;ecundi tecti, quindecim pedum: tertij, qua&shy;<lb/>tuordecim: quarti, tredecim: quinti, duodecim: &longs;exti, vndecim: <lb/>&longs;eptimi, decem: octaui, nouem: noni, octo: decimi&queacute;, &longs;eptem pedum <lb/>erit. </s>
<s>attamen c&ugrave;m vltimi tecti area quadrata quinta pars are&aelig; <lb/>quadrat&aelig; ip&longs;ius ba&longs;is e&longs;&longs;e debeat, quam 51. 1/5, eius&queacute; latus <expan abbr="tetra-gonic&utilde;">tetra&shy;<lb/>gonicum</expan> 7 1/6 e&longs;&longs;e iam o&longs;tendimus: non immerito reliqua nouem te&shy;<lb/>cta &longs;ingula pedem auferentia ex ip&longs;is &longs;edecim, &longs;eptem proxim&egrave; <lb/>relinquere dixit. </s>
<s>quandoquidem reuera 7 1/6 proxim&egrave; relinque&shy;<lb/>re debent. </s>
<s>quod e&longs;t quint&aelig; ip&longs;ius 256 partis latus tetragoni&shy;<lb/>cum, vt mod&ograve; declarauimus. </s>
<s>vnd&egrave; profecto &longs;ingula po&longs;tremi te&shy;<lb/>cti latera minus qu&agrave;m vnum pedem ex ip&longs;is &longs;edecim auferre ne&shy;<lb/>ce&longs;&longs;ari&ograve; debent, nempe 5/6 vnius pedis. </s>
<s>Non e&longs;t autem pr&aelig;tereun&shy;<lb/>dum qu&ograve;d huius quidem turris altitudo 115 pedum e&longs;&longs;e colligitur: <lb/>vniu&longs;cuiu&longs;que ver&ograve; eius tectorum area quadrata ex vnoquoque <lb/>laterum numero in &longs;eip&longs;um multiplicato producitur: eorumdem <lb/>autem area cubica ex multiplicatione vniu&longs;cuiu&longs;que laterum in <lb/>&longs;uam quadratam aream gignitur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note92"/></s></p><p type="margin">
<s><margin.target id="note92"/>k</s></p><p type="main">
<s><emph type="italics"/>[ip&longs;as ver&ograve; tectorum diui&longs;iones &amp;c.] Hac in parte videtur <lb/>Autor explicare tectorum diui&longs;iones aliter factas fui&longs;&longs;e &agrave; Diade,<emph.end type="italics"/>
<pb xlink:href="052/01/062.jpg"/><emph type="italics"/>&amp; Charia Polyidis Thetali di&longs;cipulis, quorum in pr&aelig;cedenti ca&shy;<lb/>pite mentionem fecit. </s>
<s>Ver&ugrave;m ea, qu&aelig; in pr&aelig;&longs;entia de tectorum di&shy;<lb/>ui&longs;ionibus ab Autore dicuntur, non in turribus, quas in pr&ecedil;ceden&shy;<lb/>ti capite iuxta Diadis, &amp; Chari&aelig; doctrinam con&longs;truxit: &longs;ed in <lb/>quadam alia turri intelligenda &longs;unt: cuius tota quidem altitudo <lb/>&longs;it cubitorum 49 2/3 1/2, hoc e&longs;t cubitorum 49 &amp; digitorum<emph.end type="italics"/> 20, <emph type="italics"/>&longs;iue <lb/>cubitorum 49 &amp; pedis vnius &amp; quart&aelig; partis pedis: latus ver&ograve; <lb/>primi tecti, ide&longs;t ip&longs;ius ba&longs;is 7 1/2: vnumquodque autem laterum <lb/>&longs;ecundi, tertij, quarti, quinti, &amp; &longs;exti tecti, quinque: vnum&shy;<lb/>quodque demum reliquorum quatuor tectorum latus, 4 1/3: ex qui&shy;<lb/>bus porr&ograve; cunctis altitudinibus totius turris altitudo cubitorum <lb/>49 2/3 1/2 colligitur. </s>
<s><expan abbr="Animaduert&etilde;dum">Animaduertendum</expan> autem e&longs;t qu&ograve;d in hac tur&shy;<lb/>re quadrata area po&longs;tremi tecti non erit quinta pars are&aelig; qua&shy;<lb/>drat&aelig; ip&longs;ius ba&longs;is. </s>
<s>quoniam area quadrata &longs;u&ecedil; ba&longs;is erit 51 1/3 &amp; <lb/>(1/36), &longs;iue 51 &amp; (13/36), cuius quidem pars quinta e&longs;t cubitorum 10 &amp; <lb/>digitorum 6 2/5 &longs;er&egrave;: quadrata ver&ograve; area po&longs;tremi tecti e&longs;t 18 7/9 <lb/>c&ugrave;m &agrave; radice 4 1/3 producatur. </s>
<s>Adnotauit in&longs;uper Autor, qu&ograve;d <lb/>ip&longs;as tectorum omnium cra&szlig;itudines altitudini connumerabant, <lb/>hoc e&longs;t in tota turris altitudine computabant: &amp; qu&ograve;d &longs;i minor <lb/>etiam turris ip&longs;a fui&longs;&longs;et, diui&longs;ionem tectorum iuxta eandem ra&shy;<lb/>tionem re&longs;pectu totius altitudinis faciebant.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note93"/></s></p><p type="margin">
<s><margin.target id="note93"/><emph type="italics"/>l<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Verum iam dictus Apollodorus &amp;c.] in hac parte propo&longs;itum <lb/>Autoris e&longs;t declarare iuxta doctrinam Apollodori men&longs;uras eo&shy;<lb/>rum lignorum, qu&ecedil; &longs;uperi&ugrave;s adh&aelig;rentia nuncupari dixit. </s>
<s>Ait <lb/>igitur qu&ograve;d Apollodorus pedibus <expan abbr="men&longs;ur&atilde;s">men&longs;urans</expan> turrim, adh&aelig;rentia pri<lb/>ma, qu&aelig; statim &agrave; ba&longs;i eriguntur pedum nouem iuxta altitudinem <lb/>fecit. </s>
<s>Pr&aelig;terea inquit qu&ograve;d &longs;i idem Apollodorus omnia adh&aelig;&shy;<lb/>rentia, &longs;cilicet in omnibus tectis adh&aelig;rentia ligna, &ecedil;qualis qui&shy;<lb/>dem altitudinis e&longs;&longs;e vult: tunc &longs;ex tectis pr&ecedil;ditam e&longs;&longs;e turrem ip&shy;<lb/>&longs;am declarat, <expan abbr="necn&otilde;">necnon</expan> &longs;uperadiectionem pedum &longs;ex tant&ugrave;m e&longs;&longs;e. </s>
<s>vo&shy;<lb/>cat autem Autor h&igrave;c &longs;uperadiectionem (quemadmodum etiam &longs;u<lb/>peri&ugrave;s id, quod vnius tecti laterum numerus addit &longs;uper alterius <lb/>tecti laterum numerum, vt &longs;uperi&ugrave;s vidimus. </s>
<s>uerbi gratia 16 <lb/>&longs;uper 15, &amp; 15 &longs;uper 14, &amp; &longs;ic in reliquis. </s>
<s>&longs;i enim turris &longs;ex te-<emph.end type="italics"/><pb xlink:href="052/01/063.jpg"/><emph type="italics"/>ctis pr&aelig;dita e&longs;t, quorum vnumquodque pedem vnum &longs;uper aliud <lb/>addit, dubio procul ip&longs;a &longs;uper. </s>
<s>diectio &longs;ex pedum erit. </s>
<s>atque huc&shy;<lb/>u&longs;que verba Autoris clara, vera&queacute; &longs;unt. </s>
<s>qu&aelig; ver&ograve; mox &longs;ubiungit <lb/>incipientia ab illis verbis [vige&longs;imamtertiam ver&ograve; partem] &amp; fi&shy;<lb/>nientia inclu&longs;iu&egrave; in illis [quadripertit&ograve; euenire] pror&longs;us fal&longs;a <lb/>mihi videntur. </s>
<s>nam in turre quidem ab Autore &longs;uperi&ugrave;s iuxta <lb/>mentem Apollodori de&longs;cripta vera nequaquam e&longs;&longs;e po&longs;&longs;unt. </s>
<s>quan&shy;<lb/>doquidem in ip&longs;a, hoc e&longs;t v&longs;que ad ip&longs;ius &longs;ex tecta (c&ugrave;m &longs;ex tectis <lb/>pr&aelig;ditam eam &longs;upponat) vige&longs;imatertia pars proxim&egrave; are&aelig; ba&longs;is <lb/>&longs;ur&longs;um minim&egrave; colligitur: neque etiam &longs;ingula decem pedum &longs;u&shy;<lb/>periora iuga po&longs;ita &longs;unt, imo vndecim: ni&longs;i ba&longs;is non connumere&shy;<lb/>tur. </s>
<s>quoui&longs;modo autem fiat, nullo pacto vige&longs;imatertia pars pro&shy;<lb/>xim&egrave; are&aelig; ba&longs;is &longs;ur&longs;um colligetur. </s>
<s>Poti&ugrave;s autem h&aelig;c duo, qu&aelig; ab <lb/>Autore dicuntur, vera e&longs;&longs;ent in quadam turri, cuius area qui&shy;<lb/>dem ip&longs;ius ba&longs;is e&longs;&longs;et 2300 pedum, area ver&ograve; &longs;upremi tecti 100. <lb/>tunc etenim area quadrata &longs;upremi tecti &longs;ur&longs;um a lateribus col&shy;<lb/>lecta reuera vige&longs;imatertia pars are&aelig; ba&longs;is e&longs;&longs;et: &amp; &longs;uperiora iu&shy;<lb/>ga nempe latera tecti &longs;upremi iam dictam vige&longs;imamtertiam par<lb/>tem comprehendentia &longs;ingula decem pedum e&longs;&longs;ent: latera ver&ograve; <lb/>are&aelig; ip&longs;ius ba&longs;is &longs;ingula pedum 48 proxim&egrave;. </s>
<s>at hucu&longs;que nullam <lb/>talis turris mentionem Autor fecit, &longs;ed videtur de iam de&longs;cripta <lb/>&longs;uperi&ugrave;s Apollodori turre &longs;tatim h&aelig;c &longs;ubiunxi&longs;&longs;e, quippe qu&aelig; nul&shy;<lb/>lo pacto in ea quidem accommodari po&longs;&longs;unt. </s>
<s>Quod autem po&longs;t <lb/>h&aelig;c &longs;ubdit, qu&ograve;d &longs;cilicet &longs;i quintam ba&longs;is partem Apollodorus in <lb/>turri &longs;ex tectis pr&aelig;dita &longs;ur&longs;um colligit, vnius cum dimidio pedis <lb/>tectorum &longs;uperadiectionem quadripertit&ograve; euenire declarat: om&shy;<lb/>nino fal&longs;um e&longs;&longs;e videtur, &amp; ijs, qu&aelig; dicit Autor minim&egrave; quadrat. <lb/>&longs;i enim vnumquodque &longs;ex laterum (vt ait Autor) ex ip&longs;o pedum <lb/>&longs;edecim latere pedem vnum cum dimidio auferat, ita vt &longs;uperad&shy;<lb/>iectio &longs;it pedis unius cum dimidio: nemo e&longs;t, qui non fateatur qu&ograve;d <lb/>&longs;ecundum latus 14 1/2, tertium 13, quartum 11 1/2, <expan abbr="quint&utilde;">quintum</expan> 10, &longs;ex<lb/>tum&queacute; <expan abbr="dem&utilde;">demum</expan> 8 1/2 erit. </s>
<s>At 8 1/2 latus in &longs;eip&longs;um <expan abbr="multiplicat&utilde;">multiplicatum</expan> pro<lb/>ducit aream quadratam 78 1/9, qu&aelig; non e&longs;t quinta pars are&aelig; <lb/>quadrat&aelig; 256 ip&longs;ius ba&longs;is. </s>
<s>Qu&ograve;d &longs;i quis dicat <expan abbr="&longs;uperadiection&etilde;">&longs;uperadiectionem</expan> <lb/>ip&longs;am de&longs;uper incipiendo &agrave; &longs;upremo turris tecto faciendam e&longs;&longs;e, <lb/>atque turrem &longs;ex tectis pr&aelig;dictam in &longs;uperiori turris decem te-<emph.end type="italics"/><pb xlink:href="052/01/064.jpg"/><emph type="italics"/>ctis pr&aelig;dit&aelig; parte &longs;u&longs;cipi, ac ba&longs;im eius non connumerari: ita vt <lb/>c&ugrave;m &longs;upremum tectum &longs;it 7 1/6, eius proximum nempe &longs;ecun&shy;<lb/>dum de&longs;cendendo latus &longs;it 8 2/3, tertium 10 1/6, <expan abbr="quart&utilde;">quartum</expan> 11 2/3, <lb/>quintum 13 1/6, &longs;extum 14 2/3, huius&queacute; demum proximum, ui&shy;<lb/>delicet &longs;eptimum, &longs;eu ba&longs;is ip&longs;a non connumerata in numero &longs;ex <lb/>tectorum 16 1/6: erit quadrata quidem area ip&longs;ius 16 1/6 lateris <lb/>(261 23/36), cuius non e&longs;t quinta pars 51 1/5 &amp; (1/36) area, qu&aelig; &agrave; 7 1/6 <lb/>producitur. </s>
<s>proximior enim quinta eius pars e&longs;t 52 1/5. ni&longs;i for <lb/>ta&longs;&longs;e dicat aliquis ip&longs;am unius cum dimidio &longs;uperadiectionem <lb/>non e&longs;&longs;e faciendam in ba&longs;i, &longs;ed in &longs;ex <expan abbr="tant&utilde;modo">tantummodo</expan> tectis. </s>
<s>tunc enim <lb/>area ba&longs;is erit &longs;icut &agrave; principio 256, cuius quinta pars e&longs;t 51 1/5, <lb/>cuius quint&aelig; partis latus tetragonicum est 7 1/6 proxim&egrave;. </s>
<s>Ver&ugrave;m <lb/>&longs;i uerba autoris &longs;ic intelligenda &longs;unt, uerum erit quod ait, &longs;cili&shy;<lb/>cet qu&ograve;d &longs;i quintam ba&longs;is partem in turri &longs;ex tectis pr&aelig;dita &longs;ur&shy;<lb/>&longs;um colligit Apollodorus, unius cum dimidio pedis tectorum &longs;u&shy;<lb/>peradiectionem quadripertit&ograve; euenire declarat. </s>
<s>Sed reuera tur<lb/>ris h&aelig;c non erit &longs;ex tectis pr&aelig;dita, &longs;ed &longs;eptem computando ba&longs;im <lb/>pro uno tecto, ut in omnibus turribus autorem &longs;eci&longs;&longs;e uidimus. </s>
<s><lb/>particula uer&ograve; illa [quadripertit&ograve;] &longs;ic intelligenda e&longs;t. </s>
<s>qu&ograve;d &longs;ci&shy;<lb/>licet quadrifariam iuxta quatuor laterum numeros &longs;uperadie&shy;<lb/>ctio facienda &longs;it. </s>
<s>Quamuis autem hoc ultimum ab autore dictum <lb/>&longs;ic intelligendo turrem ingenios&egrave; uerum o&longs;tendi potest, illa duo ta&shy;<lb/>men ab eo &longs;uperi&ugrave;s dicta nullo modo in &longs;e ueritatem contine&shy;<lb/>re po&longs;&longs;unt: ni&longs;i in ea, qu&agrave;m diximus turre, cuius autor nullam <lb/>mentionem &longs;ecit. </s>
<s>Quapropter ego potius crediderim ante illa <lb/>uerba [uige&longs;imam tertiam uer&ograve; partem] nonnulla intextu de&longs;ide <lb/>rari. </s>
<s>Qu&ecedil; c&ugrave;m ita dixerit autor &longs;equitur propo&longs;itum &longs;uum his <lb/>verbis [&longs;i autem decem tectis pr&ecedil;ditam &amp;c.] ubi prim&ugrave;m repe&shy;<lb/>tit ea, qu&aelig; &longs;uperi&ugrave;s de turri decem tectis pr&aelig;dita ab Apollodoro <lb/>con&longs;tructa dixerat: qu&ograve;d &longs;cilicet Apollodorus declarat &longs;ingu&shy;<lb/>lam pedis unius &longs;uperadiectionem euenire, &amp; quintam ba&longs;is par&shy;<lb/>tem &longs;ur&longs;um ab ip&longs;o intercipi, ita ut &longs;uperiora iuga &longs;ingula pedum <lb/>&longs;eptem &amp; &longs;ext&aelig; partis fiant: Deinde declarat in hac turri, &longs;ci-<emph.end type="italics"/><pb xlink:href="052/01/065.jpg"/><emph type="italics"/>licet decem tectis pr&aelig;dita men&longs;uras adh&aelig;rentium lignorum ab <lb/>Apollodoro traditas, dicens qu&ograve;d Apollodorus inferiora adh&aelig;ren&shy;<lb/>tia &longs;ingula pedum nouem fieri declarat: ip&longs;a ver&ograve;, qu&aelig; in &longs;upe&shy;<lb/>rioribus quatuor tectis &longs;unt, &longs;ingula pedum &longs;ex tantum: ip&longs;a de&shy;<lb/>mum, qu&aelig; in quatuor reliquis (c&ugrave;m adh&aelig;rentia ligna &longs;int nouem <lb/>ordinum) adhuc &longs;uperiora &longs;unt, &longs;ingula quinque, &amp; partis. </s>
<s>qu&aelig; <lb/>quidem pars, qu&aelig; nam &longs;it tertia &longs;cilicet, an quarta, vel quinta, <lb/>vel qu&aelig;uis alia, ne&longs;citur, c&ugrave;m Autor eam minim&egrave; po&longs;uerit, aut <lb/>forta&longs;&longs;e in textu deficiat.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note94"/></s></p><p type="margin">
<s><margin.target id="note94"/><emph type="italics"/>m<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Hoc itaque pacto &amp;c.] in pr&aelig;&longs;enti parte prim&ugrave;m epilogat Au&shy;<lb/>tor breuiter ea, qu&aelig; de tectorum diui&longs;ionibus, &longs;iue altitudinibus <lb/>edocuit: deinde declarat turres ex tectis c&ugrave;m &aelig;qualis, tum in&aelig;&shy;<lb/>qualis altitudinis iuxta cubitos ac pedes con&longs;tructas adinuicem <lb/>proportionales, &amp; commen&longs;urabiles e&longs;&longs;e. </s>
<s>Epilogans igitur inquit. <lb/>[Hoc itaque pacto] &longs;cilicet quemadmodum iam docuimus [non <lb/>&longs;ol&ugrave;m ea, qu&aelig; iuxta numerum di&longs;crepant turrium tecta] hoc est, <lb/>qu&aelig; modo &longs;ex, modo decem numero &longs;unt in turribus &longs;cilicet, qu&aelig; <lb/>quandoque &longs;ex, quandoque decem tectis pr&aelig;dit&aelig; &longs;upponuntur. <lb/>[ad &longs;exaginta pedum altitudinem] videlicet in turri ip&longs;ius Apol&shy;<lb/>lodori, quam &longs;exaginta pedum altitudinis con&longs;truxit, vt in prin&shy;<lb/>cipio pr&aelig;&longs;entis capitis Autor declarauit. [c&ugrave;m &aelig;qualis] nempe in <lb/>turri &longs;ex tectis pr&aelig;dita, in qua omnia adh&aelig;rentia ligna, quibus <lb/>tectorum altitudo di&longs;tinguitur, &longs;ingula pedum nouem ab Apollo&shy;<lb/>doro ponuntur. [tum in&aelig;qualis altitudinis] vt puta in turri de&shy;<lb/>cem tectis pr&aelig;dita, in qua (vt paul&ograve; &longs;uperi&ugrave;s dictum e&longs;t) infe&shy;<lb/>riora quidem adh&aelig;rentia, pedum nouem: &longs;uperiora autem qua&shy;<lb/>tuor, pedum &longs;ex: reliqua ver&ograve; quatuor adhuc &longs;uperiora, quinque, <lb/>&amp; partis ab Apollodoro po&longs;ita &longs;unt. [exi&longs;tentia reperientur.] hoc <lb/>est ita vt iam diximus &longs;e &longs;e habere inuenientur. </s>
<s>qu&aelig; quidem c&ugrave;m <lb/>&longs;ic epilogauerit, &longs;ubiungit. [verumetiam e&aelig;, qu&aelig; ex vtri&longs;que] &longs;ci&shy;<lb/>licet tum &aelig;qualis, tum in&aelig;qualis altitudinis tectis [iuxta cubi&shy;<lb/>tos] quales &longs;unt Diadis, &amp; Chari&aelig; [&amp; pedes con&longs;truuntur,] qua&shy;<lb/>les Apollodori &longs;unt. [ac iuxta magnitudinem di&longs;crepant turres] <lb/>quandoquidem iuxta cubitos con&longs;truct&aelig; iuxta pedes con&longs;tructis <lb/>maiores &longs;unt, vt nobis per&longs;picuum erit. [commen&longs;urabiles ad &longs;e <lb/>&longs;e inuicem &longs;ecundum proportionem ostendentur] hoc e&longs;t commu&shy;<lb/>nibus men&longs;uris proportionaliter men&longs;urari demonstrabuntur. </s>
<s>ve-<emph.end type="italics"/><pb xlink:href="052/01/066.jpg"/><emph type="italics"/>r&ugrave;m vt id, quod ait Autor clarum fiat, &longs;int exempli gratia du&aelig; <lb/>Diadis, &amp; Chari&ecedil; turres iuxta cubitos ab eis con&longs;truct&aelig;, qua&shy;<lb/>rum altera quidem nonaginta, altera ver&ograve; &longs;exaginta cubitorum <lb/>altitudinem habebant. </s>
<s><expan abbr="h&ccedil;">haec</expan> igitur adinuicem <expan abbr="c&otilde;men&longs;urabiles">commen&longs;urabiles</expan> &longs;unt. </s>
<s><lb/>quoniam non &longs;ol&ugrave;m communi men&longs;ura, nempe cubito men&longs;uran&shy;<lb/>tur, verumetiam &agrave; triginta cubitibus tamquam vna communi <lb/>earum men&longs;ura &longs;u&longs;ceptis altera quidem ter, altera ver&ograve; bis men&shy;<lb/>&longs;uratur. </s>
<s>Rur&longs;us autem adinuicem in ratione &longs;e&longs;quialtera &longs;unt, <lb/>c&ugrave;m nonaginta altitudo, &longs;exaginta altitudinem &longs;emel, ac eius di&shy;<lb/>midiam partem contineat. </s>
<s>Similiter &longs;int ali&aelig; du&aelig; turres iuxta pe&shy;<lb/>des &longs;ecundum Apollodorum con&longs;truct&aelig;, quarum altera quidem <lb/>nonaginta, altera ver&ograve; &longs;exaginta pedum altitudine pr&aelig;dita &longs;it. </s>
<s><lb/>h&aelig; itaque turres eodem modo, quo du&aelig; priores, tum commen&longs;ura&shy;<lb/>biles, tum adinuicem in ratione &longs;e&longs;quialtera &longs;unt. </s>
<s>Pr&aelig;terea ver&ograve; <lb/>&longs;i quatuor i&longs;t&aelig; turres adinuicem comparentur, du&aelig; quidem prio&shy;<lb/>res duabus po&longs;terioribus, tum commen&longs;urabiles, tum in ratione <lb/>&longs;e&longs;quialtera reperientur. </s>
<s>commen&longs;urabiles enim &longs;unt, quoniam <lb/>octo digiti cubitum quidem ter, pedem ver&ograve; bis men&longs;urant: c&ugrave;m <lb/>pes 16, cubitus 24 digitis con&longs;tet: vnd&egrave; etiam cubitus ad pedem <lb/>&longs;e&longs;quialter e&longs;t. </s>
<s>in ratione ver&ograve; &longs;e&longs;quialtera &longs;unt, quandoquidem <lb/>altitudo nonaginta cubitorum altitudinis nonaginta pedum, &longs;imi&shy;<lb/>liter&queacute; altitudo &longs;exaginta cubitorum altitudinis &longs;exaginta <expan abbr="pe-d&utilde;">pe&shy;<lb/>dum</expan>, necnon <expan abbr="&longs;ept&etilde;decim">&longs;eptendecim</expan> cubitorum longitudo ba&longs;is <expan abbr="&longs;ept&etilde;decim">&longs;eptendecim</expan> pe&shy;<lb/>dum longitudinis ba&longs;is &longs;e&longs;quialtera e&longs;t. </s>
<s>quemadmodum enim &longs;e <lb/>habet cubitus ad pedem, ita etiam 90, vel 60, vel 17, vel quot&shy;<lb/>cumque cubiti ad 90, vel 60, vel 17, vel quotcumque pedes &longs;e &longs;e <lb/>habebunt. </s>
<s>Non &longs;ol&ugrave;m autem iuxta altitudines, &amp; ba&longs;ium longi&shy;<lb/>tudines: verumetiam iuxta reliquas omnes earum partes iam di&shy;<lb/>ct&aelig; quatuor turres, tum <expan abbr="c&otilde;men&longs;urabilitatem">commen&longs;urabilitatem</expan>, tum eam rationum <lb/>po&szlig;ident conuententiam, qu&aelig; proportio dicitur. </s>
<s>atque propterea <lb/>&longs;ubiunxit Autor, [&amp; &longs;icut &longs;e habent 24 ad 16, &longs;ic etiam rot&aelig; ad <lb/>&longs;einuicem tum iuxta numerum, tum etiam iuxta magnitudinem: <lb/>necnon ba&longs;is ad ba&longs;im &longs;icuti etiam tria ad duo.] hoc e&longs;t ip&longs;e quoque <lb/>turrium rationem adinuicem &longs;e&longs;quialteram habentium rot&aelig; in <lb/>ratione &longs;e&longs;quialtera e&longs;&longs;e debent [tum iuxta numerum] vt &longs;cilicet <lb/>rot&aelig; &longs;e&longs;quialter&aelig; turris, &longs;ex numero: &longs;ub &longs;e&longs;quialter&aelig; ver&ograve;, qua&shy;<lb/>tuor &longs;int, [tum etiam iuxta magnitudinem] vt nempe rot&aelig; &longs;e&longs;-<emph.end type="italics"/><pb xlink:href="052/01/067.jpg"/><emph type="italics"/>quialter&aelig; turris rotis &longs;ub&longs;e&longs;quialter&aelig; maiores in ratione &longs;e&longs;qui&shy;<lb/>altera &longs;int, quemadmodum 24 ad 16. Similiter autem &amp; ba&longs;is <lb/>&longs;e&longs;quialter&aelig; turris ad ba&longs;im &longs;ub&longs;e&longs;quialter&aelig; &longs;icut tria ad duo ra&shy;<lb/>tionem &longs;e&longs;quialteram habere debet. </s>
<s>Qu&aelig; quidem concludens <lb/>Autor ait, [o&longs;ten&longs;&aelig; &longs;unt igitur ip&longs;&aelig; quoque men&longs;urantes turres,] <lb/>nempe &longs;ub&longs;e&longs;quialter&aelig;, &longs;iue iuxta pedes con&longs;truct&ecedil; [ad &longs;einui&shy;<lb/>cem eam, quam e&aelig;, qu&aelig; men&longs;urantur] hoc e&longs;t &longs;e&longs;quialter&aelig;, &longs;iue <lb/>iuxta cubitos fabricat&aelig; [iuxta proportionem] ide&longs;t rationum &longs;i&shy;<lb/>militudinem, atque conuenientiam, &longs;iue proportionaliter [habere <lb/>rationem] vtpot&egrave; videlicet &longs;e&longs;quialteram. </s>
<s>vocat autem &longs;ub&longs;e&longs;&shy;<lb/>quialteras quidem men&longs;urantes, &longs;e&longs;quialteras ver&ograve; men&longs;uratas <lb/>hac ratione: quia &longs;cilicet &longs;e&longs;quialter&aelig; ab earum &longs;ub&longs;e&longs;quialte&shy;<lb/>ris, videlicet ab earum dimidijs partibus ter men&longs;urantur. </s>
<s>po&shy;<lb/>&longs;tea ver&ograve; concludens Autor cuncta ea, qu&aelig; in hac vltima capitis <lb/>parte de commen&longs;urabilitate, proportione&queacute; turrium ab eo dicta <lb/>&longs;unt ait, qu&ograve;d non &longs;ol&ugrave;m iuxta commen&longs;urationem, verumetiam <lb/>iuxta conuenientiam, &longs;cilicet rationum, &longs;eu proportionem ip&longs;am, <lb/>turrium ferri idonearum con&longs;tructiones. </s>
<s>Diodorus, necnon Dia&shy;<lb/>des, &amp; Charias fecerunt. </s>
<s>vbi qu&aelig;rendum e&longs;t qui&longs;nam &longs;uerit i&longs;te <lb/>Diodorus, cuius nullibi ni&longs;i hoc in loco mentionem Autor fecit: an <lb/>poti&ugrave;s Apollodorus legendum &longs;it, cuius poti&szlig;im&ugrave;m doctrina de <lb/>con&longs;tructione turrium in toto pr&aelig;&longs;enti capite traditur. </s>
<s>Po&longs;th&aelig;c <lb/>demum ex ijs, qu&aelig; hucu&longs;que dicta &longs;unt <expan abbr="corollari&utilde;">corollarium</expan> quoddam Au&shy;<lb/>tor excerp&longs;it dicens manife&longs;tum e&longs;&longs;e [qu&ograve;d Antiqui Mechanici] <lb/>&longs;cilicet profe&longs;&longs;ores eius Mathematic&aelig; &longs;cienti&aelig; partis, qu&ecedil; Me&shy;<lb/>chanica nuncupatur [eruditi&szlig;imi&queacute; architecti] hoc e&longs;t ip&longs;i machi&shy;<lb/>narum bellicarum artifices iam dict&ecedil; Mechanic&aelig; &longs;cienti&aelig; peri&shy;<lb/>ti&szlig;imi, vel ab alijs eiu&longs;dem &longs;cienti&aelig; periti&szlig;imis coadiuuati [&longs;cien <lb/>tific&egrave;] hoc e&longs;t cum debitis proportionibus, ac men&longs;uris ab ip&longs;a &longs;cien<lb/>tia traditis [&amp; non ab&longs;que ratione] nempe fortuit&ograve; [<expan abbr="Machinar&utilde;">Machinarum</expan>] </s></p><p type="main">
<s><arrow.to.target n="note95"/><lb/>vtique bellicarum [con&longs;tructiones faciebant. [Turre &longs;ic quoad <lb/>con&longs;tructionem con&longs;tructa] in hac po&longs;trema pr&aelig;&longs;entis capitis par&shy;<lb/>te de quibu&longs;dam ad ip&longs;arum turrium confirmationem, deffen&longs;io&shy;<lb/>nem&que; pr&ecedil;uidendis, ac pr&aelig;parandis &longs;ermonem habet Autor, cu&shy;<lb/>ius verba per&longs;picua &longs;unt. </s>
<s>finis autem huiu&longs;ce capitis, &amp; princi&shy;<lb/>pium &longs;equentis, ac forta&longs;&longs;e quoddam aliud integrum caput de&shy;<lb/>&longs;iderantur in omnibus qu&aelig; vidimus gr&aelig;cis exemplaribus, ve-<emph.end type="italics"/><pb xlink:href="052/01/068.jpg"/><emph type="italics"/>r&ugrave;m h&aelig;c &agrave; nobis pro dilucidatione pr&aelig;&longs;entis capitis omnium qu&aelig; <lb/>in toto pr&aelig;&longs;enti opere continentur tum longi&szlig;imi, tum ob&longs;curi&szlig;i&shy;<lb/>mi dicta &longs;int.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note95"/>n</s></p><p type="main">
<s><emph type="center"/>De &longs;calis Arietem ge&longs;tantibus. </s>
<s>Cap. </s>
<s>XV.<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Principium huius Capitis de&longs;ideratur.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s>* * * partes Arietem &longs;u&longs;tentatum ferri. </s>
<s>&agrave; tertio uer&ograve; <lb/>gradu &longs;uperioris &longs;cal&aelig; ad alterius tertium, &amp; &aelig;qualis altitu&shy;<lb/>dinis exi&longs;tentem tabulis, uel uirgis textis teguntur: utri&longs;que <lb/>autem creta &longs;uperillitis, aut corijs bouum recens occi&longs;o&shy;<lb/>rum coopertis, tum propter tormenta ignem iaculantia, <lb/>tum propter lapidum iactus. </s>
<s>at paul&ograve; infra tertium <expan abbr="grad&utilde;">gradum</expan> <lb/>po&longs;t octo decim, aut <expan abbr="&etilde;t">etiam</expan> uiginti pedes, contingentes gradus <lb/>aliud tectum &longs;u&longs;cipiunt, non ad totam graduum latitudi&shy;<lb/>nem. </s>
<s>locus enim ad a&longs;cen&longs;um pertinens ab&longs;que tecto relin<lb/>quetur. </s>
<s>Oportet <expan abbr="a&utilde;t">aut</expan> eos, <expan abbr="&qtail;">quod</expan> ad <expan abbr="&longs;calar&utilde;">&longs;calarum</expan> crura imponuntur cla<lb/>uos, mult&ugrave;m ad latera foras prodire: ut lati&ugrave;s &longs;calarum &longs;pa<lb/>tium tegatur. </s>
<s>nam Aries ibi maxim&egrave; aget, &agrave; &longs;upremo te&shy;<lb/><arrow.to.target n="note96"/><lb/>cto pendens duobus &longs;u&longs;tentaculis &aelig;qualis fer&egrave; altitudinis, <lb/>ut qui Arietem pellunt &longs;uper pauimento &longs;patii tabulis co&shy;<lb/>operti &longs;tantes, ad &longs;uperiores murorum partes Ariete oppu<lb/>gnent. </s>
<s>nam omne erectum, &amp; excedens tanquam liberum, <lb/><expan abbr="haud&qacute;ue">haudque</expan> coniunctum facil&egrave; frangi, <expan abbr="de&longs;trui&qacute;ue">de&longs;truique</expan> pote&longs;t. </s>
<s>cu&shy;<lb/>iu&longs;modi &longs;unt murorum pinn&aelig;, <expan abbr="turrium&qacute;ue">turriumque</expan> propugnacu&shy;<lb/>la, ac demum qu&aelig;cunque non adinuicem continuata &longs;u&shy;<lb/>&longs;tentantur. </s>
<s>atque per ip&longs;um Arietem quadrangulum exi&shy;<lb/>&longs;tentem ad murum peruenire facil&egrave; poterint, non aliter <lb/>quam ij, qui per eas, qu&aelig; in turribus iam dict&aelig; &longs;unt ad la&shy;<lb/>tera circum&longs;eptiones, perueniunt. </s>
<s>nam huiu&longs;cemodi &longs;cal&aelig; <lb/>non circumflectuntur ad crura <expan abbr="circ&utilde;uer&longs;&aelig;">circumuer&longs;&aelig;</expan>, &longs;ed &longs;emper ere&shy;<lb/>ct&aelig;, <expan abbr="eadem&qacute;ue">eademque</expan> ad &longs;einuicem interualla con&longs;eruantes per&shy;<arrow.to.target n="note97"/><lb/>manent. </s>
<s>&amp; de&longs;criptio propo&longs;ita e&longs;t. </s></p>
<pb xlink:href="052/01/069.jpg"/><p type="margin">
<s><margin.target id="note96"/>a</s></p><p type="margin">
<s><margin.target id="note97"/>b</s></p><figure id="id.052.01.069.1.jpg" xlink:href="052/01/069/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>MAchin&aelig; ex &longs;calis con&longs;truct&aelig;, arietem&queacute; ge&longs;tantis, de qua <lb/>loquitur Autor in hoc capite, constructione caremus, quo&shy;<lb/>niam in ea parte, qu&aelig; in principio capitis huius de&longs;idera&shy;<lb/>tur ea tradi debebat. </s>
<s>habemus <expan abbr="a&utilde;t">aut</expan> <expan abbr="e&atilde;">eam</expan> ab Apollodoro traditam in <lb/>libro &longs;uo de machinis ob&longs;idionalibus, quam h&igrave;c po&longs;ui&longs;&longs;emus &longs;i fi&shy;<lb/>gur&aelig; ab Autore propo&longs;it&aelig; corre&longs;ponderet. </s>
<s>c&ugrave;m <expan abbr="aut&etilde;">autem</expan> ei minim&egrave; cor&shy;<lb/>re&longs;pondeat, &longs;ed ab ea long&egrave; diuer&longs;a &longs;it, pluribus&queacute; figuris indigeat,<emph.end type="italics"/>
<pb xlink:href="052/01/070.jpg"/><emph type="italics"/>noluimus eam h&igrave;c inter&longs;erere, ne Autoris <expan abbr="ordin&etilde;">ordinem</expan> peruerteremus. </s>
<s><lb/>ver&ugrave;m ip&longs;a etiam &aelig;detur c&ugrave;m &agrave; nobis iam dictus Apolloderi li&shy;<lb/>ber vn&agrave; cum Ath&aelig;nei, Cte&longs;ibij, Bitonis, diuer&longs;orum&queacute; aliorum au&shy;<lb/>torum opera varia de re bellica &egrave; gr&aelig;co &longs;ermone in latinum iam <lb/>conuer&longs;a impre&longs;&longs;oribus excudenda tradentur.<emph.end type="italics"/><lb/><arrow.to.target n="note98"/></s></p><p type="margin">
<s><margin.target id="note98"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[fer&egrave;] particulam hanc appo&longs;uit Autor, vt nobis o&longs;tenderet, <lb/>qu&ograve;d illa duo &longs;u&longs;tentacula, quibus aries ip&longs;a pendet, in&aelig;qualis al&shy;<lb/>titudinis e&longs;&longs;e debent; ita &longs;cilicet qu&ograve;d anterius &longs;u&longs;tentaculum po&shy;<lb/>&longs;teriore breuius aliquantulum &longs;it, vt aries ad &longs;uperiores muro&shy;<lb/>rum partes tendat, maiorem&queacute; percu&szlig;ionem efficiat: quemadmo&shy;<lb/>dum &longs;uperi&ugrave;s in <expan abbr="te&longs;tudin&utilde;">te&longs;tudinum</expan> arietem <expan abbr="ge&longs;tanti&utilde;">ge&longs;tantium</expan> con&longs;tructione docuit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note99"/></s></p><p type="margin">
<s><margin.target id="note99"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Dubitandum an pr&aelig;&longs;ens figura in fine huius capitis ab Autore <lb/>po&longs;ita fuerit, quoniam in fine omnium huius operis capitum v&longs;us <lb/>e&longs;t Autor his verbis [&amp; figura &longs;ubiecta e&longs;t.] vel [&longs;ub&longs;cripta e&longs;t] <lb/>vel [huiu&longs;cemodi e&longs;t] h&igrave;c autem ait [propo&longs;ita e&longs;t] quod indicat <lb/>figuram hanc ante hunc locum ab Autore &longs;ui&longs;&longs;e collocatam: for&shy;<lb/>&longs;an in ijs, qu&aelig; inter finem pr&aelig;cedentis, &amp; initium pr&aelig;&longs;entis ca&shy;<lb/>pitis de&longs;unt. </s>
<s>nos ver&ograve; c&ugrave;m hoc in loco eam apud gr&aelig;cum exem&shy;<lb/>plar inuenimus, h&igrave;c etiam ponendam e&longs;&longs;e voluimus.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Alia &longs;calarum de&longs;criptio duos Arietes ge&longs;tantium. </s>
<s><lb/>Cap. </s>
<s>XVI.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note100"/></s></p><p type="margin">
<s><margin.target id="note100"/>a</s></p><p type="main">
<s>RVr&longs;us alium ordinem, <expan abbr="&longs;itum&qacute;ue">&longs;itumque</expan> &longs;cal&aelig; &longs;u&longs;ci&shy;<lb/>piunt, eum &longs;cilicet, qui ver&longs;us murum adue&shy;<lb/>niat, &aelig;qualis exi&longs;tens, &amp; parallelus, aut &longs;ecun&shy;<lb/>dum faciem erectus: &amp; ip&longs;os quidem gradus <lb/>iuxta muri faciem, <expan abbr="retro&qacute;ue">retroque</expan> re&longs;picientes ha&shy;<lb/>bent: ip&longs;a ver&ograve; &agrave; &longs;einuicem tum &longs;ur&longs;um, tum deor&longs;um in&shy;<lb/>terualla, non quemadmodum prim&aelig; in&aelig;qualia habent, &longs;ed <lb/>ex &aelig;quali idem interuallum con&longs;eruant. </s>
<s>At tecta eadem, <lb/>qu&aelig; priores habent: variant <expan abbr="aut&etilde;">autem</expan> iuxta hoc. </s>
<s>nam vice vnius <lb/>arietis, qui inter priores duas &longs;calas fertur, duo extrin&longs;ec&ugrave;s <lb/>ad crurium latera po&longs;iti feruntur. </s>
<s>Hi autem arietes c&ugrave;m ali&shy;<lb/>quid peregerint &longs;iue commouentes, &longs;iue rumpentes aliquid <lb/>eorum, qu&aelig; in muri faciem pr&aelig;ponuntur: eos funes, qui ex <lb/>po&longs;terioribus &longs;unt relaxabant, &amp; &longs;imul du&aelig; &longs;cal&aelig; muro ap-<pb xlink:href="052/01/071.jpg"/>portantur. </s>
<s>ver&ugrave;m anterior quidem <expan abbr="ear&utilde;">earum</expan> penes gradus &longs;uos <lb/>muro appropinquat: altera ver&ograve; di&longs;tat ab ip&longs;a, quant&ugrave;m <lb/>etiam id, quod e&longs;t inter eas adinuicem interuallum iuxta <lb/><expan abbr="connexion&etilde;">connexionem</expan> remouetur. </s>
<s>ac <expan abbr="dem&utilde;">demum</expan> ea, qu&aelig; de&longs;uper e&longs;t &longs;cala&shy;<lb/>rum connexio, tamquam pauimentum tabulis pro&longs;tratis <lb/>facta, &amp; circumquaque cooperta, efficax ad murum &longs;can&longs;o&shy;<lb/>rium fit. </s>
<s><expan abbr="figura&qacute;ue">figuraque</expan> ip&longs;a &longs;ubijcitur. </s></p><figure id="id.052.01.071.1.jpg" xlink:href="052/01/071/1.jpg"/>
<pb xlink:href="052/01/072.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note101"/></s></p><p type="margin">
<s><margin.target id="note101"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>VErb&aelig; illa [e&utilde; &longs;cilicet, qui ver&longs;us murum adueniat, &aelig;qua&shy;<lb/>lis exi&longs;tens, &amp; parallelus, aut &longs;ecundum faciem erectus] <lb/>aliquantulum ob&longs;cura &longs;unt &longs;i ordini, &longs;itui&queacute; applicentur, <lb/>vt verborum &longs;eries exigit. </s>
<s>durum e&longs;t enim dicere qu&ograve;d ordo, &longs;i&shy;<lb/>tus&queacute; &longs;calarum talis &longs;it, qui ver&longs;us murum adueniat, &aelig;qualis <lb/>exi&longs;tens, &amp; parallelus, ac &longs;ecundum faciem erectus. </s>
<s>c&ugrave;m enim <lb/>ordo, ac &longs;itus corporis accidentia &longs;int: nec ad murum aduenire, <lb/>neque pror&longs;us moueri ni&longs;i vn&agrave; cum aliquo corpore po&longs;&longs;unt. </s>
<s>pr&aelig;te&shy;<lb/>rea c&ugrave;m &aelig;quale, parallelum, &amp; erectum e&longs;&longs;e magnitudinis pa&longs;&shy;<lb/>&longs;iones &longs;int: &longs;itus autem, ac ordo &longs;ub pr&aelig;dicamento quantitatis <lb/>cadere minime queant, nulli dubium qu&ograve;d iam dict&aelig; pa&szlig;iones de <lb/>his pr&aelig;dicari non po&longs;&longs;unt. </s>
<s>Quapropter pa&szlig;iones i&longs;t&aelig; &longs;calis ip&longs;is <lb/>applicand&aelig; &longs;unt. </s>
<s>ita vt eorum verborum &longs;ententia &longs;it huiu&longs;modi. </s>
<s><lb/>qu&ograve;d &longs;cilicet talem ordinem, &longs;itum&queacute; &longs;cale &longs;u&longs;cipiunt: qui eas ad <lb/>murum aduenire, &aelig;quales muri altitudini exi&longs;tere, &amp; parallelas <lb/>tum muro, tum <expan abbr="&longs;ibiinuic&etilde;">&longs;ibiinuicem</expan>, aut &longs;ecundum faciem erectas e&longs;&longs;e faciat.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Alia &longs;calarum de&longs;criptio vnicum arietem, &longs;ed in de&longs;truen&shy;<lb/>do vehementiorem ge&longs;tantium. </s>
<s>Cap. </s>
<s>XVII.<emph.end type="center"/></s></p><p type="main">
<s>QV&ugrave;m in hac po&longs;itione, tum in prima (excepta <lb/>iam dicta &longs;ecunda, qu&aelig; &longs;itu, ac ordine paral&shy;<lb/>lela ad murum e&longs;t) eorum, qui arietibus addi&shy;<lb/>cati &longs;unt illi, qui &longs;uper <expan abbr="pauim&etilde;to">pauimento</expan> &longs;tant, &amp; arie&shy;<lb/>te &longs;ur&longs;um oppugnant turbantur, ac propu&shy;<lb/>gnantes ho&longs;tes extime&longs;cunt. </s>
<s>ver&ugrave;m duos de&shy;<lb/>&longs;uper eminentes gradus in eo, cui &longs;it arietis motu, corijs <lb/>circum operientes, propugnaculum, &amp; cu&longs;todiam <expan abbr="t&atilde;quam">tanquam</expan> <lb/>muri pinnas &longs;ibi ip&longs;is pr&aelig;bebunt. </s>
<s>Non paruam autem vti&shy;<lb/>litatem ad indubitatum auxilium, ac &longs;eruitium dupl&aelig; &longs;ca&shy;<lb/>l&aelig; pr&aelig;&longs;tabunt, &longs;i in vnaquaque compo&longs;itarum ab &aelig;qualis <lb/>altitudinis clauo ad alterius ex aduers&ograve; &aelig;qualis altitudinis <lb/>clauum, &longs;iue in eiu&longs;dem ordinis gradum <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> &longs;e&shy;<lb/>cundum eandem men&longs;uram ab eodemmet alterius gradu
<pb xlink:href="052/01/073.jpg"/>ligna parte altera latiora indirectum accommodabimus: <lb/>ad ea, qu&aelig; ad latera extra excedunt clauium extrema, pe&shy;<lb/>netrantia: &amp; immutabiles con&longs;eruantia eos interceptos lo&shy;<lb/>cos, qui ab ip&longs;is inuicem &longs;calis ad crura di&longs;tant, quique nec </s></p><p type="main">
<s><arrow.to.target n="note102"/><lb/>adaperiri in ip&longs;o lationis motu po&longs;&longs;unt, neque tota machi&shy;<lb/>na claudi. </s>
<s>At ne ligna ip&longs;a di&longs;rumpantur, neque decidant <arrow.to.target n="note103"/><lb/>&agrave; loco, quem po&longs;&longs;ident: chelonaria impo&longs;ita &longs;uper &longs;cala&shy;<lb/>rum cruribus, clauis affigantur, quemadodum iam dicta <lb/>in&longs;culpta hemi&longs;ph&aelig;ria, &longs;iue pugilli iuxta medium circum&shy;<lb/>&longs;ecti ad a&longs;tringendum, &amp; continendum ligna, qu&aelig; clauis <lb/><expan abbr="tr&atilde;sfixa">transfixa</expan> &longs;unt. </s>
<s>ver&ugrave;m aries quam iuxta medium &longs;cal&ecedil; ferunt, <lb/>ex vtri&longs;que lateribus iuxta anterius extremum &longs;u&longs;cipiat <lb/>duas tabellas quadrangulas tamquam maxillas erectas ad <lb/>altitudinem, &longs;uper arietem v&longs;que ad cubitum eminentes, <lb/>in ip&longs;a ver&ograve; clauorum affixione, atque inferi&ugrave;s propter ex&shy;<lb/>ten&longs;ionis <expan abbr="vehementi&atilde;">vehementiam</expan> confirmatas. </s>
<s>H&aelig; <expan abbr="itaq;">itaque</expan> indirectum ex <lb/>aduer&longs;o &longs;ibiinuicem circa medium forentur, atque ad ex&shy;<lb/>trin&longs;ecas foraminum partes coron&aelig; &longs;olid&aelig; tamquam anuli <arrow.to.target n="note104"/><lb/>clauis affigantur, qu&aelig; modiolos vocatos iuxta medium &longs;u&shy;<lb/>&longs;cipiant, quoad figuras fictilibus tubeculis &longs;imiles, ex &aelig;re <lb/>interi&ugrave;s tornatiles, vel ex fortibus lignis factos, ferreis ex&shy;<lb/>trin&longs;ec&ugrave;s laminis alligatos, ampliores ba&longs;es circa po&longs;itio&shy;<lb/>nem habentes, ac demum iuxta circum uolutionem ab anu&shy;<lb/>lis, qui clauis affixi &longs;int, impeditos ne ab ip&longs;is foraminum lo<lb/>cis excidant. </s>
<s>ip&longs;&aelig; ver&ograve; modiolorum bucul&aelig; repercutian&shy;<lb/>tur, <expan abbr="&longs;u&longs;cipiant&qacute;ue">&longs;u&longs;cipiantque</expan> paruas regulas quadrangulas penetran&shy;<arrow.to.target n="note105"/><lb/>tes tamquam peri&longs;tomidas ver&longs;us bucularum extrema ex&shy;<lb/>cedentes. </s>
<s>ad quas neruis humerarijs, &longs;iue dor&longs;alibus om&shy;<lb/>nium animalium (exceptis porcorum) per medium modio&shy;<lb/>lorum tran&longs;euntibus, in ip&longs;a circum uolutionis vehemen&shy;<lb/>tia propter fortitudinem eos circumuolui oportet: aut eis <lb/>robu&longs;tioribus chordis, qu&aelig; ex &longs;ericis textis fiunt, vel ex li&shy;<arrow.to.target n="note106"/><lb/>no netilibus, iuxta medium &longs;u&longs;cipientibus lignum longum <lb/><expan abbr="interpo&longs;it&utilde;">interpo&longs;itum</expan>, in figura reflexi angonis, &egrave; contrario retror&longs;us <lb/>conuer&longs;um, &amp; iuncturam retinens: quales &longs;unt ij, qui lapi&shy;<arrow.to.target n="note107"/><lb/>des iaciunt monangones, quos nonnulli fundas appellant. </s>
<s><lb/>vectem autem ferreum anulari radice pr&aelig;ditum ad iam di-
<pb xlink:href="052/01/074.jpg"/>ctas peri&longs;tomidas interpo&longs;itum violentam circumuolutio&shy;<lb/>nem in ip&longs;is modiolis agere, <expan abbr="fortem&qacute;ue">fortemque</expan> violentiam perfice&shy;<lb/>re opus e&longs;t. </s>
<s>aries ver&ograve;, qu&aelig; &agrave; &longs;calis pellitur, &amp; muro affer&shy;<lb/>tur, inijciet ijs, qui murum cu&longs;todiunt demi&longs;&longs;um monan&shy;<lb/>gonem, &amp; multam a&longs;&longs;i&longs;tentium expugnationem faciet. </s>
<s>at&shy;<lb/>que figura de&longs;cripta e&longs;t. </s></p><p type="margin">
<s><margin.target id="note102"/>a</s></p><p type="margin">
<s><margin.target id="note103"/>b</s></p><p type="margin">
<s><margin.target id="note104"/>c</s></p><p type="margin">
<s><margin.target id="note105"/>d</s></p><p type="margin">
<s><margin.target id="note106"/>e</s></p><p type="margin">
<s><margin.target id="note107"/>f</s></p><figure id="id.052.01.074.1.jpg" xlink:href="052/01/074/1.jpg"/>
<pb xlink:href="052/01/075.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note108"/></s></p><p type="margin">
<s><margin.target id="note108"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[tota machina claudi] &longs;ic in gr&aelig;co codice legitur. </s>
<s>&longs;ed meli&ugrave;s <lb/>e&longs;&longs;et legere [totam machinam claudere.]<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note109"/></s></p><p type="margin">
<s><margin.target id="note109"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[chelonaria h&igrave;c intelligenda &longs;unt parua chelonia, qu&aelig; quidem <lb/>cuiu&longs;modi &longs;int in pr&aelig;cedenti capite declarauimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note110"/></s></p><p type="margin">
<s><margin.target id="note110"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Modiolus, qui gr&aelig;c&egrave;<emph.end type="italics"/> <foreign lang="greek">xoiniki\s</foreign> <emph type="italics"/>dicitur, e&longs;t rot&aelig; pars axim cir&shy;<lb/>cumambiens, cui affixi &longs;unt radij.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note111"/></s></p><p type="margin">
<s><margin.target id="note111"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Ea ligna, qu&aelig; &longs;uperi&ugrave;s in nono, ac pr&aelig;cedenti capite perito&shy;<lb/>midas Autor vocauit, nunc peri&longs;tomidas non immerito nuncupat: <lb/>quandoquidem circa &longs;tomium, hoc e&longs;t buculam ip&longs;orum modio&shy;<lb/>lorar: ponenda &longs;unt. </s>
<s>ver&ugrave;m peritomid&aelig; quoque dicuntur<emph.end type="italics"/> <foreign lang="greek">a)po\ <lb/>tou_ perite/mnein</foreign>, <emph type="italics"/>hoc e&longs;t circumincidere, quoniam circuminci&longs;a, <lb/>in&longs;culpta&queacute; circumquaque iam dicta ligna &longs;unt, quemadmodum <lb/>in duobus &longs;uperioribus locis declarauimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note112"/></s></p><p type="margin">
<s><margin.target id="note112"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Angon e&longs;t qu&aelig;dam &longs;pecies arcus reflexi, qui cum chordam <lb/>non habet, &egrave; contrario retror&longs;um conuertitur. </s>
<s>cuiu&longs;modi arcus ij <lb/>&longs;unt, quibus nunc gr&aelig;ci, turc&aelig;&queacute; &longs;agittarij vtuntur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note113"/></s></p><p type="margin">
<s><margin.target id="note113"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Monangon e&longs;t quoddam iaculatorium in&longs;trumentum balli&longs;t&aelig; <lb/>&longs;imile, cuius exqui&longs;itam con&longs;tructionem Athen&aelig;us quidem tra&shy;<lb/>dit: Auior ver&ograve; breuiter in &longs;equenti capite mentionem facturus <lb/>e&longs;t. </s>
<s>hoc autem in&longs;trumentum quidam (vt ait Autor) antiquorum <lb/>Mechanicorum fundam etiam appellarunt: licet funda propri&egrave; <lb/>&longs;it in&longs;trumentum ex lino factum, quo long&egrave; lapides iactantur.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>De quibu&longs;dam iaculatorijs in&longs;trumentis breuis <lb/>enarratio. </s>
<s>Cap. </s>
<s>XVIII.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note114"/></s></p><p type="margin">
<s><margin.target id="note114"/>a</s></p><p type="main">
<s>IP&longs;a ver&ograve; monangonis con&longs;tructio ad catapul&shy;<lb/>ticam etiam contemplationem volentes in&longs;ti&shy;<arrow.to.target n="note115"/><lb/>tuet. </s>
<s>quandoquidem ad longi&ugrave;s iaculandum <lb/>tum rect&egrave; exten&longs;is, tum reflexis: &longs;iue tum la&shy;<lb/>pides iacientibus, tum &longs;agittas celeriter iacu&shy;<lb/>lantibus in&longs;trumentis mult&ugrave;m confert. </s>
<s>nam ip&longs;a modiolo&shy;<lb/>rum appo&longs;itio parte altera oblongius per chordam in&longs;tru&shy;<lb/>mentum: &amp; circa vehementiam, fortiorem emi&longs;&longs;ionem effi&shy;<pb xlink:href="052/01/076.jpg"/>cit. </s>
<s>quant&ugrave;m enim chorda iuxta longitudinem ad augetur, <lb/>tant&ugrave;m &longs;agitt&aelig; quoque emi&longs;&longs;io extendi innata e&longs;t: chorda <lb/>ip&longs;ius arcus omnia peragente, <expan abbr="ip&longs;i&ugrave;s&qacute;ue">ip&longs;i&ugrave;sque</expan> emi&longs;&longs;ionis violen&shy;<lb/>tiam &longs;u&longs;tinente. </s>
<s>quamobrem huius contexionem ex robu&shy;<lb/>&longs;tioribus, &amp; quamplurim&ugrave;m exercitatis neruis animalis <lb/>fieri dicunt. </s>
<s>verbi gratia Cerui quidem, ex ijs, qui in cruri&shy;<lb/>bus, pedibus&qgrave;ue: Tauri ver&ograve;, ex ijs, qui in humero &longs;unt. <arrow.to.target n="note116"/><lb/>atque ip&longs;as quidem erect&egrave; exten&longs;orum chordas rotundas <lb/>quoad contexionem e&longs;&longs;e, vt inter &longs;agittarum forficulas in&shy;<lb/>cidant: ip&longs;as vero reflexorum, latas zonarum in&longs;tar, an&longs;as <lb/>ex earum extremis habentes, ad quas angones ip&longs;i ingre&shy;<lb/>diuntur. </s>
<s>vt lapis &agrave; medietate chord&aelig; &longs;ecundum <expan abbr="latitudin&etilde;">latitudinem</expan> <lb/>percu&longs;&longs;us, ben&egrave; emittatur, non excidens ver&longs;us extrema. </s>
<s><lb/>Ip&longs;am autem, qu&aelig; in angonibus e&longs;t chordam ex commis <lb/>etiam muliebribus texi dicunt. </s>
<s>&longs;ubtiles enim exi&longs;tentes, <arrow.to.target n="note117"/><lb/>atque long&aelig;, <expan abbr="multo&qacute;ue">multoque</expan> oleo educat&aelig;: c&ugrave;m context&aelig; fue&shy;<lb/>rint, multum roborem &longs;u&longs;cipiunt: ita vt ab ip&longs;a, qu&aelig; ner&shy;<lb/>uis fit fortitudine non di&longs;crepent. </s>
<s>Verumtamen de his <expan abbr="n&utilde;c">nunc</expan> <arrow.to.target n="note118"/><lb/>&longs;atis. </s>
<s><expan abbr="n&atilde;">nam</expan> in iaculorum effectrice tractatione &longs;ubtiliter curio&shy;<lb/>&longs;ioribus ad con&longs;tructionem non &longs;ol&ugrave;m h&aelig;c, verumetiam <lb/>foraminum in in&longs;trumentis dimetientes, necnon ij, qui in <lb/>triplicata ratione dimetientium in ba&longs;ibus exi&longs;tentium &longs;i&shy;<lb/>miles, adinuicem o&longs;tenduntur cylindri, ac demum diuul&shy;<lb/>gata cubi duplatio: quibus iaculorum magnitudines iuxta <lb/>magnitudines contingentium in&longs;trumentorum dupl&aelig;, vel <lb/>etiam tripl&aelig; c&ugrave;m fiant, ad ea&longs;dem longitudines emittun&shy;<lb/>tur: mathematic&egrave; ibi, ac in&longs;trumentaliter cuncta ab Ale&shy;<arrow.to.target n="note119"/><lb/>xandrino Herone per demon&longs;trationem enarrata &longs;unt. </s></p><p type="margin">
<s><margin.target id="note115"/>b</s></p><p type="margin">
<s><margin.target id="note116"/>c</s></p><p type="margin">
<s><margin.target id="note117"/>d</s></p><p type="margin">
<s><margin.target id="note118"/>e</s></p><p type="margin">
<s><margin.target id="note119"/>f</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note120"/></s></p><p type="margin">
<s><margin.target id="note120"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>QVis nam &longs;it Angon, &amp; Monangon &longs;uperi&ugrave;s quidem dixi&shy;<lb/>mus: nunc ver&ograve; &longs;ciendum e&longs;t qu&ograve;d catapulta e&longs;t qu&aelig;dam <lb/>machina bellica, qua tela, aut &longs;axa excuti &longs;olent. </s>
<s>h&aelig;c <lb/>autem machina (vt docet Athen&aelig;us) varijs modis con&longs;truitur, <lb/>eius&queacute; mult&aelig; &longs;unt &longs;pecies, de quibus pertractans &longs;cientia cata-<emph.end type="italics"/>
<pb xlink:href="052/01/077.jpg"/><emph type="italics"/>pultica vocatur. </s>
<s>Ver&ugrave;m animaduertendum e&longs;t qu&ograve;d<emph.end type="italics"/> <foreign lang="greek">belopoii+kh\</foreign>, <lb/><emph type="italics"/>ide&longs;t iaculatoria, &longs;eu<emph.end type="italics"/> <foreign lang="greek">belopoii/a</foreign>, <emph type="italics"/>hoc e&longs;t iaculorum effectrix &longs;cien&shy;<lb/>tia differt &agrave; catapultica tamquam genus &agrave; &longs;pecie. </s>
<s>nam ip&longs;a qui&shy;<lb/>dem iaculatoria docet cuncta ea in&longs;trumenta conficere, qu&aelig; &longs;agit&shy;<lb/>tas, tela, &longs;axa, &amp; cuiu&longs;cumque generis iacula longi&ugrave;s excutiunt: <lb/>catapultica ver&ograve; ea tantum iaculatoria con&longs;truit in&longs;trumenta, <lb/>qu&aelig; proprio nomine catapult&aelig; dicuntur. </s>
<s>Quoniam autem Mo&shy;<lb/>nangon quoad eius con&longs;tructionem catapult&aelig; &longs;imilis e&longs;t, idcirco <lb/>dixit Autor, qu&ograve;d Monangonis con&longs;tructio ad <expan abbr="catapultic&atilde;">catapulticam</expan> etiam <lb/>contemplationem volentes in&longs;tituet. </s>
<s>cuius equidem rei rationem </s></p><p type="main">
<s><arrow.to.target n="note121"/><lb/>reddens ait [quandoquidem ad longi&ugrave;s iaculandum, tum rect&egrave; <lb/>exten&longs;is, tum reflexis: &longs;iue tum lapides iacientibus, tum &longs;agittas <lb/>celeriter iaculantibus in&longs;trumentis mult&ugrave;m confert.] hoc e&longs;t Mo&shy;<lb/>nangonis con&longs;tructio ad catapulticam contemplationem volentes <lb/>in&longs;tituet, hac &longs;cilicet ratione, quoniam mult&ugrave;m ip&longs;a Monangonis <lb/>con&longs;tructio nobis confert ad longi&ugrave;s <expan abbr="iaculand&utilde;">iaculandum</expan> in&longs;trumentis tum <lb/>rect&egrave; exten&longs;is, tum reflexis: &longs;iue tum lapides iacientibus, tum &longs;a&shy;<lb/>gittas celeriter iaculantibus. </s>
<s>vt ver&ograve; per&longs;picuum fiat qu&aelig;nam &longs;int <lb/>ista in&longs;trumenta rect&egrave; exten&longs;a, &amp; reflexa: &longs;iue lapides iactantia, <lb/>&amp; &longs;agittas celeriter mittentia, de quibus Autor in pr&aelig;&longs;entia lo&shy;<lb/>quitur : &longs;ciendum est qu&ograve;d multa, varia&queacute; &longs;unt in&longs;trumenta ia&shy;<lb/>culatoria, de quibus ip&longs;a<emph.end type="italics"/> <foreign lang="greek">belopoii/a</foreign>, <emph type="italics"/>ide&longs;t iaculorum effectrix <lb/>&longs;cientia pertractat: vt Angones, Monangones, catapult&aelig;, Balli&shy;<lb/>&longs;t&aelig;, &amp; alia id genus. </s>
<s>quorum in&longs;trumentorum alia &longs;unt rect&egrave; ex&shy;<lb/>ten&longs;a iuxta eorum chordas, qu&aelig; quidem &agrave; gr&aelig;cis Euthitona, hoc <lb/>e&longs;t rect&egrave; exten&longs;a, &longs;iue rect&egrave; exten&longs;as eorum chordas habentia: alia <lb/>ver&ograve; iuxta eorum chordas reflexa, qu&aelig; ab ei&longs;dem Palintona, hoc <lb/>est reflexa, &longs;eu reflexas eorum chordas habentia nominantur. </s>
<s>ho&shy;<lb/>rum autem reflexa quidem lapides longi&ugrave;s iactandi, rect&egrave; exten&shy;<lb/>&longs;a ver&ograve; &longs;agittas, tela, &amp; cuiu&longs;cumque generis iacula celeriter <arrow.to.target n="note122"/><lb/>iaculandi vim habent. </s>
<s>Quapropter paul&ograve; inferi&ugrave;s in pr&aelig;&longs;enti <lb/>capite ait Autor qu&ograve;d rect&egrave; exten&longs;orum in&longs;trumentorum chord&aelig; <lb/>rotund&aelig; contexend&aelig; &longs;unt, vt inter <expan abbr="&longs;agittar&utilde;">&longs;agittarum</expan> forficulas incidant: <lb/>ip&longs;&aelig; ver&ograve; reflexorum chord&aelig; lat&aelig; Zonarum hoc est fa&longs;ciarum, vel <lb/>cingulorum in&longs;tar e&longs;&longs;e debent, vt lapis &agrave; medietate chord&aelig; &longs;ecun&shy;<lb/>dum latitudinem percu&longs;&longs;us, ben&egrave; emittatur, non excidens ver&longs;us <lb/>extrema. </s>
<s>ait pr&aelig;terea qu&ograve;d an&longs;as etiam ex earum extremis,<emph.end type="italics"/>
<pb xlink:href="052/01/078.jpg"/><emph type="italics"/>&longs;cilicet reflexis, confectas habere debent, vt ad eas ingrediantur <lb/>Angones ip&longs;i, videlicet arcus, quos &longs;uperi&ugrave;s declarauimus, quip&shy;<lb/>pe qui in fronte i&longs;torum reflexorum in&longs;trumentorum coaptantur.<emph.end type="italics"/><lb/><arrow.to.target n="note123"/></s></p><p type="margin">
<s><margin.target id="note121"/>b</s></p><p type="margin">
<s><margin.target id="note122"/>c</s></p><p type="margin">
<s><margin.target id="note123"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[multo oleo educat&aelig;] commas muliebres multo oleo nutritas <lb/>e&longs;&longs;e ait, quoniam gr&aelig;cis mulieribus mos est commas &longs;uas oleo co&shy;<lb/>tidie perungere, tum vt cre&longs;cant, <expan abbr="t&utilde;">tum</expan> vt robustiores con&longs;eruentur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note124"/></s></p><p type="margin">
<s><margin.target id="note124"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in iaculorum effectrice tractatione] h&aelig;c est<emph.end type="italics"/> <foreign lang="greek">belopoii+kh\</foreign>, <emph type="italics"/>&longs;eu<emph.end type="italics"/><lb/><foreign lang="greek">belopoii/a</foreign> <emph type="italics"/>ab Athen&aelig;o, &amp; Bitone, &amp; Alexandrino Herone, <lb/>alijs&queacute; antiquioribus Mechanicis tradita: in qua quidem non &longs;o&shy;<lb/>l&ugrave;m h&aelig;c, qu&aelig; ad <expan abbr="iaculatorior&utilde;">iaculatoriorum</expan> in&longs;trumentorum con&longs;tructionem <lb/>&longs;pectant (de quibus Autor etiam in pr&aelig;&longs;enti capite &longs;ermonem ha&shy;<lb/>buit) &longs;ubtiliter curio&longs;ioribus demon&longs;trantur: ver&ugrave;m etiam fora&shy;<lb/>minum in in&longs;trumentis ip&longs;is exi&longs;tentium dimetientes, ac reliqua <lb/>omnia, qu&aelig; in fine huius capitis breuiter Autor tetigit, mathema&shy;<lb/>tic&egrave;, ac in&longs;trumentaliter ab Alexandrino Herone per demon&longs;tra&shy;<lb/>tionem enarrata &longs;unt. </s>
<s>C&aelig;ter&ugrave;m vt ea, qu&aelig; in fine pr&aelig;&longs;entis ca&shy;<lb/>pitis Autor recen&longs;et, dilucidiora nobis reddantur, ignorandum <lb/>non e&longs;t qu&ograve;d (quemadmodum Athen&aelig;us in primo, &amp; &longs;ecundo <lb/>libro de machinis bellicis docet) ip&longs;i Mechanici maxima cum pro&shy;<lb/>portione tum in&longs;trumenta iaculatoria, tum etiam tela, ac iacula <lb/>ip&longs;a con&longs;truebant. </s>
<s>nam &longs;ecundum locorum di&longs;tantias, ad quas <lb/>iacula mittenda erant, instrumenta ip&longs;a modo maiora, modo mi&shy;<lb/>nora proportionaliter faciebant. </s>
<s>alterum quidem eorum alterius <lb/>iuxta omnes &longs;uas partes duplum, aut triplum, vel quotuplum li&shy;<lb/>buerit con&longs;truentes, ad mittenda longi&ugrave;s duplo, vel triplo, vel quo&shy;<lb/>uis alio &longs;patio iacula ip&longs;a. </s>
<s>non &longs;ol&ugrave;m autem in&longs;trumenta iam di&shy;<lb/>cta &longs;ecundum proportionem, quam habent adinuicem augebant, <lb/>ac minuebant: ver&ugrave;m etiam iacula ip&longs;a, tela, ac &longs;axa &longs;uis in&longs;tru&shy;<lb/>mentis proportione quoad eorum longitudinem, cra&szlig;itiem, ac pon&shy;<lb/>dero&longs;itatem corre&longs;pondentia ponebant. </s>
<s>Vnde etiam ip&longs;a iacula ean<lb/>dem inter &longs;e rationem, quam eorum in&longs;trumenta &longs;eruabant: tum <lb/>quoad eorum magnitudinem, ac pondus, tum etiam quoad lon&shy;<lb/>gitudines &longs;patiorum, quas ab in&longs;trumentis emi&longs;&longs;a percurrere de&shy;<lb/>bebant. </s>
<s>Has autem c&ugrave;m in&longs;trumentorum, &amp; eorum partium, tum <lb/>iaculorum proportiones duabus poti&szlig;im&ugrave;m geometricis propo&shy;<lb/>&longs;itionibus vtentes inueniebant. </s>
<s>quarum altera quidem e&longs;t Theo&shy;<lb/>rema duodecimum libri duodecimi Elementorum Euclidis, in quo<emph.end type="italics"/>
<pb xlink:href="052/01/079.jpg"/><emph type="italics"/>demon&longs;tratur qu&ograve;d &longs;imiles coni, &amp; cylindri in triplicata &longs;unt ad&shy;<lb/>inuicem ratione dimetientium in &longs;uis ba&longs;ibus exi&longs;tentium. </s>
<s>alte&shy;<lb/>ra ver&ograve; propo&longs;itio e&longs;t illud diuulgati&szlig;imum, ad cubique duplatio&shy;<lb/>nem nece&longs;&longs;arium problema, qu&ograve;d inter duas datas rectas lineas <lb/>alias duas medias proportionales inuenire docet. </s>
<s>quippe quod ab <lb/>antiquis <expan abbr="n&otilde;">non</expan> &longs;cientific&egrave;, &longs;ed cum in&longs;trumentis demon&longs;tratum fuit. </s>
<s><lb/>His enim duabus propo&longs;itionibus foraminum, per qu&aelig; tum chor&shy;<lb/>d&aelig;, tum iacula in in&longs;trumentis pertran&longs;eunt: necnon &longs;agittarum, <lb/>ac iaculorum, rotundarum&queacute; chordarum cylindricam formam ha<lb/>bentium dimetientes in quauis ratione periti&szlig;imi Mechanici re&shy;<lb/>periebant. </s>
<s>His itaque declaratis ea, qu&aelig; in pr&aelig;&longs;entia breuiter <lb/>Autor enucleat, per&longs;picua nobis erunt. </s>
<s>ait enim qu&ograve;d in ip&longs;a ia&shy;<lb/>culorum effectrice tractatione non &longs;ol&ugrave;m h&aelig;c, &longs;cilicet qu&aelig; ip&longs;e de <lb/>iaculatoriorum in&longs;trumentorum con&longs;tructione in pr&aelig;&longs;enti capite <lb/>breuiter enarrauit: &longs;ubtiliter ijs, qui ad con&longs;tructionem curio&longs;io&shy;<lb/>res &longs;unt, per demon&longs;trationem enarrata fuere: ver&ugrave;metiam fo&shy;<lb/>raminum in ip&longs;is in&longs;trumentis exi&longs;tentium dimetientes: necnon ij <lb/>&longs;imiles cylindri, qui in triplicata adinuicem dimetientium in &longs;uis <lb/>ba&longs;ibus exi&longs;tentium in ratione e&longs;&longs;e o&longs;tenduntur: ac demum diuul&shy;<lb/>gata cubi duplatio: quibus &longs;cilicet duabus propo&longs;itionibus, ia&shy;<lb/>culorum magnitudines, iuxta magnitudines contingentium, hoc <lb/>e&longs;t quorumcumque in&longs;trumentorum, dupl&aelig;, vel etiam tripl&aelig;, vi&shy;<lb/>delicet adinuicem, c&ugrave;m fiant, ad ea&longs;dem, nempe duplas, vel tri&shy;<lb/>plas, longitudines, idest locorum di&longs;tantias emittuntur: cuncta <lb/>in quam h&aelig;c mathematic&egrave;, ac in&longs;trumentaliter, nempe tum ma&shy;<lb/>thematicis &longs;cientificis propo&longs;itionibus, qualis e&longs;t iam dicta duode&shy;<lb/>cima duodecimi Euclidis Elementorum, tum in&longs;trumentalibus, <lb/>qualis e&longs;t diuulgata cubi duplatio, quam in&longs;trumentorum admi&shy;<lb/>niculo pri&longs;ci geometr&aelig; faciebant: ab Alexandrino Herone per <lb/>demon&longs;trationem enarrata &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note125"/></s></p><p type="margin">
<s><margin.target id="note125"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Pr&aelig;terea h&igrave;c adnotandum e&longs;t qu&ograve;d Heron qui &longs;crip&longs;it hunc de <lb/>machinis bellicis librum, quem nunc pr&aelig;manibus habemus, non <lb/>e&longs;t Heron Alexandrinus, qui &longs;crip&longs;it librum<emph.end type="italics"/> <foreign lang="greek">peri\ belopii/as</foreign>,&shy;<lb/><emph type="italics"/>ide&longs;t de iaculorum effectrice tractatione, libros quatuor de aqua&shy;<lb/>ticis horologijs, libros duos de&longs;piritalibus, librum<emph.end type="italics"/> <foreign lang="greek">peri\ a)uto<lb/>matikw_n poii+tikw_n</foreign>, <emph type="italics"/>hoc e&longs;t de ijs, qu&aelig; per &longs;e fieri, moueri&queacute; inna&shy;<lb/>ta &longs;unt, librum de Mechanicis, librum de re ru&longs;tica, libros de<emph.end type="italics"/>
<pb xlink:href="052/01/080.jpg"/><emph type="italics"/>Geometria. </s>
<s>quandoquidem Alexandrinus Heron long&egrave; anterior <lb/>fuit hoc Herone, qui pr&aelig;&longs;entem librum compo&longs;uit. </s>
<s>Quare non &longs;o&shy;<lb/>l&ugrave;m hoc in loco, ver&uacute;m etiam inferi&ugrave;s pr&aelig;&longs;ens Heron illius anti&shy;<lb/>quioris Heronis Alexandrini mentionem facit. </s>
<s>Hoc autem ad&shy;<lb/>notandum e&longs;&longs;e duximus, ne qui&longs;piam in eundem cum Conrado <lb/>Ge&longs;nero in &longs;ua Bibliotheca, &amp; cum Conrado Lyco&longs;thene in eiu&longs;&shy;<lb/>dem Bibliothec&aelig; epitome, incidat errorem: qui de vnico tant&ugrave;m <lb/>Alexandrino &longs;cilicet Herone mentionem fecerunt, a&longs;&longs;erentes <lb/>eundem Heronem Alexandrinum, qui iam dicta &longs;uperi&ugrave;s opera <lb/>&longs;crip&longs;it, pr&aelig;&longs;entem etiam de machinis bellicis librum &longs;crip&longs;i&longs;&longs;e. </s>
<s><lb/>quem dicunt Bononii&aelig; in Bibliotheca Sancti Saluatoris gr&aelig;cum <lb/>vn&agrave; cum figuris eleganter de&longs;criptum extare. </s>
<s>quod quam &longs;it &agrave; <lb/>veritate alienum, pr&aelig;&longs;ens locus declarat. </s>
<s>H&ecedil;c autem ad pr&aelig;&longs;en&shy;<lb/>tis etiam capitis dilucidationem breuiter &agrave; nobis dicta &longs;int.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>De &longs;cala rotis &longs;urrepente, <expan abbr="pontem&qacute;ue">pontemque</expan> ferente. </s>
<s><lb/>Cap. </s>
<s>XIX.<emph.end type="center"/></s></p><p type="main">
<s>FIt etiam alia iuxta formam &longs;cala rotis &longs;urre&shy;<lb/>pens, ex lignis c&ugrave;m fortibus, tum leuibus ip&longs;a <lb/>quoque con&longs;tructa. </s>
<s>ad quam alia pontis in&longs;tar <lb/>iuxta medium &longs;ur&longs;um interpo&longs;ita, per dime&shy;<lb/>tientem cylindrica &amp; polyta ex torno facta <lb/>ea, qu&aelig; cruribus copulantur extrema po&longs;&longs;identem conne&shy;<lb/>ctitur. </s>
<s>vt &longs;olubiliter ver&longs;us alteram deor&longs;um lata reclinetur, <lb/><expan abbr="rur&longs;us&qacute;ue">rur&longs;usque</expan> ad ip&longs;am &longs;ur&longs;um erect&egrave; feratur, dum &agrave; funibus <lb/>retror&longs;um retinetur, ac torcularibus ijs, qu&aelig; mult&ugrave;m con&shy;<lb/>torta dicuntur, &longs;iue trochleis volubilibus violentam vim <lb/>in remi&longs;&longs;ione, <expan abbr="inten&longs;ione&qacute;ue">inten&longs;ioneque</expan> funium ip&longs;a rotularum adhe&shy;<lb/>rentium appo&longs;itione inna&longs;ci facientibus commen&longs;urabili&shy;<lb/>ter pr&aelig;betur, atque attrahitur. </s>
<s>impedimenta ver&ograve; &longs;ur&longs;um <lb/>in ea, qu&aelig; &longs;tat erecta, fiant: vel prominenti&aelig; qu&aelig;dam reci&shy;<lb/>pientes eam, qu&aelig; erigitur &longs;calam dum retror&longs;um conuer&shy;<lb/>titur. </s>
<s>ne raptim &longs;uper alterius verticem eleuata, ca&longs;um in&shy;<lb/>operantibus poti&ugrave;s &longs;it minatura. </s>
<s>At &longs;i quidem &longs;implicibus <lb/>lignis con&longs;tans fuerit &longs;cala, qu&aelig; deor&longs;um erecta &longs;tare de&shy;<lb/>bet: gradus habeat &longs;ingulos &longs;ingulis alternatim pr&aelig;termi&longs;&shy;<pb xlink:href="052/01/081.jpg"/>&longs;is excedentes crura, &amp; in exce&longs;&longs;u foratos, vt per foramina <lb/>funis robu&longs;tus exten&longs;us pertran&longs;iens infrangibilem ip&longs;am </s></p><p type="main">
<s><arrow.to.target n="note126"/><lb/>&longs;eruet: &longs;i ver&ograve; compo&longs;ita fuerit, iam dictarum &longs;calarum con<lb/>&longs;tructionem &longs;u&longs;cipiat. </s>
<s>Ip&longs;a autem qu&aelig; &longs;ur&longs;um eleuanda e&longs;t, <lb/>iuxta totam eius longitudinem tabulis pro&longs;ternatur, &amp; fu&shy;<lb/>nibus circundata confirmetur, <expan abbr="indubitata&qacute;ue">indubitataque</expan> &longs;uper mu&shy;<lb/>rum traiectio fiat. </s>
<s>c&ugrave;m enim ip&longs;a &longs;uper alteram eleuata, <expan abbr="ere-cte&qacute;ue">ere&shy;<lb/>cteque</expan> portata fuerit: amb&aelig; muro &longs;imul afferuntur. </s>
<s>atque <lb/>ea quidem, qu&aelig; deor&longs;um erecta &longs;tat, <expan abbr="gradus&qacute;ue">gradusque</expan> ad a&longs;cen&shy;<lb/>&longs;um habet, &agrave; muro di&longs;tet quantum amu&longs;&longs;i quadam, ac men&shy;<lb/>&longs;ura funibus relaxatis ip&longs;ius pro&longs;trat&aelig; extremum de&longs;cen&shy;<lb/>dens muro applicetur, <expan abbr="volentibus&qacute;ue">volentibusque</expan> &longs;it aditus. </s>
<s>Latitudo <lb/>autem tum &longs;cal&aelig;, tum pontis &longs;ufficiens fiat, ita vt ordina&shy;<lb/>tim quinque, &longs;eu quatuor, vel ad minus tres viri feriatim <lb/>a&longs;cendant &longs;uper ponte pertran&longs;euntes: adhoc vt vnanimi&shy;<lb/>ter &longs;uper murum propugnantibus ex aduer&longs;o repugnent. </s>
<s><lb/>Circum&longs;eptiones ver&ograve; ex corijs ad vtra&longs;que partes tum &longs;ca<lb/>l&aelig;, tum pontis fiant, propter &longs;agittas, qu&aelig; &agrave; lateribus effe&shy;<lb/>runtur. </s>
<s>Oper&aelig;pretium e&longs;t autem &longs;calam deor&longs;um &longs;tantem <lb/>palis infixis &longs;tabiliri, <expan abbr="funibus&qacute;ue">funibusque</expan> exten&longs;is confirmari, nec&shy;<lb/>non altiorem muro reperiri tribus ad minus pedibus: vt <lb/>ea, qu&aelig; &agrave; muro de&longs;upter veniunt, ad altum peruenire, <expan abbr="c&aelig;-dem&qacute;ue">c&aelig;&shy;<lb/>demque</expan> in a&longs;cendentibus agere nequeant. </s>
<s>Ver&ugrave;m ponte <lb/>decliui &longs;upra murum exi&longs;tente, promptiores, <expan abbr="audaciore&longs;-&qacute;ue">audaciore&longs;&shy;<lb/>que</expan> milites ad de&longs;cen&longs;um erunt. </s>
<s>&longs;i ver&ograve; depre&longs;&longs;ior muro <lb/>&longs;cala fuerit, hi&longs;ce contraria euenient, <expan abbr="figur&aelig;&qacute;ue">figur&aelig;que</expan> ip&longs;&aelig; &longs;ubie&shy;<lb/>ct&aelig; &longs;unt. </s></p>
<pb xlink:href="052/01/082.jpg"/><p type="margin">
<s><margin.target id="note126"/>a</s></p><figure id="id.052.01.082.1.jpg" xlink:href="052/01/082/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note127"/></s></p><p type="margin">
<s><margin.target id="note127"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[iam dictarum &longs;calarum con&longs;tructionem] con&longs;tructio compo&longs;ita&shy;<lb/>rum &longs;calarum, de qua h&igrave;c loquitur Autor, &longs;uperi&ugrave;s in quartide&shy;<lb/>cimi capitis initio de&longs;ideratur. </s>
<s>apud Apollodorum autem eam <lb/>habemus.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/083.jpg"/><p type="main">
<s><emph type="center"/>De aggere te&longs;tudine pontem ferente. </s>
<s>Cap. </s>
<s>XX.<emph.end type="center"/></s></p><p type="main">
<s>Flet autem vtilis pons &longs;ola quoque iam dicta <lb/>traiectio, quando &longs;cilicet fo&longs;&longs;as latas, aut pro&shy;<lb/>fundas, <expan abbr="aquarum&qacute;ue">aquarumque</expan> plenas aggerare <expan abbr="n&otilde;">non</expan> po&longs;&shy;<lb/>&longs;umus: &longs;i longitudine commen&longs;urabilis ad fo&longs;&shy;<arrow.to.target n="note128"/><lb/>&longs;arum latitudines fiat, atque vt iam didicimus <lb/>&longs;olubiliter connexa fuerit, ante aggerem te&longs;tudinem ere&shy;<lb/>ct&egrave; &longs;tans, &agrave; funibus retror&longs;um attracta, ac tradita, vel &agrave; iam <lb/>dictis &longs;uperi&ugrave;s mult&ugrave;m contortis torcularibus: quando vi&shy;<lb/>delicet magnitudo, ac onus ponderis ip&longs;ius traiectionis tan<lb/>t&aelig; molis fuerit. </s>
<s>c&ugrave;m enim &agrave; te&longs;tudine ge&longs;tata fuerit, <expan abbr="ante-riori&qacute;ue">ante&shy;<lb/>riorique</expan> fo&longs;&longs;&aelig; labro &longs;uperuenerit: funes retror&longs;um relaxan&shy;<lb/>tur, <expan abbr="extremum&qacute;ue">extremumque</expan> de&longs;cendens, &longs;uper oppo&longs;ito labro poni&shy;<lb/>tur, <expan abbr="via&qacute;ue">viaque</expan> tuta fit volentibus prompt&egrave; cum parmis creta, <lb/>aut cinere &longs;anguini admi&longs;to circa contexiones illitis, corij&longs;&shy;<lb/>que bouum rec&egrave;ns occi&longs;orum coopertis pertransire: tum <lb/>propter <expan abbr="torm&etilde;ta">tormenta</expan> ignem iaculantia, tum etiam propter eos, <lb/>qui infunduntur feruidos liquores. </s>
<s>&amp; quemadmodum in <lb/>fo&longs;&longs;orijs te&longs;tudinibus iam o&longs;ten&longs;um e&longs;t, ita etiam parma&shy;<lb/>rum abinuicem di&longs;tantiam viginti pedibus minorem fieri: <lb/>necnon &agrave; tribus pedibus &longs;upra terram incipiendo eam, <lb/>qu&aelig; ad murum fit fodinam agere oportet. </s>
<s>&amp; figura &longs;ubie&shy;<lb/>cta e&longs;t. </s></p>
<pb xlink:href="052/01/084.jpg"/><p type="margin">
<s><margin.target id="note128"/>a</s></p><figure id="id.052.01.084.1.jpg" xlink:href="052/01/084/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note129"/></s></p><p type="margin">
<s><margin.target id="note129"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;i longitudine commen&longs;urabilis ad fo&longs;&longs;arum latitudines fiat] <lb/>commen&longs;urabilitas in pr&aelig;&longs;entia non eodem modo, quo docet Eu&shy;<lb/>clides in definitionibus decimi libri Elementorum accipienda e&longs;t: <lb/>qu&ograve;d &longs;cilicet pontis longitudo, &amp; fo&longs;&longs;arum latitudines tamquam <lb/>recta line&aelig; &longs;u&longs;cept&aelig; longitudine commen&longs;urabiles fiant, hoc e&longs;t <lb/>communi men&longs;ura quoad earum longitudinem men&longs;urentur. </s>
<s>nam <lb/>fieri pote&longs;t, vt tam dict&aelig; rect&aelig; line&aelig; iuxta doctrinam Euclidis lon&shy;<lb/>gitudine commen&longs;urabiles &longs;int, ip&longs;ius tamen pontis longitudo qua&shy;<lb/>cumque fo&longs;&longs;arum latitudine minor existat: ac propterea c&ugrave;m ip&longs;e <lb/>pons &agrave; te&longs;tudine ge&longs;tatus anteriori fo&longs;&longs;&aelig; labro &longs;uperuenerit, fu&shy;<lb/>nibus retror&longs;um relaxatis, extrema&queacute; pontis parte de&longs;cendente, <lb/>&longs;uper oppo&longs;ito fo&longs;&longs;a labro minim&egrave; ponatur, &longs;ed intra fo&longs;&longs;am inci&shy;<lb/>dat: quod vtique pr&aelig;ter Autoris intentionem erit. </s>
<s>Quamobrem <lb/>verba hac [&longs;i longitudine commen&longs;urabilis ad fo&longs;&longs;arum latitudi&shy;<lb/>nes fiat] &longs;ic intelligenda &longs;unt: qu&ograve;d &longs;cilicet pons ip&longs;e iuxta &longs;ui <lb/>longitudinem &agrave; quacumque fo&longs;&longs;arum latitudine pluribus vici&shy;<lb/>bus. </s>
<s>aut &longs;altem &longs;emel commen&longs;uretur. </s>
<s>C&ugrave;m enim fo&longs;&longs;arum lati&shy;<pb xlink:href="052/01/085.jpg"/>tudines eiu&longs;dem ciuitatis vari&aelig; po&szlig;int e&longs;&longs;e, nece&longs;&longs;e e&longs;t vt iam di&shy;<lb/>cti pontis longitudo maximam fo&longs;&longs;arum latitudinem aliquantu&shy;<lb/>lum excedat: ita vt &longs;altem &longs;emel quidem ab ip&longs;a, pluries autem <lb/>&agrave; minoribus etiam commen&longs;uretur: vnd&egrave; &longs;an&egrave; commen&longs;urabili&shy;<lb/>tas in pr&aelig;&longs;enti loco pro &longs;implici line&aelig; rect&aelig; maioris &agrave; minoribus <lb/>rectis lineis commen&longs;uratione &longs;u&longs;cipienda est, non quidem qu&ograve;d <lb/>ab eis ita men&longs;uretur, vt toties ip&longs;&aelig; &longs;u&longs;cept&aelig; &longs;eu repetita hanc in&shy;<lb/>tegram con&longs;tituant: &longs;ed qu&ograve;d h&aelig;c c&ugrave;m illis maior &longs;it eas in &longs;e <lb/>comprehendat, quamuis <expan abbr="eti&atilde;">etiam</expan> illis longitudine incommen&longs;urabilis <lb/>e&longs;&longs;et. </s>
<s>quemadmodum etiam dimetiens quadrati c&ugrave;m costa maior <lb/>&longs;it eam in &longs;e continet, longitudine tamen adinuicem incommen&shy;<lb/>&longs;urabiles &longs;unt, vt in eodem decimo Euclidis libro docetur. </s>
<s>forta&longs;&shy;<lb/>&longs;e namque po&longs;&longs;et euenire qu&ograve;d longitudo pontis ip&longs;ius ad aliquam <lb/>fo&longs;&longs;arum latitudinem, vel vna fo&longs;&longs;arum latitudo ad aliam earun&shy;<lb/>dem fo&longs;&longs;arum latitudinem, eam haberet rationem, quam habet <lb/>dimetiens quadrati ad eius co&longs;tam. </s>
<s>hoc autem adnotatu dignum <lb/>cen&longs;uimus, nequis credat Autorem huiu&longs;ce rei nos a&longs;tringere, vt <lb/>nempe longitudinem ip&longs;ius pontis fo&longs;&longs;arum latitudinibus commen<lb/>&longs;urabilem longitudine faciamus: quod nimirum in quibu&longs;dam <lb/>ciuitatum fo&szlig;is nequaquam fieri po&longs;&longs;et.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>De aggere te&longs;tudine ratem habente &longs;ecundum Philo&shy;<lb/>nem Bizantium. </s>
<s>Cap. </s>
<s>XXI.<emph.end type="center"/></s></p><p type="main">
<s>PHilon autem Bizantius prope huiu&longs;cemodi <lb/>fo&longs;&longs;as te&longs;tudines aggeres ponens, iuxta ip&longs;as <lb/>rates connectit, &amp; ad quamcumque muti par&shy;<lb/>tem voluerit milites adducit, ferreos palos af&shy;<lb/>figentes. </s>
<s>quippe qui obdurati, acutique facti, <lb/>ad murorum c&ugrave;m lapideorum, tum lateritiorum commi&longs;&shy;<lb/>&longs;uras, <expan abbr="compagines&qacute;ue">compaginesque</expan> penetrant, ferreis malleis ab a&longs;cen&shy;<lb/>dentibus percu&longs;&longs;i. </s>
<s>atque hamis in&longs;uperfactis, qui in extre&shy;<lb/>mitatibus funium exi&longs;tentes vn&agrave; cum retibus ad mari pin&shy;<lb/>nas inijciuntur: ita vt militibus poti&longs;&longs;imum a&longs;&longs;uetis haud <lb/>difficilis &longs;it <expan abbr="a&longs;c&etilde;&longs;us">a&longs;cen&longs;us</expan>. </s>
<s>tali <expan abbr="n&atilde;q;">namque</expan> methodo vtentes Aegyptij <expan abbr="n&otilde;">non</expan> <lb/>paratas, ac <expan abbr="n&otilde;">non</expan> fortes, &amp; quoad altitudinem humiles ciuita&shy;<lb/>tes facil&egrave; ob&longs;idere con&longs;ueuerunt. </s>
<s><expan abbr="figura&qacute;">figuraque</expan>; ip&longs;a &longs;ubiecta e&longs;t. </s></p>
<pb xlink:href="052/01/086.jpg"/><figure id="id.052.01.086.1.jpg" xlink:href="052/01/086/1.jpg"/><p type="main">
<s><emph type="center"/>De quibu&longs;dam animaduer&longs;ionibus ad omnes &longs;calas, &amp; <lb/>pontes pertinentibus. </s>
<s>Cap. </s>
<s>XXII.<emph.end type="center"/></s></p><p type="main">
<s>OPer&aelig;pretium e&longs;t autem in omnibus &longs;calis, &amp; <lb/>eis, qu&aelig; ad murum fiunt a&longs;cen&longs;ionibus, &longs;iue <lb/>pontibus animaduertere ea, qu&aelig; ex lino pr&aelig;&shy;<lb/>parantur cra&longs;&longs;a verricula. </s>
<s>nam iniecta, <expan abbr="colle-ctim&qacute;ue">colle&shy;<lb/>ctimque</expan> rur&longs;us retracta a&longs;cendentes, vel in&shy;<lb/>gredientes viuos venantur, <expan abbr="inimicis&qacute;ue">inimicisque</expan> captiuos pr&aelig;&longs;en&shy;<arrow.to.target n="note130"/><lb/>tant. </s>
<s>Verum in ip&longs;is quidem &longs;calis inoffen&longs;um a&longs;cen&longs;um <lb/>con&longs;eruauimus, quemadmodum in trabibus in anchor&aelig; <lb/>modum incuruatis  de&longs;cendentium ponderum &longs;uperi&ugrave;s <lb/>&longs;truendo determinauimus. </s>
<s>Ad ip&longs;os autem pontes duo <lb/>anteri&ugrave;s ligua erigenda &longs;unt, &longs;olubiliter deor&longs;um conne&shy;<lb/>xa, aduer&longs;us quidem inimicorum faciem facil&egrave; inciden&shy;<arrow.to.target n="note131"/><lb/>tia, <expan abbr="retror&longs;um&qacute;ue">retror&longs;umque</expan> re&longs;i&longs;tentia, &longs;uperi&ugrave;s ver&ograve; ad unguem ab&shy;<lb/>&longs;ci&longs;&longs;a, ad verticem coeuntia, atque ad acutum angulum ac&shy;<lb/>commodata, triangulam figuram vn&agrave; cum ba&longs;i perficien&shy;<lb/>tia, <expan abbr="necn&otilde;">necnon</expan> clauos ferreos &agrave; lateribus &longs;u&longs;cipientia, vt iniecta <lb/>verricula illius implicentur, non amplius ad contrariam
<pb xlink:href="052/01/087.jpg"/>attractionem, <expan abbr="collectionem&qacute;ue">collectionemque</expan> reuertentia. </s>
<s>C&aelig;ter&ugrave;m qui <lb/>mutum in&longs;cendere debent aduer&longs;us inimicorum <expan abbr="faci&etilde;">faciem</expan> h&aelig;c <lb/>inijcientes ad ingre&longs;&longs;um ill&aelig;&longs;i con&longs;eruabuntur. </s>
<s>At &longs;i non&shy;<lb/>nulli eorum, qui &longs;uper ponte &longs;tant cum conuertibilibus <arrow.to.target n="note132"/><lb/>manuarijs ignem iaculantibus tormentis aduer&longs;us ho&longs;tium <lb/>faciem igne infe&longs;tauerint: eos, qui muro pr&aelig;a&longs;&longs;i&longs;tunt tan&shy;<lb/>to terrore afficient, vt pugn&aelig; aggre&longs;&longs;ionem, ac ignis impe&shy;<lb/>tum minim&egrave; &longs;u&longs;tinentes, celeriter locum &longs;ubterfugiant. </s>
<s>&amp; <lb/>figura de&longs;cripta e&longs;t. </s></p><p type="margin">
<s><margin.target id="note130"/>a</s></p><p type="margin">
<s><margin.target id="note131"/>b</s></p><p type="margin">
<s><margin.target id="note132"/>c</s></p><figure id="id.052.01.087.1.jpg" xlink:href="052/01/087/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note133"/></s></p><p type="margin">
<s><margin.target id="note133"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>HAec qu&aelig; in pr&aelig;&longs;entia dicit Autor &longs;e &longs;uperi&ugrave;s determi&shy;<lb/>na&longs;&longs;e, forta&longs;&longs;e ex ijs &longs;unt, qu&aelig; in principio quintidecimi <lb/>capitis de&longs;iderantur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note134"/></s></p><p type="margin">
<s><margin.target id="note134"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ad vnguem] ide&longs;t obliqu&egrave; ad unguis &longs;imilitudinem, quemad&shy;<lb/>modum etiam &longs;uperi&ugrave;s in capite tertio dixit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note135"/></s></p><p type="margin">
<s><margin.target id="note135"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[manuarijs] hoc e&longs;t in&longs;trumentis, qu&aelig; manu teneri, vibrari&queacute; <lb/>po&longs;&longs;unt. </s>
<s>enchiridium enim (vt in gr&aelig;co textu legitur) e&longs;t omne <lb/>in&longs;trumentum, quod manu tenetur.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/088.jpg"/><p type="main">
<s><emph type="center"/>De curru &longs;eu te&longs;tudine quatuor rotis &longs;urrepente, <expan abbr="canalem-&qacute;ue">canalem&shy;<lb/>que</expan> murum in&longs;cendentem ferente. </s>
<s>Cap. </s>
<s>XXIII.<emph.end type="center"/></s></p><p type="main">
<s>VErumenimuero fieri pote&longs;t, vt etiam ab&longs;que <lb/>&longs;calis &longs;upra murum a&longs;cendatur, quemadmo&shy;<lb/>dum A&longs;cr&aelig;us Cte&longs;ibius Heronis Alexandri&shy;<lb/>ni magi&longs;ter in &longs;uis commentarijs declarauit, <arrow.to.target n="note136"/><lb/>per huiu&longs;cemodi <expan abbr="machin&atilde;">machinam</expan>, &longs;icut inquit Athe&shy;<lb/>n&aelig;us, qu&ograve;d &longs;cilicet currum rotis quatuor pr&aelig;ditum, vnde&shy;<lb/>quaque circumtectum exi&longs;tentem, &longs;eu te&longs;tudinem arietem <lb/>ge&longs;tantem con&longs;truere oportet. </s>
<s>&amp; ad vtramque harum dua&shy;<lb/>rum machinum iuxta medium duo ligna erecta &longs;tantia &longs;unt <lb/>affigenda, &amp; aliud tran&longs;uer&longs;um altera parte latius de&longs;uper <lb/>ad ip&longs;a interiacens iuxta latitudinem &longs;uperimponendum <lb/>e&longs;t. </s>
<s>quippe quod ab&longs;ci&longs;iones rotundas habeat ex vtri&longs;que <lb/>partibus, <expan abbr="&longs;u&longs;cipiat&qacute;ue">&longs;u&longs;cipiatque</expan> veluti canalem quendam &longs;uperiacen<lb/>tem tubo &longs;imilem, <expan abbr="arcuatis&qacute;ue">arcuatisque</expan> lignis con&longs;tructum, &agrave; late&shy;<lb/>ribus autem clauis affixum, ac tabulis exteri&ugrave;s clauis affi&shy;<lb/>xis &longs;uperalligatum, aut &longs;olis corijs cra&longs;&longs;is, ac robu&longs;tis tam&shy;<lb/>quam leuioribus circumopertum: ita vt armati viri erecti <lb/>ingredientis, &amp; mod&ograve; quidem progredientis, mod&ograve; ver&ograve; <lb/>regredientis capax &longs;it. </s>
<s>quo facto canalis &longs;ur&longs;um eleuandus <lb/>e&longs;t, ac transferendus in quacumque parte qui&longs;piam volue&shy;<lb/>rit. </s>
<s>cuius vna parte ver&longs;us pauimentum declinante, reliqua <lb/>in altum eleuabitur: eo qu&ograve;d &longs;uper ip&longs;as &longs;uperiacentis li&shy;<lb/>gni ab&longs;ci&longs;iones ferreis catenis ad eius vtrumque latus at&shy;<lb/>tracta circumuertitur. </s>
<s>dum autem canalis ip&longs;e &longs;ublimis fer&shy;<lb/>tur, c&ugrave;m os eius prope <expan abbr="mur&utilde;">murum</expan> aduenerit: adducta rotis qua&shy;<lb/>tuor pr&aelig;dita te&longs;tudine, &longs;eu curru: is, qui intus e&longs;t eam, qu&aelig; <lb/>anteri&ugrave;s e&longs;t ianuam adaperire, <expan abbr="murum&qacute;ue">murumque</expan> armatus in&longs;cen&shy;<lb/>dere debet. </s>
<s>&longs;imile ver&ograve; faciundum e&longs;t &agrave; pluribus etiam, qui <lb/>per eandem canalis ba&longs;im intus progrediuntur. </s>
<s>At canalis <lb/>ip&longs;e, qui iuxta tabulas clauis affixas e&longs;t roborem &longs;u&longs;cipiens <lb/>robu&longs;tis funibus vndequaque &longs;ubcingitur, necnon corijs, <lb/>ac madidis pellibus concinnatur, vt &agrave; tormentis ignem fer&shy;<lb/>rentibus ill&aelig;&longs;us &longs;eruetur. </s>
<s>Verumtamen huiu&longs;ce problema&shy;<lb/>tis men&longs;uras quoad con&longs;tructionem <expan abbr="Cte&longs;ibi&utilde;">Cte&longs;ibium</expan> minim&egrave; com<pb xlink:href="052/01/089.jpg"/>po&longs;ui&longs;&longs;e: &longs;ed commentarium &longs;olum veluti mathematicis <lb/>gerentibus architectis h&aelig;c imponentem inuenimus. </s>
<s>ad eos <lb/>enim &longs;pectat in&longs;trumentorum commen&longs;urabilitatem tran&longs;&shy;<lb/>formare, ad <expan abbr="conuenientem&qacute;ue">conuenientemque</expan> loci v&longs;um transferre. </s>
<s>Nos <lb/>autem exercitationis gratia ijs, qui in&longs;tituuntur ad pr&aelig;&longs;en&shy;<lb/>tis problematis con&longs;tructionem huiu&longs;cemodi commen&longs;u&shy;<lb/>rabilitatem expo&longs;uimus. </s>
<s>Fiat itaque pauimentum &longs;uperia&shy;<lb/>cens in curru, &longs;iue te&longs;tudine quatuor, vel &longs;ex rotis pr&aelig;dita <lb/>quoad longitudinem quidem cubitorum quindecim: quo&shy;<lb/>ad latitudinem ver&ograve;, decem. </s>
<s>rotarum autem dimetientes <lb/>cubitorum duorum cum dimidio fiant. </s>
<s>ligna ver&ograve; duo ere&shy;<lb/>cta &longs;tantia fiant cubitorum viginti. </s>
<s>lignum autem tran&longs;uer&shy;<lb/>&longs;um, quod inter ip&longs;a mouetur vn&agrave; cum &longs;uperpo&longs;ito canali <lb/>cubitorum quoad longitudinem triginta, latitudinem ha&shy;<lb/>bens iuxta ba&longs;im pedis vnius cum dimidio, cra&longs;&longs;itiem ver&ograve; <lb/>vnius dodrantis. </s>
<s>vt quam rationem habet longitudo paui&shy;<lb/>menti ad latitudinem, eandem etiam habeat quod moue&shy;<lb/>tur tran&longs;uer&longs;um lignum ad ligna erecta &longs;tantia. </s>
<s>&amp; <expan abbr="qu&atilde;">quam</expan> rur&shy;<lb/>&longs;us habet rationem ip&longs;um, quod mouetur tran&longs;uer&longs;um li&shy;<lb/>gnum ad pauimenti longitudinem, eandem etiam ligna <arrow.to.target n="note137"/><lb/>erecta &longs;tantia ad eandem latitudinem rationem habeat. </s>
<s><expan abbr="n&atilde;">nam</expan> <lb/>&longs;icut quindecim ad decem, &longs;ic triginta ad viginti: &amp; &longs;icuti <lb/>triginta ad quindecim, ita viginti ad decem. </s>
<s>&longs;e&longs;quialter au&shy;<lb/>tem e&longs;t numerus quindecim numeri denarij, quando qui&shy;<lb/>dem denarium, ac dimidium eius in &longs;e continet. </s>
<s>&longs;e&longs;quialter <lb/>igitur e&longs;t etiam ip&longs;e triginta numerus ip&longs;ius viginti nume&shy;<lb/>ri. </s>
<s>rur&longs;us autem ip&longs;e triginta ip&longs;ius quindecim duplus e&longs;t, <arrow.to.target n="note138"/><lb/>duplus ergo ip&longs;e viginti ip&longs;ius denarij. </s>
<s>&longs;imiliter autem la&shy;<lb/>titudo <expan abbr="quoq;">quoque</expan> ip&longs;ius ba&longs;is ad eius cra&longs;&longs;itudinem dupla erit. <arrow.to.target n="note139"/><lb/>Ver&ugrave;m ip&longs;&aelig; quoque rotarum dimetientes commen&longs;urabi&shy;<lb/>les iuxta commen&longs;urationem, &amp; conuenientes in ratione <lb/>o&longs;tendentur. </s>
<s>etenim duo cum dimidio cubiti ip&longs;ius dime&shy;<lb/>tientis &longs;exies quidem ip&longs;um quindecim numerum metiun&shy;<lb/>tur, quater vero denarium, &amp; duodecies quidem ip&longs;um tri&shy;<lb/>ginta, octies ver&ograve; ip&longs;um viginti. </s>
<s>atque veluti &longs;e habet &longs;ena&shy;<lb/>rius ad quaternarium, ita ip&longs;e triginta ad ip&longs;um viginti, &amp; <lb/>quindecim ad decem: &amp; quemadmodum numerus quin&shy;<pb xlink:href="052/01/090.jpg"/>decim ad &longs;enarium, eodem modo denarius ad quaterna&shy;<lb/>rium. </s>
<s>&longs;e&longs;quialter <expan abbr="aut&etilde;">autem</expan> e&longs;t &longs;enarius quaternarij, habet enim <lb/>ip&longs;um, &amp; eius dimidium: &longs;e&longs;quialter igitur e&longs;t ip&longs;e etiam <lb/>quindecim ip&longs;ius denarij. </s>
<s>at ip&longs;e quindecim &longs;enarij duplus <lb/>&longs;e&longs;quialter exi&longs;tit, duplus &longs;e&longs;quialter ergo denarius etiam <lb/>quaternarij erit. </s>
<s>Quapropter ip&longs;a quoque dimetientis ro&shy;<arrow.to.target n="note140"/><lb/>tarum commen&longs;uratio conueniens ad magnitudinis con&shy;<lb/>&longs;tructionem reperitur. </s>
<s>quandoquidem eandem ip&longs;a cum <arrow.to.target n="note141"/><lb/>ijs, qu&aelig; men&longs;urantur rationem &longs;ecundum proportionem <lb/>&longs;eruat. </s>
<s>figura autem &longs;ub&longs;cripta e&longs;t. </s></p><p type="margin">
<s><margin.target id="note136"/>a</s></p><p type="margin">
<s><margin.target id="note137"/>b</s></p><p type="margin">
<s><margin.target id="note138"/>c</s></p><p type="margin">
<s><margin.target id="note139"/>d</s></p><p type="margin">
<s><margin.target id="note140"/>e</s></p><p type="margin">
<s><margin.target id="note141"/>f</s></p><figure id="id.052.01.090.1.jpg" xlink:href="052/01/090/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note142"/></s></p><p type="margin">
<s><margin.target id="note142"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>CTe&longs;ibius patria A&longs;cr&aelig;us Heronis Alexandrini pr&aelig;ceptor <lb/>&longs;crip&longs;it commentaria de rebus bellicis, necnon<emph.end type="italics"/> <foreign lang="greek">belopii+ka\</foreign><lb/><emph type="italics"/>nempe iaculatoria, qu&aelig; in Athenei volumine in&longs;erta ha&shy;<lb/>bentur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note143"/></s></p><p type="margin">
<s><margin.target id="note143"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ad eandem latitudinem] hoc e&longs;t <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> pauimenti <expan abbr="latitudin&etilde;">latitudinem</expan>.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note144"/></s></p><p type="margin">
<s><margin.target id="note144"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;imiliter latitudo quoque ip&longs;ius ba&longs;is] nempe latitudo ba&longs;is<emph.end type="italics"/>
<pb xlink:href="052/01/091.jpg"/><emph type="italics"/>ip&longs;ius canalis. [ad eius cra&szlig;itiem dupla erit] c&ugrave;m enim iam di&shy;<lb/>cta latitudo pedis vnius cum dimidio, hoc e&longs;t digitorum viginti&shy;<lb/>quatuor, cra&szlig;ities ver&ograve; vnius dodrantis, ide&longs;t duodecim digito&shy;<lb/>rum ab Autore &longs;uppo&longs;it&aelig; &longs;int: dubio procul duplam adinuicem ra&shy;<lb/>tionem habebunt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note145"/></s></p><p type="margin">
<s><margin.target id="note145"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ver&ugrave;m ip&longs;&aelig; quoque rotarum &amp;c.] qu&aelig; in hac vltima capitis <lb/>parte de dimetientium rotarum commen&longs;urabilitate, &amp; quoad <lb/>rationem conuenientia re&longs;pectu aliarum huius machin&aelig; men&longs;u&shy;<lb/>rarum declarat Autor: ex ijs, qu&aelig; nos in &longs;cholio quintidecimi <lb/>capitis de commen&longs;urabilitate, proportione&queacute; turrium diximus, <lb/>per&longs;picua cuilibet erunt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note146"/></s></p><p type="margin">
<s><margin.target id="note146"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[conueniens] &longs;cilicet in ratione.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note147"/></s></p><p type="margin">
<s><margin.target id="note147"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[cum ijs, qu&aelig; men&longs;urantur] videlicet reliquarum machin&aelig; <lb/>partium quoad longitudinem, &amp; latitudinem, atque cra&szlig;itiem <lb/>men&longs;uris, quippe qu&aelig; ab ip&longs;is rotarum dimetientibus men&longs;u&shy;<lb/>rantur.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Alia &longs;uperius iam de&longs;cripti canalis exqui&longs;itior de&shy;<lb/>&longs;criptio. </s>
<s>Cap. </s>
<s>XXIIII.<emph.end type="center"/></s></p><p type="main">
<s>IDem autem canalis efficatior ad ob&longs;idionem <lb/>fiet, &longs;i maior iuxta magnitudinem in anteriori <lb/>bucula fuerit, &amp; &agrave; duobus o&longs;tiolis exitum ha&shy;<lb/>buerit: ita vt etiam duos armatos uiros mu&shy;<lb/>rum un&agrave; in&longs;cen&longs;uros uici&longs;&longs;im adinuicem &longs;tan&shy;<lb/>tes &longs;u&longs;cipiat. </s>
<s>eiu&longs;dem autem bucul&aelig; o&longs;tia extrin&longs;ec&ugrave;s hor&shy;<lb/>ribilia apparenti &longs;culptura, <expan abbr="uer&longs;icolori&qacute;ue">uer&longs;icolorique</expan> pictura in ante&shy;<lb/>riori canalis parte fiant: draconis, aut leonis ignem ferens <lb/>caput ad terrorem, ac metum ho&longs;tium adueniens offeren&shy;<lb/>tia. </s>
<s>vt etiam ante ingre&longs;&longs;ionem terrore affecti muro a&longs;&longs;i&longs;ten<lb/>tes &agrave; murorum &longs;patijs inter turres exi&longs;tentibus effugiant. </s>
<s><lb/>At &longs;ciendum e&longs;t qu&ograve;d &longs;i indirectum quidem &aelig;qualis alti&shy;<lb/>tudinis canalis &longs;uper erectis lignis interiacens muro adue&shy;<lb/>niat, indirectum quoque ba&longs;im o&longs;tendet: &longs;i autem muro &longs;u&shy;<lb/>perior quoad &longs;itum reperiatur, paul&ograve; ante deductus, ac de&shy;<lb/>clinans, actionem perficiet: &longs;i uer&ograve; muro depre&longs;&longs;ior quoad <lb/>altitudinem forta&longs;&longs;e &longs;it, productus adhuc anteri&ugrave;s, atque
<pb xlink:href="052/01/092.jpg"/>erectus adductus ex minori, <expan abbr="po&longs;teriori&qacute;ue">po&longs;teriorique</expan> parte &agrave; catena <lb/>&longs;ubtractus, ad <expan abbr="&longs;uperna&qacute;ue">&longs;upernaque</expan> tendens paul&ograve; &longs;uper murum pro&shy;<lb/>minens, ip&longs;um quoque ad maiorem altitudinem a&longs;cendere <lb/>volentibus v&longs;um complebit. </s>
<s>atque figura &longs;ub&longs;cripta e&longs;t. </s></p><figure id="id.052.01.092.1.jpg" xlink:href="052/01/092/1.jpg"/><p type="main">
<s><emph type="center"/>De machinis maritimas ciuitates deua&longs;tantibus. </s>
<s><lb/>Cap. </s>
<s>XXV.<emph.end type="center"/></s></p><p type="main">
<s>EAs, qu&aelig; ex nauigijs aguntur machinas inquit <arrow.to.target n="note148"/><lb/>Athen&aelig;us, quas nonnulli Sambucas appel&shy;<lb/>lant ex metaphora mu&longs;icorum in&longs;trumento&shy;<lb/>rum figuratas, &longs;imiles quoad arcuatam con&shy;<lb/>&longs;tructionem iam dicto canali exi&longs;tentes, nil in <lb/>&longs;e &longs;criptu dignum habere, eo qu&ograve;d omnibus cognitu faci&shy;<lb/>les, <expan abbr="manife&longs;t&aelig;&qacute;ue">manife&longs;t&aelig;que</expan> &longs;int: potius autem eo qu&ograve;d nec etiam &longs;e&shy;<lb/>pius ip&longs;&aelig; fiant, vel irrationabiliter, ac incommen&longs;urabili&shy;<lb/>ter con&longs;truct&aelig; &longs;int. </s>
<s>etenim qui in ob&longs;idione circa Chium <lb/>vrbem facta coniecturando &agrave; &longs;copo aberrarunt, <expan abbr="altiores&qacute;">altioresque</expan>; <lb/>turribus Sambucas adduxerunt: eos, qui in ip&longs;as a&longs;cende&shy;<lb/>runt ab igne enecari fecere. </s>
<s>quippe c&ugrave;m ab altitudine tur&shy;<lb/>res in&longs;cendere minim&egrave; potui&longs;&longs;ent. </s>
<s>vt deprimerentur ver&ograve; <lb/><expan abbr="nequaqu&atilde;">nequaquam</expan> fieri poterat, quin nauigia &longs;ubuerterentur one&shy;<lb/>re, quod &longs;uperimpo&longs;itum e&longs;t extra ponderante ge&longs;tato. <arrow.to.target n="note149"/><lb/>quapropter hortatur non e&longs;&longs;e ignaros optic&aelig; tractationis <lb/>eos, qui huiu&longs;cemodi machinis vti debent. </s>
<s>&amp; qu&ograve;d &longs;i qui-<pb xlink:href="052/01/093.jpg"/>dam architectorum maritimam ciuitatem a&longs;&longs;equi decreue&shy;<lb/>rint, duo nauigia tamquam ad iugum iungendo &longs;uper ip&longs;is <lb/>ad altitudinem machinam ponunt, atque in maris tran&shy;<lb/>quillitatibus muris ip&longs;am adducere con&longs;ueuere. </s>
<s>ver&ugrave;m &longs;i <lb/>&agrave; contrario vento nauigia aggre&longs;&longs;a fuerint, &amp; vnda fracta <lb/>ad ip&longs;a &longs;ubrepat: obruit, &amp; circumactu euertit concutien&shy;<lb/>do machinam, qu&aelig; in nauigijs firmata fuerat. </s>
<s>nauigia nam&shy;<lb/>que non eundem, ac &longs;imilem &longs;emper motum efficiunt: &longs;ed <lb/>alterum quidem eorum in und&aelig; culmine quandoque, al&shy;<lb/>terum ver&ograve; in depre&longs;&longs;ione exi&longs;tit. </s>
<s>vnd&egrave; c&ugrave;m di&longs;cerpantur, <lb/>franguntur machin&aelig; ab ip&longs;a per &longs;e in&longs;idiante machinatio&shy;<lb/>ne concu&longs;&longs;&aelig;: ho&longs;tes autem audacia poti&ugrave;s, <expan abbr="fiducia&qacute;ue">fiduciaque</expan> affi&shy;<lb/>ciunt. </s>
<s>At quoniam anima humana quadam, qua per&longs;e <lb/>mouetur excitatione pr&aelig;dita e&longs;t, non &longs;ol&ugrave;m qu&aelig; bene ab <lb/>alijs inuenta &longs;unt nos agno&longs;cere, ver&ugrave;metiam aliquid eo&shy;<lb/>rum, qu&aelig; ad vtilitatem &longs;pectant adinuenire oportet. </s>
<s>qua&shy;<lb/>propter ad &longs;uffulciendam machinam ip&longs;am conati &longs;umus, <lb/>adinuenientes hoc, qu&ograve;d vtique iuxta medium connexio&shy;<arrow.to.target n="note150"/><lb/>nis duorum nauigiorum coaptetur illud, quod pithicium <lb/>dicitur. </s>
<s>quippe quod pondus quoddam quoad magnitu&shy;<arrow.to.target n="note151"/><lb/>dinem quidem figur&aelig; &longs;imile, pendulum inferi&ugrave;s, ac pon&shy;<lb/>dero&longs;um propter &aelig;quilibrium e&longs;t. </s>
<s>vt marina fluctuatione <lb/>vndequaque mouente, <expan abbr="quatiente&qacute;ue">quatienteque</expan> nauigia, machina <lb/>ip&longs;a erecta, ac indeclinabilis con&longs;eruetur. </s>
<s>aduer&longs;us autem <lb/>ventos, atque ad habendum in con&longs;tructione in promptu <lb/>ea, qu&aelig; ad ob&longs;idionem pertinent pr&aelig;&longs;idia: paru&aelig; machi&shy;<lb/><arrow.to.target n="note152"/>n&aelig; (qu&aelig; a gr&aelig;cis Elepolis, hoc e&longs;t vrbium deua&longs;tatrices <lb/><arrow.to.target n="note153"/>dicuntur) pr&aelig;&longs;truend&aelig; &longs;unt, tamquam thoracia qu&aelig;dam <lb/>turribus &longs;imilia, vel a&longs;cen&longs;oria, iuxta altitudinem com&shy;<lb/>men&longs;urabilia, <expan abbr="prompta&qacute;ue">promptaque</expan> exi&longs;tentia. </s>
<s>vt c&ugrave;m nauigia pro&shy;<lb/>pe murum aduenerint, tunc funibus, aut iam dictis mul&shy;<lb/>t&ugrave;m contortis torcularibus huiu&longs;cemodi machin&aelig;, &longs;upra <lb/>murum aditum pr&aelig;parantes, erigantur. </s>
<s>efficax autem ad <lb/>huiu&longs;cemodi v&longs;um iam dictus etiam canalis o&longs;tendetur &longs;i <lb/>magnitudine commen&longs;urabilis exi&longs;tens ad coniuncta na&shy;<lb/>uigia in lignis erect&egrave; &longs;tabilitis &longs;ur&longs;um feratur tran&longs;motus <arrow.to.target n="note154"/><lb/>(vt iam o&longs;ten&longs;um e&longs;t) aut &longs;uper charche&longs;io vocato, potens
<pb xlink:href="052/01/094.jpg"/><arrow.to.target n="note155"/>&longs;uper ip&longs;o &longs;ex motus facere, quemadmodum etiam in&longs;tru&shy;<lb/><arrow.to.target n="note156"/>menta, qu&aelig; grues, &longs;iue ciconi&aelig; dicuntur: aut etiam &longs;uper <lb/><arrow.to.target n="note157"/>circumcurrente clauiculo, quod &longs;uper circumuoluto cau&shy;<lb/><arrow.to.target n="note158"/>le impo&longs;itum &longs;it, qui &longs;an&egrave; caulis operario circumuolutio&shy;<lb/><arrow.to.target n="note159"/>nem ad altum, ad <expan abbr="imum&qacute;ue">imumque</expan> faciat. </s>
<s>&longs;ic itaque Damis etiam <lb/>Colophonius &longs;uper caulibus Sambucas ponebat, quemad&shy;<lb/>modum mechanicus Biton in &longs;uis commentarijs ob&longs;iden&shy;<lb/>di arte tradit. </s>
<s>iam dict&aelig; ver&ograve; quinque configurat&aelig; machi&shy;<lb/>n&aelig; expo&longs;it&aelig; &longs;unt. </s></p>
<pb xlink:href="052/01/095.jpg"/><p type="margin">
<s><margin.target id="note148"/>a</s></p><p type="margin">
<s><margin.target id="note149"/>b</s></p><p type="margin">
<s><margin.target id="note150"/>c</s></p><p type="margin">
<s><margin.target id="note151"/>d</s></p><p type="margin">
<s><margin.target id="note152"/>e</s></p><p type="margin">
<s><margin.target id="note153"/>f</s></p><p type="margin">
<s><margin.target id="note154"/>g</s></p><p type="margin">
<s><margin.target id="note155"/>h</s></p><p type="margin">
<s><margin.target id="note156"/>i</s></p><p type="margin">
<s><margin.target id="note157"/>k</s></p><p type="margin">
<s><margin.target id="note158"/>l</s></p><p type="margin">
<s><margin.target id="note159"/>m</s></p><figure id="id.052.01.095.1.jpg" xlink:href="052/01/095/1.jpg"/>
<pb xlink:href="052/01/096.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note160"/></s></p><p type="margin">
<s><margin.target id="note160"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>SAmbuca e&longs;t quoddam mu&longs;icum in&longs;trumentum triangula&shy;<lb/>rem formam habens ex in&aelig;qualibus tum longitudine, tum <lb/>cra&szlig;itie neruis effectum, vt Porphyrius &longs;cribit. </s>
<s>pr&aelig;&shy;<lb/>terea instrumentum est ob&longs;idionale oppugnandis vrbibus ido&shy;<lb/>neum apud Polybium. </s>
<s>in pr&aelig;&longs;entia ver&ograve; machina bellica e&longs;t ma&shy;<lb/>ritimarum ciuitatum deua&longs;tatrix, quam Autor diligenter de&shy;<lb/>&longs;cribit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note161"/></s></p><p type="margin">
<s><margin.target id="note161"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[quapropter hortatur] ip&longs;e &longs;cilicet Athen&aelig;us [non e&longs;&longs;e igna&shy;<lb/>ros optic&aelig; tractationis] optica tractatio non e&longs;t h&igrave;c accipienda <lb/>pro &longs;cientia optica, &longs;eu per&longs;pectiua, qu&aelig; vi&longs;us pa&szlig;iones demon&shy;<lb/>&longs;trat, ab Euclide, Sereno, Vitellione alijs&queacute; autoribus tradita: &longs;ed <lb/>pro illa &longs;cienti&aelig; mathematic&aelig; parte Geod&aelig;&longs;ia dicta, qu&aelig; vi&longs;u, &longs;iue <lb/>radio vi&longs;uali coadiuuantibus varijs in&longs;trumentis <expan abbr="t&utilde;">tum</expan> longitudines <lb/>altitudinum, planitierum, ac profunditatum: tum longitudi&shy;<lb/>nes, &amp; latitudines &longs;imul &longs;uperficierum: tum etiam longitudines, <lb/>latitudines, cra&szlig;itudines&queacute; &longs;imul corporum metiri docet. </s>
<s>quam <lb/>porr&ograve; &longs;cientiam multi quidem c&ugrave;m antiqui, tum recentiores au&shy;<lb/>tores locupleti&szlig;im&egrave; tradidere: Autor ver&ograve; in fine pr&aelig;&longs;entis ope&shy;<lb/>ris, quatenus rei bellic&aelig; nece&longs;&longs;ariam &longs;ubiunxit. </s>
<s>Qui enim ci&shy;<lb/>uitates expugnaturi &longs;unt, prius earum &longs;itus, ambitus, m&oelig;nium <lb/>altitudines, fo&longs;&longs;arum latitudines, ac profunditates &agrave; longe iam <lb/>dict&aelig; &longs;cienti&aelig; pr&aelig;ceptis, ac regulis &longs;cire debent: vt machinas <lb/>antiquorum more, vel terrea ca&longs;tra iuxta recentiorum v&longs;um ad <lb/>earum expugnationem proportionaliter, <expan abbr="commen&longs;urabiliter&qacute;ue">commen&longs;urabiliterque</expan> <lb/>pr&aelig;&longs;truere po&szlig;int. </s>
<s>Quamobrem non immerito Athen&aelig;us hor&shy;<lb/>tatur non e&longs;&longs;e ignaros iam dict&aelig; optic&aelig; tractationis eos, qui huiu&shy;<lb/>&longs;cemodi machinis bellicis, quales Autor in hoc opere de&longs;cribit, vti <lb/>debent. </s>
<s>ne idem inconueniens eis accidat, quod Chium ciuitatem <lb/>temere ob&longs;identibus eueni&longs;&longs;e Autor inquit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note162"/></s></p><p type="margin">
<s><margin.target id="note162"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Pithicium e&longs;t quoddam pondus &longs;axeum, aut ferreum, vel <lb/>plumbeum, cuius formam Author declarat.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note163"/></s></p><p type="margin">
<s><margin.target id="note163"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ figur&aelig; ] hoc e&longs;t form&aelig;, quam habet tota machina, de qua <lb/>h&igrave;c agitur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note164"/></s></p><p type="margin">
<s><margin.target id="note164"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Elepolis est qu&aelig;dam machina bellica ciuitatum deua&longs;tatrix,<emph.end type="italics"/>
<pb xlink:href="052/01/097.jpg"/><emph type="italics"/>quam Athen&aelig;us ex Apollodori doctrina con&longs;truere diligenti&longs;&shy;<lb/>&longs;im&egrave; docet. </s>
<s>h&aelig;c autem tum magna, tum parua fit, vt nece&szlig;itas, <lb/>v&longs;us&queacute; po&longs;tulat.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note165"/></s></p><p type="margin">
<s><margin.target id="note165"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Quid nam &longs;it thoracium &longs;uperi&ugrave;s in vndecimo capite decla&shy;<lb/>rauimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note166"/></s></p><p type="margin">
<s><margin.target id="note166"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Charche&longs;ium e&longs;t quoddam poculi genus, necnon &longs;ummitas <lb/>mali, vel anten&aelig; nauis.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note167"/></s></p><p type="margin">
<s><margin.target id="note167"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;ex motus] &longs;cilicet dextror&longs;um, &longs;ini&longs;tror&longs;um, ante, retro, <lb/>&longs;ur&longs;um, atque deor&longs;um.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note168"/></s></p><p type="margin">
<s><margin.target id="note168"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Grues, &longs;iue ciconi&aelig; gr&aelig;c&egrave;<emph.end type="italics"/> <foreign lang="greek">ge/ranoi</foreign>, <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="greek">khlo/nia</foreign>, <emph type="italics"/>&longs;unt in&longs;tru&shy;<lb/>menta, quibus aqua &egrave; puteis hauritur, &longs;ubleuandis etiam pon&shy;<lb/>deribus apta.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note169"/></s></p><p type="margin">
<s><margin.target id="note169"/>k</s></p><p type="main">
<s><emph type="italics"/>Caulis h&igrave;c intelligendus e&longs;t fu&longs;tis, &longs;iue fu&longs;us &longs;piricis, aut he&shy;<lb/>lici &longs;imilibus &longs;calptura factis circumuolutionibus pr&aelig;ditus. </s>
<s>cu&shy;<lb/>iu&longs;modi &longs;unt ij, quibus in torcularibus etiam vtimur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note170"/></s></p><p type="margin">
<s><margin.target id="note170"/><emph type="italics"/>l<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Operario] videlicet in&longs;trumento illo, quod eleuandi trahen&shy;<lb/>di&queacute; pondera vim habet, atque Italica lingua Argana vocatur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note171"/></s></p><p type="margin">
<s><margin.target id="note171"/><emph type="italics"/>m<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Damis colophonius antiquus fuit &longs;criptor, cuius nullum vi&shy;<lb/>dimus volumen. </s>
<s>Bitonis autem commentarij de con&longs;tructione bel&shy;<lb/>licorum in&longs;trumentorum extant inter Athenai libros in&longs;erti.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>De Rate fluuio, &longs;iue fo&longs;&longs;&aelig; aqua plen&aelig; imponenda. </s>
<s><lb/>Cap. </s>
<s>XXVI.<emph.end type="center"/></s></p><p type="main">
<s>FIat Ratis longitudinem habens paul&ograve; maio&shy;<lb/>rem latitudine fluuij, cui pons imponendus <lb/>e&longs;t: <expan abbr="in&longs;ternatur&qacute;ue">in&longs;ternaturque</expan> tabulis clauis ligneis affi&shy;<lb/>xis ne iuxta varios fluuialis vnd&aelig; motus amo&shy;<lb/>ueatur, <expan abbr="diuul&longs;a&qacute;ue">diuul&longs;aque</expan> decidat. </s>
<s>Et maior qui&shy;<lb/>dem pars lignorum ip&longs;ius ratis funibus alligatis, &amp; ligneis <lb/>clauis raris affixis &longs;tabiliat&ugrave;r. </s>
<s>tota ver&ograve; ratis longitudo, qu&ecedil; <lb/>ante inimicorum faciem ventura e&longs;t, vn&agrave; cum duobus <lb/><expan abbr="vtrobiq;">vtrobique</expan> exi&longs;tentibus lateribus, propugnaculum ligneum, <lb/>cardinibus volubile. </s>
<s>altitudinis pedum duodecim habeat. </s>
<s><lb/>Fit autem per affixionem erectorum &longs;tantium lignorum, ro<lb/>tunda foramina inferi&ugrave;s &longs;u&longs;cipientium, <expan abbr="politis&qacute;ue">politisque</expan> clauis <lb/>connexorum ad laterales tabulas extrin&longs;ec&ugrave;s confixas, qui&shy;<pb xlink:href="052/01/098.jpg"/>bus porr&ograve; clauis extractis propugnaculum etiam vn&agrave; co&shy;<lb/>incidit. </s>
<s>Appendantur autem &amp; coria, &longs;iue panni laceres <lb/>in ip&longs;is tabulis extrin&longs;ec&egrave; parum excedentia. </s>
<s>necnon &longs;cal&aelig; <lb/>intus apponantur, &longs;uperna quidem crura ad erecta ligna <lb/>clauis affixa habentes, ip&longs;is <expan abbr="eti&atilde;">etiam</expan> erectis lignis &longs;upern&egrave; per&shy;<lb/>foratis exi&longs;tentibus: inferna ver&ograve; in pauimento funibus <lb/>alligata. </s>
<s>vt &longs;calis erectis ex aduer&longs;o &longs;tantibus occurrens <lb/>propugnaculum erectum permaneat. </s>
<s>Sic igitur qui &longs;uper <lb/>&longs;calis &longs;tant ante inimicorum faciem altiores exi&longs;tentes, <expan abbr="an-teriores&qacute;ue">an&shy;<lb/>terioresque</expan> turres in eorum cu&longs;todiam, ac tutellam ex pro&shy;<lb/>pugnaculo habentes, prompt&egrave; in aduer&longs;um oppugnabunt. </s>
<s><lb/>Non vniatur autem totum quod erectum &longs;tat propugnacu&shy;<lb/>lum, &longs;ed ad qua&longs;dam partes haud colligatum &longs;it. </s>
<s>vt &longs;i &longs;ecun&shy;<lb/>d&ugrave;m aggre&longs;&longs;ionem nece&longs;&longs;e fuerit, altera quidem eius pars <lb/>&longs;tet, altera ver&ograve; decidat. </s>
<s>qu&ograve;d &longs;i fuerit opus vt totum quo&shy;<lb/>que decidat, &longs;calas omnes oppugnantes, &longs;uper <expan abbr="propugna-culo&qacute;ue">propugna&shy;<lb/>culoque</expan> re&longs;i&longs;tentes &longs;oluendo, ex inferioribus cruribus &longs;ub&shy;<lb/>trahemus, &longs;uper pauimento eas reponentes. </s>
<s>Hanc autem <lb/>ratem palis terr&aelig; procul infixis per funes retinendo firma&shy;<lb/>bimus. </s>
<s>atque &agrave; ripa nobis proxima vnum eius extremum <lb/>paululum tradentes expellemus, cuneo, qui de&longs;uper ip&longs;am <lb/>retinet ab&longs;oluto. </s>
<s>atque hoc modo ratis ip&longs;a in&longs;tar ianu&aelig; &longs;e <lb/>adaperiens, exercitu plena exi&longs;tens ab aqu&aelig; decur&longs;u pau&shy;<lb/>latim protrahitur, ac denique vnum eius extremum ad flu&shy;<lb/>minis ripam ho&longs;tibus proximam aduenit. </s>
<s>At quoniam lon&shy;<lb/>gior fluminis latitudine &longs;uppo&longs;ita fuit, non pote&longs;t ab vnda <lb/>ad defluxum iterum conuerti. </s>
<s>intra propugnaculum ver&ograve; <lb/>in pauimento relicta &longs;unt foramina qua&longs;dam ad partes, ac <lb/>ad terram v&longs;que peruenientia, ad qu&aelig; lignei pali acurat&egrave; <lb/>figuntur, <expan abbr="ip&longs;a&qacute;ue">ip&longs;aque</expan> ratis latenter alligatur. </s>
<s>ac demum figu&shy;<lb/>ra talis e&longs;t. </s></p>
<pb xlink:href="052/01/099.jpg"/><figure id="id.052.01.099.1.jpg" xlink:href="052/01/099/1.jpg"/><p type="main">
<s><emph type="center"/>De quibu&longs;dam &longs;uperioris machin&aelig; additamentis, eiu&longs;que <lb/>motu, &amp; v&longs;u. </s>
<s>Cap. </s>
<s>XXVII.<emph.end type="center"/></s></p><p type="main">
<s>OVum autem vnum ratis extremum ad contra&shy;<lb/>riam fluminis ripam aduenerit, atque ex inte&shy;<lb/>riore propugnaculi parte in terra firmatum <lb/>fuerit, vt iam dictum e&longs;t: tunc ab extremitate <lb/>alterum quoque extremum ab&longs;oluitur, <expan abbr="ite-rum&qacute;ue">ite&shy;<lb/>rumque</expan> ip&longs;ius vnd&aelig; decur&longs;us tran&longs;uer&longs;am ip&longs;am impedit, <lb/>atque ad alterum fluminis litus totam &longs;ecund&ugrave;m longitu&shy;<lb/>dinem coaptatam apponit. </s>
<s>multitudine collecta, <expan abbr="prompta-&qacute;ue">prompta&shy;<lb/>que</expan> ad pugn&aelig; contrariam aciem exi&longs;tente. </s>
<s>qui ver&ograve; &longs;uper <lb/>&longs;calas a&longs;cenderunt tamquam &longs;uper muro &longs;tantes, audacter <lb/>in aduers&ugrave;m certabunt. </s>
<s>C&ugrave;m autem perterrens &agrave; propu&shy;<lb/>gnaculo congre&longs;&longs;us ho&longs;tes auerterit, inferiora &longs;calarum li&shy;<lb/>gna &longs;oluuntur, <expan abbr="totus&qacute;ue">totusque</expan> propugnaculi paries pedetentim <lb/>obliquatur, &longs;ubtractis &longs;cilicet &longs;calis, ac &longs;uper pauimentum <lb/>incidentibus. </s>
<s><expan abbr="totum&qacute;ue">totumque</expan> interiectum &longs;patium, via inciden&shy;<lb/>tis propugnaculi fit, ac demum hoc pacto continua traie&shy;<pb xlink:href="052/01/100.jpg"/>ctio erit. </s>
<s>Foretur autem latenter infern&egrave; quoque propu&shy;<lb/>gnaculum in lateralibus tabulis iuxta faciem affixis, ita vt <lb/>ab inferiori etiam parte ad ho&longs;tes iacula, <expan abbr="&longs;agitt&aelig;&qacute;ue">&longs;agitt&aelig;que</expan> diri&shy;<lb/>gantur: occultis autem certantibus exi&longs;tentibus, duplici <lb/>&longs;erie iuxta faciem certent: ad &longs;olam ver&ograve; &longs;upernam ho&longs;tes <lb/>re&longs;piciant, atque repugnent. </s>
<s>Expo&longs;uimus itaque quonam <lb/>pacto figura rect&egrave; de&longs;cribitur, vt c&ugrave;m &longs;calarum po&longs;itio, tum <lb/>propugnaculi &longs;itus per&longs;picuus fiat. </s>
<s>ip&longs;i autem rati dum ex <lb/>proxima nobis ripa &longs;oluitur, ac tamquam ianua adaperi&shy;<lb/>tur, in fluuialis vnd&aelig; defluxu auxiliari oportet, ne raptim <lb/>ad reliquam fluminis ripam ver&longs;us ho&longs;tes exi&longs;tentem ad&shy;<lb/>ueniat. </s>
<s>quapropter &agrave; proxima nobis ripa retinendo fr&aelig;&shy;<lb/>nanda, <expan abbr="coercenda&qacute;ue">coercendaque</expan> e&longs;t: funium vero traditio paulatine <lb/>facienda: vt leniter, <expan abbr="&longs;en&longs;im&qacute;ue">&longs;en&longs;imque</expan> progrediens, alteram flu&shy;<lb/>minis ripam ab omni periculo immunis occupet. </s>
<s>atque fi&shy;<lb/>gura &longs;ubijcitur. </s></p>
<pb xlink:href="052/01/101.jpg"/><figure id="id.052.01.101.1.jpg" xlink:href="052/01/101/1.jpg"/><p type="main">
<s><emph type="center"/>Operis conclu&longs;io.<emph.end type="center"/></s></p><p type="main">
<s>HAs igitur ob&longs;idionales machinas, qu&aelig; &agrave; nobis <lb/>quoad de&longs;criptionem, <expan abbr="configurationem&qacute;ue">configurationemque</expan> </s></p><p type="main">
<s><arrow.to.target n="note172"/><lb/>per electionem iam con&longs;truct&aelig; &longs;unt, ip&longs;i exer&shy;<lb/>cituum pr&aelig;&longs;ides cum ratione, <expan abbr="a&longs;&longs;idua&qacute;ue">a&longs;&longs;iduaque</expan> me&shy;<lb/>ditatione accurat&egrave; conficientes: diuinam vbi&shy;<lb/>que locorum vltionem illuce&longs;cere facientes: iu&longs;titia, ac pie&shy;<lb/>tate ornati: &amp; forti manu, atque mutua opera, <expan abbr="bellica&qacute;ue">bellicaque</expan> <lb/>&longs;ocietate Dei cultorum, <expan abbr="Chri&longs;ti&qacute;ue">Chri&longs;tique</expan> amatorum Romano&shy;<pb xlink:href="052/01/102.jpg"/>rum Imperatorum conuale&longs;centes, ac pr&aelig;&longs;idijs cu&longs;toditi: <lb/>facil&egrave; ip&longs;ius poti&longs;&longs;im&ugrave;m Agar ciuitates capient, nullum ip&shy;<lb/>&longs;i in commodum &agrave; de&longs;truentibus diuinum cultum inimicis <arrow.to.target n="note173"/><lb/>patientes. </s></p><p type="margin">
<s><margin.target id="note172"/>a</s></p><p type="margin">
<s><margin.target id="note173"/>b</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note174"/></s></p><p type="margin">
<s><margin.target id="note174"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>PEr electionem non ab re dixit, quoniam non omnes ob&longs;i&shy;<lb/>dionales machinas ab antiquioribus autoribus traditas <lb/>ip&longs;e de&longs;crip&longs;it: &longs;ed eas <expan abbr="tant&utilde;">tantum</expan>, quas eligere &longs;ibi vi&longs;um fuit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note175"/></s></p><p type="margin">
<s><margin.target id="note175"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Chri&longs;ti&queacute; amatorum] hoc e&longs;t Chri&longs;tianorum Romanorum Im&shy;<lb/>peratorum Chri&longs;ti fidem contra Gentiles defendentium. </s>
<s>vnd&egrave; ad&shy;<lb/>notandum est quod Autor no&longs;ter po&longs;t Chri&longs;ti aduentum floruit, vt <lb/>in fine &longs;equentis &longs;ui operis per&longs;picuum nobis erit.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Operis de machinis bellicis finis.<emph.end type="italics"/><emph.end type="center"/></s></p>
<pb xlink:href="052/01/103.jpg"/><figure id="id.052.01.103.1.jpg" xlink:href="052/01/103/1.jpg"/><p type="main">
<s><emph type="center"/>HERONIS MECHANICI <lb/>LIBER DE GEODAESIA. <lb/>PROEMIVM.<emph.end type="center"/></s></p><p type="main">
<s>QVONIAM autem non licet ob&longs;idere <lb/>volentibus &agrave; longe murorum altitu&shy;<lb/>dines, ac &longs;patiorum interualla, nec&shy;<lb/>non fluuiorum latitudines in men&longs;u&shy;<lb/>ratione &longs;upputare: &longs;ed exercitatos li&shy;<arrow.to.target n="note176"/><lb/>nearum peritia, <expan abbr="Dioptric&aelig;&qacute;ue">Dioptric&aelig;que</expan> facul&shy;<lb/>tatis cognitione con&longs;iderationem fa&shy;<lb/>cere: ad hoc vt Elepolis &aelig;qualem <lb/>cum muris &longs;taturam habentes, <expan abbr="com-men&longs;urabiles&qacute;ue">com&shy;<lb/>men&longs;urabilesque</expan> pontes ratibus ad <lb/>fluuiorum latitudines inducantur: vt tamquam in ponte, <lb/>vel traiectione innocu&egrave; exercitus ordinatim pertran&longs;igat: <lb/>quandoquidem multi &longs;&aelig;pe maiores, vel minores qu&agrave;m de&shy;<lb/>cebat machinas c&ugrave;m con&longs;truxi&longs;&longs;ent, <expan abbr="atq;">atque</expan> attuli&longs;&longs;ent (quem&shy;<arrow.to.target n="note177"/><lb/>admodum etiam in pr&aelig;cedenti opere claruit) eos, qui in <lb/>ip&longs;is propugnaturi &longs;unt, &agrave; contrarijs enecari fecerunt: &longs;en&shy;<lb/>&longs;u temerario, <expan abbr="coniectura&qacute;ue">coniecturaque</expan> per&longs;ua&longs;i: propterea decreui&shy;<arrow.to.target n="note178"/><lb/>mus ip&longs;am Dioptri&aelig; cum ratione vim, ac eam ip&longs;ius par&shy;<lb/>tem, qu&aelig; multis in rebus vitam humanam maxim&egrave; iuuat: <lb/>ex antiquioribus, <expan abbr="eruditi&longs;&longs;imis&qacute;ue">eruditi&longs;&longs;imisque</expan> &longs;impliciora colligentes, <arrow.to.target n="note179"/><lb/>nudis linearibus indaginibus explicare, in <expan abbr="paucis&qacute;ue">paucisque</expan> dia&shy;<lb/>grammatibus demon&longs;trationes facere, quonam pacto ex&shy;<arrow.to.target n="note180"/><lb/>tra iaculum ho&longs;tium &longs;tantes, altitudines, ac longitudines, <lb/><expan abbr="interuala&qacute;">interualaque</expan>; reuera &longs;ine mendacio connumerare valeamus.
<pb xlink:href="052/01/104.jpg"/>H&aelig;c autem con&longs;ideratio <expan abbr="n&otilde;">non</expan> &longs;ol&ugrave;m ad militarem &longs;cientiam <lb/>addi&longs;cendi cupidos in&longs;tituet, ver&ugrave;metiam ad aqu&aelig; dedu&shy;<lb/>ctiones, ac murorum con&longs;tructiones, &amp; lacuum circum&longs;cri&shy;<arrow.to.target n="note181"/><lb/>ptiones vtili&longs;&longs;ima: necnon ad Geod&aelig;&longs;iam, <expan abbr="c&oelig;le&longs;tium&qacute;ue">c&oelig;le&longs;tiumque</expan> <lb/>contemplationem non parum conferens apparebit. </s>
<s>Atque <lb/>oper&aelig;pretium e&longs;t nos prolixitatem, ac multiloquium effu&shy;<lb/>gientes, id quidem, quod ob&longs;curum, ac inexplicabile circa <lb/>dictiones pri&longs;corum &longs;cientia pr&aelig;ditorum e&longs;t, &longs;ecernere, at&shy;<lb/>que in rudius tran&longs;mutare: eam ver&ograve;, qu&aelig; circa demon&shy;<lb/>&longs;trationes mathematic&egrave; dicta e&longs;t orationum compendio ca<lb/>ptu <expan abbr="facili&utilde;">facilium</expan> dilatationem aggredi: ac tandem id, quod eius, <lb/>qu&aelig; circa mentis conceptus ver&longs;atur contemplationis al&shy;<lb/>tum e&longs;t, ad humile, <expan abbr="magis&qacute;ue">magisque</expan> &longs;en&longs;uale deferre: con&longs;picuam <lb/>ip&longs;am tractationem facientes viris, qui facil&egrave; in&longs;idiari vo&shy;<lb/>lunt, &amp; quibu&longs;cumque alijs, qui for&longs;an hanc &longs;tudio pro&longs;e&shy;<lb/>quuntur, pr&aelig;cipu&egrave; ver&ograve; ijs, qui quomodocumque Geo&shy;<lb/>metriam ob&longs;eruant. </s></p><p type="margin">
<s><margin.target id="note176"/>a</s></p><p type="margin">
<s><margin.target id="note177"/>b</s></p><p type="margin">
<s><margin.target id="note178"/>c</s></p><p type="margin">
<s><margin.target id="note179"/>d</s></p><p type="margin">
<s><margin.target id="note180"/>e</s></p><p type="margin">
<s><margin.target id="note181"/>f</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note182"/></s></p><p type="margin">
<s><margin.target id="note182"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>DIoptrica facultas (vt docet Proculus in 14. cap. </s>
<s>primi li&shy;<lb/>bri &longs;uorum commentariorum in primum Euclides Ele&shy;<lb/>mentorum) dicitur illa pars A&longs;trologi&aelig;, qu&aelig; &longs;olis, ac <lb/>lun&aelig; c&aelig;terarum&queacute; &longs;tellarum di&longs;tantias dioptricis in&longs;trumentis di&shy;<lb/>gno&longs;cit. </s>
<s>Dioptrica ver&ograve; in&longs;trumenta &longs;unt ea, in quibus exi&longs;tunt <lb/>duo parua foramina, per qu&aelig; radij vi&longs;uales oculorum no&longs;trorum <lb/>tran&longs;eunt dum aliquod interuallum metiri volumus. </s>
<s>quoniam <lb/>autem huiu&longs;cemodi in&longs;trumentis Geod&aelig;&longs;ia &longs;cienti&aelig; mathematic&aelig; <lb/>pars operatur, idcirco dioptricam facultatem h&igrave;c eam Autor vo&shy;<lb/>cat. </s>
<s>quam in 25 capite pr&aelig;cedentis operis opticam etiam nuncu&shy;<lb/>pauit, quemadmodum ibi iam adnotauimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note183"/></s></p><p type="margin">
<s><margin.target id="note183"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in pr&aelig;cedenti opere claruit] &longs;cilicet in principio vige&longs;imi&shy;<lb/>quinti capitis vbi loquebatur de ijs, qui temere <expan abbr="Chi&utilde;">Chium</expan> ob&longs;idebant.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note184"/></s></p><p type="margin">
<s><margin.target id="note184"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Dioptriam h&igrave;c appellat eam, quam &longs;uperius dioptricam fa&shy;<lb/>cultatem vocauit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note185"/></s></p><p type="margin">
<s><margin.target id="note185"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Diagramma propri&egrave; h&igrave;c accipiendum e&longs;t pro figura lineis, ac<emph.end type="italics"/>
<pb xlink:href="052/01/105.jpg"/><emph type="italics"/>elementis de&longs;ignata: cuiu&longs;modi &longs;unt figur&aelig;, in quibus geometr&aelig; <lb/>propo&longs;itiones &longs;uas demon&longs;trant.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note186"/></s></p><p type="margin">
<s><margin.target id="note186"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[extra iaculum ho&longs;tium &longs;tantes] hoc e&longs;t extra terminum illum <lb/>&longs;tantes, ad quem ho&longs;tium iacula peruenire po&longs;&longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note187"/></s></p><p type="margin">
<s><margin.target id="note187"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[necnon ad Geod&aelig;&longs;iam, c&oelig;le&longs;tium&queacute; contemplationem] Qu&aelig;&shy;<lb/>nam &longs;it Geod&aelig;&longs;ia &longs;cientia nos quidem in pr&aelig;cedentis operis 25 <lb/>capite diximus, Proclus autem in tam dicto loco declarat. </s>
<s>C&oelig;le&shy;<lb/>&longs;tium vero contemplationem hic intelligit Autor cam, quam mo&shy;<lb/>d&ograve; diximus dioptricam A&longs;trologi&aelig; partem. </s>
<s>H&aelig;c ad faciliorem hu&shy;<lb/>iu&longs;ce proemij perceptionem adnotanda e&longs;&longs;e duximus. </s>
<s>ver&ugrave;m ani&shy;<lb/>maduertendum e&longs;t, qu&ograve;d hoc in loco magna pr&aelig;&longs;entis operis ha&shy;<lb/>betur imperfectio. </s>
<s>quandoquidem &longs;equentis propo&longs;itionis prin&shy;<lb/>cipium de&longs;ideratur, necnon inter proemium, ip&longs;am&queacute; propo&longs;itio&shy;<lb/>nem qu&aelig;dam alt&aelig; propo&longs;itiones de&longs;unt, vt ex &longs;ine iam dict&aelig; &longs;e&shy;<lb/>quentis propo&longs;itionis, ex alijs&queacute; &longs;equentibus propo&longs;itionibus pa&shy;<lb/>tet. </s>
<s>forta&longs;&longs;e ver&ograve; proemium etiam hoc prolixius ab Autore com&shy;<lb/>po&longs;itum &longs;uit, eius&queacute; &longs;inis de&longs;ideratur.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Propo&longs;itio earum, qu&aelig; extant prima, cuius principium <lb/>de&longs;ideratur.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s>* * * &amp; cd ba&longs;im. </s>
<s>&longs;imiliter autem ip&longs;um etiam li&shy;<lb/>ne&aelig; ab ad lineam bd. </s>
<s>atque rur&longs;us in qua ratione e&longs;t ip&shy;<lb/>&longs;a bd ad vtramlibet ip&longs;arum dc, dg, in eadem e&longs;t ip&longs;a <lb/><expan abbr="quoq;">quoque</expan> ab ad vtramlibet ip&longs;arum hg, ec altitudinem. </s>
<s>opor<lb/>tet autem vt palus, qui perpendiculariter ante &longs;tat ad ma&shy;<lb/>iores altitudines, &amp; aquarum deductionem iuxta h &longs;ignum <lb/>ad clauum quaedam &longs;u&longs;pen&longs;am &longs;u&longs;cipiat dioptram, qu&aelig; <arrow.to.target n="note188"/><lb/>etiam lychnia vocatur. </s>
<s>c&ugrave;m autem ip&longs;as dc, dg minoris <lb/>trianguli ba&longs;es ver&longs;us nos exi&longs;tentes meritus fuero, <expan abbr="ip&longs;as&qacute;">ip&longs;asque</expan>; <lb/>iuxta longitudinem inuenero: ip&longs;as etiam ce, gh cogni&shy;<lb/>tas habebo, tamquam cas, qu&aelig; ip&longs;ius dioptr&aelig;, ac pali alti&shy;<lb/>tudines vniunt. </s>
<s>&amp; &longs;i ba&longs;im altitudinis decuplam inuenero, <lb/>decuplam totam etiam db ip&longs;ius ab enuntiabo. </s>
<s>po&longs;&longs;um <arrow.to.target n="note189"/><lb/>autem totam quoque db reperire quemadmodum in lon&shy;<lb/>gitudine, ac latitudine didicimus. </s>
<s>&amp; c&ugrave;m ip&longs;am <expan abbr="pa&longs;iu&utilde;">pa&longs;&longs;uum</expan> 120 <lb/>reperiero, ip&longs;am etiam ab 12 affirmabo. </s>
<s>qu&aelig; quidem ea
<pb xlink:href="052/01/106.jpg"/>e&longs;t muri altitudo, qu&aelig; in extremo propugnaculi qu&aelig;ritur, <lb/>tam quam ip&longs;ius &agrave; portarum pauimento &longs;uppo&longs;iti b &longs;igni <arrow.to.target n="note190"/><lb/>ad id, quod ad quandam quadrigalis curriculi partem &longs;i&shy;<arrow.to.target n="note191"/><lb/>gnatum e&longs;t a &longs;ignum. </s>
<s>De partibus autem, ac particulis &longs;uf&shy;<lb/>ficienter qu&aelig;rentibus per arithmeticos methodos &longs;uperi&ugrave;s <lb/>di&longs;&longs;eruimus. </s></p><p type="margin">
<s><margin.target id="note188"/>a</s></p><p type="margin">
<s><margin.target id="note189"/>b</s></p><p type="margin">
<s><margin.target id="note190"/>c</s></p><p type="margin">
<s><margin.target id="note191"/>d</s></p><figure id="id.052.01.106.1.jpg" xlink:href="052/01/106/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>NI&longs;i materia h&aelig;c. </s>
<s>de qua in pr&aelig;&longs;enti opu&longs;culo agit Autor, <lb/>&agrave; multis c&ugrave;m antiquis, t&ugrave;m recentioribus autoribus locu&shy;<lb/>pleti&szlig;im&egrave; tradita fui&longs;&longs;et: plena huius, &longs;equentium&queacute; pro&shy;<lb/>po&longs;itionum componeremus commentaria, vt geometricas earum <lb/>demon&longs;trationes iuxta Euclidis doctrinam rudioribus faciliores, <lb/>dilucidiores&queacute; redderemus. </s>
<s>quoniam autem ab alijs &longs;ufficienter <lb/>hanc materiam traditam habemus, nos iam inceptum ordinem <lb/>no&longs;trum &longs;equentes ea duntaxat breuibus &longs;cholijs exponemus, qu&aelig; <lb/>penitus ob&longs;cura nobis e&longs;&longs;e videbuntur.<emph.end type="italics"/><lb/><arrow.to.target n="note192"/></s></p><p type="margin">
<s><margin.target id="note192"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Dioptram, hoc e&longs;t in&longs;trumentum dioptricum lychniam etiam <lb/>antiqui vocabant, ab ip&longs;is lucern&aelig; &longs;imilitudine: quippe c&ugrave;m in <lb/>men&longs;urando tamquam lucerna libere pendeat, duobus&queacute; forami&shy;<lb/>nibus lucem oculis no&longs;tris offerat.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note193"/></s></p><p type="margin">
<s><margin.target id="note193"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[quemadmodum in longitudine, ac latitudine didicimus] nem<lb/>pe in propo&longs;itionibus ijs, in quibus longitudinem, ac latitudinem <lb/>interuallorum ip&longs;e metiri docuit, qu&ecedil; inter proemium, <expan abbr="pr&aelig;&longs;entem-&qacute;ue">pr&aelig;&longs;entem&shy;<lb/>que</expan> mutilam propo&longs;itionem de&longs;iderantur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note194"/></s></p><p type="margin">
<s><margin.target id="note194"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Quadrigale, &longs;iue quadrigarium curriculum e&longs;t &longs;patium &longs;uper <lb/>muros ciuitatum, &longs;uper quod quadrig&aelig; circumcurrunt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note195"/></s></p><p type="margin">
<s><margin.target id="note195"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[De partibus autem, ac particulis] hoc e&longs;t minutis, &longs;ecun&shy;<lb/>dis, tertijs, c&aelig;teris&queacute; minoribus partium minutijs ait &longs;e &longs;uperi&ugrave;s <lb/>&longs;ufficienter per arithmeticos methodos di&longs;&longs;erui&longs;&longs;e. </s>
<s>vnd&egrave; manife-<emph.end type="italics"/><pb xlink:href="052/01/107.jpg"/><emph type="italics"/>&longs;tum nobis e&longs;t multa inter proemium, pr&aelig;&longs;entem&queacute; principio ca&shy;<lb/>rentem propo&longs;itionem de&longs;iderari. </s>
<s>c&ugrave;m enim men&longs;urandi facul&shy;<lb/>tatem Autor pertractaturus e&longs;&longs;et, qu&ecedil; &longs;ine &longs;upputatione integro&shy;<lb/>rum, fractorum&queacute; numerorum tradi non poterat: nece&longs;&longs;arium ei <lb/>fuerat de arte &longs;upputandi, tum integros, tum fractos numeros per <lb/>minuta, &longs;ecunda, tertia, c&aelig;tera&queacute; hi&longs;ce adhuc minora more gr&aelig;&shy;<lb/>corum A&longs;tronomorum pri&ugrave;s &longs;ermonem habui&longs;&longs;e.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Secunda.<emph.end type="center"/></s></p><p type="main">
<s>OStendemus autem quonam pacto etiam duo&shy;<arrow.to.target n="note196"/><lb/>bus &longs;ignis longe &agrave; nobis datis, <expan abbr="atq;">atque</expan> vi&longs;is: quod <arrow.to.target n="note197"/><lb/>inter ea iuxta circinum interiacet interuallum <lb/>capere po&longs;&longs;imus, non appropinquantes datis <lb/>&longs;ignis. </s>
<s>Sint &longs;igna vi&longs;a ab, qu&aelig; in ip&longs;a cancel&shy;<arrow.to.target n="note198"/><arrow.to.target n="note199"/><lb/>lorum di&longs;tantia ob&longs;eruentur. </s>
<s>ip&longs;um quidem a in tertio, ip&shy;<arrow.to.target n="note200"/><lb/>&longs;um vero b in nono. </s>
<s>firmans itaque dioptram in &longs;uperna <lb/>orbita ver&longs;us tertium &longs;ignum, atque ad &longs;itum plani dato&shy;<arrow.to.target n="note201"/><lb/>rum &longs;ignorum tympanum con&longs;tituens: duas rectas lineas <arrow.to.target n="note202"/><lb/>per foramina regul&aelig; diduco: ad tertium quidem ip&longs;am ca, <lb/>ad nonum ver&ograve; ip&longs;am cb. </s>
<s>atque harum vnam regula me&shy;<arrow.to.target n="note203"/><lb/>tior, vel <expan abbr="qu&etilde;amodum">quemamodum</expan> etiam &longs;uperi&ugrave;s o&longs;ten&longs;um e&longs;t. </s>
<s>&amp; &longs;i for&shy;<lb/>ta&longs;&longs;e pa&longs;&longs;uum octoginta eam inuenero, &longs;eco ip&longs;am iuxta <lb/>quam cumque partem voluero. </s>
<s>&longs;it &longs;ectio iuxta decimam par<lb/>tem earum, qu&aelig; ver&longs;us orbitam &longs;unt rectarum linearum, ad <lb/>pa&longs;&longs;us octo, iuxta d &longs;ignum. </s>
<s>&amp; c&ugrave;m dioptram ad ip&longs;um <expan abbr="tra&longs;&shy;po&longs;uero">tra&longs;&shy;<lb/>po&longs;uero</expan>, ip&longs;am de <expan abbr="rect&atilde;">rectam</expan> <expan abbr="line&atilde;">lineam</expan> per <expan abbr="regul&atilde;">regulam</expan> diduco, qu&aelig; &longs;imi&shy;<lb/>liter ip&longs;am cb iuxta <expan abbr="decim&atilde;">decimam</expan> partem ad e &longs;ignum &longs;ecet. </s>
<s>Erit <lb/>igitur ip&longs;a <expan abbr="quoq;">quoque</expan> de decima pars ip&longs;ius ab di&longs;tanti&aelig;. </s>
<s><expan abbr="qu&etilde;-admodum">quem&shy;<arrow.to.target n="note204"/><lb/>admodum</expan> enim ip&longs;a ac ad ip&longs;am cd, &amp; ip&longs;a bc ad ip&longs;am <lb/>ce, ita etiam ip&longs;a ab ad ip&longs;am de erit at veluti etiam ip&longs;a d <lb/>e ad ip&longs;am ec, &longs;ic ip&longs;a quoque ab ad ip&longs;am bc. </s>
<s>c&ugrave;m autem <lb/>ip&longs;am etiam ed ver&longs;us nos exi&longs;tentem men&longs;urauero, &amp; pa&longs;&shy;<lb/>&longs;uum quatuor eam cognitam inuenero: ip&longs;am quoque ab <lb/>tamquam decuplam quadraginta pa&longs;&longs;uum exi&longs;tentem ha&shy;<lb/>bebo. </s>
<s>Quapropter quod qu&aelig;ritur inter ab &longs;igna interia&shy;<arrow.to.target n="note205"/><lb/>cens interuallum quadraginta pa&longs;&longs;uum repertum e&longs;t. </s></p>
<pb xlink:href="052/01/108.jpg"/><p type="margin">
<s><margin.target id="note196"/><emph type="italics"/>Propo&longs;i&shy;<lb/>tio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note197"/>a</s></p><p type="margin">
<s><margin.target id="note198"/><emph type="italics"/>Con&longs;tru&shy;<lb/>ctio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note199"/>b</s></p><p type="margin">
<s><margin.target id="note200"/>c</s></p><p type="margin">
<s><margin.target id="note201"/>d</s></p><p type="margin">
<s><margin.target id="note202"/>e</s></p><p type="margin">
<s><margin.target id="note203"/>f</s></p><p type="margin">
<s><margin.target id="note204"/><emph type="italics"/>Demon&shy;<lb/>&longs;tratio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note205"/><emph type="italics"/><expan abbr="C&otilde;clu&longs;io">Conclu&longs;io</expan>.<emph.end type="italics"/></s></p><figure id="id.052.01.108.1.jpg" xlink:href="052/01/108/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note206"/></s></p><p type="margin">
<s><margin.target id="note206"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[iuxta circinum] ide&longs;t iuxta quandam circini aperturam.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note207"/></s></p><p type="margin">
<s><margin.target id="note207"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ip&longs;um quidem a in tertio, ip&longs;um ver&ograve; b in nono] intelligen&shy;<lb/>dum e&longs;t cancello.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note208"/></s></p><p type="margin">
<s><margin.target id="note208"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in &longs;uperna orbita] du&aelig; &longs;unt in Dioptra, &longs;iue dioptrico in&longs;tru&shy;<lb/>mento partes, quarum altera quidem vocatur orbita &longs;uperna, <lb/>altera ver&ograve; orbita inferna. </s>
<s>h&aelig; autem &longs;unt du&aelig; &longs;emicircumferen&shy;<lb/>ti&aelig;, &longs;uperna &longs;cilicet, ac inferna: in quibus etiam in A&longs;trolabij <lb/>dor&longs;o &longs;unt du&aelig; ill&aelig; vnius rect&aelig; line&aelig; partes, quarum &longs;uperna qui&shy;<lb/>dem vocatur linea medij c&oelig;li, &longs;iue medi&aelig; diei: inferna ver&ograve;, linea <lb/>medi&aelig; noctis, &longs;iue angulus terr&aelig;.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/109.jpg"/><p type="main">
<s><arrow.to.target n="note209"/></s></p><p type="margin">
<s><margin.target id="note209"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Tympana &longs;unt rotul&aelig; in A&longs;trolabij matre content&aelig;, in quibus <lb/>diuer&longs;orum climatum tabul&aelig; de&longs;ignantur. </s>
<s>in pr&ecedil;&longs;entia uer&ograve; tym&shy;<lb/>panum accipiendum e&longs;t pro plana &longs;uperficie ip&longs;ius dioptr&aelig;, &longs;eu <lb/>dioptrici in&longs;trumenti, quo Autor utitur. </s>
<s>quod autem ait [ad &longs;i&shy;<lb/>tum plani datorum &longs;ignorum] &longs;ic intelligendum e&longs;t. </s>
<s>qu&ograve;d &longs;cilicet <lb/>tympanum ip&longs;um ita &longs;ituetur, vt in eodem plano tympanum, ocu&shy;<lb/>lus, men&longs;urantis, data&queacute; &longs;igna &longs;int.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note210"/></s></p><p type="margin">
<s><margin.target id="note210"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Regul&aelig;] hoc e&longs;t alidad&aelig;, &longs;eu voluell&aelig;, in qua du&aelig; pinnul&aelig; <lb/>paruis foraminibus pr&aelig;dit&aelig; &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note211"/></s></p><p type="margin">
<s><margin.target id="note211"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;uperi&ugrave;s o&longs;ten&longs;um e&longs;t] videlicet in propo&longs;itionibus ijs, qu&aelig; <lb/>de&longs;iderantur.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Tertia.<emph.end type="center"/></s></p><p type="main">
<s>ALiter etiam interuallum inter data duo &longs;igna <arrow.to.target n="note212"/><lb/>interiacens percipi pote&longs;t iuxta diagramma, <lb/>quod nunc exponitur. </s>
<s>Intelligatur per &longs;up&shy;<lb/>po&longs;itionem ip&longs;um quidem a &longs;ignum, quod <arrow.to.target n="note213"/><lb/>iuxta latitudinem hippici ad &longs;ini&longs;tram fund&aelig; <lb/>partem ob&longs;eruetur: ip&longs;um ver&ograve; b ad dexteram. </s>
<s>Statuo igi&shy;<arrow.to.target n="note214"/><arrow.to.target n="note215"/><lb/>tur ad eum, qui inacce&longs;&longs;ibilis vocatur dioptram parum di&shy;<lb/>&longs;tantem &agrave; &longs;uperna &egrave; contrario iacente orbita, vt ad c <expan abbr="&longs;ign&utilde;">&longs;ignum</expan>. </s>
<s><lb/>ita vt vi&longs;us ad rectam datorum &longs;ignorum in&longs;pectionem ne&shy;<lb/>quaquam impediatur. </s>
<s>c&ugrave;m autem tympanum ad &longs;itum pla&shy;<lb/>ni ba&longs;is fund&aelig; con&longs;tituero, diduco duas rectas lineas per <lb/>regulam ad &longs;ini&longs;trum quidem terminum ip&longs;am ca: ad dex&shy;<lb/>trum ver&ograve; ip&longs;am cb. </s>
<s>atque harum vnam (vt iam dictum <lb/>e&longs;t) c&ugrave;m partitus fuero, &amp; forta&longs;&longs;e pa&longs;&longs;uum 126 inuenero: <arrow.to.target n="note216"/><lb/>ad alterum regul&aelig; radium me confero. </s>
<s>atque immobilibus <lb/>cunctis, qu&aelig; in dioptra &longs;unt permanentibus, &longs;uper tympa&shy;<lb/>num oculos paululum attollo: &amp; in ip&longs;a bc recta linea, vt <lb/>puta ad eius decimamoctauam partem ad &longs;ini&longs;tras ip&longs;ius <lb/>inacce&longs;&longs;ibilis partes iuxta &longs;eptem pa&longs;&longs;us &longs;ignum d perci&shy;<lb/>pio: &longs;imiliter autem ad dexteras etiam partes in ip&longs;a ac re&shy;<lb/>cta linea, &longs;ignum e: <expan abbr="ip&longs;am&qacute;ue">ip&longs;amque</expan> ed connecto. </s>
<s>Et quoniam <arrow.to.target n="note217"/><lb/>ip&longs;a ec ip&longs;ius ca, &amp; ip&longs;a dc ip&longs;ius cb decimaoctaua <lb/>pars e&longs;t: ip&longs;ius quoque de interuallum ad ip&longs;ius ab in&shy;<pb xlink:href="052/01/110.jpg"/>teruallum decimaoctaua pars erit. </s>
<s>quemadmodum enim <lb/>minora latera duorum, qu&aelig; &egrave; contrario aduerticem figu&shy;<lb/>rantur <expan abbr="triangulor&utilde;">triangulorum</expan> ad maiora &longs;e &longs;e <expan abbr="hab&etilde;t">habent</expan>: ita <expan abbr="eti&atilde;">etiam</expan> ba&longs;is trian<lb/>guli minoris, ad maioris ba&longs;em &longs;e habebit. </s>
<s>c&ugrave;m <expan abbr="aut&etilde;">autem</expan> ip&longs;am <lb/>de minoris trianguli ba&longs;im <expan abbr="t&atilde;qu&atilde;">tamquam</expan> apud nos <expan abbr="exi&longs;tent&etilde;">exi&longs;tentem</expan> men lb/&gt;&longs;urauero, ac forta&longs;&longs;e pa&longs;&longs;uum duorum cum dimidio ip&longs;am <lb/>inuenero: ip&longs;a <expan abbr="quoq;">quoque</expan> ab <expan abbr="t&atilde;quam">tanquam</expan> octodecupla exi&longs;tens mi<arrow.to.target n="note218"/><lb/>hi cognita erit. </s>
<s>Quamobrem rur&longs;us ip&longs;um inter ab &longs;igna <lb/>interiacens <expan abbr="interuall&utilde;">interuallum</expan> iuxta extremitatem latitudinis hip&shy;<lb/>pici ad ba&longs;im fund&aelig; pa&longs;&longs;uum 45 repertum e&longs;t. </s></p><p type="margin">
<s><margin.target id="note212"/><emph type="italics"/>Propo&longs;i&shy;<lb/>tio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note213"/>a b</s></p><p type="margin">
<s><margin.target id="note214"/><emph type="italics"/>Con&longs;tru&shy;<lb/>ctio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note215"/>c</s></p><p type="margin">
<s><margin.target id="note216"/>d</s></p><p type="margin">
<s><margin.target id="note217"/><emph type="italics"/>Demon&shy;<lb/>stratio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note218"/><emph type="italics"/><expan abbr="C&otilde;clu&longs;io">Conclu&longs;io</expan>.<emph.end type="italics"/></s></p><figure id="id.052.01.110.1.jpg" xlink:href="052/01/110/1.jpg"/>
<pb xlink:href="052/01/111.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note219"/></s></p><p type="margin">
<s><margin.target id="note219"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>HIppicum est equitatus men&longs;ura quatuor cubitos conti&shy;<lb/>nens, quod etiam pro quocumque &longs;tadiorum quatuor in&shy;<lb/>teruallo &longs;u&longs;cipitur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note220"/></s></p><p type="margin">
<s><margin.target id="note220"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[fund&aelig;] hoc e&longs;t Monangonis in&longs;trumenti iaculatorij, quod in <lb/>17 capite pr&aelig;cedentis operis fundam etiam &agrave; nonnullis appellari <lb/>dixit. </s>
<s>de hac etenim funda h&igrave;c intelligenda &longs;unt ea, qu&aelig; ab Au&shy;<lb/>tore dicuntur: non autem de funda ex lino facta.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note221"/></s></p><p type="margin">
<s><margin.target id="note221"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ad eum, qui inacce&szlig;ibilis vocatur] hoc e&longs;t ver&longs;us eum, &longs;cilicet <lb/>locum, quem peragrare nobis minim&egrave; licet propter varia impe&shy;<lb/>dimenta, qui &agrave; geometris inacce&szlig;ibilis nuncupatur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note222"/></s></p><p type="margin">
<s><margin.target id="note222"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[radium] hoc e&longs;t pinnul&aelig; foramen, per quod vi&longs;ualis radius <lb/>tran&longs;it.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Quarta.<emph.end type="center"/></s></p><p type="main">
<s>FIeri autem pote&longs;t, vt <expan abbr="n&otilde;">non</expan> &longs;ol&ugrave;m interiacens in&shy;<arrow.to.target n="note223"/><lb/>ter data duo &longs;igna interuallum &longs;u&longs;cipiamus, <lb/>ver&ugrave;metiam vt rect&aelig; line&aelig; &longs;igna connectentis <lb/>&longs;itum reperiamus, alicui datorum &longs;ignorum <lb/>non approximantes. </s>
<s>Sint &longs;igna qu&aelig; videntur <arrow.to.target n="note224"/><arrow.to.target n="note225"/><lb/>ab, ip&longs;um quidem a ad vnum ex &longs;eptem Euripi &longs;egmentis <arrow.to.target n="note226"/><lb/>in pectorum ba&longs;i ob&longs;eruatum: ip&longs;um vero b ad id, quod in <arrow.to.target n="note227"/><lb/>regali &longs;ede e&longs;t pauimentum, aut in vna earum, qu&aelig; vtro&shy;<arrow.to.target n="note228"/><lb/>bique in cur&longs;oribus iuxta gymnicos agones in&longs;tructiones <lb/>appellantur. </s>
<s>c&ugrave;m ita que dioptram ad infern&aelig; orbit&aelig; &egrave; con&shy;<lb/>trario circumductionem &egrave; regione &longs;igni b ad c &longs;ignum con<lb/>&longs;tituero, per regulam di&longs;picio, donec in recta linea iam di&shy;<lb/>ctum a &longs;ignum ab extremitate con&longs;pexero. </s>
<s>&amp; c&ugrave;m ad la&shy;<lb/>tus dioptr&aelig;, quod in orbita e&longs;t, me contulerim, &longs;uper tym&shy;<lb/>panum paululum oculos attollo, &amp; rectam diduco lineam <arrow.to.target n="note229"/><lb/>ex oppo&longs;ito &longs;cal&aelig; graduum ip&longs;am cd tamquam ad paui&shy;<lb/>mentum ante &longs;tantium pectorum iuxta d &longs;ignum re&longs;picien<lb/>tem, ad rectos exi&longs;tentem angulos ip&longs;i ac rect&aelig; line&aelig; in <lb/>recto angulo, qui ad c &longs;ignum e&longs;t. </s>
<s>atque dioptram in ip&longs;a
<pb xlink:href="052/01/112.jpg"/>cd recta linea deduco, donec in recta linea b &longs;ignum a&longs;pi&shy;<arrow.to.target n="note230"/><lb/>ciam. </s>
<s>&longs;ituetur dioptra ad e &longs;ignum. </s>
<s>Ip&longs;a igitur be ip&longs;i qui&shy;<lb/>dem cd ad rectos e&longs;t angulos, ip&longs;i ver&ograve; ac parallela. </s>
<s>po&longs;&shy;<lb/>&longs;um autem id, quod &agrave; &longs;igno c ad &longs;ignum a, &amp; quod &agrave; &longs;igno <lb/>e ad &longs;ignum b e&longs;t interuallum capere, quemadmodum &longs;&aelig;&shy;<lb/>pe triangularem figuram faciens &longs;uppo&longs;ui. </s>
<s>&amp; &longs;i &aelig;qualem <lb/>quidem ip&longs;am ca ip&longs;i eb inuenero, &aelig;quale ip&longs;um quoque <lb/>ce interuallum ip&longs;i ab enuntiabo: &longs;i ver&ograve; vnam ip&longs;arum <lb/>altera maiorem, exce&longs;&longs;um &agrave; maiore aufero, deinde mino&shy;<lb/>rem connecto. </s>
<s>verbi gratia &longs;i ip&longs;am ce rectam latitudinis <lb/>lineam pa&longs;&longs;uum duodecim inuenero, ip&longs;am ver&ograve; ca 90, &amp; <lb/>81 ip&longs;am eb: excedentes pa&longs;&longs;us nouem &agrave; &longs;igno c ad <expan abbr="&longs;ign&utilde;">&longs;ignum</expan> <lb/>f aufero, deinde minorem ip&longs;a fe connecto &aelig;quale, &amp; pa&shy;<lb/>rallela iuxta &longs;itum ip&longs;i ab exi&longs;tente. </s>
<s>nam &longs;i &aelig;qualis qui&shy;<lb/>dem e&longs;&longs;et ac ip&longs;i be, duodecim <expan abbr="vtiq;">vtique</expan> pa&longs;&longs;uum ip&longs;um quo&shy;<lb/>que line&aelig; ab, quemadmodum ip&longs;um line&aelig; ce interual&shy;<lb/>lum e&longs;&longs;et. </s>
<s>at quoniam excedens ip&longs;a ca ip&longs;am eb nouem <lb/>pa&longs;&longs;ibus reperta e&longs;t, hos ip&longs;a fe re&longs;ecat, &amp; angulum rectum <lb/>ad c &longs;ignum exi&longs;tentem &longs;ubtendit. </s>
<s>e&longs;t autem ip&longs;a quoque <lb/>ce ba&longs;is pa&longs;&longs;uum duodecim: quare quindecim ip&longs;a fe erit, <arrow.to.target n="note231"/><lb/>tamquam ea, qu&aelig; &longs;ecundum potentiam duobus circa re&shy;<lb/>ctum angulum iacentibus lateribus ad&aelig;quatur. </s>
<s>eorundem <lb/>igitur pa&longs;&longs;uum erit ip&longs;um etiam, quod ab a &longs;igno ad b &longs;i&shy;<arrow.to.target n="note232"/><lb/>gnum e&longs;t interuallum. </s>
<s>Quare non &longs;ol&ugrave;m interiacens inter <lb/>ab &longs;igna interuallum iuxta magnitudinem repertum e&longs;t, <lb/>ver&ugrave;m etiam &longs;itus rect&aelig; line&aelig; &longs;igna connectentis: quemad&shy;<lb/>modum propo&longs;itum etiam diagramma &longs;uppo&longs;uit. </s></p>
<pb xlink:href="052/01/113.jpg"/><p type="margin">
<s><margin.target id="note223"/><emph type="italics"/>Propo&longs;i<lb/>tio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note224"/><emph type="italics"/>Constru<lb/>ctio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note225"/>a</s></p><p type="margin">
<s><margin.target id="note226"/>b. </s>
<s>c</s></p><p type="margin">
<s><margin.target id="note227"/>d</s></p><p type="margin">
<s><margin.target id="note228"/>e.f. </s>
<s>g</s></p><p type="margin">
<s><margin.target id="note229"/>h</s></p><p type="margin">
<s><margin.target id="note230"/><emph type="italics"/>Demon&shy;<lb/>&longs;tratio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note231"/>i</s></p><p type="margin">
<s><margin.target id="note232"/><emph type="italics"/><expan abbr="C&otilde;clu&longs;io">Conclu&longs;io</expan>.<emph.end type="italics"/></s></p><figure id="id.052.01.113.1.jpg" xlink:href="052/01/113/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>QVibu&longs;dam antiquioribus, <expan abbr="ob&longs;curioribus&qacute;ue">ob&longs;curioribusque</expan> vocabulis in <lb/>principio pr&aelig;&longs;entis propo&longs;itionis v&longs;us e&longs;t Autor, qu&aelig; ni&longs;i <lb/>declarentur, forta&longs;&longs;e minis ob&longs;cura legentibus videbun&shy;<lb/>tur: &longs;unt autem h&aelig;c.<emph.end type="italics"/><lb/><arrow.to.target n="note233"/></s></p><p type="margin">
<s><margin.target id="note233"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Euripus Autore Mela e&longs;t fretum, &longs;eu mare angu&longs;tum inter <lb/>Aulidem B&oelig;oti&aelig; portum, &amp; Euboeam in&longs;ulam &longs;itum, quod vi&shy;<lb/>gintiquatuor horarum &longs;patio &longs;epties recurrit eo impetu, vt naui&shy;<lb/>gia repugnantibus etiam ventis plena &longs;ecum rapiat: vnd&egrave; &longs;e&shy;<lb/>ptem agit in recur&longs;ibus ip&longs;is in terra &longs;egmenta &longs;inuum in&longs;tar.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note234"/></s></p><p type="margin">
<s><margin.target id="note234"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[pectorum] gr&aelig;c&egrave;<emph.end type="italics"/> <foreign lang="greek">sthqe/wn</foreign> <emph type="italics"/>legitur, quod nil aliud latin&egrave; &longs;onat, <lb/>qu&agrave;m pectorum, quemadmodum ego conuerti, vt &longs;im &longs;idus inter&shy;<emph.end type="italics"/><pb xlink:href="052/01/114.jpg"/><emph type="italics"/>pres. </s>
<s>ver&ugrave;m metaphoric&egrave; hoc ab Autore dictum e&longs;&longs;e mihi videtur. </s>
<s><lb/>quandoquidem in pr&aelig;&longs;entia vocabulum<emph.end type="italics"/> <foreign lang="greek">sth/qos</foreign>, <emph type="italics"/>quod propri&egrave; pe&shy;<lb/>ctus &longs;ignificat, pro dictione<emph.end type="italics"/> <foreign lang="greek">ko/lloy</foreign>, <emph type="italics"/>&longs;iue<emph.end type="italics"/> <foreign lang="greek">ko/lpos</foreign>, <emph type="italics"/>hoc e&longs;t &longs;inus <lb/>accipiendum e&longs;t. </s>
<s>nam quemadmodum &longs;inus vocatur litus curuum <lb/>duobus qua&longs;i brachijs longi&ugrave;s in mare procurrentibus inclu&longs;um <lb/>per tran&longs;lationem de&longs;umptam &agrave; curuitate illa, qu&aelig; e&longs;t intra pe&shy;<lb/>ctoris, brachiorum&queacute; complexum: ita etiam hoc in loco Autor pe&shy;<lb/>ctus pro &longs;inu maris conuer&longs;a metaphora &longs;u&longs;cepit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note235"/></s></p><p type="margin">
<s><margin.target id="note235"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Ba&longs;im pectorum vocat intimam &longs;inuum partem.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note236"/></s></p><p type="margin">
<s><margin.target id="note236"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ad id, quod in regali &longs;ede e&longs;t pauimentum] hoc e&longs;t ad ip&longs;ius <lb/>regalis &longs;edis, nempe pallatij ba&longs;im, ac fundamentum.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note237"/></s></p><p type="margin">
<s><margin.target id="note237"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Cur&longs;ores in pr&aelig;&longs;entia pro locis, &longs;iue interuallis accepit, vbi in <lb/>ludis publicis cur&longs;atur, qui proprio nomine curricula dicuntur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note238"/></s></p><p type="margin">
<s><margin.target id="note238"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Gymnici Agones &longs;unt loci, in quibus Scenica, Mu&longs;ica, Dioni&longs;ia&shy;<lb/>ca, bellica, alia&queacute; varia &longs;pectacula, necnon certamina exerceban&shy;<lb/>tur: quorum quatuor pr&aelig;cipui in Gr&aelig;cia fuere, &longs;cilicet Nem&aelig;us, <lb/>Pythius, I&longs;thmius, ac Olimpius.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note239"/></s></p><p type="margin">
<s><margin.target id="note239"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in&longs;tructiones] ide&longs;t apparatus gradibus con&longs;tructi, cuiu&longs;mo&shy;<lb/>di &longs;unt Theatra, Amphitheatra, Aren&aelig;, Palestr&aelig;, ali&aelig;&queacute; id genus <lb/>machin&aelig;.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>His ita declaratis quod ait Autor nobis per&longs;picuum erit. </s>
<s>nam <lb/>excogitans ip&longs;e &longs;e prope quandam e&longs;&longs;e maritimam, opulentam&queacute; <lb/>ciuitatem in Euripi litore po&longs;itam, cuius &longs;itus &agrave; longe &longs;ibi capien&shy;<lb/>dus &longs;it: ait duo &longs;igna per dioptram ob&longs;eruanda e&longs;&longs;e, quorum al&shy;<lb/>terum quidem &longs;it ad vnum ex &longs;eptem Euripi &longs;egmentis in ba&longs;i <lb/>pectorum ip&longs;orum &longs;egmentorum: reliquum ver&ograve;, ad <expan abbr="pauiment&utilde;">pauimentum</expan>, <lb/>quod in regali &longs;ede e&longs;t, aut ad pauimentum, quod in vna earum <lb/>machinarum e&longs;t, qu&aelig; vtrobique in cur&longs;oribus iuxta gymnicos <lb/>Agones in&longs;tructiones appellantur. </s>
<s>talis itaque &longs;it ordo, &longs;en&longs;us&queacute; <lb/>pr&aelig;&longs;entium ob&longs;curorum Autoris verborum. </s>
<s>Animaduertendum <lb/>autem e&longs;t qu&ograve;d tam in hac, qu&agrave;m in pr&aelig;cedentibus, ac &longs;equen&shy;<lb/>tibus huius operis propo&longs;itionibus dioptram mod&ograve; pro toto dioptri&shy;<lb/>co in&longs;trumento, mod&ograve; pro voluella, aut ea <expan abbr="in&longs;trum&etilde;ti">in&longs;trumenti</expan> parte, in qua <lb/>duo, per qu&aelig; in&longs;picimus parua foramina &longs;unt, Autor accipere <lb/>videtur. </s>
<s>quod di&longs;tinguendum prudenti legentium iuditio relin&shy;<lb/>quimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note240"/></s></p><p type="margin">
<s><margin.target id="note240"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;cal&aelig; graduum] hoc est &longs;cal&aelig; altimetrs in ip&longs;o dioptrico in-<emph.end type="italics"/>
<pb xlink:href="052/01/115.jpg"/><emph type="italics"/>&longs;trumento de&longs;ignat&aelig;, in qua gradus vmbr&aelig; rect&aelig;, &amp; vmbr&aelig; ver&shy;<lb/>&longs;&aelig; in &longs;uis partibus, ac particulis diui&longs;i &longs;unt, quemadmodum <lb/>etiam in dor&longs;o A&longs;trolabij.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note241"/></s></p><p type="margin">
<s><margin.target id="note241"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;ecundum potentiam] potentia rectarum linearum nil aliud <lb/>est ni&longs;i quadratum ab ip&longs;is de&longs;criptum, , vt ex decimo libro Ele&shy;<lb/>mentorum Euclidis patet. </s>
<s>quoniam autem in omni rectangulo <lb/>triangulo quadratum &agrave; latere rectum angulum &longs;ubtendente de&shy;<lb/>&longs;criptum &aelig;quale est ijs, qu&aelig; &agrave; reliquis lateribus <expan abbr="de&longs;crib&utilde;tur">de&longs;cribuntur</expan> qua&shy;<lb/>dratis, vt Euclides in penultima propo&longs;itione primi Elementorum <lb/>demon&longs;trat: idcirco inquit Autor qu&ograve;d ip&longs;a fe rectum angulum <lb/>&longs;ubtendens recta linea quindecim pa&longs;&longs;uum erit, quandoquidem <lb/>&longs;ecundum potentiam duobus circa rectum angulum iacentibus <lb/>lateribus ad&aelig;quatur, hoc e&longs;t quadratum eius quadratis eorum <lb/>duorum laterum &aelig;quale exi&longs;tit. </s>
<s>c&ugrave;m enim alterum quidem ip&longs;o&shy;<lb/>rum duorum laterum nouem, alterum ver&ograve; duodecim pa&longs;&longs;uum <lb/>&longs;uppo&longs;ita &longs;int: quadratum alterius quidem 81, reliqui vero 144 <lb/>erit, qu&aelig; &longs;imuliuncta 225 efficiunt, totidem igitur quadratum <lb/>etiam a latere ef de&longs;criptum continet. </s>
<s>quare latus ef 15 pa&longs;&shy;<lb/>&longs;uum erit. </s>
<s>H&aelig;c autem pro dilucidatione huiu&longs;ce propo&longs;itionis bre&shy;<lb/>uiter adnotata &longs;int.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Quinta.<emph.end type="center"/></s></p><p type="main">
<s>AT ip&longs;am quidem rectarum linearum men&longs;u&shy;<lb/>rationem hoc modo cognitam habebimus. </s>
<s>ip&shy;<lb/>&longs;a ver&ograve;, qu&aelig; tum &agrave; rectilineis, tum &agrave; curuili&shy;<lb/>neis figuris continentur plana &longs;patia hoc pa&shy;<arrow.to.target n="note242"/><lb/>cto men&longs;urabuntur. </s>
<s>in quadrangulis quidem <lb/>tum &aelig;quilateris, tum altera parte longioribus oportet lon&shy;<lb/>gitudinis latus in latitudinis latus multiplicare, vel etiam <arrow.to.target n="note243"/><lb/>&egrave; conuers&ograve;: &amp; eum, qui ex duobus ip&longs;is lateribus fit <expan abbr="plan&utilde;">planum</expan> <arrow.to.target n="note244"/><lb/>numerum, figur&aelig; aream, &longs;iue &longs;patium, quod &agrave; quatuor la&shy;<lb/>teribus circum qua que terminatur, enuntiare. </s>
<s>quemadmo&shy;<lb/>dum in iamdicto diagrammate o&longs;tendetur. </s>
<s>Quum enim la&shy;<lb/>tus ac pa&longs;&longs;uum &longs;it nonaginta, duodecim ver&ograve; latus ce: &longs;i <lb/>in &longs;einuicem multiplicentur 1080 faciunt, quod e&longs;t totum <arrow.to.target n="note245"/><lb/>alterapartelongioris &longs;patium. </s>
<s>idem autem modus in &aelig;qui-<pb xlink:href="052/01/116.jpg"/><arrow.to.target n="note246"/><lb/>lateris etiam quadrangulis fiat. </s>
<s>Qua&longs;i &longs;imilem autem, ac <lb/>euidentem men&longs;urationem habebunt ip&longs;a etiam quadran&shy;<lb/>gula, qu&aelig; Rhombi vocantur: tamquam ij, qui ex quadran&shy;<lb/>gulorum &aelig;quilaterorum, <expan abbr="quemadmod&utilde;">quemadmodum</expan> etiam ip&longs;&aelig; Rhom <lb/>boides figur&aelig; ex ip&longs;arum alterapartelongiorum <expan abbr="figurar&utilde;">figurarum</expan> <lb/>di&longs;tortione fiunt. </s>
<s>etenim latera terminata, vnamque dia&shy;<arrow.to.target n="note247"/><lb/>goniorum datam habent. </s>
<s>nam Rhombus quidem, ex duo&shy;<lb/>bus &aelig;quicruribus: Rhomboides ver&ograve;, ex duobus acutan&shy;<lb/>gulis, vel obtu&longs;angulis triangulis componitur. </s>
<s>vt in dia&shy;<lb/>grammate qui&longs;que per&longs;picere pote&longs;t ip&longs;um quadrangulum <lb/>ab af, fe, eb, &amp; ab lateribus <expan abbr="c&otilde;tentum">contentum</expan>, ex ip&longs;ius altera&shy;<lb/>partelongioris di&longs;tortione in Rhomboides <expan abbr="tr&atilde;sfiguratum">transfiguratum</expan>: <lb/>&amp; ab ip&longs;a quidem fb diagonio in duo acutangula, ab ip&longs;a <arrow.to.target n="note248"/><lb/>vero ae in duo obtu&longs;angula triangula diui&longs;um. </s>
<s>At ip&longs;a <lb/>triangulorum &longs;patia &agrave; dimidio quadrangulorum, qu&aelig; ex ip <lb/>&longs;is de&longs;cribuntur, &longs;upputare oportet. </s>
<s>quandoquidem omne <lb/>etiam quadrangulum &agrave; diagonio in duo triangula &longs;ecatur, <lb/>quinquangulum ver&ograve; in tria, &longs;exangulum in quatuor, &amp; &longs;ic <lb/>deinceps diui&longs;iones fiant. </s>
<s>&amp; &longs;i area quidem quadranguli <lb/>1000 reperta fuerit, 500 trianguli area erit. </s>
<s>ver&ugrave;m qu&ograve;d <arrow.to.target n="note249"/><lb/>omne triangulum, quod tum intelligentia, tum &longs;en&longs;u per&shy;<lb/>cipitur tres angulos duobus rectis &aelig;quales habet, h&igrave;c mani <lb/>fe&longs;tum e&longs;t. </s>
<s>&longs;i enim omne quadrangulum quatuor rectis &aelig;&shy;<lb/>quales &longs;uos angulos habet, &agrave; diagonio ver&ograve; in duo di&longs;tin&shy;<lb/>guitur triangula, atque in &longs;ex angulos, alios quidem rectos, <lb/>alios ver&ograve; &longs;ecundum magis &amp; minus acutiores, <expan abbr="obtu&longs;iore&longs;-&qacute;ue">obtu&longs;iore&longs;&shy;<lb/>que</expan> euadentes: hi autem &longs;ex in omni quadrangulo quatuor <lb/>rectis &aelig;quales &longs;unt: vtrumque igitur duorum, qu&aelig; di&longs;tin<lb/>guuntur triangulorum tres angulos duobus rectis &aelig;quales <lb/>habebit: vnd&egrave; etiam omne, quod tum &longs;en&longs;u, tum phanta&shy;<arrow.to.target n="note250"/><lb/>&longs;ia percipi pote&longs;t. </s>
<s>De men&longs;uratione ver&ograve; earum, qu&aelig; Tra&shy;<lb/>pezi&aelig;, &amp; trapezoide&aelig; vocantur tamquam ab angulorum <lb/>&aelig;qualitate ordinatarum: <expan abbr="c&aelig;terarum&qacute;ue">c&aelig;terarumque</expan> c&ugrave;m ordinatarum, <lb/>tum inordinatarum figurarum Archimedes, &amp; Heron in <arrow.to.target n="note251"/><lb/>vniuer&longs;ali tractatione eruditioribus demon&longs;trarunt. </s>
<s>nos <lb/>autem eos, qui ad Mathematicas di&longs;ciplinas in&longs;tituuntur <lb/>excitare volentes, metricas commentationes floribus col-
<pb xlink:href="052/01/117.jpg"/>lectis compo&longs;uimus, an&longs;as &longs;uppo&longs;itionis propter prompti&shy;<lb/>tudinem pr&aelig;bentes, &amp; quod &longs;ane iuxta prouerbium dici&shy;<lb/>tur, in latere <expan abbr="figulin&atilde;">figulinam</expan> <expan abbr="art&etilde;">artem</expan> ip&longs;os addi&longs;cere iam &longs;uppo&longs;uimus. </s></p><p type="margin">
<s><margin.target id="note242"/>a</s></p><p type="margin">
<s><margin.target id="note243"/>b</s></p><p type="margin">
<s><margin.target id="note244"/>c</s></p><p type="margin">
<s><margin.target id="note245"/>d</s></p><p type="margin">
<s><margin.target id="note246"/>e</s></p><p type="margin">
<s><margin.target id="note247"/>f</s></p><p type="margin">
<s><margin.target id="note248"/>g</s></p><p type="margin">
<s><margin.target id="note249"/>h</s></p><p type="margin">
<s><margin.target id="note250"/>i</s></p><p type="margin">
<s><margin.target id="note251"/>k</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note252"/></s></p><p type="margin">
<s><margin.target id="note252"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>QVamuis quadrangulum &longs;it nomen genericum omnes figu&shy;<lb/>ras angulis quatuor pr&aelig;ditas in &longs;e continens, quadran&shy;<lb/>gulum tamen per excellentiam &agrave; Geometris vocatur <lb/>illa quadrilatera, quadrangula&queacute; figura, qu&aelig; &aelig;quilatera, necnon <lb/>rectangula e&longs;t. </s>
<s>vt docet Proclus in 18 commentario libri &longs;ecundi <lb/>in primum librum Elementorum Euclidis. </s>
<s>Autor autem in pr&aelig;&shy;<lb/>&longs;entia nomen hoc neque pro genere omnium quadrangularum fi&shy;<lb/>gurarum, neque pro iam dicta &longs;pecie &longs;u&longs;cepit, qu&aelig; per excellen&shy;<lb/>tiam quadrangulum dicitur: &longs;ed pro quadrangulo rectangulo, <lb/>cuius du&aelig; &longs;unt &longs;pecies, altera quidem iam dictum &aelig;quilaterum <lb/>&amp; rectangulum, quod &agrave; Gr&aelig;cis<emph.end type="italics"/> <foreign lang="greek">tetra/gwnon</foreign>, <emph type="italics"/>hoc est quadrangu&shy;<lb/>lum per excellentiam, &agrave; latinis quadratum appellatur: altera ve&shy;<lb/>r&ograve; rectangulum &amp; non &aelig;quilaterum, quod alterapartelongius <lb/>nuncupatur. </s>
<s>in his enim duobus tant&ugrave;m quadrangulis verum e&longs;t <lb/>quod ait Autor, nempe qu&ograve;d ex multiplicatione longitudinis in la&shy;<lb/>titudinem eorum area producitur. </s>
<s>in alijs autem quadrangulis, <lb/>qu&aelig; rectangula non &longs;unt, hoc verum e&longs;&longs;e minim&egrave; pote&longs;t.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note253"/></s></p><p type="margin">
<s><margin.target id="note253"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Planus numerus (vt docet Euclides in 16 definitione libri &longs;e&shy;<lb/>ptimi Elementorum) e&longs;t, qui ex duorum numerorum in &longs;e &longs;e in&shy;<lb/>uicem multiplicatione producitur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note254"/></s></p><p type="margin">
<s><margin.target id="note254"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Area figur&aelig; in Geometria (vt ip&longs;emet Autor in pr&aelig;&longs;entia <lb/>declarat) e&longs;t &longs;patium, qu&ograve;d &agrave; lateribus ip&longs;ius figur&aelig; circumqua&shy;<lb/>que terminatur, &longs;i figura plura habuerit latera: &longs;i ver&ograve; ab vnica <lb/>linea fuerit comprehen&longs;a, vt circulus, eius area &longs;patium illud e&longs;t, <lb/>quod &agrave; circumferentia continetur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note255"/></s></p><p type="margin">
<s><margin.target id="note255"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in &aelig;quilateris etiam quadrangulis] hoc e&longs;t in quadratis.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note256"/></s></p><p type="margin">
<s><margin.target id="note256"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Qua&longs;i &longs;imilem men&longs;urationem habere dicit Rhombos, &amp; Rhom&shy;<lb/>boides quadrangulas figuras iam dict&aelig; men&longs;urationi quadrati, <lb/>&amp; alterapartelongioris: quoniam non per multiplicationem qui&shy;<lb/>dem eorum longitudinis in latitudinem quemadmodum iam di-<emph.end type="italics"/>
<pb xlink:href="052/01/118.jpg"/><emph type="italics"/>cta duo rectangula quadrangula <expan abbr="men&longs;ur&atilde;tur">men&longs;urantur</expan>. </s>
<s>&longs;ed Rhombus qui&shy;<lb/>dem per multiplicationem vnius &longs;uarum diagoniorum in dimi&shy;<lb/>dium alterius earundem diagoniorum (qu&aelig; quidem men&longs;urandi <lb/>regula Rhombo, &amp; quadrato communis e&longs;t) Rhomboides ver&ograve; per <lb/>inuentionem are&aelig; alterius duorum, in quibus &agrave; diagonio diuidi&shy;<lb/>tur triangulorum, eiu&longs;dem&queacute; are&aelig; duplicationem: vt apud Auto&shy;<lb/>res materiam hanc diligenter pertractantes videre licet. </s>
<s>quod <lb/>etiam Autor innuens in pr&aelig;&longs;entia dixit [etenim latera termina&shy;<lb/>ta, vnam&queacute; diagonium datam habent] hoc e&longs;t latera terminata, <lb/>ideo&queacute; nobis cognita: vnam&queacute; diagonium datam, &longs;cilicet ex late&shy;<lb/>ribus repertam habent. </s>
<s>Cum enim latera terminata &longs;int, ea men&shy;<lb/>&longs;urare po&longs;&longs;umus: ex ip&longs;orum autem longitudine reperta, diago&shy;<lb/>niorum etiam longitudo data, ide&longs;t cognita nobis erit. </s>
<s>Diagonius <lb/>autem dicitur illa recta linea, qu&aelig; in figuris angularibus ab vno <lb/>earum angulo ad alterum earum angulum ex oppo&longs;ito iacentem <lb/>ducta figuram per medium diuidit. </s>
<s>qu&aelig; etiam diameter, &longs;iue di&shy;<lb/>metiens communiter appellatur. </s>
<s>nam Dimetiens quidem commu<lb/>ni nomine dicitur omnis recta linea figuram aliquam &longs;iue <expan abbr="plan&amacr;">planam</expan>, <lb/>&longs;iue &longs;olidam per medium diuidens: Diagonius ver&ograve; propri&egrave; in an&shy;<lb/>gularibus figuris: quemadmodum etiam dimetiens quidem pro&shy;<lb/>pri&egrave; in circulo, Axis vero in &longs;olidis figuris dicitur. </s>
<s>vt docet Pro&shy;<lb/>clus in 14 commentario &longs;ecundi libri in primum Elementorum <lb/>Euclidis. </s>
<s>Non immerito autem dixit Autor, qua&longs;i &longs;imilem e&longs;&longs;e <lb/>men&longs;urationem Rhombi, ac Rhomboidis men&longs;urationi quadrati, <lb/>&amp; alterapartelongioris: quoniam omnes i&longs;t&aelig; men&longs;urationes per <lb/>multiplicationem fiunt, &longs;ed diuer&longs;imode. </s>
<s>nempe rectangulorum <lb/>quidem, per multiplicationem lateris longitudinis in latus latitu&shy;<lb/>dinis eorum: non rectangulorum ver&ograve;, per multiplicationem dia&shy;<lb/>gonij vnius in dimidium alterius diagonij, vt in Rhombo: vel per <lb/>duplicationem vnius <expan abbr="eor&utilde;">eorum</expan>, in quibus a diagonio diui&longs;um e&longs;t trian&shy;<lb/>gulorum, vt in Rhomboide, qu&aelig; porr&ograve; duplicatio nil aliud qu&agrave;m <lb/>multipticatio per binarium e&longs;t. </s>
<s>Hanc autem men&longs;urationum i&longs;ta&shy;<lb/>rum &longs;imilitudinem ait Autor ex ea prouenire &longs;imilitudine, quam <lb/>Rhombus cum quadrato, &amp; Romboides cum alterapartelongiore <lb/>habet quandoquidem Rhombus quidem ex quadrati, Rhomboides <lb/>ver&ograve; ex alterapartelongioris distortione fiunt. </s>
<s>vt ip&longs;e quoque <lb/>Proclus in &longs;uperi&ugrave;s dicto 18 commentario declarauit. </s>
<s>Pote&longs;t au-<emph.end type="italics"/>
<pb xlink:href="052/01/119.jpg"/><emph type="italics"/>tem Rhombus, ac Rhomboides qua&longs;i &longs;imilem, ac cuidentem (vt <lb/>ait Autor) men&longs;urationem habere, men&longs;urationi &longs;cilicet qua&shy;<lb/>drati, &amp; altera parte longioris, hoc etiam modo. </s>
<s>qu&ograve;d nempe &longs;u&shy;<lb/>per vno Rhombi, vel Rhomboidis latere, &amp; in ei&longs;dem Parallelis <lb/>eorum lateribus, altero videlicet producto, alterapartelongius <lb/>con&longs;tituatur, quod per 35 propo&longs;itionem primi Elementorum Eu&shy;<lb/>clidis &aelig;quale ip&longs;is erit. </s>
<s>huius enim alterapartelongioris area (vt <lb/>docet Autor) men&longs;urata, Rhombi quoque, &longs;eu Rhomboidis eius <lb/>&aelig;qualis aream habebimus. </s>
<s>atque h&aelig;c etiam Rhombi, <expan abbr="Rhomboidi&longs;-&qacute;ue">Rhomboidi&longs;&shy;<lb/>que</expan> men&longs;uratio quadrati, &amp; altera parte longioris men&longs;urationi <lb/>qua&longs;i &longs;imilis, ac euidens erit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note257"/></s></p><p type="margin">
<s><margin.target id="note257"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Animaduertendum autem e&longs;t, qu&ograve;d c&ugrave;m dicit Autor <expan abbr="rhomb&utilde;">rhombum</expan> <lb/>quidem ex duobus &aelig;quicruribus, rhomboides uer&ograve; ex duobus acu&shy;<lb/>tangulis, vel obtu&longs;angulis triangulis componi: non e&longs;t hoc ita in&shy;<lb/>telligendum qu&ograve;d non po&szlig;it etiam rhombus quidem ex duobus &aelig;&shy;<lb/>quilateris, rhomboides ver&ograve; ex duobus rectangulis componi trian<lb/>gulis quandoquidem quadratum quidem, &amp; alterapartelongius <arrow.to.target n="note258"/><lb/>c&ugrave;m rectangula &longs;int, ex duobus rectangulis triangulis alterum <lb/>quidem &aelig;quicruribus, alterum ver&ograve; &longs;calenis &longs;emper componun&shy;<lb/>tur, in qu&aelig; etiam di&longs;&longs;oluuntur: Rhombus ver&ograve; ex duobus &aelig;quila&shy;<lb/>teris acutangulis, vel &aelig;quicruribus tum acutangulis, tum obtu&shy;<lb/>&longs;angulis, &longs;ed numquam ex rectangulis, vel &longs;calenis: Rhomboides <lb/>autem, &longs;emper ex &longs;calenis tum acutangulis, tum obtu&longs;angulis, <lb/>tum etiam rectangulis. </s>
<s>Qu&ograve;d enim rhombus ex &aelig;quilateris etiam <lb/>triangulis componi po&szlig;it manifestum nobis erit, &longs;i in eadem recta <lb/>linea duo &aelig;quilatera triangula alterum quidem &longs;ur&longs;um, alterum <lb/>ver&ograve; deor&longs;um con&longs;tituantur, quippe qu&aelig; dubio procul rhombum <lb/>efficient. </s>
<s>qu&ograve;d autem rhomboides ex duobus etiam rectangulis <lb/>triangulis componatur per&longs;picuum nobis erit &longs;i dato &longs;caleno re&shy;<lb/>ctangulo triangulo ab eius angulo recto recta linea parallela, &amp; <lb/>&aelig;qualis eius lateri rectum angulum &longs;ubtendenti ad eas partes <lb/>ducatur, in quibus e&longs;t angulus eius minimus, &amp; cum iam dicto la&shy;<lb/>tere per aliam rectam lineam coniungatur. </s>
<s>&longs;ic enim ex duobus <lb/>rectangulis triangulis rhomboides componetur. </s>
<s>vt ijs, qui ali&shy;<lb/>quantulum in Geometria ver&longs;ati &longs;unt, ignotum non e&longs;t. </s>
<s>Ver&ugrave;m <arrow.to.target n="note259"/><lb/>pr&aelig;tereundum etiam non e&longs;&longs;e exi&longs;timo qu&ograve;d illud quod ait Autor, <lb/>qu&ograve;d &longs;cilicet in pr&aelig;cedenti diagrammate rhomboides a b e f, ab<emph.end type="italics"/>
<pb xlink:href="052/01/120.jpg"/><emph type="italics"/>ip&longs;a fb diagonio in duo acutangula triangula diuiditur, omnino <lb/>fal&longs;um e&longs;t. </s>
<s>&longs;i enim hoc verum e&longs;&longs;et, &longs;equeretur per penultimam <lb/>propo&longs;itionem &longs;ecundi libri Elementorum Euclidis qu&ograve;d quadra&shy;<lb/>tum lateris af e&longs;&longs;et minus quadratis ip&longs;arum ab &amp; bf &longs;imul <lb/>iunctis: &longs;imiliter&queacute; quadratum ip&longs;ius be minus e&longs;&longs;et quadratis <lb/>ip&longs;arum ef, fb &longs;imul iunctis, quod fal&longs;um e&longs;t. </s>
<s>quoniam qua&shy;<lb/>dratum quidem tum ip&longs;ius af, tum ip&longs;ius be, 6561: quadratum <lb/>autem ip&longs;ius ab, necnon ip&longs;ius fe, 225: quadratum ver&ograve; ip&longs;ius <lb/>fb, 5328 vt patet per penultimam primi libri Elementorum Eu&shy;<lb/>clidis, ducta &longs;cilicet perpendiculari &agrave; &longs;igno f ad ip&longs;am be. </s>
<s>quare <lb/>quadratum 6561 quadratis 5328, &amp; 225 &longs;imul iunctis, hoc e&longs;t <lb/>ip&longs;is 5553 minus e&longs;&longs;e non potest. </s>
<s>patet igitur fal&longs;itas eius qu&ograve;d <lb/>dicit Autor. </s>
<s>forta&longs;&longs;e autem h&aelig;c ab Autore in pr&ecedil;&longs;entia non ita di&shy;<lb/>ligenter quemadmodum &agrave; Geometris con&longs;iderata &longs;unt.<emph.end type="italics"/><lb/><arrow.to.target n="note260"/></s></p><p type="margin">
<s><margin.target id="note258"/>Regula <lb/>generalis</s></p><p type="margin">
<s><margin.target id="note259"/><expan abbr="No'&atilde;d&utilde;">Notandum</expan>.</s></p><p type="margin">
<s><margin.target id="note260"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Pr&aelig;terea ver&ograve; adnotandum e&longs;t qu&ograve;d illud, quod ait Autor [at <lb/>ip&longs;a triangulorum &longs;patia &agrave; dimidio quadrangulorum, qu&aelig; ex ip&longs;is <lb/>de&longs;cribuntur, &longs;upputare oportet.] &longs;ic intelligendum e&longs;t. </s>
<s>qu&ograve;d &longs;ci&shy;<lb/>licet dato <expan abbr="quocumq;">quocumque</expan> triangule, cuius aream men&longs;urare debemus, <lb/>quadrangulum ex ip&longs;o de&longs;cribendum e&longs;t, hoc e&longs;t ab vno eius angu&shy;<lb/>lorum vni eius laterum parallela &amp; &aelig;qualis recta linea producen<lb/>da est, parallelogramum&queacute; complendum: cuius area modis qui&shy;<lb/>bus &longs;uperi&ugrave;s diximus reperienda, <expan abbr="eius&qacute;ue">eiusque</expan> dimidium quantitas <lb/>are&aelig; trianguli propo&longs;iti affirmanda e&longs;t. </s>
<s>quoniam omne parallelo<lb/>grammum &longs;uper eadem ba&longs;i, &amp; in ei&longs;dem parallelis cum triangu&shy;<lb/>lo exi&longs;tens, duplum ip&longs;ius trianguli e&longs;t, vt Euclides in 41 propo&longs;i&shy;<lb/>tione primi Elementorum demon&longs;trauit. </s>
<s>&amp; hoc quidem est, quod <lb/>ait Autor, quod &longs;cilicet ip&longs;a triangulorum &longs;patia &agrave; dimidio qua&shy;<lb/>drangulorum, qu&aelig; ex ip&longs;is de&longs;cribuntur &longs;upputare oportet. </s>
<s>atque <lb/>hoc pacto triangulorum omnium areas facil&egrave; men&longs;urare po&longs;&longs;u&shy;<lb/>mus. </s>
<s>quamuis etiam multis alijs pulcherrimis regulis men&longs;urari <lb/>po&szlig;int, quas multi alij Autores diligenti&szlig;imi tradidere.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note261"/></s></p><p type="margin">
<s><margin.target id="note261"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[omne triangulum, quod tum intelligentia, tum &longs;en&longs;u percipi&shy;<lb/>tur] De duplici triangulo &longs;ermonem hic habet Autor, altero qui&shy;<lb/>dem, quod intelligentia percipitur, hoc e&longs;t in phanta&longs;ia tamquam <lb/>in materia intelligibili mathematicis formis &longs;ubiecta impre&longs;&longs;um <lb/>&agrave; cognitatione intelligitur: altero ver&ograve;, quod &longs;en&longs;u deprehenditur, <lb/>hoc e&longs;t in aliqua &longs;en&longs;ibili materia cernitur. </s>
<s>de hoc auiem &longs;en&longs;ibili<emph.end type="italics"/>
<pb xlink:href="052/01/121.jpg"/><emph type="italics"/>triangulo pr&aelig;&longs;ens de men&longs;uratione tractatio, &longs;iue Geod&aelig;&longs;ia ip&longs;a <lb/>pertractat. </s>
<s>quare paul&ograve; inferi&ugrave;s per inductionem concludens Au&shy;<lb/>tor inquit [vnd&egrave; etiam omne, quod tum phanta&longs;ia, tum &longs;en&longs;u per&shy;<lb/>cipi pote&longs;t] &longs;cilicet triangulum, tres angulos duobus rectis &aelig;qua&shy;<lb/>les habet.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note262"/></s></p><p type="margin">
<s><margin.target id="note262"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Qu&aelig;nam &longs;int Trapezi&aelig;, &amp; Trapezoide&aelig; figur&aelig;, earum&queacute; &longs;pe&shy;<lb/>cies eleganti&szlig;im&egrave; docet Proclus in commentario 18 &longs;ecundi libri <lb/>in primum librum Elementorum Euclidis. </s>
<s>quas quidem ordina&shy;<lb/>tas e&longs;&longs;e dicit Autor ab angulorum &aelig;qualitate, quoniam quidam in <lb/>eis anguli &longs;ibiinuicem &aelig;quales extant: ad differentiam aliarum <lb/>figurarum inordinatarum nullos angulos &aelig;quales habentium. </s>
<s><lb/>Harum autem omnium c&ugrave;m ordinatarum, tum inordinatarum <lb/>figurarum nullam tradidit Autor men&longs;urationem, duabus de cau<lb/>&longs;is. </s>
<s>prim&ograve; quoniam (vt ait ip&longs;e) Archimedes, &amp; Heron, &longs;cilicet <lb/>Alexandrinus eam eruditioribus demon&longs;trarunt in vniuer&longs;ali <lb/>tractatione. </s>
<s>hoc e&longs;t in quadam tractatione, qu&aelig; non de men&longs;ura&shy;<lb/>tione linearum, &longs;uperficierum, &amp; corporum &longs;en&longs;ibilium ad rem mi <lb/>litarem &longs;pectante tractat: &longs;ed in vniuer&longs;um de <expan abbr="m&etilde;&longs;uratione">men&longs;uratione</expan> linea&shy;<lb/>rum, &longs;uperficierum, &amp; corporum intelligibilium quatenus line&aelig;, <lb/>&longs;uperficies, &amp; corpora &longs;unt. </s>
<s>h&aelig;c autem Archimedis, &amp; Heronis <lb/>vniuer&longs;alis de men&longs;uratione tractatio de&longs;ideratur. </s>
<s>&longs;ecund&ograve; quo&shy;<lb/>niam omnes Trapezi&aelig;, &amp; Trapezoide&aelig;, necnon c&aelig;ter&aelig; tum ordi&shy;<lb/>nat&aelig;, tum inordinat&aelig; rectiline&aelig; figur&aelig; in triangula re&longs;&longs;olui, per <lb/>ip&longs;a&queacute;, (&longs;icut ip&longs;e docuit) men&longs;urari po&longs;&longs;unt. </s>
<s>c&ugrave;m enim propo&longs;itum <lb/>Autoris in hoc opere &longs;it men&longs;urationem linearum &longs;uperficierum, <lb/>&amp; corporum &longs;en&longs;ibilium docere, quatenus rei militari nece&longs;&longs;aria <lb/>e&longs;t: noluit amplam, ac perfectam men&longs;urandi doctrinam (quem&shy;<lb/>admodum alij Autores fecerunt) tradere: &longs;ed (vt ip&longs;e ait) flo&shy;<lb/>&longs;culis collectis ha&longs;ce metricas, hoc est aliquam men&longs;urandi doctri&shy;<lb/>nam continentes commentationes compo&longs;uit: an&longs;as &longs;uppo&longs;itionis, <lb/>ide&longs;t &longs;ubiect&aelig;, de qua nunc agit, materi&aelig;, pr&aelig;bens, &longs;cilicet ijs, qui <lb/>vt ob&longs;idionis gratia prompti &longs;int in capiendis men&longs;urando ciuita&shy;<lb/>tum &longs;itibus ad mathematicas di&longs;ciplinas in&longs;tituuntur. </s>
<s>ac demum <lb/>quodam antiquo pulcherrimo&queacute; prouerbio inquit &longs;e &longs;uppo&longs;ui&longs;&longs;e ip&shy;<lb/>&longs;os in latere figulinam artem addi&longs;cere, hoc e&longs;t in rerum bellica&shy;<lb/>rum v&longs;u men&longs;urandi facultatem aquirere, eius instar, qui <expan abbr="figu-lin&atilde;">figu&shy;<lb/>linam</expan> artem in latere conficiendo addi&longs;cit. </s>
<s>c&ugrave;m enim aliquam &longs;cien<emph.end type="italics"/><pb xlink:href="052/01/122.jpg"/><emph type="italics"/>tiam addi&longs;cimus in eo human&aelig; vit&aelig; v&longs;u, cui vtilis, ac nece&longs;&longs;aria <lb/>e&longs;t: tunc in latere figulinam artem addi&longs;cere iuxta iam dictum <lb/>antiquum prouerbium dicimur. </s>
<s>Ver&ugrave;m &longs;i de quadrilaterorum <lb/>&longs;patiorum men&longs;uratione perfectam h&igrave;c doctrinam tradere velle&shy;<lb/>mus. </s>
<s>plura nobis e&longs;&longs;ent dicenda: quoniam autem ab alijs autoribus <lb/>materia h&aelig;c diligenti&szlig;im&egrave; pertracta fuit, &amp; pr&aelig;&longs;ertim &agrave; Saua&longs;&shy;<lb/>&longs;orda hebreo docti&szlig;imo viro, in libro de dimen&longs;ionibus arearum: <lb/>&amp; ab Er&longs;emide in libro de dimen&longs;ionibus, quos nos iam re&longs;taura&shy;<lb/>uimus, &amp; impre&longs;&longs;oribus excudendos annuente Deo tradituri &longs;u&shy;<lb/>mus: necnon &agrave; nobis in quodam no&longs;tro de hac re opu&longs;culo, quod <lb/>etiam &aelig;dituri &longs;umus: idcirco paucula h&aelig;c pro dilucidatione pr&aelig;&shy;<lb/>&longs;entis propo&longs;itionis breuiter &agrave; nobis adnotata &longs;ufficiant.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>SCHOLIVM ANTIQVVM<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>INCERTI AVTORIS IN PRAESENTEM<emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>quintam propo&longs;itionem &agrave; Franci&longs;co Batocio &egrave; gr&aelig;co <lb/>in latinum &longs;ermonem conuer&longs;um.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note263"/></s></p><p type="margin">
<s><margin.target id="note263"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>NAm ea, qu&aelig; ad men&longs;urationem, ac figurationem &agrave; longe <lb/>incert&aelig; magnitudinis &longs;uper terra iacent &longs;patia, milita&shy;<lb/>rem &longs;cientiam c&ugrave;m ad ob&longs;idionem, tum ad pugn&aelig; re&longs;i&longs;ten&shy;<lb/>tiam ordinatim in&longs;tituere con&longs;ueuere. </s>
<s>etenim qui exercitui pr&aelig;&shy;<lb/>e&longs;t ad quadratorum, &longs;iue alterapartelongiorum &longs;patiorum ma&shy;<lb/>gnitudines re&longs;piciens, quot milites iuxta pede&longs;trem ordinem tum <lb/>velites, tum cetratos, vel tum ha&longs;tatos, tum iaculatores iuxta <arrow.to.target n="note264"/><lb/>phalangarchiam &longs;u&longs;cipient: necnon rhomboidum ad turm&aelig; ordi&shy;<lb/>nes quot milites &longs;imul eorum, qui tamquam ad iugum &longs;ecundum <lb/>longitudinem coniunguntur, quos gr&aelig;ci<emph.end type="italics"/> <foreign lang="greek">zugoiw/tas</foreign>, <emph type="italics"/>&amp; qui in &longs;e&shy;<lb/>rie &longs;ecundum cra&szlig;itiem collocantur, quos gr&aelig;ci<emph.end type="italics"/> <foreign lang="greek">stoixoiw/tas</foreign> <emph type="italics"/><expan abbr="vo-c&atilde;t">vo&shy;<lb/>cant</expan>, ex impari numero: &longs;iue<emph.end type="italics"/> <foreign lang="greek">zugoiw/tas</foreign> <emph type="italics"/><expan abbr="quid&etilde;">quidem</expan> &amp; <expan abbr="n&otilde;">non</expan><emph.end type="italics"/> <foreign lang="greek">stoixoiw/tas</foreign>, <lb/><emph type="italics"/>vel&egrave; contra, expari: &amp; quonam pacto &agrave; medio iugo lateralibus cu <arrow.to.target n="note265"/><lb/>&longs;todibus in duo di&longs;&longs;ectis embola, &longs;iue &longs;phinoideas &agrave; tergo figuras <arrow.to.target n="note266"/><lb/>nominatas iuxta turmarium, iuxta ver&ograve; ductorem extrema par&shy;<lb/>tis, &longs;iue &longs;ini&longs;tri cornu, vel caud&aelig; exercitus<emph.end type="italics"/> <foreign lang="greek">ou)rago/n</foreign> <emph type="italics"/>&agrave; gr&aelig;cis di&shy;<lb/>ctum, retror&longs;um: &amp; quomodo oporteat phalangem ad locorum &longs;i&shy;<lb/>tus iuxta dextrum, ac &longs;ini&longs;trum cornu in decurias di&longs;tinguere,<emph.end type="italics"/>
<pb xlink:href="052/01/123.jpg"/><emph type="italics"/>contrari&aelig; progre&szlig;ionis, &longs;eu alterius cornu ho&longs;tium circumuentio&shy;<lb/>nis gratia. </s>
<s>&amp; quoniam iuxta cra&szlig;itudinem agmen &longs;ingulum octo <lb/>vel duodecim virorum propter bipertitam diui&longs;ionem &longs;ecundum <lb/>quo&longs;dam ordinatur: plurium ver&ograve; <expan abbr="quandoq;">quandoque</expan>, ac pauciorum iux&shy;<lb/>ta parem numerum, qui iuxta ip&longs;am pede&longs;trium, &amp; eque&longs;trium <arrow.to.target n="note267"/><lb/>multitudinem ad unitatem v&longs;que diuiditur. </s>
<s>&longs;it igitur agmen, to&shy;<lb/>ta ver&ograve; phalanx &longs;edecim milium trecentorum octogintaquatuor. </s>
<s><lb/>quare 1024 &longs;unt qui &agrave; tergo phalangis de&longs;ignati existunt mani&shy;<lb/>pulares. </s>
<s>manife&longs;tum e&longs;t autem qu&ograve;d ordinati quidem, &longs;eu ver&oacute; <lb/>gratia &agrave; cubitis quatuor di&longs;tantes, 4096 iuxta confinium habe&shy;<lb/>bunt, c&ugrave;m &longs;tadia <expan abbr="dec&etilde;">decem</expan>, &amp; cubiti 96 &longs;int: contracti ver&ograve; vt &agrave; duo&shy;<lb/>bus cubitis, &longs;tadia quinque, &amp; cubiti 48: &longs;ecund&ugrave;m autem cubi&shy;<lb/>tum vnum conglutinati, duo cum dimidio, &amp; cubiti vigintiqua&shy;<arrow.to.target n="note268"/><lb/>tuor. </s>
<s>stadio quidem centum pa&longs;&longs;uum, pa&longs;&longs;u cubitorum quatuor, <lb/>&amp; cubito dodrantium duorum, digitorum autem <expan abbr="eti&atilde;">etiam</expan> vigintiqua&shy;<lb/>tuor exi&longs;tente. </s>
<s>H&aelig;c &longs;cientes exercituum ductores, ip&longs;os ver&ograve; lo&shy;<lb/>corum &longs;itus iuxta figuram, ac magnitudinem eligentes &agrave; longe: <lb/>ordinat&egrave;, ac &longs;ine periculo itinera facient, tum in ob&longs;idionibus, tum <lb/>in re&longs;i&longs;tentijs contrarios deuincentes.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note264"/>b</s></p><p type="margin">
<s><margin.target id="note265"/>c d</s></p><p type="margin">
<s><margin.target id="note266"/>e</s></p><p type="margin">
<s><margin.target id="note267"/>f</s></p><p type="margin">
<s><margin.target id="note268"/>g</s></p><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>SVperius antiquum incerti Autoris &longs;cholium in libri mar&shy;<lb/>gine &longs;criptum inuenimus, forta&longs;&longs;e autem ip&longs;iu&longs;met Hero&shy;<lb/>nis e&longs;t c&ugrave;m propter phra&longs;is &longs;imilitudinem, tum propter do&shy;<lb/>ctrinam in eo contentam. </s>
<s>multa enim hoc in &longs;cholio magna cum <lb/>breuitate, non parua&queacute; ob&longs;curitate tanguntur, qu&aelig; ex ip&longs;ius &longs;cien&shy;<lb/>ti&aelig; militaris vi&longs;ceribus excerpta fuerunt: vt ijs per&longs;picuum e&longs;t, <lb/>qui in ip&longs;a militari doctrina diu ver&longs;ati &longs;unt. </s>
<s>nos autem ne pr&aelig;&shy;<lb/>ter in&longs;titutum in pr&aelig;&longs;entia nimis prolixo &longs;ermone vtamur, pau&shy;<lb/>cula qu&aelig;dam ad iam dicti &longs;cholij faciliorem intelligentiam breui&shy;<lb/>ter explicabimus. </s>
<s>&longs;unt autem h&aelig;c.<emph.end type="italics"/><lb/><arrow.to.target n="note269"/></s></p><p type="margin">
<s><margin.target id="note269"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Nam ea, qu&aelig; ad men&longs;urationem &amp;c.] Propo&longs;itio h&aelig;c licet qua&shy;<lb/>dam verborum ob&longs;curitate propo&longs;ita &longs;it, &longs;ic tamen intelligenda <lb/>e&longs;t. </s>
<s>qu&ograve;d &longs;cilicet camporum, locorum, &longs;ituum&queacute; &longs;patia incert&aelig; ma&shy;<lb/>gnitudinis, qu&aelig; &longs;uper terra circumcirca ciuitatem ob&longs;idendam<emph.end type="italics"/>
<pb xlink:href="052/01/124.jpg"/><emph type="italics"/>iacent, ad men&longs;urationem, ac figurationem &agrave; longe, ide&longs;t apta na&shy;<lb/>ta vt &agrave; longe men&longs;urentur, atque figurentur, nempe vt geometri&shy;<lb/>cis regulis, ac in&longs;trumentis men&longs;urerentur quanta &longs;int, ad figu&shy;<lb/>ras&queacute; geometricas reducantur: h&aelig;c (inquam) men&longs;uranda, fi&shy;<lb/>guranda&queacute; &longs;patia militarem &longs;cientiam c&ugrave;m ad ob&longs;idionem, tum ad <lb/>pugn&aelig; re&longs;i&longs;tentiam ordinatim in&longs;tituere con&longs;ueuere. </s>
<s>quoniam &longs;ci&shy;<lb/>licet ab&longs;que iam dictorum &longs;patiorum men&longs;uratione, ac figuratio&shy;<lb/>ne militaris &longs;cientia neque ob&longs;idionem, neque pugn&aelig; re&longs;i&longs;tentiam <lb/>ordinatim edocere pote&longs;t. </s>
<s>talis e&longs;t h&aelig;c propo&longs;itio, qu&aelig; in toto pr&aelig;&shy;<lb/>&longs;enti &longs;cholio rationibus confirmatur. </s>
<s>c&ugrave;m o&longs;tendatur qu&ograve;d &longs;ine <lb/>quadratorum, alterapartelongiorum, rhomborum, <expan abbr="atq;">atque</expan> rhomboi&shy;<lb/>dorum figuratione, ac men&longs;uratione qui exercitui pr&aelig;e&longs;t quanti&shy;<lb/>tatem diuer&longs;orum c&ugrave;m pede&longs;trium tum eque&longs;trium militum, qu&aelig; <lb/>in iam dictis quadrangulis &longs;patijs collocanda e&longs;t, multa&queacute; alia h&igrave;c <lb/>breuiter enucleata militaris &longs;cienti&aelig; nece&longs;&longs;aria &longs;cire minim&egrave; po&shy;<lb/>te&longs;t. </s>
<s>H&aelig;c e&longs;t totius pr&aelig;&longs;entis antiqui &longs;cholij &longs;ententia, quod qu&agrave;m <lb/>nece&longs;&longs;aria militari &longs;cienti&aelig; &longs;uperior quinta propo&longs;itio &longs;it, nobis <lb/>o&longs;tendit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note270"/></s></p><p type="margin">
<s><margin.target id="note270"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Phalangarchia e&longs;t acies quadrata continens armatos milites <lb/>4096. ex quatuor autem phalangarchijs vna phalanx componi&shy;<lb/>tur continens armatos milites 16384.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note271"/></s></p><p type="margin">
<s><margin.target id="note271"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[lateralibus cu&longs;todibus] hoc e&longs;t eius phalangis, qu&aelig; plagia vo&shy;<lb/>catur, latera cu&longs;todientibus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note272"/></s></p><p type="margin">
<s><margin.target id="note272"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Embolum e&longs;t dimidium rhombi militibus pleni.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note273"/></s></p><p type="margin">
<s><margin.target id="note273"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Sphinoides e&longs;t rhomboides figura exercitus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note274"/></s></p><p type="margin">
<s><margin.target id="note274"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;it igitur agmen, &amp;c.] in hac poti&szlig;im&ugrave;m &longs;cholij parte demon<lb/>&longs;tratur qu&agrave;m nece&longs;&longs;aria &longs;it cognitio men&longs;urationis, ac figurationis <lb/>quadratorum et, qui exercitus ordinaturus e&longs;t. </s>
<s>Ponitur enim pha&shy;<lb/>lanx 16384 militum ex quatuor phalangarchijs con&longs;tans, <expan abbr="quar&utilde;">quarum</expan> <lb/>quodlibet latus 1024 milites continet. </s>
<s>&longs;i igitur quatuor cubitis &agrave; <lb/>&longs;einuicem ip&longs;i 1024 milites di&longs;titerint, dubio procul 4096 cubito&shy;<lb/>rum quoad longitudinem eorum confinium erit. </s>
<s>hoc est decem &longs;ta&shy;<lb/>diorum, &amp; 96 cubitorum. </s>
<s>&longs;iquidem quodlibet &longs;tadium 400 cubi&shy;<lb/>tos in &longs;e continet. </s>
<s>&longs;i ver&ograve; milites ip&longs;i ita contrahantur vt duobus <lb/>cubitis abinuicem di&longs;tent, stadia quinque &amp; cubiti 48 eorum con&shy;<lb/>finium erit. </s>
<s>&longs;i autem &longs;ecund&ugrave;m cubitum vnum conglutinentur, <lb/>&longs;tadia duo cum dimidio, &amp; cubitos 24 eorum confinium contine-<emph.end type="italics"/>
<pb xlink:href="052/01/125.jpg"/><emph type="italics"/>bit. </s>
<s>Confinium autem h&igrave;c pro longitudine totius lateris ip&longs;ius pha&shy;<lb/>langarchi&aelig; &longs;u&longs;cipitur. </s>
<s>vnd&egrave; adnotandum e&longs;t qu&ograve;d numerus mi&shy;<lb/>litum phalangarchi&aelig; numquam variat, quandoquidem &longs;emper <lb/>est 4096. &amp; hic e&longs;t numerus <expan abbr="milit&utilde;">militum</expan> quatuor quadrati latera com&shy;<lb/>pletium. </s>
<s>numerus ver&ograve; confinij quandoque idem e&longs;t cum phalan&shy;<lb/>garchi&aelig; numero, quandoque ab eo di&longs;crepat. </s>
<s>&longs;i enim quatuor cu&shy;<lb/>bitis milites inuicem di&longs;titerint, idem erit numerus confinij cum <lb/>phalangarchi&aelig; numero: &longs;i ver&ograve; duobus, vel vnico tant&ugrave;m, aut <lb/>etiam pluribus qu&agrave;m quatuor di&longs;titerint cubitis, tunc numerus <lb/>confinij &agrave; phalangarchi&aelig; numero differt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note275"/></s></p><p type="margin">
<s><margin.target id="note275"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[stadio quidem centum pa&longs;&longs;uum &amp;c.] Quoniam hic geometri&shy;<lb/>carum men&longs;urarum &longs;it mentio, adnotandum e&longs;&longs;e cen&longs;eo, qu&ograve;d di&shy;<lb/>gitus e&longs;t omnium geometricarum men&longs;urarum minima, <expan abbr="qu&etilde;">quem</expan> qua&shy;<lb/>tuor grana hordei <expan abbr="&longs;ecund&atilde;">&longs;ecundam</expan> latitudinem contigu&egrave; po&longs;ita conficiunt. </s>
<s><lb/>vncia ver&ograve; habet tres digitos: palmus, quatuor; dichas, duos pal&shy;<lb/>mos: &longs;pithame, &longs;iue dodrans, tres palmos: pes, quatuor palmos: <lb/>&longs;e&longs;quipes, &longs;iue cubitus, &longs;expalmos: gradus pedes duos. </s>
<s>pa&longs;&longs;us, <expan abbr="a&utilde;t">aut</expan> <lb/>duplex e&longs;t, alter &longs;implex, alter Geometricus: &longs;implex quidem ha&shy;<lb/>bet duos pedes cum dimidio, Geometricus ver&ograve; dupliciter etiam <lb/>ab autoribus acceptus e&longs;&longs;e videtur: &agrave; gracis enim &longs;ex pedes, &agrave; la&shy;<lb/>tinis ver&ograve; quinque tant&ugrave;m continere dicitur. </s>
<s>pertica duos habet <lb/>pedes. </s>
<s>&longs;tadium &longs;ecund&ugrave;m Gr&aelig;cos centum, &longs;ecund&ugrave;m latinos 125 <lb/>pa&szlig;ibus con&longs;tat. </s>
<s>leuca 1500 pa&longs;&longs;us continet. </s>
<s>milliarius italicus <lb/>1000 pa&longs;&longs;us habet. </s>
<s>vnde iuxta Gr&aelig;cos quidem &longs;tadium decima, <lb/>iuxta Latinos autem octaua milliarii pars e&longs;t. </s>
<s>Quibus &longs;ic adnota&shy;<lb/>tis manife&longs;tum e&longs;t qu&ograve;d digiti duodecim dodrantem <expan abbr="vn&utilde;">vnum</expan>, duo do&shy;<lb/>drantes vnum cubitum, quatuor cubiti &longs;ecund&ugrave;m Gr&aelig;cos, vel tres <lb/>&amp; pars tertia &longs;ecundum Latinos, pa&longs;&longs;um vnum: centum pa&longs;&longs;us <lb/>&longs;ecund&ugrave;m Gr&aelig;cos, vel 125 &longs;ecundum Latinos vnum &longs;tadium: octo <lb/>&longs;tadij &longs;ecund&ugrave;m Gr&aelig;cos, aut decem &longs;ecundum Latinos vnum mil&shy;<lb/>liarium efficiunt. </s>
<s>Quare per&longs;picuum e&longs;t iuxta Gr&aelig;cos quod in <lb/>&longs;cholio dicitur, nempe qu&ograve;d &longs;tadium quidem 100 pa&longs;&longs;uum exi&longs;tit, <lb/>pa&longs;&longs;us cubitorum quatuor, &amp; cubitus dodrantium duorum, vel <lb/>etiam 24 digitorum. </s>
<s>H&aelig;c quoque pro dilucidatione pr&aelig;&longs;entis an&shy;<lb/>tiqui &longs;cholij breuiter &agrave; nobis enucleata &longs;int.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/126.jpg"/><p type="main">
<s><emph type="center"/>Propo&longs;itio Sexta.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note276"/></s></p><p type="margin">
<s><margin.target id="note276"/>a</s></p><p type="main">
<s>CIrculi autem dimetientem, &amp; eum, qui ad ip&shy;<arrow.to.target n="note277"/><lb/>&longs;am fit ambitum, ac totum &longs;patium cum dio&shy;<lb/>ptra reperiemus in circuli centro &longs;tantes, cir&shy;<lb/>cumferenti&aelig; non appropinquantes. </s>
<s>Sit igitur <arrow.to.target n="note278"/><lb/>circuli centrum a, in quo dioptram &longs;tatuo, &amp; <lb/>c&ugrave;m con&longs;tituero tympanum, quod in ip&longs;a e&longs;t, ad &longs;itum pla&shy;<lb/>ni, &longs;uper quo is, qui ex dioptria circulus de&longs;cribendus e&longs;t: <lb/>&longs;u&longs;cipio &longs;ignum per foramina regul&aelig; in directum ip&longs;um b, <lb/>&amp; ab eodem &longs;igno circulariter tympanum vn&agrave; cum regula <arrow.to.target n="note279"/><lb/>circumduco per incumbentem modio modiolum, aut per <arrow.to.target n="note280"/><lb/>caulem in dioptra for&longs;an exi&longs;tente: donec rur&longs;us in eodem <lb/>&longs;igno &longs;ecund&ugrave;m datum planum circumductio fiat, &agrave; quo <lb/>etiam moueri c&ecedil;perat. </s>
<s>in hac autem circulari circumuolu&shy;<lb/>tione &longs;i&shy;<lb/><arrow.to.target n="fig1"/><lb/>gna qu&ecedil;&shy;<lb/>dam <expan abbr="cir-cul&utilde;">cir&shy;<lb/>culum</expan> <expan abbr="cir-cumter-min&atilde;tia">cir&shy;<lb/>cumter&shy;<lb/>minantia</expan> <lb/>ad &longs;axa, <lb/>vel arbu<lb/>&longs;ta, vel <lb/><expan abbr="quo&longs;d&atilde;">quo&longs;dam</expan> <lb/>alios fa&shy;<lb/>cil&egrave; ex&shy;<lb/>plorabi&shy;<lb/>les &longs;co&shy;<lb/>pos a&longs;pi<lb/>cientur. </s>
<s><lb/>qualia <lb/>&longs;unt bc <lb/>defgi <lb/>klmnx <lb/>op. </s>
<s><expan abbr="atq;">atque</expan> <lb/>h&aelig;c in ip&longs;a circuli circumterminatione c&ugrave;m annotauero,
<pb xlink:href="052/01/127.jpg"/>illud, quod ab a &longs;igno ad b &longs;ignum, &longs;iue id, quod &agrave; centro <lb/>ad circumferentiam e&longs;t interuallum metior, <expan abbr="quemadmod&utilde;">quemadmodum</expan> <lb/>in longitudine, <expan abbr="latitudinem&qacute;ue">latitudinemque</expan> didicimus. </s>
<s>&amp; c&ugrave;m ip&longs;um <arrow.to.target n="note281"/><lb/>pa&longs;&longs;uum forta&longs;&longs;e 105 inuenero, totam etiam circuli dime&shy;<arrow.to.target n="note282"/><lb/>tientem 210 habeo, tamquam eius, qu&aelig; ex centro, duplam. </s>
<s><lb/>quoniam autem omnis dimetientis triplus&longs;e&longs;qui&longs;eptimus <lb/>e&longs;t ip&longs;e ambitus, manife&longs;tus e&longs;t, 660 ip&longs;e quoque exi&longs;tens, <lb/>tamquam is, qui ip&longs;um 210 numerum ter, eiu&longs;que partem <arrow.to.target n="note283"/><lb/>&longs;eptimam habet. </s>
<s>ver&ugrave;m quoniam rur&longs;us quod ex dimetien&shy;<lb/>te &amp; quarta ambitus parte, &aelig;quum e&longs;t are&aelig; circuli, vt Ar&shy;<arrow.to.target n="note284"/><lb/>chimedes in quit. </s>
<s>qu&ograve;d omnis circulus &aelig;qualis e&longs;t triangu&shy;<lb/>lo rectangulo, cuius qu&aelig; ex centro, &aelig;qualis e&longs;t vni eorum, <lb/>qu&aelig; circa rectum angulum &longs;unt laterum, ambitus ver&ograve; ba&shy;<arrow.to.target n="note285"/><lb/>&longs;i: quod autem &agrave; dimetiente, <expan abbr="toto&qacute;ue">totoque</expan> ambitu, quadruplum <lb/>circuli e&longs;t. </s>
<s>&longs;i ita que ip&longs;i dimetientis pa&longs;&longs;us 210 ad ip&longs;os 165 <lb/>quart&aelig; partis ip&longs;ius ambitus multiplicentur, 34650 fient, <arrow.to.target n="note286"/><lb/>qu&aelig; circuli area e&longs;t. </s>
<s><expan abbr="n&atilde;">nam</expan> &longs;i 200 in 100 <expan abbr="multiplic&etilde;tur">multiplicentur</expan>, 20000 <lb/>efficiunt: &longs;i ver&ograve; in 60, 12000: &amp; in quinque, 1000: ac rur&shy;<lb/>&longs;us 10 in 100, 1000: in 60 ver&ograve;, 600: necnon in quinque, <lb/>50. Quapropter reperta e&longs;t qu&aelig; quidem ex centro circuli <arrow.to.target n="note287"/><lb/>105: dimetiens autem, 210: &amp; ambitus 660: area ver&ograve;, <lb/>&longs;iue totum &longs;patium &agrave; dimetiente &amp; quarta ambitus parte <lb/>factum, pa&longs;&longs;uum 34650. Facili&ugrave;s autem ab&longs;que etiam <lb/>dioptra circuli tum dimetientem, tum ambitum, tum etiam <lb/>&longs;patium agno&longs;cemus &agrave; fune quodam iuxta longitudinem <arrow.to.target n="note288"/><arrow.to.target n="note289"/><lb/>dato. </s>
<s>Sit itaque datus funis <expan abbr="pa&longs;&longs;u&utilde;">pa&longs;&longs;uum</expan> iuxta longitudinem 35, <lb/>aut quant&ugrave;m qui&longs;que propria &longs;ponte de&longs;iderat. </s>
<s>atque ad <lb/>vnum quidem extremum annulum ferreum cum clauo ha&shy;<lb/>beat, quippe qui clauus centri loco terr&aelig; affigatur, vt per <lb/>alterum extremum circularis <expan abbr="circ&utilde;&longs;criptio">circun&longs;criptio</expan> ordinatim per&shy;<lb/>ficiatur: donec &agrave; quo c&oelig;perat &longs;igno in eodem rur&longs;us funis <arrow.to.target n="note290"/><lb/>exten&longs;a circumducatur. </s>
<s>Quare ea, qu&aelig; in principio, &amp; &agrave; <arrow.to.target n="note291"/><lb/>principio, &amp; ad principium triadic&egrave; in circuli circum&longs;cri&shy;<lb/>ptione per&longs;picietur. </s>
<s>in principio quidem, ip&longs;um centrum, <lb/>circa quod funis extremum &longs;uper clauo per annulum cir&shy;<arrow.to.target n="note292"/><lb/>cumagitur: &agrave; principio ver&ograve;, alterum funis <expan abbr="extrem&utilde;">extremum</expan>, quod <lb/>circa eam, qu&aelig; ad principium &longs;ecund&ugrave;m &aelig;qualem di&longs;tan&shy;<pb xlink:href="052/01/128.jpg"/>tiam circulariter ad ip&longs;a bcdefgh &longs;igna circumuertitur. <arrow.to.target n="note293"/><lb/>Sic igitur circulo patefacto, reperietur quidem eius dime&shy;<lb/>tiens pa&longs;&shy;<arrow.to.target n="fig2"/><lb/>&longs;uum 70, <lb/><expan abbr="t&atilde;quam">tanquam</expan> <lb/>dupla e&shy;<lb/>ius, qu&aelig; <lb/>&agrave; centro: <lb/>ip&longs;ius <expan abbr="au-t&etilde;">au&shy;<lb/>tem</expan> dime&shy;<lb/>tientis tri<lb/>plus &longs;e&longs;&shy;<lb/>qui&longs;epti&shy;<lb/>mus am&shy;<lb/>bitus, pa&longs; <lb/><expan abbr="&longs;u&utilde;">&longs;uum</expan> 220 <lb/>exi&longs;tens: <lb/>necnon <lb/>quod &agrave; <lb/>dimetien<lb/>te &amp; quar<lb/>ta ambi&shy;<lb/>tus parte, 3850, qu&aelig; circuli area e&longs;t. </s>
<s>nam 70 pa&longs;&longs;us dime&shy;<lb/>tientis in ip&longs;os 50 pa&longs;&longs;us quart&aelig; partis ip&longs;ius ambitus <lb/>multiplicati, 3500 faciunt: &amp; in ip&longs;os quinque, 350. Quam&shy;<lb/>obrem &agrave; dato fune pa&longs;&longs;uum 35 reperta e&longs;t ip&longs;a quidem cir&shy;<lb/>culi dimetiens pa&longs;&longs;uum 70, 220 autem ambitus, &amp; 3850 <lb/>&longs;patium, quod comprehenditur. </s></p><p type="margin">
<s><margin.target id="note277"/><emph type="italics"/>Propo&longs;i&shy;<lb/>tio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note278"/><emph type="italics"/>Constru&shy;<lb/>ctio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note279"/>b</s></p><p type="margin">
<s><margin.target id="note280"/>c</s></p><p type="margin">
<s><margin.target id="note281"/><emph type="italics"/>Demon&shy;<lb/>&longs;tratio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note282"/>d</s></p><p type="margin">
<s><margin.target id="note283"/>e</s></p><p type="margin">
<s><margin.target id="note284"/>f</s></p><p type="margin">
<s><margin.target id="note285"/>g</s></p><p type="margin">
<s><margin.target id="note286"/>h</s></p><p type="margin">
<s><margin.target id="note287"/><emph type="italics"/><expan abbr="C&otilde;clu&longs;io">Conclu&longs;io</expan>.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note288"/><emph type="italics"/>Aliter <lb/><expan abbr="ead&etilde;">eadem</expan> pro <lb/>po&longs;itio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note289"/>i</s></p><p type="margin">
<s><margin.target id="note290"/>k</s></p><p type="margin">
<s><margin.target id="note291"/><emph type="italics"/>Pulchr&aelig; <lb/><expan abbr="c&otilde;&longs;idera-tio">con&longs;idera&shy;<lb/>tio</expan>.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note292"/><emph type="italics"/>[eam] &longs;. </s>
<s><lb/>circum&longs;e&shy;<lb/>rentiam.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note293"/><emph type="italics"/>Demon&shy;<lb/>&longs;tratio.<emph.end type="italics"/></s></p><figure id="id.052.01.128.1.jpg" xlink:href="052/01/128/1.jpg"/><figure id="id.052.01.128.2.jpg" xlink:href="052/01/128/2.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note294"/></s></p><p type="margin">
<s><margin.target id="note294"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>AMbitus figur&aelig; in Geometria e&longs;t linea ex omnibus ip&longs;ius fi&shy;<lb/>gur&aelig; lateribus compo&longs;ita, &longs;i latera habuerit: &longs;i ver&ograve; ab <lb/>vnico termino fuerit contenta veluti circulus, terminus <lb/>ille, ambitus vocatur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note295"/></s></p><p type="margin">
<s><margin.target id="note295"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Modius qui gr&ecedil;c&egrave;<emph.end type="italics"/> <foreign lang="greek">to/rmos</foreign> <emph type="italics"/>dicitur, est illa pars rot&aelig;, qu&aelig; e&longs;t &longs;i-<emph.end type="italics"/>
<pb xlink:href="052/01/129.jpg"/><emph type="italics"/>milis va&longs;i, quod modius dicitur, in qua voluitur Axis. </s>
<s>Modiolus <lb/>ver&ograve; (vt etiam in &longs;uperiori opere declarauimus) e&longs;t paruus mo&shy;<lb/>dius ip&longs;i modio &longs;uperimpo&longs;itus, in quo radij rot&aelig; affiguntur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note296"/></s></p><p type="margin">
<s><margin.target id="note296"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[per caulem in dioptra for&longs;an exi&longs;tentem] regula, qu&aelig; in dio&shy;<lb/>ptra &longs;iue dioptrico in&longs;trumento circumuoluitur, duplici modo po&shy;<lb/>te&longs;t in in&longs;trumento accommodari: aut ita vt per &longs;uperpo&longs;itum mo&shy;<lb/>dio modiolum, aut &longs;ic vt per caulem &longs;ibi affixum circumuertatur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note297"/></s></p><p type="margin">
<s><margin.target id="note297"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[eius, qu&aelig; ex centro] ide&longs;t &longs;emidimetientis. </s>
<s>nam gr&aelig;ci &longs;&aelig;pe <lb/>&longs;emidimetientem, lineam qu&aelig; ex centro vocant.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note298"/></s></p><p type="margin">
<s><margin.target id="note298"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[quod ex dimetiente, &amp; quarta ambitus parte] &longs;cilicet fit pa&shy;<lb/>rallelogrammum rectangulum &longs;patium.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note299"/></s></p><p type="margin">
<s><margin.target id="note299"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Archimedes demon&longs;trat ea, qu&aelig; h&igrave;c dicit Autor, in libro de <lb/>circuli dimen&longs;ione, in quo doctrinam hanc diligenti&szlig;im&egrave; tradidit. </s>
<s><lb/>qu&agrave;m etiam &agrave; Saua&longs;&longs;orda, &amp; Er&longs;emeide locupleti&szlig;im&egrave; pertracta&shy;<lb/>tam habemus. </s>
<s>ver&ugrave;m adnotandum e&longs;t, qu&ograve;d non e&longs;t ambitus cir&shy;<lb/>culi ad dimetientem triplus&longs;e&longs;qui&longs;eptimus (vt ait Autor) &longs;ed mi&shy;<lb/>nor quam triplus&longs;e&longs;qui&longs;eptimus, &amp; maior qu&agrave;m triplus&longs;uper&shy;<lb/>deciespartiens&longs;eptuage&longs;imasprimas, vt Archimedes in tertia <lb/>propo&longs;itione iam dicti libri de circuli dimen&longs;ione demon&longs;trauit. </s>
<s><lb/>quoniam autem h&aelig;c parui&szlig;ima differentia qua&longs;i in&longs;en&longs;ibilem er&shy;<lb/>rorem in dimen&longs;ionibus efficere potest, idcirco viri hac in &longs;cientia <lb/>periti&szlig;imi ambitum circuli triplam&longs;e&longs;qui&longs;eptimam rationem ad <lb/>dimetientem habere &longs;uppo&longs;uerunt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note300"/></s></p><p type="margin">
<s><margin.target id="note300"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[quod autem &agrave; dimetiente, toto&queacute; ambitu] &longs;cilicet fit paralle&shy;<lb/>logrammum rectangulum &longs;patium.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note301"/></s></p><p type="margin">
<s><margin.target id="note301"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[nam &longs;i 200 in 100 multiplicentur, &amp;c.] Multiplicationem nu&shy;<lb/>meri 210 per numerum 165, qu&aelig; &agrave; recentioribus Arithmeticis <lb/>practicis hoc modo fit:<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Multiplicatio &longs;ecundum recentiores Arithmeticos<emph.end type="center"/></s></p><p type="table">
<s>TABELLE WAR HIER</s></p>
<pb xlink:href="052/01/130.jpg"/><p type="main">
<s><emph type="center"/><emph type="italics"/>alio vetu&longs;tiori quodam pacto facit Autor, &longs;ic.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="center"/>Multiplicatio &longs;ecundum Autorem.<emph.end type="center"/></s></p><p type="table">
<s>TABELLE WAR HIER</s></p><p type="main">
<s><emph type="italics"/>[dato] &longs;cilicet nobis cognito.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note302"/></s></p><p type="margin">
<s><margin.target id="note302"/>k</s></p><p type="main">
<s><emph type="italics"/>[Quare ea, qu&aelig; in principio, &amp; &agrave; principio, &amp; ad principium] <lb/>&longs;ubintelligitur exornatio [triadic&egrave; in circuli <expan abbr="circ&utilde;&longs;criptione">circum&longs;criptione</expan> per&shy;<lb/>&longs;picietur.] hoc e&longs;t in circum&longs;cribendo circulo illa trina, &longs;iue tria&shy;<lb/>dica <expan abbr="rer&utilde;">rerum</expan> omnium exornatio, quam Platonici gr&aelig;c&egrave;<emph.end type="italics"/> <foreign lang="greek">diako/smhsin</foreign><lb/><emph type="italics"/>vocant, ea &longs;cilicet, qu&aelig; in principio, &agrave; principio, &amp; ad principium <lb/>e&longs;t, triadic&egrave; per&longs;picietur. </s>
<s>nempe centro, lineis ex centro, &amp; cir&shy;<lb/>cumferentia, &longs;iue ambitu. </s>
<s>nam <expan abbr="centr&utilde;">centrum</expan> quidem e&longs;&longs;entiam in prin&shy;<lb/>cipio exi&longs;tentem, linea ex centro e&longs;&longs;entiam &agrave; principio promanan&shy;<lb/>tem, circumferentia&queacute; e&longs;&longs;entiam ad principium reuertentem ex&shy;<lb/>primunt. </s>
<s>quippe qu&aelig; tria o&longs;tendunt nobis triadicam in vnico cir&shy;<lb/>culo rerum omnium exornationem, necnon Dei Optimi Maximi <lb/>triadicam in vnum e&longs;&longs;entiam: ad cuius <expan abbr="vtiq;">vtique</expan> &longs;imilitudinem men&shy;<lb/>tem etiam no&longs;tra triadicam, ac vnam ip&longs;e creauit. </s>
<s><expan abbr="quemadmod&utilde;">quemadmodum</expan> <lb/>enim in Deo &longs;ic <expan abbr="eti&atilde;">etiam</expan> in mente no&longs;tra tria h&aelig;c <expan abbr="vn&utilde;">vnum</expan> &longs;unt, intelligens, <lb/>intellectio, &amp; res intellecta. </s>
<s>idcirco mens etiam no&longs;tra immorta&shy;<lb/>lis, trina, &amp; vna ad &longs;ui opificis &aelig;terni, trini, &amp; vni imaginem, ac <lb/>&longs;imilitudinem creata fuit. </s>
<s>Hanc itaque Trinitatis, ac vnitatis <lb/>&longs;imul alti&szlig;imam, vix&queacute; perceptibilem, ac explicabilem materiam <lb/>Autor in circuli de&longs;criptione tetigit: quam profecto &longs;i ad plenum <lb/>declarare nunc vellemus, ab in&longs;tituto no&longs;tro long&egrave; aberraremus. </s>
<s><lb/>idcirco eos, qui hanc pulcherrimam con&longs;iderationem perfect&egrave; gu&shy;<lb/>&longs;tare cupiunt, ad Platonem ip&longs;um, &amp; Proclum eius expo&longs;itorem,<emph.end type="italics"/>
<pb xlink:href="052/01/131.jpg"/><emph type="italics"/>c&aelig;teros&queacute; Platonicos, necnon ad eundem Proclum in 13 commen&shy;<lb/>tario &longs;ecundi libri in primum librum Elementorum Euclidis re&shy;<lb/>mittimus. </s>
<s>H&aelig;c autem pro dilucidatione huiu&longs;ce propo&longs;itionis di&shy;<lb/>cta &longs;int.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Septima.<emph.end type="center"/></s></p><p type="main">
<s>SOlid&aelig; ver&ograve; figur&aelig; non quemadmodum iam <lb/>dict&aelig; plan&aelig; iuxta duas tantummodo, &longs;ed ne&shy;<lb/>ce&longs;&longs;ari&ograve; iuxta tres dimen&longs;iones con&longs;iderabun<lb/>tur. </s>
<s>quandoquidem omne corpus triplici di&shy;<lb/>men&longs;ione di&longs;tat longitudinem habens, &amp; lati&shy;<lb/>tudinem, <expan abbr="atq;">atque</expan> cra&longs;&longs;itudinem, idem autem ac &longs;i dicamus pro&shy;<lb/>funditatem, aut altitudinem. </s>
<s>nam eum, qui ex longitudi&shy;<lb/>ne, ac latitudine fit planum numerum, in tertiam altitudi&shy;<lb/>nis dimen&longs;ionem multiplicantes, &longs;olidas figuras &longs;upputare <lb/>nos oportet. </s>
<s>Ac prim&ugrave;m quidem in cubica figura men&longs;u&shy;<lb/>ratio fiat. </s>
<s>Cubus enim e&longs;t figura &longs;olida &agrave; &longs;ex quadrangu&shy;<lb/>lis &aelig;qualibus comprehen&longs;a, qu&ecedil; in latera <expan abbr="quid&etilde;">quidem</expan> duodecim, <arrow.to.target n="note303"/><lb/>angulos autem rectos octo, &amp; plana &longs;ex in tribus dimen&longs;io&shy;<arrow.to.target n="note304"/><lb/>nibus &longs;ecund&ugrave;m &aelig;qualitatem con&longs;ideratur. </s>
<s>vnd&egrave; <expan abbr="eti&atilde;">etiam</expan> har&shy;<lb/>monicas in con&longs;onantia, <expan abbr="diuinas&qacute;ue">diuinasque</expan> rationes in huiu&longs;cemo<lb/>di figura Pythagorei o&longs;tendunt, harmoniam ip&longs;um cubum <lb/>nominantes. </s>
<s>ver&ugrave;m ip&longs;a figur&aelig; &longs;oliditas ita reperietur. </s>
<s>Si <lb/>enim ba&longs;is cubi 28 vnitatum iuxta longitudinem fuerit, ea&shy;<lb/>rundem iuxta latitudinem <arrow.to.target n="fig3"/><lb/>etiam erit, necnon iuxta al&shy;<lb/>titudinem &longs;imiliter. </s>
<s>ip&longs;as au<lb/>tem longitudinis 28 in ea&longs;&shy;<lb/>dem latitudinis multiplican<lb/>tes, ip&longs;um ba&longs;is planum vni&shy;<lb/>tatum 784 habebimus: <expan abbr="atq;">atque</expan> <lb/>hoc rur&longs;us in ip&longs;as altitudi&shy;<lb/>nis 28 multiplicantes, colli&shy;<lb/>gimus vnitates 21952, quas <lb/>vtique cubi &longs;oliditatem e&longs;&longs;e <arrow.to.target n="note305"/><lb/>pronuntiabimus. </s>
<s>Si autem in eodem cubo <expan abbr="cylindr&utilde;">cylindrum</expan> &ecedil;qu&egrave;<pb xlink:href="052/01/132.jpg"/><arrow.to.target n="note306"/><lb/>altum excogitauerimus in&longs;cribi, qui etiam &longs;ph&aelig;ram in me&shy;<lb/>dio circumambiat, ita vt &longs;ph&aelig;ra &longs;ecundum maximum ip&shy;<lb/>&longs;ius &longs;ph&aelig;r&aelig; circulum cylindri &longs;uperficiem tangat: o&longs;ten de&shy;<lb/>tur cubi ba&longs;is ad cylindri ba&longs;em rationem habere eam, <expan abbr="qu&atilde;">quam</expan> <arrow.to.target n="note307"/><lb/>in minimis, <expan abbr="primis&qacute;ue">primisque</expan> numeris ip&longs;e 14 numerus ad ip&longs;um <lb/>11 numerum habet. </s>
<s>Similiter autem ip&longs;a quoque &longs;ex cubi <lb/>plana ad cylindri &longs;uperficiem vn&agrave; cum duabus ba&longs;ibus &longs;e &longs;e <lb/>habebunt: necnon quatuor, &longs;ine ba&longs;ibus: &amp; &longs;olidum ad <expan abbr="&longs;o-lid&utilde;">&longs;o&shy;<lb/>lidum</expan> &longs;e habebit. </s>
<s>at ip&longs;a cylindri &longs;uperficies &longs;ine ba&longs;ibus qui&shy;<lb/>dem &aelig;qualis e&longs;t &longs;uperficiei &longs;ph&aelig;r&aelig;, qu&aelig; ab ip&longs;o circumam&shy;<lb/>bitur: vn&agrave; ver&ograve; cum ba&longs;ibus, &longs;e&longs;quialter ip&longs;ius &longs;ph&aelig;r&aelig; cy&shy;<lb/>lindrus tum iuxta &longs;uperficiem, tum iuxta &longs;oliditatem inue&shy;<lb/>nietur. </s>
<s>Ver&ugrave;m ip&longs;a cylindri ba&longs;is agno&longs;cetur ex dimetien&shy;<lb/>te, &amp; quarta ambitus parte, quemadmodum &longs;uperi&ugrave;s iam <lb/>dictum fuit. </s>
<s>c&ugrave;m enim ip&longs;a dimetiens 28 data &longs;it, 88 am&shy;<lb/>bitus erit, triplus&longs;e&longs;qui&longs;eptimus exi&longs;tens. </s>
<s>atque pars eius <lb/>quarta 22. ip&longs;&aelig; igitur 28 &longs;i in ip&longs;as 22 vnitates multiplicen&shy;<lb/>tur, aream ba&longs;is 616 faciunt. </s>
<s>e&longs;t autem ba&longs;is etiam cubi 784. <lb/>ba&longs;is ergo cubi ad ba&longs;im cylindri &longs;ic &longs;e habet, quemadmo&shy;<lb/>dum in minimis, <expan abbr="primis&qacute;ue">primisque</expan> (vti iam diximus) numeris ip&longs;e <lb/>14 ad ip&longs;um 11. nam ip&longs;e 784 numerus ip&longs;um 616 nume&shy;<arrow.to.target n="note308"/><lb/>rum, <expan abbr="eius&qacute;ue">eiusque</expan> partem quartam 154, necnon partem quadra&shy;<lb/>ge&longs;imamquartam, qu&aelig; e&longs;t 14, habet. </s>
<s>Hoc itaque pacto ip&longs;&aelig; <lb/>etiam quatuor &longs;uperficies, qu&aelig; ab ip&longs;ius cubi ba&longs;i &longs;urrexe&shy;<lb/>runt ad cylindricam &longs;uperficiem &longs;e &longs;e habebunt: ac rur&longs;us <lb/>&longs;ex cubi plana ad cylindri &longs;uperficiem, <expan abbr="ba&longs;ium&qacute;ue">ba&longs;iumque</expan> plana: <lb/>necnon &longs;olidum ad &longs;olidum. </s>
<s>nam &longs;i ip&longs;a cubic&aelig; ba&longs;is qua&shy;<lb/>tuor latera in ip&longs;as 28 altitudinis vnitates multiplicentur, <lb/>3136 fiunt: necnon &longs;i ip&longs;&aelig; 88 vnitates ambitus cylindric&aelig; <lb/>ba&longs;is in ea&longs;dem 28 altitudinis, 2464 efficiunt, in <expan abbr="eadem&qacute;ue">eademque</expan> <lb/>ratione &longs;unt. </s>
<s>eodem modo &longs;ex <expan abbr="quoq;">quoque</expan> plana cubi, qu&aelig; 4704 <lb/>fiunt, ad ip&longs;am cylindri &longs;uperficiem vn&agrave; cum ba&longs;ibus in in&shy;<lb/>ferna, <expan abbr="&longs;uperna&qacute;ue">&longs;upernaque</expan> &longs;ede exi&longs;tentibus, earum 3696, qu&aelig; col&shy;<lb/>liguntur, vnitatum. </s>
<s>&longs;imiliter autem ip&longs;a etiam cubi &longs;olidi&shy;<lb/>tas, qu&aelig; ab ip&longs;ius ba&longs;is plano ip&longs;arum 784 vnitatum, in ip&shy;<lb/>&longs;as altitudinis 28 vnitates multiplicato, 21952 reperitur, ad <lb/>cylindri &longs;oliditatem, qu&aelig; ab ip&longs;is 616 ip&longs;ius ba&longs;is vnitati-<pb xlink:href="052/01/133.jpg"/>bus in ea&longs;dem 28 altitudinis vnitates multiplicatis, 17248 <lb/>fit. </s>
<s>ita vt in eadem ratione vndequaque cubus circa eum, <lb/>qui in ip&longs;o in&longs;cribitur &aelig;qu&egrave; altum cylindrum per&longs;piciatur. </s>
<s><lb/>Ver&ugrave;menimuero qu&ograve;d cylindrus &longs;e&longs;quialter &longs;it &longs;ph&aelig;r&aelig;, <lb/>qu&aelig; in ip&longs;o in&longs;cribitur, &longs;ic o&longs;tendemus. </s>
<s>c&ugrave;m enim cylindri <lb/>&longs;uperficies vn&agrave; cum ba&longs;ium planis 3696 exi&longs;tat, 17248 ve&shy;<lb/>r&ograve; &longs;oliditas: o&longs;tendetur etiam &longs;ph&aelig;r&aelig; &longs;uperficies, qu&aelig; ex <lb/>ip&longs;is 88 ip&longs;ius ambitus maximi circuli in ip&longs;a exi&longs;tentis, &amp; <lb/>ex ip&longs;is 28 ip&longs;ius Axis altitudinis vnitatibus fit, 2464: &longs;oli&shy;<lb/>ditas autem ip&longs;ius &longs;ph&aelig;r&aelig;, qu&aelig; ab area maximi circuli ip&shy;<lb/>&longs;arum 616 in duas tertias ip&longs;ius Axis, &longs;iue in 18 2/3 multi&shy;<lb/>plicata fit, 11498 2/3. atque &longs;uperficies ad &longs;uperficiem, &amp; &longs;o&shy;<lb/>lidum ad &longs;olidum (vt iam dictum e&longs;t) in ratione &longs;e&longs;quialte&shy;<lb/>ra &longs;unt. </s>
<s>quare &longs;ph&aelig;ra du&aelig; terti&aelig; partes circumambientis ip<lb/>&longs;am &aelig;qu&egrave; alti cylindri reperta e&longs;t. </s>
<s>Omnis autem &longs;ph&aelig;rica <lb/>&longs;uperficies are&aelig; quidem &longs;ui maximi circuli quadrupla e&longs;t. </s>
<s><lb/>ip&longs;ius ver&ograve; circuli ambitum tot vicibus continet, quot <expan abbr="eti&atilde;">etiam</expan> <lb/>axis in ip&longs;a exi&longs;tens iuxta longitudinem vnitates in &longs;e com&shy;<lb/>prehendit. </s>
<s>nam ip&longs;&aelig; 2464 numerus quadruplus quidem <lb/>e&longs;t ip&longs;ius 616: vigincuplus octuplus ver&ograve; ip&longs;ius 88. E&longs;t au&shy;<lb/>tem omnis etiam &longs;ph&aelig;ra quadrupla coni ba&longs;im quidem ha<lb/>bentis maximum &longs;pher&aelig; circulum, altitudinem ver&ograve; &ecedil;qua&shy;<lb/>lem ei, qu&aelig; ex centro &longs;ph&aelig;r&aelig;. </s>
<s>etenim conic&aelig; ba&longs;is ambitus <lb/>88 exi&longs;tens, &longs;i in axis dimidium, vt &agrave; centro ad altitudinem, <lb/>14, multiplicetur, 1232 efficiunt. </s>
<s>necnon ip&longs;&aelig; are&aelig; ba&longs;is <arrow.to.target n="note309"/><lb/>616 vnitates, in ea&longs;dem 14 axis dimidi&aelig; partis, 8624. </s>
<s>Qu&aacute;m&shy;<lb/>obrem hemi&longs;ph&aelig;rium c&ugrave;m iuxta &longs;uperficiem, tum iuxta &longs;o<lb/>liditatem duobus conis &aelig;quale repertum e&longs;t: &longs;phaera ver&ograve;, <arrow.to.target n="note310"/><lb/>quatuor. </s>
<s>Conus autem e&longs;t figura &longs;olida &agrave; circulari ba&longs;i ad <lb/>vnum &longs;ublime &longs;ignum contracta. </s>
<s>&longs;ecund&ugrave;m ver&ograve; <expan abbr="Euclid&etilde;">Euclidem</expan>: <lb/>c&ugrave;m altero rectanguli trianguli latere eorum, qu&aelig; circa re&shy;<lb/>ctum &longs;unt angulum quie&longs;cente circumuolutum <expan abbr="tri&atilde;gulum">triangulum</expan> <lb/>in eundem rur&longs;us locum re&longs;titutum fuerit, vnd&egrave; moueri c&ecedil;&shy;<lb/>perat, circum&longs;cripta figura conus vocatur. </s>
<s><expan abbr="atq;">atque</expan> &longs;i quie&longs;cens <lb/>recta linea &aelig;qualis &longs;it reliqu&aelig;, qu&aelig; circumrectum angulum <lb/>conuertitur, rectangulus erit conis: &longs;in minor obtu&longs;angu-<pb xlink:href="052/01/134.jpg"/>lus: &longs;i uer&ograve; maior, acutangulus. </s>
<s>axis <expan abbr="aut&etilde;">autem</expan> coni e&longs;t quie&longs;cens <lb/>illa recta linea, circumquam triangulum uertitur: ba&longs;is ue&shy;<arrow.to.target n="note311"/><lb/>r&ograve;, circulus, qui &agrave; circumducta linea recta de&longs;cribitur. </s>
<s>Re&shy;<lb/>peritur autem omnis etiam cylindrus triplus coni eandem <lb/>cum ip&longs;o ba&longs;im, &amp; &aelig;qualem <expan abbr="altitudin&etilde;">altitudinem</expan> habentis. </s>
<s>c&ugrave;m enim <lb/>cylindri &longs;uperficies 2464 &longs;it, &longs;oliditas uero 17248: ip&longs;a <expan abbr="au-t&etilde;">au&shy;<lb/>tem</expan> coni &longs;uperficies ex eodem 88 unitatum ambitu, &amp; tertia <lb/><expan abbr="unitat&utilde;">unitatum</expan> 9 1/3 axis parte, 821 1/3 &longs;it, ex ip&longs;is uer&ograve; 616 are&aelig; <lb/>ba&longs;is unitatibus in eandem tertiam axis partem multiplica&shy;<lb/>tis 5749 1/3 &longs;oliditas reperiatur, in triplaque ratione adin&shy;<lb/>uicem &longs;int: tertia pars igitur &aelig;qu&egrave; alti cylindri conus de&shy;<arrow.to.target n="note312"/><lb/>mon&longs;tratus e&longs;t. </s>
<s>Quinetiam pri&longs;ma <expan abbr="parallelepiped&utilde;">parallelepipedum</expan> exi&longs;tens <lb/>pyramidis eandem cum ip&longs;o ba&longs;em, &amp; &aelig;qualem <expan abbr="altitudin&etilde;">altitudinem</expan> <arrow.to.target n="note313"/><lb/>habentis triplum inuenitur. </s>
<s>Atque centrum grauitatis cy&shy;<lb/>lindri e&longs;t in bipertita &longs;ectione ip&longs;ius axis. </s>
<s>&longs;imiliter autem in <lb/>pri&longs;mate <expan abbr="&etilde;t">etiam</expan> erit. </s>
<s>ip&longs;um uer&ograve; <expan abbr="conicentr&utilde;">conicentrum</expan> grauitatis e&longs;t in axe <lb/>ita diui&longs;o, ut &longs;egmentum uer&longs;us <expan abbr="uertic&etilde;">uerticem</expan> exi&longs;tens reliqui tri&shy;<lb/>plum &longs;it. </s>
<s>eadem igitur ip&longs;ius axis diui&longs;o in pyramide quo&shy;<lb/>que fiat. </s>
<s>Pyramis autem e&longs;t figura &longs;olida, qu&aelig; planis conti&shy;<lb/>netur ab ip&longs;ius ba&longs;is plano ad vnum &longs;ignum collecta: aut &agrave; <lb/>ba&longs;i triangula, vel quadrangula, vel multangula ad vnum <lb/>&longs;ublime &longs;ignum contracta. </s>
<s>Pri&longs;ma ver&ograve; e&longs;t figura &longs;olida, <lb/>qu&aelig; planis comprehenditur, quorum duo nempe ex ad&shy;<lb/>uer&longs;o iacentia c&ugrave;m &aelig;qualia, tum &longs;imilia, tum etiam paral&shy;<lb/>lela &longs;unt: reliqua ver&ograve; parallelogramma. </s></p>
<pb xlink:href="052/01/135.jpg"/><p type="margin">
<s><margin.target id="note303"/>a</s></p><p type="margin">
<s><margin.target id="note304"/>b</s></p><p type="margin">
<s><margin.target id="note305"/>c</s></p><p type="margin">
<s><margin.target id="note306"/>d</s></p><p type="margin">
<s><margin.target id="note307"/>e</s></p><p type="margin">
<s><margin.target id="note308"/>f</s></p><p type="margin">
<s><margin.target id="note309"/>g</s></p><p type="margin">
<s><margin.target id="note310"/>h</s></p><p type="margin">
<s><margin.target id="note311"/>i</s></p><p type="margin">
<s><margin.target id="note312"/>k</s></p><p type="margin">
<s><margin.target id="note313"/>l</s></p><figure id="id.052.01.135.1.jpg" xlink:href="052/01/135/1.jpg"/><p type="caption">
<s>Cylindrus in cubo in&shy;<lb/>&longs;criptus &longs;ph&aelig;ram am&shy;<lb/>biens conum in hemi&shy;<lb/>&longs;ph&aelig;rio habentem. </s>
<s>&amp; <lb/>conus in eadem cum <lb/>cylindro ba&longs;i, &amp; alti&shy;<lb/>tudine tacens.</s></p><figure id="id.052.01.135.2.jpg" xlink:href="052/01/135/2.jpg"/><p type="caption">
<s>Nota qu&ograve;d in infe&shy;<lb/>riori diagramma&shy;<lb/>te .m. </s>
<s>quidem mul&shy;<lb/>tiplicationem, .p. </s>
<s><lb/>ver&ograve; partitionem <lb/>&longs;ignificat.</s></p><p type="main">
<s><emph type="center"/>Diagramma cunctas, de quibus Autor in hac propo&longs;itione loquitur cor&shy;<lb/>porum, <expan abbr="eorum&qacute;ue">eorumque</expan> partium quantitates o&longs;tendens.<emph.end type="center"/></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"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note314"/></s></p><p type="margin">
<s><margin.target id="note314"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[angulos autem rectos octo] Quemadmodum angulus planus <lb/>triplex e&longs;t, rectus &longs;cilicet, acutus, ac obtu&longs;us: ita etiam angu&shy;<lb/>lus &longs;olidus (c&ugrave;m ex planis con&longs;tituatur angulis) triplex erit, <lb/>nempe rectus, qui ex rectis: acutus, qui ex acutis: obtu&longs;us, qui <lb/>ex obtu&longs;is planis angulis con&longs;tat. </s>
<s>quamobrem angulos rectos octo <lb/>in pr&aelig;&longs;entia &longs;olidos, non <expan abbr="aut&etilde;">autem</expan> planos e&longs;&longs;e intelligere debemus. </s>
<s>quan<lb/>doquidem 24 rectos angulos planos quilibet cubus habet.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note315"/></s></p><p type="margin">
<s><margin.target id="note315"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Quonam pacto diuinas rationes in cubo iuxta rectitudinem, <lb/>&aelig;qualitatem, ac trinam dimen&longs;ionem Pythagorei o&longs;tendant, lon&shy;<lb/>gum e&longs;&longs;et in pr&aelig;&longs;entia declarare: quomodo ver&ograve; harmonicas in <lb/>con&longs;onantia exi&longs;tentes rationes, in cubo indicent, c&ugrave;m ip&longs;um <lb/>harmoniam nuncupent, paucis explicabo. </s>
<s>C&ugrave;m itaque cubus late&shy;<lb/>ribus duodecim, angulis octo, planis&queacute; &longs;ex con&longs;tet, dubio procul om&shy;<lb/>nes quinque pr&aelig;cipu&aelig; con&longs;onantiarum harmonic&aelig; rationes in hi&shy;<lb/>&longs;ce tribus numeris. </s>
<s>6.8.12. reperiuntur. </s>
<s>nam 8 quidem ad 6 &longs;e&longs;&shy;<lb/>quitertiam habet rationem, in qua Diate&longs;&longs;aron con&longs;onantia e&longs;t: <lb/>12 ver&ograve; ad 8 &longs;e&longs;quialteram, in qua Diapente: 12 autem ad 6 du&shy;<lb/>plam, in qua Diapa&longs;&longs;on: 12 rur&longs;us ad exce&longs;&longs;um, quo duo denarius <lb/>octonarium &longs;uperat, nempe ad 4, triplam, in qua Diapa&longs;&longs;on cum <lb/>diapente: S demum ad exce&longs;&longs;um, quo &longs;enarium octonarius exce&shy;<lb/>dit, &longs;cilicet ad 2, quadruplam, in qua Bi&longs;diapa&longs;&longs;on. </s>
<s>Quapropter <lb/>c&ugrave;m harmonic&aelig; con&longs;onantiarum rationes in cubo &longs;int, non imme&shy;<lb/>rito Pythagorei harmoniam ip&longs;um nominarunt. </s>
<s>H&aelig;c autem obiter <lb/>&agrave; nobis dicta sint, quoniam non &longs;unt pr&aelig;&longs;entis contemplationis.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note316"/></s></p><p type="margin">
<s><margin.target id="note316"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Cylindrus, &longs;ph&aelig;ra, &amp; conus, ac c&aelig;tera &longs;olida, <expan abbr="eorum&qacute;ue">eorumque</expan> par&shy;<lb/>tes ab Euclide in definitionibus vndecimi libri Elementorum dili&shy;<lb/>genti&szlig;im&egrave; definiuntur. </s>
<s>quorum &longs;an&egrave; corporum aream, &longs;eu capaci<lb/>tatem Autor &longs;olidum, &longs;iue &longs;oliditatem appellat.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note317"/></s></p><p type="margin">
<s><margin.target id="note317"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&aelig;qu&egrave; altum] hoc e&longs;t cuius altitudo &longs;it &aelig;qualis altitudini cubi.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note318"/></s></p><p type="margin">
<s><margin.target id="note318"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in minimis, primis&queacute; numeris &amp;c.] Dupliciter numeri pri&shy;<lb/>mi dicuntur, aut per &longs;e, aut adinuicem con&longs;iderati. </s>
<s>&amp; qui nam <lb/>&longs;int numeri primi per &longs;e con&longs;iderati docet Euclides in undecima <lb/>definitione &longs;eptimi libri Elementorum: qui ver&ograve; &longs;int primi adin-<emph.end type="italics"/>
<pb xlink:href="052/01/137.jpg"/><emph type="italics"/>uicem, in duodecima definitione eiu&longs;dem. </s>
<s>h&igrave;c autem non de pri&shy;<lb/>mis per &longs;e, &longs;ed de primis adinuicem con&longs;ideratis Autor loquitur. </s>
<s><lb/>quippe qui etiam minimi &longs;emper &longs;unt omnium eandem cum eis <lb/>rationem habentium, ut idem Euclides in 23 propo&longs;itione eiu&longs;dem <lb/>&longs;eptimi demon&longs;trat. </s>
<s>Quomodo autem datis quotcumque numeris <lb/>minini omnium eandem cum eis rationem habentium reperian&shy;<lb/>tur demon&longs;trat Euclides in 35 propo&longs;itione libri eiu&longs;dem.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note319"/></s></p><p type="margin">
<s><margin.target id="note319"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Adnotandum qu&ograve;d melius e&longs;t dicere, qu&ograve;d 784 ad 616 ha&shy;<lb/>bet rationem &longs;upertripartientem vndecimas, &longs;iue &longs;upertriunde&shy;<lb/>cimas &longs;icut 14 ad 11: qu&agrave;m dicere qu&ograve;d continet cum, ac eius par <lb/>tem quartam, &amp; quadrage&longs;imam quartam. </s><s>nam quemadmo&shy;<lb/>dum 14 continet 11 &amp; eius (3/11), &longs;ic <expan abbr="&etilde;t">etiam</expan> 784 continet 616 &amp; eius <lb/>(3/11): qu&aelig; &longs;unt 168, exce&longs;&longs;us videlicet, quo ip&longs;e 784 ip&longs;um 616 &longs;u&shy;<lb/>perat. </s>
<s>ter enim 56, 168: &amp; undecies 56, 616 faciunt.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Pr&aelig;terea notandum qu&ograve;d illud, quod ait Autor [quamobrem <arrow.to.target n="note320"/><lb/>hemi&longs;ph&aelig;rium c&ugrave;m iuxta &longs;uperficiem, tum iuxta &longs;oliditatem <lb/>duobus conis &aelig;quale repertum e&longs;t: &longs;ph&aelig;ra ver&ograve;, quatuor.] fal&longs;um <lb/>e&longs;t in ea parte [c&ugrave;m iuxta &longs;uperficiem] quandoquidem &longs;uperfi&shy;<lb/>cies hemi&longs;ph&aelig;rij, qu&aelig; e&longs;t 1232, non e&longs;t (ut ait Autor) &aelig;qualis <lb/>duplo &longs;uperficiei coni in hemi&longs;ph&aelig;rio in&longs;cripti, quod e&longs;t 821 1/3, &longs;ed <lb/>&longs;e&longs;quialtera ip&longs;ius e&longs;t. </s>
<s>quamobrem nec etiam tota &longs;ph&aelig;rica &longs;uper&shy;<lb/>ficies, qu&aelig; e&longs;t 2464 ad totam iam dicti in hemi&longs;ph&aelig;rio con&longs;tituti co<lb/>ni &longs;uperficiem 410 2/3 exi&longs;t entem quadrupla (quemadmodum ait <lb/>Autor) &longs;ed reuera &longs;excupla quidem erit. </s>
<s>C&ugrave;m enim cylindri &longs;u&shy;<lb/>perficies, qu&aelig; &longs;uperficiei &longs;ph&aelig;r&aelig; in ip&longs;o in&longs;cript&aelig; &aelig;qualis o&longs;ten&longs;a <lb/>e&longs;t, tripla &longs;uperficiei coni eandem cum ip&longs;o ba&longs;im, &amp; &aelig;qualem alti&shy;<lb/>tudinem <expan abbr="hab&etilde;tis">habentis</expan> demon&longs;trata &longs;it, qui conus duplus e&longs;t per 14 pro&shy;<lb/>po&longs;itionem duodecimi elementorum coni in hemi&longs;ph&aelig;rio in&longs;cripti: <lb/>nemini dubium qu&ograve;d &longs;ph&aelig;r&aelig; &longs;uperficies ad in&longs;cripti in hemi&longs;ph&aelig;&shy;<lb/>rio coni &longs;uperficiem &longs;exculpam rationem habebit. </s>
<s>non e&longs;t igitur <lb/>uerum quod ait Autor, qu&ograve;d &longs;cilicet hemi&longs;p&aelig;rium iuxta &longs;uperfi&shy;<lb/>ciem duobus, &longs;ph&aelig;ra uer&ograve; quatuor conis <expan abbr="eor&utilde;">eorum</expan>, qui in hemi&longs;ph&aelig;rio <lb/>in&longs;cribuntur, &ecedil;qualis reperta &longs;it, &longs;ed iuxta &longs;oliditatem dumtaxat <lb/>hoc verum. </s>
<s>Soliditas et enim &longs;ph&aelig;r&aelig;, qu&aelig; e&longs;t 11498 2/3 &longs;oliditatis <lb/>iam dicti coni in hemi&longs;ph&aelig;rio constituti, qu&aelig; e&longs;t 2874 2/3, qua-<emph.end type="italics"/>
<pb xlink:href="052/01/138.jpg"/><emph type="italics"/>drupla dubio procul existit. </s>
<s>aut ergo textus corrupt&egrave; legitur, aut <lb/>bonus dormitauit Homerus.<emph.end type="italics"/><lb/><arrow.to.target n="note321"/></s></p><p type="margin">
<s><margin.target id="note320"/>g</s></p><p type="margin">
<s><margin.target id="note321"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>H&igrave;c dupliciter conum Autor definit, prim&ograve; definitioue forma&shy;<lb/>li, deinde Euclidis definitione, qu&aelig; ab efficienti cau&longs;a de&longs;umitur. </s>
<s><lb/>Apollonius autem Perg&aelig;us aliter, &amp; exqui&longs;iti&ugrave;s conum, eius&queacute; <lb/>partes, ac &longs;pecies definiuit in definitionibus primi libri conicorum, <lb/>vt nos alibi &longs;atis &longs;uper&queacute; declarauimus.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note322"/></s></p><p type="margin">
<s><margin.target id="note322"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Reperitur autem &amp;c.] hanc propo&longs;itionem demon&longs;trauit Eu&shy;<lb/>clides in decimo theoremate duodecimi libri Elementorum.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note323"/></s></p><p type="margin">
<s><margin.target id="note323"/>k</s></p><p type="main">
<s><emph type="italics"/>Quinetiam Pri&longs;ma &amp;c.] h&aelig;c propo&longs;itio e&longs;t corollarium &longs;epti&shy;<lb/>m&aelig; propo&longs;itionis iam dicti duodecimi, quod demon&longs;trauit Campa&shy;<lb/>nus in &longs;uis additionibus &longs;uper octauam propo&longs;itionem eiu&longs;dem li&shy;<lb/>bri. </s>
<s>ver&ugrave;m quid nam &longs;it Pri&longs;ma, atque pyramis in fine propo&longs;itio&shy;<lb/>nis declarat Autor iuxta <expan abbr="doctrin&atilde;">doctrinam</expan> duodecim&aelig;, &amp; terti&aelig;decim&aelig; <lb/>definitionis vndecimi <expan abbr="Elementor&utilde;">Elementorum</expan> Euclidis. </s>
<s><expan abbr="Parallelepiped&utilde;">Parallelepipedum</expan> <expan abbr="a&utilde;t">aut</expan> <lb/>e&longs;t figura &longs;olida parallelis planis <expan abbr="c&otilde;tenta">contenta</expan>, qu&aelig; pri&longs;matis &longs;pecies e&longs;t.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note324"/></s></p><p type="margin">
<s><margin.target id="note324"/><emph type="italics"/>l<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Centrum grauitatis duplex e&longs;t, alterum planorum, alte&shy;<lb/>rum &longs;olidorum. </s>
<s>quidnam &longs;it autem centrum grauitatis plano&shy;<lb/>rum patet ex Archimedis libro de centris grauitatis plano&shy;<lb/>rum, in quo de iam dictis centris exacti&szlig;imam doctrinam tradi&shy;<lb/>dit. </s>
<s>quid &longs;it ver&ograve; centrum grauitatis &longs;olidorum eleganti&szlig;im&egrave; de&shy;<lb/>clarauit Federicus Commandinus Mathematicarum eruditi&szlig;i&shy;<lb/>mus in prima definitione &longs;ui opu&longs;culi de centro grauitatis &longs;olido&shy;<lb/>rum, in quo doctrinam hanc hactenus in tenebris latentem docti&longs;&shy;<lb/>&longs;im&egrave; dilucidauit. </s>
<s>h&aelig;c autem, qu&aelig; h&igrave;c ab Autore de centris gra&shy;<lb/>uitatis cylindri, pri&longs;matis, coni, &amp; pyramidis dicuntur ip&longs;e Com&shy;<lb/>mandinus in octaua, &amp; vige&longs;ima&longs;ecunda propo&longs;itionibus iam di&shy;<lb/>cti &longs;ui opu&longs;culi diligenti&szlig;im&egrave; demon&longs;trauit.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Verumtamen animaduer&longs;ione dignum e&longs;t, qu&ograve;d po&longs;tquam ex <lb/>cubi lateribus &longs;uperficies, &amp; aream &longs;olidam eius inuenire docuit: <lb/>comparans eum cum alijs corporibus, <expan abbr="eor&utilde;">eorum</expan> <expan abbr="&etilde;t">et</expan> &longs;uperficies, ac &longs;olidi&shy;<lb/>tates reperire docet. </s>
<s>vnd&egrave; &longs;eptem pulcherrimas Geometricas pro&shy;<lb/>po&longs;itiones, ac vnum corollarium proponit, eas&queacute; demon&longs;trationi&shy;<lb/>bus Arithmeticis demon&longs;trat. </s>
<s>&longs;unt autem h&aelig;, qu&aelig; ordinatim &longs;e&shy;<lb/>quuntur, quemadmodum etiam ab Autore proponuntur.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/139.jpg"/><p type="main">
<s><emph type="center"/><emph type="italics"/>Propo&longs;itio prima.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Omnis cubi ba&longs;is ad cylindri in ip&longs;o in&longs;cripti ba&longs;im, &amp; &longs;ex eiu&longs;&shy;<lb/>dem cubi plana ad eiu&longs;dem cylindri &longs;uperficiem vn&agrave; cum dua&shy;<lb/>bus cylindri ba&longs;ibus, necnon quatuor cubi plana ad eandem cylin&shy;<lb/>dri &longs;uperficiem &longs;ine duabus cylindri ba&longs;ibus, ac demum cubi &longs;oli&shy;<lb/>ditas ad cylindri &longs;oliditatem rationem eam, quam numerus 14 ad <lb/>11 numerum habent.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Secunda.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Omnis cylindri &longs;uperficies &longs;ine ba&longs;ibus &longs;uperficiei &longs;ph&aelig;r&aelig; in ip&shy;<lb/>&longs;o in&longs;cript&aelig; &aelig;qualis e&longs;t.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Tertia.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Omnis cylindrus &longs;ph&aelig;r&aelig; in ip&longs;o in&longs;cript&aelig; <expan abbr="t&utilde;">tum</expan> iuxta &longs;uperficiem <lb/>vn&agrave; cum ba&longs;ibus, tum iuxta &longs;oliditatem &longs;e&longs;quialter e&longs;t.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Vnde con&longs;tat qu&ograve;d omnis &longs;ph&aelig;ra tum iuxta &longs;uperficiem, tum <lb/>iuxta &longs;oliditatem du&aelig;terti&aelig; partes est circumambientis ip&longs;am <lb/>&aelig;qu&egrave; alti cylindri.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Quarta.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Omnis &longs;ph&aelig;rica &longs;uperficies are&aelig; quidem &longs;ui maximi circuli <lb/>quadrupla e&longs;t: iam dicti ver&ograve; circuli ambitum tot vicibus conti&shy;<lb/>net, quot in eius axe iuxta longitudinem vnitates &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Quinta.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Omnis &longs;ph&aelig;ra iuxta &longs;oliditatem e&longs;t quadrupla coni ba&longs;im qui&shy;<lb/>dem habentis maximum ip&longs;ius &longs;ph&aelig;r&aelig; circulum, altitudinem ver&ograve; <lb/>&aelig;qualem dimidio axis eiu&longs;dem &longs;ph&aelig;r&aelig;: dupla autem coni ba&longs;im <lb/>quidem habentis maximum ip&longs;ius &longs;ph&aelig;r&aelig; circulum, altitudinem <lb/>ver&ograve; totum eiu&longs;dem &longs;ph&aelig;r&aelig; axem.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Sexta.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Omnis cylindrus triplus e&longs;t coni eandem <expan abbr="c&utilde;">cum</expan> ip&longs;o ba&longs;im, &amp; &aelig;qua&shy;<lb/>lem altitudinem habentis tum iuxta &longs;uperficiem &longs;ine ba&longs;ibus, tum <lb/>iuxta &longs;oliditatem.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>Septima.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>Omne pri&longs;ma parallelepipedum pyramidis eandem cum ip&longs;o ba<emph.end type="italics"/>
<pb xlink:href="052/01/140.jpg"/><emph type="italics"/>&longs;em, &amp; &aelig;qualem altitudinem habentis triplum exi&longs;tit.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Quarum quidem propo&longs;itionum geometric&ecedil; demon&longs;trationes <lb/>partim apud Euclidem iam dictis in locis, partim apud Archi&shy;<lb/>medem in &longs;uis de &longs;ph&aelig;ra, &amp; cylindro libris habentur. </s>
<s>Arithm&egrave;&shy;<lb/>tic&aelig; ver&ograve; earundem demon&longs;trationes ab Autore breuiter enarra&shy;<lb/>t&aelig;, in figura, ac diagrammate in fine pr&aelig;&longs;entis &longs;eptim&aelig; propo&longs;i&shy;<lb/>tionis &agrave; nobis appo&longs;itis &agrave; quouis explicari facil&egrave; po&longs;&longs;unt. </s>
<s><expan abbr="H&ecedil;c">Haec</expan> <expan abbr="eti&atilde;">etiam</expan> <lb/>pro dilucidatione propo&longs;itionis huiu&longs;ce dicenda nobis erant.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Octaua.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note325"/></s></p><p type="margin">
<s><margin.target id="note325"/><emph type="italics"/>Propo&longs;i&shy;<lb/>tio.<emph.end type="italics"/></s></p><p type="main">
<s>OPus itaque &longs;it in parallelogrammo, &amp; altera <lb/>parte longiori &aelig;dificio, vel humoris recepta&shy;<arrow.to.target n="note326"/><lb/>culo &longs;imilis figur&aelig;, vt in Aetia ci&longs;terna &longs;olidi&shy;<lb/>tatis men&longs;urationem manife&longs;tare: facili&ugrave;s au&shy;<lb/>tem in pi&longs;cina propter dimen&longs;ionum circa ba&shy;<lb/>&longs;im exi&longs;tentium &aelig;qualitatem lateritia figura ip&longs;a exi&longs;tente. </s>
<s><lb/>Later autem e&longs;t figura &longs;olida &agrave; &longs;ex planis <expan abbr="c&otilde;tenta">contenta</expan> &aelig;qualem <lb/>ba&longs;is longitudinem, ac latitudinem habens, minorem ver&ograve; <lb/>altitudinem. </s>
<s>&longs;i enim &aelig;qualis iuxta altitudinem etiam exi&shy;<lb/>&longs;teret, cubus quidem e&longs;&longs;et: &longs;i autem maior, trabs figurare&shy;<lb/>tur. </s>
<s>Trabs enim e&longs;t, qu&aelig; altitudinem longitudine ba&longs;is ac <arrow.to.target n="note327"/><lb/>latitudine <expan abbr="maior&etilde;">maiorem</expan> habet. </s>
<s>Supponatur igitur ba&longs;is ip&longs;ius pi&shy;<lb/>&longs;cin&aelig;, &longs;eu ci&longs;tern&aelig; iuxta longitudinem pa&longs;&longs;uum 70, latitu&shy;<lb/>dinem &longs;imiliter eandem habens, &amp; altitudinem <expan abbr="pa&longs;&longs;u&utilde;">pa&longs;&longs;uum</expan> 12. <arrow.to.target n="note328"/><lb/>Qu&aelig;ro igitur inuenire quot pa&longs;&longs;uum e&longs;t ci&longs;tern&aelig; &longs;oliditas, <lb/>&amp; quot amphoras humoris capere pote&longs;t. </s>
<s>Multiplicans ip&shy;<arrow.to.target n="note329"/><lb/>&longs;os 70 longitudinis in eo&longs;dem latitudinis pa&longs;&longs;us, habeo pla&shy;<lb/>num iuxta ba&longs;im exi&longs;tens pa&longs;&longs;uum 4900. </s><s>hos itaque rur&longs;us <lb/>in ip&longs;os altitudinis, 12 pa&longs;&longs;us multiplico, <expan abbr="fiunt&qacute;ue">fiuntque</expan> 58800. <arrow.to.target n="note330"/><lb/>At quoniam ea, qu&aelig; longitudine quaprupla &longs;unt, potentia <lb/>&longs;exdecupla exi&longs;tunt, &longs;oliditate ver&ograve; &longs;exagincuplaquadru&shy;<arrow.to.target n="note331"/><lb/>pla: pa&longs;&longs;us autem e&longs;t digitorum 96, cubitus ver&ograve; 24: qua&shy;<lb/>druplus ergo pa&longs;&longs;us ip&longs;ius cubiti iuxta longitudinem e&longs;t: <lb/>&amp; ba&longs;is longitudo cubitorum 280 exi&longs;tit. </s>
<s>ex his autem in&shy;<lb/>uenietur <expan abbr="plan&utilde;">planum</expan> 78400. etenim 16 in 4900 faciunt 78400. <lb/>ex his autem rur&longs;us &longs;oliditas fit 3763200. ita enim 64 in
<pb xlink:href="052/01/141.jpg"/><arrow.to.target n="note332"/><lb/>58800 faciunt. </s><s>At quoniam rur&longs;um ea, qu&aelig; longitudine <lb/>&longs;excupla &longs;unt, potentia trigincupla&longs;excupla o&longs;tenduntur, <lb/>&longs;oliditate ver&ograve; ducentupla&longs;exdecupla erunt. </s><s>e&longs;t enim pes <lb/>16 quoad longitudinem digitorum &longs;exta pa&longs;&longs;us pars exi&shy;<lb/>&longs;tens. </s>
<s>vnd&egrave; rur&longs;us longitudo iuxta ba&longs;im iacens, <expan abbr="ped&utilde;">pedum</expan> 420 <lb/>fit: planum vero, 176400: <expan abbr="tota&qacute;">totaque</expan>; &longs;oliditas <expan abbr="ped&utilde;">pedum</expan> 12700800. <lb/><expan abbr="n&atilde;">nam</expan> 36 in 4900 faciunt 176400, &amp; 216 in 58800, 12700800. <lb/>Et quoniam &longs;olidus pes, qui &longs;ecundum Mechanicorum <arrow.to.target n="note333"/><lb/><expan abbr="con&longs;titution&etilde;">con&longs;titutionem</expan> ab ip&longs;is 16 longitudinis digitis cubatur, 4096 <arrow.to.target n="note334"/><lb/>reperitur. </s>
<s>ip&longs;i autem 16 digiti per &longs;e &longs;e quatuor aqu&aelig; vn&shy;<lb/>cias fer&egrave; &longs;u&longs;cipiunt, digiti ver&ograve; 51 1/5 ip&longs;am duodecim vn&shy;<arrow.to.target n="note335"/><lb/>ciarum italicarum libram continebunt: ip&longs;i autem 256 ip&shy;<lb/>&longs;ius plani digiti, libras quinque: necnon ip&longs;ius &longs;oliditatis di&shy;<lb/>giti 4096, libras 80. Reperitur itaque &longs;olidus pes humoris <arrow.to.target n="note336"/><lb/>capax quoad men&longs;uram amphor&aelig; librarum italicarum 80. <arrow.to.target n="note337"/><lb/>Quamobrem quot pedum &longs;olidorum ip&longs;um humoris rece&shy;<lb/>ptaculum computatum e&longs;t, tot etiam amphorarum humo&shy;<lb/>ris e&longs;t capax. </s>
<s>Similiter autem ad quamlibet <expan abbr="eti&atilde;">etiam</expan> profundi&shy;<lb/>tatis partem &longs;ignum adnotantes, aqu&aelig; molem connumera&shy;<lb/>bimus. </s>
<s>Cylindri ver&ograve; figura <expan abbr="exi&longs;t&etilde;te">exi&longs;tente</expan>, circuli aream (vt iam <lb/>diximus) accipere oportet: &amp; eos, qui iuxta ip&longs;am ba&longs;im re&shy;<lb/>periuntur pedes in altitudinem multiplicare: eum autem, <lb/>qui fit numerum, in ip&longs;o quidem humoris receptaculo, de <lb/>ip&longs;a aqu&aelig; mole pronuntiare: in &longs;imilis autem figur&aelig; &aelig;difi&shy;<lb/>cio &longs;ine &longs;uperimpo&longs;ito tecto triticum, &amp; hordeum, &amp; legu&shy;<lb/>mina, ac demum quotcumque ex di&longs;ret&aelig; quantitatis for&shy;<arrow.to.target n="note338"/><lb/>mis iuxta medimnos, &amp; modios, ac &longs;emodios, <expan abbr="&longs;impliciore&longs;-&qacute;ue">&longs;impliciore&longs;&shy;<lb/>que</expan> men&longs;uras con&longs;iderantur, ad pondus, &amp; magnitudinem <lb/>ex eo, qui con&longs;truitur &longs;olido pede, re&longs;picientes &longs;upputare. </s></p>
<pb xlink:href="052/01/142.jpg"/><p type="margin">
<s><margin.target id="note326"/>a</s></p><p type="margin">
<s><margin.target id="note327"/><emph type="italics"/>Expo&longs;i&shy;<lb/>tio et <expan abbr="c&otilde;-&longs;tructio">con&shy;<lb/>&longs;tructio</expan>.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note328"/><emph type="italics"/>Determi&shy;<lb/>natio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note329"/><emph type="italics"/>Demon&shy;<lb/>&longs;tratio.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note330"/>b</s></p><p type="margin">
<s><margin.target id="note331"/>c</s></p><p type="margin">
<s><margin.target id="note332"/>d</s></p><p type="margin">
<s><margin.target id="note333"/>e</s></p><p type="margin">
<s><margin.target id="note334"/>f</s></p><p type="margin">
<s><margin.target id="note335"/>g</s></p><p type="margin">
<s><margin.target id="note336"/>h</s></p><p type="margin">
<s><margin.target id="note337"/><emph type="italics"/><expan abbr="C&otilde;clu&longs;io">Conclu&longs;io</expan>.<emph.end type="italics"/></s></p><p type="margin">
<s><margin.target id="note338"/>k.i</s></p><p type="caption">
<s>Ci&longs;terna &longs;eu pi&longs;cina lateris figuram habens.<lb/><arrow.to.target n="fig4"/></s></p><figure id="id.052.01.142.1.jpg" xlink:href="052/01/142/1.jpg"/><p type="table">
<s>TABELLE WAR HIER</s></p>
<pb xlink:href="052/01/143.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note339"/></s></p><p type="margin">
<s><margin.target id="note339"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Aetia] hoc e&longs;t Aegyptiaca, iuxta formam &longs;cilicet Aegy&shy;<lb/>ptiacarum ci&longs;ternarum fabricata. </s>
<s>nam Aetia dicta est Aegyptus <lb/>&agrave; quodam Indo Aeto, vt Stefanus adnotauit. </s>
<s>Melior autem lectio <lb/>e&longs;t Y etia, hoc e&longs;t pluuio&longs;a.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note340"/></s></p><p type="margin">
<s><margin.target id="note340"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ea, qu&aelig; longitudine quadrupla &amp;c.] ip&longs;&aelig; &longs;cilicet rect&aelig; line&aelig;, <lb/>qu&aelig; longitudine <expan abbr="quadrupl&atilde;">quadruplam </expan>inter &longs;e rationem habent: potentia, <lb/>videlicet iuxta earum quadrata, &longs;exdecuplam rationem &longs;eruant: <lb/>&longs;oliditate ver&ograve;, nempe iuxta &longs;olida ex ip&longs;is producta, &longs;exdecuplam <lb/>rationem &longs;ortit&aelig; &longs;unt. </s>
<s>H&aelig;c autem regula vera, &amp; vniuer&longs;alis <lb/>e&longs;t, <expan abbr="demon&longs;trari&qacute;ue">demon&longs;trarique</expan> geometric&egrave; pote&longs;t per quintam definitionem <lb/>&longs;exti, &amp; &longs;ecundam partem vige&longs;im&aelig; propo&longs;itionis eiu&longs;dem, &amp; de&shy;<lb/>cimam definitionem quinti Elementorum Euclidis.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note341"/></s></p><p type="margin">
<s><margin.target id="note341"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[pa&longs;&longs;us autem e&longs;t digitorum 96 &amp;c.] pa&longs;&longs;um h&igrave;c non &longs;impli&shy;<lb/>cem, &longs;ed geometricum intelligere debemus, quem &longs;ex pedes iuxta <lb/>gr&aelig;corum &longs;ententiam continere &longs;uperi&ugrave;s diximus. </s>
<s>c&ugrave;m autem <lb/>pes quidem quatuor palmis, palmus ver&ograve; quatuor digitis con&longs;tet: <lb/>nemo e&longs;t, qui non fateatur iam dictum pa&longs;&longs;um 96 digitis comple&shy;<lb/>ri. </s>
<s>Similiter etiam cubitus c&ugrave;m &longs;ex palmos contineat, dubio pro&shy;<lb/>cul 24 digitis con&longs;tat. </s>
<s>vnd&egrave; etiam pa&longs;&longs;us ip&longs;e cubiti iuxta longi&shy;<lb/>tudinem quadruplus e&longs;t.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note342"/></s></p><p type="margin">
<s><margin.target id="note342"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ea, qu&aelig; longitudine &longs;excupla &longs;unt &amp;c.] H&aelig;c etiam regula <lb/>vera &amp; vniuer&longs;alis e&longs;t, iam dictis&queacute; geometricis rationibus demon <lb/>&longs;trari pote&longs;t.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note343"/></s></p><p type="margin">
<s><margin.target id="note343"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[cubare] gr&aelig;c&egrave;<emph.end type="italics"/> <foreign lang="greek">kubi/zein</foreign>, <emph type="italics"/>verbum hoc licet apud latinos alias <lb/>habeat &longs;ignificationes, tamen apud Mathematicos nil aliud &longs;igni&shy;<lb/>ficat, ni&longs;i numerum cubum ex aliquo numero producere, vel figu&shy;<lb/>ram cubicam ex aliqua recta linea de&longs;ignare. </s>
<s>Adnotandum au&shy;<lb/>tem e&longs;t qu&ograve;d omnes men&longs;ur&aelig; geometric&aelig; tripliciter con&longs;iderari <lb/>po&longs;&longs;unt, vel quatenus linearum longitudinem, vel quatenus &longs;u&shy;<lb/>perficierum aream, vel quatenus corporum &longs;oliditatem <expan abbr="men&longs;ur&atilde;t">men&longs;urant</expan>. </s>
<s><lb/>Quapropter cuiu&longs;cumque generis men&longs;ura geometrica tum li&shy;<lb/>nearis vel recta, vel circularis, vel ex hi&longs;ce mi&longs;ta: tum &longs;uperfi&shy;<lb/>cialis vel plana, vel &longs;ph&aelig;rica, vel mi&longs;ta: tum etiam &longs;olida vel hu&shy;<lb/>ius, vel illius form&aelig; iuxta corporum diuer&longs;itatem appellari pote&longs;t.<emph.end type="italics"/>
<pb xlink:href="052/01/144.jpg"/><emph type="italics"/>atque talis e&longs;t &longs;olidus pes, de quo Autor in pr&aelig;&longs;entia loquitur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note344"/></s></p><p type="margin">
<s><margin.target id="note344"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[quatuor aqu&aelig; vncias fer&egrave;] vnciam h&igrave;c non pro geometrica <lb/>illa men&longs;ura &longs;u&longs;cipienda e&longs;t, quam tribus con&longs;tare digitis &longs;upe&shy;<lb/>ri&ugrave;s diximus: &longs;ed pro duodecima ip&longs;ius a&szlig;is, &longs;iue libr&aelig; parte. </s>
<s>quo&shy;<lb/>niam autem qu&aelig;libet humoris libra 51 1/5 digitis con&longs;tat, non im&shy;<lb/>merito quatuor fer&egrave; vncias aqu&aelig; (&longs;icut ait Autor) ip&longs;i 16 digiti <lb/>habent. </s>
<s>c&ugrave;m enim quatuor vnci&aelig; &longs;int tertia libr&aelig; pars, libra ve&shy;<lb/>r&ograve; 51 1/5 digitis con&longs;tet, dubio procul digiti 17 &amp; tertia pars vnius <lb/>quint&aelig; digiti partis vncias quatuor <expan abbr="contin&etilde;t">continent</expan>. </s>
<s>quare 16 digiti fe&shy;<lb/>r&egrave; quatuor vncias habent, vt Autor inquit.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[italicarum] c&ugrave;m italorum libr&aelig; &agrave; libris gr&aelig;corum iuxta quan<arrow.to.target n="note345"/><lb/>titatem di&longs;crepent, non immerito vnci&aelig; quoque diuer&longs;&aelig; &longs;unt. </s>
<s>quo&shy;<lb/>niam autem italica libra e&longs;t digitorum 51 1/5, idcirco vnciarum, <lb/>ac librarum italicarum Autor dixit.<emph.end type="italics"/><lb/><arrow.to.target n="note346"/></s></p><p type="margin">
<s><margin.target id="note345"/>g</s></p><p type="margin">
<s><margin.target id="note346"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Amphora e&longs;t Autore Budeo men&longs;ura congios quidem octo, &longs;ex&shy;<lb/>tarios ver&ograve; 48 continens. </s>
<s>&longs;extarius enim e&longs;t &longs;exta congij pars. </s>
<s>h&igrave;c <lb/>autem Amphoram Autor pro va&longs;e fictili libras 80 italicas humo&shy;<lb/>ris, &longs;iue pedem vnum &longs;olidum recipiente &longs;u&longs;cipere videtur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note347"/></s></p><p type="margin">
<s><margin.target id="note347"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Medimnus est men&longs;ura <expan abbr="capi&etilde;s">capiens</expan> quinos modios &longs;ecund&ugrave;m &longs;icu&shy;<lb/>lam men&longs;uram, vel &longs;enos &longs;ecund&ugrave;m Atticam, aut Romanam te&longs;te <lb/>Budeo libro quinto de A&longs;&longs;e.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note348"/></s></p><p type="margin">
<s><margin.target id="note348"/>k</s></p><p type="main">
<s><emph type="italics"/>Simpliciores men&longs;uras h&igrave;c intelligere debemus modij partes &longs;e <lb/>modio minores, ex quibus modius componitur, &amp; in quas re&longs;&longs;olui&shy;<lb/>tur. </s>
<s>H&aelig;c autem pro pr&aelig;&longs;entis etiam propo&longs;itionis intelligentia <lb/>breuiter &agrave; nobis dicta &longs;ufficiant. </s>
<s>nam ex figura, &amp; diagramma&shy;<lb/>te, quod in eius calce appo&longs;uimus, clara &longs;unt ea, qu&aelig; ab Autore <lb/>demon&longs;trationibus Arithmeticis o&longs;tenduntur.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Nona.<emph.end type="center"/></s></p><p type="main">
<s><arrow.to.target n="note349"/></s></p><p type="margin">
<s><margin.target id="note349"/>a</s></p><p type="main">
<s>COgno&longs;cemus autem fontis quoque defluxum <lb/>&longs;ecundum Heronem, quantu&longs;cumque &longs;it. </s>
<s>ve&shy;<lb/>r&ugrave;m &longs;cire quidem oportet qu&ograve;d non &longs;emper <lb/>eadem &longs;caturigo permanet. </s>
<s><expan abbr="n&atilde;">nam</expan> imbribus qui&shy;<lb/>dem exi&longs;tentibus intenditur, e&ograve; quod in api&shy;<lb/>cibus montium aqua &longs;uperabundans, violenti&ugrave;s eliditur:
<pb xlink:href="052/01/145.jpg"/>&longs;iccitatibus autem exi&longs;tentibus deficit. </s>
<s>At fontes illi, qui <lb/>&longs;uapte natura &longs;caturiendi vim habent, non multam &longs;caturi&shy;<lb/>ginem &longs;ortit&aelig; &longs;unt. </s>
<s>Oper&aelig;pretium e&longs;t igitur totam fontis <lb/>aquam circumambientes, vt nu&longs;quam defluat: tubum <expan abbr="plumbe&utilde;">plum<lb/>beum</expan> quadrangulum facere, qui defluxu iuxta receptionem <lb/>mult&ograve; maior exi&longs;tat. </s>
<s><expan abbr="ip&longs;um&qacute;ue">ip&longs;umque</expan> vni loco &longs;ic adaptare, vt per <lb/>ip&longs;um fontis aqua defluat. </s>
<s>Opus e&longs;t autem tubum ip&longs;um <lb/>ad depre&longs;&longs;iorem fontis locum iacere, vt facilem defluxum <lb/>habeat. </s>
<s>ip&longs;um autem depre&longs;&longs;iorem locum per dioptram <lb/>agno&longs;cemus. </s>
<s>ip&longs;a ver&ograve; defluens aqua, in bucula tubi iuxta <arrow.to.target n="note350"/><lb/>altitudinem manife&longs;ta fiet. </s>
<s>Sit itaque iuxta altitudinem di&shy;<lb/>gitorum trium, habeat autem &amp; latitudinem ip&longs;a bucula di&shy;<lb/>gitorum &longs;ex. </s>
<s>at digiti tres in &longs;ex digitos multiplicati, 18 fa&shy;<lb/>ciunt. </s>
<s>ip&longs;am ergo fontis &longs;caturiginem 18 <expan abbr="digitor&utilde;">digitorum</expan> e&longs;&longs;e pro&shy;<lb/>nuntiabimus. </s>
<s>Ver&ugrave;menimuero &longs;ciendum e&longs;t, qu&ograve;d non &longs;uf&shy;<lb/>ficit ad agno&longs;cendum quantam fons exhibet aquam, ip&longs;ius <lb/>defluxus molem inuenire: &longs;ed ip&longs;a quoque velocitas repe&shy;<lb/>rienda e&longs;t. </s>
<s>nam velociori defluxu quidem exi&longs;tente, plus <lb/>aqu&aelig; pr&aelig;betur: tardiori ver&ograve;, minus. </s>
<s>Quare &longs;ub fontis de&shy;<lb/>fluxum fo&longs;&longs;am effodientes ob&longs;eruare oportet ex &longs;olari ho&shy;<lb/>rologio, quanta per vnamquamque horam aqua in fo&longs;&longs;a <lb/>defluit: &amp; &longs;ic aquam, qu&aelig; per totam diem exhibetur, con&shy;<lb/>&longs;iderare quanta iuxta molem &longs;it. </s>
<s>Quamobrem non &longs;ol&ugrave;m <lb/>defluxus molem, ver&ugrave;metiam velocitatem ob&longs;eruare ne&shy;<lb/>ce&longs;&longs;um e&longs;t. </s>
<s>nam per horarium tempus diurnam etiam aqu&aelig; <lb/>contributionem explo<arrow.to.target n="fig5"/><lb/>ratam habebimus, &longs;i <lb/>enim omne <foreign lang="greek">nuxqh/meron</foreign><arrow.to.target n="note351"/><lb/>hoc e&longs;t diei &longs;imul &amp; no<lb/>ctis &longs;patium &aelig;quino&shy;<arrow.to.target n="note352"/><lb/>ctialium <expan abbr="t&etilde;por&utilde;">temporum</expan> 360, <lb/>horarum ver&ograve; 24 e&longs;t: <lb/>qu&ecedil;libet hora quinde&shy;<lb/>cim &aelig;quinoctialia tem <lb/>pora continebit: plu&shy;<lb/>ra ver&ograve; quandoque, <expan abbr="pauciora&qacute;ue">paucioraque</expan> &longs;uppeditatio ip&longs;a. </s>
<s>quo&shy;<lb/>niam hyeme quidem exi&longs;tente maior defluxus fit, &aelig;&longs;tate
<pb xlink:href="052/01/146.jpg"/>ver&ograve;, minor. </s>
<s>Si igitur in qualibet hora aquam in fo&longs;&longs;a de&shy;<arrow.to.target n="note353"/><lb/>fluentem 20 forta&longs;&longs;e cadorum e&longs;&longs;e perceperimus, quadri&shy;<lb/>gentorum ergo &amp; octoginta fontis exhibitionem per diem, <lb/><expan abbr="noctem&qacute;ue">noctemque</expan> pronuntiabimus. </s></p><p type="margin">
<s><margin.target id="note350"/>b</s></p><p type="margin">
<s><margin.target id="note351"/>c</s></p><p type="margin">
<s><margin.target id="note352"/>d</s></p><p type="margin">
<s><margin.target id="note353"/>e</s></p><figure id="id.052.01.146.1.jpg" xlink:href="052/01/146/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/><lb/><arrow.to.target n="note354"/></s></p><p type="margin">
<s><margin.target id="note354"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>QVi&longs;nam fuerit Heron, cuius h&igrave;c, &amp; multis alijs in locis <lb/>Autor no&longs;ter mentionem facit, in &longs;uperioribus &longs;atis &longs;u&shy;<lb/>per&queacute; diximus. </s>
<s>fontium autem defluxum men&longs;urare do&shy;<lb/>cuit ille Alexandrinus Heron in libris quatuor, quos de aquati&shy;<lb/>cis horologijs &longs;crip&longs;it.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note355"/></s></p><p type="margin">
<s><margin.target id="note355"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;it it aque] &longs;cilicet ip&longs;a aqua, qu&aelig; in tubo e&longs;t dum fluit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note356"/></s></p><p type="margin">
<s><margin.target id="note356"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Dies h&igrave;c intelligendus e&longs;t artificialis, videlicet ab ortu &longs;olis ad <lb/>occa&longs;um v&longs;que.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note357"/></s></p><p type="margin">
<s><margin.target id="note357"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Aequinoctialia tempora vocat Autor ip&longs;as 360 particulas <lb/>&aelig;quinoctialis circuli c&aelig;le&longs;tis, quas A&longs;trologi latini gradus ap&shy;<lb/>pellant.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note358"/></s></p><p type="margin">
<s><margin.target id="note358"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Cadus e&longs;t vinarium vas congios decem, vel (vt <expan abbr="quid&atilde;">quidam</expan> volunt) <lb/>duodecim continens. </s>
<s>H&aelig;c paucula pro huiu&longs;ce dilucid&aelig; per &longs;e pro&shy;<lb/>po&longs;itionis faciliori perceptione dicta &longs;int.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/>Propo&longs;itio Decima, &amp; vltima.<emph.end type="center"/></s></p><p type="main">
<s>QVandoquidem igitur promi&longs;&longs;os &longs;uperi&ugrave;s dio&shy;<lb/>ptricos v&longs;us enarrauimus, propter commo&shy;<lb/>dum huiu&longs;cemodi dioptr&aelig; v&longs;um ad <expan abbr="c&oelig;le&longs;ti&utilde;">c&oelig;le&longs;tium</expan> <lb/>etiam contemplationem eleuari poterimus: <lb/>c&ugrave;m &longs;olis, tum lun&ecedil; magnitudinem ip&longs;a di&longs;cer<lb/>nentes: necnon &longs;tellarum abinuicem di&longs;tantias tum <expan abbr="fixar&utilde;">fixarum</expan> <lb/>ad fixas ac errantes, tum errantium ad errantes &amp; fixas per&shy;<lb/>&longs;picere. </s>
<s>nam ex ea, qu&aelig; in tympano facta e&longs;t ip&longs;orum 360 <lb/>graduum, &amp; iacentium inter ip&longs;os minutorum de&longs;criptio&shy;</s></p><p type="main">
<s><arrow.to.target n="note359"/><lb/>ne: magnitudines, qu&aelig; qu&aelig;runtur &longs;imul a&longs;picere valebi&shy;<lb/>mus. </s>
<s>Qu&ugrave;m itaque di&longs;tantiam inter duas &longs;tellas exi&longs;tentem <lb/>ob&longs;eruare voluerimus, quot partium exi&longs;tat: tympani par&shy;<pb xlink:href="052/01/147.jpg"/>tem ver&longs;us nos iacentem inclinabimus, ad altum alteram <lb/>attollentes, donec vtique per idem planum ambarum &longs;tel&shy;<lb/>larum &longs;itus con&longs;pexerimus: atque cunctis, qu&aelig; in dioptra <lb/>&longs;unt, immobilibus permanentibus regulam &longs;uper tympano <lb/>circumuoluemus donec vnam &longs;tellarum per duo foramina <lb/>di&longs;piciamus: &amp; c&ugrave;m gradum, &longs;eu minutum adnotaueri&shy;<lb/>mus, in eo loco, vbi graduum index exi&longs;tit: regulam &longs;tatim <lb/>circumuertemus, <expan abbr="quou&longs;q;">quou&longs;que</expan> per duo foramina reliquam quo&shy;<lb/>que per&longs;piciamus: <expan abbr="gradum&qacute;ue">gradumque</expan> demum illum, qui iuxta gra&shy;<lb/>duum indicem iacet c&ugrave;m &longs;imiliter adnotauerimus, &amp; gra&shy;<arrow.to.target n="note360"/><lb/>dus inter iam dicta duo &longs;igna iacentes &longs;uper tympano nu&shy;<lb/>merauerimus, ip&longs;as &longs;tellarum abinuicem di&longs;tantias enun&shy;<lb/>tiabimus. </s>
<s>c&ugrave;m autem ad aliquem Zodiaci locum vnam &longs;tel&shy;<arrow.to.target n="note361"/><lb/>larum di&longs;pexerimus, &longs;i quidem iuxta longitudinem ad an&shy;<lb/>tecedentia, vt ab oriente ad occidentem: ad partes dexte&shy;<lb/>ras regulam in tympano exi&longs;tentem circumagentes, hanc <lb/>di&longs;picimus: &longs;i ver&ograve; ad con&longs;equentia, vt ab occidente ad <lb/>c&oelig;li medium, &longs;iue ad horo&longs;copum: ad partes &longs;ini&longs;tras. </s>
<s>An&shy;<lb/>tecedentia autem &longs;igna vocantur, qu&ecedil; &longs;unt ab Ariete ad Pi&shy;<lb/>&longs;ces, Aquarium, Sagittarium, &amp; c&aelig;tera: con&longs;equentia ver&ograve;, <lb/>qu&aelig; &longs;unt ab Ariete ad Taurum, Geminos, Cancrum, &amp; re&shy;<lb/>liqua. </s>
<s>&amp; &longs;i quidem &longs;ecund&ugrave;m Zodiaci longitudinem di&longs;tan&shy;<lb/>tiam con&longs;ideramus haud fortuit&ograve; di&longs;piciemus: &longs;ed &longs;uper li&shy;<lb/>nea meridiana parallelam dioptram con&longs;tituentes. </s>
<s>&longs;i ver&ograve; <arrow.to.target n="note362"/><lb/>&longs;ecund&ugrave;m latitudinem qu&aelig;&longs;tionem facimus, vt &agrave; Borea ad <lb/>Au&longs;trum, aut &egrave; contrario: &longs;uper linea &aelig;quinoctiali. </s>
<s>H&aelig; au&shy;<lb/>tem line&aelig; in admiratione digno regali ver&longs;us Au&longs;trum cu&shy;<lb/>biculo ijs, qui de hoc curant, &agrave; nobis in&longs;cript&aelig;, &longs;uper viri&shy;<lb/>dibus iacent. </s>
<s>harum autem inuentionem in po&longs;itione &longs;ola&shy;<arrow.to.target n="note363"/><lb/>rium horologiorum con&longs;crip&longs;imus. </s>
<s>C&ugrave;m igitur &longs;uper cir&shy;<lb/>culo hemi&longs;ph&aelig;rium &longs;uper terram exi&longs;tens definiente ad <lb/>ortus ip&longs;os, vel occa&longs;us c&ugrave;m tropica, tum &aelig;quinoctialia, <arrow.to.target n="note364"/><lb/>tum etiam ea, qu&aelig; inter h&aelig;c men&longs;trua &longs;unt &longs;igna &longs;u&longs;cipere <lb/>voluerimus: ad lineam meridianam dioptram parallelam <lb/>&longs;tatuentes, regulam ip&longs;am dirigimus: &amp; per duo foramina <lb/>ad ortum, &amp; occa&longs;um indirect&ugrave;m di&longs;picientes, h&aelig;c in no&shy;<lb/>&longs;tro orizonte ob&longs;eruabimus: vbi Sol c&ugrave;m in primum Arie
<pb xlink:href="052/01/148.jpg"/>tis, vel Libr&aelig; gradum aduenerit, tum vernalia, tum autum&shy;<arrow.to.target n="note365"/><lb/>nalia facit &aelig;quinoctia. </s>
<s>&amp; quoniam parallelum orizonti <lb/>tympanum apponitur, c&ugrave;m &agrave; &longs;itu indicis regul&aelig; ad partes <lb/>boreales gradus 32 numerauerimus, ad <expan abbr="ip&longs;os&qacute;ue">ip&longs;osque</expan> regulam <lb/>direxerimus: &aelig;&longs;tiua tropica &longs;igna &longs;u&longs;cipiemus. </s>
<s>ibi enim Sol <lb/>in primum Cancri gradum veniens &aelig;&longs;tiuas efficit conuer&shy;<lb/>&longs;iones. </s>
<s>qu&aelig; ver&ograve; in medio interiacent men&longs;trua &longs;igna ab <lb/>&aelig;quinoctiali per 16, &amp; 28 gradus accipiemus. </s>
<s>&amp; &egrave; contra&shy;<arrow.to.target n="note366"/><lb/>rio ab &aelig;quinoctiali ad partes au&longs;trales eo&longs;dem gradus nu&shy;<lb/>merantes, ad <expan abbr="ip&longs;os&qacute;ue">ip&longs;osque</expan> regulam deducentes: c&ugrave;m hyema&shy;<lb/>lia tropica, tum medio interiacentia men&longs;trua &longs;igna con&longs;pi<lb/>cere poterimus. </s>
<s>At quoniam per 180 &longs;emicirculi gradus <lb/>&longs;igna &longs;ecund&ugrave;m dimetientem oppo&longs;ita &longs;uper orizontem <lb/>oriuntur, &amp; occidunt: Cancro &longs;iquidem oriente, Capri&shy;<lb/>cornus occidit: Aquario ver&ograve; occidente, oritur Leo: volui <lb/>ob&longs;eruare quot gradibus di&longs;tet in <expan abbr="anteced&etilde;tibus">antecedentibus</expan> &longs;ignorum <arrow.to.target n="note367"/><lb/>lucida Hyadum &longs;tella (qu&aelig; etiam Lambauras, hoc e&longs;t fax <lb/>ardens dicitur) ab ea, qu&aelig; in corde Leonis e&longs;t, vocatur au&shy;<lb/>tem Ba&longs;ili&longs;cus: <expan abbr="atq;">atque</expan> circa &longs;ecundam horam nocturnam c&ugrave;m <lb/>orientem ver&longs;us di&longs;pexerim, ac <expan abbr="t&atilde;quam">tanquam</expan> manife&longs;tam cam, <lb/>qu&aelig; in corde Leonis e&longs;t &longs;tellam acceperim: adnotaui gra&shy;<lb/>dum in tympano, iuxta quem regul&aelig; index extitit: &amp; c&ugrave;m <lb/>ad antecedentia regulam conuerterim, di&longs;pexi in Tauro ip <lb/>&longs;am <expan abbr="Lambaur&atilde;">Lambauram</expan>, hoc e&longs;t facem <expan abbr="ardent&etilde;">ardentem</expan>, c&ugrave;m <expan abbr="grad&utilde;">gradum</expan>, qui apud <lb/>ip&longs;am e&longs;t &longs;imiliter adnotarim. </s>
<s>&amp; <expan abbr="c&utilde;">cum</expan> in tympano gradus in&shy;<lb/>ter &longs;igna <expan abbr="iac&etilde;tes">iacentes</expan> enumerauerim, eos 80 fer&egrave; inueni. </s>
<s>quot <expan abbr="&etilde;t">etiam</expan> <arrow.to.target n="note368"/><lb/>&longs;unt ij, quibus amb&aelig; &longs;telle abinuicem di&longs;tant. </s>
<s>nam ip&longs;e <lb/>Ba&longs;ili&longs;cus un&agrave; cum additamento motus eorum, qu&aelig; ab <lb/>&aelig;tate Ptolem&cedil;i &longs;unt temporum, gradus 10 1/2 in Leone <expan abbr="n&utilde;c">nunc</expan> <lb/>po&longs;&longs;idens reperitur: Et lucida Hyadum in Tauro, 20 <arrow.to.target n="note369"/><lb/>2/3. </s><s>C&ugrave;m autem ip&longs;os 10 1/2 gradus leonis in antecedentia <lb/>tum Cancri, tum Geminorum &longs;ingula 30, &amp; in 9 1/3 Tau<lb/>ri connumerauerim, eo&longs;dem 80 fer&egrave; gradus inueni: </s><s>Simili&shy;<lb/>ter autem in con&longs;equentia quoque, vt &agrave; Tauro ad <expan abbr="Leon&etilde;">Leonem</expan>. </s>
<s><lb/>Rur&longs;us autem circa mediam noctem c&ugrave;m ab ea, qu&aelig; in cor <lb/>de Leonis e&longs;t &longs;tella ad con&longs;equentia Arcturum, qui Boo-<pb xlink:href="052/01/149.jpg"/><arrow.to.target n="note370"/><lb/>tes etiam uocatur, in libra, borealiorem autem &aelig;quino&shy;<lb/>ctiali gradus 31 exi&longs;tentem di&longs;pexerim: adnotaui, <expan abbr="reperi-&qacute;ue">reperi&shy;<lb/>que</expan> in medio gradus 54 fer&egrave;, quot &longs;unt ij, quibus etiam <lb/>Arcturus ad con&longs;equentia &agrave; Ba&longs;ili&longs;co di&longs;tat. </s>
<s>Arcturus enim <lb/>hac no&longs;tra <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> un&agrave; cum iam dicto motus additamen&shy;<lb/>to quintum Libr&aelig; gradum obtinet. </s>
<s><expan abbr="Sunt&qacute;ue">Suntque</expan> Leonis qui&shy;<lb/>dem ad con&longs;equentia 19 1/2, virginis 30, &amp; quinque Li&shy;<lb/>br&aelig;, quot etiam in tympano ferre connumerati fuere. </s>
<s><lb/>Idem itaque modus in reliquis etiam fixis &longs;tellis prim&aelig;, <arrow.to.target n="note371"/><lb/><expan abbr="&longs;ecund&aelig;&qacute;ue">&longs;ecund&aelig;que</expan> magnitudinis exi&longs;tentibus, ac in quinque pla&shy;<lb/>netis &longs;emper fiat. </s>
<s>Lun&aelig; ver&ograve; di&longs;tantiam non &longs;ol&ugrave;m ad pla&shy;<arrow.to.target n="note372"/><lb/>netas, &amp; eas fixarum, qu&aelig; manife&longs;t&aelig;, <expan abbr="&longs;imilem&qacute;ue">&longs;imilemque</expan> ad ip&longs;am <lb/>Lunam, vel contrariam temperiem adept&aelig; &longs;unt, ob&longs;eruare <lb/>oportet: ver&ugrave;metiam ad eas, qu&aelig; nebulo&longs;&aelig; dicuntur con&shy;<arrow.to.target n="note373"/><lb/>&longs;tellationes, verbi gratia ad Pr&aelig;&longs;epium, vel <expan abbr="Crin&etilde;">Crinem</expan>, aut eas, <arrow.to.target n="note374"/><lb/>qu&aelig; in bipertita &longs;ectione Tauri Pleiades vocantur, aut eas, <arrow.to.target n="note375"/><lb/>qu&aelig; in cornibus propter ip&longs;ius Y elementi figuram Hya&shy;<lb/>das, &amp; pluuiarum, ac imbrium effectrices. </s>
<s>Pr&aelig;&longs;ertim autem <arrow.to.target n="note376"/><lb/>ob&longs;eruanda e&longs;t luna circum quas etiam &longs;tellas ad &longs;olem <arrow.to.target n="note377"/><lb/>a&longs;pectus &longs;eptem facit: &longs;i hi&longs;ce proxima e&longs;t, aut graduatim <lb/>ad ip&longs;am &longs;tell&aelig; figurantur, aut coniunctores a&longs;pectus ad <lb/>&longs;olem efficiunt. </s>
<s>H&aelig;c igitur qui circa dioptriam, &amp; Ph&aelig;no&shy;<lb/>mena con&longs;iderarunt, <expan abbr="&longs;itus&qacute;ue">&longs;itusque</expan> &longs;yderum ex prompta regula <lb/>&longs;u&longs;cipiunt: non &longs;ol&ugrave;m &longs;tellarum di&longs;tantias enuntiabunt, <lb/>ver&ugrave;metiam aur&aelig; con&longs;titutiones, &amp; in&aelig;quabilitates, nec&shy;<lb/>non intemperies, ac temperies per eas, qu&aelig; fiunt quotan&shy;<lb/>nis &longs;tellarum &longs;ignificationes, intelligentes pr&aelig;&longs;agient. </s></p>
<pb xlink:href="052/01/150.jpg"/><p type="margin">
<s><margin.target id="note359"/>a</s></p><p type="margin">
<s><margin.target id="note360"/>b</s></p><p type="margin">
<s><margin.target id="note361"/>c</s></p><p type="margin">
<s><margin.target id="note362"/>d</s></p><p type="margin">
<s><margin.target id="note363"/>e</s></p><p type="margin">
<s><margin.target id="note364"/>f</s></p><p type="margin">
<s><margin.target id="note365"/>g</s></p><p type="margin">
<s><margin.target id="note366"/>h</s></p><p type="margin">
<s><margin.target id="note367"/>i</s></p><p type="margin">
<s><margin.target id="note368"/>k</s></p><p type="margin">
<s><margin.target id="note369"/>l</s></p><p type="margin">
<s><margin.target id="note370"/>m</s></p><p type="margin">
<s><margin.target id="note371"/>n</s></p><p type="margin">
<s><margin.target id="note372"/>o</s></p><p type="margin">
<s><margin.target id="note373"/>p. </s>
<s>q</s></p><p type="margin">
<s><margin.target id="note374"/>r</s></p><p type="margin">
<s><margin.target id="note375"/>s</s></p><p type="margin">
<s><margin.target id="note376"/>t</s></p><p type="margin">
<s><margin.target id="note377"/>u</s></p><figure id="id.052.01.150.1.jpg" xlink:href="052/01/150/1.jpg"/><p type="main">
<s><emph type="center"/>FRANCISCI BAROCII <lb/>SCHOLIVM.<emph.end type="center"/></s></p><p type="main">
<s><emph type="italics"/>MVlta nobis e&longs;&longs;ent hoc in loco dicenda pro perfecta pr&aelig;&longs;en&shy;<lb/>tis propo&longs;itionis intelligentia &longs;i plenos &agrave; principio commen<lb/>tarios in&longs;titui&longs;&longs;emus. </s>
<s>Ver&ugrave;m c&ugrave;m institutum no&longs;trum fue&shy;<lb/>rit breui&szlig;ima quoad fieri potuit &longs;cholia locos ob&longs;curos dilucidan&shy;<lb/>tia componere, iam inceptum ordinem &longs;equentes, nonnulla dum&shy;<lb/>taxat ob&longs;curior a verba declarabimus. </s>
<s>hoc pri&ugrave;s adnotantes, qu&ograve;d <lb/>propo&longs;itum Autoris in hac propo&longs;itione e&longs;t o&longs;tendere quomodo per<emph.end type="italics"/>
<pb xlink:href="052/01/151.jpg"/><emph type="italics"/>dioptram, &longs;iue dioptricum in&longs;trumentum c&oelig;le&longs;tes quoque di&longs;tan&shy;<lb/>tias metiri po&longs;&longs;umus. </s>
<s>in quo quidem o&longs;tendendo tali procedit or&shy;<lb/>dine. </s>
<s>prim&ugrave;m demon&longs;trat <expan abbr="quon&atilde;">quonam</expan> pacto di&longs;tantia inter duas qua&longs;&shy;<lb/>libet stellas per dioptram ob&longs;eruatur. </s>
<s>Secund&ograve; demon&longs;trat quo&shy;<lb/>modo duo &aelig;quinoctialia, &amp; duo tropica, &amp; qu&aelig; inter h&aelig;c &longs;unt men<lb/>&longs;trua puncta, tum orientalia, tum occidentalia in Orizonte no&longs;tro <lb/>per eandem dioptram ob&longs;eruari po&longs;&longs;unt. </s>
<s>Terti&ograve; cau&longs;a exempli de&shy;<lb/>mon&longs;trat quomodo di&longs;tantia inter qua&longs;dam &longs;tellas fixas per dio&shy;<lb/>ptram reperiri pote&longs;t. </s>
<s>Dioptram autem h&igrave;c, &amp; in &longs;uperioribus pro&shy;<lb/>po&longs;itionibus intelligere debemus fui&longs;&longs;e quoddam antiquum in&longs;tru&shy;<lb/>mentum ab a&longs;trolabij dor&longs;o parum di&szlig;imile, aptum ad men&longs;uran&shy;<lb/>das <expan abbr="qua&longs;cumq;">qua&longs;cumque</expan> di&longs;tantias. </s>
<s>cuius figuram qualem in veteri exem&shy;<lb/>plari inuenimus, talem in fine huius propo&longs;itionis appo&longs;uimus. </s>
<s><lb/>commodi&ugrave;s autem, ac facili&ugrave;s iam dict&aelig; di&longs;tanti&aelig; capiuntur, mul&shy;<lb/>ta&queacute; alia Geometrica, &amp; A&longs;trologica problemata fiunt per dor&longs;um <lb/>a&longs;trolabij. </s>
<s>vt multi Autores locupleti&szlig;im&egrave; docuere.<emph.end type="italics"/><lb/><arrow.to.target n="note378"/></s></p><p type="margin">
<s><margin.target id="note378"/><emph type="italics"/>a<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[magnitudines, qu&aelig; qu&aelig;runtur] &longs;cilicet stellarum &longs;oliditates, <lb/>atque di&longs; antias.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note379"/></s></p><p type="margin">
<s><margin.target id="note379"/><emph type="italics"/>b<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Signa h&igrave;c pro punctis, &longs;iue gradibus, &amp; inferi&ugrave;s mod&ograve; pro pun&shy;<lb/>ctis, &longs;ine gradibus, mod&ograve; pro &longs;ignis Zodiaci &longs;u&longs;cipienda &longs;unt.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note380"/></s></p><p type="margin">
<s><margin.target id="note380"/><emph type="italics"/>c<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Antecedentia vocat Autor &longs;igna Zodiaci, qu&aelig; contra &longs;ucce&longs;&shy;<lb/>&longs;ionem ip&longs;orum &longs;ignorum: con&longs;equentia ver&ograve;, qu&aelig; &longs;ecundum &longs;uc&shy;<lb/>ce&szlig;ionem eorumdem &longs;equuntur, vt ip&longs;emet exempto declarauit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note381"/></s></p><p type="margin">
<s><margin.target id="note381"/><emph type="italics"/>d<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Qu&aelig;nam &longs;int i&longs;t&aelig; du&aelig; line&aelig;, &longs;cilicet meridiana, &amp; &aelig;quinoctia&shy;<lb/>lis A&longs;trologi, Co&longs;mographi, &amp; Horologiographi pa&szlig;im &longs;atis &longs;uper&queacute; <lb/>declarant. </s>
<s>Sunt enim (vt breuiter dicam) duo maximi terre&longs;tris <lb/>globi circuli, qui &longs;e &longs;e ad angulos rectos &longs;ph&aelig;rales inter&longs;ecant, al&shy;<lb/>ter quidem &longs;ub c&oelig;le&longs;ti meridiano in terra iacens, alter ver&ograve; &longs;ub <lb/>eo c&oelig;le&longs;ti circulo, qui per &aelig;quinoctialia puncta, &amp; Zenith habitan<lb/>tium tran&longs;it. </s>
<s>quas vtique duas lineas Autor in quodam admiran&shy;<lb/>do regalis palatij ver&longs;us au&longs;trum exi&longs;tente cubiculo &longs;uper qua&shy;<lb/>dam virids &longs;uperficie ad eorum commoditatem, qui de hac re &longs;oli&shy;<lb/>citi &longs;unt, &longs;e de&longs;igna&longs;&longs;e inquit. </s>
<s>harum autem duarum linearum <lb/>inuentionem, quam multi docti&szlig;imi viri diuer&longs;is pulcherrimis re&shy;<lb/>gulis tradidere, ip&longs;e etiam Autor in libro de &longs;olarium <expan abbr="horologior&utilde;">horologiorum</expan> <lb/>po&longs;itione (qui adhuc de&longs;ideratur) &longs;e con&longs;crip&longs;i&longs;&longs;e ait.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note382"/></s></p><p type="margin">
<s><margin.target id="note382"/><emph type="italics"/>e<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[circulo hemi&longs;ph&aelig;rium &longs;uper terram existens definiente] hoc<emph.end type="italics"/>
<pb xlink:href="052/01/152.jpg"/><emph type="italics"/>e&longs;t Orizonte, quippe qui no&longs;trum &longs;upernum hemi&longs;ph&aelig;rium ab in&shy;<lb/>ferno no&longs;trorum antipodum hemi&longs;ph&aelig;rio &longs;eparat, atque di&longs;tinguit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note383"/></s></p><p type="margin">
<s><margin.target id="note383"/><emph type="italics"/>f<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Qu&aelig;nam &longs;int intelligenda &longs;igna tropica, &aelig;quinoctialia, &amp; in&shy;<lb/>ter h&aelig;c iacentia men&longs;trua, paucis ab&longs;oluam. </s>
<s>Duo itaque &longs;unt &aelig;qui<lb/>noctialia &longs;igna &longs;iue puncta, &longs;cilicet primus gradus Arietis, &amp; pri&shy;<lb/>mus gradus libr&aelig;, in quibus c&ugrave;m Sol fuerit, vernale, &amp; autum&shy;<lb/>nale &aelig;quinoctium facit. </s>
<s>Duo pr&aelig;terea &longs;unt tropica, &longs;iue &longs;ol&longs;titialia <lb/>puncta, videlicet principium Cancri, &amp; principium Capricorni, <lb/>in quibus c&ugrave;m Sol fuerit, &aelig;&longs;tiuale, hyemale&queacute; &longs;ol&longs;titium efficit. </s>
<s>vo&shy;<lb/>cantur autem tropica<emph.end type="italics"/> <foreign lang="greek">a)po\ th_s troph_s</foreign>, <emph type="italics"/>hoc e&longs;t &agrave; conuer&longs;ione, quo&shy;<lb/>niam c&ugrave;m in eis Sol fuerit, incipit &longs;e conuertere &agrave; parte boreali <lb/>ad au&longs;tralem, aut ab au&longs;trali ad borealem. </s>
<s>inter h&aelig;c ver&ograve; quatuor <lb/>iam dicta puncta reliqui omnes 356 Zodiaci gradus &longs;unt, in quo&shy;<lb/>rum vnoquoque c&ugrave;m Sol cotidie moueatur cau&longs;at ip&longs;as 178 &longs;pi&shy;<lb/>ras, qu&aelig; inter &aelig;quinoctialem, ac tropicos ab a&longs;trologis fieri exco&shy;<lb/>gitantur. </s>
<s>ex his itaque 356 Zodiaci punctis omnia principia &longs;iue <lb/>primi gradus &longs;ignorum menstrua puncta nuncupantur, quoniam <lb/>&longs;patio men&longs;is vnius ab uno eorum ad aliud Sol migrat. </s>
<s>Quare per&shy;<lb/>&longs;picuum nobis e&longs;t qu&aelig;nam &longs;int puncta &longs;iue &longs;igna &aelig;quinoctialia, <lb/>tropica, &amp; inter h&aelig;c media iacentia men&longs;trua. </s>
<s>Adnotatu ver&ograve; <lb/>dignum e&longs;t <expan abbr="&qtail;">quae</expan> <expan abbr="o&itilde;a">omnia</expan> h&aelig;c &longs;igna tripliciter con&longs;iderantur, nempe aut in <lb/>Zodiaco, aut in Meridiano, aut in Orizonte: necnon in vnoquoque <lb/>etiam i&longs;torum circulorum dupliciter in Zodiaco quidem aut in&longs;i&shy;<lb/>gnis borealibus, vbi Sol exi&longs;tens dies noctibus longiores: aut in au&shy;<lb/>&longs;tralibus, vbi dies breuiores qu&agrave;m noctes nobis efficit. </s>
<s>in Meri&shy;<lb/>diano ver&ograve;, aut in &longs;uperno hemi&longs;ph&aelig;rio, vbi no&longs;trum meridiem: <lb/>aut in inferno, vbi no&longs;tram mediam noctem agit. </s>
<s>in orizonte de&shy;<lb/>mum, aut in oriente, vbi &longs;ui ortus: aut in occidente vbi eiu&longs;dem <lb/>occa&longs;us varietatem cotidi&egrave; nobis indicat. </s>
<s>h&aelig;c igitur qu&aelig; in ori&shy;<lb/>zonte con&longs;iderantur orientalia, &amp; occidentalia c&ugrave;m &aelig;quinoctia&shy;<lb/>lia, tum tropica, tum inter h&aelig;c iacentia men&longs;trua &longs;igna, &longs;iue pun&shy;<lb/>cta &longs;unt, qu&aelig; per dioptram in orizonte no&longs;tro reperire nos Au&shy;<lb/>tor docet.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note384"/></s></p><p type="margin">
<s><margin.target id="note384"/><emph type="italics"/>g<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&amp; quoniam parallelum orizonti &amp;c.] h&aelig;c Autoris demon&longs;tra&shy;<lb/>tio in in&longs;trumento dioptrico, &longs;iue in &longs;ph&aelig;ra materiali clara e&longs;t. </s>
<s><lb/>Animaduertendum autem e&longs;t qu&ograve;d ea, qu&aelig; dicit Autor ibi [gra&shy;<lb/>dus 32 numerauerimus &amp;c.] vera non &longs;unt apud omnes mundi<emph.end type="italics"/>
<pb xlink:href="052/01/153.jpg"/><emph type="italics"/>habitantes, &longs;ed apud eos tant&ugrave;m, qui habent polum arcticum, &longs;eu <lb/>borealem eleuatum 35 gradibus. </s>
<s>vnd&egrave; manife&longs;tum nobis e&longs;t Au&shy;<lb/>torem no&longs;trum in aliqua regionum iam dictum polum &longs;upra ori&shy;<lb/>zontem 35 gradibus altum habentium fui&longs;&longs;e dum pr&aelig;&longs;ens opus <lb/>componebat. </s>
<s>Adnotandum pr&aelig;terea qu&ograve;d illud [16, &amp; 28 gra&shy;<lb/>dus accipiemus] non ita intelligendum e&longs;t, qu&ograve;d &longs;cilicet per ho&shy;<lb/>&longs;ce tant&ugrave;m duos graduum numeros ip&longs;a interiacentia men&shy;<lb/>&longs;trua &longs;igna &longs;u&longs;cipienda &longs;unt: &longs;ed per omnes etiam reliquos, qui <lb/>ab vnitate v&longs;que ad 32 &longs;unt. </s>
<s>ho&longs;ce ver&ograve; duos Autor exempli gra&shy;<lb/>tia fortuit&ograve; &longs;u&longs;cepit, tamquam eos, quorum vterque ab ip&longs;o 32 <lb/>numero comprehenditur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note385"/></s></p><p type="margin">
<s><margin.target id="note385"/><emph type="italics"/>h<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[eo&longs;dem gradus] &longs;cilicet 32, &amp; eos qui &agrave; 32 continentur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note386"/></s></p><p type="margin">
<s><margin.target id="note386"/><emph type="italics"/>i<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Hyadum stellam lucidam &longs;iue Lambauram h&igrave;c intelligere de&shy;<lb/>bemus eam stellam fixam prim&aelig; magnitudinis, qu&aelig; oculus Tauri <lb/>vocatur. </s>
<s>Animaduertendum e&longs;t autem qu&ograve;d h&aelig;c &longs;tella non e&longs;t ex <lb/>eis &longs;tellis inter cornua Tauri iacentibus, qu&aelig; Hyades vocantur, <lb/>vt videtur velle h&igrave;c Autor: ill&aelig; enim &longs;unt quint&aelig; magnitudinis, <lb/>vt ex Hyginio, Ptolem&aelig;o&queacute; patet.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note387"/></s></p><p type="margin">
<s><margin.target id="note387"/><emph type="italics"/>k<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[Nam ip&longs;e Ba&longs;ili&longs;cus &amp;c.] illius &longs;tell&aelig; fix&aelig;, qu&aelig; cor Leonis <lb/>vocatur in octau&aelig; &longs;ph&aelig;r&aelig; Zodiaco exi&longs;tentis &longs;itus in Zodiaco de&shy;<lb/>cim&aelig; &longs;ph&aelig;r&aelig; non fuit idem tempore, quo &longs;crip&longs;it Autor hoc opus, <lb/>qui fuerat etiam Ptolem&aelig;i temporibus: &longs;ed orientalior propter <lb/>motum proprium non&aelig; &longs;ph&aelig;r&aelig;. </s>
<s>idcirco ait Autor qu&ograve;d ip&longs;e Ba&longs;i&shy;<lb/>li&longs;cus, &longs;cilicet octau&aelig; &longs;ph&aelig;r&aelig; vn&agrave; cum additamento motus eorum, <lb/>qu&aelig; ab &aelig;tate Ptolem&aelig;i &longs;unt temporum, gradus 10 1/2 in Leone vi&shy;<lb/>delicet decim&aelig; &longs;ph&aelig;r&aelig;, nunc, &longs;cilicet Autoris temporibus, po&szlig;i&shy;<lb/>dens reperitur. </s>
<s>&longs;ic autem intelligendum <expan abbr="eti&atilde;">etiam</expan> e&longs;t quod ait [&amp; luci&shy;<lb/>da Hyadum in Tauro 20 2/3]<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note388"/></s></p><p type="margin">
<s><margin.target id="note388"/><emph type="italics"/>l<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[c&ugrave;m autem ip&longs;os 10 1/2 gradus &amp;c.] verba h&aelig;c &longs;ic intelli&shy;<lb/>genda &longs;unt. </s>
<s>qu&ograve;d &longs;cilicet ip&longs;os 10 1/2 gradus Leonis decim&aelig; &longs;ph&aelig;&shy;<lb/>r&aelig; vn&agrave; cum antecedentibus 30 cancri, &amp; 30 Geminorum, &amp; 9 1/3 <lb/>Tauri gradibus in vnum coaceruando: 80 fer&egrave; graduum di&longs;tan&shy;<lb/>tiam inter iam dictas duas stellas fixas reperi&longs;&longs;e ait. </s>
<s>eadem au&shy;<lb/>tem e&longs;t di&longs;tantia in con&longs;equentia quoque &longs;igna, &agrave; Tauro ad Leo&shy;<lb/>nem. </s>
<s>nempe &longs;i&agrave; Tauri 20 1/3 gradibus enumerationem facere<emph.end type="italics"/>
<pb xlink:href="052/01/154.jpg"/><emph type="italics"/>c&aelig;perimus, v&longs;que ad 10 1/2 Leonis gradus progredientes.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note389"/></s></p><p type="margin">
<s><margin.target id="note389"/><emph type="italics"/>m<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[borealiorem autem &aelig;quinoctiali gradus 31 exi&longs;tentem] Ad&shy;<lb/>notandum h&igrave;c e&longs;t, qu&ograve;d quamuis paul&ograve; po&longs;t dicat Arcturum tem&shy;<lb/>pore &longs;uo quintum Libr&aelig; gradum in decima &longs;ph&aelig;ra occupare, po&shy;<lb/>te&longs;t attamen etiam 31 gradibus ab &aelig;quinoctiali di&longs;tare, &longs;i &longs;igna li&shy;<lb/>br&aelig; in decim&aelig; &longs;ph&aelig;r&aelig; Zodiaco &longs;u&longs;cipiantur h&igrave;c &longs;ecundum <expan abbr="terti&atilde;">tertiam</expan> <lb/>&longs;ignorum &longs;ignificationem declaratam &agrave; Ioanne de Sacrobo&longs;co in <lb/>&longs;ecundo capitulo &longs;ph&aelig;r&aelig;. </s>
<s>Adnotandum pr&aelig;terea qu&ograve;d ex hi&longs;ce <lb/>iam dictarum stellarum fixarum &longs;itibus &longs;ic tempore Autoris exi&shy;<lb/>&longs;tentibus quilibet a&longs;trologicarum tabularum peritus &longs;upputando <lb/>in cognitionem venire poterit &aelig;ui, quo no&longs;ter Autor pr&aelig;&longs;entem li&shy;<lb/>brum con&longs;crip&longs;it. </s>
<s>floruit enim po&longs;t Chri&longs;ti aduentum. </s>
<s>quandoqui&shy;<lb/>dem tempore quo Chri&longs;tus redemptor no&longs;ter ortus e&longs;t, reperiebatur <lb/>&longs;ecundum Ptolem&cedil;i ob&longs;eruationem principium Arietis octau&aelig;, &amp; <lb/>non&aelig;, &amp; decim&aelig; &longs;ph&aelig;r&aelig; &longs;imul iuncta. </s>
<s>vnd&egrave; etiam principium Tau&shy;<lb/>ri octau&aelig; &longs;ph&aelig;r&aelig; vn&agrave; cum principio Tauri decim&ecedil; coniunctum <lb/>erat. </s>
<s>tempore ver&ograve; Autoris initium Tauri octau&aelig; &longs;ph&aelig;r&aelig; erat in <lb/>gradu 20 1/3 Tauri decim&aelig; &longs;ph&aelig;r&aelig;.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note390"/></s></p><p type="margin">
<s><margin.target id="note390"/><emph type="italics"/>n<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[in quinque planetis] dixit, quoniam inter &longs;olem, &amp; c&aelig;tera &longs;i&shy;<lb/>dera di&longs;tantias per dioptram ob&longs;eruare die non po&longs;&longs;umus c&ugrave;m &longs;tel&shy;<lb/>l&aelig; &longs;ole &longs;uper no&longs;trum orizontem exi&longs;tente non luceant. </s>
<s>de luna <lb/>ver&ograve; mox &longs;ubiungit.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note391"/></s></p><p type="margin">
<s><margin.target id="note391"/><emph type="italics"/>o<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Stellarum fixarum ali&aelig; manifest&aelig;, ali&aelig; nebulo&longs;&aelig; &longs;unt: ali&aelig; ean&shy;<lb/>dem cum planetis, ali&aelig; contrariam cis naturam, temperiem&queacute; ha&shy;<lb/>bent, vt ab A&longs;trologis declaratur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note392"/></s></p><p type="margin">
<s><margin.target id="note392"/><emph type="italics"/>p<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/><expan abbr="Pr&aelig;&longs;epi&utilde;">Pr&aelig;&longs;epium</expan> e&longs;t <expan abbr="qu&ecedil;d&atilde;">qu&ecedil;dam</expan> nubilo&longs;a con&longs;tellatio in &longs;igno Cancri <expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan>.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note393"/></s></p><p type="margin">
<s><margin.target id="note393"/><emph type="italics"/>q<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Crinis autem, &longs;cilicet Berenices, &longs;imiliter alia con&longs;tellatio e&longs;t <lb/>in Leone iacens.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note394"/></s></p><p type="margin">
<s><margin.target id="note394"/><emph type="italics"/>r<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Pleiades ver&ograve; e&longs;t con&longs;tellatio exi&longs;tens in bipertita &longs;ectione Tau&shy;<lb/>ri, in qua &longs;i Taurus iuxta latitudinem &longs;ecandus &longs;it, bifariam &longs;e&shy;<lb/>cabitur.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note395"/></s></p><p type="margin">
<s><margin.target id="note395"/><emph type="italics"/>&longs;<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>Hyades <expan abbr="a&utilde;t">aut</expan> e&longs;t alia &longs;tellarum <expan abbr="fixar&utilde;">fixarum</expan> con&longs;tellatio in faciem Tau<lb/>ri inter eius cornua exi&longs;tens, quam Autor ab ip&longs;ius y elementi fi&shy;<lb/>gura &longs;ic dictam e&longs;&longs;e vult, quamuis etiam alijs de cau&longs;is ita dica&shy;<lb/>tur, vt apud Autores materiam hanc pertractantes legitur.<emph.end type="italics"/></s></p>
<pb xlink:href="052/01/155.jpg"/><p type="main">
<s><arrow.to.target n="note396"/></s></p><p type="margin">
<s><margin.target id="note396"/><emph type="italics"/>t<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[ad &longs;olem a&longs;pectus &longs;eptem] &longs;eptem a&longs;pectus lun&aelig; ad &longs;olem <lb/>&longs;unt ij, qui in quolibet men&longs;e lunari fiunt: &longs;cilicet duo trini, duo <lb/>quadrati, duo &longs;extiles, &amp; vnica oppo&longs;itio. </s>
<s>Coniunctionem enim <lb/>lun&aelig; cum &longs;ole non connumerauit, quoniam c&ugrave;m inui&longs;ibilis nobis <lb/>tunc luna &longs;it, per dioptram &agrave; nobis ob&longs;eruari minim&egrave; pote&longs;t.<emph.end type="italics"/></s></p><p type="main">
<s><arrow.to.target n="note397"/></s></p><p type="margin">
<s><margin.target id="note397"/><emph type="italics"/>u<emph.end type="italics"/></s></p><p type="main">
<s><emph type="italics"/>[&longs;i hi&longs;ce proxima e&longs;t &amp;c.] Hoc est tria h&aelig;c de Luna re&longs;pectu <lb/>earum &longs;tellarum fixarum, circum quas iam dictos &longs;eptem ad &longs;o&shy;<lb/>lem a&longs;pectus facit, per dioptram ob&longs;eruanda &longs;unt: nempe &longs;i &longs;tel&shy;<lb/>lis ip&longs;is proxima e&longs;t, videlicet &longs;i in eodem c&oelig;li loco cum ip&longs;is exi&shy;<lb/>&longs;tat: aut &longs;i graduatim ad ip&longs;am &longs;tell&aelig; figurantur, ide&longs;t &longs;i per gra&shy;<lb/>dus aliquot ab ip&longs;a Luna di&longs;tantes ip&longs;&ecedil; &longs;tell&aelig; in a&longs;pectu quodam <lb/>figurantur: aut &longs;i coniunctores a&longs;pectus ad &longs;olem efficiunt, hoc e&longs;t <lb/>&longs;i ip&longs;&aelig; &longs;tell&aelig; in coniunctione cum &longs;ole &longs;unt. </s>
<s>Ver&ugrave;m h&ecedil;c etiam pro <lb/>pr&aelig;&longs;entis vltim&aelig;, ac pulcherrima, <expan abbr="doctrina&qacute;ue">doctrinaque</expan> a&longs;trologica plen&ecedil; <lb/>propo&longs;itionis dilucidationem dicta &longs;ufficiant.<emph.end type="italics"/></s></p><p type="main">
<s><emph type="center"/><emph type="italics"/>FINIS.<emph.end type="italics"/><emph.end type="center"/></s></p>

			</chap>
		</body>
		<back/>
	</text>
</archimedes>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Thu, 02 May 2013 11:38:23 +0200
parents	22d6a63640c6
children