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| <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Baldi, Bernadino</author> <title>In Mechanica Aristotelis problemata exercitationes</title> <date>1621</date> | <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> |
| | <author>Baldi, Bernardino</author> |
| | <title>In mechanica Aristotelis problemata exercitationes</title> |
| <place>Mainz</place> <translator></translator> <lang>la</lang> <cvs_file>baldi_mecha_01_la_1621.xml</cvs_file><cvs_version>1.11</cvs_version> <locator>0000000007</locator> </info> <text> <front> </front> <body> <chap> <pb/><pb id="p.0002"/><p type="head"> | <date>1621</date> |
| | <place>Mainz</place> |
| | <translator></translator> |
| | <lang>la</lang> |
| | <cvs_file>baldi_mecha_01_la_1621</cvs_file> |
| | <cvs_version></cvs_version> |
| | <locator>0000000007.xml</locator> |
| | </info> <text> <front> </front> <body> <chap> <pb/><pb id="p.0002"/><p type="head"> |
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| <s>BERNARDINI</s></p><p type="head"> | <s>BERNARDINI</s></p><p type="head"> |
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| <s>Verum enimuero cum inge­<lb/>nuiilli fuerint homines, & nullatenus obtrecta­<lb/>tores, credendum potius est, Comment ariolum i­<lb/>&longs;tud, eorum æuo, paucis cognitum, alicubi in Bi­<lb/>bliothecis latui&longs;&longs;e: etenim cætera quoque Ari&longs;tote­<lb/>lis &longs;cripta, po&longs;t vetu&longs;tailla tempora, ante Ale­<lb/>xandrum Aphrodi&longs;ien&longs;em, àmultis fui&longs;&longs;e igno-<pb/>rata non dubitamus. </s> | <s>Verum enimuero cum inge­<lb/>nuiilli fuerint homines, & nullatenus obtrecta­<lb/>tores, credendum potius est, Comment ariolum i­<lb/>&longs;tud, eorum æuo, paucis cognitum, alicubi in Bi­<lb/>bliothecis latui&longs;&longs;e: etenim cætera quoque Ari&longs;tote­<lb/>lis &longs;cripta, po&longs;t vetu&longs;tailla tempora, ante Ale­<lb/>xandrum Aphrodi&longs;ien&longs;em, àmultis fui&longs;&longs;e igno-<pb/>rata non dubitamus. </s> |
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| <s>Habemus &longs;iquidem, Stra­<lb/>bone te&longs;te, lib. </s> | <s>Habemus &longs;iquidem, Stra­<lb/>bone te&longs;te, lib. |
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| <s>13. Ari&longs;totelis, & Theophra&longs;ti bi­<lb/>bliothecam, po&longs;t ip&longs;ius Theophra&longs;ti dece&longs;&longs;um, ad <lb/>Neleum quendam Scep&longs;ium, Cori&longs;cifilium, qui <lb/>eius fuerat auditor, perueni&longs;&longs;e; po&longs;t hæc libros, <lb/>blattis olim, & humore corruptos, Apelliconi Te­<lb/>io venditos, & ab eo Athenas translatos, tum <lb/>Athenis captis in Syllæ pote&longs;tatem deacni&longs;&longs;e, eo&longs;­<lb/>que tandem à Sylla acceptos, Tyrannionem <lb/>Grammaticum, vt potuit meliùs emendatos, <lb/>promulga&longs;&longs;e. </s> | 13. Ari&longs;totelis, & Theophra&longs;ti bi­<lb/>bliothecam, po&longs;t ip&longs;ius Theophra&longs;ti dece&longs;&longs;um, ad <lb/>Neleum quendam Scep&longs;ium, Cori&longs;cifilium, qui <lb/>eius fuerat auditor, perueni&longs;&longs;e; po&longs;t hæc libros, <lb/>blattis olim, & humore corruptos, Apelliconi Te­<lb/>io venditos, & ab eo Athenas translatos, tum <lb/>Athenis captis in Syllæ pote&longs;tatem deacni&longs;&longs;e, eo&longs;­<lb/>que tandem à Sylla acceptos, Tyrannionem <lb/>Grammaticum, vt potuit meliùs emendatos, <lb/>promulga&longs;&longs;e. </s> |
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| <s>Exquibus colligimus, mirum non <lb/>e&longs;&longs;e, Archimedi, Heroni, & alijs qui ante Syllam <lb/>vixêre, fui&longs;&longs;e incognitos. </s> | <s>Exquibus colligimus, mirum non <lb/>e&longs;&longs;e, Archimedi, Heroni, & alijs qui ante Syllam <lb/>vixêre, fui&longs;&longs;e incognitos. </s> |
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| <s>Pe&longs;tilentia ex co Gymna&longs;io exactus in Pa­<lb/>triam redijt, vbi quin quennium integrum Federico <expan abbr="Cō-mandino">Con­<lb/>mandino</expan> affixus omnes Mathe&longs;eos partes perdidicit, cui <lb/>viro in delinean dis figuris ad Euclidis, Pappi, & Heronis <lb/>monumenta manum commodauit: ex eiu&longs;dem obitu do­<lb/>lorem vix con&longs;olabilem &longs;u&longs;tinuit, &longs;u&longs;ceptoque eius vitam <lb/>&longs;cribendi con&longs;ilio, &longs;ubinde ad omnium Mathematicorum <lb/>vitas con&longs;cribendas animum adplicuit, quod & duode­<lb/>cim annorum &longs;patio præ&longs;titit felici&longs;&longs;imè. </s> | <s>Pe&longs;tilentia ex co Gymna&longs;io exactus in Pa­<lb/>triam redijt, vbi quin quennium integrum Federico <expan abbr="Cō-mandino">Con­<lb/>mandino</expan> affixus omnes Mathe&longs;eos partes perdidicit, cui <lb/>viro in delinean dis figuris ad Euclidis, Pappi, & Heronis <lb/>monumenta manum commodauit: ex eiu&longs;dem obitu do­<lb/>lorem vix con&longs;olabilem &longs;u&longs;tinuit, &longs;u&longs;ceptoque eius vitam <lb/>&longs;cribendi con&longs;ilio, &longs;ubinde ad omnium Mathematicorum <lb/>vitas con&longs;cribendas animum adplicuit, quod & duode­<lb/>cim annorum &longs;patio præ&longs;titit felici&longs;&longs;imè. </s> |
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| <s>cum vero Ma­<lb/>thematicarum di&longs;ciplinarum amore torqueretur, ami&longs;&longs;o <lb/>Commandino Præceptore, amicum nactus fuit præ&longs;tan­<lb/>ti&longs;&longs;imum & &longs;ymmy&longs;tam Guidum Vbaldum è Marchioni­<lb/>bus Montis, in cuius &longs;e con&longs;uetudinem daret: quantum <lb/>profeci&longs;&longs;et, o&longs;tendunt ij commentarij quos anno 1582. in <lb/>Ari&longs;t. </s> | <s>cum vero Ma­<lb/>thematicarum di&longs;ciplinarum amore torqueretur, ami&longs;&longs;o <lb/>Commandino Præceptore, amicum nactus fuit præ&longs;tan­<lb/>ti&longs;&longs;imum & &longs;ymmy&longs;tam Guidum Vbaldum è Marchioni­<lb/>bus Montis, in cuius &longs;e con&longs;uetudinem daret: quantum <lb/>profeci&longs;&longs;et, o&longs;tendunt ij commentarij quos anno 1582. in <lb/>Ari&longs;t. Mechanica &longs;crip&longs;it. </s> |
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| <s>Mechanica &longs;crip&longs;it. </s> | |
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| <s>Vt po&longs;tea à grauioribus &longs;tudijs <lb/>ad amœniora animum abduceret, de re nautica poëma I­<lb/>talicè <gap/>onfecit. </s> | <s>Vt po&longs;tea à grauioribus &longs;tudijs <lb/>ad amœniora animum abduceret, de re nautica poëma I­<lb/>talicè <gap/>onfecit. </s> |
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| <s>Earumdem vitarum Epitomen Chronologicum confecit. </s></p><p type="main"> | <s>Earumdem vitarum Epitomen Chronologicum confecit. </s></p><p type="main"> |
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| <s>In Ari&longs;tot. </s> | <s>In Ari&longs;tot. Mechan. Commentar. </s></p><p type="main"> |
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| <s>Mechan. </s> | |
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| <s>Commentar. </s></p><p type="main"> | |
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| <s>De Renautica Poëmation. </s></p><p type="main"> | <s>De Renautica Poëmation. </s></p><p type="main"> |
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| <s>De vniuer&longs;ali Diluuio poemation. </s></p><p type="main"> | <s>De vniuer&longs;ali Diluuio poemation. </s></p><p type="main"> |
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| <s>Nouæ Gnomonices lib. </s> | <s>Nouæ Gnomonices lib. |
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| <s>quin que. </s></p><p type="main"> | quin que. </s></p><p type="main"> |
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| <s>Hieremiæ Threnos vertit, & ex Heb. </s> | <s>Hieremiæ Threnos vertit, & ex Heb. </s> |
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| <s>Epigrammata alia. </s></p><p type="main"> | <s>Epigrammata alia. </s></p><p type="main"> |
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| <s>Heronis lib. </s> | <s>Heronis lib. |
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| <s>de Balli&longs;tis conuer&longs;io. </s></p><p type="main"> | de Balli&longs;tis conuer&longs;io. </s></p><p type="main"> |
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| <s>Exercitationes in Ari&longs;totelis Mechan. </s></p><p type="main"> | <s>Exercitationes in Ari&longs;totelis Mechan. </s></p><p type="main"> |
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| <s>Centrum grauitatis <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> corporis e&longs;t pun­<lb/>ctum quod dam intra po&longs;itum, à quo &longs;i graue, mente ap­<lb/>pen&longs;um concipiatur, dum fertur, quie&longs;cit, & &longs;eruat eam <lb/>quam in prin cipio habuit po&longs;itionem; neque in ip&longs;a latio­<lb/>ne circumuertitur. </s> | <s>Centrum grauitatis <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> corporis e&longs;t pun­<lb/>ctum quod dam intra po&longs;itum, à quo &longs;i graue, mente ap­<lb/>pen&longs;um concipiatur, dum fertur, quie&longs;cit, & &longs;eruat eam <lb/>quam in prin cipio habuit po&longs;itionem; neque in ip&longs;a latio­<lb/>ne circumuertitur. </s> |
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| <s>Commandinus verò in lib. </s> | <s>Commandinus verò in lib. |
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| <s>de centro <lb/>grauitatis &longs;olidorum hoc pacto: Centrum grauitatis v­<lb/>niu&longs;cuiu&longs;que &longs;olidæ figuræ, e&longs;t punctum illud intra po&longs;i­<lb/>tum, circa quod vndique partes æqualium momentorum <lb/>ad&longs;i&longs;tunt. </s> | de centro <lb/>grauitatis &longs;olidorum hoc pacto: Centrum grauitatis v­<lb/>niu&longs;cuiu&longs;que &longs;olidæ figuræ, e&longs;t punctum illud intra po&longs;i­<lb/>tum, circa quod vndique partes æqualium momentorum <lb/>ad&longs;i&longs;tunt. </s> |
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| <s>Sienim per tale centrum ducatur planum, fi­<lb/>guram quomodolibet &longs;ecans, in partes æ què ponderantes <lb/>eam diuidit. </s> | <s>Sienim per tale centrum ducatur planum, fi­<lb/>guram quomodolibet &longs;ecans, in partes æ què ponderantes <lb/>eam diuidit. </s> |
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| <s>Punctum autem, quod &longs;tat, &longs;emidia­<lb/>metri pars nulla e&longs;t. </s> | <s>Punctum autem, quod &longs;tat, &longs;emidia­<lb/>metri pars nulla e&longs;t. </s> |
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| <s>Et &longs;anè cur moto <lb/><expan abbr="&longs;emidiamētro">&longs;emidiamentro</expan> fiat circulus, non ideo accidit, quod <expan abbr="alterū">alterum</expan> <lb/>extremum &longs;tet, alterum verò moueatur:led ideo quòd &longs;e­<lb/>midiameter perpetuò candem &longs;eruct longitudinem. </s> | <s>Et &longs;anè cur moto <lb/><expan abbr="&longs;emidiamētro">&longs;emidiamentro</expan> fiat circulus, non ideo accidit, quod <expan abbr="alterū">alterum</expan> <lb/>extremum &longs;tet, alterum verò moueatur:led ideo quòd &longs;e­<lb/>midiameter perpetuò eandem &longs;eruct longitudinem. </s> |
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| <s>Elli­<lb/>p&longs;is &longs;anè centrum habet, &longs;ed ab eo ad circumferentiam <lb/>quatuor tantùm &longs;emidiametri quomodolibet &longs;umpti du­<lb/>cuntur æ quales. </s> | <s>Elli­<lb/>p&longs;is &longs;anè centrum habet, &longs;ed ab eo ad circumferentiam <lb/>quatuor tantùm &longs;emidiametri quomodolibet &longs;umpti du­<lb/>cuntur æ quales. </s> |
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| <s>Semperigi­<lb/>tur punctum A &longs;i duabus lationibus feratur, laterum pro­<lb/>portione &longs;eruata, lineam producet rectam, diametrum <lb/>nempe AGC. </s> | <s>Semperigi­<lb/>tur punctum A &longs;i duabus lationibus feratur, laterum pro­<lb/>portione &longs;eruata, lineam producet rectam, diametrum <lb/>nempe AGC. </s> |
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| <s>Et hoc &longs;anè nullam habet dubitationem, <lb/>ex ijs quæ docet Euclides 1. 6. prop. </s> | <s>Et hoc &longs;anè nullam habet dubitationem, <lb/>ex ijs quæ docet Euclides 1. 6. prop. |
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| <s>24. </s></p><p type="main"> | 24. </s></p><p type="main"> |
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| <s>His ita demon&longs;tratis hac vti videtur Philo&longs;ophus <pb pagenum="11"/>argumentatione: Si mixtus motus proportione &longs;emotâ, <lb/>rectam producir, &longs;i nun quam &longs;emota, efficiet circulum; &longs;i <lb/>enim modo &longs;eruaretur, modo non, partim recta partim <lb/>non recta produceretur. </s> | <s>His ita demon&longs;tratis hac vti videtur Philo&longs;ophus <pb pagenum="11"/>argumentatione: Si mixtus motus proportione &longs;emotâ, <lb/>rectam producir, &longs;i nun quam &longs;emota, efficiet circulum; &longs;i <lb/>enim modo &longs;eruaretur, modo non, partim recta partim <lb/>non recta produceretur. </s> |
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| <s>Sit <lb/>autem, cum AC &longs;uo motu peruenerit <lb/>in D, punctum A, &longs;imiliter &longs;uo motu per eam latum perue­<lb/>nitle in E erit eigo ex mixto motu, non quidem in D, nec <lb/>in E, &longs;ed in F, eritque punctum F in circum ferentia circu­<lb/>li, cuius e&longs;t diameter ip&longs;a linea AB, quod quidem demon­<lb/>&longs;tratur ex conuer&longs;a propo&longs;. </s> | <s>Sit <lb/>autem, cum AC &longs;uo motu peruenerit <lb/>in D, punctum A, &longs;imiliter &longs;uo motu per eam latum perue­<lb/>nitle in E erit eigo ex mixto motu, non quidem in D, nec <lb/>in E, &longs;ed in F, eritque punctum F in circum ferentia circu­<lb/>li, cuius e&longs;t diameter ip&longs;a linea AB, quod quidem demon­<lb/>&longs;tratur ex conuer&longs;a propo&longs;. </s> |
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| <s>13. lib. </s> | <s>13. lib. |
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| <s>6. Elem. </s> | 6. Elem. </s> |
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| <s>E&longs;t enim AE <lb/>hoce&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>& DB. </s> | <s>E&longs;t enim AE <lb/>hoce&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>& DB. </s> |
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| <s>Modò quod pollicebamur, nempe minorem e&longs;&longs;e <lb/>BT, quàm q M, ita demon&longs;tramus. </s> | <s>Modò quod pollicebamur, nempe minorem e&longs;&longs;e <lb/>BT, quàm q M, ita demon&longs;tramus. </s> |
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| <s><expan abbr="quoniã">quoniam</expan> ST. ex prop. </s> | <s><expan abbr="quoniã">quoniam</expan> ST. ex prop. |
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| <s>13. <lb/>1. 6. media proportionalis e&longs;t inter BT & TE, erit qua­<lb/>dratum TS æquale <expan abbr="parallelogrãmo">parallelogrammo</expan> &longs;eu rectangulo BT, <lb/>TE, item, quoniam q L media proportionalis e&longs;t inter <lb/>M q, & q O. erit quadratum q L æquale rectangulo M q, <lb/>q O, æqualia ergo &longs;unt rectangula BTE, M q O, itaque <lb/>reciprocalatera habent proportionalia. </s> | 13. <lb/>1. 6. media proportionalis e&longs;t inter BT & TE, erit qua­<lb/>dratum TS æquale <expan abbr="parallelogrãmo">parallelogrammo</expan> &longs;eu rectangulo BT, <lb/>TE, item, quoniam q L media proportionalis e&longs;t inter <lb/>M q, & q O. erit quadratum q L æquale rectangulo M q, <lb/>q O, æqualia ergo &longs;unt rectangula BTE, M q O, itaque <lb/>reciprocalatera habent proportionalia. </s> |
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| <s>quare, vt TE, ad <lb/>q O, ita M q ad TB, &longs;ed TE maior e&longs;t ip&longs;a q O, quippe <lb/>quòd pars &longs;it q O ip&longs;ius TE, maior ergo & M q ip&longs;a TB, <lb/>quod o&longs;tendendum fuerat. </s></p><p type="main"> | <s>quare, vt TE, ad <lb/>q O, ita M q ad TB, &longs;ed TE maior e&longs;t ip&longs;a q O, quippe <lb/>quòd pars &longs;it q O ip&longs;ius TE, maior ergo & M q ip&longs;a TB, <lb/>quod o&longs;tendendum fuerat. </s></p><p type="main"> |
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| <s>At quia linea DFCB, à centro mundi, <lb/>quod e&longs;t extra circulum, BEF, circulum ip&longs;um per cen­<lb/>trum C &longs;ecat, erit pars eius DF quidem breui&longs;&longs;ima, ip&longs;a <lb/>verò DB longi&longs;&longs;ima, ex propo&longs;. </s> | <s>At quia linea DFCB, à centro mundi, <lb/>quod e&longs;t extra circulum, BEF, circulum ip&longs;um per cen­<lb/>trum C &longs;ecat, erit pars eius DF quidem breui&longs;&longs;ima, ip&longs;a <lb/>verò DB longi&longs;&longs;ima, ex propo&longs;. </s> |
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| <s>8. lib. </s> | <s>8. lib. |
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| <s>3. Elem. </s> | 3. Elem. </s> |
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| <s>Pondus igi­<lb/>tur A conuer&longs;um &longs;eu liberè motum circa centrum C, in <lb/>duobus tantum locis perpendicularis lineæ &longs;tabit remo­<lb/>ti&longs;&longs;imo altero, vt e&longs;t B, altero verò cidem quamproximo, <lb/>vt e&longs;t F. </s></p><p type="main"> | <s>Pondus igi­<lb/>tur A conuer&longs;um &longs;eu liberè motum circa centrum C, in <lb/>duobus tantum locis perpendicularis lineæ &longs;tabit remo­<lb/>ti&longs;&longs;imo altero, vt e&longs;t B, altero verò cidem quamproximo, <lb/>vt e&longs;t F. </s></p><p type="main"> |
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| <s>Demit­<lb/>tatur enim, à puncto B <lb/>horizonti perpendicula­<lb/>ris BG, & ab F item per­<lb/>pendicularis FH, Tum <lb/>iuncta DB, centro D, eo­<lb/>dem vero &longs;patio DB, circuli portio de&longs;cribatur BI, item <lb/>iuncta DF eodem centro D, &longs;patio DF, portio circuli de­<lb/>&longs;cribatu: FK. e&longs;t autem maior DB ip&longs;a DF ex propo&longs;. <lb/></s> | <s>Demit­<lb/>tatur enim, à puncto B <lb/>horizonti perpendicula­<lb/>ris BG, & ab F item per­<lb/>pendicularis FH, Tum <lb/>iuncta DB, centro D, eo­<lb/>dem vero &longs;patio DB, circuli portio de&longs;cribatur BI, item <lb/>iuncta DF eodem centro D, &longs;patio DF, portio circuli de­<lb/>&longs;cribatu: FK. e&longs;t autem maior DB ip&longs;a DF ex propo&longs;. <lb/></s> |
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| <s>21. lib. </s> | <s>21. lib. |
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| <s>1. Elem. </s> | 1. Elem. |
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| <s>quare maiotis circuli portio e&longs;t BI quàm <lb/>FK. </s> | quare maiotis circuli portio e&longs;t BI quàm <lb/>FK. </s> |
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| <s>Obliquior autem, hoc e&longs;t, à perpendiculariremotior <lb/>e&longs;t motus per FK quàm per BI. maior &longs;i quidem e&longs;t angu­<lb/>lus KFH angulo IBG. quod nos ita probamus. </s> | <s>Obliquior autem, hoc e&longs;t, à perpendiculariremotior <lb/>e&longs;t motus per FK quàm per BI. maior &longs;i quidem e&longs;t angu­<lb/>lus KFH angulo IBG. quod nos ita probamus. </s> |
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| <s>Soluit Philo&longs;ophus, inquiens: An quia malus quidem <lb/>&longs;it vectis, fulcimentum verò mali &longs;edes, in qua colloca­<lb/>tur, pondus autem quod moueri debet, ip&longs;um nauigium: <lb/>mouens verò is, qui vela tendit &longs;piritus? </s> | <s>Soluit Philo&longs;ophus, inquiens: An quia malus quidem <lb/>&longs;it vectis, fulcimentum verò mali &longs;edes, in qua colloca­<lb/>tur, pondus autem quod moueri debet, ip&longs;um nauigium: <lb/>mouens verò is, qui vela tendit &longs;piritus? </s> |
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| <s>Si igitur quanto <lb/>remotior fuerit fulcimentum facilius cadem potentia, & <lb/>citiùs idem mouet pondus, altius certè &longs;ublatâ antennâ, <lb/>velum à mali &longs;ede, quae fulcimentum e&longs;t remotius faciens, <lb/>id efficiet. </s> | <s>Si igitur quanto <lb/>remotior fuerit fulcimentum facilius eadem potentia, & <lb/>citiùs idem mouet pondus, altius certè &longs;ublatâ antennâ, <lb/>velum à mali &longs;ede, quae fulcimentum e&longs;t remotius faciens, <lb/>id efficiet. </s> |
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| <s>Hæcille. </s> | <s>Hæcille. </s> |
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| <s>Ap­<lb/>plicata igitur potentia in H erit pondus inter fulcimen­<lb/>tum & potentiam, quare vt IE ad IH ita potentla &longs;u&longs;ti­<lb/>nens in H ad pondus in E, quod demon&longs;trandum fuerat. </s></p><p type="main"> | <s>Ap­<lb/>plicata igitur potentia in H erit pondus inter fulcimen­<lb/>tum & potentiam, quare vt IE ad IH ita potentla &longs;u&longs;ti­<lb/>nens in H ad pondus in E, quod demon&longs;trandum fuerat. </s></p><p type="main"> |
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| <s>Quippiam &longs;imile o&longs;ten dit Pappus 1. 8. prop. </s> | <s>Quippiam &longs;imile o&longs;ten dit Pappus 1. 8. prop. |
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| <s>9. alijs <lb/>tamen &longs;uppo&longs;itis & con&longs;ideratis. </s> | 9. alijs <lb/>tamen &longs;uppo&longs;itis & con&longs;ideratis. </s> |
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| <s>Dico præterea, ij&longs;dem <lb/>&longs;tantibus angulum ECI æqualem e&longs;&longs;e angulo inclinatio­<lb/>nis CBF. </s> | <s>Dico præterea, ij&longs;dem <lb/>&longs;tantibus angulum ECI æqualem e&longs;&longs;e angulo inclinatio­<lb/>nis CBF. </s> |
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| <s>Secus enim <lb/>axium & Rotarum fieret offen&longs;atio, cuius offen&longs;ationis <lb/>vim & effectum cum nouerit Ari&longs;toteles, vel hoc ip&longs;o lo­<lb/>co te&longs;te, mirum e&longs;t, nihil de ea egi&longs;&longs;e quæ&longs;tione 9. vbi nos <lb/>hac de re fu&longs;i&longs;&longs;imè tractauimus. </s></p><p type="main"> | <s>Secus enim <lb/>axium & Rotarum fieret offen&longs;atio, cuius offen&longs;ationis <lb/>vim & effectum cum nouerit Ari&longs;toteles, vel hoc ip&longs;o lo­<lb/>co te&longs;te, mirum e&longs;t, nihil de ea egi&longs;&longs;e quæ&longs;tione 9. vbi nos <lb/>hac de re fu&longs;i&longs;&longs;imè tractauimus. </s></p><p type="main"> |
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| <s>Cæterùm quod de rotatis &longs;cytalis &longs;cribit Philo&longs;o­<lb/>phus, notandum, à Pappo quidem lib. </s> | <s>Cæterùm quod de rotatis &longs;cytalis &longs;cribit Philo&longs;o­<lb/>phus, notandum, à Pappo quidem lib. |
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| <s>8. & à no&longs;tris Me­<lb/>chanicis pa&longs;&longs;im ab&longs;que rotis Cylindrica &longs;implici videli­<lb/>cet, & tereti formâ ad v&longs;um adhiberi. </s> | 8. & à no&longs;tris Me­<lb/>chanicis pa&longs;&longs;im ab&longs;que rotis Cylindrica &longs;implici videli­<lb/>cet, & tereti formâ ad v&longs;um adhiberi. </s> |
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| <s>E&longs;to igitur Ari­<lb/><figure id="fig14"></figure><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi verò &longs;eu vul­<lb/>garis, & communis CD. <lb/></s> | <s>E&longs;to igitur Ari­<lb/><figure id="fig14"></figure><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi verò &longs;eu vul­<lb/>garis, & communis CD. <lb/></s> |
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| <s>QVAESTIO XV.</s></p><p type="head"> | <s>QVAESTIO XV.</s></p><p type="head"> |
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| <s><emph type="italics"/>Proponitur inueftigandum, Cur litterales crocæ (glareas dicunt <lb/>Latini, velcalculos, quos vmbilicos appellat Cicero lib. </s> | <s><emph type="italics"/>Proponitur inueftigandum, Cur litterales crocæ (glareas dicunt <lb/>Latini, velcalculos, quos vmbilicos appellat Cicero lib. |
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| <s>2. de Orat.) <lb/>rotundâ&longs;int figurâ, cum aliquando ex magnis &longs;int la­<lb/>pidibus te&longs;tisue?<emph.end type="italics"/></s></p><p type="main"> | 2. de Orat.) <lb/>rotundâ&longs;int figurâ, cum aliquando ex magnis &longs;int la­<lb/>pidibus te&longs;tisue?<emph.end type="italics"/></s></p><p type="main"> |
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| <s>A It Philo&longs;ophus, ideo forta&longs;&longs;e fieri, quòd ca quæ à me­<lb/>dio magis recedunt, in motionibus, celerius feran­<lb/>tur; me dium e&longs;&longs;e centrum, interuallum vero quæ à cen­<lb/>tro, &longs;emper autem maiorem ab æ quali motione maiorem <lb/>de&longs;cribere circulum; quod autem maius in æquali tem­<lb/>pore &longs;patium tran&longs;it, celerius ferri; quæ autem celerius ex <lb/>æquali feruntur &longs;patio vehementius impetere, quæ <expan abbr="autē">autem</expan> <lb/>impetunt, impeti magis, & ideo quæ magis à centro di­<lb/>&longs;tant, nece&longs;&longs;e e&longs;&longs;e confringi, quod cum glareæ &longs;eu croc æ <lb/>patiantur, nece&longs;&longs;ariò rotundas fieri. </s> | <s>A It Philo&longs;ophus, ideo forta&longs;&longs;e fieri, quòd ca quæ à me­<lb/>dio magis recedunt, in motionibus, celerius feran­<lb/>tur; me dium e&longs;&longs;e centrum, interuallum vero quæ à cen­<lb/>tro, &longs;emper autem maiorem ab æ quali motione maiorem <lb/>de&longs;cribere circulum; quod autem maius in æquali tem­<lb/>pore &longs;patium tran&longs;it, celerius ferri; quæ autem celerius ex <lb/>æquali feruntur &longs;patio vehementius impetere, quæ <expan abbr="autē">autem</expan> <lb/>impetunt, impeti magis, & ideo quæ magis à centro di­<lb/>&longs;tant, nece&longs;&longs;e e&longs;&longs;e confringi, quod cum glareæ &longs;eu croc æ <lb/>patiantur, nece&longs;&longs;ariò rotundas fieri. </s> |
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| <s>Hinc etiam no&longs;trates Architecti, in arcium propu­<lb/>gnaculis efformandis a cutos angulos <expan abbr="deuitãt">deuitant</expan>, vtpote de­<lb/>biliores, & magis offen&longs;ionibus obnoxios. </s> | <s>Hinc etiam no&longs;trates Architecti, in arcium propu­<lb/>gnaculis efformandis a cutos angulos <expan abbr="deuitãt">deuitant</expan>, vtpote de­<lb/>biliores, & magis offen&longs;ionibus obnoxios. </s> |
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| <s>quod nec Vi­<lb/>truuium latuit, qui ideo lib. </s> | <s>quod nec Vi­<lb/>truuium latuit, qui ideo lib. |
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| <s>1. cap. </s> | 1. cap. |
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| <s>5. ita &longs;cribit: <emph type="italics"/>Turresitaque<lb/>rotundæ aut polygoniæ &longs;unt faciendæ, quadrat as enim machinæ <lb/>celerius di&longs;&longs;ipant; & angulos, Arietes tundendo frangunt, inro­<lb/>tundationibus autem, vti cuneos adcentrum adigendo lædere non <lb/>po&longs;&longs;unt.<emph.end type="italics"/> Hæcille. </s> | 5. ita &longs;cribit: <emph type="italics"/>Turresitaque<lb/>rotundæ aut polygoniæ &longs;unt faciendæ, quadrat as enim machinæ <lb/>celerius di&longs;&longs;ipant; & angulos, Arietes tundendo frangunt, inro­<lb/>tundationibus autem, vti cuneos adcentrum adigendo lædere non <lb/>po&longs;&longs;unt.<emph.end type="italics"/> Hæcille. </s> |
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| <s>Cur autem no&longs;tri rotundas figuras alias <lb/>vtiles reijciant, ab ijs petendum qui in ea facultate ver­<lb/>&longs;antur. </s> | <s>Cur autem no&longs;tri rotundas figuras alias <lb/>vtiles reijciant, ab ijs petendum qui in ea facultate ver­<lb/>&longs;antur. </s> |
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| <s>Quoniam igitur vt EC, ad EA, ita CD ad <lb/>AB per 4. propo&longs;. </s> | <s>Quoniam igitur vt EC, ad EA, ita CD ad <lb/>AB per 4. propo&longs;. </s> |
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| <s>lib. </s> | <s>lib. |
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| <s>6. maior erit CD ip&longs;a AB, & eâdem <lb/>de cau&longs;&longs;a maior AB, ip&longs;a HI, & idcirco maius ABDC &longs;pa­<lb/>tium, &longs;patio AHIB. </s> | 6. maior erit CD ip&longs;a AB, & eâdem <lb/>de cau&longs;&longs;a maior AB, ip&longs;a HI, & idcirco maius ABDC &longs;pa­<lb/>tium, &longs;patio AHIB. </s> |
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| <s>Non igitur pote&longs;t linea CD, fieri in <lb/>AB, neque AB, in HI, neque &longs;patium totum CABD, tran&longs;­<lb/>ferri in &longs;patium AHIB non data (quod naturæ ip&longs;i repu­<pb pagenum="106"/>gnat) corporum penetratione. </s> | <s>Non igitur pote&longs;t linea CD, fieri in <lb/>AB, neque AB, in HI, neque &longs;patium totum CABD, tran&longs;­<lb/>ferri in &longs;patium AHIB non data (quod naturæ ip&longs;i repu­<pb pagenum="106"/>gnat) corporum penetratione. </s> |
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| <s>Verumenimuero, debilis hæc &longs;tructura e&longs;t, & eo de­<lb/>bilior, quo vani latitudo fucrit maior, cuneorum verò al­<lb/>titudo minor. </s> | <s>Verumenimuero, debilis hæc &longs;tructura e&longs;t, & eo de­<lb/>bilior, quo vani latitudo fucrit maior, cuneorum verò al­<lb/>titudo minor. </s> |
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| <s>Idem enim patitur quod epi&longs;tylia in &longs;pecie <lb/>Aræos&longs;tyla, quæ, vt&longs;cribit Vitruuius lib. </s> | <s>Idem enim patitur quod epi&longs;tylia in &longs;pecie <lb/>Aræos&longs;tyla, quæ, vt&longs;cribit Vitruuius lib. |
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| <s>3. c. </s> | 3. c. </s> |
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| <s>2. propter in­<lb/>teruallorum magnitudinem franguntur. </s> | <s>2. propter in­<lb/>teruallorum magnitudinem franguntur. </s> |
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| <s>circa medium autem pote&longs;t videri debilior, <lb/>quippe quod ellip&longs;isibi circulo curuetur minus. </s></p><p type="main"> | <s>circa medium autem pote&longs;t videri debilior, <lb/>quippe quod ellip&longs;isibi circulo curuetur minus. </s></p><p type="main"> |
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| <s>Ea verò forma, qua mirum in modum delectati &longs;unt <lb/>Barbari, qui declinante imperio Italiam inua&longs;erunt, & <lb/>bonam emendati&longs;&longs;imamqueue antiquorum ædificandi ra­<lb/>tionem deturparunt, ex duobus con&longs;tat circuli portioni­<lb/>bus, quamobrem Albertus lib. </s> | <s>Ea verò forma, qua mirum in modum delectati &longs;unt <lb/>Barbari, qui declinante imperio Italiam inua&longs;erunt, & <lb/>bonam emendati&longs;&longs;imamqueue antiquorum ædificandi ra­<lb/>tionem deturparunt, ex duobus con&longs;tat circuli portioni­<lb/>bus, quamobrem Albertus lib. |
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| <s>3. ho&longs;ce arcus, compo&longs;itos, <lb/>appellat. </s> | 3. ho&longs;ce arcus, compo&longs;itos, <lb/>appellat. </s> |
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| <s>Circinantur autem hoc pacto, diui&longs;a nempe <lb/>&longs;ubten&longs;a, in partes tres, ea&longs;que æquales, ponitur circini <lb/>pes in altero diui&longs;ionum puncto & pars circuli de&longs;cribi­<lb/>tur, mox in altero puncto circini pede collocato alia cir­<lb/>culi portio lineatur, quibus arcus ip&longs;e integratur. </s> | <s>Circinantur autem hoc pacto, diui&longs;a nempe <lb/>&longs;ubten&longs;a, in partes tres, ea&longs;que æquales, ponitur circini <lb/>pes in altero diui&longs;ionum puncto & pars circuli de&longs;cribi­<lb/>tur, mox in altero puncto circini pede collocato alia cir­<lb/>culi portio lineatur, quibus arcus ip&longs;e integratur. </s> |
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| <s>Centro <lb/>igitur G fiet euer&longs;io portio­<lb/>num fornicum, MD, HD, <lb/>Ducantur GA, GE & producta AD in N ip&longs;i AN perpen­<lb/>dicularis ducatur GN. quoniam igitur GE cadit in trian­<lb/>gulo AGN erit ex 21. propo&longs;. </s> | <s>Centro <lb/>igitur G fiet euer&longs;io portio­<lb/>num fornicum, MD, HD, <lb/>Ducantur GA, GE & producta AD in N ip&longs;i AN perpen­<lb/>dicularis ducatur GN. quoniam igitur GE cadit in trian­<lb/>gulo AGN erit ex 21. propo&longs;. </s> |
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| <s>lib. </s> | <s>lib. |
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| <s>1. elem. </s> | 1. elem. </s> |
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| <s>GA, maior GE. <lb/></s> | <s>GA, maior GE. <lb/></s> |
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| <s>A­<lb/>ri&longs;totelis mentem clarè <lb/>& fusè explicat G. V­<lb/>bald. </s> | <s>A­<lb/>ri&longs;totelis mentem clarè <lb/>& fusè explicat G. V­<lb/>bald. </s> |
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| <s>in Mechan. </s> | <s>in Mechan. vbi de <lb/>Cuneo peculiariter a­<lb/>git. </s></p><p type="main"> |
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| <s>vbi de <lb/>Cuneo peculiariter a­<lb/>git. </s></p><p type="main"> | |
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| <s>E&longs;to igitur &longs;cindendum quippiam ABCD, Cuneus <lb/>EFG, cuius pars HFI &longs;ci&longs;&longs;uræ in&longs;erta HI, facta igitur vali­<lb/>da percu&longs;&longs;ione in EG, fiet vt cum EG fuerit in NO, H &longs;it v­<lb/>bi N, A vbi P, itemque I vbi O, D verò vbi Q & facta erit <lb/>&longs;ci&longs;&longs;io NSO, toti nempe cuneo EFG, æqualis. </s> | <s>E&longs;to igitur &longs;cindendum quippiam ABCD, Cuneus <lb/>EFG, cuius pars HFI &longs;ci&longs;&longs;uræ in&longs;erta HI, facta igitur vali­<lb/>da percu&longs;&longs;ione in EG, fiet vt cum EG fuerit in NO, H &longs;it v­<lb/>bi N, A vbi P, itemque I vbi O, D verò vbi Q & facta erit <lb/>&longs;ci&longs;&longs;io NSO, toti nempe cuneo EFG, æqualis. </s> |
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| <s>Tract. </s> | <s>Tract. </s> |
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| <s>de Vecte <lb/>prop. </s> | <s>de Vecte <lb/>prop. |
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| <s>3. Po&longs;ita nempe inter fulcimentum & pondus &longs;u&longs;ti­<lb/>nente potentiâ. </s> | 3. Po&longs;ita nempe inter fulcimentum & pondus &longs;u&longs;ti­<lb/>nente potentiâ. </s> |
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| <s>Præterea quod a&longs;&longs;eruit Ari&longs;toteles, Tro­<lb/>chleas ad vectem reduci, verum quidem e&longs;t, &longs;ed aptius di­<lb/>xi&longs;&longs;et ad libram, etenim vectis vtcunque à ful cimento di­<lb/>uiditur. </s> | <s>Præterea quod a&longs;&longs;eruit Ari&longs;toteles, Tro­<lb/>chleas ad vectem reduci, verum quidem e&longs;t, &longs;ed aptius di­<lb/>xi&longs;&longs;et ad libram, etenim vectis vtcunque à ful cimento di­<lb/>uiditur. </s> |
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| <s>Quod autem addit Ari&longs;toteles, eo maiorem fieri <lb/>vectium eleuationem, hoc e&longs;t, in&longs;trumenti aperitionem, <lb/>quo magis nux quæ frangitur, fuerit propior fulcimento, <lb/>hoc e&longs;t, ip&longs;i vertebræ, facile o&longs;tenditur ex conuer&longs;a 21. <lb/>propo&longs;. </s> | <s>Quod autem addit Ari&longs;toteles, eo maiorem fieri <lb/>vectium eleuationem, hoc e&longs;t, in&longs;trumenti aperitionem, <lb/>quo magis nux quæ frangitur, fuerit propior fulcimento, <lb/>hoc e&longs;t, ip&longs;i vertebræ, facile o&longs;tenditur ex conuer&longs;a 21. <lb/>propo&longs;. </s> |
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| <s>lib. </s> | <s>lib. |
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| <s>1. Elem. </s> | 1. Elem. |
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| <s>&longs;i enim ab extremitatibus vnius line æ <lb/>ad ea&longs;dem partes con&longs;tituantur duæ line æ maiores con­<lb/>currentes in angulo, & ab ij&longs;dem extremitatibus duæ a­<lb/>liæ minores, quæ intra triangulum à maioribus con&longs;titu­<lb/>tum cadant, maiorem angulum continebunt. </s> | &longs;i enim ab extremitatibus vnius line æ <lb/>ad ea&longs;dem partes con&longs;tituantur duæ line æ maiores con­<lb/>currentes in angulo, & ab ij&longs;dem extremitatibus duæ a­<lb/>liæ minores, quæ intra triangulum à maioribus con&longs;titu­<lb/>tum cadant, maiorem angulum continebunt. </s> |
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| <s>At talis e&longs;t <lb/>angulus qui fit in in &longs;trumento, cum partes vectis à verte­<lb/>bra adnucem fuerint breuiores. </s> | <s>At talis e&longs;t <lb/>angulus qui fit in in &longs;trumento, cum partes vectis à verte­<lb/>bra adnucem fuerint breuiores. </s> |
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| <s>Huius quoque &longs;peculationis e&longs;t inue&longs;tigare, Cur <lb/>quadrupedia dum gradiuntur, pedes diametraliter mo­<lb/>ueant. </s> | <s>Huius quoque &longs;peculationis e&longs;t inue&longs;tigare, Cur <lb/>quadrupedia dum gradiuntur, pedes diametraliter mo­<lb/>ueant. </s> |
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| <s>Cuius rei verba fecitip&longs;e quoque Philo&longs;ophus lib. <lb/></s> | <s>Cuius rei verba fecitip&longs;e quoque Philo&longs;ophus lib. <lb/> |
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| <s>de animalium in ce&longs;&longs;u cap. </s> | de animalium in ce&longs;&longs;u cap. |
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| <s>12. Nos autem ad maiorem de­<lb/>clarationem, quodip&longs;e Phy&longs;icis principijs fecit, mecha­<lb/>nicis demon&longs;trabimus. </s></p><p type="main"> | 12. Nos autem ad maiorem de­<lb/>clarationem, quodip&longs;e Phy&longs;icis principijs fecit, mecha­<lb/>nicis demon&longs;trabimus. </s></p><p type="main"> |
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| <s>Sint duæ in plano parallelæ AB, CD, in quibus qua­<lb/>drupedis pedes E, F, B, D, quorum EF, anteriores, BD vero <lb/>po&longs;teriores. </s> | <s>Sint duæ in plano parallelæ AB, CD, in quibus qua­<lb/>drupedis pedes E, F, B, D, quorum EF, anteriores, BD vero <lb/>po&longs;teriores. </s> |
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| <s>Certe cau&longs;&longs;am velocitatis auctæ eam e&longs;&longs;e, quod <lb/>potentia mouens rem motam in motu ip&longs;o moueat, nemo <lb/>vtarbitror, inficias ibit, acquirit enim corpus motum <expan abbr="pō-">pon-</expan><pb pagenum="179"/>dero&longs;itatem quan dam accidentalem, quæ cum ex motu <lb/>perinde augeatur, ip&longs;um motum faciliorem, eoque velo­<lb/>ciorem facit. </s> | <s>Certe cau&longs;&longs;am velocitatis auctæ eam e&longs;&longs;e, quod <lb/>potentia mouens rem motam in motu ip&longs;o moueat, nemo <lb/>vtarbitror, inficias ibit, acquirit enim corpus motum <expan abbr="pō-">pon-</expan><pb pagenum="179"/>dero&longs;itatem quan dam accidentalem, quæ cum ex motu <lb/>perinde augeatur, ip&longs;um motum faciliorem, eoque velo­<lb/>ciorem facit. </s> |
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| <s>Di&longs;putat hæc & Simplicius lib. </s> | <s>Di&longs;putat hæc & Simplicius lib. |
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| <s>7. Phy&longs;ic. </s> | 7. Phy&longs;ic. </s> |
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| <s>c. <lb/></s> | <s>c. <lb/></s> |
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| <s>Hocitidem problema e&longs;t mere Phy&longs;icum. </s> | <s>Hocitidem problema e&longs;t mere Phy&longs;icum. </s> |
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| <s>Ad quod ea <lb/>pertinent quæ à Philo&longs;opho tractantur libro Natu­<lb/>ralium 8. & lib. </s> | <s>Ad quod ea <lb/>pertinent quæ à Philo&longs;opho tractantur libro Natu­<lb/>ralium 8. & lib. |
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| <s>1. de Cœlo. </s> | 1. de Cœlo. </s> |
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| <s>Tres autem affert &longs;ubdubitan­<lb/>do rationes, An quia impellens de&longs;init potentia, vel pro­<lb/>pter retractionem, vel propter rei proiectæ in <expan abbr="clinationē">clinationem</expan>, <lb/>quando ea valentior fuerit quam proijcientis vires? </s></p><p type="main"> | <s>Tres autem affert &longs;ubdubitan­<lb/>do rationes, An quia impellens de&longs;init potentia, vel pro­<lb/>pter retractionem, vel propter rei proiectæ in <expan abbr="clinationē">clinationem</expan>, <lb/>quando ea valentior fuerit quam proijcientis vires? </s></p><p type="main"> |
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| <s>Erit igitur FI (prop. <lb/></s> | <s>Erit igitur FI (prop. <lb/></s> |
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| <s>18. lib. </s> | <s>18. lib. |
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| <s>3. elem.) ip&longs;i GH plano perpendicularis. </s> | 3. elem.) ip&longs;i GH plano perpendicularis. </s> |
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| <s>Ducatur <lb/>item peri, ip&longs;i EC, parallela IK, &longs;ecans pilæ circumferen­<lb/>tiam in K. </s> | <s>Ducatur <lb/>item peri, ip&longs;i EC, parallela IK, &longs;ecans pilæ circumferen­<lb/>tiam in K. </s> |
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| <s>Atque e&longs;t ip&longs;ius AB dimidi<gap/> AL, & ip&longs;ius BC, du­<lb/>pla CG, e&longs;t igitur vt MA ad AL, ita GC ad C<emph type="italics"/>K<emph.end type="italics"/>. </s> | <s>Atque e&longs;t ip&longs;ius AB dimidi<gap/> AL, & ip&longs;ius BC, du­<lb/>pla CG, e&longs;t igitur vt MA ad AL, ita GC ad C<emph type="italics"/>K<emph.end type="italics"/>. </s> |
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| <s>Sed vt GC <lb/>ad C<emph type="italics"/>K<emph.end type="italics"/>, ita FH ad H<emph type="italics"/>K<emph.end type="italics"/> propter lineas parallelas GF, CH. <lb/>quare & componendo vt ML, ad LA, ita F<emph type="italics"/>K<emph.end type="italics"/> ad <emph type="italics"/>K<emph.end type="italics"/>H, &longs;ed <lb/>AL ponitur æqualis H<emph type="italics"/>K<emph.end type="italics"/>, quoniam & ip&longs;i CF, ergo & ML <lb/>per 9. lib. </s> | <s>Sed vt GC <lb/>ad C<emph type="italics"/>K<emph.end type="italics"/>, ita FH ad H<emph type="italics"/>K<emph.end type="italics"/> propter lineas parallelas GF, CH. <lb/>quare & componendo vt ML, ad LA, ita F<emph type="italics"/>K<emph.end type="italics"/> ad <emph type="italics"/>K<emph.end type="italics"/>H, &longs;ed <lb/>AL ponitur æqualis H<emph type="italics"/>K<emph.end type="italics"/>, quoniam & ip&longs;i CF, ergo & ML <lb/>per 9. lib. |
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| <s>5. æqualis erit F<emph type="italics"/>K<emph.end type="italics"/>, & quadratum ex ML, æquale <lb/>quadrato ex F<emph type="italics"/>K<emph.end type="italics"/>. </s> | 5. æqualis erit F<emph type="italics"/>K<emph.end type="italics"/>, & quadratum ex ML, æquale <lb/>quadrato ex F<emph type="italics"/>K<emph.end type="italics"/>. </s> |
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| <s>e&longs;t autem quadrato ex ML, æquale re­<lb/>ctangulum BMA vna cum quadrato ex AL & quadrato <lb/>ex Fk æquale o&longs;ten&longs;um e&longs;t rectangulum BkC vna cum. <pb pagenum="194"/>quadrato ex CF, quorum quidem quadratum ex AL æ­<lb/>quale e&longs;t quadrato ex CF, ponitur enim AL, ip&longs;i CF æ­<lb/>qualis, ergo reliquum BMA rectangulum æquale e&longs;t reli­<lb/>quo BkC. </s> | <s>e&longs;t autem quadrato ex ML, æquale re­<lb/>ctangulum BMA vna cum quadrato ex AL & quadrato <lb/>ex Fk æquale o&longs;ten&longs;um e&longs;t rectangulum BkC vna cum. <pb pagenum="194"/>quadrato ex CF, quorum quidem quadratum ex AL æ­<lb/>quale e&longs;t quadrato ex CF, ponitur enim AL, ip&longs;i CF æ­<lb/>qualis, ergo reliquum BMA rectangulum æquale e&longs;t reli­<lb/>quo BkC. </s> |
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