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

version 1.13, 2005/11/03 11:53:52

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<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. </s><s><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"/> </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>

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<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>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. </s><s>Fit hoc aëre mediante, <lb/>aquæ immi&longs;to. </s><s>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="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. </s><s>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. </s><s>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. </s><s>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. </s><s>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. </s><s>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>

<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. </s><s>Iterum remove vas <lb/>AB, & ingredietur per os G alius <lb/>aër, &longs;equeturque aquam. </s><s>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>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. </s><s>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. </s><s>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>

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<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>

<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. </s><s>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="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. </s><s><emph type="italics"/>Non videtur quippe e&longs;&longs;e motus, ni&longs;i &longs;it inane. </s><s><lb/>Quod enim plenum e&longs;t, admittere in &longs;e mobile non pote&longs;t. </s><s>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="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. </s><s>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>

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<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/>

<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. </s><s>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="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

<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. </s><s><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>

<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. </s><s>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. </s><s>Neque dicas, e&longs;&longs;e in mundo rara, <lb/>liquida, fluxaque corpora, quæ cedere magis quàm &longs;ilices po&longs;<lb/>&longs;int. </s><s>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. </s><s>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>HIs quid reponendum, viderint Philo&longs;ophi. </s><s>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="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. </s><s>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-

<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. </s><s><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. </s><s>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>

<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. </s><s>Videmus follibus compre&longs;&longs;is erumpere <lb/>aërem, & aquam etiam, &longs;i aquâ erant repleti. </s><s>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. </s><s><lb/>Taceo centena exempla alia. </s><s>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. </s><s>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>

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<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

<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. </s><s>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>

<pb xlink:href="051/01/078.jpg" pagenum="47"/>aqua effluere po&longs;&longs;it. </s><s>Va&longs;a A & F habeant in operculis forami<lb/>na C & E, vt per ea infundi po&longs;&longs;it aqua, & iterum obturari. </s><s><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. </s><s>Habeat præterea epi&longs;tomium K. </s><s>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. </s><s>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. </s><s>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 &

<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. </s><s>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. </s><s>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. </s><s>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>

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<arrow.to.target n="fig11"/><lb/>porum impenetra<lb/>bilitatem; ideoque <lb/>Tyrones diligenter <lb/>procurare debent, <lb/>vt illud intelligant: <lb/>quare nonnulla cir<lb/>ca <expan abbr="ips&utilde;">ipsum</expan> &longs;unt adver<lb/>tenda. </s>

<s>Primum e&longs;t, ex<lb/>pedire vt vas A non <lb/>&longs;it minùs capax <expan abbr="quã">quam</expan> <lb/>vas F, & vt tubus <lb/>FG non &longs;it amplior <lb/>tubo AB: &longs;ic enim <lb/>fiet, vt quàmdiu a<lb/>qua ex va&longs;e F <expan abbr="de&longs;c&etilde;-dit">de&longs;cen<lb/>dit</expan> intra G, tamdiu <lb/>&longs;aliat aqua ex vase A <lb/>per tubum AB. Hoc <lb/><expan abbr="tam&etilde;">tamen</expan> non e&longs;t omni<lb/>nò nece&longs;&longs;arium. </s>

<s>Primum e&longs;t, ex<lb/>pedire vt vas A non <lb/>&longs;it minùs capax <expan abbr="quã">quam</expan> <lb/>vas F, & vt tubus <lb/>FG non &longs;it amplior <lb/>tubo AB: &longs;ic enim <lb/>fiet, vt quàmdiu a<lb/>qua ex va&longs;e F <expan abbr="de&longs;c&etilde;-dit">de&longs;cen<lb/>dit</expan> intra G, tamdiu <lb/>&longs;aliat aqua ex vase A <lb/>per tubum AB. </s><s>Hoc <lb/><expan abbr="tam&etilde;">tamen</expan> non e&longs;t omni<lb/>nò nece&longs;&longs;arium. </s>

<s>Secundum e&longs;t, Non e&longs;&longs;e nece&longs;&longs;arium, vt fiat vas F, &longs;ed fie<lb/>ri pote&longs;t&longs;olus canalis &longs;eu tubus FG, qui apud F habeat infun<lb/>dibulum, vt aqua infundi po&longs;&longs;it; dummodò &longs;it longior quàm <lb/>tubus AB; vt mox dicam. </s>

<s>Tertium e&longs;t, omninò <expan abbr="nece&longs;&longs;ari&utilde;">nece&longs;&longs;arium</expan> e&longs;&longs;e, vt tubus FG longi<lb/>or &longs;it quam tubus AB, quia, vt diximus Protheoria I. §. VI. & di<lb/>cemus iterum infrà Protheoria IV. cap. 2. Propo&longs;it. 14. hîc et<lb/>iam, vt vbiq, in hydraulicis, perpendiculis certatur, non verò <expan abbr="a-quar&utilde;">a<lb/>quarum</expan> copiâ. <expan abbr="Perpendicul&utilde;|aut&etilde;">Perpendiculun|autem</expan> tubi FG computatur ab F <expan abbr="v&longs;q;">v&longs;que</expan> ad </s>

<s>Tertium e&longs;t, omninò <expan abbr="nece&longs;&longs;ari&utilde;">nece&longs;&longs;arium</expan> e&longs;&longs;e, vt tubus FG longi<lb/>or &longs;it quam tubus AB, quia, vt diximus Protheoria I. §. VI. & di<lb/>cemus iterum infrà Protheoria IV. cap. 2. Propo&longs;it. 14. hîc et<lb/>iam, vt vbiq, in hydraulicis, perpendiculis certatur, non verò <expan abbr="a-quar&utilde;">a<lb/>quarum</expan> copiâ. </s><s><expan abbr="Perpendicul&utilde;|aut&etilde;">Perpendiculun|autem</expan> tubi FG computatur ab F <expan abbr="v&longs;q;">v&longs;que</expan> ad </s>

<s>

<arrow.to.target n="marg108"/><lb/>&longs;upremam <expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> aquæ de&longs;cendentis & quie&longs;centis in va&longs;e G. <lb/>Quò verò longius fuerit perpendiculum FG &longs;upra perpendicu<lb/>lum AB eò altiùs &longs;alit aqua ex o&longs;culo B. Quare cùm in prin<lb/>cipio, quando incipit de&longs;cendere aqua intra vas G, longius &longs;it <lb/>perpendiculum FG, quàm po&longs;tea (repleto paulatim va&longs;e G) <lb/>& id <expan abbr="&longs;&etilde;per">&longs;emper</expan> magis ac magis minuatur; con&longs;equens e&longs;t, vtin prin<lb/>cipio altiùs &longs;aliat aqua ex B, quàm po&longs;t principium, & vt &longs;em<lb/>per minùs & minùs altè ex&longs;iliat. Vide etiam quæ dicimus in<lb/>frà Parte 2. Cla&longs;se I. cap. 2. Machina I. Annot. 2. </s>

<arrow.to.target n="marg108"/><lb/>&longs;upremam <expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> aquæ de&longs;cendentis & quie&longs;centis in va&longs;e G. </s><s><lb/>Quò verò longius fuerit perpendiculum FG &longs;upra perpendicu<lb/>lum AB eò altiùs &longs;alit aqua ex o&longs;culo B. </s><s>Quare cùm in prin<lb/>cipio, quando incipit de&longs;cendere aqua intra vas G, longius &longs;it <lb/>perpendiculum FG, quàm po&longs;tea (repleto paulatim va&longs;e G) <lb/>& id <expan abbr="&longs;&etilde;per">&longs;emper</expan> magis ac magis minuatur; con&longs;equens e&longs;t, vtin prin<lb/>cipio altiùs &longs;aliat aqua ex B, quàm po&longs;t principium, & vt &longs;em<lb/>per minùs & minùs altè ex&longs;iliat. </s><s>Vide etiam quæ dicimus in<lb/>frà Parte 2. Cla&longs;se I. cap. 2. Machina I. Annot. 2. </s>

<s><margin.target id="marg108"/><emph type="italics"/>Perpendi<lb/>culis, non a<lb/>qudrum co<lb/>piâ certatur <lb/>in hydrau<lb/>licis.<emph.end type="italics"/></s>

<s>Quartum e&longs;t, Non &longs;olùm &longs;ervandam e&longs;&longs;e proportionem <lb/>quoad longitudinem inter tubos AB, & GF, &longs;ed etiam quoad <lb/>capacitatem, nè &longs;cilicet AB laxior &longs;it quàm GF; alioquin gra<lb/>vior erit aqua intra ip&longs;um, quàm vt elevari po&longs;&longs;it ab aëre modi<lb/>co intra vas A pul&longs;o à modica aqua cadente intra vas G. Si <lb/>verò FG tubus laxior e&longs;&longs;e<gap/> quàm AB, nimis citò repleretur <lb/>vas G, & antequam tota aqua va&longs;is A expelleretur per AB. </s>

<s>Quartum e&longs;t, Non &longs;olùm &longs;ervandam e&longs;&longs;e proportionem <lb/>quoad longitudinem inter tubos AB, & GF, &longs;ed etiam quoad <lb/>capacitatem, nè &longs;cilicet AB laxior &longs;it quàm GF; alioquin gra<lb/>vior erit aqua intra ip&longs;um, quàm vt elevari po&longs;&longs;it ab aëre modi<lb/>co intra vas A pul&longs;o à modica aqua cadente intra vas G. </s><s>Si <lb/>verò FG tubus laxior e&longs;&longs;e<gap/> quàm AB, nimis citò repleretur <lb/>vas G, & antequam tota aqua va&longs;is A expelleretur per AB. </s>

<s>Quintum e&longs;t, Nihil referre quantæ &longs;it altitudinis tubus HD, <lb/>per quem aër defertur, quia nihil confert ad perpendiculum. Pro<lb/>curandum tamen e&longs;t, nè &longs;it nimis laxus, aliàs multùm aëris intra <lb/>ip&longs;um ab&longs;orberetur, qui alioquin expelli deberet intra vas A. </s>

<s>Quintum e&longs;t, Nihil referre quantæ &longs;it altitudinis tubus HD, <lb/>per quem aër defertur, quia nihil confert ad perpendiculum. </s><s>Pro<lb/>curandum tamen e&longs;t, nè &longs;it nimis laxus, aliàs multùm aëris intra <lb/>ip&longs;um ab&longs;orberetur, qui alioquin expelli deberet intra vas A. </s>

<s>Sextum e&longs;t, prædictum artificium elevandi aquam vi ex<lb/>pul&longs;iva propter corporum impenetra bilitatem, e&longs;&longs;e typum & <lb/>exemplar omnium Machinarum Hydro-pnevmaticarum præ<lb/>dicta virtute animatarum; ac proinde &longs;emperante oculos <lb/>in &longs;imilibus Machinis fabricandis e&longs;&longs;e habendum, <lb/>vtin principio dicebam. </s>

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<s><emph type="center"/>Heronis error in elevando oleo vi Expul&longs;ivâ <lb/>in lucerna.<emph.end type="center"/></s>

<s>HEro Alexandrinus in libello de Spiritalibus cap. 72. proponit <lb/>hanc Machinam. <emph type="italics"/>Lucernæ con&longs;tructio, vt ellychnio impo<lb/>&longs;ito, quando oleum deficiat, ex aure eius oleum in ellychnium infun<lb/>datur, quantum quis voluerit, nullo ip&longs;i appo&longs;ito va&longs;e, ex quo oleum in<lb/>

<s>HEro Alexandrinus in libello de Spiritalibus cap. 72. proponit <lb/>hanc Machinam. </s><s><emph type="italics"/>Lucernæ con&longs;tructio, vt ellychnio impo<lb/>&longs;ito, quando oleum deficiat, ex aure eius oleum in ellychnium infun<lb/>datur, quantum quis voluerit, nullo ip&longs;i appo&longs;ito va&longs;e, ex quo oleum in<lb/>

<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="fig12"/><lb/>errandi occa&longs;io. </s><s>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. </s><s>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"/>

<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. </s><s>Sic ergo di&longs;currit Hero. </s><s><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. </s><s><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. </s><s>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, 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>

<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. </s><s>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. </s><s>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. </s><s>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. </s><s>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. </s><s>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. </s><s>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. </s><s>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. </s><s>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>

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<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,

<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. </s><s>Non potui in venire Græcum <lb/>Heronis textum, vt vt diù quæ&longs;iverim. </s><s>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. </s><s>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/>

<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. </s><s>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. </s><s>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. </s><s>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. </s><s>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>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. </s><s>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/>

<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. </s><s>Diximus præterea Protheoria I. <lb/>§. VI. perpendiculum aquæ cadentis & trahentis aërem, debe<lb/>re &longs;uperare longitudine perpendiculum aquæ attractæ. </s><s>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. </s><s>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>

<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. </s><s>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. </s><s>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>

<s>Sit ex va&longs;e B elevanda <lb/>aqua v&longs;que ad vas E, ad <lb/>altitudinem centum pe<lb/>dum, mediante perpen<lb/>diculo 50. pedum aquæ <lb/>cadentis. Fiant alia duo <lb/>va&longs;a A, & C, in eodem <lb/>plano horizontali cum <lb/>va&longs;e B con&longs;tituta, <expan abbr="eju&longs;d&etilde;">eju&longs;dem</expan> <lb/>capacitatis cum B; & in<lb/>fra ip&longs;a con&longs;tituatur vas <lb/>D, cujus &longs;uprema oper<lb/>culi pars di&longs;tet à fundis di<lb/>ctorum va&longs;orum 50. pedi<lb/>bus. Ex va&longs;e A de&longs;cen<lb/>dat in vas D tubus GX, 50.

<s>Sit ex va&longs;e B elevanda <lb/>aqua v&longs;que ad vas E, ad <lb/>altitudinem centum pe<lb/>dum, mediante perpen<lb/>diculo 50. pedum aquæ <lb/>cadentis. </s><s>Fiant alia duo <lb/>va&longs;a A, & C, in eodem <lb/>plano horizontali cum <lb/>va&longs;e B con&longs;tituta, <expan abbr="eju&longs;d&etilde;">eju&longs;dem</expan> <lb/>capacitatis cum B; & in<lb/>fra ip&longs;a con&longs;tituatur vas <lb/>D, cujus &longs;uprema oper<lb/>culi pars di&longs;tet à fundis di<lb/>ctorum va&longs;orum 50. pedi<lb/>bus. </s><s>Ex va&longs;e A de&longs;cen<lb/>dat in vas D tubus GX, 50.

<arrow.to.target n="fig13"/><lb/><expan abbr="ped&utilde;">pedum</expan>; qui tamen ab X ex<lb/>tendi ac prolongari pote&longs;t <lb/>u&longs;que ad H, dummodò <lb/>tantum di&longs;tet à fundo, ut <lb/>aqua effluere po&longs;&longs;it. Ha<lb/>beat autem hic tubus epi<lb/>&longs;tomium V. Ex va&longs;e B de<lb/>&longs;cendat in idem vas D ali<lb/>us tubus KI, incipiens <lb/>paulò infra operculum <lb/>apud K, & de&longs;inens pau<lb/>lò infra operculum apud <lb/>I. Ex va&longs;e C de&longs;cendat <lb/>tubus OP 50. pedum, <lb/>habens epi&longs;tomium T. Ex <lb/>va&longs;e E de&longs;cendant in va<lb/>&longs;a B & C duo tubi: pri<lb/>mus NC, incipiens infra operculum apud N, & de&longs;inens in<lb/>fra operculum apud C: alter ML, incipiens immediatè infra <lb/>operculum apud M, & de&longs;inens &longs;upra fundum apud L. Lon<lb/>gitudo verò hujus tubi ML ab operculo M u&longs;que ad punctum <lb/>L &longs;it centum pedum. Tria va&longs;a A, B, C, habeant &longs;ua forami<lb/>na cum infundibulis F, per quæ aqua infundi po&longs;&longs;it intra va&longs;a, <lb/>& obturari. Vas tamen A pote&longs;t manere apertum. Duo va&longs;a <lb/>D & E habeant &longs;ua epi&longs;tomia H & S. Omnia præterea va<lb/>&longs;a, excepto A, debent e&longs;&longs;e undique ac diligenti&longs;&longs;imè clau&longs;a; <lb/>ideoque tubi debent in loco tran&longs;itus accurati&longs;&longs;imè adferrumi<lb/>nari ip&longs;orum va&longs;orum operculis, & fundis. His ita con&longs;titutis, <lb/>repleantur tria va&longs;a A, B, C, aquâ, & claudantur, clau&longs;is priùs <lb/>omnibus epi&longs;tomijs omnium va&longs;orum ac tuborum: reliqua ve<lb/>rò duo va&longs;a, D & E, maneant vacua. Deinde aperiatur <lb/>epi&longs;tomium T; & aqua va&longs;is C de&longs;cendet ver&longs;us P, &longs;ecum<lb/>que trahet, ad vacuum vitandum, aërem va&longs;is E, per tubum <lb/>NC, &longs;imulque aquam va&longs;is B u&longs;que ad altitudinem 50. pedum

<arrow.to.target n="fig13"/><lb/><expan abbr="ped&utilde;">pedum</expan>; qui tamen ab X ex<lb/>tendi ac prolongari pote&longs;t <lb/>u&longs;que ad H, dummodò <lb/>tantum di&longs;tet à fundo, ut <lb/>aqua effluere po&longs;&longs;it. </s><s>Ha<lb/>beat autem hic tubus epi<lb/>&longs;tomium V. </s><s>Ex va&longs;e B de<lb/>&longs;cendat in idem vas D ali<lb/>us tubus KI, incipiens <lb/>paulò infra operculum <lb/>apud K, & de&longs;inens pau<lb/>lò infra operculum apud <lb/>I. </s><s>Ex va&longs;e C de&longs;cendat <lb/>tubus OP 50. pedum, <lb/>habens epi&longs;tomium T. </s><s>Ex <lb/>va&longs;e E de&longs;cendant in va<lb/>&longs;a B & C duo tubi: pri<lb/>mus NC, incipiens infra operculum apud N, & de&longs;inens in<lb/>fra operculum apud C: alter ML, incipiens immediatè infra <lb/>operculum apud M, & de&longs;inens &longs;upra fundum apud L. </s><s>Lon<lb/>gitudo verò hujus tubi ML ab operculo M u&longs;que ad punctum <lb/>L &longs;it centum pedum. </s><s>Tria va&longs;a A, B, C, habeant &longs;ua forami<lb/>na cum infundibulis F, per quæ aqua infundi po&longs;&longs;it intra va&longs;a, <lb/>& obturari. </s><s>Vas tamen A pote&longs;t manere apertum. </s><s>Duo va&longs;a <lb/>D & E habeant &longs;ua epi&longs;tomia H & S. </s><s>Omnia præterea va<lb/>&longs;a, excepto A, debent e&longs;&longs;e undique ac diligenti&longs;&longs;imè clau&longs;a; <lb/>ideoque tubi debent in loco tran&longs;itus accurati&longs;&longs;imè adferrumi<lb/>nari ip&longs;orum va&longs;orum operculis, & fundis. </s><s>His ita con&longs;titutis, <lb/>repleantur tria va&longs;a A, B, C, aquâ, & claudantur, clau&longs;is priùs <lb/>omnibus epi&longs;tomijs omnium va&longs;orum ac tuborum: reliqua ve<lb/>rò duo va&longs;a, D & E, maneant vacua. </s><s>Deinde aperiatur <lb/>epi&longs;tomium T; & aqua va&longs;is C de&longs;cendet ver&longs;us P, &longs;ecum<lb/>que trahet, ad vacuum vitandum, aërem va&longs;is E, per tubum <lb/>NC, &longs;imulque aquam va&longs;is B u&longs;que ad altitudinem 50. pedum

<pb xlink:href="051/01/086.jpg" pagenum="55"/>ubi V, quantum nimirum e&longs;t perpendiculum tubl OP, per <lb/>quem aqua cadit. Po&longs;tquam verò aqua de&longs;cenderit hinc u&longs;que <lb/>ad P, inde u&longs;que ad V, hærebit utrimque velut in æquilibrio <lb/>immobilis, propter perpendiculorum æqualitatem. Tum verò <lb/>aperiatur epi&longs;tomium V, & aqua va&longs;is A de&longs;cendet intra vas <lb/>D, indeque expellet aërem per tubum IK intra vas B; qui aër <lb/>premet aquam, atque propellet &longs;ur&longs;um per tubum LM ver&longs;us <lb/>M, &longs;icque elevabitur aqua ultra punctum V, effluetque aqua <lb/>ex tubo OP, penitu&longs;que a&longs;cendet aqua va&longs;is B, per tubum LM, <lb/>intra vas E; nec ce&longs;&longs;abit fluxus, donec tria va&longs;a A, B, C, &longs;imul <lb/>fuerint evacuata, totaque aqua B a&longs;cenderitin E. Sijam aqua <lb/>va&longs;orum D & E per &longs;ua epi&longs;tomia depromatur, & va&longs;a A, B, C, <lb/>denuò repleantur; in&longs;titui poterit eadem circulatio, idque to<lb/>ties, quoties libuerit. Hæc e&longs;t praxis Portæ; ingenio&longs;us atque <lb/>indu&longs;trius artifex addere, demere, mutare poterit, quæ libuerit, <lb/>ornatûs aut commoditatis gratia, modò non alteretur rel &longs;ub<lb/>&longs;tantia, quam nos præcisè hîc dedimus. </s>

<pb xlink:href="051/01/086.jpg" pagenum="55"/>ubi V, quantum nimirum e&longs;t perpendiculum tubl OP, per <lb/>quem aqua cadit. </s><s>Po&longs;tquam verò aqua de&longs;cenderit hinc u&longs;que <lb/>ad P, inde u&longs;que ad V, hærebit utrimque velut in æquilibrio <lb/>immobilis, propter perpendiculorum æqualitatem. </s><s>Tum verò <lb/>aperiatur epi&longs;tomium V, & aqua va&longs;is A de&longs;cendet intra vas <lb/>D, indeque expellet aërem per tubum IK intra vas B; qui aër <lb/>premet aquam, atque propellet &longs;ur&longs;um per tubum LM ver&longs;us <lb/>M, &longs;icque elevabitur aqua ultra punctum V, effluetque aqua <lb/>ex tubo OP, penitu&longs;que a&longs;cendet aqua va&longs;is B, per tubum LM, <lb/>intra vas E; nec ce&longs;&longs;abit fluxus, donec tria va&longs;a A, B, C, &longs;imul <lb/>fuerint evacuata, totaque aqua B a&longs;cenderitin E. </s><s>Sijam aqua <lb/>va&longs;orum D & E per &longs;ua epi&longs;tomia depromatur, & va&longs;a A, B, C, <lb/>denuò repleantur; in&longs;titui poterit eadem circulatio, idque to<lb/>ties, quoties libuerit. </s><s>Hæc e&longs;t praxis Portæ; ingenio&longs;us atque <lb/>indu&longs;trius artifex addere, demere, mutare poterit, quæ libuerit, <lb/>ornatûs aut commoditatis gratia, modò non alteretur rel &longs;ub<lb/>&longs;tantia, quam nos præcisè hîc dedimus. </s>

<s>Nota hîc, ut aperto epi&longs;tomio T de&longs;cendat aqua va&longs;is C <lb/>ver&longs;us P, laxandum &longs;imul e&longs;&longs;e epi&longs;tomium V va&longs;is A; alio<lb/>quin nunquam de&longs;cendet aqua va&longs;is C, nè detur vacuum, ut <lb/>con&longs;ideranti patebit. </s>

Line 1603

Line 1602

<s>HEro cap. 55. Spiritalium ait, <emph type="italics"/>quædam va&longs;a à principio humore <lb/>injecto fluunt, intermi&longs;&longs;ione verò facta non ampliùs fluunt injecto <lb/>humore, quou&longs;&queacute; ad dimidium repleta fuerint; tunc enim incipiunt flue<lb/>re: At intermi&longs;&longs;ione facta, non ampliùs fluunt, quou&longs;&que; impleantur.<emph.end type="italics"/><lb/>Hujus rei probandæ gratia proponit huju&longs;modi machinam.

<arrow.to.target n="marg114"/><lb/>

<arrow.to.target n="fig14"/><lb/><emph type="italics"/>Sit enim vas<emph.end type="italics"/> AB, <emph type="italics"/>habens in &longs;eip&longs;<gap/><lb/>tres &longs;iphones inflexos<emph.end type="italics"/> C, D, E, <emph type="italics"/>in ven<lb/>tre occultatos, quorum altera quidem <lb/>crura &longs;int ad fundum va&longs;is, altera ve<lb/>rò extra ferantur in canales efforma<lb/>ta; atque eorum extremis apponantur <lb/>va&longs;a<emph.end type="italics"/> F, H, G, <emph type="italics"/>quorum fundum di&longs;tet <lb/>ab o&longs;culis, quantum ad aquæ fluxum &longs;a<lb/>tis &longs;it. Omnia verò comprehendantur <lb/>alio quodam va&longs;e, tanquam ba&longs;i<emph.end type="italics"/> KLMN, <lb/><emph type="italics"/>quæ canalem<emph.end type="italics"/> X <emph type="italics"/>habeat. Et &longs;iphonis <lb/>quidem<emph.end type="italics"/> C <emph type="italics"/>curvit as &longs;it ad fundum va<lb/>&longs;is; &longs;iphonis verò<emph.end type="italics"/> D <emph type="italics"/>curvitas ad di<lb/>midium altitudinis ejus & &longs;iphonis<emph.end type="italics"/> E <lb/><emph type="italics"/>ad ip&longs;um collum. Si igitur in vas<emph.end type="italics"/> AB <lb/><emph type="italics"/>aquam infundamus, à principio <expan abbr="quid&etilde;">quidem</expan> <lb/>fluet per &longs;iphonem<emph.end type="italics"/> C, <emph type="italics"/>quoniam cur<lb/>vitas ip&longs;ius e&longs;t ad fundum. Quòd &longs;i <lb/>intermittamus, evacuabitur humidum <lb/>infu&longs;um per canalem<emph.end type="italics"/> X, <emph type="italics"/>& vas<emph.end type="italics"/> F <emph type="italics"/>relin quetur aqua plenum, &longs;iphonis <lb/>verò<emph.end type="italics"/> C <emph type="italics"/>reliqua pars aëre plena erit. Rur&longs;um cùm aquam infunda<lb/>mus, non procedet per &longs;iphonem<emph.end type="italics"/> C, <emph type="italics"/>propterea quòd aër in eo contine<lb/>tur inter aquam infu&longs;am, & eam quæ e&longs;t in va&longs;e<emph.end type="italics"/> F. <emph type="italics"/>A&longs;cendet ergo <lb/>humidum u&longs;que ad &longs;iphonis<emph.end type="italics"/> D <emph type="italics"/>curvitatem, quæ e&longs;t ad dimidium alti<lb/>tudinis va&longs;is; & tunc fluere incipiet: &longs;ed inter mi&longs;&longs;ione facta, rur&longs;us <lb/>idem continget quod in &longs;iphone<emph.end type="italics"/> C <emph type="italics"/>jam dictum e&longs;t. Eadem & in &longs;i<lb/>phone<emph.end type="italics"/> E <emph type="italics"/>intelligantur. Oportebit autem humidum &longs;en&longs;im infunde<lb/>re, nè aër, qui in &longs;iphonibus comprehen&longs;us e&longs;t, &longs;umma vi expellatur.<emph.end type="italics"/><lb/>Hæc Hero; Quæ tamen, & quidem optimè, atque ex Hydro<lb/>pnevmaticæ artis principijs, Salomon Caus in &longs;uis hydraulicis, <lb/>

<arrow.to.target n="fig14"/><lb/><emph type="italics"/>Sit enim vas<emph.end type="italics"/> AB, <emph type="italics"/>habens in &longs;eip&longs;<gap/><lb/>tres &longs;iphones inflexos<emph.end type="italics"/> C, D, E, <emph type="italics"/>in ven<lb/>tre occultatos, quorum altera quidem <lb/>crura &longs;int ad fundum va&longs;is, altera ve<lb/>rò extra ferantur in canales efforma<lb/>ta; atque eorum extremis apponantur <lb/>va&longs;a<emph.end type="italics"/> F, H, G, <emph type="italics"/>quorum fundum di&longs;tet <lb/>ab o&longs;culis, quantum ad aquæ fluxum &longs;a<lb/>tis &longs;it. </s><s>Omnia verò comprehendantur <lb/>alio quodam va&longs;e, tanquam ba&longs;i<emph.end type="italics"/> KLMN, <lb/><emph type="italics"/>quæ canalem<emph.end type="italics"/> X <emph type="italics"/>habeat. </s><s>Et &longs;iphonis <lb/>quidem<emph.end type="italics"/> C <emph type="italics"/>curvit as &longs;it ad fundum va<lb/>&longs;is; &longs;iphonis verò<emph.end type="italics"/> D <emph type="italics"/>curvitas ad di<lb/>midium altitudinis ejus & &longs;iphonis<emph.end type="italics"/> E <lb/><emph type="italics"/>ad ip&longs;um collum. </s><s>Si igitur in vas<emph.end type="italics"/> AB <lb/><emph type="italics"/>aquam infundamus, à principio <expan abbr="quid&etilde;">quidem</expan> <lb/>fluet per &longs;iphonem<emph.end type="italics"/> C, <emph type="italics"/>quoniam cur<lb/>vitas ip&longs;ius e&longs;t ad fundum. </s><s>Quòd &longs;i <lb/>intermittamus, evacuabitur humidum <lb/>infu&longs;um per canalem<emph.end type="italics"/> X, <emph type="italics"/>& vas<emph.end type="italics"/> F <emph type="italics"/>relin quetur aqua plenum, &longs;iphonis <lb/>verò<emph.end type="italics"/> C <emph type="italics"/>reliqua pars aëre plena erit. </s><s>Rur&longs;um cùm aquam infunda<lb/>mus, non procedet per &longs;iphonem<emph.end type="italics"/> C, <emph type="italics"/>propterea quòd aër in eo contine<lb/>tur inter aquam infu&longs;am, & eam quæ e&longs;t in va&longs;e<emph.end type="italics"/> F. </s><s><emph type="italics"/>A&longs;cendet ergo <lb/>humidum u&longs;que ad &longs;iphonis<emph.end type="italics"/> D <emph type="italics"/>curvitatem, quæ e&longs;t ad dimidium alti<lb/>tudinis va&longs;is; & tunc fluere incipiet: &longs;ed inter mi&longs;&longs;ione facta, rur&longs;us <lb/>idem continget quod in &longs;iphone<emph.end type="italics"/> C <emph type="italics"/>jam dictum e&longs;t. </s><s>Eadem & in &longs;i<lb/>phone<emph.end type="italics"/> E <emph type="italics"/>intelligantur. </s><s>Oportebit autem humidum &longs;en&longs;im infunde<lb/>re, nè aër, qui in &longs;iphonibus comprehen&longs;us e&longs;t, &longs;umma vi expellatur.<emph.end type="italics"/><lb/>Hæc Hero; Quæ tamen, & quidem optimè, atque ex Hydro<lb/>pnevmaticæ artis principijs, Salomon Caus in &longs;uis hydraulicis, <lb/>

<arrow.to.target n="marg115"/><lb/>&longs;eu lib. 1. de viribus motricibus, reprehendit, dicens effluere <lb/>aquam per &longs;iphonem C, etiam po&longs;t &longs;ecundam infu&longs;ionem in<lb/>tra vas, eò quòd aër contentus intra &longs;iphonem C pellatur ab <lb/>aqua extra inferius o&longs;culum, erumpatque extra aquam va&longs;is F

<pb xlink:href="051/01/088.jpg" pagenum="57"/>Quod quidem <expan abbr="veri&longs;&longs;im&utilde;">veri&longs;&longs;imum</expan> e&longs;t, cùm aqua infu&longs;a intra vas AB per &longs;e<lb/>cundam <expan abbr="infu&longs;ion&etilde;">infu&longs;ionem</expan>, facillimè a&longs;cendat per crus internum <expan abbr="u&longs;q;">u&longs;que</expan> ad <lb/><expan abbr="curvitat&etilde;">curvitatem</expan> C, non re&longs;i&longs;tente aëre; qui aër intra <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> CF compre&longs;<lb/>&longs;us cedit aquæ a&longs;cendenti primùm u&longs;q, ad <expan abbr="curvitat&etilde;">curvitatem</expan> C, <expan abbr="indeq;">indeque</expan> <lb/>de&longs;cendenti pondere &longs;uo, pul&longs;o aëre, erumpente per aquam va<lb/>&longs;is F. Adde quòd &longs;i tam altum e&longs;&longs;et va&longs;culum F, ut aër per ejus <lb/>aquam exitum non inveniret; a&longs;cenderet is per &longs;iphonem aquæ <lb/>mixtus, prout fieri videmus in canali vitreo quantumvis gracili <lb/>atque longo: &longs;i enim aquâ aliquòusque eum repleas, & ob<lb/>tùrato utroque orificio invertas, ut aqua &longs;uperiorem, aër inferio<lb/>rem occupat locum; &longs;tatim de&longs;cendit aqua, & a&longs;cenditaër, aper<lb/>tâ &longs;ibi vel per medias aquas viâ, ut te&longs;tantur bullæ frequentes in<lb/>ter aquas erumpentes; & qui paulò antè &longs;uccumbebat aquæ, ei<lb/>dem paulò po&longs;t incumbit aër. </s>

<pb xlink:href="051/01/088.jpg" pagenum="57"/>Quod quidem <expan abbr="veri&longs;&longs;im&utilde;">veri&longs;&longs;imum</expan> e&longs;t, cùm aqua infu&longs;a intra vas AB per &longs;e<lb/>cundam <expan abbr="infu&longs;ion&etilde;">infu&longs;ionem</expan>, facillimè a&longs;cendat per crus internum <expan abbr="u&longs;q;">u&longs;que</expan> ad <lb/><expan abbr="curvitat&etilde;">curvitatem</expan> C, non re&longs;i&longs;tente aëre; qui aër intra <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> CF compre&longs;<lb/>&longs;us cedit aquæ a&longs;cendenti primùm u&longs;q, ad <expan abbr="curvitat&etilde;">curvitatem</expan> C, <expan abbr="indeq;">indeque</expan> <lb/>de&longs;cendenti pondere &longs;uo, pul&longs;o aëre, erumpente per aquam va<lb/>&longs;is F. </s><s>Adde quòd &longs;i tam altum e&longs;&longs;et va&longs;culum F, ut aër per ejus <lb/>aquam exitum non inveniret; a&longs;cenderet is per &longs;iphonem aquæ <lb/>mixtus, prout fieri videmus in canali vitreo quantumvis gracili <lb/>atque longo: &longs;i enim aquâ aliquòusque eum repleas, & ob<lb/>tùrato utroque orificio invertas, ut aqua &longs;uperiorem, aër inferio<lb/>rem occupat locum; &longs;tatim de&longs;cendit aqua, & a&longs;cenditaër, aper<lb/>tâ &longs;ibi vel per medias aquas viâ, ut te&longs;tantur bullæ frequentes in<lb/>ter aquas erumpentes; & qui paulò antè &longs;uccumbebat aquæ, ei<lb/>dem paulò po&longs;t incumbit aër. </s>

<s><margin.target id="marg114"/><emph type="italics"/>Heronis Ma <lb/>china defe<lb/>ctuo&longs;a.<emph.end type="italics"/></s>

Line 1616

Line 1615

<s><emph type="center"/>Idem perpendiculum aquæ cadentis non pote&longs;t &longs;ervire <lb/>&longs;imul attractioni & expul&longs;ioni.<emph.end type="center"/></s>

<s>POrta loco &longs;æpe citato de &longs;piritalibus Cap. VIII. ait, &longs;e fre<lb/>quenter tenta&longs;&longs;e ut aquam eodem perpendiculo mediante <lb/>elevaret ad majorem altitudinem, quàm perpendiculum erat, <lb/>partim attractione, partim expul&longs;ione. Eum in finem fecit vas <lb/>A, ex quo elevare volebat aquam u&longs;que ad vas B, ad alti<lb/>tudinem pedum centum verbi gratia. Con&longs;truxit igitur aliud <lb/>æquale vas C in eodem plano, & aliud DF demi&longs;&longs;ius utroque <lb/>pedibus 50. va&longs;a con&longs;tructa in&longs;truxit tubis & epi&longs;tomijs, prout <lb/>figura mon&longs;trat. Hi&longs;ce peractis, replevit va&longs;a C & A aquis, & <lb/>diligenter clau&longs;it utrumque, clau&longs;is etiam eadem diligentia va&longs;is <lb/>B & DE. Deinde aperuit tubum ED, ut de&longs;cendente aqua va&longs;is C <lb/>intra vas DE, traheretur aër ex tubo CK, va&longs;e B, & tubo <lb/>IH, &longs;imulque attraheretur aqua va&longs;is A &longs;altem ad L, altitu<lb/>dinem pedum 50; quod & factum fuit. Sperabat|autem ut aër <lb/>va&longs;is DF pul&longs;us per tubum EG, intra vas A, expelleret inde

<s>POrta loco &longs;æpe citato de &longs;piritalibus Cap. VIII. ait, &longs;e fre<lb/>quenter tenta&longs;&longs;e ut aquam eodem perpendiculo mediante <lb/>elevaret ad majorem altitudinem, quàm perpendiculum erat, <lb/>partim attractione, partim expul&longs;ione. </s><s>Eum in finem fecit vas <lb/>A, ex quo elevare volebat aquam u&longs;que ad vas B, ad alti<lb/>tudinem pedum centum verbi gratia. </s><s>Con&longs;truxit igitur aliud <lb/>æquale vas C in eodem plano, & aliud DF demi&longs;&longs;ius utroque <lb/>pedibus 50. va&longs;a con&longs;tructa in&longs;truxit tubis & epi&longs;tomijs, prout <lb/>figura mon&longs;trat. </s><s>Hi&longs;ce peractis, replevit va&longs;a C & A aquis, & <lb/>diligenter clau&longs;it utrumque, clau&longs;is etiam eadem diligentia va&longs;is <lb/>B & DE. </s><s>Deinde aperuit tubum ED, ut de&longs;cendente aqua va&longs;is C <lb/>intra vas DE, traheretur aër ex tubo CK, va&longs;e B, & tubo <lb/>IH, &longs;imulque attraheretur aqua va&longs;is A &longs;altem ad L, altitu<lb/>dinem pedum 50; quod & factum fuit. </s><s>Sperabat|autem ut aër <lb/>va&longs;is DF pul&longs;us per tubum EG, intra vas A, expelleret inde

<arrow.to.target n="fig15"/><lb/>aliam aquam, & &longs;ublatam <lb/>jam antea aquam v&longs;que ad <lb/>L, attolleret vlteriùs v&longs;que <lb/>ad vas B; at nunquam id <lb/>obtinere potuit: nam po&longs;t<lb/>quam a&longs;cenderat aqua v&longs;<lb/>que ad L, hæ&longs;it &longs;u&longs;pen&longs;a, <lb/>& aqua va&longs;is C non deflu<lb/>xit ampliùs per tubum ED. <lb/>Collegit inde, idem per<lb/>pendiculum ED non po&longs;<lb/>&longs;e in&longs;ervire attractioni & <lb/>expul&longs;ioni &longs;imul, &longs;ed vel <lb/>&longs;oli attractioni, vel &longs;oli ex<lb/>pul&longs;ioni; quod benè notan<lb/>dum e&longs;t. Cau&longs;am dabi<lb/>mus infrà Protheoria IV. <lb/>capite 2. Propo&longs;it. 13. & 14. <lb/>quam tamen ignora&longs;&longs;e Por<lb/>ta videtur, quoniam nul<lb/>lam ad&longs;ignat. </s>

<arrow.to.target n="fig15"/><lb/>aliam aquam, & &longs;ublatam <lb/>jam antea aquam v&longs;que ad <lb/>L, attolleret vlteriùs v&longs;que <lb/>ad vas B; at nunquam id <lb/>obtinere potuit: nam po&longs;t<lb/>quam a&longs;cenderat aqua v&longs;<lb/>que ad L, hæ&longs;it &longs;u&longs;pen&longs;a, <lb/>& aqua va&longs;is C non deflu<lb/>xit ampliùs per tubum ED. </s><s><lb/>Collegit inde, idem per<lb/>pendiculum ED non po&longs;<lb/>&longs;e in&longs;ervire attractioni & <lb/>expul&longs;ioni &longs;imul, &longs;ed vel <lb/>&longs;oli attractioni, vel &longs;oli ex<lb/>pul&longs;ioni; quod benè notan<lb/>dum e&longs;t. </s><s>Cau&longs;am dabi<lb/>mus infrà Protheoria IV. <lb/>capite 2. Propo&longs;it. 13. & 14. <lb/>quam tamen ignora&longs;&longs;e Por<lb/>ta videtur, quoniam nul<lb/>lam ad&longs;ignat. </s>

<s><emph type="center"/>Error apud Ioannem Bapti&longs;tam Portam, indicatur.<emph.end type="center"/></s>

<s>APud Ioannem Bapti&longs;tam Portam lib 2. Spiritalium cap. 10. <lb/>traditur modus elevandi aquam per expul&longs;ionem ad &longs;tellas <lb/>v&longs;que, vt ibi dicitur, mediante &longs;olo vnico perpendiculo quin<lb/>quaginta verbi gratia pedum altitudinis: qui tamen e&longs;t omnino <lb/>fal&longs;us, & repugnat doctrinæ Portæ in præcedentibus traditæ; <lb/>Vnde &longs;u&longs;picabar ab Hi&longs;pano traductore fuiffe additum: crede<lb/>re enim nulla ratione poteram, à Porta tam enormem errorem <lb/>potui&longs;&longs;e committi. Reperi tamen deinde eundem modum in

<arrow.to.target n="fig16"/><lb/>editione latina cap. 9. Modus hic <lb/>e&longs;t. E&longs;to vas C, & &longs;upra ip&longs;um <lb/>ad di&longs;tantiam pedum verbi gratia <lb/>quinquaginta, va&longs;a D & K, cum <lb/>&longs;uis infundibulis; & &longs;upra hæc ali<lb/>ud G; aliudque &longs;upra hoc; & &longs;ic <lb/>deinceps ad quamvis altitudinem, <lb/>etiam v&longs;que ad &longs;tellas. Conjun<lb/>gantur dicta va&longs;a tubis, vt mon<lb/>&longs;trat figura, habeatque tubus DB <lb/>&longs;uum epi&longs;tomium, vt & vas C &longs;u<lb/>um; & va&longs;a D & K repleantur a<lb/>quâ. Deinde aperiatur epi&longs;tomi<lb/>um tubi DB, & aqua de&longs;cendens <lb/>intra vas C expellet inde aërem <lb/>per tubum FK intra vas K; qui <lb/>aër inde expellet aquam per tu<lb/>bum FG in vas G, & ex G per <lb/>tubum HI expelletur aqua in aliud <lb/>vas, & &longs;ic vlteriùs. Sed hæc pror<lb/>

<arrow.to.target n="fig16"/><lb/>editione latina cap. 9. Modus hic <lb/>e&longs;t. </s><s>E&longs;to vas C, & &longs;upra ip&longs;um <lb/>ad di&longs;tantiam pedum verbi gratia <lb/>quinquaginta, va&longs;a D & K, cum <lb/>&longs;uis infundibulis; & &longs;upra hæc ali<lb/>ud G; aliudque &longs;upra hoc; & &longs;ic <lb/>deinceps ad quamvis altitudinem, <lb/>etiam v&longs;que ad &longs;tellas. </s><s>Conjun<lb/>gantur dicta va&longs;a tubis, vt mon<lb/>&longs;trat figura, habeatque tubus DB <lb/>&longs;uum epi&longs;tomium, vt & vas C &longs;u<lb/>um; & va&longs;a D & K repleantur a<lb/>quâ. </s><s>Deinde aperiatur epi&longs;tomi<lb/>um tubi DB, & aqua de&longs;cendens <lb/>intra vas C expellet inde aërem <lb/>per tubum FK intra vas K; qui <lb/>aër inde expellet aquam per tu<lb/>bum FG in vas G, & ex G per <lb/>tubum HI expelletur aqua in aliud <lb/>vas, & &longs;ic vlteriùs. </s><s>Sed hæc pror<lb/>

<arrow.to.target n="marg116"/><lb/>&longs;us &longs;unt erronea, & contra princi<lb/>pia hydraulica. Perpendiculum <lb/>enim DB aquæ cadentis pedum quinquaginta, non pote&longs;t ele<lb/>vare aliam præter aquam va&longs;is K per tubum FG pedum etiam <lb/>50. ad &longs;ummum, v&longs;que ad vas G, vbi quie&longs;cet aqua. Dato dein<lb/>de quòd ex G po&longs;&longs;et elevari aqua eodem perpendiculo DB, de<lb/>beret tubus IH pertingere ferè v&longs;que ad fundum va&longs;is G, vt <lb/>aqua pre&longs;&longs;a intrare po&longs;&longs;et. Fal&longs;us ergo e&longs;t hic modus. Alium nos <lb/>trademus infrà Cla&longs;se I. cap. 2. Machina 4. & 11. </s>

<arrow.to.target n="marg116"/><lb/>&longs;us &longs;unt erronea, & contra princi<lb/>pia hydraulica. </s><s>Perpendiculum <lb/>enim DB aquæ cadentis pedum quinquaginta, non pote&longs;t ele<lb/>vare aliam præter aquam va&longs;is K per tubum FG pedum etiam <lb/>50. ad &longs;ummum, v&longs;que ad vas G, vbi quie&longs;cet aqua. </s><s>Dato dein<lb/>de quòd ex G po&longs;&longs;et elevari aqua eodem perpendiculo DB, de<lb/>beret tubus IH pertingere ferè v&longs;que ad fundum va&longs;is G, vt <lb/>aqua pre&longs;&longs;a intrare po&longs;&longs;et. </s><s>Fal&longs;us ergo e&longs;t hic modus. </s><s>Alium nos <lb/>trademus infrà Cla&longs;se I. cap. 2. Machina 4. & 11. </s>

<s><margin.target id="marg116"/><emph type="italics"/>Error apud <lb/>Portam.<emph.end type="italics"/></s>

Line 1640

Line 1639

<s><margin.target id="marg117"/><emph type="italics"/>Modui ele<lb/>vandi <expan abbr="aquã">aquam</expan> <lb/>etiam bru <lb/>tis notus.<emph.end type="italics"/></s>

<s>ESt & alia ratio aquam quie&longs;centem atque infu&longs;am va&longs;is ele<lb/>vandi, in altum, atque in fontes efformandi, quam vel ip&longs;a <lb/>bruta do cent animalia. De Cervis quippe Lybicis narratur, quòd

<pb xlink:href="051/01/091.jpg" pagenum="60"/>dum &longs;itientes foveam offendunt <expan abbr="aquã">aquam</expan> plenam, culus tamen &longs;u<lb/>prema &longs;uperficies humilior <expan abbr="atq;">atque</expan> profundior e&longs;t, quàm vt capite <lb/>ac collo proten&longs;o eam attingere po&longs;&longs;int, calculos ore & vnguibus <lb/>a&longs;portantes foveæ injiciant, vt de&longs;identibus in fundum lapidi<lb/>bus humor &longs;ub&longs;identium corporum occupatione elevetur, &longs;u<lb/>perioremque elatus repleat vacuitatem; ita &longs;olerti machinatio<lb/>ne reficiuntur. Va&longs;is <expan abbr="itaq;">itaque</expan> puteisque &longs;i &longs;olida injicias corpora, quæ <lb/>fundum petant vel &longs;ponte, vel vi depre&longs;&longs;a; elevabitur aqua, & <lb/>per tubos &longs;uperiùs applicatos effluens in fontem formabitur. <lb/>Hoc artificio con&longs;tructus erat olim fons ad S. Georg. Venetijs, </s>

<pb xlink:href="051/01/091.jpg" pagenum="60"/>dum &longs;itientes foveam offendunt <expan abbr="aquã">aquam</expan> plenam, culus tamen &longs;u<lb/>prema &longs;uperficies humilior <expan abbr="atq;">atque</expan> profundior e&longs;t, quàm vt capite <lb/>ac collo proten&longs;o eam attingere po&longs;&longs;int, calculos ore & vnguibus <lb/>a&longs;portantes foveæ injiciant, vt de&longs;identibus in fundum lapidi<lb/>bus humor &longs;ub&longs;identium corporum occupatione elevetur, &longs;u<lb/>perioremque elatus repleat vacuitatem; ita &longs;olerti machinatio<lb/>ne reficiuntur. </s><s>Va&longs;is <expan abbr="itaq;">itaque</expan> puteisque &longs;i &longs;olida injicias corpora, quæ <lb/>fundum petant vel &longs;ponte, vel vi depre&longs;&longs;a; elevabitur aqua, & <lb/>per tubos &longs;uperiùs applicatos effluens in fontem formabitur. </s><s><lb/>Hoc artificio con&longs;tructus erat olim fons ad S. Georg. Venetijs, </s>

<s>

<arrow.to.target n="marg118"/><lb/>te&longs;te Io&longs;epho Ceredo Di&longs;cur&longs;u primo de Modo elevandi aquas <lb/>è locishumilibus, pag. 11. Binæ enim fabricatæ erant ci&longs;ternæ, <lb/>&longs;eu pi&longs;cinæ, humilior ac profundior vna, altera elatior ad prioris <lb/>latus. Humilior latera habebat angu&longs;ta, & putei in&longs;tar erecta; <lb/>è cuius fundo v&longs;que ad collateralis &longs;uprema labra deduceban<lb/>tur tubi plumbei. Habebat præterea operculum ligneum atque <lb/>gravi&longs;&longs;imum, quod ci&longs;ternæ latera vacua implebat, & aquæ in<lb/>cumbens &longs;uo paulatim pondere de&longs;cendebat, atque aquam <expan abbr="cõ-primens">con<lb/>primens</expan> eam intra tubos compellebat; per quos a&longs;cendens, &longs;ub<lb/>&longs;equentibus alijs aquis pul&longs;a, exonerabat &longs;e&longs;e intra &longs;uperiorem <lb/>collateralem ci&longs;ternam, indeque pondere &longs;uo naturaliter dela<lb/>bens per fi&longs;tulas efforma batur in fontem. Multas alias Machi<lb/>nas hydraulicas eodem con&longs;tructas artificio enumerat ibidem <lb/>citatus Ceredus, & vnam hac ratione adornatam Machinulam <lb/>Scaliger Exercitat. 42. contra Cardanum; ex qua tamen fal&longs;um <lb/>deducit modum o&longs;tendendi fontium originem ex mari. Hac <lb/>porrò ratione in altum elevatur aqua per antlias, quarum ingen<lb/>tem copiam affert Augu&longs;tinus Ramellus in&longs;uo de Machi<lb/>nis hydraulicis opere, & nos aliquas adduce<lb/>mus Cla&longs;se I. cap. 2. Machina 6. </s>

<arrow.to.target n="marg118"/><lb/>te&longs;te Io&longs;epho Ceredo Di&longs;cur&longs;u primo de Modo elevandi aquas <lb/>è locishumilibus, pag. 11. </s><s>Binæ enim fabricatæ erant ci&longs;ternæ, <lb/>&longs;eu pi&longs;cinæ, humilior ac profundior vna, altera elatior ad prioris <lb/>latus. </s><s>Humilior latera habebat angu&longs;ta, & putei in&longs;tar erecta; <lb/>è cuius fundo v&longs;que ad collateralis &longs;uprema labra deduceban<lb/>tur tubi plumbei. </s><s>Habebat præterea operculum ligneum atque <lb/>gravi&longs;&longs;imum, quod ci&longs;ternæ latera vacua implebat, & aquæ in<lb/>cumbens &longs;uo paulatim pondere de&longs;cendebat, atque aquam <expan abbr="cõ-primens">con<lb/>primens</expan> eam intra tubos compellebat; per quos a&longs;cendens, &longs;ub<lb/>&longs;equentibus alijs aquis pul&longs;a, exonerabat &longs;e&longs;e intra &longs;uperiorem <lb/>collateralem ci&longs;ternam, indeque pondere &longs;uo naturaliter dela<lb/>bens per fi&longs;tulas efforma batur in fontem. </s><s>Multas alias Machi<lb/>nas hydraulicas eodem con&longs;tructas artificio enumerat ibidem <lb/>citatus Ceredus, & vnam hac ratione adornatam Machinulam <lb/>Scaliger Exercitat. 42. contra Cardanum; ex qua tamen fal&longs;um <lb/>deducit modum o&longs;tendendi fontium originem ex mari. </s><s>Hac <lb/>porrò ratione in altum elevatur aqua per antlias, quarum ingen<lb/>tem copiam affert Augu&longs;tinus Ramellus in&longs;uo de Machi<lb/>nis hydraulicis opere, & nos aliquas adduce<lb/>mus Cla&longs;se I. cap. 2. Machina 6. </s>

<s><margin.target id="marg118"/><emph type="italics"/>Fons ad S. <lb/>Georgium <lb/>Venetijs.<emph.end type="italics"/></s>

Line 1660

Line 1659

<s><emph type="center"/>Rarefactionis vis, & effectus mirabiles.<emph.end type="center"/></s>

<s>RArefactionem ingentes &longs;uppeditare vires vt <lb/>alijs corporibus, ita aquæ & aëri, ad ea in omnem &longs;i<lb/>tus differentiam impellendam, multòque magis ad <lb/>hydro-pnevmatica omnis generis techna&longs;mata mo<lb/>lienda; is &longs;olus ignorare pote&longs;t, qui &longs;tupendos ip&longs;ius effectus igno<lb/>rat. videmus quotidie, miramurque, ac plangimus &longs;tragem, <lb/>

<arrow.to.target n="marg119"/><lb/>quam <foreign lang="greek">polio<gap/>xh|tai\</foreign> nitrato & &longs;ulphureo pulvere intra bombarda<lb/>rum militarium angu&longs;tias rarefacto edunt, in &longs;ternendis non ho<lb/>minibus tantùm, fed ædibus, turribus, propugnaculis, atque <lb/>adeo vrbibus integris. Non Iovis tantummodo fulmina imita<lb/>tur rarefactio in bombardis, &longs;ed Plutonis etiam iras æmulatur in <lb/>&longs;ubterraneis cuniculis; tantò pernicio&longs;iore &longs;trage, quantò mi<lb/>nùs patente. Excavant Martiales Architecti à loco ob&longs;idionis <lb/>

<arrow.to.target n="marg119"/><lb/>quam <foreign lang="greek">polio<gap/>xh|tai\</foreign> nitrato & &longs;ulphureo pulvere intra bombarda<lb/>rum militarium angu&longs;tias rarefacto edunt, in &longs;ternendis non ho<lb/>minibus tantùm, fed ædibus, turribus, propugnaculis, atque <lb/>adeo vrbibus integris. </s><s>Non Iovis tantummodo fulmina imita<lb/>tur rarefactio in bombardis, &longs;ed Plutonis etiam iras æmulatur in <lb/>&longs;ubterraneis cuniculis; tantò pernicio&longs;iore &longs;trage, quantò mi<lb/>nùs patente. </s><s>Excavant Martiales Architecti à loco ob&longs;idionis <lb/>

<arrow.to.target n="marg120"/><lb/>ad v&longs;que propugnaculum, cui ruinam minantur, viam anfra<lb/>ctuo&longs;am, angu&longs;tamque, magneticæ pixidis ductu, uti inter alios <lb/>docet P. Athana&longs;ius Kircherus lib. 2. de Arte Magnet. par. 2. cap. 1. <lb/>Probl 7. & nos in Pantometro Kircherianolib. 5. Ichnographi<lb/>co Probl. 8. Sub loco deinde ruinæ de&longs;tinato Cameram con<lb/>&longs;truunt laxiorem, eamque implent pulveris tormentarij va&longs;is, <lb/>& o&longs;tium claudunt, relicto exiguo foramine, perque viam totam <lb/>ignis pabulum &longs;ternunt, & egre&longs;&longs;i ignem applicant; qui &longs;erpens <lb/>per viam accendit pulveris ma&longs;&longs;am omnem Camerâ conclu&longs;am, <lb/>itàque rarefacit, dilatatque, ut angu&longs;tiarum impatiens, & laxio<lb/>rem quærens locum, impo&longs;itam &longs;ibi molem di&longs;iiciat horribili <lb/>

<arrow.to.target n="marg121"/><lb/>fremitu, nec minori terrore, quàm damno. Nihil unquam <lb/>magis &longs;imile terræ motui, qui & ip&longs;e rarefactionis e&longs;t effectus lu-

<arrow.to.target n="marg121"/><lb/>fremitu, nec minori terrore, quàm damno. </s><s>Nihil unquam <lb/>magis &longs;imile terræ motui, qui & ip&longs;e rarefactionis e&longs;t effectus lu-

<pb xlink:href="051/01/093.jpg" pagenum="62"/>culenti&longs;&longs;imus, excogitatum fuit. Eodem enim pror&longs;us modo <lb/>in terræ concu&longs;&longs;ione flamma ex aliqua &longs;ubterranea fornace, vel <lb/>interno calore, per venulam aliquam nitri aut &longs;ulphuris &longs;erpit, <lb/>donec perveniat ad locum, in quo maiorem huiu&longs;ce materiæ <lb/>copiam inveniat; quâ &longs;ubitò accen&longs;a & rarefactâ, dum maio<lb/>rem quærit locum, &longs;ibi impo&longs;itas concutit, & di&longs;jicit non rarò, <lb/>moles. Sæpe etiam iam antea accen&longs;us in terræ vi&longs;ceribus ignis, <lb/>dum nova augetur aliunde attracta materia, montes &longs;ibi impo&longs;i<lb/>

<pb xlink:href="051/01/093.jpg" pagenum="62"/>culenti&longs;&longs;imus, excogitatum fuit. </s><s>Eodem enim pror&longs;us modo <lb/>in terræ concu&longs;&longs;ione flamma ex aliqua &longs;ubterranea fornace, vel <lb/>interno calore, per venulam aliquam nitri aut &longs;ulphuris &longs;erpit, <lb/>donec perveniat ad locum, in quo maiorem huiu&longs;ce materiæ <lb/>copiam inveniat; quâ &longs;ubitò accen&longs;a & rarefactâ, dum maio<lb/>rem quærit locum, &longs;ibi impo&longs;itas concutit, & di&longs;jicit non rarò, <lb/>moles. </s><s>Sæpe etiam iam antea accen&longs;us in terræ vi&longs;ceribus ignis, <lb/>dum nova augetur aliunde attracta materia, montes &longs;ibi impo&longs;i<lb/>

<arrow.to.target n="marg122"/><lb/>tos concutit, finditque, vt non &longs;emel audivi, vidique in Ætna Si<lb/>ciliæ, duorum annorum accola olim, & nunc hoc ip&longs;o anno 1654. <lb/>quo hæc &longs;cribo, hîc Romæ, quam (raro exe n<gap/>o) concu&longs;&longs;it mo<lb/>tusille ingens, qui tantam Soræ &longs;tragem <gap/>lit, & Romam hinc <lb/>inde Neapolim, omnes que interiacent<gap/> regiones tremefecit. </s>

<s><margin.target id="marg119"/><emph type="italics"/>Rarefactio<lb/>nis vis in <lb/>bombardis.<emph.end type="italics"/></s>

Line 1681

Line 1680

<s><margin.target id="marg123"/><emph type="italics"/>Rare&longs;actio<lb/>nis exempla <lb/>d<gap/>.<emph.end type="italics"/></s>

<s>NArrat P. Nicolaus Cabæus lib. 4. Meteor. Ari&longs;t. text. 12. <expan abbr="q.">que</expan> 1. <lb/>vidi&longs;&longs;e &longs;e marmoreum vas maximum atque duri&longs;&longs;imum ab <lb/>aqua conglaciata di&longs;ci&longs;&longs;um, eò quòd <expan abbr="cõgelatione">congelatione</expan> rarefactæ fue<lb/>rint aliquæ internæ partes aquæ: factà enim illâ &longs;ubitâ congela<lb/>tione, ob&longs;titerunt attenuationi & rarefactioni partium latera va<lb/>&longs;is, <expan abbr="ce&longs;&longs;it&qacute;ue">ce&longs;&longs;itque</expan> durities vehementiæ rarefactionis, & fractum e&longs;t <lb/>vas, quod non di&longs;rupi&longs;&longs;ent centum juga boum, &longs;i in diver&longs;as par<lb/>tes traxi&longs;&longs;ent. Idem Cabæus ibidem a&longs;&longs;erit, &longs;e vidi&longs;&longs;e columnam <lb/>marmoream, quam tres homines dilatatis brachijs &longs;imul non <lb/>poterant complecti, quamque mille juga boum, &longs;i in diver&longs;as <lb/>partes, toto juncto impetu traxi&longs;&longs;ent, frangere non potui&longs;&longs;ent, <lb/>fractam tamen pror&longs;us mediam atque truncatam, eò quòd ligna <lb/>quædam columnæ illi proxima fuerint combu&longs;ta, ideoque ex vi<lb/>cino calore &longs;piritulus aliquis in marmore inclu&longs;us intus in meati<lb/>bus fuerit rarefactus, & ex rarefactione maiorem &longs;ibi <expan abbr="loc&utilde;">locum</expan> quæ<lb/>&longs;iverit. </s>

<s>NArrat P. Nicolaus Cabæus lib. 4. Meteor. Ari&longs;t. text. 12. <expan abbr="q.">que</expan> 1. <lb/>vidi&longs;&longs;e &longs;e marmoreum vas maximum atque duri&longs;&longs;imum ab <lb/>aqua conglaciata di&longs;ci&longs;&longs;um, eò quòd <expan abbr="cõgelatione">congelatione</expan> rarefactæ fue<lb/>rint aliquæ internæ partes aquæ: factà enim illâ &longs;ubitâ congela<lb/>tione, ob&longs;titerunt attenuationi & rarefactioni partium latera va<lb/>&longs;is, <expan abbr="ce&longs;&longs;it&qacute;ue">ce&longs;&longs;itque</expan> durities vehementiæ rarefactionis, & fractum e&longs;t <lb/>vas, quod non di&longs;rupi&longs;&longs;ent centum juga boum, &longs;i in diver&longs;as par<lb/>tes traxi&longs;&longs;ent. </s><s>Idem Cabæus ibidem a&longs;&longs;erit, &longs;e vidi&longs;&longs;e columnam <lb/>marmoream, quam tres homines dilatatis brachijs &longs;imul non <lb/>poterant complecti, quamque mille juga boum, &longs;i in diver&longs;as <lb/>partes, toto juncto impetu traxi&longs;&longs;ent, frangere non potui&longs;&longs;ent, <lb/>fractam tamen pror&longs;us mediam atque truncatam, eò quòd ligna <lb/>quædam columnæ illi proxima fuerint combu&longs;ta, ideoque ex vi<lb/>cino calore &longs;piritulus aliquis in marmore inclu&longs;us intus in meati<lb/>bus fuerit rarefactus, & ex rarefactione maiorem &longs;ibi <expan abbr="loc&utilde;">locum</expan> quæ<lb/>&longs;iverit. </s>

<s>Notum jam p&oelig;nè e&longs;t omnibus, quod refert Petrus Ca&longs;tel<lb/>lus in Libello de Incendio Ve&longs;uvij Italicè con&longs;cripto, & exip&longs;o <lb/>Kircherus lib. 3. Artis Magnet, part. 2. cap. 3. circa finem, de pul-

<pb xlink:href="051/01/094.jpg" pagenum="63"/>vere pyrio ex auro confecto, quod aurum fulminans appellat Ca</s>

<s>

<arrow.to.target n="marg124"/><lb/>&longs;tellus, & aurum volatile Crollius. E&longs;t id nihil aliud quàm au<lb/>rum calcinatum aquâ forti &longs;eu regiâ, &longs;ale armoniaco, & oleo tar<lb/>tari præcipitati. Hæc calx quàm primùm &longs;entit etiam calorem <lb/>ignis, concipit &longs;ponte &longs;ua flammam, & in auras abit, cum ingenti <lb/>fragore & &longs;trepitu: & &longs;i vel vnum aut alterum huius pulveris gra<lb/>num cultro impo&longs;ueris, & candelam infrà applicueris, vtinca. <lb/>le&longs;cat; tantum edit fragorem, ac &longs;i magnam explo&longs;i&longs;&longs;es bombar<lb/>dam. Facit autem effectum contrarium ordinario pulveri pyrio, <lb/>quia non &longs;ur&longs;um, &longs;ed deor&longs;um tendit; vnde &longs;erupulus vnicus hu<lb/>ius volatilis auri po&longs;itus &longs;upra laminam ferream <expan abbr="nõ">non</expan> modicæ cra&longs;<lb/>&longs;itiei, & carbone de&longs;uper applicato accen&longs;us, penetrat & per<lb/>foratip&longs;am laminam. </s>

<arrow.to.target n="marg124"/><lb/>&longs;tellus, & aurum volatile Crollius. </s><s>E&longs;t id nihil aliud quàm au<lb/>rum calcinatum aquâ forti &longs;eu regiâ, &longs;ale armoniaco, & oleo tar<lb/>tari præcipitati. </s><s>Hæc calx quàm primùm &longs;entit etiam calorem <lb/>ignis, concipit &longs;ponte &longs;ua flammam, & in auras abit, cum ingenti <lb/>fragore & &longs;trepitu: & &longs;i vel vnum aut alterum huius pulveris gra<lb/>num cultro impo&longs;ueris, & candelam infrà applicueris, vtinca. <lb/>le&longs;cat; tantum edit fragorem, ac &longs;i magnam explo&longs;i&longs;&longs;es bombar<lb/>dam. </s><s>Facit autem effectum contrarium ordinario pulveri pyrio, <lb/>quia non &longs;ur&longs;um, &longs;ed deor&longs;um tendit; vnde &longs;erupulus vnicus hu<lb/>ius volatilis auri po&longs;itus &longs;upra laminam ferream <expan abbr="nõ">non</expan> modicæ cra&longs;<lb/>&longs;itiei, & carbone de&longs;uper applicato accen&longs;us, penetrat & per<lb/>foratip&longs;am laminam. </s>

<s><margin.target id="marg124"/><emph type="italics"/>Aurum ful<lb/>minans.<emph.end type="italics"/></s>

<s>Nolo hîc ommittere aliud rarefactionis exemplum, quo <lb/>ego ip&longs;e multis in locis, coram viris etiam Principibus, exiguâ <lb/>machinulâ non exiguum excita vi fragorem, bombardulæ mi<lb/>noris fragori pror&longs;us æqualem ac &longs;imilem. Vitreas Sphærulas <lb/>

<arrow.to.target n="marg125"/><lb/>nucis avellanæ magnitudine, aut etiam minores, fieri curavi ad <lb/>lampadem Romæ à quodam Germano artifice, vitrum in omnes <lb/>colores omnes que figuras florum, fructuum, avium, animalium <lb/>omnis generis, jcuncularum quarumlibet affabrè elaboratarum <lb/>efformante, idemque in &longs;ubtili&longs;&longs;ima fila ad rotam <expan abbr="circumactã">circumactam</expan> <lb/>diducente. In eas vitreas Sphærulas acetum, aut nitratum &longs;a<lb/>lem aquâ di&longs;&longs;olutum ac liquefactum infundi iu&longs;fi, & ad medieta<lb/>tem repleri, ac deinde hermeticè claudi ad eandem lampadem. <lb/>Harum &longs;phærularum vnam &longs;i carbonibus non nimiùm accen&longs;is, <lb/>aut calidis cineribus (vt paulatim calefiat) impo&longs;ueris; rarefit <lb/>&longs;pirito&longs;a materia intus clau&longs;a, & majorem quærens locum, po&longs;t <lb/>&longs;patium circiter temporis quo P&longs;almus 50. <emph type="italics"/>Mi&longs;erere mei Deus,<emph.end type="italics"/> re<lb/>citari pote&longs;t, tanto cum impetu ac fragore viam &longs;ibi aperit, vt <lb/>non tantùm vitrum in mille minuti&longs;&longs;imas particulas diffringat, <lb/>&longs;ed cineres etiam & carbones toto conclavi di&longs;&longs;ipet, nullius <lb/>damno, ni&longs;i &longs;i quis vultum propè applicet. Cùm experientiam <lb/>Romæ coram Sereni&longs;&longs;imi Hol&longs;atiæ Ducis Filio primogenito fa-

<arrow.to.target n="marg125"/><lb/>nucis avellanæ magnitudine, aut etiam minores, fieri curavi ad <lb/>lampadem Romæ à quodam Germano artifice, vitrum in omnes <lb/>colores omnes que figuras florum, fructuum, avium, animalium <lb/>omnis generis, jcuncularum quarumlibet affabrè elaboratarum <lb/>efformante, idemque in &longs;ubtili&longs;&longs;ima fila ad rotam <expan abbr="circumactã">circumactam</expan> <lb/>diducente. </s><s>In eas vitreas Sphærulas acetum, aut nitratum &longs;a<lb/>lem aquâ di&longs;&longs;olutum ac liquefactum infundi iu&longs;fi, & ad medieta<lb/>tem repleri, ac deinde hermeticè claudi ad eandem lampadem. </s><s><lb/>Harum &longs;phærularum vnam &longs;i carbonibus non nimiùm accen&longs;is, <lb/>aut calidis cineribus (vt paulatim calefiat) impo&longs;ueris; rarefit <lb/>&longs;pirito&longs;a materia intus clau&longs;a, & majorem quærens locum, po&longs;t <lb/>&longs;patium circiter temporis quo P&longs;almus 50. <emph type="italics"/>Mi&longs;erere mei Deus,<emph.end type="italics"/> re<lb/>citari pote&longs;t, tanto cum impetu ac fragore viam &longs;ibi aperit, vt <lb/>non tantùm vitrum in mille minuti&longs;&longs;imas particulas diffringat, <lb/>&longs;ed cineres etiam & carbones toto conclavi di&longs;&longs;ipet, nullius <lb/>damno, ni&longs;i &longs;i quis vultum propè applicet. </s><s>Cùm experientiam <lb/>Romæ coram Sereni&longs;&longs;imi Hol&longs;atiæ Ducis Filio primogenito fa-

<pb xlink:href="051/01/095.jpg" pagenum="64"/>cerem, foco a&longs;&longs;identi more ibidem &longs;olito, famuli ante cubicu<lb/>lum præ&longs;tolantes accurrebant attoniti, bombardulam in Princi<lb/>pem &longs;uum explo&longs;am credentes. Alius magnus quidam Prin<lb/>ceps cùm nonnullas à me accepi&longs;&longs;et, ac domi die quodam cum <lb/>multis alijs nobilibus foco a&longs;&longs;ideret, vnam o&longs;tendit, ac videnti<lb/>bus omnibus igni iniecit, a&longs;&longs;erens, vbi calefieret, grati&longs;&longs;imum <lb/>&longs;par&longs;uram odorem. Cùm omnes arrectis naribus, & ore hi<lb/>ante odorem ex&longs;pectarent, derepente fit crepitus, & carbonum <lb/>disiectio, diffugientibus omnibus in timorem primò, deinde in <lb/>ri&longs;um di&longs;&longs;olutis. Alio tempore coram Cardinale quodam & <lb/>magno Nobilium comitatu, admonito priùs clanculum &longs;olo <lb/>Cardinale, vnam explo&longs;i; & ita omnes alij præter dictum <lb/>Cardinalem territi fuêre, vt auctorem (ignorabant me e&longs;&longs;e) <lb/>ad p&oelig;nam quærerent. </s>

<pb xlink:href="051/01/095.jpg" pagenum="64"/>cerem, foco a&longs;&longs;identi more ibidem &longs;olito, famuli ante cubicu<lb/>lum præ&longs;tolantes accurrebant attoniti, bombardulam in Princi<lb/>pem &longs;uum explo&longs;am credentes. </s><s>Alius magnus quidam Prin<lb/>ceps cùm nonnullas à me accepi&longs;&longs;et, ac domi die quodam cum <lb/>multis alijs nobilibus foco a&longs;&longs;ideret, vnam o&longs;tendit, ac videnti<lb/>bus omnibus igni iniecit, a&longs;&longs;erens, vbi calefieret, grati&longs;&longs;imum <lb/>&longs;par&longs;uram odorem. </s><s>Cùm omnes arrectis naribus, & ore hi<lb/>ante odorem ex&longs;pectarent, derepente fit crepitus, & carbonum <lb/>disiectio, diffugientibus omnibus in timorem primò, deinde in <lb/>ri&longs;um di&longs;&longs;olutis. </s><s>Alio tempore coram Cardinale quodam & <lb/>magno Nobilium comitatu, admonito priùs clanculum &longs;olo <lb/>Cardinale, vnam explo&longs;i; & ita omnes alij præter dictum <lb/>Cardinalem territi fuêre, vt auctorem (ignorabant me e&longs;&longs;e) <lb/>ad p&oelig;nam quærerent. </s>

<s><margin.target id="marg125"/><emph type="italics"/>Vitrea &longs;phæ <lb/>rula mino<lb/>ris bombar<lb/>dulæ crepi<lb/>tum amu<lb/>lantes.<emph.end type="italics"/></s>

<s>Innumeros alios effectus rarefactionis, &longs;icut & conden&longs;a<lb/>tionis, adducere po&longs;&longs;em; &longs;ed hi &longs;ufficiunt ad ad&longs;truendam effica<lb/>ciam in commovendis corporibus. Quæ efficacia &longs;i tanta e&longs;t, <lb/>quantam vidimus; quis neget, eandem in aëre & aquis elucere <lb/>po&longs;&longs;e, dilatando & con&longs;tringendo elementa ip&longs;a, & in fontes a<lb/>liaque hydraulica, pnevmaticaque artificia animando? &longs;ed hæc <lb/>evidenti&longs;&longs;imè o&longs;tendemus in multis ex &longs;equentibus Machinis <lb/>Partis 2. p<gap/>ertim Cla&longs;. <expan abbr="&Itilde;">Im</expan>. cap. 3. Mach. 1.2.5.6.8. & alijsmultis. </s>

<s>Innumeros alios effectus rarefactionis, &longs;icut & conden&longs;a<lb/>tionis, adducere po&longs;&longs;em; &longs;ed hi &longs;ufficiunt ad ad&longs;truendam effica<lb/>ciam in commovendis corporibus. </s><s>Quæ efficacia &longs;i tanta e&longs;t, <lb/>quantam vidimus; quis neget, eandem in aëre & aquis elucere <lb/>po&longs;&longs;e, dilatando & con&longs;tringendo elementa ip&longs;a, & in fontes a<lb/>liaque hydraulica, pnevmaticaque artificia animando? &longs;ed hæc <lb/>evidenti&longs;&longs;imè o&longs;tendemus in multis ex &longs;equentibus Machinis <lb/>Partis 2. p<gap/>ertim Cla&longs;. <expan abbr="&Itilde;">Im</expan>. cap. 3. Mach. 1.2.5.6.8. & alijsmultis. </s>

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

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<s>PLurima, jucundi&longs;&longs;ima, vtili&longs;&longs;imaque circa A<lb/>quæ fluxum naturalem, &longs;eu libera ea &longs;it, &longs;eu aquædu<lb/>ctibus, canalibus, tubis, &longs;iphonibus, fi&longs;tulis, & qui<lb/>bus cunque alijs meatibus con&longs;tricta, dicenda occur<lb/>runt noc ioco, quæ Hydro-pnevmaticarum Machinarum Arti-</s>

<s><emph type="center"/>Protheoria IV.<emph.end type="center"/><lb/>ficibus non minùs nece&longs;&longs;aria, quàm vtilia &longs;unt. Nos ex omni<lb/>bus ea tantùm, quæ fini no&longs;tro conducere videbuntur, &longs;elegimus; <lb/>cætera ad Mechanicam no&longs;tram Magiam re&longs;ervabimus. </s>

<s><emph type="center"/>Protheoria IV.<emph.end type="center"/><lb/>ficibus non minùs nece&longs;&longs;aria, quàm vtilia &longs;unt. </s><s>Nos ex omni<lb/>bus ea tantùm, quæ fini no&longs;tro conducere videbuntur, &longs;elegimus; <lb/>cætera ad Mechanicam no&longs;tram Magiam re&longs;ervabimus. </s>

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

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

<s><emph type="italics"/>LIberè fluit aqua, dum nullis con&longs;tricta<emph.end type="italics"/><lb/>

<arrow.to.target n="marg126"/><lb/><emph type="italics"/>e&longs;t meatibus ceu vinculis. Huiu&longs;ce proprie<lb/>tates, fini no&longs;tro conducentes, vt a&longs;&longs;ignem, <lb/>Suppono duo, quæ licet in dubium revocentur <lb/>ab aliquibus, conceduntur tamen à me<gap/><lb/>notæ Philo&longs;ophis & Mathematicis.<emph.end type="italics"/></s>

<arrow.to.target n="marg126"/><lb/><emph type="italics"/>e&longs;t meatibus ceu vinculis. </s><s>Huiu&longs;ce proprie<lb/>tates, fini no&longs;tro conducentes, vt a&longs;&longs;ignem, <lb/>Suppono duo, quæ licet in dubium revocentur <lb/>ab aliquibus, conceduntur tamen à me<gap/><lb/>notæ Philo&longs;ophis & Mathematicis.<emph.end type="italics"/></s>

<s><margin.target id="marg126"/>Aqua libe<lb/>rè fluere <lb/>quæ dica<lb/>tur.</s>

<s><emph type="italics"/>Primum e&longs;t, Ordinem Elementorum, naturæ eorum con<emph.end type="italics"/><lb/>

<arrow.to.target n="marg127"/><lb/><emph type="italics"/>gruentem hunc e&longs;&longs;e, vt Terra &longs;it in medio omnium, Aqua circa <lb/>Terram, circa Aquam Aër, & circa Aërem putatus lgnis. Ac <lb/>principio quidem rerum, quando<emph.end type="italics"/> Creavit DEVS c&oelig;lum & <lb/>terram, <emph type="italics"/>Genes. C. I. prædictum &longs;ervarunt ordinem, v&longs;que ad <lb/>diem Mundi tertium, quo die Deus benedictus Terram, anteà <lb/>&longs;phæricè rotundam, in cavitates varias deformavit, in easque <lb/>Aquam omnem &longs;ubterc&oelig;le&longs;tem, maribus, lacubus, fluminibus, <lb/>fontibus di&longs;cretam, derivavit, vnumque ex Terra & Aqua <lb/>globum con&longs;tituit, vnicâ contentum &longs;phæricâ &longs;uperficie, terrenâ<emph.end type="italics"/><lb/>

<arrow.to.target n="marg127"/><lb/><emph type="italics"/>gruentem hunc e&longs;&longs;e, vt Terra &longs;it in medio omnium, Aqua circa <lb/>Terram, circa Aquam Aër, & circa Aërem putatus lgnis. </s><s>Ac <lb/>principio quidem rerum, quando<emph.end type="italics"/> Creavit DEVS c&oelig;lum & <lb/>terram, <emph type="italics"/>Genes. C. I. prædictum &longs;ervarunt ordinem, v&longs;que ad <lb/>diem Mundi tertium, quo die Deus benedictus Terram, anteà <lb/>&longs;phæricè rotundam, in cavitates varias deformavit, in easque <lb/>Aquam omnem &longs;ubterc&oelig;le&longs;tem, maribus, lacubus, fluminibus, <lb/>fontibus di&longs;cretam, derivavit, vnumque ex Terra & Aqua <lb/>globum con&longs;tituit, vnicâ contentum &longs;phæricâ &longs;uperficie, terrenâ<emph.end type="italics"/><lb/>

<arrow.to.target n="marg128"/><lb/><emph type="italics"/>hinc, inde aqueâ, prout Aquæ diver&longs;imodè Terram di&longs;ci&longs;&longs;am <lb/>interfluunt, aut circumfluunt. Qui quidem globus ex Terra <lb/>& Aqua coagmentatus (quem ob id rectè <expan abbr="Terraque&utilde;">Terraqueum</expan> appellare <lb/>po&longs;&longs;umus) in prima &longs;ui coagmentatione, quando die Mundi<emph.end type="italics"/>

<arrow.to.target n="marg128"/><lb/><emph type="italics"/>hinc, inde aqueâ, prout Aquæ diver&longs;imodè Terram di&longs;ci&longs;&longs;am <lb/>interfluunt, aut circumfluunt. </s><s>Qui quidem globus ex Terra <lb/>& Aqua coagmentatus (quem ob id rectè <expan abbr="Terraque&utilde;">Terraqueum</expan> appellare <lb/>po&longs;&longs;umus) in prima &longs;ui coagmentatione, quando die Mundi<emph.end type="italics"/>

<pb xlink:href="051/01/097.jpg" pagenum="66"/><emph type="italics"/>tertio<emph.end type="italics"/> dixit DEUS: congre gentur aquæ, quæ &longs;ub c&oelig;lo &longs;unt, <lb/>in locum vnum, & appareat Arida; & factum e&longs;t ita; <emph type="italics"/>in <lb/>medio Vniver&longs;i, hoc est, in centro &longs;upremi, & omnia ambien<lb/>tis Cæli collocatus fui&longs;&longs;e videtur; in medio, inquam, non &longs;olùm <lb/>quoad &longs;en&longs;um (quod nullus, aut vix vllus, &longs;altem alicuius no<lb/>minis, negat) &longs;ed revera ac mathematicè, ita vt centrum gra<lb/>vitatis Terraquæ congruerit tunc perfectè centro Vniver&longs;i, exi-<emph.end type="italics"/><lb/>

<arrow.to.target n="marg129"/><lb/><emph type="italics"/>gente id naturali ip&longs;ius gravitate. Nunc verò licet ob conti<lb/>nuam gravium in Terra Marique mutationem, centrique gra<lb/>vitatis variationem prædicta Terraqua non &longs;it forta&longs;&longs;e &longs;emper <lb/>præcisè & mathematicè in Mundi medio in &longs;en&longs;u dicto (non <lb/>enim certò constat, ad centrum gravitatis mutatum continuò, <lb/>&longs;equi continuam, licet exiguam, trepidationem ip&longs;ius, nitentis <lb/>ad mundi centrum) tam parum tamen ab illo centro distat, <lb/>quàm multùm di&longs;tat à tota mole Terraquæ quodcunque pon<lb/>dus defacto additum aut ablatum de novo. Ex quibus dedu<lb/>citur, &longs;i centrum gravitatis Terraquæ differt à centro magni<lb/>tudinis eiusdem (vt probabile e&longs;t differre, cùm Terra pondero<lb/>&longs;ior &longs;it quàm Aqua, nec omnes Terræ partes, æqualis &longs;int ponde<lb/>ris) differre &longs;olùm in&longs;en&longs;ibiliter; ac proinde idem cen&longs;eri po&longs;&longs;e; <lb/>&longs;altem phy&longs;icè & ad &longs;en&longs;um, vtrumque centrum. Sed de his <lb/>&longs;usè tractatum vide à Kirchero in Mundo &longs;ubterranneo, libro 1. <lb/>de Centro&longs;ophia, & à nobis in Mechanica Vniver&longs;ali lib. 1. <lb/>aut in Magia Mechanica.<emph.end type="italics"/><lb/>

<arrow.to.target n="marg129"/><lb/><emph type="italics"/>gente id naturali ip&longs;ius gravitate. </s><s>Nunc verò licet ob conti<lb/>nuam gravium in Terra Marique mutationem, centrique gra<lb/>vitatis variationem prædicta Terraqua non &longs;it forta&longs;&longs;e &longs;emper <lb/>præcisè & mathematicè in Mundi medio in &longs;en&longs;u dicto (non <lb/>enim certò constat, ad centrum gravitatis mutatum continuò, <lb/>&longs;equi continuam, licet exiguam, trepidationem ip&longs;ius, nitentis <lb/>ad mundi centrum) tam parum tamen ab illo centro distat, <lb/>quàm multùm di&longs;tat à tota mole Terraquæ quodcunque pon<lb/>dus defacto additum aut ablatum de novo. </s><s>Ex quibus dedu<lb/>citur, &longs;i centrum gravitatis Terraquæ differt à centro magni<lb/>tudinis eiusdem (vt probabile e&longs;t differre, cùm Terra pondero<lb/>&longs;ior &longs;it quàm Aqua, nec omnes Terræ partes, æqualis &longs;int ponde<lb/>ris) differre &longs;olùm in&longs;en&longs;ibiliter; ac proinde idem cen&longs;eri po&longs;&longs;e; <lb/>&longs;altem phy&longs;icè & ad &longs;en&longs;um, vtrumque centrum. </s><s>Sed de his <lb/>&longs;usè tractatum vide à Kirchero in Mundo &longs;ubterranneo, libro 1. <lb/>de Centro&longs;ophia, & à nobis in Mechanica Vniver&longs;ali lib. 1. <lb/>aut in Magia Mechanica.<emph.end type="italics"/><lb/>

<arrow.to.target n="marg130"/></s>

<s><margin.target id="marg127"/><gap/>o<lb/><gap/>do <lb/>naturalis<gap/></s>

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<s><margin.target id="marg130"/>Centrum <lb/>commune <lb/>omnium <lb/>gravium <lb/>ac levium</s>

<s><emph type="italics"/>Alterum quod &longs;uppono est, centrum Vniver&longs;i, adeoque <lb/>Centrum Terraquei globi, quem in Mundi medio &longs;tatuimus, <lb/>cen&longs;eri po&longs;&longs;e centrum commune omnium gravium ac levium, quò<emph.end type="italics"/>

<pb xlink:href="051/01/098.jpg" pagenum="67"/><emph type="italics"/>nimirum omnia gravia per &longs;e tendunt appetitu innato, & à quo <lb/>levia recedunt, vtraque per rectas ac brevi&longs;&longs;imas lineas, ni&longs;i <lb/>impediantur, aut cogantur per obliquam ac longiorem viam <lb/>ver&longs;us illud de&longs;cendere, vel ab illo recedere. Cùm igitur aqua <lb/>omnis &longs;it gravis, vt experientiâ patet; tendet appetitu naturali <lb/>ad centrum Terraquæ, id e&longs;t, ad centrum Vniver&longs;i. Idem di<lb/>cendum e&longs;t de alijs liquoribus. His præmi&longs;&longs;is accedimus ad <lb/>propo&longs;itum.<emph.end type="italics"/></s>

<pb xlink:href="051/01/098.jpg" pagenum="67"/><emph type="italics"/>nimirum omnia gravia per &longs;e tendunt appetitu innato, & à quo <lb/>levia recedunt, vtraque per rectas ac brevi&longs;&longs;imas lineas, ni&longs;i <lb/>impediantur, aut cogantur per obliquam ac longiorem viam <lb/>ver&longs;us illud de&longs;cendere, vel ab illo recedere. Cùm igitur aqua <lb/>omnis &longs;it gravis, vt experientiâ patet; tendet appetitu naturali <lb/>ad centrum Terraquæ, id e&longs;t, ad centrum Vniver&longs;i. </s><s>Idem di<lb/>cendum e&longs;t de alijs liquoribus. </s><s>His præmi&longs;&longs;is accedimus ad <lb/>propo&longs;itum.<emph.end type="italics"/></s>

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

<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>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. </s><s>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="marg131"/><lb/>impedimentis, eò fluit aqua, quia naturaliter eò inclinat. </s><s>Con<lb/>&longs;i&longs;tentem porrò aquam appello, quæ &longs;itum obtinet naturalem. </s><s><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>

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<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/>

<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. </s><s>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>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. </s><s>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>

Line 1778

Line 1777

<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>

<arrow.to.target n="marg136"/><lb/><expan abbr="cõvexa">convexa</expan> centrum. </s><s>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>

<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. </s><s>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>

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<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>

<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. </s><s>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>

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<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>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. </s><s>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/>

<s>AS&longs;erit hoc Archimedes loco proximè citato. </s><s><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>

<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. </s><s>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. </s><s>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>

Line 1817

Line 1816

<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>PAtet hoc ex multis &longs;ignis. </s><s>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. </s><s><lb/>Secundò, vrinatores infra aquam exi&longs;tentes non &longs;entiunt pon<lb/>dus aquarum incumbentium &longs;ibi. </s><s>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. </s><s>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. </s><s>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>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. </s><s>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-

<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. </s><s>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. </s><s>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. </s><s>Hinc e&longs;t, quòd aqua effluatè <lb/>foramine in fundo aut latere va&longs;is. </s><s>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>

<pb xlink:href="051/01/102.jpg" pagenum="71"/>dum tenue va&longs;is incurvetur, ac tandem frangatur. </s><s>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. </s><s>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>

Line 1836

Line 1835

<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>PAtet experientia. </s><s>Et ratio e&longs;t, quia vna non premit alteram, <lb/>vt dictum in præcedenti Proprietate. </s><s>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>

Line 1852

Line 1851

<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

<arrow.to.target n="marg143"/><lb/>& &longs;equitur ex dictis Proprietate I. & II. </s><s>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>

<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. </s><s>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>

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

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<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="marg145"/><lb/>&longs;as figuras, vt apparet in appo&longs;itis &longs;chemati&longs;mis. </s><s>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>Siphon erectus e&longs;t, cuius omnia crura &longs;ur&longs;um &longs;unt. </s><s>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>Siphon inver&longs;us e&longs;t, cuius omnia crura deor&longs;um &longs;unt. </s><s>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>Siphon mixtus e&longs;t, cuius crura partim &longs;ur&longs;um, partim de<lb/>or&longs;um &longs;unt. </s><s>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>Siphones tam erecti, quàm inver&longs;i, vel habent vtrumque <lb/>erus æquale, vel inæquale. </s><s>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>

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<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/>

<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. </s><s>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>

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<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-

<arrow.to.target n="fig17"/><lb/>crure &longs;int in eadem <lb/>linea horizontali. </s><s><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>

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<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>

<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. </s><s>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>

<s><emph type="italics"/>Quarta.<emph.end type="italics"/> Si cruri breviori, licet capaciori, nempe cruri <lb/>EFCD, jam pleno addas plùs aquæ |; ea non attollet aquam <lb/>cruris longioris vltra punctum G, &longs;ed effluet ex ore EF, licet <lb/>aqua cruris EFCD &longs;it longè maior & pondero&longs;ior, quàm <lb/>aqua cruris AB. Patet itidem experientiâ, & ratio e&longs;t eadem. </s>

<s><emph type="italics"/>Quarta.<emph.end type="italics"/> Si cruri breviori, licet capaciori, nempe cruri <lb/>EFCD, jam pleno addas plùs aquæ |; ea non attollet aquam <lb/>cruris longioris vltra punctum G, &longs;ed effluet ex ore EF, licet <lb/>aqua cruris EFCD &longs;it longè maior & pondero&longs;ior, quàm <lb/>aqua cruris AB. </s><s>Patet itidem experientiâ, & ratio e&longs;t eadem. </s>

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

<s>COlligitur hinc primò, aquam maioris perpendiculi pellere <lb/>

<arrow.to.target n="marg153"/><lb/>aquam minoris perpendiculi, non ob&longs;tante maiore copia, & <lb/>maiore pondere huius: ideo enim aqua cruris AB primæ & tertiæ <lb/>figuræ expellit aquam cruris CDEF, licet longè maiorem & <lb/>pondero&longs;iorem, quia perpendiculum illius e&longs;t maius &longs;eu longius, <lb/>quàm perpendiculum huius. Aquæ perpendiculum hic, & in <lb/>

<arrow.to.target n="marg154"/><lb/>&longs;equentibus, appello altitudinem aquæ &longs;upra horizontem, &longs;eu <lb/>&longs;upra centrum Terræ, ita vt illa dicatur habere maius perpendi-

<pb xlink:href="051/01/107.jpg" pagenum="76"/>culum, quàm altera, cuius altitudo ab infima ad &longs;upremam &longs;u<lb/>perficiem maior e&longs;t, in eodem horizonte. </s>

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<s><margin.target id="marg155"/><emph type="italics"/>Aqua ma<lb/>gis aut, mi <lb/>nùs pre&longs;&longs;a <lb/>in &longs;iphoni<lb/>bus, <expan abbr="quanã">quanam</expan> <lb/>dicatur.<emph.end type="italics"/></s>

<s>COlligitur &longs;ecundò, Quænam aqua in &longs;iphone erecto dicatur <lb/>magis aut minùs pre&longs;&longs;a: Nam cùm con&longs;tet, Aquam minùs <lb/>pre&longs;&longs;am expelli à magis pre&longs;&longs;a, per dicta Capite primo, Propriet. <lb/>3. con&longs;tet præterea, Aquam minoris perpendiculi in &longs;iphone e<lb/>recto premi atque expelli ab aqua maioris perpendiculi; clarum <lb/>e&longs;t, Aquam minoris perpendiculi dici minùs, <expan abbr="aquã">aquam</expan> verò maioris <lb/>perpendiculi dici magis pre&longs;sam. Ex his formo &longs;equens </s>

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

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<s>COlligltur quar<lb/>

<arrow.to.target n="fig18"/><lb/>tò, Quomodo <lb/>&longs;cire po&longs;&longs;is præcisè <lb/>quou&longs;que dolium <lb/>aliquod <expan abbr="exinanit&utilde;">exinanitum</expan> <lb/>&longs;it, manente obtu<lb/>ramento &longs;uperiore <lb/>clauso, <expan abbr="nulloq;">nulloque</expan> alio <lb/>foramine facto <lb/>præterid, cui epi<lb/>&longs;tomium immitti

<pb xlink:href="051/01/108.jpg" pagenum="77"/>&longs;olet. Sit enim dolium DC, exinanitum v&longs;que ad lineam FG; <lb/>quod tu ignores: &longs;cies id, &longs;i tubum oblongum AB incurves in<lb/>feriùs iuxta B, & doleo iuxta C in&longs;eras epi&longs;tomij loco; liquor <lb/>enim dolij effluens a&longs;cendet per tubum, donec perveniat <expan abbr="v&longs;q;">v&longs;que</expan> ad <lb/>E, & æquetur &longs;upremæ &longs;uperficiei liquoris in dolio contenti. </s>

<pb xlink:href="051/01/108.jpg" pagenum="77"/>&longs;olet. </s><s>Sit enim dolium DC, exinanitum v&longs;que ad lineam FG; <lb/>quod tu ignores: &longs;cies id, &longs;i tubum oblongum AB incurves in<lb/>feriùs iuxta B, & doleo iuxta C in&longs;eras epi&longs;tomij loco; liquor <lb/>enim dolij effluens a&longs;cendet per tubum, donec perveniat <expan abbr="v&longs;q;">v&longs;que</expan> ad <lb/>E, & æquetur &longs;upremæ &longs;uperficiei liquoris in dolio contenti. </s>

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

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<s><margin.target id="marg159"/><emph type="italics"/>Dolium im <lb/>plere per e<lb/>pi&longs;tomium <lb/>ope &longs;iphonis.<emph.end type="italics"/></s>

<s>COlligitur quintò, Quomodo repleri po&longs;&longs;it prædictum doli<lb/>um per foramen C epi&longs;tomij. Si enim tubum AB incur<lb/>vatum in&longs;eras dolio iuxta C, & &longs;uperiùs iuxta A infundas li<lb/>quorem; a&longs;cendet is in dolio, donec æquetur &longs;ummitati tubi, <lb/>aut donec dolium &longs;it omnino repletum, &longs;i tubus altior e&longs;t dolio. <lb/>Bene tamen Schvventerus monet in fuis Recreationibus Mathe<lb/>maticis parte 13. quæ&longs;t. 3. debere in &longs;ummitate dolij foramen a<lb/>periri, per quod aër elabatur, impediturus alioquin liquoris in<lb/>fu&longs;ionem, &longs;i non po&longs;&longs;it erumpere per foramen C & tubum BA. </s>

<s>COlligitur quintò, Quomodo repleri po&longs;&longs;it prædictum doli<lb/>um per foramen C epi&longs;tomij. </s><s>Si enim tubum AB incur<lb/>vatum in&longs;eras dolio iuxta C, & &longs;uperiùs iuxta A infundas li<lb/>quorem; a&longs;cendet is in dolio, donec æquetur &longs;ummitati tubi, <lb/>aut donec dolium &longs;it omnino repletum, &longs;i tubus altior e&longs;t dolio. </s><s><lb/>Bene tamen Schvventerus monet in fuis Recreationibus Mathe<lb/>maticis parte 13. quæ&longs;t. 3. debere in &longs;ummitate dolij foramen a<lb/>periri, per quod aër elabatur, impediturus alioquin liquoris in<lb/>fu&longs;ionem, &longs;i non po&longs;&longs;it erumpere per foramen C & tubum BA. </s>

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

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

<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. </s><s>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. </s><s>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"/>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. </s><s>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. </s><s><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. </s><s><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="italics"/>Opportuna monitio, nec menti meæcontraria. </s><s>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>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. </s><s>In<lb/>tellige, in ca&longs;u & &longs;en&longs;u explicato. </s>

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

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<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>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. </s><s>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. </s><s>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. </s><s>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. </s><s>Exhac, & præcedente Proprietate, formari pote&longs;t <lb/>aliud. </s>

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

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<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>AQua per longius crus &longs;iphonis inver&longs;i eò currit celeriùs, quò <lb/>longius fuerit crus. </s><s>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. </s><s>Hinc formo &longs;equens </s>

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

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<s><margin.target id="marg164"/><emph type="italics"/>Aqua per <lb/><expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> fluit <lb/>difformi <lb/>celeritate.<emph.end type="italics"/></s>

<s>AQua per longius crus &longs;iphonis inver&longs;i non effluit celeritate v<lb/>niformi, &longs;ed difformi; augetur enim continuò celeritas de<lb/>&longs;cen&longs;us, donec exhau&longs;tum &longs;it crus oppo&longs;itum: nunquam tamen <lb/>de&longs;cendit tam celeriter aqua, quàm &longs;i liberè, hoc e&longs;t, non per <lb/>&longs;iphonem, &longs;ed per tubum, aut extra tubum vel canalem de&longs;cen<lb/>deret. Ratio e&longs;t, quia aqua effluens per crus longius AB, in an<lb/>tea po&longs;ito, & in quocunque alio &longs;iphone, debet &longs;ecum trahere <lb/>contranitentem aquam cruris brevioris CB, nè detur vacuum <lb/>intra &longs;iphonem; quæ aqua cruris brevioris quoniam continuò <lb/>minuitur effluente aqua per os A, ideo faciliùs &longs;emper ac faci<lb/>liùs attrahitur ab aqua cruris longioris AB; cuius proinde <expan abbr="de&longs;c&etilde;-dentis">de&longs;cen<lb/>dentis</expan> celeritas continuò intenditur, donec exhau&longs;tum &longs;it to<lb/>tum crus CB. Non æquat tamen celeritatem eam, quâ liberè <lb/>de&longs;cenderet, non trahendo &longs;ecum aquam alterius cruris; quia <lb/>quàm diu re&longs;tat aliquid aquæ in crure breviori CB, attrahere <lb/>illud debet, vt po&longs;&longs;it effluere, ac proin de &longs;emper aliquid retinet <lb/>impedimenti; quo caret, dum liberè cadit. Adde quòd quò <lb/>diutiùs aqua effluit per A, eò aquæ cruris CB &longs;uperficies ex<lb/>trema C magis a&longs;cendit ver&longs;us B, adeoque & perpendiculum <lb/>aquæ cruris CB continuò minuitur, aquæ interim, quæ ex crure <lb/>AB fluit, perpendiculo manente eodem. Augetur ergo a&longs;&longs;iduè <lb/>proportio perpendiculi BA ad perpendiculum BC, adeoque &

<s>AQua per longius crus &longs;iphonis inver&longs;i non effluit celeritate v<lb/>niformi, &longs;ed difformi; augetur enim continuò celeritas de<lb/>&longs;cen&longs;us, donec exhau&longs;tum &longs;it crus oppo&longs;itum: nunquam tamen <lb/>de&longs;cendit tam celeriter aqua, quàm &longs;i liberè, hoc e&longs;t, non per <lb/>&longs;iphonem, &longs;ed per tubum, aut extra tubum vel canalem de&longs;cen<lb/>deret. </s><s>Ratio e&longs;t, quia aqua effluens per crus longius AB, in an<lb/>tea po&longs;ito, & in quocunque alio &longs;iphone, debet &longs;ecum trahere <lb/>contranitentem aquam cruris brevioris CB, nè detur vacuum <lb/>intra &longs;iphonem; quæ aqua cruris brevioris quoniam continuò <lb/>minuitur effluente aqua per os A, ideo faciliùs &longs;emper ac faci<lb/>liùs attrahitur ab aqua cruris longioris AB; cuius proinde <expan abbr="de&longs;c&etilde;-dentis">de&longs;cen<lb/>dentis</expan> celeritas continuò intenditur, donec exhau&longs;tum &longs;it to<lb/>tum crus CB. </s><s>Non æquat tamen celeritatem eam, quâ liberè <lb/>de&longs;cenderet, non trahendo &longs;ecum aquam alterius cruris; quia <lb/>quàm diu re&longs;tat aliquid aquæ in crure breviori CB, attrahere <lb/>illud debet, vt po&longs;&longs;it effluere, ac proin de &longs;emper aliquid retinet <lb/>impedimenti; quo caret, dum liberè cadit. </s><s>Adde quòd quò <lb/>diutiùs aqua effluit per A, eò aquæ cruris CB &longs;uperficies ex<lb/>trema C magis a&longs;cendit ver&longs;us B, adeoque & perpendiculum <lb/>aquæ cruris CB continuò minuitur, aquæ interim, quæ ex crure <lb/>AB fluit, perpendiculo manente eodem. </s><s>Augetur ergo a&longs;&longs;iduè <lb/>proportio perpendiculi BA ad perpendiculum BC, adeoque &

<pb xlink:href="051/01/112.jpg" pagenum="81"/>proportio pre&longs;&longs;ionis aquæ BA ad pre&longs;&longs;ionem aquæ BC au<lb/>getur; ergo, &c. Dixi, donec exhau&longs;tum &longs;it totum crus CB <lb/>oppo&longs;itum: nam illo exhau&longs;to, minuitur &longs;emper magis ac magis <lb/>celeritas effluxus per os A, quoniam minuitur perpendiculum <lb/>aquæ, ac proinde &longs;emper minùs ac minùs premitur aqua apud A. </s>

<pb xlink:href="051/01/112.jpg" pagenum="81"/>proportio pre&longs;&longs;ionis aquæ BA ad pre&longs;&longs;ionem aquæ BC au<lb/>getur; ergo, &c. </s><s>Dixi, donec exhau&longs;tum &longs;it totum crus CB <lb/>oppo&longs;itum: nam illo exhau&longs;to, minuitur &longs;emper magis ac magis <lb/>celeritas effluxus per os A, quoniam minuitur perpendiculum <lb/>aquæ, ac proinde &longs;emper minùs ac minùs premitur aqua apud A. </s>

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

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<s>SIphonum mixtorum crura vel &longs;unt omnia æqualia, vel omnia </s>

<s>

<arrow.to.target n="marg165"/><lb/>inæqualia, vel aliqua æqualia, aliqua inæqualia. De proprie<lb/>tatibus &longs;iphonis, cuius omnia crura &longs;unt æqualia, agemus Pro<lb/>po&longs;it. &longs;equenti; de reliquorum proprietatibus hîc agemus. Sit <lb/>igitur &longs;iphon AKDI. Hic &longs;i integer maneat, habebit omnia cru<lb/>ra inæqualia: &longs;i truncetur in E, aut in B, habebit aliqua crura <lb/>æqualia, alia inæqualia: &longs;i truncetur in F, aut N, habebit iterum <lb/>omnia crura inæqualia. </s>

<arrow.to.target n="marg165"/><lb/>inæqualia, vel aliqua æqualia, aliqua inæqualia. </s><s>De proprie<lb/>tatibus &longs;iphonis, cuius omnia crura &longs;unt æqualia, agemus Pro<lb/>po&longs;it. </s><s>&longs;equenti; de reliquorum proprietatibus hîc agemus. </s><s>Sit <lb/>igitur &longs;iphon AKDI. </s><s>Hic &longs;i integer maneat, habebit omnia cru<lb/>ra inæqualia: &longs;i truncetur in E, aut in B, habebit aliqua crura <lb/>æqualia, alia inæqualia: &longs;i truncetur in F, aut N, habebit iterum <lb/>omnia crura inæqualia. </s>

<s><margin.target id="marg165"/><emph type="italics"/>Siphonis mi<lb/>xti variæ <lb/>&longs;pecies.<emph.end type="italics"/></s>

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<s>SI crus DI truncetur in B, ita vtos B &longs;it eiusdem altitudinis <lb/>&longs;upra horizontom cum ore A, & totus &longs;iphon AKDB replea<lb/>tur aquá; e&longs;t qui putat non effluere ex B, &longs;ed effluere ex A, du<lb/>rareque fluxum donec &longs;uperficies aquæ B pervenerit ad C, <lb/>hoc e&longs;t, donec effluxerit tantum aquæ, quantum e&longs;tintra BDC,

<arrow.to.target n="fig20"/><lb/>tunc enim, ait, ce&longs;&longs;abit fluxus ex A, <lb/>&longs;tabitque aqua in æquilibrio intra <lb/>AKC. Quòd non effluat aqua ex B, <lb/>clarum e&longs;t, quia perpendiculum BD <lb/>brevius e&longs;t quàm <expan abbr="perpendicul&utilde;">perpendiculum</expan> DK, <lb/>ergò aqua DB non pote&longs;t trahere a<lb/>quam DK, & multò minùs <expan abbr="aquã">aquam</expan> DKA. <lb/>Quòd autem effluat ex A, <expan abbr="ration&etilde;">rationem</expan> <lb/>a&longs;&longs;ignat, quia perdendiculum DK <lb/>longius e&longs;t quàm perpendiculum AK; <lb/>ergo aqua DK fortiùs premit deor<lb/>&longs;um ver&longs;us K, quàm aqua AK, ac <lb/>proinde aqua AK debet cedere, & <lb/>effluere ex A, ac &longs;equi tota reliqua <lb/>aqua, nè vacuum detur. Quòd de<lb/>nique ce&longs;&longs;et fluxus aquæ ex A, quan<lb/>do &longs;uperficies B pervenerit ad C, <lb/>rationem dat, quia tunc perpendicu<lb/>la CK, AK, &longs;unt æqualia. </s>

<arrow.to.target n="fig20"/><lb/>tunc enim, ait, ce&longs;&longs;abit fluxus ex A, <lb/>&longs;tabitque aqua in æquilibrio intra <lb/>AKC. </s><s>Quòd non effluat aqua ex B, <lb/>clarum e&longs;t, quia perpendiculum BD <lb/>brevius e&longs;t quàm <expan abbr="perpendicul&utilde;">perpendiculum</expan> DK, <lb/>ergò aqua DB non pote&longs;t trahere a<lb/>quam DK, & multò minùs <expan abbr="aquã">aquam</expan> DKA. </s><s><lb/>Quòd autem effluat ex A, <expan abbr="ration&etilde;">rationem</expan> <lb/>a&longs;&longs;ignat, quia perdendiculum DK <lb/>longius e&longs;t quàm perpendiculum AK; <lb/>ergo aqua DK fortiùs premit deor<lb/>&longs;um ver&longs;us K, quàm aqua AK, ac <lb/>proinde aqua AK debet cedere, & <lb/>effluere ex A, ac &longs;equi tota reliqua <lb/>aqua, nè vacuum detur. </s><s>Quòd de<lb/>nique ce&longs;&longs;et fluxus aquæ ex A, quan<lb/>do &longs;uperficies B pervenerit ad C, <lb/>rationem dat, quia tunc perpendicu<lb/>la CK, AK, &longs;unt æqualia. </s>

<s>Experentiâ tamen con&longs;tat, in dicto ca&longs;u <expan abbr="nullã">nullam</expan> effluere aquam <lb/>ex Siphone AKDB, neque per os B, neque per os A. Rationem <lb/>ad&longs;igno, quia aqua quæ e&longs;t in AKC, ita e&longs;t librata, vt à poten<lb/>tia quantumvis parva moveri, & ex vna parte attolli po&longs;&longs;it; qua<lb/>re humido CD &longs;upra &longs;e po&longs;ito non re&longs;i&longs;tit. I am verò quoniam <lb/>perpendicula crurium DC, DB æqualia &longs;unt, aqua in C æquè <lb/>premitur ac in B; quare cùm nec infra B, nec infra C vllum <lb/>&longs;it impedimentum extrin&longs;ecum, præter aërem (iam enim o&longs;ten<lb/>&longs;um e&longs;t, aquam CKA non re&longs;i&longs;tere humido CD de&longs;cendenti) <lb/>pariter ex A & B aqua deberet effluere; quod fieri non pote&longs;t <lb/>absque vacuo. Patet ergo cur aqua con&longs;i&longs;tat. Dices, in hoc <lb/>di&longs;cur&longs;u committitur manife&longs;tus paralogi&longs;mus; dividitur enim <lb/>mente crus DK in puncto C, & di&longs;curritur ac &longs;i realiter ibidem <lb/>e&longs;&longs;et facta divi&longs;io; Natura non dividit aquam cruris DK in pun<lb/>cto C, nec propter no&longs;tras intellectuales divi&longs;iones mutat ope-

<s>Experentiâ tamen con&longs;tat, in dicto ca&longs;u <expan abbr="nullã">nullam</expan> effluere aquam <lb/>ex Siphone AKDB, neque per os B, neque per os A. </s><s>Rationem <lb/>ad&longs;igno, quia aqua quæ e&longs;t in AKC, ita e&longs;t librata, vt à poten<lb/>tia quantumvis parva moveri, & ex vna parte attolli po&longs;&longs;it; qua<lb/>re humido CD &longs;upra &longs;e po&longs;ito non re&longs;i&longs;tit. I am verò quoniam <lb/>perpendicula crurium DC, DB æqualia &longs;unt, aqua in C æquè <lb/>premitur ac in B; quare cùm nec infra B, nec infra C vllum <lb/>&longs;it impedimentum extrin&longs;ecum, præter aërem (iam enim o&longs;ten<lb/>&longs;um e&longs;t, aquam CKA non re&longs;i&longs;tere humido CD de&longs;cendenti) <lb/>pariter ex A & B aqua deberet effluere; quod fieri non pote&longs;t <lb/>absque vacuo. </s><s>Patet ergo cur aqua con&longs;i&longs;tat. </s><s>Dices, in hoc <lb/>di&longs;cur&longs;u committitur manife&longs;tus paralogi&longs;mus; dividitur enim <lb/>mente crus DK in puncto C, & di&longs;curritur ac &longs;i realiter ibidem <lb/>e&longs;&longs;et facta divi&longs;io; Natura non dividit aquam cruris DK in pun<lb/>cto C, nec propter no&longs;tras intellectuales divi&longs;iones mutat ope-

<pb xlink:href="051/01/114.jpg" pagenum="83"/>randi vim, cùm non ob&longs;tante illa divi&longs;ione revera crus DK lon<lb/>gius &longs;it, quàm crus AK. Re&longs;pondeo, quamvis DK longius &longs;it <lb/>quàm crus AK, eius tamen activitati &longs;eu pre&longs;&longs;ioni deor&longs;um non <lb/>&longs;olùm re&longs;i&longs;tit crus AK, &longs;ed etiam crus DB; illud, nè aqua KA <lb/>pellatur &longs;ur&longs;um; hoc, nèaqua AD trahatur &longs;ur&longs;um: vnde per<lb/>pendiculum DK habet duplicem re&longs;i&longs;tentiam, &longs;cilicet DB, & AK; <lb/>quæ duæ re&longs;i&longs;tentiæ æquant eius activitatem, & con&longs;equenter <lb/>impediunt motum aquæ DK, eiusque fluxum, &longs;ive per os A, &longs;i<lb/>ve per os B. Divi&longs;io autem intellectualis cruris DK in puncto <lb/>C fit &longs;olùm ad o&longs;ten dendum quomodo duplex prædicta <expan abbr="re&longs;i&longs;t&etilde;-tia">re&longs;i&longs;ten<lb/>tia</expan> æquivaleat activitati totius cruris DK. </s>

<pb xlink:href="051/01/114.jpg" pagenum="83"/>randi vim, cùm non ob&longs;tante illa divi&longs;ione revera crus DK lon<lb/>gius &longs;it, quàm crus AK. </s><s>Re&longs;pondeo, quamvis DK longius &longs;it <lb/>quàm crus AK, eius tamen activitati &longs;eu pre&longs;&longs;ioni deor&longs;um non <lb/>&longs;olùm re&longs;i&longs;tit crus AK, &longs;ed etiam crus DB; illud, nè aqua KA <lb/>pellatur &longs;ur&longs;um; hoc, nèaqua AD trahatur &longs;ur&longs;um: vnde per<lb/>pendiculum DK habet duplicem re&longs;i&longs;tentiam, &longs;cilicet DB, & AK; <lb/>quæ duæ re&longs;i&longs;tentiæ æquant eius activitatem, & con&longs;equenter <lb/>impediunt motum aquæ DK, eiusque fluxum, &longs;ive per os A, &longs;i<lb/>ve per os B. </s><s>Divi&longs;io autem intellectualis cruris DK in puncto <lb/>C fit &longs;olùm ad o&longs;ten dendum quomodo duplex prædicta <expan abbr="re&longs;i&longs;t&etilde;-tia">re&longs;i&longs;ten<lb/>tia</expan> æquivaleat activitati totius cruris DK. </s>

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

<s>SI crus DI truncetur in F, vt os F &longs;it inferius quàm os A; <lb/>idem qui &longs;uprà putat non effluere aquam ex F, &longs;ed ex A, du<lb/>rareque ut antea fluxum, donec &longs;uperficies F pervenerit v&longs;que <lb/>ad C. Rationem eandem dat cum illa, quam ad&longs;ignavit paulò <lb/>antè. </s>

<s>SI crus DI truncetur in F, vt os F &longs;it inferius quàm os A; <lb/>idem qui &longs;uprà putat non effluere aquam ex F, &longs;ed ex A, du<lb/>rareque ut antea fluxum, donec &longs;uperficies F pervenerit v&longs;que <lb/>ad C. </s><s>Rationem eandem dat cum illa, quam ad&longs;ignavit paulò <lb/>antè. </s>

<s>Eâdem tamen experientiä con&longs;tat, aquam in hoc ca&longs;u ef<lb/>fluere ex F, donec aqua cruris AK de&longs;cenderit in H ad pa<lb/>rem cum F altitudinem. Ratio e&longs;t, quia humidum in F ma<lb/>gis premitur, quàm in C, id e&longs;t, quàm in A, ob longius per<lb/>pendiculum DF, quàm DC; quare humidum in F de&longs;cen<lb/>det, <expan abbr="trahet&qacute;ue">trahetque</expan> humidum reliquum, nè detur vacuum. Nec re<lb/>fert, quòd dividatur intellectu crus DK in puncto C, & compa<lb/>retur crus DF cum parte DC &longs;olùm, ac &longs;i & Natura ibidem <lb/>divi&longs;i&longs;&longs;et crus DK; hoc enim &longs;olùm fit ob rationem paulò antè <lb/>allatam. </s>

<s>Eâdem tamen experientiä con&longs;tat, aquam in hoc ca&longs;u ef<lb/>fluere ex F, donec aqua cruris AK de&longs;cenderit in H ad pa<lb/>rem cum F altitudinem. </s><s>Ratio e&longs;t, quia humidum in F ma<lb/>gis premitur, quàm in C, id e&longs;t, quàm in A, ob longius per<lb/>pendiculum DF, quàm DC; quare humidum in F de&longs;cen<lb/>det, <expan abbr="trahet&qacute;ue">trahetque</expan> humidum reliquum, nè detur vacuum. </s><s>Nec re<lb/>fert, quòd dividatur intellectu crus DK in puncto C, & compa<lb/>retur crus DF cum parte DC &longs;olùm, ac &longs;i & Natura ibidem <lb/>divi&longs;i&longs;&longs;et crus DK; hoc enim &longs;olùm fit ob rationem paulò antè <lb/>allatam. </s>

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

<s>SI crus DI truncetur in E, vt os E habeat eandem altitudinem <lb/>cum puncto K; ille idem qui &longs;uprà exi&longs;timat nihil effluere, <expan abbr="neq;">neque</expan> <lb/>ex E, neque ex A. Ratio eius e&longs;t, quia perpendicula DE, DK &longs;unt <lb/>æqualia; ergo aqua apud E non plùs premitur quàm apud K, nec <lb/>apud K plùs quàm apud E; ergo neque ex E, neque ex A <lb/>effluere pote&longs;t aqua, nè æqualis potentia dicatur &longs;upera&longs;&longs;e æ<lb/>qualem. </s>

<s>SI crus DI truncetur in E, vt os E habeat eandem altitudinem <lb/>cum puncto K; ille idem qui &longs;uprà exi&longs;timat nihil effluere, <expan abbr="neq;">neque</expan> <lb/>ex E, neque ex A. </s><s>Ratio eius e&longs;t, quia perpendicula DE, DK &longs;unt <lb/>æqualia; ergo aqua apud E non plùs premitur quàm apud K, nec <lb/>apud K plùs quàm apud E; ergo neque ex E, neque ex A <lb/>effluere pote&longs;t aqua, nè æqualis potentia dicatur &longs;upera&longs;&longs;e æ<lb/>qualem. </s>

<s>Dicendum tamen, eâdem experientiá duce, effluxuram <lb/>aquam ex E, duraturumque fluxum, donec &longs;uperficies A per<lb/>venlat ad K, & non vltrà. Rationem ad&longs;igno, quia perpen<lb/>diculum DE longius e&longs;t, quàm DC, dum plenus e&longs;t tubus. Dum <lb/>autem aqua de&longs;cenderit ad K, perpendicula DK, DE &longs;unt æ<lb/>qualia. </s>

<s>Dicendum tamen, eâdem experientiá duce, effluxuram <lb/>aquam ex E, duraturumque fluxum, donec &longs;uperficies A per<lb/>venlat ad K, & non vltrà. </s><s>Rationem ad&longs;igno, quia perpen<lb/>diculum DE longius e&longs;t, quàm DC, dum plenus e&longs;t tubus. </s><s>Dum <lb/>autem aqua de&longs;cenderit ad K, perpendicula DK, DE &longs;unt æ<lb/>qualia. </s>

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

<s>Si crus DI truncetur in N, effluet aqua ex A, donec <lb/>&longs;uperficies N perveniat in C, vbi con&longs;i&longs;tet. Ratio e&longs;t, quia <lb/>altitudo aquæ DK, vel potiùs DC, maior e&longs;t, quàm altitudo DN. </s>

<s>Si crus DI truncetur in N, effluet aqua ex A, donec <lb/>&longs;uperficies N perveniat in C, vbi con&longs;i&longs;tet. </s><s>Ratio e&longs;t, quia <lb/>altitudo aquæ DK, vel potiùs DC, maior e&longs;t, quàm altitudo DN. </s>

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

Line 2125

Line 2124

<s><emph type="center"/>Siphonis mixti æqualium crurium proprieta<lb/>tes a&longs;&longs;ignare.<emph.end type="center"/></s>

<s>EX &longs;iphone mixto æqualium crurium, qua<lb/>lis e&longs;t ABCD, in appo&longs;ito &longs;chemate, &longs;i a<lb/>quâ totus repleatur; effluit aqua ex D. Ra<lb/>tio e&longs;t, quia licet tam perpendicula AB, CB, <lb/>quàm perpendicula CD, CB, &longs;int æqualia; <lb/>quia tamen aqua CB æquilibrata e&longs;t ab aqua <lb/>AB, poterit à qualibet potentia facillimè <lb/>moveri, ideoque ab aqua CD deor&longs;um ni<lb/>tente poterittrahi, & effluere ex D; & ita de <lb/>facto contingit, vt experientia docet. </s>

<s>EX &longs;iphone mixto æqualium crurium, qua<lb/>lis e&longs;t ABCD, in appo&longs;ito &longs;chemate, &longs;i a<lb/>quâ totus repleatur; effluit aqua ex D. </s><s>Ra<lb/>tio e&longs;t, quia licet tam perpendicula AB, CB, <lb/>quàm perpendicula CD, CB, &longs;int æqualia; <lb/>quia tamen aqua CB æquilibrata e&longs;t ab aqua <lb/>AB, poterit à qualibet potentia facillimè <lb/>moveri, ideoque ab aqua CD deor&longs;um ni<lb/>tente poterittrahi, & effluere ex D; & ita de <lb/>facto contingit, vt experientia docet. </s>

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

Line 2134

Line 2133

<s><margin.target id="marg166"/><emph type="italics"/>Crus inter<lb/>num, & <lb/>crus exter<lb/>num &longs;ipho<lb/>nis<emph.end type="italics"/></s>

<s>OBvia &longs;unt quæ dicam, ideò breviter expediam. E&longs;to igitur <lb/>vas aquâ plenum ABCD, cui inver&longs;i &longs;iphonis crus vnum FE <lb/>immergatur, alterum FN foris maneat. Vocetur autem crus

<s>OBvia &longs;unt quæ dicam, ideò breviter expediam. </s><s>E&longs;to igitur <lb/>vas aquâ plenum ABCD, cui inver&longs;i &longs;iphonis crus vnum FE <lb/>immergatur, alterum FN foris maneat. </s><s>Vocetur autem crus

<arrow.to.target n="fig21"/><lb/>FE internum, crus verò FN <lb/>externum. Huius fiphonis <lb/>variæ &longs;unt proprietates, provt <lb/>variè difponi poterit crus eius <lb/>externum. </s>

<arrow.to.target n="fig21"/><lb/>FE internum, crus verò FN <lb/>externum. </s><s>Huius fiphonis <lb/>variæ &longs;unt proprietates, provt <lb/>variè difponi poterit crus eius <lb/>externum. </s>

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

<s>Si enim crus exter<lb/>num FN maneat integrum, <lb/>& ex ore N ex&longs;ugatur aër; &longs;e<lb/>quetur a<gap/> va&longs;is, ob vacui <lb/>metum, & tota effluet, aut p&oelig;<lb/>nè tota (donec nimirum aquæ <lb/>&longs;uperficies &longs;uperior CD de&longs;cen<lb/>derit v&longs;que ad o&longs;culum E) &longs;i <lb/>internum crus fundum p&oelig;nè <lb/>tangat. Ratio e&longs;t, quia per<lb/>pendiculum externi cruris e&longs;t <lb/>longius quàm interni. Si to<lb/>tus &longs;iphon aquâ impleatur, & <lb/>vtrumque orificium claudatur, ac deinde minus crus EF aquæ <lb/>imponatur, maiori foras prominente, & &longs;imul vtrumque orifi<lb/>cium aperiatur; idem fiet. </s>

<s>Si enim crus exter<lb/>num FN maneat integrum, <lb/>& ex ore N ex&longs;ugatur aër; &longs;e<lb/>quetur a<gap/> va&longs;is, ob vacui <lb/>metum, & tota effluet, aut p&oelig;<lb/>nè tota (donec nimirum aquæ <lb/>&longs;uperficies &longs;uperior CD de&longs;cen<lb/>derit v&longs;que ad o&longs;culum E) &longs;i <lb/>internum crus fundum p&oelig;nè <lb/>tangat. </s><s>Ratio e&longs;t, quia per<lb/>pendiculum externi cruris e&longs;t <lb/>longius quàm interni. </s><s>Si to<lb/>tus &longs;iphon aquâ impleatur, & <lb/>vtrumque orificium claudatur, ac deinde minus crus EF aquæ <lb/>imponatur, maiori foras prominente, & &longs;imul vtrumque orifi<lb/>cium aperiatur; idem fiet. </s>

<s>Effluet tamen inæqualiter, cum perpetuo <expan abbr="nimir&utilde;">nimirum</expan> celerita<lb/>tis decremento, quia perpendiculum aquæ cruris interni, altitu<lb/>do nempe aquæ à puncto P u&longs;que ad &longs;uperficiem &longs;uperiorem <lb/>aquæ va&longs;is (hæc enim &longs;ola premit actu, reliquæ verò inferiores <lb/>actu non premunt, per dicta cap. 1. Proprietate V.) &longs;emper ma<lb/>gis ac magis cre&longs;cit, ac proinde &longs;emper magis magi&longs;que re&longs;i&longs;tit <lb/>perpendiculo aquæ cruris externi. </s>

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

<s>

<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-

<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. </s><s>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>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. </s><s>Ratio e&longs;t, quia perpendiculum cruris externi longius <lb/>e&longs;t quàm interni. </s><s>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. </s><s>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>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. </s><s>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. </s><s>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>

Line 2194

Line 2193

<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>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. </s><s>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/>

<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. </s><s>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>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. </s><s>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. </s><s>Non ergo externum crus &longs;uperat in<lb/>ternum, quòd aquæ plùs contineat. </s><s>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

<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. </s><s>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>

<s>

<arrow.to.target n="marg172"/><lb/>externum crus e&longs;t æquale interno quoad longitudinem, u&longs;que <lb/>ad aquæ &longs;uperficiem &longs;upremam va&longs;is, aqua non effluat ex crure <lb/>externo, etiam&longs;i &longs;iphon &longs;it plenus aquâ, e&longs;&longs;e, quia tunc aqua &longs;i<lb/>phonis continuatur cum aqua va&longs;is, & utriu&longs;que &longs;uperficies ex<lb/>trema æqualiter di&longs;tat à centro Mundi: Cau&longs;am verò cur, quan<lb/>do externi cruris orificium e&longs;t demi&longs;&longs;ius &longs;uperficie extrema aquæ <lb/>va&longs;is, effluat, e&longs;&longs;e, quia tunc &longs;uperficies aquæ va&longs;is e&longs;t altior, quàm <lb/>&longs;uperficies aquæ cruris externi, cum cujus aqua continuatur, ac <lb/>proinde tam diu fluere debet aqua va&longs;is, po&longs;tquam &longs;emel fluere <lb/>c&oelig;pit, donec &longs;uperficies fiant æqualiter di&longs;tantes à centro Ter<lb/>ræ. Ob contrariam ergo cau&longs;am, &longs;ecundùm Heronem non <lb/>effluit aqua ex crure externo breviore, &longs;ed refluit intra vas quia <lb/>nimirum &longs;uprema &longs;uperficies aquæ va&longs;is e&longs;t declivior, quàm &longs;u<lb/>perficies aquæ cruris externi. </s>

<arrow.to.target n="marg172"/><lb/>externum crus e&longs;t æquale interno quoad longitudinem, u&longs;que <lb/>ad aquæ &longs;uperficiem &longs;upremam va&longs;is, aqua non effluat ex crure <lb/>externo, etiam&longs;i &longs;iphon &longs;it plenus aquâ, e&longs;&longs;e, quia tunc aqua &longs;i<lb/>phonis continuatur cum aqua va&longs;is, & utriu&longs;que &longs;uperficies ex<lb/>trema æqualiter di&longs;tat à centro Mundi: Cau&longs;am verò cur, quan<lb/>do externi cruris orificium e&longs;t demi&longs;&longs;ius &longs;uperficie extrema aquæ <lb/>va&longs;is, effluat, e&longs;&longs;e, quia tunc &longs;uperficies aquæ va&longs;is e&longs;t altior, quàm <lb/>&longs;uperficies aquæ cruris externi, cum cujus aqua continuatur, ac <lb/>proinde tam diu fluere debet aqua va&longs;is, po&longs;tquam &longs;emel fluere <lb/>c&oelig;pit, donec &longs;uperficies fiant æqualiter di&longs;tantes à centro Ter<lb/>ræ. </s><s>Ob contrariam ergo cau&longs;am, &longs;ecundùm Heronem non <lb/>effluit aqua ex crure externo breviore, &longs;ed refluit intra vas quia <lb/>nimirum &longs;uprema &longs;uperficies aquæ va&longs;is e&longs;t declivior, quàm &longs;u<lb/>perficies aquæ cruris externi. </s>

<s><margin.target id="marg172"/><emph type="italics"/>Heronis opi<lb/>nio circa a<lb/>quæ fluxum <lb/>è crure ex<lb/>terno &longs;ipho<lb/>nis.<emph.end type="italics"/></s>

<s>C&oelig;terùm cur aqua in &longs;ecundo ca&longs;u, ex va&longs;e a&longs;cendat ad <lb/>&longs;iphonis &longs;ummitatem, contra ejus naturam, indeque de&longs;cendat <lb/>ad orificium u&longs;que externi cruris, non e&longs;t ob cau&longs;am jam ad&longs;igna<lb/>tam, &longs;ed ut impleat, aut impediat vacuum, &longs;eu quia trahitur vio<lb/>lenter ad impediendum, aut implendum vacuum. Quoniam <lb/>enim ex crure externo extrahitur aër, trahit is &longs;ecum, nè vacuus <lb/>maneat &longs;iphon, & di&longs;continuentur corpora, nempe aër & aqua, <lb/>trahit inquam &longs;ecum aquam u&longs;que ad orificium cruris externi; <lb/>quò ubi pervenerit, nullam ampliùs violentiam patitur ab aëre, <lb/>nec ab alio extrin&longs;eco agente, &longs;ed naturæ &longs;uæ relinquitur, ut pars <lb/>illa incipiat, aut pro&longs;equatur fluxum, cujus &longs;uperficies extre<lb/>ma minùs di&longs;tat à centro Mundi, duretque fluxus, donec am<lb/>bæ &longs;uperficies æquales fiant. </s>

<s>C&oelig;terùm cur aqua in &longs;ecundo ca&longs;u, ex va&longs;e a&longs;cendat ad <lb/>&longs;iphonis &longs;ummitatem, contra ejus naturam, indeque de&longs;cendat <lb/>ad orificium u&longs;que externi cruris, non e&longs;t ob cau&longs;am jam ad&longs;igna<lb/>tam, &longs;ed ut impleat, aut impediat vacuum, &longs;eu quia trahitur vio<lb/>lenter ad impediendum, aut implendum vacuum. </s><s>Quoniam <lb/>enim ex crure externo extrahitur aër, trahit is &longs;ecum, nè vacuus <lb/>maneat &longs;iphon, & di&longs;continuentur corpora, nempe aër & aqua, <lb/>trahit inquam &longs;ecum aquam u&longs;que ad orificium cruris externi; <lb/>quò ubi pervenerit, nullam ampliùs violentiam patitur ab aëre, <lb/>nec ab alio extrin&longs;eco agente, &longs;ed naturæ &longs;uæ relinquitur, ut pars <lb/>illa incipiat, aut pro&longs;equatur fluxum, cujus &longs;uperficies extre<lb/>ma minùs di&longs;tat à centro Mundi, duretque fluxus, donec am<lb/>bæ &longs;uperficies æquales fiant. </s>

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

<s>ES&longs;e porrò hanc, quam ad&longs;ignavit Hero, genuinam dicti <lb/>phænomeni cau&longs;am, confirmat ip&longs;e tali Experimento. <emph type="italics"/>Si <lb/>

<s>ES&longs;e porrò hanc, quam ad&longs;ignavit Hero, genuinam dicti <lb/>phænomeni cau&longs;am, confirmat ip&longs;e tali Experimento. </s><s><emph type="italics"/>Si <lb/>

<arrow.to.target n="marg173"/><lb/>&longs;umentes,<emph.end type="italics"/> inquit, <emph type="italics"/>duo va&longs;a<emph.end type="italics"/> (cuju&longs;modi &longs;unt A & B in appo<lb/>&longs;itis figuris) <emph type="italics"/>injiciemus humidum in utrumque ip&longs;orum, & implentes<emph.end type="italics"/>

<pb xlink:href="051/01/121.jpg" pagenum="90"/><emph type="italics"/>&longs;iphonem, digiti&longs;que ip&longs;ius o&longs;cula comprehendentes, demittemus alte<lb/>rum crus in unum dictorum va&longs;orum adeo, ut aquâ demergatur; alte<lb/>rum verò in alterum vas,<emph.end type="italics"/> (ut aqua etiam demergatur, prout in <lb/>appo&longs;itis figuris apparet;) <emph type="italics"/>fiet tota aqua continua; utrumque enim <lb/>humidorum, quæ &longs;unt in væ&longs;ibus,<emph.end type="italics"/> (ita interpres) <emph type="italics"/>conjungitur cum eo, <lb/>quod e&longs;t in &longs;iphone, ita ut totum continuum fiat. Si igitur &longs;uperficies<emph.end type="italics"/><lb/>

<pb xlink:href="051/01/121.jpg" pagenum="90"/><emph type="italics"/>&longs;iphonem, digiti&longs;que ip&longs;ius o&longs;cula comprehendentes, demittemus alte<lb/>rum crus in unum dictorum va&longs;orum adeo, ut aquâ demergatur; alte<lb/>rum verò in alterum vas,<emph.end type="italics"/> (ut aqua etiam demergatur, prout in <lb/>appo&longs;itis figuris apparet;) <emph type="italics"/>fiet tota aqua continua; utrumque enim <lb/>humidorum, quæ &longs;unt in væ&longs;ibus,<emph.end type="italics"/> (ita interpres) <emph type="italics"/>conjungitur cum eo, <lb/>quod e&longs;t in &longs;iphone, ita ut totum continuum fiat. </s><s>Si igitur &longs;uperficies<emph.end type="italics"/><lb/>

<arrow.to.target n="fig22"/><lb/><emph type="italics"/>humidorum, quæ priùs erant in va<lb/>&longs;ibus, in una &longs;uperficie con&longs;i&longs;tant,<emph.end type="italics"/><lb/>ut in prima figura; <emph type="italics"/>quie&longs;cet & &longs;ic <lb/>utraque ip&longs;arum demer&longs;o &longs;iphone: <lb/>&longs;in minùs,<emph.end type="italics"/> ut in &longs;ecunda figura; <lb/><emph type="italics"/>quoniam aqua continua facta e&longs;t, <lb/>nece&longs;&longs;ariò ob continuitatem in hu<lb/>miliorem locum fluet, quou&longs;&queacute; vel <lb/>omnis aqua, quæ in va&longs;ibus, in una <lb/>&longs;uperficie &longs;it, vel alterum va&longs;orum <lb/><expan abbr="exinãiat">exinaniat</expan><gap/>r,<emph.end type="italics"/> illud videlicet, quod <lb/>altiori fuerit loco. <emph type="italics"/>Fiant igitur <lb/>in una &longs;uperficie humida, quæ &longs;unt <lb/>in va&longs;ibus; quie&longs;cent utique, ita <lb/>ut etiam humidum, quod e&longs;t in &longs;i<lb/>phone, &longs;imul quie&longs;cat. Quòd &longs;i<emph.end type="italics"/><lb/>

<arrow.to.target n="fig22"/><lb/><emph type="italics"/>humidorum, quæ priùs erant in va<lb/>&longs;ibus, in una &longs;uperficie con&longs;i&longs;tant,<emph.end type="italics"/><lb/>ut in prima figura; <emph type="italics"/>quie&longs;cet & &longs;ic <lb/>utraque ip&longs;arum demer&longs;o &longs;iphone: <lb/>&longs;in minùs,<emph.end type="italics"/> ut in &longs;ecunda figura; <lb/><emph type="italics"/>quoniam aqua continua facta e&longs;t, <lb/>nece&longs;&longs;ariò ob continuitatem in hu<lb/>miliorem locum fluet, quou&longs;&queacute; vel <lb/>omnis aqua, quæ in va&longs;ibus, in una <lb/>&longs;uperficie &longs;it, vel alterum va&longs;orum <lb/><expan abbr="exinãiat">exinaniat</expan><gap/>r,<emph.end type="italics"/> illud videlicet, quod <lb/>altiori fuerit loco. </s><s><emph type="italics"/>Fiant igitur <lb/>in una &longs;uperficie humida, quæ &longs;unt <lb/>in va&longs;ibus; quie&longs;cent utique, ita <lb/>ut etiam humidum, quod e&longs;t in &longs;i<lb/>phone, &longs;imul quie&longs;cat. </s><s>Quòd &longs;i<emph.end type="italics"/><lb/>

<arrow.to.target n="marg174"/><lb/><emph type="italics"/>quis mente concipiat &longs;iphonem <gap/>&longs;<lb/>&longs;ectum juxta &longs;uperficies humidorum, quæ &longs;unt in va&longs;ibus; & ita qui<lb/>e&longs;cet humidum, quod e&longs;t in &longs;iphone: ergo & &longs;iphone ip&longs;o &longs;u&longs;pen&longs;o, & <lb/>in neutram partem inclinato, rur&longs;us quie&longs;cet humidum, &longs;ive æqualem <lb/>omnino habens latitudinem, &longs;ive alterum crus altero multo majus &longs;it; <lb/>non enim in hoc cau&longs;a e&longs;t, cur humidum quie&longs;cat, &longs;ed in eo, quòd ip<lb/>&longs;ius o&longs;cula æqualiter jaceant.<emph.end type="italics"/> Hæc Hero. lege etiam quæ &longs;equun<lb/>tur apud ip&longs;um in eodem cap. 1. </s>

<s><margin.target id="marg173"/>Experimen <lb/>tum circa <lb/>aquæ <expan abbr="flux&utilde;">fluxum</expan> <lb/>ex &longs;iphone.</s>

Line 2232

Line 2231

<s>Sed hæc cau&longs;a ex Herone ad&longs;ignata non videtur e&longs;&longs;e ve<lb/>

<arrow.to.target n="marg175"/><lb/>ra, aut &longs;altem non e&longs;t adæquata. Primò enim, &longs;i ideo fluit <lb/>aqua ex crure longiore, AD, &longs;eu potius CD, &longs;ecundæ figuræ, <lb/>quia &longs;uperfies extrema aquæ ip&longs;ius non e&longs;t æqualis &longs;uperficiei

<arrow.to.target n="marg175"/><lb/>ra, aut &longs;altem non e&longs;t adæquata. </s><s>Primò enim, &longs;i ideo fluit <lb/>aqua ex crure longiore, AD, &longs;eu potius CD, &longs;ecundæ figuræ, <lb/>quia &longs;uperfies extrema aquæ ip&longs;ius non e&longs;t æqualis &longs;uperficiei

<pb xlink:href="051/01/122.jpg" pagenum="91"/>extremæ aquæ alterius cruris, BF, &longs;eu potius EF, &longs;ed demi&longs;&longs;ior; <lb/>ergo quando &longs;iphon &longs;ive æqualium, &longs;ive inæqualium crurium, <lb/>aqu&adot; plenus, & utrimque compre&longs;&longs;is digitis obturatus, imponi<lb/>tur duobus prædictis va&longs;is aqu&adot; plenis, quorum unius &longs;uperficies <lb/>&longs;uprema aquæ altior e&longs;t, quàm alterius, effluitque aqua intra vas <lb/>demi&longs;&longs;ius, eò quòd alterius &longs;uperficies &longs;uprema altior e&longs;t, & ad <lb/>decliviorem locum tendit, nititurque &longs;uperficiem &longs;uam adæ<lb/>quare &longs;uperficiei alterius va&longs;is humilioris; ergo inquam, quando <lb/>hoc contingit, aqua ex va&longs;e altiore a&longs;cendit naturaliter & inna<lb/>to appetitu ad &longs;iphonis &longs;uperiorem partem, indeque de&longs;cendit <lb/>intra vas humilius; naturaliter enim aquæ partes altiores fluunt <lb/>ad loca decliviora. Deinde &longs;i illa e&longs;t cau&longs;a adæquata, cur quan<lb/>do &longs;iphon ina qualium crurium repletur aquâ, & &longs;ecundùm <lb/>longius crus immergitur aquæ, <gap/>revius verò extra <lb/>in aëre relinquitur, cur<gap/>quam, no<gap/>uit aqua per externum, <lb/>ubi nullum e&longs;t impedimentum pr<gap/>te<gap/>erem? pote&longs;t enim aqua <lb/>per exte num fluere <gap/>d loca decliviora, & fundare unam conti<lb/>nuam &longs;uperficiem di&longs;tinctam à &longs;uperficie, quæ in va&longs;e e&longs;t; & <lb/>præterea inclinationem habet ad de&longs;cendendum, non verò ad <lb/>a&longs;cendendum. Præterea, cur quando &longs;iphon inæqualium cru<lb/>rium repletur aqua, & tenetur inver&longs;us in aëre, non effluit aqua <lb/>ex crure breviori, cum ejus aqua plùs di&longs;tet à centro Terræ, <lb/>quàm aqua cruris longioris? Alia ergo cau&longs;a ad&longs;ignari debet, cur <lb/>aqua cruris longioris, &longs;eu externi, &longs;eu interni, vincataquam cru<lb/>ris brevioris; quam paulò po&longs;t dabimus. </s>

<pb xlink:href="051/01/122.jpg" pagenum="91"/>extremæ aquæ alterius cruris, BF, &longs;eu potius EF, &longs;ed demi&longs;&longs;ior; <lb/>ergo quando &longs;iphon &longs;ive æqualium, &longs;ive inæqualium crurium, <lb/>aqu&adot; plenus, & utrimque compre&longs;&longs;is digitis obturatus, imponi<lb/>tur duobus prædictis va&longs;is aqu&adot; plenis, quorum unius &longs;uperficies <lb/>&longs;uprema aquæ altior e&longs;t, quàm alterius, effluitque aqua intra vas <lb/>demi&longs;&longs;ius, eò quòd alterius &longs;uperficies &longs;uprema altior e&longs;t, & ad <lb/>decliviorem locum tendit, nititurque &longs;uperficiem &longs;uam adæ<lb/>quare &longs;uperficiei alterius va&longs;is humilioris; ergo inquam, quando <lb/>hoc contingit, aqua ex va&longs;e altiore a&longs;cendit naturaliter & inna<lb/>to appetitu ad &longs;iphonis &longs;uperiorem partem, indeque de&longs;cendit <lb/>intra vas humilius; naturaliter enim aquæ partes altiores fluunt <lb/>ad loca decliviora. </s><s>Deinde &longs;i illa e&longs;t cau&longs;a adæquata, cur quan<lb/>do &longs;iphon ina qualium crurium repletur aquâ, & &longs;ecundùm <lb/>longius crus immergitur aquæ, <gap/>revius verò extra <lb/>in aëre relinquitur, cur<gap/>quam, no<gap/>uit aqua per externum, <lb/>ubi nullum e&longs;t impedimentum pr<gap/>te<gap/>erem? pote&longs;t enim aqua <lb/>per exte num fluere <gap/>d loca decliviora, & fundare unam conti<lb/>nuam &longs;uperficiem di&longs;tinctam à &longs;uperficie, quæ in va&longs;e e&longs;t; & <lb/>præterea inclinationem habet ad de&longs;cendendum, non verò ad <lb/>a&longs;cendendum. </s><s>Præterea, cur quando &longs;iphon inæqualium cru<lb/>rium repletur aqua, & tenetur inver&longs;us in aëre, non effluit aqua <lb/>ex crure breviori, cum ejus aqua plùs di&longs;tet à centro Terræ, <lb/>quàm aqua cruris longioris? Alia ergo cau&longs;a ad&longs;ignari debet, cur <lb/>aqua cruris longioris, &longs;eu externi, &longs;eu interni, vincataquam cru<lb/>ris brevioris; quam paulò po&longs;t dabimus. </s>

<s><margin.target id="marg175"/><emph type="italics"/>Heronis opi<lb/>nio exami<lb/>natur.<emph.end type="italics"/></s>

<s>Qui tamen Heronis &longs;ententiam tueri volet, ad has ratio<lb/>nes in contrarium allatas re&longs;pondere poterit, ut &longs;equitur. Nem<lb/>pe ad primam, aquam cruris brevioris non a&longs;cendere naturali<lb/>ter, &longs;ed tractam ab aqua cruris longioris AD, &longs;eu CD, ad va<lb/>cuum in &longs;iphone impediendum, & ad tuendam continuitatem <lb/>partium aquæ aqua enim cruris longioris AD, &longs;eu CD, de&longs;cen<lb/>dit naturaliter (utpote tendens ad locum decliviorem) &longs;ecum<lb/>que trahit reliquam aquam, quia &longs;uprema &longs;uperficies va&longs;is A, <lb/>cum qua continuatur aqua &longs;iphonis, & va&longs;is B, e&longs;t declivior,

<s>Qui tamen Heronis &longs;ententiam tueri volet, ad has ratio<lb/>nes in contrarium allatas re&longs;pondere poterit, ut &longs;equitur. </s><s>Nem<lb/>pe ad primam, aquam cruris brevioris non a&longs;cendere naturali<lb/>ter, &longs;ed tractam ab aqua cruris longioris AD, &longs;eu CD, ad va<lb/>cuum in &longs;iphone impediendum, & ad tuendam continuitatem <lb/>partium aquæ aqua enim cruris longioris AD, &longs;eu CD, de&longs;cen<lb/>dit naturaliter (utpote tendens ad locum decliviorem) &longs;ecum<lb/>que trahit reliquam aquam, quia &longs;uprema &longs;uperficies va&longs;is A, <lb/>cum qua continuatur aqua &longs;iphonis, & va&longs;is B, e&longs;t declivior,

<pb xlink:href="051/01/123.jpg" pagenum="92"/>&longs;uprema verò &longs;uperficies va&longs;is B e&longs;t altior, & debet fieri æqua<lb/>litas inter ip&longs;as: quæ non fieret, &longs;i aqua &longs;iphonis BF, &longs;eu EF, de<lb/>&longs;cenderet. </s>

<s>Ad &longs;ecundam, non effluere aquam per brevius, &longs;ed per lon<lb/>gius crus, quia aqua amat continuitatem &longs;uarum partium, & ap<lb/>petit habere &longs;uperficiem &longs;upremam omnium partium æqualiter <lb/>di&longs;tantem à centro Terræ; quorum utrumque obtinet, &longs;i ef<lb/>fluit aqua per longius crus; neutrum, &longs;i per brevius. </s>

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<s><margin.target id="marg176"/><emph type="italics"/>Authoris o<lb/>pinio circa <lb/>aquæ <expan abbr="flux&utilde;">fluxum</expan> <lb/>è crure ex<lb/>terno longio <lb/>re &longs;iphonis.<emph.end type="italics"/></s>

<s>Sed quidquid &longs;it de hac Heronis &longs;ententia, mihi magis pla<lb/>cet &longs;equens ratio allati phænomeni, quæ univer&longs;alis e&longs;t & in <lb/>omnibus &longs;imilibus ca&longs;ibus locum habet, ut vidimus in præce<lb/>dentibus, & iterum videbimus infrà hoc eodem capite Propo<lb/>&longs;it. 13. & 14. Pro qua recolendum e&longs;t, quod diximus &longs;uprà Ca<lb/>pite 1. Proprietate IV. ex Archimede, aquæ & humidi cuju&longs;cun<lb/>que partem unamquamque premi humido &longs;upra ip&longs;am exi&longs;tente <lb/>ad perpendiculum, &longs;i humidum &longs;it de&longs;cendens in aliquo, aut cer<lb/>tè nullum habeat impedimentum, ut de&longs;cendat. </s>

<s>Sed quidquid &longs;it de hac Heronis &longs;ententia, mihi magis pla<lb/>cet &longs;equens ratio allati phænomeni, quæ univer&longs;alis e&longs;t & in <lb/>omnibus &longs;imilibus ca&longs;ibus locum habet, ut vidimus in præce<lb/>dentibus, & iterum videbimus infrà hoc eodem capite Propo<lb/>&longs;it. 13. & 14. </s><s>Pro qua recolendum e&longs;t, quod diximus &longs;uprà Ca<lb/>pite 1. Proprietate IV. ex Archimede, aquæ & humidi cuju&longs;cun<lb/>que partem unamquamque premi humido &longs;upra ip&longs;am exi&longs;tente <lb/>ad perpendiculum, &longs;i humidum &longs;it de&longs;cendens in aliquo, aut cer<lb/>tè nullum habeat impedimentum, ut de&longs;cendat. </s>

<s>Dico itaque, cau&longs;am hujus rei e&longs;&longs;e eandem cum ea, quæ <lb/>ad&longs;ignata fuit in præcedentibus, quia nimirum aqua cruris lon<lb/>gioris potentior e&longs;t ad de&longs;cendendum, &longs;ecumque trahendum <lb/>aquam cruris brevioris, quàm aqua cruris alterius; & hoc ideo, <lb/>quia aqua premit ac premitur, dum premit ac premitur, ad per<lb/>pendiculum, hoc e&longs;t, &longs;ecundùm lineam quæ tran&longs;it per centrum <lb/>Mundi. Cujus ergo aquæ perpendiculum longius e&longs;t, illa ma<lb/>gis premit ac vincit, hoc e&longs;t, de&longs;cendit, &longs;i nihil ob&longs;tet de&longs;cen<lb/>&longs;um impediens, ut in no&longs;tro ca&longs;u contingit. Hîc ergo verum <lb/>etiam e&longs;t, quòd <emph type="italics"/>in Hydraulicis pugnatur & vincitur non pondere, <lb/>aut copi aquarum, &longs;ed perpendiculis,<emph.end type="italics"/> juxta Axioma hydraulicum, <lb/>2. quod &longs;uprà Propo&longs;itione 2, formatum fuit. </s>

<s>Dico itaque, cau&longs;am hujus rei e&longs;&longs;e eandem cum ea, quæ <lb/>ad&longs;ignata fuit in præcedentibus, quia nimirum aqua cruris lon<lb/>gioris potentior e&longs;t ad de&longs;cendendum, &longs;ecumque trahendum <lb/>aquam cruris brevioris, quàm aqua cruris alterius; & hoc ideo, <lb/>quia aqua premit ac premitur, dum premit ac premitur, ad per<lb/>pendiculum, hoc e&longs;t, &longs;ecundùm lineam quæ tran&longs;it per centrum <lb/>Mundi. </s><s>Cujus ergo aquæ perpendiculum longius e&longs;t, illa ma<lb/>gis premit ac vincit, hoc e&longs;t, de&longs;cendit, &longs;i nihil ob&longs;tet de&longs;cen<lb/>&longs;um impediens, ut in no&longs;tro ca&longs;u contingit. </s><s>Hîc ergo verum <lb/>etiam e&longs;t, quòd <emph type="italics"/>in Hydraulicis pugnatur & vincitur non pondere, <lb/>aut copi aquarum, &longs;ed perpendiculis,<emph.end type="italics"/> juxta Axioma hydraulicum, <lb/>2. quod &longs;uprà Propo&longs;itione 2, formatum fuit. </s>

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

<s><emph type="center"/>Siphonem ad Libram &longs;eu vectem revocare, <lb/>filtrum ad &longs;iphonem.<emph.end type="center"/></s>

<s>ESto recta linea AB, divi&longs;a bifariam in puncto C. Si huic <lb/>puncto C &longs;upponatur hypomochlion G, aut alligetur fi<lb/>

<s>ESto recta linea AB, divi&longs;a bifariam in puncto C. </s><s>Si huic <lb/>puncto C &longs;upponatur hypomochlion G, aut alligetur fi<lb/>

<arrow.to.target n="fig23"/><lb/>lum FG; &longs;tabit, hærebitque li<lb/>nea AB in æquilibrio horizon<lb/>ti parallela, & neutra pars præ<lb/>valebit. Si prolongetur pars <lb/>CB u&longs;que ad D, prævalebit pars <lb/>CD parti CA, & de&longs;cendet. Si <lb/>prolongetur eadem pars CB, u&longs;<lb/>que ad E, adhuc magis prævale<lb/>bit pars C parti CA, <expan abbr="cele-riu&longs;&qacute;ue">cele<lb/>riu&longs;que</expan> de&longs;cendet; & quò ma<lb/>gis prolongabitur pars longior, <lb/>eò magis prævalebit breviori, <lb/>magi&longs;que celeriter de&longs;cendet. <lb/>Linea porrò AB, aut AD, aut <lb/>AE, &longs;i hypomochlio G impo<lb/>natur, repræ&longs;entatvectem; &longs;i è <lb/>filo FC &longs;u&longs;pendatur, repræ&longs;entat <lb/>libram, aut &longs;tateram. </s>

<arrow.to.target n="fig23"/><lb/>lum FG; &longs;tabit, hærebitque li<lb/>nea AB in æquilibrio horizon<lb/>ti parallela, & neutra pars præ<lb/>valebit. </s><s>Si prolongetur pars <lb/>CB u&longs;que ad D, prævalebit pars <lb/>CD parti CA, & de&longs;cendet. </s><s>Si <lb/>prolongetur eadem pars CB, u&longs;<lb/>que ad E, adhuc magis prævale<lb/>bit pars C parti CA, <expan abbr="cele-riu&longs;&qacute;ue">cele<lb/>riu&longs;que</expan> de&longs;cendet; & quò ma<lb/>gis prolongabitur pars longior, <lb/>eò magis prævalebit breviori, <lb/>magi&longs;que celeriter de&longs;cendet. </s><s><lb/>Linea porrò AB, aut AD, aut <lb/>AE, &longs;i hypomochlio G impo<lb/>natur, repræ&longs;entatvectem; &longs;i è <lb/>filo FC &longs;u&longs;pendatur, repræ&longs;entat <lb/>libram, aut &longs;tateram. </s>

<s>E&longs;to jam &longs;iphon ACB, &longs;ive <lb/>

<arrow.to.target n="marg177"/><lb/>erectus, &longs;ive inver&longs;us, divi&longs;us <lb/>mente in duas æquales partes AC, BC, & repleatur totus aquâ; <lb/>ex neutro crure effluet, ut vidimus atque probavimus, &longs;ed aqua <lb/>&longs;tabit, hærebitve in duobus cruribus AC, BC, in æquilibrio. <lb/>Si prolongetur crus CB, u&longs;que ad D, & repleatur totus &longs;i<lb/>phon aquâ; prævalebit crus CD, & aqua ejus in inver&longs;o &longs;ipho<lb/>ne effluens &longs;ecum trahet reliquam; in erecto verò &longs;iphone de<lb/>&longs;cendet & expellet reliquam per os A. Si prolongetur idem <lb/>crus CB u&longs;que ad E, adhuc magis prævalebit crus CE, ma<lb/>gi&longs;que celeriter de&longs;cendet ejus aqua, & vel &longs;ecum trahet reli<lb/>quam, vel illam &longs;ub&longs;idendo expellet. </s>

<arrow.to.target n="marg177"/><lb/>erectus, &longs;ive inver&longs;us, divi&longs;us <lb/>mente in duas æquales partes AC, BC, & repleatur totus aquâ; <lb/>ex neutro crure effluet, ut vidimus atque probavimus, &longs;ed aqua <lb/>&longs;tabit, hærebitve in duobus cruribus AC, BC, in æquilibrio. </s><s><lb/>Si prolongetur crus CB, u&longs;que ad D, & repleatur totus &longs;i<lb/>phon aquâ; prævalebit crus CD, & aqua ejus in inver&longs;o &longs;ipho<lb/>ne effluens &longs;ecum trahet reliquam; in erecto verò &longs;iphone de<lb/>&longs;cendet & expellet reliquam per os A. </s><s>Si prolongetur idem <lb/>crus CB u&longs;que ad E, adhuc magis prævalebit crus CE, ma<lb/>gi&longs;que celeriter de&longs;cendet ejus aqua, & vel &longs;ecum trahet reli<lb/>quam, vel illam &longs;ub&longs;idendo expellet. </s>

<s><margin.target id="marg177"/><emph type="italics"/>Siphon tam <lb/>erectus. qu<gap/><lb/>inver&longs;us, re <lb/>vecatur ad <lb/>libram.<emph.end type="italics"/></s>

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<s>Patet ergo, quomodo &longs;iphon <lb/>tam erectus, quàm inver&longs;us, re<lb/>vocetur ad libram, aut vectem </s>

<s>Filtrum appellamus panni <lb/>

<arrow.to.target n="marg178"/><lb/>laciniam ACB, pendentem ex <lb/>va&longs;e A, ita ut pars AC &longs;it in<lb/>tra vas, & aquæ immer&longs;a, &longs;al<lb/>tem ex parte; pars verò altera <lb/>CB extra vas pendeat. Hæc <lb/>panni lacinia &longs;i priùs madefiat <lb/>tota, deinde modo dicto ex va<lb/>&longs;e aquâ pleno &longs;u&longs;pendatur; tra<lb/>hit aquam non &longs;ecus ac &longs;iphon, <lb/>&longs;i pars exterior fuerit longior <lb/>quàm interior; &longs;i æqualis, aut <lb/>brevior, non trahit. Con&longs;tat <lb/>ergo, filtrum ad &longs;iphonem re<lb/>duci. </s>

<arrow.to.target n="marg178"/><lb/>laciniam ACB, pendentem ex <lb/>va&longs;e A, ita ut pars AC &longs;it in<lb/>tra vas, & aquæ immer&longs;a, &longs;al<lb/>tem ex parte; pars verò altera <lb/>CB extra vas pendeat. </s><s>Hæc <lb/>panni lacinia &longs;i priùs madefiat <lb/>tota, deinde modo dicto ex va<lb/>&longs;e aquâ pleno &longs;u&longs;pendatur; tra<lb/>hit aquam non &longs;ecus ac &longs;iphon, <lb/>&longs;i pars exterior fuerit longior <lb/>quàm interior; &longs;i æqualis, aut <lb/>brevior, non trahit. </s><s>Con&longs;tat <lb/>ergo, filtrum ad &longs;iphonem re<lb/>duci. </s>

<s><margin.target id="marg178"/><emph type="italics"/>Filtrum re<lb/>vocatur ad <lb/>&longs;iphonem.<emph.end type="italics"/></s>

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<s><emph type="center"/>Diabetem &longs;piritalem de&longs;cribere, eju&longs;que <lb/>proprietates ad&longs;ignare.<emph.end type="center"/></s>

<s>EO&longs;dem ferè effectus, quos præ&longs;tat &longs;iphon inflexus, cujus <lb/>unum crus va&longs;i imponitur, præ&longs;tat etiam tubus certo mo<lb/>do va&longs;i implantatus, quem Hero Alexandrinus vocat medium <lb/>&longs;piritalem diabetem, qua&longs;i dicas, pera&longs;cen&longs;orem; alij verò vo<lb/>cant tubum &longs;uffocabilem. Sic autem con&longs;truitur. </s>

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