texts/archimedes/xml/schot_mecha_051_la_1657.xml - Colored diff

Main History Search Repository tree

Return to schot_mecha_051_la_1657.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/schot_mecha_051_la_1657.xml between version 1.5 and 1.12

version 1.5, 2005/10/19 09:06:46

version 1.12, 2005/10/25 11:08:16

Line 67

<s><emph type="center"/>ACCESSIT<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Experimentum novum Magdeburgicum, quo vacuum alij &longs;ta<lb/>bilire, alij evertere conan<gap/>r.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Experimentum novum Magdeburgicum, quo vacuum alij &longs;ta<lb/>bilire, alij evertere conantur.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/>Sumptu Heredum JOANNIS GODEFRIDI Schôn wetteri,<emph.end type="center"/></s>

Line 91

<s><emph type="center"/>Archiepi&longs;copo, S. Rom. Imp. per Germani<lb/>am Archi-Cancellario, & Principi Electori; Epi&longs;copo <lb/>Herbipolen&longs;i, Franciæ Orientalis Duci, <lb/>Domino meo clementi&longs;&longs;imo.<emph.end type="center"/></s>

<s>EMINENTISSIME PRIN<lb/>CEPS. Fontes quos Natura <lb/>producit ad hominum utilitatem, <lb/><emph type="italics"/>Mare<emph.end type="italics"/> petunt, ut fluant. <emph type="italics"/>Omnia quippe <lb/>flumina,<emph.end type="italics"/> ac proinde & fontes flumi-

<pb xlink:href="051/01/007.jpg"/>num origines, <emph type="italics"/>intrant in Mare, & Mare non <lb/>redundat; ad locum, unde exeunt flumina, revertun<lb/>tur, vt iterum fluant.<emph.end type="italics"/> Fontes quos hoc <lb/>in Opere produco ex Hydrotech<lb/>nica Arte ad Principum delecta<lb/>tionem, ut &longs;aliant, FONTEM petunt <lb/>PULCHRUM, Te inquam, EMI<lb/>NENTISSIME DOMINE, <expan abbr="Tuumq;">Tuumque</expan> <lb/>favorem ac benevolentiam. Ni&longs;i <lb/>enim ope Tua, qui FONS es PUL<lb/>CHERRIMUS, foveantur, & <lb/>Tua augeantur ditenturque co<lb/>pia; exare&longs;cant nece&longs;&longs;e e&longs;t, ma<lb/>gno licet labore, nec minori <lb/>Arte, in fluxum ac &longs;altum àme <lb/>animati. Pateat igitur Fontibus

<s>EMINENTISSIME PRIN<lb/>CEPS. Fontes quos Natura <lb/>producit ad hominum utilitatem, <lb/><emph type="italics"/>Mare<emph.end type="italics"/> petunt, ut fluant. </s><s><emph type="italics"/>Omnia quippe <lb/>flumina,<emph.end type="italics"/> ac proinde & fontes flumi-

<pb xlink:href="051/01/008.jpg"/>meis FONS PULCHER; <expan abbr="deriv&etilde;tur">deriventur</expan> <lb/>in eos Humanitatis Tuæ aquæ, ut <lb/>gloriari liceat, ac dicere: FONS <lb/>PULCHER SUFFICIT UNDAS. <lb/>Dixi quod volebain, & hîc finio, <lb/>nè peccare cogar peccatum quo <lb/>Scriptorum plerique reos &longs;e con<lb/>&longs;tituunt, dum in Mecænatum <lb/>&longs;uorum laudes ip&longs;o in Librorum <lb/>ve&longs;tibulo quàm pro loci oppor<lb/>tunitate longiùs excurrunt. Ma<lb/>jor e&longs;t virtutum Tuarum &longs;plen<lb/>dor, majora in Eccle&longs;iam & Im<lb/>perium Romanum merita, quàm <lb/>ut exili calamo meo, præ&longs;ertim <lb/>hoc loco, exarentur. </s>

<pb xlink:href="051/01/007.jpg"/>num origines, <emph type="italics"/>intrant in Mare, & Mare non <lb/>redundat; ad locum, unde exeunt flumina, revertun<lb/>tur, vt iterum fluant.<emph.end type="italics"/> </s><s>Fontes quos hoc <lb/>in Opere produco ex Hydrotech<lb/>nica Arte ad Principum delecta<lb/>tionem, ut &longs;aliant, FONTEM petunt <lb/>PULCHRUM, Te inquam, EMI<lb/>NENTISSIME DOMINE, <expan abbr="Tuumq;">Tuumque</expan> <lb/>favorem ac benevolentiam. </s><s>Ni&longs;i <lb/>enim ope Tua, qui FONS es PUL<lb/>CHERRIMUS, foveantur, & <lb/>Tua augeantur ditenturque co<lb/>pia; exare&longs;cant nece&longs;&longs;e e&longs;t, ma<lb/>gno licet labore, nec minori <lb/>Arte, in fluxum ac &longs;altum àme <lb/>animati. </s><s> Pateat igitur Fontibus

<pb xlink:href="051/01/008.jpg"/>meis FONS PULCHER; <expan abbr="deriv&etilde;tur">deriventur</expan> <lb/>in eos Humanitatis Tuæ aquæ, ut <lb/>gloriari liceat, ac dicere: FONS <lb/>PULCHER SUFFICIT UNDAS. </s><s><lb/>Dixi quod volebain, & hîc finio, <lb/>nè peccare cogar peccatum quo <lb/>Scriptorum plerique reos &longs;e con<lb/>&longs;tituunt, dum in Mecænatum <lb/>&longs;uorum laudes ip&longs;o in Librorum <lb/>ve&longs;tibulo quàm pro loci oppor<lb/>tunitate longiùs excurrunt. </s><s>Ma<lb/>jor e&longs;t virtutum Tuarum &longs;plen<lb/>dor, majora in Eccle&longs;iam & Im<lb/>perium Romanum merita, quàm <lb/>ut exili calamo meo, præ&longs;ertim <lb/>hoc loco, exarentur. </s>

<s>Vale PRINCEPS EMINEN<lb/>TISSIME, Imperii columen, <lb/>& Eccle&longs;iæ decus; ae bono utrius<lb/>que quàm diutis&longs;imè vive. Ita <lb/>optat Herbipoli Die VIII. Julij, <lb/>Anno MDCL VII. </s>

<s>Vale PRINCEPS EMINEN<lb/>TISSIME, Imperii columen, <lb/>& Eccle&longs;iæ decus; ae bono utrius<lb/>que quàm diutis&longs;imè vive. </s><s> Ita <lb/>optat Herbipoli Die VIII. Julij, <lb/>Anno MDCL VII. </s>

<s>EMINENTISSIMÆ <lb/>TUÆ </s>

Line 118

Line 119

<s><emph type="center"/>PEGASUS.<emph.end type="center"/></s>

<s><emph type="center"/>Riget in&longs;tar pumicis, qui Parna&longs;&longs;um irrigavit: <lb/>Qui infantium etiam linguas fecerat di&longs;ertas, <lb/>Dudum, prô pudor, e&longs;t de&longs;ertus. <lb/>Pone cri&longs;tas Heliconis Nympha;<emph.end type="center"/></s>

<s><emph type="center"/>Riget in&longs;tar pumicis, qui Parna&longs;&longs;um irrigavit: <lb/>Qui infantium etiam linguas fecerat di&longs;ertas, <lb/>Dudum, prô pudor, e&longs;t de&longs;ertus. </s><s><lb/>Pone cri&longs;tas Heliconis Nympha;<emph.end type="center"/></s>

<s><emph type="center"/>HIPPOCRENE FUIT!<emph.end type="center"/></s>

Line 156

Line 157

<s><emph type="center"/>Verùm quid Mu&longs;as, Nymphásque memoro? <lb/>Ip&longs;a adeò Natura hoc fonte haurit, <lb/>Ut parturientem juvet Artem:<emph.end type="center"/></s>

<s><emph type="center"/>Hinc Ars bibit, ut languentem fulciat Naturam, <lb/>Experti di&longs;cimus: <lb/>Quod non &longs;ola Natura audet. <lb/>Nec Ars &longs;ola pote&longs;t, <lb/>Et pote&longs;t cum Arte Natura & audet. <lb/>Verùm deficerent, ni&longs;i &longs;ufficeret,<emph.end type="center"/></s>

<s><emph type="center"/>Hinc Ars bibit, ut languentem fulciat Naturam, <lb/>Experti di&longs;cimus: <lb/>Quod non &longs;ola Natura audet. </s><s><lb/>Nec Ars &longs;ola pote&longs;t, <lb/>Et pote&longs;t cum Arte Natura & audet. </s><s><lb/>Verùm deficerent, ni&longs;i &longs;ufficeret,<emph.end type="center"/></s>

<s><emph type="center"/>FONS PULCHER<emph.end type="center"/></s>

<s><emph type="center"/>Undas, Animos, Vires. <lb/>Hoc manante animatur emortuus Æolus, <lb/>Et &longs;pirat:<emph.end type="center"/></s>

<s><emph type="center"/>Undas, Animos, Vires. </s><s><lb/>Hoc manante animatur emortuus Æolus, <lb/>Et &longs;pirat:<emph.end type="center"/></s>

<s><emph type="center"/>Hoc &longs;tillante lique&longs;cunt, licet ære fu&longs;æ, Phaëtontiades, <lb/>Et lacrymantur:<emph.end type="center"/></s>

Line 191

Line 192

<s><emph type="center"/>Hoc &longs;tratagemate, <lb/><emph type="italics"/>Rotas Moganas<emph.end type="italics"/> firmavit, <lb/>Ut bene verterentur, <lb/>Quæ à procellis, quia rapiebantur, <lb/>Pæne evertebantur.<emph.end type="center"/></s>

<s><emph type="center"/>Pluris &longs;cilicet &longs;æpe e&longs;t e&longs;&longs;e humanum quàm fortem, <lb/>Ubi gloria e&longs;t major, <lb/>Vincere amoribus quàm viribus. <lb/>In fontibus reliquis eximium hoc habet<emph.end type="center"/></s>

<s><emph type="center"/>Pluris &longs;cilicet &longs;æpe e&longs;t e&longs;&longs;e humanum quàm fortem, <lb/>Ubi gloria e&longs;t major, <lb/>Vincere amoribus quàm viribus. </s><s><lb/>In fontibus reliquis eximium hoc habet<emph.end type="center"/></s>

<s><emph type="center"/>FONS PULCHER,<emph.end type="center"/></s>

Line 243

Line 244

<s><emph type="center"/><emph type="italics"/>PRÆPOSITUS GENERALIS.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>CUm Opus, quod in&longs;cribitur<emph.end type="italics"/> Mechanica <lb/>Hydraulico-pnevmatica, à P. GASPARE <lb/>SCHOTT <emph type="italics"/>noftræ Societatis Sacerdote compo&longs;i<lb/>tum, aliquot eju&longs;dem Societatis Religio&longs;i recognove<lb/>rint, & in lucem edi po&longs;&longs;e probaverint; facultatem <lb/>concedimus vt typis mandetur, &longs;i ijs ad quos pertinet, <lb/>ita videbitur. In cujus rei te&longs;timonium has litteras <lb/>manu no&longs;trâ &longs;ub&longs;criptas, &longs;igillo&queacute; no&longs;tro munitas da<lb/>mus Romæ,<emph.end type="italics"/> 23. <emph type="italics"/>Januarij<emph.end type="italics"/> 1655. </s>

<s><emph type="italics"/>CUm Opus, quod in&longs;cribitur<emph.end type="italics"/> Mechanica <lb/>Hydraulico-pnevmatica, à P. GASPARE <lb/>SCHOTT <emph type="italics"/>noftræ Societatis Sacerdote compo&longs;i<lb/>tum, aliquot eju&longs;dem Societatis Religio&longs;i recognove<lb/>rint, & in lucem edi po&longs;&longs;e probaverint; facultatem <lb/>concedimus vt typis mandetur, &longs;i ijs ad quos pertinet, <lb/>ita videbitur. </s><s>In cujus rei te&longs;timonium has litteras <lb/>manu no&longs;trâ &longs;ub&longs;criptas, &longs;igillo&queacute; no&longs;tro munitas da<lb/>mus Romæ,<emph.end type="italics"/> 23. <emph type="italics"/>Januarij<emph.end type="italics"/> 1655. </s>

<s>GOSWINUS NICKEL. </s>

Line 254

Line 255

<s><emph type="center"/>Per Rheni Superioris Provinciam Bi<lb/>bliopolæ facta.<emph.end type="center"/></s>

<s><emph type="italics"/>CUm ex Mandato Sacræ Cæ&longs;areæ Maje&longs;tatis omnibus <lb/>& &longs;ingulis Typographis, Bibliopolis, ac aliis quamcun<lb/>que librariam negotiationem exercentibus, &longs;eriò firmiterque in<lb/>hibeatur, nè qui&longs;quam libros ullos<emph.end type="italics"/> à SOCIETATIS <emph type="italics"/>no&longs;træ Pa<lb/>tribus hactenus editos, aut impo&longs;terum edendos intra S.R. Im<lb/>perij, Regnorum, & Dominiorum Suæ Cæ&longs;areæ Maje&longs;tatis hæ<lb/>reditariorum fines, &longs;imili aliovè charactere aut formâ, &longs;ive in <lb/>toto, &longs;ive in parte recudere, vel aliò recudendos mittere, aut ali<lb/>bi etiam impre&longs;&longs;os adducere, vendere, & di&longs;trahere, clàm &longs;eu <lb/>palàm, citrà &longs;upradictorum Patrum con&longs;en&longs;um ac te&longs;timonium, <lb/>audeat, vel præ&longs;umat: Ego<emph.end type="italics"/> NITHARDUS BIBERUS, <lb/>SOCIETATIS JESU <emph type="italics"/>per Rheni &longs;uperioris Provinciam Pro<lb/>vincialis, concedo<emph.end type="italics"/> Joanni Godefrido Schôn wettero <emph type="italics"/>fa<lb/>cultatem, &longs;uis &longs;umptibus excudendi<emph.end type="italics"/> P. GASPARIS SCHOTTI <lb/>è SOCIEIATE JESU Mechanicam Hydraulico-pnev<lb/>maticam. <emph type="italics"/>In quorum fidem hoc ei te&longs;timonium manu no&longs;trâ <lb/>&longs;ub&longs;criptum, & Sigillo munitum dare voluimus. Herbipoli<emph.end type="italics"/><lb/>21. <emph type="italics"/>Fanuarij<emph.end type="italics"/> 1656. </s>

<s><emph type="italics"/>CUm ex Mandato Sacræ Cæ&longs;areæ Maje&longs;tatis omnibus <lb/>& &longs;ingulis Typographis, Bibliopolis, ac aliis quamcun<lb/>que librariam negotiationem exercentibus, &longs;eriò firmiterque in<lb/>hibeatur, nè qui&longs;quam libros ullos<emph.end type="italics"/> à SOCIETATIS <emph type="italics"/>no&longs;træ Pa<lb/>tribus hactenus editos, aut impo&longs;terum edendos intra S.R. Im<lb/>perij, Regnorum, & Dominiorum Suæ Cæ&longs;areæ Maje&longs;tatis hæ<lb/>reditariorum fines, &longs;imili aliovè charactere aut formâ, &longs;ive in <lb/>toto, &longs;ive in parte recudere, vel aliò recudendos mittere, aut ali<lb/>bi etiam impre&longs;&longs;os adducere, vendere, & di&longs;trahere, clàm &longs;eu <lb/>palàm, citrà &longs;upradictorum Patrum con&longs;en&longs;um ac te&longs;timonium, <lb/>audeat, vel præ&longs;umat: Ego<emph.end type="italics"/> NITHARDUS BIBERUS, <lb/>SOCIETATIS JESU <emph type="italics"/>per Rheni &longs;uperioris Provinciam Pro<lb/>vincialis, concedo<emph.end type="italics"/> Joanni Godefrido Schôn wettero <emph type="italics"/>fa<lb/>cultatem, &longs;uis &longs;umptibus excudendi<emph.end type="italics"/> P. GASPARIS SCHOTTI <lb/>è SOCIEIATE JESU Mechanicam Hydraulico-pnev<lb/>maticam. </s><s><emph type="italics"/>In quorum fidem hoc ei te&longs;timonium manu no&longs;trâ <lb/>&longs;ub&longs;criptum, & Sigillo munitum dare voluimus.</s><s> Herbipoli<emph.end type="italics"/><lb/>21. <emph type="italics"/>Fanuarij<emph.end type="italics"/> 1656. </s>

<s>NITHARDUS BIBERUS. </s>

Line 398

Line 399

<s>I. Aqua decurrit per tubi verticalis foramen ba&longs;is, in&longs;tar columnæ aqueæ, cuius <lb/>ba&longs;is æqualis foramini, altitudo perpendiculares à ba&longs;i erectæ; &longs;ive tubi &longs;int <lb/>&longs;emper pleni, &longs;ive non. 111 </s>

<s>II. Per tubos <gap/>m &longs;emper, quàm non &longs;emper plenos æqualis altitudinis, & æqua<lb/>lium foraminum, effluit æqualis aquæ copia, eodem vel æquali tempore, <lb/>cujuscunque capacitatis & formæ &longs;int tubi. 113 </s>

<s>II. Per tubos tam &longs;emper, quàm non &longs;emper plenos æqualis altitudinis, & æqua<lb/>lium foraminum, effluit æqualis aquæ copia, eodem vel æquali tempore, <lb/>cujuscunque capacitatis & formæ &longs;int tubi. 113 </s>

<s>III. Per tubos tam &longs;emper, quàm non &longs;emper plenos æqualium luminum, &longs;ed <lb/>inæqualium altitudinum, effluit eodem, vel æquali tempore, inæqualis aquæ <lb/>copia. 114 </s>

Line 421

Line 422

<s>XII. Tempora quibus æqualis aquæ quantitas è tubis æqualium luminum, &longs;ed <lb/>inæqualium altitudinum effluit, habent &longs;ubduplicatam rationem tubo<lb/>rum. ibid. </s>

<s>XIII. Si tubi, &longs;ive &longs;emper pleni, &longs;ive non &longs;emper pleni, &longs;int ejusdem altitudinis, <lb/>&longs;ed inæqualium foraminum, e&longs;t <gap/>dem ratio aquæ ad aquam, quæ foraminis <lb/>ad foramen, phy&longs;icè &longs;eu ad &longs;en&longs;um. 127 </s>

<s>XIII. Si tubi, &longs;ive &longs;emper pleni, &longs;ive non &longs;emper pleni, &longs;int ejusdem altitudinis, <lb/>&longs;ed inæqualium foraminum, e&longs;t eadem ratio aquæ ad aquam, quæ foraminis <lb/>ad foramen, phy&longs;icè &longs;eu ad &longs;en&longs;um. 127 </s>

<s>XIV. Tubi non &longs;emper pleni æquè alti, & æqualium foraminum; &longs;ed inæquali<lb/>um ba&longs;ium, evacuantur inæqualibus temporibus, e&longs;tque eadem ratio tem<lb/>porum, quæ ba&longs;ium. 129 </s>

Line 462

Line 463

<s>V. Aliter invenire tertiam proportionalem. 147 </s>

<s>VI. Adhuc aliter invenire tertiam proportionalem. ibid </s>

<s>VI. Adhuc aliter invenire tertiam proportionalem. ibid. </s>

<s>VII. Datis tribus numeris invenire quartum proportionalem. 148 </s>

Line 589

Line 590

<s>II. Clep&longs;ydra Heroniana. 195 </s>

<s>III. Fons Heronis in va&longs;is mediatis: item &longs;cyphus diver&longs;os ejiciens liquores. 197. </s>

<s>III. Fons Heronis in va&longs;is mediatis: item &longs;cyphus diver&longs;os ejiciens liquores. 197 </s>

<s>IV. Fons novus Poly&longs;iphonius. 201 </s>

Line 629

Line 630

<s>I. Pyrobolus fons, incale&longs;centis per ignem aëris vi aquam expellens. 226 </s>

<s>II. Fons alius pyrobolus, projectum liquorem convertens in aërem, autignem. <lb/>226. Item Meteorologicæ impre&longs;&longs;iones igneæ. 229 </s>

<s>II. Fons alius pyrobolus, projectum liquorem convertens in aërem, autignem <lb/>226 </s><s>Item Meteorologicæ impre&longs;&longs;iones igneæ. 229 </s>

<s>III. Thermo&longs;copium progno&longs;ticum Hybernum. 229. & Æ&longs;tivum. 231 </s>

<s>III. Thermo&longs;copium progno&longs;ticum Hybernum. 229 </s><s>& Æ&longs;tivum. 231 </s>

<s>IV. <gap/>umentum novum, gradus humidi & &longs;icciindicans. 232 </s>

<s>IV. In&longs;trumentum novum, gradus humidi & &longs;icci indicans. 232 </s>

<s>V. Cacabus ejiciens, & retrahens eandem aquam. 236 </s>

Line 650

Line 651

<s>XI. Ara a&longs;pide adornata, in qua igne po&longs;ito I&longs;is & O&longs;iris vinum & lac &longs;acrificant <lb/>a&longs;pis verò &longs;ibilando applaudit. 244 </s>

<s>XII. Valvæ &longs;acelli &longs;uccen&longs;o &longs;acrificii igne &longs;ponte aperibiles, & extincto clau&longs;æ. 246. </s>

<s>XII. Valvæ &longs;acelli &longs;uccen&longs;o &longs;acrificii igne &longs;ponte aperibiles, & extincto clau&longs;æ. 246 </s>

<s>XIII. Ara Deorum imagines tripudiantes exhibens. 247 </s>

Line 672

Line 673

<s>III. Rota ver&longs;atilis, aquam lu&longs;trationi nece&longs;&longs;ariam fundens. 257 </s>

<s>IV. Cycocephalus Ægyptius ex veretillo aquam fundens, quæ horas æq<gap/><lb/>ctiales in &longs;ubjecto va&longs;e mon&longs;trat. 259 </s>

<s>IV. Cycocephalus Ægyptius ex veretillo aquam fundens, quæ horas æquino<lb/>ctiales in &longs;ubjecto va&longs;e mon&longs;trat. 259 </s>

<s>V. Hydrologium horarum antiquarum, &longs;eu inæqualium. 261 </s>

Line 767

Line 768

<s>III. Horarium hydraulicum, motum perpetuum adumbrans. 346 </s>

<s>IV. Kircheriana Machinula, motus perpetui rarefactionis & conden&longs;ationis <lb/>&longs;pecim<gap/>n exhibens. 351 </s>

<s>IV. Kircheriana Machinula, motus perpetui rarefactionis & conden&longs;ationis <lb/>&longs;pecimen exhibens. 351 </s>

<s>V. Fonticulus motum perpetuum vi rarefactionis & conden&longs;ationis aëris e<lb/>mentitus. 353 </s>

Line 861

Line 862

<s>§. V. P. Athana&longs;ii Kircheri de novo Experimento judicium. 452 </s>

<s>§. VI. Litteræ Auctoris Experimenti, ejusdemque ad varia quæ&longs;ita re&longs;pon&longs;io. 453. </s>

<s>§. VI. Litteræ Auctoris Experimenti, ejusdemque ad varia quæ&longs;ita re&longs;pon&longs;io. 453 </s>

<s>§. VII. Ejusdem Authoris re&longs;pon&longs;io ad no&longs;trum quæ&longs;itum. 450 </s>

<s>§. VIII. P. Nicolai Zucchii è Societate Je&longs;u de novo Experimento judicium. 463. </s>

<s>§. VIII. P. Nicolai Zucchii è Societate Je&longs;u de novo Experimento judicium. 463 </s>

<s>§. IX. P. Melchioris Cornæi è Societate Je&longs;u de eodem Experimento judi<lb/>cium. 465 </s>

Line 873

Line 874

<s><emph type="center"/><emph type="italics"/>In<emph.end type="italics"/><lb/>MECHANICAM HYDRAU<lb/>LICAM<emph.end type="center"/></s>

<s><emph type="center"/>Odarion Encomia&longs;ticon.<emph.end type="center"/><lb/><emph type="italics"/>CEdat &longs;uperbas Amphitryonides <lb/>Palmas Minervæ. Vis jacet: Artium <lb/>Tropæa clarent. Cuncta nut us <lb/>Jam Dominæ venerantur Artis. <lb/>Non ille no&longs;tri temporis Hercules, <lb/>Qui frangit armis cornua fluminum, <lb/>Dum cana &longs;eclorum &longs;enectus <lb/>Ingeniis animis <expan abbr="&qacute;ue">que</expan> floret. <lb/>Quid? ergò Reges nè furor incitet <lb/>Vincire Pontum. Nil ni&longs;i fabulam <lb/>Seris propinabit nepotum <lb/>Fa&longs;tus Achæmenidæ cachinnis. <lb/>Risêre &longs;tultas æquora compedes <lb/>Manare ritu certa &longs;uo, licet <lb/>Ringatur & flagro rebelles <lb/>Mulctet aquæ male&longs;anus iras. <lb/>In&longs;anientis quid Domini minæ <lb/>Tangunt proteruum marmor? Herus jubet? <lb/>Surde&longs;cit, & plaudente fluctu <lb/>Ludificat pelagus Tyrannum. <lb/>At non & Artem vis Acheloia <lb/>Impunè ludet. Capta &longs;uis Aqua <lb/>Technis tenetur, liberosque <lb/>Victa jocos, patiturque ri&longs;us.<emph.end type="italics"/>

<s><emph type="center"/>Odarion Encomia&longs;ticon.<emph.end type="center"/><lb/><emph type="italics"/>CEdat &longs;uperbas Amphitryonides <lb/>Palmas Minervæ. </s><s>Vis jacet: Artium <lb/>Tropæa clarent. </s><s>Cuncta nutus <lb/>Jam Dominæ venerantur Artis. </s><s><lb/>Non ille no&longs;tri temporis Hercules, <lb/>Qui frangit armis cornua fluminum, <lb/>Dum cana &longs;eclorum &longs;enectus <lb/>Ingeniis animis <expan abbr="&qacute;ue">que</expan> floret. </s><s><lb/>Quid? </s><s>ergò Reges nè furor incitet <lb/>Vincire Pontum. </s><s>Nil ni&longs;i fabulam <lb/>Seris propinabit nepotum <lb/>Fa&longs;tus Achæmenidæ cachinnis. </s><s><lb/>Risêre &longs;tultas æquora compedes <lb/>Manare ritu certa &longs;uo, licet <lb/>Ringatur & flagro rebelles <lb/>Mulctet aquæ male&longs;anus iras. </s><s><lb/>In&longs;anientis quid Domini minæ <lb/>Tangunt proteruum marmor? Herus jubet? <lb/>Surde&longs;cit, & plaudente fluctu <lb/>Ludificat pelagus Tyrannum. </s><s><lb/>At non & Artem vis Acheloia <lb/>Impunè ludet. </s><s>Capta &longs;uis Aqua <lb/>Technis tenetur, liberosque <lb/>Victa jocos, patiturque ri&longs;us.<emph.end type="italics"/>

<pb xlink:href="051/01/030.jpg"/><emph type="italics"/>Et quas domando non potuit mari <lb/>Sevùm fremi&longs;cens ardor adoreas, <lb/>Has lenè &longs;olers Machinator <lb/>Præripuit meliore ni&longs;u. <lb/>Spectare ge&longs;tin? en tibi panditur <lb/>Hoc &longs;cena libro, quâ &longs;trepitu procul, <lb/>Quæ dulce &longs;it &longs;pecta&longs;&longs;e, &longs;pectes, <lb/>Quæque juvet didici&longs;&longs;e, di&longs;cas, <lb/>Quàm f&oelig;deratum non violabilis <lb/>Lex nectat orbem; &longs;i qua pericula <lb/>Vexent, ut imis &longs;umma, raris <lb/>Den&longs;a, levi grave det &longs;alutem. <lb/>Quò pondus vnd<gap/> vergat, & aëris; <lb/>Quod pellat; aut quod corpora jus trahat; <lb/>Cur i&longs;te gurges ructet vndas, <lb/>Quas avido bibit ales ore; <lb/>Quid mille lu&longs;us, mille jocos aquæ <lb/>Fundet, docebit<emph.end type="italics"/> SCHOTTVS <emph type="italics"/>Hydraulicæ <lb/>Con&longs;ultus artis, doctas idem <lb/>Ingenium fluitantis auræ. <lb/>Non Ille nomen fluctibus apprimat, <lb/>Quod turbet Au&longs;ter, dignus aheneis <lb/>Scribi columnis, quæ nec ævi <lb/>Dente, nec invidiæ terantur.<emph.end type="italics"/></s>

<pb xlink:href="051/01/030.jpg"/><emph type="italics"/>Et quas domando non potuit mari <lb/>Sevùm fremi&longs;cens ardor adoreas, <lb/>Has lenè &longs;olers Machinator <lb/>Præripuit meliore ni&longs;u. </s><s><lb/>Spectare ge&longs;tin? en tibi panditur <lb/>Hoc &longs;cena libro, quâ &longs;trepitu procul, <lb/>Quæ dulce &longs;it &longs;pecta&longs;&longs;e, &longs;pectes, <lb/>Quæque juvet didici&longs;&longs;e, di&longs;cas, <lb/>Quàm f&oelig;deratum non violabilis <lb/>Lex nectat orbem; &longs;i qua pericula <lb/>Vexent, ut imis &longs;umma, raris <lb/>Den&longs;a, levi grave det &longs;alutem. </s><s><lb/>Quò pondus vnd<gap/> vergat, & aëris; <lb/>Quod pellat; aut quod corpora jus trahat; <lb/>Cur i&longs;te gurges ructet vndas, <lb/>Quas avido bibit ales ore; <lb/>Quid mille lu&longs;us, mille jocos aquæ <lb/>Fundet, docebit<emph.end type="italics"/> SCHOTTVS <emph type="italics"/>Hydraulicæ <lb/>Con&longs;ultus artis, doctas idem <lb/>Ingenium fluitantis auræ. </s><s><lb/>Non Ille nomen fluctibus apprimat, <lb/>Quod turbet Au&longs;ter, dignus aheneis <lb/>Scribi columnis, quæ nec ævi <lb/>Dente, nec invidiæ terantur.<emph.end type="italics"/></s>

<s><emph type="center"/><emph type="italics"/>MONITIO AD LECTOREM.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Opu&longs;culum hoc Appendice exceptâ Romæ <lb/>con&longs;criptum, acprælo præparatum fuit; <lb/>ideo in eo pa&longs;sim ita loquitur Auctor, <lb/>qua&longs;i Romæ adhuc degeret. Vale, & nè <lb/>quid te moretur, errores paucos in calce <lb/>Librinotatos, priùs corrige. </s>

<s>Opu&longs;culum hoc Appendice exceptâ Romæ <lb/>con&longs;criptum, acprælo præparatum fuit; <lb/>ideo in eo pa&longs;sim ita loquitur Auctor, <lb/>qua&longs;i Romæ adhuc degeret. </s><s>Vale, & nè <lb/>quid te moretur, errores paucos in calce <lb/>Librinotatos, priùs corrige. </s>

Line 897

Line 898

<s>

<arrow.to.target n="marg1"/><lb/><emph type="italics"/>mus mihi est, benevole Lector, è Viri <lb/>Docti&longs;&longs;imi, toto&queacute; orbe noti&longs;&longs;imi Atha<lb/>na&longs;ij Kircheri Libris, quà typo excu&longs;is, <lb/>quà exar atis manu collectam; at&que; ex omnibus eius<lb/>dem Adver&longs;ariis ac Schediasmatis, quæ penes me <lb/>&longs;unt; nec non ex alijs probatorum Auctorum monu<lb/>mentis, nostris&queacute; inventis, fide &longs;ummâ, pari&queacute; &longs;tudio <lb/>concinnatam, propriis&queacute; & aliorum experimentis <lb/>&longs;tabilitam: illam inquam Magiam Naturalem, cuius<emph.end type="italics"/>

<pb xlink:href="051/01/033.jpg" pagenum="2"/><emph type="italics"/>in Catalogo Librorum posthàc à prædicto Docti&longs;&longs;imo <lb/>Auctore edendorum Magneticæ Arti denuò hîc Ro<lb/>mæ nuper editæ appo&longs;ito feci mentionem. Spartam <lb/>hanc ab ip&longs;o Auctore mihi commi&longs;&longs;am præ alijs a&longs;&longs;um<lb/>p&longs;i excolendam, quoniam præterquàm quòd omnium <lb/>ab ip&longs;o con&longs;criptorum librorum, &longs;eu prælo <expan abbr="commi&longs;&longs;or&utilde;">commi&longs;&longs;orum</expan>, <lb/>&longs;eu in Adver&longs;aria coniectorum, copiam habeo, quo<lb/>tidianâ eiusdem vtor con&longs;uetudine, vtpote inre litte<lb/>rariâ &longs;ocius; cuius proinde &longs;ententiam aut minùs <lb/>intellectam, aut breviùs &longs;ubinde explicatam, exquire<lb/>re nullo negotio po&longs;&longs;um. Opus erit ingens, multi&queacute; la<lb/>boris ac &longs;tudij, nec minùs reconditâ rerum cùm natu<lb/>ralium, tùm arte factarum refertum &longs;cientiâ. Habe<lb/>bis in eo varia, curio&longs;a, exotica admir andorum effe<lb/>ctuum &longs;pectacula, reconditarúmque inventionum mi<lb/>racula, & quæ meritò cen&longs;ebuntur magica; ab omni <lb/>tamen imposturâ, & illicitæ artis &longs;u&longs;picione aliena. <lb/>Habebis Magiam Arithmeticam; at non vulgarem: <lb/>Habebis Geometricam; at paucis perviam: Habebis <lb/>Astronomicam; at penitùs abstru&longs;am Invenies Ma<lb/>giam Magneticam, Gnomonicam, Staticam, Opti<lb/>cam, Dioptricam, Catoptricam, Hydraulicam, Pnev-<emph.end type="italics"/>

<pb xlink:href="051/01/033.jpg" pagenum="2"/><emph type="italics"/>in Catalogo Librorum posthàc à prædicto Docti&longs;&longs;imo <lb/>Auctore edendorum Magneticæ Arti denuò hîc Ro<lb/>mæ nuper editæ appo&longs;ito feci mentionem. </s><s>Spartam <lb/>hanc ab ip&longs;o Auctore mihi commi&longs;&longs;am præ alijs a&longs;&longs;um<lb/>p&longs;i excolendam, quoniam præterquàm quòd omnium <lb/>ab ip&longs;o con&longs;criptorum librorum, &longs;eu prælo <expan abbr="commi&longs;&longs;or&utilde;">commi&longs;&longs;orum</expan>, <lb/>&longs;eu in Adver&longs;aria coniectorum, copiam habeo, quo<lb/>tidianâ eiusdem vtor con&longs;uetudine, vtpote inre litte<lb/>rariâ &longs;ocius; cuius proinde &longs;ententiam aut minùs <lb/>intellectam, aut breviùs &longs;ubinde explicatam, exquire<lb/>re nullo negotio po&longs;&longs;um. </s><s>Opus erit ingens, multi&queacute; la<lb/>boris ac &longs;tudij, nec minùs reconditâ rerum cùm natu<lb/>ralium, tùm arte factarum refertum &longs;cientiâ. </s><s>Habe<lb/>bis in eo varia, curio&longs;a, exotica admir andorum effe<lb/>ctuum &longs;pectacula, reconditarúmque inventionum mi<lb/>racula, & quæ meritò cen&longs;ebuntur magica; ab omni <lb/>tamen imposturâ, & illicitæ artis &longs;u&longs;picione aliena. </s><s><lb/>Habebis Magiam Arithmeticam; at non vulgarem: <lb/>Habebis Geometricam; at paucis perviam: Habebis <lb/>Astronomicam; at penitùs abstru&longs;am Invenies Ma<lb/>giam Magneticam, Gnomonicam, Staticam, Opti<lb/>cam, Dioptricam, Catoptricam, Hydraulicam, Pnev-<emph.end type="italics"/>

<pb xlink:href="051/01/034.jpg" pagenum="3"/><emph type="italics"/>maticam, Pyrobolicam, <expan abbr="Harmonicã">Harmonicam</expan>, <expan abbr="Phonocampticã">Phonocampticam</expan> <lb/><expan abbr="Anacãpticã">Anacampticam</expan>, Anaclasticam, <expan abbr="Phy&longs;iognomicã">Phy&longs;iognomicam</expan>, Mecha<lb/>nicam, Sympathicam, Steganologicam, Cryptographi<lb/>cam, Divinatoriam, Cabalicam, Hieroglyphicam, <lb/>Sacram. Miraberis in eodem Opere &longs;ecreta Ani<lb/>malium, Herbarum, Plantarum, Lapidum, aliarúm<lb/>que rerum per variam activorum cum pa&longs;&longs;ivis appli<lb/>cationem, virtutum occultarum combinationem, Na<lb/>turæ & Artis connubium, Paranymphâ Experientiâ. <lb/>Jdeam aliquam in fine huius Operis invenies.<emph.end type="italics"/></s>

<pb xlink:href="051/01/034.jpg" pagenum="3"/><emph type="italics"/>maticam, Pyrobolicam, <expan abbr="Harmonicã">Harmonicam</expan>, <expan abbr="Phonocampticã">Phonocampticam</expan> <lb/><expan abbr="Anacãpticã">Anacampticam</expan>, Anaclasticam, <expan abbr="Phy&longs;iognomicã">Phy&longs;iognomicam</expan>, Mecha<lb/>nicam, Sympathicam, Steganologicam, Cryptographi<lb/>cam, Divinatoriam, Cabalicam, Hieroglyphicam, <lb/>Sacram. </s><s>Miraberis in eodem Opere &longs;ecreta Ani<lb/>malium, Herbarum, Plantarum, Lapidum, aliarúm<lb/>que rerum per variam activorum cum pa&longs;&longs;ivis appli<lb/>cationem, virtutum occultarum combinationem, Na<lb/>turæ & Artis connubium, Paranymphâ Experientiâ. </s><s><lb/>Jdeam aliquam in fine huius Operis invenies.<emph.end type="italics"/></s>

<s><margin.target id="marg1"/>Magia Na<lb/>turalis Au<lb/>ctoris.</s>

<s><emph type="italics"/>Quoniam verò Opus, vt dixi, vastum erit, mul<lb/>ti&queacute; laboris ac &longs;tudij, nec ni&longs;i &longs;ubci&longs;ivis horis, quas <lb/>ordinariis occupationibus &longs;ubtr ahere licebit, perfici<lb/>endum; operæ pretium me facturum, gratúmque Rei<lb/>publicæ Litterariæ existimavi, &longs;iquæ paulatim elabo<lb/>ra&longs;&longs;em, per partes protruderem. Ab Hydraulicis igi<lb/>tur atque Pnevmaticis initium &longs;umere decrevi, id&queacute; <lb/>non tàm meâ, quàm aliorum voluntate. Scribendi <lb/>occa&longs;io hæc fuit. Est in &longs;upradicti Docti&longs;&longs;imi Auctoris<emph.end type="italics"/><lb/>

<s><emph type="italics"/>Quoniam verò Opus, vt dixi, vastum erit, mul<lb/>ti&queacute; laboris ac &longs;tudij, nec ni&longs;i &longs;ubci&longs;ivis horis, quas <lb/>ordinariis occupationibus &longs;ubtr ahere licebit, perfici<lb/>endum; operæ pretium me facturum, gratúmque Rei<lb/>publicæ Litterariæ existimavi, &longs;iquæ paulatim elabo<lb/>ra&longs;&longs;em, per partes protruderem. </s><s>Ab Hydraulicis igi<lb/>tur atque Pnevmaticis initium &longs;umere decrevi, id&queacute; <lb/>non tàm meâ, quàm aliorum voluntate. </s><s>Scribendi <lb/>occa&longs;io hæc fuit. </s><s>Est in &longs;upradicti Docti&longs;&longs;imi Auctoris<emph.end type="italics"/><lb/>

<arrow.to.target n="marg2"/><lb/><emph type="italics"/>Mu&longs;eo &longs;anè celeberrimo, frequentati&longs;&longs;imóque (quod <lb/>brevi typis evulgabimus) non exigua <expan abbr="Hydraulicar&utilde;">Hydraulicarum</expan> <lb/>ac Pnevmaticarum Machinarum copia, quas &longs;um-<emph.end type="italics"/>

<pb xlink:href="051/01/035.jpg" pagenum="4"/><emph type="italics"/>mâ animi voluptate &longs;pectant atque mirantur ij, qui <lb/>ex omnibus Vrbis & Orbis partibus ad ip&longs;um vi&longs;en<lb/>dum accurrunt Viri Principes ac Litter ati, avidé<lb/>que &longs;cire de&longs;iderant, & Machinarum constructa<lb/>rum rationes, & machinalium motionum cau&longs;as. Ho<lb/>rum de&longs;iderìo vt &longs;atisfacerem, omnium dicti Mu&longs;ej <lb/>Machinarum fabricam & qua&longs;i anatomiam edoce<lb/>re, aut alicubi jam ab ip&longs;o Auctore edoctam enarrare, <lb/>brevi opu&longs;culo aggre&longs;&longs;us &longs;um. Quod dum faciebam, <lb/>tam multa <expan abbr="ejusd&etilde;">ejusdem</expan> argumenti animo <expan abbr="calamóq;">calamóque</expan> occur<lb/>rebant, quæ alibi videram, legeram, excogitaveram <lb/>ip&longs;e, nec vulgaria, nec injucunda, vt difficiliùs mihi <lb/>fuerit &longs;istere, quàm pro&longs;equi inceptum cur&longs;um; nec mi<lb/>nor in non &longs;eribendo, quàm in &longs;cribendo labor &longs;ubeun<lb/>dus: multóque plurafuerunt omittenda, quàm char<lb/>tæ committenda, vt &longs;umptibus & tempori parceretur.<emph.end type="italics"/></s>

<pb xlink:href="051/01/035.jpg" pagenum="4"/><emph type="italics"/>mâ animi voluptate &longs;pectant atque mirantur ij, qui <lb/>ex omnibus Vrbis & Orbis partibus ad ip&longs;um vi&longs;en<lb/>dum accurrunt Viri Principes ac Litter ati, avidé<lb/>que &longs;cire de&longs;iderant, & Machinarum constructa<lb/>rum rationes, & machinalium motionum cau&longs;as. </s><s>Ho<lb/>rum de&longs;iderìo vt &longs;atisfacerem, omnium dicti Mu&longs;ej <lb/>Machinarum fabricam & qua&longs;i anatomiam edoce<lb/>re, aut alicubi jam ab ip&longs;o Auctore edoctam enarrare, <lb/>brevi opu&longs;culo aggre&longs;&longs;us &longs;um. </s><s>Quod dum faciebam, <lb/>tam multa <expan abbr="ejusd&etilde;">ejusdem</expan> argumenti animo <expan abbr="calamóq;">calamóque</expan> occur<lb/>rebant, quæ alibi videram, legeram, excogitaveram <lb/>ip&longs;e, nec vulgaria, nec injucunda, vt difficiliùs mihi <lb/>fuerit &longs;istere, quàm pro&longs;equi inceptum cur&longs;um; nec mi<lb/>nor in non &longs;eribendo, quàm in &longs;cribendo labor &longs;ubeun<lb/>dus: multóque plurafuerunt omittenda, quàm char<lb/>tæ committenda, vt &longs;umptibus & tempori parceretur.<emph.end type="italics"/></s>

<s><margin.target id="marg2"/>Mu&longs;eum <lb/>Kircheria<lb/>num.</s>

Line 912

Line 913

<s><emph type="italics"/>Cùm verò vt in aliis &longs;cientiis & artibus, ita in Hydrauli<lb/>cis atque Pnevmaticis, vel maximè Praxis & Theoria<emph.end type="italics"/><lb/>

<arrow.to.target n="marg3"/><lb/><emph type="italics"/>conjunctionem ita ambiant, vt vna &longs;i alteram de&longs;tituat, meri<lb/>tò vtraque cadat; & nec &longs;ola Praxis &longs;uam &longs;ine Theoria obtine<lb/>at exi&longs;timationem, nec &longs;ine Praxi&longs;ola &longs;uam Theoria; <expan abbr="vtram&qacute;">vtramque</expan>; <lb/>coniungendam putavi; præ&longs;ertim cùm vix vllum id hactenus <lb/>factita&longs;&longs;e videam, <expan abbr="tu&qacute;ue">tuque</expan> mecum per&longs;picies, Lector, &longs;ievolves,<emph.end type="italics"/>

<pb xlink:href="051/01/036.jpg" pagenum="5"/><emph type="italics"/>quotquot de Aquaticis ac Spiritalibus quoquo modo <expan abbr="tractâr&utilde;t">tractârunt</expan> <lb/>Auctores, quorum Elenchum po&longs;tea dabimus. Plerique enim <lb/>nudam duntaxat tradunt Praxin, non per&longs;criptis, ac nè indi<lb/>catis quidem operandi principijs &longs;eu fundamentis, quæ veligno<lb/>rarunt ip&longs;i, vel alijs inviderunt: quò fit, vt alijs &longs;æpe errandi <lb/>præbeant occa&longs;ionem, & ip&longs;i <expan abbr="nõ">non</expan> rarò pudendos committant erro<lb/>res, vel tunc etiam, cùm aliorum errores detegere <expan abbr="at&qacute;ue">atque</expan> corri<lb/>gere præ&longs;umptuo&longs;iùs attentant. In duas igitur partes Opus to<lb/>tum dividimus. In prima theoriam damus ad omnis generis <lb/>Machinas Hydraulicas, Pnevmaticas, & Mixtas ex Vtris<lb/>que con&longs;truendas facilitate &longs;ummâ, &longs;ucce&longs;&longs;u infallibili. In &longs;e<lb/>cunda fabricam docemus, & praxim exhibemus innumera<lb/>rum Machinarum, &longs;eu purè Hydraulicarum, &longs;eu purè <lb/>Pnevmaticarum, &longs;eu Hydro-pnevmaticarum, hoc e&longs;t, ex v<lb/>tris que Mixtarum, ex traditis principijs con&longs;tructarum, con<lb/>&longs;truendarumvè, ad hortorum delicias, <expan abbr="domorum&qacute;ue">domorumque</expan> vtilita<lb/>tes, commoditates, ornamenta, virorum præ&longs;ertim Principum, <lb/>qui magis oculorum inde, <expan abbr="animi&qacute;ue">animique</expan> oblectamentum, quàm rei <lb/>familiaris quæ&longs;tum ex&longs;pectant. Nec oculos tantum modò pa<lb/>&longs;<gap/>ere &longs;atagimus; auribus etiam &longs;ua paramus delinimenta, <expan abbr="va-ria&qacute;ue">va<lb/>riaque</expan> Organa atque Jn&longs;trumenta automata, & autophona, <lb/>&longs;olo aquarum lap&longs;u, aëris <expan abbr="&qacute;ue">que</expan> allap&longs;u, in motum ac &longs;onum con<lb/>citamus, non minori facilitate, quàm arte. Et quoniam in-<emph.end type="italics"/><lb/>

<pb xlink:href="051/01/036.jpg" pagenum="5"/><emph type="italics"/>quotquot de Aquaticis ac Spiritalibus quoquo modo <expan abbr="tractâr&utilde;t">tractârunt</expan> <lb/>Auctores, quorum Elenchum po&longs;tea dabimus. </s><s>Plerique enim <lb/>nudam duntaxat tradunt Praxin, non per&longs;criptis, ac nè indi<lb/>catis quidem operandi principijs &longs;eu fundamentis, quæ veligno<lb/>rarunt ip&longs;i, vel alijs inviderunt: quò fit, vt alijs &longs;æpe errandi <lb/>præbeant occa&longs;ionem, & ip&longs;i <expan abbr="nõ">non</expan> rarò pudendos committant erro<lb/>res, vel tunc etiam, cùm aliorum errores detegere <expan abbr="at&qacute;ue">atque</expan> corri<lb/>gere præ&longs;umptuo&longs;iùs attentant. </s><s>In duas igitur partes Opus to<lb/>tum dividimus. </s><s>In prima theoriam damus ad omnis generis <lb/>Machinas Hydraulicas, Pnevmaticas, & Mixtas ex Vtris<lb/>que con&longs;truendas facilitate &longs;ummâ, &longs;ucce&longs;&longs;u infallibili. </s><s>In &longs;e<lb/>cunda fabricam docemus, & praxim exhibemus innumera<lb/>rum Machinarum, &longs;eu purè Hydraulicarum, &longs;eu purè <lb/>Pnevmaticarum, &longs;eu Hydro-pnevmaticarum, hoc e&longs;t, ex v<lb/>tris que Mixtarum, ex traditis principijs con&longs;tructarum, con<lb/>&longs;truendarumvè, ad hortorum delicias, <expan abbr="domorum&qacute;ue">domorumque</expan> vtilita<lb/>tes, commoditates, ornamenta, virorum præ&longs;ertim Principum, <lb/>qui magis oculorum inde, <expan abbr="animi&qacute;ue">animique</expan> oblectamentum, quàm rei <lb/>familiaris quæ&longs;tum ex&longs;pectant. </s><s>Nec oculos tantum modò pa<lb/>&longs;<gap/>ere &longs;atagimus; auribus etiam &longs;ua paramus delinimenta, <expan abbr="va-ria&qacute;ue">va<lb/>riaque</expan> Organa atque Jn&longs;trumenta automata, & autophona, <lb/>&longs;olo aquarum lap&longs;u, aëris <expan abbr="&qacute;ue">que</expan> allap&longs;u, in motum ac &longs;onum con<lb/>citamus, non minori facilitate, quàm arte. </s><s>Et quoniam in-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg4"/><lb/><emph type="italics"/>credibilis e&longs;t hodie, &longs;i unquam aliàs, ne&longs;cio an manuum, an ve<lb/>rò ingeniorum pruritus, motum, quem vocant perpetuum (quem <lb/>tot modis ac vijs <expan abbr="nõ">non</expan> pauci hactenus quæ&longs;iverunt, &longs;ed fru&longs;trà, per<lb/>ennis quietis potiùs quàm motionis Architecti) reap&longs;e exhibendi,<emph.end type="italics"/>

<pb xlink:href="051/01/037.jpg" pagenum="6"/><emph type="italics"/>& Mundo iam dudum eius exæ&longs;tuanti de&longs;iderio obtrudendi; <lb/><expan abbr="multi&qacute;ue">multique</expan> putant, non alijs &longs;aciliùs Machinis quàm hydrauli<lb/>cis in opus deduci id po&longs;&longs;e; in vnum collegi <expan abbr="refutavi&qacute;ue">refutavique</expan>, quot<lb/>quot videre, audire, legere potui aliorum artificia, qui eâ in re <lb/>&longs;e aliquid præ&longs;titi&longs;&longs;e putarunt, aut præ&longs;tari po&longs;&longs;e &longs;ibi per&longs;ua&longs;e<lb/>runt; vt visâ alieni conatus vanitate, curio&longs;us Lector judi<lb/>cium ferre de alijs queat, & à &longs;imili vano labore &longs;ibi temperet. <lb/>Tres igitur Cla&longs;&longs;es habebit Pars &longs;ecunda Operis.<emph.end type="italics"/></s>

<pb xlink:href="051/01/037.jpg" pagenum="6"/><emph type="italics"/>& Mundo iam dudum eius exæ&longs;tuanti de&longs;iderio obtrudendi; <lb/><expan abbr="multi&qacute;ue">multique</expan> putant, non alijs &longs;aciliùs Machinis quàm hydrauli<lb/>cis in opus deduci id po&longs;&longs;e; in vnum collegi <expan abbr="refutavi&qacute;ue">refutavique</expan>, quot<lb/>quot videre, audire, legere potui aliorum artificia, qui eâ in re <lb/>&longs;e aliquid præ&longs;titi&longs;&longs;e putarunt, aut præ&longs;tari po&longs;&longs;e &longs;ibi per&longs;ua&longs;e<lb/>runt; vt visâ alieni conatus vanitate, curio&longs;us Lector judi<lb/>cium ferre de alijs queat, & à &longs;imili vano labore &longs;ibi temperet. </s><s><lb/>Tres igitur Cla&longs;&longs;es habebit Pars &longs;ecunda Operis.<emph.end type="italics"/></s>

<s><margin.target id="marg3"/>Divi&longs;io O<lb/>peris præ<lb/>&longs;entis bi<lb/>partita.</s>

Line 928

Line 929

<s><emph type="italics"/>MEchanicam porrò Hydraulico-pnevmaticam vocamus <lb/>hoc Opus; & Machinas Hydro pnevmaticas, &longs;eu Hydrau<lb/>lico-pnevmaticas, quas in eodem producimus, appellamus, <lb/>quòd pleræque tales &longs;int, taliumque tradantur in prima Operis <lb/>parte principia ac regulæ; Hydraulico-pnevmaticas, inquam, <lb/>qua&longs;i dicas, Aquatico-Spiritales, hoc e&longs;t, aqua & &longs;piritu &longs;eu aëre<emph.end type="italics"/></s>

<s>

<arrow.to.target n="marg6"/><lb/><emph type="italics"/>animatas. Aquaticæ etenim Machinæ, hauriendis è profun<lb/>do, deducendis per planitiem, educendis in altum per fi&longs;tulas ac <lb/>tubos<emph.end type="italics"/> (<foreign lang="greek">a)ul<gap/>\s</foreign> <emph type="italics"/>Græci appellant) aquis excogitatæ, triplicis &longs;unt<emph.end type="italics"/><lb/>

<arrow.to.target n="marg6"/><lb/><emph type="italics"/>animatas. </s><s>Aquaticæ etenim Machinæ, hauriendis è profun<lb/>do, deducendis per planitiem, educendis in altum per fi&longs;tulas ac <lb/>tubos<emph.end type="italics"/> (<foreign lang="greek">a)ul<gap/>\s</foreign> <emph type="italics"/>Græci appellant) aquis excogitatæ, triplicis &longs;unt<emph.end type="italics"/><lb/>

<arrow.to.target n="marg7"/><lb/><emph type="italics"/>generis. Aliæ iumentorum, hominum, ponderum ope, rotis <lb/>variè inter &longs;e&longs;e implicatis, moventur; cuiusmodi &longs;unt tympa<lb/>na, antliæ, cochleæ, tollenones, &longs;imiliaque, quæ Vitruvius pro<lb/>ducit libro<emph.end type="italics"/> 10. <emph type="italics"/>Capite<emph.end type="italics"/> 9, 10, 11, 13, <emph type="italics"/>&<emph.end type="italics"/> 14. <emph type="italics"/>alijque <lb/>Auctores multi<emph.end type="italics"/>

<arrow.to.target n="marg7"/><lb/><emph type="italics"/>generis. </s><s>Aliæ iumentorum, hominum, ponderum ope, rotis <lb/>variè inter &longs;e&longs;e implicatis, moventur; cuiusmodi &longs;unt tympa<lb/>na, antliæ, cochleæ, tollenones, &longs;imiliaque, quæ Vitruvius pro<lb/>ducit libro<emph.end type="italics"/> 10. <emph type="italics"/>Capite<emph.end type="italics"/> 9, 10, 11, 13, <emph type="italics"/>&<emph.end type="italics"/> 14. <emph type="italics"/>alijque <lb/>Auctores multi<emph.end type="italics"/>

<arrow.to.target n="marg8"/><lb/><emph type="italics"/>ad nau&longs;eam vsque confarcinatis libris inculcant. Aliæ &longs;olo aqua<lb/>rum lap&longs;u fontes exhibent am&oelig;ni&longs;&longs;imos, & aquas per &longs;iphones <lb/>tubosque variè configuratos protru&longs;as nunc expandunt in &longs;ub<lb/>tili&longs;&longs;imum lucidi&longs;&longs;imum que velum, nunc diffundunt in radios,<emph.end type="italics"/>

<arrow.to.target n="marg8"/><lb/><emph type="italics"/>ad nau&longs;eam vsque confarcinatis libris inculcant. </s><s>Aliæ &longs;olo aqua<lb/>rum lap&longs;u fontes exhibent am&oelig;ni&longs;&longs;imos, & aquas per &longs;iphones <lb/>tubosque variè configuratos protru&longs;as nunc expandunt in &longs;ub<lb/>tili&longs;&longs;imum lucidi&longs;&longs;imum que velum, nunc diffundunt in radios,<emph.end type="italics"/>

<pb xlink:href="051/01/038.jpg" pagenum="7"/><emph type="italics"/>figurant in &longs;tellas, effingunt in flores, extendunt in iacula, cri<lb/>&longs;pant in pluvias, conglobant in grandines, &longs;ummâ oculorum <lb/>voluptate, vt pa&longs;&longs;im in vrbanis ac &longs;uburbanis Romæ vide<lb/>mus hortis.<emph.end type="italics"/></s>

<s><margin.target id="marg6"/>Aquaticæ <lb/>Machinæ <lb/>triphcis <expan abbr="&longs;&utilde;t">&longs;unt</expan> <lb/>generis.</s>

Line 940

Line 941

<s><margin.target id="marg8"/>Hydrauli<lb/>cæ.</s>

<s><emph type="italics"/>Aliæ denique inclu&longs;i intru&longs;ive äeris violentiâ eiaculan-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg9"/><lb/><emph type="italics"/>tur in altum aquas, inflant tibias, tubasque, volucrum ani<lb/>maliumque aliorum imitantur motum ac Cantum, aliaque præ<lb/>&longs;tant tam mira atque exotica, vix vt ab humano ingenio præ<lb/>&longs;tari po&longs;&longs;e videantur. Eius generis fuit apud Cornelium Seve<lb/>rum in Ætna Triton, qui aquarum a&longs;&longs;ultu auram concipiebat, <lb/>ac per buccinam ori admotam vocem edebat, &longs;ive vt ait Poëta, <lb/>irriguum Carmen. Tales etiam &longs;unt, quas magno numero, nec <lb/>minori ingenio prodit Hero in &longs;uo de Spiritalibus libello Machi<lb/>nas, ab antiquis (quos Ægyptios interpretatur Kircherus in <lb/>Mechanica Ægyptiaca tom.<emph.end type="italics"/> 2. <emph type="italics"/>Oedipi parte<emph.end type="italics"/> 2.) <emph type="italics"/>excogitatas: <lb/>cuiusmodi &longs;unt &longs;tatuæ ad aras vinum & lac &longs;acrificantes, va<lb/>&longs;a melancoryphi vocem edentia, Syringæ mentientes vocem a<lb/>vicularum multarum per ordinem di&longs;po&longs;itarum, quibus a&longs;&longs;idet <lb/>noctua, quæ &longs;ua &longs;ponte ad aviculas conver&longs;a eas terret, & à <lb/>cantu ab&longs;terret; <expan abbr="aliæ&qacute;ue">aliæque</expan> multæ. Tales denique, quas toto hoc <lb/>Opere magno numero producimus.<emph.end type="italics"/></s>

<arrow.to.target n="marg9"/><lb/><emph type="italics"/>tur in altum aquas, inflant tibias, tubasque, volucrum ani<lb/>maliumque aliorum imitantur motum ac Cantum, aliaque præ<lb/>&longs;tant tam mira atque exotica, vix vt ab humano ingenio præ<lb/>&longs;tari po&longs;&longs;e videantur. </s><s>Eius generis fuit apud Cornelium Seve<lb/>rum in Ætna Triton, qui aquarum a&longs;&longs;ultu auram concipiebat, <lb/>ac per buccinam ori admotam vocem edebat, &longs;ive vt ait Poëta, <lb/>irriguum Carmen. </s><s>Tales etiam &longs;unt, quas magno numero, nec <lb/>minori ingenio prodit Hero in &longs;uo de Spiritalibus libello Machi<lb/>nas, ab antiquis (quos Ægyptios interpretatur Kircherus in <lb/>Mechanica Ægyptiaca tom.<emph.end type="italics"/> 2. <emph type="italics"/>Oedipi parte<emph.end type="italics"/> 2.) <emph type="italics"/>excogitatas: <lb/>cuiusmodi &longs;unt &longs;tatuæ ad aras vinum & lac &longs;acrificantes, va<lb/>&longs;a melancoryphi vocem edentia, Syringæ mentientes vocem a<lb/>vicularum multarum per ordinem di&longs;po&longs;itarum, quibus a&longs;&longs;idet <lb/>noctua, quæ &longs;ua &longs;ponte ad aviculas conver&longs;a eas terret, & à <lb/>cantu ab&longs;terret; <expan abbr="aliæ&qacute;ue">aliæque</expan> multæ. </s><s>Tales denique, quas toto hoc <lb/>Opere magno numero producimus.<emph.end type="italics"/></s>

<s><margin.target id="marg9"/>Hydrauli<lb/>co-pnev<lb/>maticæ.</s>

<s><emph type="italics"/>Primi generis Machinas appellamus nos cum alijs Tracto<lb/>rias: & de illis non agimus hoc Opere; pertinent enim ad illam <lb/>Mechanicæ partem, quæ <expan abbr="viponder&utilde;">viponderum</expan> atque rotarum &longs;uas perfi<lb/>cit operationes, & &longs;ine ip&longs;ius principijs nec tradi, nec ab alijs <lb/>percipi po&longs;&longs;unt: quare Magiæ no&longs;træ Mechanicæ eas re&longs;erva<lb/>mus. Secundi generis Machinas appellamus Hydraulicas.<emph.end type="italics"/>

<s><emph type="italics"/>Primi generis Machinas appellamus nos cum alijs Tracto<lb/>rias: & de illis non agimus hoc Opere; pertinent enim ad illam <lb/>Mechanicæ partem, quæ <expan abbr="viponder&utilde;">viponderum</expan> atque rotarum &longs;uas perfi<lb/>cit operationes, & &longs;ine ip&longs;ius principijs nec tradi, nec ab alijs <lb/>percipi po&longs;&longs;unt: quare Magiæ no&longs;træ Mechanicæ eas re&longs;erva<lb/>mus. </s><s>Secundi generis Machinas appellamus Hydraulicas.<emph.end type="italics"/>

<pb xlink:href="051/01/039.jpg" pagenum="8"/><emph type="italics"/>Tertij denique generis Hydraulico-pnevmaticas. Quoniam <lb/>igitur pleræque Machinæ, quas producimus, huiu&longs;modi &longs;unt,<emph.end type="italics"/><lb/>

<pb xlink:href="051/01/039.jpg" pagenum="8"/><emph type="italics"/>Tertij denique generis Hydraulico-pnevmaticas. </s><s>Quoniam <lb/>igitur pleræque Machinæ, quas producimus, huiu&longs;modi &longs;unt,<emph.end type="italics"/><lb/>

<arrow.to.target n="marg10"/><lb/><emph type="italics"/>hoc e&longs;t, aquæ & aëris &longs;ub&longs;idio con&longs;tructæ; ideo Hydraulico<lb/>pnevmaticas, vt dicebam, appellamus hoc Opere traditas <lb/>Machinas. Dico, plerasque aquæ & aëris &longs;ub&longs;idio e&longs;&longs;e con<lb/>&longs;tructas; non omnes: &longs;unt enim & purè hydraulicæ multæ, & <lb/>purè pnevmaticæ non paucæ; imò nonnullæ, quæ licet aquæ au<lb/>xilio fiant, hydraulicæ tamen propriè ac rigorosè, juxta &longs;en&longs;um <lb/>expo&longs;itum, cen&longs;eri non po&longs;&longs;unt, vt videbis in Operis decur&longs;u, <lb/>& ex Machinarum indice apparebit.<emph.end type="italics"/></s>

<arrow.to.target n="marg10"/><lb/><emph type="italics"/>hoc e&longs;t, aquæ & aëris &longs;ub&longs;idio con&longs;tructæ; ideo Hydraulico<lb/>pnevmaticas, vt dicebam, appellamus hoc Opere traditas <lb/>Machinas. </s><s>Dico, plerasque aquæ & aëris &longs;ub&longs;idio e&longs;&longs;e con<lb/>&longs;tructas; non omnes: &longs;unt enim & purè hydraulicæ multæ, & <lb/>purè pnevmaticæ non paucæ; imò nonnullæ, quæ licet aquæ au<lb/>xilio fiant, hydraulicæ tamen propriè ac rigorosè, juxta &longs;en&longs;um <lb/>expo&longs;itum, cen&longs;eri non po&longs;&longs;unt, vt videbis in Operis decur&longs;u, <lb/>& ex Machinarum indice apparebit.<emph.end type="italics"/></s>

<s><margin.target id="marg10"/>Machinæ <lb/>huius Ope <lb/>ris <expan abbr="pleræq;">pleræque</expan> <lb/><expan abbr="&longs;&utilde;t">&longs;unt</expan> hydrau<lb/>lico-pnev<lb/>maticæ.</s>

Line 955

Line 956

<s><emph type="italics"/>SCriptores quod attinet, qui de Hydraulicis, <expan abbr="Pnevmaticis-&qacute;ue">Pnevmaticis<lb/>que</expan> quoquo modo &longs;crip&longs;erunt, & ad manus meas pervene<lb/>runt, &longs;unt &longs;equentes, Alphabeti ordine.<emph.end type="italics"/> Archimedes, Atha<lb/>na&longs;ius Kircherus, Augu&longs;tinus Ramellus, Benedictus Ca<lb/>&longs;tellus, Daniel Lip&longs;torpius, Daniel Schvventerus, Evan<lb/>geli&longs;ta Torricellus, Galilæus Galilæi, Ga&longs;par Ens, Ge<lb/>orgius Agricola, Georgius Philippus Har&longs;torfferus, Ge<lb/>orgius Valla, Hero Alexandrinus, Hieronymus Carda<lb/>nus, Iacobus Be&longs;&longs;on, Ioannes Bapti&longs;ta Porta, Ioannes Ba<lb/>pti&longs;ta Balianus, Ioannes Bapti&longs;ta Aleottus, Ioannes Iaco<lb/>bus Weckerus, Ioannes Leurechon, Io&longs;ephus Ceredus, <lb/>Ioannes Branca, Marinus Ghetaldus, Marinus Mer&longs;en<lb/>nus, Marius Bettinus, Nicolaus Cabæus, Petrus Herigo<lb/>nius, Raphaël Magiottus, Robertus Valturius, Rober-

<pb xlink:href="051/01/040.jpg" pagenum="9"/>tus à Fluctibus, Salomon Caus, Simon Stevinus, Theo<lb/>dorus Muretus, Va&longs;&longs;or Arabs, Vitruvius, <expan abbr="eius&qacute;ue">eiusque</expan> Com<lb/>mentatores, vt Philander, Barbarus, Cæ&longs;arinus, <expan abbr="alij&qacute;ue">alijque</expan>. <lb/><emph type="italics"/>Hæc Auctorum nomina.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ex his Archimedes duos per&longs;crip&longs;it libros<emph.end type="italics"/> <foreign lang="greek">peri\ <gap/>w_n o)x<gap/>me/nwn</foreign>, <lb/>

<s><emph type="italics"/>Ex his Archimedes duos per&longs;crip&longs;it libros<emph.end type="italics"/> <foreign lang="greek">peri\ tw=n o)xoume/nwn</foreign>, <lb/>

<arrow.to.target n="marg11"/><lb/><emph type="italics"/>hoc e&longs;t, de In&longs;identibus in humido, ex quibus pauca no&longs;tro in<lb/>&longs;erviunt propo&longs;ito. Athana&longs;ius Kircherus Societ. Je&longs;u multa<emph.end type="italics"/><lb/>

<arrow.to.target n="marg12"/><lb/><emph type="italics"/>pa&longs;&longs;im hydraulica atque pnevmatica machinamenta in&longs;erit &longs;uis <lb/>docti&longs;&longs;imis libris, præ&longs;ertim de Arte Magnetica, de Lumine & <lb/>Vmbra, de Con&longs;ono & Di&longs;&longs;ono, ac novi&longs;&longs;imè &longs;uo incompara<lb/>bili de Ægyptiorum hieroglyphicis Operi quem Oedipum Ægy<lb/>ptiacuin in&longs;crip&longs;it: multa quoque inter eius Manu&longs;cripta re<lb/>peri, <expan abbr="multa&qacute;ue">multaque</expan> oretenus ab eodem percepi. Augu&longs;tinus Ra-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg12"/><lb/><emph type="italics"/>pa&longs;&longs;im hydraulica atque pnevmatica machinamenta in&longs;erit &longs;uis <lb/>docti&longs;&longs;imis libris, præ&longs;ertim de Arte Magnetica, de Lumine & <lb/>Vmbra, de Con&longs;ono & Di&longs;&longs;ono, ac novi&longs;&longs;imè &longs;uo incompara<lb/>bili de Ægyptiorum hieroglyphicis Operi quem Oedipum Ægy<lb/>ptiacuin in&longs;crip&longs;it: multa quoque inter eius Manu&longs;cripta re<lb/>peri, <expan abbr="multa&qacute;ue">multaque</expan> oretenus ab eodem percepi. </s><s>Augu&longs;tinus Ra-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg13"/><lb/><emph type="italics"/>mellus ingens &longs;crip&longs;it Opus de Machinis Italico & Gallico idio<lb/>mate, <expan abbr="inter&qacute;ue">interque</expan> illas ingentem habet copiam Antliarum diver&longs;is <lb/>modis con&longs;tructarum, <expan abbr="alias&qacute;ue">aliasque</expan> nonnullas praxes ad elevandas <lb/>aquas, &longs;ed omnes tractoriæ &longs;unt Machinæ ad primum pertinen<lb/>tes genus. Benedictus Castellus, olim Mathematicus Pon-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg13"/><lb/><emph type="italics"/>mellus ingens &longs;crip&longs;it Opus de Machinis Italico & Gallico idio<lb/>mate, <expan abbr="inter&qacute;ue">interque</expan> illas ingentem habet copiam Antliarum diver&longs;is <lb/>modis con&longs;tructarum, <expan abbr="alias&qacute;ue">aliasque</expan> nonnullas praxes ad elevandas <lb/>aquas, &longs;ed omnes tractoriæ &longs;unt Machinæ ad primum pertinen<lb/>tes genus. </s><s>Benedictus Castellus, olim Mathematicus Pon-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg14"/><lb/><emph type="italics"/>tificius, libellum compo&longs;uit Italico idiomate de aqua cur<lb/>rente, &longs;ed per alveos, aquæductus, & tubos inclinatos; quæ <lb/>proinde ad nos non pertinent. Daniel Lip&longs;torpius Lubecen&longs;is<emph.end type="italics"/><lb/>

<arrow.to.target n="marg14"/><lb/><emph type="italics"/>tificius, libellum compo&longs;uit Italico idiomate de aqua cur<lb/>rente, &longs;ed per alveos, aquæductus, & tubos inclinatos; quæ <lb/>proinde ad nos non pertinent. </s><s>Daniel Lip&longs;torpius Lubecen&longs;is<emph.end type="italics"/><lb/>

<arrow.to.target n="marg15"/><lb/><emph type="italics"/>edidit Specimina Philo&longs;ophiæ Carte&longs;ianæ, in cuius parte<emph.end type="italics"/> 3. <emph type="italics"/>c.<emph.end type="italics"/> 3. <lb/><emph type="italics"/>multas adducit Machinas hydraulico-pnevmaticas, easque <lb/>explicat ex Carte&longs;ij principijs. Daniel Schvventerus, & Ge-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg15"/><lb/><emph type="italics"/>edidit Specimina Philo&longs;ophiæ Carte&longs;ianæ, in cuius parte<emph.end type="italics"/> 3. <emph type="italics"/>c.<emph.end type="italics"/> 3. <lb/><emph type="italics"/>multas adducit Machinas hydraulico-pnevmaticas, easque <lb/>explicat ex Carte&longs;ij principijs. </s><s>Daniel Schvventerus, & Ge-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg16"/><lb/><emph type="italics"/>orgius Philippus Harstorfferus Norimbergen&longs;is Patritius, in<emph.end type="italics"/><lb/>

<arrow.to.target n="marg17"/><lb/><emph type="italics"/>Delicijs Mathematicis multas afferunt, <expan abbr="eas&qacute;ue">easque</expan> iucundi&longs;&longs;imas <lb/>Machinas hydraulicas, & pnevmaticas. Multas etiam in<emph.end type="italics"/>

<arrow.to.target n="marg18"/><lb/><emph type="italics"/>Thaumaturgo &longs;uo Mathematico adducit ex alijs Ga&longs;par Ens;<emph.end type="italics"/><lb/>

<arrow.to.target n="marg19"/><lb/><emph type="italics"/>vt & Weckerus in &longs;uis Secretis nonnullas ex Cardano de&longs;um-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg20"/><lb/><emph type="italics"/>ptas, quas dictus Cardanus in&longs;erit &longs;uis de &longs;ubtilitate libris. E-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg21"/><lb/><emph type="italics"/>vangelista Torricellus, Magni Hetruriæ Ducis Mathemati<lb/>cus, & Benedicti Ca&longs;telli di&longs;cipulus, &longs;crip&longs;it libros<emph.end type="italics"/> 3. <emph type="italics"/>de Motu <lb/>proiectorum; quorum &longs;ecundo inter&longs;erit nonnulla de motu a<lb/>quarum per tubos, &longs;ed quàm &longs;ubtilia, tàm parum ad praxin v-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg22"/><lb/><emph type="italics"/>tilia, vt ip&longs;emet fatetur. Galilæus Galilæi edidit Archimedem <lb/><expan abbr="rediviv&utilde;">redivivum</expan>, quem ex latino <expan abbr="Italic&utilde;">Italicum</expan> fecit <expan abbr="Ioañes">Ioannes</expan> Baptista Hodierna <lb/>Siculus, Vir rerum Astronomicarum apprimè gnarus, & &longs;ide<lb/>rum, adeoque Naturæ totius &longs;crutator indefe&longs;&longs;us, <expan abbr="amicus&qacute;ue">amicusque</expan> <lb/>&longs;inceri&longs;&longs;imus. Opu&longs;culum e&longs;t ad Hydrostaticam pertinens;<emph.end type="italics"/><lb/>

<arrow.to.target n="marg22"/><lb/><emph type="italics"/>tilia, vt ip&longs;emet fatetur. </s><s>Galilæus Galilæi edidit Archimedem <lb/><expan abbr="rediviv&utilde;">redivivum</expan>, quem ex latino <expan abbr="Italic&utilde;">Italicum</expan> fecit <expan abbr="Ioañes">Ioannes</expan> Baptista Hodierna <lb/>Siculus, Vir rerum Astronomicarum apprimè gnarus, & &longs;ide<lb/>rum, adeoque Naturæ totius &longs;crutator indefe&longs;&longs;us, <expan abbr="amicus&qacute;ue">amicusque</expan> <lb/>&longs;inceri&longs;&longs;imus. </s><s>Opu&longs;culum e&longs;t ad Hydrostaticam pertinens;<emph.end type="italics"/><lb/>

<arrow.to.target n="marg23"/><lb/><emph type="italics"/>quale etiam e&longs;t Archimedes promotus Marini Ghetaldi; vt &<emph.end type="italics"/><lb/>

<arrow.to.target n="marg24"/><lb/><emph type="italics"/>quæ habet Simon Stevinus; ideoque nobis nullam hîc &longs;uppetunt <lb/>materiam. Georgius Agricola libro<emph.end type="italics"/> 6. <emph type="italics"/>de rebus metallicis in-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg24"/><lb/><emph type="italics"/>quæ habet Simon Stevinus; ideoque nobis nullam hîc &longs;uppetunt <lb/>materiam. </s><s>Georgius Agricola libro<emph.end type="italics"/> 6. <emph type="italics"/>de rebus metallicis in-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg25"/><lb/><emph type="italics"/>&longs;erit nonnullas Machinas hydraulicas, nonnullas Robertus <lb/>Valturius &longs;uis de Militia libris, nonnullas Iacobus Be&longs;&longs;on Del-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg26"/><lb/><emph type="italics"/>phinas &longs;uo de In&longs;trumentis Mathematicis ac Mechanicis tracta<lb/>tui; &longs;ed omnes &longs;unt tractoriæ, & alienæ à no&longs;tro instituto. Ge-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg27"/><lb/><emph type="italics"/>orgius Valla Placentinus libro<emph.end type="italics"/> 15. <emph type="italics"/>Expetendorum & fugiendo<lb/>rum, qui e&longs;t &longs;extus Geometriæ, &longs;eu Spiritalium vnicus, multas <lb/>habet Machinas Spiritales, &longs;ed ad vnam omnes ex Herone Ale<lb/>xandrino decerptas, nè nominato quidem Herone. Habebat <lb/>vir bonus, vt Io&longs;ephus Ceredus te&longs;tatur, Heronis librum græ<lb/>cum de Spiritalibus, nondum tunc à Federico Commandino, <lb/>aliovè Latinitati donatum, <expan abbr="putabat&qacute;ue">putabatque</expan> &longs;ecurè atque impunè &longs;e <lb/>po&longs;&longs;e in alienam me&longs;&longs;em mittere falcem &longs;uam.<emph.end type="italics"/></s>

<arrow.to.target n="marg27"/><lb/><emph type="italics"/>orgius Valla Placentinus libro<emph.end type="italics"/> 15. <emph type="italics"/>Expetendorum & fugiendo<lb/>rum, qui e&longs;t &longs;extus Geometriæ, &longs;eu Spiritalium vnicus, multas <lb/>habet Machinas Spiritales, &longs;ed ad vnam omnes ex Herone Ale<lb/>xandrino decerptas, nè nominato quidem Herone. </s><s>Habebat <lb/>vir bonus, vt Io&longs;ephus Ceredus te&longs;tatur, Heronis librum græ<lb/>cum de Spiritalibus, nondum tunc à Federico Commandino, <lb/>aliovè Latinitati donatum, <expan abbr="putabat&qacute;ue">putabatque</expan> &longs;ecurè atque impunè &longs;e <lb/>po&longs;&longs;e in alienam me&longs;&longs;em mittere falcem &longs;uam.<emph.end type="italics"/></s>

<s><margin.target id="marg11"/>Archime<lb/>des.</s>

Line 1011

Line 1012

<s><margin.target id="marg27"/>Valla.</s>

<s><emph type="italics"/>Hero Alexandrinus Auctor antiquus, græcè edidit libel-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg28"/><lb/><emph type="italics"/>lum de Spiritalibus, in quo quæ ab antiquis (quos Ægyptios <lb/>interpretatur Kircherus, vt &longs;uprà dicebam) tradita in illo ge<lb/>nere fuêre, in ordinem redegit; & quæ ip&longs;emet invenit, expo<lb/>&longs;uit: quæ quidem omnia pulcherrima &longs;unt, & ingenio plena. <lb/>Idem Auctor ait &longs;e quatuor libros con&longs;crip&longs;i&longs;&longs;e de aquaticis horo<lb/>&longs;copijs; quos tamen temporum iniquitas nobis invidit. De-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg28"/><lb/><emph type="italics"/>lum de Spiritalibus, in quo quæ ab antiquis (quos Ægyptios <lb/>interpretatur Kircherus, vt &longs;uprà dicebam) tradita in illo ge<lb/>nere fuêre, in ordinem redegit; & quæ ip&longs;emet invenit, expo<lb/>&longs;uit: quæ quidem omnia pulcherrima &longs;unt, & ingenio plena. </s><s><lb/>Idem Auctor ait &longs;e quatuor libros con&longs;crip&longs;i&longs;&longs;e de aquaticis horo<lb/>&longs;copijs; quos tamen temporum iniquitas nobis invidit. </s><s>De-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg29"/><lb/><emph type="italics"/>&longs;cribit autem Hero nudam praxim, nec vllibi præcepta & regu<lb/>las tradit, ni&longs;i quòd in principio de vacuo agat; ideoque & <lb/>ip&longs;e &longs;ubinde errat, (&longs;i tamen ip&longs;ius, & non Interpretis &longs;unt er<lb/>rores) & alios in errorem inducit; nec omnia quæ promittit, <lb/>effectum &longs;ortiuntur. E&longs;t nihilominùs ip&longs;e de Republica litteraria <lb/>egregiè meritus, & vnicus qui ex antiquis de rebus hydraulicis<emph.end type="italics"/><lb/>

<arrow.to.target n="marg29"/><lb/><emph type="italics"/>&longs;cribit autem Hero nudam praxim, nec vllibi præcepta & regu<lb/>las tradit, ni&longs;i quòd in principio de vacuo agat; ideoque & <lb/>ip&longs;e &longs;ubinde errat, (&longs;i tamen ip&longs;ius, & non Interpretis &longs;unt er<lb/>rores) & alios in errorem inducit; nec omnia quæ promittit, <lb/>effectum &longs;ortiuntur. </s><s>E&longs;t nihilominùs ip&longs;e de Republica litteraria <lb/>egregiè meritus, & vnicus qui ex antiquis de rebus hydraulicis<emph.end type="italics"/><lb/>

<arrow.to.target n="marg30"/><lb/><emph type="italics"/>& pnevmaticis &longs;ua ad nos monumenta transmi&longs;it. Reperies <lb/>in hoc Opere no&longs;tro nonnullas ex ip&longs;o de&longs;umptas Machinas; quas <lb/>ideo adducimus, quòd aliquæ indigent correctione, vtpote fal&longs;æ: <lb/>aliquæ explicatione, vtpote ob&longs;curiùs traditæ; aliquæ excu&longs;a<lb/>tione ac defen&longs;ione, vtpote &longs;ini&longs;trâ ab alijs cen&longs;urâ notatæ; aliæ <lb/>commendatione, vtpote no&longs;trarum ectypa; aliæ denique ad<lb/>miratione, vtpote ingenio pleni&longs;&longs;imæ. Heronem Latinum fe<lb/>cit Federicus Commandinus Vrbinas; Italicum Joannes Ba-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg30"/><lb/><emph type="italics"/>& pnevmaticis &longs;ua ad nos monumenta transmi&longs;it. </s><s>Reperies <lb/>in hoc Opere no&longs;tro nonnullas ex ip&longs;o de&longs;umptas Machinas; quas <lb/>ideo adducimus, quòd aliquæ indigent correctione, vtpote fal&longs;æ: <lb/>aliquæ explicatione, vtpote ob&longs;curiùs traditæ; aliquæ excu&longs;a<lb/>tione ac defen&longs;ione, vtpote &longs;ini&longs;trâ ab alijs cen&longs;urâ notatæ; aliæ <lb/>commendatione, vtpote no&longs;trarum ectypa; aliæ denique ad<lb/>miratione, vtpote ingenio pleni&longs;&longs;imæ. </s><s>Heronem Latinum fe<lb/>cit Federicus Commandinus Vrbinas; Italicum Joannes Ba-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg31"/><lb/><emph type="italics"/>pti&longs;ta Aleottus, qui & in fine addidit quinque Problemata no<lb/>va, &longs;anè jucundi&longs;&longs;ima, pariterque ingenio&longs;a.<emph.end type="italics"/></s>

Line 1026

Line 1027

<s><emph type="italics"/>Ioannes Bapti&longs;ta Porta Neapolitanus tres latinè &longs;crip&longs;it<emph.end type="italics"/><lb/>

<arrow.to.target n="marg32"/><lb/><emph type="italics"/>egregios libellos de Spiritalibus, qui tamen pe&longs;&longs;imum nacti &longs;unt <lb/>Interpretem Joannem E&longs;crivanum Hi&longs;panum, qui eos Italicè <lb/>at que Hi&longs;panicè vertit; &longs;ed cùm Italicam linguam non calleret,<emph.end type="italics"/>

<pb xlink:href="051/01/043.jpg" pagenum="12"/><emph type="italics"/>mirum e&longs;t, quàm barbarum vbique, quàm ob&longs;curum, quàm <lb/>mutilum reddiderit optimum Auctorem. Addidit nonnulla <lb/>de &longs;uo, oretenus à Porta, &longs;ed malè intellecta, & peiùs per&longs;cri<lb/>pta, itáque alienis permixta, vt di&longs;cerni nequeant, ni&longs;i cum <lb/>genuino comparentur partu. Tradit Porta Spiritalium prin<lb/>cipia, tradit machinamenta multa; vtraque longis experi<lb/>mentis, nec &longs;ine expen&longs;is, confirmata. Huic ego primas inter <lb/>omnes Spiritalium Scriptores dandas cen&longs;eo. Latinum exem<lb/>plar Neapoli impre&longs;&longs;um Anno<emph.end type="italics"/> 1601. <emph type="italics"/>innumeris &longs;catet erroribus <lb/>typographicis, qui &longs;en&longs;um &longs;æpe pror&longs;us pervertunt. Idem Au<lb/>ctor lib.<emph.end type="italics"/> 18. <emph type="italics"/>&<emph.end type="italics"/> 19. <emph type="italics"/>Magiæ Naturalis multas alias habet Machi<lb/>nas Hydraulicas & Pnevmaticas.<emph.end type="italics"/><lb/>

<pb xlink:href="051/01/043.jpg" pagenum="12"/><emph type="italics"/>mirum e&longs;t, quàm barbarum vbique, quàm ob&longs;curum, quàm <lb/>mutilum reddiderit optimum Auctorem. </s><s>Addidit nonnulla <lb/>de &longs;uo, oretenus à Porta, &longs;ed malè intellecta, & peiùs per&longs;cri<lb/>pta, itáque alienis permixta, vt di&longs;cerni nequeant, ni&longs;i cum <lb/>genuino comparentur partu. </s><s>Tradit Porta Spiritalium prin<lb/>cipia, tradit machinamenta multa; vtraque longis experi<lb/>mentis, nec &longs;ine expen&longs;is, confirmata. </s><s>Huic ego primas inter <lb/>omnes Spiritalium Scriptores dandas cen&longs;eo. </s><s>Latinum exem<lb/>plar Neapoli impre&longs;&longs;um Anno<emph.end type="italics"/> 1601. <emph type="italics"/>innumeris &longs;catet erroribus <lb/>typographicis, qui &longs;en&longs;um &longs;æpe pror&longs;us pervertunt. </s><s>Idem Au<lb/>ctor lib.<emph.end type="italics"/> 18. <emph type="italics"/>&<emph.end type="italics"/> 19. <emph type="italics"/>Magiæ Naturalis multas alias habet Machi<lb/>nas Hydraulicas & Pnevmaticas.<emph.end type="italics"/><lb/>

<arrow.to.target n="marg33"/></s>

Line 1036

Line 1037

<s><emph type="italics"/>Joannes Bapti&longs;ta Balianus Patritius Genuen&longs;is, &longs;cri<lb/>p&longs;it libros &longs;ex de motu naturali gravium & liquidorum quorum <lb/>tres vltimi &longs;unt de liquidorum fluxu per canales & foramina; <lb/>è quorum vltimo nonnulla in Protheoriam no&longs;tram quartam<emph.end type="italics"/></s>

<s>

<arrow.to.target n="marg34"/><lb/><emph type="italics"/>derivavimus. P. Ioannes Leurechon è Societ ate no&longs;tra, Lo<lb/>tharingus &longs;crip&longs;it gallico idiomate, tacito nomine &longs;uo, Recreatio<lb/>nes Mathematicas; quas deinde germanicas fecit Daniel<emph.end type="italics"/><lb/>

<arrow.to.target n="marg34"/><lb/><emph type="italics"/>derivavimus. </s><s>P. Ioannes Leurechon è Societ ate no&longs;tra, Lo<lb/>tharingus &longs;crip&longs;it gallico idiomate, tacito nomine &longs;uo, Recreatio<lb/>nes Mathematicas; quas deinde germanicas fecit Daniel<emph.end type="italics"/><lb/>

<arrow.to.target n="marg35"/><lb/><emph type="italics"/>Schvventer, latinas verò Ga&longs;par Ens. Io&longs;ephus Ceredus, <lb/>Medicus Placentinus, &longs;crip&longs;it tres egregios di&longs;cur&longs;us de Cochleæ <lb/>Archimedææ compo&longs;itione & vtilitate, ad elevandas magnâ<emph.end type="italics"/><lb/>

<arrow.to.target n="marg36"/><lb/><emph type="italics"/>quantitate ac facilitate aquas. Ioannes Branca civis Roma<lb/>nus, & Architectus Lauretanæ domus, librum &longs;crip&longs;it Italico <lb/>ac Latino &longs;ermone de Machinis, quas inter multæ &longs;unt hydrau<lb/>licæ, & nonnullæ hydro-pnevmaticæ, at pleræque fal&longs;æ, & hy-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg36"/><lb/><emph type="italics"/>quantitate ac facilitate aquas. </s><s>Ioannes Branca civis Roma<lb/>nus, & Architectus Lauretanæ domus, librum &longs;crip&longs;it Italico <lb/>ac Latino &longs;ermone de Machinis, quas inter multæ &longs;unt hydrau<lb/>licæ, & nonnullæ hydro-pnevmaticæ, at pleræque fal&longs;æ, & hy-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg37"/><lb/><emph type="italics"/>dro-pnevmaticis principijs contrariæ. Marinus Mer&longs;ennus<emph.end type="italics"/>

<arrow.to.target n="marg37"/><lb/><emph type="italics"/>dro-pnevmaticis principijs contrariæ. </s><s>Marinus Mer&longs;ennus<emph.end type="italics"/>

<pb xlink:href="051/01/044.jpg" pagenum="13"/><emph type="italics"/>&longs;crip&longs;it Ph&oelig;nomena hydraulica & pnevmatica, <expan abbr="multas&qacute;ue">multasque</expan> ex<lb/>perientias à &longs;e in illa materia factas, ex quibu⋅ multa deducit <lb/><expan abbr="docti&longs;&longs;ima&qacute;">docti&longs;&longs;imaque</expan>; Theoremata atque Problemata; & nos <expan abbr="noñulla">nonnulla</expan> ex<emph.end type="italics"/><lb/>

<arrow.to.target n="marg38"/><lb/><emph type="italics"/>ip&longs;o in&longs;eruimus quartæ no&longs;træ Protheoriæ. Nicolaus Cabæus <lb/>Commentarijs &longs;uis in Ari&longs;totelis Meteora, nonnulla habet hy-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg38"/><lb/><emph type="italics"/>ip&longs;o in&longs;eruimus quartæ no&longs;træ Protheoriæ. </s><s>Nicolaus Cabæus <lb/>Commentarijs &longs;uis in Ari&longs;totelis Meteora, nonnulla habet hy-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg39"/><lb/><emph type="italics"/>draulica: nonnulla Marius Bettinus in Apiarijs Mathematicis <lb/>Apiario<emph.end type="italics"/> 4. <emph type="italics"/>Progymnas.<emph.end type="italics"/> 1. <emph type="italics"/>Nonnulla denique Petrus Herigo<lb/>nius to.<emph.end type="italics"/> 3. <emph type="italics"/>Cur&longs;us Mathematici tract. de Mechanica. Raphael<emph.end type="italics"/><lb/>

<arrow.to.target n="marg40"/><lb/><emph type="italics"/>Magiottus, Mathematicus Excellenti&longs;&longs;imus, Opu&longs;culum &longs;cri-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg41"/><lb/><emph type="italics"/>p&longs;it Italicum de aquæ Renitentia compre&longs;&longs;ioni; in quo tradit <lb/>Experimentum novum, quod nos adducimus Part.<emph.end type="italics"/> 2. <emph type="italics"/>Cla&longs;&longs;e<emph.end type="italics"/> 1. <lb/><emph type="italics"/>cap.<emph.end type="italics"/> 5. <emph type="italics"/>Machina<emph.end type="italics"/> 6. <emph type="italics"/>Robertus à Fluctibus in &longs;ua Philo&longs;ophia<emph.end type="italics"/><lb/>

<arrow.to.target n="marg42"/><lb/><emph type="italics"/>Mo&longs;aica alijs&qtail; Operibus, multas pa&longs;&longs;im inter&longs;erit Machinas, a<lb/>liâ occa&longs;ione. Salomon à Caus &longs;crip&longs;it Gallico idiomate libros tres<emph.end type="italics"/><lb/>

<arrow.to.target n="marg42"/><lb/><emph type="italics"/>Mo&longs;aica alijs&qtail; Operibus, multas pa&longs;&longs;im inter&longs;erit Machinas, a<lb/>liâ occa&longs;ione. </s><s>Salomon à Caus &longs;crip&longs;it Gallico idiomate libros tres<emph.end type="italics"/><lb/>

<arrow.to.target n="marg43"/><lb/><emph type="italics"/>de hydraulicis quos ip&longs;e de viribus motricibus intitulat: Opus <lb/>est egregium, in eoque theoria aliqualiter cum praxi conjungi-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg44"/><lb/><emph type="italics"/>tur. Theodorus Muretus, è Societate IESV, in Pragen&longs;i Vni<lb/>ver&longs;itate Mathematicæ Profe&longs;&longs;or, edidit Problema Mathema-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg44"/><lb/><emph type="italics"/>tur. </s><s>Theodorus Muretus, è Societate IESV, in Pragen&longs;i Vni<lb/>ver&longs;itate Mathematicæ Profe&longs;&longs;or, edidit Problema Mathema-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg45"/><lb/><emph type="italics"/>ticum de Fontibus. Vitruvius lib.<emph.end type="italics"/> 8. <emph type="italics"/>Architecturæ cap.<emph.end type="italics"/> 6 <emph type="italics"/>&<emph.end type="italics"/> 7. <lb/><emph type="italics"/>agit de perductionibus & librationibus aquarum, & in&longs;trumen<lb/>tis ad hunc v&longs;um; & libro<emph.end type="italics"/> 10. <emph type="italics"/>varia habet in&longs;trumenta hy<lb/>draulica, at pleraque tractoria. Va&longs;&longs;or Arabs habet varias<emph.end type="italics"/><lb/>

<arrow.to.target n="marg45"/><lb/><emph type="italics"/>ticum de Fontibus. </s><s>Vitruvius lib.<emph.end type="italics"/> 8. <emph type="italics"/>Architecturæ cap.<emph.end type="italics"/> 6 <emph type="italics"/>&<emph.end type="italics"/> 7. <lb/><emph type="italics"/>agit de perductionibus & librationibus aquarum, & in&longs;trumen<lb/>tis ad hunc v&longs;um; & libro<emph.end type="italics"/> 10. <emph type="italics"/>varia habet in&longs;trumenta hy<lb/>draulica, at pleraque tractoria. </s><s>Va&longs;&longs;or Arabs habet varias<emph.end type="italics"/><lb/>

<arrow.to.target n="marg46"/><lb/><emph type="italics"/>praxes Spiritales ad aquas in altum educendas: Liber e&longs;t Ma<lb/>nu&longs;criptus, latinus, quem reperi inter libros P. Athana&longs;ij Kir<lb/>cheri, at mutilum, & &longs;ine figuris nece&longs;&longs;a<gap/>ijs: Su&longs;picor e&longs;&longs;e <lb/>fragmentum Scriptoris cuiusdam Græci antiqui, à Ua&longs;&longs;ore in <lb/>Arabicam, ab alio in Latinam linguam translatum. Edidi&longs;-<emph.end type="italics"/>

<pb xlink:href="051/01/045.jpg" pagenum="14"/><emph type="italics"/>&longs;em vnà cum hoc Opere, &longs;i operæ pretium me facturum judica&longs;<lb/>&longs;em.<emph.end type="italics"/></s>

<s><margin.target id="marg34"/>Leurechon</s>

Line 1078

Line 1079

<s><margin.target id="marg46"/>Va&longs;&longs;or A<lb/>rabs.</s>

<s><emph type="italics"/>Hi &longs;unt Auctores, qui de Hydraulicis atque pnevmati<lb/>cis &longs;crip&longs;erunt, &longs;eu ex profe&longs;&longs;o, &longs;eu incidenter. Ex quibus ta<lb/>men, &longs;i Kircherum, Portam, Mer&longs;ennum, aliosque nonnullos <lb/>excipias, pauci no&longs;trum triverunt iter, & vix vllus theoriam <lb/>cum praxi conjunxit; quod nos facimus. Aliorum Auctorum <lb/>nomina, qui vnam aut alteram Machinam &longs;uis inter&longs;erue<lb/>runt Operibus, proferemus &longs;uis locis: Cuiusmodi &longs;unt Oron-<emph.end type="italics"/><lb/>

<s><emph type="italics"/>Hi &longs;unt Auctores, qui de Hydraulicis atque pnevmati<lb/>cis &longs;crip&longs;erunt, &longs;eu ex profe&longs;&longs;o, &longs;eu incidenter. </s><s>Ex quibus ta<lb/>men, &longs;i Kircherum, Portam, Mer&longs;ennum, aliosque nonnullos <lb/>excipias, pauci no&longs;trum triverunt iter, & vix vllus theoriam <lb/>cum praxi conjunxit; quod nos facimus. </s><s>Aliorum Auctorum <lb/>nomina, qui vnam aut alteram Machinam &longs;uis inter&longs;erue<lb/>runt Operibus, proferemus &longs;uis locis: Cuiusmodi &longs;unt Oron-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg47"/><lb/><emph type="italics"/>tius Finæus, & Bonaventura Cavallerius, eximius vterque<emph.end type="italics"/><lb/>

<arrow.to.target n="marg48"/><lb/><emph type="italics"/>Mathematicus; quorum ille in fine tractatus de Horologijs <lb/>vnicam habet hydraulicam Machinam; hic alteram in fine <lb/>Exercitationis &longs;extæ Geometricæ; quarum vtram<lb/>que nos infrà Parte<emph.end type="italics"/> 2. <emph type="italics"/>afferimus.<emph.end type="italics"/><lb/>

<arrow.to.target n="fig2"/></s>

Line 1100

Line 1101

<s><emph type="italics"/>QUatuor reperio Machinarum Hydrau-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg49"/><lb/><emph type="italics"/>lico-pnevmaticarum principia, quibus <lb/>ab Arte animantur in motum, illósque <lb/>præstant effectus, quos tantâ voluptate <lb/>miramur quotidie, tantâ pa&longs;&longs;im experimur vtilita-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg50"/><lb/><emph type="italics"/>te. Primum est vis Attractiva, ad vacuum vel fu<lb/>giendum, velreplendum; quâ vi Aqua, elementu&mtail;<emph.end type="italics"/>

<arrow.to.target n="marg50"/><lb/><emph type="italics"/>te. </s><s>Primum est vis Attractiva, ad vacuum vel fu<lb/>giendum, velreplendum; quâ vi Aqua, elementu&mtail;<emph.end type="italics"/>

<pb xlink:href="051/01/047.jpg" pagenum="16"/><emph type="italics"/>alioquingrave, iners, lentum, & humi repens, tracta <lb/>accurrit non invita, vt videtur, &longs;uæ&queacute; oblita naturæ <lb/>in &longs;ublime nititur, tripudianti &longs;imilis, vacui <expan abbr="velrepl&etilde;-">velreplen-</expan><emph.end type="italics"/><lb/>

<arrow.to.target n="marg51"/><lb/><emph type="italics"/>di, vel impediendi causâ. Alterum est vis expul<lb/>&longs;iva, ad corporum penetrationem fugiendam; quâ vi <lb/>eadem Aqua, dum aëri alterivé corpori validè in<lb/>cumbenticedere cogitur ho&longs;pitio, expul&longs;a fugam prori<lb/>pit eò celeriorem, excel&longs;iorémque, quò vehementiori-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg51"/><lb/><emph type="italics"/>di, vel impediendi causâ. </s><s>Alterum est vis expul<lb/>&longs;iva, ad corporum penetrationem fugiendam; quâ vi <lb/>eadem Aqua, dum aëri alterivé corpori validè in<lb/>cumbenticedere cogitur ho&longs;pitio, expul&longs;a fugam prori<lb/>pit eò celeriorem, excel&longs;iorémque, quò vehementiori-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg52"/><lb/><emph type="italics"/>bus &longs;e&longs;timulis agitatam &longs;en&longs;erit. Tertium est vis ‘Ra<lb/>refactiva; quâ ob&longs;e&longs;&longs;um elementum in tantas &longs;ubin<lb/>de redigitur angustias, vt dum &longs;e&longs;e, quâ data porta, <lb/>vel &longs;ubducit, vel ingerit, alas indui&longs;&longs;e videatur, abje<lb/>ctis gravitatis propriæ compedibus. Quartum de-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg52"/><lb/><emph type="italics"/>bus &longs;e&longs;timulis agitatam &longs;en&longs;erit. </s><s>Tertium est vis ‘Ra<lb/>refactiva; quâ ob&longs;e&longs;&longs;um elementum in tantas &longs;ubin<lb/>de redigitur angustias, vt dum &longs;e&longs;e, quâ data porta, <lb/>vel &longs;ubducit, vel ingerit, alas indui&longs;&longs;e videatur, abje<lb/>ctis gravitatis propriæ compedibus. </s><s>Quartum de-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg53"/><lb/><emph type="italics"/>ni&queacute; estgravitas Aquæ naturalis, ad decliviora loca <lb/>tendentis, & æquilibrium affectantis; quæ gravitas <lb/>non rarò (quod mirêre) in altum attollit ip&longs;am, quam <lb/>paulò antè depre&longs;&longs;er at in profundum.<emph.end type="italics"/></s>

<s><margin.target id="marg49"/>Principia <lb/><expan abbr="Machinar&utilde;">Machinarum</expan> <lb/><expan abbr="Hydrau-lico-pnev-maticar&utilde;">Hydrau<lb/>lico-pnev<lb/>maticarum</expan> <lb/>quatuor.</s>

Line 1118

Line 1119

<s><emph type="italics"/>Hæc quatuor principia qui applicare ritè nove<lb/>rit, quaslibet ingenio&longs;as Machinas, ad Naturæ ne&longs;cio <lb/>an æmulationem, an invidiamfabricari poterit faci<lb/>litate &longs;ummâ, &longs;ucce&longs;&longs;u infallibili; cùm nulla Machina <lb/>hydraulica, aut pnevmatica, aut ex vtrisque mixta<emph.end type="italics"/>

<pb xlink:href="051/01/048.jpg" pagenum="17"/><emph type="italics"/>ad&longs;ignari po&longs;&longs;it quæ non aliquâ harumfacultatum in-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg54"/><lb/><emph type="italics"/>&longs;tituatur. Jmò multis par a&longs;angis Naturæ &longs;uper abit co<lb/>natus<emph.end type="italics"/> <foreign lang="greek">u(dro texni/ths</foreign>. <emph type="italics"/>Natura etenim non ni&longs;i vno motus <lb/>principio aquas terrâ eijcit, at&que; in fontes efformat, na<lb/>turali videlicet fluxu aquæ <expan abbr="de&longs;cend&etilde;tis">de&longs;cendentis</expan> <expan abbr="prim&utilde;">primum</expan>, ac de<lb/>inde a&longs;cendentis: at verò Ars non vno, &longs;ed multiplici, <lb/>vt dixi, &longs;cilicet &longs;uctu &longs;eu attractione, pre&longs;&longs;ione, dila<lb/>tatione, præcipitatione: queis artibus, vel potiùs &longs;tra<lb/>tagematis, in valles, in montes, in hortos, in domos de<lb/>ducit, non fontes tantummodò, &longs;ed machinamenta a<lb/>lia varia, jucunda, ac pror&longs;us<emph.end type="italics"/> <foreign lang="greek"><gap/>aumasiw/tata</foreign>, <emph type="italics"/>aliorum vel <lb/>nece&longs;&longs;itati, vel vtilitati, vel delectationi: Veri&longs;&longs;imum <lb/>quippe est illud Antiphontis,<emph.end type="italics"/> <foreign lang="greek">te/xnh| ga/r xra<gap/>men, w(_n fu/sei nixai/<lb/>meda</foreign>. <emph type="italics"/>At hæc ip&longs;a quatuor hydro-pnevmaticarum <lb/>Machinarum principia &longs;eu fundamenta, antequam <lb/>vlteriùs progrediamur, paulô fu&longs;iùs explicare <lb/>lubet, vt &longs;ecuriùs deinde in praxi pro<lb/>cedamus.<emph.end type="italics"/></s>

<arrow.to.target n="marg54"/><lb/><emph type="italics"/>&longs;tituatur. </s><s>Jmò multis par a&longs;angis Naturæ &longs;uper abit co<lb/>natus<emph.end type="italics"/> <foreign lang="greek">u(dro texni/ths</foreign>. </s><s><emph type="italics"/>Natura etenim non ni&longs;i vno motus <lb/>principio aquas terrâ eijcit, at&que; in fontes efformat, na<lb/>turali videlicet fluxu aquæ <expan abbr="de&longs;cend&etilde;tis">de&longs;cendentis</expan> <expan abbr="prim&utilde;">primum</expan>, ac de<lb/>inde a&longs;cendentis: at verò Ars non vno, &longs;ed multiplici, <lb/>vt dixi, &longs;cilicet &longs;uctu &longs;eu attractione, pre&longs;&longs;ione, dila<lb/>tatione, præcipitatione: queis artibus, vel potiùs &longs;tra<lb/>tagematis, in valles, in montes, in hortos, in domos de<lb/>ducit, non fontes tantummodò, &longs;ed machinamenta a<lb/>lia varia, jucunda, ac pror&longs;us<emph.end type="italics"/> <foreign lang="greek">qaumasiw/tata</foreign>, <emph type="italics"/>aliorum vel <lb/>nece&longs;&longs;itati, vel vtilitati, vel delectationi: Veri&longs;&longs;imum <lb/>quippe est illud Antiphontis,<emph.end type="italics"/> <foreign lang="greek">te/xnh| ga/r xratou=men, w(=n fu/sei nixw/<lb/>meqa</foreign>. </s><s><emph type="italics"/>At hæc ip&longs;a quatuor hydro-pnevmaticarum <lb/>Machinarum principia &longs;eu fundamenta, antequam <lb/>vlteriùs progrediamur, paulô fu&longs;iùs explicare <lb/>lubet, vt &longs;ecuriùs deinde in praxi pro<lb/>cedamus.<emph.end type="italics"/></s>

<s><margin.target id="marg54"/>Ars vin<gap/><lb/>Naturam <lb/>infontibus <lb/>producen<lb/>dis.</s>

<s><margin.target id="marg54"/>Ars vincit <lb/>Naturam <lb/>infontibus <lb/>producen<lb/>dis.</s>

Line 1133

Line 1134

<s><margin.target id="marg55"/><emph type="italics"/><expan abbr="Vacu&utilde;">Vacuum</expan> Phi<lb/>lo&longs;ophorum <lb/>alij admit <lb/>tunt, alij <lb/>respuunt.<emph.end type="italics"/></s>

<s>VAcuum appellat vulgus quodlibet vas, aut lo<lb/>cum, in quo nullum cernunt vi&longs;ibile corpus, etiam&longs;i <lb/>aëre &longs;int plena. At Philo&longs;ophi <emph type="italics"/>Vacuum<emph.end type="italics"/> definiunt <emph type="italics"/>locum <lb/>nullo repletum corpore.<emph.end type="italics"/> Hoc po&longs;terius, quod <expan abbr="&longs;ol&utilde;">&longs;olum</expan> vacui <lb/>nomen meretur propriè, non tam invi&longs;um Naturæ e&longs;t vi&longs;um De<lb/>mocrito, Leucippo, Epicuro, alijsque, vt eliminandum penitus <lb/>cen&longs;uerint è rerum cen&longs;u. Alij verò <expan abbr="pleri&qacute;ue">plerique</expan> Philo&longs;ophi cum <lb/>Stagyrita &longs;uo adeo Naturæ adver&longs;um, adeo pernicio&longs;um exi&longs;ti<lb/>mant Vacuum, vt ad evitandum ip&longs;um dicant, eandem <expan abbr="Naturã">Naturam</expan> <lb/><expan abbr="null&utilde;">nullum</expan> non movere <expan abbr="lapid&etilde;">lapidem</expan>, & omnia <expan abbr="&longs;usq;">&longs;usque</expan> <expan abbr="de&qacute;ue">deque</expan> vertere corpora, <lb/><expan abbr="ip&longs;a&qacute;ue">ip&longs;aque</expan> permi&longs;cere elementa. Qui de hydraulicis, <expan abbr="pnevma-ticis&qacute;ue">pnevma<lb/>ticisque</expan> tractant Machinis, vnanimi con&longs;en&longs;u fatentur omnes </s>

<s>VAcuum appellat vulgus quodlibet vas, aut lo<lb/>cum, in quo nullum cernunt vi&longs;ibile corpus, etiam&longs;i <lb/>aëre &longs;int plena. </s><s>At Philo&longs;ophi <emph type="italics"/>Vacuum<emph.end type="italics"/> definiunt <emph type="italics"/>locum <lb/>nullo repletum corpore.<emph.end type="italics"/> Hoc po&longs;terius, quod <expan abbr="&longs;ol&utilde;">&longs;olum</expan> vacui <lb/>nomen meretur propriè, non tam invi&longs;um Naturæ e&longs;t vi&longs;um De<lb/>mocrito, Leucippo, Epicuro, alijsque, vt eliminandum penitus <lb/>cen&longs;uerint è rerum cen&longs;u. </s><s>Alij verò <expan abbr="pleri&qacute;ue">plerique</expan> Philo&longs;ophi cum <lb/>Stagyrita &longs;uo adeo Naturæ adver&longs;um, adeo pernicio&longs;um exi&longs;ti<lb/>mant Vacuum, vt ad evitandum ip&longs;um dicant, eandem <expan abbr="Naturã">Naturam</expan> <lb/><expan abbr="null&utilde;">nullum</expan> non movere <expan abbr="lapid&etilde;">lapidem</expan>, & omnia <expan abbr="&longs;usq;">&longs;usque</expan> <expan abbr="de&qacute;ue">deque</expan> vertere corpora, <lb/><expan abbr="ip&longs;a&qacute;ue">ip&longs;aque</expan> permi&longs;cere elementa. </s><s>Qui de hydraulicis, <expan abbr="pnevma-ticis&qacute;ue">pnevma<lb/>ticisque</expan> tractant Machinis, vnanimi con&longs;en&longs;u fatentur omnes </s>

<s>

<arrow.to.target n="marg56"/><lb/>(&longs;i Lip&longs;torpium cum Carte&longs;io &longs;uo excipias) vim attractivam, <lb/>quam in Machinis nonnullis aperti&longs;&longs;im è elucere videmus, aliun<lb/>de non provenire, ni&longs;i quòd Aqua, & Aër, Naturæ ob&longs;ecunda<lb/>turi, accurrant tracti &longs;eu &longs;ponte, &longs;eu invitè, vel ad replendum va<lb/>cuum quod oderunt, vel ad impediendum quod timent. Vtra<lb/>que igitur &longs;ententia, & quæ vacuum recipit, & quæ rejicit, Hy<lb/>draulicorum ac Pnevmaticorum Artificibus favet; ac proinde <lb/>ex vtrius que placitis vis attractiva prædicta e&longs;t explicanda. </s>

<arrow.to.target n="marg56"/><lb/>(&longs;i Lip&longs;torpium cum Carte&longs;io &longs;uo excipias) vim attractivam, <lb/>quam in Machinis nonnullis aperti&longs;&longs;im è elucere videmus, aliun<lb/>de non provenire, ni&longs;i quòd Aqua, & Aër, Naturæ ob&longs;ecunda<lb/>turi, accurrant tracti &longs;eu &longs;ponte, &longs;eu invitè, vel ad replendum va<lb/>cuum quod oderunt, vel ad impediendum quod timent. </s><s>Vtra<lb/>que igitur &longs;ententia, & quæ vacuum recipit, & quæ rejicit, Hy<lb/>draulicorum ac Pnevmaticorum Artificibus favet; ac proinde <lb/>ex vtrius que placitis vis attractiva prædicta e&longs;t explicanda. </s>

<s><margin.target id="marg56"/><emph type="italics"/>Attractiva <lb/>vis ex appe<lb/><gap/>itu vacui <lb/>vel replen<lb/>di, vel fu<lb/>giendi ori<lb/>tur in Ma<lb/>chinis hy<lb/>dro-pnev<lb/>maticis.<emph.end type="italics"/></s>

<s><margin.target id="marg56"/><emph type="italics"/>Attractiva <lb/>vis ex appet<lb/>itu vacui <lb/>vel replen<lb/>di, vel fu<lb/>giendi ori<lb/>tur in Ma<lb/>chinis hy<lb/>dro-pnev<lb/>maticis.<emph.end type="italics"/></s>

<s><emph type="center"/>Protheoria I.<emph.end type="center"/></s>

Line 1148

Line 1149

<s><emph type="center"/>Hero Alexandrinus Vacuum in aëre & aqua <lb/>di&longs;seminatum agno&longs;cit.<emph.end type="center"/></s>

<s>HEro Alexandrinus, &longs;imul Spiritalium Magi&longs;trum agens, &longs;i<lb/>

<arrow.to.target n="marg57"/><lb/>mul Democritici, <expan abbr="Epicurei&qacute;ue">Epicureique</expan> Philo&longs;ophi per&longs;onam, prio<lb/>rem de Vacuo &longs;ententiam doctè non minùs quàm fusè explicat, <lb/>atque tuetur, in Præfatione Libelli &longs;ui de Pnevmaticis &longs;eu Spi<lb/>ritalibus, vbi ait<emph type="italics"/>: Alij enim vnivërsè nullum omnino vacuum e&longs;&longs;e <lb/>affirmant; alij coacervatum quidem naturâ nullum e&longs;&longs;e vacuum, &longs;ed <lb/>&longs;ecundùm exiguas partes di&longs;&longs;eminatum in aëre, humido, & ig<gap/> alijsque <lb/>corporibus; quibus maximè a&longs;&longs;entiri convenit.<emph.end type="italics"/> Vacuum coacerva<lb/>tum veteres vocabant <foreign lang="greek">a)<gap/>n</foreign>, di&longs;&longs;eminatum verò <foreign lang="greek">parespa<gap/>me/non</foreign>, vt <lb/>notat Petrus Ga&longs;lendus in Philo&longs;ophia Epicuri; à quo Epicuro <lb/>

<arrow.to.target n="marg57"/><lb/>mul Democritici, <expan abbr="Epicurei&qacute;ue">Epicureique</expan> Philo&longs;ophi per&longs;onam, prio<lb/>rem de Vacuo &longs;ententiam doctè non minùs quàm fusè explicat, <lb/>atque tuetur, in Præfatione Libelli &longs;ui de Pnevmaticis &longs;eu Spi<lb/>ritalibus, vbi ait<emph type="italics"/>: Alij enim vnivërsè nullum omnino vacuum e&longs;&longs;e <lb/>affirmant; alij coacervatum quidem naturâ nullum e&longs;&longs;e vacuum, &longs;ed <lb/>&longs;ecundùm exiguas partes di&longs;&longs;eminatum in aëre, humido, & igne, alijsque <lb/>corporibus; quibus maximè a&longs;&longs;entiri convenit.<emph.end type="italics"/> Vacuum coacerva<lb/>tum veteres vocabant <foreign lang="greek">a)<gap/>n</foreign>, di&longs;&longs;eminatum verò <foreign lang="greek">parespa<gap/>me/non</foreign>, vt <lb/>notat Petrus Ga&longs;lendus in Philo&longs;ophia Epicuri; à quo Epicuro <lb/>

<arrow.to.target n="marg58"/><lb/>Hero &longs;ontentiam &longs;uam mutuatus e&longs;t. <foreign lang="greek">*alla\ me\n</foreign>, inquit Epicurus <lb/>Epi&longs;tola ad <expan abbr="Herodot&utilde;">Herodotum</expan>, <foreign lang="greek">kai\| to\ pa_n e)si\ ph_ me/n *sw_ma, ph_| de\ xeno\n</foreign> <emph type="italics"/>vniver&longs;um <lb/>autem partim quidem Corpus, partim verò inane e&longs;t.<emph.end type="italics"/></s>

<arrow.to.target n="marg58"/><lb/>Hero &longs;ontentiam &longs;uam mutuatus e&longs;t. </s><s><foreign lang="greek">*alla\ me\n</foreign>, inquit Epicurus <lb/>Epi&longs;tola ad <expan abbr="Herodot&utilde;">Herodotum</expan>, <foreign lang="greek">kai\| to\ pa_n e)si\ ph_ me/n *sw_ma, ph_| de\ xeno\n</foreign> <emph type="italics"/>vniver&longs;um <lb/>autem partim quidem Corpus, partim verò inane e&longs;t.<emph.end type="italics"/></s>

<s><margin.target id="marg57"/><emph type="italics"/>Hero vacu<lb/>um admit<lb/>tit in aëre <lb/>& aqua di&longs; <lb/>&longs;eminatum<emph.end type="italics"/></s>

<s><margin.target id="marg58"/><emph type="italics"/>Epicuriu <lb/>vacuum ad <lb/>mittit.<emph.end type="italics"/></s>

<s>Suam porrò de vacuo &longs;ententiam Hero tot probat rationi<lb/>bus & experientijs, vt demon&longs;tratam exi&longs;timet, easque dignas <lb/>cen&longs;uit Marinus Mer&longs;ennus, quas Hydraulicis &longs;uis præmitteret <lb/>

<arrow.to.target n="marg59"/><lb/>Ph&oelig;nomenis. Ac principio quidem o&longs;tendit Hero. <emph type="italics"/>Va&longs;a, quæ <lb/>multis vacua videntur,<emph.end type="italics"/> eò quòd nullum in ijs vi&longs;ibile deprehen<lb/>dunt Corpus, <emph type="italics"/>non e&longs;&longs;e vacua, vt putant, &longs;ed aëre plena.<emph.end type="italics"/> Quod <lb/>quidem patet ex eo, inquit Hero, quòd <emph type="italics"/>&longs;i vas, quod vacuum vide<lb/>tur, quis inver&longs;um in aquam depre&longs;&longs;erit, rectumque &longs;ervarit, aqua in <lb/>ip&longs;um non ingredietur, quamvis totum occultatum fuerit.<emph.end type="italics"/> Vtique <lb/>non alia de Cau&longs;a, ni&longs;i quia aër, cum Corpus &longs;it, & totum vas <lb/>occupet, non permittit aquam ingredi, vt ip&longs;emet &longs;ubjungit. <lb/>Idem patetin phialis vitreis, ollis, alijsque va&longs;is, &longs;i inver&longs;a aquis <lb/>immergantur: non enim ni&longs;i difficulter admodum demergun<lb/>tur; & dum retrahuntur, latera interiora habent &longs;icca; non ob <lb/>aliud profectò, ni&longs;i quia inclu&longs;us aër ingre&longs;&longs;um prohibuit aquæ. </s>

<arrow.to.target n="marg59"/><lb/>Ph&oelig;nomenis. </s><s>Ac principio quidem o&longs;tendit Hero. </s><s><emph type="italics"/>Va&longs;a, quæ <lb/>multis vacua videntur,<emph.end type="italics"/> eò quòd nullum in ijs vi&longs;ibile deprehen<lb/>dunt Corpus, <emph type="italics"/>non e&longs;&longs;e vacua, vt putant, &longs;ed aëre plena.<emph.end type="italics"/> Quod <lb/>quidem patet ex eo, inquit Hero, quòd <emph type="italics"/>&longs;i vas, quod vacuum vide<lb/>tur, quis inver&longs;um in aquam depre&longs;&longs;erit, rectumque &longs;ervarit, aqua in <lb/>ip&longs;um non ingredietur, quamvis totum occultatum fuerit.<emph.end type="italics"/> Vtique <lb/>non alia de Cau&longs;a, ni&longs;i quia aër, cum Corpus &longs;it, & totum vas <lb/>occupet, non permittit aquam ingredi, vt ip&longs;emet &longs;ubjungit. </s><s><lb/>Idem patetin phialis vitreis, ollis, alijsque va&longs;is, &longs;i inver&longs;a aquis <lb/>immergantur: non enim ni&longs;i difficulter admodum demergun<lb/>tur; & dum retrahuntur, latera interiora habent &longs;icca; non ob <lb/>aliud profectò, ni&longs;i quia inclu&longs;us aër ingre&longs;&longs;um prohibuit aquæ. </s>

<s><margin.target id="marg59"/><emph type="italics"/>Va&longs;a ina<lb/>nia aëre e&longs;&longs;e <lb/>plena, vari<lb/>is probatur <lb/>experimen<lb/>tis.<emph.end type="italics"/></s>

<s>Quòd &longs;i prædictorum Va&longs;orum inver&longs;orum aquis immer<lb/>&longs;orum <emph type="italics"/>fundum quis perforet, aqua quidem per os demer&longs;um in ip&longs;a in<lb/>gredietur, aër verò per foramen exibit,<emph.end type="italics"/> adeo manife&longs;tè, vt non &longs;o-

<pb xlink:href="051/01/051.jpg" pagenum="20"/>lùm manui admotæ &longs;en&longs;um inferat, &longs;ed etiam aures &longs;ono de<lb/>mulceat, & quidem harmonico, &longs;i foramini aptentur fi&longs;tulæ <lb/>&longs;ono Harmonico edendo aptæ, prout ip&longs;emet Hero fieri <lb/>jubet in multis, quas de&longs;cribit in citato Libello, hydraulicis at<lb/>que pnevmaticis Machinis. Quod etiam quotidie experimur <lb/>in Hortis Romanis, Tu&longs;culanis, Tiburtinis, & in ip&longs;o etiam <lb/>P. Athana&longs;ij Kircheri mu&longs;eo. <emph type="italics"/>Non igitur <gap/>rbitrandum e&longs;t,<emph.end type="italics"/> infert <lb/>Hero, <emph type="italics"/>in his quæ&longs;unt, vacui naturam quandam coacervatam ip&longs;am per<lb/>&longs;e ip&longs;am exi&longs;tere &longs;ed&longs;ecundùm exiguas partes in aëre, & humido, alijsque <lb/>corporib<gap/> di&longs;&longs;eminatam,<emph.end type="italics"/> etiam in ip&longs;o adamante, duri&longs;&longs;imo licet, <lb/>den&longs;i&longs;&longs;<gap/>oque, <emph type="italics"/>quippe qui neque igniri, neque rumpi pote&longs;t, & percu&longs;<lb/>

<pb xlink:href="051/01/051.jpg" pagenum="20"/>lùm manui admotæ &longs;en&longs;um inferat, &longs;ed etiam aures &longs;ono de<lb/>mulceat, & quidem harmonico, &longs;i foramini aptentur fi&longs;tulæ <lb/>&longs;ono Harmonico edendo aptæ, prout ip&longs;emet Hero fieri <lb/>jubet in multis, quas de&longs;cribit in citato Libello, hydraulicis at<lb/>que pnevmaticis Machinis. </s><s>Quod etiam quotidie experimur <lb/>in Hortis Romanis, Tu&longs;culanis, Tiburtinis, & in ip&longs;o etiam <lb/>P. Athana&longs;ij Kircheri mu&longs;eo. </s><s><emph type="italics"/>Non igitur <gap/>rbitrandum e&longs;t,<emph.end type="italics"/> infert <lb/>Hero, <emph type="italics"/>in his quæ&longs;unt, vacui naturam quandam coacervatam ip&longs;am per<lb/>&longs;e ip&longs;am exi&longs;tere &longs;ed&longs;ecundùm exiguas partes in aëre, & humido, alijsque <lb/>corporib<gap/> di&longs;&longs;eminatam,<emph.end type="italics"/> etiam in ip&longs;o adamante, duri&longs;&longs;imo licet, <lb/>den&longs;i&longs;&longs;<gap/>oque, <emph type="italics"/>quippe qui neque igniri, neque rumpi pote&longs;t, & percu&longs;<lb/>

<arrow.to.target n="marg60"/><lb/>&longs;us in incudes & malleos totus ing reditur<emph.end type="italics"/> (vt cum Pl<gap/>io putat Hero; <lb/>quod tamen, Mer&longs;enno te&longs;te, experientiæ repugnat, nam ictu <lb/>mallei in varias partes di&longs;&longs;ilit, & ita pote&longs;t iguiri, vt pereat.<emph type="italics"/>) Hoc <lb/><expan abbr="aut&etilde;">autem</expan> ip&longs;iaccidit,<emph.end type="italics"/> &longs;ubiungit Hero, <emph type="italics"/>non quòd vacuo careat, &longs;ed ob conti<lb/>nuatam den&longs;itatem.<emph.end type="italics"/> Corpora porro illa (aëris præ&longs;ertim) quæ <lb/>partes &longs;uas habent inter &longs;e&longs;e cohærentes, <emph type="italics"/>non|tamen ex omni parte, <lb/>&longs;ed interiecta habent inter valla quædam vacua,<emph.end type="italics"/> (quæ vacuola appel<lb/>lat Mer&longs;ennus) bellè comparat Hero arenarum cumulo, inter <lb/>

<arrow.to.target n="marg61"/><lb/>cuius grana multæ aëris particulæ intercedunt; aitque, arenæ par<lb/>ticulas particulis aëris &longs;imiles e&longs;&longs;e, <expan abbr="aër&etilde;">aërem</expan> verò, qui inter arenas in<lb/>terjicitur, &longs;imilem vacuolis intra aërem contentis; quæ quidem <lb/>vocuola tunc di&longs;inere putat in aëre (alijsque corporibus) cùm <lb/>accedente vi quapiam conden&longs;atur aër; redire verò, cùm facta <lb/>remi&longs;&longs;ione in pri&longs;tinum ordinem re&longs;tituitur aër ob naturalem <lb/>contentionem, quâ, velut arcus inflexus, aut &longs;icca &longs;pongia vi <lb/>pre&longs;&longs;a, molem ab ip&longs;o rerum conditu &longs;ibi tributam repetit, &longs;ta<lb/>

<arrow.to.target n="marg62"/><lb/>tim atque vis externa de&longs;init. <emph type="italics"/>At aëris corpora,<emph.end type="italics"/> inquit Hero, <emph type="italics"/>inter <lb/>&longs;e&longs;e quidem cohærent, non tamen ex omni parte, &longs;edinteriecta habent <lb/>intervalla quædam vacua, &longs;icut arena, quæ e&longs;t in littoribus. Itaque a<lb/>nimo concipiendum e&longs;t, arenæ particulas corporibus aëris &longs;imiles e&longs;&longs;e, aë<lb/>rem vero, qui inter particulas arenæ interiicitur, &longs;imilem vacuis intra <lb/>aërem contentis. Quamobrem vi quadam accedente äerem den&longs;ari con<lb/>tingit, & in vacuorum loca re&longs;idere, corporibus præter naturam inter <lb/>&longs;e&longs;e compre&longs;&longs;is: remi&longs;sione verò factârar&longs;us in cun dem ordinem re&longs;titui-<emph.end type="italics"/>

<arrow.to.target n="marg62"/><lb/>tim atque vis externa de&longs;init. </s><s><emph type="italics"/>At aëris corpora,<emph.end type="italics"/> inquit Hero, <emph type="italics"/>inter <lb/>&longs;e&longs;e quidem cohærent, non tamen ex omni parte, &longs;edinteriecta habent <lb/>intervalla quædam vacua, &longs;icut arena, quæ e&longs;t in littoribus. </s><s>Itaque a<lb/>nimo concipiendum e&longs;t, arenæ particulas corporibus aëris &longs;imiles e&longs;&longs;e, aë<lb/>rem vero, qui inter particulas arenæ interiicitur, &longs;imilem vacuis intra <lb/>aërem contentis. </s><s>Quamobrem vi quadam accedente äerem den&longs;ari con<lb/>tingit, & in vacuorum loca re&longs;idere, corporibus præter naturam inter <lb/>&longs;e&longs;e compre&longs;&longs;is: remi&longs;sione verò factârar&longs;us in cun dem ordinem re&longs;titui-<emph.end type="italics"/>

<pb xlink:href="051/01/052.jpg" pagenum="21"/><emph type="italics"/>tur, ob naturalem Corporum contentionem; quemadmodum & in cor<lb/>nuum ramentis, & in &longs;pongiis &longs;iccis, quæ&longs;i compre&longs;&longs;a remittantur, rur<lb/>&longs;us in cundem locum redeunt, eandem que accipiunt molem. Similiter <lb/>&longs;i aliqua vi aëris particulæ à &longs;e in vicem di&longs;tractæ fuerint, & maior præ<lb/>ter naturam locus vacuus fiat, rur&longs;us ad &longs;e&longs;e recurrunt, per vacuum e<lb/>nim celerem corporum lationem fieri contingit, nullo ob&longs;tunte, aut re<lb/>pellente, quóusque corpora ad &longs;e&longs;e applicentur.<emph.end type="italics"/></s>

<pb xlink:href="051/01/052.jpg" pagenum="21"/><emph type="italics"/>tur, ob naturalem Corporum contentionem; quemadmodum & in cor<lb/>nuum ramentis, & in &longs;pongiis &longs;iccis, quæ&longs;i compre&longs;&longs;a remittantur, rur<lb/>&longs;us in cundem locum redeunt, eandem que accipiunt molem. </s><s>Similiter <lb/>&longs;i aliqua vi aëris particulæ à &longs;e in vicem di&longs;tractæ fuerint, & maior præ<lb/>ter naturam locus vacuus fiat, rur&longs;us ad &longs;e&longs;e recurrunt, per vacuum e<lb/>nim celerem corporum lationem fieri contingit, nullo ob&longs;tunte, aut re<lb/>pellente, quóusque corpora ad &longs;e&longs;e applicentur.<emph.end type="italics"/></s>

<s><margin.target id="marg60"/>Adamas i<lb/>gni & mal<lb/>len cedit.</s>

Line 1206

Line 1207

<s><margin.target id="marg68"/><emph type="italics"/>Sphæra con<lb/>cava, & aë<lb/>replena, cur <lb/>plùs <gap/>ris <lb/>per inflatio<lb/>nem recipi<lb/>at <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <lb/>Heronem.<emph.end type="italics"/></s>

<s>Quartò, <emph type="italics"/>con&longs;truatur Sphæra cra&longs;&longs;itudinem habens laminæ, vt nè <lb/>facilè rumpatur, continensque circiter cotylas octo, & vndique præclu<lb/>&longs;a;<emph.end type="italics"/> & per foramen in ip&longs;a factum immittamus <emph type="italics"/>Siphonem æreum, <lb/>hoc e&longs;t, tubum gracilem, non contingentem locum, qui puncto perfora<lb/>to &longs;ecundùm diametrum opponitur, ita vt aqua fluere po&longs;&longs;it; alia autem <lb/>ip&longs;ius pars extra &longs;phæram emineat circiter digitos tres, ip&longs;i&queacute; diligenter <lb/>adferruminetur, ambitu foraminis circa tubum &longs;tanno præclu&longs;o, vt cùm <lb/>volumus ore per &longs;iphonem inflare, &longs;piritus ex &longs;phærâ nullo modo excidat.<emph.end type="italics"/><lb/>His factis,, <emph type="italics"/>in&longs;piciamus quæ contingunt. Aëre enim in ip&longs;a exi&longs;tente<emph.end type="italics"/><lb/>(quemadmodum & in aliis va&longs;is quæ vacua appellantur) <emph type="italics"/>totum<lb/>que qui in ipsa locum replente, & per continuationem quandam ad eius <lb/>ambitum applicato, nullo denique loco, ut arbitrantur, penitus exi&longs;ten<lb/>te vacuo; neque aquam immittere po&longs;&longs;emus, neque alium aërem, non <lb/>excedente priori aëre qui in ipsa erat; & &longs;i multa vi immi&longs;&longs;ionem facia<lb/>mus, priùs di&longs;rumpetur vas, quàm aliquid &longs;u&longs;cipiat, cùm plenum &longs;it: ne<lb/>que enim aëris corpora in minorem magnitudinem contrahi po&longs;&longs;unt: <lb/>quare nece&longs;&longs;e erit, vt in &longs;eip&longs;is habeant quædam intervalla, in quæ com<lb/>pre&longs;&longs;a minorem obtineant molem; hoc autem veri&longs;imile non e&longs;t, nullo <lb/>penitus exi&longs;tente vacuo: & cùm corpora ad &longs;e&longs;e applicentur &longs;ecundùm <lb/>omnes &longs;uperficies, & &longs;imiliter ad va&longs;is ambitum, non po&longs;&longs;unt expul&longs;a lo<lb/>cum alicui facere, non exi&longs;tente vacuo aliquo, quamobrem nullo modo <lb/>in &longs;phæram immittetur aliquid eorum, quæ &longs;unt extra, ni&longs;i excedat ali<lb/>qua pars aëris priùs in ea contenti, &longs;iquidem totus locus con&longs;tipatus est, <lb/>& continuatus, vt arbitrantur. At<emph.end type="italics"/> experientiâ con&longs;tat contrari<lb/>um: nam <emph type="italics"/>&longs;i quis &longs;iphonem ori admovens &longs;phæraminflet, multum im<lb/>mittit &longs;piritum, non excedente aëre, qui in ea e&longs;t. Quod cùm ita &longs;em<lb/>per contingat; manife&longs;tò o&longs;tenditur, <expan abbr="contraction&etilde;">contractionem</expan> fieri <expan abbr="corpor&utilde;">corporum</expan> in &longs;phæra <lb/>exi&longs;tentium in vacua implicata: contractio autem præter naturam fit, <lb/>ob immi&longs;&longs;ionis violentiam. Si igitur aliquis infla<gap/>, & ad ip&longs;um os ma<lb/>num apponens, &longs;tatim digito &longs;iphonem obturet; manebit omni tempore<emph.end type="italics"/>

<s>Quartò, <emph type="italics"/>con&longs;truatur Sphæra cra&longs;&longs;itudinem habens laminæ, vt nè <lb/>facilè rumpatur, continensque circiter cotylas octo, & vndique præclu<lb/>&longs;a;<emph.end type="italics"/> & per foramen in ip&longs;a factum immittamus <emph type="italics"/>Siphonem æreum, <lb/>hoc e&longs;t, tubum gracilem, non contingentem locum, qui puncto perfora<lb/>to &longs;ecundùm diametrum opponitur, ita vt aqua fluere po&longs;&longs;it; alia autem <lb/>ip&longs;ius pars extra &longs;phæram emineat circiter digitos tres, ip&longs;i&queacute; diligenter <lb/>adferruminetur, ambitu foraminis circa tubum &longs;tanno præclu&longs;o, vt cùm <lb/>volumus ore per &longs;iphonem inflare, &longs;piritus ex &longs;phærâ nullo modo excidat.<emph.end type="italics"/><lb/>His factis,, <emph type="italics"/>in&longs;piciamus quæ contingunt. </s><s>Aëre enim in ip&longs;a exi&longs;tente<emph.end type="italics"/><lb/>(quemadmodum & in aliis va&longs;is quæ vacua appellantur) <emph type="italics"/>totum<lb/>que qui in ipsa locum replente, & per continuationem quandam ad eius <lb/>ambitum applicato, nullo denique loco, ut arbitrantur, penitus exi&longs;ten<lb/>te vacuo; neque aquam immittere po&longs;&longs;emus, neque alium aërem, non <lb/>excedente priori aëre qui in ipsa erat; & &longs;i multa vi immi&longs;&longs;ionem facia<lb/>mus, priùs di&longs;rumpetur vas, quàm aliquid &longs;u&longs;cipiat, cùm plenum &longs;it: ne<lb/>que enim aëris corpora in minorem magnitudinem contrahi po&longs;&longs;unt: <lb/>quare nece&longs;&longs;e erit, vt in &longs;eip&longs;is habeant quædam intervalla, in quæ com<lb/>pre&longs;&longs;a minorem obtineant molem; hoc autem veri&longs;imile non e&longs;t, nullo <lb/>penitus exi&longs;tente vacuo: & cùm corpora ad &longs;e&longs;e applicentur &longs;ecundùm <lb/>omnes &longs;uperficies, & &longs;imiliter ad va&longs;is ambitum, non po&longs;&longs;unt expul&longs;a lo<lb/>cum alicui facere, non exi&longs;tente vacuo aliquo, quamobrem nullo modo <lb/>in &longs;phæram immittetur aliquid eorum, quæ &longs;unt extra, ni&longs;i excedat ali<lb/>qua pars aëris priùs in ea contenti, &longs;iquidem totus locus con&longs;tipatus est, <lb/>& continuatus, vt arbitrantur. </s><s>At<emph.end type="italics"/> experientiâ con&longs;tat contrari<lb/>um: nam <emph type="italics"/>&longs;i quis &longs;iphonem ori admovens &longs;phæraminflet, multum im<lb/>mittit &longs;piritum, non excedente aëre, qui in ea e&longs;t. </s><s>Quod cùm ita &longs;em<lb/>per contingat; manife&longs;tò o&longs;tenditur, <expan abbr="contraction&etilde;">contractionem</expan> fieri <expan abbr="corpor&utilde;">corporum</expan> in &longs;phæra <lb/>exi&longs;tentium in vacua implicata: contractio autem præter naturam fit, <lb/>ob immi&longs;&longs;ionis violentiam. </s><s>Si igitur aliquis infla<gap/>, & ad ip&longs;um os ma<lb/>num apponens, &longs;tatim digito &longs;iphonem obturet; manebit omni tempore<emph.end type="italics"/>

<pb xlink:href="051/01/054.jpg" pagenum="23"/><emph type="italics"/>con&longs;tipatus aër in &longs;phæra: quod&longs;i quis aperiat, rur&longs;us extra erump<gap/>t cum <lb/><gap/>agno &longs;trepitu & clamore immi&longs;&longs;us aër, propterea quòd, vt propo&longs;uimus, <lb/>expellitur à dilatatione pr<gap/>exi&longs;tentis aëris impetu quodam factâ.<emph.end type="italics"/></s>

<s>Quintò, <emph type="italics"/>&longs;i quis velit aërem, qui in Sphæra e&longs;t, per &longs;iphonem at</s>

<s>

<arrow.to.target n="marg69"/><lb/>trahere, magna copia con&longs;equetur, nullâ aliâ&longs;ub&longs;tantiâ in &longs;phæram &longs;uc<lb/>cedente, quemadmodum in ovo antè dictum e&longs;t. Quare ex hoc per &longs;pi<lb/>cuè o&longs;tenditur, magnam vacui coacervationem in &longs;phæra factam e&longs;&longs;e: <lb/>non enim aëris corpora, quærelinquuntur eo tempore, maiora fieri po&longs;<lb/>&longs;unt, ita vt expul&longs;orum corporum locum repleant: nam&longs;i augerentur, <lb/>cùm nulla ip&longs;is &longs;ub&longs;tantia extrin&longs;ecus accedat, veri&longs;imile e&longs;&longs;et, augmen<lb/>tum fieri per rarefactionem; hoc autem e&longs;&longs;et implicatio &longs;ecundùm eva<lb/>cuationem; &longs;ed vacuum nullum e&longs;&longs;e dicunt; non igitur augebuntur Cor<lb/>pora; neque enim aliud augmentum ip&longs;is accidere mente concipi pote&longs;t. <lb/>Ex quibus per &longs;picuum e&longs;t, in aëris corporibus di&longs;&longs;eminata e&longs;&longs;e quædam <lb/>vacua intermedia, & vi quadam adveniente ea præter naturam in va<lb/>cua reclinare.<emph.end type="italics"/></s>

<arrow.to.target n="marg69"/><lb/>trahere, magna copia con&longs;equetur, nullâ aliâ&longs;ub&longs;tantiâ in &longs;phæram &longs;uc<lb/>cedente, quemadmodum in ovo antè dictum e&longs;t. </s><s>Quare ex hoc per &longs;pi<lb/>cuè o&longs;tenditur, magnam vacui coacervationem in &longs;phæra factam e&longs;&longs;e: <lb/>non enim aëris corpora, quærelinquuntur eo tempore, maiora fieri po&longs;<lb/>&longs;unt, ita vt expul&longs;orum corporum locum repleant: nam&longs;i augerentur, <lb/>cùm nulla ip&longs;is &longs;ub&longs;tantia extrin&longs;ecus accedat, veri&longs;imile e&longs;&longs;et, augmen<lb/>tum fieri per rarefactionem; hoc autem e&longs;&longs;et implicatio &longs;ecundùm eva<lb/>cuationem; &longs;ed vacuum nullum e&longs;&longs;e dicunt; non igitur augebuntur Cor<lb/>pora; neque enim aliud augmentum ip&longs;is accidere mente concipi pote&longs;t. </s><s><lb/>Ex quibus per &longs;picuum e&longs;t, in aëris corporibus di&longs;&longs;eminata e&longs;&longs;e quædam <lb/>vacua intermedia, & vi quadam adveniente ea præter naturam in va<lb/>cua reclinare.<emph.end type="italics"/></s>

<s><margin.target id="marg69"/>Sphæra con <lb/>cava ex&longs;u<lb/>cto aëre, va <lb/>cua conti<lb/>net inter<lb/>valla <expan abbr="&longs;ec&utilde;-dum">&longs;ecun<lb/>dum</expan> Hero<lb/>nem.</s>

<s>Sextò, <emph type="italics"/>vacuis non exi&longs;tentibus, neque per aquam, neque per <lb/>

<arrow.to.target n="marg70"/><lb/>aërem, neque per aliud corpus vllum po&longs;&longs;et lumen tranfire, aut calidit as, <lb/>aut alia potentia<emph.end type="italics"/> &longs;eu qualitas <emph type="italics"/>corporea. </s><s>Nam quomodo radij &longs;olares <lb/>per aquam in fundam va&longs;is penetrarent? Si enim aqua non haberet <lb/>poros, &longs;ed radij aquam vi &longs;cinderent, contingeret vasa plena &longs;uperfun<lb/>di; quod fieri non videmus: Ad hæc &longs;i aquam vi &longs;cinderent, non vti<lb/>que radiorum alij ad&longs;uperiorem locum frangerentur, alij deor&longs;um cade<lb/>rent: nunc autem quicunque aquæ particulis occurrunt, franguntur ad <lb/>&longs;uperiorem locum; quicunque verò incidunt in aquæ vacua, paucis par<lb/>ticulis occurrentes in va&longs;is fundum pervadunt.<emph.end type="italics"/> Adde quòd &longs;i nulla <lb/>e&longs;&longs;ent in corporibus vacua, nullum corpus per alia corpora tran<lb/>&longs;ire po&longs;&longs;et: quod tamen oleis contingit, quorum aliqua tam &longs;ub<lb/>tilia, &longs;unt vt omnia metalla, <expan abbr="ip&longs;um&qacute;">ip&longs;umque</expan>; <expan abbr="etiã">etiam</expan> vitrum penetrent. </s><s>Idem <lb/>etiam fieri ab igne, nemo ne&longs;cit, qui ferrum, aurum, & vitrum <lb/>candentia vidit. </s><s>Idem præterea à virtute magnetica fieri, quo<lb/>tidie experimur. <lb/>

<arrow.to.target n="marg71"/></s>

<s><margin.target id="marg70"/>Corpora & <lb/>qualitates <lb/>corporeæ, pe<lb/>netrant a<lb/>lia corpora, <lb/>&longs;ecundùm <lb/>Heronem, <lb/>propter va<lb/>cua interie<lb/>cta.</s>

<s><margin.target id="marg71"/><emph type="italics"/>Vinum mi<lb/>&longs;cetur aquæ <lb/>ob inte<gap/>er <lb/>&longs;a vacua <lb/><gap/>uxta He<lb/>ronem.<emph.end type="italics"/></s>

<s>Septimò, <emph type="italics"/>Vinum in aquam iniectum videtur &longs;ecundùm fu&longs;io<lb/>nem quandam per totum aquæ locum per meare; quod non fieret, ni&longs;i va<lb/>cua aquæ ine&longs;&longs;ent. </s><s>Lumen quoque alterum per alterum fertur: nam<emph.end type="italics"/>

<pb xlink:href="051/01/055.jpg" pagenum="24"/><emph type="italics"/>cùm plures lucernas quis accenderit, omnia magis illu&longs;tr abuntur, ijsdem <lb/>quoquò ver&longs;us per &longs;e invicem penetrantibus. </s><s>Sed & per æs, per ferrum, <lb/>& per alia corpora omnia penetratio fit; quemadmodum & quod in tor<lb/>pedine marina contingit.<emph.end type="italics"/></s>

<s>

<arrow.to.target n="marg72"/></s>

<s><margin.target id="marg72"/><emph type="italics"/>Argumen<lb/>ta aliorum <lb/><gap/>o vac<gap/>o.<emph.end type="italics"/></s>

<s>Hæ &longs;unt rationes Heronis, quibus probat. </s><s><emph type="italics"/><gap/>mne corpus ex <lb/>tenuibus con&longs;tare corporibus, inter quæ&longs;unt vacua di&longs;&longs;eminata particulis <lb/>minora.<emph.end type="italics"/> Quibus addi pote&longs;t vlteriùs, quòd eadem vacuola vi<lb/>dentur admittenda inter aquæ partes frigore con&longs;trictas in gla<lb/>ciem: etenim aqua in congelatione ad maius intervallum occu<lb/>pandum extenditur; va&longs;a enim licet benè compacta, &longs;ià &longs;inu <lb/>latiori in angu&longs;tum a&longs;&longs;urgant, & repleantur aquâ ad maximam il<lb/>lam latitudinem, vel vltra; in congelatione diffringuntur: non <lb/>&longs;ic, &longs;i infra illam latitudinem repleantur, vtdilatationi <expan abbr="&longs;pati&utilde;">&longs;patium</expan> de<lb/>tur. </s><s>In maioribus etiam va&longs;is, &longs;ed recurvo intus labro, validius <lb/>re&longs;i&longs;tentibus, ip&longs;a glacies curvatur, &longs;ur&longs;um &longs;ecundùm convexum <lb/>elevata. </s><s>Omnis etiam glacies aquæ iniecta &longs;uperna<gap/> Dila<lb/>tatur ergo in congelatione aqua, & vacuitates parvas intus ha<lb/>bet. </s>

<s>Addi præterea in confirmationem dictorum pote&longs;t duplex <lb/>Experimentum, vnum argenti vivi, alterum aquæ tubo inclusæ; <lb/>de quibus agemus infrà Cla&longs;se 1. cap. 6. Machina 7. Item expe<lb/>rimentum Thermo&longs;copij, de quo ibidem cap. 3. Mach 3. </s>

<s>

<arrow.to.target n="marg73"/></s>

<s><margin.target id="marg73"/><emph type="italics"/>Vis attra<lb/>ctiva quo<lb/>modo ab He <lb/>rone expli<lb/>cetur.<emph.end type="italics"/></s>

<s>Ex his alijsque argumentis atque experimentis, quæ vide<lb/>ri po&longs;&longs;unt apud alios, præ&longs;ertim Neotericos <expan abbr="noñullos">nonnullos</expan>, <expan abbr="cõ&longs;tare">con&longs;tare</expan> po<lb/>te&longs;t, quomodoex Heronis & <expan abbr="eor&utilde;">eorum</expan> &longs;ententia, qui <expan abbr="vacu&utilde;">vacuum</expan> admittunt, <lb/>Natura adnitatur trahere alia corpora, aquam præ&longs;ertim & aë<lb/>rem, ad vacuum replendum, quod vi extrin&longs;eca præter naturam <lb/>e&longs;t alicubi coacervatum; & quomodo corporibus omnibus in<lb/>&longs;it vis quædam attractiva, vt repleant vacuum illud; ac denique <lb/>quomodo vis attractiva corporum, aquæ inquam & aëris, cau&longs;a <lb/>e&longs;&longs;e po&longs;&longs;it ac principium Machinarum hydro-pnev<lb/>maticarum. </s><s>Lege Heronis Spiritalia. </s>

<s><emph type="center"/>Experimenta quibus vacuum nullum e&longs;&longs;e <lb/>probatur<emph.end type="center"/></s>

<s>HIs tamen non ob&longs;tantibus, communior & &longs;anior Philo&longs;o</s>

<s>

<arrow.to.target n="marg74"/><lb/>phorum Veterum ac Recentiorum &longs;en&longs;us e&longs;t, nullum in re<lb/>rum natura vacuum e&longs;&longs;e, neque coacervatum in vnum, neque <lb/>di&longs;&longs;eminatum inter partes corporum di&longs;ci&longs;&longs;as; & neque &longs;pontè <lb/>ortum, neque productum violenter; adeoque corporum tra<lb/>ctionem, quæ in allatis Experimentis elucet, non fieri ad replen<lb/>dum vacuum, quod nullibi &longs;t, neque e&longs;&longs;e pote&longs;t; &longs;ed ad impe<lb/>diendam, quam Natura tantopere abhorret, inanitatem. </s><s>Sua<lb/>dent hæc tum experientia Philo&longs;ophiæ Magi&longs;tra, tum rationes. </s><s><lb/>Experientias adducam paucas ex multis; rationes apud alios <lb/>leges. </s>

<s><margin.target id="marg74"/><emph type="italics"/>Argumen<lb/>ta contra <lb/>vacuum.<emph.end type="italics"/></s>

<s>Primò, Latera follium, &longs;i arctè con&longs;tricta &longs;int, & inter &longs;e <lb/>

<arrow.to.target n="marg75"/><lb/>contigua, nulla vi diduci po&longs;&longs;unt, etiam Angelica, &longs;i obturetur <lb/>orificium, per quod aër inter iectum inter diducenda latera &longs;pa<lb/>tium occupaturus &longs;ubeat. </s><s>Cur hoc, ni&longs;i quia vacuum dari non <lb/>pote&longs;t? quod tamen dari deberet, &longs;i occlu&longs;o orificio aër, & <lb/>quodcunque aliud corpus &longs;ubiturum excluderetur, & tamen la<lb/>tera diducerentur. </s><s>Eâdem de cau&longs;a duæ tabulæ plani&longs;&longs;imæ, <lb/>

<arrow.to.target n="marg76"/><lb/>& &longs;ibi mutuò &longs;ecundùm planitiem cohærentes, divelli non po&longs;<lb/>&longs;unt, &longs;i ita tentetur divul&longs;io, vt aër aut aliud corpus inter &longs;uper<lb/>ficies &longs;ubintrare tempe&longs;tivè non po&longs;&longs;it. </s><s><emph type="italics"/>Iuveni lacertorum &longs;uorum <lb/>robur iactanti<emph.end type="italics"/> (inquit P. Nicolaus Zucchius in &longs;ua de vacuo do<lb/>cti&longs;&longs;ima Diatribe) <emph type="italics"/>propo&longs;ita-&longs;emel e&longs;t lamina ærea per an&longs;am in me<lb/>dio extantem apprehen&longs;am elevanda è tabula marmorea, cui optimè con<lb/>gruebat: qui primò tanquam rem ludicram puero committendam con<lb/>temp&longs;it: tum in&longs;tantibus amicis manum vtramque admovens, cùm lu<lb/>ctatus diu hærentem non removi&longs;&longs;et, excu&longs;avit impotentiam, obiectâ <lb/>peregrini & potenti&longs;&longs;imi glutinis interpo&longs;itione, quo forti&longs;&longs;imè copulan<lb/>te nequiret divelli; donec vidit ab alio per tabulam facillimè laminam <lb/>deduci, & ad extrema productam, & actam in transver&longs;um, inde de<lb/>portari.<emph.end type="italics"/> Pa&longs;&longs;im etiam experimur, dum duo corpora &longs;ecundùm

<pb xlink:href="051/01/057.jpg" pagenum="26"/>planas &longs;uperficies coniuncta &longs;unt, vt vnum illorum elevatur, &longs;e<lb/>qui etiam alterum, quantumvis grave, atque in aëre libero ve<lb/>luti &longs;u&longs;pen&longs;um hærere. </s>

<s><margin.target id="marg75"/><emph type="italics"/>Latera fol<lb/>lium diauci <lb/>non po&longs;&longs;unt, <lb/>ore occlu&longs;e, <lb/>ob metum <lb/>vacus.<emph.end type="italics"/></s>

<s><margin.target id="marg76"/><emph type="italics"/>Tabulæ pla<lb/>næ metu va <lb/>cui divelli <lb/>non po&longs;&longs;unt.<emph.end type="italics"/></s>

<s>Secundò, Si vas vitreum aquæ immergas atque impleas & <lb/>

<arrow.to.target n="marg77"/><lb/>deinde intra aquam invertas, vt patens os deor&longs;um vergat, tum <lb/>æqualiter ita inver&longs;um eleves, & extrahere tentes; &longs;pectabis a<lb/>quam illo inclu&longs;am &longs;ur&longs;um intra illud &longs;imul attolli; & &longs;i vas illud <lb/>ex parte iam extractum, & ex parte adhuc immer&longs;um, manu &longs;u<lb/>&longs;tineas, videbis etiam aquam inclu&longs;am in illo per&longs;i&longs;tere &longs;ic eleva<lb/>tam &longs;upra ambientis aquæ &longs;uperficiem æquilibratam, & &longs;uo et<lb/>iam pondere manum &longs;u&longs;tinentis aggravare. Cur hoc? Quia <lb/>non pote&longs;t aër &longs;uccedere ad occupandum locum inter aquam <lb/>de&longs;cendentem, & partes va&longs;is, quæ aquâ de&longs;cendente de&longs;ere<lb/>rentur. Idem continget in quolibet alio va&longs;e, &longs;ed in vitreo et<lb/>iam oculis patebit experimentum. Quòd &longs;i in fundo va&longs;is fora<lb/>men aliquod &longs;it clau&longs;um, vt po&longs;&longs;it aperiri; eo aperto, & aëre li<lb/>berè &longs;ubintrante, aqua intra vas &longs;u&longs;pen&longs;um de&longs;cendet, & de&longs;i<lb/>net gravare manum. <lb/>

<arrow.to.target n="marg77"/><lb/>deinde intra aquam invertas, vt patens os deor&longs;um vergat, tum <lb/>æqualiter ita inver&longs;um eleves, & extrahere tentes; &longs;pectabis a<lb/>quam illo inclu&longs;am &longs;ur&longs;um intra illud &longs;imul attolli; & &longs;i vas illud <lb/>ex parte iam extractum, & ex parte adhuc immer&longs;um, manu &longs;u<lb/>&longs;tineas, videbis etiam aquam inclu&longs;am in illo per&longs;i&longs;tere &longs;ic eleva<lb/>tam &longs;upra ambientis aquæ &longs;uperficiem æquilibratam, & &longs;uo et<lb/>iam pondere manum &longs;u&longs;tinentis aggravare. </s><s>Cur hoc? </s><s> Quia <lb/>non pote&longs;t aër &longs;uccedere ad occupandum locum inter aquam <lb/>de&longs;cendentem, & partes va&longs;is, quæ aquâ de&longs;cendente de&longs;ere<lb/>rentur. </s><s>Idem continget in quolibet alio va&longs;e, &longs;ed in vitreo et<lb/>iam oculis patebit experimentum. </s><s>Quòd &longs;i in fundo va&longs;is fora<lb/>men aliquod &longs;it clau&longs;um, vt po&longs;&longs;it aperiri; eo aperto, & aëre li<lb/>berè &longs;ubintrante, aqua intra vas &longs;u&longs;pen&longs;um de&longs;cendet, & de&longs;i<lb/>net gravare manum. <lb/>

<arrow.to.target n="marg78"/></s>

<s><margin.target id="marg77"/><emph type="italics"/>Vas inver<lb/>&longs;um difficul <lb/>ter extrahi<lb/>tur ex aqua <lb/>ob vacui <lb/>metum.<emph.end type="italics"/></s>

<s><margin.target id="marg78"/><emph type="italics"/>Va&longs;a &longs;ub<gap/>s <lb/>pertu&longs;a, &longs;u<lb/>periùs occlu <lb/>&longs;a, aquam <lb/>retinent v<gap/><lb/>uí metu.<emph.end type="italics"/></s>

<s>Tertiò, In va&longs;is ad irrigandos hortos pa&longs;&longs;im adhiberi &longs;oli<lb/>tis (cuiu&longs;modi proponimus infrà Cla&longs;s. 1. cap. 6. Mach 2, & Cri<lb/>brum Ve&longs;talium vocamus) licet fundum ip&longs;orum &longs;it perforatum, <lb/>& multis foraminibus pervium, dum aquâ plena, æqualiter ele<lb/>vantur in libero aëre, aqua non defluit, quàm diu digitus fora<lb/>mini illorum &longs;upernè in collo patenti adpre&longs;&longs;us non permittit in<lb/>gre&longs;&longs;um aëri ad replendum locum, qui, &longs;i deflueret aqua, relin<lb/>queretur inter &longs;uperiorem va&longs;is &longs;uperficiem, & defluentem a<lb/>quam. Et in tali con&longs;i&longs;tentia permanente aquâ intra vas, tan<lb/>tum gravat, & deor&longs;um nititur aqua, quantum &longs;i fundo integro <lb/>& collo aperto, &longs;imul cum va&longs;e &longs;u&longs;tineretur. Remoto verò di<lb/>gito, & permi&longs;&longs;o ingre&longs;&longs;u aëri per &longs;uperius foramen, &longs;tatim de<lb/>fluit aqua ex fundi foraminibus. Quòd &longs;i in medio defluxu ite<lb/>rum appo&longs;ito digito foramen ob&longs;truatur, pendet iterum aqua, <lb/>contra inclinacionem &longs;uæ gravitatis, tunc etiam manum gra<lb/>vantis, nec defluit in apertum aërem. </s>

<s>Tertiò, In va&longs;is ad irrigandos hortos pa&longs;&longs;im adhiberi &longs;oli<lb/>tis (cuiu&longs;modi proponimus infrà Cla&longs;s. 1. cap. 6. Mach 2, & Cri<lb/>brum Ve&longs;talium vocamus) licet fundum ip&longs;orum &longs;it perforatum, <lb/>& multis foraminibus pervium, dum aquâ plena, æqualiter ele<lb/>vantur in libero aëre, aqua non defluit, quàm diu digitus fora<lb/>mini illorum &longs;upernè in collo patenti adpre&longs;&longs;us non permittit in<lb/>gre&longs;&longs;um aëri ad replendum locum, qui, &longs;i deflueret aqua, relin<lb/>queretur inter &longs;uperiorem va&longs;is &longs;uperficiem, & defluentem a<lb/>quam. </s><s>Et in tali con&longs;i&longs;tentia permanente aquâ intra vas, tan<lb/>tum gravat, & deor&longs;um nititur aqua, quantum &longs;i fundo integro <lb/>& collo aperto, &longs;imul cum va&longs;e &longs;u&longs;tineretur. </s><s>Remoto verò di<lb/>gito, & permi&longs;&longs;o ingre&longs;&longs;u aëri per &longs;uperius foramen, &longs;tatim de<lb/>fluit aqua ex fundi foraminibus. </s><s>Quòd &longs;i in medio defluxu ite<lb/>rum appo&longs;ito digito foramen ob&longs;truatur, pendet iterum aqua, <lb/>contra inclinacionem &longs;uæ gravitatis, tunc etiam manum gra<lb/>vantis, nec defluit in apertum aërem. </s>

<s>Quartò, Si fi&longs;tulæ vnam extremitatem aquæ immergas, </s>

Line 1242

Line 1284

<s><margin.target id="marg79"/><emph type="italics"/>Fi&longs;tula ex<lb/>&longs;ucto aëre <expan abbr="a-quã">a<lb/>quam</expan> recipit <lb/>vacui metu<emph.end type="italics"/></s>

<s>Quintò, Si phialam cupream firmis lateribus compactam, <lb/>

<arrow.to.target n="marg80"/><lb/>nè facilè rumpatur, igni admotam calefacias, vt aër intus con<lb/>tentus vehementer rarefiat, eamque deinde frigidæ immergas, <lb/>vt aër phialæ à violenta rarefactione &longs;e recolligens conden&longs;etur, <lb/>& minorem occupet locum; intus attrahitur aqua, dum alius <lb/>aër in locum <expan abbr="relinquend&utilde;">relinquendum</expan> &longs;uccedere non pote&longs;t, ne &longs;cilicet detur <lb/>vacuum in phiala. Sic &longs;i ex fi&longs;tula, cuius vnum orificium occlu<lb/>

<arrow.to.target n="marg80"/><lb/>nè facilè rumpatur, igni admotam calefacias, vt aër intus con<lb/>tentus vehementer rarefiat, eamque deinde frigidæ immergas, <lb/>vt aër phialæ à violenta rarefactione &longs;e recolligens conden&longs;etur, <lb/>& minorem occupet locum; intus attrahitur aqua, dum alius <lb/>aër in locum <expan abbr="relinquend&utilde;">relinquendum</expan> &longs;uccedere non pote&longs;t, ne &longs;cilicet detur <lb/>vacuum in phiala. </s><s>Sic &longs;i ex fi&longs;tula, cuius vnum orificium occlu<lb/>

<arrow.to.target n="marg81"/><lb/>&longs;um, alterum apertum, aut ex clave f&oelig;minea benè compacta, <lb/>ex&longs;ugas fortiter & continuato tractu aërem, & ce&longs;&longs;ante &longs;uctione <lb/>&longs;tatim apponas fi&longs;tulæ orificio patenti digitum aut labrum, nè <lb/>&longs;uccedat ambiens aër; attrahitur intra fi&longs;tulam, aut clavem, <lb/>caro digiti aut labri, vt notabiliter vellicet, & de carne depende<lb/>at. Non alia de cau&longs;a, ni&longs;i quia durante ex&longs;uctione rarefit rema<lb/>nens intus aër, & violenter <expan abbr="tot&utilde;">totum</expan> illud &longs;patium &longs;olus implet; ce&longs;<lb/>&longs;ante verò &longs;uctu recolligit &longs;e à violenta rarefactione, & <expan abbr="minor&etilde;">minorem</expan> <lb/>locum occupans advocat aliud, quod ip&longs;i proximum e&longs;t, ad lo<lb/>cum de&longs;ertum replendum. <expan abbr="Eadem&qacute;ue">Eademque</expan> cau&longs;a e&longs;t, cur cucurbi<lb/>

<arrow.to.target n="marg81"/><lb/>&longs;um, alterum apertum, aut ex clave f&oelig;minea benè compacta, <lb/>ex&longs;ugas fortiter & continuato tractu aërem, & ce&longs;&longs;ante &longs;uctione <lb/>&longs;tatim apponas fi&longs;tulæ orificio patenti digitum aut labrum, nè <lb/>&longs;uccedat ambiens aër; attrahitur intra fi&longs;tulam, aut clavem, <lb/>caro digiti aut labri, vt notabiliter vellicet, & de carne depende<lb/>at. </s><s>Non alia de cau&longs;a, ni&longs;i quia durante ex&longs;uctione rarefit rema<lb/>nens intus aër, & violenter <expan abbr="tot&utilde;">totum</expan> illud &longs;patium &longs;olus implet; ce&longs;<lb/>&longs;ante verò &longs;uctu recolligit &longs;e à violenta rarefactione, & <expan abbr="minor&etilde;">minorem</expan> <lb/>locum occupans advocat aliud, quod ip&longs;i proximum e&longs;t, ad lo<lb/>cum de&longs;ertum replendum. </s><s><expan abbr="Eadem&qacute;ue">Eademque</expan> cau&longs;a e&longs;t, cur cucurbi<lb/>

<arrow.to.target n="marg82"/><lb/>tulæ, quæ Chirurgis in v&longs;u e&longs;&longs;e &longs;olent, carnem &longs;ur&longs;um attrahant; <lb/>nimirum quia aêr, qui priùs igne incaluerat, & in raritatem abi<lb/>erat, extincta flamma frigiditatem & den&longs;itatem recipit, atque <lb/>in minorem contractus molem inane &longs;patium relinqueret, ni&longs;i <lb/>ad id replendum caro elevaretur. </s>

<s><margin.target id="marg80"/><emph type="italics"/>Phiala cale <lb/>facta, & a<lb/>quæ immer<lb/>&longs;a, attrahit <lb/>ip&longs;am va<lb/>cui metu.<emph.end type="italics"/></s>

Line 1259

Line 1301

<s>Atque hæc &longs;ecunda &longs;ententia, quæ Naturæ vacuum tan<lb/>toperè fugientis partes tuendas &longs;u&longs;cipit, meritò à melioris notæ <lb/>Philo&longs;ophis, vt olim, ita nunc quoque præfertur: quidquid ob-

<pb xlink:href="051/01/059.jpg" pagenum="28"/>ganniant Neoterici quidam, qui ne&longs;cio quo novitatis &longs;tudio in<lb/>

<arrow.to.target n="marg84"/><lb/>citati, <foreign lang="greek">xenodoci/as</foreign> vento inflati, nova quotidie dogmata cudere, <lb/>aut ob&longs;oleta <expan abbr="veter&utilde;">veterum</expan> commenta recoquere non verecundantur. <lb/>Satiùs enim ac faciliùs e&longs;&longs;e exi&longs;timatur, admittere contra di&longs;po<lb/>&longs;itiones particulares corporum gravium elevationem, levium <lb/>depre&longs;&longs;ionem, den&longs;iorum dilatationem, rariorum conden&longs;a<lb/>tionem, durorum inflectionem, & &longs;imilia, quàm vacuum, quod <lb/>Naturam adeo abhorrere con&longs;picitur, vt nulla vi naturalis agen<lb/>tis, nullo Machinæ artificio dari po&longs;&longs;it. Huiu&longs;modi autem na<lb/>turæ pugnas & &longs;tratagemata multa &longs;pectabis manife&longs;tè infrà in <lb/>multis Machinis, quibus hæc Naturæ inanitatem fugientis &longs;o<lb/>lertia &longs;ummam præbet commoditatem. Alia etiam paulò po&longs;t <lb/>afferam, &longs;i priùs, quæuam &longs;it vis illa Attractiva corporum, quâ <lb/>Natura vtitur ad vacuum impediendum, o&longs;tendero. </s>

<arrow.to.target n="marg84"/><lb/>citati, <foreign lang="greek">xenodoci/as</foreign> vento inflati, nova quotidie dogmata cudere, <lb/>aut ob&longs;oleta <expan abbr="veter&utilde;">veterum</expan> commenta recoquere non verecundantur. </s><s><lb/>Satiùs enim ac faciliùs e&longs;&longs;e exi&longs;timatur, admittere contra di&longs;po<lb/>&longs;itiones particulares corporum gravium elevationem, levium <lb/>depre&longs;&longs;ionem, den&longs;iorum dilatationem, rariorum conden&longs;a<lb/>tionem, durorum inflectionem, & &longs;imilia, quàm vacuum, quod <lb/>Naturam adeo abhorrere con&longs;picitur, vt nulla vi naturalis agen<lb/>tis, nullo Machinæ artificio dari po&longs;&longs;it. </s><s>Huiu&longs;modi autem na<lb/>turæ pugnas & &longs;tratagemata multa &longs;pectabis manife&longs;tè infrà in <lb/>multis Machinis, quibus hæc Naturæ inanitatem fugientis &longs;o<lb/>lertia &longs;ummam præbet commoditatem. </s><s>Alia etiam paulò po&longs;t <lb/>afferam, &longs;i priùs, quæuam &longs;it vis illa Attractiva corporum, quâ <lb/>Natura vtitur ad vacuum impediendum, o&longs;tendero. </s>

<s><margin.target id="marg84"/><emph type="italics"/>Vacuum da <lb/>rinaturali<lb/>ter non po<lb/>te&longs;t.<emph.end type="italics"/></s>

Line 1267

Line 1309

<s><emph type="center"/>Vis attractiva|ob vacui metum, primum Machinarum <lb/>hydro-pnevmaticarum principium, quæ, & qua<lb/>lis, quibusvè in&longs;it corporibus.<emph.end type="center"/></s>

<s>HÆ &longs;unt binæ de vacuo &longs;ententiæ, quarum vtraque fontium <lb/>artificialium, <expan abbr="aliarum&qacute;ue">aliarumque</expan> hydro-pnevmaticarum Machina<lb/>rum con&longs;tructioni, & effectuum mirabilium patrationi viam a<lb/>perit & &longs;ubmini&longs;trat arma; quamvis evidentiùs &longs;ecunda, quàm <lb/>prima, cui & illam idcirco prætulimus. Quæ&longs;tio tamen non le<lb/>

<arrow.to.target n="marg85"/><lb/>vis remanet inter &longs;ecundæ huius &longs;ententiæ fautores circa vim il<lb/>lam, quæ cogit corpora gravia accurrere ad vacuum impedi<lb/>endum, etiam contra propriam inclinationem; <expan abbr="dubitatur&qacute;ue">dubitaturque</expan>, <lb/>quibusnam illa vis in&longs;it ceu &longs;ubiectis; trahentibusnè, an tractis <lb/>corporibus? </s>

<s><margin.target id="marg85"/><emph type="italics"/>Vis attra<lb/>ctiva aquæ <lb/>quibus in&longs;it <lb/>corporibus.<emph.end type="italics"/></s>

<s>Alij enim putant, e&longs;&longs;e virtutem motivam ip&longs;is corporibus <lb/>

<arrow.to.target n="marg86"/><lb/>accurrentibus intrin&longs;ecam, quæ in bonum Vniver&longs;i corpora gra<lb/>via in altum, contra con&longs;uetum modum, ad vacuum impedien<lb/>dum, vrgeat atque impellat. At hoc experientia ip&longs;a &longs;atis con<lb/>vellit, & fal&longs;itatis arguit; &longs;iquidem, vt benè advertunt Cabæus

<arrow.to.target n="marg86"/><lb/>accurrentibus intrin&longs;ecam, quæ in bonum Vniver&longs;i corpora gra<lb/>via in altum, contra con&longs;uetum modum, ad vacuum impedien<lb/>dum, vrgeat atque impellat. </s><s>At hoc experientia ip&longs;a &longs;atis con<lb/>vellit, & fal&longs;itatis arguit; &longs;iquidem, vt benè advertunt Cabæus

<pb xlink:href="051/01/060.jpg" pagenum="29"/>& Zucchius, aqua <expan abbr="a&longs;cend&etilde;s">a&longs;cendens</expan> intra tubum, ad vacuum <expan abbr="impediend&utilde;">impediendum</expan> <lb/>

<arrow.to.target n="marg87"/><lb/>(quod in &longs;equentibus Machinis frequenti&longs;&longs;imum e&longs;t) tantundem <lb/>gravat, <expan abbr="quant&utilde;">quantum</expan> gravaret in libero aëre <expan abbr="&longs;u&longs;p&etilde;&longs;a">&longs;u&longs;pen&longs;a</expan>. Quòd benè adver<lb/>terejubet Cabæus illos, qui &longs;pecio&longs;o nimis nomine &longs;e Ingenie<lb/>ros appellari volunt; & Zucchius ait, &longs;e huius rei experimento <lb/>coëgi&longs;&longs;e, <emph type="italics"/>virum alioqui non ineruditum, vt fallaciam agno&longs;ceret in <lb/>via, quâ motum perpetuum &longs;e inveni&longs;&longs;e putabat, & iam dicandum Ma<lb/>gno Principi &longs;chema in æs incidi curaverat, &longs;upponendo aquam ad impe<lb/>diendum vacuum &longs;ua vi <expan abbr="a&longs;c&etilde;dentem">a&longs;cendentem</expan> non egere virtute æquilibrante, ne<lb/>dum &longs;uperante pondus illius, qua eget cùm &longs;i&longs;tenda vel elevanda e&longs;t in <lb/>aëre, liberè accurrente ad replendum &longs;patium inter eam, & alia corpora <lb/>relinquendum.<emph.end type="italics"/></s>

<arrow.to.target n="marg87"/><lb/>(quod in &longs;equentibus Machinis frequenti&longs;&longs;imum e&longs;t) tantundem <lb/>gravat, <expan abbr="quant&utilde;">quantum</expan> gravaret in libero aëre <expan abbr="&longs;u&longs;p&etilde;&longs;a">&longs;u&longs;pen&longs;a</expan>. </s><s>Quòd benè adver<lb/>terejubet Cabæus illos, qui &longs;pecio&longs;o nimis nomine &longs;e Ingenie<lb/>ros appellari volunt; & Zucchius ait, &longs;e huius rei experimento <lb/>coëgi&longs;&longs;e, <emph type="italics"/>virum alioqui non ineruditum, vt fallaciam agno&longs;ceret in <lb/>via, quâ motum perpetuum &longs;e inveni&longs;&longs;e putabat, & iam dicandum Ma<lb/>gno Principi &longs;chema in æs incidi curaverat, &longs;upponendo aquam ad impe<lb/>diendum vacuum &longs;ua vi <expan abbr="a&longs;c&etilde;dentem">a&longs;cendentem</expan> non egere virtute æquilibrante, ne<lb/>dum &longs;uperante pondus illius, qua eget cùm &longs;i&longs;tenda vel elevanda e&longs;t in <lb/>aëre, liberè accurrente ad replendum &longs;patium inter eam, & alia corpora <lb/>relinquendum.<emph.end type="italics"/></s>

<s><margin.target id="marg86"/><emph type="italics"/>Vis attra<lb/>ctiva non <lb/>ine&longs;t corpo<lb/>ribus attra <lb/>Hic.<emph.end type="italics"/></s>

Line 1283

Line 1325

<s>Alij igitur, & meliùs, exi&longs;timant, omnibus corporibus <lb/>

<arrow.to.target n="marg88"/><lb/>contiguis hanc ine&longs;&longs;e vim, à Natura attributam, ad Vniver&longs;i <lb/>bonum ac con&longs;ervationem, vt quotiescunque vnum illorum lo<lb/>co cedit, &longs;eu tractum ab extrin&longs;eco agente violenter, &longs;eu &longs;ponte <lb/>& innatâ inclinatione recedens, pondere videlicet, autlevitate: <lb/>trahat &longs;ecum alterum &longs;ibi contiguum, quantumvis reluctans, <lb/>quoties inter ip&longs;um & contiguum non pote&longs;t &longs;ubintrare corpus <lb/>aliud, quod partium Vniver&longs;i contiguitatem tueatur, & impedi<lb/>at inanitatem; adeoque trahentibus, non tractis corporibus <lb/>

<arrow.to.target n="marg89"/><lb/>vim illam motivam ine&longs;&longs;e. Et hanc vim appellant vim attracti<lb/>vam, e&longs;tque illa ip&longs;a quam nos primum <expan abbr="Machinar&utilde;">Machinarum</expan> hydro-pnev<lb/>maticarum principium &longs;eu fundamentum dicimus, vnaque e&longs;t <lb/>ex cau&longs;is vacui impeditivis. Dico, vna ex cau&longs;is, non enim v<lb/>nica e&longs;t via atque indu&longs;tria, quâ vacuum Natura evitare adni<lb/>titur. Modò enim vtitur prædicta vi attractiva: modò ad&longs;ci&longs;cit <lb/>operam alteratricium qualitatum, quæ corpora rarefaciunt, & <lb/>in ampliorem molem diffundunt: non nunquam magno impe<lb/>tu va&longs;a frangit, aut alia id genus media, prout occa&longs;io & nece&longs;<lb/>&longs;itas fert, accommodat: quin etiam haud rarò nullo motu, nulla <lb/>actione, nulla denique vi effectrice, &longs;ed per negativam <expan abbr="quandã">quandam</expan> <lb/>ob&longs;i&longs;tentiam vacuo repugnat; vt cùm Iatera follium compre&longs;&longs;a <lb/>clau&longs;o orificio, vt diximus &longs;uprà, divellinon &longs;init. Semper ta-

<arrow.to.target n="marg89"/><lb/>vim illam motivam ine&longs;&longs;e. </s><s>Et hanc vim appellant vim attracti<lb/>vam, e&longs;tque illa ip&longs;a quam nos primum <expan abbr="Machinar&utilde;">Machinarum</expan> hydro-pnev<lb/>maticarum principium &longs;eu fundamentum dicimus, vnaque e&longs;t <lb/>ex cau&longs;is vacui impeditivis. </s><s>Dico, vna ex cau&longs;is, non enim v<lb/>nica e&longs;t via atque indu&longs;tria, quâ vacuum Natura evitare adni<lb/>titur. </s><s>Modò enim vtitur prædicta vi attractiva: modò ad&longs;ci&longs;cit <lb/>operam alteratricium qualitatum, quæ corpora rarefaciunt, & <lb/>in ampliorem molem diffundunt: non nunquam magno impe<lb/>tu va&longs;a frangit, aut alia id genus media, prout occa&longs;io & nece&longs;<lb/>&longs;itas fert, accommodat: quin etiam haud rarò nullo motu, nulla <lb/>actione, nulla denique vi effectrice, &longs;ed per negativam <expan abbr="quandã">quandam</expan> <lb/>ob&longs;i&longs;tentiam vacuo repugnat; vt cùm Iatera follium compre&longs;&longs;a <lb/>clau&longs;o orificio, vt diximus &longs;uprà, divellinon &longs;init. </s><s>Semper ta-

<pb xlink:href="051/01/061.jpg" pagenum="30"/>men Natura in his, vtin cæteris rebus, <expan abbr="cõpendio">compendio</expan> &longs;tudet, & quan<lb/>tum pote&longs;t, facilioribus ac &longs;implicioribus vtitur medijs; vt &longs;i ad <lb/>fugam vacui corpus &longs;ur&longs;um attrahere, quàm den&longs;atione impedi<lb/>re promptius &longs;it, illud præ&longs;tat, non hoc; &longs;i contrà, hoc, non il<lb/>lud: item &longs;i per &longs;olum motum localem &longs;ine rarefactione corpus <lb/>aliunde trahere &longs;ufficit, rarefactioni parcit; alioquin vtrumque <lb/>mi&longs;cet. <lb/>

<arrow.to.target n="marg90"/></s>

Line 1304

Line 1346

<s>INfrà Cla&longs;se 1. cap. 1. Machina 11. Modum præ&longs;cribimus <expan abbr="aquã">aquam</expan> </s>

<s>

<arrow.to.target n="marg91"/><lb/>ad certam ac determinatam aliquam altitudinem evehendi, <lb/>eumque appellamus Siphonem inver&longs;um interruptum: qui mo<lb/>dus cùm nitatur vi Attractivâ orta ex vacui metu, multaque im<lb/>plicet notatu digni&longs;&longs;ima, & ad vim Attractivam penitiùs intelli<lb/>gendam omninò nece&longs;&longs;aria, hîc eum paulò fu&longs;iùs explicandum <lb/>cen&longs;ui; ibi enim breviter tantùm, & quantum ad praxin &longs;ufficit, <lb/>illum proponimus. Sit itaque in ci&longs;terna, puteo, pi&longs;cina, aut <lb/>va&longs;e quocunque B, aquâ pleno, elevanda ad pedes ex.g.cent&utilde; (di<lb/>co, exempli gratia, nam alioquin non pote&longs;t ad <expan abbr="tantã">tantam</expan> <expan abbr="altitudin&etilde;">altitudinem</expan> <lb/>attolli per vim attractivam) aqua in vas KA, quod &longs;it con&longs;titu-

<arrow.to.target n="marg91"/><lb/>ad certam ac determinatam aliquam altitudinem evehendi, <lb/>eumque appellamus Siphonem inver&longs;um interruptum: qui mo<lb/>dus cùm nitatur vi Attractivâ orta ex vacui metu, multaque im<lb/>plicet notatu digni&longs;&longs;ima, & ad vim Attractivam penitiùs intelli<lb/>gendam omninò nece&longs;&longs;aria, hîc eum paulò fu&longs;iùs explicandum <lb/>cen&longs;ui; ibi enim breviter tantùm, & quantum ad praxin &longs;ufficit, <lb/>illum proponimus. </s><s>Sit itaque in ci&longs;terna, puteo, pi&longs;cina, aut <lb/>va&longs;e quocunque B, aquâ pleno, elevanda ad pedes ex.g.cent&utilde; (di<lb/>co, exempli gratia, nam alioquin non pote&longs;t ad <expan abbr="tantã">tantam</expan> <expan abbr="altitudin&etilde;">altitudinem</expan> <lb/>attolli per vim attractivam) aqua in vas KA, quod &longs;it con&longs;titu-

<arrow.to.target n="fig3"/><lb/>tum in parte &longs;uperiore domus, <expan abbr="habeat&qacute;ue">habeatque</expan> epi&longs;tomium H, per <lb/>quod, vbi repletum fuerit vas, depleri po&longs;&longs;it. Fiat vas C, cu<lb/>iuscunque capacitatis (quamvis meliùs &longs;it, vt &longs;it æqualis capa<lb/>citatis cum va&longs;e KA, aut &longs;altem non minoris) ex eoque derive<lb/>tur ad vas KA, &longs;iphon &longs;eu tubus OI, qui in va&longs;e C, incipiat im<lb/>mediatè infra operculum ip&longs;ius, in va&longs;e verò KA, de&longs;inat paulò <lb/>infra eiu&longs;dem operculum, tantum ab illo di&longs;tans, quantum &longs;uf<lb/>ficit vt aër permeare po&longs;&longs;it. Deinde ex va&longs;e B, derivetur ad vas <lb/>KA, tubus BK; qui in va&longs;e B, incipiat paulò &longs;upra fundum ip&longs;i-

<arrow.to.target n="fig3"/><lb/>tum in parte &longs;uperiore domus, <expan abbr="habeat&qacute;ue">habeatque</expan> epi&longs;tomium H, per <lb/>quod, vbi repletum fuerit vas, depleri po&longs;&longs;it. </s><s>Fiat vas C, cu<lb/>iuscunque capacitatis (quamvis meliùs &longs;it, vt &longs;it æqualis capa<lb/>citatis cum va&longs;e KA, aut &longs;altem non minoris) ex eoque derive<lb/>tur ad vas KA, &longs;iphon &longs;eu tubus OI, qui in va&longs;e C, incipiat im<lb/>mediatè infra operculum ip&longs;ius, in va&longs;e verò KA, de&longs;inat paulò <lb/>infra eiu&longs;dem operculum, tantum ab illo di&longs;tans, quantum &longs;uf<lb/>ficit vt aër permeare po&longs;&longs;it. </s><s>Deinde ex va&longs;e B, derivetur ad vas <lb/>KA, tubus BK; qui in va&longs;e B, incipiat paulò &longs;upra fundum ip&longs;i-

<arrow.to.target n="fig4"/><lb/>us, in va&longs;e verò KA, de&longs;inat paulò infra operculum; vbi etiam <lb/>nonnihil in curvetur, vti in figura apparet. Tandem ex va&longs;e C, <lb/>derivetur alius tubus EF, cum epi&longs;tomio E, habens longitudi<lb/>nem paulò majorem longitudine tubi BK, capacitatem verò <lb/>&longs;eu amplitudinem eidem BK, omnino æqualem. Debent autem <lb/>omnes tres tubi diligenti&longs;&longs;imè <expan abbr="adferr&utilde;inari">adferruninari</expan> &longs;eu coarctari plum<lb/>bo, aliavè materia, &longs;uis va&longs;is in loco tran&longs;itus; & tam vas C, quam <lb/>vas KA, claudi <expan abbr="obturari&qacute;ue">obturarique</expan> vndiq, &longs;tudio&longs;i&longs;&longs;imè, nè aërem ali<lb/>unde, quàm per tubos, recipere aut ejicere valeant. His ita

<arrow.to.target n="fig4"/><lb/>us, in va&longs;e verò KA, de&longs;inat paulò infra operculum; vbi etiam <lb/>nonnihil in curvetur, vti in figura apparet. </s><s>Tandem ex va&longs;e C, <lb/>derivetur alius tubus EF, cum epi&longs;tomio E, habens longitudi<lb/>nem paulò majorem longitudine tubi BK, capacitatem verò <lb/>&longs;eu amplitudinem eidem BK, omnino æqualem. </s><s>Debent autem <lb/>omnes tres tubi diligenti&longs;&longs;imè <expan abbr="adferr&utilde;inari">adferruninari</expan> &longs;eu coarctari plum<lb/>bo, aliavè materia, &longs;uis va&longs;is in loco tran&longs;itus; & tam vas C, quam <lb/>vas KA, claudi <expan abbr="obturari&qacute;ue">obturarique</expan> vndiq, &longs;tudio&longs;i&longs;&longs;imè, nè aërem ali<lb/>unde, quàm per tubos, recipere aut ejicere valeant. </s><s>His ita

<pb xlink:href="051/01/064.jpg" pagenum="33"/>præparatis, impleatur vas C. aquâ per foramen O, immi&longs;&longs;o ip&longs;i <lb/>foramini iufundibulo; & vbi repletum fuerit, claudatur vt di<lb/>ctum. Deinde clau&longs;o epi&longs;tomio H, aperiatur epi&longs;tomium E, <lb/>tubi EF; <expan abbr="defluet&qacute;ue">defluetque</expan> aqua ex va&longs;e C, & in locum ip&longs;ius, nè va<lb/>cuum in va&longs;e admittatur, &longs;equetur per &longs;iphonem IO, aër in va<lb/>&longs;e KA, contentus; in locum verò aëris extracti è va&longs;e KA, &longs;eque<lb/>tur, propter vacui metum, aqua va&longs;is &longs;eu ci&longs;ternæ aut pi&longs;cinæ B, <lb/>per &longs;iphonem BK; & tam diu durabit a&longs;cen<gap/>s aquæ per <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> <lb/>BK, in vas KA, quàm diu de&longs;cendet aqua per &longs;iphonem EF ex va<lb/>&longs;e C. Lege quæ dicimus infrà loco cit. En ergo, quomodo aq ia, <lb/>ad vacuum impediendum, a&longs;cendat contra naturalem &longs;uam in<lb/>clinationem, & quomodo propter <expan abbr="eand&etilde;">eandem</expan> cau&longs;am aër de&longs;cendat. </s>

<pb xlink:href="051/01/064.jpg" pagenum="33"/>præparatis, impleatur vas C. aquâ per foramen O, immi&longs;&longs;o ip&longs;i <lb/>foramini iufundibulo; & vbi repletum fuerit, claudatur vt di<lb/>ctum. </s><s>Deinde clau&longs;o epi&longs;tomio H, aperiatur epi&longs;tomium E, <lb/>tubi EF; <expan abbr="defluet&qacute;ue">defluetque</expan> aqua ex va&longs;e C, & in locum ip&longs;ius, nè va<lb/>cuum in va&longs;e admittatur, &longs;equetur per &longs;iphonem IO, aër in va<lb/>&longs;e KA, contentus; in locum verò aëris extracti è va&longs;e KA, &longs;eque<lb/>tur, propter vacui metum, aqua va&longs;is &longs;eu ci&longs;ternæ aut pi&longs;cinæ B, <lb/>per &longs;iphonem BK; & tam diu durabit a&longs;cen<gap/>s aquæ per <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> <lb/>BK, in vas KA, quàm diu de&longs;cendet aqua per &longs;iphonem EF ex va<lb/>&longs;e C. </s><s>Lege quæ dicimus infrà loco cit. </s><s>En ergo, quomodo aq ia, <lb/>ad vacuum impediendum, a&longs;cendat contra naturalem &longs;uam in<lb/>clinationem, & quomodo propter <expan abbr="eand&etilde;">eandem</expan> cau&longs;am aër de&longs;cendat. </s>

<s><margin.target id="marg91"/><emph type="italics"/>Experimen <lb/>tum vim <lb/><expan abbr="attractivã">attractivam</expan> <lb/>o&longs;tendens <lb/>ad vacuum <lb/>impedien<lb/>dum.<emph.end type="italics"/></s>

Line 1319

Line 1361

<s><emph type="center"/>Notantur nonnulla circa prædictum experimentum, <expan abbr="&longs;i-mul&qacute;">&longs;i<lb/>mulque</expan>; &longs;tabilitur, in attractione aquæ metu vacui habendam <lb/>e&longs;&longs;e rationem perpendiculi aquarum.<emph.end type="center"/></s>

<s>DIximus, meliùs e&longs;&longs;e vt vas C, &longs;it æq<gap/>lis capacitatis cum va&longs;e <lb/>KA, aut&longs;altem non minoris: & præterea &longs;iphonem EF debe<lb/>re e&longs;&longs;e paulò longiorem &longs;iphone BK, capacitatis verò &longs;eu ampli<lb/>tudinis æqualis. Ratio quoad capacitatem va&longs;orum & &longs;ipho<lb/>num e&longs;t, quia tamdiu a&longs;cendit aqua per BK, quàm diu de&longs;cen<lb/>dit per EF, vt dixi (tam diu enim, & non ampliùs, duratvacui <lb/>metus, ob quam aqua a&longs;cendit per tubum BK:) &longs;i ergo vas C mi<lb/>nus e&longs;&longs;et quàm vas KA, aut tubus EF capacior quàm tubus BK; ef<lb/>flueret tota aqua ex C, antequam repleretur KA. Accedit & <lb/>hoc commodi ex æquali vtrorumque capacitate, quòd &longs;cire po&longs;<lb/>&longs;it apud C exi&longs;tens, quandonam plenum &longs;it vas KA; quando ni<lb/>mirum effluxerit tota aqua C. Ratio verò cur tubus EF, debeat <lb/>

<s>DIximus, meliùs e&longs;&longs;e vt vas C, &longs;it æq<gap/>lis capacitatis cum va&longs;e <lb/>KA, aut&longs;altem non minoris: & præterea &longs;iphonem EF debe<lb/>re e&longs;&longs;e paulò longiorem &longs;iphone BK, capacitatis verò &longs;eu ampli<lb/>tudinis æqualis. </s><s>Ratio quoad capacitatem va&longs;orum & &longs;ipho<lb/>num e&longs;t, quia tamdiu a&longs;cendit aqua per BK, quàm diu de&longs;cen<lb/>dit per EF, vt dixi (tam diu enim, & non ampliùs, duratvacui <lb/>metus, ob quam aqua a&longs;cendit per tubum BK:) &longs;i ergo vas C mi<lb/>nus e&longs;&longs;et quàm vas KA, aut tubus EF capacior quàm tubus BK; ef<lb/>flueret tota aqua ex C, antequam repleretur KA. </s><s>Accedit & <lb/>hoc commodi ex æquali vtrorumque capacitate, quòd &longs;cire po&longs;<lb/>&longs;it apud C exi&longs;tens, quandonam plenum &longs;it vas KA; quando ni<lb/>mirum effluxerit tota aqua C. </s><s>Ratio verò cur tubus EF, debeat <lb/>

<arrow.to.target n="marg92"/><lb/>e&longs;&longs;e longior tubo BK, patebit ex dicendis Protheoria IV. capite <lb/>2. Propo&longs;it. 13. interim hîc id confirmo hoc Experimento. Ac<lb/>cipe vas aquâ plenum, eique in&longs;ere &longs;iphonem inver&longs;um ABCD <lb/>æqualium crurium. Accipe deinde tubum rectum DE aquâ <lb/>plenum, eumque, obturato priùs ore E, in&longs;ere extremitati D,

<arrow.to.target n="marg92"/><lb/>e&longs;&longs;e longior tubo BK, patebit ex dicendis Protheoria IV. capite <lb/>2. Propo&longs;it. 13. interim hîc id confirmo hoc Experimento. </s><s>Ac<lb/>cipe vas aquâ plenum, eique in&longs;ere &longs;iphonem inver&longs;um ABCD <lb/>æqualium crurium. </s><s>Accipe deinde tubum rectum DE aquâ <lb/>plenum, eumque, obturato priùs ore E, in&longs;ere extremitati D,

<arrow.to.target n="fig5"/><lb/>cruris CD, & diligenter coarcta in<lb/>ter &longs;e&longs;e, nè aër inter <expan abbr="vtrumq;">vtrumque</expan> <expan abbr="trã&longs;ire">tran&longs;ire</expan> <lb/>po&longs;&longs;it. His factis aperios inferius. <lb/>Et &longs;i quidem tubus rectus DE lon<lb/>gior fuerit quàm crus AB à &longs;upre<lb/>ma &longs;uperficie aquæ va&longs;is <expan abbr="vsq;">vsque</expan> ad B; <lb/>effluet aqua ex E, <expan abbr="a&longs;cendet&qacute;ue">a&longs;cendetque</expan> a<lb/>qua va&longs;is A, per crus AB, <expan abbr="inde&qacute;ue">indeque</expan> <lb/>per CD, crus de&longs;cendet, donec <lb/>tota effluxerit ex ore E. Si aut de<lb/>urtetur tubus DE in F, fiatque <lb/>æqualis cruri AB; a&longs;endet aqua va<lb/>&longs;is A &longs;olùm u&longs;que ad B, quàm diu vi<lb/>delicet aqua ex F effluit; quâ elapsâ, <lb/>relabetur aqua cruris AB intra vas <lb/>A, Si idem tubus DE decurtetur <lb/>in G, aut H, <expan abbr="fiat&qacute;ue">fiatque</expan> brevior quàm <lb/>crus AB; a&longs;cendet aqua per AB &longs;o<lb/>lùm aliquòu&longs;que, & deinde rela<lb/>betur. Experientiam quilibet fa<lb/>cilè poterit facere. </s>

<arrow.to.target n="fig5"/><lb/>cruris CD, & diligenter coarcta in<lb/>ter &longs;e&longs;e, nè aër inter <expan abbr="vtrumq;">vtrumque</expan> <expan abbr="trã&longs;ire">tran&longs;ire</expan> <lb/>po&longs;&longs;it. </s><s>His factis aperios inferius. </s><s><lb/>Et &longs;i quidem tubus rectus DE lon<lb/>gior fuerit quàm crus AB à &longs;upre<lb/>ma &longs;uperficie aquæ va&longs;is <expan abbr="vsq;">vsque</expan> ad B; <lb/>effluet aqua ex E, <expan abbr="a&longs;cendet&qacute;ue">a&longs;cendetque</expan> a<lb/>qua va&longs;is A, per crus AB, <expan abbr="inde&qacute;ue">indeque</expan> <lb/>per CD, crus de&longs;cendet, donec <lb/>tota effluxerit ex ore E. </s><s>Si aut de<lb/>urtetur tubus DE in F, fiatque <lb/>æqualis cruri AB; a&longs;endet aqua va<lb/>&longs;is A &longs;olùm u&longs;que ad B, quàm diu vi<lb/>delicet aqua ex F effluit; quâ elapsâ, <lb/>relabetur aqua cruris AB intra vas <lb/>A, Si idem tubus DE decurtetur <lb/>in G, aut H, <expan abbr="fiat&qacute;ue">fiatque</expan> brevior quàm <lb/>crus AB; a&longs;cendet aqua per AB &longs;o<lb/>lùm aliquòu&longs;que, & deinde rela<lb/>betur. </s><s>Experientiam quilibet fa<lb/>cilè poterit facere. </s>

<s><margin.target id="marg92"/><emph type="italics"/>Experimë<lb/>tum aliud: <lb/>o&longs;tendens <lb/>vim attra<lb/>ctivam a<lb/>quæ in <expan abbr="alt&utilde;">altum</expan>.<emph.end type="italics"/></s>

<s>Nec &longs;ufficit vt tubus EF, &longs;upe<lb/>rioris figuræ &longs;it <expan abbr="quacunq;">quacunque</expan> ratione longior tubo BK, &longs;ed nece&longs;&longs;ari<lb/>um e&longs;t, vt <expan abbr="perpendicul&utilde;">perpendiculum</expan> ip&longs;ius EF, &longs;it longius quàm perpendicu<lb/>lum BK, hoc e&longs;t, vt tubus EF perpendiculariter de&longs;cendat <lb/>profundiùs infra vas C, quàm tubus BK a&longs;cendat perpendi<lb/>culariter &longs;upra vas B. Quare &longs;i tubus EF centum & vnius pe<lb/>

<arrow.to.target n="marg93"/><lb/>dum inclinaretur infra vas C, aut convolveretur in helicem, <lb/>vt hîc apparet, ita vt perpendiculum ip&longs;ius &longs;olùm e&longs;&longs;et pedum <lb/>v.g. 60. ab E v&longs;que ad D v.g. & non v&longs;que ad N; neutiquam <lb/>&longs;ufficeret; &longs;ed omnino nece&longs;&longs;arium e&longs;t, vt perpendiculum &longs;it <lb/>etiam ad minimùm centum pedum, & pertingat v&longs;que ad N. Et <lb/>hæc perpendiculi men&longs;ura adeo e&longs;t nece&longs;&longs;aria in hydraulicis hi<lb/>&longs;ce operationibus, vt Natura falli nulla arte, nullo dolo, <expan abbr="nulla&qacute;">nullaque</expan>; <lb/>experientia po&longs;&longs;it. Ioannes Bapti&longs;ta Porta lib. 2. Spirital. cap.

<arrow.to.target n="marg93"/><lb/>dum inclinaretur infra vas C, aut convolveretur in helicem, <lb/>vt hîc apparet, ita vt perpendiculum ip&longs;ius &longs;olùm e&longs;&longs;et pedum <lb/>v.g. 60. ab E v&longs;que ad D v.g. & non v&longs;que ad N; neutiquam <lb/>&longs;ufficeret; &longs;ed omnino nece&longs;&longs;arium e&longs;t, vt perpendiculum &longs;it <lb/>etiam ad minimùm centum pedum, & pertingat v&longs;que ad N. </s><s>Et <lb/>hæc perpendiculi men&longs;ura adeo e&longs;t nece&longs;&longs;aria in hydraulicis hi<lb/>&longs;ce operationibus, vt Natura falli nulla arte, nullo dolo, <expan abbr="nulla&qacute;">nullaque</expan>; <lb/>experientia po&longs;&longs;it. </s><s>Ioannes Bapti&longs;ta Porta lib. 2. Spirital. cap.

<arrow.to.target n="fig6"/><lb/>1. ait, &longs;e, cúm indigeret determi<lb/>nato perpendiculo infra vas de<lb/>&longs;cendente, nec locum haberet <lb/>ad demittendum perpendicula<lb/>riter tubum, multis viis tenta&longs;&longs;e, <lb/>vt defectum &longs;uppleret; præcipuè <lb/>verò duabus memoratis, nimi<lb/>rum inclinando primùm, deinde <lb/>in helicem convolvendo tubum <lb/>requi&longs;itæ longitudinis; &longs;ed nun<lb/>quam de&longs;ideratum effectum fu<lb/>i&longs;&longs;e con&longs;ecutum, nec vnquam <lb/>a&longs;cendi&longs;&longs;e aquam ad maiorem <lb/>altitudinem quàm erat perpen<lb/>diculum tubi inclinati, aut tor<lb/>tuo&longs;i. Demi&longs;it etiam infra vas <lb/>canalem capaciorem, licet bre<lb/>viorem illo, qui erat &longs;upra vas: <lb/>præterea loco vnius longioris <lb/>demi&longs;it multos breviores, qui &longs;i<lb/>mul &longs;uperabant longitudinem <lb/>&longs;uperioris; &longs;ed vano &longs;emper labore. Adeo &longs;ui juris tenax e&longs;t <lb/>Natura, & vt non fallit nos in &longs;uis operationibus, ita nec falli à <lb/>nobis vult. Infrà tamen Cla&longs;se 1. cap. 1. Machina 7. Modum do<lb/>cebo elevandi aquam ad quamvis <expan abbr="altitudin&etilde;">altitudinem</expan> perpendiculis bre<lb/>vibus multiplicatis, &longs;ed vtrisque, de&longs;cendentis nimirum & a&longs;cen<lb/>dentis aquæ. Notandum præterea e&longs;t hoc loco, Tubum OI, <lb/>aut CI, po&longs;&longs;e e&longs;&longs;e quantævis longitudinis, vt infrà iterum dicam <lb/>§. IX. Quomodo autem vi attractiva & expul&longs;iva &longs;imul elevari <lb/>po&longs;&longs;it aqua ad maiorem altitudinem quàm &longs;it perpen<lb/>diculum aquæ de&longs;cendentis, dicemus infrà <lb/>Protheoria II. </s>

<arrow.to.target n="fig6"/><lb/>1. ait, &longs;e, cúm indigeret determi<lb/>nato perpendiculo infra vas de<lb/>&longs;cendente, nec locum haberet <lb/>ad demittendum perpendicula<lb/>riter tubum, multis viis tenta&longs;&longs;e, <lb/>vt defectum &longs;uppleret; præcipuè <lb/>verò duabus memoratis, nimi<lb/>rum inclinando primùm, deinde <lb/>in helicem convolvendo tubum <lb/>requi&longs;itæ longitudinis; &longs;ed nun<lb/>quam de&longs;ideratum effectum fu<lb/>i&longs;&longs;e con&longs;ecutum, nec vnquam <lb/>a&longs;cendi&longs;&longs;e aquam ad maiorem <lb/>altitudinem quàm erat perpen<lb/>diculum tubi inclinati, aut tor<lb/>tuo&longs;i. </s><s>Demi&longs;it etiam infra vas <lb/>canalem capaciorem, licet bre<lb/>viorem illo, qui erat &longs;upra vas: <lb/>præterea loco vnius longioris <lb/>demi&longs;it multos breviores, qui &longs;i<lb/>mul &longs;uperabant longitudinem <lb/>&longs;uperioris; &longs;ed vano &longs;emper labore. </s><s>Adeo &longs;ui juris tenax e&longs;t <lb/>Natura, & vt non fallit nos in &longs;uis operationibus, ita nec falli à <lb/>nobis vult. </s><s>Infrà tamen Cla&longs;se 1. cap. 1. Machina 7. </s><s>Modum do<lb/>cebo elevandi aquam ad quamvis <expan abbr="altitudin&etilde;">altitudinem</expan> perpendiculis bre<lb/>vibus multiplicatis, &longs;ed vtrisque, de&longs;cendentis nimirum & a&longs;cen<lb/>dentis aquæ. </s><s>Notandum præterea e&longs;t hoc loco, Tubum OI, <lb/>aut CI, po&longs;&longs;e e&longs;&longs;e quantævis longitudinis, vt infrà iterum dicam <lb/>§. </s><s>IX. Quomodo autem vi attractiva & expul&longs;iva &longs;imul elevari <lb/>po&longs;&longs;it aqua ad maiorem altitudinem quàm &longs;it perpen<lb/>diculum aquæ de&longs;cendentis, dicemus infrà <lb/>Protheoria II. </s>

<s><margin.target id="marg93"/><emph type="italics"/>Perpendicu <lb/>lum aquæ <lb/>de&longs;cenden<lb/>tis debet e&longs;&longs;e <lb/>longius, <lb/>quàm a&longs;cen <lb/>dentis.<emph.end type="italics"/></s>

Line 1343

Line 1385

<s><margin.target id="marg94"/><emph type="italics"/>Error He<lb/>ronis.<emph.end type="italics"/></s>

<s>HEro Alexandrinus cap. 53. libri de Spiritalibus modum præ<lb/>&longs;cribit elevandi aquam per vim attractivam ex vacui metu; <lb/>&longs;ed vehementer hallucinatur, ob perpendiculi prædicti <expan abbr="defect&utilde;">defectum</expan>; <lb/>&longs;i tamen Heronis e&longs;t error ille, & non potiùs interpretis, qui &longs;che<lb/>ma appo&longs;uit, vt notavit etiam Ioannes Bapti&longs;ta Porta lib. 2. de <lb/>Spirital. cap. 2. Affero verba vnà cum Schemate Heronis, ex ver<lb/>&longs;ione & editione Federici Commandini Vrbinatis, qui ex Græco <lb/>in latinum eum tran&longs;tulit quem errorem repetit etiam Ioannes <lb/>Bapti&longs;ta Aleottus in ver&longs;ione Italica. </s>

<s>HEro Alexandrinus cap. 53. libri de Spiritalibus modum præ<lb/>&longs;cribit elevandi aquam per vim attractivam ex vacui metu; <lb/>&longs;ed vehementer hallucinatur, ob perpendiculi prædicti <expan abbr="defect&utilde;">defectum</expan>; <lb/>&longs;i tamen Heronis e&longs;t error ille, & non potiùs interpretis, qui &longs;che<lb/>ma appo&longs;uit, vt notavit etiam Ioannes Bapti&longs;ta Porta lib. 2. de <lb/>Spirital. cap. 2. </s><s>Affero verba vnà cum Schemate Heronis, ex ver<lb/>&longs;ione & editione Federici Commandini Vrbinatis, qui ex Græco <lb/>in latinum eum tran&longs;tulit quem errorem repetit etiam Ioannes <lb/>Bapti&longs;ta Aleottus in ver&longs;ione Italica. </s>

<s><emph type="italics"/>E&longs;t etiam alia con&longs;tructio,<emph.end type="italics"/> inquit Hero, <emph type="italics"/>in qua humidum &longs;en<lb/>&longs;im fertur, & manet, ita vt &longs;emper a&longs;cendens videatur.<emph.end type="italics"/><lb/>

<arrow.to.target n="fig7"/><lb/><emph type="italics"/>Sit ba&longs;is<emph.end type="italics"/> AB <emph type="italics"/>vndique præclu&longs;a, quæ dia<lb/>phragma habeat<emph.end type="italics"/> CD, <emph type="italics"/>& vitreum oper<lb/>culum Cylindri forma<emph.end type="italics"/> EF <emph type="italics"/>&longs;imiliter vndi<lb/>que præclu&longs;um. In operculo autem<emph.end type="italics"/> EF <emph type="italics"/>&longs;it <lb/>tubus<emph.end type="italics"/> GH, <emph type="italics"/>ab ip&longs;ius tecto parum di&longs;tans, <lb/>& &longs;imul perforatus cum diaphragmate. A<lb/>lius etiam tubus<emph.end type="italics"/> KL <emph type="italics"/>&longs;imul perforetur cum <lb/>tecto ba&longs;is, & à diaphragmate parum di&longs;tet. <lb/>In&longs;it autem ba&longs;i extra vitreum operculum <lb/>foramen<emph.end type="italics"/> M, <emph type="italics"/>per quod vas<emph.end type="italics"/> AB, <emph type="italics"/>impleatur: <lb/>& ba&longs;is<emph.end type="italics"/> AB <emph type="italics"/>ad fundum canalem habeat<emph.end type="italics"/><lb/>N. <emph type="italics"/>Sit præterea alius tubus<emph.end type="italics"/> XO, <emph type="italics"/>&longs;imul <lb/>perforatus cum diaphragmate, parumque <lb/>à ba&longs;i di&longs;tans, per quem implebitur vas<emph.end type="italics"/> CB. <lb/><emph type="italics"/>Itaque ob&longs;tructo canali<emph.end type="italics"/> N, <emph type="italics"/>aër qui e&longs;t in<emph.end type="italics"/> CB, <emph type="italics"/>per tubos, & per fora<lb/>men<emph.end type="italics"/> M <emph type="italics"/>excedet extra. Et cùm vas<emph.end type="italics"/> CB <emph type="italics"/>repletum fuerit, implebi<lb/>mus<emph.end type="italics"/> AD <emph type="italics"/>per foramen<emph.end type="italics"/> M, <emph type="italics"/>aër enim qui in ip&longs;o e&longs;t, per idem foramen <lb/>excedit. Si igitur canalem<emph.end type="italics"/> N <emph type="italics"/>fluere dimittamus, in locum<emph.end type="italics"/> CB <emph type="italics"/>exina<lb/>nitum, aër ex vitreo operculo procedet per tubum<emph.end type="italics"/> GH: <emph type="italics"/>in locum autem <lb/>vitrei operculi exinanitum ex<emph.end type="italics"/> AD <emph type="italics"/>humidum a&longs;cendet per tubum<emph.end type="italics"/> KL, <emph type="italics"/>&<emph.end type="italics"/>

<arrow.to.target n="fig7"/><lb/><emph type="italics"/>Sit ba&longs;is<emph.end type="italics"/> AB <emph type="italics"/>vndique præclu&longs;a, quæ dia<lb/>phragma habeat<emph.end type="italics"/> CD, <emph type="italics"/>& vitreum oper<lb/>culum Cylindri forma<emph.end type="italics"/> EF <emph type="italics"/>&longs;imiliter vndi<lb/>que præclu&longs;um. </s><s>In operculo autem<emph.end type="italics"/> EF <emph type="italics"/>&longs;it <lb/>tubus<emph.end type="italics"/> GH, <emph type="italics"/>ab ip&longs;ius tecto parum di&longs;tans, <lb/>& &longs;imul perforatus cum diaphragmate. </s><s>A<lb/>lius etiam tubus<emph.end type="italics"/> KL <emph type="italics"/>&longs;imul perforetur cum <lb/>tecto ba&longs;is, & à diaphragmate parum di&longs;tet. </s><s><lb/>In&longs;it autem ba&longs;i extra vitreum operculum <lb/>foramen<emph.end type="italics"/> M, <emph type="italics"/>per quod vas<emph.end type="italics"/> AB, <emph type="italics"/>impleatur: <lb/>& ba&longs;is<emph.end type="italics"/> AB <emph type="italics"/>ad fundum canalem habeat<emph.end type="italics"/><lb/>N. </s><s><emph type="italics"/>Sit præterea alius tubus<emph.end type="italics"/> XO, <emph type="italics"/>&longs;imul <lb/>perforatus cum diaphragmate, parumque <lb/>à ba&longs;i di&longs;tans, per quem implebitur vas<emph.end type="italics"/> CB. </s><s><lb/><emph type="italics"/>Itaque ob&longs;tructo canali<emph.end type="italics"/> N, <emph type="italics"/>aër qui e&longs;t in<emph.end type="italics"/> CB, <emph type="italics"/>per tubos, & per fora<lb/>men<emph.end type="italics"/> M <emph type="italics"/>excedet extra. </s><s>Et cùm vas<emph.end type="italics"/> CB <emph type="italics"/>repletum fuerit, implebi<lb/>mus<emph.end type="italics"/> AD <emph type="italics"/>per foramen<emph.end type="italics"/> M, <emph type="italics"/>aër enim qui in ip&longs;o e&longs;t, per idem foramen <lb/>excedit. </s><s>Si igitur canalem<emph.end type="italics"/> N <emph type="italics"/>fluere dimittamus, in locum<emph.end type="italics"/> CB <emph type="italics"/>exina<lb/>nitum, aër ex vitreo operculo procedet per tubum<emph.end type="italics"/> GH: <emph type="italics"/>in locum autem <lb/>vitrei operculi exinanitum ex<emph.end type="italics"/> AD <emph type="italics"/>humidum a&longs;cendet per tubum<emph.end type="italics"/> KL, <emph type="italics"/>&<emph.end type="italics"/>

<pb xlink:href="051/01/068.jpg" pagenum="37"/><emph type="italics"/>a<gap/>r per foramen<emph.end type="italics"/> M <emph type="italics"/>ingredietur. Atque hoc vsque eò fiet, quoad vitreum <lb/>operculum repletum fuerit. Oportebit autem loca<emph.end type="italics"/> AD, CB, EF, <emph type="italics"/>inter <lb/>&longs;e æqualia e&longs;&longs;e, vt ad invicem & aër, & humidum transferantur. Quan<lb/>do autem vas<emph.end type="italics"/> CB <emph type="italics"/>exinanitum fuertt, & con&longs;titerit aër is continuitas, <lb/>rur&longs;us ex vitreo operculo aqua in vas<emph.end type="italics"/> AD <emph type="italics"/>deferetur, aëre per canalem<emph.end type="italics"/><lb/>N, <emph type="italics"/>& per<emph.end type="italics"/> GH <emph type="italics"/>tubum in vitreum operculum ingrediente, qui verò <lb/>e&longs;t in vase<emph.end type="italics"/> AD <emph type="italics"/>aër per foramen<emph.end type="italics"/> M <emph type="italics"/>excedet.<emph.end type="italics"/></s>

<pb xlink:href="051/01/068.jpg" pagenum="37"/><emph type="italics"/>a<gap/>r per foramen<emph.end type="italics"/> M <emph type="italics"/>ingredietur. </s><s>Atque hoc vsque eò fiet, quoad vitreum <lb/>operculum repletum fuerit. </s><s>Oportebit autem loca<emph.end type="italics"/> AD, CB, EF, <emph type="italics"/>inter <lb/>&longs;e æqualia e&longs;&longs;e, vt ad invicem & aër, & humidum transferantur. </s><s>Quan<lb/>do autem vas<emph.end type="italics"/> CB <emph type="italics"/>exinanitum fuertt, & con&longs;titerit aër is continuitas, <lb/>rur&longs;us ex vitreo operculo aqua in vas<emph.end type="italics"/> AD <emph type="italics"/>deferetur, aëre per canalem<emph.end type="italics"/><lb/>N, <emph type="italics"/>& per<emph.end type="italics"/> GH <emph type="italics"/>tubum in vitreum operculum ingrediente, qui verò <lb/>e&longs;t in vase<emph.end type="italics"/> AD <emph type="italics"/>aër per foramen<emph.end type="italics"/> M <emph type="italics"/>excedet.<emph.end type="italics"/></s>

<s>Ita Hero; &longs;ed errat autip&longs;e, aut eius interpres: debete<lb/>nim canalis N de&longs;cendere infra vas perpendiculariter ad tantam <lb/>profunditatem, quanta e&longs;t longitudo KL, vt attrahatur tota a<lb/>qua va&longs;is AD; alioquin po&longs;tquam effluxerit aliquantulum a<lb/>quæ ex canali N, traxeritque aliquantulum aëris ex cylindro <lb/>EF, & aquæ ex va&longs;e AD, ce&longs;&longs;abit omnino aquæ fluxus, ob de<lb/>fectum perpendiculi æqualis perpendiculo KL, &longs;altem ab &longs;u<lb/>prema &longs;uperficie aquæ va&longs;is AD, v&longs;que ad orificium K tubi <lb/>prædict KL Qui defectus &longs;i &longs;uppleatur, &longs;equetur effectus de&longs;ide<lb/>ratus. Porta tamen loco citato, occa&longs;ione huius Heronianæ <lb/>indu&longs;triæ, alium excogita vit modum elevandi vi attractiva ex <lb/>inferiori ad &longs;uperius vas aquam: quem legere poteris apud <expan abbr="ips&utilde;">ipsum</expan>. </s>

<s>Ita Hero; &longs;ed errat autip&longs;e, aut eius interpres: debete<lb/>nim canalis N de&longs;cendere infra vas perpendiculariter ad tantam <lb/>profunditatem, quanta e&longs;t longitudo KL, vt attrahatur tota a<lb/>qua va&longs;is AD; alioquin po&longs;tquam effluxerit aliquantulum a<lb/>quæ ex canali N, traxeritque aliquantulum aëris ex cylindro <lb/>EF, & aquæ ex va&longs;e AD, ce&longs;&longs;abit omnino aquæ fluxus, ob de<lb/>fectum perpendiculi æqualis perpendiculo KL, &longs;altem ab &longs;u<lb/>prema &longs;uperficie aquæ va&longs;is AD, v&longs;que ad orificium K tubi <lb/>prædict KL Qui defectus &longs;i &longs;uppleatur, &longs;equetur effectus de&longs;ide<lb/>ratus. </s><s>Porta tamen loco citato, occa&longs;ione huius Heronianæ <lb/>indu&longs;triæ, alium excogita vit modum elevandi vi attractiva ex <lb/>inferiori ad &longs;uperius vas aquam: quem legere poteris apud <expan abbr="ips&utilde;">ipsum</expan>. </s>

Line 1359

Line 1401

<s>ALium errorem committit Hero lib. cit. de Spiritalibus cap. 5. </s>

<s>

<arrow.to.target n="marg95"/><lb/>&longs;i tamen & hic non e&longs;t ad&longs;cribendus interpreti. Docere <lb/>vult Hero modum elevandi atque attrahendi humidum ex va&longs;e <lb/>per &longs;iphonem inver&longs;um, cuius vnum crus &longs;it humido <expan abbr="immer&longs;&utilde;">immer&longs;um</expan>, <lb/>alterum extra vas promineat, non attrahendo prius per os no<lb/>&longs;trum aërem ex &longs;iphone, &longs;ed appendendo vas quodpiam aquâ <lb/>plenum: Sic ergo di&longs;currit. </s>

<arrow.to.target n="marg95"/><lb/>&longs;i tamen & hic non e&longs;t ad&longs;cribendus interpreti. </s><s>Docere <lb/>vult Hero modum elevandi atque attrahendi humidum ex va&longs;e <lb/>per &longs;iphonem inver&longs;um, cuius vnum crus &longs;it humido <expan abbr="immer&longs;&utilde;">immer&longs;um</expan>, <lb/>alterum extra vas promineat, non attrahendo prius per os no<lb/>&longs;trum aërem ex &longs;iphone, &longs;ed appendendo vas quodpiam aquâ <lb/>plenum: Sic ergo di&longs;currit. </s>

<s><margin.target id="marg95"/><emph type="italics"/>Error alius <lb/>Heronis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit &longs;merismation aliquod, cuius ma&longs;culum quidem apponatur <lb/>extrin&longs;eco &longs;iphonis cruri, ita vt per ip&longs;um fluat, &longs;itque<emph.end type="italics"/> TV; <emph type="italics"/>faminave-<emph.end type="italics"/>

<arrow.to.target n="fig8"/><lb/><emph type="italics"/>rò<emph.end type="italics"/> TYV <emph type="italics"/>priùs adglutinata va&longs;i<emph.end type="italics"/><lb/>LZ, <emph type="italics"/>quod paulò plùs aquæ, quàm <lb/>&longs;iphon capiat; habeat autem ad <lb/>fundum effluxionem<emph.end type="italics"/> <foreign lang="greek">*w</foreign> <emph type="italics"/>Quan<lb/>do igitur volumus per &longs;iphonem e<lb/>ducere aquam, quæ e&longs;t in va&longs;e<emph.end type="italics"/> AB, <lb/><emph type="italics"/>effluxionem va&longs;is<emph.end type="italics"/> LZ <emph type="italics"/>di<gap/>ito <expan abbr="cõ-prehendentes">con<lb/>prehendentes</expan>, ip&longs;um aquâ imple<lb/>bimus. Po&longs;tea f&oelig;mineum &longs;meri<lb/>&longs;ma ma&longs;culo aptantes effluxionem<emph.end type="italics"/><lb/><foreign lang="greek">*w</foreign> <emph type="italics"/>dimittemus. Evacuato au<lb/>tem<emph.end type="italics"/> LZ <emph type="italics"/>va&longs;e, aër in &longs;iphone <lb/>exi&longs;tens in evacuatum locum pro<lb/>cedet; quem con&longs;equetur humi<lb/>dum quod in va&longs;e<emph.end type="italics"/> AB, <emph type="italics"/>ita vt <expan abbr="&longs;iphõ">&longs;iphom</expan> <lb/>impleatur. Deinde aufferentes <lb/>vas<emph.end type="italics"/> LZ <emph type="italics"/>Siphonem fluere &longs;ine<lb/>mus. Oportet autem &longs;iphonem rectè de&longs;cendere, &longs;i officium &longs;uum præ<lb/>&longs;tare debeat; illud autem erit, quando ad va&longs;is<emph.end type="italics"/> AB <emph type="italics"/>labrum duas regu<lb/>las rectas compingemus, atque inter ip&longs;as intrin&longs;ecum &longs;iphonis crus <lb/>con&longs;tituemus, ita vt vtrasque contingat; ad idem verò &longs;iphonis crus <lb/>intrin&longs;ecum vtrimque clauvicuulam affigemus, regulas continentem <lb/>parte interiori: ita enim neque obliquum, neque in <gap/>nteriorem par<lb/>tem declinabit; rectò enim & exqui&longs;itè de&longs;cendet, claviculis regulas <lb/>atterentibus.<emph.end type="italics"/></s>

<arrow.to.target n="fig8"/><lb/><emph type="italics"/>rò<emph.end type="italics"/> TYV <emph type="italics"/>priùs adglutinata va&longs;i<emph.end type="italics"/><lb/>LZ, <emph type="italics"/>quod paulò plùs aquæ, quàm <lb/>&longs;iphon capiat; habeat autem ad <lb/>fundum effluxionem<emph.end type="italics"/> <foreign lang="greek">*w</foreign> <emph type="italics"/>Quan<lb/>do igitur volumus per &longs;iphonem e<lb/>ducere aquam, quæ e&longs;t in va&longs;e<emph.end type="italics"/> AB, <lb/><emph type="italics"/>effluxionem va&longs;is<emph.end type="italics"/> LZ <emph type="italics"/>di<gap/>ito <expan abbr="cõ-prehendentes">con<lb/>prehendentes</expan>, ip&longs;um aquâ imple<lb/>bimus. </s><s>Po&longs;tea f&oelig;mineum &longs;meri<lb/>&longs;ma ma&longs;culo aptantes effluxionem<emph.end type="italics"/><lb/><foreign lang="greek">*w</foreign> <emph type="italics"/>dimittemus. </s><s>Evacuato au<lb/>tem<emph.end type="italics"/> LZ <emph type="italics"/>va&longs;e, aër in &longs;iphone <lb/>exi&longs;tens in evacuatum locum pro<lb/>cedet; quem con&longs;equetur humi<lb/>dum quod in va&longs;e<emph.end type="italics"/> AB, <emph type="italics"/>ita vt <expan abbr="&longs;iphõ">&longs;iphom</expan> <lb/>impleatur. </s><s>Deinde aufferentes <lb/>vas<emph.end type="italics"/> LZ <emph type="italics"/>Siphonem fluere &longs;ine<lb/>mus. </s><s>Oportet autem &longs;iphonem rectè de&longs;cendere, &longs;i officium &longs;uum præ<lb/>&longs;tare debeat; illud autem erit, quando ad va&longs;is<emph.end type="italics"/> AB <emph type="italics"/>labrum duas regu<lb/>las rectas compingemus, atque inter ip&longs;as intrin&longs;ecum &longs;iphonis crus <lb/>con&longs;tituemus, ita vt vtrasque contingat; ad idem verò &longs;iphonis crus <lb/>intrin&longs;ecum vtrimque clauvicuulam affigemus, regulas continentem <lb/>parte interiori: ita enim neque obliquum, neque in <gap/>nteriorem par<lb/>tem declinabit; rectò enim & exqui&longs;itè de&longs;cendet, claviculis regulas <lb/>atterentibus.<emph.end type="italics"/></s>

<s>Hæc Hero; quæ tamen fal&longs;a &longs;unt, & contraria experien<lb/>tiæ, rationi, & hydro-pnevmaticis principijs. Ni&longs;i enim va&longs;is <lb/>altitudo ab V ad <foreign lang="greek">*w</foreign> tanta &longs;it, quantum e&longs;t crus internum CD <lb/>Siphonis; non a&longs;cendet aqua per crus CD, ni&longs;i ad tantam al<lb/>titudinem, quanta e&longs;t altitudo va&longs;is prædicta ab Y, v&longs;que ad <foreign lang="greek">*w</foreign>. <lb/>Et ratio e&longs;t, quia cùm perpendiculum Y <foreign lang="greek">*w</foreign> minus &longs;it, quàm <lb/>perpendiculum CD; non pote&longs;t aqua attolli ad altitudinem <lb/>CD, &longs;ed po&longs;tquam a&longs;cenderit ad altitudinem æqualem perpen<lb/>diculo Y <foreign lang="greek">*w</foreign>, relabetur intra vas AB. Ioannes Bapti&longs;ta Porta

<s>Hæc Hero; quæ tamen fal&longs;a &longs;unt, & contraria experien<lb/>tiæ, rationi, & hydro-pnevmaticis principijs. </s><s>Ni&longs;i enim va&longs;is <lb/>altitudo ab V ad <foreign lang="greek">*w</foreign> tanta &longs;it, quantum e&longs;t crus internum CD <lb/>Siphonis; non a&longs;cendet aqua per crus CD, ni&longs;i ad tantam al<lb/>titudinem, quanta e&longs;t altitudo va&longs;is prædicta ab Y, v&longs;que ad <foreign lang="greek">*w</foreign>. </s><s><lb/>Et ratio e&longs;t, quia cùm perpendiculum Y <foreign lang="greek">*w</foreign> minus &longs;it, quàm <lb/>perpendiculum CD; non pote&longs;t aqua attolli ad altitudinem <lb/>CD, &longs;ed po&longs;tquam a&longs;cenderit ad altitudinem æqualem perpen<lb/>diculo Y <foreign lang="greek">*w</foreign>, relabetur intra vas AB. </s><s>Ioannes Bapti&longs;ta Porta

<pb xlink:href="051/01/070.jpg" pagenum="39"/>lib. 2. de &longs;pirital. cap. 3. ait. aquam non effluxuram è va&longs;e LZ, ab<lb/>

<arrow.to.target n="marg96"/><lb/>lato impedimento apud <foreign lang="greek">*w</foreign>, propter defectum &longs;cilicet perpendi<lb/>culi prædicti. Sed ratio & experientia convincit, effluere aquam <lb/>è va&longs;e; & a&longs;cendere aquam per crus internum ad altitudinem ex<lb/>plicatam; quod ip&longs;emet Porta alibi fatetur. </s>

<arrow.to.target n="marg96"/><lb/>lato impedimento apud <foreign lang="greek">*w</foreign>, propter defectum &longs;cilicet perpendi<lb/>culi prædicti. </s><s>Sed ratio & experientia convincit, effluere aquam <lb/>è va&longs;e; & a&longs;cendere aquam per crus internum ad altitudinem ex<lb/>plicatam; quod ip&longs;emet Porta alibi fatetur. </s>

<s><margin.target id="marg96"/><emph type="italics"/>Error Ioan<lb/>nis Bapti&longs;tæ <lb/>Porta.<emph.end type="italics"/></s>

<s>Ut igitur ex va&longs;e AB extrahi po&longs;&longs;it aqua per &longs;iphonem ab&longs;<lb/>que eo quòd ore attrahatur aër, oportet loco Va&longs;is LZ adhibere <lb/>tubum tantæ longitudinis, quantæ e&longs;t crus CD, imò paulò ma<lb/>joris: tunc enim effluente aquâ ex tubo appen&longs;o a&longs;cendet paula<lb/>tim aqua per &longs;iphonem, donec pervenerit u&longs;que ad &longs;ignum V, <lb/>quod &longs;uppono e&longs;&longs;e &longs;emper demi&longs;&longs;ius quàm e&longs;t &longs;uprema &longs;uperfi<lb/>cies aquæ in Va&longs;e AB: tunc enim &longs;i aufferatur tubus appen&longs;us, ef<lb/>fluxus aquæ ex &longs;iphone tam diu durabit, donec tota aqua ex <lb/>va&longs;e AB effluxerit, &longs;i os C ad fundum v&longs;que va&longs;is pertigerit. </s><s>Vi<lb/>de Salomonem de Caus lib. 1. de viribus motricibus. </s><s>Vide præ<lb/>terea quæ &longs;cribimus de fluxu aquæ per &longs;iphones infrà Protheo<lb/>ria IV. Cap. 2. præ&longs;ertim Propo&longs;it. </s><s>XI. ubi in Annotatione 2. no<lb/>tamus errorem Marini Mer&longs;enni <expan abbr="&longs;imil&etilde;">&longs;imilem</expan> prædicti Heronis errori. </s>

<s>Monuit hîc, & optimè, <expan abbr="acuti&longs;&longs;ime&qacute;ue">acuti&longs;&longs;imeque</expan> P. Paulus Ca&longs;atus <lb/>Mathe&longs;eos in Romano no&longs;tro Collegio Profe&longs;&longs;or, quæ diximus <lb/>contra Heronem hoc loco, tunc &longs;olùm haberelocum, quando <lb/>&longs;uprema aquæ &longs;uperficies non e&longs;&longs;et multùm &longs;upra punctum C. </s><s><lb/>Cæterùm &longs;i vas AB e&longs;t plenum, & <expan abbr="perpendicul&utilde;">perpendiculum</expan> <foreign lang="greek">*y*w</foreign> &longs;uperat per<lb/>pendiculum à &longs;uprema aquæ &longs;uperficie u&longs;q<gap/> ad D; poterit a&longs;cen<lb/>dere aqua, & per crus DY defluere<gap/> quâ &longs;emel defluente, &longs;em<lb/>per deinde defluet, donec evacuetur vas vsque ad punctum C, <lb/>quoniam perpendiculum DY &longs;emper manebit longius quàm <lb/>perpendiculum CD. </s>

<s><emph type="center"/>In aquarum elevatione vi attractivâ, habenda e&longs;t ratio <lb/>perpendiculi &longs;olùm illorum tuborum, per quos aqua, <lb/>non per quos aër vehitur.<emph.end type="center"/><lb/>

<arrow.to.target n="marg97"/></s>

<s><margin.target id="marg97"/><emph type="italics"/>Tubi per <lb/>quos aër de<lb/>fertur in<emph.end type="italics"/></s>

<s>NOtat optimè Ioannes Bapti&longs;ta Porta lib 2. de Spiritalibus. C. 6. <lb/>& nos etiam &longs;uprà in fine §. VI. in&longs;inuavimus, in Machinis </s>

<s>

<arrow.to.target n="marg98"/><lb/>

<arrow.to.target n="fig9"/><lb/>vi attractiva elevan<lb/>tibus aquam, haben<lb/>dam e&longs;&longs;e rationem <lb/>longitudinis ac bre<lb/>vitatis &longs;olùm illorum <lb/>tuborum &longs;eu canali<lb/>um, qui conferunt <lb/>ad aquarum perpen<lb/>diculum, & per quos <lb/>tran&longs;ire debet aqua, <lb/>atque adeo quorum <lb/>aquæ &longs;e mutuò tra<lb/>here ac v<gap/> de<lb/>bent, <gap/><lb/>quoru<gap/><lb/>&longs;olù<gap/><lb/>bet. </s><s><gap/>eli<lb/>ùs intelligatur, in<gap/><lb/>ciat<gap/> figura porta <lb/>&longs;uprà §. citato, in qua <lb/>figura h<gap/>enda e&longs;t <lb/>&longs;olùm ratio <expan abbr="tubor&utilde;">tuborum</expan> <lb/>BK, & EF; hi enim <lb/>duo continent aquas <lb/>quarum perpendi<lb/>cula ad invicem pu<lb/>gnant, juxta dicenda infrà Protheoria IV. cap. 2. Propo&longs;it. 13. <lb/>tubus verò OI pote&longs;t e&longs;&longs;e quantævis longitudinis aut brevita<lb/>tis, ac proinde vas C pote&longs;t e&longs;&longs;e & infra & &longs;upra vas B. </s><s>Patet <lb/>hoc experientia, vt dicemus loco citato; vbi etiam experientiæ <lb/>cau&longs;am dabimus. </s>

<s><margin.target id="marg98"/><emph type="italics"/>Machinis <lb/>attractivis <lb/>metu vacui <lb/>po&longs;&longs;unt e&longs;&longs;e <lb/>quantævis <lb/>longitudinis<emph.end type="italics"/></s>

<s><emph type="center"/>Vi attractivâ elevari pote&longs;t aqua vltra perpen<lb/>culi altitudinem, aëre mediante.<emph.end type="center"/></s>

<s>Ingenio&longs;&longs;imum &longs;anè modum <expan abbr="Naturã">Naturam</expan> quodamodo decipiendi, <lb/>& aquam vltra perpendiculi à Natura requi&longs;iti altitudinem e<lb/>levandi vi attractiva, affert Porta loco proximè citato, cap. 11. <lb/>aitque &longs;e illum ca&longs;u reperi&longs;&longs;e inter cont<gap/>uas hydraulicas atque <lb/>pnevmaticas experientias quas fecit. Fit hoc aëre mediante, <lb/>aquæ immi&longs;to. Hac ratione, inquit Porta, perpendiculo 50. <lb/>pedum elevari pote&longs;t aqua ad altitudinem pedum 80. Modus <lb/>hic e&longs;t. </s>

<s>Sit ex va&longs;e AB portatili e<lb/>

<arrow.to.target n="marg99"/><lb/>levanda aqua ad vas D, ad alti<lb/>tudinem pedum 80. Fiat canalis <lb/>vitreus GK (vt&longs;pectari, oculis<lb/>que percipi manife&longs;tè po&longs;&longs;itar<lb/>tificium) vtrimque apertus, & <lb/>va&longs;i D optimè coarctatus a<lb/>pud K. Fiat deinde vas C, æ<lb/>qualis aut maioris capacitatis, <lb/>quàm vas D; <expan abbr="in&longs;eratur&qacute;ue">in&longs;eraturque</expan> v<lb/>trique canalis PQ vtrimque a<lb/>pertus immediatè &longs;ub operculis <lb/>&longs;eu tectis va&longs;orum. Tandem <lb/>ex va&longs;e C de&longs;cendat perpendi<lb/>culariter canalis EF quinqua<lb/>ginta pedum longitudinis, ha<lb/>bens epi&longs;tomium E, & &longs;it opti<lb/>mè adferruminatus fundo va&longs;is C. His factis, impleantur va&longs;a <lb/>AB, & C, aquâ, <expan abbr="admoveatur&qacute;ue">admoveaturque</expan> vas AB tubo GK, ita vt o<lb/>&longs;culum G &longs;it aquæ immer&longs;um, & aperiatur epi&longs;tomium E; de<lb/>&longs;cendet aqua ex va&longs;e C, &longs;ecumque trahet aërem ex tubis QP, <lb/>& KG, & ex va&longs;e D, &longs;imulque aquam ex va&longs;e AB. Po&longs;tquam <lb/>a&longs;cenderit aqua intra canalem GK v&longs;que ad aliquod &longs;patium <lb/>exiguum, v.g. v&longs;que ad H; remove aliquantulùm vas AB; & <lb/>aqua canalis a&longs;cendet vlteriús, tracta &longs;cilicet ab aqua effluente <lb/>per FE) & po&longs;t aquam &longs;equetur aër. Admove deinde iterum

<arrow.to.target n="fig10"/><lb/>vas AB, & attrahetur alia aqua, <lb/><expan abbr="erit&qacute;ue">eritque</expan> aër HI inter aquam <lb/>GH, & IM. Iterum remove vas <lb/>AB, & ingredietur per os G alius <lb/>aër, &longs;equeturque aquam. Quo <lb/>facto, &longs;i vas iterum admôris, <expan abbr="di-ctamq;">di<lb/>ctamque</expan> operationem repetive<lb/>ris; a&longs;cendent tandem aqua & <lb/>aër mi&longs;ti inter &longs;e, v&longs;que ad vas D, <lb/>illudque replebunt, <expan abbr="antequã">antequam</expan> ef<lb/>fluat tota aqua va&longs;is C, quod ob <lb/>id minus e&longs;&longs;e debet quam vas D. </s>

<s><margin.target id="marg99"/><emph type="italics"/>Experimen <lb/>tum Porta <lb/>ad aquam <lb/>elevandam <lb/>vltra <expan abbr="perp&etilde;-diculi">perpen<lb/>diculi</expan> alti<lb/>tudinem.<emph.end type="italics"/></s>

<s>Procedendum e&longs;t autem <lb/>valde cautè in hoc negotio, nè <lb/>nimium aéris ingrediatur per os <lb/>G, & levitate &longs;ua &longs;ur&longs;um ten<lb/>dens pellat modicam aquam <lb/>antea in tromiffam, repleatque totum canalem GK, &longs;icque de<lb/>&longs;truatur continuitas aquæ & aëris intra canalem: hoc enim &longs;i <lb/>fieret, non repleretur vas D, ni&longs;i po&longs;t longi&longs;&longs;imum tempus, & <lb/>multas operationes, deberetque &longs;æpius repleri vas C. Nun<lb/>quam præterea tantum aquæ &longs;imul continere debet canalis <lb/>GK, vt ejus perpendiculum &longs;uperet perpendiculum aquæ ca<lb/>n alis EF. Ex hac praxi deducit Porta modum mirabilem, & <lb/>omnibus antiquis ignotum, ut ip&longs;e ait, elevandi per &longs;iphonem <lb/>inver&longs;um aquam è montis radice ad ejus verticem; quem mo<lb/>dum afferam infrà Protheoria IV. cap. 2. Propo&longs;it. 12. ex <lb/>quo etiam loco meliùs intelligetur hoc <lb/>præ&longs;ens Experimentum. </s>

<s><emph type="center"/>Protheoria II.<emph.end type="center"/></s>

<s><emph type="center"/>PROTHEORIA <lb/>SECVNDA.<emph.end type="center"/></s>

<s><emph type="center"/>De vi Expul&longs;iva propter corporum impe<lb/>netrabilitatem; &longs;eu de &longs;ecundo Machinarum Hy<lb/>dropnevmaticarum principio.<emph.end type="center"/></s>

<s><emph type="center"/>Omnia Vniver&longs;i corpora &longs;unt inter &longs;e <lb/>contigua.<emph.end type="center"/></s>

<s>COrpora omnia, quæ DEVS Optimus Maximus <lb/>

<arrow.to.target n="marg100"/><lb/>in prima rerum conditione intra præ&longs;titutum in Vni<lb/>ver&longs;i ambitu conclu&longs;it locum, C&oelig;lum dico, Elemen<lb/>ta, & Mixta, tali &longs;unt ordine di&longs;po&longs;ita, ut multi, nec <lb/>vulgares Philo&longs;ophi, exi&longs;timent, motum localem in Mundo non <lb/><expan abbr="futur&utilde;">futurum</expan> ullum, ni&longs;i aut concedatur di&longs;per&longs;um per omnia vacuum <lb/>(quale vidimus invehere Heronem, alio&longs;que nonnullos) aut <lb/>corporum mutua penetratio, aut rerum omnium commotio, <lb/>atque permixtio. Audi Epicurum apud Diogenem Laêrtium <lb/>lib. 10. in Epi&longs;tola ad Herodotum, ubi ait. <foreign lang="greek">*ei) de\ mh\ h)_n o( kai\ xeno\s, kai\ <lb/>xw/<gap/>an, kai\ a)naf<gap/> fu/sin o)noma/comen, <gap/>x a)/n ei)_xe ta\ sw/mata o(/p<gap/>n <gap/>de\ di) <gap/><lb/>exinei_to, xa<gap/>a/pe<gap/> fa/inetw xin<gap/>mena</foreign> <emph type="italics"/>Ni&longs;i verò id e&longs;&longs;et quoque, quod & <lb/>inane,<emph.end type="italics"/> &longs;eu vacuum, <emph type="italics"/>& regionem,<emph.end type="italics"/> &longs;eu &longs;patium, <emph type="italics"/>ac locum & intacti<lb/>lem<emph.end type="italics"/> &longs;ive in corpoream <emph type="italics"/>naturam vocamus; non haberent corpora ne<lb/>que ubi e&longs;&longs;ent, neque quà motus &longs;uos obirent; cùm moveri ea quidem <lb/>manife&longs;tum &longs;it.<emph.end type="italics"/></s>

<s><margin.target id="marg100"/><emph type="italics"/>Corpora o<lb/>mnia Vni<lb/>ver&longs;i conti<lb/>gua inter &longs;e.<emph.end type="italics"/></s>

<s>Hanc autem, quam petitam ex motu rationem in&longs;inuat <lb/>

<arrow.to.target n="marg101"/><lb/>&longs;olummodò Epicurus, deducunt manife&longs;tiùs Democritus atque <lb/>Leucippus (quos &longs;ecutus e&longs;t Epicurus) apud Ari&longs;totelem lib. 4. <lb/>Phy&longs;. tex. 6. (ubi etiam alteram de corporum penetratione ur<lb/>gent) his verbis <foreign lang="greek"><gap/> ga\<gap/> a)\n doxo/ih ei)/nai ei) m<gap/> xeno\n. to\ ga/<gap/> pl<gap/>es a)du/na<lb/>ton ei)/nai de/ca<gap/></foreign>, &c. <emph type="italics"/>Non videtur quippe e&longs;&longs;e motus, ni&longs;i &longs;it inane. <lb/>Quod enim plenum e&longs;t, admittere in &longs;e mobile non pote&longs;t. Nam &longs;i ad-<emph.end type="italics"/>

<arrow.to.target n="marg102"/><lb/><emph type="italics"/>mittat, & fuerint in eodem loco duo corpora; nihil repugnabit, quò mi<lb/>nùs quotquot libuerit, &longs;imul &longs;int; quia dici, cur id non valeat evenire, <lb/>minimè pote&longs;t. Sin autem eveniat, tunc quod minimum, id admittet <lb/>quod maximum; quando ip&longs;um magnum multa parva e&longs;t: adeo ut &longs;i <lb/>multa æqualia in eodem e&longs;&longs;e contigerit, e&longs;&longs;e & in æqualia contingat.<emph.end type="italics"/> Ean<lb/>dem <expan abbr="con&longs;ecution&etilde;">con&longs;ecutionem</expan> deducit Lucretius in &longs;ua ver&longs;ibus ligata Phi<lb/>

<arrow.to.target n="marg103"/><lb/>lo&longs;ophia; additque non &longs;olùm, &longs;i Inane &longs;eu Vacuum non admit<lb/>tatur, rem nullam exijs quæ &longs;unt, moveri, &longs;ed nec ullam denuò <lb/>na&longs;ci po&longs;&longs;e in mundo. </s>

<s><margin.target id="marg101"/><emph type="italics"/>Argumen<lb/>tum Epicuri <lb/>Leucippi, ac <lb/>Democriti <lb/>pro vacuo.<emph.end type="italics"/></s>

<s><margin.target id="marg102"/><emph type="italics"/>Corporum <lb/>penetratio <lb/>non pote&longs;t <lb/>fieri natu<lb/>raliter.<emph.end type="italics"/></s>

<s><margin.target id="marg103"/><emph type="italics"/>Vacuum <expan abbr="nõ">non</expan> <lb/>admittit <lb/>Lucretius.<emph.end type="italics"/></s>

<s><emph type="center"/><emph type="italics"/>Quæ &longs;i non e&longs;&longs;et Inane,<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>Non tam &longs;olicito motu privata careret, Quàm genita omninò nulla ra<lb/>tione fui&longs;&longs;et, vndique materies quoniam &longs;tipata fui&longs;&longs;et.<emph.end type="italics"/> Cogita enim <lb/>vniver&longs;um mundum (ait vir docti&longs;&longs;imus Petrus Ga&longs;&longs;endus in <lb/>&longs;uis de Phy&longs;iologia Epicuri Animad ver&longs;ionibus, ex Epicuri men<lb/>te,) &longs;i nihil Inanis inter&longs;per&longs;um habeat, conferti&longs;&longs;imam e&longs;&longs;e mo<lb/>lem, adeo ut nè minimum quidem corpu&longs;culum valeat de novo <lb/>&longs;u&longs;cipere (quod quidem a&longs;&longs;erendum nece&longs;&longs;ariò e&longs;t, &longs;i nullum in <lb/>rebus Inane, &longs;i nihil non plenum, &longs;i locus nullus re&longs;tat complen<lb/>dus.) Quare aut corpus non admittetur denuò genitum, aut in <lb/>illo loco collocabitur, in quo aliud jam &longs;itum e&longs;t; &longs;icque idem <lb/>locus duo corpora &longs;e&longs;e undique penetrantia capiet. Quod &longs;anè <lb/>per vires Naturæ fieri po&longs;&longs;e non dixeris, ut ut alij id a&longs;&longs;erant, in<lb/>ducti exemplo panis, &longs;pongiæque &longs;iccæ aquam, cui injiciuntur, <lb/>in&longs;ugentis; & cinerum tantundem aquæ in con&longs;ortium &longs;uum ad<lb/>mittentium in va&longs;e, quantum &longs;ine cineribus vas recipere pote&longs;t. <lb/>

<arrow.to.target n="marg104"/></s>

<s><margin.target id=

<s><margin.target id="marg104"/><emph type="italics"/>Argumen<lb/>tum Epicu <lb/>reorum ac <lb/>Democriti <lb/>torum pro <lb/>vacuo.<emph.end type="italics"/></s>

<s>Si ab&longs;onum videtur vacuum admittere, &longs;i <foreign lang="greek">a)du/naton</foreign> corpo<lb/>rum dari penetrationem, & tamen motum admittimus localem; <lb/>&longs;u&longs;que deque verti corpora omnia, quæ Univer&longs;o concluduntur, <lb/>fateamur nece&longs;&longs;e e&longs;t toties, quoties eorum unum movebitur, di<lb/>cet Democriticus qui&longs;piam, aut Epicureus: moveatur enim <lb/>quodcunque eorum, quæ &longs;unt, de &longs;uo quem occupat loco, alte<lb/>riu&longs;que in vadere tentet &longs;tationem; &longs;anè cùm locum plenum <lb/>offendat, nece&longs;&longs;e erit, ex eo pellat, quod corpus illum occupat. <lb/>Illud porrò quónam concedat, &longs;i omnia quidem plena &longs;unt? An

<pb xlink:href="051/01/076.jpg" pagenum="45"/>non ip&longs;um rur&longs;us expellet aliud? At de eo par redibit difficultas: <lb/>hoc enim, aliud expellere loco debebit; & illud aliud; &longs;icque con<lb/>tinuari nece&longs;&longs;e erit inchoatam &longs;omel corporum commotionem <lb/>in ævum, & totum commoveri Vniver&longs;um vel ad mu&longs;cæ vola<lb/>tum. Si enim vel unum corpus cedere loco non valeat, aut non <lb/>volet, omnis ce&longs;&longs;abit illicò motus, eritque unaquæque res mun<lb/>di &longs;ic in&longs;erta in aliam, ut magis è loco excedere nequeat, quàm <lb/>mytuli (inquit Ga&longs;&longs;endus paulò antè citatus) &longs;eu cochleæ illæ, <lb/>quæ intra &longs;ilices na&longs;cuntur. Neque dicas, e&longs;&longs;e in mundo rara, <lb/>liquida, fluxaque corpora, quæ cedere magis quàm &longs;ilices po&longs;<lb/>&longs;int. Sint enim quantum vis rara, fluxa, & cedere nata; &longs;i admi<lb/>&longs;tum Inane non habent, &longs;i particulæ omnes illorum contiguita<lb/>tem undique, &longs;eu &longs;ecundùm totas &longs;uperficies habent; tale con<lb/>tinuum corpus facient, ut perinde &longs;it &longs;eu ex &longs;ilice, &longs;eu ex aqua, &longs;eu <lb/>ex aëre illud dicas: neque enim aër vel paucioribus, vel minùs <lb/>compactis &longs;ui partibus occupabit locum minorem, quàm &longs;ilex, <lb/>cùm quotcunque loci particulas feceris, tam nulla earum &longs;it aë<lb/>ris, quàm &longs;ilicis particulæ expers. Hactenus Democritici, & <lb/>Epicurei. </s>

<s><emph type="center"/>Corpora &longs;e mutuò expellunt.<emph.end type="center"/></s>

<s>HIs quid reponendum, viderint Philo&longs;ophi. Ari&longs;toteles certe, </s>

<s>

<arrow.to.target n="marg105"/><lb/>qui nec vacuum admittit, nec corporum penetrationem <lb/>mutuam, nequaquam timet rerum omnium ad quemlibet mo<lb/>tum commotionem; quoniam liquida non &longs;olùm pelluntur, &longs;ed <lb/>dividuntur etiam dum urgentur; & quæ antror&longs;um vergebant <lb/>partes, latera lambentes claudunt terga. At quidquid &longs;it, tam <lb/>evidens e&longs;t, corpus unum expellere alterum è &longs;uo, quem occu<lb/>pat, loco, ni &longs;ponte excedere velit, quàm e&longs;t manife&longs;tum, mo<lb/>

<arrow.to.target n="marg106"/><lb/>tum dari localem; idque verum e&longs;t non tantùm in duris &longs;oli<lb/>di&longs;vé, &longs;ed liquidis etiam ac fluidis corporibus, aëre dico, & aqua. <lb/>videmus enim quotidie, aquam va&longs;i, tuboque aëre pleno illa<lb/>bentem, expellere aërem, &longs;i exeundi locum habet; & &longs;i non ha<lb/>bet, neque aquam po&longs;&longs;e, aut velle infundi. Videmus item aë-

<pb xlink:href="051/01/077.jpg" pagenum="46"/>rem inflatum va&longs;i per os unum, expellere aquam per alterum, aut <lb/>etiam per idem, &longs;i elabendi detur locus; qui &longs;i non datur, nec aë<lb/>ri patere ingre&longs;&longs;um. Videmus follibus compre&longs;&longs;is erumpere <lb/>aërem, & aquam etiam, &longs;i aquâ erant repleti. Videmus, &longs;i va&longs;i <lb/>aquâ pleno operculum in medio perforatum imponamus, de<lb/>primamu&longs;que, aquam pre&longs;&longs;am, &longs;i inter latera va&longs;is & opercu<lb/>lum erumpere non pote&longs;t, ex&longs;ilire per foramen magno impetu. <lb/>Taceo centena exempla alia. Atque hæc mutua corporum ex<lb/>pul&longs;io alterum e&longs;t Machinarum Hydro-pnevmaticarum prin<lb/>cipium, quo innumera, & non minùs iucunda, quàm admiran<lb/>da exhibentur &longs;pectacula pa&longs;&longs;im, vt apparebit aperti&longs;&longs;imè ex &longs;e<lb/>quentibus Machinis. Interim&longs;equens accipe Experimentum. </s>

<s><margin.target id="marg105"/><emph type="italics"/>Corpora ex<lb/>pellunt &longs;e <lb/>mutuò.<emph.end type="italics"/></s>

<s><margin.target id="marg106"/><emph type="italics"/><expan abbr="Experim&etilde;-ta">Experimen<lb/>ta</expan> varia, <lb/>quibus pro<lb/>batur cor<lb/>pora&longs;e mu<lb/>mutuò ex<lb/>pellere.<emph.end type="italics"/></s>

<s><emph type="center"/>Experimentum, quo o&longs;tenditur vis expul&longs;iva, propter <lb/>corporum impenetrabilitatem, ad aquas elevan<lb/>das in altum.<emph.end type="center"/></s>

<s>FAcex&longs;tanno, cu<lb/>pro, creta, ligno, <lb/>aut alia quacunque <lb/>materia aquis re&longs;i<lb/>&longs;tente tria va&longs;cula <lb/>A, F, & G, columnis <lb/>inter&longs;e di&longs;tincta, vt <lb/>mon&longs;trat figura; aut <lb/>alia ratione, prout <lb/>placuerit, aut com<lb/>modiùs fuerit: <expan abbr="&longs;int-&qacute;ue">&longs;int<lb/>que</expan> hæc va&longs;cula vn<lb/>dique clau&longs;a quàm <lb/>diligenti&longs;&longs;ime, nè <lb/>aër po&longs;&longs;it aut ingre<lb/>di, aut elabi, &longs;altem <lb/>ex A & G. Vas infe<lb/>rius G habeat <expan abbr="epi-&longs;tomi&utilde;">epi<lb/>&longs;tomium</expan> I. per quod

<pb xlink:href="051/01/078.jpg" pagenum="47"/>aqua effluere po&longs;&longs;it. Va&longs;a A & F habeant in operculis forami<lb/>na C & E, vt per ea infundi po&longs;&longs;it aqua, & iterum obturari. <lb/>Exva&longs;e A egrediatur tubulus AB vtrimque, apertus qui apud <lb/>A fundum va&longs;is non attingat, &longs;ed tantum ab illo di&longs;tet, vt <lb/>aqua interfluere po&longs;&longs;it: apud B verò habeat o&longs;culum &longs;tricti&longs;&longs;i<lb/>mum. Habeat præterea epi&longs;tomium K. Ex eodem va&longs;e A de<lb/>&longs;cendat intra vas inferius G alius tubulus DN, vtrimque aper<lb/>tus, qui apud D non attingat operculum va&longs;is A, &longs;ed tantum <lb/>ab illo di&longs;tet, vt po&longs;&longs;it egredi aër: apud H verò tran&longs;eat &longs;olum <lb/>operculum va&longs;is G, & non extendatur vlteriùs.| Ex va&longs;e deni<lb/>que F de&longs;cendatintra vas G alius tubus FG vtrimque aper<lb/>tus, qui apud F tran&longs;eat &longs;olùm fundum va&longs;is, & non progredia<lb/>tur vlteriùs; apud G verò di&longs;tet tantum à fundo, vt aqua ef<lb/>fluere po&longs;&longs;it, habeatque vas G epi&longs;tominm L. Hi tres tubi <lb/>debentita &longs;tanno alia vè materia coarctari, & adferruminari va<lb/>&longs;is in loco tran&longs;itus, vt nullus aër penetrare intra va&longs;a, aut elabi <lb/>ex ijsdem po&longs;&longs;it. Cavendum præterea diligenter e&longs;t, nè tubu<lb/>lus AB &longs;it longior, aut æquè longus, ac tubulus FG; quare <lb/>meliùs erit, &longs;i inter B & K decurtetur quantum pote&longs;t, & quàm <lb/>minimum extra vas A protendatur. </s>

<s>His ita ritè præparatis, repleantur aqua duo va&longs;a A & F, per <lb/>foramina C & E, & obturentur quàm diligenti&longs;&longs;imè, maximè <lb/>foramen C (foramen enim E pote&longs;t manere apertum;) vas <lb/>verò G maneatvacuum; & omnia epi&longs;tomia &longs;int clau&longs;a. De<lb/>inde aperiatur epi&longs;tomium L, vt aqua va&longs;is F defluere po&longs;&longs;it <lb/>intra vas G: & po&longs;tquam defluxit aliquantulum aquæ, aperia<lb/>tur epi&longs;tomium K; <expan abbr="erumpet&qacute;ue">erumpetque</expan> maximo impetu aqua va<lb/>&longs;is A per tubulum AB, pro&longs;ilietque in altum, vi expul&longs;iva, pro<lb/>pter corporum impetrabilitatem. Nàm aqua va&longs;is F de&longs;cen<lb/>dens intra vas G, expellit inde aërem per tubum HD intra vas <lb/>A; qui aer expellit inde aquam per tubulum AB, quoniam ne<lb/>que in G, neque in A, aër & aqua &longs;imul in eodem loco manere <lb/>po&longs;&longs;unt, &longs;ed nece&longs;&longs;ariò vnum corpus expellit alterum, propter <lb/>eorum impenetrabilitatem. Vides igitur quomodo vis expul<lb/>&longs;iva propter corporum impenetrabilitatem &longs;it principium &

<pb xlink:href="051/01/079.jpg" pagenum="48"/>cau&longs;a Machinarum Hydro-pnevmaticarum? Vbi de&longs;cenderit <lb/>aqua va&longs;is F intra vas G, & ex&longs;iliuerit aqua va&longs;is A per tubum <lb/>AB; depromi poterit aqua va&longs;is G per epi&longs;tomium I, & reple<lb/>ri iterum va&longs;a A & F, vt antea, & in&longs;titui idem lu&longs;us. </s>

Line 1413

Line 1557

<arrow.to.target n="marg109"/><lb/>fluat.<emph.end type="italics"/> Qua quidem in con&longs;tructione errorem committit gravi&longs;<lb/>&longs;imum (&longs;i tamen ip&longs;ius e&longs;t error, & non potiùs Interpretis, qui <lb/>figuras appo&longs;uit) quem hîc detegere oportet, ne alijs etiam &longs;it <lb/>

<arrow.to.target n="fig12"/><lb/>errandi occa&longs;io. Quod eò et<lb/>iam libentiùs facio, quòd nec <lb/>Federicus Commandinus, qui <lb/>ex Græco in latinum tran&longs;tulit <lb/>Heronem; nec Ioannes Bapti<lb/>&longs;ta Aleottus, qui Commandini <lb/>interpretationem red didit Itali<lb/>cam; nec Ioannes Bapti&longs;ta Porta, <lb/>qui Heronis errorem etiam ob<lb/>&longs;ervavit, genuinam lucernæ de<lb/>lineationem dederunt. Eam <lb/>verò hîc dare conabimur, allatis <lb/>

<arrow.to.target n="marg110"/><lb/>Heronis verbis ex Commandini <lb/>translatione, addendo nonnulla <lb/>verba majoris claritatis gratia, <lb/>quæ a&longs;teri&longs;cis in margine no<lb/>tantur. Sic ergo di&longs;currit Hero. <lb/><emph type="italics"/>Con&longs;truatur lucerna, ba&longs;im habens <lb/>concavam, & triangularem in&longs;tar <lb/>pyramidis; &longs;it que ba&longs;is concava<emph.end type="italics"/> AB <lb/>CD, <emph type="italics"/>& in ea diaphragma<emph.end type="italics"/> EF. <emph type="italics"/>Lu<lb/>cernæ autem caulis &longs;it<emph.end type="italics"/> GH, <emph type="italics"/>& ip&longs;e <lb/>concavus; &longs;upra quem &longs;it concavus <lb/>calathus<emph.end type="italics"/> KL, <emph type="italics"/>plurimum olei conti<lb/>nens. Ex diaphragmate<emph.end type="italics"/> EF <emph type="italics"/>pro-<emph.end type="italics"/>

<pb xlink:href="051/01/082.jpg" pagenum="51"/><emph type="italics"/>cedat<emph.end type="italics"/> MN <emph type="italics"/>tubus, &longs;imul cum eo perforatus, tantu

<pb xlink:href="051/01/082.jpg" pagenum="51"/><emph type="italics"/>cedat<emph.end type="italics"/> MN <emph type="italics"/>tubus, &longs;imul cum eo perforatus, tantum di&longs;tans à calathi <lb/>operculo<emph.end type="italics"/> KL <emph type="italics"/>(in quo ellychnium imponitur) quantum ad aër is <lb/>exitum &longs;ufficiat. Alius autem tubulus<emph.end type="italics"/> XO <emph type="italics"/>demittatur per opercu<lb/>l<gap/>m<emph.end type="italics"/> KL <emph type="italics"/>di&longs;tans à fundo calathi, quantum &longs;atis &longs;it ad aquæ fluxum <lb/>& ex operculo paululum excedens. Exce&longs;&longs;ui verò aptetur alius tubulus<emph.end type="italics"/><lb/>P <emph type="italics"/>habens &longs;uperius o&longs;culum ob&longs;tructum; qui tubulus per fundum lychnij <lb/> impul&longs;us coagmentetur lychno. At tubum autem<emph.end type="italics"/> P <emph type="italics"/>adglutine<lb/>tur alius tubulus exilis, procedens ad extremitatem auris, & &longs;imul com ea <lb/>perforetur, vt in fluat in concavitatem ellychnij, foramen habens <lb/>quemadmodum & alij. Et&longs;ub diaphragmate<emph.end type="italics"/> EF <emph type="italics"/>conglutinetur clavi<lb/>cula deferens in locum<emph.end type="italics"/> CDEF, <emph type="italics"/>ita, vt &longs;i aperiatur, aqua ex loco<emph.end type="italics"/><lb/>ABEF, <emph type="italics"/>in ip&longs;um<emph.end type="italics"/> CDEF <emph type="italics"/>tran&longs;eat. Sit autem in operculo<emph.end type="italics"/> AB <emph type="italics"/>par<lb/>rum foramen, per quod locum<emph.end type="italics"/> ABEF <emph type="italics"/>implebimus aquâ<gap/>& qui <lb/>in ip&longs;o e&longs;t aër, per dictum foramen excedet. Itaque &longs;ublato ellych<lb/>nio, calathum oleo imple bimus per tubum<emph.end type="italics"/> XO, <emph type="italics"/>aëre per<emph.end type="italics"/> NM <emph type="italics"/>tubulum <lb/>excedente, & adhuc per clavem apertam, quæ e&longs;t in fundo<emph.end type="italics"/> C.D, <lb/> <emph type="italics"/>quando & quæ e&longs;t in<emph.end type="italics"/> CDEF <emph type="italics"/>aqua effluet. Impo&longs;ito igitur el<lb/>lychnio per &longs;meri&longs;ma<emph.end type="italics"/> P, <emph type="italics"/>quando opus &longs;it oleum infundere, aperiemus <lb/>clavem, quæ in fundo<emph.end type="italics"/> CD; <emph type="italics"/>& aquâ ex loco<emph.end type="italics"/> ABEF <emph type="italics"/>in locum<emph.end type="italics"/><lb/>CDEF <emph type="italics"/>&longs;ecedente, a&edot;r qui e&longs;t in ip&longs;o, per tubum<emph.end type="italics"/> MN <emph type="italics"/>ad cala<lb/>thum perveniens elidet oleum; quod quidem per tubulum<emph.end type="italics"/> XO, <emph type="italics"/>& <lb/>per alium ip&longs;i cohærentem ad ellychnium procedet. Quando au<lb/>tem non amplùs fluere volumus, clavicula claudetur, & ce&longs;&longs;abit; & <lb/>rur&longs;us quando opus &longs;it, idem faciemus.<emph.end type="italics"/></s>

<s><margin.target id="marg109"/>Error He<lb/>ronis in lu<lb/>cernæ con<lb/>&longs;tructione.</s>

<s><margin.target id="marg110"/><emph type="italics"/>Lucernæ <lb/>Heronis ge<lb/>auina figu<lb/>ra.<emph.end type="italics"/></s>

<s>Hæc Commandinus Heronis Interpres; quæ ego omni<lb/>

<arrow.to.target n="marg111"/><lb/>no mendo&longs;a e&longs;&longs;e exi&longs;timo: puto enim vbique lychnum pro el<lb/>lychnio ponendum e&longs;&longs;e, & alia pleraque legenda prout in mar<lb/>gine &longs;unt po&longs;ita a&longs;teri&longs;cis notata. Non potui in venire Græcum <lb/>Heronis textum, vt vt diù quæ&longs;iverim. Tubuli etiam &longs;upra ca<lb/>lathi operculum di&longs;ponendi &longs;unt &longs;ine dubio, vt nos di&longs;po&longs;uimus, <lb/><expan abbr="quoniã">quoniam</expan> Heronis textus latinus apud <expan abbr="ip&longs;u&mtilde;et">ip&longs;umnet</expan> Commandinum id <lb/>exigit. Nec mireris Lector, &longs;i &longs;u&longs;picer Commandini præ&longs;entem <lb/>Latinum de lucerna textum non e&longs;&longs;e vndequaque corre&longs;pon<lb/>dentem græco textui; po&longs;thumum enim e&longs;t Opus Commandini,

<pb xlink:href="051/01/083.jpg" pagenum="52"/>nec po&longs;tremam ip&longs;ius manum expertum, vt habetur initio libelli <lb/>in præfatiuncula ad Lectorem. E&longs;t autem in Commandini te<lb/>xtu ac &longs;chemate in&longs;ignis error in eo, quòd clavicula R trans<lb/>mittit aquam quæ e&longs;t in ABEF intra ba&longs;im EFCD per aper<lb/>tum &longs;olùm foramen &longs;ine tubulo, qui paulò longior &longs;it quàm tu<lb/>bulus OX; quod tamen omnino requiritur, vt diximus paulò <lb/>antè §. IV. & cau&longs;am dabimusintrà Protheoria IV. cap. 2. Pro<lb/>po&longs;it. 14. experientia &longs;iquidem con&longs;tat, cylindrum aquæ per fo<lb/>ramen <expan abbr="de&longs;cendent&etilde;">de&longs;cendentem</expan> (&longs;i quandoque de&longs;cendit aëre &longs;uccedente) <lb/>in aêre libero non habere eandem vim, ac de&longs;cendentem per <lb/>tubum; tamet&longs;i vtrobique &longs;it eadem aquæ quantitas, cum eodem <lb/>perpendiculo. Cau&longs;a e&longs;t, quia &longs;i liberè & &longs;ine tubo defluit a queus <lb/>cylindrus, <expan abbr="&longs;ign&utilde;">&longs;ignum</expan> e&longs;t aërem &longs;ubintrare; &longs;i aër &longs;ubintrat, ce&longs;&longs;at me<lb/>tus vacui, ac proinde aqua debet elevari vt <expan abbr="laborãti">laboranti</expan> Naturæ &longs;uc<lb/>currat. Quòd &longs;i tam &longs;trictum e&longs;t foramen, vt aër &longs;ubintrare non <lb/>po&longs;&longs;it, nè gutta quidem aquæ effluet, vt experientia quotidiana <lb/>docet, idque propter vacui metum. Hunc tamen errorem ego <lb/>

<arrow.to.target n="marg112"/><lb/>nequaquam Heroni ad&longs;cribendum putem, vt Porta facit, &longs;ed <lb/>exi&longs;timo Heronem produxi&longs;&longs;e tubulum R ferè v&longs;que fundum <lb/>CD; &longs;ic enim major erit quàm tubulus XO, & aqua per ip&longs;am <lb/>R decideus habebit perpendiculum præponderans perpendi<lb/>culo aquæ &longs;eu olei a&longs;cendentis per XO. </s>

<s><margin.target id="marg111"/><emph type="italics"/>Heronis lo<lb/>cus apud <lb/>Comman<lb/>dinum men <lb/>do&longs;<gap/>.<emph.end type="italics"/></s>

<s><margin.target id="marg112"/><emph type="italics"/>Heronis er<lb/>ror excu&longs;a<lb/>tur.<emph.end type="italics"/></s>

<s>Similis error reperitur apud Heronem cap. 36. vbi docet <lb/>&longs;atyri&longs;cum con&longs;truere &longs;uper quadam ba&longs;i, vtrem in manibus <expan abbr="te-nent&etilde;">te<lb/>nentem</expan>, cui adiacet labellum; vt infu&longs;o in labellum humore, ita <lb/>vt repleatur, aqua per vtrem in idem labellum in fluat, & non &longs;u<lb/>perfundatur, quòusque tota per vtrem aqua evacuata fuerit. Ex <lb/>qua quidem con&longs;tructione de&longs;umpta e&longs;t praxis con&longs;truendi fon<lb/>tem Heronis, de quo infrà Parte 2. Cla&longs;se I. cap. 2. Machi<lb/>na 1. 2. & 3. vbi errorem Heronis detegemus; <lb/>&longs;i tamen Heronis e&longs;t, & non In<lb/>terpretis. </s>

<s><emph type="center"/>Attractione & expul&longs;ione &longs;imul aquam ele<lb/>vare po&longs;&longs;umus.<emph.end type="center"/></s>

<s>DIximus §. IV præcedente, perpen diculum aquæ cadentis & <lb/>pellentis aërem, longius e&longs;&longs;e debere perpendiculo aquæ <lb/>a&longs;cendentis per expul&longs;ionem. Diximus præterea Protheoria I. <lb/>§. VI. perpendiculum aquæ cadentis & trahentis aërem, debe<lb/>re &longs;uperare longitudine perpendiculum aquæ attractæ. Infrâ <lb/>Parte 2. Cla&longs;se I. cap. 1. Machina 7. & cap. 2. Machina 10. & 11. di<lb/>cemus, qua ratione per multiplicationem plurium <expan abbr="perp&etilde;">perpem</expan> dicu<lb/>lorum brevium elevari po&longs;&longs;it aqua, tam per expul&longs;ionem, quàm <lb/>per attractionem, ad quam vis altitudinem. Nunc &longs;ubjiciam <lb/>modum attollendi aquam per attractionem & expul&longs;ionem &longs;i<lb/>

<arrow.to.target n="marg113"/><lb/>fimul ad duplam altitudinem aquæ cadentis, quoniam ingenio<lb/>fus e&longs;t, & ad multa pote&longs;t e&longs;&longs;e vtilis. Refert illum Porta lib. 2. <lb/>Spiritalium cap. 2. eumque magnificè extollit, tanquam à &longs;e in<lb/>ventum; & ait &longs;uperare omnem humanum intellectum, nec vn<lb/>quam in mentem veni&longs;&longs;e antiquis, &longs;e verò po&longs;t expen&longs;as multas, <lb/>& labores plurimos illum tandem reperi&longs;&longs;e. Modus hic e&longs;t. </s>

<s><margin.target id="marg113"/><emph type="italics"/>Modus in<lb/>genio&longs;us e<lb/>levandi <lb/>aquam in <lb/>quam vis al <lb/>titudinem <lb/>per attracti <lb/>onem & ex<lb/>pul&longs;ionem, <lb/>&longs;imul.<emph.end type="italics"/></s>

Line 1576

Line 1743

<s><emph type="center"/>Proprietas I.<emph.end type="center"/></s>

<s><emph type="center"/>Aqua

<s><emph type="center"/>Aqua tendit ad loca decliviora.<emph.end type="center"/></s>

<s>AQuam, & omnem alium humorem, fluentem <lb/><gap/>iberè, currere ad loca decliviora, & centro Mundi ac <lb/>Terraquæ propinquiora, &longs;i patetip&longs;is liber aditus, &longs;ive <lb/><gap/>us ac perpendicularis, &longs;ive obliquus; patet expe<lb/>rientia quotidiaua, nec indiget probatione. Ex quo deduci<lb/>tur, aquæ etiam con&longs;i&longs;tentis partes omnes inclinare innato ap<lb/>petitu ad eadem loca decliviora: ideo enim de facto, &longs;ublatis </s>

<s>

<arrow.to.target n="marg131"/><lb/>impedimentis, eò fluit aqua, quia naturaliter eò inclinat. Con<lb/>&longs;i&longs;tentem porrò aquam appello, quæ &longs;itum obtinet naturalem. <lb/>Situs autem &longs;eu po&longs;itio naturalis aquæ e&longs;t, quem dum naturali <lb/>

<arrow.to.target n="marg132"/><lb/>&longs;uo fluxui & con&longs;i&longs;tentiæ permittitur, &longs;ua &longs;ponte a&longs;&longs;umit, tam in <lb/>&longs;uperficie &longs;uperiore, quàm in inferiore, & lateralibus. </s>

<s><margin.target id="marg131"/><emph type="italics"/>Aqua con<lb/>&longs;i&longs;tens qua <lb/>dicatur.<emph.end type="italics"/></s>

<s><margin.target id="marg132"/><emph type="italics"/>Aqua &longs;itus <lb/>naturalis <lb/>quis &longs;it.<emph.end type="italics"/></s>

<s><emph type="center"/>Proprietas II.<emph.end type="center"/></s>

<s><emph type="center"/>Aquæ &longs;uperficies &longs;uperior, ce&longs;&longs;ante fluxu, &longs;phærica <lb/>e&longs;t; reliquæ conformantur va&longs;is & rece<lb/>ptaculis,<emph.end type="center"/></s>

<s>AQua liberè fluens tam diu fluit, donec partium continuata<lb/>

<arrow.to.target n="marg133"/><lb/>rum extima &longs;eu &longs;uperior &longs;uperficies &longs;phærica &longs;it, habens idem <lb/><expan abbr="centr&utilde;">centrum</expan> cum centro Terraquæ & Vniver&longs;i, hoc e&longs;t, donec omnes <lb/>extimæ &longs;uperficiei partes æqualiter di&longs;tenta Centro Mundi. De-

<pb xlink:href="051/01/099.jpg" pagenum="68"/>mon&longs;trat hoc &longs;ubtili&longs;&longs;imè Archimedes lib 1. de in&longs;identibus hu<lb/>mido Propo&longs;it. 2. & Ari&longs;tot. lib. 2. de C&oelig;lo text. 31. & &longs;equitur <lb/>ex præcedente Proprietate. Si enim ce&longs;&longs;ante fluxu, & con&longs;i<lb/>&longs;tente iam aquâ, pars vna &longs;uperficiei extimæ altior e&longs;&longs;et, & altera <lb/>humilior, hoc e&longs;t, &longs;i non omnes æquè di&longs;tarent à centro Mundi <lb/>(quod e&longs;t &longs;phæricam habere &longs;uperficiem, habentem idem Cen<lb/>trum commune Mundi;) non omnes aquæ partes, &longs;ublatis im<lb/>pedimentis, fluerent ad loca decliviora, nec aquæ con&longs;i&longs;tentis <lb/>partes omnes eò naturali appetitu inclinarent; aut certè violen<lb/>ter in tali &longs;tatu, & nullo præ&longs;ente impedimento, detinerentur; <lb/>

<arrow.to.target n="marg134"/><lb/>quod incongruum e&longs;t, & naturis rerum repugnans. </s>

<s><margin.target id="marg133"/><emph type="italics"/>Aqua con&longs;i<lb/>&longs;tentis &longs;uper <lb/>ficies &longs;uperi<lb/>or &longs;pharica <lb/>e&longs;t.<emph.end type="italics"/></s>

<s><margin.target id="marg134"/><emph type="italics"/>Aquæ va&longs;is <lb/>contentæ &longs;u <lb/>perficies con <lb/>formantur <lb/>va&longs;orum in <lb/>ternis figu<lb/>ris.<emph.end type="italics"/></s>

<s>Inferior porrò aquæ &longs;uperficies, & laterales, conforman<lb/>tur &longs;uperficiebus internis va&longs;orum & receptaculorum, quibus <lb/>aqua continetur: Vnde &longs;i vna pars fundi va&longs;orum ac recepta<lb/>culorum e&longs;t altior alterâ (prout in mari, lacubus, fluminibus, <lb/>& va&longs;is ordinariè fit) etiam talis erit aquæ illis contentæ infe<lb/>rior &longs;uperficies. Idem intellige de lateralibus &longs;uperficiebus. </s>

<s><emph type="center"/>Pori&longs;ma I.<emph.end type="center"/><lb/>

<arrow.to.target n="marg135"/></s>

<s><margin.target id="marg135"/><emph type="italics"/>Aquarum <lb/>omnium Su <lb/>perficies &longs;u<lb/>perior e&longs;t <lb/>&longs;phærica.<emph.end type="italics"/></s>

<s>COlligitur hinc, Oceani, Marium, lacuum, & aquarum qua<lb/>rumcunque continuatarum, & in quibuscunque receptacu<lb/>lis contentarum, ac con&longs;i&longs;tentium, &longs;uperficies &longs;uperiores atque <lb/>externas e&longs;&longs;e &longs;phæricas, habentes idem cum Terraquæ &longs;uperficie </s>

<s>

<arrow.to.target n="marg136"/><lb/><expan abbr="cõvexa">convexa</expan> centrum. In va&longs;is tamen & receptaculis exiguis adeo exi<lb/>gua e&longs;t & in&longs;en&longs;ibilis&longs;phæricitas i&longs;tius &longs;uperficiei, vt meritò &longs;up<lb/>poni po&longs;&longs;it e&longs;&longs;e planam, &longs;eu horizonti parallelam: vnde & nos <lb/>in &longs;equentibus id nobis concedi po&longs;tulabimus, & ita &longs;uppone<lb/>mus. </s>

<s><margin.target id="marg136"/><emph type="italics"/>In va&longs;is ta<lb/>men exiguis <lb/>cen&longs;eri po<lb/>te&longs;t plana.<emph.end type="italics"/></s>

<s><emph type="center"/>Pori&longs;ma II.<emph.end type="center"/></s>

<s>COlligitur iterum, idem vas ad turris aut montis radicem po<lb/>

<arrow.to.target n="marg137"/><lb/>&longs;itum, & aquâ omnino plenum, plùs aquæ continere, mathe<lb/>maticè loquendo, quàm po&longs;itum in turris aut montis vertice, & <lb/>aquâ itidem omnino plenum. Ratio e&longs;t, quia major e&longs;t &longs;phæri<lb/>citas aquæ in primo, quàm &longs;ecundo ca&longs;u. </s>

<s><margin.target id="marg137"/><emph type="italics"/>Aquæ plus <lb/><expan abbr="cõtinet">continet</expan> vas <lb/>plenù infe<lb/>riori, quàm <lb/>&longs;uperiori <lb/>loco.<emph.end type="italics"/></s>

<s><emph type="center"/>Pori&longs;ma III.<emph.end type="center"/></s>

<s>COlligitur tertiò, &longs;i aqua ad libellam con&longs;tituta e&longs;&longs;et alicubi, <lb/>

<arrow.to.target n="marg138"/><lb/>non po&longs;&longs;e con&longs;i&longs;tere, &longs;ed nece&longs;&longs;ariò moveri, quia tunc non <lb/>omnes partes extimæ & &longs;uperioris &longs;uperficiei e&longs;&longs;ent æquè vicinæ <lb/>centro Terraquæ. Athoc meliùs explicabitur in Pantometro <lb/>no&longs;tro Kircheriano lib. 9. Hydragogico, vbi delibellatione a<lb/>quarum agemus, <expan abbr="iterumq;">iterumque</expan> in Mechanica no&longs;tra Vniver&longs;ali, libro <lb/>quem in&longs;cribemus Mechanicam Hydragogicam. </s>

<s><margin.target id="marg138"/><emph type="italics"/>Aqu<gap/> con<lb/>&longs;i&longs;tere non <lb/>pote&longs;i ad li<lb/>bellam con<lb/>&longs;tituta.<emph.end type="italics"/></s>

<s><emph type="center"/>Proprietas III.<emph.end type="center"/></s>

<s><emph type="center"/>Aqua minùs pre&longs;&longs;a expellitur à magis pre&longs;&longs;a.<emph.end type="center"/></s>

<s>AQuæ, & humidi cuiuscunque, ea e&longs;t natura, inquit Archi<lb/>medes lib. 1. de In&longs;identibus humido, Hypothe&longs;i I, vt par<lb/>tibus ip&longs;ius æqualiter iacentibus & continuatis inter &longs;e&longs;e; minùs <lb/>pre&longs;&longs;a à magis pre&longs;&longs;a expellatur; & quidem tantò fortiùs, quantò <lb/>aut minùs illa, aut magis hæc pre&longs;&longs;a fuerit. Hoc quomodo &longs;it in<lb/>telligendum, patebit ex &longs;equentibus Proprietatibus huius capitis, <lb/>& etiam ex dicendis capite &longs;equenti, Propo&longs;itione 2. </s>

<s><emph type="center"/>Proprietas IV.<emph.end type="center"/></s>

<s><emph type="center"/>Aquæ, & humidi cuiu&longs;cunque, pars vnaquæ que premi<lb/>tur humido &longs;upra ip&longs;am exi&longs;tente ad perpendiculum, &longs;i hu<lb/>midum &longs;it de&longs;cendens in aliquo, aut ab alio ali<lb/>quo pre&longs;&longs;um.<emph.end type="center"/></s>

<s>AS&longs;erit hoc Archimedes loco proximè citato. <expan abbr="Itaq;">Itaque</expan> quando <lb/>

<arrow.to.target n="marg139"/><lb/>humidum non e&longs;t de&longs;cendens in aliquo, aut non e&longs;t ab ali<lb/>quo alio pre&longs;&longs;um, &longs;ed con&longs;i&longs;tit in &longs;uo &longs;itu naturali, vna pars non <lb/>premit alteram, vt mox dicemus. Si autem humidum <lb/>e&longs;t de&longs;cendens in aliquo, vt &longs;i effluit per foramen va&longs;is, aut in<lb/>fluit in vas coniunctum: tunc partes &longs;upra foramen premuntur <lb/>à partibus ad perpendiculum ip&longs;is incumbentibus, non verò ab <lb/>alijs collateralibus. Similiter &longs;i humidum premitur ab aliquo, <lb/>partes pre&longs;&longs;æ premunt &longs;olùm quæ ip&longs;is ad perpendiculum &longs;ub<lb/>&longs;tant. </s>

<s><margin.target id="marg139"/><emph type="italics"/>Aquæ par<lb/>tes inferio<lb/>res <expan abbr="prem&utilde;-tur">premun<lb/>tur</expan> à &longs;upe<lb/>rioribus ad <lb/>perpendicu<lb/>lum incum <lb/>bentibus.<emph.end type="italics"/></s>

<s><emph type="center"/>Proprietas V.<emph.end type="center"/></s>

<s><emph type="center"/>Aquâ in &longs;itu naturali con&longs;i&longs;tente, partes &longs;uperiores non <lb/>premunt inferiores.<emph.end type="center"/></s>

<s>PAtet hoc ex multis &longs;ignis. Primò enim alioquin partes aquæ <lb/>inferiores e&longs;&longs;ent den&longs;iores &longs;uperioribus, quia <expan abbr="cõpre&longs;&longs;æ">compre&longs;&longs;æ</expan> e&longs;&longs;ent. <lb/>Secundò, vrinatores infra aquam exi&longs;tentes non &longs;entiunt pon<lb/>dus aquarum incumbentium &longs;ibi. Tertiò, herbæ levi&longs;&longs;imæ intra <lb/>aquam cre&longs;centes, & in altum a&longs;&longs;urgentes, non &longs;ternuntur ab <lb/>aqua &longs;uperincumbente. Quartò, corpus grave fune alligatum <lb/>& infra aquam demer&longs;um, &longs;u&longs;tinetur à manu, & extrahitur, tan<lb/>ta facilitate, quanta &longs;u&longs;tineretur & extraheretur, &longs;i nulla aqua illi <lb/>incumberet; imò maiorietiam facilitate, quoniam gravia mi<lb/>nùs ponderantintra, quàm extra aquam. Quintò, &longs;itula aquâ <lb/>plena levior e&longs;t intra aquam, quàm extra: Curhoc, ni&longs;i quia <lb/>aqua intra aquam non ponderat? </s>

<s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/><lb/>

<arrow.to.target n="marg140"/></s>

<s><margin.target id="marg140"/><emph type="italics"/>Aquæ con <lb/>&longs;i&longs;tentis par<lb/>tes &longs;uperio<lb/>res non pre<lb/>munt actu <lb/>inferiores.<emph.end type="italics"/></s>

<s>COlligitur hinc, quando Archimedes, alijque dicunt, omnes <lb/>aquæ partes, dum ea in &longs;itu con&longs;i&longs;tit naturali, a qualiter pre<lb/>mi, non e&longs;&longs;e &longs;ermonem de actuali pre&longs;&longs;ione, &longs;ed &longs;olùm de aptitu<lb/>dinali. Premi vnum ab alio aptitudinaliter, e&longs;t, habere &longs;upra <lb/>&longs;e grave non &longs;u&longs;tentatum; at premi actualiter e&longs;t ita habere &longs;u</s>

<s>

<arrow.to.target n="marg141"/><lb/>pra &longs;e grave non &longs;u&longs;tentatum, vt ablato impedimento cedere co<lb/>gatur corpori incumbenti; & ni&longs;i cedat, comprimatur. Vel di<lb/>cendum e&longs;t, premi quidem partes humidi inferiores à &longs;uperio<lb/>ribus &longs;ibi &longs;uperin cumbentibus, at non comprimi. Solùm ergo <lb/>partes &longs;uperiores aquæ actu premunt inferiores, quando vel ab <lb/>alio premuntur &longs;uperiores, vel quando &longs;unt altiores alijs partibus <lb/>contiguis in eodem va&longs;e, aut in duobus va&longs;is inter &longs;e communi<lb/>cantibus, vt videbimus, cùm de Siphonibus agetur; vel denique <lb/>quando infra &longs;e habent inferiores immediatè corpus levius &longs;e in <lb/>&longs;pecie, v.g. aërem, aut tenui&longs;&longs;imum fundum; in omnibus enim <lb/>hi&longs;ce ca&longs;ibus partes inferiores cedunt quidem &longs;uperioribus, at <lb/>minimè ab illis comprimuntur. Hinc e&longs;t, quòd aqua effluatè <lb/>foramine in fundo aut latere va&longs;is. Hinc etiam e&longs;t, quòd fun-

<pb xlink:href="051/01/102.jpg" pagenum="71"/>dum tenue va&longs;is incurvetur, ac tandem frangatur. Hinc deni<lb/>que e&longs;t, quòd dum partes aquæ &longs;uperiores premuntur, & partes <lb/>inferiores non habent effugium aut infrà, aut è latere va&longs;is, rum<lb/>patur potiùs vas, quàm partes inferiores comprimantur. Vide <lb/>quæ dicimus infrà parte 2. Cla&longs;se 1. cap. 5. Machina 6. </s>

<s><margin.target id="marg141"/><emph type="italics"/>Premi actu, <lb/>& premi <lb/>aptitudina<lb/>liter, quid <lb/>&longs;it.<emph.end type="italics"/></s>

<s><emph type="center"/>Proprietas VI.<emph.end type="center"/></s>

<s><emph type="center"/>Aquæ in &longs;itu naturali po&longs;itæ vna pars non <lb/>expellit alteram.<emph.end type="center"/></s>

<s>PAtet experientia. Et ratio e&longs;t, quia vna non premit alteram, <lb/>vt dictum in præcedenti Proprietate. Quòd &longs;i in va&longs;is con<lb/>jugatis altior aqua pellit minùs altam, cau&longs;a e&longs;t, quòd non &longs;it <lb/>po&longs;ita in &longs;itu naturali, quia &longs;cilicet non habet omnes partes æ<lb/>què di&longs;tantes à centro Mundi. </s>

<s><emph type="center"/>Proprietas VII.<emph.end type="center"/></s>

<s><emph type="center"/>Non omnes aquæ æquales magnitudine, &longs;unt <lb/>æquales pondere.<emph.end type="center"/></s>

<s>SUnt enim &longs;alsæ graviores dulcibus, & frigidæ calidis eiu&longs;dem <lb/>

<arrow.to.target n="marg142"/><lb/>&longs;peciei, &longs;eu individui; & tam &longs;alsæ, quàm dulces, aliæ alijs gra<lb/>viores &longs;unt, vt patet experientia, & fatentur etiam nautæ, vi<lb/>dentes naves è fluminibus impuris ad pura, aut è mari ad flumina <lb/>transeuntes &longs;ub&longs;idere profundiùs, & &longs;ubinde cum &longs;ubmer&longs;ionis <lb/>periculo. </s>

<s><margin.target id="marg142"/><emph type="italics"/>Aqua &longs;alsa <lb/>frigida, im<lb/>pura, gra<lb/>vior e&longs;t <expan abbr="quã">quam</expan> <lb/>dulcis &c.<emph.end type="italics"/></s>

<s><emph type="center"/>Proprietas VIII.<emph.end type="center"/></s>

<s><emph type="center"/>Aqua naturaliter non a&longs;cendit ad locum altio<lb/>rem &longs;uâ origine.<emph.end type="center"/></s>

<s><emph type="italics"/>IMò nec fluit naturaliter ab vno ad alterum locum, ni&longs;i terminus à quo <lb/>altior &longs;it, quàm terminùs ad quem.<emph.end type="italics"/> Vtrumque patet experientiä, <lb/>

<arrow.to.target n="marg143"/><lb/>& &longs;equitur ex dictis Proprietate I. & II. Hinc Hydragogi a&longs;&longs;e<lb/>runt, non po&longs;&longs;e deduciaquam de loco in locum, &longs;ive per alveum, <lb/>&longs;ive per aquæductus, canales, ac tubos deducenda &longs;it, &longs;i &longs;patium <lb/>&longs;it æquilibratum, &longs;eu ad libellam con&longs;titutum; nec &longs;ufficere <expan abbr="Ma-thematicã">Ma<lb/>thematicam</expan>, aut quam cunque phy&longs;icam declivitatem, &longs;ed requiri <lb/>in &longs;ingulis milliaribus cadentiam &longs;eu declivitatem quatuor ad

<pb xlink:href="051/01/103.jpg" pagenum="72"/>minimùm vnciarum vnius pedis, (e&longs;t vncia pars duodecima pe<lb/>dis) ita vt terminus ad quem in fine milliaris &longs;it vicinior centro <lb/>Terræ quatuorvncijs, quàm terminus à quo; &p o&longs;t alterum mil<lb/>liare alijs quatuor vncijs &longs;it vicinior, & &longs;ic deinceps &longs;emper, e&longs;t<lb/>que hæc regula à <expan abbr="pleris&qacute;ue">plerisque</expan> recepta tanquam Axioma hydra<lb/>gogicum. Sed de hac re fusè agemus in Pantometro no&longs;tro <lb/>Kircheriano lib. 9. vbi agemus ex profe&longs;&longs;o de Hydragogia & li. <lb/>bellatione aquarum; & in Mechanica Vniver&longs;ali. </s>

<s><margin.target id="marg143"/><emph type="italics"/>Aqua non <lb/>pote&longs;t decur <lb/>rereper &longs;pa<lb/>tium æqui<lb/>libratum.<emph.end type="italics"/></s>

<s><emph type="center"/>CAPVT II. <lb/>DE <lb/>Proprietatibus Aquæ fluentis per <lb/>&longs;iphones.<emph.end type="center"/></s>

<s>QUamvis in Machinis no&longs;tris Hydro-pnevmati<lb/>cis, Parte 2. indifferenter & pro eodem fumamus no<lb/>men &longs;iphonis, & tubi, pro fi&longs;tula &longs;cilicet, per quam <lb/>aqua fluit, &longs;ive recta illa &longs;it, &longs;ive curva; hîc tamen, <lb/>

<arrow.to.target n="marg144"/><lb/>maioris di&longs;tinctionis gratia, &longs;iphonem à tubo di&longs;tinguimus. <lb/>E<gap/>gitur Siphon nihil aliud quàm tubus inflexus. Huius variæ <lb/>&longs;unt &longs;pecies, vt &longs;equitur. </s>

<s><margin.target id="marg144"/><emph type="italics"/>Siphon quid<emph.end type="italics"/></s>

<s><emph type="center"/>Propo&longs;itio I.<emph.end type="center"/></s>

<s><emph type="center"/>Siphonis varias divi&longs;iones a&longs;&longs;ignare.<emph.end type="center"/></s>

<s>SIphon igitur, &longs;eu tubus in flexus, dividitur variè, & habet diver<lb/>

<arrow.to.target n="marg145"/><lb/>&longs;as figuras, vt apparet in appo&longs;itis &longs;chemati&longs;mis. Alius enim <lb/>dicitur &longs;iphon erectus, alius in ver&longs;us, aliusmixtus, alius æquali<lb/>um, alius in æqualium crurium. <lb/>

<arrow.to.target n="marg146"/></s>

<s><margin.target id="marg145"/><emph type="italics"/>Siphonis <lb/>&longs;pecies va<lb/>ria.<emph.end type="italics"/></s>

<s><margin.target id="marg146"/><emph type="italics"/>Siphon ere<lb/>ctus.<emph.end type="italics"/></s>

<s>Siphon erectus e&longs;t, cuius omnia crura &longs;ur&longs;um &longs;unt. Huius<lb/>modi &longs;unt &longs;eptem priores, & vltimus ex hîc appo&longs;itis. </s>

<s>

<arrow.to.target n="marg147"/></s>

<s><margin.target id="marg147"/><emph type="italics"/>Siphon in<lb/>ver&longs;us.<emph.end type="italics"/></s>

<s>Siphon inver&longs;us e&longs;t, cuius omnia crura deor&longs;um &longs;unt. Hu<lb/>iusmodi &longs;untijdem, &longs;i inver &longs;i intelligantur, hoc e&longs;t, &longs;i B &longs;ur&longs;um, <lb/>C & A deor&longs;um &longs;pectent. </s>

<s>

<arrow.to.target n="marg148"/></s>

<s><margin.target id="marg148"/><emph type="italics"/>Siphon mi<lb/>xtus.<emph.end type="italics"/></s>

<s>Siphon mixtus e&longs;t, cuius crura partim &longs;ur&longs;um, partim de<lb/>or&longs;um &longs;unt. Huiu&longs;modi &longs;unt tres penultimi ex appo&longs;itis, &longs;eu 8. 9. <lb/>& 10. </s>

<s>Siphones tam erecti, quàm inver&longs;i, vel habent vtrumque <lb/>erus æquale, vel inæquale. Si æqualia &longs;unt crura, vellongitu<lb/>dine & capacitate &longs;untæqualia, vt apparet in prima, tertia, & </s>

<s>

<arrow.to.target n="marg149"/><lb/>&longs;eptima figura: vel &longs;ola longitudine æqualia, capacitate verò <lb/>inæqualia, vt apparet in &longs;ecunda, quarta, quinta, &longs;exta, & vlti<lb/>ma figura. </s>

<s><margin.target id="marg149"/><emph type="italics"/>Siphones a<lb/>qualium, <lb/>& inaqua<lb/>lium cruri<lb/>um.<emph.end type="italics"/></s>

<s>Siphones mixti, vel habent omnia crura æqualia longitu<lb/>dine, vt in octava figura apparet; vel aliqua tantùm, utin nona <lb/>figura; vel nulla, ut in decima figura patet. Hæc eadem crura <lb/>po&longs;&longs;unt e&longs;&longs;e diver&longs;æ capacitatis inter &longs;e. <lb/>

<arrow.to.target n="marg150"/></s>

<s><margin.target id="marg150"/><emph type="italics"/>Siphon con<lb/>iugatus.<emph.end type="italics"/></s>

<s>Nota. Siphonem quartum aliqui vocant coniugatum, re<lb/>liquos verò inflexos appellant. </s>

<s><emph type="center"/>Propo&longs;itio II.<emph.end type="center"/></s>

<s><emph type="center"/>Siphonis erecti proprietates a&longs;&longs;ignare.<emph.end type="center"/></s>

<s>

<arrow.to.target n="marg151"/></s>

<s><margin.target id="marg151"/><emph type="italics"/>Siphonis e<lb/>recti proprie <lb/>tates.<emph.end type="italics"/></s>

<s><emph type="italics"/>PRima.<emph.end type="italics"/> Aqua vni &longs;iphonis erecti cruri infu&longs;a de&longs;cendit pri<lb/>mùm, deinde a&longs;cendit per alterum crus, donec &longs;upremæ &longs;u<lb/>perficies in vtroque <lb/>

<arrow.to.target n="fig17"/><lb/>crure &longs;int in eadem <lb/>linea horizontali. <lb/>Sint &longs;iphones erecti <lb/>ABCDEF, &longs;ive æ<lb/>qualium, &longs;ive inæ<lb/>qualium crurium, <lb/>tam quoad longitu<lb/>dinem, quàm quoad <lb/>capacitatem; vn<gap/><expan abbr="q;">que</expan> <lb/>crutium, &longs;ive longi<lb/>ori, &longs;ive breviori, <lb/>&longs;ive æquali, & &longs;ive <lb/>largiori, &longs;ive &longs;tricti<lb/>ori, v.g. cruri AB, <lb/>infundatur aqua: <lb/>de&longs;cendet ea <expan abbr="prim&utilde;">primum</expan> <lb/>v&longs;que ad B, <expan abbr="indeq;">indeque</expan> <lb/>per C & D a&longs;cen<lb/>det, donec &longs;upremæ <lb/>aqu&ecedil; &longs;uperficies &longs;int <lb/>in vtroque crure in <lb/>eadem linea Hori-

<pb xlink:href="051/01/106.jpg" pagenum="75"/>zontali, v.g. in linea HIK; hoc e&longs;t, donec omnes dictarum &longs;u<lb/>perficierum partes di&longs;tent æqualiter à centro terræ, juxta dicta <lb/>cap. 1. Proprietat. 2. Ratio de&longs;umitur ex dictis ibidem. Ex his <lb/>formo &longs;equens. </s>

<s><emph type="center"/>Axioma Hydraulicum I.<emph.end type="center"/></s>

<s><emph type="italics"/>QVantùm aqua de&longs;cendit per vnum &longs;iphonis erecti crus, tantundem </s>

<s>

<arrow.to.target n="marg152"/><lb/>a&longs;cendit per alterum.<emph.end type="italics"/> Idem contingit in omnibus canalibus, <lb/>alveis, & meatibus quibuscunque incurvatis. </s>

<s><margin.target id="marg152"/>Axioma hy <lb/>draulicum.</s>

<s><emph type="italics"/>Secunda.<emph.end type="italics"/> Si vni crurium, &longs;ive longiori, &longs;ive breviori, &longs;ive <lb/>æquali, & &longs;ive capaciori, &longs;ive minùs capaci, addas aliquid aquæ, <lb/>v.g. cruri AB; attollitur etiam alterius cruris aqua, donec rur<lb/>&longs;us &longs;uperficies di&longs;tent æqualiter a centrro terræ, &longs;eu &longs;int in eadem <lb/>linea horizontali, v.g. in linea GFE. Ratio e&longs;t eadem. </s>

<s><emph type="italics"/>Tertia.<emph.end type="italics"/> Si cruri longiori, &longs;ive id capacius &longs;it altero iam <lb/>pleno, &longs;ive non, addas plùs aquæ, v.g. cruri AB; de&longs;cendet ea <lb/>p<gap/> B, <expan abbr="elevabit&qacute;ue">elevabitque</expan> aquam cruris CDEF, & expellet per os <lb/>EF, donec ce&longs;&longs;ante infu&longs;ione &longs;it iterum vtraque &longs;uperficies in li<lb/>nea GFE. Patet experientiâ, & ratio e&longs;t eadem, ne &longs;cilicet &longs;u<lb/>perficies vnius cruris di&longs;tet plùs aut minùs, à centro terræ, quàm <lb/>alterius. </s>

Line 1648

Line 2004

<s>

<arrow.to.target n="marg160"/></s>

<s><margin.target id="marg160"/><emph type="

<s><margin.target id="marg160"/><emph type="italics"/>Siphonis in<lb/>ver&longs;i pro<lb/>prietates.<emph.end type="italics"/></s>

<s>PLurimas proprietates, easque plerumque miras habet Siphon <lb/>ever&longs;us, tam æqualium quoad longitudinem & capacitatem <lb/>crurium, quàm inæqualium. Nos præcipuas referemus. </s>

<s><emph type="center"/>Prima Proprietas.<emph.end type="center"/></s>

<s>SI crura &longs;iphonis inver&longs;i inæqualia &longs;unt quoad longitudinem, <lb/>& totus &longs;iphon repleatur aquâ, & invertatur; effluit ea tota per <lb/>cruslongius, licet &longs;it minus capacitate. E&longs;to Siphon inver&longs;us <lb/>ABC inæqualium crurium, aquâ plenus, & crus AB longius <lb/>&longs;it quàm crus CB, hoc e&longs;t, extremæ aquarum &longs;uperficies A & C <lb/>inæqualiter di&longs;tent à Centro Mundi, &longs;cilicet AB minùs, CB <lb/>plùs; dico, totam aquam effluere per crus AB, licet capacitate <lb/>&longs;it minus quàm CB. Ratio e&longs;t, quia cùm aquæ AB perpendi<lb/>culum, &longs;it longius, quàm aquæ CB perpendiculum, ma<lb/>gis premitur aqua apud A, quàm apud C, per corollarlum I.

<arrow.to.target n="fig19"/><lb/>Propo&longs;itione. II. <lb/>præcedentis; ac pro<lb/>indeper Propr. III. <lb/>cap. 1. aqua AB ex<lb/>pellet aquam CB, <lb/>non <expan abbr="quid&etilde;">quidem</expan> per pre&longs;<lb/>&longs;ionem, &longs;ed per at<lb/>tractionem; hoc e&longs;t, <lb/>effluetaqua AB, &longs;e<lb/>cumque <expan abbr="trahetaquã">trahetaquam</expan> <lb/>CB, & quidem to<lb/>tam, tum propter <lb/>rationem dictam, <lb/>tum nè detur vacu<lb/>um in &longs;iphone. </s>

<s><emph type="center"/>Annotatio I.<emph.end type="center"/></s>

<s><emph type="italics"/>MOnuit hîc P. Athana&longs;ius Kircherus, ea quæ diximus hoc loco, &longs;o<lb/>lùm e&longs;&longs;e intelligenda in eo ca&longs;u, in quo tubi<emph.end type="italics"/> ABC <emph type="italics"/>laxior portio<emph.end type="italics"/> BC <lb/><emph type="italics"/>inferiùs e&longs;t clau&longs;a, &longs;olo foramine<emph.end type="italics"/> I. <emph type="italics"/>relicto. Si enim totum orificium a<lb/>pertum fuerit; aqua nulla ratione &longs;i&longs;tipoterit quin effluat &longs;ecumque tra<lb/>hat aquam cruris<emph.end type="italics"/> BA. <emph type="italics"/>Rationem ad&longs;ignat, quia quando &longs;olum fora<lb/>men<emph.end type="italics"/> I <emph type="italics"/>e&longs;t apertum, &longs;ola columna aquea<emph.end type="italics"/> BI <emph type="italics"/>in fig.<emph.end type="italics"/> I. <emph type="italics"/>habet rationem per<lb/>pendiculi, eò quòd &longs;olum illa premat &longs;upra<emph.end type="italics"/> I. <emph type="italics"/>At quando totum orifi<lb/>cium e&longs;t apertum, tota aqua<emph.end type="italics"/> BHICG <emph type="italics"/>habet rationem perpendiculi, <lb/>quia tota premit &longs;upra orificium apertum, ac proinde æquivalet pluribus <lb/>perpendiculis æqualibus perpendiculo<emph.end type="italics"/> BI; <emph type="italics"/>quæ &longs;imul &longs;umpta &longs;uperant <lb/>perpendiculum longius<emph.end type="italics"/> BA. <emph type="italics"/>Addidit, hæc &longs;e longa experientia didici&longs;&longs;e.<emph.end type="italics"/></s>

<s><emph type="italics"/>Opportuna monitio, nec menti meæcontraria. Puto tamen, a<lb/>quam ex orificio<emph.end type="italics"/> CI <emph type="italics"/>penitus aperto effluere non tam obrationem ad&longs;ig<lb/>natam, quàm quòd aëri facillimus pateat ingre&longs;&longs;us ob laxitatem orificij; <lb/>quo ingrediente di&longs;continuatur aqua, & per vtrumque orificium <expan abbr="apert&utilde;">apertum</expan> <lb/>effluit.<emph.end type="italics"/></s>

<s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s>

<s>COnfirmatur hinc Axioma hydraulicum præcedens, quòd in <lb/>&longs;iphonibus (& etiam tubis, & quibuscunque va&longs;is) non pu<lb/>gnatur ponderibus, &longs;ed altitudinibus, &longs;eu perpendiculis. In<lb/>tellige, in ca&longs;u & &longs;en&longs;u explicato. </s>

<s><emph type="center"/>Annotatio II.<emph.end type="center"/></s>

<s><emph type="italics"/>DIcere quis po&longs;&longs;et, quando &longs;olùm patet foramen<emph.end type="italics"/> I, <emph type="italics"/>tunc attracto cy<lb/>lindrulo aqueo<emph.end type="italics"/> BI, <emph type="italics"/>faciliùs &longs;uccedit aër per foramen attractus, <lb/>quàm aqua lateralis<emph.end type="italics"/> HI, <emph type="italics"/>vel<emph.end type="italics"/> GI; <emph type="italics"/>immi&longs;&longs;oque aëre, aqua illa lateralis <lb/>facillimè effluet per foramen<emph.end type="italics"/> I. <emph type="italics"/>Quare in nullo ca&longs;u videtur po&longs;&longs;e ve<lb/>rificari, quòd aqua<emph.end type="italics"/> AB <emph type="italics"/>attrahat totam aquam<emph.end type="italics"/> BC <emph type="italics"/>Nego tamen id <lb/>recte dici, quia aër ingrediens per foramen<emph.end type="italics"/> I <emph type="italics"/>adhærebit &longs;olùm vltimæ <lb/>&longs;uperficiei aquæ fugientis.<emph.end type="italics"/></s>

<s><emph type="center"/>Secunda Proprietas.<emph.end type="center"/></s>

<s>SI crura &longs;iphonis inver&longs;i æqualia &longs;int quoad longitudinem, li<lb/>cetinæqualia capacitate (cum limitatione tamen po&longs;ita) & <lb/>totus repleatur aquâ, <expan abbr="invertatur&qacute;ue">invertaturque</expan>; nihil effluit. Decurtetur <lb/>in præcedente &longs;chemate crus AB in D, & repleatur totus&longs;iphon <lb/>aquâ, ita vt extremæ aquæ &longs;uperficies C & D æqualiter di&longs;tent <lb/>à centro mundi; dico, nihil effluere, licet cruris CB maior aqua <lb/>& pondero&longs;ior &longs;it, quàm aqua cruris AB. Idem fiet, &longs;i absque cru<lb/>ris AB decurtatione, extrema aquæ &longs;uperficies in illo æquè di<lb/>&longs;tetà centro Mundi, atque in crure CB, vt &longs;i vtro<gap/> e&longs;&longs;et in <lb/>linea horizontali CD, aut in linea GHE. Ratio e&longs;t, quia cùm <lb/>in vtroque crure æquale &longs;it <expan abbr="perpendicul&utilde;">perpendiculum</expan> &longs;eu altitudo aquæ, pre<lb/>metur vtrobique æqualiter; vel ergo vtriu&longs;que cruris aqua &longs;imul <lb/>de&longs;cendere deberet, quod fieri non pote&longs;t absque vacuo; vel <lb/>neutrius. Exhac, & præcedente Proprietate, formari pote&longs;t <lb/>aliud. </s>

<s><emph type="center"/>Axioma hydraulicum III.<emph.end type="center"/></s>

<s><emph type="italics"/>IN hydraulicis æqualia perpendicula æqualiter premunt, inæqualia </s>

<s>

<arrow.to.target n="marg161"/><lb/>inæqualiter, &longs;cilicet longius plùs, brevius minùs.<emph.end type="italics"/></s>

<s><margin.target id="marg161"/>Axioma by <lb/>draulicum.</s>

<s><emph type="center"/>Tertia Proprietas.<emph.end type="center"/><lb/>

<arrow.to.target n="marg162"/></s>

<s><margin.target id="marg162"/><emph type="italics"/>Aqua per <lb/>longius crus <lb/>&longs;iphonis ce<lb/>leriùs cur<lb/>rit, quàm <lb/>per brevius.<emph.end type="italics"/></s>

<s>AQua per longius crus &longs;iphonis inver&longs;i eò currit celeriùs, quò <lb/>longius fuerit crus. Ratio e&longs;t, quia quò longius e&longs;t crus, eò <lb/>longius e&longs;t aquæ de&longs;cendentis <expan abbr="perpendicul&utilde;">perpendiculum</expan>, ac proinde eò ma<lb/>ius pondus incumbit aquæ prope os, eòque magis premitur a<lb/>qua in egre&longs;lu, celeriúsque propterea effluit, & con&longs;equenter ce<lb/>leriùs de&longs;cendit. Hinc formo &longs;equens </s>

<s><emph type="center"/>Axioma Hydraulicum IV.<emph.end type="center"/></s>

Line 1747

Line 2148

<s>Quò verò crus externum longius fuerit infra &longs;uperficiem </s>

<s>

<arrow.to.target n="marg167"/><lb/>&longs;uperiorem aquæ va&lo

<arrow.to.target n="marg167"/><lb/>&longs;uperiorem aquæ va&longs;is, eò fluet aqua celeriùs, & æqualibus tem<lb/>poribus copio&longs;iùs: quia tunc eò magis perpendiculum externi <lb/>&longs;uperabit perpendiculum interni cruris in longitudine, & vi pre<lb/>mendi deor&longs;um. Non tamen &longs;ufficit, ut crus externum &longs;it qua-

<pb xlink:href="051/01/117.jpg" pagenum="86"/>cunque ratione longius crure interno, &longs;ed nece&longs;&longs;arium omnino <lb/>e&longs;t ut perpendiculum externi cruris longius &longs;it perpendiculo in<lb/>terni, juxta dicta &longs;uprà Protheoria I. §. VI. </s>

<s><margin.target id="marg167"/><emph type="italics"/>Aqua in<gap/><lb/>quali cele<lb/>ritate efflu<lb/>it ex crure <lb/>externo &longs;i<lb/>phonis,<emph.end type="italics"/></s>

<s><emph type="center"/>Secunda Proprietas.<emph.end type="center"/></s>

<s>Si crus externum FN decurtetur in K, & internum tan<lb/>gat ferè fundum in E, & ex ore K extrahatur aer; &longs;equetur <lb/>aqua u&longs;que ad os K, propter vacui metum, & tota ferè effluet, <lb/>donec <expan abbr="nimir&utilde;">nimirum</expan> perveniat &longs;uprema aquæ &longs;uperficies <expan abbr="u&longs;q;">u&longs;que</expan> ad o&longs;cu<lb/>lum E. Ratio e&longs;t, quia perpendiculum cruris externi longius <lb/>e&longs;t quàm interni. At po&longs;tquam aqua pervenerit u&longs;que ad o&longs;cu<lb/>lum E, nihil amplius effluit, quia perpendicula FE, FK &longs;unt <lb/>æqualia. Hærebit ergo aqua in æquilibrio in utroque crure. </s>

<s><emph type="center"/>Tertia Proprietas.<emph.end type="center"/></s>

<s>Si crus externum FN decurtetur in H, & internum <gap/><lb/>infra lineam LM, aut pertingat &longs;olummodò u&longs;que ad d<gap/><lb/>lineam; vas tamen &longs;it plenum u&longs;que ad lineam CD, aut<gap/><lb/>aqua &longs;it &longs;upra lineam LM; effluet aqua per os H, donec &longs;upre<lb/>ma aquæ va&longs;is &longs;uperficies perveniat u&longs;que ad lineam LM, & non <lb/>ampliùs. Ratio e&longs;t, quia antequam dicta aquæ &longs;uperficies per<lb/>veniat ad lineam LM, perpendiculum cruris externi e&longs;t &longs;em<lb/>per longius perpendiculo cruris interni; quando verò de&longs;cendit <lb/>jam ad dictam lineam, am bo perpendicula &longs;untæqualia. Fluxus <lb/>porrò difformitas quoad celeritatem aut tarditatem eadem e&longs;t, <lb/>quæ antea. </s>

<s><emph type="center"/>Quarta Proprietas.<emph.end type="center"/></s>

<s>Si crus externum decurtetur in G, ut &longs;it eju&longs;dem altitudi<lb/>nis &longs;upra Horizontem cum &longs;uperficie humidi CD, & aqua at<lb/>trahatur in G; nihil effluet, quia perpendicula &longs;unt æqualia: <lb/>quare aqua hærebit in æquilibrio in utroque crure. </s>

<s><emph type="center"/>Corollarium I.<emph.end type="center"/></s>

<s>Ex his colligitur primò, Si vas &longs;it plenum &longs;olummodò u&longs;que <lb/>

<arrow.to.target n="marg168"/><lb/>ad lineam LM, & &longs;iphonis crus externum decurtetur in H, vel <lb/>G, vel O, internum verò pertingat u&longs;que ad fundum; nihil <lb/>po&longs;&longs;e effluere ex crure externo. </s>

<s><margin.target id="marg168"/><emph type="italics"/>Perpendicu <lb/>li exce&longs;&longs;um <lb/>tuetur Na<lb/>tura in a<lb/>quæ fluxu.<emph.end type="italics"/></s>

<s><emph type="center"/>Corollarium II.<emph.end type="center"/></s>

<s>Colligitur &longs;ecundò, quàm pertinax &longs;it Natura, vel con&longs;tans <lb/>potiùs, in retinendo atque tuendo perpendiculi exce&longs;&longs;u, nè mi<lb/>

<arrow.to.target n="marg169"/><lb/>nor aut æqualis potentia dicatur vici&longs;&longs;e majorem. </s>

<s><margin.target id="marg169"/><emph type="italics"/>Perpendicu<lb/>lo, non copia <lb/>aquæ Natu<lb/>ra pugnat, <lb/>ac vincit, in <lb/>hydrauli<lb/>cis.<emph.end type="italics"/></s>

<s><emph type="center"/>Corollarium III.<emph.end type="center"/></s>

<s>Colligitur tertiò, quomodo Natura in Hydraulicis pugnet, <lb/>ac &longs;uperet, non aquarum copiâ, &longs;ed altitudine perpendiculari. </s>

<s><emph type="center"/>Corollarium IV.<emph.end type="center"/></s>

<s>Colligitur quartò, &longs;iphonis operationes hydraulicas ad li<lb/>bræ operationes commodè revocari po&longs;le, uti mox dicemus <lb/>Propo&longs;it: VIII. <expan abbr="&longs;eq.">&longs;eque</expan> </s>

<s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/><lb/>

<arrow.to.target n="marg170"/></s>

<s><margin.target id="marg170"/><emph type="italics"/>Fonticulus <lb/>duplex ope <lb/>&longs;iphonis in<lb/>ver&longs;i.<emph.end type="italics"/></s>

<s>Hinc etiam patet, <lb/>qua ratione &longs;iphonis <lb/>inver&longs;i præ&longs;idio fonti<lb/>culus duplex exhiberi <lb/>po&longs;&longs;it, &longs;i nimirum crus <lb/>brevius AB indatur <lb/>vitreo protuberanti <lb/>ventri BC, habeatque <lb/>intra ventrem &longs;tricti&longs;&longs;i<lb/>mum o&longs;culum B aper<lb/>tum; deinde ex eodem <lb/>ventre derivetur crus <lb/>longius DE in curva<lb/>tum inferiùs, & apud E <lb/><expan abbr="de&longs;in&etilde;s">de&longs;inens</expan> in o&longs;culum an<lb/>gu&longs;tum. Si enim hu<lb/>ju&longs;modi &longs;iphon impo<lb/>natur va&longs;i pleno, & ex <lb/>o&longs;culo E &longs;ugatur aër; <lb/>a&longs;cendet aqua per crus AB, & in ventre exiliet radiosâ virgulâ <lb/>vix a&longs;pectabili, indeque &longs;e demittet in crus alterum longius DE, <lb/>cogeturque &longs;ua propendente demi&longs;&longs;ione ad ejectionem eò altio<lb/>rem, quò profundiùs de&longs;cendet. </s>

<s><emph type="center"/>Propo&longs;itio VII.<emph.end type="center"/></s>

<s><emph type="center"/>Cau&longs;am ad&longs;ignare, cur quando o&longs;culum externi cruris <lb/>&longs;iphonis inver&longs;i, e&longs;t altius, aut æquè altum ac aquæ &longs;uperficies <lb/>&longs;uprema in va&longs;e, aqua non fluat; quando verò <lb/>e&longs;t demi&longs;&longs;ius, fluat.<emph.end type="center"/></s>

<s>VIdimus, experientiam docere, quando perpendiculum cru<lb/>ris externi &longs;iphonis inver&longs;i, e&longs;t minus, aut æquale perpendi<lb/>culo cruris interni, u&longs;que ad &longs;upremam aquæ &longs;uperficiem aquam <lb/>non effluere po&longs;&longs;e per os externi cruris, ce&longs;&longs;ante &longs;uctu, &longs;eu attra<lb/>ctione; quando verò perpendiculum externi e&longs;t majus quàm in<lb/>terni cruris in &longs;en&longs;u expo&longs;ito, fluere donec æqualia fiant perpen<lb/>dicula, aut donec tota effluxerit aqua ex va&longs;e. Quæritur nunc <lb/>hujus phænomeni cau&longs;a. <lb/>

<arrow.to.target n="marg171"/></s>

<s><margin.target id="marg171"/><emph type="italics"/>Siphonis <lb/>crus longius <lb/>&longs;uperat bre<lb/>vius, non <lb/>capacius mi <lb/><gap/> capax.<emph.end type="italics"/></s>

<s>Hero Alexandrinus in libello de Spiritalibus cap 1. ait, <lb/>quo&longs;dam putare, cau&longs;am e&longs;&longs;e, quòd aqua cruris externi debeat <lb/>trahere aquam cruris interni, ac proinde illa debeat e&longs;&longs;e major <lb/>ac copio&longs;ior, quàm hæc. Sed hoc minimè verum e&longs;&longs;e, patet ex <lb/>eo (quod etiam Hero advertit) quòd licet crus externum &longs;it lon<lb/>gè amplius atque capacius interno, <expan abbr="multo&qacute;ue">multoque</expan> plùs aquæ conti<lb/>neat; &longs;i tamen longius non e&longs;t, nequaquam effluit ex ip&longs;o aqua, <lb/>&longs;ed ubi ce&longs;&longs;at violenta &longs;uctio, &longs;eu tractio, tota refluit per crus in<lb/>ternum longius intra vas. Non ergo externum crus &longs;uperat in<lb/>ternum, quòd aquæ plùs contineat. Itaque videamus natura<lb/>lem cau&longs;am & genuinam, ex Heronis primò, deinde ex no&longs;tra <lb/>&longs;ententia. </s>

<s>Diximus cap. 1. Propriet. II. aquæ continuæ & quie&longs;centis <lb/>&longs;uperficiem &longs;uperiorem e&longs;&longs;e &longs;phæricam (etiam in parvis va&longs;is, & <lb/>receptaculis, licet in&longs;enfibiliter) centrum habentem idem quod <lb/>Terra, &longs;eu globus Terraqueus; non quie&longs;centem verò aquam <lb/>tam diu fluere, donec partes continuæ in una &longs;uperficie &longs;phærica <lb/>con&longs;tituantur, hoc e&longs;t, donec omnes extimæ &longs;uperficiei partes <lb/>continuæ æqualiter di&longs;tent à centro Terræ. Hoc po&longs;ito putat <lb/>Hero, cau&longs;am ob quam, quando externi cruris orificium e&longs;t

<pb xlink:href="051/01/120.jpg" pagenum="89"/>æquè altum ac &longs;uperficies &longs;uperior aquæ va&longs;is, hoc e&longs;t, quando </s>

Line 2133

Line 2592

<s><emph type="center"/>Pori&longs;ma I.<emph.end type="center"/></s>

<s>SEquitur hinc, ex eodem tubo, aut va&longs;e, non &longs;emper pleno, <lb/>æqualibus temporibus, non æqualem effluere aquam ex eo<lb/>dem foramine, &longs;ed in &longs;ecundo tempore minorem, quàm in pri<lb/>mo, & in tertio minorem, quàm in &longs;ecundo, & &longs;ic deinceps. <lb/>Vide Propo&longs;it. 24. </s>

<s><emph type="center"/>Pori&longs;ma II.<emph.end type="center"/></s>

<s>SEquitur præterea, &longs;patia quæ æqualibus temporibus evacu<lb/>antur in dicto ca&longs;u, non e&longs;&longs;e æqualia, &longs;ed &longs;ecundum &longs;patium <lb/>corre&longs;pondens &longs;ecundo tempori, e&longs;&longs;e minus primo; & tertium <lb/>&longs;patium corre&longs;pondens tertio tempori, minus &longs;ecundo; & &longs;ic de <lb/>cæteris. Vide ibidem. </s>

<s><emph type="center"/>Propo&longs;itio VII. Phænomenon VII.<emph.end type="center"/></s>

<s><emph type="center"/>Tubus altitudine quadrupedalis, cui pro ba&longs;is diametro <lb/>pedis Pari&longs;ien&longs;is vncia, aquâ &longs;emper plenus, effundit per lumen <lb/>lineare in ba&longs;i &longs;itum aquæ libram &longs;patio tredecim mi<lb/>nutorum &longs;ecundorum temporis.<emph.end type="center"/></s>

<s>OB&longs;ervavit hoc Marinus Mer&longs;ennus, ut a&longs;&longs;erit ip&longs;e in Hydrau<lb/>licis &longs;uis Phænomenis Propo&longs;it. 1. </s>

<s><emph type="center"/>Annotatio I.<emph.end type="center"/></s>

<s><emph type="italics"/>VTitur autem Mer&longs;ennus tam pede, quàm libra (heminam vocat ip&longs;e)<emph.end type="italics"/><lb/>

<arrow.to.target n="marg208"/><lb/><emph type="italics"/>Pari&longs;ien&longs;i. Et pedem quidem, uti in aliarum Nationum pedibus fie<lb/>ri&longs;olet, dividit in duodecim æquales partes, quas uncias appellat; & <lb/>quamlíbet vnciam &longs;ubdividit in alias duodecim partes æquales, quas <lb/>

<arrow.to.target n="marg209"/><lb/>ip&longs;e lineas, alij &longs;crupulos vocant. Vncia, &longs;eu duodecima pedis pars ap<lb/>pellatur etiam pollex; ab aliquibus verò cum Mer&longs;enno digitus: rectiùs <lb/>tamen digitus e&longs;t decima &longs;exta pars pedis, vt con&longs;tat ex Vitruvio, Iulio <lb/>Frontino, Columella, & alijs apud Villalpandum tom.<emph.end type="italics"/> 3. <emph type="italics"/>Apparatus <lb/>Part.<emph.end type="italics"/> 2. <emph type="italics"/>lib.<emph.end type="italics"/> 3. <emph type="italics"/>cap.<emph.end type="italics"/> 16. <lb/>

<arrow.to.target n="marg210"/></s>

<s><margin.target id="marg208"/><emph type="italics"/>Pes dividi<lb/>tur in vnci<lb/><gap/><emph.end type="italics"/> 12. <emph type="italics"/>& di<lb/>gitos<emph.end type="italics"/> 16.</s>

<s><margin.target id="marg209"/>Linea e&longs;t <lb/>duodecima <lb/>pars vncia.</s>

<s><margin.target id="marg210"/><emph type="italics"/>Minuti &longs;e<lb/><gap/>undi dura <lb/>tio, quanta <lb/>&longs;it.<emph.end type="italics"/></s>

<s><emph type="italics"/>Minutum &longs;ecundum e&longs;t &longs;exage&longs;ima pars unius minuti primi, &longs;eu<emph.end type="italics"/><lb/>3600. <emph type="italics"/>pars vnius horæ, & proximè re&longs;pondet lento arteriæ &longs;eu cordis <lb/>pul&longs;ui, ut Mer&longs;ennus a&longs;&longs;erit.<emph.end type="italics"/></s>

<s><emph type="center"/>Annotatio II.<emph.end type="center"/></s>

<s><emph type="italics"/>NOn e&longs;t nece&longs;&longs;e, ut ba&longs;is tubi quadrupedalis, quo fit ob&longs;ervatio, &longs;it </s>

<s>

<arrow.to.target n="marg211"/><lb/>pedalis, aut uncialis, aut alterius determinatæ amplitudinis atque <lb/>capacitatis, &longs;ed &longs;ufficit quantalibet latitudo tubi, dummodò foramen &longs;it <lb/>lineare. Ratio e&longs;t, quia; ut vidimus Propo&longs;itione<emph.end type="italics"/> 2. <emph type="italics"/>huius capitis, ea<lb/>dem aquæ quantitas eodem, vel æquali tempore, fluit ex tubo &longs;emper <lb/>pleno quantum vis arcto, vel lato, dummodò foramen &longs;it lineare, & al-<emph.end type="italics"/>

<pb xlink:href="051/01/148.jpg" pagenum="117"/><emph type="italics"/>titudo &longs;it quadrupedalis; adeo ut &longs;i totus Oceanus, ut &longs;uprà innuimus in <lb/>

<arrow.to.target n="marg212"/><lb/>Corollario I. Propo&longs;it.<emph.end type="italics"/> 2. <emph type="italics"/>e&longs;&longs;et inclu&longs;us va&longs;i quatuor pedum æltitudinis & <lb/>luminis linearis, non effunderet ni&longs;i vnicam heminam &longs;eu libram Pari<lb/>&longs;ien&longs;em &longs;patio tredecim minutorum &longs;ecundorum; Si tamen addas, inquit <lb/>Mer&longs;ennus, pro horis &longs;ingulis vnam quadrage&longs;imam quintam libræ <lb/>partem, quâ&longs;olet aqua marina &longs;uperare aquam fontium ac fluviorum in <lb/>pondere, & con&longs;equenter vi premendi, & vehementiùs è foramine e<lb/>rumpendi.<emph.end type="italics"/></s>

<s><margin.target id="marg211"/>Vas ampli<lb/>us non effu<lb/>dit plùs a <lb/>quæ per fora <lb/>men, quàm <lb/>minù, am-</s>

<s><margin.target id="marg212"/>plum, &longs;i al<lb/>titudo & fo<lb/>ramè æqua <lb/>lia &longs;unt.</s>

<s><emph type="center"/>Annotatio III.<emph.end type="center"/></s>

<s><emph type="italics"/>QVod dicit Mer&longs;ennus de tubo quadrupedali, & de libra aquæ, in<lb/>telligi debet &longs;olùm loquendo de pede & libra Pari&longs;ien&longs;i, non ve<lb/>rò aliarum Nationum, &longs;ed unu&longs;qui&longs;que in &longs;ua natione experientiam <lb/>facere debet, ut &longs;ciat quantum aquæ, quanto tempore, ex quantæ al<lb/>

<arrow.to.target n="marg213"/><lb/>titudinis, quantique foraminis tubo, ejiciatur. Cæterùm cùm diffe<lb/>rentia pedum, atque librarum apud diver&longs;as Nationes tanta &longs;it, quan<lb/>ta ip&longs;arum Nationum; cum&queacute; difficulter exacta men&longs;ura unius certi <lb/>ac determinati pedis, v. g. Romani, aut Pari&longs;ien&longs;is, ad alias Nationes <lb/>tran&longs;mitti libris impre&longs;&longs;is po&longs;&longs;it, quòd chartæ priùs madefactæ, ac dein<lb/>de &longs;iccatæ, non reddant fideliter longitudinem linearum impre&longs;&longs;arum; <lb/>nolo diutiùs huic rei inhærere, comparando pedem Pari&longs;ien&longs;em cum <lb/>pedibus aliarum Nationum. Faciat, qui volet, aut cujus intere&longs;t, <lb/>experientiam, ut videat quanto tempore tubus quatuor pedum regio<lb/>nis &longs;uæ ejiciat per lumen lineare aquæ libram itidem regionis &longs;uæ. De <lb/>exacta pedis Romani men&longs;ura, & de modo tran&longs;mittendi illum ad <lb/>alias nationes, di&longs;&longs;eram in Pantometro Kircheriano Lib.<emph.end type="italics"/> 1. <emph type="italics"/>Technico <lb/>Parte<emph.end type="italics"/> 2. <emph type="italics"/>Cap.<emph.end type="italics"/> 4. </s>

<s><margin.target id="marg213"/>Podis men<lb/>&longs;ura diver<lb/>&longs;a apud di<lb/>ver&longs;as na<lb/>tiones.</s>

<s><emph type="center"/>Propo&longs;itio VIII. Phænomenon VIII.<emph.end type="center"/></s>

<s><emph type="center"/>Aquæ fluentes ex tubis tam &longs;emper, quàm non &longs;em<lb/>per plenis æqualium foraminum, &longs;ed inæqualium altitudinum, <lb/>habent rationem &longs;ubduplicatam altitudinum tuborum; <lb/><expan abbr="habent&qacute;ue">habentque</expan> dicti tubi duplicatam rationem <lb/>aquarum, quas fundunt.<emph.end type="center"/></s>

<s>RAtio &longs;eu proportio duplicata quæcunque, e&longs;t ratio quæ<lb/>

<arrow.to.target n="marg214"/><lb/>cunque &longs;implex &longs;emel repetita, &longs;eu bis continuè &longs;umpta:

<pb xlink:href="051/01/149.jpg" pagenum="118"/>quemadmodum ratio quæcunque triplicata, quadruplicata, &c. <lb/>e&longs;t ratio quæcunque &longs;implex bis, ter &c. repetita, &longs;eu ter, <lb/>quater continuè &longs;umpta. Exemplum. Inter 2 & 1 reperitur <lb/>ratio dupla; hæc ratio &longs;i &longs;emel repetatur, &longs;eu adhuc &longs;emel <lb/>accipiatur, hoc e&longs;t, &longs;i bis continuè &longs;umatur hoc modo, 4, <lb/>2, 1; erit inter 4 & 1 ratio &longs;eu proportio duplicata illius pro<lb/>portionis, quæ e&longs;t inter 2 & 1, quandoquidem inter 4 & 1 <lb/>reperitur ratio dupla &longs;emel repetita, &longs;eu bis continuè <lb/>&longs;umpta, hoc e&longs;t, duplicata, &longs;cilicet &longs;emel inter 4 & 2, & ite<lb/>rum inter 2 & 1. Similiter inter 8 & 1 e&longs;t ratio triplicata il<lb/>lius, quæ e&longs;t inter 2 & 1, quia inter 8 & 1, intercedit ter <lb/>ratio dupla, nempe 8 ad 4, 4 ad 2, 2 ad 1. Sic 16 ad 1 ha<lb/>bet rationem quadruplicatam, & 32 ad 1 rationem quintu<lb/>plicatam rationis illius, quam habet 2 ad 1. Aliud exemplum. <lb/>Inter 6 ad 4 reperitur ratio &longs;e&longs;quialtera &longs;implex; hæc ratio <lb/>duplicatur, &longs;i adhuc &longs;emel repetatur, &longs;eu &longs;i bis continuè &longs;uma<lb/>tur, ut apparet in his numeris 9, 6, 4: nam quia ut 6 ad 4, <lb/>ita 9 ad 6; ideo inter 9 & 4 bis reperitur ratio &longs;e&longs;quialtera. <lb/>Si verò eadem ratio &longs;e&longs;quialtera bis repetatur, &longs;eu ter conti<lb/>nuè ponatur; erit inter extremos terminos ratio &longs;e&longs;quialtera <lb/>triplicata, ut apparet in his numeris, 13<gap/>, 9, 6, 4; quam pro<lb/>portionem ab&longs;que fractione habebis, &longs;i duplicaveris ho&longs;ce <lb/>numeros &longs;ic, 27, 18, 12, 8: nam ut 12 continet 8 &longs;emel cum <lb/>dimidio, ita 18 continet 12 &longs;emel cum dimidio, & 27 etiam <lb/>continet 18 &longs;emel cum dimidio. <lb/>

<arrow.to.target n="marg215"/></s>

Line 2198

Line 2710

<pb xlink:href="051/01/153.jpg" pagenum="122"/>Mundi, & Balianus lib 1. de Motu naturali gravium, Propo&longs;it. 6. <lb/>(licet deinde lib. 4. à pag. 110. ad 113. aliter &longs;tatuat) & po&longs;tip&longs;os <lb/>Ga&longs;&longs;endus in Epi&longs;tolis de motu impre&longs;&longs;o à motore, & Kirche<lb/>rus in Mu&longs;urgia lib. 6. parte 1. Lemmate 3. & con&longs;tat experien<lb/>

<arrow.to.target n="marg223"/><lb/>tiâ. Numeri pariter impares ab unitate numerati, &longs;unt hi: 1, <lb/>3, 5, 7, 9, 11, 13, 15 &c. Itaque &longs;i grave aliquod de&longs;cendens con<lb/>ficit in primo minuto temporis unum &longs;tadium &longs;patij; in &longs;ecundo <lb/>minuto conficiet tria ftadia, in tertio quinque, in quarto &longs;e<lb/>ptem, &c. Sic enim &longs;patia æqualibus temporibus confecta, <lb/>erunt inter &longs;e, ut quadrata temporum: nam quadratum mi<lb/>nuti primi e&longs;t 1; & quadratum minuti &longs;ecundi, 4; & quadra<lb/>tum minuti tertij, 9; & quadratum minuti quarti, 16 &c. ut <lb/>apparet inappo&longs;ita tabella.

<arrow.to.target n="table1"/><lb/>Cùm igitur grave de&longs;cen<lb/>dens in primo minuto con<lb/>ficiat unum &longs;patium, & in <lb/>&longs;ecundo minuto tria &longs;patia, <lb/>quæ cum uno conficiunt <lb/>quatuor; & in tertio minu<lb/>to quinque &longs;patia, quæ cum <lb/>quatuor efficiunt novem; & in quarto minuto &longs;eptem &longs;patia, <lb/>quæ cum novem efficiunt &longs;exdecim; & in quinto minuto no<lb/>vem &longs;patia, quæ cum &longs;exdecim efficiunt viginti quinque, &c. <lb/>apparet manife&longs;tè, &longs;patia tran&longs;mi&longs;&longs;a à gravi de&longs;cendente, ha<lb/>bere &longs;e, ut quadrata temporum æqualium, quibus percurrun<lb/>tur illa &longs;patia. In idem autem recidit, &longs;i dicas, &longs;patia tran&longs;<lb/>mi&longs;&longs;a certis temporibus habere inter &longs;e duplicatam rationem <lb/>&longs;eu proportionem illius proportionis, quam habent tempora, <lb/>quibus &longs;patia illa men&longs;urata fuerint: nam tempus &longs;eu minutum <lb/>&longs;ecundum ad primum, ut apparet ex tabella præcedente, ha<lb/>bet rationem &longs;eu proportionem duplam, &longs;patia verò &longs;ecundo <lb/>minuto confecta, nempe 1 ad 3 (quæ &longs;imul juncta efficiunt 4) <lb/>ad primum minutum habent rationem duplicatam rationis <lb/><gap/>plæ. Eadem e&longs;t ratio de cæteris. Lege etiam Mundum &longs;u<gap/>-

<pb xlink:href="051/01/154.jpg" pagenum="123"/>terraneum P. Athana&longs;ij Kircheri, ubi in Libro Centro&longs;ophico <lb/>fu&longs;i&longs;&longs;imè pertractat hanc materiam. Lege præterea Joannem <lb/>Caramuelem

<s><margin.target id="marg222"/>Lex II. gra<lb/>vium <expan abbr="de-&longs;cendenti&utilde;">de<lb/>&longs;cendentium</expan>.</s>

<s><margin.target id="marg223"/><emph type="italics"/>Numeri pa<lb/>riter impa<lb/>res ab unita <lb/>te numera<lb/>ti.<emph.end type="italics"/></s>

<table>

<row><cell>Tempora</cell><cell>Quadrata</cell><cell>Spatia</cell></row>

<s><emph type="center"/>Leges aquæ naturali motu de&longs;cendentis <lb/>& effluentis per tubos.<emph.end type="center"/></s>

<s>SIt jam tubus ABCD, &longs;ive &longs;emper, &longs;ive non &longs;emper plenus, <lb/>

<arrow.to.target n="marg224"/><lb/>cujus foramen B; <expan abbr="tempu&longs;&qacute;ue">tempu&longs;que</expan> in quo aqua ab A de&longs;cendit <lb/>u&longs;que ad B, dividatur in quinque æquales partes, in quarum <lb/>prima confecerit &longs;patium A1; Dico, eandem aquam in &longs;e<lb/>cunda parte temporis conficere &longs;patium A4, in tertia parte <lb/>

<arrow.to.target n="fig30"/><lb/>A9, in quarta &longs;patium A16, in quinta &longs;patium A25; <lb/>atque adeo &longs;patia æqualibus quinque temporibus <lb/>confecta, habere &longs;e ut quadrata quinque illorum <lb/>temporum, ut ex appo&longs;itis utrimque numeris ap<lb/>paret; &longs;eu velocitatem de&longs;cen&longs;us aquæ cre&longs;cere &longs;e<lb/>cundùm progre&longs;&longs;ionem numerorum imparium, <lb/>prout indicant numeri intra tubum notati; &longs;eu <lb/>&longs;patia confecta habere duplicatam rationem illius, <lb/>quam habent tempora, ut apparet &longs;i conferas nu<lb/>meros externos lateris AB, cum numeris lateris <lb/>CD. Ratio e&longs;t, quia aqua gravis e&longs;t, & intra tu<lb/>bum naturali motu de&longs;cendit, nullumque ade&longs;t <lb/>impedimentum motus; ergo imitari debet leges aliorum gra<lb/>vium naturali motu de&longs;cendentium. </s>

<s><margin.target id="marg224"/><emph type="italics"/>Leges aqua <lb/>naturali <lb/>motu de<lb/>&longs;cendentis <lb/>per tubos.<emph.end type="italics"/></s>

<s><emph type="center"/>Corollarium I.<emph.end type="center"/></s>

<s>COlligitur hinc primò, Aquam è foramine B, tubi &longs;emper <lb/>

<arrow.to.target n="marg225"/><lb/>pleni, effluere tantâ velocitate, quantâ de&longs;cendit ab A ad <lb/>B. Ratio e&longs;t, quia ut &longs;upponitur, tantum effluit per B, quan<lb/>tum influit per A, & è contrario tantum per A influit, quan<lb/>tum per B effluit, & in de&longs;cen&longs;u ab A ad B nulla fit inter<lb/>ruptio; ergo tam velociter effluit per B, quàm velociter de<lb/>&longs;cendit ab A ad B. </s>

<s><margin.target id="marg225"/><emph type="italics"/>Leges aquæ <lb/>effluentis <lb/>per <expan abbr="foram&etilde;">foramen</expan> <lb/>tubi &longs;emper <lb/>pleni.<emph.end type="italics"/></s>

<s><emph type="center"/>Corollarium II.<emph.end type="center"/></s>

<s>COlligitur &longs;ecundò, Aquam apud B, in utroque tubo, hoc e&longs;t, <lb/>&longs;emper & non &longs;emper pleno, tantâ &longs;olùm vi premi prope <lb/>foramen B, quanta e&longs;t vis &longs;eu pondus aquæ à B u&longs;que ad &longs;u<lb/>premam aquæ &longs;uperficiem, id e&longs;t, columnæ aqueæ habentis <lb/>pro ba&longs;i latitudinem foraminis B, pro altitudine perpendicu<lb/>larem à B ad dictam &longs;uperficiem. Ratio e&longs;t, quia &longs;olùm illa <lb/>columna premit &longs;upra B, per dicta Propo&longs;it. 1. Intellige, ni&longs;i <lb/>illa aliunde impetum recipiat, ut &longs;i ip&longs;i affunderetur aqua ex <lb/>tubo inclinato, &longs;ive conjuncto, &longs;ive di&longs;iuncto. </s>

<s><emph type="center"/>Corollarium. III.<emph.end type="center"/></s>

<s>COlligitur tertiò, Leges prædictas de&longs;cen&longs;us gravium &longs;ervari <lb/>

<arrow.to.target n="marg226"/><lb/>ab aqua in tubo &longs;emper pleno, de&longs;cendendo ab A ad B, &longs;o<lb/>lùm in primo de&longs;cen&longs;u, non verò in de&longs;cen&longs;u continuato; item <lb/>&longs;olùm à prima parte aquæ de&longs;cendentis, <expan abbr="nõ">non</expan> à partibusip&longs;i conti<lb/>guis & &longs;ub&longs;equentibus. Explico De&longs;cendat aqua ab A ad B, effi<lb/>ciatque de&longs;cen&longs;us columnam aqueam AB, quæ dividatur in vi<lb/>ginti <expan abbr="quinq;">quinque</expan> æquales partes &longs;ecundùm longitudinem &longs;eu altitu<lb/>dinem ab A ad B. Dico, &longs;olùmvige&longs;imam quintam partem, quæ <lb/>e&longs;t apud B, &longs;ervare prædictam legem de&longs;cen&longs;us gravium cre<lb/>&longs;centis in velocitate &longs;ecundùm numeros impares ab unitate <lb/>numeratos; & quidem illam &longs;olam vige&longs;imam quintam par<lb/>tem, quæ e&longs;t in prima columna aquea à de&longs;cen&longs;u aquæ for<lb/>mata, non verò quæ e&longs;t in reliquis columnis &longs;ub&longs;equentibus. <lb/>Ratio e&longs;t, quia cùm nulla pars ex viginti quinque egrediatur <lb/>è foramine B, quin ingrediatur alia per orificium A priori <lb/>æqualis; & nulla tran&longs;eat vige&longs;imum quintum & ultimum &longs;pa<lb/>tiolum lateris AB, quin eodem tempore tran&longs;eat alia æqualis <lb/>primum &longs;patiolum, & alia &longs;ecundum, & alia tertium, ac reli<lb/>qua omma; nece&longs;sè e&longs;t ut omnes reliquæ partes eâdem velo<lb/>citate conficiant &longs;ingula &longs;patiola, qua velocitate ultima con<lb/>ficit ultimum; & eâdem velocitate unaquæque pertran&longs;eat <lb/>&longs;patiolum &longs;ibi corre&longs;pondens, qua velocitate ultima pars per<lb/>tran&longs;it ultimum &longs;patiolum. Patet ergo propo&longs;itum. </s>

<s><margin.target id="marg226"/><emph type="italics"/>Lex de&longs;cen <lb/>&longs;us aquæ è <lb/>tubo expli<lb/>catur.<emph.end type="italics"/></s>

<s><emph type="center"/>Corollarium IV.<emph.end type="center"/></s>

<s>COlligitur quartò, Aquam è foramine B efflue<lb/>

<arrow.to.target n="marg227"/><lb/>re eò majori velocitate, quò altior fuerit tu<lb/>bus. Ratio e&longs;t, quia quò altior e&longs;t tubus, eò ma<lb/>jorem velocitatem adquirit prima pars aquæ de<lb/>&longs;cendentis in &longs;uo de&longs;cen&longs;u, & con&longs;equenter reli<lb/>quæ &longs;ub&longs;equentes; item quò altior e&longs;t tubus, eò <lb/>altior e&longs;t columna aquea premens apud B. ideo<lb/>que eò vehementiùs premit apud idem B. Vide <lb/>quæ diximus Propo&longs;it. VI. </s>

<s><margin.target id="marg227"/><emph type="italics"/>Aqua è tu<lb/>bo eò velo<lb/>ciùs effluit, <lb/>quò altior <lb/>e&longs;t tubus.<emph.end type="italics"/></s>

<s><emph type="center"/>Corollarium V.<emph.end type="center"/></s>

<s>COlligitur quintò, Aquam ex æqualibus tubis, quoad fora<lb/>

<arrow.to.target n="marg228"/><lb/>mina & altitudines, effluere æquali velocitate. </s>

<s><margin.target id="marg228"/><emph type="italics"/>Aqua ex æ<lb/>qualibus tu<lb/>bis quoad o<lb/>mnia, æqua<lb/>li velocita<lb/>te effluit,<emph.end type="italics"/></s>

<s><emph type="center"/>Propo&longs;itio X. Theorema II.<emph.end type="center"/></s>

<s><emph type="center"/>Velocitates motus aquæ de&longs;cendentis & effluentis per <lb/>tubos æqualium foraminum, &longs;ed inæqualium altitu<lb/>dinum, habent &longs;ubduplicatam rationem <lb/>altitudinum.<emph.end type="center"/></s>

<s>ESto tubus AB altus uno pede, & alius CD al<lb/>tus quatuor pedibus, &longs;ed uterque æqualium <lb/>foraminum, &longs;ive &longs;emper, &longs;ive non &longs;emper pleni, è <lb/>quibus effluat aqua inæquali velocitate, juxta di<lb/>cta Propo&longs;itione præcedente, Corollario IV. Dico, <lb/>velocitates motus & effluxus aquarum e&longs;&longs;e in &longs;ub<lb/>duplicata ratione tuborum, hoc e&longs;t, aquam per <lb/>tubum CD de&longs;cendere, & effluere duplo velo<lb/>ciùs, quàm per tubum AB. Quoniam enim aquæ <lb/>

<arrow.to.target n="marg229"/><lb/>motus per tubos æmulatur leges gravium de&longs;cen<lb/>dentium motu naturali, per dicta Propo&longs;it. IX. <lb/>præcedente, hoc e&longs;t, cre&longs;cit in velocitate &longs;ecun-

<arrow.to.target n="fig31"/><lb/>dùm progre&longs;&longs;ionem numerorumim parium ab un<gap/><lb/>tate numeratorum; &longs;i aqua in primo tempore d<gap/><lb/>terminato, v.g. in primo minuto de&longs;cendit à C i<gap/><lb/>E, hoc e&longs;t, ab A in B; in &longs;ecundo minuto d<gap/><lb/>&longs;cendet ab E ad D, ac proinde in fine quarti pa<gap/><lb/>mi mota erit duplo velociùs, quàm in fine prin<gap/><lb/>palmi; Ergo velocitas motus aquæ per tubum CI<gap/><lb/>ad velocitatem aquæ per tubum AB, habet &longs;ul<gap/><lb/>duplicatam rationem altitudinum. Eadem e<gap/><lb/>ratio in alijs inæqualibus altitudinibus, quamcu<gap/><lb/>que habeant inter &longs;e proportionem. </s>

<s><margin.target id="marg229"/><emph type="italics"/>Proportio <lb/>velocitatis <lb/>motus aquæ <lb/>de&longs;cenden<lb/>tis per tubos: <lb/><expan abbr="inæquali&utilde;">inæqualium</expan> <lb/>foraminum.<emph.end type="italics"/></s>

<s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/><lb/> </s>

<s>TUbi ergo duplicatam habent rationem illius, quam haben<gap/><lb/>velocitates motus de&longs;cendentis, & effluentis per ip&longs;os aquæ<gap/></s>

<s><emph type="center"/>Propo&longs;itio XI. Theorema III.<emph.end type="center"/></s>

<s><emph type="center"/>Cau&longs;am a&longs;&longs;ignare, cur aquæ fluentes per tubos æqua <lb/>lium luminum, &longs;ed inæqualium altitudinum, habeantra<lb/>tionem &longs;ubduplicatam altitudinum tuborum.<emph.end type="center"/></s>

<s>

<arrow.to.target n="marg230"/></s>

<s><margin.target id="marg230"/><emph type="italics"/>Proportio<lb/>nis prædicta <lb/>cau&longs;a.<emph.end type="italics"/></s>

<s>QUod a&longs;&longs;eruimus Propo&longs;it. VIII. huius capitis, demon&longs;tran<gap/><lb/>dum hîc e&longs;t, utfidemibi obligatam &longs;olvamus. </s>

<s>Ratio igitur ad&longs;ignati hîc & ibi Phænomeni e&longs;t, quòd flu<gap/><lb/>xus aquæ per foramen, &longs;eu quantitas aquæ effluentis, pendet<gap/><lb/>velocitate aquæ eiusdem de&longs;cendentis per tubum, per dict<gap/><lb/>Propo&longs;it. IX. Corollario. I. Velocitas autem illa e&longs;t &longs;ubduplicata<gap/><lb/>altitudinum, per dicta Propo&longs;it. X; ergo & quantitas aquæ efflu<lb/>entis ex tubis inæqualium altitudinum &longs;ubduplicata erit <expan abbr="tubor&utilde;">tuborum</expan>. </s>

<s><emph type="center"/>Propo&longs;itio XII. Theorema IV.<emph.end type="center"/></s>

<s><emph type="center"/>Tempora quibus æqualis aquæ quantitas è tubis æqua<lb/>lium luminum, &longs;ed inæqualium altitudinum effluit, ha<lb/>bent &longs;ubduplicatam rationem tuborum.<emph.end type="center"/></s>

<s>

<arrow.to.target n="marg231"/></s>

<s><margin.target id="marg231"/><emph type="italics"/>Proportio <lb/>temporum <lb/>quibus a<lb/>qua effluit è <lb/>tubis.<emph.end type="italics"/></s>

<s>SItut antea tubus AB vnius, & tubus CD quatuor pedum in <lb/>altitudine, &longs;ed æqualium luminum, &longs;ive &longs;emper, &longs;ive non &longs;em-

<pb xlink:href="051/01/158.jpg" pagenum="127"/>per pleni; fluatque ex tubo AB vna libra aquæ &longs;patio duorum <lb/>minutorum. Dico, eandem aquam effluere ex tubo CD &longs;pa<lb/>tio vnius minuti, <expan abbr="e&longs;&longs;e&qacute;ue">e&longs;&longs;eque</expan> propterea tempus fluxus aquæ ex tubo <lb/>CD, ad tempus fluxus aquæ ex tubo AB, ut 1 ad 2, quæ e&longs;t ratio <lb/>&longs;ubduplicata tuborum. Ratio ex dictis patet. Quoniam enim <lb/>velocitates effluxûs aquæ ex æquali lumine habent &longs;ubduplica<lb/>tam rationem tuborum, ut demon&longs;travimus Propo&longs;it. X, fluet in <lb/>dimidio temporis tantum ex tubo CD, quantum in toto tem<lb/>pore ex tubo AB, po&longs;ita æqualitate luminum; ac proinde in <lb/>toto tempore duplum effluet ex tubo CD. Eadem e&longs;t ratio in <lb/>alijs tuborum æqualium luminum proportionibus. </s>

<s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s>

<s>TUbi ergo quilibet æqualium luminum, &longs;ed inæqualium alti</s>

<s>

<arrow.to.target n="marg232"/><lb/>tudinum, habent rationem duplicatam temporum, quibus <lb/>effluit æqualis aquæ quantitas. </s>

<s><margin.target id="marg232"/><emph type="italics"/>Proportio <lb/>tuborum <gap/><lb/>tempora fl<gap/><lb/>xus aquæ.<emph.end type="italics"/></s>

<s><emph type="center"/>Propo&longs;itio XIII. Theorema V.<emph.end type="center"/></s>

<s><emph type="center"/>Si tubi, &longs;ive &longs;emper pleni, &longs;ive non &longs;emper pleni, &longs;int <lb/>eiu&longs;dem altitudinis, &longs;ed inæqualium foraminum, e&longs;t eadem ra<lb/>tio aquæ ad aquam, quæ foraminis ad foramen, <lb/>phy&longs;icè &longs;eu ad &longs;en&longs;um.<emph.end type="center"/></s>

<s>ESt Mer&longs;enni in hydraulicis Phænomenis Propo&longs;it. IV. quem <lb/>

<arrow.to.target n="marg233"/><lb/>&longs;equitur P. Andreas Tacquet in &longs;uis hydraulicis Manu&longs;cri<lb/>ptis cap. 4. Phænomen. 7. Ratio e&longs;t, quòd licet ex maiori lu<lb/>mine &longs;eu foramine fluat eodem tempore maior aquea columna <lb/>quàm ex minori, tantòque maior exillo quàm ex hoc, quantò <lb/>fuerit maius lumen &longs;eu <expan abbr="foram&etilde;">foramen</expan> illud quàm hoc, quoad aream, per <lb/>dicta Propo&longs;it. 4. huius eapitis; tamen vtraque columna fluit <lb/>ex æquali altitudine tuborum æquâ velocitate phy&longs;icè & ad <lb/>&longs;en&longs;um. </s>

<s><margin.target id="marg233"/><emph type="italics"/>Proportio <gap/><lb/>quæ ad <gap/><lb/><expan abbr="quã">quam</expan> eadem. <lb/>quæ forami<lb/>num in tu<lb/>bu æquè <gap/><lb/>tis.<emph.end type="italics"/></s>

<s>Dixi phy&longs;icè & ad &longs;en&longs;um, quia licet gravia eiusdem &longs;pe<lb/>ciei, &longs;ed inæqualis molis ac ponderis, ab eodem ad eundem

<pb xlink:href="051/01/159.jpg" pagenum="128"/>terminum non de&longs;cendant æquè velociter, revera & mathema<lb/>ticè, quemadmodum &longs;entiunt Galilæus Dialogo 2. de Sy&longs;tem. <lb/>Mundi, Ioannes Bapti&longs;ta Balianus lib. 1. de motu naturali gravi<lb/>um &longs;olidorum in Præfat. Nicolaus Cabæus lib. 1. Meteoror. textu <lb/>17. <expan abbr="q.">que</expan> 5. & 6. Arriaga di&longs;put. 4. de Generat. &longs;ect. 5. &longs;ub&longs;ect. 3. <lb/>Ma&longs;trius, Bellutus, & alij (quod ego fal&longs;um exi&longs;timo, mathe. <lb/>maticè loquendo, cum Patre Ioanne Bapti&longs;ta Ricciolo, qui <lb/>tom. 1. Almage&longs;ti Novi lib. 2. cap. 21. Propo&longs;it. 2. & lib. 9. &longs;ect. 4. <lb/>num. 24. a&longs;&longs;erit, <emph type="italics"/>duorum gravium eiusdem &longs;peciei & figuræ &longs;ea inæ<lb/>qualis molis ac ponderis, ex eadem altitudine momento eodem dimi&longs;<lb/>&longs;orum, illud naturali motu citiùs de&longs;cendere ad eundem terminum, quod <lb/>e&longs;t gravius;<emph.end type="italics"/> ubi etiam Experimenta multa diver&longs;is annis coram <lb/>multis viris doctis incredibili diligentiâ peracta Bononiæ refert <lb/>num. 13.) tamen in parvis altitudinibus, quales &longs;unt tuborum <lb/>in omni ferè ca&longs;u, tam exigua e&longs;t differentia velocitatum, ut pro <lb/>eâdem &longs;eu æquali cen&longs;eri meritò po&longs;&longs;it. </s>

Line 2287

Line 2917

<s>SUppono hîc id, quod notavi &longs;uprà Pro<lb/>po&longs;it. XIII. tam exiguam e&longs;&longs;e differen<lb/>tiam inter velocitates aquarum ex tubis <lb/>eiusdem altitudinis, & diver&longs;orum fora<lb/>minum, <expan abbr="effluenti&utilde;">effluentium</expan>, ut cen&longs;eri meritò po&longs;<lb/>&longs;it, aquam ad aquam e&longs;&longs;e, utforamen ad <lb/>foramen. Quo po&longs;ito. <lb/>

<arrow.to.target n="marg239"/></s>

<s><margin.target id="marg239"/><emph type="italics"/>Data alti<lb/>tudine & <lb/>foramine tu <lb/>bi, invenire <lb/>aquæ quan<lb/>titatem da<lb/>to tempore <lb/>effluentem.<emph.end type="italics"/></s>

<s>Sit, exempli gratia, altitudo tubi <lb/>ADB pedum 64, luminis &longs;eu foraminis <lb/>diameter DB digitalis, tempus hora una. <lb/>Oporteat igitur reperire, quantum aquæ <lb/>tribuat, &longs;eu quantam ci&longs;ternam impleat, <lb/>prædictus tubus, intra unam horam. So<lb/>lutio pendet ex dictis Propo&longs;it. VII. XIII. <lb/>& VIII. & præterea ex Propo&longs;it. 2. lib. 12. Eu<lb/>clidis. Igitur tubum 4 pedes altum, & <lb/>luminis linearis, repræ&longs;entet CPK. Ex <lb/>tubo ADB. &longs;ume EDB portionem <expan abbr="etiã">etiam</expan> <lb/>4 pedes altam. Et quoniam diameter DB <lb/>digitalis, e&longs;t ad linearem PK, ut 12 ad 1; <lb/>eritper Propo&longs;it. &longs;ecundam lib. 12. Eucli<lb/>dis, lumen DB ad lumen KP, utquadra<lb/>tum diametri DB, ad quadratum diame<lb/>tri PK, hoc e&longs;t, ut 144 ad 1. Quare cùm <lb/>per Propo&longs;it. XIII. præcedentem, in tubis <lb/>æquè altis & &longs;emper plenis, &longs;ed inæquali<lb/>um luminum, aqua ab uno effu&longs;a, fit ad a<lb/>quam ab altero effu&longs;am, tempore eodem, <lb/>utlumen ad lumen; dabit EDB. centies <lb/>quadragies quater plus aquæ, quàm det <lb/>eodem tempore tubus CPK: Sed tubus <lb/>CPK, per Propo&longs;it. VII. præcedentem, <lb/>&longs;patio tredecim &longs;ecundorum temporis dat <lb/>unam libram aquæ: Ergo tubus EDB

<arrow.to.target n="fig33"/><lb/>&longs;patio tredecim &longs;ecundorum tomporis da<lb/>bit 144 libras. <expan abbr="Quoniã">Quoniam</expan> autem in una hora, <lb/>&longs;eu in 60. minutis primis, hoc e&longs;t, in 3600 <lb/>minutis &longs;ecundis, tredecim &longs;ecunda con<lb/>tinentur ducenties &longs;eptuagies &longs;exies, rema<lb/>nentque <gap/>, &longs;ive (facilioris calculi gratia) <lb/>ducenties &longs;eptuagies &longs;epties; &longs;i 144 libras, <lb/>quas tredecim &longs;ecundis dat tubus EDB, <lb/>multiplices per 277, fient ferè 39888. li<lb/>bræ, quas horæ &longs;patio fundit tubus EDB. <lb/>Inveniatur iam inter 64, altitudinem nem<lb/>pe tubi ADB, & inter 4, altitudinem ni<lb/>mirum portionis EDB, media proporti<lb/>onalis 16. Quoniam igitur per Propo&longs;it. <lb/>VIII. præcedentem, aquæ quas tubi ADB, <lb/>& EDB &longs;emper pleni, eodem tempore <lb/>fundunt, &longs;unt in &longs;ubduplicata ratione eius <lb/>quam habent altitudines ADB, & EDB; <lb/>erit aqua quam horæ &longs;patio dat tubus <lb/>EDB, ad aquam quam eodem tempore <lb/>dabit tubus ADB, ut 4 ad 16, &longs;eu ut 1 ad 4. <lb/>Itaque &longs;i fiat, ut 1 ad 4, ita 39888 (tot enim <lb/>aquæ libras iam o&longs;tendimus horæ &longs;patio <lb/>dare tubum EDP) ad alium numerum, <lb/>nempe ad 159552, quot hic continet vni<lb/>tates, tot aquæ libras horæ &longs;patio dabit tu<lb/>bus ABD &longs;emper plenus, lumen habens <lb/>digitale, altitudinem pedum 64; atque <lb/>adeo tubus prædictus implebit horæ &longs;pa<lb/>tio ci&longs;ternam capacem librarum <lb/>aquæ 159552. </s>

<s><emph type="center"/>Annotatio.<emph.end type="center"/></s>

<s>

<arrow.to.target n="marg240"/></s>

<s><margin.target id="marg240"/><emph type="italics"/>Pari&longs;ien&longs;es <lb/>libra<emph.end type="italics"/> 72. <emph type="italics"/>ef<lb/>ficiunt pe<lb/>dem <expan abbr="cubis&utilde;">cubisum</expan> <lb/>aquæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>MEr&longs;ennus ait, heminas &longs;eu libras Pari&longs;ien&longs;es<emph.end type="italics"/> 72. <emph type="italics"/>efficere pedem <lb/>cubicum aquæ. Itaque &longs;i placet prædictas libras ad pedes cubi<lb/>cos reducere, divide numerum<emph.end type="italics"/> 159552 <emph type="italics"/>per<emph.end type="italics"/> 72, <emph type="italics"/>& quotiens<emph.end type="italics"/> 2216 <emph type="italics"/>da<lb/>bit aquæ pedes cubicos quos horæ &longs;patio fundet tubus<emph.end type="italics"/> ADB. </s>

<s><emph type="center"/>Propo&longs;itio XVIII. Problema II.<emph.end type="center"/></s>

<s><emph type="center"/>Datis altitudine & lumine tubi &longs;emper pleni, invenire <lb/>tempus quo datam aquæ quantitatem effundat, &longs;i<lb/>ve quo datam ci&longs;ternam impleat.<emph.end type="center"/></s>

<s>SIt tubus &longs;emper plenus ADB, v.g. 16 pedes altus, lumen </s>

<s>

<arrow.to.target n="marg241"/><lb/>habens digitale DB; &longs;it verò quantitas aquæ à tubo ADB <lb/>effundendæ, aut ci&longs;terna ab eodem replenda, 3000 pedum cu<lb/>bicorum. Oporteat invenire tempus quo dictam aquam ef<lb/>fundat, aut dictam ci&longs;ternam impleat. </s>

<s><margin.target id="marg241"/><emph type="italics"/>Data alti<lb/>tudine & <lb/>foramine <lb/>tubi, inve<lb/>nire tempus <lb/>quo data a<lb/>qua effluit.<emph.end type="italics"/></s>

<s>Revocentur primò 3000 pedes cubici aquæ ad heminas <lb/>

<arrow.to.target n="fig34"/><lb/>&longs;eu libras (quod fiet, &longs;i 3000 multiplica<lb/>bis per 72. fiatq, numerus librarum 216000, <lb/>(quandoquidem unus pes cubicus conficit <lb/>72 libras, ut diximus Propo&longs;it: præceden<lb/>te in Annotat:) Deinde &longs;umatur ex ADB, <lb/>tubus quadrupedalis EDB: Demum inter <lb/>ADB altitudinem, id e&longs;t, 16, & EDB alti<lb/>tudinem, id e&longs;t, 4, inveniatur medius nu<lb/>merus proportionalis 8. Igitur, per Pro<lb/>po&longs;it. VIII. præcedentem, aqua fluens per <lb/>tubum EDB, e&longs;t ad aquam per tubum <lb/>ADB eodem tempore fluentem, ut 4 ad 8, <lb/>in ratione videlicet &longs;ubduplicata altitudi<lb/>num EDB 4 pedum, & ADB 16 pedum. <lb/>Quo ergo tempore dat tubus ADB 3000 <lb/>pedes cubicos aquæ, id e&longs;t, 216000 hemi<lb/>nas &longs;eu libras; eodem tempore EDB dabit duplò minus, &longs;eu

<arrow.to.target n="fig35"/><lb/>heminas &longs;olùm 108000. A&longs;&longs;umatur jam, <lb/>ut antea, tubus quadrupedalis CPK lu<lb/>minis linearis. Tubi EDB, CPK, &longs;unt æ<lb/>què alti; & lumina DB, PK, dantur, per <gap/><lb/>Propo&longs;it. lib. 12. Euclid. nempe 1, & 144 <lb/>lineæ quadratæ; aqua etiam quam CPK <lb/>fundit&longs;patio 13 &longs;ecundorum, datur, per VII. <lb/>præcedentem, una nimirum libra: Qua<lb/>re cùm quantitates aquæ à tubis æquè al<lb/>tis eodem tempore effu&longs;æ &longs;int ut lumina, <lb/>per Propo&longs;it. XIII. præcedentem, &longs;i fiat ut <lb/>lumen PK, ad lumen DB, id e&longs;t, ut 1 ad <lb/>144, ita aqua unius ad aquam alterius; pro<lb/>ducetur numerus heminarum &longs;eu libra<lb/>rum, quas effundit tubus EDB &longs;patio tre<lb/>decim &longs;ecundorum, nempe 144. Quo<lb/>niam igitur tubus EDB 144 libras dat &longs;patio tredecim &longs;ecundo<lb/>rum; libras 108000 quanto tempore dabit? Fiat, ut 144 libræ <lb/>ad <gap/> hoc e&longs;t, ad tredecim &longs;ecunda, ita 108000 ad 9750; dabit <lb/>hic numerus &longs;ecunda, quibus tubus EDB dat libras 108000. <lb/>Sed o&longs;ten&longs;um e&longs;t &longs;uprà, quo tempote tubus EDB dat 108000 <lb/>libras, tubum ADB dare libras 216000, id e&longs;t, 3000 pedes cu<lb/>bicos aquæ; Inventum e&longs;t igitur tempus, quo tubus ADB &longs;em<lb/>per plenus fundit datam aquam 3000 pedum cubicorum, nem<lb/>pe 9750 &longs;ecunda, &longs;eu 162 prima; quæ faciunt horas 2, & 42 <lb/>minuta prima. </s>

<s><emph type="center"/>Propo&longs;itio XIX. Problema III.<emph.end type="center"/></s>

<s><emph type="center"/>Datis tempore, quantitate aquæ, &longs;eu Ci&longs;ternâ, & lu<lb/>mine tubi, invenire altitudinem tubi, qui &longs;emper <lb/>plenus ci&longs;ternam dato tempore repleat.<emph.end type="center"/><lb/>

<arrow.to.target n="marg242"/></s>

<s><margin.target id="marg242"/><emph type="italics"/>Dato tem<lb/>pore, & <lb/>quantitate <lb/>aquæ, inve<lb/>nire tubum <lb/>ex quo ef<lb/>fluat.<emph.end type="italics"/></s>

<s>SIt datum tempus unius horæ & 21 minutorum primorum, <lb/>aqua data 3000 pedum cubicorum, &longs;eu 216000 librarum <lb/>capax ci&longs;terna, & lumen &longs;eu foramen tubi digitale, &longs;eu duo-

<pb xlink:href="051/01/168.jpg" pagenum="137"/>decim linearum. Oporteat invenire altitudinem tubi qui unâ <lb/>horâ & 21 minutis primis ex foramine digitali ejiciat 216000 <lb/>libras aquæ, &longs;eu repleat ci&longs;teruam 3000 pedum cubicorum. </s>

<s>Quoniam tubus quadrupedalis, cujus lumen digitale, eji<lb/>cit tredecim &longs;ecundorum &longs;patio libras 144, ut vidimus Pro<lb/>po&longs;it. XVII. præcedente, & idem tubus &longs;patio duarum hora<lb/>rum, ac 42 minutorum primorum ejicit libras 108000, ut vi<lb/>dimus Propo&longs;it. XVIII. præcedente; ergo duplum hujus aquæ, <lb/>hoc e&longs;t, libræ 216000, ejicientur à tubo eju&longs;dem luminis alto <lb/>pedes 16. eò quòd tuborum æqualium foraminum altitudines <lb/>debeant e&longs;&longs;e in duplicata ratione aquarum, ut duplo plùs aquæ <lb/>eodem tempore fundant, prout diximus Propo&longs;it. VIII. Pori<lb/>&longs;mate 1. Ut verò eadem aqua effluat ex tubo eju&longs;dem fora<lb/>minis duplo velociùs, hoc e&longs;t, intra horam unam, minuta 21; <lb/>debet tubus e&longs;&longs;e altus pedes 64, ut patet ex Pori&longs;mate Propo<lb/>&longs;it. X. & XII. </s>

<s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s>

<s>SImili ratione datis tempore, ci&longs;terna, & altitudine tubi, in<lb/>venitur foramen tubi, qui ci&longs;ternam datam repleat in illo <lb/>tempore. </s>

<s><emph type="center"/>Propo&longs;itio XX. Problema IV.<emph.end type="center"/></s>

<s><emph type="center"/>Dato Va&longs;e, & foramine per quod effluit aqua, <lb/>invenire tempus quo evacuatur.<emph.end type="center"/></s>

<s>SIt datum vas pri&longs;maticum ABCD, cujus tam longitudo, </s>

<s>

<arrow.to.target n="marg243"/><lb/>quàm latitudo &longs;it decem pedum, altitudo vero 16 pedum, <lb/>ac proinde capacitas totius va&longs;is &longs;it 1600 pedum cubicorum, <lb/>ba&longs;is verò &longs;it 100 pedum quadratorum; lumen denique &longs;eu <lb/>foramen E in fundo va&longs;is &longs;it digitale. Oporteat invenire tem<lb/>pus quo dictum vas, &longs;i aquâ fuerit plenum, per lumen E eva<lb/>cuetur. </s>

<s><margin.target id="marg243"/><emph type="italics"/>Dato va&longs;e, <lb/>& forami<lb/>ne, inveni<lb/>re tempus <lb/>quo evacua <lb/>tur.<emph.end type="italics"/></s>

<s>Con&longs;tat ex dictis Pro<lb/>po&longs;it. XIV. in Annotat. tu<lb/>bum quadrupedalem, cu<lb/>jus ba&longs;is pedalis, & lumen <lb/>lineare, &longs;patio 144. minu<lb/>torum, &longs;eu duabus horis <lb/>& 24 minutis, totum ex<lb/>hauriri, &longs;i non &longs;it &longs;emper <lb/>plenus. Con&longs;tat præterea <lb/>ex eadem Propo&longs;itione, <lb/>tubos non &longs;emper plenos, <lb/>æquè altos, & æqualium <lb/>foraminum, &longs;ed inæqua<lb/>lium ba&longs;ium, evacuari in<lb/>æqualibus temporibus; <lb/>& tempora quibus evacuantur, e&longs;&longs;e inter &longs;e, vt ba&longs;es. A&longs;&longs;uma<lb/>tur igitur tubus pri&longs;maticus quadrupedalis KL, ba&longs;im habens <lb/>pedalem, & lumen lineare. A&longs;&longs;umatur præterea ex va&longs;e dato <lb/>ABCD, pars CFDH alta pedes quatuor, ba&longs;&longs;im habens ean<lb/>dem cumtoto va&longs;e centum pedum, lumen verò 1 lineare. Quo<lb/>niam igitur, per Propo&longs;itionem XIV. dictam, tempora quibus <lb/>vas CFDH, & tubus KL exhauriuntur per lumen lineare, &longs;unt <lb/>inter &longs;e ut ba&longs;es ip&longs;orum; ba&longs;es autem ex hypothe&longs;i habent pro<lb/>portionem ut 100. ad 1; nece&longs;&longs;e e&longs;t, tempus quo evacuatur vas <lb/>CFDH per lineare lumen 1, ad tempus quo evacuatur tubus <lb/>KL per lumen etiam lineare, e&longs;&longs;e ut 100 ad 1. Quare cùm tu<lb/>bus KL per lineare lumen evacuetur &longs;patio 144 minutorum, <lb/>ut vidimus; evacuabitur vas CFDH, per lineare lumen 1, &longs;pa<lb/>tio 14400 minutorum, (tot enim producuntur, &longs;i 144 multi<lb/>plicentur per 100) &longs;eu horarum 240, vel dierum decem. Iam <lb/>verò quoniam per Propo&longs;it. XVI. tempus quo effluitaqua ex va<lb/>&longs;e CFDH per lumen digitale E, ad tempus quo effluit eadem <lb/>aqua ex eodem va&longs;e per lumen lineare 1, e&longs;t reciprocè, &longs;icut <lb/>e&longs;t foramen 1 ad foramen E, nempe ut 1 ad 144; &longs;i dividatur

<pb xlink:href="051/01/170.jpg" pagenum="139"/>tempus quo effluit aqua per foramen 1, nempe 14400 minuta, <lb/>per 144; hoc e&longs;t, &longs;i accipiatur cente&longs;ima quadrage&longs;ima quarta <lb/>pars minutorum 14400, nempe minuta 100; habebitur tem<lb/>pus quo exhauritur vas CFDH, per digitale lumen E. Tan<lb/>dem quoniam per Propo&longs;it. XV. præcedentem, tempora qui<lb/>bus deplentur va&longs;a ABCD, CFDH. æqualium ba&longs;ium, &longs;ed non <lb/>æqualium altitudinum, per idem foramen E, &longs;unt in &longs;ubdu<lb/>plicata ratione altitudinum, nempe pedum 4, & pedum 16; <lb/>&longs;i inter 4 & 16 inveniatur medius numerus proportionalis, nem<lb/>pe 8; erit tempus quo evacuatur vas CFDH, per lumen digita<lb/>le E, nimirum 100 minutorum, ad tempus quo evacuatur vas <lb/>ABCD per idem lumen digitale E, ut 4 ad 8, &longs;eu ut 1 ad 2, <lb/>nempe ut minuta 100, ad minuta 200, quæ efficiunt horas 3. <lb/>min. 20. </s>

<s><emph type="center"/>Annotatio.<emph.end type="center"/></s>

<s><emph type="italics"/>QVod diximus de va&longs;e pri&longs;matico, debet etiam intelligi de cylindrico, <lb/>& cuiuscunque alterius figuræ; &longs;ed tunc a&longs;&longs;umi debet tubus quadru<lb/>pedalis va&longs;i &longs;imilis.<emph.end type="italics"/></s>

<s><emph type="center"/>Propo&longs;itio XXI. Problema V.<emph.end type="center"/></s>

<s><emph type="center"/>Dato va&longs;e, & tempore, invenire foramen per quod <lb/>evacuetur tempore dato.<emph.end type="center"/></s>

<s>SIt data ci&longs;terna A, 1600. pe

<arrow.to.target n="table1"/><lb/>

<arrow.to.target n="marg244"/><lb/>dum cubicorum; & tempus <lb/>B, quo evacuandum e&longs;t totum, <lb/>&longs;it horarum 40 & minutorum <lb/>16; &longs;itque inveniendum foramen, per quod evacuetur ci&longs;ter<lb/>na A data, in tempore B dato. A&longs;&longs;umatur quodvis lumen &longs;eu <lb/>foramen notæ magnitudinis, v.g. lineare; & per Propo&longs;itionem <lb/>XX. præcedentem inveniatur tempus C, quo ci&longs;terna A hu<lb/>mido plena, evacuetur tota per lumen lineare. Quoniam igi<lb/>tur, per Propo&longs;it. XVI. præcedentem, tempora quibus evacuan<lb/>tur va&longs;a non &longs;emper plena, &longs;imilia, & æqualia quoad altitudinem

<pb xlink:href="051/01/171.jpg" pagenum="140"/>& ba&longs;es, per lumina &longs;imilia inæqualia, &longs;unt reciprocè ut lumina; <lb/>& è contrario, lumina prædictorum va&longs;orum &longs;unt reciprocè ut <lb/>tempora, quibus evacuantur, ut diximus in Pori&longs;mate dictæ <lb/>Propo&longs;itionis XVI; &longs;i fiat ut tempus B, ad tempus C, quo per <lb/>lineare lumen effluit ci&longs;terna A, ita lumen lineare ad aliud; <lb/>hoc ip&longs;um erit lumen quod quærebatur. </s>

<s><margin.target id="marg244"/><emph type="italics"/>Dato va&longs;e <lb/>& tempore, <lb/>invenire <lb/>foramen.<emph.end type="italics"/></s>

Line 2436

Line 3146

<s>Si e&longs;&longs;ent propo&longs;itæ duæ rectæ CB, <lb/>BE, deberent ip&longs;æ coniungi ad angu<lb/>lum rectum CBE, & ductâ rectâ CE, <lb/>productaque CB, deberet duci per<lb/>pendicularis AE, ad rectam CE, <expan abbr="e&longs;&longs;et&qacute;ue">e&longs;&longs;etque</expan> AB tertia quæ&longs;ita. </s>

<s><emph type="center"/>Annotatio.<emph.end type="center"/>

<s><emph type="center"/>Annotatio.<emph.end type="center"/></s>

<s><emph type="italics"/>INventâ alterutro modorum tertiâ continuè proportionali, &longs;i primam <lb/>omi&longs;eris, & alijs duabus tertiam inveneris; habebis quatuor leneas <lb/>continuè proportionales. Eodemque modo invenies quintam, &longs;extam, <lb/>&longs;eptimam, & quamcunque aliam.<emph.end type="italics"/></s>

<s><emph type="center"/>Propo&longs;itio VI.<emph.end type="center"/></s>

<s><emph type="center"/>Adhuc aliter invenire tertiam proportionalem.<emph.end type="center"/></s>

<s>SI difficile tibi videtur ducere tot perpendiculares ad inveni<lb/>

<arrow.to.target n="marg255"/><lb/>endamtertiam proportionalem, uti poteris modo præ&longs;cripto <lb/>ab Euclide lib. 6. Propo&longs;it. 11. &longs;ic: </s>

<s><margin.target id="marg255"/><emph type="italics"/>Adhuc ali<lb/>ter item pre <lb/>&longs;tare.<emph.end type="italics"/></s>

<s>Sint duæ rectæ AB, AE. <lb/><expan abbr="Di&longs;ponãtur">Di&longs;ponantur</expan> eæita, ut efficiant <lb/>angulum A quemcunque, <lb/>producaturque AB quam vis <lb/>e&longs;&longs;e antecedentem &longs;eu <expan abbr="primã">primam</expan>, <lb/>& capiatur BC æqualis ip&longs;i <lb/>AE, quæ con&longs;equens e&longs;&longs;e de-

<arrow.to.target n="fig38"/><lb/>bet, &longs;ive &longs;ecunda, aut media. <lb/>Deinde ductâ rectâ AB, aga<lb/>tur illi ex C parallela CD, <lb/>occurrensip&longs;i AE productæ, <lb/>in D; eritque ED tertia <lb/>proportionalis quæ&longs;ita. </s>

<s><emph type="center"/>Annotatio.<emph.end type="center"/></s>

<s><emph type="italics"/>SIduæ datæ&longs;int nimis longæ, &longs;ervetur id, quod diximus in Annota<lb/>tione Propo&longs;itionis quartæ præcedentis.<emph.end type="italics"/></s>

<s><emph type="center"/>Propo&longs;itio VII.<emph.end type="center"/></s>

<s><emph type="center"/>Datis tribus numeris, invenire quartum pro<lb/>portionalem.<emph.end type="center"/><lb/>

<arrow.to.target n="marg256"/></s>

<s><margin.target id="marg256"/><emph type="italics"/>Numeris <lb/>tribus datis <lb/>quartum <lb/>proportiona<lb/>lem inveni<lb/>re.<emph.end type="italics"/></s>

<s>UTere Regulâ proportionum apud Arithmeticos noti&longs;&longs;ima, <lb/>quam Auteam vocant; & habebis intentum. </s>

<s><emph type="center"/>Propo&longs;itio VIII.<emph.end type="center"/></s>

<s><emph type="center"/>Datis tribus rectia lineis, quartam propor<lb/>tionaleminvenirc.<emph.end type="center"/></s>

<s>

<arrow.to.target n="marg257"/></s>

<s><margin.target id="marg257"/><emph type="italics"/>Lineis tri<lb/>bus datis, <lb/><expan abbr="quartã">quartam</expan> pro<lb/>portiona<lb/>lem inveni<lb/>re.<emph.end type="italics"/></s>

<s>SInt tres lineæ rectæ, AB, BC, <lb/>AD, quibus invenienda &longs;it <lb/>quarta. proportionalis, ad <lb/>quàm &longs;it tertia AD, ut e&longs;t <lb/>prima AB, ad &longs;ecundam BC. <lb/><expan abbr="Di&longs;ponãtur">Di&longs;ponantur</expan> primæ duæ, AB, <lb/>BC, &longs;ecundùm lineam <expan abbr="rectã">rectam</expan> <lb/>quæ &longs;it AC; tertia verò AD, <lb/>cum prima AB, faciatangulum A quemcunque: deinde ex B <lb/>ad D ducatur recta BD, cui per C ducatur parallela CE, oc<lb/>currens rectæ AD productæ, in E puncto. Dico, DE, e&longs;&longs;e <lb/>quartam proportionalem. Demon&longs;trationem vide apud <lb/>Euclidem lib. 6. Propo&longs;it. 12. </s>

<s><emph type="center"/>CAPVT IV.<emph.end type="center"/></s>

<s><emph type="center"/>De proprietatibus aquæ &longs;alientis ex tubis. <lb/>PROOEMIVM.<emph.end type="center"/></s>

<s><emph type="italics"/>CApite præceden<lb/>

<arrow.to.target n="marg258"/><lb/>ti egimuo de pro<lb/>prietatibus a<lb/>quæ fluentis per tubos <lb/>verticales, hoc e&longs;t, efflu<lb/>entis ex foramine facto in <lb/>ba&longs;ibus tuborum: hoc Ca<lb/>pite agemus de proprieta<lb/>tibus eju&longs;dem aquæ &longs;ali<lb/>entis ex tubis verticali<lb/>bus, hoc e&longs;t, effluentis ex <lb/>foraminibus lateralib<emph type="sup"/>9<emph.end type="sup"/> <expan abbr="tu-bor&utilde;">tu<lb/>borum</expan>, &longs;eu per tubos inferi<lb/>ùs inflexos. Po&longs;&longs;unt <expan abbr="aut&etilde;">autem</expan> <lb/>tubi verticales inferiùs <lb/>inflecti triplici modo, ho<lb/>

<arrow.to.target n="marg259"/><lb/>rizontaliter, verticali<lb/>ter, & medio modo. Ho<lb/>rizontaliter inflexus dici<lb/>tur, &longs;i pars inferior infle<lb/>xa &longs;it horizonti parallela <lb/>re&longs;pectupartis reliquæ ver<emph.end type="italics"/>

<arrow.to.target n="fig39"/><lb/><emph type="italics"/>ticaliter erectæ; &longs;eu&longs;i pars <lb/>inferior inflexa faciat cum <lb/>reliquæ angulum rectum. <lb/>Talis e&longs;t in appo&longs;ito &longs;che<lb/>mate tubus<emph.end type="italics"/> ABC. <emph type="italics"/>Ver<lb/>ticaliter inflexus dicitur, <lb/>&longs;i pars inferior inflexa &longs;it <lb/>horizonti perpendicularis <lb/>re&longs;pectu reliquæ partis et<lb/>iam perpendiculariter e<lb/>rectæ. Talis e&longs;t in &longs;che<lb/>mate præ&longs;enti tubus<emph.end type="italics"/> ABE. <lb/><emph type="italics"/>Medio modo inflexus di<lb/>citur, &longs;ipars inferior ne<lb/>que parallela e&longs;t horizon<lb/>ti, neque perpendicula<lb/>ris, &longs;ed inter utrumque <lb/>&longs;itum facit angulum &longs;e<lb/>mirectum &longs;eu<emph.end type="italics"/> 45 <emph type="italics"/>gradu<lb/>um. Talis e&longs;t tubus<emph.end type="italics"/> ABD. </s>

<s><margin.target id="marg258"/>Proprieta<lb/>tes aquæ &longs;a<lb/>lientis ex tu <lb/>bis vertica<lb/>libus.</s>

<s><margin.target id="marg259"/>Tubi verti<lb/>cale, tripli<lb/>citer inflecti <lb/>po&longs;&longs;unt in<lb/>feriùs.</s>

<s><emph type="italics"/>Easdem appellatio<lb/>nes &longs;ubibit tubusinflexus, <lb/>&longs;i pars inferior habeat tria <lb/>epi&longs;tomia,<emph.end type="italics"/> E, D, C, <emph type="italics"/>quorum<emph.end type="italics"/> E <emph type="italics"/>&longs;it erectum perpendiculariter,<emph.end type="italics"/><lb/>C <emph type="italics"/>pro&longs;tratum horizontaliter,<emph.end type="italics"/> D <emph type="italics"/>inclinatum inter utrum<lb/>que, ad dictum angulum. Quod fit per tria epi&longs;tomia dicta, <lb/>fieri pote&longs;t per unum, &longs;i ita in&longs;eratur parti inferiori tubi inflexi, <lb/>ut verti atque dirigi po&longs;&longs;it in quemcunque &longs;itum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Radij aquæ, qui ex inflexo tubo, aut ex epi&longs;tomiis præ-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg260"/><lb/><emph type="italics"/>dictis exiliunt, quales &longs;unt in præcedenti <expan abbr="diagra&mtilde;ate">diagramnate</expan> radij<emph.end type="italics"/> EF, <lb/>DI, DK, CG, CH, <emph type="italics"/>appellari po&longs;&longs;unt aqueæ virgulæ, aquei ecdro<lb/>mi, hoc e&longs;t, excur&longs;us &longs;eu &longs;altus aquæ, & &longs;imilibus nominibus. <lb/>Marinus tamen Mer&longs;ennus in Hydraulicis &longs;uis Phænomenis <lb/>appellat eos<emph.end type="italics"/> &longs;alientes, <emph type="italics"/>aitque eo nomine appellari à Iulio Fron<lb/>tino, aliis que veteribus; quare & nos eo vocabulo utemur.<emph.end type="italics"/><lb/>

<arrow.to.target n="marg261"/><lb/><emph type="italics"/>Radius igitur<emph.end type="italics"/> EF <emph type="italics"/>dicatur &longs;aliens verticalis, Radius<emph.end type="italics"/> CG, <lb/><emph type="italics"/>&<emph.end type="italics"/> CH, <emph type="italics"/>&longs;aliens Horizontalis; radius denique<emph.end type="italics"/> DI, <emph type="italics"/>&<emph.end type="italics"/> DK, <lb/><emph type="italics"/>&longs;aliens Medius, et licet &longs;alientes<emph.end type="italics"/> CG, CH, <emph type="italics"/>nonprocedant ho<lb/>rizontaliter, &longs;ed ob aquæ gravitatem &longs;tatim deprimantur, at<lb/>que curventur; vocantur tamen &longs;alientes horizontales, propter <lb/>epi&longs;tomium aut tubulum<emph.end type="italics"/> C <emph type="italics"/>horizontaliter di&longs;po&longs;itum.<emph.end type="italics"/></s>

<s><margin.target id="marg260"/>Radij aqu&ecedil; <lb/>ex inflexo <lb/>tubo exili<lb/>entes.</s>

Legend:

Removed from v.1.5
changed lines
	Added in v.1.12