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version 1.4, 2006/05/24 07:10:28

version 1.5, 2006/05/24 09:22:55

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<s><emph type="center"/>De Percu&longs;&longs;ione & motu orbiculorum.<emph.end type="center"/></s>

<s>ORbiculi &longs;unt figuræ circulares, <expan abbr="utrâq;">utrâque</expan> &longs;uperficie planâ <lb/>& parallelâ terminatæ; &longs;eu portiones cylindri habentes <lb/>partem axis re&longs;ecti minorem &longs;emidiametro circuli. </s><s>E&longs;t autem <lb/>hoc illis commune cum globis; ut ordine di&longs;po&longs;iti, <expan abbr="&longs;ibiq;">&longs;ibique</expan> con<lb/>tigui eadem ratione moveantur: percu&longs;&longs;o enim primo, &longs;i æ<lb/>quales &longs;int, medijs immotis ultimus movetur. </s><s><expan abbr="Atq;">Atque</expan> inde ra<lb/>tio con&longs;tat, quamobrem eiu&longs;modi orbiculis ludentes ab <lb/>eadem plagâ, non eundem effectum con&longs;equantur. </s><s><expan abbr="Quan-doq;">Quan<lb/>doque</expan> enim ad finem tabulæ orbiculum in&longs;eq<gap/>itur ille, qui <lb/>percu&longs;&longs;it: <expan abbr="quandoq;">quandoque</expan> immotus manet. </s><s>Hoc enim fit ob in æ<lb/>qualem gravitatem: in&longs;equitur enim maior minorem, non

<s>ORbiculi &longs;unt figuræ circulares, <expan abbr="utrâq;">utrâque</expan> &longs;uperficie planâ <lb/>& parallelâ terminatæ; &longs;eu portiones cylindri habentes <lb/>partem axis re&longs;ecti minorem &longs;emidiametro circuli. </s><s>E&longs;t autem <lb/>hoc illis commune cum globis; ut ordine di&longs;po&longs;iti, <expan abbr="&longs;ibiq;">&longs;ibique</expan> con<lb/>tigui eadem ratione moveantur: percu&longs;&longs;o enim primo, &longs;i æ<lb/>quales &longs;int, medijs immotis ultimus movetur. </s><s><expan abbr="Atq;">Atque</expan> inde ra<lb/>tio con&longs;tat, quamobrem eiu&longs;modi orbiculis ludentes ab <lb/>eadem plagâ, non eundem effectum con&longs;equantur. </s><s><expan abbr="Quan-doq;">Quan<lb/>doque</expan> enim ad finem tabulæ orbiculum in&longs;equitur ille, qui <lb/>percu&longs;&longs;it: <expan abbr="quandoq;">quandoque</expan> immotus manet. </s><s>Hoc enim fit ob in æ<lb/>qualem gravitatem: in&longs;equitur enim maior minorem, non

<pb xlink:href="063/01/105.jpg"/>verò &longs;ibi æqualem aut maiorem. </s><s>Suppono verò motum fi<lb/>eri in lineâ centri: nam &longs;i inclinet; quia non totam dat plagam, <lb/>motum continuabit. </s><s>At verò hoc peculiare habent; quòd <lb/>non tantùm in lineâ rectâ &longs;ibi contigui fiant; &longs;ed etiam illâ &longs;u<lb/>perficie planâ in &longs;imilitudinem cylindri a&longs;&longs;urgant. </s><s>Quòd &longs;i <lb/>ergo his ita cumulatis illum orbiculum, qui ba&longs;is e&longs;t reliquo<lb/>rum, percutiat æqualis; eadem ratione movebitur huic con<lb/>tiguus, quantumvis illorum numerus, qui ba&longs;i incumbunt, au<lb/>geatur: quin etiam quovis onere accepto impul&longs;um tran&longs;mit<lb/>tit nihilo minorem. </s><s>At verò ba&longs;is excuti non eadem facilita<lb/>te pote&longs;t: verùm pro numero orbiculorum, aut oneris appen<lb/>&longs;i ratione, nece&longs;&longs;e plagam fieri maiorem. </s><s>Quòd &longs;i orbicu<lb/>lus gravitatem habeat æqualem illi, quâ ba&longs;is gravatur, eadem <lb/>facilitate illam loco movebit: verùm ip&longs;e <expan abbr="quoq;">quoque</expan> tran&longs;ito illo <lb/>hiatu, motum ba&longs;is &longs;equetur. </s><s>Cuius ratio e&longs;&longs;e videtur: <lb/>quòd impul&longs;us nece&longs;&longs;ariò fiat iuxta determinationem plagæ; <lb/>licet &longs;ubiectum non moveatur ex eo impul&longs;u: & &longs;i maior &longs;it <lb/>quàm ut in &longs;ubiecto terminetur, aliud percutit &longs;ibi contiguum. <lb/><expan abbr="Neq;">Neque</expan> minor e&longs;t impul&longs;us &longs;i ab a lienâ gravitate detineatur; non <lb/>enim gravitas ab extra veniens, &longs;ed nativa hunc attenuat: quæ <lb/>multam materiam habet coniunctam. </s><s><expan abbr="Itaq;">Itaque</expan> &longs;i magnitudi<lb/>ne non verò gravitate &longs;int pares; orbiculus maior à minori <lb/>percu&longs;&longs;us, minorem ex eadem plagâ impul&longs;um reliquis dabit, <lb/>quàm &longs;i ab æquali percutiatur: propterea, quòd in multâ ma<lb/>teriâ magis hebetatur. </s><s>Vt verò &longs;ubiectum moueatur, ne<lb/>ce&longs;&longs;e & gravitatem nativam, & impul&longs;um contrarium &longs;upera<lb/>re. </s><s><expan abbr="Itaq;">Itaque</expan> fit ut ba&longs;is illius cylindri orbiculati motui renita<lb/>tur: quæ & &longs;uâ & illorum, à quibus premitur, gravitate de<lb/>tinetur. </s><s>Quòd &longs;i gravitas orbiculi augeatur, ut gravitati illius <lb/>cylindri &longs;it æqualis: quæ tota in ba&longs;im colligitur, <expan abbr="atq;">atque</expan> illius vi <lb/>à motu detinetur, percu&longs;&longs;io tum fit æqualis: <expan abbr="quou&longs;q;">quou&longs;que</expan> nimirum

<pb xlink:href="063/01/106.jpg"/>à nexu illorum orbiculorum &longs;e expediat: tum enim motu a<lb/>gitur multò velociore, quàm &longs;i plaga fiat ab æquali: amotâ e<lb/>nim illâ re&longs;i&longs;tentiâ, impul&longs;us ad gravitatem multò iam mino<lb/>rem, maiorem habet exce&longs;&longs;um. </s>

<s><emph type="italics"/>Dices. </s><s>Quid &longs;i orbiculi percutiant illum sylindrum, à quo &longs;unt re&longs;ecti; <lb/>an non movebunt alios huic contiguos eadem ratione, quà in cylindro <lb/>orbiculato? Videtur enim eadem ratio e&longs;&longs;e illius &longs;egmenti, quod percu<lb/>titur ab æquali, &longs;i<gap/> re&longs;ectum &longs;it, &longs;iue continuum: propterea, quòd ma<lb/>teria una, ac proinde impul&longs;us, qui viam &longs;equitur plagæ, æqualiter per<lb/>tran&longs;it. </s><s>Illa autem continuitas non videtur mutare naturam impul<lb/>&longs;us: qui non ni&longs;i vi dimovetur à lineâ rectâ: at&queacute; eâdem gravitate à <lb/>motu detinetur pars re&longs;ecta & continua: eadem ergo plaga, quæ orbicu<lb/>lum excludit, cylindrum quo&que; &longs;olidum movebit.<emph.end type="italics"/></s>

<s><emph type="italics"/>Dices. </s><s>Quid &longs;i orbiculi percutiant illum cylindrum, à quo &longs;unt re&longs;ecti; <lb/>an non movebunt alios huic contiguos eadem ratione, quà in cylindro <lb/>orbiculato? Videtur enim eadem ratio e&longs;&longs;e illius &longs;egmenti, quod percu<lb/>titur ab æquali, &longs;iue re&longs;ectum &longs;it, &longs;iue continuum: propterea, quòd ma<lb/>teria una, ac proinde impul&longs;us, qui viam &longs;equitur plagæ, æqualiter per<lb/>tran&longs;it. </s><s>Illa autem continuitas non videtur mutare naturam impul<lb/>&longs;us: qui non ni&longs;i vi dimovetur à lineâ rectâ: at&queacute; eâdem gravitate à <lb/>motu detinetur pars re&longs;ecta & continua: eadem ergo plaga, quæ orbicu<lb/>lum excludit, cylindrum quo&que; &longs;olidum movebit.<emph.end type="italics"/></s>

<s>Re&longs;pondeo impul&longs;um, cùm à principio fiat interno mobi<lb/>lis, totum &longs;ubiectum afficere. </s><s>Licet ergo viam &longs;equatur pla<lb/>gæ; quia tamen in altum <expan abbr="quoq;">quoque</expan> a&longs;&longs;urgit: quantum virium <lb/>huc confert, tantum decedit plagæ oppo&longs;itæ. </s><s>Percu&longs;&longs;o <lb/><expan abbr="itaq;">itaque</expan> cylindro &longs;olido, minori vi moventur orbiculi contigui; <lb/>decre&longs;cente plagâ pro altitudine cylindri. </s><s>Quòd &longs;i orbiculi <lb/>inter &longs;e glutinentur; quia tum extrema fiunt unum, rationem <lb/>habent continui: unde eadem his, quæ cylindro &longs;olido <lb/>conveniunt. </s><s>Verùm de his cùm &longs;citu digna vi<lb/>deantur continere. enucleatiùs di&longs;&longs;eren<lb/>dum. </s>

Line 855

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

<s><emph type="italics"/>Si duo Orbiculi &longs;imul iuncti & æquales percutiant alium maiorem, <lb/>duobus autem illis &longs;imul &longs;umptis æqualem; orbiculo &longs;uperiori reflexo, <lb/>motum continuat b<gap/>s.<emph.end type="italics"/></s>

<s>Difficultas hic e&longs;t, quòd cùm orbiculus &longs;olidus percutit ali<lb/>um &longs;ibi æqualem, illo moto quie&longs;cit: cur igitur non idem fit, <lb/>cùm duo &longs;imul iuncti, <expan abbr="atq;">atque</expan> eidem æquales hunc percutiunt, ve. <lb/>rùm <expan abbr="uterq;">uterque</expan> inæqualiter movetur ex illâ plagâ? Nam eodem <lb/>impul&longs;u agi videntur: nece&longs;&longs;e ergo eandem inferre plagam: <lb/>Et cùm gravitas orbiculi maioris &longs;it dupla, & impul&longs;um reci<lb/>piat duplum illius, quo &longs;inguli moventur; erit <expan abbr="quoq;">quoque</expan> eadem ve<lb/>locitas motûs. </s><s>At verò &longs;i ba&longs;is &longs;equitur motum maioris; ne<lb/>ce&longs;&longs;e huius motum e&longs;&longs;e velociorem quàm ba&longs;is motum: quæ <lb/>ab incipiente & necdum perfectâ plagâ movetur. </s><s>Et &longs;i refle<lb/>ctit alter orbiculus: quia peractâ huius plagâ necdum incipit <lb/>moveri maior; velocitatem habebit minorem. </s><s>Pro &longs;olutione <lb/>dico, impul&longs;um in <expan abbr="utroq;">utroque</expan> orbiculo e&longs;&longs;e æqualem. </s><lb/><s>Secundô inæqualiter moveri, <expan abbr="magisq;">magisque</expan> impediri motum ba&longs;is <lb/>per 1 Theor: huius; & cùm impul&longs;um determinet motus; ma <lb/>iori tempore plagam perficiet ba&longs;is. </s><s>Cùm ergò maior orbi<lb/>culus gravitatem habeat duplam; ad illam velocitatem mo<lb/>tûs, non ni&longs;i ab impul&longs;u duplo perducitur: perfectâ autem pla<lb/>gâ unius orbiculi, necdum percu&longs;&longs;it alter: <expan abbr="neq;">neque</expan> igitur ex illâ <lb/>plagâ &longs;e abducit orbiculus maior: ac proinde orbiculus, qui <lb/>iam percu&longs;&longs;it, reflectit. </s><s>Et quia minor e&longs;t velocitas motûs <lb/>ba&longs;is, velociùs movebitur ab <expan abbr="utraq;">utraque</expan> plagâ. igitur ad illam ve<lb/>locitatem, quâ movetur ba&longs;is, ab incipiente & necdum perfe<lb/>ctâ huius plagâ perducetur: ac proinde reliquus impul&longs;us mo<lb/>tum continuabit. </s><s>Idem autem fit, &longs;i alter orbiculus &longs;it paulo

<pb xlink:href="063/01/110.jpg"/>levior, &longs;eu ba&longs;is, &longs;eu qui &longs;uperiori loco &longs;itum habet. </s><s>At &longs;i <lb/>magnus &longs;it exce&longs;&longs;us; ut cùm ligneo metallicum adiungimus, <lb/>gravior in omni &longs;itu motum &longs;equitur maioris. </s><s>Quòd &longs;i duo <lb/>orbiculi &longs;imuliuncti <expan abbr="atq;">atque</expan> inter &longs;e æquales deficiant à gravitate <lb/>maioris: minùs quidem movetur ba&longs;is, <gap/>is autem reflectit <lb/>alter orbiculus. E contra &longs;i gravitas excedit: hic quidem mi<lb/>nùs reflectit, ille verò motum magis producit. </s><s>Cuius ratio <lb/>e&longs;t, quòd horum impul&longs;us maiorem rationem habet ad orbi<lb/>culum minùs gravem: igitur cùm à minori plagâ eadem ve<lb/>locitas motûs &longs;equatur; erit maior impul&longs;us reliquus ad mo<lb/>tum continuandum. </s><s>Et quia velociùs à plagâ &longs;e abducit, erit <lb/>minor reflexio motûs-Cùm verò impul&longs;us minorem habet <lb/>rationem; non ni&longs;i à maiori plagâ ad motum æquè velocem <lb/>cietur maior, & non ni&longs;i tardè à plagâ &longs;e abducit: magis proin<lb/>de reflectit motus, minùs autem à reliquo impul&longs;u movetur <lb/>ba&longs;is. </s>

<pb xlink:href="063/01/110.jpg"/>levior, &longs;eu ba&longs;is, &longs;eu qui &longs;uperiori loco &longs;itum habet. </s><s>At &longs;i <lb/>magnus &longs;it exce&longs;&longs;us; ut cùm ligneo metallicum adiungimus, <lb/>gravior in omni &longs;itu motum &longs;equitur maioris. </s><s>Quòd &longs;i duo <lb/>orbiculi &longs;imul iuncti <expan abbr="atq;">atque</expan> inter &longs;e æquales deficiant à gravitate <lb/>maioris: minùs quidem movetur ba&longs;is, magis autem reflectit <lb/>alter orbiculus. E contra &longs;i gravitas excedit: hic quidem mi<lb/>nùs reflectit, ille verò motum magis producit. </s><s>Cuius ratio <lb/>e&longs;t, quòd horum impul&longs;us maiorem rationem habet ad orbi<lb/>culum minùs gravem: igitur cùm à minori plagâ eadem ve<lb/>locitas motûs &longs;equatur; erit maior impul&longs;us reliquus ad mo<lb/>tum continuandum. </s><s>Et quia velociùs à plagâ &longs;e abducit, erit <lb/>minor reflexio motûs-Cùm verò impul&longs;us minorem habet <lb/>rationem; non ni&longs;i à maiori plagâ ad motum æquè velocem <lb/>cietur maior, & non ni&longs;i tardè à plagâ &longs;e abducit: magis proin<lb/>de reflectit motus, minùs autem à reliquo impul&longs;u movetur <lb/>ba&longs;is. </s>

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

Line 875

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

<s><emph type="italics"/>Si plures orbiculi &longs;imul iuncti<gap/> percutiant alium maiorem, & à <lb/>plagâ illâ immotum; ad minus intervallum reflectunt ba&longs;i propiores.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si plures orbiculi &longs;imul iuncti percutiant alium maiorem, & à <lb/>plagâ illâ immotum; ad minus intervallum reflectunt ba&longs;i propiores.<emph.end type="italics"/></s>

<s>Cùm omnes orbiculi percutiant, <expan abbr="neq;">neque</expan> ad ullius plagam <lb/>moveatur ille orbiculus: recipient à percu&longs;&longs;o æqualem illi, <lb/>quam <expan abbr="quisq;">quisque</expan> dedit plagam. </s><s>At verò ba&longs;is per Theor: 2. mo<lb/>tum habet magis impeditum: igitur cùm velocitas motûs de<lb/>terminet plagam; minor erit huius, quàm reliquorum plaga.

<pb xlink:href="063/01/112.jpg"/>Et quia propiores illi ba&longs;i, quæ tangit planum, remotioribus <lb/>&longs;unt pro ba&longs;i; erit minor illorum plaga: ac proinde ad minus <lb/>intervallum reflectunt. </s><s>Idem verò contingit &longs;iue eandem <lb/>habeant gravitatem orbiculi reliqui, &longs;iue præponderet ba&longs;is, <lb/>aut minus &longs;it gravis. </s><s>Nam licet ba&longs;is magis pondero&longs;a ma<lb/>iorem dat plagam; cùm non ni&longs;i à maiori impul&longs;u moveatur <lb/>eodem cum minoris gravitatis motu: quia tamen in ordine <lb/>ad motum hanc expendimus; <expan abbr="at&qacute;">atque</expan>; in eadem ratione &longs;unt mo<lb/>tus reflexi, minor autem huius motus; minorem <expan abbr="quoq;">quoque</expan> in or<lb/>dine ad &longs;uum motum dicetur dare & referre plagam. </s>

Line 889

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

<s><emph type="italics"/>Si duo orbiculi &longs;imul iuncti & æqual<gap/>s percutiant alios duos, &longs;imul <lb/>quo&que; iunctos & prioribus æquales, <gap/>abe<gap/> verò à tergo orbiculum ma<lb/>iorem; immotâ ba&longs;iprimâ, movetur ba&longs;i, &longs;ecunda.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si duo orbiculi &longs;imul iuncti & æquales percutiant alios duos, &longs;imul <lb/>quo&que; iunctos & prioribus æquales, habeant verò à tergo orbiculum ma<lb/>iorem; immotâ ba&longs;i primâ, movetur ba&longs;i, &longs;ecunda.<emph.end type="italics"/></s>

<s>Cùm duo orbiculi æquales &longs;imuliuncti percutiunt alios du<lb/>os &longs;imul <expan abbr="quoq;">quoque</expan> iunctos & æquales: licet inæqualem afferant <lb/>plagam; quia tamen <expan abbr="uterq;">uterque</expan> orbiculus ex illâ inæquali plagâ &longs;e <lb/>abducit; <expan abbr="qui&longs;q;">qui&longs;que</expan> &longs;uo orbiculo expul&longs;o à motu conquie&longs;cit. </s><lb/><s>At cùm alius orbiculus maior accedit: in quem impetus &longs;e ex<lb/>onerat illorum orbiculorum: quia inæqualem <expan abbr="atq;">atque</expan> minorem <lb/>á ba&longs;i recipit plagam; per theor: 2. huius, refiexo altero orbi<lb/>c<gap/>lo movebitur ba&longs;is. </s><s>Cùm igitur hæc ba&longs;is &longs;ecunda à pla<lb/>gâ &longs;e abducat; quie&longs;cet à percu&longs;&longs;ione ba&longs;is prima. </s><s>Con&longs;tat <lb/>verò illo orbiculo reflexo, reflecti <expan abbr="quoq;">quoque</expan> o<gap/>biculum priorem <lb/><gap/>ic contiguum. </s>

<s>Cùm duo orbiculi æquales &longs;imuliuncti percutiunt alios du<lb/>os &longs;imul <expan abbr="quoq;">quoque</expan> iunctos & æquales: licet inæqualem afferant <lb/>plagam; quia tamen <expan abbr="uterq;">uterque</expan> orbiculus ex illâ inæquali plagâ &longs;e <lb/>abducit; <expan abbr="qui&longs;q;">qui&longs;que</expan> &longs;uo orbiculo expul&longs;o à motu conquie&longs;cit. </s><lb/><s>At cùm alius orbiculus maior accedit: in quem impetus &longs;e ex<lb/>onerat illorum orbiculorum: quia inæqualem <expan abbr="atq;">atque</expan> minorem <lb/>á ba&longs;i recipit plagam; per theor: 2. huius, reflexo altero orbi<lb/>culo movebitur ba&longs;is. </s><s>Cùm igitur hæc ba&longs;is &longs;ecunda à pla<lb/>gâ &longs;e abducat; quie&longs;cet à percu&longs;&longs;ione ba&longs;is prima. </s><s>Con&longs;tat <lb/>verò illo orbiculo reflexo, reflecti <expan abbr="quoq;">quoque</expan> orbiculum priorem <lb/>huic contiguum. </s>

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

Line 935

<s><emph type="italics"/>Si orbiculus æqualis percutiat ba&longs;im cylindri orbiculati minùs gra<lb/>vem; habeat verò impul&longs;um duplo maiorem gravitate &longs;ecunda; ex<lb/>clusâ à cylindro ba&longs;i pertran&longs;ibit.<emph.end type="italics"/></s>

<s>Nam &longs;i impul&longs;um habeat æqualem gravitati &longs;ecundæ; per <lb/>12 huius, &longs;uccedit in locum ba&longs;is à cylindro exclu&longs;æ: Cùm igi<lb/>tur eadem gravitate detineatur, quâ ba&longs;is exclu&longs;a; non ni&longs;i ab <lb/>impul&longs;u æquali excludi valebit. </s><s>Vt ergo exclusâ ba&longs;i ip&longs;e <lb/><expan abbr="quoq;">quoque</expan> eluctetur; impul&longs;um habebit duplo maiorem. </s><s>Quòd <lb/>&longs;i verò impul&longs;um habeat illâ gravitate maiorem, minorem ve<lb/>rò quàm duplum; exclusâ ba&longs;i non totus, &longs;ed pro ratione ex<lb/>ce&longs;&longs;ûs plus, minuù&longs;uè à cylindro prominebit. </s><s>Priu&longs;quam <lb/>hunc motum orbiculorum finiam; admonere volui, ne quis <lb/>ab uno experimento obiter facto, <expan abbr="neq;">neque</expan> ni&longs;i omnibus propo<lb/>&longs;itionibus priùs expen&longs;is, facile pronuntiet: cùm hæ inter<lb/>dum illas limitent. </s><s><expan abbr="Icaq;">Icaque</expan> cùm dico orbiculum, &longs;i alium per<lb/>cutiat &longs;ibi æqualem, illo expul&longs;o quie&longs;cere; id non pror&longs;us ve<lb/>ritati con&longs;onum videbitur, &longs;i experimentum fiat in orbiculis <lb/>magis pondero&longs;is: cuiu&longs;modi metallici, ex argento, ferro, ære, <lb/>plumbo, &longs;tanno, auro. </s><s>Percu&longs;&longs;o enim æquali non quie&longs;cunt, <lb/>&longs;ed aliquantulum ex illâ plagâ &longs;equuntur: idq magis minù&longs;ue <lb/>pro ratione ponderis. </s><s>Quod quidem ad finem theor: 6 monui <lb/>Quia nimirum rationem cylindri habent eiu&longs;modi orbiculi: <lb/><expan abbr="magi&longs;q;">magi&longs;que</expan> pondero&longs;us æquivalet cylindro longi<gap/>ri. </s><s><expan abbr="Itaq;">Itaque</expan> diffe<lb/>rentia plagæ in his maior; quæ in orbiculis levi<gap/>bus evane<lb/>&longs;cit, & ob exiguitatem &longs;en&longs;um latet. </s><s>Idem fit in globis magni <lb/>ponderis & molis. </s><s>Quia vel centrum gravitatis n<gap/> e&longs;t idem <lb/>cum centro molis: vel quòd &longs;aperficiem minùs &longs;phæricam <lb/>habentes non in puncto, &longs;ed parte aliquâ dividuâ &longs;e tangunt,

<s>Nam &longs;i impul&longs;um habeat æqualem gravitati &longs;ecundæ; per <lb/>12 huius, &longs;uccedit in locum ba&longs;is à cylindro exclu&longs;æ: Cùm igi<lb/>tur eadem gravitate detineatur, quâ ba&longs;is exclu&longs;a; non ni&longs;i ab <lb/>impul&longs;u æquali excludi valebit. </s><s>Vt ergo exclusâ ba&longs;i ip&longs;e <lb/><expan abbr="quoq;">quoque</expan> eluctetur; impul&longs;um habebit duplo maiorem. </s><s>Quòd <lb/>&longs;i verò impul&longs;um habeat illâ gravitate maiorem, minorem ve<lb/>rò quàm duplum; exclusâ ba&longs;i non totus, &longs;ed pro ratione ex<lb/>ce&longs;&longs;ûs plus, minuù&longs;uè à cylindro prominebit. </s><s>Priu&longs;quam <lb/>hunc motum orbiculorum finiam; admonere volui, ne quis <lb/>ab uno experimento obiter facto, <expan abbr="neq;">neque</expan> ni&longs;i omnibus propo<lb/>&longs;itionibus priùs expen&longs;is, facile pronuntiet: cùm hæ inter<lb/>dum illas limitent. </s><s><expan abbr="Icaq;">Icaque</expan> cùm dico orbiculum, &longs;i alium per<lb/>cutiat &longs;ibi æqualem, illo expul&longs;o quie&longs;cere; id non pror&longs;us ve<lb/>ritati con&longs;onum videbitur, &longs;i experimentum fiat in orbiculis <lb/>magis pondero&longs;is: cuiu&longs;modi metallici, ex argento, ferro, ære, <lb/>plumbo, &longs;tanno, auro. </s><s>Percu&longs;&longs;o enim æquali non quie&longs;cunt, <lb/>&longs;ed aliquantulum ex illâ plagâ &longs;equuntur: idq magis minù&longs;ue <lb/>pro ratione ponderis. </s><s>Quod quidem ad finem theor: 6 monui <lb/>Quia nimirum rationem cylindri habent eiu&longs;modi orbiculi: <lb/><expan abbr="magi&longs;q;">magi&longs;que</expan> pondero&longs;us æquivalet cylindro longiori. </s><s><expan abbr="Itaq;">Itaque</expan> diffe<lb/>rentia plagæ in his maior; quæ in orbiculis levioribus evane<lb/>&longs;cit, & ob exiguitatem &longs;en&longs;um latet. </s><s>Idem fit in globis magni <lb/>ponderis & molis. </s><s>Quia vel centrum gravitatis non e&longs;t idem <lb/>cum centro molis: vel quòd &longs;uperficiem minùs &longs;phæricam <lb/>habentes non in puncto, &longs;ed parte aliquâ dividuâ &longs;e tangunt,

<pb xlink:href="063/01/118.jpg"/>vel quòd plaga aliquantulum inclinet. </s><s>Quin & volubilitas <lb/>&longs;peciem motûs continuati <expan abbr="quandoq;">quandoque</expan> præ&longs;tat. </s>

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

Line 943

<s><emph type="italics"/>Orbiculorum in cylindro di&longs;po&longs;itorum quemcun&que; imperatum exclu<lb/>dere, alijs non exclu&longs;is.<emph.end type="italics"/></s>

<s>In cylindro orbiculato AI &longs;it excludenda ba&longs;is A. id con&longs;e<lb/>quemur cum orbiculo æquali M factâ plagâ per 1 Pori&longs;: At <lb/>&longs;i tertius à ba&longs;i C excludi debeat: appone duos à tergo pla<lb/>

<arrow.to.target n="fig21"/><lb/>gæ KL: & cum tribus orbiculis percute cylindrum: namre<lb/>liquis immotis tertius ex&longs;iliet: propterea, quòd impetus prio<lb/>rum in illas anterides &longs;e exonerat. </s><s>Quòd &longs;i artem magis la<lb/>tere velis; &longs;int orbiculi mole, non etiam pondere æquales. </s><lb/><s>Duobus ergo levioribus tertio æquali &longs;ubie<gap/>, &longs;i percu<lb/>tiatur cylindrus; quia minor plaga levior<gap/>, non ni&longs;i tertium <lb/>excludes. </s><s>Eodem modo &longs;i quartus, aut q<gap/> <gap/>o&longs;tuletur; <lb/>cum totidem numero orbiculis plagá ind<gap/>ce un<gap/> minus <lb/>à tergo cylindri <expan abbr="plagã">plagam</expan> excipies: aut certè totidem leviores, <lb/>quot &longs;upere&longs;&longs;e velis, ultimo &longs;uppone. </s>

<arrow.to.target n="fig21"/><lb/>gæ KL: & cum tribus orbiculis percute cylindrum: namre<lb/>liquis immotis tertius ex&longs;iliet: propterea, quòd impetus prio<lb/>rum in illas anterides &longs;e exonerat. </s><s>Quòd &longs;i artem magis la<lb/>tere velis; &longs;int orbiculi mole, non etiam pondere æquales. </s><lb/><s>Duobus ergo levioribus tertio æquali &longs;ubiectis, &longs;i percu<lb/>tiatur cylindrus; quia minor plaga leviorum, non ni&longs;i tertium <lb/>excludes. </s><s>Eodem modo &longs;i quartus, aut quintus po&longs;tuletur; <lb/>cum totidem numero orbiculis <expan abbr="plagã">plagam</expan> induces: uno verô minus <lb/>à tergo cylindri <expan abbr="plagã">plagam</expan> excipies: aut certè totidem leviores, <lb/>quot &longs;upere&longs;&longs;e velis, ultimo &longs;uppone. </s>

Line 957

<s><emph type="italics"/>Orbiculos plures non contiguos à cylindro orbiculato excludere, alijs <lb/>non exclu&longs;is.<emph.end type="italics"/></s>

<s>Sint orbiculi tres excludendi, nimirum 1. 3 & 5 omnibus <lb/>alijs immotis ex illâ plagâ. </s><s>Quod quidem duobus modis con<lb/>&longs;equimur. uno, &longs;i orbiculi plagam afferentes &longs;int inæquales: <lb/><expan abbr="levioré&longs;q;">levioré&longs;que</expan> percutiant eos, quos manere volumus. </s><s>Secundo <lb/>modo, &longs;i his æqualiter habentibus &longs;equantur inæquales: <expan abbr="atq;">atque</expan> <lb/>illorum plaga, quos excuti volumus, &longs;e recipiat in minores: <lb/>tum enim per Pori&longs;: 2 motum minoris &longs;equitur maior. </s><s>Cùm <lb/>autem dicimus reliquos orbiculos e&longs;&longs;e <expan abbr="ab&longs;q;">ab&longs;que</expan> motu; de illo in<lb/>tellige, qui provenit à percu&longs;&longs;ione: nece&longs;&longs;e enim in illa inter<lb/>valla, à quibus orbiculi &longs;unt eiecti, alios &longs;e recipere à gravita<lb/>te depre&longs;&longs;os. </s><s>Quòd &longs;i tamen dextrè plaga inferatur, omn<gap/>; <lb/>orbiculi inter &longs;e &longs;int æquales & ad libellam complanati; <expan abbr="ab&longs;q;">ab&longs;que</expan>

<s>Sint orbiculi tres excludendi, nimirum 1. 3 & 5 omnibus <lb/>alijs immotis ex illâ plagâ. </s><s>Quod quidem duobus modis con<lb/>&longs;equimur. uno, &longs;i orbiculi plagam afferentes &longs;int inæquales: <lb/><expan abbr="levioré&longs;q;">levioré&longs;que</expan> percutiant eos, quos manere volumus. </s><s>Secundo <lb/>modo, &longs;i his æqualiter habentibus &longs;equantur inæquales: <expan abbr="atq;">atque</expan> <lb/>illorum plaga, quos excuti volumus, &longs;e recipiat in minores: <lb/>tum enim per Pori&longs;: 2 motum minoris &longs;equitur maior. </s><s>Cùm <lb/>autem dicimus reliquos orbiculos e&longs;&longs;e <expan abbr="ab&longs;q;">ab&longs;que</expan> motu; de illo in<lb/>tellige, qui provenit à percu&longs;&longs;ione: nece&longs;&longs;e enim in illa inter<lb/>valla, à quibus orbiculi &longs;unt eiecti, alios &longs;e recipere à gravita<lb/>te depre&longs;&longs;os. </s><s>Quòd &longs;i tamen dextrè plaga inferatur, <expan abbr="omne&longs;q;">omne&longs;que</expan> <lb/>orbiculi inter &longs;e &longs;int æquales & ad libellam complanati; <expan abbr="ab&longs;q;">ab&longs;que</expan>

<pb xlink:href="063/01/120.jpg"/>&longs;uccu&longs;&longs;ione fit cylindri: qui non ni&longs;i ex inæquali orbiculorum <lb/>lap&longs;u, aut cùm plaga in alios impingit, dilabitur. </s>

<s><emph type="italics"/>Verùm dubitatio non levis occurrit. </s><s>Nam &longs;i orbiculi inter &longs;e æqua<lb/>les & contigui longî &longs;erie di&longs;ponantur in lineâ; rectà; percu&longs;&longs;o primo ul<lb/>timus movetur non eadem ratione: verùm pro numero orbiculorum <lb/>minùs, quou&longs;&que; omnes à plagâ &longs;int immoti. </s><s>Marce&longs;cit ergo illâ exten<lb/>&longs;ione impul&longs;us; ne&que; totaplaga in &longs;ingulos propagatur. </s><s>Atqui eadem <lb/>ratio videtur &longs;phærularum: quomodo ergo per infinitas hunc extendi <lb/>volumus, quem in orbiculis cito videmus terminari.<emph.end type="italics"/></s>

<s>Re&longs;pondeo dici po&longs;&longs;e, quòd &longs;i orbiculi per omnia &longs;int æqua<lb/>les, in lineâ centri gravitatis &longs;itum habentes, eadem ratione, <lb/>quâ in &longs;phærulis interminabilem fore motum. </s><s>Verùm <lb/>quia illorum centrum non nece&longs;&longs;ariò e&longs;t idem cum centro <lb/>gravitatis; cùm partes habeant à &longs;e differentes: inde fieri ut <lb/>centrum gravitatis <expan abbr="plerumq;">plerumque</expan> &longs;it extra illam lineam, quæ tran<lb/>&longs;it per centra orbiculorum. </s>

<s>Quôd &longs;i ita: non <gap/>am una omninm e&longs;t plaga; &longs;ed minor qu<gap/><lb/>percutit obliquè: nece&longs;&longs;e ergo dum eâ ratione mutatur cen<lb/>trum gravitatis, impul&longs;um minui, ac demum deficere. </s>

<s>Quôd &longs;i ita: non iam una omninm e&longs;t plaga; &longs;ed minor quæ <lb/>percutit obliquè: nece&longs;&longs;e ergo dum eâ ratione mutatur cen<lb/>trum gravitatis, impul&longs;um minui, ac demum deficere. </s>

<s>Re&longs;pondeo &longs;ecundò, illam po&longs;itionem de interminabili mo<lb/>tu &longs;phærularum non ni&longs;i ut probabilem a&longs;&longs;umi. </s><s>Vt verò <lb/>gratiam ineamus etiam cum his, qui eam aver&longs;antur; videa<lb/>mus &longs;i quâ ratione hunc motum, omnibus immotis, quæ pro <lb/>fundamento &longs;unt adducta, terminare valeamus. </s><lb/><s>Cùm ergo &longs;phærula prima &longs;ecundam hæc tertiam percutit; <lb/>dico inæqualem fieri plagam. </s><s>Nam q<gap/>a impul&longs;us inæquali<lb/>ter recipitur in mobili; prout nimirum partes magis, minù&longs;uè <lb/>ab&longs;unt à plagâ; quæ tamen æquationem habent à centro gra-

<s>Re&longs;pondeo &longs;ecundò, illam po&longs;itionem de interminabili mo<lb/>tu &longs;phærularum non ni&longs;i ut probabilem a&longs;&longs;umi. </s><s>Vt verò <lb/>gratiam ineamus etiam cum his, qui eam aver&longs;antur; videa<lb/>mus &longs;i quâ ratione hunc motum, omnibus immotis, quæ pro <lb/>fundamento &longs;unt adducta, terminare valeamus. </s><lb/><s>Cùm ergo &longs;phærula prima &longs;ecundam hæc tertiam percutit; <lb/>dico inæqualem fieri plagam. </s><s>Nam quia impul&longs;us inæquali<lb/>ter recipitur in mobili; prout nimirum partes magis, minù&longs;uè <lb/>ab&longs;unt à plagâ; quæ tamen æquationem habent à centro gra-

<pb xlink:href="063/01/121.jpg"/>vitatis; quo omnes æqualiter moventur: minor erit vis in <lb/>centro quàm in loco plagæ. </s><s>Quòd &longs;i enim motui veloci&longs;<lb/>&longs;imo accedat minùs velox; hunc quidem incitari, illum verò <lb/>retardari contingit. </s><s>Igitur cùm per cu&longs;&longs;io fiat à centro, mi<lb/>nor erit plaga à &longs;ecundo quàm à primo. </s><s>Ratio in oppo<lb/>&longs;itum facta ita di&longs;&longs;olvitur. </s><s>Impul&longs;um à plagâ 20 ad totum <lb/>impul&longs;um maiorem rationem habere, quàm &longs;ubvigecuplam. </s><lb/><s>Licet enim plaga &longs;ecunda &longs;it minor quàm prima: non tamen <lb/>illud decrementum e&longs;t æquale magnitudini, quam pertran&longs;it, <lb/>&longs;ed exce&longs;&longs;ui, quo plaga maior e&longs;t æquatione centri gravitatis: <lb/>quæ differentia in eiu&longs;modi &longs;phærulis e&longs;t valde exigua. </s><s><expan abbr="Itaq;">Itaque</expan> <lb/>fit ut globus libr: 20. moveri nequeat à plagâ unius libræ: im<lb/>pul&longs;us tamen tran&longs;iens per globos librales 20. ultimum mo<lb/>veat. </s>

<s><emph type="center"/>THEOREMA XIV.<emph.end type="center"/></s>

Line 986

<s><emph type="italics"/>Tres orbiculos percutere eadem plagâ: qui in motu percutiant alios <lb/>tres quolibet intervallo &longs;eiunctos: â quibus rur&longs;um alij tres percutian<lb/>tur in quouis &longs;itu.<emph.end type="italics"/></s>

<s>Sint tres orbiculi in &longs;ltu <emph type="italics"/>a.b.c:<emph.end type="italics"/> quos alij <emph type="italics"/>g.h.i<emph.end type="italics"/> percutere de<lb/>bent in motu: à quibus rur&longs;um alij tres <emph type="italics"/>d.e.f<emph.end type="italics"/> percutiantur: a

<pb xlink:href="063/01/123.jpg"/>&longs;ingulis &longs;inguli. nempe ab <emph type="italics"/>a<emph.end type="italics"/> ip&longs;um <emph type="italics"/>d,<emph.end type="italics"/> & à <emph type="italics"/>b<emph.end type="italics"/> ip&longs;um <emph type="italics"/>e,<emph.end type="italics"/> at&que; de<lb/>mum <emph type="italics"/>f<emph.end type="italics"/>à<emph type="italics"/>c.<emph.end type="italics"/> Ducantur per illorum centra rectæ <emph type="italics"/>da. eb. fc:<emph.end type="italics"/> & <lb/>producantur extra circulum in <emph type="italics"/>o.p.q,<emph.end type="italics"/> adintervallum &longs;emidia<lb/>metri eiu&longs;dem circuli: à quibus ducantur aliæ rectæ <emph type="italics"/>ok. pk. qk<emph.end type="italics"/><lb/>per centrum orbiculi <emph type="italics"/>k<emph.end type="italics"/> maioris. </s><s>Quòd &longs;i <expan abbr="itaq;">itaque</expan> orbiculi <emph type="italics"/>g. h. i<emph.end type="italics"/><lb/>contigui orbiculo <emph type="italics"/>k<emph.end type="italics"/> habeant centra in ei&longs;dem lineis <emph type="italics"/>ok. pk. qk:<emph.end type="italics"/><lb/>percutiat verò orbiculum <emph type="italics"/>k<emph.end type="italics"/> alius æqualis, vel maior <emph type="italics"/>l<emph.end type="italics"/> in <gap/>: di<lb/>co orbiculos <emph type="italics"/>g.h.i<emph.end type="italics"/> exillâ plagâ percutere orbiculos <emph type="italics"/>a.b.c:<emph.end type="italics"/> ab <lb/>his verò rur&longs;um percuti orbiculos <emph type="italics"/>d.e.f.<emph.end type="italics"/><lb/>Cùm enim orbiculi <emph type="italics"/>g.h.i<emph.end type="italics"/> &longs;int minores quàm <emph type="italics"/>k;<emph.end type="italics"/> movebuntur <lb/>exillâ plagâ per coroll: Theor: 14. </s><s>Et quia percu&longs;&longs;io, & qui <lb/>hanc &longs;equitur impul&longs;us, fit per linean<gap/>ectam productam à con<lb/>tactu per centrum corporis percu&longs;&longs;i per 5 Theor: 2 part: erit <lb/>motus orbiculi <emph type="italics"/>g<emph.end type="italics"/> in lineâ <emph type="italics"/>go.<emph.end type="italics"/> Ducatur per contactum linea <emph type="italics"/>rs<emph.end type="italics"/><lb/>parallela ip&longs;i <emph type="italics"/>ok:<emph.end type="italics"/> quæ &longs;i &longs;ecet orbiculum <emph type="italics"/>a,<emph.end type="italics"/> erit linea hypomo<lb/>chlij, & complementum <emph type="italics"/>os<emph.end type="italics"/> eiu&longs;dem plaga: quæ ex demon&longs;tra<lb/>tis orbiculum <emph type="italics"/>a<emph.end type="italics"/> movebit per rectam <emph type="italics"/>ad.<emph.end type="italics"/> Quòd &longs;i verò recta <lb/><emph type="italics"/>rs<emph.end type="italics"/> cadat extra <expan abbr="utrumq;">utrumque</expan> orbiculam; problema locum non ha<lb/>bebit. </s><s>Non e&longs;t tamen nece&longs;se per <expan abbr="utrumq;">utrumque</expan> centrum duci li<lb/>neam rectam; ni&longs;i cùm totum impul&longs;um dare volumus orbi<lb/>culo percu&longs;lo: &longs;ed &longs;ufficit, &longs;i ex centro unius producta linea re<lb/>cta tangat, vel &longs;ecet <expan abbr="quacunq;">quacunque</expan> ratione alterum orbiculum. </s><lb/><s>Eadem ratione o&longs;tendemus orbiculos <emph type="italics"/>b<emph.end type="italics"/> & <emph type="italics"/>c<emph.end type="italics"/> percuti ab<emph type="italics"/>h<emph.end type="italics"/> & <emph type="italics"/>i:<emph.end type="italics"/><lb/>percutere verò eo&longs;dem <emph type="italics"/>e<emph.end type="italics"/> & <emph type="italics"/>f.<emph.end type="italics"/></s>

<pb xlink:href="063/01/123.jpg"/>&longs;ingulis &longs;inguli. nempe ab <emph type="italics"/>a<emph.end type="italics"/> ip&longs;um <emph type="italics"/>d,<emph.end type="italics"/> & à <emph type="italics"/>b<emph.end type="italics"/> ip&longs;um <emph type="italics"/>e,<emph.end type="italics"/> at&que; de<lb/>mum <emph type="italics"/>f<emph.end type="italics"/>à<emph type="italics"/>c.<emph.end type="italics"/> Ducantur per illorum centra rectæ <emph type="italics"/>da. eb. fc:<emph.end type="italics"/> & <lb/>producantur extra circulum in <emph type="italics"/>o.p.q,<emph.end type="italics"/> adintervallum &longs;emidia<lb/>metri eiu&longs;dem circuli: à quibus ducantur aliæ rectæ <emph type="italics"/>ok. pk. qk<emph.end type="italics"/><lb/>per centrum orbiculi <emph type="italics"/>k<emph.end type="italics"/> maioris. </s><s>Quòd &longs;i <expan abbr="itaq;">itaque</expan> orbiculi <emph type="italics"/>g. h. i<emph.end type="italics"/><lb/>contigui orbiculo <emph type="italics"/>k<emph.end type="italics"/> habeant centra in ei&longs;dem lineis <emph type="italics"/>ok. pk. qk:<emph.end type="italics"/><lb/>percutiat verò orbiculum <emph type="italics"/>k<emph.end type="italics"/> alius æqualis, vel maior <emph type="italics"/>l<emph.end type="italics"/> in <emph type="italics"/>w<emph.end type="italics"/>: di<lb/>co orbiculos <emph type="italics"/>g.h.i<emph.end type="italics"/> ex illâ plagâ percutere orbiculos <emph type="italics"/>a.b.c:<emph.end type="italics"/> ab <lb/>his verò rur&longs;um percuti orbiculos <emph type="italics"/>d.e.f.<emph.end type="italics"/><lb/>Cùm enim orbiculi <emph type="italics"/>g.h.i<emph.end type="italics"/> &longs;int minores quàm <emph type="italics"/>k;<emph.end type="italics"/> movebuntur <lb/>exillâ plagâ per coroll: Theor: 14. </s><s>Et quia percu&longs;&longs;io, & qui <lb/>hanc &longs;equitur impul&longs;us, fit per lineam rectam productam à con<lb/>tactu per centrum corporis percu&longs;&longs;i per 5 Theor: 2 part: erit <lb/>motus orbiculi <emph type="italics"/>g<emph.end type="italics"/> in lineâ <emph type="italics"/>go.<emph.end type="italics"/> Ducatur per contactum linea <emph type="italics"/>rs<emph.end type="italics"/><lb/>parallela ip&longs;i <emph type="italics"/>ok:<emph.end type="italics"/> quæ &longs;i &longs;ecet orbiculum <emph type="italics"/>a,<emph.end type="italics"/> erit linea hypomo<lb/>chlij, & complementum <emph type="italics"/>os<emph.end type="italics"/> eiu&longs;dem plaga: quæ ex demon&longs;tra<lb/>tis orbiculum <emph type="italics"/>a<emph.end type="italics"/> movebit per rectam <emph type="italics"/>ad.<emph.end type="italics"/> Quòd &longs;i verò recta <lb/><emph type="italics"/>rs<emph.end type="italics"/> cadat extra <expan abbr="utrumq;">utrumque</expan> orbiculum; problema locum non ha<lb/>bebit. </s><s>Non e&longs;t tamen nece&longs;se per <expan abbr="utrumq;">utrumque</expan> centrum duci li<lb/>neam rectam; ni&longs;i cùm totum impul&longs;um dare volumus orbi<lb/>culo percu&longs;lo: &longs;ed &longs;ufficit, &longs;i ex centro unius producta linea re<lb/>cta tangat, vel &longs;ecet <expan abbr="quacunq;">quacunque</expan> ratione alterum orbiculum. </s><lb/><s>Eadem ratione o&longs;tendemus orbiculos <emph type="italics"/>b<emph.end type="italics"/> & <emph type="italics"/>c<emph.end type="italics"/> percuti ab<emph type="italics"/>h<emph.end type="italics"/> & <emph type="italics"/>i:<emph.end type="italics"/><lb/>percutere verò eo&longs;dem <emph type="italics"/>e<emph.end type="italics"/> & <emph type="italics"/>f.<emph.end type="italics"/></s>

<s><emph type="center"/>DE <lb/>PROPORTIONE MOTVS ORBICVLO<lb/>RVM TAM AD SE, QVAM AD MOTVM <lb/>ORBICVLI CONTIGVI, A QVO <lb/>IMPELLVNTVR.<emph.end type="center"/></s>

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

<s><emph type="italics"/>Si i<gap/> diametro orbiculi productâ fiat contactus orbiculorum; percu<lb/>tiat verò hunc alius æqualis in parte oppo&longs;itâ diametri; eo immoto u<lb/>ter&que; contiguorum movetur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si in diametro orbiculi productâ fiat contactus orbiculorum; percu<lb/>tiat verò hunc alius æqualis in parte oppo&longs;itâ diametri; eo immoto u<lb/>ter&que; contiguorum movetur.<emph.end type="italics"/></s>

<s>Percutiat orbiculum A alius æqualis in F: in cuius diametro <lb/>productâ FQ fiat contactus orbiculorum CD: dico immo<lb/>to A <expan abbr="utrumq;">utrumque</expan> orbiculum C & D moveri ex illâ plagâ. </s><s>Du<lb/>catur linea hypomochlij HG: & ad eam perpendicularis AN <lb/>quæ &longs;ecabitur in duo &longs;egmenta æqualia AS. NS. propterea <lb/>quòd AS &longs;it &longs;inus rectus grad: 30. &longs;emi&longs;&longs;is nimirum GI grad: <lb/>60. habebit ergo plaga &longs;emi&longs;&longs;em totius impul&longs;ûs: qui per po<lb/>&longs;it:4 velocitate feretur &longs;ubduplâ illius velocitatis. quâ orbicu<lb/>lus A moveretur. </s><s>Quod idem dicendum de orbiculo D. </s><lb/><s>Cùm <expan abbr="itaq;">itaque</expan> duo orbiculi C&D &longs;imul contineant totum impul<lb/>&longs;um ex A; erit plaga perfecta: ac proinde orbiculus A à motu <lb/>conquie&longs;cet. </s>

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<s><emph type="center"/>THEOREMA XX.<emph.end type="center"/></s>

<s><emph type="italics"/>Si plures orbiculi tangant alium maiorem; percutiat verò hunc æ<lb/>qualis; omnes contigui unà cum orbiculo maiore movebu<gap/>tur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si plures orbiculi tangant alium maiorem; percutiat verò hunc æ<lb/>qualis; omnes contigui unà cum orbiculo maiore movebuntur.<emph.end type="italics"/></s>

<s>Tangant orbiculum <emph type="italics"/>k<emph.end type="italics"/> quotlibet alij minores <emph type="italics"/>g. b. m. i:<emph.end type="italics"/> per<lb/>cutiat verò hunc æqualis <emph type="italics"/>l:<emph.end type="italics"/> dico orbiculos <emph type="italics"/>g. h. m. i<emph.end type="italics"/> unà cum <lb/>orbiculo <emph type="italics"/>k<emph.end type="italics"/> moveri ex illâ plagâ. </s><s>Erit enim ex demon&longs;tratis <lb/>Theor: 16 ut <emph type="italics"/>kz<emph.end type="italics"/> ad <emph type="italics"/>nz<emph.end type="italics"/> ita plaga orbiculi <emph type="italics"/>h<emph.end type="italics"/> ad plagam orbi<lb/>culi <emph type="italics"/>m:<emph.end type="italics"/> & ut <emph type="italics"/>nz<emph.end type="italics"/> ad <emph type="italics"/>yz,<emph.end type="italics"/> ita plaga in <emph type="italics"/>m<emph.end type="italics"/> ad plagam in <emph type="italics"/>i.<emph.end type="italics"/> Quòd <lb/>idem de plagâ orbiculi <emph type="italics"/>g<emph.end type="italics"/> dicendum. maior <expan abbr="itaq;">itaque</expan> omnibus pla<lb/>ga e&longs;t in <emph type="italics"/>h.<emph.end type="italics"/> Quia verò plaga &longs;equitur impul&longs;um, quo percu-

<s>Tangant orbiculum <emph type="italics"/>k<emph.end type="italics"/> quotlibet alij minores <emph type="italics"/>g. b. m. i:<emph.end type="italics"/> per<lb/>cutiat verò hunc æqualis <emph type="italics"/>l:<emph.end type="italics"/> dico orbiculos <emph type="italics"/>g. h. m. i<emph.end type="italics"/> unà cum <lb/>orbiculo <emph type="italics"/>k<emph.end type="italics"/> moveri ex illâ plagâ. </s><s>Erit enim ex demon&longs;tratis <lb/>Theor: 16 ut <emph type="italics"/>kz<emph.end type="italics"/> ad <emph type="italics"/>nz<emph.end type="italics"/> ita plaga orbiculi <emph type="italics"/>h<emph.end type="italics"/> ad plagam orbi<lb/>culi <emph type="italics"/>m:<emph.end type="italics"/> & ut <emph type="italics"/>nz<emph.end type="italics"/> ad <emph type="italics"/>yz,<emph.end type="italics"/> ita plaga in <emph type="italics"/>m<emph.end type="italics"/> ad plagam in <emph type="italics"/>i.<emph.end type="italics"/> Quòd <lb/>idem de plagâ orbiculi <emph type="italics"/>g<emph.end type="italics"/> dicendum. maior <expan abbr="itaq;">itaque</expan> omnibus pla<lb/>ga e&longs;t in <emph type="italics"/>h.<emph.end type="italics"/> Quia verò plaga &longs;equitur impul&longs;um, quo percu-

<pb xlink:href="063/01/130.jpg"/>tiens erat moturum; percutit verò <emph type="italics"/>k<emph.end type="italics"/> orbiculum minorem <emph type="italics"/>h;<emph.end type="italics"/><lb/>movebitur hic<gap/>ab incipiente & necdum perfectâ plagâ: orbicu<lb/>lus ergo <emph type="italics"/>k<emph.end type="italics"/> per pori<gap/>ma 2. motum continuabit. </s><s>Simili modo <lb/>orbiculi. reliqui <emph type="italics"/>g. m. i<emph.end type="italics"/> quia minores quàm <emph type="italics"/>k;<emph.end type="italics"/> movebuntur ab <lb/>impul&longs;u minori: ac proinde à plagâ incipiente: unde huius ex<lb/>ce&longs;&longs;us erit principium motûs orbiculi <emph type="italics"/>k,<emph.end type="italics"/></s>

<pb xlink:href="063/01/130.jpg"/>tiens erat moturum; percutit verò <emph type="italics"/>k<emph.end type="italics"/> orbiculum minorem <emph type="italics"/>h;<emph.end type="italics"/><lb/>movebitur hic ab incipiente & necdum perfectâ plagâ: orbicu<lb/>lus ergo <emph type="italics"/>k<emph.end type="italics"/> per pori&longs;ma 2. motum continuabit. </s><s>Simili modo <lb/>orbiculi. reliqui <emph type="italics"/>g. m. i<emph.end type="italics"/> quia minores quàm <emph type="italics"/>k;<emph.end type="italics"/> movebuntur ab <lb/>impul&longs;u minori: ac proinde à plagâ incipiente: unde huius ex<lb/>ce&longs;&longs;us erit principium motûs orbiculi <emph type="italics"/>k,<emph.end type="italics"/></s>

<s><emph type="center"/>DE GYRATIONE ORBICVLI.<emph.end type="center"/></s>

<s>Si orbiculus percu&longs;&longs;us alium impellat &longs;ibi contiguum & æ<lb/>qualem; duplici motu videtur ferri ex illâ plagâ: nimirum <lb/>recto & circulari. </s><s>Nam cùm A movetur per lineam AI, pun<lb/>ctum H in peripheriâ transfertur in F. K &c. </s><s>Quod quidem <lb/>erit manife&longs;tum &longs;i punctum contactûs aliquo &longs;igno notetur. </s><lb/><s>Huius autem motûs ratio videtur referri ad librationem. </s><s>Nam <lb/>cùm ex plagâ in G dece&longs;&longs;erit impul&longs;us æqualis PT; nece&longs;se <lb/>præpondium fieri in K, <expan abbr="atq;">atque</expan> ita revolui orbiculum circa mobi<lb/>le centrum A. </s>

<s><emph type="italics"/>Obijcies. </s><s>Si ob librationem circumagitur orbiculus, neceße buius mo<lb/>tum e&longs;&longs;e æqualem plagæ. cui æquatur exce&longs;&longs;us in parte oppo&longs;itâ. igitur quò <lb/>contactui propior diameter, quia tum maior plaga; erit quo&que; circulatio <lb/>maior: quod tamen non fit. </s><s>Verùm quò maius intervallum, eò arcum <lb/>de&longs;cribit maiorem. </s><s>Deinde verò &longs;i duo orbiculi contigui inaqualiter ab<lb/>&longs;int à diametro, cuin&longs;modi in LV, circulatio procedit ex H in N. e&longs;t au<lb/>tem maior plaga in V quàm in L: oportebat ergo hunc motum fieri ex <lb/>H in F, &longs;i illa circulatio pr<gap/>veniret ab exce&longs;&longs;u.<emph.end type="italics"/></s>

<s><emph type="italics"/>Obijcies. </s><s>Si ob librationem circumagitur orbiculus, neceße buius mo<lb/>tum e&longs;&longs;e æqualem plagæ. cui æquatur exce&longs;&longs;us in parte oppo&longs;itâ. igitur quò <lb/>contactui propior diameter, quia tum maior plaga; erit quo&que; circulatio <lb/>maior: quod tamen non fit. </s><s>Verùm quò maius intervallum, eò arcum <lb/>de&longs;cribit maiorem. </s><s>Deinde verò &longs;i duo orbiculi contigui inæqualiter ab<lb/>&longs;int à diametro, cuiu&longs;modi in LV, circulatio procedit ex H in N. e&longs;t au<lb/>tem maior plaga in V quàm in L: oportebat ergo hunc motum fieri ex <lb/>H in F, &longs;i illa circulatio proveniret ab exce&longs;&longs;u.<emph.end type="italics"/></s>

<s>Re&longs;pondeo cùm motus hic circularis fluat ab eodem impul<lb/>&longs;u, quem retinet centrum ad &longs;e movendum; hic autem acce&longs;&longs;u <lb/>ad diametrum continuò minuatur; nece&longs;sc <expan abbr="quoq;">quoque</expan> circulatio-

<pb xlink:href="063/01/131.jpg"/>nem æ&longs;timari minorem. </s><s>Deinde verò cùm per Theor: 19 <lb/>ab intervallo grad: 60 motus centri fiat per tangentem circu<lb/>li; nece&longs;&longs;e hanc librationem magis augeri. </s><s>Vnde etiam ratio <lb/>petenda, quòd circulatio <expan abbr="quandoq;">quandoque</expan> fiat in partem plagæ maio<lb/>ris: cùm videlicet duo orbiculi inæqualiter ab&longs;unt à lineâ mo <lb/>tûs centri: Hic enim oppo&longs;ita circulatio prævalet: quam deter<lb/>minat motus centri per tangentem. </s>

<s>Po&longs;&longs;everò mi&longs;ceri motui recto circularem, manife&longs;tum in <lb/>eodem orbiculo; &longs;i convexâ parte tangat planum. á digito e<lb/>nim compre&longs;&longs;us & eli&longs;us <expan abbr="quandoq;">quandoque</expan> eidem puncto in&longs;i&longs;tens ro<lb/><gap/>ari, <expan abbr="quandoq;">quandoque</expan> à procur&longs;u recurrere, aut etiam retro agi vide<lb/>

<s>Po&longs;&longs;e verò mi&longs;ceri motui recto circularem, manife&longs;tum in <lb/>eodem orbiculo; &longs;i convexâ parte tangat planum. á digito e<lb/>nim compre&longs;&longs;us & eli&longs;us <expan abbr="quandoq;">quandoque</expan> eidem puncto in&longs;i&longs;tens ro<lb/>tari, <expan abbr="quandoq;">quandoque</expan> à procur&longs;u recurrere, aut etiam retro agi vide<lb/>

<arrow.to.target n="fig23"/><lb/>tur. </s><s>Quòd &longs;i enim motus circularis fiat æqualis motui recto; <lb/>videbitur orbiculus in eodem puncto A circa immobile cen<lb/>trum gyrari. </s><s>Dividatur peripheria orbiculi in &longs;ex partes æqua<lb/>les <emph type="italics"/>abcdef:<emph.end type="italics"/> & &longs;umantur his æqualia &longs;egmenta in lineâ re<lb/>ctâ <emph type="italics"/>aghikl.<emph.end type="italics"/> Cùm <expan abbr="itaq;">itaque</expan> motus in <emph type="italics"/>ab<emph.end type="italics"/> &longs;it æqualis motui centri <lb/>eiu&longs;dem orbiculi in <emph type="italics"/>ag;<emph.end type="italics"/> gyratio autem non ni&longs;i per contactum

<pb xlink:href="063/01/132.jpg"/>fiat eiu&longs;dem plani; nece&longs;se ubi ex <emph type="italics"/>a<emph.end type="italics"/> promovit in <emph type="italics"/>g,<emph.end type="italics"/> ip&longs;um <emph type="italics"/>b<emph.end type="italics"/><lb/>revolui in <emph type="italics"/>a.<emph.end type="italics"/> Similiter ubi <emph type="italics"/>b<emph.end type="italics"/> perventurum eratex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>g,<emph.end type="italics"/> ip&longs;um <lb/><emph type="italics"/>c<emph.end type="italics"/> attinget punctum <emph type="italics"/>a.<emph.end type="italics"/> Quòd &longs;i maior &longs;it motus circuli, quàm <lb/>eiu&longs;dem centri; contingit ip&longs;um retroagi. </s><s>Nam cùm ex <emph type="italics"/>a<emph.end type="italics"/><lb/>movetur in <emph type="italics"/>g;<emph.end type="italics"/> motus in peripheriâ fit per maius <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> <emph type="italics"/>ab:<emph.end type="italics"/> ac <lb/>proinde orbiculus tangit planum in puncto medio inter <emph type="italics"/>b<emph.end type="italics"/> & <emph type="italics"/>c.<emph.end type="italics"/><lb/>Demum &longs;i maior &longs;it motus centri quàm gyrationis; videbitur <lb/>motus rectus, & punctum <emph type="italics"/>b<emph.end type="italics"/> inter <emph type="italics"/>a<emph.end type="italics"/> & <emph type="italics"/>g.<emph.end type="italics"/> Inde ergo ratio reddi<lb/>tur; quòd motus centri ab illatâ plagâ deflectat à lineâ rectâ <lb/><emph type="italics"/>AI<emph.end type="italics"/> etiam ante grad: 60. </s><s>Cùm enim motus orbiculi circularis <lb/>in plano firmetur, <expan abbr="eaq;">eaque</expan> ratione motui centri reluctetur; ne<lb/>ce&longs;&longs;e motum mixtum inde procreari. </s>

Line 1076

<s><emph type="center"/>De Levigatione & Politura.<emph.end type="center"/></s>

<s>COrpora polita dicuntur, quæ &longs;uperficiem habent illius fi<lb/>guræ, quâ terminantur, æquabilem: ut in cubo perfectè <lb/>planam, in globo &longs;phæricam. </s><s>His opponitur a&longs;perum &longs;eu &longs;ca<lb/>brum: cuius &longs;uperficies partes habet inæqualiter &longs;itas, magis <lb/>& minùs depre&longs;&longs;as aut elevatas. </s><s><expan abbr="Neq;">Neque</expan> omnia corpora æqua<lb/>liter: &longs;ed alia magis, alia minùs, alia nullâ indu&longs;triâ poliuntur: <lb/>ut thophus, pumex, &longs;uber, panni lanei &c. </s><s>Et cùm &longs;cabrities <lb/>&longs;eu inæqualitas à duobus proveniat: cùm vel partes in&longs;unt <lb/>verruco&longs;æ, vel pori &longs;eu cavernulæ &longs;uperficiem perforantes, <lb/>quantum vis &longs;en&longs;um lateant: polituram obtinemus contrariâ <lb/>affectione: verrucarum quidem, & quæ prominent, ablatione: <lb/>&longs;patiorum verò inanium repletione. </s><s>Quòd &longs;i eiu&longs;modi um<lb/>bilici & verruculæ tolli nequeant: aut lacunæ expleri, impo<lb/>libile dicetur corpus, Talia &longs;unt <foreign lang="greek">a)pie<gap/>a\</foreign>, & quæ dividi neque<lb/>unt in partes minimas: quia <expan abbr="neq;">neque</expan> compre&longs;&longs;ioni cedunt ad po<lb/>rum &longs;olidandum, receptâ in eas vacuitates parte magis pre&longs;sâ:

<pb xlink:href="063/01/133.jpg"/>ut vitrum, gemmæ, lapides, <expan abbr="omniaq;">omniaque</expan> <foreign lang="greek">qrau<gap/>a</foreign>: <expan abbr="neq;">neque</expan> pars minima <lb/>re&longs;ecari valet, cuiu&longs;modi e&longs;t thophus. </s><s><expan abbr="Atq;">Atque</expan> illa quidem &longs;olá <lb/>partium ablatione poliuntur: & &longs;i quidem poro&longs;a &longs;int, nullâ <lb/>ratione &longs;uam perfectionem a&longs;&longs;equitur politura: quemadmo<lb/>dum <expan abbr="neq;">neque</expan> individua in partes minimas: ablatâ enim parte ma<lb/>iori, quàm &longs;it exce&longs;&longs;us; eadem inæqualitas manet. </s><s>Corporaer<lb/>go <foreign lang="greek">paxume/rea</foreign> & quæ glutinosâ vi&longs;ciditate tenaciùs cohærent, <lb/>ut cera, pix, tela linea, papyrus; &longs;olâ levigatione proficiunt: <lb/>partibus à compre&longs;&longs;ione in eodem &longs;itu manentibus. </s><s>Vnde <lb/>panni lanei, ob pilos à compre&longs;&longs;ione &longs;urrigentes, non levigan<lb/>tur. metalla <expan abbr="quoq;">quoque</expan> omnia, <expan abbr="atq;">atque</expan> ligna alia magis, alia minùs le<lb/>vigationi parent. </s><s>Quæ enim mollia &longs;unt, <expan abbr="neq;">neque</expan> compre&longs;&longs;a <lb/>manent in eo &longs;itu, <gap/>t medulla &longs;ambuci, aut &longs;pongia, non levi<lb/>gantur. </s><s>Nece&longs;&longs;e enim reniti aliquas partes: quibus aliæ inni<lb/>tantur. </s><s>Quod non fit, &longs;i omnes à compre&longs;&longs;ione moveantur <expan abbr="ce-dantq;">ce<lb/>dantque</expan> <expan abbr="Itaq;">Itaque</expan> ligna duriora, cuiu&longs;modi hebenus, præ alijs levi<lb/>gantur. </s><s>Cùm igitur illa corpora vel partium ablatione, vel <lb/>illarum &longs;itu permutato &longs;uperficiem politam con&longs;equantur; <lb/>manife&longs;tum levigationem & polituram non <expan abbr="ab&longs;q;">ab&longs;que</expan> motu & im<lb/>pul&longs;u fieri. </s><s>Cuiu&longs;modi verò &longs;it motus, & quâ ratione fiat, <lb/>nunc dicam, à levigatione incipiendo. </s>

<pb xlink:href="063/01/133.jpg"/>ut vitrum, gemmæ, lapides, <expan abbr="omniaq;">omniaque</expan> <foreign lang="greek">qrau<gap/>a</foreign>: <expan abbr="neq;">neque</expan> pars minima <lb/>re&longs;ecari valet, cuiu&longs;modi e&longs;t thophus. </s><s><expan abbr="Atq;">Atque</expan> illa quidem &longs;olá <lb/>partium ablatione poliuntur: & &longs;i quidem poro&longs;a &longs;int, nullâ <lb/>ratione &longs;uam perfectionem a&longs;&longs;equitur politura: quemadmo<lb/>dum <expan abbr="neq;">neque</expan> individua in partes minimas: ablatâ enim parte ma<lb/>iori, quàm &longs;it exce&longs;&longs;us; eadem inæqualitas manet. </s><s>Corporaer<lb/>go <foreign lang="greek">paxume/rea</foreign> & quæ glutinosâ vi&longs;ciditate tenaciùs cohærent, <lb/>ut cera, pix, tela linea, papyrus; &longs;olâ levigatione proficiunt: <lb/>partibus à compre&longs;&longs;ione in eodem &longs;itu manentibus. </s><s>Vnde <lb/>panni lanei, ob pilos à compre&longs;&longs;ione &longs;urrigentes, non levigan<lb/>tur. metalla <expan abbr="quoq;">quoque</expan> omnia, <expan abbr="atq;">atque</expan> ligna alia magis, alia minùs le<lb/>vigationi parent. </s><s>Quæ enim mollia &longs;unt, <expan abbr="neq;">neque</expan> compre&longs;&longs;a <lb/>manent in eo &longs;itu, ut medulla &longs;ambuci, aut &longs;pongia, non levi<lb/>gantur. </s><s>Nece&longs;&longs;e enim reniti aliquas partes: quibus aliæ inni<lb/>tantur. </s><s>Quod non fit, &longs;i omnes à compre&longs;&longs;ione moveantur <expan abbr="ce-dantq;">ce<lb/>dantque</expan> <expan abbr="Itaq;">Itaque</expan> ligna duriora, cuiu&longs;modi hebenus, præ alijs levi<lb/>gantur. </s><s>Cùm igitur illa corpora vel partium ablatione, vel <lb/>illarum &longs;itu permutato &longs;uperficiem politam con&longs;equantur; <lb/>manife&longs;tum levigationem & polituram non <expan abbr="ab&longs;q;">ab&longs;que</expan> motu & im<lb/>pul&longs;u fieri. </s><s>Cuiu&longs;modi verò &longs;it motus, & quâ ratione fiat, <lb/>nunc dicam, à levigatione incipiendo. </s>

<s><emph type="italics"/>E&longs;t autem levigatio motus reciprocus in &longs;uperficie levigandà, factus <lb/>à corpore polito, non &longs;ine compreßione.<emph.end type="italics"/></s>

Line 1085

<s>Re&longs;pondeo, licet partes continuò mutentur: quia tamen <lb/>aliæ <expan abbr="atq;">atque</expan> aliæ &longs;uccedunt eiu&longs;dem rationis, motum continuan<lb/>tes; per æquivalentiam idem videri movens. </s><s>E&longs;t autem dif<lb/>ferétia inter ea, quæ <foreign lang="greek">xi/nhsin</foreign> habent <foreign lang="greek">a)po\ tg_s a(/yews</foreign>, & quæ <foreign lang="greek">a)po\ tg_s <lb/>plhgh_s xino<gap/>_nt<gap/></foreign>: quòd hæc in motu &longs;eparantur à movente: ac <lb/>proinde acceptâ plagâ non &longs;it in pote&longs;tate moventis ille mo<lb/>tus. </s><s>Quæ verò <foreign lang="greek">a)po\ th_s a(/yews</foreign> moventur; impul&longs;um habent <lb/>fluentem: qui non ni&longs;i illis motis e&longs;&longs;e pote&longs;t: <expan abbr="moxq;">moxque</expan> ubi cæpit, <lb/>ex illo contactu finit: & non ni&longs;i impul&longs;u continuato &longs;ervari <lb/>pote&longs;t. </s><s><expan abbr="Atq;">Atque</expan> inde fit, ut nulla particula inter poliendum, &longs;eu <lb/>levigandum divellatur: cùm motus in ip&longs;a plagâ finiat, <expan abbr="neq;">neque</expan> <lb/>ullus re&longs;tet impul&longs;us. </s><s>Et licet non &longs;ine aliquâ tractione par<lb/>tes levigatæ extendantur; non tamen e&longs;t motus exce&longs;&longs;ivus: <lb/><expan abbr="neq;">neque</expan> per &longs;e, &longs;ed à compre&longs;&longs;ione na&longs;cens: <expan abbr="Itaq;">Itaque</expan> &longs;i excedat, ut <lb/>dum chartam minùs cautè levigamus; partes divelluntur. </s>

<s><emph type="italics"/>Dices. A quo ergo partes compreßa detinentur in co &longs;itu? ne&que; enim &longs;o-<emph.end type="italics"/>

<s><emph type="italics"/>Dices. A quo ergo partes compreßa detinentur in eo &longs;itu? ne&que; enim &longs;o-<emph.end type="italics"/>

<pb xlink:href="063/01/135.jpg"/><emph type="italics"/>la<emph.end type="italics"/> <foreign lang="greek">p<gap/>esa\</foreign> <emph type="italics"/>levigantur: ne&que; illa filamenta linteorum & minutuli &longs;locci <lb/>in compreßione uniu<gap/>tur, &longs;uperficiem unam habentes: verùm contigui <lb/>inter &longs;e manent: ita&queacute; linteis excußis rur&longs;um à &longs;e di&longs;iungi, & &longs;uperfici<lb/>em hi&longs;pidam reddi videmus.<emph.end type="italics"/></s>

<pb xlink:href="063/01/135.jpg"/><emph type="italics"/>la<emph.end type="italics"/> <foreign lang="greek">p<gap/>esa\</foreign> <emph type="italics"/>levigantur: ne&que; illa filamenta linteorum & minutuli &longs;locci <lb/>in compreßione uniuntur, &longs;uperficiem unam habentes: verùm contigui <lb/>inter &longs;e manent: ita&queacute; linteis excußis rur&longs;um à &longs;e di&longs;iungi, & &longs;uperfici<lb/>em hi&longs;pidam reddi videmus.<emph.end type="italics"/></s>

<s>Re&longs;pondeo illum &longs;itum non ni&longs;i à novo motu turbari: mo<lb/>tum verò non <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; impul&longs;u advenire. </s><s>Quòd &longs;i ergo partes <lb/><expan abbr="neq;">neque</expan> à &longs;e, <expan abbr="neq;">neque</expan> ab extra habeant principium motûs; nece&longs;&longs;e illá <lb/>&longs;uperficiem, in quam terminavit motus, retinere. </s><s><expan abbr="Itaq;">Itaque</expan> lin<lb/>tea agitata turbantur: dum ex illo motu impetum concipiunt <lb/>particulæ, ab eo &longs;itu di&longs;trahentem. </s><s>Quæ autem rigidiu&longs;cula <lb/>&longs;unt: quia in &longs;e ip&longs;is habent principium motús; à compre&longs;&longs;io<lb/>ne eo modo, quo arcus à curvaturá, rea&longs;&longs;urgunt. </s><s>Sicuti ve<lb/>rò duobus modis levigatio fit; <expan abbr="nimir&utilde;">nimirum</expan> depre&longs;&longs;ione & <expan abbr="cõpre&longs;&longs;io-ne">compre&longs;&longs;io<lb/>ne</expan> <expan abbr="atomor&utilde;">atomorum</expan>; ita <expan abbr="quoq;">quoque</expan> duobus motibus oppo&longs;itis tu<gap/>batur: cùm <lb/>vel eriguntur: vel partes pre&longs;&longs;æ retume&longs;cunt. </s><s>Superficié le viga<lb/>tam &longs;equitur tanquam proprietas &longs;plendor: lucis nimirum uni<lb/>tæ confertim facta evibratio. </s><s>Nam quæ &longs;uperficiem habent <lb/>a&longs;peram, lucem incidentem di&longs;trahunt & inæqualiter <expan abbr="reflect&utilde;t">reflectunt</expan>. <lb/><expan abbr="Neq;">Neque</expan> enim ab aliquâ parte radij uniti, &longs;ed à &longs;e divul&longs;i, <expan abbr="&longs;eq;">&longs;eque</expan> in<lb/>ter&longs;ecantes in retinam feruntur: &longs;inguli non ni&longs;i luce tenui &longs;en<lb/>&longs;um afficientes. </s>

<s>Re&longs;pondeo illum &longs;itum non ni&longs;i à novo motu turbari: mo<lb/>tum verò non <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; impul&longs;u advenire. </s><s>Quòd &longs;i ergo partes <lb/><expan abbr="neq;">neque</expan> à &longs;e, <expan abbr="neq;">neque</expan> ab extra habeant principium motûs; nece&longs;&longs;e illá <lb/>&longs;uperficiem, in quam terminavit motus, retinere. </s><s><expan abbr="Itaq;">Itaque</expan> lin<lb/>tea agitata turbantur: dum ex illo motu impetum concipiunt <lb/>particulæ, ab eo &longs;itu di&longs;trahentem. </s><s>Quæ autem rigidiu&longs;cula <lb/>&longs;unt: quia in &longs;e ip&longs;is habent principium motús; à compre&longs;&longs;io<lb/>ne eo modo, quo arcus à curvaturá, rea&longs;&longs;urgunt. </s><s>Sicuti ve<lb/>rò duobus modis levigatio fit; <expan abbr="nimir&utilde;">nimirum</expan> depre&longs;&longs;ione & <expan abbr="cõpre&longs;&longs;io-ne">compre&longs;&longs;io<lb/>ne</expan> <expan abbr="atomor&utilde;">atomorum</expan>; ita <expan abbr="quoq;">quoque</expan> duobus motibus oppo&longs;itis turbatur: cùm <lb/>vel eriguntur: vel partes pre&longs;&longs;æ retume&longs;cunt. </s><s>Superficié le viga<lb/>tam &longs;equitur tanquam proprietas &longs;plendor: lucis nimirum uni<lb/>tæ confertim facta evibratio. </s><s>Nam quæ &longs;uperficiem habent <lb/>a&longs;peram, lucem incidentem di&longs;trahunt & inæqualiter <expan abbr="reflect&utilde;t">reflectunt</expan>. <lb/><expan abbr="Neq;">Neque</expan> enim ab aliquâ parte radij uniti, &longs;ed à &longs;e divul&longs;i, <expan abbr="&longs;eq;">&longs;eque</expan> in<lb/>ter&longs;ecantes in retinam feruntur: &longs;inguli non ni&longs;i luce tenui &longs;en<lb/>&longs;um afficientes. </s>

<s><emph type="italics"/>An igitur inferre licet omnia, quæ luce alienâ re&longs;plendent &longs;uperfici<lb/>em habere levigatam? Nitent enim margaritæ, conchylia, opera item <lb/>figulina vitreata, avium pennæ, atramentum, picturæ &c. in quibus <lb/>tæmen a&longs;peritatem notamus.<emph.end type="italics"/></s>

<s>Re&longs;pondeo &longs;plendorem non ni&longs;i ex multâ luce unitâ na&longs;ci: <lb/>multa autem fit ratione &longs;ubiecti. nam &longs;ubiectum magis den<lb/>&longs;um plus lucis continet. </s><s>Corpus ergo den&longs;i&longs;&longs;imum & &longs;ummè <lb/>politum &longs;plendorem habet &longs;ummum. </s><s><expan abbr="Itaq;">Itaque</expan> aurum p<gap/>fectè <lb/>levigatum præ omnibus alijs &longs;plendet, <expan abbr="aciemq;">aciemque</expan> oculorum per-

<s>Re&longs;pondeo &longs;plendorem non ni&longs;i ex multâ luce unitâ na&longs;ci: <lb/>multa autem fit ratione &longs;ubiecti. nam &longs;ubiectum magis den<lb/>&longs;um plus lucis continet. </s><s>Corpus ergo den&longs;i&longs;&longs;imum & &longs;ummè <lb/>politum &longs;plendorem habet &longs;ummum. </s><s><expan abbr="Itaq;">Itaque</expan> aurum perfectè <lb/>levigatum præ omnibus alijs &longs;plendet, <expan abbr="aciemq;">aciemque</expan> oculorum per-

<pb xlink:href="063/01/136.jpg"/>cellit: plumbum verò licet alijs metallis magis den&longs;um; quia <lb/>tamen ob partes terreas minùs levigari pote&longs;t, & colori atro <lb/>magis mi&longs;cetur; minùs re&longs;plendet. </s><s>Fieri ergo pote&longs;t ut cor<lb/>pus den&longs;um, & &longs;i minùs politum, magis &longs;plendeat, quàm rarum, <lb/>& è co<gap/>tra: at &longs;ummè levigatum nece&longs;&longs;ariò &longs;uperat den&longs;i&longs;&longs;i<lb/>mum; &longs;i pror&longs;us &longs;it impolitum. </s><s>Deinde levigatum &longs;eu poli<lb/>tum duobus modis &longs;umitur: ab&longs;olutè, & &longs;ecundum quid. </s><lb/><s>Ab&longs;olutè quidem, cuius &longs;uperficies <expan abbr="undiq;">undique</expan> e&longs;t ter&longs;a & æqualis: <lb/>&longs;ecundùm quid autem, quod non totam &longs;uperficiem, &longs;ed tan<lb/>tum aliquas partes habet levigatas, non continuas inter &longs;e, ve<lb/>rum partibus &longs;cabris interci&longs;as. </s><s>Multa ergo licet &longs;uperficiem <lb/>habeant &longs;cabram & inæqualem; quia tamen eiu&longs;modi umbili<lb/>cos continent leves & politos; re&longs;plendent. </s><s>Ita enim figulina <lb/>poliuntur: dum metallicus humot illitus, <expan abbr="atq;">atque</expan> igne lique&longs;cens <lb/>&longs;uperficiem inungit: & demum æqualiter concretus &longs;peciem <lb/>vitri a&longs;&longs;umit. </s><s>Similiter panis humido inunctus, cru&longs;tam in igne <lb/>trahit re&longs;plendentem. </s><s>Ita atramentum &longs;criptorium admi&longs;to <lb/>gummi &longs;plendet. quia ob vi&longs;ciditatem minùs &longs;orbetur humor: <lb/>& partes vitriolicæ ceu vi&longs;co cohærentes, inter &longs;iccandum mi<lb/>nùs hiulcæ fiunt. </s><s>Colores <expan abbr="quoq;">quoque</expan> & picturæ glutine pellucido <lb/>affu&longs;o, aut permixto &longs;imili ratione re&longs;plendent, </s>

<pb xlink:href="063/01/136.jpg"/>cellit: plumbum verò licet alijs metallis magis den&longs;um; quia <lb/>tamen ob partes terreas minùs levigari pote&longs;t, & colori atro <lb/>magis mi&longs;cetur; minùs re&longs;plendet. </s><s>Fieri ergo pote&longs;t ut cor<lb/>pus den&longs;um, & &longs;i minùs politum, magis &longs;plendeat, quàm rarum, <lb/>& è contra: at &longs;ummè levigatum nece&longs;&longs;ariò &longs;uperat den&longs;i&longs;&longs;i<lb/>mum; &longs;i pror&longs;us &longs;it impolitum. </s><s>Deinde levigatum &longs;eu poli<lb/>tum duobus modis &longs;umitur: ab&longs;olutè, & &longs;ecundum quid. </s><lb/><s>Ab&longs;olutè quidem, cuius &longs;uperficies <expan abbr="undiq;">undique</expan> e&longs;t ter&longs;a & æqualis: <lb/>&longs;ecundùm quid autem, quod non totam &longs;uperficiem, &longs;ed tan<lb/>tum aliquas partes habet levigatas, non continuas inter &longs;e, ve<lb/>rum partibus &longs;cabris interci&longs;as. </s><s>Multa ergo licet &longs;uperficiem <lb/>habeant &longs;cabram & inæqualem; quia tamen eiu&longs;modi umbili<lb/>cos continent leves & politos; re&longs;plendent. </s><s>Ita enim figulina <lb/>poliuntur: dum metallicus humot illitus, <expan abbr="atq;">atque</expan> igne lique&longs;cens <lb/>&longs;uperficiem inungit: & demum æqualiter concretus &longs;peciem <lb/>vitri a&longs;&longs;umit. </s><s>Similiter panis humido inunctus, cru&longs;tam in igne <lb/>trahit re&longs;plendentem. </s><s>Ita atramentum &longs;criptorium admi&longs;to <lb/>gummi &longs;plendet. quia ob vi&longs;ciditatem minùs &longs;orbetur humor: <lb/>& partes vitriolicæ ceu vi&longs;co cohærentes, inter &longs;iccandum mi<lb/>nùs hiulcæ fiunt. </s><s>Colores <expan abbr="quoq;">quoque</expan> & picturæ glutine pellucido <lb/>affu&longs;o, aut permixto &longs;imili ratione re&longs;plendent, </s>

<s><emph type="italics"/>Sed dices. aquam e&longs;&longs;e &longs;ummè levigatam, minùs tamen alijs &longs;plendere.<emph.end type="italics"/></s>

<s>Re&longs;pondeo &longs;plendorem e&longs;&longs;e lucem à &longs;uperficie reflexam: <lb/>ut autem reflecti po&longs;&longs;it nece&longs;&longs;e priùs terminari. </s><s>At verò aquam <lb/>pellucidam lux pertran&longs;it: minùs ergo lucis à reflexione. </s><s>De<lb/>inde cùm aqua &longs;it fluens & minùs den&longs;a corporibus ex eâ con<lb/>cretis; minor copia lucis in eâ colligi pote&longs;t. </s><s>Nec refert mul<lb/>ta corpora e&longs;&longs;e rariora: hæc enim &longs;uam concretionem aëri de<lb/>bent<gap/>ui in his prædominatur: cuiu&longs;modi volucrum pennæ, <lb/>& &longs;ambuci medulla. </s>

<s>Re&longs;pondeo &longs;plendorem e&longs;&longs;e lucem à &longs;uperficie reflexam: <lb/>ut autem reflecti po&longs;&longs;it nece&longs;&longs;e priùs terminari. </s><s>At verò aquam <lb/>pellucidam lux pertran&longs;it: minùs ergo lucis à reflexione. </s><s>De<lb/>inde cùm aqua &longs;it fluens & minùs den&longs;a corporibus ex eâ con<lb/>cretis; minor copia lucis in eâ colligi pote&longs;t. </s><s>Nec refert mul<lb/>ta corpora e&longs;&longs;e rariora: hæc enim &longs;uam concretionem aëri de<lb/>bent, qui in his prædominatur: cuiu&longs;modi volucrum pennæ, <lb/>& &longs;ambuci medulla. </s>

<s>Hæc de levigatione. </s><s>Politura eundem finem habet; nimi<lb/>rum &longs;uperficiem erugatam, <expan abbr="ter&longs;ámq;">ter&longs;ámque</expan>: differentia e&longs;t in modo <lb/>& medijs ad hunc finem. </s><s>Nam levigatio deprimit, aut in lacu<lb/>nas transfert: politura adimit &longs;cabritiem efficientes partes. </s><lb/><s>Quæ quidem differentia in materiâ fundatur: cuius partes <expan abbr="neq;">neque</expan> <lb/>comprimi valent, <expan abbr="neq;">neque</expan> aliò transferri: Talia &longs;unt vitra, gemmæ, <lb/>lapides, <expan abbr="atq;">atque</expan> omnia <foreign lang="greek">a)pies a\ x<gap/>\ qzau<gap/>a\</foreign>. </s><s>Igitur quædam <expan abbr="utroq;">utroque</expan> <lb/>modo hunc finem con&longs;equuntur, & politurâ & levigatione, ut <lb/>metalla: quædam &longs;olâ levigatione, ut papyrus, lintea, cera: <lb/>quædam non ni&longs;i politurâ, ut gemmæ, lapides, vitra. </s><s>Ratio <lb/>e&longs;t quia nequeunt dividi in partes minimas: &longs;iue ob vi&longs;cidita<lb/>tem magis tenacem, &longs;iue ob cra&longs;&longs;itiem. </s><s><expan abbr="Itaq;">Itaque</expan> fit, ut dum plus, <lb/>minú&longs;ue à &longs;cabritie aufert politura; prior inæqualitas con<lb/>tinuò aliâ permutetur. </s><s>Deinde levigatio in multis incipit à <lb/>politurâ: cùm nimirum maior e&longs;t a&longs;peritas, quàm compre&longs;&longs;io <lb/>e&longs;&longs;e po&longs;&longs;it; nece&longs;&longs;e ergo illum exce&longs;&longs;um adimi, quò reliqua &longs;u<lb/>perficies levigationem habeat mag<gap/> expeditam: ita enim ligna <lb/><expan abbr="atq;">atque</expan> metalla non ni&longs;i ferro acci&longs;a levigantur. </s><s><expan abbr="Neq;">Neque</expan> idem e&longs;t <lb/>modus polituræ in omnibus; <expan abbr="neq;">neque</expan> idem principium. </s><s>Nam pro<lb/>ut materiâ, & &longs;uperficie magis & minùs a&longs;perâ à &longs;e differunt; <lb/><expan abbr="atq;">atque</expan> ab alijs plus, ab alijs minùs e&longs;t auferendum; ita <expan abbr="quoq;">quoque</expan> in&longs;tru<lb/>menta varia &longs;unt inventa. </s><s>Saxa enim & marmora malleo de<lb/>cu&longs;&longs;is, aut ferro acci&longs;is promontorijs æquantur: gemmæ verò <lb/>affricatione adlapidem arenarium molâ circumactum, corti<lb/>cem priùs, quò ve&longs;tiuntur, exuunt; inde &longs;errâ obtusâ in <expan abbr="&longs;egm&etilde;-ta">&longs;egmen<lb/>ta</expan> dividuntur: demum arenâ <expan abbr="atq;">atque</expan> huius <gap/>polline levigantur. </s><lb/><s>Ligna verò &longs;ecuri, cuneo, &longs;errâ finduntur & &longs;ecantur: dein<lb/>de a&longs;ciâ, tornóve poliuntur. </s><s>E&longs;t autem nobis propo&longs;itum non <lb/>ni&longs;i de motu & impul&longs;u agere, quo &longs;uperficiem politam obti<lb/>nemus; nequaquam verò de arte poliendi, quæ &longs;uis Magi&longs;tris <lb/>e&longs;t relinquenda. </s><s>Incipiam verò à Lignorum politurâ, utpo-

<s>Hæc de levigatione. </s><s>Politura eundem finem habet; nimi<lb/>rum &longs;uperficiem erugatam, <expan abbr="ter&longs;ámq;">ter&longs;ámque</expan>: differentia e&longs;t in modo <lb/>& medijs ad hunc finem. </s><s>Nam levigatio deprimit, aut in lacu<lb/>nas transfert: politura adimit &longs;cabritiem efficientes partes. </s><lb/><s>Quæ quidem differentia in materiâ fundatur: cuius partes <expan abbr="neq;">neque</expan> <lb/>comprimi valent, <expan abbr="neq;">neque</expan> aliò transferri: Talia &longs;unt vitra, gemmæ, <lb/>lapides, <expan abbr="atq;">atque</expan> omnia <foreign lang="greek">a)pies a\ x<gap/>\ qzau<gap/>a\</foreign>. </s><s>Igitur quædam <expan abbr="utroq;">utroque</expan> <lb/>modo hunc finem con&longs;equuntur, & politurâ & levigatione, ut <lb/>metalla: quædam &longs;olâ levigatione, ut papyrus, lintea, cera: <lb/>quædam non ni&longs;i politurâ, ut gemmæ, lapides, vitra. </s><s>Ratio <lb/>e&longs;t quia nequeunt dividi in partes minimas: &longs;iue ob vi&longs;cidita<lb/>tem magis tenacem, &longs;iue ob cra&longs;&longs;itiem. </s><s><expan abbr="Itaq;">Itaque</expan> fit, ut dum plus, <lb/>minú&longs;ue à &longs;cabritie aufert politura; prior inæqualitas con<lb/>tinuò aliâ permutetur. </s><s>Deinde levigatio in multis incipit à <lb/>politurâ: cùm nimirum maior e&longs;t a&longs;peritas, quàm compre&longs;&longs;io <lb/>e&longs;&longs;e po&longs;&longs;it; nece&longs;&longs;e ergo illum exce&longs;&longs;um adimi, quò reliqua &longs;u<lb/>perficies levigationem habeat magis expeditam: ita enim ligna <lb/><expan abbr="atq;">atque</expan> metalla non ni&longs;i ferro acci&longs;a levigantur. </s><s><expan abbr="Neq;">Neque</expan> idem e&longs;t <lb/>modus polituræ in omnibus; <expan abbr="neq;">neque</expan> idem principium. </s><s>Nam pro<lb/>ut materiâ, & &longs;uperficie magis & minùs a&longs;perâ à &longs;e differunt; <lb/><expan abbr="atq;">atque</expan> ab alijs plus, ab alijs minùs e&longs;t auferendum; ita <expan abbr="quoq;">quoque</expan> in&longs;tru<lb/>menta varia &longs;unt inventa. </s><s>Saxa enim & marmora malleo de<lb/>cu&longs;&longs;is, aut ferro acci&longs;is promontorijs æquantur: gemmæ verò <lb/>affricatione adlapidem arenarium molâ circumactum, corti<lb/>cem priùs, quò ve&longs;tiuntur, exuunt; inde &longs;errâ obtusâ in <expan abbr="&longs;egm&etilde;-ta">&longs;egmen<lb/>ta</expan> dividuntur: demum arenâ <expan abbr="atq;">atque</expan> huius polline levigantur. </s><lb/><s>Ligna verò &longs;ecuri, cuneo, &longs;errâ finduntur & &longs;ecantur: dein<lb/>de a&longs;ciâ, tornóve poliuntur. </s><s>E&longs;t autem nobis propo&longs;itum non <lb/>ni&longs;i de motu & impul&longs;u agere, quo &longs;uperficiem politam obti<lb/>nemus; nequaquam verò de arte poliendi, quæ &longs;uis Magi&longs;tris <lb/>e&longs;t relinquenda. </s><s>Incipiam verò à Lignorum politurâ, utpo-

<pb xlink:href="063/01/138.jpg"/>te minùs operosâ. </s><s>Cuius principium <foreign lang="greek">sxi/sis x<gap/>\ tm<gap/>_sis<gap/></foreign>: in eo à <lb/>&longs;e differentes: quòd <foreign lang="greek">sxi/sis</foreign> &longs;it <foreign lang="greek">diai/zesi<gap/>)pi\ to\ pl<gap/>on. sxiset<gap/> ga\z</foreign>, <lb/>inquit Ari&longs;toteles, <foreign lang="greek">o(/tan e)pi\ to\ pl<gap/>on di<gap/>zh_t<gap/> h(' to/ di<gap/>zo_un di<gap/>z<gap/>, xa<gap/><lb/>pzohg<gap/>tai h( diai/zesis</foreign>. </s><s>In fi&longs;&longs;ione ergo e&longs;t maior divi&longs;io, |quàm <lb/>ut ad <expan abbr="illã">illam</expan> <expan abbr="plagã">plagam</expan> referri po&longs;&longs;it: <expan abbr="eamq;">eamque</expan> divi&longs;io anteit. </s><s>E&longs;t enim <foreign lang="greek">xi/<lb/>nhsis a)po\ th_s a(\yews</foreign>: cùm plaga in&longs;equitur <expan abbr="mot&utilde;">motum</expan>: <expan abbr="atq;">atque</expan> impul&longs;um <lb/>habet <expan abbr="fluent&etilde;">fluentem</expan>, & à plagâ in&longs;eparabilem. </s><s>Igitur cùm fi&longs;&longs;ura ultra <lb/>plagam &longs;e extendat, non e&longs;&longs;e pote&longs;t à plagâ. </s><s>Huius autem ra<lb/>tio. quia <foreign lang="greek">to\ di<gap/>z<gap/>_n</foreign> habet vim cunei: cuius ingre&longs;&longs;u in eam pla<lb/>gam partes di&longs;trahuntur. </s><s>Et cùm fibræ in longitudinem ex<lb/>currentes flecti nequeant; nece&longs;&longs;e ultra cuneum agi fi&longs;&longs;uram: <lb/><expan abbr="atq;">atque</expan> eò magis, quò fibras habent rigidiores, & minùs lentas. <lb/><expan abbr="Itaq;">Itaque</expan> ligna duriora magis finduntur, quàm mollia ac lenta: quæ <lb/>magis obliquari & flecti <gap/>alent. </s><s>Vnde angulo obtu&longs;iore, illa <lb/>verò acutiore, fi&longs;&longs;urâ magis productâ finiunt plagam. </s><s>Cùm <lb/>ergo inci&longs;io fit, ferrum in fi&longs;&longs;urâ conquie&longs;cit: partes verò hu<lb/>ius ingre&longs;&longs;u di&longs;tractæ, quia flecti nequeunt ob rigiditatem, <expan abbr="neq;">neque</expan> <lb/>comprimi vulneris labra: quemadmodum fit in plumbi &longs;ectu<lb/>râ, illam rectitudinem &longs;ervantes findunt partes ulteriores: <lb/><foreign lang="greek">sxista/</foreign> autem dicit Ari&longs;toteles <foreign lang="greek">o(/sa xata\ mh_xos e)/x<gap/> t<gap/>s po/z<gap/>s xa<gap/><lb/>su(\s pzosfu/et<gap/> a)llh/lois,<gap/> a)lla\ mh<gap/>xata\ pla/tos</foreign>. </s><s>Eiu&longs;modi &longs;unt li<lb/>gna ferè omnia fibris in longitudinem proten&longs;is: inter quas <lb/>pori &longs;ub&longs;tantiâ molliori & veluti fungosâ pleni inter&longs;unt, per <lb/>quas agitur fi&longs;&longs;ura: non verò in tran&longs;ver&longs;um per illas fibras, <lb/>in quibus non continuantur eiu&longs;modi pori. </s><s>Plaga autem fit à <lb/>&longs;ectione pro ratione compre&longs;&longs;ionis. </s><s>Igitu<gap/> ligna, quæ fibras <lb/>habent directas, fi&longs;&longs;uram <expan abbr="quoq;">quoque</expan> agunt rectam: quòd &longs;i tortuosè <lb/>procedant, inæqualiter finduntur: cùm plaga viam &longs;equatur <lb/>mediam inter illas fibras. </s><s>At cùm &longs;errâ dividuntur, à &longs;ectio<lb/>ne etiam inter fibras ductâ nulla &longs;equitur fi&longs;&longs;ura: quia &longs;erratio <lb/>partes fibro&longs;as non di&longs;trahit, &longs;ed di&longs;continuas facit. </s><s>E&longs;t au-

<pb xlink:href="063/01/138.jpg"/>te minùs operosâ. </s><s>Cuius principium <foreign lang="greek">sxi/sis x<gap/>\ tm<gap/>_sis<gap/></foreign>: in eo à <lb/>&longs;e differentes: quòd <foreign lang="greek">sxi/sis</foreign> &longs;it <foreign lang="greek">diai/zesi<gap/>)pi\ to\ pl<gap/>on. sxiset<gap/> ga\z</foreign>, <lb/>inquit Ari&longs;toteles, <foreign lang="greek">o(/tan e)pi\ to\ pl<gap/>on di<gap/>zh_t<gap/> h(' to/ di<gap/>zo_un di<gap/>z<gap/>, xa<gap/><lb/>pzohg<gap/>tai h( diai/zesis</foreign>. </s><s>In fi&longs;&longs;ione ergo e&longs;t maior divi&longs;io, |quàm <lb/>ut ad <expan abbr="illã">illam</expan> <expan abbr="plagã">plagam</expan> referri po&longs;&longs;it: <expan abbr="eamq;">eamque</expan> divi&longs;io anteit. </s><s>E&longs;t enim <foreign lang="greek">xi/<lb/>nhsis a)po\ th_s a(\yews</foreign>: cùm plaga in&longs;equitur <expan abbr="mot&utilde;">motum</expan>: <expan abbr="atq;">atque</expan> impul&longs;um <lb/>habet <expan abbr="fluent&etilde;">fluentem</expan>, & à plagâ in&longs;eparabilem. </s><s>Igitur cùm fi&longs;&longs;ura ultra <lb/>plagam &longs;e extendat, non e&longs;&longs;e pote&longs;t à plagâ. </s><s>Huius autem ra<lb/>tio. quia <foreign lang="greek">to\ di<gap/>z<gap/>_n</foreign> habet vim cunei: cuius ingre&longs;&longs;u in eam pla<lb/>gam partes di&longs;trahuntur. </s><s>Et cùm fibræ in longitudinem ex<lb/>currentes flecti nequeant; nece&longs;&longs;e ultra cuneum agi fi&longs;&longs;uram: <lb/><expan abbr="atq;">atque</expan> eò magis, quò fibras habent rigidiores, & minùs lentas. <lb/><expan abbr="Itaq;">Itaque</expan> ligna duriora magis finduntur, quàm mollia ac lenta: quæ <lb/>magis obliquari & flecti valent. </s><s>Vnde angulo obtu&longs;iore, illa <lb/>verò acutiore, fi&longs;&longs;urâ magis productâ finiunt plagam. </s><s>Cùm <lb/>ergo inci&longs;io fit, ferrum in fi&longs;&longs;urâ conquie&longs;cit: partes verò hu<lb/>ius ingre&longs;&longs;u di&longs;tractæ, quia flecti nequeunt ob rigiditatem, <expan abbr="neq;">neque</expan> <lb/>comprimi vulneris labra: quemadmodum fit in plumbi &longs;ectu<lb/>râ, illam rectitudinem &longs;ervantes findunt partes ulteriores: <lb/><foreign lang="greek">sxista/</foreign> autem dicit Ari&longs;toteles <foreign lang="greek">o(/sa xata\ mh_xos e)/x<gap/> t<gap/>s po/z<gap/>s xa<gap/><lb/>su(\s pzosfu/et<gap/> a)llh/lois,<gap/> a)lla\ mh<gap/>xata\ pla/tos</foreign>. </s><s>Eiu&longs;modi &longs;unt li<lb/>gna ferè omnia fibris in longitudinem proten&longs;is: inter quas <lb/>pori &longs;ub&longs;tantiâ molliori & veluti fungosâ pleni inter&longs;unt, per <lb/>quas agitur fi&longs;&longs;ura: non verò in tran&longs;ver&longs;um per illas fibras, <lb/>in quibus non continuantur eiu&longs;modi pori. </s><s>Plaga autem fit à <lb/>&longs;ectione pro ratione compre&longs;&longs;ionis. </s><s>Igitur ligna, quæ fibras <lb/>habent directas, fi&longs;&longs;uram <expan abbr="quoq;">quoque</expan> agunt rectam: quòd &longs;i tortuosè <lb/>procedant, inæqualiter finduntur: cùm plaga viam &longs;equatur <lb/>mediam inter illas fibras. </s><s>At cùm &longs;errâ dividuntur, à &longs;ectio<lb/>ne etiam inter fibras ductâ nulla &longs;equitur fi&longs;&longs;ura: quia &longs;erratio <lb/>partes fibro&longs;as non di&longs;trahit, &longs;ed di&longs;continuas facit. </s><s>E&longs;t au-

<pb xlink:href="063/01/139.jpg"/>tem &longs;erratio motus compo&longs;itus ex inci&longs;ione & fractione. </s><s><expan abbr="Neq;">Neque</expan> <lb/>enim huius dentes a&longs;periu&longs;culi inter &longs;e &longs;unt paralleli; &longs;ed alter<lb/>natim ad latus <expan abbr="utrinq;">utrinque</expan> reflexi: quò divi&longs;io ex obliquo facta oc<lb/>currat plagæ oppo&longs;itæ. </s><s><expan abbr="Itaq;">Itaque</expan> partes quidem medias inciden<lb/>do, partes verò laterales &longs;uâ a&longs;peritate radendo auferunt: <expan abbr="eaq;">eaque</expan> <lb/>ratione vulneris labra, quo motum habeant liberiorem, adau<lb/>gent. </s><s>Inci&longs;io enim &longs;implex e&longs;t divi&longs;io continui <expan abbr="ab&longs;q;">ab&longs;que</expan> deper<lb/>ditione alicuius particulæ: ut cùm pomum per medium &longs;eca<lb/>mus. </s><s>Differt à &longs;ectione &longs;ci&longs;&longs;ura: quòd hæc &longs;it plaga continu<lb/>ata; &longs;ectio verò &longs;implex & interrupta: quæ tamen ob <expan abbr="vehem&etilde;-tiam">vehemen<lb/>tiam</expan> excedere pote&longs;t illam. </s><s><expan abbr="Vtraq;">Vtraque</expan> e&longs;t &longs;olutio unionum, &longs;eu <lb/>di&longs;continuatio cum aliquâ compre&longs;&longs;ione: nece&longs;&longs;e enim quod <lb/>incidit recipi in <expan abbr="illãm">illamm</expan> plagam, <expan abbr="partésq;">partésque</expan> medias comprimi in la<lb/>tus <expan abbr="utrumq;">utrumque</expan>. </s><s>Corpus &longs;erratile e&longs;t <foreign lang="greek">xataxto\n<gap/> xai\ qzauso\n</foreign> <expan abbr="neq;">neque</expan> enim <lb/>lapides, vitrum, gemmæ &longs;errantur. </s><s>Nam &longs;erra, quâ gemmæ <lb/>mediâ arenâ &longs;ecantur, quia dentibus caret, non ni&longs;i impropriè <lb/>dicitur. </s><s>Igitur lignis in hunc modum &longs;errâ <expan abbr="atq;">atque</expan> &longs;ecuri divi&longs;is, <lb/>aut cultro inci&longs;is a&longs;cia &longs;uccedit: quâ &longs;uperficies a&longs;pera & inæ<lb/>qualis aufertur. </s><s><expan abbr="E&longs;tq;">E&longs;tque</expan> huius motus idem cum inci&longs;ione; ma<lb/>gis tamen limitatus, ad men&longs;uram ferri inci&longs;orij ab eâ promi<lb/>nentis. </s><s>Non enim profundiùs agitur plaga, quàm &longs;it illa fer<lb/>ri longitudo: quæ contrahi & augeri pro libitu pote&longs;t. </s><s>Im<lb/>pul&longs;um verò habet fluentem: cùm &longs;it <foreign lang="greek">xi/nhsis a)po\ th_s a(/y<gap/>ws</foreign>: <lb/>quam a&longs;cia manu librata dirigit, impul&longs;um cohibens, quò mi<lb/>nùs latè evagetur. </s><s>Vnde maioribus a&longs;cijs utuntur in politu<lb/>râ: quò maior compre&longs;&longs;io à pondere, & à parte huius planâ & <lb/>politâ levigatio &longs;imul fiat. </s><s>Huic &longs;imilis videtur motus à tor<lb/>no factus: idem enim e&longs;t &longs;eu ferrum incidens, &longs;eu corpus inci<lb/>dendum moveatur. </s><s>E&longs;t ergo manus veluti a&longs;cia, quæ fulcro <lb/>innixa aciem ferri pro voto inci&longs;uræ libratam &longs;u&longs;tinet: Velo<lb/>cior tamen huius, quàm a&longs;ciæ motus <expan abbr="atq;">atque</expan> in circulum reductus: <lb/>qualis quidem e&longs;&longs;e nequit a&longs;ciæ motus ad globum poliendum.

<pb xlink:href="063/01/140.jpg"/>ita quidem &longs;e habet politura in lignis, & quæ his &longs;unt cogna<lb/>ta. </s><s>At verò torno poliuntur etiam metalla: nequaquam gem<lb/>mæ, lapides, aut <expan abbr="vitr&utilde;">vitrum</expan>: quòd hæc <foreign lang="greek">a<gap/>tmhta</foreign> &longs;int <foreign lang="greek">xa<gap/> qzausa\</foreign>: & non <lb/>ni&longs;i in plures partes friantur. </s><s><expan abbr="Itaq;">Itaque</expan> <expan abbr="neq;">neque</expan> a&longs;ciâ aut cultro &longs;ecari <lb/>valent: cùm &longs;ectio in duo terminetur, <expan abbr="unámq;">unámque</expan> particulam ab <lb/>alijs avellat. </s>

<s><emph type="italics"/>Sed cur metalla ab a&longs;ciâ non poliuntur, eandem vim cum torno ha<lb/>bente?<emph.end type="italics"/></s>

<s>Re&longs;pondeo in torno e&longs;&longs;e motum velociorem; quo re&longs;i&longs;ten<lb/>tia & durities metallorum &longs;uperatur. </s><s>Idem enim e&longs;t cùm tor<lb/>no circumagitur mobile, quemadmodum &longs;i ferrum celerrimè <lb/>moveretur: ut cùm gemmæ orbiculis circumactis poliuntur. </s><lb/><s>Et licet illarum politura torno fieri videatur; ob motum cir<lb/>cularem illorum orbiculorum, quibus gemmæ &longs;e affricantes <lb/>atteruntur: e&longs;t tamen longè diver&longs;us <expan abbr="atq;">atque</expan> alius motus. </s><s>Non <lb/>enim orbiculi &longs;eu umbilici, quibus præpilantur cylindri ver<lb/>&longs;atiles, incidunt: &longs;ed arenulæ his intermixtæ: quo modo in a<lb/>lijs orbiculis contingit horizonti parallelis. lutum enim arenu<lb/>latum continuò affu&longs;um &longs;uâ a&longs;peritate radit &longs;uperficiem ma<lb/>gis eminentem. </s><s>Cùm verò hæc omnia &longs;int <foreign lang="greek">qzausa<gap/></foreign>; erit illo<lb/>rum divi&longs;io <foreign lang="greek">q<gap/>rau_s s</foreign> non <foreign lang="greek">xa/ta<gap/>is</foreign>. quia non una particula, &longs;ed <lb/>plures &longs;imul avelluntur: illæ nimirum, quæ impul&longs;um <expan abbr="mot&utilde;q;">motunque</expan> <lb/>recipiunt à plagâ, pro numero arenularum, non unâ. </s><s>Vide<lb/>tur autem motus compo&longs;itus ex inci&longs;ione & fracturâ: com<lb/>pre&longs;&longs;ione quidem in profundum: tractu verò in latum agen<lb/>te plagam, ab impul&longs;u fluente inductam. </s><s>Cùm igitur &longs;it <foreign lang="greek">xi/nh<lb/>sis a)po\ th_s a(/yews</foreign>, nequaquam altè penetrat; &longs;ed mox à com<lb/>pre&longs;&longs;ione & contactu impul&longs;us cohibetur. </s><s>Cui accedit humi<lb/>ditas ex polline arenularum continuò affu&longs;a gemmis, impul<lb/>&longs;um hebetans: alioquin fragilibus, &longs;i arenulâ &longs;iccâ poliantur.

<pb xlink:href="063/01/141.jpg"/>quæ & calorem ex illo motu na&longs;centem, quo corpora tene<lb/>re&longs;cunt, magisq, fragilia fiunt, obtundit. </s><s>Vnde adamantes, qui<lb/>bus gemmæ &longs;olidiores poliuntur, ex illâ velocitate motûs &longs;pe<lb/>ciem carbonis igniti a&longs;&longs;umunt. </s><s>Differentia autem plagæ fit <lb/>pro ratione arenularum: cra&longs;&longs;iores enim & magis duræ ma<lb/>iora auferunt &longs;egmenta. </s><s><expan abbr="Itaq;">Itaque</expan> gemmas rudiores, <expan abbr="multúmq;">multúmque</expan> <lb/>a&longs;peritatis habentes priùs &longs;axis arenulatis, quæ molis circum<lb/>aguntur, affricantes, illâ attritione complanant: inde lapide <lb/>&longs;miri in farinam trito poliunt: & magis &longs;ubtili eiu&longs;dem polline <lb/>levigantes, demum perfectionem terrâ tripolitanâ inducunt. </s><lb/><s>Vitra tamen quia molliora, calce &longs;tanni levigantur. </s><lb/><s>Nec differt illarum &longs;ectio per &longs;erram æream edentulam facta, <lb/>lenti&longs;&longs;imo tractu arenulis interfu&longs;is radente: pro <expan abbr="quar&utilde;">quarum</expan> diver&longs;i<lb/>tate mutatur <expan abbr="quoq;">quoque</expan> vulneris amplitudo. </s><s>Nam cra&longs;&longs;ior arena, <lb/>inquit Plinins, laxioribus &longs;egmentis terit, & plus erodit mar<lb/>moris, <expan abbr="maiú&longs;q;">maiú&longs;que</expan> opus &longs;cabritia polituræ relinquit. </s><s>Ita &longs;ectæ atte<lb/>nuantur cru&longs;tæ. </s><s>Duplex ergo incommodum ab arenâ cra&longs;&longs;io<lb/>re: nam & plus decedit gemmis à plagâ latiore: & &longs;uperficies <lb/>a&longs;pera maiorem in poliendo laborem exigit. </s><s><expan abbr="Itaq;">Itaque</expan> olim <gap/>&longs;q, <lb/>ad Æthiopas, & Indos arena petebatur: quarum Æthiopica <lb/>mollior, <expan abbr="nullâq;">nullâque</expan> &longs;cabritie &longs;ecans. </s><s>Nunc verò lapis &longs;miri & <lb/>terra tripolitana in u&longs;um polituræ &longs;ucce&longs;&longs;it. </s><s><expan abbr="Neq;">Neque</expan> &longs;olum gem<lb/>mæ, marmora, & vitrum arenâ, &longs;eu lapide areno&longs;o poliuntur; <lb/>&longs;ed etiam metalla: cotibus enim ferrum atteri & pulvere &longs;mi<lb/>ri levigari con&longs;tat. </s><s>Verùm hæc in&longs;uper limam &longs;entiunt: <lb/>quòd gemmis non convenit. </s><s>Tamet&longs;i dicat Plinius nobili<lb/>um gemmarum &longs;oli Topazio id accidere: reliquas verò coti<lb/>bus Naxijs poliri. </s><s>Quod quidem de politurâ rudiori & incho<lb/>atâ intelligendum: <expan abbr="neq;">neque</expan> enim aut reliquas gemmas cotibus: <lb/>aut topazium limâ perfici potui&longs;&longs;e credendum. </s><s>No&longs;tratem <lb/><expan abbr="quoq;">quoque</expan> topazium licet molliorem reliquis gemmis, limam re-

<pb xlink:href="063/01/141.jpg"/>quæ & calorem ex illo motu na&longs;centem, quo corpora tene<lb/>re&longs;cunt, magisq, fragilia fiunt, obtundit. </s><s>Vnde adamantes, qui<lb/>bus gemmæ &longs;olidiores poliuntur, ex illâ velocitate motûs &longs;pe<lb/>ciem carbonis igniti a&longs;&longs;umunt. </s><s>Differentia autem plagæ fit <lb/>pro ratione arenularum: cra&longs;&longs;iores enim & magis duræ ma<lb/>iora auferunt &longs;egmenta. </s><s><expan abbr="Itaq;">Itaque</expan> gemmas rudiores, <expan abbr="multúmq;">multúmque</expan> <lb/>a&longs;peritatis habentes priùs &longs;axis arenulatis, quæ molis circum<lb/>aguntur, affricantes, illâ attritione complanant: inde lapide <lb/>&longs;miri in farinam trito poliunt: & magis &longs;ubtili eiu&longs;dem polline <lb/>levigantes, demum perfectionem terrâ tripolitanâ inducunt. </s><lb/><s>Vitra tamen quia molliora, calce &longs;tanni levigantur. </s><lb/><s>Nec differt illarum &longs;ectio per &longs;erram æream edentulam facta, <lb/>lenti&longs;&longs;imo tractu arenulis interfu&longs;is radente: pro <expan abbr="quar&utilde;">quarum</expan> diver&longs;i<lb/>tate mutatur <expan abbr="quoq;">quoque</expan> vulneris amplitudo. </s><s>Nam cra&longs;&longs;ior arena, <lb/>inquit Plinins, laxioribus &longs;egmentis terit, & plus erodit mar<lb/>moris, <expan abbr="maiú&longs;q;">maiú&longs;que</expan> opus &longs;cabritia polituræ relinquit. </s><s>Ita &longs;ectæ atte<lb/>nuantur cru&longs;tæ. </s><s>Duplex ergo incommodum ab arenâ cra&longs;&longs;io<lb/>re: nam & plus decedit gemmis à plagâ latiore: & &longs;uperficies <lb/>a&longs;pera maiorem in poliendo laborem exigit. </s><s><expan abbr="Itaq;">Itaque</expan> olim <expan abbr="u&longs;q;">u&longs;que</expan> <lb/>ad Æthiopas, & Indos arena petebatur: quarum Æthiopica <lb/>mollior, <expan abbr="nullâq;">nullâque</expan> &longs;cabritie &longs;ecans. </s><s>Nunc verò lapis &longs;miri & <lb/>terra tripolitana in u&longs;um polituræ &longs;ucce&longs;&longs;it. </s><s><expan abbr="Neq;">Neque</expan> &longs;olum gem<lb/>mæ, marmora, & vitrum arenâ, &longs;eu lapide areno&longs;o poliuntur; <lb/>&longs;ed etiam metalla: cotibus enim ferrum atteri & pulvere &longs;mi<lb/>ri levigari con&longs;tat. </s><s>Verùm hæc in&longs;uper limam &longs;entiunt: <lb/>quòd gemmis non convenit. </s><s>Tamet&longs;i dicat Plinius nobili<lb/>um gemmarum &longs;oli Topazio id accidere: reliquas verò coti<lb/>bus Naxijs poliri. </s><s>Quod quidem de politurâ rudiori & incho<lb/>atâ intelligendum: <expan abbr="neq;">neque</expan> enim aut reliquas gemmas cotibus: <lb/>aut topazium limâ perfici potui&longs;&longs;e credendum. </s><s>No&longs;tratem <lb/><expan abbr="quoq;">quoque</expan> topazium licet molliorem reliquis gemmis, limam re-

<pb xlink:href="063/01/142.jpg"/>&longs;puere experientia docet. </s><s>Fuerit ergo alterius generis Plinij <lb/>gemma à no&longs;trâ: quam in&longs;uo genere virentem, <expan abbr="eiu&longs;q;">eiu&longs;que</expan> <lb/>&longs;imilitudinem, ad porri &longs;uccum dirigi te&longs;tatur: cùm <lb/>no&longs;tra &longs;it coloris aurei. </s><s>Motus, quem lima inducit, e&longs;t <lb/>compo&longs;itus ab inci&longs;ione cancellatâ & <foreign lang="greek">xla/te<gap/></foreign>. </s><s>Nam &longs;ulci præ<lb/>tenues inci&longs;i ab a&longs;peritate tra&longs;versâ eiu&longs;dem limæ raduntur. </s><lb/><s>Maior ergo durities nobilioribus gemmis ine&longs;t, cuiu&longs;modi a<lb/>damas, calcedonius, &longs;apphyrus, heliotropia, rubinus: quæ <expan abbr="neq;">neque</expan> <lb/>ferro incidi, <expan abbr="neq;">neque</expan> limâ radi &longs;u&longs;tinent: quam tamen &longs;entiunt <lb/>marmora, lapides, vitrum, & gemmæ ignobiliores. A cotibus <lb/>verò hæc univer&longs;a poliuntur: propterea quòd &longs;uperficiem <lb/>habeant cotes &longs;cabram & areno&longs;am: quæ &longs;i polita, <expan abbr="miniméq;">miniméque</expan> <lb/>friabilis e&longs;&longs;ed, haud quaquam attererentur. </s><s>Mutuâ ergo <lb/>affrictone arenulæ coacervantur: quarum ab&longs;ce&longs;&longs;u minui <lb/>cotes, & demum longo u&longs;u ab&longs;umi con&longs;tat. </s><s>Saxa verò duri<lb/>ora, quia atteri non valent, <expan abbr="neq;">neque</expan> u&longs;um cotis habent. </s><s>Sed <lb/>quæ&longs;tio hic e&longs;t: quamobrem cotes Naxiæ, & quæ nobis &longs;unt in <lb/>u&longs;u, aquâ; Creticæ verò & Laconicæ, ut Plinius te&longs;tatur, oleo <lb/>temperentur: an eiu&longs;modi cotes naturam habent olei, &longs;eu <lb/>bituminis pinguedinem continentes aquæ incommi&longs;cibilem? <lb/>ine&longs;&longs;e enim quibu&longs;dam lapidibus &longs;uccum pinguem & oleo&longs;um <lb/>con&longs;tat exinflammatione. </s><s>Lapis <expan abbr="quoq;">quoque</expan> nephriticus, quem <lb/>I&longs;adam vocant, multùm pingue&longs;cit inter poliendum: quan<lb/>quam huius pinguedo non oleo&longs;a, &longs;ed quale gummi, aquæ <lb/>commi&longs;cetur. </s><s>At quomodo ergo cotes Ciliciæ, eodem Plinio <lb/>te&longs;te, oleo & aquâ pollent: an <expan abbr="utramq;">utramque</expan> naturam eo modo <lb/>permi&longs;tam habent, quo &longs;migma? quod & pingue in &longs;e tra<lb/>hit, & aquâ eluitur. </s><s>Ita cotes ton&longs;trinarum humore non quo<lb/>uis &longs;ed vi&longs;co&longs;o, cuiu&longs;modi &longs;putum, proficiunt. </s><s>Aquas autem <lb/>in Italiâ repertas, aciem trahentes acerrimo &longs;en&longs;u, minerales <lb/>fui&longs;le credo, eiu&longs;dem naturæ cum aquâ forti. </s><s>Magis tamen

<pb xlink:href="063/01/143.jpg"/>mirandum, quod tradit Ferdinandus Corte&longs;ius, in Mexico e&longs;&longs;e <lb/>lapidem coloris flavi; ex quo novaculæ fiant acuti&longs;&longs;imæ: quæ <lb/>non à ferro, aut cote, &longs;ed ex aquâ illam aciem trahant. </s><lb/><s>Videtur autem hæc proprietas innuere huius cognationem <lb/>cum aquâ; <expan abbr="e&longs;&longs;éq;">e&longs;&longs;éque</expan> veluti glaciem ex aquâ concretam: à quâ <lb/>rur&longs;um atteratur & liquefiat: mox tamen ab aëre eo modo, <lb/>quo ovorum cortices, indurari. A motibus iam dictis differt <lb/>terebratio & perforatio: <expan abbr="fitq;">fitque</expan> duobus modis. </s><s>Vt cùm cavi<lb/>tas inducitur <expan abbr="ab&longs;q;">ab&longs;que</expan> deperditione alicuius particulæ: & cùm <lb/>partes ab illâ cavitate excluduntur. </s><s>Et primo quidem modo <lb/>cavitas fit per compre&longs;&longs;ionem: quam &longs;ola <foreign lang="greek">pies a\</foreign> admittunt, cu<lb/>iu&longs;modi metalla & ligna: nequaquam verò <foreign lang="greek">ta\ qzau<gap/>a\</foreign> at gem<lb/>mæ, lapides, vitra. </s><s>Cùm deperditione verò &longs;ub&longs;tantiæ & hæc <lb/>& reliqua omnia cavantur: licet non uno modo omnia. </s><lb/><s>Nam gemmæ quidem & vitra non ni&longs;i politurâ, <expan abbr="&longs;en&longs;imq;">&longs;en&longs;imque</expan> ra<lb/>dendo perforantur: terebratione verò ligna, metalla, o&longs;&longs;a. </s><lb/><s>Et &longs;icuti terebra figurâ à &longs;e differunt; ita etiam modus perfo<lb/>randi. </s><s>Alia enim circulo; alia formâ &longs;emilunari terminan<lb/>tur: alia cochleatim &longs;triata, ab acuto &longs;en&longs;im augentur & late<lb/>&longs;cunt. </s><s><expan abbr="Atq;">Atque</expan> hæc quidem à perforatione incipiendo <foreign lang="greek">sxi/sei x<gap/>/ <lb/>xla/sei</foreign> terminant motum. </s><s>Dum enim cochlea circum acta <lb/>in partem compre&longs;&longs;am vulnus agit, & quæ à tergo &longs;equitur <lb/>helix, ambit latiore plagâ; in tenues & friabiles lamellas eâ <lb/>ratione &longs;cobinatur helicoides, à plagâ inci&longs;us conus: <expan abbr="eoq;">eoque</expan> in <lb/>helicem cavam recepto terebratio procedit, <expan abbr="quou&longs;q;">quou&longs;que</expan> cochlea <lb/>repleta &longs;cobe, educi & expurgari debeat. </s><s>Videtur autem hic <lb/>ratio vectis intervenire: cuius hypomochlium in centro mo<lb/>tûs: extrema verò &longs;unt circelli &longs;en&longs;im aucti & in conum late<lb/>&longs;centes. </s><s>Verùm huiu&longs;modi terebella &longs;uperficiem, quæ am<lb/>bit plagam, minùs æqualem relinquunt: calorem verò ob <lb/>multiplicem motum adaugent. </s><s><expan abbr="Itaq;">Itaque</expan> minùs apta cranio per-

<pb xlink:href="063/01/144.jpg"/>forando: ne huius medulla nimiùm exæ&longs;tuet. </s><s>Quæ autem <lb/>circulo finiunt: quia unâ inci&longs;ione auferunt quidquid inclu<lb/>ditur illo circulo, <expan abbr="unóq;">unóque</expan> motu &longs;implici peragunt inci&longs;ionem; <lb/>in hunc u&longs;um veniunt. </s><s>Nam cùm in gyrum agitur hic cir<lb/>culus; <expan abbr="unaquæq;">unaquæque</expan> particula incidit: & cùm aliæ eiu&longs;dem rati<lb/>onis &longs;equantur; vulnus continuò fit maius: <expan abbr="atq;">atque</expan> eò magis, <lb/>quo <foreign lang="greek">qli/yis</foreign> &longs;eu compre&longs;&longs;io maior, motus autem velocior. </s><lb/><s>Differt ab his terebellum, quo metalla perforantur. </s><s>Stylus e<lb/>nim <foreign lang="greek">amfi/<gap/>zus</foreign> cylindro infixus veluti torno circumagitur, non <lb/>&longs;ine compre&longs;&longs;ione ad corpus terebrandum. </s><s>Qui motus <lb/>inci&longs;ione perficitur: <expan abbr="duritiémq;">duritiémque</expan> metalli &longs;uperat ob <lb/>illam velocitatem. </s>

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