texts/archimedes/xml/gueva_mecha_005_la_1627.xml - Colored diff

Main History Search Repository tree

Return to gueva_mecha_005_la_1627.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/gueva_mecha_005_la_1627.xml between version 1.11 and 1.16

version 1.11, 2004/09/08 15:36:20

version 1.16, 2004/10/15 12:30:10

Line 2910

<s id="N16159">Quamobrem quando hæc quidam <lb/>ip&longs;i GM pertran&longs;iuerit, illa verò ip&longs;i FI, & rur&longs;um facta <lb/>fuerit recta ip&longs;a FA ad ip&longs;am FL, & ip&longs;a AG rur&longs;um re<lb/>cta, velut à principio erant in ip&longs;is MI. </s>

<s id="N16162">Hoc autem neque <lb/>alia intercedente mora maioris ad minorem, vbi &longs;cilicet per <lb/>aliquod temporis &longs;patium &longs;taret in eodem puncto, neque tran&longs;i<lb/>liente minore aliquod punctum, maiorem quidem æqualem mi<lb/>nori pertran&longs;ire, hunc autem maiori, ab&longs;urdum e&longs;t. </s>

<s id="N1616F">Præterea <lb/>vnica etiam &longs;emper existente motione, centrorum motum inter<lb/>dum quidem magnam, nonnunquam verò minorem conuerti, <lb/>admirandum est. </s>

<s id="N16178">I dem enim celeritate eadem latum æqualem <lb/>natum boc e&longs;t pertran&longs;ire: eadem autem celeritate vtroque <lb/>modo æqualem licet mouere. </s>

<s id="N16178">I dem enim celeritate eadem latum æqualem <lb/>natum hoc e&longs;t pertran&longs;ire: eadem autem celeritate vtroque <lb/>modo æqualem licet mouere. </s>

<s id="N1617F">Principium autem &longs;umendum <lb/>est circa i&longs;torum cau&longs;am, quod eadem potentia, & æqualit <lb/>bans quidem tardius mouet magnitudinem, illam verò cel<gap/><lb/>rius. </s>

<s id="N1617F">Principium autem &longs;umendum <lb/>est circa i&longs;torum cau&longs;am, quod eadem potentia, & æqualis <lb/>hanc quidem tardius mouet magnitudinem, illam verò cele<lb/>rius. </s>

<s id="N1618A">Si enim fuerit quippiam, quod à &longs;eip&longs;o moueri, natum <lb/><gap/>n &longs;it, &longs;i &longs;imul & illud mouerit, quod natum e&longs;t mouert, tar<lb/>dius mouebitur, quàm &longs;i ip&longs;um per &longs;e moueretur. </s>

<s id="N1618A">Si enim fuerit quippiam, quod à &longs;eip&longs;o moueri, natum <lb/>non &longs;it, &longs;i &longs;imul & illud mouerit, quod natum e&longs;t moueri, tar<lb/>dius mouebitur, quàm &longs;i ip&longs;um per &longs;e moueretur. </s>

<s id="N16192">Et &longs;iquidem <lb/><gap/>atum fuerit moueri, non &longs;imul autem moueatur, &longs;imiliter <lb/>&longs;e habebit. </s>

<s id="N16192">Et &longs;iquidem <lb/>natum fuerit moueri, non &longs;imul autem moueatur, &longs;imiliter <lb/>&longs;e habebit. </s>

<s id="N1619A">Et impo&longs;&longs;ibile certè e&longs;t, plus moueri quàm mouem, <lb/><gap/>on enim &longs;uam ip&longs;ius mouetur motionem. </s>

<s id="N1619A">Et impo&longs;&longs;ibile certè e&longs;t, plus moueri quàm mouem, <lb/>non enim &longs;uam ip&longs;ius mouetur motionem. </s>

<s id="N161A0">Sit igitur e reu'us <lb/>maior vbi A, minor autem vbi B, &longs;i minor maiorem impel<lb/>let non reuolutum ex &longs;e, manife&longs;tum e&longs;t, quod tantum ip&longs;ius <lb/>rectæ maior pertran&longs;it, quantum e&longs;t impul&longs;us. </s>

<s id="N161A9">T antum autem <lb/>e&longs;t impul&longs;us, quantum paruus est motus æqualem igitur ip&longs;ius <lb/>rectæ pertran&longs;iuerunt. </s>

<s id="N161B0">Nece&longs;ie igitur e&longs;t &longs;i reuolutus minor <lb/>maiorem impellet, reuoluti &longs;imul cum impul&longs;ione; tantum <lb/>autem, quantum minor reuolutus e&longs;t, &longs;i nibil ip&longs;e &longs;ui ip&longs;ius <lb/>motione mouetur. </s>

<s id="N161B0">Nece&longs;&longs;e igitur e&longs;t &longs;i reuolutus minor <lb/>maiorem impellet, reuoluti &longs;imul cum impul&longs;ione; tantum <lb/>autem, quantum minor reuolutus e&longs;t, &longs;i nihil ip&longs;e &longs;ui ip&longs;ius <lb/>motione mouetur. </s>

<s id="N161B9">Quomodo enim & quantum mouit, tantum <lb/>motum e&longs;&longs;e nece&longs;&longs;e e&longs;t, quod mouetur ab illo. </s>

<s id="N161BE">Sed profectò par<lb/>uus circulus tantum jeip&longs;um circulariter mouit, quantum est <lb/>pedalis quantitas (tantum enim &longs;it id, quod motus e&longs;t) & ma<lb/>gnus igitur tantum motus erit. </s>

<s id="N161BE">Sed profectò par<lb/>uus circulus tantum &longs;eip&longs;um circulariter mouit, quantum est <lb/>pedalis quantitas (tantum enim &longs;it id, quod motus e&longs;t) & ma<lb/>gnus igitur tantum motus erit. </s>

<s id="N161C7"><expan abbr="Similiq.">Similique</expan> modo &longs;i magnus par<lb/>uum mouebit, motus erit paruus quemadmodum maior. </s>

<s id="N161CF">Per <lb/>&longs;e autem motus illorum vtrumlibet, &longs;iue celeriter, &longs;eu tardè <lb/>eadem velocitate, statim quando maior natus e&longs;t circumferri <lb/>lineam, quod difficultatem facit, quod non &longs;imiliter faciunt <lb/>quando fuerint connexi. </s>

<s id="N161DA">Hoc autem e&longs;t, &longs;i alter ab altero mo<lb/>ueatur, non quam natus e&longs;t, neque peculiarem motionem: nibil <lb/>enim refert cireumponere, & annectere, aut <expan abbr="eõiungere">eoniungere</expan> vtrum<lb/>libet alteri. </s>

<s id="N161DA">Hoc autem e&longs;t, &longs;i alter ab altero mo<lb/>ueatur, non quam natus e&longs;t, neque peculiarem motionem: nihil <lb/>enim refert circumponere, & annectere, aut <expan abbr="eõiungere">coniungere</expan> vtrum<lb/>libet alteri. </s>

<s id="N161E7">Similiter enim quando bic quidem mouet, ille ve<lb/>rò mouelur ab isto, quantum vtique mouerit, alt<gap/>r, tantum<emph.end type="italics"/><pb pagenum="207" xlink:href="005/01/215.jpg"/><emph type="italics"/>alter mouebitur. </s>

<s id="N161E7">Similiter enim quando hic quidem mouet, ille ve<lb/>rò mouetur ab isto, quantum vtique mouerit, alter, tantum <emph.end type="italics"/><pb pagenum="207" xlink:href="005/01/215.jpg"/><emph type="italics"/>alter mouebitur. </s>

<s id="N161F7">Quandoquidem igitur adiacens mouerit, aut <lb/>propen&longs;us, non &longs;emper conuoluitur, quando verò circa idem <lb/>po&longs;iti fuerint centrum, alterum ab illo &longs;emper conuolui nece&longs;<lb/>&longs;e est. </s>

<s id="N16200">Sed nihileminus non &longs;uam ip&longs;ius motionem mouetur al<lb/>ter, &longs;ed velut nullam baberet motionem: & &longs;i babuerit, illa <lb/>autem non vtatur, tantundem accidit. </s>

<s id="N16200">Sed nihil e minus non &longs;uam ip&longs;ius motionem mouetur al<lb/>ter, &longs;ed velut nullam haberet motionem: & &longs;i habuerit, illa <lb/>autem non vtatur, tantundem accidit. </s>

<s id="N16207">Quandoquidem igitur <lb/>magnus mouerit &longs;ibi <expan abbr="alligat&utilde;">alligatum</expan> paruum, paruus mouetur quan<lb/>tum ille: quando autem paruus, rur&longs;us magnus quantum i&longs;te, <lb/>&longs;eparatus autem vterque &longs;eip&longs;um mouet. </s>

<s id="N16214">Quod autem eodem <lb/>exi&longs;tente centro, & mouente eadem velocitate, accidit inæqua<lb/>lem illos pertran&longs;ire lineam, paralogi&longs;mo &longs;opbi&longs;ticè vtitur is, <lb/>qui dubitat: idem enim ambobus e&longs;t centrum, verùm per acci<lb/>dens, veluti mu&longs;icum, & album. </s>

<s id="N16214">Quod autem eodem <lb/>exi&longs;tente centro, & mouente eadem velocitate, accidit inæqua<lb/>lem illos pertran&longs;ire lineam, paralogi&longs;mo &longs;ophi&longs;ticè vtitur is, <lb/>qui dubitat: idem enim ambobus e&longs;t centrum, verùm per acci<lb/>dens, veluti mu&longs;icum, & album. </s>

<s id="N1621F">E&longs;&longs;e enim vtriu&longs;que circuli <lb/>centro non eodem vtitur. </s>

<s id="N16224">Quandoquidem igitur mouens fue<lb/>rit paruus, vt illius centrum, & principium: quando verò <lb/>magnus, vt illius. </s>

<s id="N1622B">Non igitur idem &longs;impliciter mouet, &longs;ed e&longs;t <lb/>quo modo.<emph.end type="italics"/></s>

Line 2939

<s id="N1623A">Qvæ&longs;tio hæc admirabilem complectitur difficulta<lb/>tem, vtpotè in&longs;tituta circa rem, quæ vix credi po&longs;&longs;et, <lb/>ni&longs;i ante oculos ob&longs;eruaretur: Vnde inter cæteras <lb/>præcipua ac omnium difficillima exi&longs;timatur, <expan abbr="multumq.">multumque</expan> pa<lb/>riter &longs;icut præcedens ad mixti motus naturam exploran<lb/>dam conducit. </s>

<s id="N1624B">Cau&longs;am igitur &longs;ci&longs;citatur Ari&longs;toteles, cur <lb/>duo circuli alter altero maior circa idem centrum &longs;imul an<lb/>nexi, & coaptati, &longs;i &longs;ecundùm ab&longs;idem volutentur (vt plau<lb/>&longs;trorum progredientium rotæ) ambo æquale pertran&longs;eant <lb/>&longs;patium: &longs;eor&longs;um verò &longs;eparati, &longs;i eodem pacto circum<lb/>uoluantur, non ita &longs;ed maior circulus maiorem lineam, mi<lb/>nor verò minorem percurrat iuxta proportionem circumfe<lb/>rentiæ vnius ad circumferentiam alterius? </s>

<s id="N1625C">Quod vt di&longs;tin<lb/>ctius ob&longs;eruetur addit Ari&longs;toteles, cir culos ip&longs;os circa idem <lb/>centrum coniunctos, <expan abbr="quandoq.">quandoque</expan> in circumuolutione tantam <lb/>lineam &longs;patij pertran&longs;ire, quantam &longs;eor&longs;um pertran&longs;iret cir<lb/>culus minor: quandoque verò quantam eodem pacto per<lb/>curreret circulus maior. </s>

<s id="N1626D">Etenim, vt quilque experiri po-<pb pagenum="208" xlink:href="005/01/216.jpg"/>te&longs;t, &longs;i ex ip&longs;is duobus circulis &longs;imul circa idem centrum <lb/>coniunctis volutetur minor &longs;ecundum ab&longs;idem &longs;uam &longs;uper <lb/>aliquod planum, ad motum ip&longs;ius conuoluetur &longs;imul & ma<lb/>ior &longs;uper aliud planum; &longs;ed vtraque linea ab ip&longs;is de&longs;cripta, <lb/>æqualis erit ei quam de&longs;criberet ip&longs;emet circulus minor &longs;i <lb/>&longs;olus per &longs;e ac &longs;eor&longs;um volutaretur. </s>

<s id="N1626D">Etenim, vt qui&longs;que experiri po-<pb pagenum="208" xlink:href="005/01/216.jpg"/>te&longs;t, &longs;i ex ip&longs;is duobus circulis &longs;imul circa idem centrum <lb/>coniunctis volutetur minor &longs;ecundum ab&longs;idem &longs;uam &longs;uper <lb/>aliquod planum, ad motum ip&longs;ius conuoluetur &longs;imul & ma<lb/>ior &longs;uper aliud planum; &longs;ed vtraque linea ab ip&longs;is de&longs;cripta, <lb/>æqualis erit ei quam de&longs;criberet ip&longs;emet circulus minor &longs;i <lb/>&longs;olus per &longs;e ac &longs;eor&longs;um volutaretur. </s>

<s id="N1627F">E contra verò &longs;i &longs;uper <lb/>planum eodem pacto volutetur &longs;ecundum ab&longs;idem &longs;uam <lb/>circulus maior, & ad motum ip&longs;ius circumuoluatur etiam <lb/>circulus minor, vtraque linea recta ab ip&longs;is de&longs;cripta æqua<lb/>lis erit ei quam per &longs;e volutatus de&longs;criberet idemmet circu<lb/>lus maior. </s>

<s id="N1628E">Manife&longs;tum autem e&longs;&longs;e, ait Ari&longs;toteles, circulum maio<lb/>rem &longs;eor&longs;um reuolutum, maius <expan abbr="&longs;paci&utilde;">&longs;pacium</expan>, &longs;eu maiorem lineam <lb/>pertran&longs;ire, quàm pertran&longs;eat circulus minor. </s>

<s id="N16299">Idque ex eo, <lb/>nam &longs;icut &longs;en&longs;u con&longs;tat, ambitum cuiu&longs;que circuli e&longs;&longs;e, at<lb/>que con&longs;titui per ip&longs;am circumferentiam, &longs;eu circumuolu<lb/>tionem propriæ cliametri eiu&longs;dem circuli, maioris quidem <lb/>maiorem, minoris verò minorem: ita &longs;en&longs;u pariter digno&longs;ci<lb/>tur eandem inter &longs;e proportionem habere lineas, quæ per <lb/>circumuolutionem ip&longs;orum circulorum de&longs;cribuntur in <lb/>plano; vt&longs;cilicet linea de&longs;cripta à maiori circumferentia <lb/>&longs;it maior, quæ verò à minori de&longs;cribitur, &longs;it minor. </s>

<s id="N16299">Idque ex eo, <lb/>nam &longs;icut &longs;en&longs;u con&longs;tat, ambitum cuiu&longs;que circuli e&longs;&longs;e, at<lb/>que con&longs;titui per ip&longs;am circumferentiam, &longs;eu circumuolu<lb/>tionem propriæ diametri eiu&longs;dem circuli, maioris quidem <lb/>maiorem, minoris verò minorem: ita &longs;en&longs;u pariter digno&longs;ci<lb/>tur eandem inter &longs;e proportionem habere lineas, quæ per <lb/>circumuolutionem ip&longs;orum circulorum de&longs;cribuntur in <lb/>plano; vt &longs;cilicet linea de&longs;cripta à maiori circumferentia <lb/>&longs;it maior, quæ verò à minori de&longs;cribitur, &longs;it minor. </s>

<s id="N162AC">Vbi <lb/>autem v&longs;i &longs;umus nomine (ambitus) textus habet (angulus) <lb/>cuius propria &longs;ignificatio difficile cohæret cum &longs;en&longs;u ip&longs;ius <lb/>orationis, <expan abbr="proindeq.">proindeque</expan> non paruam &longs;u&longs;picionem præbuit er<lb/>roris librariorum, qui forta&longs;&longs;e angulum pro ambitu &longs;crip&longs;e<lb/>runt: Cum alioquin vox ambitus contextui planè coh&etail;reat, <lb/><expan abbr="explicetq.">explicetque</expan> magis ac breuius quod auctor intendit. </s>

Line 2960

<s id="N1631A">Sint circa <lb/>idem <expan abbr="p&utilde;ctum">punctum</expan> <lb/>A ip&longs;i duo cir<lb/>culi <expan abbr="coni&utilde;cti">coniuncti</expan>, <lb/>maior <expan abbr="quid&etilde;">quidem</expan> <lb/>BCDE, minor <lb/>verò FGHI. <lb/></s>

<s id="N16336">Sintque dia<lb/>metri maioris <lb/>BD, & EC; <lb/>minoris verò <lb/>FH, & IG &longs;e&longs;e <lb/>inuicem inter&longs;ecantes ad angulos rectos in cenrro A. </s>

<s id="N16336">Sintque dia<lb/>metri maioris <lb/>BD, & EC; <lb/>minoris verò <lb/>FH, & IG &longs;e&longs;e <lb/>inuicem inter&longs;ecantes ad angulos rectos in centro A. </s>

<s id="N16344">Ideo<lb/>que quadrans circuli maioris &longs;it CD, minoris verò GH. <lb/></s>

<s id="N1634A">Deinde con&longs;tituamus vtrunque circulum ad dexteram &longs;i<lb/>mul moueri cum &longs;uo communi centro, rotando alterum <pb pagenum="210" xlink:href="005/01/218.jpg"/>quidem per &longs;e &longs;uper rectam lineam DK, alterum verò ad <lb/>motum illius, de&longs;cribendo aliam rectam huic parallelam, <lb/>quæ &longs;it HL. </s>

<s id="N16358">Rur&longs;us con&longs;tituamus, maiorem circulum per <lb/>&longs;e moueri &longs;ecundum ab&longs;idem quadrantis CD &longs;uper lineam <lb/>DK, ita vt aliquando punctum C perueniat in M, percur<lb/>rendo &longs;patium DM æquale ip&longs;i CD. </s>

Line 2984

<s id="N163F1">Præterea quòd vnica exi&longs;tente motione vtriu&longs;que cir<lb/>culi connexi, centrum commune commotum, interdum <lb/>quidem maiorem, interdum verò minorem lineam percur<lb/>rat iuxta ab&longs;idem, &longs;cilicet maioris, aut minoris circuli &longs;e<lb/>cundum quam mouetur: cum tamen idem eadem celerita<lb/>te latum, æqualem lineam regulariter debeat pertran&longs;ire. </s>

<s id="N16400">Pro &longs;olultione igitur quæ&longs;tionis ad explicandam cau&longs;am <lb/>tam mirifici effectus, duo &longs;upponit Ari&longs;toteles fundamenta. <lb/></s>

<s id="N16400">Pro &longs;olutione igitur quæ&longs;tionis ad explicandam cau&longs;am <lb/>tam mirifici effectus, duo &longs;upponit Ari&longs;toteles fundamenta. <lb/></s>

<s id="N16406">Vnum e&longs;t eandem, vel æqualem potentiam, tardius quidem <lb/>mouere vnam magnitudinem, quàm aliam. </s>

<s id="N1640B">Licet enim illæ <lb/>æquè ex &longs;e mobiles &longs;int, &longs;i tamen vna &longs;imul cum alia ad <lb/>motum inepta vel difficili reperiatur coniuncta, tardius mo<lb/>uebitur, quàm illa, quæ reperitur &longs;oluta, vel quam ip&longs;amet <lb/>&longs;eor&longs;um moueretur ab eadem potentia. </s>

<s id="N16416">Quod &longs;i magni<lb/>tudo, quæ moueri debet ad motum alterius, cui reperi<lb/>tur connexa, mobilis quidem facilè ex &longs;e &longs;it, nihil tamen <lb/>ex &longs;e moueatur, vel ad motum alterius conferat, perin<lb/>de e&longs;t, ac &longs;i minimè apta e&longs;&longs;et ad motum: vnde & altera, <lb/>quæ &longs;imul cum ip&longs;a moueri debet, tardius non minus mo<lb/>uebitur. </s>

Line 2995

<s id="N1643C">Quibus po&longs;itis Ari&longs;toteles quæ&longs;tionem &longs;oluendo prædi<lb/>ctum effectum ex eo inquit contingere. </s>

<s id="N16441">Nam &longs;i circulus ma<lb/>ior non moueatur ni&longs;i ad motum minoris cui e&longs;t annexus, <lb/>tantum &longs;patium poterit pertran&longs;ire, quantum delatus fuerit <lb/>ex impullu illius: tantum autem deferri poterit quantum <lb/>minor ip&longs;e circulus ex &longs;e motus impulerit, & non amplius. <lb/></s>

<s id="N16441">Nam &longs;i circulus ma<lb/>ior non moueatur ni&longs;i ad motum minoris cui e&longs;t annexus, <lb/>tantum &longs;patium poterit pertran&longs;ire, quantum delatus fuerit <lb/>ex impul&longs;u illius: tantum autem deferri poterit quantum <lb/>minor ip&longs;e circulus ex &longs;e motus impulerit, & non amplius. <lb/></s>

<s id="N1644D">Quomodo enim & quantum ex &longs;e motus fuerit mouens, <lb/>tantundem nece&longs;&longs;e e&longs;t moueri, qui mouetur ab illo. </s>

<s id="N16452">Aequa<lb/>lem igitur viam vterque circulus rotando conficiet dum <lb/>maior mouetur ad motum minoris. </s>

<s id="N16459"><expan abbr="Idemq.">Idemque</expan> infert contin<lb/>gere &longs;i minor circulus moueatur ad motum maioris &longs;ibi an<lb/>nexi, & eodem pacto &longs;ecundum ab&longs;idem lati. </s>

<s id="N16463">Nam tantum <lb/>ip&longs;e minor circulus, & non minus moueri poterit, quantum <lb/>à maiori deportabitur. </s>

<s id="N1646A">Rapitur enim iugiter ab illo in &longs;ua <lb/>rotatione v&longs;que ad vltimum terminum, <expan abbr="æqualemq.">æqualemque</expan> propte<lb/>rea lineam rectam <expan abbr="c&utilde;">cum</expan> illo de&longs;cribet, quamuis minorem pe<lb/>ripheriam obtineat. </s>

<s id="N1647B">Quod &longs;i vtrumlibet ip&longs;orum circulo<lb/>rum &longs;eor&longs;um ex &longs;e &longs;ecundum propriam ab&longs;idem eadem ve<lb/>locitate moueatur, tunc maior circulus maiorem rectam, <lb/>minor verò minorem &longs;ua volutatione conficiet iuxta men<lb/>&longs;utam &longs;ecundum quam natus e&longs;t circumferri. </s>

<s id="N1647B">Quod &longs;i vtrumlibet ip&longs;orum circulo<lb/>rum &longs;eor&longs;um ex &longs;e &longs;ecundum propriam ab&longs;idem eadem ve<lb/>locitate moueatur, tunc maior circulus maiorem rectam, <lb/>minor verò minorem &longs;ua volutatione conficiet iuxta men<lb/>&longs;uram &longs;ecundum quam natus e&longs;t circumferri. </s>

<s id="N16488">Cæterum eam, ac profectò <expan abbr="arduã">arduam</expan> difficultatem &longs;ibi obij<lb/>cit Philo&longs;ophus. </s>

Line 3022

<s id="N1652A">Hucu&longs;que ex mente, ac doctrina Ari&longs;totelis, qui tamen <lb/>mul<gap/>orum iudicio non videtur obiectam &longs;ibi difficultatem <lb/>&longs;atis infringere, vt quæ adhuc magna ex parte maneat in &longs;uo <lb/>robore. </s>

<s id="N1652A">Huiu&longs;que ex mente, ac doctrina Ari&longs;totelis, qui tamen <lb/>multorum iudicio non videtur obiectam &longs;ibi difficultatem <lb/>&longs;atis infringere, vt quæ adhuc magna ex parte maneat in &longs;uo <lb/>robore. </s>

<s id="N16535">Nam hoc quod e&longs;t proprio, vel alieno motu cieri, <lb/><expan abbr="centrumq.">centrumque</expan> circuli deferentis per accidens e&longs;&longs;e etiam cen<lb/>trum circuli delati, non tollit, vtrunque circulum &longs;ecun<lb/>dum ab&longs;idem codem pacto rotari, ac propriam lineam <lb/>rectam in &longs;uo plano de&longs;cribere: vnde videtur inferri eodem <lb/>etiam pacto vtramque lineam de&longs;criptam propriæ periphe<lb/>riæ à qua de&longs;cribitur debere commen&longs;urari. </s>

<s id="N16547">Parum enim <lb/>refert, circulum per &longs;e rotari circa proprium centrum ad <lb/>impul&longs;um axis immediatè, vel per accidens mediante alio <lb/>circulo, dummodo eodem pacto per circumuolutionem &longs;u&etail; <lb/>ab&longs;idis circa idem centrum lineam de&longs;cribat, cui illa debeat <lb/>commen&longs;urari. </s>

<s id="N16554">Sphæra namque &longs;uper planum rotando &longs;i<lb/>ue proprio nutu, &longs;iue alieno impul&longs;u, tardius, aut velocius, <lb/>&longs;icut omnes plani partes, per quas tran&longs;it debet attingere; <lb/>ita per totidem partes &longs;uas illis debet corre&longs;pondere, & ad <lb/>æqualitatem in tran&longs;itu adaptari. </s>

Line 3031

<s id="N1657F"><expan abbr="Idemq.">Idemque</expan> è conuer&longs;o applicari pote&longs;t in contactu pe<lb/>ripheriæ maioris circuli cum recta breuiori, quam conficit <lb/>ad motum minoris circuli &longs;uper ab&longs;idem per &longs;e lati. </s>

<s id="N1658B">Ad diluendam igitur omnino prædictam difficultatem, <lb/>quæ multorum quippe vexauit ingenia, & pene in&longs;uperabi-<pb pagenum="215" xlink:href="005/01/223.jpg"/>lis apud aliquos extimatur, liceat aliunde totum negocium <lb/>au&longs;picari, nouumque aliquid in medium affere in eiu&longs;dem <lb/>Ari&longs;totelis, ac veterum Philo&longs;ophorum princip<gap/>s funda <lb/>tum. </s>

<s id="N1659D">Ac primò quidem &longs;tabiliatur, motum cuiu&longs;libet circu<lb/>li &longs;ecundum ab&longs;idem, e&longs;&longs;e motum quendam mixtum ex du<lb/>plici latione; vna qua circumuoluitur, &longs;eu circa proprium <lb/>centrum fertur in gyrum; altera verò qua ad motum axis <lb/>rectà fertur &longs;uper planum quo ver&longs;us tendit ip&longs;emet axis. <lb/></s>

<s id="N165A9">Etenim &longs;i circulus &longs;tans ab&longs;que &longs;ui rotatione raperetur &longs;u<lb/>per <expan abbr="plan&utilde;">planum</expan>, verè moueretur motu recto, ac per vnicum pun<lb/>ctum totam plani longitudinem &longs;uper quam fertur attinge<lb/>ret. </s>

<s id="N165B6">Si verò circumuolueretur ab&longs;que progre&longs;&longs;u, aut latio<lb/>ne axis, verè moueretur circulariter ac per omnes partes, <lb/><expan abbr="punctaq.">punctaque</expan> &longs;uæ peripheriæ, eandem plani partem, vel punctum <lb/>in quo &longs;i&longs;tebat attingeret. </s>

<s id="N165C2">Cum itaque ad motum axis re<lb/>ctà &longs;uper planum trahitur, ac &longs;imul rotatur, ex vtraque la<lb/>tione mixtus quidam motus producitur, per quem tota <lb/>circumferentia toti longitudini &longs;uper quam fertur ada<lb/>ptatur. </s>

<s id="N165CF">Deinde verò &longs;tabiliatur lineam, quæ à circulo, prædicto <lb/>modo de&longs;cribitur &longs;uper planum, ab&longs;trahendo à rotatione <lb/>&longs;pontanea, vel coacta ad motum alterius, ex natura &longs;ua non <lb/>de&longs;cribinisi luxta men&longs;uram lationis, &longs;eu motus recti, qui &longs;imui <lb/>cum axe conficitur in anteriora, & cuius virtute de&longs;cribitur. <lb/></s>

<s id="N165CF">Deinde verò &longs;tabiliatur lineam, quæ à circulo, prædicto <lb/>modo de&longs;cribitur &longs;uper planum, ab&longs;trahendo à rotatione <lb/>&longs;pontanea, vel coacta ad motum alterius, ex natura &longs;ua non <lb/>de&longs;cribi nisi iuxta men&longs;uram lationis, &longs;eu motus recti, qui &longs;imul <lb/>cum axe conficitur in anteriora, & cuius virtute de&longs;cribitur. <lb/></s>

<s id="N165DB">Etenim ip&longs;a de&longs;cribi po&longs;&longs;et ab eodem circulo etiam &longs;ine ro<lb/>tatione, per vnicum punctum vt diximus, non autem &longs;ine re<lb/>cta aliqua latione. </s>

<s id="N165E2">Quamobrem in de&longs;criptione ip&longs;ius lineæ <lb/>rectæ &longs;uper planum, per &longs;e, & ab&longs;olutè loquendo, non habe<lb/>tur ratio de motu circulari, nec de &longs;patio circulariter pera<lb/>grato ab ip&longs;o circulo, &longs;ed de motu recto, ac &longs;patio, quod ip<lb/>&longs;e circulus &longs;imul <expan abbr="c&utilde;">cum</expan> axe percurrit, & ad cuius &longs;emper men<lb/>&longs;uram ip&longs;a recta linea excitatur. </s>

<s id="N165F3">Quamuis per accidens con<lb/>tingat, circulum deferentem, vel alium ex &longs;e, ac &longs;eor&longs;um ro<lb/>tando, tantum &longs;patium &longs;imul cum axe recta tran&longs;inittere, <lb/>quantum ip&longs;emet circulariter eodem tempore peragrare <lb/>valuerit. </s>

<s id="N165F3">Quamuis per accidens con<lb/>tingat, circulum deferentem, vel alium ex &longs;e, ac &longs;eor&longs;um ro<lb/>tando, tantum &longs;patium &longs;imul cum axe recta tran&longs;mittere, <lb/>quantum ip&longs;emet circulariter eodem tempore peragrare <lb/>valuerit. </s>

<s id="N165FE">Quia &longs;cilicet cum tota progre&longs;&longs;io à &longs;ua ip&longs;ius ro<pb pagenum="216" xlink:href="005/01/224.jpg"/>tatione dependeat, &longs;icut motus rectus progre&longs;&longs;ionis nece&longs;<lb/>&longs;ariò proportionatur motui circulari à quo pendet, ita <lb/>etiam linea de&longs;cripta per talem motum proportionari, & <lb/>adæquari debet lineæ de&longs;criptæ, &longs;eu peragratæ per circui<lb/>tionem. </s>

<s id="N16610">His itaque &longs;ic &longs;tabilitis, atque &longs;uppo&longs;itis tanquam certis, <lb/>& cuidentibus, ad primam partem quæ&longs;tionis &longs;imul, ac dif<lb/>ficultatis propo&longs;itæ re&longs;pondetur, circulum delatum &longs;emper <lb/>æquale &longs;patium, ac circulum deferentem &longs;uper planum ro<lb/>tando, rectà tran&longs;initrere, &longs;iue maior eo fuerit, &longs;iue minor; <lb/>quia illud non tran&longs;mittit ex vi &longs;uæ rotationis, ac iuxta <lb/>men&longs;uram &longs;uæ circumferentiæ, &longs;ed ex vi &longs;ui raptus, & a&longs;por<lb/>tationis. </s>

<s id="N16610">His itaque &longs;ic &longs;tabilitis, atque &longs;uppo&longs;itis tanquam certis, <lb/>& cui dentibus, ad primam partem quæ&longs;tionis &longs;imul, ac dif<lb/>ficultatis propo&longs;itæ re&longs;pondetur, circulum delatum &longs;emper <lb/>æquale &longs;patium, ac circulum deferentem &longs;uper planum ro<lb/>tando, rectà tran&longs;mittere, &longs;iue maior eo fuerit, &longs;iue minor; <lb/>quia illud non tran&longs;mittit ex vi &longs;uæ rotationis, ac iuxta <lb/>men&longs;uram &longs;uæ circumferentiæ, &longs;ed ex vi &longs;ui raptus, & a&longs;por<lb/>tationis. </s>

<s id="N16621">Siquidem tantum rectà progreditur, quantum à <lb/>deferente rapitur, & a&longs;portatur, licet aliàs eodem tempore <lb/>maiorem, aut minorem &longs;imul peragrat circuitum, de quo <lb/>nulla per &longs;e haberi debet ratio, vt præmonuimus. </s>

<s id="N1662A">Vnde nec <lb/>requiritur, vt cius motus circumuolutionis &longs;it æqualis mo<lb/>tui recto, nec vt linea recta, quam percurrit &longs;it æqualis cir<lb/>cunferentiæ &longs;ecundum quam rotando conuoluitur. </s>

<s id="N1662A">Vnde nec <lb/>requiritur, vt eius motus circumuolutionis &longs;it æqualis mo<lb/>tui recto, nec vt linea recta, quam percurrit &longs;it æqualis cir<lb/>cunferentiæ &longs;ecundum quam rotando conuoluitur. </s>

<s id="N16635">Ad &longs;ecundam verò partem quæ&longs;tionis re&longs;pondetur, cir<lb/>culum deferentem, vel alium, qui &longs;eor&longs;um per &longs;e &longs;uper pla<lb/>num circumuoluatur, quò maior ip&longs;e fuerit, maius &longs;patium <lb/>rectà in &longs;ua reuolutione percurrere, quò verò minor, minus. <lb/></s>

Line 3056

<s id="N16655">Adhuc tamen ex ei&longs;dem principijs <expan abbr="re&longs;põderi">re&longs;ponderi</expan> pote&longs;t, præ<lb/>fata nos experiri, quia minor circulus quando mouetur ad <lb/>motum alterius maioris motu mixto iam explicato, magis <lb/>participat de latione recta, quàm circulari; citius videlicet <lb/>progrediendo quàm rorando. </s>

<s id="N16664">Cogitur enim rectà progre-<pb pagenum="217" xlink:href="005/01/225.jpg"/>di iuxta progre&longs;&longs;um axis, ac circuli maioris, <expan abbr="&longs;imulq.">&longs;imulque</expan> tardius <lb/>rotari quàm ille, minus &longs;patium eodem tempore tran&longs;init<lb/>tendo in &longs;ua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb/>rotationem, rectam quandam lineam de&longs;cribit maiorem, <lb/>quam &longs;it eius circunferentia propria. </s>

<s id="N16664">Cogitur enim rectà progre-<pb pagenum="217" xlink:href="005/01/225.jpg"/>di iuxta progre&longs;&longs;um axis, ac circuli maioris, <expan abbr="&longs;imulq.">&longs;imulque</expan> tardius <lb/>rotari quàm ille, minus &longs;patium eodem tempore tran&longs;mit<lb/>tendo in &longs;ua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb/>rotationem, rectam quandam lineam de&longs;cribit maiorem, <lb/>quam &longs;it eius circunferentia propria. </s>

<s id="N1667C">E contra verò, nam <lb/>cum circulus maior mouetur ad motum minoris, magis par<lb/>ticipat de latione circulari, quàm recta. </s>

<s id="N16683">Siquidem, cogitur <lb/>citius moueri circulariter quàm rectà, cum eodem tempo<lb/>re maiorem ambitum, quàm circulus minor, æqualemque <lb/>rectam debeat percurrere: <expan abbr="ideoq.">ideoque</expan> minorem rectam in &longs;ua <lb/>circumuolutione de&longs;cribit, quàm &longs;it eiu&longs;inet circum&longs;erentia<lb/>qua illam attingit. </s>

<s id="N16683">Siquidem, cogitur <lb/>citius moueri circulariter quàm rectà, cum eodem tempo<lb/>re maiorem ambitum, quàm circulus minor, æqualemque <lb/>rectam debeat percurrere: <expan abbr="ideoq.">ideoque</expan> minorem rectam in &longs;ua <lb/>circumuolutione de&longs;cribit, quàm &longs;it eiu&longs;met circum&longs;erentia<lb/> qua illam attingit. </s>

<s id="N16694">Demum quia &longs;i circulus ex &longs;e, & inde<lb/>pendenter ab alio duplici hac latione feratur, &longs;iue maior &longs;it, <lb/>&longs;iue minor, &longs;emper æquè de vtraque participat. </s>

<s id="N1669B">Etenim tan<lb/>tum rectà progreditur quantum rotatur, nec aliunde rapi<lb/>tur, aut detinetur, vt magis vna quàm altera latione dimo<lb/>ueatur. </s>

<s id="N166A4">Quo fit vt linea quam &longs;uper planum de&longs;cribit, æqua<lb/>lis &longs;it propriæ circumferentiæ eique &longs;ecundum omnes par<lb/>tes commen&longs;urata. </s>

<s id="N166AD">Verum vt non &longs;olum cau&longs;a tam admirabilis effectus, &longs;ed <lb/>etiam modus quo ip&longs;e ab illa procedit expre&longs;&longs;ius innote<lb/>&longs;cat, ac difficultas vltimò propo&longs;ita ex directo penitus eua<lb/>datur, vlterius dicendum e&longs;t, circulum delatum non minus <lb/>ac deferentem, omnia ac &longs;ingula puncta, quæ &longs;unt in linea re<lb/>cta &longs;uper quam fertur per totidem puncta propria &longs;ucce&longs;&longs;i<lb/>uè attingere; ita vt in quolibet in&longs;tanti per nouum punctum <lb/>&longs;<gap/>æ peripheriæ attingat nouum punctum plani. </s>

<s id="N166C0">Etenim cum <lb/>planum à circulo attingatur per puncta, quæ &longs;unt extremita<lb/>tes diametrorum, & vterque circulus ex infinitis diametris <lb/>con&longs;tet; imò diametri cir culi maioris includant diametros <lb/>minoris; tot erunt puncta terminatiua diametrorum in cir<lb/>culo minori, quot &longs;unt in maiori, &longs;iue delato per quæ &longs;imili<lb/>ter omnia puncta &longs;ui plani valebit attingere. </s>

<s id="N166D1">Rur&longs;us dicendum e&longs;t tam circulum deferentem, quàm <lb/>circulum delatum omnes, ac &longs;ingulas partes diui&longs;ibiles, qu&etail; <lb/>&longs;unt in eadem linea plani per totidem partes &longs;uas &longs;ucce&longs;&longs;iuè <pb pagenum="218" xlink:href="005/01/226.jpg"/>attingere: hoc tamen di&longs;crimine, quod circulus deferens <lb/>illas attingit commen&longs;uratiuè, & adæquatè, circulus verò <lb/>delatus nonni&longs;i inadæquatè. </s>

<s id="N166E1">Sicut enim circulus deferens <lb/>&longs;iue maior &longs;it, &longs;iue minor con&longs;tat ex infinitis partibus inde<lb/>terminatis, quæ mediant inter infinita puncta, ita etiam cir<lb/>culus delatus, per ea&longs;que non minus attingere poterit infi<lb/>nitas partes, quæ &longs;unt in plano. </s>

<s id="N166EC">Diximus tamen attingere <lb/>inadæquatè. </s>

<s id="N166F1">Nam contactus adæquatus, & commen&longs;ura<lb/>tus duarum quantitatum, fit per æqualem applicationem <lb/>partium æqualium vtriu&longs;que quantitatis ad coexi&longs;tendum <lb/>&longs;imul in eodem &longs;patio loci: partes autem æqualiter appli<lb/>carinon po&longs;&longs;ant per lationes inæquales, nam ea e&longs;t inæqua<lb/>litas in applicatione, quæ e&longs;t in ip&longs;is lationibus, &longs;iue lationes <lb/>cadant in vtramque quantitatem, &longs;iue in alteram tantùm. <lb/></s>

<s id="N166F1">Nam contactus adæquatus, & commen&longs;ura<lb/>tus duarum quantitatum, fit per æqualem applicationem <lb/>partium æqualium vtriu&longs;que quantitatis ad coexi&longs;tendum <lb/>&longs;imul in eodem &longs;patio loci: partes autem æqualiter appli<lb/>cari non po&longs;&longs;unt per lationes inæquales, nam ea e&longs;t inæqua<lb/>litas in applicatione, quæ e&longs;t in ip&longs;is lationibus, &longs;iue lationes <lb/>cadant in vtramque quantitatem, &longs;iue in alteram tantùm. <lb/></s>

<s id="N16701">Quapropter cum tota applicatio partium circumferentiæ <lb/>ad attingendas partes plani &longs;uper quod rotatur, fiat tum ex <lb/>vi ip&longs;ius rotationis, qua &longs;ucce&longs;&longs;iuè ip&longs;æ partes inclinantur <lb/>ad illas, tum ex vi motus recti quo &longs;ucce&longs;&longs;iuè etiam progre<lb/>diendo ad ca&longs;dem perueniunt: hinc fit, vt &longs;i lationes ip&longs;æ <lb/>æqualiter procedant, quemadmo dum in motu mixto circuli <lb/>deferentis, aut alterius per &longs;e &longs;eor&longs;um rotantis, æqualiter <lb/>etiam alterius quantitatis partes, ad partes alterius appli<lb/>centur, ac &longs;e tangendo ad inuicem commen&longs;urentur, & <lb/>adæquentur: E contra verò &longs;i non procedant æqualiter ip<lb/>&longs;æ lationes, &longs;ed vna alteram excedat in velocitate, aut tardi<lb/>tate, vt in motu mixto cuiu&longs;libet circuli delati, inæqualiter <lb/>etiam partes ip&longs;ius ad partes plani applicentur, ac inadæ<lb/>quatè adinuicem commen&longs;urentur. </s>

<s id="N16701">Quapropter cum tota applicatio partium circumferentiæ <lb/>ad attingendas partes plani &longs;uper quod rotatur, fiat tum ex <lb/>vi ip&longs;ius rotationis, qua &longs;ucce&longs;&longs;iuè ip&longs;æ partes inclinantur <lb/>ad illas, tum ex vi motus recti quo &longs;ucce&longs;&longs;iuè etiam progre<lb/>diendo ad ea&longs;dem perueniunt: hinc fit, vt &longs;i lationes ip&longs;æ <lb/>æqualiter procedant, quemadmodum in motu mixto circuli <lb/>deferentis, aut alterius per &longs;e &longs;eor&longs;um rotantis, æqualiter <lb/>etiam alterius quantitatis partes, ad partes alterius appli<lb/>centur, ac &longs;e tangendo ad inuicem commen&longs;urentur, & <lb/>adæquentur: E contra verò &longs;i non procedant æqualiter ip<lb/>&longs;æ lationes, &longs;ed vna alteram excedat in velocitate, aut tardi<lb/>tate, vt in motu mixto cuiu&longs;libet circuli delati, inæqualiter <lb/>etiam partes ip&longs;ius ad partes plani applicentur, ac inadæ<lb/>quatè adinuicem commen&longs;urentur. </s>

<s id="N16720">Quod &longs;i non po&longs;&longs;it coexi&longs;tere in &longs;patio, exempli gratia <lb/>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb/>paimaris, vel tripalmaris, quacunque rotatione ad inuicem <lb/>applicentur; hoc profectò intelligitur in quiete, atque in <lb/>termino ip&longs;ius motus: alioquin in tran&longs;itu, ac &longs;ucce&longs;siuè id <lb/>nullo modo repugnat, &longs;icutnec punctum globirectà &longs;uper <lb/>planum delati po&longs;t punctum ip&longs;ius plani, attingere partem <lb/>diui&longs;ibilem eiu&longs;dem plani, eique coexi&longs;tendo inadæquatè <pb pagenum="219" xlink:href="005/01/227.jpg"/>& &longs;ucce&longs;siuè commen&longs;urari, vt omnes penè Philo&longs;ophi fa<lb/>tentur. </s>

<s id="N16720">Quod &longs;i non po&longs;&longs;it coexi&longs;tere in &longs;patio, exempli gratia <lb/>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb/>palmaris, vel tripalmaris, quacunque rotatione ad inuicem <lb/>applicentur; hoc profectò intelligitur in quiete, atque in <lb/>termino ip&longs;ius motus: alioquin in tran&longs;itu, ac &longs;ucce&longs;siuè id <lb/>nullo modo repugnat, &longs;icutnec punctum globi rectà &longs;uper <lb/>planum delati po&longs;t punctum ip&longs;ius plani, attingere partem <lb/>diui&longs;ibilem eiu&longs;dem plani, eique coexi&longs;tendo inadæquatè <pb pagenum="219" xlink:href="005/01/227.jpg"/>& &longs;ucce&longs;siuè commen&longs;urari, vt omnes penè Philo&longs;ophi fa<lb/>tentur. </s>

<s id="N16738">Maior enim vel minor velocitas atque &longs;ucce&longs;sio in <lb/>tran&longs;itu, & in partium applicatione, ex vi alterius lationis <lb/>æquipollet maiori, vel minori exten&longs;ioni ip&longs;ius quantitatis <lb/>ad replendum æquale &longs;patium ei, quod occupatur ab alia <lb/>quantitate in eodem tempore, qua ratione dicuntur coexi<lb/>&longs;tere, ac inter &longs;e coaptari. </s>

<s id="N16747">Res itaque &longs;ic e&longs;t concipienda, vt in reuolutione circuli <lb/>minoris ad motum maioris &longs;emper pars minor ip&longs;ius attin, <lb/>gat partem plani maiorem, quia velocius tran&longs;it per illam <lb/>motu recto, quàm rotando æqualem <expan abbr="dimen&longs;ion&etilde;">dimen&longs;ionem</expan> proptiam <lb/>po&longs;sit exponere, atque &longs;ecundum ip&longs;am &longs;e applicare. </s>

<s id="N16747">Res itaque &longs;ic e&longs;t concipienda, vt in reuolutione circuli <lb/>minoris ad motum maioris &longs;emper pars minor ip&longs;ius attin<lb/>gat partem plani maiorem, quia velocius tran&longs;it per illam <lb/>motu recto, quàm rotando æqualem <expan abbr="dimen&longs;ion&etilde;">dimen&longs;ionem</expan> proptiam <lb/>po&longs;sit exponere, atque &longs;ecundum ip&longs;am &longs;e applicare. </s>

<s id="N16756">Vnde <lb/>quod illi dee&longs;t exten&longs;ionis compen&longs;atur velociori &longs;ucce&longs;sio<lb/>ne, & applicatione &longs;ecundum lationem rectam ad coaptan<lb/>dum &longs;e parti majori. </s>

<s id="N1675F">Quod certè non e&longs;t intelligendum <lb/>fieri per raptationem, qua&longs;i per vnicum delati circuli pun<lb/>ctum plura plani puncta, vel per <expan abbr="eand&etilde;">eandem</expan>. </s>

<s id="N1676A">omnino circuli par<lb/>tem, plures plani partes attingerentur; &longs;ed per propriam, <lb/>rotationem. </s>

<s id="N16771">Quia ita rapitur, ac fertur &longs;uper illud motu re<lb/>cto, vt &longs;imul quamuis tardius feratur latione circulari per <lb/>quam partes, ac puncta ip&longs;ius peripheriæ iugiter mutantur. <lb/></s>

<s id="N16779">Cumque numerus in&longs;inities in&longs;initus punctorum, ac indeter<lb/>minatarum partium vtriu&longs;que circuli &longs;ufficiat ad mutatio<lb/>nem ip&longs;am continuam, & corre&longs;pondentiam, quam præ&longs;ta<lb/>re debet infinitis punctis, ac partibus plani, nullum relinqui<lb/>tur inconueniens, minorem circumferentiam maiori &longs;pario, <lb/>plani ob di&longs;parem lationem, & applicationem inadæquatè <lb/>in tran&longs;itu coaptari. </s>

<s id="N16779">Cumque numerus infinities infinitus punctorum, ac indeter<lb/>minatarum partium vtriu&longs;que circuli &longs;ufficiat ad mutatio<lb/>nem ip&longs;am continuam, & corre&longs;pondentiam, quam præ&longs;ta<lb/>re debet infinitis punctis, ac partibus plani, nullum relinqui<lb/>tur inconueniens, minorem circumferentiam maiori &longs;patio, <lb/>plani ob di&longs;parem lationem, & applicationem inadæquatè <lb/>in tran&longs;itu coaptari. </s>

<s id="N16788">Idemque è conuer&longs;o dici pote&longs;t in re<lb/>uolutione circuli maioris ad <expan abbr="mot&utilde;">motum</expan> minoris, vt &longs;cilicet &longs;em<lb/>per pars maior ip&longs;ius co re&longs;pondeat parti minori in plano <lb/>&longs;uper quod fertur, quia tardius tran&longs;it per illam motu recto, <lb/>quàm rotando æ qualem &longs;ibi dimen&longs;ionem po&longs;&longs;it attingere. <lb/></s>

<s id="N16788">Idemque è conuer&longs;o dici pote&longs;t in re<lb/>uolutione circuli maioris ad <expan abbr="mot&utilde;">motum</expan> minoris, vt &longs;cilicet &longs;em<lb/>per pars maior ip&longs;ius eo re&longs;pondeat parti minori in plano <lb/>&longs;uper quod fertur, quia tardius tran&longs;it per illam motu recto, <lb/>quàm rotando æqualem &longs;ibi dimen&longs;ionem po&longs;&longs;it attingere. <lb/></s>

<s id="N16798">Siquidem velocius rotando, quàm progrediendo, nequit at<lb/>tingere tantam dimen&longs;ionem in plano, quantam ip&longs;e exhi<lb/>bet per circumuolutionem. </s>

<s id="N1679F">Vnde quod ei &longs;upere&longs;t exten<lb/>&longs;ionis circularis compen&longs;atur tardiori &longs;ucce&longs;&longs;ione, & appli-<pb pagenum="220" xlink:href="005/01/228.jpg"/>cationem &longs;ecundum lationem rectam ad proportionandum <lb/>&longs;e parti minori. </s>

<s id="N167AB">Atque hæc in re tam ambigua &longs;i minus <lb/>demon&longs;tra&longs;&longs;e, &longs;altem indica&longs;&longs;e, vel tenta&longs;&longs;e &longs;ufficiat. </s>

Line 3095

<s id="N167BB">Nimirum cur in prædicta latione <lb/>duorum circulorum circa idem centrum &longs;ecundùm ab&longs;idem <lb/>circuli maioris, aliqua puncta circumferentiæ maioris, mi<lb/>nus progrediantur, quàm corre&longs;pondentia &longs;ibi puncta cir<lb/>cumferentiæ minoris; aliqua verò magis. </s>

<s id="N167C6">In maiori enim <lb/>circulo puncta vnius &longs;emicirculi minus progrediuntur, quam <lb/>puncta &longs;emicirculi corre&longs;pondentis in circulo minori. </s>

<s id="N167CD">Con<lb/>tra verò, puncta alterius &longs;emicirculi magis progrediuntur in <lb/>circulo maiori, quàm in minori, vt de motu particulari Epi<lb/>cyclorum docere &longs;olent A&longs;tronomi. </s>

<s id="N167D7">Quod maximè vide<lb/>tur admirandum <expan abbr="c&umacr;">cum</expan> vterque circulus &longs;impliciter, ac &longs;ecun<lb/>dum &longs;e totum ad motum axis progrediendo, æquale &longs;pa<lb/>rium percurrat, vt vidimus, ac probatum e&longs;t in præcedenti<lb/>bus. </s>

<s id="N167D7">Quod maximè vide<lb/>tur admirandum <expan abbr="c&umacr;">cum</expan> vterque circulus &longs;impliciter, ac &longs;ecun<lb/>dum &longs;e totum ad motum axis progrediendo, æquale &longs;pa<lb/>tium percurrat, vt vidimus, ac probatum e&longs;t in præcedenti<lb/>bus. </s>

<s id="N167E6">Ita tamen rem &longs;e habere &longs;ic o&longs;tenditur. </s>

Line 3105

<s id="N16815">Dicimus ergo punctum C in hac reuolutione <lb/>minus dextror&longs;um promoueri, quàm punctum G. </s>

<s id="N1681B">Demit<lb/>tatur enim à puncto C linea CO perpendicularis pariter <lb/>ip&longs;i KL, & à puncto G alia perpendicularis GP: & tunc <lb/>apparebit punctum C dextror&longs;um peragra&longs;&longs;e &longs;patium CM, <lb/>vel OL, quæ &longs;unt latera oppo&longs;ita, ac proinde æqualia re<lb/>ctanguli CMLO, vt pater per 34. propo&longs;it. </s>

<s id="N16828">primi. </s>

<s id="N1682B">Pun<lb/>ctum verò G con&longs;tabit peragraffe &longs;patium GM, &longs;eu PL <lb/>æquale huic. </s>

<s id="N1682B">Pun<lb/>ctum verò G con&longs;tabit peragra&longs;&longs;e &longs;patium GM, &longs;eu PL <lb/>æquale huic. </s>

<s id="N16832">At GM maior e&longs;t, quàm CM, eo quod <lb/>illam contineat, &longs;icut PL maior e&longs;t ip&longs;a OL propter ean<lb/>dem rationem. </s>

<s id="N16839">Ergo per talem circumuolutionem minus <lb/>dextror&longs;um progreditur punctum C, quod e&longs;t extremum <lb/>diainetri circuli maioris, quàm punctum G extremum <lb/>diametri contenti cit culi minoris. </s>

<s id="N16839">Ergo per talem circumuolutionem minus <lb/>dextror&longs;um progreditur punctum C, quod e&longs;t extremum <lb/>diametri circuli maioris, quàm punctum G extremum <lb/>diametri contenti sit culi minoris. </s>

<s id="N16844">Rur&longs;us verò dicimus punctum D eiu&longs;dem circuli maio<lb/>ris, minus pariter dextror&longs;um progredi, quam punctum H, <lb/>quod illi corre&longs;pondet in circulo minori. </s>

<s id="N1684B">Etenim po&longs;t præ<lb/>dictam reuolutionem centro I tran&longs;lato in M, ac C in <lb/>L, punctum D erit in linea AM vbi Q, (nempe in loco, <lb/>qui tantum &longs;anè di&longs;ter à puncto M, quantum di&longs;tat extre<lb/>mum D ip&longs;ius &longs;emidiametri DI ab ip&longs;o centro I,) pun<lb/>ctum verò H &longs;imiliter erit in R; ita vt &longs;emidiameter IHD <lb/>reperiatur in <expan abbr="MRq.">MRque</expan> Quapropter &longs;i ex duobus punctis QR <lb/>demittantur duæ perpendiculares in planum DL, quæ &longs;int <lb/>QS, & RT, &longs;patium progre&longs;&longs;ionis ip&longs;ius puncti D, erit <lb/>linea IQ, æqualis ip&longs;i DS: Spatium verò progre&longs;&longs;ionis <lb/>puncti H, erit linea IR, &longs;iue DT. C<gap/> lgitur minor &longs;it linea <lb/>DS ip&longs;a DT, &longs;iquidem continetur in illa, remanet vt pun<lb/>ctum D circuli maioris, minus. </s>

<s id="N1684B">Etenim po&longs;t præ<lb/>dictam reuolutionem centro I tran&longs;lato in M, ac C in <lb/>L, punctum D erit in linea AM vbi Q, (nempe in loco, <lb/>qui tantum &longs;anè di&longs;ter à puncto M, quantum di&longs;tat extre<lb/>mum D ip&longs;ius &longs;emidiametri DI ab ip&longs;o centro I,) pun<lb/>ctum verò H &longs;imiliter erit in R; ita vt &longs;emidiameter IHD <lb/>reperiatur in <expan abbr="MRq.">MRque</expan> Quapropter &longs;i ex duobus punctis QR <lb/>demittantur duæ perpendiculares in planum DL, quæ &longs;int <lb/>QS, & RT, &longs;patium progre&longs;&longs;ionis ip&longs;ius puncti D, erit <lb/>linea IQ, æqualis ip&longs;i DS: Spatium verò progre&longs;&longs;ionis <lb/>puncti H, erit linea IR, &longs;iue DT. Cum igitur minor &longs;it linea <lb/>DS ip&longs;a DT, &longs;iquidem continetur in illa, remanet vt pun<lb/>ctum D circuli maioris, minus. </s>

<s id="N1686C">dextror&longs;um promoueatur <lb/>quàm punctum H &longs;ibi corre&longs;pondens circuli minoris. </s>

Line 3123

<s id="N1689D">Id ip&longs;um tandem demon&longs;tratur de puncto B, quod cer<lb/>tè magis progreditur quàm F. </s>

<s id="N168A3">Quandoquidem in de&longs;cri<lb/>pta reuolutione &longs;emidiarneter IB con&longs;titueretur in MY in <lb/>qua cum contineatur &longs;emidiameter IF, ip&longs;um F con&longs;titue<lb/>retur in Z: completi&longs;que rectangulis BY, & BZ, erit &longs;pa<lb/>tium dextror&longs;um peragratum à B quantum IY; peragra<lb/>tum verò ab F; quantum IZ contentum in ip&longs;o IY, quod <lb/>propterea maius e&longs;t. </s>

<s id="N168A3">Quandoquidem in de&longs;cri<lb/>pta reuolutione &longs;emidiameter IB con&longs;titueretur in MY in <lb/>qua cum contineatur &longs;emidiameter IF, ip&longs;um F con&longs;titue<lb/>retur in Z: completi&longs;que rectangulis BY, & BZ, erit &longs;pa<lb/>tium dextror&longs;um peragratum à B quantum IY; peragra<lb/>tum verò ab F; quantum IZ contentum in ip&longs;o IY, quod <lb/>propterea maius e&longs;t. </s>

<s id="N168B2">Erunt igitur duo puncta circuli maio<lb/>ris, quæ minus dextror&longs;um progrediuntur, quàm puncta &longs;ibi <lb/>corre&longs;pondentia circuli minoris: alia verò duo quæ magis. <lb/></s>

<s id="N168BA">Quod etiam demon&longs;trari poterit de reliquis punctis eiu&longs;<lb/>dem &longs;emicirculi cum &longs;uo corre&longs;pondenti in vtroque circulo <lb/>&longs;i vterque bifariam &longs;ecetur per diametrum 3, 4, cuius extre<lb/>mitates nempe 3, & 4, in circulo maiori medient inter A, <lb/>& D, ac inter B & C. </s>

<s id="N168C6">Sicut in circulo minori extremita<lb/>tes 5, 6. medient inter E, & H, ac inter F, & G. </s>

Line 3143

<s id="N16945">Quod &longs;i puncta, quæ &longs;unt in arcubus 4 C, & 6 G dex<lb/>tror&longs;um vtraque pariter latione ferantur, &longs;icut reliqua pun<lb/>cta, quæ &longs;unt in &longs;emicirculis ABC, & EFG; & tamen pun<lb/>cta inter 4 C circuli maioris minus progrediantur, quàm <lb/>&longs;ibi corre&longs;pondentia in 6 G circuli minoris; hoc quidem <lb/>fit; nam cum ip&longs;i arcus maximè declinent deor&longs;um, parum <lb/>ambo progrediuntur ad dexteram virtute &longs;uæ circumuolu<lb/>tionis; <expan abbr="multumq.">multumque</expan> virtute motus recti, & a&longs;portantis ad mo<lb/>tum axis. </s>

<s id="N1695C">Cumque ratione &longs;itus, terminus à quo incipit mo<lb/>ueri prædictus arcus circuli minoris, magis di&longs;tet à termino, <pb pagenum="224" xlink:href="005/01/232.jpg"/>à quo incipit moueri arcus maioris, quàm &longs;it exce&longs;&longs;us pto<lb/>gre&longs;&longs;ionis ip&longs;ius arcus maioris ratione termini, ad quem <lb/>po&longs;tea pertingit, &longs;equitur ab&longs;olutè loquendo, magis progre<lb/>di dextror&longs;um prædictum arcum circuli minoris, quàm ar<lb/>cum circuli maioris. </s>

<s id="N1695C">Cumque ratione &longs;itus, terminus à quo incipit mo<lb/>ueri prædictus arcus circuli minoris, magis di&longs;tet à termino, <pb pagenum="224" xlink:href="005/01/232.jpg"/>à quo incipit moueri arcus maioris, quàm &longs;it exce&longs;&longs;us pro<lb/>gre&longs;&longs;ionis ip&longs;ius arcus maioris ratione termini, ad quem <lb/>po&longs;tea pertingit, &longs;equitur ab&longs;olutè loquendo, magis progre<lb/>di dextror&longs;um prædictum arcum circuli minoris, quàm ar<lb/>cum circuli maioris. </s>

<s id="N1696E"><expan abbr="Idemq.">Idemque</expan> è conuer&longs;o applicari pote&longs;t in <lb/>arcubus 3 A, 5 E ad o&longs;tendendum, cur puncta arcus <lb/>3 A circuli maioris, magis progrediantur quàm puncta ar<lb/>cus 5 E circuli minoris. </s>

<s id="N1697A">Nam licet vterque arcus per mo<lb/>tum circularem retrocedat, ac retrocedendo velocius mo<lb/>ueatur arcus maioris, quàm minoris; nihilominus ratione <lb/>&longs;itus, ac termini à quo, <expan abbr="c&utilde;">cum</expan> minor &longs;it exce&longs;&longs;us retroce&longs;&longs;ionis, <lb/>quàm antece&longs;&longs;ionis virtute motus rect, eo quod à remotio<lb/>ri termino arcus maioris promoueatur; hinc pariter fit, vt <lb/>maior &longs;it progre&longs;&longs;us dextror&longs;um maioris, quàm minoris ar<lb/>cus prædicti, &longs;icut & totius &longs;emicirculi 3 AB 4, quàm 5 <lb/>EF 6, vt dicebamus. </s>

<s id="N1697A">Nam licet vterque arcus per mo<lb/>tum circularem retrocedat, ac retrocedendo velocius mo<lb/>ueatur arcus maioris, quàm minoris; nihilominus ratione <lb/>&longs;itus, ac termini à quo, <expan abbr="c&utilde;">cum</expan> minor &longs;it exce&longs;&longs;us retroce&longs;&longs;ionis, <lb/>quàm antece&longs;&longs;ionis virtute motus recti, eo quod à remotio<lb/>ri termino arcus maioris promoueatur; hinc pariter fit, vt <lb/>maior &longs;it progre&longs;&longs;us dextror&longs;um maioris, quàm minoris ar<lb/>cus prædicti, &longs;icut & totius &longs;emicirculi 3 AB 4, quàm 5 <lb/>EF 6, vt dicebamus. </s>

<s id="N16993">Quæ&longs;tio Vige&longs;imaquinta.</s>

<s id="N16998">C<emph type="italics"/>vr lectulorum &longs;pondas &longs;ecundum duplam fa<lb/>ciunt proportionem, hanc quidem &longs;ex pedum, <lb/>vel paulò ampliorem, illam verò trium? </s>

<s id="N169A2">Curvè <lb/>non &longs;ecundum diametcum illos restibus exten<lb/>dunt? </s>

<s id="N169A2">Curvè <lb/>non &longs;ecundum diametrum illos restibus exten<lb/>dunt? </s>

<s id="N169A9">An tantos quidem magnitudine faciunt, <lb/>vt corporibus &longs;int proportionem babentes? <lb/></s>

<s id="N169A9">An tantos quidem magnitudine faciunt, <lb/>vt corporibus &longs;int proportionem habentes? <lb/></s>

<s id="N169AF">fiunt enim &longs;ic &longs;ecundum &longs;pondas dupli, longitudine quidem <lb/>cubitorum, latitudine verò duorum. </s>

<s id="N169B4">Extendunt autem illos <lb/>non &longs;ecundum diametrum, &longs;ed ex oppo&longs;ito, vt & ligna <lb/>minus di&longs;trabantur. </s>

<s id="N169B4">Extendunt autem illos <lb/>non &longs;ecundum diametrum, &longs;ed ex oppo&longs;ito, vt & ligna <lb/>minus di&longs;trahantur. </s>

<s id="N169BB">Celerrimè enim &longs;cinduntur &longs;ecundum na<lb/>turam diui&longs;a, & eodem modo distenta laborant maximè. </s>

<s id="N169C0">Am<lb/>plius quonia n opus e&longs;t, vt re&longs;tes pondus ferre po&longs;sint, &longs;i certè <lb/>pondere impo&longs;ito minus <expan abbr="laborab&utilde;t">laborabunt</expan>, &longs;i tran&longs;uer&longs;im, quàm &longs;i obli<lb/>què extendantur. </s>

<s id="N169C0">Am<lb/>plius quoniam opus e&longs;t, vt re&longs;tes pondus ferre po&longs;sint, &longs;i certè <lb/>pondere impo&longs;ito minus <expan abbr="laborab&utilde;t">laborabunt</expan>, &longs;i tran&longs;uer&longs;im, quàm &longs;i obli<lb/>què extendantur. </s>

<s id="N169CD">Præterea hoc etiam modo minus ab&longs;umitur <lb/>restium. </s>

<s id="N169D2">Sit enim lectulus AFGK, & bifariam diuidatur ip<lb/>&longs;a FG &longs;ecundum B: æqualia certè foramina &longs;unt in ip&longs;a <lb/>FA: latera enim &longs;unt æqualia, nam totum FG duplum est. <lb/></s>

<s id="N169DA">Extendunt autem, vt de&longs;criptum e&longs;t, ab ip&longs;o A ad ip&longs;um B: ita <lb/>vbi e&longs;t C ita e&longs;t D, ita vbi H, po&longs;tea vbi E, & <expan abbr="eod&etilde;">eodem</expan> &longs;emper mo-<emph.end type="italics"/><pb pagenum="225" xlink:href="005/01/233.jpg"/><emph type="italics"/>do, donee ad angulum peruenerint <expan abbr="ali&utilde;">alium</expan>. </s>

<s id="N169DA">Extendunt autem, vt de&longs;criptum e&longs;t, ab ip&longs;o A ad ip&longs;um B: ita <lb/>vbi e&longs;t C ita e&longs;t D, ita vbi H, po&longs;tea vbi E, & <expan abbr="eod&etilde;">eodem</expan> &longs;emper mo-<emph.end type="italics"/><pb pagenum="225" xlink:href="005/01/233.jpg"/><emph type="italics"/>do, donec ad angulum peruenerint <expan abbr="ali&utilde;">alium</expan>. </s>

<s id="N169F0">Duo enim anguli restis <lb/>babent capita: æquales autem &longs;unt re&longs;tes &longs;ecundum curuatu<lb/>ras, videlicet AB, & BC, ip&longs;is CD, & DH: & aliæ &longs;imi<lb/>li &longs;e babent modo, quoniam eadem demon&longs;tratio: ip&longs;a enim <lb/>AB æqualis est ip&longs;i HE, æqualia enim &longs;unt latera &longs;patÿ BG, <lb/>MA, & foramina æquè distant. </s>

<s id="N169F0">Duo enim anguli restis <lb/>habent capita: æquales autem &longs;unt re&longs;tes &longs;ecundum curuatu<lb/>ras, videlicet AB, & BC, ip&longs;is CD, & DH: & aliæ &longs;imi<lb/>li &longs;e habent modo, quoniam eadem demon&longs;tratio: ip&longs;a enim <lb/>AB æqualis est ip&longs;i HE, æqualia enim &longs;unt latera &longs;patij BG, <lb/>MA, & foramina æquè distant. </s>

<s id="N169FD">Ip&longs;a autem BG æqualis e&longs;t <lb/>ip&longs;i MA. </s>

<s id="N16A02">Angulus enim B æqualis e&longs;t angulo G. </s>

<s id="N16A06">In æquali<lb/>bus enim hic quidem intus, ille verò extra, & B quidem est <lb/>&longs;emirectus. </s>

<s id="N16A0D">Est enim FB æqualis ip&longs;i FA. </s>

<s id="N16A10">Et angulus vbi <lb/>F, rectus e&longs;t, B autem angulus æqualis ei, vbi e&longs;t G quo<lb/>niam quadratum altera parte longius, duplum e&longs;t: & ad me<lb/>dium e&longs;t curuatura, quamobrem AD ip&longs;i EG e&longs;t æqualis, bui<gap/><lb/>verò ip&longs;a HM. <expan abbr="Similiq.">Similique</expan> modo demon&longs;trantur aliæ, quoniam <lb/>æquales &longs;unt duæ, quæ &longs;ecundum euruaturas &longs;unt, duabus. <lb/></s>

<s id="N16A10">Et angulus vbi <lb/>F, rectus e&longs;t, B autem angulus æqualis ei, vbi e&longs;t G quo<lb/>niam quadratum altera parte longius, duplum e&longs;t: & ad me<lb/>dium e&longs;t curuatura, quamobrem AD ip&longs;i EG e&longs;t æqualis, huic <lb/>verò ip&longs;a HM. <expan abbr="Similiq.">Similique</expan> modo demon&longs;trantur aliæ, quoniam <lb/>æquales &longs;unt duæ, quæ &longs;ecundum curuaturas &longs;unt, duabus. <lb/></s>

<s id="N16A23">Quare manifestum e&longs;t, quod tot &longs;unt re&longs;tes in lectulo, quot <lb/>&longs;unt quatuor, &longs;icut AB. </s>

<s id="N16A29">Quanta autem foraminum e&longs;t mul<lb/>titudo in ip&longs;o FG laters, & in eius dimidio FB e&longs;t medietas. <lb/></s>

<s id="N16A29">Quanta autem foraminum e&longs;t mul<lb/>titudo in ip&longs;o FG latere, & in eius dimidio FB e&longs;t medietas. <lb/></s>

<s id="N16A2F">Quamobrem in dimidiato lectulo tantæ re&longs;tium magnitudines <lb/>erunt, quantum e&longs;t AB, multitudine verò tot, quot in BG &longs;unt <lb/>foramina. </s>

<s id="N16A36">Hoc autem nihil refert dicere, quàm quot &longs;unt in <lb/>ip&longs;is AF, & BF &longs;imul &longs;umptis. </s>

<s id="N16A3B">Si autem &longs;ecundum diame<lb/>trum extendantur re&longs;tes, quemadmodum &longs;e babet in lectulo <lb/>ABCD: dimidia non tot &longs;unt, quot amborum latera FAFG, <lb/>æqualia autem quot in ip&longs;is FB, FA, &longs;unt foramina. </s>

<s id="N16A3B">Si autem &longs;ecundum diame<lb/>trum extendantur re&longs;tes, quemadmodum &longs;e habet in lectulo <lb/>ABCD: dimidia non tot &longs;unt, quot amborum latera FAFG, <lb/>æqualia autem quot in ip&longs;is FB, FA, &longs;unt foramina. </s>

<s id="N16A44">Maio<lb/>res autem &longs;unt ip&longs;æ AF, BF, duæ exi&longs;tentes, quam AB. </s>

<s id="N16A4A">Qua<lb/>re re&longs;tis in tantùm maior, quantùm ambo latera diametro &longs;unt <lb/>maiora.<emph.end type="italics"/></s>

Line 3185

<s id="N16A7F">Philo&longs;ophus de lectulis minoribus cum qui ad vnum dum<lb/>taxat capiendum hominem cubantem efficiuntur, tum qui <lb/>re&longs;tibus, &longs;eu funibus quibu&longs;dam ad &longs;u&longs;tinendam culcitram <lb/>&longs;uper quam ille iaceat &longs;unt intexti, quemadmodum adhuc <lb/>in Italia licet rarò, frequentius tamen in Gallia, atque Hi&longs;pa<lb/>nia con&longs;piciuntur in v&longs;um traducti. </s>

<s id="N16A8E">Hinc itaque rur&longs;us qu<gap/>rit cur in huiu&longs;modi lectulis mu<lb/>niendis, re&longs;tes per tran&longs;uer&longs;um, & ex oppo&longs;ito, non autem <lb/>per diametrum extendantur. </s>

<s id="N16A8E">Hinc itaque rur&longs;us quaerit cur in huiu&longs;modi lectulis mu<lb/>niendis, re&longs;tes per tran&longs;uer&longs;um, & ex oppo&longs;ito, non autem <lb/>per diametrum extendantur. </s>

<s id="N16A97"><expan abbr="Aitq.">Aitque</expan> triplici ex cau&longs;a id fieri; <lb/>vel pariter in con&longs;uetudinem abij&longs;&longs;e. </s>

<s id="N16A9F">Primò nimirum, vt <lb/>&longs;pondarum ligna ab ip&longs;is re&longs;tibus minus di&longs;trahantur atque <lb/>&longs;cindantur; quandoquidem &longs;ci&longs;&longs;ioni magis obnoxia &longs;unt cum <lb/>per diametrum in eis funes inditi fuerint, ac di&longs;tenti. </s>

<s id="N16AA8">Nam <lb/>tunc qua&longs;i per longum iuxta naturales venulas, ac rimulas, <lb/>quibus ob&longs;equendo facilè &longs;equitur &longs;ci&longs;sio, ligna ip&longs;a vim pa<lb/>terentur, ac veluti &longs;ecarentur; &longs;ecus ac &longs;i per tran&longs;uer&longs;um, <lb/>ac &longs;ecundum latitudinem terebrata &longs;int, funesq per ip&longs;a <lb/>foramina <expan abbr="traducãtur">traducantur</expan>. </s>

<s id="N16AA8">Nam <lb/>tunc qua&longs;i per longum iuxta naturales venulas, ac rimulas, <lb/>quibus ob&longs;equendo facilè &longs;equitur &longs;ci&longs;sio, ligna ip&longs;a vim pa<lb/>terentur, ac veluti &longs;ecarentur; &longs;ecus ac &longs;i per tran&longs;uer&longs;um, <lb/>ac &longs;ecundum latitudinem terebrata &longs;int, <expan abbr="funesq">funesque</expan> per ip&longs;a <lb/>foramina <expan abbr="traducãtur">traducantur</expan>. </s>

<s id="N16AB9">Quia &longs;emper lignorum tramites tran&longs;<lb/>uer&longs;i funium pre<gap/>&longs;&longs;ioni magis re&longs;i&longs;tunt. </s>

<s id="N16AB9">Quia &longs;emper lignorum tramites tran&longs;<lb/>uer&longs;i funium pre&longs;&longs;ioni magis re&longs;i&longs;tunt. </s>

<s id="N16AC2">Secundo id fieri docet ex eo quod &longs;ic funes traducti, mi<lb/>nus laborant, pondus &longs;uperimpo&longs;itum &longs;u&longs;tinendo. </s>

Line 3198

<s id="N16AD8">Tertio denique id ip&longs;um iccirco v&longs;ui e&longs;&longs;e inquit, vt in ip<lb/>&longs;a lectulorum textura minus re&longs;tium, &longs;eu funium ab&longs;umatur. <lb/></s>

<s id="N16ADE">Quod licet implexè admodum videatur probare ob textus <lb/>corruptionem; Satis tamen &longs;en&longs;us probationis tenctur, at<lb/>que optimè à Piccolomineo dilucidatur. </s>

<s id="N16ADE">Quod licet implexè admodum videatur probare ob textus <lb/>corruptionem; Satis tamen &longs;en&longs;us probationis tenetur, at<lb/>que optimè à Piccolomineo dilucidatur. </s>

<s id="N16AE7">Summatim verò ad hoc, vt clarius probatio ip&longs;a perci<lb/>piatur, &longs;upponimus primò cum ip&longs;o Ari&longs;torele, quod lectu<lb/>lus &longs;uis re&longs;tibus per tran&longs;uer&longs;um intextus exempli gratia <pb pagenum="227" xlink:href="005/01/235.jpg"/><figure id="id.005.01.235.1.jpg" xlink:href="005/01/235/1.jpg"/><lb/>&longs;it <expan abbr="rectãgul&utilde;">rectangulum</expan> IGAO, <lb/><expan abbr="eiusq.">eiusque</expan> <expan abbr="lõgiores">longiores</expan> <expan abbr="&longs;põ-dæ">&longs;pon<lb/>dæ</expan>, nempe &longs;ex <expan abbr="ped&utilde;">pedum</expan> <lb/>&longs;int IG, & AO; bre<lb/>uiores verò <expan abbr="tri&utilde;">trium</expan> pe<lb/>dum IA, & GO, &longs;in<lb/>gulæ in totidem pe<lb/>des diui&longs;æ per &longs;ua <lb/>foramina, quibus re<lb/>&longs;tes indantur, prout <lb/>hic litteris con&longs;ignantur. </s>

<s id="N16AE7">Summatim verò ad hoc, vt clarius probatio ip&longs;a perci<lb/>piatur, &longs;upponimus primò cum ip&longs;o Ari&longs;totele, quod lectu<lb/>lus &longs;uis re&longs;tibus per tran&longs;uer&longs;um intextus exempli gratia <pb pagenum="227" xlink:href="005/01/235.jpg"/><figure id="id.005.01.235.1.jpg" xlink:href="005/01/235/1.jpg"/><lb/>&longs;it <expan abbr="rectãgul&utilde;">rectangulum</expan> IGAO, <lb/><expan abbr="eiusq.">eiusque</expan> <expan abbr="lõgiores">longiores</expan> <expan abbr="&longs;põ-dæ">&longs;pon<lb/>dæ</expan>, nempe &longs;ex <expan abbr="ped&utilde;">pedum</expan> <lb/>&longs;int IG, & AO; bre<lb/>uiores verò <expan abbr="tri&utilde;">trium</expan> pe<lb/>dum IA, & GO, &longs;in<lb/>gulæ in totidem pe<lb/>des diui&longs;æ per &longs;ua <lb/>foramina, quibus re<lb/>&longs;tes indantur, prout <lb/>hic litteris con&longs;ignantur. </s>

<s id="N16B24">Deinde &longs;upponimus ex eodem, <lb/>hoc pacto re&longs;tes ip&longs;os per tran&longs;uer&longs;um extendi. </s>

<s id="N16B29">Sumitur ini<lb/>tium re&longs;tis, & obfirmatur in A, tunc re&longs;tis ip&longs;a ducitur ad B, <lb/>ex quo po&longs;tea per C flectitur in D; hinc per E ad F; exinde <lb/>verò per G ad H: ex H autem rur&longs;us ducitur in I, & ex I per <lb/>K in L; vnde per M ad N; & ex N per B, <expan abbr="tand&etilde;">tandem</expan> peruenitur <lb/>in O; vbi &longs;imiliter <expan abbr="alter&utilde;">alterum</expan> re&longs;tis caput de&longs;inendo obfirmatur. </s>

Line 3223

<s id="N16BBD">Quæ&longs;tio Vige&longs;ima&longs;exta.</s>

<s id="N16BC2">C<emph type="italics"/>vr diffi ilius e&longs;t longa ligna ab extremo &longs;upe<gap/><lb/>humeros ferre, quàm &longs;ecundum medium, <lb/>æquali existente pondere? </s>

<s id="N16BC2">C<emph type="italics"/>vr difficilius e&longs;t longa ligna ab extremo &longs;uper <lb/>humeros ferre, quàm &longs;ecundum medium, <lb/>æquali existente pondere? </s>

<s id="N16BCD">An quia vibrato li<lb/>gno ip&longs;um extremum prohibet ferre, vibratio<lb/>ne magis retrahens lationem? </s>

<s id="N16BD4">An quoniam li<lb/>cet nihil inflectatur, neque multam habeat lon<lb/>gitudinem, difficilius tamen ad ferendum e&longs;t <lb/><gap/> extremo, quoniam facilius ex medio eleuatur, quàm ab ex<lb/>tremo, & ideo &longs;ic ferre e&longs;l facilius. </s>

<s id="N16BE0">Cau&longs;a autem quoniam <lb/>&longs;ecundum medium quidem eleuato ligno &longs;emper &longs;e&longs;e inuicem <lb/>&longs;u&longs;pendunt extrema, & altera pars alteram bene &longs;ubleuat. <lb/></s>

<s id="N16BE8">Medium enim veluti centrum fit, vbi babet is qui eleuat, <lb/>aut fert. </s>

<s id="N16BE8">Medium enim veluti centrum fit, vbi habet is qui eleuat, <lb/>aut fert. </s>

<s id="N16BED">Extremorum igitur vtrumque deor&longs;um vergens, <lb/>&longs;ur&longs;um &longs;u&longs;penditur. </s>

<s id="N16BF2">Quod &longs;i ab extremo eleuetur, aut fe<lb/>ratur, non &longs;anè facit: &longs;ed vniuer&longs;um pondus ad vnum ver<lb/>git medium, quo eleuatur, aut fertur. </s>

<s id="N16BF9">Sit medium vbi A, <lb/>extrema B, C. </s>

<s id="N16BFF">Eleuato igitur aut portato &longs;ecundum A,<emph.end type="italics"/><pb pagenum="229" xlink:href="005/01/237.jpg"/><emph type="italics"/>ip&longs;um quidem B deor&longs;um nutans, &longs;ur&longs;um eleuat C, ip&longs;um au<lb/>tem C aeor&longs;um nutans, B &longs;ur&longs;um eleuat, ambo autem &longs;ur&longs;um <lb/>eleuata hoc faciunt.<emph.end type="italics"/></s>

<s id="N16BFF">Eleuato igitur aut portato &longs;ecundum A,<emph.end type="italics"/><pb pagenum="229" xlink:href="005/01/237.jpg"/><emph type="italics"/>ip&longs;um quidem B deor&longs;um nutans, &longs;ur&longs;um eleuat C, ip&longs;um au<lb/>tem C deor&longs;um nutans, B &longs;ur&longs;um eleuat, ambo autem &longs;ur&longs;um <lb/>eleuata hoc faciunt.<emph.end type="italics"/></s>

<s id="N16C13">COMMENTARIVS.</s>

<s id="N16C19">Dvplicem Ari&longs;totel<gap/>cau&longs;am affert, ob <expan abbr="quã">quam</expan> difficilius <lb/>procera ligna ab extremo &longs;uper <expan abbr="humer&utilde;">humerum</expan> ge&longs;tantur, <lb/>quàm è medio, æquali exi&longs;tente pondere, à quo to<lb/>ta ge&longs;tandi difficultas na&longs;ci videretur. </s>

<s id="N16C19">Dvplicem Ari&longs;toteles<gap/>cau&longs;am affert, ob <expan abbr="quã">quam</expan> difficilius <lb/>procera ligna ab extremo &longs;uper <expan abbr="humer&utilde;">humerum</expan> ge&longs;tantur, <lb/>quàm è medio, æquali exi&longs;tente pondere, à quo to<lb/>ta ge&longs;tandi difficultas na&longs;ci videretur. </s>

<s id="N16C2C">Vna e&longs;t, quia procera <lb/>ligna, vt plurimùm ex &longs;e flexibiliora &longs;unt, ac vibrationi, & flu<lb/>ctuationi magis obnoxia, quàm breuiora. </s>

<s id="N16C33">Quapropter &longs;i to<lb/>ta ferè longitudo ligni &longs;uper humerum ge&longs;tati, à tergo po<lb/>natur, parte tantum ante relicta qua manu &longs;u&longs;tineatur, cre<lb/>&longs;cit cum ip&longs;a longitudine flexibilitas: vnde magis agitatio<lb/>ne ip&longs;a portantis fluctuando vibratur: vibratio autem non <lb/>parum ge&longs;tationem impedit, retrahendo quodammodo la<lb/>tionem, dum frequenti&longs;&longs;imo motu &longs;ur&longs;um, ac deor&longs;um vi<lb/>brati ligni extremitas tendit, <expan abbr="proindeq.">proindeque</expan> non ad partes ante<lb/>riores, iuxta motum progre&longs;&longs;iuum ferentis. </s>

<s id="N16C4A">De quo vibra<lb/>tionis effectu iterum redibit &longs;ermo quæ&longs;tione &longs;equenti vbi <lb/>fu&longs;iùs, ac luculentiùs declarabitur. </s>

<s id="N16C51">Interim concluditur ex <lb/>Ari&longs;totele, propter maiorem huiu&longs;modi fluctuationem, ac <lb/>vibrationem difficilius procera ligna ab extremo &longs;uper hu<lb/>merum ge&longs;tari, quàm &longs;i è medio &longs;u&longs;tinerentur, atque a&longs;por<lb/>tarentur, cum hoc pacto, minus ab humero, feu fulcimen<lb/>to producta, minus vibrationi e&longs;&longs;ent obnoxia. </s>

<s id="N16C51">Interim concluditur ex <lb/>Ari&longs;totele, propter maiorem huiu&longs;modi fluctuationem, ac <lb/>vibrationem difficilius procera ligna ab extremo &longs;uper hu<lb/>merum ge&longs;tari, quàm &longs;i è medio &longs;u&longs;tinerentur, atque a&longs;por<lb/>tarentur, cum hoc pacto, minus ab humero, seu fulcimen<lb/>to producta, minus vibrationi e&longs;&longs;ent obnoxia. </s>

<s id="N16C60">Quoniam verò cau&longs;a hæc vniuer&longs;alis non e&longs;t, nec adæ<lb/>quata, &longs;iquidem nec omnia ligna quantumuis procera fle<lb/>xibilia &longs;unt, aut vibrari po&longs;&longs;unt; nec difficultas ge&longs;tationis <lb/>à &longs;ola vibratione <expan abbr="interced&etilde;te">intercedente</expan> procedit; hinc e&longs;t, quod Ari&longs;to<lb/>teles alteram propo&longs;itæ difficultatis cau&longs;am, tanquam vni<lb/>uer&longs;aliorem in medium afferat. </s>

<s id="N16C71">Ea autem e&longs;t, quia quæ<lb/>cumque difficilius eleuantur, difficilius pariter po&longs;tquam <lb/>eleuata fuerint &longs;u&longs;tinentur, aut ge&longs;tantur, cum tàm latio, <lb/>quàm &longs;u&longs;tentatio &longs;it veluti continuata quædam eleuatio ob <pb pagenum="230" xlink:href="005/01/238.jpg"/>longa autem ligna difficilius ab extremo eleuantur, quam <lb/>ex medio, &longs;iquidem eleuato ligno ab eius medio &longs;emper <lb/>&longs;e&longs;e inuicem &longs;u&longs;tentant extrema, & altera pars alteram &longs;ub<lb/>leuat, ait ip&longs;e <gap/>hilo&longs;cphus. </s>

<s id="N16C87">Medium enim qua&longs;i centrum <lb/>con&longs;tituitur, quod fulcitur in manu eleuantis, aut in humero <lb/>deferentis. </s>

<s id="N16C8E">Quapropter ad depre&longs;sionem alterius extremi, <lb/>alterum eleuatur, & &longs;ic vici&longs;sim mutuo &longs;u&longs;tolluntur. </s>

<s id="N16C93">At &longs;i <lb/>ab extremo idem lignum eleuetur, vel deferatur, vniuer&longs;o <lb/>pondere deor&longs;um vergente, nulla e&longs;&longs;et pars, quæ ad graui<lb/>tationem alterius eleuatetur, proindeque laborio&longs;a magis <lb/>e&longs;&longs;et ge&longs;tatio. </s>

<s id="N16CA0">Verùm contra huiu&longs;modi di&longs;cur&longs;um, ac doctrinam Ari<lb/>&longs;totelis illud obijci po&longs;&longs;et, quod tamet&longs;i extrema proceri <lb/>ligni è puncto medio delati &longs;e&longs;e inuicem &longs;u&longs;tollant vtrum <lb/>libet alterum &longs;uperando: nihilominus ip&longs;a &longs;imul &longs;umpta <lb/>cum toto ligno &longs;emper eodem modo grauitant re&longs;pectu <lb/>deferentis, &longs;iue in &etail;quilibrio, &longs;iue &longs;ecus con&longs;tituantur. </s>

<s id="N16CAD">Quan<lb/>doquidem deferens tam excedens, quàm exce&longs;&longs;um &longs;u&longs;ti<lb/>net, ac defert: proindeq pondus ip&longs;ius ligni, non minus gra<lb/>uitare concluditur cum lignum ip&longs;um è medio &longs;u&longs;tollitur, ac <lb/>cum ab extremo. </s>

<s id="N16CAD">Quan<lb/>doquidem deferens tam excedens, quàm exce&longs;&longs;um &longs;u&longs;ti<lb/>net, ac defert: <expan abbr="proindeq">proindeque</expan> pondus ip&longs;ius ligni, non minus gra<lb/>uitare concluditur cum lignum ip&longs;um è medio &longs;u&longs;tollitur, ac <lb/>cum ab extremo. </s>

<s id="N16CBA">Huic tamen obiectioni occurritur di&longs;tinguendo grauita<lb/>tionem procedentem ab ip&longs;o pondere ligni delati &longs;ecun<lb/>dum &longs;e &longs;umpto ab ea, quæ procedit ratione di&longs;tantiæ à ful<lb/>cimento quò &longs;u&longs;tinetur. </s>

Line 3263

<s id="N16CE1">Quandoquidem hæc augetur ad <lb/>augmentum di&longs;tantiæ, ac minuitur per approximationem; <lb/>imò omninò deperditur per <expan abbr="æquilibration&etilde;">æquilibrationem</expan>. </s>

<s id="N16CEC">Porrò brachia <pb pagenum="231" xlink:href="005/01/239.jpg"/>libræ, &longs;iue magis &longs;iue minus protendantur, dummodo &etail;qua<lb/>lia inter &longs;e &longs;int, nihil ponderis, aut grauitationis augent, vel <lb/>minuunt; &longs;ecus autem &longs;i alterum &longs;it protentius, licet æqualis <lb/>ponderis naturalis. </s>

<s id="N16CFA">Nam libram vertet per exce&longs;&longs;um &longs;uæ <lb/>di&longs;tantiæ à fulcimento, vt &longs;upra quæ&longs;t. </s>

<s id="N16CFF">prima explic uimus. </s>

<s id="N16CFF">prima explicauimus. </s>

<s id="N16D04">Rectè igitur argumentatur Philo&longs;ophus, dum ex mutua <lb/>victoria, ac &longs;ubleuatione extremorum ligni in medio fulti, <lb/>minorem difficultatem, &longs;eu grauitationem infert, quàm &longs;i <lb/>ab extremo &longs;u&longs;tolleretur, ac in &longs;itu &longs;imili &longs;u&longs;tentaretur per <lb/>lineam horizonti paralellam, &longs;eu qua&longs;i paralellam. </s>

Line 3282

<s id="N16D5D">C<emph type="italics"/>vr &longs;i valde procerum fuerit idem pondus, dif<lb/>ficilius &longs;uper humeros gestatur, etiam&longs;i me<lb/>dium qui&longs;piam illud ferat, quàm &longs;i breuius <lb/>&longs;it? </s>

<s id="N16D69">Quod enim dudum dictum e&longs;t, cau&longs;a non <lb/>e&longs;t, &longs;ed vibratio nunc est cau&longs;a. </s>

<s id="N16D6E">Quando enim <lb/>productius fuerit, vibrantur extrema, quam<lb/>obrem contingit portantem difficilius ge&longs;tare. </s>

<s id="N16D75">Vibrationis au<lb/>tem cau&longs;a e&longs;t, quoniam ab eadem motione magis transferuntur <lb/>extrema; quanto proceriu<gap/> fuerit lignum. </s>

<s id="N16D75">Vibrationis au<lb/>tem cau&longs;a e&longs;t, quoniam ab eadem motione magis transferuntur <lb/>extrema; quanto procerius fuerit lignum. </s>

<s id="N16D7E">Humerus quidem <lb/>&longs;it centrum vbi A manet enim is; ip&longs;æ autem A B, A C, quæ <lb/>&longs;unt ex centro, quantò autem maius fuerit id, quod ex centro <lb/>e&longs;t, &longs;iuè A B, &longs;eu A C, plus transfertur &longs;patÿ. </s>

<s id="N16D87">Demon&longs;tratum <lb/>autem e&longs;t boc prius.<emph.end type="italics"/></s>

<s id="N16D87">Demon&longs;tratum <lb/>autem e&longs;t hoc prius.<emph.end type="italics"/></s>

<s id="N16D90">COMMENTARIVS.</s>

Line 3293

<s id="N16D96">Qvamuis idemmet lignum, vel aliud graue corpus <lb/>oblongum facilius ex medio &longs;u&longs;tineatur, ac defera<lb/>tur, quam ab extremo, vt in præcedenti quæ&longs;t. </s>

<s id="N16D9D">di<lb/>ctum e&longs;t: nihilominus cum hoc etiam pacto delatum, quò <lb/>procerius illud fuerit, eò difficilius ge&longs;tetur, quærit hic Ari<lb/>&longs;toteles vnde maior hæc difficultas oriatur. </s>

<s id="N16DA6">Concluditque, <lb/>vibrationem huius rei cau&longs;am e&longs;&longs;e. </s>

<s id="N16DAB">Nam quanto produ<lb/>ctius fuerit lignum, tantò imbecillius redditur, ac vibrationi <lb/>obnoxius: magis enim in&longs;lectitur, vt quæ&longs;t. </s>

<s id="N16DAB">Nam quanto produ<lb/>ctius fuerit lignum, tantò imbecillius redditur, ac vibrationi <lb/>obnoxius: magis enim inflectitur, vt quæ&longs;t. </s>

<s id="N16DB2">16. probatum <lb/>e&longs;t magi&longs;que eius extrema iactantur tanquam à centro re<lb/>motiora. </s>

<s id="N16DB9">Magis autem iactatis, ac vibratis extremis, diffi<lb/>cilior euadit ge&longs;tatio; Idque duplici ex capite, vt rectè Bal<lb/>dus ob&longs;eruat. </s>

<s id="N16DC0">Tum &longs;cilicet quia motus vibrationis, vt præ<lb/>cedenti quæ&longs;t. </s>

<s id="N16DC5">docuerat Ari&longs;toteles, morum progre&longs;sionis, <lb/>&longs;ur&longs;um ac deor&longs;um tendendo impedit, ac quod ammodo <lb/>prohibet, retrahendo ip&longs;um delatum, quod in anteriora fer<lb/>tur: tum etiam quia impetum quendam producit quo vltra <pb pagenum="233" xlink:href="005/01/241.jpg"/><expan abbr="põdus">pondus</expan> grauatus humerus <expan abbr="defer&etilde;tis">deferentis</expan>. </s>

<s id="N16DDA">Etenim extrema ip&longs;ius <lb/>ligni valde ab eius medio, &longs;eu centro remota, dum inferius, <lb/>quantum ex &longs;e e&longs;t, vibrando flectuntur ip&longs;ummet centrum, <lb/>&longs;eu medium &longs;ecum rapere, ac detrahere conantur. </s>

<s id="N16DE3">Quam<lb/>obrem humerus, qui medio &longs;upponitur, non modo totius li<lb/>gni &longs;u&longs;tinet pondus, quod in ip&longs;o grauitatis centro coacer<lb/>uatur, &longs;ed impetum quoque per eandem extremorum in<lb/>flexionem ei illatum. </s>

<s id="N16DEE">Tamet&longs;i hoc totum intelligatur non <lb/>iugiter, &longs;ed per interualla tantum contingere, vt idem Bal<lb/>dus animaduertit; Quandoquidem impetus ex ip&longs;o motu <lb/>vibrationis acqui&longs;itus quemadmodum deor&longs;um tendendo <lb/>deprimit, ita &longs;ur&longs;um attollens ip&longs;a extrema, portantem alle<lb/>uiat, humerumq aliquanti&longs;per nonnihil exonerat, vt milites <lb/>&longs;ari&longs;&longs;am in humero ge&longs;tantes pa&longs;sim experiuntur. </s>

<s id="N16DEE">Tamet&longs;i hoc totum intelligatur non <lb/>iugiter, &longs;ed per interualla tantum contingere, vt idem Bal<lb/>dus animaduertit; Quandoquidem impetus ex ip&longs;o motu <lb/>vibrationis acqui&longs;itus quemadmodum deor&longs;um tendendo <lb/>deprimit, ita &longs;ur&longs;um attollens ip&longs;a extrema, portantem alle<lb/>uiat, humerumque aliquanti&longs;per nonnihil exonerat, vt milites <lb/>&longs;ari&longs;&longs;am in humero ge&longs;tantes pa&longs;sim experiuntur. </s>

<s id="N16DFF">Quæ&longs;tio Vige&longs;imaoctaua.</s>

Line 3311

<s id="N16E13">An quo<lb/>niam duobus temporibus hauriendi diui&longs;o ope<lb/>re (intingere enim oportet, & id &longs;ur&longs;um <lb/>trahere) continget demittere quidem vacuum faciliter, <lb/>trahere verò plenum difficulter. </s>

<s id="N16E1E">Commodum igitur est pau<lb/>lò tardius illud demittere, cùm multò leuiùs effectum &longs;u&longs;tol<lb/>latur pondus: id autem facit in extremo celonio adiunctum: <lb/>plumbum, aut lapis. </s>

<s id="N16E27">Demittendi quidem maius &longs;it pon<lb/>dus, quàm &longs;i &longs;olummodò vacuum oporteret demittere: <lb/>cùm verò plenum fuerit &longs;ur&longs;um id rapii plumbum, aut quic<lb/>quid illi ponderis inerit. </s>

<s id="N16E30">Quamobrem faciliora boc modo <lb/>ambo &longs;unt, quàm illo.<emph.end type="italics"/></s>

<s id="N16E30">Quamobrem faciliora hoc modo <lb/>ambo &longs;unt, quàm illo.<emph.end type="italics"/></s>

Line 3328

<s id="N16EA2">His itaque non aliter &longs;e habentibus, quærit hic Ari&longs;tote<lb/>les, cur ad huiu&longs;modi machinam facilius promouendam, & <lb/>& aquam eius motione exhauriendam, onus oneri adiunga<lb/>tur, plumbum nimirum, aut lapidem apponendo in alte<lb/>ro extremo tran&longs;uer&longs;arij ligni, cum alioquin tota ip&longs;a ma<lb/>china &longs;it per &longs;e grauis, ac præ&longs;ertim idemmet tran&longs;uer<lb/>&longs;arium lignum, quod adhuc prægrauatur pondere va&longs;is ap<lb/>pen&longs;i, &longs;iue vacui, &longs;iue repleti. </s>

<s id="N16EB3">Difficilius namque e&longs;t mo<lb/>uere machinam grauiorem, quàm leuiorem. </s>

<s id="N16EB8">Quamob<lb/>rem &longs;it in de&longs;cripta Tellenonis figura A B C D tignum <pb pagenum="235" xlink:href="005/01/243.jpg"/>arrectarium &longs;uper <lb/><figure id="id.005.01.243.1.jpg" xlink:href="005/01/243/1.jpg"/><lb/>planum <expan abbr="erect&utilde;">erectum</expan> AB: <lb/>tran&longs;uer&longs;arium ve<lb/>rò CD; ac funis <lb/>propendens DE, <lb/>in cuius ima extre<lb/>mitate vbi E, alli<lb/>gata &longs;it vrna, vel &longs;i<lb/>tula, aut &longs;imile <lb/>aliud vas <expan abbr="aquari&utilde;">aquarium</expan>: <lb/><expan abbr="Puteusq.">Puteusque</expan> &longs;ubiectus, <lb/>&longs;it vbi F. </s>

<s id="N16EEA">Tunc in<lb/>quam &longs;i in extremo <lb/>C tran&longs;uer&longs;arij li<lb/>gni adiungatur <expan abbr="põ-dus">pon<lb/>dus</expan> lapidis, aut <expan abbr="pl&utilde;-bi">plun<lb/>bi</expan>, vt in figura refertur, manus funi admota ad demittendum <lb/>vas aquarium, difficilius deprimet extremum D, vnde fu<lb/>nis ip&longs;e propendet, cum vltra propriam grauitatem ligni <lb/>AC, &longs;uperare, ac eleuare etiam debeat pondus illi adiun<lb/>ctum. </s>

<s id="N16EEA">Tunc in<lb/>quam &longs;i in extremo <lb/>C tran&longs;uer&longs;arij li<lb/>gni adiungatur <expan abbr="põ-dus">pon<lb/>dus</expan> lapidis, aut <expan abbr="pl&utilde;-bi">plum<lb/>bi</expan>, vt in figura refertur, manus funi admota ad demittendum <lb/>vas aquarium, difficilius deprimet extremum D, vnde fu<lb/>nis ip&longs;e propendet, cum vltra propriam grauitatem ligni <lb/>AC, &longs;uperare, ac eleuare etiam debeat pondus illi adiun<lb/>ctum. </s>

<s id="N16F07">Quare ex huiu&longs;modi ponderis additione, potius vi<lb/>detur, motionem ip&longs;am explicatæ machinæ retardari, quàm <lb/>facilius con&longs;equi, & expediri. </s>

Line 3350

<s id="N16FA3">C<emph type="italics"/>vr quando &longs;uper ligno, aut huiu&longs;modi quo<lb/>piam duo portauerint homines æquale pondus <lb/>non &longs;imiliter præmuntur, &longs;i ad vnum non de<lb/>clinet pondus, &longs;ed magis quanti vicinius fue<lb/>rit gestantibus? </s>

<s id="N16FB1">An quoniam vectis quidem <lb/>lignum efficitur: pondus verò hypomochlion: <lb/>qui autem propior e&longs;t ponderi ex ÿs, qui illud ge&longs;tant, id qua<lb/>re mouetur: alter vero portantium, quod mouet? </s>

<s id="N16FB1">An quoniam vectis quidem <lb/>lignum efficitur: pondus verò hypomochlion: <lb/>qui autem propior e&longs;t ponderi ex ijs, qui illud ge&longs;tant, id qua<lb/>re mouetur: alter vero portantium, quod mouet? </s>

<s id="N16FBA">Quantò igitur <lb/>plus di&longs;tat à pondere, tanto facilius mouet, & alterum premit <lb/>magis inferius, velut contranitente pondere impo&longs;ito quod hy<lb/>pomochlion factum e&longs;t, &longs;i autem in medio inerit pondus, nihilo <lb/>magis alter alteri fit pondus, aut mouet: &longs;ed eodem modo alteri <lb/>alter fit pondus.<emph.end type="italics"/></s>

Line 3360

<s id="N16FD1">Cau&longs;am hic inquirit Ari&longs;toteles cur duo baiuli idem <lb/>pondus &longs;uper lignum, vel quidpiam aliud &longs;imile fe<lb/>rentes, <expan abbr="nõ">non</expan> æquè grauentur, atque <expan abbr="pr&etail;mãtur">pr&etail;mantur</expan> &longs;i in <expan abbr="eo-r&utilde;">eo<lb/>rum</expan> medio <expan abbr="nõ">non</expan> extiterit ip&longs;um pondus, &longs;ed magis præmatur is, <lb/>cui ip&longs;um proximius con&longs;tituitur. </s>

<s id="N16FEC"><expan abbr="Eamq.">Eamque</expan> mox e&longs;&longs;e ait, quo<lb/>niam huiu&longs;modi lignum in ip&longs;a a&longs;portatione efficitur vectis, <lb/>cuius fulcimentum con&longs;tituitur ip&longs;ummet pondus quod ge<lb/>&longs;tatur: Onus verò baiulus, qui ponderi e&longs;t propinquior, ac <lb/>veluti potentia mouens, baiulus, qui e&longs;t ab illo remotior. <lb/></s>

<s id="N16FFB">Etenim cum onus quodlibet, vecte adhibito, tanto facilius <lb/>moueatur, quanto proximius fuerit centro, &longs;eu fulcimen<lb/>to locatum, ac motrix potentia remotius fuerit applicata, <lb/>vt &longs;upra o&longs;ten&longs;um e&longs;t quæ&longs;t. </s>

<s id="N17004">3. hinc fit, vt baiulus, qui one<lb/>tis loco &longs;uccedit, hoc ip&longs;o, quod pr<gap/>pinquius centro con<lb/>&longs;tituitur, quàm alter qui potentiæ vices obtinet, magis <lb/>præmatur, contranitente pondere impo&longs;ito, tanquam fulci<lb/>mento validè obfirmato, cui vectis innititur in ip&longs;o motu. <pb pagenum="238" xlink:href="005/01/246.jpg"/><figure id="id.005.01.246.1.jpg" xlink:href="005/01/246/1.jpg"/><lb/>Quod vt præ ocu<lb/>lis habeatur e&longs;to <lb/>lignum AB, pon<lb/>dus C appen&longs;um <lb/>in D proximius <lb/>ip&longs;i A; baiulorum <lb/>verò alter hume<lb/>rum, vel manum <lb/>&longs;upponat in A; al<lb/>ter in B. </s>

<s id="N17004">3. hinc fit, vt baiulus, qui one<lb/>ris loco &longs;uccedit, hoc ip&longs;o, quod propinquius centro con<lb/>&longs;tituitur, quàm alter qui potentiæ vices obtinet, magis <lb/>præmatur, contra nitente pondere impo&longs;ito, tanquam fulci<lb/>mento validè obfirmato, cui vectis innititur in ip&longs;o motu. <pb pagenum="238" xlink:href="005/01/246.jpg"/><figure id="id.005.01.246.1.jpg" xlink:href="005/01/246/1.jpg"/><lb/>Quod vt præ ocu<lb/>lis habeatur e&longs;to <lb/>lignum AB, pon<lb/>dus C appen&longs;um <lb/>in D proximius <lb/>ip&longs;i A; baiulorum <lb/>verò alter hume<lb/>rum, vel manum <lb/>&longs;upponat in A; al<lb/>ter in B. </s>

<s id="N1702E">Dicimus ergo cum Ari&longs;totele, lignum ip&longs;um AB, <lb/>vectem con&longs;titui &longs;uffultum in D, tanquam fulcimento in<lb/>uer&longs;o ad deprimendum humerum a&longs;portantis in A, per mo<lb/>tum a&longs;portantis in B, qui baiulando, &longs;emper eleuare cona<lb/>tur extremitatem &longs;ibi incumbentem in B. </s>

<s id="N17039">Quandoquidem <lb/>punctum D, quod con&longs;tituitur centrum in motione ip&longs;ius <lb/>vectis, ita à pendente pondere præmitur, & figitur, ac &longs;i im<lb/>mobile omnino e&longs;&longs;et ad fulciendum ip&longs;um vectem. </s>

<s id="N17042">Quod <lb/>ueidentius fiet &longs;i eundem vectem inuer&longs;o modo con&longs;idere<lb/><figure id="id.005.01.246.2.jpg" xlink:href="005/01/246/2.jpg"/><lb/>mus, in &longs;equenti fi<lb/>gura; Nimirum vt <lb/>&longs;i vectis A B &longs;u<lb/>&longs;pendatur in C ex <lb/>puncto intermedio <lb/>vbi D, ad eleuan<lb/>dum onus impo<lb/>&longs;itum in extremo A <lb/>per depre&longs;sionem alterius extremi B. </s>

<s id="N17042">Quod <lb/>euidentius fiet &longs;i eundem vectem inuer&longs;o modo con&longs;idere<lb/><figure id="id.005.01.246.2.jpg" xlink:href="005/01/246/2.jpg"/><lb/>mus, in &longs;equenti fi<lb/>gura; Nimirum vt <lb/>&longs;i vectis A B &longs;u<lb/>&longs;pendatur in C ex <lb/>puncto intermedio <lb/>vbi D, ad eleuan<lb/>dum onus impo<lb/>&longs;itum in extremo A <lb/>per depre&longs;sionem alterius extremi B. </s>

<s id="N1705F">His namque po<lb/>&longs;itis ad primam figuram redeuntes facilè intelligitur cur <lb/>baiulus ge&longs;tans in A magis grauetur à pondere C, <lb/>quàm ge&longs;tans in B. </s>

<s id="N17068">Quanto enim longior e&longs;t pars vectis <lb/>DB, ip&longs;a DA, eo facilius ge&longs;tans in B eleuat, vel &longs;u&longs;ti<lb/>net ip&longs;um extremum B re&longs;pectu &longs;u&longs;tinentis in A tanquam <lb/>in loco centro vectis propinquiori quàm &longs;it ip&longs;um B. </s>

<s id="N17073">Quod autem cum Ari&longs;totele explicuimus per rationem <lb/>vnius vectis, Piccolomineus explicat per rationem duplicis <pb pagenum="239" xlink:href="005/01/247.jpg"/>vectis, ita vt idem lignum AB rationem &longs;ubeat vtriu&longs;que <lb/>vectis, vnius nempe per quem ge&longs;tans in A prematur ad <lb/>motum ge&longs;tantis in B: alterius verò per quem ge&longs;tans in <lb/>B, prematur ad motum ge&longs;tantis in A, eodem &longs;emper exi<lb/>&longs;tente fulcimento D. </s>

<s id="N17086">Siquidem ambo ge&longs;tantes eleuare <lb/>conantur &longs;ua extrema, & ambo deprimuntur adinuicem, <lb/>ita vt alter alteri con&longs;tituatur onus, ac mouens potentia; li<lb/>cetille magis moueat, minu&longs;que grauetur, qui longius di&longs;tat <lb/>à fulcimento. </s>

<s id="N17091">Quæ profectò explicatio à mente Ari&longs;totelisc <lb/>tradita doctrina non abhorret, imò maximè congruit cum <lb/>co, quod ip&longs;emet Philo&longs;ophus tandem adiecit: Nimirum <lb/>quòd &longs;i pondus in medio vectis con&longs;titueretur, non magis <lb/>vnus, quam alter baiulus grauaretur; atque moueret; &longs;ed <lb/>eodem pacto alter alteri e&longs;&longs;et onus, & potentia. </s>

<s id="N17091">Quæ profectò explicatio à mente Ari&longs;totelise <lb/>tradita doctrina non abhorret, imò maximè congruit cum <lb/>eo, quod ip&longs;emet Philo&longs;ophus tandem adiecit: Nimirum <lb/>quòd &longs;i pondus in medio vectis con&longs;titueretur, non magis <lb/>vnus, quam alter baiulus grauaretur; atque moueret; &longs;ed <lb/>eodem pacto alter alteri e&longs;&longs;et onus, & potentia. </s>

<s id="N170A0">Baldus verò eandem Piccolominei expo&longs;itionem appro<lb/>bando doctrinam Ari&longs;totelis à qua illa de&longs;umpta e&longs;t, & cui <lb/>omnino congruit, reprobat, rationem fulcimenti in ip&longs;o <lb/>pondere con&longs;ideratam, <expan abbr="figment&utilde;">figmentum</expan> vocans Ari&longs;totelis. </s>

Line 3383

<s id="N170DF">Nihil enim pro<lb/>hibet idem lignum &longs;ecundum diuer&longs;as con&longs;iderationes <lb/>adhuc in diuer&longs;o genere vectis con&longs;titui. </s>

<s id="N170E8">Ad hæc idem Baldus affines qua&longs;dam huic dubitationes, <lb/><expan abbr="eanumq.">eanumque</expan> &longs;olutiones &longs;ubnectit, quarum illa præcipuè ad rem <lb/>facit; Num &longs;cilicet pondere in vectis medio con&longs;tituto, <pb pagenum="240" xlink:href="005/01/248.jpg"/>idem pror&longs;us contingat &longs;i alterum eorum, qui &longs;u&longs;tinent &longs;it <lb/>&longs;tatura procerior, alrer verò humilior: Vel &longs;i &longs;tatura quidem <lb/>pares fuerine, per viam tamen accliuem, aut decliuem ince<lb/>dant. </s>

<s id="N170E8">Ad hæc idem Baldus affines qua&longs;dam huic dubitationes, <lb/><expan abbr="eanumq.">eanumque</expan> &longs;olutiones &longs;ubnectit, quarum illa præcipuè ad rem <lb/>facit; Num &longs;cilicet pondere in vectis medio con&longs;tituto, <pb pagenum="240" xlink:href="005/01/248.jpg"/>idem pror&longs;us contingat &longs;i alterum eorum, qui &longs;u&longs;tinent &longs;it <lb/>&longs;tatura procerior, alter verò humilior: Vel &longs;i &longs;tatura quidem <lb/>pares fueritne, per viam tamen accliuem, aut decliuem ince<lb/>dant. </s>

<s id="N170FD">Etenim &longs;i pondus liberè pendeat optimè re&longs;pondet, <lb/>idem omnino contingere, quia &longs;emper eadem &longs;eruaretur <lb/>æqualitas partium vectis, ac di&longs;tantia baiulorum à loco vbi <lb/>pondus deprimeret, vt clarè ip&longs;e demon&longs;trat: Si autem <lb/>pondus nequaquam liberè pendeat, &longs;ed fir miter &longs;it infra <lb/>vectem alligatum, tunc magis grauari eum, qui extremum <lb/>vectis magis ab horizonte eleuatum &longs;u&longs;tinet. </s>

<s id="N1710C">Quando qui<lb/>dem pondus grauitat in parte vectis propinquiori ip&longs;i ex<lb/>tremo magis eleuato, quamuis in medio &longs;it con&longs;titurum. <lb/></s>

<s id="N17114">Cuius oppo&longs;itum contingeret &longs;i pondus &longs;upra vectem, li<lb/>cet pariter in medio collocaretur, quod non tetigit Baldus, <lb/>& vtrumque facilè erit &longs;imul probare. </s>

Line 3404

<s id="N17188">C<emph type="italics"/>vr &longs;urgentes omnes femori eius ad acutum <lb/>con&longs;tituentes angulum, & thoraci &longs;imiliter fe<lb/>mur &longs;urgunt? </s>

<s id="N17192">quod &longs;i non, baudquaquam &longs;ur<lb/>gere poterunt. </s>

<s id="N17192">quod &longs;i non, haudquaquam &longs;ur<lb/>gere poterunt. </s>

<s id="N17197">An quia id quod æquale e&longs;t, quie<lb/>tis <expan abbr="vbiq.">vbique</expan> e&longs;t cau&longs;a: rectus autem angulus æqua<lb/>litatis e&longs;t, <expan abbr="&longs;tationemq.">&longs;tationemque</expan> facit, quamobrem ad &longs;i<lb/>miles fertur angulos ip&longs;i terræ circumferentiæ, <lb/>non enim quod ad rectum est ip&longs;i pauimento. </s>

<s id="N171AA">An quoniam &longs;ur<lb/>gens &longs;it rectus, &longs;tantem verò nece&longs;&longs;e e&longs;t perpendiculum e&longs;&longs;e ad <lb/>terram. </s>

<s id="N171B1">Siquidem igitur ad rectum debet e&longs;&longs;e, hoc autem e&longs;t ca<lb/>put &longs;ecundum pedes habere, & fieri oportet cum &longs;urgit. </s>

<s id="N171B6">Quan<lb/>doquidem igitur fuerit &longs;edens, &longs;ecundum paralellam pedes <lb/>babet & caput, & non inæquali. </s>

<s id="N171B6">Quan<lb/>doquidem igitur fuerit &longs;edens, &longs;ecundum paralellam pedes <lb/>habet & caput, & non inæquali. </s>

<s id="N171BD">Caput &longs;it A, thorax AB, &longs;e<lb/>mur BC, crura CD. </s>

<s id="N171C3">Ad rectum autem fit & thorax vbi AB <lb/>ip&longs;i femori, & cruri femur, &longs;ic &longs;edente. </s>

<s id="N171C8">Quamobrem eo &longs;e <lb/>babentem modo &longs;urgere est impo&longs;sibile. </s>

<s id="N171C8">Quamobrem eo &longs;e <lb/>habentem modo &longs;urgere est impo&longs;sibile. </s>

<s id="N171CD">Nece&longs;&longs;e autem est crus <lb/><expan abbr="r&emacr;elinare">renelinare</expan>, <expan abbr="pedesq.">pedesque</expan> con&longs;tituere &longs;ub capite, hoc autem erit, &longs;i<emph.end type="italics"/><pb pagenum="242" xlink:href="005/01/250.jpg"/><emph type="italics"/>CD fiet, vbi CF, & &longs;imul &longs;urgere continget, & in eadem <lb/>æquali babere caput, & pedes, ip&longs;a autem CF acutum facit <lb/>angulum ad ip&longs;am BG.<emph.end type="italics"/></s>

<s id="N171CD">Nece&longs;&longs;e autem est crus <lb/><expan abbr="r&emacr;elinare">rem elinare</expan>, <expan abbr="pedesq.">pedesque</expan> con&longs;tituere &longs;ub capite, hoc autem erit, &longs;i<emph.end type="italics"/><pb pagenum="242" xlink:href="005/01/250.jpg"/><emph type="italics"/>CD fiet, vbi CF, & &longs;imul &longs;urgere continget, & in eadem <lb/>æquali habere caput, & pedes, ip&longs;a autem CF acutum facit <lb/>angulum ad ip&longs;am BG.<emph.end type="italics"/></s>

<s id="N171EB">COMMENTARIVS.</s>

<s id="N171F1">Svpponit Ari&longs;toteles, quod &longs;atis per &longs;e notum e&longs;t, <lb/>commodè, & appo&longs;itè &longs;edentes duos angulos rectos <lb/>po&longs;itione &longs;ui corporis con&longs;tituere iuxta propriam &longs;e<lb/>dis formam: Vnum quippe quem facit thorax cum femore, <lb/>alterum verò quem efficit femur cum tibia. </s>

<s id="N171FC">Vt exempli <lb/>gratia &longs;i linea AB rectitudinem <lb/>humani corporis referat à capite <lb/><figure id="id.005.01.250.1.jpg" xlink:href="005/01/250/1.jpg"/><lb/>v&longs;que ad ventrem, BC verò fe<lb/>morum longitudinem v&longs;que ad <lb/>genua, tanquam duo latera recti <lb/>anguli ABC; & CD crurium al<lb/>titudinem de&longs;ignet, quæ pariter <lb/>cum BC alterum angulum re<lb/>ctum con&longs;tituat BCD. </s>

<s id="N171FC">Vt exempli <lb/>gratia &longs;i linea AB rectitudinem <lb/>humani corporis referat à capite <lb/><figure id="id.005.01.250.1.jpg" xlink:href="005/01/250/1.jpg"/><lb/>v&longs;que ad ventrem, BC verò fe<lb/>morum longitudinem v&longs;que ad <lb/>genua, tanquam duo latera recti <lb/>anguli ABC; & CD crucium al<lb/>titudinem de&longs;ignet, quæ pariter <lb/>cum BC alterum angulum re<lb/>ctum con&longs;tituat BCD. </s>

<s id="N17218">Quo &longs;up<lb/>po&longs;ito quærit cur &longs;edentes cum <lb/>&longs;urgere voluerint, in ip&longs;o &longs;urgendi <lb/>actu prædictos angulos rectos in <lb/>acutos commutare &longs;oleant, nec <lb/>aliter &longs;urgere valeant? </s>

<s id="N17225">Vt &longs;i&longs;ten<lb/>do in eadem figura propo&longs;ita, ca<lb/>put ab A declinando in E ad <lb/>efficiendum angulum acutum <lb/>EBC, ac tibias retrahendo cum pedibus ex D in F ad con<lb/>&longs;tituendum acutum angulum BCF. </s>

Line 3429

<s id="N17244">tex. 4 8. debet e&longs;&longs;e ab inæquali proportione. <lb/></s>

<s id="N1724A">Angulus autem rectus, e&longs;t angulus æqualitatis non modò <lb/>quia cuilibet alterirecto &longs;emper e&longs;t æqualis, &longs;ed quia æqui-<pb pagenum="243" xlink:href="005/01/251.jpg"/>ponderantiam in corporibus cau&longs;at, velcertè con&longs;equitur, <lb/>vt patet in libra, quæ dum in æquilibrio con&longs;tituitur duos <lb/>vtrinque efficit angulos rectos cum trutina. </s>

<s id="N17258"><expan abbr="Itemq.">Itemque</expan> nam <lb/>corpora perpendiculariter ad angulos rectos &longs;uper planum <lb/>horizontis con&longs;tituta, dum terræ &longs;uperficiei incumbunt, <lb/>æqualiter omni ex parte di&longs;tant à &longs;olo, <expan abbr="&longs;tareq.">&longs;tareque</expan> propterea <lb/>dicuntur, hoc e&longs;t in &longs;ua propria mole con&longs;i&longs;tere. </s>

<s id="N1726A">Quare cu<lb/>bus eo quod non ni&longs;i ex rectis angulis con&longs;tet, & vndique <lb/>&longs;it æqualis, maximè omnium corporum valet con&longs;i&longs;tere, at<lb/>que &longs;olo inhærédo quie&longs;cere: Ita vt Pythagorici ad tuendam <lb/>terræ immobilitatem, eam dixerint e&longs;&longs;e cubicam. </s>

<s id="N1726A">Quare cu<lb/>bus eo quod non ni&longs;i ex rectis angulis con&longs;tet, & vndique <lb/>&longs;it æqualis, maximè omnium corporum valet con&longs;i&longs;tere, at<lb/>que &longs;olo inhæréndo quie&longs;cere: Ita vt Pythagorici ad tuendam <lb/>terræ immobilitatem, eam dixerint e&longs;&longs;e cubicam. </s>

<s id="N17275">Quod <lb/>autem dicitur de toto corpore &longs;tante, idem re&longs;pectiuè dici <lb/>pote&longs;t de partibus, quæ &longs;imiliter ad angulos rectos &longs;upra <lb/>planum horizontis erectæ quie&longs;cunt, vt thorax, vel tibiæ in <lb/>homine &longs;edente. </s>

<s id="N17280">Cum igitur à &longs;e&longs;&longs;ione &longs;urgentes, quietem <lb/>qua &longs;edendo ad angulos rectos potiebantur a&longs;&longs;urgendo re<lb/>linquant, ip&longs;os angulos rectos in acutos commutare co<lb/>guntur, hoc ip&longs;o quod moueantur, & acuti anguli, non au<lb/>tem obtu&longs;i ad ip&longs;um &longs;urrectionis motum &longs;int idonei, at que <lb/>accommodati, vt mox infrà con&longs;tabit. </s>

<s id="N1728F">Secundò igitur id fieri docet Philo&longs;ophus, nam qui &longs;ur<lb/>git, ad hoc tendit, vt totus con&longs;tituatur erectus, ac perpen<lb/>dicularis &longs;uperficiei terræ &longs;ecundum eandem rectitud nem <lb/>vnius lineæ cadentis ad centrum, &longs;ecus ac cum &longs;ederet. <lb/></s>

<s id="N1728F">Secundò igitur id fieri docet Philo&longs;ophus, nam qui &longs;ur<lb/>git, ad hoc tendit, vt totus con&longs;tituatur erectus, ac perpen<lb/>dicularis &longs;uperficiei terræ &longs;ecundum eandem rectitudinem <lb/>vnius lineæ cadentis ad centrum, &longs;ecus ac cum &longs;ederet. <lb/></s>

<s id="N17299">Quantumuis enim tunc caput & thorax, &longs;icut & crura per<lb/>pendiculariter haberet &longs;upra horizontem erecta, non tamen <lb/>femora &longs;ic erant con&longs;tituta, nec crura in eadem erant linea, <lb/>ac thorax & caput, &longs;ed in alia paralella. </s>

<s id="N172A2">Quare vt totus <lb/>erigatur, & &longs;ecundum eandem lineam perpendiculariter <lb/>horizonti in&longs;i&longs;tat, opus e&longs;t, pedes retrahere, vt dicebamus, <lb/>ex D in F, <expan abbr="caputq.">caputque</expan> cum &longs;ubiecto thorace reclinare ex A <lb/>in E; quod e&longs;t prædictos angulos rectos in acutos conuerte<lb/>re, vt pedibus &longs;ub capite con&longs;titutis, per eandem perper di<lb/>cularem EF totum corpus erigi po&longs;&longs;it, ac &longs;tare. </s>

<s id="N172B5">Alioquia <lb/>eandem angulorum rectitudinem &longs;eruando, non &longs;ieret mo<lb/>tus; atque rectos angulos in obtu&longs;os commutando, non mo<pb pagenum="244" xlink:href="005/01/252.jpg"/>do pedes &longs;ub thorace, vel capite perpendiculariter, vt opus <lb/>e&longs;t, con&longs;tituerentur; &longs;ed magis à perpen diculo, in quo con<lb/>uenire debent ad erectionem pedes, & caput, di&longs;tarent, vt <lb/>per &longs;e patet. </s>

<s id="N172B5">Alioquia <lb/>eandem angulorum rectitudinem &longs;eruando, non fieret mo<lb/>tus; atque rectos angulos in obtu&longs;os commutando, non mo<pb pagenum="244" xlink:href="005/01/252.jpg"/>do pedes &longs;ub thorace, vel capite perpendiculariter, vt opus <lb/>e&longs;t, con&longs;tituerentur; &longs;ed magis à perpen diculo, in quo con<lb/>uenire debent ad erectionem pedes, & caput, di&longs;tarent, vt <lb/>per &longs;e patet. </s>

<s id="N172C9">Cæterum Baldus obijcit Ari&longs;toteli; &longs;edentem non ideo <lb/>quie&longs;cere quod rectus angulus quietis &longs;it cau&longs;a, &longs;ed propte<lb/>rea quod cius thoracis tum etiam femorum pondus ab ip<lb/>&longs;a &longs;ede &longs;u&longs;tineatur; crura verò & pedes ideo non laborent, <lb/>quod partim &longs;u&longs;pen&longs;a &longs;int, partim ip&longs;i &longs;olo innitantur. </s>

<s id="N172C9">Cæterum Baldus obijcit Ari&longs;toteli; &longs;edentem non ideo <lb/>quie&longs;cere quod rectus angulus quietis &longs;it cau&longs;a, &longs;ed propte<lb/>rea quod eius thoracis tum etiam femorum pondus ab ip<lb/>&longs;a &longs;ede &longs;u&longs;tineatur; crura verò & pedes ideo non laborent, <lb/>quod partim &longs;u&longs;pen&longs;a &longs;int, partim ip&longs;i &longs;olo innitantur. </s>

<s id="N172D4">Sed <lb/>hoc nihil contra ip&longs;ius Philo&longs;ophi doctrinam concludit. <lb/></s>

<s id="N172DA">Non enim dixit Ari&longs;toteles, &longs;edentem ab&longs;olutè quie&longs;cere <lb/>ex eo, quod rectus angulus quietis &longs;it cau&longs;a, nulla habi<lb/>ta ratione fulcimenti, cui &longs;edens innititur, &longs;ed præ&longs;up<lb/>po&longs;ita &longs;ede, cui &longs;edens incumbendo ad angulos rectos <lb/>quie&longs;cit, ait illum ad hoc vt &longs;urgat, angulos rectos in <lb/>acutos nece&longs;&longs;ariò commutare. </s>

<s id="N172E7">Quando quidem &longs;eruata re<lb/>ctitudine angulorum moueri non po&longs;&longs;et, nec &longs;e totum ere<lb/>ctum con&longs;tituere &longs;uper planum horizontis per angulos re<lb/>ctos. </s>

Line 3453

<s id="N17320">C<emph type="italics"/>vr faciliùs mouetur commotum, quàm ma<lb/>nens? </s>

<s id="N17328">V eluti currus citiùs commotos agitant, <lb/>quàm moueri incipientes. </s>

<s id="N1732D">An quia difficilli<lb/>mum est pondus mouere, quod in contrarium <lb/>mouetur, aufert enim quiddam ex motoris po<lb/>tentia, licet multò &longs;it velocior, nece&longs;&longs;e namque <lb/>e&longs;t tardiorem e&longs;&longs;e impulfionem illius, quod re<lb/>pellitur. </s>

<s id="N1733A">Secundo autem loco &longs;i quieuerit, re&longs;isiit enim ip&longs;um <lb/>quie&longs;cens. </s>

<s id="N1733A">Secundo autem loco &longs;i quieuerit, re&longs;istit enim ip&longs;um <lb/>quie&longs;cens. </s>

<s id="N1733F">Quod autem mouetur ad id ip&longs;um ad quod impelli<lb/>tur, impellenti &longs;imile facit, ceu &longs;i qui&longs;ptam mouentis poten<lb/>tiam, & ceberitatem augeret, quod enim ab illo pateretur, vti<lb/>que ip&longs;um facit ex &longs;e commotum.<emph.end type="italics"/></s>

<s id="N1733F">Quod autem mouetur ad id ip&longs;um ad quod impelli<lb/>tur, impellenti &longs;imile facit, ceu &longs;i qui&longs;piam mouentis poten<lb/>tiam, & celeritatem augeret, quod enim ab illo pateretur, vti<lb/>que ip&longs;um facit ex &longs;e commotum.<emph.end type="italics"/></s>

<s id="N1734C">COMMENTARIVS.</s>

Line 3472

<s id="N1738D">Ex &longs;e <pb pagenum="246" xlink:href="005/01/254.jpg"/>namque graue quodlibet quie&longs;cendo, corpori cui adiacet <lb/>adhæret, ac perpetua quadam pre&longs;&longs;ione deor&longs;um mundi <lb/>centrum iugiter petit. </s>

<s id="N17399">Quapropter dum aliò transferri con<lb/>tigerit, re&longs;i&longs;tit qua&longs;i per contrarium motum. </s>

<s id="N1739E">Vice autem <lb/>ver&longs;a cum iam moueri c&oelig;perit per impul&longs;um tunc acce<lb/>ptum, non modò adhuc refrænatur grauitas, <expan abbr="minuiturq.">minuiturque</expan> ef<lb/>fectus pre&longs;sionis illius qua tendit deor&longs;um, &longs;ed iam graue <lb/>ip&longs;um ad vlteriorem motum progre&longs;sionis reperitur di&longs;po<lb/>&longs;itum, vt adueniente nouo impetu qua&longs;i duplicato principio <lb/>transferatur. </s>

<s id="N173B1">Imo ip&longs;a quoque grauitas in corpore agita<lb/>to &longs;i ex parte illud tendat deor&longs;um, vt in decliue vrget quo <lb/>ver&longs;um graae proijcitur, ita vt vis quæ merè deor&longs;um ten<lb/>debat, in vim quæ aliò transfert per accidens refundatur. <lb/></s>

<s id="N173B1">Imo ip&longs;a quoque grauitas in corpore agita<lb/>to &longs;i ex parte illud tendat deor&longs;um, vt in decliue vrget quo <lb/>ver&longs;um graue proijcitur, ita vt vis quæ merè deor&longs;um ten<lb/>debat, in vim quæ aliò transfert per accidens refundatur. <lb/></s>

<s id="N173BB">Facilius ergo deinceps fertur graue proximè commotum <lb/>quàm cum primò quietem relinquit: quia mouetur ad no<lb/>uum ip&longs;um impul&longs;um &longs;imul cum reliquijs impetus prius im<lb/>pre&longs;si, quo adhuc grauitas compe&longs;citur, ac moderatur ne <lb/>progre&longs;sioni ob&longs;i&longs;tat, &longs;ed potius ad illam <expan abbr="quandoq.">quandoque</expan> per ac<lb/>cidens conferat, at que concurrat. </s>

Line 3482

<s id="N173F7">Nam is cum celerrimè fiat, impingere videtur in <pb pagenum="247" xlink:href="005/01/255.jpg"/>ip&longs;um mobile, <expan abbr="proindeq.">proindeque</expan> impetu incu&longs;&longs;o, motum eius acce<lb/>lerare; ex qua acceleratione velocior adhuc redditur no<lb/>uus accur&longs;us, quo rur&longs;us mobile magis impellitur, & &longs;ic <lb/>deinceps. </s>

<s id="N17409"><expan abbr="Citaturq.">Citaturque</expan> pro hac &longs;ententia Ari&longs;toteles 3. de cæ<lb/>lo tex. 28. vbi loquendo de di&longs;tinctione motus naturalis à <lb/>violento, & acceleratione vtriu&longs;que inquit: Ad ambo au<lb/>tem tanquam in&longs;trumento vtitur aere: nempe ip&longs;um princi<lb/>pium à quo principaliter prouenit motus. </s>

<s id="N17419"><expan abbr="Rur&longs;umq.">Rur&longs;umque</expan> paulò <lb/>inferius loquens adhuc de aere, &longs;ubdit: Veluti enim impri<lb/>mens tradit vtrique. </s>

<s id="N17423">Impul&longs;um &longs;cilicet vtriq<gap/>e mobili ad <lb/>proprium motum impertiendo. </s>

<s id="N17423">Impul&longs;um &longs;cilicet vtrique mobili ad <lb/>proprium motum impertiendo. </s>

<s id="N1742A">Verum ex hoc loco ad &longs;um<lb/>mum tantum colligitur de mente Ari&longs;totelis, aerem ad <lb/>vtrunque motum perficiendum, videlicet tam naturalem, <lb/>quàm violentum de&longs;eruire, ac tanquam in&longs;trumentum con<lb/>currere. </s>

<s id="N17435">Alioquin præcisè loquendo de maiori celeritate <lb/>motus naturalis deor&longs;um quò proprius graue ad imum ac<lb/>ce&longs;&longs;erit, potius ibidem docet Philo&longs;ophus, eam ab adiuncta <lb/>virtute præternaturali oriri; inquiens, eum motum, qui e&longs;t <lb/>&longs;ecundum naturam (vt in lapide dum fertur deor&longs;um) velo<lb/>ciorem fieri ab eo, qui e&longs;t &longs;ecundum potentiam: vocat au<lb/>tem potentiam ip&longs;am virtutem motiuam, quæ per violen<lb/>tiam imprimitur, aut producitur in corporibus, vt patet ex <lb/>contextu. </s>

Line 3498

<s id="N17496">Præ<lb/>tereaidem Philo&longs;ophus lib.

1. de c&oelig;lo tex. 88. docet <expan abbr="cele-ritat&etilde;">cele<lb/>ritatem</expan> motus naturalis in progre&longs;&longs;u augeri propter <expan abbr="augmen-t&utilde;">augmen<lb/>tum</expan> virtutis motiuæ grauitatis, aut leuitatis, quæ &longs;cilicet <expan abbr="au-g&etilde;tur">au<lb/>gentur</expan> in motu. </s>

<s id="N174AF">Vnde infert, quod &longs;i motus pcederet in <expan abbr="infi-nit&utilde;">infi<lb/>nitum</expan>, <expan abbr="etiã">etiam</expan> grauitas, aut leuitas, & velocitas ex illis orta cre&longs;ce <lb/>ret in <expan abbr="infinit&utilde;">infinitum</expan>. </s>

<s id="N174AF">Vnde infert, quod &longs;i motus prederet in <expan abbr="infi-nit&utilde;">infi<lb/>nitum</expan>, <expan abbr="etiã">etiam</expan> grauitas, aut leuitas, & velocitas ex illis orta cre&longs;ce <lb/>ret in <expan abbr="infinit&utilde;">infinitum</expan>. </s>

<s id="N174C2">Loquitur <expan abbr="aut&etilde;">autem</expan> de <expan abbr="augm&etilde;to">augmento</expan>, & <expan abbr="increm&etilde;to">incremento</expan> gra. <lb/></s>

<s id="N174D2">uitatis <expan abbr="accid&etilde;talis">accidentalis</expan>, &longs;eu impetus acqui&longs;iti; <expan abbr="c&utilde;">cum</expan> &longs;atis <expan abbr="cõ&longs;tet">con&longs;tet</expan>, nec <lb/><expan abbr="grauitat&etilde;">grauitatem</expan>, nec <expan abbr="leuitat&etilde;">leuitatem</expan> naturalem formaliter in &longs;eip&longs;a augeri. </s>

Line 3510

<s id="N17539">Quod cum &longs;en&longs;u con&longs;tet, & <lb/>à graui&longs;simis Philo&longs;ophis acceperimus ob&longs;eruatum, gratis à <lb/>nonnullis negatur, qui parui quoque momenti faciunt vim <lb/>aeris &longs;ub&longs;equentis cum per poros lanæ inquiunt illum in&longs;i<lb/>nuari, & &longs;ic graue depellere ab&longs;que vlla lanæ depre&longs;sione. </s>

<s id="N17546">Cum igitur hiu&longs;modi accur&longs;us aeris &longs;uccedentis in eun<lb/>dem locum non &longs;uffragetur; nec &longs;ufficiat minor illa re&longs;i&longs;ten<lb/>tia explicata; grauitas verò ip&longs;a corporis augeri non po&longs;sit <lb/>à &longs;eip&longs;a, &longs;icut nec vlla qualitas per acqui&longs;itionem noui gra<lb/>dus eiu&longs;dem &longs;pecificæ qualitatis, qui &longs;i daretur, per&longs;euera<lb/>ret etiam po&longs;t motum, quod experientiæ repugnat; aliaque <lb/>non appareat probabilis cau&longs;a ip&longs;ius maioris velocitatis, <lb/>quam graue acquirit in motu; remanet vt illam non ni&longs;i ab <lb/>impetu ab eodem graui in ip&longs;a naturali motione producto <lb/>oriri dicamus cum Ari&longs;totele, <expan abbr="alijsq.">alijsque</expan> magni nominis tum <lb/>veteribus, tum neotericis Philo&longs;ophis, qui hac de re fusè <lb/>&longs;crip&longs;erunt. </s>

<s id="N17546">Cum igitur huiu&longs;modi accur&longs;us aeris &longs;uccedentis in eun<lb/>dem locum non &longs;uffragetur; nec &longs;ufficiat minor illa re&longs;i&longs;ten<lb/>tia explicata; grauitas verò ip&longs;a corporis augeri non po&longs;sit <lb/>à &longs;eip&longs;a, &longs;icut nec vlla qualitas per acqui&longs;itionem noui gra<lb/>dus eiu&longs;dem &longs;pecificæ qualitatis, qui &longs;i daretur, per&longs;euera<lb/>ret etiam po&longs;t motum, quod experientiæ repugnat; aliaque <lb/>non appareat probabilis cau&longs;a ip&longs;ius maioris velocitatis, <lb/>quam graue acquirit in motu; remanet vt illam non ni&longs;i ab <lb/>impetu ab eodem graui in ip&longs;a naturali motione producto <lb/>oriri dicamus cum Ari&longs;totele, <expan abbr="alijsq.">alijsque</expan> magni nominis tum <lb/>veteribus, tum neotericis Philo&longs;ophis, qui hac de re fusè <lb/>&longs;crip&longs;erunt. </s>

<s id="N17565">Secundum verò fundamentum eiu&longs;dem veritatis, ac no<lb/>&longs;træ &longs;ententiæ &longs;umendum e&longs;t ab ob&longs;eruationibus, & expe<lb/>rientijs. </s>

<s id="N1756C">Primò enim con&longs;tat, grauia quò ex altiori loco <lb/>deciderint, non modò eo velocius ferri prope &longs;inem, quàm <lb/>in principio, &longs;ed etiam validius obuiantia pellere <expan abbr="fortiusq.">fortiusque</expan> <lb/>impingere: quod non contingit quando ad latera, vel &longs;ur<lb/>&longs;um feruntur, langue&longs;cente impetu prope finem. </s>

<s id="N1756C">Primò enim con&longs;tat, grauia quò ex altiori loco <lb/>deciderint, non modò eo velocius ferri prope finem, quàm <lb/>in principio, &longs;ed etiam validius obuiantia pellere <expan abbr="fortiusq.">fortiusque</expan> <lb/>impingere: quod non contingit quando ad latera, vel &longs;ur<lb/>&longs;um feruntur, langue&longs;cente impetu prope finem. </s>

<s id="N1757B"><expan abbr="Indiciumq.">Indiciumque</expan> <lb/>propterea e&longs;t, non prouenire à &longs;ola grauitate, eodem &longs;em<lb/>per modo &longs;e habente, &longs;ed etiam ab impetu acqui&longs;ito, qui <lb/>cum in motu naturali &longs;ucce&longs;siuè &longs;emper intendatur, in vio<lb/>lento verò remittatur, magis præualet in illo, quàm in i&longs;to, <lb/>quo longius ip&longs;a grauia à principio fuerint remota. </s>

<s id="N1758D">Deinde ob&longs;eruamus ip&longs;a grauia quanto ex &longs;ublimiori &longs;i<lb/>tu demittantur, tantò altius re&longs;ilire, quod euenire nequit <pb pagenum="250" xlink:href="005/01/258.jpg"/>ex vi præci&longs;æ grauitatis, quæ &longs;anè vbi primò &longs;olum vel de<lb/>tinens quippiam attingeret, &longs;i&longs;teret, nec &longs;ineret graue ip&longs;um <lb/>rur&longs;us attolli. </s>

<s id="N1759B">Contra verò admi&longs;&longs;a productione impetus in <lb/>de&longs;cen&longs;u illorum, cum hic &longs;ucce&longs;siuè intendatur in progre&longs;<lb/>fu, facilè intelligitur magis ea re&longs;ilire iuxta maiorem impe<lb/>tum acqui&longs;itum in maiori via. </s>

<s id="N1759B">Contra verò admi&longs;&longs;a productione impetus in <lb/>de&longs;cen&longs;u illorum, cum hic &longs;ucce&longs;siuè intendatur in progre&longs;<lb/>su, facilè intelligitur magis ea re&longs;ilire iuxta maiorem impe<lb/>tum acqui&longs;itum in maiori via. </s>

<s id="N175A4">Quod &longs;i dicas impetum ad <lb/>re&longs;iliendum produci ab ip&longs;o plano, vel &longs;olo in <expan abbr="pilã">pilam</expan> lu&longs;oriam, <lb/>vel decidens quodlibet corpus, quod re&longs;ilit: hoc in primis <lb/>expre&longs;sè e&longs;t contra Ari&longs;totelem 8. phy&longs;ic. </s>

<s id="N175B1">tex. 32. Qui <lb/>&longs;phæram ait à proijciente, non à pariete virtutem accipere <lb/>ad re&longs;iliendum: nec minus contra experientiam cum te&longs;ta <lb/>impetu lata, & obliquè in aquarum &longs;uper&longs;iciem incidens, <lb/>longius inde re&longs;iliat, tamet&longs;i paruam, aut nullam in fluido <lb/>corpore adinuenerit re&longs;i&longs;tentiam, <expan abbr="nullumq.">nullumque</expan> propterea pro<lb/>prii impetus acqui&longs;ierit incrementum. </s>

<s id="N175B1">tex. 32. Qui <lb/>&longs;phæram ait à proijciente, non à pariete virtutem accipere <lb/>ad re&longs;iliendum: nec minus contra experientiam cum te&longs;ta <lb/>impetu lata, & obliquè in aquarum &longs;uperficiem incidens, <lb/>longius inde re&longs;iliat, tamet&longs;i paruam, aut nullam in fluido <lb/>corpore adinuenerit re&longs;i&longs;tentiam, <expan abbr="nullumq.">nullumque</expan> propterea pro<lb/>prii impetus acqui&longs;ierit incrementum. </s>

<s id="N175C6">Corpus enim quod <lb/>&longs;eritur, aut percutitur à proiectis, repellere illa dicitur non <lb/>producendo, nec augendo, &longs;ed retorquendo in eis impe<lb/>tum incu&longs;&longs;um à proijciente. </s>

<s id="N175CF">Item non &longs;atis intelligitur im<lb/>pul&longs;um ad re&longs;iliendum effici ab&longs;que motu locali impellentis <lb/>&longs;icut in reliquis omnibus impul&longs;ibus experimur. </s>

<s id="N175D6"><expan abbr="Probaturq.">Probaturque</expan> <lb/>ex recepti&longs;simo illo Ari&longs;totelis axiomate, quod nullum <lb/>moueat ni&longs;i commotum, vt quæ&longs;t. </s>

Line 3529

<s id="N175E5">Præterea videmus corpus fune appen&longs;um huc atque il<lb/>luc circumferri, per vnum quippe arcum de&longs;cendendo, ac <lb/>per alium a&longs;cendendo: &longs;ed nequit a&longs;cendere virtute graui<lb/>tatis, qua &longs;olùm pote&longs;t de&longs;cendere: Ergo nece&longs;&longs;ariò conce<lb/>denda e&longs;t alia virtus motiua, qua po&longs;sit a&longs;cendere; & hanc <lb/>vocamus impetum. </s>

<s id="N175F2">Qui cum à nulla alia cau&longs;a tunc po&longs;sit <lb/>ori<gap/>i, remanet, vt producatur ab eodem corpore agitato in <lb/>ip&longs;o de&longs;cen&longs;u virtute &longs;uæ grauitatis, quæ e&longs;t illi ratio princi<lb/>paliter agendi, vt infra rur&longs;us patebit. </s>

<s id="N175F2">Qui cum à nulla alia cau&longs;a tunc po&longs;sit <lb/>orir<gap/>i, remanet, vt producatur ab eodem corpore agitato in <lb/>ip&longs;o de&longs;cen&longs;u virtute &longs;uæ grauitatis, quæ e&longs;t illi ratio princi<lb/>paliter agendi, vt infra rur&longs;us patebit. </s>

<s id="N175FF">Neminem denique fugit cel&longs;is ex cacuminibus montium <lb/>cadentia &longs;axa di&longs;cindi per aera, nullis alijs illi&longs;a corporibus; <lb/>& aquam &longs;upernè cadentem in progre&longs;&longs;u magis ac magis <lb/>d uelli, & in guttas re&longs;olui. </s>

Line 3543

<s id="N17647">Nec ob&longs;tat qualitatem impetus e&longs;&longs;e præter naturam gra<lb/>uium ad hoc, vt dicamus ab ip&longs;ismet per motum naturalem <lb/>deor&longs;um tendendo produci. </s>

<s id="N1764E">Quandoquidem multa per <lb/>accidens producuntur à cau&longs;is naturalibus, quæ illis con<lb/>ueniunt præter naturam. </s>

<s id="N17655">Vt cum per motum localem pro<lb/>ducitur in &longs;e calor ab aqua, vel ferro, quibus conuenit præ<lb/>ter naturam; &longs;icut & præfentia localis in &longs;patio à centro re<lb/>motiori, quæ producitur ab ei&longs;dem grauibus &longs;ur&longs;um ten<lb/>dentibus, at que promotis; & &longs;imilia. </s>

<s id="N17655">Vt cum per motum localem pro<lb/>ducitur in &longs;e calor ab aqua, vel ferro, quibus conuenit præ<lb/>ter naturam; &longs;icut & præferentia localis in &longs;patio à centro re<lb/>motiori, quæ producitur ab ei&longs;dem grauibus &longs;ur&longs;um ten<lb/>dentibus, at que promotis; & &longs;imilia. </s>

<s id="N17662">Nec tandem &longs;equitur, quod &longs;i talis impetus à de&longs;cenden<lb/>te graui produceretur, natura &longs;ua tenderet in eundem Io<lb/>cum in quem tendit grauitas, à qua propterea non &longs;atis po&longs;<lb/>&longs;et di&longs;tin gui. </s>

Line 3551

<s id="N17674">Vnde &longs;icut indifferens e&longs;t ex natura &longs;ua, vt <lb/>producatur à proijciente, vel à graui de&longs;cendente, aut leui <lb/>a&longs;cendente: ita pariter e&longs;t in differens ad tenden dum potius <pb pagenum="252" xlink:href="005/01/260.jpg"/>i&longs;tuc quàm illuc; determinatur autem à cau&longs;a impellente <lb/>per modum quo applicatur, ac iuxta po&longs;itionem qua vrget, <lb/>ac diligit mobile in ip&longs;a impul&longs;ione. </s>

<s id="N17686">Cæterum ex dictis in hac quæ&longs;tione colligitur, non e&longs;&longs;e <lb/>eandem rationem de maiori facilitate motus violenti, ac <lb/>naturalis po&longs;t principium motus; cum maior facilitas, quæ <lb/>reperitur in violenta motione corporis iam commoti, oria<lb/>tur ex reduplicatione illa impetus explicata: maior autem <lb/>facilitas, ac velocitas motus naturalis <expan abbr="po&longs;tquã">po&longs;tquam</expan> corpus mo<lb/>ueri c&oelig;perit in &longs;<gap/>urn <expan abbr="loc&utilde;">locum</expan>, procedat ab impetu aduenien<lb/>te vltra grauitatem, aut leuitatem, qui adhuc &longs;ucce&longs;&longs;iuè in<lb/>tenditur, <expan abbr="promouetq.">promouetque</expan> magis ac magis v&longs;que in <expan abbr="fin&etilde;">finem</expan>. </s>

<s id="N17686">Cæterum ex dictis in hac quæ&longs;tione colligitur, non e&longs;&longs;e <lb/>eandem rationem de maiori facilitate motus violenti, ac <lb/>naturalis po&longs;t principium motus; cum maior facilitas, quæ <lb/>reperitur in violenta motione corporis iam commoti, oria<lb/>tur ex reduplicatione illa impetus explicata: maior autem <lb/>facilitas, ac velocitas motus naturalis <expan abbr="po&longs;tquã">po&longs;tquam</expan> corpus mo<lb/>ueri c&oelig;perit in &longs;olum <expan abbr="loc&utilde;">locum</expan>, procedat ab impetu aduenien<lb/>te vltra grauitatem, aut leuitatem, qui adhuc &longs;ucce&longs;&longs;iuè in<lb/>tenditur, <expan abbr="promouetq.">promouetque</expan> magis ac magis v&longs;que in <expan abbr="fin&etilde;">finem</expan>. </s>

<s id="N176AB">Quam<lb/>obrem ab&longs;que fundamento nonnulli oppo&longs;itum putantes, <lb/>aiunt eandem e&longs;&longs;e vtrique motui facilitatis, ac velocitatis <lb/>rationem, <expan abbr="eamq.">eamque</expan> con&longs;i&longs;tere in di&longs;po&longs;itione prioris motus, <lb/>quo di&longs;ponatur &longs;ubiectum ad motum po&longs;teriorem: cum <lb/>nec motus, nec alia actio per &longs;e di&longs;ponere valeat &longs;ubiectum <lb/>ab&longs;que formæ alicuius productione; nec vlla forma produ<lb/>ci po&longs;&longs;it per motum localem præter: præ&longs;entiam ip&longs;am lo<lb/>calem, quæ ad nihil di&longs;ponit. </s>

Line 3560

<s id="N176C9">C<emph type="italics"/>vr ea quæ proijciuntur, ce&longs;&longs;ant à latione? <lb/></s>

<s id="N176D0">An quia impellens de&longs;init potentia, vel pro<lb/>pter retractionem, vel propter rei proiectæ in<lb/>clinarionem, quando ea valentior fuerit, <lb/>quàm pro<03>cientis vires. </s>

<s id="N176D9">Aut istbæc ambi<lb/>gere, principium relinquentes, ab&longs;urdum e&longs;t.<emph.end type="italics"/></s>

<s id="N176D9">Aut isthæc ambi<lb/>gere, principium relinquentes, ab&longs;urdum e&longs;t.<emph.end type="italics"/></s>

<s id="N176E2">COMMENTARIVS.</s>

Line 3580

<s id="N17744">Nonnulli tamen re&longs;pondent, virtutem illam impre&longs;&longs;am <lb/>in proiectis paulatim remitti, ac tandem penitus corrumpi <lb/>per reproductionem deperditæ grauitatis ad impre&longs;&longs;ionem <lb/>illius. </s>

<s id="N1774D">Putant enim in ip&longs;o actu impre&longs;sionis impetus, mul<lb/>tùm minui de grauitate naturali ip<gap/>us corporis proiecti; <lb/>quod cùm violenter fiat, <expan abbr="ip&longs;u&mtilde;">ip&longs;umm</expan> & corpus cum primò &longs;epa<lb/>ratur à proijciente paulatim <gap/>e reducit in pri&longs;tinam grauita<lb/>tem, per <expan abbr="quã">quam</expan> &longs;en&longs;im etiam expellitur virtus illa à proijcien<lb/>te impre&longs;&longs;a, quæ vocatur impetus, &longs;iue impul&longs;us, & &longs;ic proie<lb/>ctum ce&longs;&longs;at à latione. </s>

<s id="N1774D">Putant enim in ip&longs;o actu impre&longs;sionis impetus, mul<lb/>tùm minui de grauitate naturali ipsius corporis proiecti; <lb/>quod cùm violenter fiat, <expan abbr="ip&longs;u&mtilde;">ip&longs;um</expan> & corpus cum primò &longs;epa<lb/>ratur à proijciente paulatim <gap/>e reducit in pri&longs;tinam grauita<lb/>tem, per <expan abbr="quã">quam</expan> &longs;en&longs;im etiam expellitur virtus illa à proijcien<lb/>te impre&longs;&longs;a, quæ vocatur impetus, &longs;iue impul&longs;us, & &longs;ic proie<lb/>ctum ce&longs;&longs;at à latione. </s>

<s id="N17768">Quod explicant atque con&longs;irmant <pb pagenum="254" xlink:href="005/01/262.jpg"/>exemplo caloris introducti in aquam, qui &longs;anè ad remotio<lb/>nem calefacientis paulatim extinguitur, dum aqua &longs;e redu<lb/>cit in pri&longs;tinam frigiditatem. </s>

<s id="N17768">Quod explicant atque confirmant <pb pagenum="254" xlink:href="005/01/262.jpg"/>exemplo caloris introducti in aquam, qui &longs;anè ad remotio<lb/>nem calefacientis paulatim extinguitur, dum aqua &longs;e redu<lb/>cit in pri&longs;tinam frigiditatem. </s>

<s id="N17776">Sed ratio e&longs;t valde diuer&longs;a, vnde faciiè hæc re&longs;pon&longs;io im<lb/>pugnatur. </s>

<s id="N17776">Sed ratio e&longs;t valde diuer&longs;a, vnde facilè hæc re&longs;pon&longs;io im<lb/>pugnatur. </s>

<s id="N1777B">Primò quia graui dum impetu feruntur, &longs;i in <lb/>medio cur&longs;u &longs;i&longs;tantur, nihil &longs;uæ naturalis grauitatis perdidi&longs;<lb/>&longs;e comperiuntur; vt manu experiri potestin paruis proie<lb/>ctis. </s>

<s id="N17784">Nec talis grauitas in in&longs;tanti ad eandem men&longs;uram <lb/>potui&longs;&longs;et reproduci, cum primo ip&longs;a grauia incipiunt deti<lb/>neri. </s>

<s id="N1778B">Nam qualitates quæ habent contrarium nonni&longs;i in <lb/>tempore intenduntur, ac remittuntur per proprium mo<lb/>tum alterationis, vt patet in eadem calefactione aquæ, ae <lb/>reproductione frigiditatis eiu&longs;dem. </s>

<s id="N1778B">Nam qualitates quæ habent contrarium nonni&longs;i in <lb/>tempore intenduntur, ac remittuntur per proprium mo<lb/>tum alterationis, vt patet in eadem calefactione aquæ, ea <lb/>reproductione frigiditatis eiu&longs;dem. </s>

<s id="N17794">Secundò quia non e&longs;t <lb/>admittenda diminutio, ac reproductio grauitatis ab&longs;que <lb/>propria contrarietate, quam ip&longs;a grauitas habeat cum virtu<lb/>te illa impre&longs;&longs;a. </s>

<s id="N1779D">Nullam autem e&longs;&longs;e huiu&longs;modi contrarie<lb/>tatem, argumento e&longs;t, quia in motu violento quo deor&longs;um <lb/>aliqua corpora depelluntur, nec aufertur, nec minuitur gra<lb/>uitas per ip&longs;am violentiam illatam, <expan abbr="virtutemq.">virtutemque</expan> motiuam in <lb/>illis impre&longs;&longs;am; nec virtus ip&longs;a motiua deperditur, aut cor<lb/>rumpitur à grauitate, quia potius augetur, <expan abbr="magisq.">magisque</expan> corrobo<lb/>ratur. </s>

<s id="N177B4">Imò ab ip&longs;o &longs;olo corpore graui operante per graui<lb/>tatem in de&longs;cen&longs;u producitur, vt quæ&longs;tione præcedenti di<lb/>cebamus: Quod certè non contingeret, &longs;i qualitas illa vir<lb/>tutis impre&longs;&longs;æ, quæ &longs;emper e&longs;t eiu&longs;dem &longs;peciei, ex natura <lb/>&longs;ua incompo&longs;sibilis e&longs;&longs;et cum grauitate, <expan abbr="contrarietatemq.">contrarietatemque</expan> <lb/>habe ent ad inuicem. </s>

Line 3595

<s id="N177C7">Præterea tota contrarietas excogitabilis inter grauita<lb/>tem, & impetum colligitur ex repugnantia, quam grauitas <lb/>habet cum illo quando grauia &longs;ur&longs;um proijciuntur: Quæ ta<lb/>men repugnantia non minus ob&longs;eruatur inter eandem qua<lb/>litatem impetus, & leuitatem, quando leuia proijciuntur <lb/>deor&longs;um. </s>

<s id="N177D4">At eadem qualitas ex genere &longs;uo non pote&longs;t e&longs;&longs;e <lb/>&longs;imul contraria duabus qualitaribus inter &longs;e contrarijs: nam <lb/>hoc ip&longs;o quod opponatur vni, non pote&longs;t opponi alteri illi <lb/>contrariæ: Ergo qualitas impetus ex genere &longs;uo nullam ha-<pb pagenum="255" xlink:href="005/01/263.jpg"/>bet contrarietatem cum grauitate, aut leuitate, quæ &longs;unt <lb/>qualitates inter &longs;e contrariæ. </s>

<s id="N177E4">Et con&longs;irmari adhuc pote&longs;t, <lb/>quia &longs;i gradus aliquis grauitatis expelleretur è proiecto, id <lb/>fierer per introductionem &longs;imilis gradus leuitatis, vt gradus <lb/>frigoris per gradum caloris; atque adeò non per introdu<lb/>ctionem qualitatis impetus, quæ indifferens e&longs;t ad coexi<lb/>&longs;tendum cum grauitate, aut leuitate. </s>

<s id="N177E4">Et confirmari adhuc pote&longs;t, <lb/>quia &longs;i gradus aliquis grauitatis expelleretur è proiecto, id <lb/>fieret per introductionem &longs;imilis gradus leuitatis, vt gradus <lb/>frigoris per gradum caloris; atque adeò non per introdu<lb/>ctionem qualitatis impetus, quæ indifferens e&longs;t ad coexi<lb/>&longs;tendum cum grauitate, aut leuitate. </s>

<s id="N177F1">Licet <expan abbr="quandoq.">quandoque</expan> ex <lb/>prædominio impediat effectum, &longs;eu motum vtriu&longs;que vel <lb/>alterutræ qualitatis oppo&longs;itæ. </s>

<s id="N177FC">Nam &longs;i dirigatur ad latera <lb/>per lineam horizonti paralellam, nec &longs;init proiectum a&longs;cen<lb/>dere, nec de&longs;cendere; ac &longs;ur&longs;um ferens pondera prohibet <lb/>de&longs;cen&longs;um, non minus ac a&longs;cen&longs;um leuium dum ea deor&longs;um <lb/>deprimit. </s>

<s id="N17807">Quod &longs;i <expan abbr="pleraq.">pleraque</expan> grauia nimia grauitate proijci <lb/>minimè valeant, <expan abbr="nullamq.">nullamque</expan> propterea impetus introductio<lb/>nem, aut productionem in &longs;e admittant: hoc certè non pro<lb/>uenit ex contrarietate, quam formaliter grauitas habeat <lb/>cum impetu; &longs;ed ex repugnantia, quam dicit ad motum <lb/>præternaturalem, ac requi&longs;itum tanquam conditionem ad <lb/>hoc vt impetus producatur, & incutiatur. </s>

<s id="N1781E">Etenim quod mo<lb/>neri nequit, nec pote&longs;t impelli, & ab&longs;que impul&longs;u, nulla &longs;ieri <lb/>valet proiectio. </s>

<s id="N1781E">Etenim quod mo<lb/>neri nequit, nec pote&longs;t impelli, & ab&longs;que impul&longs;u, nulla fieri <lb/>valet proiectio. </s>

<s id="N17825">Sicut contrà quantò plus, aut velociùs <lb/>graue aliquod à proijciente agitatur, tantò maiorem ab eo <lb/>impetum recipit, <expan abbr="longiusq.">longiusque</expan> proijcitur. </s>

<s id="N17832">Soluit igitur quæ&longs;tionem Ari&longs;toteles dicens, proiecta ex <lb/>co à latione ce&longs;&longs;are, quod virtus motiua impellens, quam <lb/>vocat potentiam, & qua ip&longs;a ferebantur, tandem de&longs;inat, <lb/>atque marce&longs;cat. </s>

<s id="N17832">Soluit igitur quæ&longs;tionem Ari&longs;toteles dicens, proiecta ex <lb/>eo à latione ce&longs;&longs;are, quod virtus motiua impellens, quam <lb/>vocat potentiam, & qua ip&longs;a ferebantur, tandem de&longs;inat, <lb/>atque marce&longs;cat. </s>

<s id="N1783B">Quod profectò duplici ex cau&longs;a euenire <lb/>po&longs;&longs;e &longs;ubiungit. </s>

<s id="N17840">Nimirum vel propter &longs;implicem retractio<lb/>nem, vt cum proiecta alterius corporis obiectu, &longs;iue repul&longs;u <lb/>retrahuntur à tali motu, ac &longs;i&longs;tere coguntur: ( Nam quippe <lb/>tunc ce&longs;&longs;ante progre&longs;&longs;u, ac motu, ce&longs;&longs;at & impetus, qui &longs;icut <lb/>præuio motu producitur, ita quamdiu durat con&longs;eruatur in <lb/>motu tanquam cum propria di&longs;po&longs;itione;) vel propter in<lb/>clinationem, quam potius ip&longs;a proiecta habeant ad alium <lb/>motum, vt &longs;ur&longs;um, vel deor&longs;um per naturalem grauitatem, <lb/>aut leuitatem quando talis inclinatio rur&longs;us coepcrit præ-<pb pagenum="256" xlink:href="005/01/264.jpg"/>ualere magis quàm virtus illa impre&longs;&longs;a à proijciente. </s>

<s id="N17840">Nimirum vel propter &longs;implicem retractio<lb/>nem, vt cum proiecta alterius corporis obiectu, &longs;iue repul&longs;u <lb/>retrahuntur à tali motu, ac &longs;i&longs;tere coguntur: ( Nam quippe <lb/>tunc ce&longs;&longs;ante progre&longs;&longs;u, ac motu, ce&longs;&longs;at & impetus, qui &longs;icut <lb/>præuio motu producitur, ita quamdiu durat con&longs;eruatur in <lb/>motu tanquam cum propria di&longs;po&longs;itione;) vel propter in<lb/>clinationem, quam potius ip&longs;a proiecta habeant ad alium <lb/>motum, vt &longs;ur&longs;um, vel deor&longs;um per naturalem grauitatem, <lb/>aut leuitatem quando talis inclinatio rur&longs;us coeperit præ-<pb pagenum="256" xlink:href="005/01/264.jpg"/>ualere magis quàm virtus illa impre&longs;&longs;a à proijciente. </s>

<s id="N17858">Quod <lb/>vtique &longs;i attentè con&longs;ideretur non pote&longs;t verificari per pro<lb/>priam contrarietatem, & incompo&longs;sibilitatem ip&longs;arum for<lb/>marum grauitatis, aut leuitatis cum impetu in eodem &longs;ubie<lb/>cto; &longs;ed potius per quandam reluctantiam ex parte effectus, <lb/>diuer&longs;orum &longs;cilicet motuum, quos cau&longs;are con&longs;ueuerunt. <lb/></s>

<s id="N17866">Idque optimè intelligitur in tractione, qua graue aliquod <lb/>hinc inde &longs;imul di&longs;trahitur. </s>

<s id="N1786B">Quandoquidem virtutes tra<lb/>hentes non &longs;unt contrariæ, &longs;ed motus ip&longs;i, &longs;eu tractiones, <lb/>quæ vel mutuò &longs;e impediunt, vel mixtum quendam motum <lb/>componunt ab vtraque diuer&longs;um: vel po&longs;t reluctantiam, al<lb/>tera tandem præualet ob validiorem virtutem à qua proce<lb/>dit. </s>

Line 3616

<s id="N17895">Alioquin &longs;i grauitas, aut leuitas proiecti, quod actu fertur <lb/>per impetum acceptum ex &longs;e ob&longs;titi&longs;&longs;et introductioni, ac <lb/>radicationi illius in &longs;ubiecto, nec &longs;ineret proiectum moueri <lb/>ad nutum illius. </s>

<s id="N1789E">Quod &longs;i non à principio, &longs;ed po&longs;tea in pro<lb/>gre&longs;&longs;u naturalis ip&longs;a inclinatio grauitatis, aut leuitatis inci<lb/>piat præualere, indicium e&longs;t, vel tunc augeri ip&longs;am graui<lb/>tatem, aut leuitatem, quod, vt diximus, e&longs;t improbabile; vel <lb/>tunc impetum langue&longs;cere, aut remitti per naturalem, ac <lb/>veluti &longs;pontaneam de&longs;itionem: qua &longs;emel admi&longs;&longs;a, iam <lb/>optimè intelligitur, effectum grauitatis, aut leuitatis præua<lb/>lere contra lationem diuer&longs;am ac violentam. </s>

<s id="N178AF">Nam tenden<lb/>tia grauis deor&longs;um, aut leuis &longs;ur&longs;um, non pote&longs;t impediri à <lb/>quacunque latione impetus remi&longs;si, &longs;ed potius impetu lan<lb/>gue&longs;cente, grauitate autem, aut leuitate in &longs;uo robore per<lb/>&longs;i&longs;tente, paulatim motus degenerat à latione violenta <lb/>quou&longs;que ab&longs;olutè fiat iuxta inclinationem naturalem, cum <lb/>&longs;cilicet impetus omninò de&longs;ierit. </s>

<s id="N178BE">Ab&longs;oluta igitur cau&longs;a <lb/>ce&longs;&longs;ationis à latione in proiectis, e&longs;t ip&longs;a de&longs;itio impetus, <pb pagenum="257" xlink:href="005/01/265.jpg"/>qui cum contrarium non habcat, <expan abbr="&longs;itq.">&longs;itque</expan> &longs;emper eiu&longs;dem &longs;pe<lb/>ciei quocunque tendat, ex &longs;e incipit langue&longs;cere, & hebeta<lb/>ri po&longs;t moram aliquam à &longs;ua productione ob defectum cau<lb/>&longs;æ con&longs;eruantis, & commune e&longs;t pluribus qualitatibus in <lb/>genere di&longs;po&longs;itionis facilè mobilis à &longs;ubiecto, ac pa&longs;&longs;ibilis <lb/>qualitatis, & pa&longs;sionis propriè dictæ; imò & in genere natu<lb/>ralis potentiæ, & impotentiæ. </s>

<s id="N178BE">Ab&longs;oluta igitur cau&longs;a <lb/>ce&longs;&longs;ationis à latione in proiectis, e&longs;t ip&longs;a de&longs;itio impetus, <pb pagenum="257" xlink:href="005/01/265.jpg"/>qui cum contrarium non habeat, <expan abbr="&longs;itq.">&longs;itque</expan> &longs;emper eiu&longs;dem &longs;pe<lb/>ciei quocunque tendat, ex &longs;e incipit langue&longs;cere, & hebeta<lb/>ri po&longs;t moram aliquam à &longs;ua productione ob defectum cau<lb/>&longs;æ con&longs;eruantis, & commune e&longs;t pluribus qualitatibus in <lb/>genere di&longs;po&longs;itionis facilè mobilis à &longs;ubiecto, ac pa&longs;&longs;ibilis <lb/>qualitatis, & pa&longs;sionis propriè dictæ; imò & in genere natu<lb/>ralis potentiæ, & impotentiæ. </s>

<s id="N178D8">Nam & &longs;onus, & odor, & &longs;a<lb/>por, po&longs;tquam aliquanti&longs;per viguerint, ex &longs;e remittuntur, ac <lb/>de&longs;inunt ab&longs;que proprio contrario expellente in eodem <lb/>&longs;ubiecto. </s>

<s id="N178E1">Sicut & rubedo, quæ procedit ex verecundia, & <lb/>ab Ari&longs;torele inter pa&longs;siones enumeratur. </s>

<s id="N178E1">Sicut & rubedo, quæ procedit ex verecundia, & <lb/>ab Ari&longs;totele inter pa&longs;siones enumeratur. </s>

<s id="N178E6">Itemque &longs;pecies <lb/>intentionales expre&longs;&longs;æ, imò & impre&longs;&longs;æ po&longs;t diuturnam ce&longs;<lb/>&longs;ationem ab v&longs;u, ac renouatione illarum. </s>

<s id="N178EF">Nec ob&longs;tat, quòd impetus lati corporis, vel proiecti in, <lb/>medio cur&longs;u detenti non vltrò ac &longs;ponte &longs;ua, &longs;ed vi detinen<lb/>ris corrumpi videatur; <expan abbr="itemq.">itemque</expan> non &longs;ucce&longs;siuè, &longs;ed in in&longs;tan<lb/>ti cum primò ce&longs;&longs;at à motu. </s>

<s id="N178FC">Nam virtus detinentis non <lb/>opponitur virtuti motiuæ, &longs;iue naturali, &longs;iue violentæ; &longs;ed <lb/>ef&longs;ectui illarum: Vnde &longs;icut per detentionem corporis non <lb/>corrumpitur grauitas, aut leuitas illius, &longs;ic neque impetus. <lb/></s>

<s id="N178FC">Nam virtus detinentis non <lb/>opponitur virtuti motiuæ, &longs;iue naturali, &longs;iue violentæ; &longs;ed <lb/>effectui illarum: Vnde &longs;icut per detentionem corporis non <lb/>corrumpitur grauitas, aut leuitas illius, &longs;ic neque impetus. <lb/></s>

<s id="N17906">Per accidens tamen acceleratur corruptio, ac de&longs;itio impe<lb/>tusin ip&longs;a detentione, quia vt diximus, ce&longs;&longs;ante motu ce&longs;&longs;at <lb/>di&longs;po&longs;itio, atque conditio, qua maximè impetus con&longs;erua<lb/>tur. </s>

<s id="N1790F"><expan abbr="Nullumq.">Nullumque</expan> e&longs;t inconueniens, effectum concurrere ad <lb/>con&longs;eruationem cau&longs;æ tanquam di&longs;po&longs;itionem, aut condi<lb/>tionem. </s>

<s id="N17919">Nec propterea talis de&longs;itio fit tota &longs;imul in in<lb/>&longs;tanti; Quandoquidem licet impetus po&longs;t primum impul<lb/>&longs;um, ac repul&longs;um amplius à detinente non &longs;entiatur, videli<lb/>der propter exuperantiam virtutis illius qua vincitur, & &longs;u<lb/>peratur: hoc tamen non arguit cum totum fimul in primo <lb/>in&longs;tanti deperij&longs;&longs;e; &longs;ed tantum propter ob&longs;taculum ad ce&longs;&longs;a<lb/>tionem motus breuimorula remi&longs;&longs;um paulatim fui&longs;&longs;e, ac <lb/>tandem penitus de&longs;i&longs;&longs;e. </s>

<s id="N17919">Nec propterea talis de&longs;itio fit tota &longs;imul in in<lb/>&longs;tanti; Quandoquidem licet impetus po&longs;t primum impul<lb/>&longs;um, ac repul&longs;um amplius à detinente non &longs;entiatur, videli<lb/>cet propter exuperantiam virtutis illius qua vincitur, & &longs;u<lb/>peratur: hoc tamen non arguit cum totum simul in primo <lb/>in&longs;tanti deperij&longs;&longs;e; &longs;ed tantum propter ob&longs;taculum ad ce&longs;&longs;a<lb/>tionem motus breui morula remi&longs;&longs;um paulatim fui&longs;&longs;e, ac <lb/>tandem penitus de&longs;i&longs;&longs;e. </s>

<s id="N1792A">Etenim ni&longs;i omni ex parte ip&longs;um <lb/>proiectum detineatur, adhuc po&longs;t acceptum repul&longs;um vide<lb/>mus illud re&longs;ilire, ac pauli&longs;per imperum eius quamuis retor<lb/>tum, ac langue&longs;centem non nibil vrgere. </s>

<s id="N1792A">Etenim ni&longs;i omni ex parte ip&longs;um <lb/>proiectum detineatur, adhuc po&longs;t acceptum repul&longs;um vide<lb/>mus illud re&longs;ilire, ac pauli&longs;per impetum eius quamuis retor<lb/>tum, ac langue&longs;centem non nihil vrgere. </s>

<s id="N17939">Sed contra etiam e&longs;t, quia &longs;i qualitas prædicta' impetus <lb/>impre&longs;si deficeret per meram de&longs;itionem ad remotionem <lb/>impellentis, vel proijcientis, &longs;tatim atque proiectum elabi<lb/>tur è manu proijcientis, inciperet ip&longs;a impetus remi&longs;sio, <lb/><expan abbr="cre&longs;ceretq.">cre&longs;ceretque</expan> v&longs;que ad totalem de&longs;itionem. </s>

<s id="N17947">At non ita con<lb/>tingit, cum potius proiecta è manibus proijcientium egre&longs;<lb/>&longs;a, tardius moueantur à principio, quàm in progre&longs;&longs;u v&longs;que <lb/>ad certum terminum, ad quem virtus impul&longs;iua valet per<lb/>tingere, <expan abbr="validiusq.">validiusque</expan> propterea feriant in proportionata qua<lb/>dam di&longs;tantia, quàm prope nimis ip&longs;um proijciens: Ergo <lb/>indicium e&longs;t ip&longs;am impetus qualitatem, non de&longs;icere, nec <lb/>remitti &longs;tatim ad defectum cau&longs;æ con&longs;eruantis, & impel<lb/>lentis, &longs;ed potius augeri per aliquod tempus, deinde paula<lb/>tim remitti.ac tandem di&longs;cedere ad expul&longs;ionem ortam ex <lb/>qualitate contraria. </s>

<s id="N17947">At non ita con<lb/>tingit, cum potius proiecta è manibus proijcientium egre&longs;<lb/>&longs;a, tardius moueantur à principio, quàm in progre&longs;&longs;u v&longs;que <lb/>ad certum terminum, ad quem virtus impul&longs;iua valet per<lb/>tingere, <expan abbr="validiusq.">validiusque</expan> propterea feriant in proportionata qua<lb/>dam di&longs;tantia, quàm prope nimis ip&longs;um proijciens: Ergo <lb/>indicium e&longs;t ip&longs;am impetus qualitatem, non deficere, nec <lb/>remitti &longs;tatim ad defectum cau&longs;æ con&longs;eruantis, & impel<lb/>lentis, &longs;ed potius augeri per aliquod tempus, deinde paula<lb/>tim remitti.ac tandem di&longs;cedere ad expul&longs;ionem ortam ex <lb/>qualitate contraria. </s>

<s id="N17964">Verùm huic obiectioni facilè occurritur dicendo, impe<lb/>tum po&longs;t remotionem impellentis, nullum ex &longs;e incremen<lb/>tum po&longs;&longs;e &longs;u&longs;cipere, &longs;iue habeat, &longs;iue non habeat qualitatem <lb/>contrariam; cau&longs;amque tarditatis, &longs;eu minoris velocitatis <lb/>prædictæ in principio, e&longs;&longs;e maiorem re&longs;i&longs;tentiam, quam &longs;ub <lb/>ip&longs;o initio proiectum reperit in intermedio. </s>

<s id="N17971">Nam aer, verbi <lb/>gratia, vel aqua quie&longs;cens, cum primo à proiecto impellitur <lb/>magis valet re&longs;i&longs;tere, quàm cum paulatim dimota per no<lb/>uum &longs;emper impul&longs;um vlterius abire cogitur, vr locum re<lb/>linquat ip&longs;i proiecto. </s>

<s id="N1797C">Impetus enim in eodem aere, vel <lb/>aqua impre&longs;&longs;us cre&longs;cit &longs;emper cum motu, quia proiectum <lb/>dum fertur &longs;emper impellit, ac impellendo &longs;ucce&longs;siuè in<lb/>tendit effectum: magis autem inten&longs;us impetus in ip&longs;o me<lb/>dio, magis ac magis dif&longs;unditur in vlteriores partes eiu&longs;dem <lb/>medij, quod propterea velocius di&longs;cedit, ac locum, quem <lb/>habet relinquendo, minus re&longs;i&longs;tit. </s>

<s id="N1797C">Impetus enim in eodem aere, vel <lb/>aqua impre&longs;&longs;us cre&longs;cit &longs;emper cum motu, quia proiectum <lb/>dum fertur &longs;emper impellit, ac impellendo &longs;ucce&longs;siuè in<lb/>tendit effectum: magis autem inten&longs;us impetus in ip&longs;o me<lb/>dio, magis ac magis dif&longs;funditur in vlteriores partes eiu&longs;dem <lb/>medij, quod propterea velocius di&longs;cedit, ac locum, quem <lb/>habet relinquendo, minus re&longs;i&longs;tit. </s>

<s id="N1798B">Quod idem in cau&longs;a <lb/>e&longs;t &longs;altem ex parte, vt motus grauium è &longs;uperno aliquo lo<lb/>co <expan abbr="decid&etilde;tium">decidentium</expan> velocior &longs;it in progre&longs;&longs;u, quàm in principio, <lb/>vt &longs;upra innuimus. </s>

<s id="N17998">Etenim inter motum grauium natura<lb/>lem, quo illa tendunt deor&longs;um, ac motum violentum, quo <lb/>tendunt &longs;ur&longs;um, vel ad latera, hoc &longs;olum intere&longs;t in propo&longs;i-<pb pagenum="259" xlink:href="005/01/267.jpg"/>to, quod motus naturalis &longs;ucce&longs;siuè &longs;emper fiat velocior, <lb/>at que velocior in partibus po&longs;terioribus v&longs;que in finem <lb/>cum &longs;emper grauitas per&longs;eueret in eadem intentione, <expan abbr="mi-nusq.">mi<lb/>nusque</expan> re&longs;i&longs;tat intermedium, nec non & maiori &longs;emper feran<lb/>tur impul&longs;u ab ei&longs;dem grauibus in eodem motu produ<lb/>cto: motus autem violentus licet in progre&longs;&longs;u v&longs;que ad <lb/>certum terminum &longs;imiliter fiat velocior, tandem lan<lb/>gue&longs;cente impetu rur&longs;us incipiat retardari quou&longs;que de&longs;i<lb/>nat in quietem, vel degeneret in motum naturalem cor<lb/>rupta penitus virtute motiua ip&longs;ius impetus à proijciente <lb/>impre&longs;&longs;a. </s>

Line 3648

<s id="N179EF">Difficultas autem in eo con&longs;i&longs;tit, quod cum huiu&longs;modi <lb/>motus ex parte &longs;it obliquus <expan abbr="quidã">quidam</expan> a&longs;cen&longs;us, & ex parte <expan abbr="de-&longs;c&etilde;&longs;us">de<lb/>&longs;cen&longs;us</expan>, nec à grauitate <expan abbr="d&utilde;taxat">duntaxat</expan> videtur po&longs;&longs;e procedere, nec <lb/>ab alia &longs;imul virtute impre&longs;&longs;a, quæ moueat in <expan abbr="cõtrari&utilde;">contrarium</expan>: præ<lb/>&longs;ertim <expan abbr="c&utilde;">cum</expan> nulla appareat cau&longs;a effectiua talis virtutis; ni&longs;i di<lb/>catur ab eodem graui manare ( vt præcedenti quæ&longs;tione <lb/>probatum e&longs;t ) quod cum operetur per grauitatem intrin&longs;e<lb/>cam, quæ iugiter per&longs;euerat in ip&longs;o, iugiter etiam talem vir<lb/>tutem in &longs;e con&longs;eruaret, quæ propterea nunquam ce&longs;&longs;aret à <lb/>motu alterno iam explicato, <expan abbr="&longs;icq.">&longs;icque</expan> corpus per funem pro<lb/>pendens, &longs;emel promotum, alternatim ac &longs;emper, &longs;eu pe<pb pagenum="260" xlink:href="005/01/268.jpg"/>renniter moueretur; partim &longs;cilicet à grauitate, ac partim <lb/>à virtute impre&longs;&longs;a, per&longs;euerante &longs;emper grauitate cum tali <lb/>virtute impul&longs;iua. </s>

<s id="N17A29"><expan abbr="Dicend&utilde;">Dicendum</expan> tàmen e&longs;t, corpus <expan abbr="prædict&utilde;">prædictum</expan> <expan abbr="&longs;tatimatq.">&longs;tatimatque</expan> relinqui<lb/>tur in &longs;ua libertate <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan> ex vi propriæ grauitatis ea via <lb/>qua pote&longs;t, nempe obliquè per arcum, <expan abbr="de&longs;crib&etilde;do">de&longs;cribendo</expan> <expan abbr="portion&etilde;">portionem</expan> <lb/>circumferentiæ circa punctum, in quo funis e&longs;t religatus <lb/>tanquam circa centrum: Per hunc autem de&longs;cen&longs;um impe<lb/>tum quendam in &longs;e ab eodem corpore produci, quod cum <lb/>vlterius deor&longs;um tendere nequeat ob funis detentionem, <lb/>qua&longs;i re&longs;ilire cogitur, ac denuò &longs;ur&longs;um attolli per oppo&longs;itum <lb/>arcum &longs;eu viam, ita vt corpus po&longs;tquam à dextris de&longs;cendit <lb/>per grauitatem; a&longs;cendit ad læuam per impetum, quo lan<lb/>gue&longs;cente, ac de&longs;inente rur&longs;us per eandem viam corpus ip<lb/>&longs;um grauitate vrgente de&longs;cendat: Per quem de&longs;cen&longs;um <lb/>nouus impetus producitur ad nouum a&longs;cen&longs;um per&longs;icien<lb/>dum, & &longs;ic deinceps. </s>

<s id="N17A29"><expan abbr="Dicend&utilde;">Dicendum</expan> tàmen e&longs;t, corpus <expan abbr="prædict&utilde;">prædictum</expan> <expan abbr="&longs;tatimatq.">&longs;tatim atque</expan> relinqui<lb/>tur in &longs;ua libertate <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan> ex vi propriæ grauitatis ea via <lb/>qua pote&longs;t, nempe obliquè per arcum, <expan abbr="de&longs;crib&etilde;do">de&longs;cribendo</expan> <expan abbr="portion&etilde;">portionem</expan> <lb/>circumferentiæ circa punctum, in quo funis e&longs;t religatus <lb/>tanquam circa centrum: Per hunc autem de&longs;cen&longs;um impe<lb/>tum quendam in &longs;e ab eodem corpore produci, quod cum <lb/>vlterius deor&longs;um tendere nequeat ob funis detentionem, <lb/>qua&longs;i re&longs;ilire cogitur, ac denuò &longs;ur&longs;um attolli per oppo&longs;itum <lb/>arcum &longs;eu viam, ita vt corpus po&longs;tquam à dextris de&longs;cendit <lb/>per grauitatem; a&longs;cendit ad læuam per impetum, quo lan<lb/>gue&longs;cente, ac de&longs;inente rur&longs;us per eandem viam corpus ip<lb/>&longs;um grauitate vrgente de&longs;cendat: Per quem de&longs;cen&longs;um <lb/>nouus impetus producitur ad nouum a&longs;cen&longs;um perficien<lb/>dum, & &longs;ic deinceps. </s>

<s id="N17A5D">Quoniam verò corpus ip&longs;ùm per im<lb/>petum in &longs;e media grauitate productum, nunquam pote&longs;t <lb/>tantum a&longs;cendere, quantum per ip&longs;am grauitatem de&longs;cen<lb/>dit ob re&longs;i&longs;tentiam, quam reperit in a&longs;cen&longs;u &longs;ecus ac in de<lb/>&longs;cen&longs;u: hinc e&longs;t, vt &longs;ecundus de&longs;cen&longs;us per minorem arcum <lb/>etiam fiat, per <expan abbr="eumq.">eumque</expan> minor impetus producatur, quàm pe<gap/><lb/>primum; ex quo minori impetu adhuc minor con&longs;tituatur <lb/>alius a&longs;cen&longs;us, ac de&longs;cen&longs;us, & &longs;ic paulatim per minores, ac <lb/>minores arcus corpus ip&longs;um dimoueacur, quou&longs;que penitus <lb/>quie&longs;cat in puncto explicato. </s>

<s id="N17A5D">Quoniam verò corpus ip&longs;ùm per im<lb/>petum in &longs;e media grauitate productum, nunquam pote&longs;t <lb/>tantum a&longs;cendere, quantum per ip&longs;am grauitatem de&longs;cen<lb/>dit ob re&longs;i&longs;tentiam, quam reperit in a&longs;cen&longs;u &longs;ecus ac in de<lb/>&longs;cen&longs;u: hinc e&longs;t, vt &longs;ecundus de&longs;cen&longs;us per minorem arcum <lb/>etiam fiat, per <expan abbr="eumq.">eumque</expan> minor impetus producatur, quàm per <lb/>primum; ex quo minori impetu adhuc minor con&longs;tituatur <lb/>alius a&longs;cen&longs;us, ac de&longs;cen&longs;us, & &longs;ic paulatim per minores, ac <lb/>minores arcus corpus ip&longs;um dimoueatur, quou&longs;que penitus <lb/>quie&longs;cat in puncto explicato. </s>

<s id="N17A79">Quæ&longs;tio Trige&longs;imatertia.</s>

<s id="N17A7E">C<emph type="italics"/>vr quippiam non pecutiarcm &longs;ibi fertur la<lb/>tionem, impul&longs;ore alioquin non con&longs;equenter <lb/>An videlicet quoniam primum id efficit, vt <lb/>alterum impellat: <expan abbr="illudq.">illudque</expan> rur&longs;um vt alte<lb/>rum? </s>

<s id="N17A7E">C<emph type="italics"/>vr quippiam non peculiarem &longs;ibi fertur la<lb/>tionem, impul&longs;ore alioquin non con&longs;equenter?</s>

<s id="N17A90">Ce<32>at autem quando non pote&longs;t am<lb/>plius facers primum impellear, id quod<emph.end type="italics"/><pb pagenum="261" xlink:href="005/01/269.jpg"/><emph type="italics"/>fertur, vt impellat: & quoniam ip&longs;ius lati grauitas nutu <lb/>&longs;uo declinat magis, quàm impellentis in ante &longs;it potentia.<emph.end type="italics"/></s>

<s id="N17A82">An videlicet quoniam primum id efficit, vt <lb/>alterum impellat: <expan abbr="illudq.">illudque</expan> rur&longs;um vt alte<lb/>rum? </s>

<s id="N17A90">Ce<32>at autem quando non pote&longs;t am<lb/>plius facere primum impelleat, id quod <emph.end type="italics"/><pb pagenum="261" xlink:href="005/01/269.jpg"/><emph type="italics"/>fertur, vt impellat: & quoniam ip&longs;ius lati grauitas nutu <lb/>&longs;uo declinat magis, quàm impellentis in ante &longs;it potentia.<emph.end type="italics"/></s>

<s id="N17AA4">COMMENTARIVS.</s>

<s id="N17AAA">Cvm frequenti&longs;&longs;imè de impetu, &longs;iue impul&longs;u, quo <lb/>grauia in diuer&longs;a loca feruntur &longs;ermo in his quæ&longs;tio<lb/>nibus incidi&longs;&longs;et, nunquam quod ille &longs;it, hucu&longs;que de<lb/>terminauerat Ari&longs;toteles. </s>

<s id="N17AAA">Cvm frequenti&longs;&longs;imè de impetu, &longs;iue impul&longs;u, quo <lb/>grauia in diuer&longs;a loca feruntur &longs;ermo in his quæ&longs;tio<lb/>nibus incidi&longs;&longs;et, nunquam quod ille &longs;it, huiu&longs;que de<lb/>terminauerat Ari&longs;toteles. </s>

<s id="N17AB4">Quod licet ob&longs;curin&longs;culè, op<lb/>portunè tamen hic præ&longs;tat agendo de motu proiectorum, <lb/>po&longs;t proximam quæ&longs;tionem, qua de ce&longs;&longs;atione illorum à <lb/>motu, ac de&longs;itione eiu&longs;dem impul&longs;us, vt vidimus pertran<lb/>&longs;iuit. </s>

Line 3707

Line 3708

<s id="N17BF7">Illud autem his in locis magnopere ob&longs;eruandum e&longs;t, <lb/>Ari&longs;totelem &longs;emper loqui de motore extrin&longs;eco, quem in <lb/>motibus quoque naturalibus grauium, & leuium ibidem <lb/>admittit, ne concedere cogatur corpora inanimata moueri <lb/>à &longs;eip&longs;is, huiu&longs;modi motus referens ad generantem grauita<lb/>tem, aut leuitatem, vel ad remouentem impedimenta. <lb/></s>

<s id="N17C05">Quamobrem &longs;icut ip&longs;e Philo&longs;ophus non per hoc negat, <lb/>grauia, & leuia habere for mam quandam inhærentem, at<lb/>que intrin&longs;ecam, quæ natura &longs;ua tendunt &longs;ur&longs;um, aut deer<lb/>&longs;um, vt apertè conc e&longs;&longs;erat tex. præcedenti nempe 8. Phy&longs;ic. <lb/>tex. 32. ita nec pote&longs;t negare, proiecta præter canfam ex<lb/>trin&longs;ecam &longs;uæ motionis piæternaturalis, videlicer primum <pb pagenum="264" xlink:href="005/01/272.jpg"/>motorem, aut aerem impellentem, habere propriam virtu<lb/>tem motiuam intrin&longs;ecam, ip&longs;is à proijciente, vel ambiente <lb/>impre&longs;&longs;am, per quam proximè feruntur quò diriguntur, &longs;icut <lb/>per leuitatem &longs;ur&longs;um, ac per grauitatem deor&longs;um. </s>

<s id="N17C05">Quamobrem &longs;icut ip&longs;e Philo&longs;ophus non per hoc negat, <lb/>grauia, & leuia habere formam quandam inhærentem, at<lb/>que intrin&longs;ecam, quæ natura &longs;ua tendunt &longs;ur&longs;um, aut deor<lb/>&longs;um, vt apertè conce&longs;&longs;erat tex. præcedenti nempe 8. Phy&longs;ic. <lb/>tex. 32. ita nec pote&longs;t negare, proiecta præter causam ex<lb/>trin&longs;ecam &longs;uæ motionis præternaturalis, videlicet primum <pb pagenum="264" xlink:href="005/01/272.jpg"/>motorem, aut aerem impellentem, habere propriam virtu<lb/>tem motiuam intrin&longs;ecam, ip&longs;is à proijciente, vel ambiente <lb/>impre&longs;&longs;am, per quam proximè feruntur quò diriguntur, &longs;icut <lb/>per leuitatem &longs;ur&longs;um, ac per grauitatem deor&longs;um. </s>

<s id="N17C22">Quam <lb/>quidem virtutem, vt vidimus, &longs;æpè ip&longs;e in&longs;inuat, & à neote<lb/>ncis rem di&longs;tinctius pertractantibus vocatur impetus, &longs;eu <lb/>impul&longs;us. </s>

<s id="N17C22">Quam <lb/>quidem virtutem, vt vidimus, &longs;æpè ip&longs;e in&longs;inuat, & à neote<lb/>ricis rem di&longs;tinctius pertractantibus vocatur impetus, &longs;eu <lb/>impul&longs;us. </s>

<s id="N17C2B">Qui cum diu non per&longs;eueret in &longs;ubiecto, nec ei <lb/>competat ex natura &longs;ua: Cumq determinatè tantum va<lb/>leat mouere iuxta proijcientis directionem, non &longs;equitur il<lb/>lud inconueniens, quod Ari&longs;toteles pro ratione dubitandi <lb/>propo&longs;uerat, nimirum fore, vt proiecta <expan abbr="mouer&etilde;tur">mouerentur</expan> à &longs;eip&longs;is, <lb/>& ab intrin&longs;eco, non &longs;ecus ac animalia, vel &longs;altem corpora, <lb/>quæ natuia mouentur, non violentia. </s>

<s id="N17C2B">Qui cum diu non per&longs;eueret in &longs;ubiecto, nec ei <lb/>competat ex natura &longs;ua: <expan abbr="Cumq">Cumque</expan> determinatè tantum va<lb/>leat mouere iuxta proijcientis directionem, non &longs;equitur il<lb/>lud inconueniens, quod Ari&longs;toteles pro ratione dubitandi <lb/>propo&longs;uerat, nimirum fore, vt proiecta <expan abbr="mouer&etilde;tur">mouerentur</expan> à &longs;eip&longs;is, <lb/>& ab intrin&longs;eco, non &longs;ecus ac animalia, vel &longs;altem corpora, <lb/>quæ natura mouentur, non violentia. </s>

<s id="N17C3E">Non &longs;ufficit enim mo<lb/>ueri à principio intrin&longs;eco ad con&longs;tituendum motum natu<lb/>ralem, &longs;ed amplius requiritur, vt ip&longs;um principium &longs;it &longs;tabi<lb/>le, acnaturæ debitum, cuiu&longs;modi non e&longs;t virtus impre&longs;&longs;a <lb/>proiectis. </s>

Line 3717

Line 3718

<s id="N17C5A">Sen&longs;u enim con&longs;tat, nulla <lb/>ventorum irruentium vi quie&longs;centem lapidem, aut plum<lb/>beam pilam po&longs;&longs;e &longs;u&longs;tolli, & in longinqua transferri, &longs;icut <lb/>nec ligneam, aut ferream rotam conuolui, & alia eiu&longs;modi <lb/>corpora promoueri; quæ tamen impetu incu&longs;&longs;o, facilè præ<lb/>&longs;tantur à manu, etiam contra omnem ventorum conatum <lb/>vehementi&longs;&longs;imè ex aduer&longs;o perflantium. </s>

<s id="N17C69">Imò & ferreas <lb/>pilas contra eundem flatum videmus è tormentis explodi, <lb/>ac non minus mænia quatere; & ingentia &longs;axa eminus ac <lb/>&longs;umma celeritate per aera ferri, ip&longs;o aere in contrarium ni<lb/>tente, ac repellente. </s>

<s id="N17C74">Vanumque videtur illud effugium, <lb/>flante vento, quamuis totus aer commoueatur, pars tamen <lb/>aeris, quæ tangit proiectum, cum vnitè magis moueatur à <lb/>proijciente, maiorem vim obtinere ad promouendum, quàm <lb/>vllum ventum in contr arium. </s>

<s id="N17C7F">Siquidem veluti per follem, <pb pagenum="265" xlink:href="005/01/273.jpg"/>aut fi&longs;tulam aer emittendus e&longs;&longs;et, ac pellendus à prijcien<lb/>te po&longs;t terga proiecti, po&longs;terioremque partem, qua neruo <lb/>aptari &longs;olet &longs;agitta ex directo feriret, tanquam ventus na<lb/>uem in puppi: <expan abbr="tantaq.">tantaque</expan> demum e&longs;&longs;et virtus ip&longs;ius aeris in <lb/>tam paruam quantitatem incidentis, vt totum corpus emi<lb/>nus impellere contra quamcunque reliqui aeris vniuer&longs;i ve<lb/>hementiam præualeret, quod e&longs;t ab&longs;urdum. </s>

<s id="N17C7F">Siquidem veluti per follem, <pb pagenum="265" xlink:href="005/01/273.jpg"/>aut fi&longs;tulam aer emittendus e&longs;&longs;et, ac pellendus à proijcien<lb/>te po&longs;t terga proiecti, po&longs;terioremque partem, qua neruo <lb/>aptari &longs;olet &longs;agitta ex directo feriret, tanquam ventus na<lb/>uem in puppi: <expan abbr="tantaq.">tantaque</expan> demum e&longs;&longs;et virtus ip&longs;ius aeris in <lb/>tam paruam quantitatem incidentis, vt totum corpus emi<lb/>nus impellere contra quamcunque reliqui aeris vniuer&longs;i ve<lb/>hementiam præualeret, quod e&longs;t ab&longs;urdum. </s>

<s id="N17C99">Accedit quia nec aquam comitari, atque impellere vi<lb/>demus nauiculas, ac triremes quemcunque cur&longs;um in mari <lb/>tenentes, quippe quæ &longs;æpius contra fluxum, ac fluctus illius <lb/>&longs;olo remorum pul&longs;u feruntur: Nec aerem circumob&longs;i&longs;ten<lb/>tem con&longs;tat, rotam figuli, vel &longs;imilem, quæ in gyrum velo<lb/>ci&longs;&longs;imè ducitur promouere, cum accen&longs;um lumen prope <lb/>illam extinguere, aut inflectere quamuis concitatus ip&longs;e <lb/>minimè valeat. </s>

Line 3729

Line 3730

<s id="N17CEB">Demum ratio à priori videtur, quoniam aer ex &longs;e quie<lb/>tus e&longs;t, nec pote&longs;t aliud mouere, ni&longs;i ip&longs;e ab alio moueatur, <lb/>& impellatur: dum autem impellitur, vel accipit virtutem <lb/>aliquam ab impellente, vel nullam: &longs;i aliquam accipit, eam <lb/>potius, vel &longs;imilem dicemus accipere proiectum immedia<lb/>tè: &longs;i nullam accipit; ergo tamdiu poterit impellere quam. <lb/></s>

<s id="N17CF9">diu actu impellitur (vt baculus, vel aliud in&longs;trumentum ma<lb/>nu dimotum ad aliud impellendum) ce&longs;&longs;ante verò impul<lb/>&longs;ore, ip&longs;e quoque ab impul&longs;u de&longs;i&longs;ter. </s>

<s id="N17D00">Quod idem conclu<lb/>ditur de pluribus, ac pluribus intermedijs, quan do alterum <lb/>ab altero nullam accipit virtutem inhærentem, &longs;ed pendent <lb/>ab actuali influxu, ac motione prioris. </s>

<s id="N17D09">At &longs;en&longs;u con&longs;tat ce&longs;<lb/>&longs;ante primo motore, &longs;eu proijciente, adhuc proiecta perfer<lb/>ri vlteriu&longs;que propelli: Ergo vel non propelluntur ab aere, <lb/>vel aer propellens non ab&longs;que virtute à proijciente recepta <lb/>propellit. </s>

<s id="N17D14">Semel autem admi&longs;&longs;a huiu&longs;modi virtute impul<lb/>&longs;iua in aere, multo magis ac potiori iure admittenda erit <lb/>in ip&longs;is proiectis. </s>

<s id="N17D1D">Quod &longs;i dicatur proiectum &longs;emper impelli ab aere &longs;ucce<lb/>dente à tergo ad replendum vacuum, quod ab ip&longs;o proiecto <lb/>relinquitur, nulla vi ab alio recepta, vel in vlteriores partes <lb/>aeris transfu&longs;a; tunc concluderetur, huiu&longs;modi motum ne<lb/>ce&longs;&longs;ario e&longs;&longs;e perennem. </s>

<s id="N17D28">Quandoquidem &longs;icut nunquam <lb/>ce&longs;lat naturalis illa propen&longs;io, qua corpora feruntur ad re<lb/>plendum vacuum, ita nunquam ce&longs;&longs;are po&longs;&longs;et effectus ma<lb/>nans ab illa; quod cum &longs;it fal&longs;um, remanet, & fal&longs;um e&longs;&longs;e il<lb/>lud, ex quo &longs;equitur. </s>

<s id="N17D28">Quandoquidem &longs;icut nunquam <lb/>ce&longs;sat naturalis illa propen&longs;io, qua corpora feruntur ad re<lb/>plendum vacuum, ita nunquam ce&longs;&longs;are po&longs;&longs;et effectus ma<lb/>nans ab illa; quod cum &longs;it fal&longs;um, remanet, & fal&longs;um e&longs;&longs;e il<lb/>lud, ex quo &longs;equitur. </s>

<s id="N17D35">Cum igitur aer commotus, vel aliud medium, tanquam <lb/>in&longs;trumentum proijcientis, non &longs;ufficiat ad <expan abbr="perfici&etilde;dum">perficiendum</expan> mo<lb/>tum proiectorum, po&longs;tquam ea ab ip&longs;o proijciente rece&longs;&longs;e<lb/>rint, nec aliud ad id præ&longs;tandam appareat, remanet cau&longs;am <lb/>proximam, ac principalem motus prædicti e&longs;&longs;e ip&longs;amet cor<lb/>pora proiecta, prout informata qualitate impetus, quem <pb pagenum="267" xlink:href="005/01/275.jpg"/>hactenus à proijciente in actu proiectionis acceperunt. </s>

Line 3744

Line 3745

<s id="N17D5E">Dicimus autem præfatum impetum, &longs;eu virtutem moti<lb/>uam impre&longs;&longs;am, e&longs;&longs;e propriam qualitatem de &longs;ecunda &longs;pe<lb/>cie, quæ dicitur potentia in prædicamento qualitatis, diuer<lb/>&longs;am tamen e&longs;&longs;entialiter à virtute motiua naturali, vt e&longs;t gra<lb/>uitas, aut leuitas. </s>

<s id="N17D69">Quatenus nimirum e&longs;t principium forma<lb/>le intrin&longs;ecum quo producitur motus localis, non debitus <lb/>naturæ, &longs;ed præter vel contra inclinationem illius fecus ac <lb/>motus, qui producitur à grauitate, aut leuitate, qui &longs;emper <lb/>e&longs;t determinatus ad vnum locum, iuxta inclinationem pro<lb/>priæ naturæ. </s>

<s id="N17D69">Quatenus nimirum e&longs;t principium forma<lb/>le intrin&longs;ecum quo producitur motus localis, non debitus <lb/>naturæ, &longs;ed præter vel contra inclinationem illius secus ac <lb/>motus, qui producitur à grauitate, aut leuitate, qui &longs;emper <lb/>e&longs;t determinatus ad vnum locum, iuxta inclinationem pro<lb/>priæ naturæ. </s>

<s id="N17D76">Motus enim productus ab impetu indifferens <lb/>e&longs;t ad quamcunque po&longs;itionem, vel locum, ita vt quoquo<lb/>uer&longs;um ab eo proiecta ferantur: Imò & pila, vt Ari&longs;toteles <lb/>aduertit. </s>

<s id="N17D7F">8. Phy&longs;icor. tex. 22. per eundem impetum à proij<lb/>ciente receptum in parietem illidit, ac inde re&longs;ilit, qui mo<lb/>tus &longs;unt inter &longs;e contrarij. </s>

<s id="N17D8A">Et crocæ, vel te&longs;tulæ eodem, <lb/>impetu, quo in &longs;uperficiem aquæ proijciuntur, vix ad con<lb/><gap/>actum peruenientes, per aliam lineam inde re&longs;iliunt, ite<lb/>rumque vlterius, tanquam per &longs;altus pluries in eandem &longs;u<lb/>perficiem incidunt, quou&longs;que impetu extincto immergan<lb/>tur. </s>

<s id="N17D8A">Et crocæ, vel te&longs;tulæ eodem, <lb/>impetu, quo in &longs;uperficiem aquæ proijciuntur, vix ad con<lb/>tactum peruenientes, per aliam lineam inde re&longs;iliunt, ite<lb/>rumque vlterius, tanquam per &longs;altus pluries in eandem &longs;u<lb/>perficiem incidunt, quou&longs;que impetu extincto immergan<lb/>tur. </s>

<s id="N17D9A">Vnde colligitur ip&longs;am qualitatem impetus eiu&longs;dem e&longs;&longs;e <lb/>infimæ &longs;peciei in omnibus proiectis, ac motibus violentis. <lb/></s>

Line 3764

Line 3765

<s id="N17E12">explicatum e&longs;t. </s>

<s id="N17E17">Ex quo pariter intelligitur, cur proiecta in vacuo non <lb/>mouerentur proprio motu, vt docet Ari&longs;toteles 4. Phy&longs;ic. <lb/>tex. 68. Nam præcipua ratio &longs;ucce&longs;sionis in motu locali <pb pagenum="269" xlink:href="005/01/277.jpg"/>prouenit à re&longs;i&longs;tentia medij locum non &longs;tatim cedentis, v<gap/><lb/>ip&longs;emet Philo&longs;ophus po&longs;tea docet tex. 70. quod cum non <lb/>e&longs;&longs;et in vacuo, non po&longs;&longs;et re&longs;i&longs;tere; <expan abbr="proindeq.">proindeque</expan> confe&longs;tim de <lb/>loco ad locum cuncta proiecta transferri contingeret per <lb/>vnicum mutatum e&longs;&longs;e. </s>

<s id="N17E17">Ex quo pariter intelligitur, cur proiecta in vacuo non <lb/>mouerentur proprio motu, vt docet Ari&longs;toteles 4. Phy&longs;ic. <lb/>tex. 68. Nam præcipua ratio &longs;ucce&longs;sionis in motu locali <pb pagenum="269" xlink:href="005/01/277.jpg"/>prouenit à re&longs;i&longs;tentia medij locum non &longs;tatim cedentis, vs <lb/>ip&longs;emet Philo&longs;ophus po&longs;tea docet tex. 70. quod cum non <lb/>e&longs;&longs;et in vacuo, non po&longs;&longs;et re&longs;i&longs;tere; <expan abbr="proindeq.">proindeque</expan> confe&longs;tim de <lb/>loco ad locum cuncta proiecta transferri contingeret per <lb/>vnicum mutatum e&longs;&longs;e. </s>

<s id="N17E35">Quod &longs;atis e&longs;t in&longs;inua&longs;&longs;e ad cuaden<lb/>das difficultates, quæ contra explicatam virtutem congere<lb/>re plerique conantur. </s>

<s id="N17E35">Quod &longs;atis e&longs;t in&longs;inua&longs;&longs;e ad suaden<lb/>das difficultates, quæ contra explicatam virtutem congere<lb/>re plerique conantur. </s>

<s id="N17E3E">Quæ&longs;tio Trige&longs;imaquarta.</s>

<s id="N17E43">C<emph type="italics"/>vr neque parua valde, neque magna longè <lb/>proÿci queunt, &longs;ed comm en&longs;urationem quan<lb/>dam illa babere oportet ad id quod proÿcit? </s>

<s id="N17E43">C<emph type="italics"/>vr neque parua valde, neque magna longè <lb/>proÿci queunt, &longs;ed commen&longs;urationem quan<lb/>dam illa habere oportet ad id quod proÿcit? </s>

<s id="N17E4D">An <lb/>quia nece&longs;&longs;e est, quod proÿcitur, & impellitur, <lb/>contraniti ei vnde impellitur <gap/> quod autem <lb/>magnitudine &longs;u<gap/> nibil cedit, cut imbecillita<lb/>te nihil contranititur, non efficit pròiectionem <lb/>neque impul&longs;ionem. </s>

<s id="N17E4D">An <lb/>quia nece&longs;&longs;e est, quod proÿcitur, & impellitur, <lb/>contraniti ei vnde impellitur quod autem <lb/>magnitudine &longs;ua nihil cedit, c ut imbecillita<lb/>te nihil contranititur, non efficit pròiectionem <lb/>neque impul&longs;ionem. </s>

<s id="N17E5E">Quod enim muliò impell<gap/>s excedit vi<lb/>res, baudquaquam cedit: quod ver<gap/>onultò e&longs;t imbe<gap/>illius, nibil <lb/>contranititur. </s>

<s id="N17E5E">Quod enim muliò impell<gap/>s excedit vi<lb/>res, haudquaquam cedit: quod veromultò e&longs;t imbec<gap/>illius, nihil <lb/>contranititur. </s>

<s id="N17E6B">An quia tantum fer<gap/>ur id quod fertur, quan<lb/>tum aëris mouerit ad pro&longs;undum: quod autem non mouetur, <lb/>neque mouebit quippiam, accidit auiem illis ambo illbæc babe<lb/>ve. </s>

<s id="N17E6B">An quia tantum fertur id quod fertur, quan<lb/>tum aëris mouerit ad profundum: quod autem non mouetur, <lb/>neque mouebit quippiam, accidit auiem illis ambo illbæc babe<lb/>ve. </s>

<s id="N17E76">Valde enim magnum, & valde paruum, ceu non mota exi<lb/>&longs;tant: alterum namque nibil mouet, alterun verò nibil no<lb/><gap/>etur.<emph.end type="italics"/></s>

<s id="N17E76">Valde enim magnum, & valde paruum, ceu non mota exi<lb/>&longs;tant: alterum namque nihil mouet, alterum verò nihil mo<lb/>uetur.<emph.end type="italics"/></s>

<s id="N17E82">COMMENTARIVS.</s>

<s id="N17E88">Qvid in cau&longs;a &longs;it quærit hic Ari&longs;toteles, vt neque <lb/>parua valde, <expan abbr="neq;">neque</expan> magna nimis longè proijci queant, <lb/>&longs;ed proportionem quandum habere debeantip&longs;a <lb/>proiecta cum proijciente. </s>

<s id="N17E95">Docetque primòid e&longs;&longs;e, quòd <lb/>in proiectione &longs;emper ac nece&longs;&longs;ariò intercedat aliqua proie<lb/>ctire&longs;i&longs;tentia, quæ tamen à proijciente viacitur, ae &longs;upera<lb/>tur. </s>

<s id="N17E95">Docetque primò id e&longs;&longs;e, quòd <lb/>in proiectione &longs;emper ac nece&longs;&longs;ariò intercedat aliqua proie<lb/>cti re&longs;i&longs;tentia, quæ tamen à proijciente vincitur, ea &longs;upera<lb/>tur. </s>

<s id="N17E9E">Vnde quod magnitudine &longs;ua, ac pondero&longs;itate ita re&longs;i<lb/>&longs;tit, vt nihil cedat, nec eius renitentia valeat &longs;uperari; a<gap/><lb/>ex oppo&longs;ito paruitate, & imbecillitate propria, mnil omni-<pb pagenum="270" xlink:href="005/01/278.jpg"/>no re&longs;i&longs;tit, nequit aliquo pacto proijci, aut ab alio moueri. </s>

<s id="N17E9E">Vnde quod magnitudine &longs;ua, ac pondero &longs;itate ita re&longs;i<lb/>&longs;tit, vt nihil cedat, nec eius renitentia valeat &longs;uperari; aut <lb/>ex oppo&longs;ito paruitate, & imbecillitate propria, nihil omni-<pb pagenum="270" xlink:href="005/01/278.jpg"/>no re&longs;i&longs;tit, nequit aliquo pacto proijci, aut ab alio moueri. </s>

<s id="N17EAD">Qua in &longs;olutione illud non paruam continet difficulta<lb/>tem, quod quæ nihil contranituntur, &longs;iue re&longs;i&longs;tunt, proijci <lb/>minime po&longs;ie Philo&longs;ophus velit. </s>

<s id="N17EB4">Cum potius ab experien<lb/>tia inferri videatur contrarium. </s>

<s id="N17EB9">Nam &longs;i quæ minus re&longs;i&longs;tunt <lb/>facilius mouentur, multò magis, <expan abbr="longèq.">longèque</expan> facilius quæ nihil <lb/>re&longs;i&longs;tunt ab&longs;olutè poterunt proijci, ac moueri. </s>

Line 3811

Line 3812

<s id="N17F68">Impul&longs;us enim, &longs;icut omnis alia &longs;imilis qua<lb/>litas, minus ex natura &longs;ua imprimi valet in parua quantitate, <lb/>quàm in maiori, <expan abbr="minusq.">minusque</expan> in leuiori, ac rariori, quàm in gra<lb/>uiori, ac den&longs;iori. </s>

<s id="N17F75">Siquidem multiplicantur partes quali<lb/>tatis ad multitudinem partium quantitatis, quæ &longs;anè plures <lb/>&longs;unt in maiori, ac den&longs;iori materia, quæ propterea etiam fit <lb/>grauior. </s>

<s id="N17F7E">Ad agendum verò non tantum valet, ac requiri<lb/>tur proportionata quædam inten&longs;io qualitatis actiuæ, &longs;ed <lb/>etiam exten&longs;io; vt patet in paruo, aut magno lumine vel ca<lb/>lore, qui licet &longs;it &longs;emper æquè inten&longs;us in igne. </s>

<s id="N17F87">minus ta<lb/>men, aut magis operatur iuxta maiorem, auc minorem ex<lb/>ten&longs;ionem, quam habet in magno, vel paruo igne. </s>

<s id="N17F87">minus ta<lb/>men, aut magis operatur iuxta maiorem, aut minorem ex<lb/>ten&longs;ionem, quam habet in magno, vel paruo igne. </s>

<s id="N17F8E">Quare <lb/>huiu&longs;modi minu&longs;cula corpora, de quibus loquebamur, po&longs;t <lb/>acceptum impul&longs;um adhuc imbecilliora remanent, quam <lb/>alia grandiora ad &longs;uperandam reluctantiam intermedij per <pb pagenum="272" xlink:href="005/01/280.jpg"/>quod debent tran&longs;ire. </s>

<s id="N17F9C">Vnde optimè intulit Ari&longs;toteles, ip<lb/>&longs;a proiecta commen&longs;urationem, ac proportionem quandam <lb/>cum proijciente requirere, vt eminus proijciantur. </s>

<s id="N17FA3">Nam <lb/>in magnis valde de&longs;icit virtus motiua ip&longs;ius proijcientis ad <lb/>&longs;uperandam inclinationem, ac pre&longs;&longs;ionem grauitatis: in ad<lb/>modum verò paruis deficit capacitas ad recipiendam tan<lb/>tam virtutem motiuam, qua pellere po&longs;&longs;int intermedium, <lb/><gap/>c per illud vlterius tran&longs;ilire. </s>

<s id="N17FA3">Nam <lb/>in magnis valde deficit virtus motiua ip&longs;ius proijcientis ad <lb/>&longs;uperandam inclinationem, ac pre&longs;&longs;ionem grauitatis: in ad<lb/>modum verò paruis deficit capacitas ad recipiendam tan<lb/>tam virtutem motiuam, qua pellere po&longs;&longs;int intermedium, <lb/>ac per illud vlterius tran&longs;ilire. </s>

<s id="N17FB3">Ex quibus perquàm facilè patebit, quod Ari&longs;toteles ad<lb/>dit po&longs;t explicatam &longs;olutionem, inquiens, idip&longs;um forta&longs;&longs;e, <lb/>ex eo adhuc contingere, quia tantum fertur id quod proij<lb/>citur, quantum aeris moucrit in profundum, videlicet ver<lb/>&longs;us eam partem, in quam tendit. </s>

<s id="N17FB3">Ex quibus perquàm facilè patebit, quod Ari&longs;toteles ad<lb/>dit po&longs;t explicatam &longs;olutionem, inquiens, idip&longs;um forta&longs;&longs;e, <lb/>ex eo adhuc contingere, quia tantum fertur id quod proij<lb/>citur, quantum aeris moucerit in profundum, videlicet ver<lb/>&longs;us eam partem, in quam tendit. </s>

<s id="N17FBE">Siquidem in eius locum, <lb/>tran&longs;eundo debet &longs;uccedere; nec po&longs;&longs;et, ni&longs;i dimouendo <lb/>illum à proprio loco. </s>

<s id="N17FC5">At valde parua, vel magna nimis, di<lb/>mouere nequeunt ip&longs;um aerem, eo quod nihil mouet im<lb/>motum; ip&longs;a autem &longs;e habeant tanquam immota: parua <lb/>quidem propter imbecillitatem impetus recepti, qui non <lb/>&longs;ufficit ad motum: magna verò propter exuperantiam gra<lb/>uitatis cuius pre&longs;&longs;ione non &longs;inuntur ab impellente moueri: <lb/>Ergo ip&longs;a valde parua, ac nimis magna proijci nullo modo <lb/>po&longs;&longs;unt, quod erat probandum. </s>

Line 3826

Line 3827

<s id="N17FDD">C<emph type="italics"/>vr ea quæ in vortico&longs;is feruntur aquis, ad me<lb/>dium tandem aguntur omnia? </s>

<s id="N17FE5">An quia magni<lb/>tudinem babet quodcunque fertur, quamobrem <lb/>illius extrema in duobus &longs;unt circulis, boc qui<lb/>dem minori, illo verò maiori: quare maior di<lb/>strabit: quoniam scleriùs fertur, & tran&longs;uer<lb/>&longs;um impellit illud ad minorem: quoniam autem id quod fer<lb/>tur, latitudinem babet, & iste rur&longs;um idem efficit, & ad inte<lb/>riorem propellit, donec ad mediam perueniat. </s>

<s id="N17FE5">An quia magni<lb/>tudinem habet quodcunque fertur, quamobrem <lb/>illius extrema in duobus &longs;unt circulis, hoc qui<lb/>dem minori, illo verò maiori: quare maior di<lb/>strahit: quoniam sceleriùs fertur, & tran&longs;uer<lb/>&longs;um impellit illud ad minorem: quoniam autem id quod fer<lb/>tur, latitudinem habet, & iste rur&longs;um idem efficit, & ad inte<lb/>riorem propellit, donec ad mediam perueniat. </s>

<s id="N17FF6">An quia quod <lb/>fertur, &longs;imili &longs;e babet modo ad omnes circulos propter medium, <lb/>medium enim in vnoquoque circulo æqualiter di&longs;tat. </s>

<s id="N17FF6">An quia quod <lb/>fertur, &longs;imili &longs;e habet modo ad omnes circulos propter medium, <lb/>medium enim in vnoquoque circulo æqualiter di&longs;tat. </s>

<s id="N17FFD">Aa <lb/>quia quorum quidem circumactæ aqu<gap/> latio non &longs;uperior pro-<emph.end type="italics"/><pb pagenum="273" xlink:href="005/01/281.jpg"/><emph type="italics"/>pter magnitudinem, &longs;ed grauitate &longs;ua circuli celeritatem ex<lb/>cellunt, ea nece&longs;&longs;e est relinqui, & tardius ferri, tardius au<lb/>tem minor circulus fertur; non idem enim in tempore æquali <lb/>magnus cum paruo reuoluitur circulus, quando circa idem <lb/>fuerint medium, quamobrem in minori circulo relinqui nece&longs;<lb/>fe e&longs;t, donec ad medium perueniant. </s>

<s id="N17FFD">An <lb/>quia quorum quidem circumactæ aqua latio non &longs;uperior pro-<emph.end type="italics"/><pb pagenum="273" xlink:href="005/01/281.jpg"/><emph type="italics"/>pter magnitudinem, &longs;ed grauitate &longs;ua circuli celeritatem ex<lb/>cellunt, ea nece&longs;&longs;e est relinqui, & tardius ferri, tardius au<lb/>tem minor circulus fertur; non idem enim in tempore æquali <lb/>magnus cum paruo reuoluitur circulus, quando circa idem <lb/>fuerint medium, quamobrem in minori circulo relinqui nece&longs;<lb/>se e&longs;t, donec ad medium perueniant. </s>

<s id="N18017">Quorumcumque autem <lb/>&longs;uperior à principio fuerit latio, & finiens idem efficiet; opor<lb/>tet enim bunc quidem &longs;tatim, alterum verò celeritate &longs;upera<lb/>re grauitatem, quamobrem ad interiorem &longs;emper circulum re<lb/>linquetur quodcumque. </s>

<s id="N18017">Quorumcumque autem <lb/>&longs;uperior à principio fuerit latio, & finiens idem efficiet; opor<lb/>tet enim hunc quidem &longs;tatim, alterum verò celeritate &longs;upera<lb/>re grauitatem, quamobrem ad interiorem &longs;emper circulum re<lb/>linquetur quodcumque. </s>

<s id="N18022">Nece&longs;&longs;e enim e&longs;t quod non &longs;uperatur, <lb/>aut in exteriori, aut in interiori moueri, in illo autem in quo <lb/>e&longs;t, impo&longs;sibile e&longs;t ferri, quod non &longs;uperatur: adbuc verò mi<lb/>nus in exteriori, celerior enim exterioris circuli e&longs;t latio, re<lb/>stat igitur, vt id quod non &longs;uperatur, ad interiorem transfe<lb/>ratur, &longs;emper autem vnumquodque proficit, vt non &longs;uperetur. <lb/></s>

<s id="N18022">Nece&longs;&longs;e enim e&longs;t quod non &longs;uperatur, <lb/>aut in exteriori, aut in interiori moueri, in illo autem in quo <lb/>e&longs;t, impo&longs;sibile e&longs;t ferri, quod non &longs;uperatur: adhuc verò mi<lb/>nus in exteriori, celerior enim exterioris circuli e&longs;t latio, re<lb/>stat igitur, vt id quod non &longs;uperatur, ad interiorem transfe<lb/>ratur, &longs;emper autem vnumquodque proficit, vt non &longs;uperetur. <lb/></s>

<s id="N18030">Quoniam verò peruenire ad medium, finem quidem efficit, vt <lb/>quippiam non moueatur, &longs;tat autem &longs;olummodò ip&longs;um cen<lb/>trum, ad boc &longs;anè-omnia congregari nece&longs;&longs;e e&longs;t.<emph.end type="italics"/></s>

<s id="N18030">Quoniam verò peruenire ad medium, finem quidem efficit, vt <lb/>quippiam non moueatur, &longs;tat autem &longs;olummodò ip&longs;um cen<lb/>trum, ad hoc &longs;anè-omnia congregari nece&longs;&longs;e e&longs;t.<emph.end type="italics"/></s>

<s id="N1803B">COMMENTARIVS.</s>

Line 3843

Line 3844

<s id="N1807B">Secundò verò idip&longs;um confirmat ex eo, nam delati cor<lb/>poris magnitudo diuer&longs;imodè &longs;ecundum diuer&longs;as &longs;ui partes <lb/>&longs;e habet ad circulos à quibus mouetur; Quandoquidem &longs;e<lb/>cundum partes à centro voiticis remctiores, velocius mo<lb/>uetur à circulis maioribus, quàm &longs;ecundum partes vicinio<lb/>res à circulis minoribus. </s>

<s id="N1807B">Secundò verò idip&longs;um confirmat ex eo, nam delati cor<lb/>poris magnitudo diuer&longs;imodè &longs;ecundum diuer&longs;as &longs;ui partes <lb/>&longs;e habet ad circulos à quibus mouetur; Quandoquidem &longs;e<lb/>cundum partes à centro vorticis remotiores, velocius mo<lb/>uetur à circulis maioribus, quàm &longs;ecundum partes vicinio<lb/>res à circulis minoribus. </s>

<s id="N18088">Ex quo fit, vt magnitudo ip&longs;a non <lb/>æqualiter &longs;uperetur, ac &longs;ecundum &longs;e totam deferri po&longs;sit ad <lb/>motum circuli maioris, <expan abbr="proindeq.">proindeque</expan> vel extra, vel intra illum <lb/>eam tran&longs;mitti debere: &longs;ed nequit extra, cum adhuc cele<lb/>rior ibi fiat latio cui non po&longs;&longs;et corre&longs;pondere &longs;ecundum <lb/>omnes &longs;uas partes; ergo re&longs;tat, vt ab ip&longs;a exuperantia cir<lb/>culi maioris in extimam eius partem incidentis, magnitu<lb/>do ip&longs;a tran&longs;mittatur intra, nempe ad interiores circulos, & <lb/>&longs;ic deinceps ad alios interiores v&longs;que ad centrum illis <lb/>commune in quo tandem omnia congregantur, atque <lb/>quie&longs;cunt. </s>

<s id="N180A5">Quod &longs;anè non ita concipiendum e&longs;t, vt ip&longs;is portionibus <lb/>circuli, quibus agitata magnitudo conuoluitur, circulum <lb/>ab&longs;oluentibus, ac perfectum motum circularem complen<lb/>tibus, diuer&longs;um ea cur&longs;um teneat, ac aliter quàm aqua ip&longs;a <lb/>deferens moueatur. </s>

<s id="N180B0">Siquidem tàm aqua, quàm corpus in <lb/>ea latum, ac &longs;upernatans, cum primò circularem motum in<lb/>choauerit ob cau&longs;am prædictam, circumferentias quas de<lb/>&longs;cribere cæperat, in &longs;piras commutat, & à perfecto motu <lb/>circulari &longs;en&longs;im degenerat. </s>

<s id="N180BB">Eodem enim e&longs;t vtriu&longs;que ra<lb/>tio, vt partes exteriores in gyrum ductæ, tanquam à centro <lb/>remotiores, velociùs ferantur, <expan abbr="prænaleantq.">prænaleantque</expan> interioribus, <lb/>quas propterea cum &longs;ecum rapere nequeant pari pa&longs;&longs;u per <lb/>lineas æquales, nec ab eis di&longs;iungi permittantur, &longs;e illis ag<lb/>glomerando interius magis, circumiendo contorqueant, <lb/>quou&longs;que &longs;imul in centrum perueniant. </s>

<s id="N180BB">Eodem enim e&longs;t vtriu&longs;que ra<lb/>tio, vt partes exteriores in gyrum ductæ, tanquam à centro <lb/>remotiores, velociùs ferantur, <expan abbr="prænaleantq.">præualeantque</expan> interioribus, <lb/>quas propterea cum &longs;ecum rapere nequeant pari pa&longs;&longs;u per <lb/>lineas æquales, nec ab eis di&longs;iungi permittantur, &longs;e illis ag<lb/>glomerando interius magis, circumiendo contorqueant, <lb/>quou&longs;que &longs;imul in centrum perueniant. </s>

<s id="N180CE">Quod e&longs;t per &longs;pi<lb/>ras tam aquam, quàm corpus in ea latum deferri, vt &longs;en&longs;u <lb/>manife&longs;ti&longs;simè con&longs;tat, ac per&longs;picuè videre e&longs;t in magnis <lb/>vorticibus fluminum, quæ rapidè fluunt, <expan abbr="amplosq.">amplosque</expan> non ha<lb/>bent &longs;inus. </s>

<s id="N180DD">Nam incidens aqua in &longs;inus ip&longs;os, angu&longs;tos, <lb/>turbinatim quidem ac per &longs;piras, non autem per ab&longs;olutos <pb pagenum="275" xlink:href="005/01/283.jpg"/>circulos cogitur circumuolui. </s>

<s id="N180E7">Id quod nec Ari&longs;toteles ne <lb/>gauit, aut tantus vir potuit ignorare; nec alienum e&longs;t à tra<lb/>dita eius doctrina, vt Baldus contendit, qua&longs;i Philo&longs;ophus <lb/>dixi&longs;&longs;et, aquam in vorticibus circumferri per circulos perfe<lb/>ctos, act<gap/><expan abbr="q.">que</expan> di&longs;tinctos, & corpus in ea latum ab vno in alium <lb/>circulum pertran&longs;ire; hoc e&longs;t ab exterioribus in interiores <lb/>appropinquando &longs;e magis ad centrum. </s>

<s id="N180E7">Id quod nec Ari&longs;toteles ne<lb/>gauit, aut tantus vir potuit ignorare; nec alienum e&longs;t à tra<lb/>dita eius doctrina, vt Baldus contendit, qua&longs;i Philo&longs;ophus <lb/>dixi&longs;&longs;et, aquam in vorticibus circumferri per circulos perfe<lb/>ctos, acta<expan abbr="q.">que</expan> di&longs;tinctos, & corpus in ea latum ab vno in alium <lb/>circulum pertran&longs;ire; hoc e&longs;t ab exterioribus in interiores <lb/>appropinquando &longs;e magis ad centrum. </s>

<s id="N180FB">Quod proculdubio <lb/>fal&longs;um e&longs;&longs;et, cum&longs;en&longs;u, vt dixiunus con&longs;&longs;et, aquam non mo<lb/>ueri per circulos, &longs;ed per &longs;piras: ac minimè con&longs;entaneum <lb/>&longs;it rati<gap/>, corpus delatum, diuer&longs;um à deferente iter tenere. <lb/></s>

<s id="N180FB">Quod proculdubio <lb/>fal&longs;um e&longs;&longs;et, cum &longs;en&longs;u, vt dixi unus con&longs;tet, aquam non mo<lb/>ueri per circulos, &longs;ed per &longs;piras: ac minimè con&longs;entaneum <lb/>&longs;it rationi<gap/>, corpus delatum, diuer&longs;um à deferente iter tenere. <lb/></s>

<s id="N18107">Præfertim cum latio corporis &longs;upernatantis in aqua, &longs;it ve<lb/>ctio, & non impul&longs;io. </s>

<s id="N18107">Præsertim cum latio corporis &longs;upernatantis in aqua, &longs;it ve<lb/>ctio, & non impul&longs;io. </s>

<s id="N1810E">Ad faciliorem tamen captum eorum, quæ de mente <lb/>Ari&longs;totelis à nobis relata &longs;unt, &longs;it aqua primò rectà decur<lb/>rens AB, quæ incidat in curuam ripam BC, vnde repul<lb/>&longs;a vergere cogatur in gyrum de&longs;cribendo qua&longs;i portionem <lb/><figure id="id.005.01.283.1.jpg" xlink:href="005/01/283/1.jpg"/><lb/>quandam circuli iuxta figuram eiu&longs;dem ripæ, cui aquæ mo<lb/>les nece&longs;lariò adaptatur, vt BCD. </s>

<s id="N18122">Sitque corpus latum in <lb/>aqua vbi E. </s>

<s id="N18128">Dicimus ergo quod aqua ceptum iter, &longs;eu mo<lb/>tum circularem &longs;ecundans nequit circulum ab&longs;olutum per<lb/>ficere, quem punctis BCDF hic expre&longs;&longs;imus, eodemque <lb/>circulo iniectam, ac &longs;upernatantem magnitudinem E &longs;ecum <pb pagenum="276" xlink:href="005/01/284.jpg"/>abripiens, circumagere: Quia po&longs;tquam aqua è loco ripæ <lb/>continentis di&longs;ce&longs;&longs;erit, & vltrò &longs;e in gyrum mouere cæperit <lb/>per impetum repul&longs;ionis inde acceptum, partes eius exte<lb/>riores, &longs;eu maioris circumferentiæ, ob maiorem velocitatem <lb/>propriam, <expan abbr="maioremq.">maioremque</expan> impetum ex incidentia receptum, ef<lb/>ficaciùs agunt quàm interiores, quæ per minorem circum<lb/>ferentiam commouentur, ac nullum immediatè repul&longs;um <lb/>acceperunt à con&longs;i&longs;tenti ripa prædicta. </s>

<s id="N18148"><expan abbr="Ideoq.">Ideoque</expan> non tantum <lb/>corre&longs;pondentem &longs;ibi partem exteriorem lati corporis E, <lb/>nempe quæ remotior e&longs;t à centro vorticis magis valent vl<lb/>terius promouere, quàm illæ partem eiu&longs;dem corporis in<lb/>teriorem; &longs;ed ip&longs;a&longs;met partes aquæ interiores, quæ per mi<lb/>nores ambitus circumuoluuntu<gap/> magis compellere, ac in <lb/>minores circuitus re&longs;tringere, quibus &longs;e&longs;e adaptando &longs;imul <lb/>in &longs;piras degenerant. </s>

<s id="N18148"><expan abbr="Ideoq.">Ideoque</expan> non tantum <lb/>corre&longs;pondentem &longs;ibi partem exteriorem lati corporis E, <lb/>nempe quæ remotior e&longs;t à centro vorticis magis valent vl<lb/>terius promouere, quàm illæ partem eiu&longs;dem corporis in<lb/>teriorem; &longs;ed ip&longs;a&longs;met partes aquæ interiores, quæ per mi<lb/>nores ambitus circumuoluuntur magis compellere, ac in <lb/>minores circuitus re&longs;tringere, quibus &longs;e&longs;e adaptando &longs;imul <lb/>in &longs;piras degenerant. </s>

<s id="N1815E">Et &longs;ic lata corporis magnitudo vnà <lb/>cum aqua tandem ad vorticis centrum reducitur. </s>

<s id="N18165">Quod &longs;i ab&longs;tractè loquendo quælibet maior, ac exterio<gap/><lb/>circumferentia velocius moueatur, quàm minor, & interior <lb/>circa idem centrum, <expan abbr="validiusq.">validiusque</expan> propterea corpora impelle<lb/>re, aut &longs;ecum rapere po&longs;&longs;e intelligatur, ab&longs;que eo, quod ad <lb/>hoc præ&longs;tandum circularem motum relinquat, ac in &longs;piras <lb/>conuertatur, compellendo etiam circumferentias interiores <lb/>ad &longs;ecum degenerandum &longs;imili modo. </s>

<s id="N18165">Quod &longs;i ab&longs;tractè loquendo quælibet maior, ac exterior <lb/>circumferentia velocius moueatur, quàm minor, & interior <lb/>circa idem centrum, <expan abbr="validiusq.">validiusque</expan> propterea corpora impelle<lb/>re, aut &longs;ecum rapere po&longs;&longs;e intelligatur, ab&longs;que eo, quod ad <lb/>hoc præ&longs;tandum circularem motum relinquat, ac in &longs;piras <lb/>conuertatur, compellendo etiam circumferentias interiores <lb/>ad &longs;ecum degenerandum &longs;imili modo. </s>

<s id="N18179">Id tamen in propo<lb/>&longs;ito locum non habet, tum quia aquæ fluenti, & ob inciden<lb/>tiam aliquam &longs;e retorquenti, nullus in rigore præ&longs;cribitur <lb/>circulus, quem debeat perficere, nec partibus eius exterio<lb/>ribus interdicitur acce&longs;&longs;us ad interiores, &longs;icut circumferen<lb/>tiæ exteriori &longs;olidi corporis ad interiorem, à qua profectò <lb/>æquè di&longs;tat in circulo: tum quia non e&longs;t eadem proportio <lb/>exce&longs;&longs;us in velocitate, & efficacitate inter circumferentiam <lb/>exteriorem, & interiorem in circulo con&longs;i&longs;tentis materiæ <lb/>dum rotatur, atque inter partes exteriores, & interiores <lb/>aquæ per incidentiam quandam circumuolutas. </s>

<s id="N18190">Quando<lb/>quidem &longs;emper e&longs;t maior exce&longs;&longs;us in i&longs;tis, quàm in illis. </s>

<s id="N18195">Vt <lb/>qui duplici ex cau&longs;a profici&longs;catur; tàm &longs;cilicet ex maiori <lb/>ambitu, quem perficiunt in æquali tempore, quàm ex maio-<pb pagenum="277" xlink:href="005/01/285.jpg"/>ri repul&longs;u, quem immediatè per incidentiam acceperunt à <lb/>ripa. </s>

Line 3879

Line 3880

<s id="N181E3">INDEX TEXTVVM <lb/>ATQVE ADDITIONVM</s>

<s id="N181EA">Primæ partis huius Mechanicæ Tra<lb/>ctationis.<lb/>O<emph type="italics"/>peris argumen<lb/>tum. pag.<emph.end type="italics"/> 1 <lb/><emph type="italics"/>Quæ &longs;it artis Me<lb/>cbanisæ facul<lb/>tas Textus pri<lb/>mus pag.<emph.end type="italics"/> 4 <lb/><emph type="italics"/>De nomine, & origine faculta<lb/>tis Mecban. </s>

<s id="N181EA">Primæ partis huius Mechanicæ Tra<lb/>ctationis.<lb/>O<emph type="italics"/>peris argumen<lb/>tum. pag.<emph.end type="italics"/> 1 <lb/><emph type="italics"/>Quæ &longs;it artis Me<lb/>chanicæ facul<lb/>tas Textus pri<lb/>mus pag.<emph.end type="italics"/> 4 <lb/><emph type="italics"/>De nomine, & origine faculta<lb/>tis Mechan. </s>

<s id="N1820D">Addit prima. </s>

<s id="N18210">pag<emph.end type="italics"/> 6 <lb/><emph type="italics"/>De obiecto circa quod Mecbani<lb/>ca facultas ver&longs;atur. </s>

<s id="N18210">pag<emph.end type="italics"/> 6 <lb/><emph type="italics"/>De obiecto circa quod Mechani<lb/>ca facultas ver&longs;atur. </s>

<s id="N1821C">Addi<lb/>tio<emph.end type="italics"/> 2. <emph type="italics"/>pag.<emph.end type="italics"/> 9 <lb/><emph type="italics"/>Qua ratione facultai Mecbani<lb/>ca con&longs;tituatur ars & &longs;eien<lb/>tia. </s>

<s id="N1821C">Addi<lb/>tio<emph.end type="italics"/> 2. <emph type="italics"/>pag.<emph.end type="italics"/> 9 <lb/><emph type="italics"/>Qua ratione facultas Mechani<lb/>ca con&longs;tituatur ars & &longs;cien<lb/>tia. </s>

<s id="N18232">Additio<emph.end type="italics"/> 3. 12 <lb/><emph type="italics"/>Mecbanicam facultatem verè, <lb/> ac propriè e&longs;&longs;e &longs;cientiam Ma<lb/>thematicam. </s>

<s id="N18232">Additio<emph.end type="italics"/> 3. 12 <lb/><emph type="italics"/>Mechanicam facultatem verè, <lb/> ac propriè e&longs;&longs;e &longs;cientiam Ma<lb/>thematicam. </s>

<s id="N18240">Addit.<emph.end type="italics"/> 4. 17 <lb/><emph type="italics"/>Quænam de&longs;criptio quidditatiua <lb/> buius facultatis colligatur ex <lb/> dictis, & quo pacto ab alÿs <lb/> &longs;eientÿs distinguatur. </s>

<s id="N18240">Addit.<emph.end type="italics"/> 4. 17 <lb/><emph type="italics"/>Quænam de&longs;criptio quid ditatiua <lb/> huius facultatis colligatur ex <lb/> dictis, & quo pacto ab alÿs <lb/> &longs;cientÿs distinguatur. </s>

<s id="N18250">Addi<lb/>tio<emph.end type="italics"/> 5. 25 <lb/><emph type="italics"/>De vnitate &longs;eientiæ Mecbanicæ, <lb/> eiu&longs;que partibus. </s>

<s id="N18250">Addi<lb/>tio<emph.end type="italics"/> 5. 25 <lb/><emph type="italics"/>De vnitate &longs;cientiæ Mechanicæ, <lb/> eiu&longs;que partibus. </s>

<s id="N1825E">Additio<emph.end type="italics"/> 6. <lb/> <emph type="italics"/>pag.<emph.end type="italics"/> 26 <lb/><emph type="italics"/>Quem gradum porfectionis, aut <lb/> dignitatis facultas Mecbani<lb/>ca obtineat. </s>

<s id="N1825E">Additio<emph.end type="italics"/> 6. <lb/> <emph type="italics"/>pag.<emph.end type="italics"/> 26 <lb/><emph type="italics"/>Quem gradum perfectionis, aut <lb/> dignitatis facultas Mechani<lb/>ca obtineat. </s>

<s id="N18274">inter &longs;eientias. <lb/> Addit.<emph.end type="italics"/> 7. <emph type="italics"/>pag.<emph.end type="italics"/> 30 <lb/><emph type="italics"/>De dignitatibus, admirandi&longs;que <lb/> circuli proprietatibus. </s>

<s id="N18274">inter &longs;cientias. <lb/> Addit.<emph.end type="italics"/> 7. <emph type="italics"/>pag.<emph.end type="italics"/> 30 <lb/><emph type="italics"/>De dignitatibus, admirandi&longs;que <lb/> circuli proprietatibus. </s>

<s id="N18288">Tex.<emph.end type="italics"/> 2. <lb/> <emph type="italics"/>pag.<emph.end type="italics"/> 33 <lb/><emph type="italics"/>De prima circuli admiranda <lb/> proprietate. </s>

<s id="N1829C">Tex.<emph.end type="italics"/> 3. 34 <lb/><emph type="italics"/>De &longs;ecunda cirouli proprietats. <lb/> Textus<emph.end type="italics"/> 4. 35 <lb/><emph type="italics"/>De tertia circuli proprietate. <lb/> Textus<emph.end type="italics"/> 5. 36 <lb/><emph type="italics"/>De quarta circuli proprietate. <lb/> Tex.<emph.end type="italics"/> 6. 39 <lb/><emph type="italics"/>Quo pacto linea circulum de&longs;eri<lb/>bens duabus feratur lationi<lb/>bus. </s>

<s id="N1829C">Tex.<emph.end type="italics"/> 3. 34 <lb/><emph type="italics"/>De &longs;ecunda circuli proprietate. <lb/> Textus<emph.end type="italics"/> 4. 35 <lb/><emph type="italics"/>De tertia circuli proprietate. <lb/> Textus<emph.end type="italics"/> 5. 36 <lb/><emph type="italics"/>De quarta circuli proprietate. <lb/> Tex.<emph.end type="italics"/> 6. 39 <lb/><emph type="italics"/>Quo pacto linea circulum de&longs;cri<lb/>bens duabus feratur lationi<lb/>bus. </s>

<s id="N182C5">Tex.<emph.end type="italics"/> 7. 40 <lb/><emph type="italics"/>Quo ratione partes diametri à <lb/> centro remotiores magis parti<lb/>cipent de motu naturali, pro<lb/>pinquiores verò magis de præ<lb/>ternaturali. </s>

<s id="N182D7">Tex.<emph.end type="italics"/> 8. 49 <lb/><emph type="italics"/>De instrumentis, ac machinis <lb/> naturam circuli in motione <lb/> partticipantibus. </s>

<s id="N182E5">Addit.<emph.end type="italics"/> 1. 53 <lb/><emph type="italics"/>De Libra.<emph.end type="italics"/> 55 <lb/><emph type="italics"/>De Veste.<emph.end type="italics"/> 56 <lb/><emph type="italics"/>De Trochlea.<emph.end type="italics"/> 58 <lb/><emph type="italics"/>De Axe in Peritrochio.<emph.end type="italics"/> 60 <lb/><emph type="italics"/>De Cuneo.<emph.end type="italics"/> 61 <lb/><emph type="italics"/>De Choclea.<emph.end type="italics"/> 63 <lb/><emph type="italics"/>De Centro grauitatis, naturaliq<lb/>mobilitate grauium, & <expan abbr="leui&utilde;">leuium</expan>. <lb/> Additio<emph.end type="italics"/> 2. 64 <lb/><emph type="italics"/>De præternaturali, & artificio&longs;a <lb/> grauium, & leuium. </s>

<s id="N182E5">Addit.<emph.end type="italics"/> 1. 53 <lb/><emph type="italics"/>De Libra.<emph.end type="italics"/> 55 <lb/><emph type="italics"/>De Veste.<emph.end type="italics"/> 56 <lb/><emph type="italics"/>De Trochlea.<emph.end type="italics"/> 58 <lb/><emph type="italics"/>De Axe in Peritrochio.<emph.end type="italics"/> 60 <lb/><emph type="italics"/>De Cuneo.<emph.end type="italics"/> 61 <lb/><emph type="italics"/>De Choclea.<emph.end type="italics"/> 63 <lb/><emph type="italics"/>De Centro grauitatis, naturalique <lb/>mobilitate grauium, & <expan abbr="leui&utilde;">leuium</expan>. <lb/> Additio<emph.end type="italics"/> 2. 64 <lb/><emph type="italics"/>De præternaturali, & artificio&longs;a <lb/> grauium, & leuium. </s>

<s id="N1832A">Additio<emph.end type="italics"/> 3. <lb/> <emph type="italics"/>pag.<emph.end type="italics"/> 68 </s>

<s id="N1833D">INDEX <lb/>QVAESTIONVM <lb/>SECVNDAE PARTIS.<lb/>Q<emph type="italics"/>vestio prima Cum <lb/> maiores libræ exa<lb/>ctiores &longs;int minori<lb/>bus. </s>

<s id="N1834F">pag.<emph.end type="italics"/> 73 <lb/>Quæ&longs;tio 2. <emph type="italics"/>Cur &longs;i &longs;partum lo<lb/>cetur &longs;upra iugum libræ ip<lb/>&longs;aque ab altero extremo depri<lb/>matur, rur&longs;um illud a&longs;cen<lb/>dat, &longs;esus ac &longs;i &longs;partum loce<lb/>tur infra.<emph.end type="italics"/> 77 <lb/>Quæ&longs;tio 3. <emph type="italics"/>Cur exiguæ vires <lb/> adhibito vecte magna moueant <lb/> pondera.<emph.end type="italics"/> 85 <lb/>Quæ&longs;tio 4. <emph type="italics"/>Cur ÿ, qui in nauis <lb/> medio &longs;unt remiges, magis na<lb/>uem moueant quam qui in alio <lb/> &longs;itu.<emph.end type="italics"/> 91 <lb/>Quæ&longs;tio 5. <emph type="italics"/>Cur paruum exi&longs;tens <lb/> gubernaculum tantas habeat <lb/> vires ad circumferenda naui<lb/>gia.<emph.end type="italics"/> 98 <lb/>Quæ&longs;tio 6. <emph type="italics"/>Cur quanto antenna <lb/> &longs;ublimior &longs;uerit ÿ&longs;dem velis, <lb/> & eodem vento, celerius fe<lb/>rantur nauigia.<emph.end type="italics"/> 118 <lb/>Quæ&longs;tio 7. <emph type="italics"/>Cur nautæ vento ex <lb/> tran&longs;uer&longs;o perflante, veli par<lb/>tem quæ ad puppim vergit <expan abbr="cõ-">con<lb/></expan> stringunt, quæ verò ad pro<lb/>ra relaxant.<emph.end type="italics"/> 124 <lb/>Quæ&longs;tio 8. <emph type="italics"/>Cux ex figuranum <lb/> genere, quæcunque rotundæ <lb/> &longs;unt facilius moueantur.<emph.end type="italics"/> 129 <lb/>Quæ&longs;tio 9. <emph type="italics"/>Cun ea quæ per maio<lb/>res circulos tolluntur citius ao <lb/> facilius moueantur.<emph.end type="italics"/> 139 <lb/>Quæ&longs;tio 10. <emph type="italics"/>Cur facilius quan<lb/>do &longs;ine pondere e&longs;t mouetur li<lb/>bra.<emph.end type="italics"/> 143 <lb/>Quæ&longs;tio 11. <emph type="italics"/>Cur &longs;uper &longs;cytalas <lb/> facilius portentur onera quàm <lb/> &longs;uper currus.<emph.end type="italics"/> 147 <lb/>Quæ&longs;tio 12. <emph type="italics"/>Cur longius feran<lb/>tur mi&longs;&longs;ilia funda, quam ma<lb/>nu mi&longs;&longs;a.<emph.end type="italics"/> 149 <lb/>Quæ&longs;tio 13. <emph type="italics"/>Cur &longs;i longiores fue<lb/>rint collopes circa. </s>

<s id="N1834F">pag.<emph.end type="italics"/> 73 <lb/>Quæ&longs;tio 2. <emph type="italics"/>Cur &longs;i &longs;partum lo<lb/>cetur &longs;upra iugum libræ ip<lb/>&longs;aque ab altero extremo depri<lb/>matur, rur&longs;um illud a&longs;cen<lb/>dat, &longs;ecus ac &longs;i &longs;partum loce<lb/>tur infra.<emph.end type="italics"/> 77 <lb/>Quæ&longs;tio 3. <emph type="italics"/>Cur exiguæ vires <lb/> adhibito vecte magna moueant <lb/> pondera.<emph.end type="italics"/> 85 <lb/>Quæ&longs;tio 4. <emph type="italics"/>Cur ÿ, qui in nauis <lb/> medio &longs;unt remiges, magis na<lb/>uem moueant quam qui in alio <lb/> &longs;itu.<emph.end type="italics"/> 91 <lb/>Quæ&longs;tio 5. <emph type="italics"/>Cur paruum exi&longs;tens <lb/> gubernaculum tantas habeat <lb/> vires ad circumferenda naui<lb/>gia.<emph.end type="italics"/> 98 <lb/>Quæ&longs;tio 6. <emph type="italics"/>Cur quanto antenna <lb/> &longs;ublimior &longs;uerit ÿ&longs;dem velis, <lb/> & eodem vento, celerius fe<lb/>rantur nauigia.<emph.end type="italics"/> 118 <lb/>Quæ&longs;tio 7. <emph type="italics"/>Cur nautæ vento ex <lb/> tran&longs;uer&longs;o perflante, veli par<lb/>tem quæ ad puppim vergit <expan abbr="cõ-">con<lb/></expan>stringunt, quæ verò ad pro<lb/>ra relaxant.<emph.end type="italics"/> 124 <lb/>Quæ&longs;tio 8. <emph type="italics"/>Cur ex figurarum <lb/> genere, quæcunque rotundæ <lb/> &longs;unt facilius moueantur.<emph.end type="italics"/> 129 <lb/>Quæ&longs;tio 9. <emph type="italics"/>Cun ea quæ per maio<lb/>res circulos tolluntur citius ac <lb/> facilius moueantur.<emph.end type="italics"/> 139 <lb/>Quæ&longs;tio 10. <emph type="italics"/>Cur facilius quan<lb/>do &longs;ine pondere e&longs;t mouetur li<lb/>bra.<emph.end type="italics"/> 143 <lb/>Quæ&longs;tio 11. <emph type="italics"/>Cur &longs;uper &longs;cytalas <lb/> facilius portentur onera quàm <lb/> &longs;uper currus.<emph.end type="italics"/> 147 <lb/>Quæ&longs;tio 12. <emph type="italics"/>Cur longius feran<lb/>tur mi&longs;&longs;ilia funda, quam ma<lb/>nu mi&longs;&longs;a.<emph.end type="italics"/> 149 <lb/>Quæ&longs;tio 13. <emph type="italics"/>Cur &longs;i longiores fue<lb/>rint collopes circa. </s>

<s id="N183F3">idem iu<lb/>gum, facilius circumagatur. <lb/> Itemque cur graciliores &longs;ut<lb/>culæ facilius pariter ab eadem, <lb/> potentia circumuoluantur. </s>

<s id="N183F3">idem iu<lb/>gum, facilius circumagatur. <lb/> Itemque cur graciliores &longs;uc<lb/>culæ facilius pariter ab eadem, <lb/> potentia circumuoluantur. </s>

<s id="N183FE">pa<lb/>gina.<emph.end type="italics"/> 154 <lb/>Quæ&longs;tio 14. <emph type="italics"/>Cur lignum faci<lb/>lius genu frangitur, cum ab <lb/> extremis apprenenditur, quàm <lb/> cum prope genu.<emph.end type="italics"/> 157 <lb/>Quæ&longs;tio 15. <emph type="italics"/>Cur ea quæ circa <lb/> litora appellantur. </s>

<s id="N183FE">pa<lb/>gina.<emph.end type="italics"/> 154 <lb/>Quæ&longs;tio 14. <emph type="italics"/>Cur lignum faci<lb/>lius genu frangitur, cum ab <lb/> extremis apprehenditur, quàm <lb/> cum prope genu.<emph.end type="italics"/> 157 <lb/>Quæ&longs;tio 15. <emph type="italics"/>Cur ea quæ circa <lb/> litora appellantur. </s>

<s id="N1841B">Croeæ, ro<lb/>tunda &longs;int figura.<emph.end type="italics"/> 160 <lb/>Quæ&longs;tio 16. <emph type="italics"/>Cur. </s>

<s id="N1841B">Crocæ, ro<lb/>tunda &longs;int figura.<emph.end type="italics"/> 160 <lb/>Quæ&longs;tio 16. <emph type="italics"/>Cur. </s>

<s id="N18429">quanto longio<lb/>ra &longs;unt ligna, tanto imbecil<lb/>liora fiant, magisque infle<lb/>ctantur.<emph.end type="italics"/> 163 <lb/>Quæ&longs;tio 17. <emph type="italics"/>Cur paruo existen-<pb xlink:href="005/01/288.jpg"/> te cuneo eius adminiculo ma<lb/>gna &longs;cindantur corpora.<emph.end type="italics"/> 167 <lb/>Quæ&longs;tio 18. <emph type="italics"/>Cur duabus tro<lb/>chleis adinuicem ex oppo&longs;ito <lb/> compo&longs;itis, ac &longs;une circumdu<lb/>cto, magna trabantur ponde<lb/>ra, quamuis imbecilla &longs;it vir<lb/>tus trabentis.<emph.end type="italics"/> 171 <lb/>Quæ&longs;tio 19. <emph type="italics"/>Cur &longs;ecuris, per<lb/>cu&longs;sione potius quàm &longs;upera<lb/>diecto pondere, lignum &longs;cin<lb/>dere valeat.<emph.end type="italics"/> 177 <lb/>Quæ&longs;tio 20. <emph type="italics"/>Cur &longs;tatera paruo <lb/> appendiculo magna trutinet <lb/> onera.<emph.end type="italics"/> 184 <lb/>Quæ&longs;tio 21. <emph type="italics"/>Cur dentes facilius <lb/> <expan abbr="extrabãtur">extrabantur</expan> dentiforcipis adhi<lb/>bito in&longs;trumento, quàm &longs;ola <lb/> manu.<emph.end type="italics"/> 189 <lb/>Quæ&longs;tio 22. <emph type="italics"/>Cur nuces ab&longs;que <lb/> ictu facile confring antur in <lb/> strumento ad eum v&longs;um in&longs;ti<lb/>tuto.<emph.end type="italics"/> 193 <lb/>Quæ&longs;tio 23. <emph type="italics"/>Cur &longs;i duo puncta <lb/> extrema vnius lateris in <lb/> Rombo duabus &longs;imul ferantu<gap/><lb/>lationibus cum eadem veloes <lb/> tate, vnum maius, alterum <lb/> minus &longs;pacium percurrat. <lb/> Item cur quod &longs;uper latus <lb/> fertur minus <expan abbr="pertrã&longs;eat">pertran&longs;eat</expan>, quàm <lb/> ip&longs;um latus.<emph.end type="italics"/> 200 <lb/>Quæ&longs;tio 24. <emph type="italics"/>Cur ex duobus cir<lb/>culis circa idem centrum coap<lb/>tati, ac reuoluti &longs;ecundum <lb/> ab&longs;idem, maior minori æqua<lb/>le &longs;pacium percurrit. </s>

<s id="N18429">quanto longio<lb/>ra &longs;unt ligna, tanto imbecil<lb/>liora fiant, magisque infle<lb/>ctantur.<emph.end type="italics"/> 163 <lb/>Quæ&longs;tio 17. <emph type="italics"/>Cur paruo existen-<pb xlink:href="005/01/288.jpg"/> te cuneo eius adminiculo ma<lb/>gna &longs;cindantur corpora.<emph.end type="italics"/> 167 <lb/>Quæ&longs;tio 18. <emph type="italics"/>Cur duabus tro<lb/>chleis adinuicem ex oppo&longs;ito <lb/> compo&longs;itis, ac fune circumdu<lb/>cto, magna trahantur ponde<lb/>ra, quamuis imbecilla &longs;it vir<lb/>tus trahentis.<emph.end type="italics"/> 171 <lb/>Quæ&longs;tio 19. <emph type="italics"/>Cur &longs;ecuris, per<lb/>cu&longs;sione potius quàm &longs;upera<lb/>diecto pondere, lignum &longs;cin<lb/>dere valeat.<emph.end type="italics"/> 177 <lb/>Quæ&longs;tio 20. <emph type="italics"/>Cur &longs;tatera paruo <lb/> appendiculo magna trutinet <lb/> onera.<emph.end type="italics"/> 184 <lb/>Quæ&longs;tio 21. <emph type="italics"/>Cur dentes facilius <lb/> <expan abbr="extrabãtur">extrabantur</expan> dentiforcipis adhi<lb/>bito in&longs;trumento, quàm &longs;ola <lb/> manu.<emph.end type="italics"/> 189 <lb/>Quæ&longs;tio 22. <emph type="italics"/>Cur nuces ab&longs;que <lb/> ictu facile confringantur in <lb/> strumento ad eum v&longs;um in&longs;ti<lb/>tuto.<emph.end type="italics"/> 193 <lb/>Quæ&longs;tio 23. <emph type="italics"/>Cur &longs;i duo puncta <lb/> extrema vnius lateris in <lb/> Rombo duabus &longs;imul ferantur <lb/>lationibus cum eadem veloci<lb/>tate, vnum maius, alterum <lb/> minus &longs;pacium percurrat. <lb/> Item cur quod &longs;uper latus <lb/> fertur minus <expan abbr="pertrã&longs;eat">pertran&longs;eat</expan>, quàm <lb/> ip&longs;um latus.<emph.end type="italics"/> 200 <lb/>Quæ&longs;tio 24. <emph type="italics"/>Cur ex duobus cir<lb/>culis circa idem centrum coap<lb/>tati, ac reuoluti &longs;ecundum <lb/> ab&longs;idem, maior minori æqua<lb/>le &longs;pacium percurrit. </s>

<s id="N184B9">Seor<lb/>&longs;um verò conuoluti, maior <lb/> maius, minor verò minus inæ<lb/>ta proportionem circumferen<lb/>tiæ vnius ad circumferentiam <lb/> alterius.<emph.end type="italics"/> 205 <lb/>Quæ&longs;tio 25. <emph type="italics"/>Cur lestulorum <lb/> &longs;pondæ &longs;ecundum duplam <lb/> proportionem longitu<gap/>inis ad <lb/> latrtudinem efficiantur. </s>

<s id="N184B9">Seor<lb/>&longs;um verò conuoluti, maior <lb/> maius, minor verò minus iux<lb/>ta proportionem circumferen<lb/>tiæ vnius ad circumferentiam <lb/> alterius.<emph.end type="italics"/> 205 <lb/>Quæ&longs;tio 25. <emph type="italics"/>Cur lectulorum <lb/> &longs;pondæ &longs;ecundum duplam <lb/> proportionem longitudinis ad <lb/> latitudinem efficiantur. </s>

<s id="N184D6">Cur <lb/> verè in illis muniendir resies <lb/> per tran&longs;uer&longs;um, non autem <lb/> per diametrum extendanlur. <lb/> pag.<emph.end type="italics"/> 225 <lb/>Quæ&longs;tio 26. <emph type="italics"/>Cur difficilius pro<lb/>cera ligna ab extremo &longs;uper <lb/> humerum ge&longs;tentur, quam <lb/> è medio, æquali exi&longs;tente pon<lb/>dere.<emph.end type="italics"/> 228 <lb/>Quæ&longs;tio 27. <emph type="italics"/>Cur &longs;i valde pro<lb/>cerum fuerit lignum, quam<lb/>uis eiu&longs;dem &longs;it ponderis, & è <lb/> nitdio &longs;uftineatur, difficilius <lb/> tamen &longs;uper bumerum ge&longs;te<lb/>tur.<emph.end type="italics"/> 232 <lb/>Quæ&longs;tio 28. <emph type="italics"/>Cur iuxta puteos <lb/> con&longs;tituta Celonia ad aquam <lb/> baurlendam facilius mouen<lb/>tur, onus in altero extremo <lb/> tran&longs;uer&longs;arÿ ligni apponendo. <lb/> pag.<emph.end type="italics"/> 233 <lb/>Quæ&longs;tio 29. <emph type="italics"/>Cur duo &longs;uper li<lb/>gnum aliquod pondus feren<lb/>tes non æquè grauentur &longs;i in <lb/> eorum medio non extiterit ip<lb/>&longs;um pondus, &longs;ed magis is cui <lb/> ip&longs;um proximius fuerit. </s>

<s id="N184D6">Cur <lb/> verè in illis muniendis resies <lb/> per tran&longs;uer&longs;um, non autem <lb/> per diametrum extendantur. <lb/> pag.<emph.end type="italics"/> 225 <lb/>Quæ&longs;tio 26. <emph type="italics"/>Cur difficilius pro<lb/>cera ligna ab extremo &longs;uper <lb/> humerum ge&longs;tentur, quam <lb/> è medio, æquali exi&longs;tente pon<lb/>dere.<emph.end type="italics"/> 228 <lb/>Quæ&longs;tio 27. <emph type="italics"/>Cur &longs;i valde pro<lb/>cerum fuerit lignum, quam<lb/>uis eiu&longs;dem &longs;it ponderis, & è <lb/> medio &longs;ustineatur, difficilius <lb/> tamen &longs;uper humerum ge&longs;te<lb/>tur.<emph.end type="italics"/> 232 <lb/>Quæ&longs;tio 28. <emph type="italics"/>Cur iuxta puteos <lb/> con&longs;tituta Celonia ad aquam <lb/> hauriendam facilius mouen<lb/>tur, onus in altero extremo <lb/> tran&longs;uer&longs;arÿ ligni apponendo. <lb/> pag.<emph.end type="italics"/> 233 <lb/>Quæ&longs;tio 29. <emph type="italics"/>Cur duo &longs;uper li<lb/>gnum aliquod pondus feren<lb/>tes non æquè grauentur &longs;i in <lb/> eorum medio non extiterit ip<lb/>&longs;um pondus, &longs;ed magis is cui <lb/> ip&longs;um proximius fuerit. </s>

<s id="N18527">pa<lb/>gina.<emph.end type="italics"/> 237 <lb/>Quæ&longs;tio 30. <emph type="italics"/>Cur à &longs;e&longs;sione &longs;ur<lb/>gentes angulos rectos, quos <lb/> efficiebat thorax cum femore, <lb/> ac femur cum tibia; in acu<lb/>tos commutant.<emph.end type="italics"/> 241 <lb/>Quæ&longs;tio 31. <emph type="italics"/>Cur facilius moue<lb/>tur commotum, quàm manens. <lb/> pag.<emph.end type="italics"/> 245 <lb/>Quæ&longs;tio 32. <emph type="italics"/>Cur ea quæ proÿ<lb/>ciuntur ce&longs;&longs;ent à latione.<emph.end type="italics"/> 252 <pb xlink:href="005/01/289.jpg"/>Quæ&longs;tio 33. <emph type="italics"/>Cur proiecta mo<lb/>ueantur quamuis impellens <lb/> ea non con&longs;equatur.<emph.end type="italics"/> 260 <lb/>Quæ&longs;tio 34. <emph type="italics"/>Cur neque parua <lb/> valde, neque magna nimis lon<lb/>gè proÿci queant.<emph.end type="italics"/> 269 <lb/>Quæ&longs;tio 35. <emph type="italics"/>Cur ea quæ in <lb/> aquarum vorticibus ferun<lb/>tur, ad medium tandem agan<lb/>tur.<emph.end type="italics"/> 272 </s>

Line 3915

Line 3916

<s id="N1858C">A<lb/>Absidem &longs;ecun<lb/>dum quam per <lb/> &longs;e <expan abbr="cõuoluitur">conuoluitur</expan> cir <lb/> culus <expan abbr="comm&etilde;&longs;u-">commen&longs;u<lb/></expan> rari plano &longs;uper <lb/> quod rotatur. <lb/> pag. 216 <lb/>Ab&longs;idem verò circuli delati ad ro<lb/>tationem alterius, non ita. </s>

<s id="N185A8">ibi<lb/>dem, & &longs;equente. <lb/></s>

<s id="N185AE">Motum circuli &longs;ecundum Ab&longs;i<lb/>dem e&longs;&longs;e motum quendam mix<lb/>tum ex duplici latione. 215 <lb/>Secundum Ab&longs;idem dimotis dir<lb/>culis, dimouetur & centrum il<lb/>lorum. 130 <lb/>Accidentia nonnulla à cau&longs;is na<lb/>turalibus producta conueniunt <lb/> illis præter naturam. </s>

<s id="N185AE">Motum circuli &longs;ecundum Ab&longs;i<lb/>dem e&longs;&longs;e motum quendam mix<lb/>tum ex duplici latione. 215 <lb/>Secundum Ab&longs;idem dimotis cir<lb/>culis, dimouetur & centrum il<lb/>lorum. 130 <lb/>Accidentia nonnulla à cau&longs;is na<lb/>turalibus producta conueniunt <lb/> illis præter naturam. </s>

<s id="N185C4">70. <lb/> & 251 <lb/>Actio debet e&longs;&longs;e ab inæquali pro<lb/>portione. 70 <lb/>Actio qua produeitur impetus <lb/> non e&longs;t motus localis, &longs;ed alte<lb/>ratio. 268 <lb/>Admiranda omnia ad duo rerum <lb/> genera po&longs;&longs;e renocari. 5 <lb/>Admirandame&longs;&longs;e natur am circuli. <lb/> pag. 33 <lb/>Aequalitas cur dicatur cau&longs;a quie<lb/>tis. 242 <lb/>Aequilibrium quid. 55 <lb/>In Aequilibris tam vectis, quam <lb/> libræ &longs;ta &longs;e haheti od <gap/>d pon<lb/>dus, vt bra, hium <gap/>brachium <lb/> ex commutata proportione. <lb/> pag. 88 <lb/>Aere inclu&longs;o varij emittuntur &longs;o<lb/>nitus ad motum, vel percu&longs;&longs;io<lb/>nem aquæ. 29 <lb/>Aëris re&longs;i&longs;tentia, & accur&longs;us in <lb/> motu grauium. 246. & 248 <lb/>Aër quid valeat ad motum natu<lb/>ralem grauium, & <expan abbr="proiector&utilde;">proiectorum</expan>. <lb/> ibid.& 265 <lb/><expan abbr="A&etilde;r">Aerr</expan> quomodo feriret &longs;agittam &longs;i <lb/> eam ip&longs;e pelleret in de&longs;tina<lb/>tum locum. 265 <lb/>Angulus <expan abbr="cõtingentiæ">contingentiæ</expan> minoris cir<lb/>cumferentiæ maior e&longs;t quàm <lb/> circunferentiæ maioris. 137 <lb/>Angulus rectus quo &longs;en&longs;u dicatur <lb/> angulus æqualitatis. 242 <lb/>Angulus circuli apud Ari&longs;totelem <lb/> quinam &longs;it. 134. & 136. & 208 <lb/>Antenna alt us &longs;ublimata, cur <lb/> celerius feratur nauigium. <lb/> pag. 119 <lb/>Antenna ab&longs;que velo quò altius <lb/> &longs;ublimatur, &longs;luctuante mare, <lb/> minus iactatur nauigium. 122 <lb/>Antennæ cornila non minus quàm <lb/> malus vrgent antror&longs;um, na<lb/>uemque trahunt per &longs;unes opi<lb/>feros ac propedes. 106 <lb/>Aquæ ead<gap/>ntes cur dinellantur. <lb/> pag. 250 <lb/>Aqua &longs;upernè cadens per aliquod <lb/> foramen cur pyramidalem &longs;i<lb/>guram referat. 251 <pb xlink:href="005/01/291.jpg"/>Archimedis opera po&longs;t Ari&longs;tote<lb/>lem facultas Mechanica in<lb/>crementa &longs;u&longs;cepit. 8 <lb/>Archimedem diuer&longs;a ab Ari&longs;tote<lb/>le principia non tradidi&longs;&longs;e. <lb/> pag. 71 <lb/>Archita ligneam columbam vo<lb/>lantem exhibuit. 8 <lb/>Ari&longs;toteles po&longs;t Architam Mecha<lb/>nicæ artismodo <expan abbr="&longs;ci&etilde;ti&longs;ico">&longs;cienti&longs;ico</expan> fun<lb/>damenta iecit. 8 <lb/>Ars quomodo & <expan abbr="quãdo">quando</expan> di&longs;tingua<lb/>tur à &longs;cientia. 12 <lb/>Arte nos &longs;uperare ea à quibus na<lb/>tura vincimur. 5 <lb/>Artis <expan abbr="raturã">raturam</expan> verè ac propriè par<lb/>ticipari à facultate Mechanica. <lb/> pag. 13 <lb/>Auctores Mechanicæ facultatis. <lb/> pag. 8. & 9 <lb/>Axis in Libra. </s>

<s id="N185C4">70. <lb/> & 251 <lb/>Actio debet e&longs;&longs;e ab inæquali pro<lb/>portione. 70 <lb/>Actio qua producitur impetus <lb/> non e&longs;t motus localis, &longs;ed alte<lb/>ratio. 268 <lb/>Admiranda omnia ad duo rerum <lb/> genera po&longs;&longs;e reuocari. 5 <lb/>Admirandam e&longs;&longs;e naturam circuli. <lb/> pag. 33 <lb/>Aequalitas cur dicatur cau&longs;a quie<lb/>tis. 242 <lb/>Aequilibrium quid. 55 <lb/>In Aequilibris tam vectis, quam <lb/> libræ ita &longs;e habet i od <gap/>d pon<lb/>dus, vt brachium <gap/>brachium <lb/> ex commutata proportione. <lb/> pag. 88 <lb/>Aere inclu&longs;o varij emittuntur &longs;o<lb/>nitus ad motum, vel percu&longs;&longs;io<lb/>nem aquæ. 29 <lb/>Aëris re&longs;i&longs;tentia, & accur&longs;us in <lb/> motu grauium. 246. & 248 <lb/>Aër quid valeat ad motum natu<lb/>ralem grauium, & <expan abbr="proiector&utilde;">proiectorum</expan>. <lb/> ibid.& 265 <lb/><expan abbr="A&etilde;r">Aer</expan> quomodo feriret &longs;agittam &longs;i <lb/> eam ip&longs;e pelleret in de&longs;tina<lb/>tum locum. 265 <lb/>Angulus <expan abbr="cõtingentiæ">contingentiæ</expan> minoris cir<lb/>cumferentiæ maior e&longs;t quàm <lb/> circunferentiæ maioris. 137 <lb/>Angulus rectus quo &longs;en&longs;u dicatur <lb/> angulus æqualitatis. 242 <lb/>Angulus circuli apud Ari&longs;totelem <lb/> quinam &longs;it. 134. & 136. & 208 <lb/>Antenna altus &longs;ublimata, cur <lb/> celerius feratur nauigium. <lb/> pag. 119 <lb/>Antenna ab&longs;que velo quò altius <lb/> &longs;ublimatur, fluctuante mare, <lb/> minus iactatur nauigium. 122 <lb/>Antennæ corolla non minus quàm <lb/> malus vrgent antror&longs;um, na<lb/>uemque trahunt per funes opi<lb/>feros ac propedes. 106 <lb/>Aquæ eade<gap/>ntes cur diuertantur. <lb/> pag. 250 <lb/>Aqua &longs;upernè cadens per aliquod <lb/> foramen cur pyramidalem fi<lb/>guram referat. 251 <pb xlink:href="005/01/291.jpg"/>Archimedis opera po&longs;t Ari&longs;tote<lb/>lem facultas Mechanica in<lb/>crementa &longs;u&longs;cepit. 8 <lb/>Archimedem diuer&longs;a ab Ari&longs;tote<lb/>le principia non tradidi&longs;&longs;e. <lb/> pag. 71 <lb/>Archita ligneam columbam vo<lb/>lantem exhibuit. 8 <lb/>Ari&longs;toteles po&longs;t Architam Mecha<lb/>nicæ artis modo <expan abbr="&longs;ci&etilde;ti&longs;ico">&longs;cientifico</expan> fun<lb/>damenta iecit. 8 <lb/>Ars quomodo & <expan abbr="quãdo">quando</expan> di&longs;tingua<lb/>tur à &longs;cientia. 12 <lb/>Arte nos &longs;uperare ea à quibus na<lb/>tura vincimur. 5 <lb/>Artis <expan abbr="raturã">raturam</expan> verè ac propriè par<lb/>ticipari à facultate Mechanica. <lb/> pag. 13 <lb/>Auctores Mechanicæ facultatis. <lb/> pag. 8. & 9 <lb/>Axis in Libra. </s>

<s id="N18677">Vide Libram. </s>

<s id="N1867B">55. <lb/> s&s 74 <lb/>Axis in Peritrochio quid. 60 <lb/>Axiculus Trochleæ 58. & 172 </s>

<s id="N18686">B<lb/>Baculi extrema permutantur <lb/> in aëre quando in eius proie<lb/>ctione anteponitur quod e&longs;t le<lb/>uius. 105 <lb/>Baculus nullc accepto impetu <expan abbr="tã-">tan<lb/></expan> tum pote&longs;t impellere, quantum <lb/> a<gap/>u mouetur à manu. 166 <lb/>Baiuli idem pondus &longs;uper lignum <lb/> &longs;imul ge&longs;tantes cur non &longs;emper <lb/> æquè grauentur. <lb/></s>

<s id="N18686">B <lb/>Baculi extrema permutantur <lb/> in aëre quando in eius proie<lb/>ctione anteponitur quod e&longs;t le<lb/>uius. 105 <lb/>Baculus nullo accepto impetu <expan abbr="tã-">tan<lb/></expan>tum pote&longs;t impellere, quantum <lb/> act<gap/>u mouetur à manu. 166 <lb/>Baiuli idem pondus &longs;uper lignum <lb/> &longs;imul ge&longs;tantes cur non &longs;emper <lb/> æquè grauentur. <lb/></s>

<s id="N186A3">Baiulorum &longs;i alter fuerit &longs;tatura <lb/> procerior, alter verò humilior, <lb/> num æquè grauentur. 240 <lb/>Item &longs;i &longs;tatura <expan abbr="quid&etilde;">quidem</expan> pares fue<lb/>rint, per viam tamen <expan abbr="acliu&etilde;">acliuem</expan> in<lb/>cedant, <expan abbr="n&utilde;">num</expan> idem contingat. </s>

<s id="N186A3">Baiulorum &longs;i alter fuerit &longs;tatura <lb/> procerior, alter verò humilior, <lb/> num æquè grauentur. 240 <lb/>Item &longs;i &longs;tatura <expan abbr="quid&etilde;">quidem</expan> pares fue<lb/>rint, per viam tamen <expan abbr="acliu&etilde;">acliue</expan> in<lb/>cedant, <expan abbr="n&utilde;">num</expan> idem contingat. </s>

<s id="N186C0">Bellica in&longs;trumenta, vel machi<lb/>nas con&longs;iderare pertinet ad Po<lb/>liorceticam. 28 <lb/>Bilancis iugum, axis, ac trutina. <lb/> 74. Vide Libram. <lb/></s>

<s id="N186CD">Bipennis vnde vim habeat ad fe<lb/>riendum. 182 <lb/>Brachia libræ in&etail; qualia quo pacto <lb/> decipiant. </s>

<s id="N186D9">76. Vide Libram. <lb/></s>

<s id="N186DE">Brachia dentiforcipis. 190 <lb/>Brachia in&longs;trumenti ad con&longs;rin<lb/>gendas nuces quo amplius dila<lb/><expan abbr="tãtur">tantur</expan>, eò velocius comprimunt. <lb/> pag. 196 </s>

<s id="N186DE">Brachia dentiforcipis. 190 <lb/>Brachia in&longs;trumenti ad confrin<lb/>gendas nuces quo amplius dila<lb/><expan abbr="tãtur">tantur</expan>, eò velocius comprimunt. <lb/> pag. 196 </s>

<s id="N186EE">C<lb/>Candelæ rectà <expan abbr="decid&etilde;t">decident</expan> is &longs;lam<lb/>mula non extinguitur, nec in<lb/>flectitur. 249 <lb/>Item nec prope rotam agitatam <lb/> po&longs;ita. 165 <lb/>Cardo in cu&longs;pide puppis <expan abbr="fulcim&etilde;-">fulcimen<lb/></expan> <expan abbr="t&utilde;">tum</expan> gubernaculi, ac temonis. 102 <lb/>Catapulta quid. 28 <lb/>Cathectus in motione libræ. 83 <lb/>Celonium quid. 234 <lb/>Ad Celonium promouendum cur <lb/> onus oneri adiungatur. ibid. <lb/></s>

<s id="N186EE">C <lb/>Candelæ rectà <expan abbr="decid&etilde;t">decident</expan> is flam<lb/>mula non extinguitur, nec in<lb/>flectitur. 249 <lb/>Item nec prope rotam agitatam <lb/> po&longs;ita. 165 <lb/>Cardo in cu&longs;pide puppis <expan abbr="fulcim&etilde;-">fulcimen<lb/></expan> <expan abbr="t&utilde;">tum</expan> gubernaculi, ac temonis. 102 <lb/>Catapulta quid. 28 <lb/>Cathectus in motione libræ. 83 <lb/>Celonium quid. 234 <lb/>Ad Celonium promouendum cur <lb/> onus oneri adiungatur. ibid. <lb/></s>

<s id="N18715">Centrobarica &longs;cientia quæ. 28 <lb/>Centrum grauitatis quid. 64 <lb/>In Centro grauitatis omnis gra<lb/>uitas corporis colligitur, & <lb/> coaceruatur. 67 <lb/>Centro grauitatis corpora recta <lb/> feruntur deor&longs;um. 67 <lb/><expan abbr="Centr&utilde;">Centrum</expan> grauitatis &longs;tatim corpus <lb/> <expan abbr="ali&utilde;de">aliunde</expan> &longs;u&longs;pen&longs;um cóuertit. ibid. <lb/></s>

<s id="N18730">Circuli proprietates quatuor, & <lb/> quæ. </s>

<s id="N18735">34. & &longs;equentibus. <lb/></s>

<s id="N18739">In Circulo quæ plus à centro di<lb/>&longs;tat linea eadem vi commota, <lb/> citius fertur. 40 <pb xlink:href="005/01/292.jpg"/>Circulos maiotes mobiliores e&longs;&longs;e <lb/> minoribus. </s>

<s id="N18739">In Circulo quæ plus à centro di<lb/>&longs;tat linea eadem vi commota, <lb/> citius fertur. 40 <pb xlink:href="005/01/292.jpg"/>Circulos maiores mobiliores e&longs;&longs;e <lb/> minoribus. </s>

<s id="N18746">pag. 133 <lb/>Circuli contrarium nixum non <lb/> habent quo re&longs;i&longs;tant motui, aut <lb/> moteri, &longs;icut corpora manen<lb/>tia. 133 <lb/>Ex duobus circulis circa idem <lb/> centrum reuolutis &longs;ecundum <lb/> <expan abbr="ab&longs;id&etilde;">ab&longs;idem</expan>, cur maior minori æqua<lb/>le &longs;patium pertran&longs;it. 207 <lb/>Circulum maiorem &longs;eor&longs;um reuo<lb/>lutum, maius &longs;patium peatran<lb/>&longs;ire. 208 <lb/>Circuli motum &longs;ecundum ab&longs;idem <lb/> e&longs;&longs;e motum quendam mixtum <lb/> ex duabus lationibus, 215 <lb/>Circulum minorem delatum ad <lb/> motum alterius maioris magis <lb/> participare de latione recta, <lb/> quàm circulari. 216 <lb/>Circulum maiorem delatum ad <lb/> motum minoris magis partici<lb/>pare de latione circulari, quàm <lb/> recta. 217 <lb/>Circulum quemlibet per &longs;e &longs;eor<lb/>&longs;um rotatum &longs;emper æquè de <lb/> <expan abbr="vtraq;">vtraque</expan> latione participare. 217 <lb/>Circunferentia idem quod ambi<lb/>tus circuli, 208 <lb/>Circunferentiæ <expan abbr="cõmen&longs;uratur">commen&longs;uratur</expan> li<lb/>nea de&longs;cripta per circumuolu<lb/>tionem circuli &longs;uper <expan abbr="plan&utilde;">planum</expan>. 209 <lb/>Cur aliqua puncta circunferentiæ <lb/> maioris &longs;ecundum <expan abbr="propriã">propriam</expan> ab<lb/>&longs;idem latæ minus <expan abbr="progrediãtur">progrediantur</expan>, <lb/> quàm puncta &longs;ibi <expan abbr="corre&longs;põden-">corre&longs;ponden<lb/></expan> tia circunferentiæ minoris &longs;e<lb/><expan abbr="c&utilde;">cum</expan> delatæ; alia verò magis. 220 <lb/>Clana cur maximè valeat ad per<lb/>cutiendom. 182 <lb/>Clcopatræ nauigium, & remi. 29 <lb/>Cochlea quid. 63 <lb/>Cochleæ v&longs;us ad mouenda ponde<lb/>ra. ibid. <lb/></s>

<s id="N18746">pag. 133 <lb/>Circuli contrarium nixum non <lb/> habent quo re&longs;i&longs;tant motui, aut <lb/> motori, &longs;icut corpora manen<lb/>tia. 133 <lb/>Ex duobus circulis circa idem <lb/> centrum reuolutis &longs;ecundum <lb/> <expan abbr="ab&longs;id&etilde;">ab&longs;idem</expan>, cur maior minori æqua<lb/>le &longs;patium pertran&longs;it. 207 <lb/>Circulum maiorem &longs;eor&longs;um reuo<lb/>lutum, maius &longs;patium pertran<lb/>&longs;ire. 208 <lb/>Circuli motum &longs;ecundum ab&longs;idem <lb/> e&longs;&longs;e motum quendam mixtum <lb/> ex duabus lationibus, 215 <lb/>Circulum minorem delatum ad <lb/> motum alterius maioris magis <lb/> participare de latione recta, <lb/> quàm circulari. 216 <lb/>Circulum maiorem delatum ad <lb/> motum minoris magis partici<lb/>pare de latione circulari, quàm <lb/> recta. 217 <lb/>Circulum quemlibet per &longs;e &longs;eor<lb/>&longs;um rotatum &longs;emper æquè de <lb/> <expan abbr="vtraq;">vtraque</expan> latione participare. 217 <lb/>Circunferentia idem quod ambi<lb/>tus circuli, 208 <lb/>Circunferentiæ <expan abbr="cõmen&longs;uratur">commen&longs;uratur</expan> li<lb/>nea de&longs;cripta per circumuolu<lb/>tionem circuli &longs;uper <expan abbr="plan&utilde;">planum</expan>. 209 <lb/>Cur aliqua puncta circunferentiæ <lb/> maioris &longs;ecundum <expan abbr="propriã">propriam</expan> ab<lb/>&longs;idem latæ minus <expan abbr="progrediãtur">progrediantur</expan>, <lb/> quàm puncta &longs;ibi <expan abbr="corre&longs;põden-">corre&longs;ponden<lb/></expan>tia circunferentiæ minoris &longs;e<lb/><expan abbr="c&utilde;">cum</expan> delatæ; alia verò magis. 220 <lb/>Claua cur maximè valeat ad per<lb/>cutiendom. 182 <lb/>Cleopatræ nauigium, & remi. 29 <lb/>Cochlea quid. 63 <lb/>Cochleæ v&longs;us ad mouenda ponde<lb/>ra. ibid. <lb/></s>

<s id="N187BC">Concauum, & conuexum &longs;e habent <lb/> &longs;icut magnum, & paruum. 35 <lb/>Con&longs;tipatio, & laxatio partium <lb/> nece&longs;&longs;aria ad inflexionem con<lb/>tinui. 165 <lb/>Crocæ quid, idemque quod vmbi<lb/>lici. 160 <lb/>Crocæ cur <expan abbr="rot&utilde;da">rotunda</expan> &longs;int figura. ibid. <lb/></s>

<s id="N187D2">Crocæ, vel te&longs;tulæ quomodo per <lb/> &longs;altus in aqua re&longs;iliant. </s>

<s id="N187D7">267. Vi<lb/>de Te&longs;ta. <lb/></s>

Line 3945

Line 3946

<s id="N187EA">D<lb/>Dedali &longs;tatua motus veluti <lb/> animatos præ&longs;tabat. 29 <lb/>Democritus Mile&longs;ius antequam <lb/> Eudoxius, & Archita opus ferè <lb/> mechan. </s>

<s id="N187F7">ediderat. 8 <lb/>Dentes cur facilius extrahantur <lb/> dentiforcipis adhibito in&longs;tru<lb/>mento, quam &longs;ola manu. 189 <lb/>Dentiforcipem duos <expan abbr="cõtinere">continere</expan> ve<lb/>ctes &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> contrarios. 190 <lb/>Dentem dentiforcipe con&longs;trictum <lb/> vnà cum ip&longs;o in&longs;trumento, <expan abbr="ali&utilde;">alium</expan> <lb/> <expan abbr="quendã">quendam</expan> con&longs;tituere <expan abbr="vect&etilde;">vectem</expan>. 191 <lb/>Dentem <expan abbr="commot&utilde;">commotum</expan> facilins manu <lb/> &longs;ola <expan abbr="quã">quam</expan> in&longs;trumento &longs;imul au<lb/>ferri, quo pacto verificeur. 192 <lb/><expan abbr="De&longs;c&etilde;&longs;us">De&longs;cen&longs;us</expan>, & deor&longs;um. </s>

<s id="N187F7">ediderat. 8 <lb/>Dentes cur facilius extrahantur <lb/> dentiforcipis adhibito in&longs;tru<lb/>mento, quam &longs;ola manu. 189 <lb/>Dentiforcipem duos <expan abbr="cõtinere">continere</expan> ve<lb/>ctes &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> contrarios. 190 <lb/>Dentem dentiforcipe con&longs;trictum <lb/> vnà cum ip&longs;o in&longs;trumento, <expan abbr="ali&utilde;">alium</expan> <lb/> <expan abbr="quendã">quendam</expan> con&longs;tituere <expan abbr="vect&etilde;">vectem</expan>. 191 <lb/>Dentem <expan abbr="commot&utilde;">commotum</expan> facilius manu <lb/> &longs;ola <expan abbr="quã">quam</expan> in&longs;trumento &longs;imul au<lb/>ferri, quo pacto verificetur. 192 <lb/><expan abbr="De&longs;c&etilde;&longs;us">De&longs;cen&longs;us</expan>, & deor&longs;um. </s>

<s id="N18831">Vide Motus. <lb/></s>

<s id="N18836">De&longs;criptio quidditatiua Mecha<lb/>nicæ facultatis. 25 <lb/><expan abbr="De&longs;ition&etilde;">De&longs;itionem</expan> impetus impre&longs;&longs;i nó fie<lb/>ri in <expan abbr="in&longs;tãti">in&longs;tanti</expan>, &longs;ed in <expan abbr="t&etilde;pore">tempore</expan>. 257 <pb xlink:href="005/01/293.jpg"/>Differentia inter Mechamcam, <lb/> Archite ctonicam, & Nauticam <lb/> facultatem. 29 <lb/>Dignitas Mechanicæ &longs;acultatis. <lb/> 30. & &longs;equen. <lb/></s>

<s id="N18836">De&longs;criptio quid ditatiua Mecha<lb/>nicæ facultatis. 25 <lb/><expan abbr="De&longs;ition&etilde;">De&longs;itionem</expan> impetus impre&longs;&longs;i nó fie<lb/>ri in <expan abbr="in&longs;tãti">in&longs;tanti</expan>, &longs;ed in <expan abbr="t&etilde;pore">tempore</expan>. 257 <pb xlink:href="005/01/293.jpg"/>Differentia inter Mechanicam, <lb/> Architectonicam, & Nauticam <lb/> facultatem. 29 <lb/>Dignitas Mechanicæ facultatis. <lb/> 30. & &longs;equen. <lb/></s>

<s id="N18857">Di&longs;tantia potentiæ à &longs;ulcimento <lb/> vectis, mouendi facilitatem au<lb/>geat. 88 <lb/>Diui&longs;io &longs;ciertiæ Mechanicæ in <lb/> &longs;uas partes. 27 <lb/>Doctrina Ari&longs;totelis'in priori par<lb/>te huius libri tradita, applica<lb/>tur in &longs;eci nda. 2. & 73 <lb/>Duplicari virtutem motiv <expan abbr="ã">am</expan> quan<lb/>do mouetur commotim. 246 <lb/>Duplicari deinceps principirm <lb/> motus in de&longs;cen&longs;u grauis deor<lb/>&longs;um. 247 </s>

<s id="N18857">Di&longs;tantia potentiæ à fulcimento <lb/> vectis, mouendi facilitatem au<lb/>geat. 88 <lb/>Diui&longs;io &longs;cientiæ Mechanicæ in <lb/> &longs;uas partes. 27 <lb/>Doctrina Ari&longs;totelis' in priori par<lb/>te huius libri tradita, applica<lb/>tur in &longs;ecunda. 2. & 73 <lb/>Duplicari virtutem motiv<expan abbr="ã">am</expan> quan<lb/>do mouetur commotim. 246 <lb/>Duplicari deinceps principium <lb/> motus in de&longs;cen&longs;u grauis deor<lb/>&longs;um. 247 </s>

<s id="N18878">E<lb/>Effectum <expan abbr="quandoq.">quandoque</expan> concurre<lb/>re ad con&longs;eruationem cau&longs;æ <lb/> <expan abbr="tanquã">tanquam</expan> di&longs;po&longs;itionem, aut con<lb/>ditionem. 257 <lb/>Efficiens cau&longs;a impetus in motu <lb/> naturali e&longs;t ip&longs;um graue, aue <lb/> leue. 247 <lb/>Efficiens cau&longs;a impetus in motu <lb/> violenco e&longs;t ip&longs;um proijciens, <lb/> vel impellens. 268 <lb/>En&longs;is ictum validiorem e&longs;&longs;e in cu<lb/>&longs;pide quam in medio. 183 <lb/>En&longs;is ictus facilius diuertitur <expan abbr="c&utilde;">cum</expan> <lb/> quis en&longs;i obuiat ver&longs;us cu&longs;pi<lb/>dem. 183 <lb/>En&longs;em non cedere &longs;ecundum pro<lb/>priam contrarietatem, &longs;ed cum <lb/> exlatere eius cu&longs;pis dimouetur <lb/> ad lat<gap/>s. ibid. <lb/></s>

<s id="N18878">E <lb/>Effectum <expan abbr="quandoq.">quandoque</expan> concurre<lb/>re ad con&longs;eruationem cau&longs;æ <lb/> <expan abbr="tanquã">tanquam</expan> di&longs;po&longs;itionem, aut con<lb/>ditionem. 257 <lb/>Efficiens cau&longs;a impetus in motu <lb/> naturali e&longs;t ip&longs;um graue, aue <lb/> leue. 247 <lb/>Efficiens cau&longs;a impetus in motu <lb/> violento e&longs;t ip&longs;um proijciens, <lb/> vel impellens. 268 <lb/>En&longs;is ictum validiorem e&longs;&longs;e in cu<lb/>&longs;pide quam in medio. 183 <lb/>En&longs;is ictus facilius diuertitur <expan abbr="c&utilde;">cum</expan> <lb/> quis en&longs;i obuiat ver&longs;us cu&longs;pi<lb/>dem. 183 <lb/>En&longs;em non cedere &longs;ecundum pro<lb/>priam contrarietatem, &longs;ed cum <lb/> exlatere eius cu&longs;pis dimouetur <lb/> ad latus. ibid. <lb/></s>

<s id="N188B0"><expan abbr="Erump&etilde;res">Erumperres</expan> ignitos lapides moue<lb/>ri motu præternaturali. 70 <lb/>Eudoxius Gnidius, & Archita Ta<lb/>rentinus primò Geometrica <lb/> principia ad v&longs;um Mechanicum <lb/> tran&longs;tulerunt. 8 <lb/>Exercitus mechanicis artibus pro <lb/> &longs;trati. 7 <lb/>Expul&longs;io quid. 70 <lb/>Extractio di&longs;&longs;icilior quàm demi&longs;<lb/>&longs;io. 236 </s>

<s id="N188B0"><expan abbr="Erump&etilde;res">Erumperis</expan> ignitos lapides moue<lb/>ri motu præternaturali. 70 <lb/>Eudoxius Gnidius, & Archita Ta<lb/>rentinus primò Geometrica <lb/> principia ad v&longs;um Mechanicum <lb/> tran&longs;tulerunt. 8 <lb/>Exercitus mechanicis artibus pro <lb/> &longs;trati. 7 <lb/>Expul&longs;io quid. 70 <lb/>Extractio di&longs;&longs;icilior quàm demi&longs;<lb/>&longs;io. 236 </s>

<s id="N188CC">F<lb/>Faber e&longs;t opi&longs;ex eotum, quæ <lb/> ingonio &longs;imul, & manibus <lb/> fiurt. 7 <lb/>Femur &longs;edertis &longs;imul cum tibia, <lb/> ac thorace duos con&longs;tituit an<lb/>gulos tectos, quos ille &longs;urgen<lb/>do cemmutat. 242 <lb/>Finis ad quem ars Methanica or<lb/>dinatur. 9 <lb/>Finis cuiufque practicæ &longs;cientiæ <lb/> e&longs;t opus. 15 <lb/>Foramen libræ cum axe triplici in <lb/> &longs;itu collocari pote&longs;t. 78. & 84 <lb/>Foramen vnde malus emergit in <lb/> naui excipit impul&longs;um ip&longs;ius <lb/> mali. 120 <lb/>Fractio ligni genu, ac manibus <lb/> vtrinque adhibitis dupliciter <lb/> pote&longs;t contingere. 157 <lb/>Et cur facilius contingat longè <lb/> quàm prope genu admotis ma<lb/>nibus. 158 <lb/>Fractio ligni per eius complica<lb/>tionem cur &longs;equatur prius ex <lb/> parte exteriori, quàm interiori<lb/>pag. 158 <lb/><expan abbr="Fulciment&utilde;">Fulcimentum</expan> græcè hypomochlion <lb/> appellatur. 56 <lb/>Fulcimentum axis vicem gerit, <lb/> <expan abbr="habetq.">habetque</expan> &longs;e tanquam centrum <lb/> immotum. 86 <pb xlink:href="005/01/294.jpg"/>Fulcimentum denti&longs;orcipis in ex<lb/>tractione dentis vbi con&longs;titua<lb/>tur. </s>

<s id="N188CC">F <lb/>Faber e&longs;t opifex eorum, quæ <lb/> ingenio &longs;imul, & manibus <lb/> fiunt. 7 <lb/>Femur sedertis &longs;imul cum tibia, <lb/> ac thorace duos con&longs;tituit an<lb/>gulos tectos, quos ille &longs;urgen<lb/>do commutat. 242 <lb/>Finis ad quem ars Mechanica or<lb/>dinatur. 9 <lb/>Finis cuiusque practicæ &longs;cientiæ <lb/> e&longs;t opus. 15 <lb/>Foramen libræ cum axe triplici in <lb/> &longs;itu collocari pote&longs;t. 78. & 84 <lb/>Foramen vnde malus emergit in <lb/> naui excipit impul&longs;um ip&longs;ius <lb/> mali. 120 <lb/>Fractio ligni genu, ac manibus <lb/> vtrinque adhibitis dupliciter <lb/> pote&longs;t contingere. 157 <lb/>Et cur facilius contingat longè <lb/> quàm prope genu admotis ma<lb/>nibus. 158 <lb/>Fractio ligni per eius complica<lb/>tionem cur &longs;equatur prius ex <lb/> parte exteriori, quàm interiori <lb/>pag. 158 <lb/><expan abbr="Fulciment&utilde;">Fulcimentum</expan> græcè hypomochlion <lb/> appellatur. 56 <lb/>Fulcimentum axis vicem gerit, <lb/> <expan abbr="habetq.">habetque</expan> &longs;e tanquam centrum <lb/> immotum. 86 <pb xlink:href="005/01/294.jpg"/>Fulcimentum dentiforcipis in ex<lb/>tractione dentis vbi con&longs;titua<lb/>tur. </s>

<s id="N1891C">pag. 191 <lb/>Fulcimentum libræ trutina, &longs;eu <lb/> &longs;partum. 55 <lb/>Fnlcimentum vectis quantò pro<lb/>pinquius oneri locatur, tantò <lb/> facilius onus ip&longs;um leuatup<lb/>pag. 56. & 87 <lb/>Fulcimentum vectis, quandoq: e&longs;t <lb/> in altera eius extremitate, vt <lb/> plurimum tamen inter onus, & <lb/> potentiam. 56 <lb/>Punda cur longius &longs;erantur mi&longs;&longs;i<lb/>lia quam manumi&longs;&longs;a. 250 <lb/>Fundatores cur tardius potius <lb/> quàm cito <expan abbr="fundã">fundam</expan> irrotare con<lb/>&longs;ueuerunt. 151 <lb/>Fundæ motus circularis quo po<lb/>cto ad motum rectum proie<lb/>ctionis vim po&longs;&longs;it adijcere. 153 <lb/>Funis ductarius vbi &longs;it alligandus <lb/> in trochleis. 172 <lb/>Fune corpus appen&longs;um qua virtu<lb/>te huc, atque illuc circumfera<lb/>tur. 250 <lb/>Item qua ratione tandem quie<lb/>&longs;eat. 259.& 260 <lb/>Funes opiferi, ac propedes. 106 </s>

<s id="N1891C">pag. 191 <lb/>Fulcimentum libræ trutina, &longs;eu <lb/> &longs;partum. 55 <lb/>Fulcimentum vectis quantò pro<lb/>pinquius oneri locatur, tantò <lb/> facilius onus ip&longs;um leuatum <lb/>pag. 56. & 87 <lb/>Fulcimentum vectis, quandoque: e&longs;t <lb/> in altera eius extremitate, vt <lb/> plurimum tamen inter onus, & <lb/> potentiam. 56 <lb/>Punda cur longius &longs;erantur mi&longs;&longs;i<lb/>lia quam manumi&longs;&longs;a. 250 <lb/>Fundatores cur tardius potius <lb/> quàm cito <expan abbr="fundã">fundam</expan> irrotare con<lb/>&longs;ueuerunt. 151 <lb/>Fundæ motus circularis quo pa<lb/>cto ad motum rectum proie<lb/>ctionis vim po&longs;&longs;it adijcere. 153 <lb/>Funis ductarius vbi &longs;it alligandus <lb/> in trochleis. 172 <lb/>Fune corpus appen&longs;um qua virtu<lb/>te huc, atque illuc circumfera<lb/>tur. 250 <lb/>Item qua ratione tandem quie<lb/>&longs;cat. 259.& 260 <lb/>Funes opiferi, ac propedes. 106 </s>

<s id="N18959">G<lb/>Geode&longs;ia quo pacto di&longs;tin<lb/>guatur à Mechanica. 26 <lb/>Geometria item in quo differat à <lb/> Mechanica. ibid. <lb/></s>

<s id="N18965">Geometricæ, & non alteri &longs;cienti&etail; <lb/> &longs;ubalternatur Mechanica. 20 <lb/>Geometricis conclu&longs;ionib<gap/>s vti<lb/>tur Mechanica tanquam pro<lb/>prijs prin<gap/>ipijs. 20 <lb/>Grauia, & leuia quomodo apud <lb/> Meclianicos v&longs;urpentur. 10 <lb/>Grauia, & leuia cum virtute qua <lb/> moueri debent con&longs;tituunt &longs;ub<lb/>iectum materiale adæquatum <lb/> Mechan. 11 <lb/>Grauia quibus præcipuè in&longs;tru<lb/>mentis à Mecliamcis mouean<lb/>tur. 54 <lb/>Graue <expan abbr="librand&utilde;">librandum</expan> tanto magis gra<lb/>uitat, quanto plus di&longs;tauerit à <lb/> catectu. 82 <lb/>Grauc cadens ex alto in &longs;e impe<lb/>tumproduon. 247 <lb/>Grauitas corporis tanquam pro<lb/>prium operandi principium, e&longs;t <lb/> illi ratio, vt moueatur deor&longs;um. <lb/> pag. 67 <lb/>Grauitas quo &longs;en&longs;u augeri dica<lb/>tur in motu. 179 <lb/>Gubernaculum quo pacto à temo<lb/>ne di&longs;tinguatnr. 100 <lb/>Et quomodo vnum cum illo con<lb/>&longs;t iouat in&longs;trumentum. 100 <lb/><expan abbr="Gubernacul&utilde;">Gubernaculum</expan> cum temone, quan<lb/>doq, &longs;e habet &longs;icut remus in <lb/> cu&longs;pide puppis. 100 <lb/>Gubernaculi virtus ad circum&longs;e<lb/>renda nauigia. </s>

<s id="N18965">Geometricæ, & non alteri &longs;cienti&etail; <lb/> &longs;ubalternatur Mechanica. 20 <lb/>Geometricis conclu&longs;ionibus vti<lb/>tur Mechanica tanquam pro<lb/>prijs princ<gap/>ipijs. 20 <lb/>Grauia, & leuia quomodo apud <lb/> Mechanicos v&longs;urpentur. 10 <lb/>Grauia, & leuia cum virtute qua <lb/> moueri debent con&longs;tituunt &longs;ub<lb/>iectum materiale adæquatum <lb/> Mechan. 11 <lb/>Grauia quibus præcipuè in&longs;tru<lb/>mentis à Mechamcis mouean<lb/>tur. 54 <lb/>Graue <expan abbr="librand&utilde;">librandum</expan> tanto magis gra<lb/>uitat, quanto plus di&longs;tauerit à <lb/> catectu. 82 <lb/>Graue cadens ex alto in &longs;e impe<lb/>tum producit. 247 <lb/>Grauitas corporis tanquam pro<lb/>prium operandi principium, e&longs;t <lb/> illi ratio, vt moueatur deor&longs;um. <lb/> pag. 67 <lb/>Grauitas quo &longs;en&longs;u augeri dica<lb/>tur in motu. 179 <lb/>Gubernaculum quo pacto à temo<lb/>ne di&longs;tinguatur. 100 <lb/>Et quomodo vnum cum illo con<lb/>&longs;t iouat in&longs;trumentum. 100 <lb/><expan abbr="Gubernacul&utilde;">Gubernaculum</expan> cum temone, quan<lb/>doque, &longs;e habet &longs;icut remus in <lb/> cu&longs;pide puppis. 100 <lb/>Gubernaculi virtus ad circum&longs;e<lb/>renda nauigia. </s>

<s id="N189B5">Vide Temonem. <lb/></s>

<s id="N189BA">Gubernator <expan abbr="quandoq.">quandoque</expan> non minus <lb/> con&longs;tituitur. </s>

<s id="N189C3">mouens quam re<lb/>miger. 102 <lb/>Gubernator quo pacto ob&longs;tare &longs;o<lb/>let nauis demer&longs;ioni cum nimis <lb/> ad latus illa vergerit ventorum <lb/> impul&longs;u. 129 </s>

<s id="N189D2">H<lb/>Hauriendi opus duobus di<lb/>&longs;tributum temporibus per<lb/>&longs;ici, & quo pacto. 235 <lb/>Helices in Cochlea quomodo <expan abbr="põ-">pon<lb/></expan> dera &longs;ubleuent. 63 <pb xlink:href="005/01/295.jpg"/>Hero Alexandrinus Philo&longs;ophus <lb/> multa monumenta Mechan. <lb/> protulit. 9 <lb/>Hero Mechanicus de Geode&longs;ia, ac <lb/> de machinis bellicis &longs;crip&longs;it. 9 <lb/>Hominem &longs;tatura proceriorem <lb/> magis grauari à pondere in&longs;ra <lb/> vectem alligatum, quod cum <lb/> alio &longs;tatura humiliori &longs;u&longs;tinet. <lb/> pag. 240 <lb/> Quod &longs;i onus &longs;upra vectem &longs;it al<lb/>ligatum magis grauari homi<lb/>nem &longs;tatura humilio<gap/>em. ibid. <lb/> Si autem onus liberè pendeat, <lb/> vtrumque hominem æquè gra<lb/>uari. ibid. <lb/></s>

<s id="N189D2">H<lb/> Hauriendi opus duobus di<lb/>&longs;tributum temporibus per<lb/>fici, & quo pacto. 235 <lb/>Helices in Cochlea quomodo <expan abbr="põ-">pon<lb/></expan> dera &longs;ubleuent. 63 <pb xlink:href="005/01/295.jpg"/>Hero Alexandrinus Philo&longs;ophus <lb/> multa monumenta Mechan. <lb/> protulit. 9 <lb/>Hero Mechanicus de Geode&longs;ia, ac <lb/> de machinis bellicis &longs;crip&longs;it. 9 <lb/>Hominem &longs;tatura proceriorem <lb/> magis grauari à pondere infra <lb/> vectem alligatum, quod cum <lb/> alio &longs;tatura humiliori &longs;u&longs;tinet. <lb/> pag. 240 <lb/> Quod &longs;i onus &longs;upra vectem &longs;it al<lb/>ligatum magis grauari homi<lb/>nem &longs;tatura humiliorem. ibid. <lb/> Si autem onus liberè pendeat, <lb/> vtrumque hominem æquè gra<lb/>uari. ibid. <lb/></s>

<s id="N18A07">Hominem &longs;cytalis, ac troobleis, <lb/> ax<gap/><expan abbr="q.">que</expan> in peritrochio, ore tan<lb/>tum perflando dimoueri po&longs;&longs;e. <lb/> pag. 177 <lb/>Homo dum commodè &longs;edet, duos <lb/> angulos rectos po&longs;itione &longs;ui <lb/> corporis efficit: cum verò &longs;ur<lb/>git, eos in acutos commutat. <lb/> pag. 242 <lb/>Humeri iunctura con&longs;tituitur cen<lb/>trum motionis qua &longs;ecuris ad <lb/> &longs;cindendum adhibetur. 180 <lb/>Humeri iunctura <expan abbr="cõ&longs;tituitur">con&longs;tituitur</expan> cen<lb/>trum motionis qua circumagi<lb/>tur funda. 151 <lb/>Hydraulicas machinas à Cte&longs;ibo <lb/> primò inuentas fui&longs;&longs;e. 9 <lb/>Hypomochlion idem quod fulci<lb/>mentum. 86 </s>

<s id="N18A07">Hominem &longs;cytalis, ac trochleis, <lb/> axe<expan abbr="q.">que</expan> in peritrochio, ore tan<lb/>tum perflando dimoueri po&longs;&longs;e. <lb/> pag. 177 <lb/>Homo dum commodè &longs;edet, duos <lb/> angulos rectos po&longs;itione &longs;ui <lb/> corporis efficit: cum verò &longs;ur<lb/>git, eos in acutos commutat. <lb/> pag. 242 <lb/>Humeri iunctura con&longs;tituitur cen<lb/>trum motionis qua &longs;ecuris ad <lb/> &longs;cindendum adhibetur. 180 <lb/>Humeri iunctura <expan abbr="cõ&longs;tituitur">con&longs;tituitur</expan> cen<lb/>trum motionis qua circumagi<lb/>tur funda. 151 <lb/>Hydraulicas machinas à Cte&longs;ibo <lb/> primò inuentas fui&longs;&longs;e. 9 <lb/>Hypomochlion idem quod fulci<lb/>mentum. 86 </s>

<s id="N18A39">I<lb/>Iacula quomodo manu emit<lb/>tantur. 150 <lb/>Iaculationem fieri non po&longs;&longs;e <expan abbr="ab&longs;q;">ab&longs;que</expan> <lb/> præuio motu iaculantis. 151 <lb/>Ictus &longs;ecuris &longs;icut & mallei, ac &longs;i<lb/>milium vnde validus con&longs;titua<lb/>tur. 179 <lb/>Ictus en&longs;is. </s>

<s id="N18A50">Vide En&longs;em. <lb/></s>

<s id="N18A55">Ignes mi&longs;&longs;iles cur huc, atque illuc <lb/> interdum di&longs;currant. 153 <lb/>Impetus, &longs;eu impul&longs;us quid. 267 <lb/>Impetum non produci &longs;ormaliter <lb/> per motum localem, &longs;ed per <lb/> aliam actionem. <gap/>68 <lb/>Impetum non produci in in&longs;tanti. <lb/> ibid. <lb/></s>

<s id="N18A55">Ignes mi&longs;&longs;iles cur huc, atque illuc <lb/> interdum di&longs;currant. 153 <lb/>Impetus, &longs;eu impul&longs;us quid. 267 <lb/>Impetum non produci formaliter <lb/> per motum localem, &longs;ed per <lb/> aliam actionem. <gap/>68 <lb/>Impetum non produci in in&longs;tanti. <lb/> ibid. <lb/></s>

<s id="N18A69">Impetum minus imprimi in par<lb/>ua quantitate quam in maiori: <lb/> minu&longs;que in leuiori, & rariori, <lb/> quàm in grauiori, ac den&longs;iori. <lb/> pag. 271 <lb/>Impetum per &longs;e ordinari ad <expan abbr="mot&utilde;">motum</expan> <lb/> rectum, ad cæteros verò per ac<lb/>cidens. 153 <lb/>Impetus ad <expan abbr="re&longs;iliend&utilde;">re&longs;iliendum</expan> à quo pro<lb/>ducatur. 250 <lb/>Impetus velis exceptus in quam <lb/> nauis partem refundatur. 119 <lb/>Impetum non corrumpi in in&longs;tan<lb/>ti, &longs;ed in tempore. </s>

<s id="N18A8E">257. Vide <lb/> Qualitas impetus. <lb/></s>

<s id="N18A94">Inflexio continui ab altero extre<lb/>mo eleuati quomodo fiat. 164 <lb/>Inflexio proceris ligni ex medio <lb/> &longs;u&longs;pen&longs;i, vel ambabus extremi<lb/>tatibus quo etiam pacto proce<lb/>dat. 166 <lb/>In&longs;trumenta naturam circuli in <lb/> motione participantia quæ. 53 <lb/>In&longs;trumenta præcipua Mechani<lb/> corum &longs;ex. ibid. <lb/></s>

Line 3985

Line 3986

<s id="N18AC6">L<lb/>Lana quamuis tenui&longs;sima de<lb/>&longs;cendenti graui po&longs;t terga <lb/> alligata ab aëre non deprimi<lb/>tur. </s>

<s id="N18AD1">pag. 249 <lb/>Lancea cur facilius &longs;u&longs;tineatur <lb/> erecta, quàm inclinata. 231 <lb/>Lancea inclinata cur facilius è <lb/> manubrio, quàm ab extremo <lb/> ge&longs;tetur. 231 <lb/>In lancea cur manubrium prope <lb/> extremum, & non in ip&longs;o extre<lb/>mo con&longs;tituatur. ibid. <lb/></s>

<s id="N18AE5">Lancea cur &longs;triari con&longs;ueuit. ibid. <lb/> Ad lanceam confringendam in<lb/>cur &longs;u quomodo robur brachij <lb/> o&longs;tentatur. ibid. <lb/></s>

<s id="N18AEF">Lances libræ non pertinent e&longs;&longs;en<lb/>tialiter ad con&longs;ticutionem li<lb/>bræ. 55 <lb/>Lapillus complanatus quomodo <lb/> eminus proijciatur. </s>

<s id="N18AEF">Lances libræ non pertinent e&longs;&longs;en<lb/>tialiter ad con&longs;titutionem li<lb/>bræ. 55 <lb/>Lapillus complanatus quomodo <lb/> eminus proijciatur. </s>

<s id="N18AFA">Vide Te&longs;ta. <lb/> pag. 152 <lb/>Latio duplex, naturalis, ac præter<lb/>naturalis. 41. & 47 <lb/>Lati continui in fine imbecilli&longs;&longs;i<lb/>mam e&longs;&longs;e lationem, quando ve. <lb/> rificetur. 105 <lb/>Lectulorum &longs;pondæ cur &longs;ecundum <lb/> duplam proportionem effician<lb/>tur. 225 <lb/>In. </s>

<s id="N18AFA">Vide Te&longs;ta. <lb/> pag. 152 <lb/>Latio duplex, naturalis, ac præter<lb/>naturalis. 41. & 47 <lb/>Lati continui in fine imbecilli&longs;&longs;i<lb/>mam e&longs;&longs;e lationem, quando ve<lb/>rificetur. 105 <lb/>Lectulorum &longs;pondæ cur &longs;ecundum <lb/> duplam proportionem effician<lb/>tur. 225 <lb/>In. </s>

<s id="N18B11">lectulis muniendis cur re&longs;tes <lb/> per tran&longs;uer&longs;um, non per dia<lb/>metrum extendantur. 226 <lb/>Libra quid & quomodo in &longs;ui mo<lb/>tione naturam circuli partici<lb/>pet. 55 <lb/>Libra cur facilius moueatur <expan abbr="qu&amacr;-">quan<lb/></expan> do e&longs;t vacua. 144 <lb/>Libræ maiorcs cur exactiores &longs;int <lb/> minoribus. 74 <lb/>Libræ inæqualibus brachijs de<lb/><expan abbr="&longs;raud&amacr;tur">&longs;raudantur</expan> <expan abbr="merci&utilde;">mercium</expan> emptores. 76 <lb/> Ad libræ <expan abbr="motion&etilde;">motionem</expan> exce&longs;&longs;us pon<lb/>deris proportionem quandam <lb/> requirit cum parte oppo&longs;ita <lb/> quam excedit. </s>

<s id="N18B11">lectulis muniendis cur re&longs;tes <lb/> per tran&longs;uer&longs;um, non per dia<lb/>metrum extendantur. 226 <lb/>Libra quid & quomodo in &longs;ui mo<lb/>tione naturam circuli partici<lb/>pet. 55 <lb/>Libra cur facilius moueatur <expan abbr="qu&amacr;-">quan<lb/></expan> do e&longs;t vacua. 144 <lb/>Libræ maiores cur exactiores &longs;int <lb/> minoribus. 74 <lb/>Libræ inæqualibus brachijs de<lb/><expan abbr="&longs;raud&amacr;tur">fraudantur</expan> <expan abbr="merci&utilde;">mercium</expan> emptores. 76 <lb/> Ad libræ <expan abbr="motion&etilde;">motionem</expan> exce&longs;&longs;us pon<lb/>deris proportionem quandam <lb/> requirit cum parte oppo&longs;ita <lb/> quam excedit. </s>

<s id="N18B40">145. & &longs;equen. <lb/></s>

<s id="N18B44">Libræ iugum &longs;u&longs;penditur &longs;parto, <lb/> vel trutina. 55 <lb/>Libræ &longs;partum locari pote&longs;t in <lb/> medio, &longs;upra vel infra lineam <lb/> iugum diuidentem per longum. <lb/> pag. 78. & 84 <lb/> Cur quando ponitur &longs;upra &longs;i al<lb/>terum extremum demittatur, <lb/> libra ex &longs;e reducitur in pri&longs;ti<lb/>num &longs;tatum. 79 <lb/> Cur quando con&longs;tituitur infra <lb/> non item. 80 <lb/> Cur quando con&longs;tituitur in pun<lb/>cto medio maneat quomodo<lb/>cunque relinquatur. 84 <lb/>Ligna oblonga cur difficilius ab <lb/> extremo &longs;uper <expan abbr="humer&umacr;">humerum</expan> ge&longs;ten<lb/>tur, quàm ex medio. 229 <lb/> Cur item difficilius ab extremo <lb/> eleuentur. 230 <lb/>Ligna cur eo difficilius quò pro<lb/>ceriora &longs;unt etiam ex medio <lb/> a&longs;portentur. 232 <lb/>Lignum cur facilius genu franga<lb/>tur &longs;i ab extremis apprehenda<lb/>tur. 157 <lb/>Ligna graciliora cur facilius fran<lb/>gantur, quàm cra&longs;&longs;iora. 158 <lb/>Ligna cur prius frangantur in <lb/> parte exteriori, quàm interiori <lb/> re&longs;pectu frangentes. 158 <lb/>Ligna cur quanto longiora &longs;unt <lb/> tanto imbecilliora fiant. 163 <lb/>Ligna ab aliquo extremo eleuata <pb xlink:href="005/01/297.jpg"/> &longs;i longiora &longs;int, cur magis infle<lb/>ctantur. 163 <lb/>Locus antennæ. 119 <lb/>Locus vbi fulcitur malus in naui. <lb/> pag. 120 <lb/>Locus proprius temonis. 105 <lb/>Locus vbi applicatur gubernacu<lb/>lum e&longs;t veluti &longs;calmus. 112 <lb/>Longitudo vectis vtrinque ex ful<lb/>cimento proten&longs;a iugum refert <lb/> libræ in partes inæquales diui<lb/>&longs;um. 86 <lb/>Longitudo patitur ad longitudi<lb/>nem, quod motum pondus ad <lb/> mouens in vecte. 88 <lb/>Lorati &longs;tipites vnde vim tantam <lb/> habeant ad percutiendum. 182 <lb/>Lumen accen&longs;um prope rotam <lb/> agitatam, ab aëre non inflecti, <lb/> nec extingui. 265 <lb/>Lumen candelæ rectà <expan abbr="decid&etilde;tis">decidentis</expan> &longs;i<lb/>militer, nec inflecti, nec extin<lb/>gui. 249 <lb/>Lu&longs;oriam pilam non re&longs;ilere per <lb/> nouum impetum acceptum à <lb/> &longs;olo vel pariete. 250 </s>

Line 4002

Line 4003

<s id="N18C6E">Motus violentus cur velocior &longs;it <lb/> in medio, quàm in principio, vel <lb/> fine. 258 <lb/>Motus productus ab impetu indif<lb/>ferens e&longs;t ad quamcunque po&longs;i<lb/>tionem. 267 <lb/>Motus acceleratio in proiectis <expan abbr="nõ">non</expan> <lb/> prouenire ab aëris &longs;ub&longs;equentis <lb/> accur&longs;u. 248 <lb/>Motus quomodo ponderi addat <lb/> pondus, & grauitas augeatur <lb/> in motu. 178 <lb/>Motus <expan abbr="re&longs;ili&etilde;di">re&longs;iliendi</expan> quomodo fiat. 250 <lb/>Motus circularis corporis fune <lb/> appen&longs;i qua virtute perficiatur. <lb/> pag. 250 <lb/>Mutatio appendiculi, vel eius <expan abbr="trã&longs;-">tran&longs;<lb/></expan> latio de loco ad locum, mutat <lb/> etiam &longs;tateram. 188 <lb/>Multiplicare trutinas in &longs;tatera <lb/> ad ponderum differentias, labo<lb/>rio&longs;um, & inutile. 188 </s>

<s id="N18CA8">N<lb/>Nauis progre&longs;&longs;us per velifi<lb/>cationem quomodo fiat. <lb/> pag. 119.& 120 <lb/>Nauis progre&longs;fus in anteriora <expan abbr="nõ">non</expan> <lb/> flante ex puppi vento. 125 <lb/>Nauis progre&longs;&longs;us per remigatio<lb/>nem quo pacto procedat. </s>

<s id="N18CA8">N <lb/>Nauis progre&longs;&longs;us per velifi<lb/>cationem quomodo fiat. <lb/> pag. 119.& 120 <lb/>Nauis progre&longs;sus in anteriora <expan abbr="nõ">non</expan> <lb/> flante ex puppi vento. 125 <lb/>Nauis progre&longs;&longs;us per remigatio<lb/>nem quo pacto procedat. </s>

<s id="N18CBD">108. <lb/> & &longs;equentib. </s>

<s id="N18CC2">Vide Remus. <lb/></s>

<s id="N18CC7">Nauis recta incedendo cur quan<lb/>doque non pertingat ad de&longs;ti<lb/>natum locum. 114 <lb/>Nauis ab&longs;que velo cur minus ia<lb/>ctetur fluctibus &longs;i altius &longs;ubli<lb/>metur antenna. 122 <lb/>Nauigia qua ratione paruo cir<lb/>cemferantur gubernaculo. </s>

<s id="N18CD8">101. <lb/> Vide Temonem. <lb/></s>

<s id="N18CDF">Nauis æquabiliter à dextris, & à <lb/> &longs;ini&longs;tris recipiendo maris im<lb/>pul&longs;um, &longs;e habet tanquam libra <lb/> in æquilibrio. 117 <lb/>Nauis con&longs;tituitur etiam onus, <lb/> quod per malum tanquam per <lb/> vectem mouetur. 119 <lb/>Nauis quo pacto ab&longs;que remis &longs;o<lb/>lo temone conuertatur in por<lb/>tu. 101 <lb/>Nixum non habet peripheria quo <lb/> retardetur à proprio motu. 133 <lb/>Nixus corporum quie&longs;centium. <lb/> ibid. <lb/></s>

<s id="N18CFD">Nuces cur ab&longs;que ictu facile in<lb/>&longs;trumento ad id opus fabrefa<lb/>cto confringantur. 194 <lb/>Nuces facilius con&longs;ringi quo lon<lb/>giora fuerint brachia huius in<lb/>&longs;trumenti à connexione ip&longs;o<lb/>rum. 195 <lb/>Nutus quem habent corpora ro <lb/> tunda ad motum. </s>

<s id="N18CFD">Nuces cur ab&longs;que ictu facile in<lb/>&longs;trumento ad id opus fabrefa<lb/>cto confringantur. 194 <lb/>Nuces facilius confringi quo lon<lb/>giora fuerint brachia huius in<lb/>&longs;trumenti à connexione ip&longs;o<lb/>rum. 195 <lb/>Nutus quem habent corpora ro<lb/>tunda ad motum. </s>

<s id="N18D10">131. & &longs;e<lb/>quentibus. <lb/></s>

<s id="N18D16">Nutu &longs;uo celerrime deor&longs;um ro<lb/>tando feruntur indecliue cor<lb/>pora orbiculata. </s>

<s id="N18D1F">O<lb/>Obiectum totale adæquatum <lb/> Mechanicæ facultatis. 11 <pb xlink:href="005/01/299.jpg"/>Obiectum formale eiu&longs;dem. ibid. <lb/></s>

<s id="N18D2B">Obliqua temonis con&longs;titutio quo<lb/>modo nauem inclinet. 103 <lb/>Obliqua, ac magna declinatio pro<lb/>ræ per paruam temonis conuer<lb/>&longs;ionem. 106.& 107 <lb/>Odor ex &longs;e remittitur, ac de&longs;init <lb/> <expan abbr="ab&longs;q;">ab&longs;que</expan> contrario expellente. 257 <lb/>Offen&longs;ant minus corpora rotunda <lb/> quàm alia &longs;uper planum. 131 <lb/>Onus, vel potentiam augeri, ac <lb/> minui iuxta maiorem, aut mi<lb/>norem di&longs;tantiam à fulcimento <lb/> vectis. 88 <lb/>Onus proportionem quandam re<lb/>quirere cum potentia. 269 <lb/>Onus oneri cur adiungatur ad ce<lb/>lonium &longs;acilius promouendum. <lb/> pag. 235 <lb/>Onus antennæ aliquando re&longs;i&longs;tit <lb/> nauis inclinationi. 123 <lb/> Aliquando verò nihil ob&longs;tat, &longs;ed <lb/> potius vicem gerit potentiæ in<lb/>clinantis. ibid. <lb/></s>

<s id="N18D2B">Obliqua temonis con&longs;titutio quo<lb/>modo nauem inclinet. 103 <lb/>Obliqua, ac magna declinatio pro<lb/>ræ per paruam temonis conuer<lb/>&longs;ionem. 106.& 107 <lb/>Odor ex &longs;e remittitur, ac de&longs;init <lb/> <expan abbr="ab&longs;q;">ab&longs;que</expan> contrario expellente. 257 <lb/>Offen&longs;ant minus corpora rotunda <lb/> quàm alia &longs;uper planum. 131 <lb/>Onus, vel potentiam augeri, ac <lb/> minui iuxta maiorem, aut mi<lb/>norem di&longs;tantiam à fulcimento <lb/> vectis. 88 <lb/>Onus proportionem quandam re<lb/>quirere cum potentia. 269 <lb/>Onus oneri cur adiungatur ad ce<lb/>lonium facilius promouendum. <lb/> pag. 235 <lb/>Onus antennæ aliquando re&longs;i&longs;tit <lb/> nauis inclinationi. 123 <lb/> Aliquando verò nihil ob&longs;tat, &longs;ed <lb/> potius vicem gerit potentiæ in<lb/>clinantis. ibid. <lb/></s>

<s id="N18D5F">Opifex eorum, quæ ingenio &longs;imul <lb/> & manibus fiunt, dicitur etiam <lb/> Mechanicus. 7 <lb/>Opiferi funes quodnam in naui <lb/> munvs exerceant. 106 <lb/>Oppugnationum a&longs;tutias in bello <lb/> ad Mechanicam pertinere. 6 <lb/>Organopetica fcientia quæ. 28 <lb/>Orbiculis multiplicatis in tro<lb/>chlea, augetur virtus motiua. <lb/> pag. 173 </s>

<s id="N18D5F">Opifex eorum, quæ ingenio &longs;imul <lb/> & manibus fiunt, dicitur etiam <lb/> Mechanicus. 7 <lb/>Opiferi funes quodnam in naui <lb/> munvs exerceant. 106 <lb/>Oppugnationum a&longs;tutias in bello <lb/> ad Mechanicam pertinere. 6 <lb/>Organopetica scientia quæ. 28 <lb/>Orbiculis multiplicatis in tro<lb/>chlea, augetur virtus motiua. <lb/> pag. 173 </s>

<s id="N18D78">P<lb/>Palmula. </s>

Line 4023

Line 4024

<s id="N18D8A">pag. 124.& 127 <lb/>Pedes retrahere, ac perpendicula<lb/>riter &longs;ub capite con&longs;tituere de<lb/>bet is, qui à &longs;e&longs;&longs;ione vult &longs;urge<lb/>re. 243 <lb/>Pila per eundem impetum à proij<lb/>ciente <expan abbr="recept&utilde;">receptum</expan> in parietem illi<lb/>dit, ac inde re&longs;ilit. 267 <lb/>Poliorcetica &longs;cientia quæ. 28 <lb/>Proiectorum latio non perficitur <lb/> ab aëre, 248. & &longs;equent. </s>

<s id="N18DA5">& 265. <lb/> & &longs;equent. <lb/></s>

<s id="N18DAB">Proiecta qua ratione è minus &longs;e<lb/>rantur. 261 <lb/>Proiecta cur ce&longs;&longs;ent à latione. 253 <lb/>Proiecta cur velocius ferantur in <lb/> progre&longs;&longs;u, quàm in principio, <lb/> vel fine. 258 <lb/> In proiectis virtutem aliquam à <lb/> proijciente imprimi, ac produ<lb/>ci. 262 <lb/>Proiectorum re&longs;i&longs;tentia in motu <lb/> locali à quo proueniat. 270 <lb/>Proiecta <expan abbr="commen&longs;uration&etilde;">commen&longs;urationem</expan> quan<lb/>dam cum proijciente require<lb/>re. 272 <lb/>Propedes veli inferiora retror &longs;um <lb/> tendere, nauemque &longs;ecum abri<lb/>pere. 106 <lb/>Propedes repentino &longs;uperuenien<lb/>te turbine relaxantur. ibid. <lb/></s>

<s id="N18DD7">Prora in eodem exiftente, totum <lb/> transferri nauigium, quomodo <lb/> intelligatur. 115 <lb/>Proræ multa &longs;it tran&longs;po&longs;itio temo<lb/>ne paululum quid tran&longs;po&longs;ito. <lb/> pag. 107.& 117 <lb/> In prora, vel puppi remigantes <lb/> minus quàm in medio nauem <lb/> promouent. 91 <lb/>Prora an <expan abbr="maior&etilde;">maiorem</expan> <expan abbr="impet&utilde;">impetum</expan> recipiat <lb/> in nauigatione <expan abbr="quã">quam</expan> puppis. 106 <pb xlink:href="005/01/300.jpg"/>Proram ver&longs;us pauciores remiges <lb/> adhibentur in triremibus. 106 <lb/>Proram ver&longs;us totus impetus it. <lb/> velo collectus etiam ex tran&longs;<lb/>uer&longs;o per&longs;lante vento refundi<lb/>tur. 128 <lb/>Puppis an maneat omnino dum <lb/> ad motum temonis circumfer<lb/>tur longitudo nauigij. 113 <lb/>Puppi parum dimota, multa &longs;it <lb/> proræ tran&longs;po&longs;itio. 106. & 113 <lb/>Puppis qua ratione feratur quo <lb/> gubernaculum vergit. 114 <lb/>Puppim ver&longs;us ad latus tenditur <lb/> velum flante vento ex tran&longs;uer<lb/>&longs;o. 124 <lb/>Puppis aliquando &longs;e habet <expan abbr="tanquã">tanquam</expan> <lb/> onus in vecte angulo&longs;o. 122 </s>

<s id="N18DD7">Prora in eodem exiftente, totum <lb/> transferri nauigium, quomodo <lb/> intelligatur. 115 <lb/>Proræ multa &longs;it tran&longs;po&longs;itio temo<lb/>ne paululum quid tran&longs;po&longs;ito. <lb/> pag. 107.& 117 <lb/> In prora, vel puppi remigantes <lb/> minus quàm in medio nauem <lb/> promouent. 91 <lb/>Prora an <expan abbr="maior&etilde;">maiorem</expan> <expan abbr="impet&utilde;">impetum</expan> recipiat <lb/> in nauigatione <expan abbr="quã">quam</expan> puppis. 106 <pb xlink:href="005/01/300.jpg"/>Proram ver&longs;us pauciores remiges <lb/> adhibentur in triremibus. 106 <lb/>Proram ver&longs;us totus impetus it. <lb/> velo collectus etiam ex tran&longs;<lb/>uer&longs;o perflante vento refundi<lb/>tur. 128 <lb/>Puppis an maneat omnino dum <lb/> ad motum temonis circumfer<lb/>tur longitudo nauigij. 113 <lb/>Puppi parum dimota, multa &longs;it <lb/> proræ tran&longs;po&longs;itio. 106. & 113 <lb/>Puppis qua ratione feratur quo <lb/> gubernaculum vergit. 114 <lb/>Puppim ver&longs;us ad latus tenditur <lb/> velum flante vento ex tran&longs;uer<lb/>&longs;o. 124 <lb/>Puppis aliquando &longs;e habet <expan abbr="tanquã">tanquam</expan> <lb/> onus in vecte angulo&longs;o. 122 </s>

<s id="N18E26">Q<lb/>Qvalitates quæ habent con<lb/>trarium non ni&longs;i in tempore <lb/> intenduntur, ac remittuntur. <lb/> pag. 254 <lb/>Qualitates nonnullæ deficientes <lb/> per propriam <expan abbr="de&longs;ition&etilde;">de&longs;itionem</expan> ab&longs;que <lb/> contrario. 257 <lb/>Qualitatem impetus e&longs;&longs;e præter <lb/> naturam grauium. 251 <lb/>Qualitatem impetus &longs;emper e&longs;&longs;e <lb/> eiu&longs;dem &longs;peciei. 267 <lb/>Qualitatem impetus non habere <lb/> qualitatem contrariam. </s>

Line 4031

Line 4032

<s id="N18E4E">Quantitas ponderis, & quantitas <lb/> virtutis motiuæ &longs;imul à Mecha<lb/>nico con&longs;ideranda. 10 <lb/>Quantitas ponderis tum grauitas <lb/> tum leuitas re&longs;pectu diuer&longs;o<lb/>rum apud Mechanicos nuncu<lb/>patur. 10 <lb/>Quæ&longs;tiones Mechanicæ quomodo <lb/> à natur alibus di&longs;tinguantur. 6 </s>

<s id="N18E63">R<lb/>Rami amputatio, quæ &longs;ur&longs;um <lb/> fit ab vnico tantum impul&longs;u <lb/> procedit. 179 <lb/>Remi longiores in medio nauis, <lb/> quàm in puppi, vel prora. 91 <lb/>Remi argentei Cleopatr&etail; Reginæ. <lb/> pag. 29 <lb/>Remi palmula, quandoq in pro<lb/>gre&longs;&longs;u nauigij non retrocedit. <lb/> pag. 109.& 111 <lb/>Remi palmula tantum <expan abbr="quandoq.">quandoque</expan> <lb/> retrocedit quantum progredi<lb/>tur nauigium. 111 <lb/>Remi palmula, vt plurimum minus <lb/> retrocedit, quàm nauis progre<lb/>diatur. ibid. <lb/></s>

<s id="N18E63">R <lb/>Rami amputatio, quæ &longs;ur&longs;um <lb/> fit ab vnico tantum impul&longs;u <lb/> procedit. 179 <lb/>Remi longiores in medio nauis, <lb/> quàm in puppi, vel prora. 91 <lb/>Remi argentei Cleopatr&etail; Reginæ. <lb/> pag. 29 <lb/>Remi palmula, quandoque in pro<lb/>gre&longs;&longs;u nauigij non retrocedit. <lb/> pag. 109.& 111 <lb/>Remi palmula tantum <expan abbr="quandoq.">quandoque</expan> <lb/> retrocedit quantum progredi<lb/>tur nauigium. 111 <lb/>Remi palmula, vt plurimum minus <lb/> retrocedit, quàm nauis progre<lb/>diatur. ibid. <lb/></s>

<s id="N18E8B">Remigantes in nauis medio, ma<lb/>gis nauem mouere. 91 <lb/>Remum in remigatione, vectis ra<lb/>tionem habere. 91 <lb/> In remigatione &longs;calmum e&longs;&longs;e ful<lb/>cimentum, mare onus. ibid. <lb/></s>

<s id="N18E99">Remigationem fieri per modum <lb/> circuli circa &longs;calmum, 97 <lb/> In remigatione ex duplici motu <lb/> circulari contrario re&longs;ultare <lb/> vnum rectum quo progreditur <lb/> nauis. 97 <lb/>Re&longs;iliendo proiectum nullus in eo <lb/> producitur impetus nouus, &longs;ed <lb/> retorquetur idem à proijciente <lb/> incu&longs;fus. 250 <lb/>Re&longs;iliendi motus. </s>

<s id="N18EB0">Vide Motus. <lb/></s>

<s id="N18EB5">Rimulæ <expan abbr="&longs;pondar&utilde;">&longs;pondarum</expan> cau&longs;a &longs;ci&longs;&longs;ionis <lb/> earum cum re&longs;tes in lectulis ex<lb/>tenduntur per diametrum. 226 <lb/>Ripa quomodo per repul&longs;um con-<pb xlink:href="005/01/301.jpg"/> currat ad circulationem aqua<lb/>rum in vorticibus. </s>

<s id="N18EC8">275. & &longs;e<lb/>quen. <lb/></s>

<s id="N18ECE">Romanos ad remigium in arena <lb/> aliquando &longs;e exercui&longs;&longs;e. 93 <lb/>Rombi puncta extrema vnius la<lb/>teris &longs;i duabus &longs;imul &longs;erantur <lb/> lationibus cum eadem veloci<lb/>tate, cur vnum maius, alterum <lb/> minus &longs;patium percurrat. 200 <lb/> In Rombo cur quod &longs;uper eius <lb/> latus fertur, minus &longs;patium per<lb/>tran&longs;it, quàm ip&longs;um latus. 204 <lb/>Rotas tripliciter in orbem po&longs;&longs;e <lb/> conucrti. 130 <lb/>Rota leuior cur facilius mouea<lb/>tur quàm grauior. 144 <lb/> Quæ per maiores rotas trahun<lb/>tur, facilius ac citius moueri. <lb/> pag. </s>

<s id="N18ECE">Romanos ad remigium in arena <lb/> aliquando &longs;e exercui&longs;&longs;e. 93 <lb/>Rombi puncta extrema vnius la<lb/>teris &longs;i duabus &longs;imul &longs;erantur <lb/> lationibus cum eadem veloci<lb/>tate, cur vnum maius, alterum <lb/> minus &longs;patium percurrat. 200 <lb/> In Rombo cur quod &longs;uper eius <lb/> latus fertur, minus &longs;patium per<lb/>tran&longs;it, quàm ip&longs;um latus. 204 <lb/>Rotas tripliciter in orbem po&longs;&longs;e <lb/> conuerti. 130 <lb/>Rota leuior cur facilius mouea<lb/>tur quàm grauior. 144 <lb/> Quæ per maiores rotas trahun<lb/>tur, facilius ac citius moueri. <lb/> pag. </s>

<s id="N18EF1">140. & 142. Vide <expan abbr="Circul&utilde;">Circulum</expan>. <lb/></s>

<s id="N18EF9">Rotunda corpora cur facilius mo<lb/>ueantur. 130.& 137 <lb/>Runca vnde efficaciam &longs;ortiatur <lb/> ad &longs;cindendum. 182 </s>

<s id="N18F04">S<lb/>Sari&longs;&longs;am ab extremo eleuatam <lb/> magis inclinari, quàm &longs;urca, <lb/> lum. 164 <lb/>Sari&longs;&longs;a perpendiculariter ad pla<lb/>num horizontis erecta, cur fa<lb/>cile ab extremo &longs;u&longs;tineatur. 231 <lb/>Cur non item per lineam hori<lb/>zonti parallelam con&longs;tituta. <lb/> ibid. <lb/></s>

<s id="N18F04">S <lb/>Sari&longs;&longs;am ab extremo eleuatam <lb/> magis inclinari, quàm furca, <lb/> lum. 164 <lb/>Sari&longs;&longs;a perpendiculariter ad pla<lb/>num horizontis erecta, cur fa<lb/>cile ab extremo &longs;u&longs;tineatur. 231 <lb/>Cur non item per lineam hori<lb/>zonti parallelam con&longs;tituta. <lb/> ibid. <lb/></s>

<s id="N18F1A">Sari&longs;&longs;am in humero ge&longs;tantes, ef<lb/>fectum vibrationis experiun<lb/>tur. 233 <lb/>Saxa <expan abbr="decid&etilde;tia">decidentia</expan> cur interdum &longs;cin<lb/>dantur per aëre. 250 <lb/>Scalmus quomodo &longs;e habeat in <lb/> remigatione. 91 <lb/>Scalmus per remigationem illuc <lb/> transfertur vbi remi e&longs;t princi<lb/>pium, &longs;eu manubrium. 172 <lb/>Scalmus con&longs;tituitur medium ma<lb/>nens inter duos motus contra<lb/>rios. 108 <lb/>Scytala quid, & quotuplex. </s>

<s id="N18F3B">141. <lb/> & 147 <lb/> Super Scytalas cur facilius por<lb/>tentur onera. 148 <lb/>Securis cur ia cta, lignum facile <lb/> &longs;cindat, &longs;ecus autem &longs;uper illud <lb/> impo&longs;ita <expan abbr="etiã">etiam</expan> ingenti &longs;uperadie<lb/>cto pondere. 178 <lb/>Securis percu&longs;&longs;io ex circulatione <lb/> vim maximam adipi&longs;citur. 179 <lb/>Securis manubrium quomodo ve. <lb/> ctis vicem &longs;ubeat. 181 <lb/>Securis in &longs;ci&longs;&longs;ione con&longs;tituitur <lb/> veluti cuneus. 182 <lb/>Securis e&longs;t malleus cuneatus, vel <lb/> cuneus malleatus. ibid. <lb/></s>

<s id="N18F3B">141. <lb/> & 147 <lb/> Super Scytalas cur facilius por<lb/>tentur onera. 148 <lb/>Securis cur ia cta, lignum facile <lb/> &longs;cindat, &longs;ecus autem &longs;uper illud <lb/> impo&longs;ita <expan abbr="etiã">etiam</expan> ingenti &longs;uperadie<lb/>cto pondere. 178 <lb/>Securis percu&longs;&longs;io ex circulatione <lb/> vim maximam adipi&longs;citur. 179 <lb/>Securis manubrium quomodo ve<lb/>ctis vicem &longs;ubeat. 181 <lb/>Securis in &longs;ci&longs;&longs;ione con&longs;tituitur <lb/> veluti cuneus. 182 <lb/>Securis e&longs;t malleus cuneatus, vel <lb/> cuneus malleatus. ibid. <lb/></s>

<s id="N18F61">Semidiametrum in de&longs;criptione <lb/> circuli moueri motu quoddam <lb/> mi&longs;to ex duabus lationibus. <lb/> 41. & 47. <lb/>Semidiameter ex quo puncto inci<lb/>pit circumduci ad idem po&longs;tre<lb/>mo reuertitur. 38 <lb/>Semidiametri puncta quo remo<lb/>tiora erunt à centro eò velo<lb/>cius mouebuntur. 41 <lb/>Semidiametri puncta à centro re<lb/>motiora, cur magis participent <lb/> de motu naturali; propinquiora <lb/> de præternaturali. 94 <lb/>Spheropeia <expan abbr="quænã">quænam</expan> &longs;cientia &longs;it. 28 <lb/>Statera quomodo paruo appendi<lb/>culo magna leuet onera. 184 <lb/>Statera, libræ &longs;imul, ac vectis ra<lb/>tionem obtinet. 185 <pb xlink:href="005/01/302.jpg"/>Stateram e&longs;&longs;e veluti libram in qua <lb/> plures &longs;int libræ, quomodo in<lb/>telligendum. 187 <lb/>Statera tanto maius onus valet <lb/> leuare quanto propinquius illi <lb/> con&longs;tituitur &longs;partum. 188 <lb/>Stipites lorati vnde tantam vim <lb/> <expan abbr="obtineãt">obtineant</expan> ad percutiendum. 182 <lb/>Stipites lorati adhiberi &longs;olent ad <lb/> enucleandum triticum. ibid. <lb/></s>

<s id="N18FA7">Succula quænam machina &longs;it. 115 <lb/>Succulæ graciliores cur facilius <lb/> ab eadem potentia circumuol<lb/>uantur. 115 <lb/>Surgentes à &longs;e&longs;&longs;ione angulos re<lb/>ctos in acutos commutant. 242 </s>

<s id="N18FB6">T<lb/>Temo quid, & quomodo con<lb/>&longs;tituat vnum in&longs;trumentum <lb/> &longs;imul cum gubernaculo. 100 <lb/>Temonis motu dupliciter nauem <lb/> po&longs;&longs;e circumferri. 100 <lb/>Temo vnde tantas vires habeat. <lb/> pag. 101 <lb/>Temonem con&longs;titui vectem, gu<lb/>bernatorem potentiam, ac ma<lb/>re, onus. 102 <lb/>Temo cur in extremo nauigij col<lb/>locetur. 104 <lb/><expan abbr="Temon&etilde;">Temonem</expan> nibil nauigio ad id quod <lb/> in ante progredi e&longs;t, conferre. <lb/> pag. 113 <lb/>Temonis motio explicatur per <lb/> eius <expan abbr="reduction&etilde;">reductionem</expan> ad libram. 117 <lb/> Per temonem nautæ cum vento <lb/> contendunt. 125 <lb/>Te&longs;ta obliquè in aquarum &longs;uper&longs;i <lb/> ciem incidens cur longius inde <lb/> re&longs;iliat. 150 <lb/><gap/> cur pluries tanquam per &longs;al<lb/>tus in eandem &longs;uperficiem inci<lb/>dat. 267 <lb/>Te&longs;ta quomodo inter digitos col<lb/>locetur ad hoc, vt eminus proij<lb/>ciatur. 152 <lb/>Taumaturgica &longs;cientia quæ. 28 <lb/> Et in quas partes diuidatur. 29 <lb/>Tollenon idem quod <expan abbr="Celoni&utilde;">Celonium</expan>. 234 <lb/>Tractio quid. 70 <lb/>Triremes cur prope puppim plu<lb/>res remiges in &longs;ingulis rcmis <lb/> habere con&longs;ueuerint. 106 <lb/>Trochlea quid. 58 <lb/>Trochleis duabus adinuicem op<lb/>po&longs;itis cur facile magna leuen<lb/>tur onera. 172 <lb/>Trochleæ orbiculum, vectis vicem <lb/> obtinere. ibid. <lb/></s>

<s id="N18FB6">T <lb/>Temo quid, & quomodo con<lb/>&longs;tituat vnum in&longs;trumentum <lb/> &longs;imul cum gubernaculo. 100 <lb/>Temonis motu dupliciter nauem <lb/> po&longs;&longs;e circumferri. 100 <lb/>Temo vnde tantas vires habeat. <lb/> pag. 101 <lb/>Temonem con&longs;titui vectem, gu<lb/>bernatorem potentiam, ac ma<lb/>re, onus. 102 <lb/>Temo cur in extremo nauigij col<lb/>locetur. 104 <lb/><expan abbr="Temon&etilde;">Temonem</expan> nihil nauigio ad id quod <lb/> in ante progredi e&longs;t, conferre. <lb/> pag. 113 <lb/>Temonis motio explicatur per <lb/> eius <expan abbr="reduction&etilde;">reductionem</expan> ad libram. 117 <lb/> Per temonem nautæ cum vento <lb/> contendunt. 125 <lb/>Te&longs;ta obliquè in aquarum &longs;uperfi<lb/>ciem incidens cur longius inde <lb/> re&longs;iliat. 150 <lb/> Et cur pluries tanquam per &longs;al<lb/>tus in eandem &longs;uperficiem inci<lb/>dat. 267 <lb/>Te&longs;ta quomodo inter digitos col<lb/>locetur ad hoc, vt eminus proij<lb/>ciatur. 152 <lb/>Taumaturgica &longs;cientia quæ. 28 <lb/> Et in quas partes diuidatur. 29 <lb/>Tollenon idem quod <expan abbr="Celoni&utilde;">Celonium</expan>. 234 <lb/>Tractio quid. 70 <lb/>Triremes cur prope puppim plu<lb/>res remiges in &longs;ingulis remis <lb/> habere con&longs;ueuerint. 106 <lb/>Trochlea quid. 58 <lb/>Trochleis duabus adinuicem op<lb/>po&longs;itis cur facile magna leuen<lb/>tur onera. 172 <lb/>Trochleæ orbiculum, vectis vicem <lb/> obtinere. ibid. <lb/></s>

<s id="N19018">Trochlearum bene&longs;icio tanto ma<lb/>ius pondus leuari, quantò plu<lb/>res extiterint in eis rotul&etail;. 173 <lb/>Trochleam &longs;uperiorem non tam <lb/> auxilium, quàm commoditatem <lb/> ad leuandum pra&longs;tare. 174 <lb/> Ex in&longs;eriori trochlea totam vim <lb/> quæ potentiæ adiungitur e&longs;&longs;e <lb/> petendam. 175 <lb/>Tylum quid. 63 <lb/>Tympanus quid. 60 </s>

<s id="N19018">Trochlearum beneficio tanto ma<lb/>ius pondus leuari, quantò plu<lb/>res extiterint in eis rotul&etail;. 173 <lb/>Trochleam &longs;uperiorem non tam <lb/> auxilium, quàm commoditatem <lb/> ad leuandum prae&longs;tare. 174 <lb/> Ex inferiori trochlea totam vim <lb/> quæ potentiæ adiungitur e&longs;&longs;e <lb/> petendam. 175 <lb/>Tylum quid. 63 <lb/>Tympanus quid. 60 </s>

<s id="N19031">V<lb/>Vectio quid & quotuplex. 70 <lb/>Vectis quid & quotuplex. 56 <lb/>Vecte adhibito cur exigua virtu<lb/>te magna leuentur pondera. 86 <lb/>Vectis quomodo habeatrationem <lb/> libræ. ibid. <lb/></s>

<s id="N19041">Vectis longitudo atque proportio <lb/> ad potentiam, & pondus. 88 <lb/>Velis antror&longs;um pergere quomo<lb/>do valeat nauis. 119 & 124 <pb xlink:href="005/01/303.jpg"/>Velificando vbi totus ventorum <lb/> impetus refundatur. 106 <lb/>Vento ex tran&longs;uer&longs;o perflante, ac <lb/> directè nihilominus nauigia in<lb/>cedendo, cur tandem non per<lb/>tingant quò præcisè tendebant. <lb/> pag. 114 <lb/>Vento ex latere &longs;lante, <expan abbr="veloq.">veloque</expan> ad <lb/> oppo&longs;itum inclinante, cur non <lb/> &longs;equatur nauis &longs;ubmer&longs;io. 128 <lb/>Imo cur &longs;ic &longs;ecurius ip&longs;a nauis <lb/> incedat. ibid. <lb/></s>

<s id="N19041">Vectis longitudo atque proportio <lb/> ad potentiam, & pondus. 88 <lb/>Velis antror&longs;um pergere quomo<lb/>do valeat nauis. 119 & 124 <pb xlink:href="005/01/303.jpg"/>Velificando vbi totus ventorum <lb/> impetus refundatur. 106 <lb/>Vento ex tran&longs;uer&longs;o perflante, ac <lb/> directè nihilominus nauigia in<lb/>cedendo, cur tandem non per<lb/>tingant quò præcisè tendebant. <lb/> pag. 114 <lb/>Vento ex latere flante, <expan abbr="veloq.">veloque</expan> ad <lb/> oppo&longs;itum inclinante, cur non <lb/> &longs;equatur nauis &longs;ubmer&longs;io. 128 <lb/>Imo cur &longs;ic &longs;ecurius ip&longs;a nauis <lb/> incedat. ibid. <lb/></s>

<s id="N19069">Verticilla ex papiro quomodo ab <lb/> aëre circumuoluantur. 101 <lb/>Vertigo quid. 70 <lb/>Vibratio quid. 229 <lb/>Vibrationis motus, ge&longs;tationem <lb/> ligni retardat. 229.& 232 <lb/>Violentia quot modis po&longs;sit in<lb/>ferri. 69 <lb/>Per violentiam mota, fieri qua&longs;i <lb/> per &longs;e mobilia. 262 <lb/>Virtus impre&longs;&longs;a cur nece&longs;&longs;ario ad <lb/> motum violentum &longs;it coceden<lb/>da, 264. Vide Impetum. <lb/></s>

<s id="N19086">Vortex per lineas &longs;pirales, non <lb/> autem per proprias circun&longs;e<lb/>rentias perfici. 274 <lb/>Vortice circumlata, cur ad me<lb/>dium tandem agantur. </s>

<s id="N19086">Vortex per lineas &longs;pirales, non <lb/> autem per proprias circunfe<lb/>rentias perfici. 274 <lb/>Vortice circumlata, cur ad me<lb/>dium tandem agantur. </s>

<s id="N19091">273. & <lb/> &longs;equentibus, </s>

Line 4066

Line 4067

<s id="N1909E">ERRATA.<lb/><emph type="italics"/>Pag. </s>

<s id="N190A9">Errata. Correctio.<emph.end type="italics"/><lb/> 13 8 pro per <lb/> 14 24 inef&longs;abiliter infallibiliter <lb/> 38 35 non e&longs;t <expan abbr="incõ-">incon-</expan> non e&longs;t <expan abbr="incõuenlens">inconuenlens</expan> cir <lb/> <expan abbr="ueni&etilde;s">ueniens</expan> ex qulum ex ip&longs;a <lb/> ip&longs;a <lb/> 51 2 paralellam parallelam, Sic lege <lb/> pag.5 2 80. 231. 243. <lb/> 255. <lb/> 71 16 enumera- enumeratas pertineat <lb/> ras <lb/><emph type="italics"/>Pag. Lin. </s>

<s id="N190D5">Errata. Correctio.<emph.end type="italics"/><lb/> 82 17 quam eleua- quam extremum <lb/> tæ partis eleuatæ <lb/> 82 33 aliena à linea <lb/>105 21 ip&longs;is ip&longs;ius <lb/>108 24 impo&longs;ito in propo&longs;ito <lb/>109 13 procedi procedere <lb/>188 29 diuer&longs;um diuj&longs;um <lb/>191 32 Philolophas philo&longs;ophatus <lb/>200 5 confert conferat <lb/>238 18 ucidentius cuidentius </s>

<s id="N190F0">REGESTVM.</s>

Legend:

Removed from v.1.11
changed lines
	Added in v.1.16