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Colored diff for /texts/archimedes/xml/fabri_tract_026_la_1646.xml between version 1.22 and 1.23

version 1.22, 2007/02/13 18:42:20

version 1.23, 2007/02/14 17:57:29

Line 16320

<s id="N26355">quod autem pennis maximè re&longs;i&longs;tat aër, patet <lb/>ex auium volatu; </s>

<s id="N2635B">imò ex ip&longs;o plumarum de&longs;cen&longs;u; </s>

<s id="N2635F">hinc pennæ illæ, qui<lb/>bus ornantur equitum pilei, &longs;emper à tergo &longs;equuntur currentem equi<lb/>tem; </s>

<s id="N26367">idem dico de fa&longs;ciis illis tran&longs;uer&longs;ariis<gap/> quibus iunguntur equites; <lb/>idem de militaribus &longs;ignis, &longs;eu vexillis. </s>

<s id="N26367">idem dico de fa&longs;ciis illis tran&longs;uer&longs;ariis, quibus iunguntur equites; <lb/>idem de militaribus &longs;ignis, &longs;eu vexillis. </s>

<s id="N26371">Tertiò, hinc ratio motus recti calami, quia, cùm &longs;emper præeat, <lb/><expan abbr="e&utilde;dem">eundem</expan> &longs;itum &longs;eruat, penna&longs;que ip&longs;as qua&longs;i reluctantes trahit, &longs;untque <lb/>ip&longs;æ ad in&longs;tar claui, qui puppim regit. </s>

Line 16363

<s id="N26411">Vndecimò, ita pennæ aptari debent, vt &longs;en&longs;im inflexæ à radice DE <lb/>ver&longs;us apices BC afflatum aëris diuer&longs;um excipiant, & di&longs;&longs;imilem: vnde <lb/>accidit, vt partes ip&longs;æ, quæ retardantur, & maiore vi pollent in vertigi<lb/>nem agantur, in eam &longs;cilicet partem, in quam aliqua inclinatio conducit <lb/>&longs;ic globus retentus à corpore oppo&longs;ito in orbem agitur propter rationem <lb/>prædictam, ne ille impetus &longs;it fru&longs;trà, qui adhuc &longs;upere&longs;t. </s>

<s id="N2641F">Hinc vides <lb/>motum orbis non imprimi calamo à pennis, &longs;ed pennis à calamo; </s>

<s id="N26425">qui <lb/>cùm ab illis retardetur, ne aliquid impetus &longs;it fru&longs;trà, &longs;upplet motu cir<lb/>culari, quod recto difficiliori propter re&longs;i&longs;tentiam orbis con&longs;cqui non <lb/>pote&longs;t; </s>

<s id="N2642F">determinatur quidem motus circularis in talem partem ab ip&longs;a <lb/>pennarum deflexione; </s>

<s id="N26435">non tamen imprimitur: </s>

<s id="N26439">hinc &longs;i fortè in via pen<lb/>næ ex &longs;ua theca decidant, calamus ip&longs;e &longs;ine nouo impul&longs;u longiùs &longs;pa<lb/>tium conficito; tribuit enim motui recto non impedito, quod circulari, <lb/>vel &longs;pirali, &longs;i pennæ ade&longs;&longs;ent tribueret. </s>

<s id="N26445">Duodecimò, &longs;i pennæ contractiores &longs;unt, & angulum acutiorem fa<lb/>ciant, calamus velociùs mauetur motu axis; </s>

<s id="N26445">Duodecimò, &longs;i pennæ contractiores &longs;unt, & angulum acutiorem fa<lb/>ciant, calamus velociùs mouetur motu axis; </s>

<s id="N2644B">ratio e&longs;t, quia re&longs;i&longs;tentia mi-<pb pagenum="360" xlink:href="026/01/394.jpg"/>nùs retardat; </s>

<s id="N26454">&longs;unt enim pauciores partes, quæ valde obliquè cadunt: </s>

<s id="N26458"><lb/>hinc minor e&longs;t appulfus, quod clarum e&longs;t; hinc, vt calamus velociùs per<lb/>gat, con&longs;tringuntur pennæ. </s>

<s id="N26458"><lb/>hinc minor e&longs;t appul&longs;us, quod clarum e&longs;t; hinc, vt calamus velociùs per<lb/>gat, con&longs;tringuntur pennæ. </s>

<s id="N26461">Decimotertiò, &longs;i contractiores &longs;unt, & rectè compo&longs;itæ, cum illa &longs;cili<lb/>cet inflexione, <expan abbr="eoq;">eoque</expan> &longs;itu, de quo n.11.non modò velocior erit motus axis, <lb/>&longs;ed etiam motus orbis; </s>

Line 16395

<s id="N264A8">Decimo&longs;eptimò, &longs;i proiicitur &longs;ur&longs;um, de&longs;cendatque deor&longs;um rectà, e&longs;t <lb/>motus mixtus ex recto & circulari; </s>

<s id="N264AE">&longs;i verò proiiciatur per horizontalem, <lb/>vel inclinatam, e&longs;t motus mixtus ex duobus rectis & circulari, vt con<lb/>&longs;tat; </s>

<s id="N264B6">ex quo motu fit linea mixta ex Parabola & Helice; </s>

<s id="N264BA">&longs;it enim cylin<lb/>drus CH, cuius motus &longs;piralis &longs;it CEFGT mixtus ex recto CT, & cir<lb/>culari orbis CD; &longs;it etiam mixtus LTQ ex accelerato LM, & æquabili <lb/><expan abbr="Mq;">Mque</expan> certè &longs;i addatur LQ circulus &longs;eu &longs;pira CEF, &c. </s>

<s id="N264BA">&longs;it enim cylin<lb/>drus CH, cuius motus &longs;piralis &longs;it CEFGT mixtus ex recto CT, & cir<lb/>culari orbis CD; &longs;it etiam mixtus LTQ ex accelerato LM, & æquabili <lb/>MQ certè &longs;i addatur LQ circulus &longs;eu &longs;pira CEF, &c. </s>

<s id="N264C7">&longs;itque RC æqua<lb/>lis IE, & VT æqualis NG, habebitur &longs;pira mixta <expan abbr="LCSVq.">LCSVque</expan> </s>

<s id="N264C7">&longs;itque RC æqua<lb/>lis IE, & VT æqualis NG, habebitur &longs;pira mixta LCSVQ </s>

<s id="N264D2">Decimooctauò, &longs;i pennæ latiores &longs;unt, &longs;eu maiorem habent &longs;uper&longs;i<lb/>ciem, minùs aptæ &longs;unt ad vtrumque motum, &longs;cllicet axis, & centri; quia <lb/>aër plùs æquo re&longs;i&longs;tit, nam plures illius pelluntur partes. </s>

<s id="N264D2">Decimooctauò, &longs;i pennæ latiores &longs;unt, &longs;eu maiorem habent &longs;uperfi<lb/>ciem, minùs aptæ &longs;unt ad vtrumque motum, &longs;cilicet axis, & centri; quia <lb/>aër plùs æquo re&longs;i&longs;tit, nam plures illius pelluntur partes. </s>

<s id="N264DC">Decimononò, &longs;i verò contractiores &longs;unt, etiam minùs aptæ videntur: <lb/>quippe aëra facilè diuidunt. </s>

Line 16469

<s id="N265CF">igitur <lb/>e&longs;t tantùm motus axis; vbi tamen vibratur per horizontalem, vel incli<lb/>natam, mouetur motu mixto ex duobus rectis, de quo iam aliàs. </s>

<s id="N265D9">Quintò, huc reuoca &longs;egittas, quæ tribus in&longs;tructæ pennis <expan abbr="e&utilde;dem">eundem</expan> <lb/>&longs;emper retinent &longs;itum in motu, vt ferrum &longs;eu mucro præeat; vnde vides <lb/>cumdem &longs;emper &longs;equi effectum, &longs;iue tres &longs;int alæ, &longs;iue quatuor. </s>

<s id="N265D9">Quintò, huc reuoca &longs;agittas, quæ tribus in&longs;tructæ pennis <expan abbr="e&utilde;dem">eundem</expan> <lb/>&longs;emper retinent &longs;itum in motu, vt ferrum &longs;eu mucro præeat; vnde vides <lb/>eumdem &longs;emper &longs;equi effectum, &longs;iue tres &longs;int alæ, &longs;iue quatuor. </s>

<s id="N265E7">Sextò, huc reuoca minima illa &longs;picula &longs;picâ in&longs;tructa, quæ per tubum <lb/>pneumaticum pueri flatu eiaculantur; </s>

Line 16528

<s id="N266AC">haud dubiè mouebitur per AD; igitur hic motus e&longs;t &longs;piralis, nec e&longs;t <lb/>alia difficultas. </s>

<s id="N266B4"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 25.<emph.end type="center"/></s>

<s id="N266B4"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 24.<emph.end type="center"/></s>

<s id="N266C2"><emph type="italics"/>Quando voluitur funis circa cylindrum, vel axem<gap/> mouetur motu <lb/>&longs;pirali, &longs;ed diuer&longs;o à prioribus<emph.end type="italics"/>; </s>

<s id="N266C2"><emph type="italics"/>Quando voluitur funis circa cylindrum, vel axem, mouetur motu <lb/>&longs;pirali, &longs;ed diuer&longs;o à prioribus<emph.end type="italics"/>; </s>

<s id="N266CF">&longs;unt enim veræ &longs;piræ ad in&longs;tar &longs;apien<lb/>tia in diuer&longs;a volumina contorti; </s>

<s id="N266D5">&longs;ic funis circa digitum fæpè <lb/>rotatur.; </s>

<s id="N266DB">e&longs;t enim motus mixtus ex diuer&longs;is circul<gap/>ilius: </s>

<s id="N266DB">e&longs;t enim motus mixtus ex diuer&longs;is circularibus: </s>

<s id="N266E1">quippè <pb pagenum="363" xlink:href="026/01/397.jpg"/>in &longs;ingulis punctis e&longs;t diuer&longs;a determinatio ad nouum circulum, quia <lb/>e&longs;t nouus radius, quia continuò radius huius vertiginis imminuitur; <lb/>porrò duobus modis pote&longs;t funis circa axem vel cylindrum conuolui. </s>

<s id="N266EE"><lb/>Primò, &longs;i &longs;emper circa <expan abbr="e&utilde;dem">eundem</expan> cylindri circulum voluatur; </s>

<s id="N266F7">tunc autem <lb/>facit veras &longs;piras, vt vides in A. Secundò, &longs;i circa diuer&longs;os eiu&longs;dem axis <lb/>circulos, vel potius diuer&longs;a eiu&longs;dem axis puncta voluatur, & hic e&longs;t mo<lb/>tus &longs;piralis conicus, vt vides in cono FDE; </s>

Line 16545

<s id="N26717"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 25.<emph.end type="center"/></s>

<s id="N26725"><emph type="italics"/>Similiter po&longs;&longs;unt explicari motus &longs;pirales &longs;pharici, quos habes in<emph.end type="italics"/>; </s>

<s id="N26725"><emph type="italics"/>Similiter po&longs;&longs;unt explicari motus &longs;pirales &longs;phærici, quos habes in<emph.end type="italics"/>; </s>

<s id="N2672E">hic au<lb/>tem motus duplex e&longs;t; </s>

<s id="N26734">primus mixtus ex recto per axem KL, quo totus <lb/>globus mouetur, & ex circulari circa axem KL, qui reuerâ e&longs;t &longs;piralis <lb/>cylindricus; </s>

<s id="N2673C">&longs;ecundus mixtus ex duobus circularibus, &longs;cilicet ex circulari <lb/>circa axem KL, & circulari per arcum IL, v.g. &longs;i punctum eo tempore <lb/>voluatur circa axem KL per arcum IO, quo &longs;ertur per arcum IL vnde <lb/>habes in hac figura tres motus &longs;pirales, quorum &longs;inguli con&longs;tant ex circu<lb/>lari circa axem KL; </s>

<s id="N2673C">&longs;ecundus mixtus ex duobus circularibus, &longs;cilicet ex circulari <lb/>circa axem KL, & circulari per arcum IL, v.g. &longs;i punctum eo tempore <lb/>voluatur circa axem KL per arcum IO, quo fertur per arcum IL vnde <lb/>habes in hac figura tres motus &longs;pirales, quorum &longs;inguli con&longs;tant ex circu<lb/>lari circa axem KL; </s>

<s id="N2674A">&longs;ed deinde con&longs;tant &longs;inguli ex &longs;ingulis motibus di<lb/>uer&longs;is, &longs;cilicet &longs;piralis cylindricus ex motu puncti I v.g. per rectam IN <lb/>parallelam KL; </s>

<s id="N26754">&longs;piralis conicus per rectam IL, & &longs;piralis &longs;phæricus <lb/>per arcum IPL; </s>

<s id="N2675A">hinc duo primi con&longs;tant ex circulari, & recto; rertius <lb/>verò ex duobus circularibus. </s>

<s id="N2675A">hinc duo primi con&longs;tant ex circulari, & recto; certius <lb/>verò ex duobus circularibus. </s>

<s id="N26762">Denique pote&longs;t e&longs;&longs;e &longs;piralis concoidicus qualem vides in i&longs;que du<lb/>plex; </s>

Line 16570

<s id="N267A6">neque hic motus <lb/>diuer&longs;us e&longs;t à motu rotæ in plano, &longs;it enim taleola centro A, circa quod <lb/>vertitur dum centrum A repit motu recto per rectam AD, perinde &longs;e <lb/>habet, atque &longs;i rota in plano BE vel CF rotaretur; </s>

<s id="N267B0">immò pote&longs;t tabella <lb/>GK ita moueri, vt eius centrum A moueatur per AD, dum reliquæ par<lb/>tes circa centrum A voluuntur; </s>

<s id="N267B8">tunc enim punctum H codem motu <lb/>moueretur, quo alia puncta peripheriæ huius rotæ; </s>

<s id="N267BE">punctum verò I eo <lb/>modo quo I in radio BA, dum rota mouetur, quod &longs;uprà &longs;usèexplicui-<pb pagenum="364" xlink:href="026/01/398.jpg"/>mus; denique ita moueri pote&longs;t taleola, vt primò B moueatur motu or<lb/>bis ver&longs;us. </s>

<s id="N267BE">punctum verò I eo <lb/>modo quo I in radio BA, dum rota mouetur, quod &longs;uprà fusè explicui-<pb pagenum="364" xlink:href="026/01/398.jpg"/>mus; denique ita moueri pote&longs;t taleola, vt primò B moueatur motu or<lb/>bis ver&longs;us. </s>

<s id="N267CB">Secundò, ver&longs;us K; Tertiò, vt motus centri &longs;it maior vel minor <lb/>motu orbis. </s>

<s id="N267D0">Quartò, vt &longs;it æqualis. </s>

<s id="N267D5">Denique, ne omittam motum illum, quo clauis &longs;eu planum &longs;olidum <lb/>in læuigata men&longs;a mouetur, dico mixtum e&longs;&longs;e ex recto alicuius centri & <lb/>circularis orbis; </s>

<s id="N267DD">&longs;it enim v.g.baculus AD, qui ita repat in plano læui<lb/>gato vt altera eius extremitas fortiùs impellatur, mouebitur motu mixto <lb/>ex circulari circa centrum C per Th.55.l.7. & recto orbis circa C; </s>

<s id="N267E5">de<lb/>&longs;cribent autem duæ extreinitates A & D lineas rotatiles diuer&longs;as; hic au<lb/>tem motus diuer&longs;us erit pro diuer&longs;a coniugatione motus orbis, & mo<lb/>tus centri, cùm hic po&longs;&longs;it e&longs;&longs;e vel maior, vel minor motu orbis, vel <lb/>æqualis, </s>

<s id="N267E5">de<lb/>&longs;cribent autem duæ extremitates A & D lineas rotatiles diuer&longs;as; hic au<lb/>tem motus diuer&longs;us erit pro diuer&longs;a coniugatione motus orbis, & mo<lb/>tus centri, cùm hic po&longs;&longs;it e&longs;&longs;e vel maior, vel minor motu orbis, vel <lb/>æqualis, </s>

<s id="N267F3"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 27.<emph.end type="center"/></s>

Line 16634

<s id="N268C8">Decimò, hinc quod iucundum e&longs;&longs;et, &longs;i huiu&longs;modi globum in datum <lb/>&longs;copum proijceres; </s>

<s id="N268CE">haud dubiè alium feriret; </s>

<s id="N268D2">igitur vt &longs;copum &longs;ignatum <lb/>tangas, aliò collimare debes; </s>

<s id="N268D8">porrò linea huius motus eadem e&longs;t, qu<gap/><lb/>e&longs;&longs;et, &longs;i globus rotaretur in linea parallela lineæ, quam de&longs;cribit cen<lb/>trum; </s>

<s id="N268D8">porrò linea huius motus eadem e&longs;t, quæ <lb/>e&longs;&longs;et, &longs;i globus rotaretur in linea parallela lineæ, quam de&longs;cribit cen<lb/>trum; </s>

<s id="N268E1">quæ vel e&longs;t &longs;pira, vel circulus, vel alia curua, iuxta diuer&longs;am con<lb/>iugationem notuum; illa autem facilè haberi pote&longs;t ex dictis &longs;uprà. </s>

<s id="N268E1">quæ vel e&longs;t &longs;pira, vel circulus, vel alia curua, iuxta diuer&longs;am con<lb/>iugationem motum; illa autem facilè haberi pote&longs;t ex dictis &longs;uprà. </s>

<s id="N268E9">Vndecimo, &longs;i in plano recto ita rotetur cylindrus, vt &longs;inguli circuli <lb/>paralleli ba&longs;i rotentur æqualiter, &longs;inguli circuli mouentur motu mixto <lb/>ex recto centri, & circulari orbis, e&longs;tque hic motus &longs;imilis motui rotæ <lb/>in plano recto, de quo &longs;uprà. </s>

Line 16658

<s id="N2692F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s>

<s id="N2693D"><emph type="italics"/>Morus di&longs;ci facilè explicasi potest;<emph.end type="italics"/>; </s>

<s id="N2693D"><emph type="italics"/>Morus di&longs;ci facilè explicari potest;<emph.end type="italics"/>; </s>

<s id="N26946">e&longs;t enim planum circulare, cuius <pb pagenum="366" xlink:href="026/01/400.jpg"/>centrum de&longs;cribit ferè Parabolam; </s>

<s id="N2694F">vnde eius motus e&longs;t mixtus ex para<lb/>bolico centri, & circulari orbis in circulo horizontali; </s>

<s id="N26955">igitur motus cen<lb/>tri con&longs;tat ex duobus rectis, &longs;cilicet ex violento, & naturali deor&longs;um; <lb/>porrò e&longs;t idem motus qui e&longs;&longs;et, &longs;i circulus verticali parallelus rotaretur <lb/>in linea parabolica de&longs;cripta in plano horizontali. </s>

Line 16667

<s id="N26961">Ob&longs;eruo autem primò motum orbis di&longs;ci e&longs;&longs;e po&longs;&longs;e maiorem motu <lb/>centri, vel minorem, vel ip&longs;i æqualem; quod quomodo fieri po&longs;&longs;it, fusè <lb/>&longs;uprà explicuimus. </s>

<s id="N2696B">Secundò, &longs;i altera eius portio &longs;it grauior motus orbis, non e&longs;t idem <lb/>cum centro di&longs;ci, vt patet; præualct enim portio grauior, &longs;ed propiùs <lb/>accedit ad portionem grauiorem. </s>

<s id="N2696B">Secundò, &longs;i altera eius portio &longs;it grauior motus orbis, non e&longs;t idem <lb/>cum centro di&longs;ci, vt patet; præualet enim portio grauior, &longs;ed propiùs <lb/>accedit ad portionem grauiorem. </s>

<s id="N26975">Tertiò, hinc cùm di&longs;cus cadit in terram, re&longs;itit altera eius portio, &longs;ci<lb/>licet leuior; </s>

Line 16687

<s id="N269AE">Primò, &longs;it ha&longs;ta in plano horizontali BG; &longs;i motu &longs;implici attollatur <lb/>extremitas B, mouebitur per arcum BA circa centrum G. </s>

<s id="N269B7">Secundò, &longs;i non modò attollatur, &longs;ed euibretur cum aliquo vi&longs;u, ele<lb/>uata &longs;cilicct tantillùm extremitate G, mouebitur vtraque extremitas; <lb/>non certè circa F, &longs;ed circa E, vel D, ita vt GE &longs;it 1/4 AG per Th.55.l.7. </s>

<s id="N269B7">Secundò, &longs;i non modò attollatur, &longs;ed euibretur cum aliquo vi&longs;u, ele<lb/>uata &longs;cilicet tantillùm extremitate G, mouebitur vtraque extremitas; <lb/>non certè circa F, &longs;ed circa E, vel D, ita vt GE &longs;it 1/4 AG per Th.55.l.7. </s>

<s id="N269C1">Tertiò, &longs;i extremitas G non adducatur &longs;ed B per aliquam Tangentem <lb/>arcus BA euibretur pro diuer&longs;a Tangente diuer&longs;us erit motus, &longs;i v.g.per <lb/>Tangentem BH punctum D a&longs;&longs;urget per DE, igitur G redibit in C, B <lb/>verò &longs;patium compo&longs;itum ex tota v. g. & eius &longs;ubdupla BC; </s>

Line 16705

<s id="N26A00">&longs;i denique minùs adducatur, por<lb/>rigi manum oportet, vt extremitates G excipiat: porrò hic motus e&longs;t <lb/>mixtus ex tribus, &longs;cilicet ex duobus rectis centri, & circulari orbis. </s>

<s id="N26A0A">Sextò, ita poterit adduci centrum D, & &longs;imul euibrari B, vt ha&longs;tæ me<lb/>dium C facto &longs;emicircuitu in dextram crectam cadat, quadretque ad in<lb/>&longs;tar iaculi mi&longs;&longs;ilis, cuius mucro deor&longs;um vergens prædæ plagam inten<lb/>tat; hoc ludi genus o&longs;tentationem Hi&longs;panicam vulgò vocant. </s>

<s id="N26A0A">Sextò, ita poterit adduci centrum D, & &longs;imul euibrari B, vt ha&longs;tæ me<lb/>dium C facto &longs;emicircuitu in dextram erectam cadat, quadretque ad in<lb/>&longs;tar iaculi mi&longs;&longs;ilis, cuius mucro deor&longs;um vergens prædæ plagam inten<lb/>tat; hoc ludi genus o&longs;tentationem Hi&longs;panicam vulgò vocant. </s>

<s id="N26A1A">Septimò, erigitur ha&longs;ta, &longs;i extremitas G tantillùm elcuata cum altera <lb/>oppo&longs;ita B, tùm &longs;tatim B deprimatur; </s>

<s id="N26A1A">Septimò, erigitur ha&longs;ta, &longs;i extremitas G tantillùm eleuata cum altera <lb/>oppo&longs;ita B, tùm &longs;tatim B deprimatur; </s>

<s id="N26A20">vnde accidit ip&longs;am G noua acce&longs;<lb/>&longs;ione impetus &longs;ur&longs;um promoueri; </s>

<s id="N26A26">quippe &longs;i deprimatur B circa aliquod <lb/>centrum, attollitur G; </s>

<s id="N26A2C">adde aliquam refluxionem ip&longs;ius G, quæ valdè <lb/>initio remouetur à manu, vt cum deinde adducitur, maiorem faciat ar<lb/>cum; </s>

Line 16720

<s id="N26A44">Octauò, duobus aliis modis erigitur ha&longs;ta è &longs;itu horizontali. </s>

<s id="N26A49">Primò, conuer&longs;o introrium brachio; </s>

<s id="N26A49">Primò, conuer&longs;o intror&longs;um brachio; </s>

<s id="N26A4D">eleuatur enim extremitas G. <lb/>& deprimitur illicò B; </s>

<s id="N26A53">vnde minore conatu deinde attollitur; </s>

<s id="N26A57">minus e&longs;t <lb/>enim momentum vectis; </s>

Line 16789

<s id="N26B85">ratio <lb/>huius motus petitur ex eo quod, neque per EF, neque per arcum EG <lb/>mouetur extremitas E; igitur per curuam de vtraque participan<lb/>tem. </s>

<s id="N26B91">Decimooctauò, cum ita proijcitur baculus, vt altera extremitas citíùs <lb/>moueatur quàm alia, &longs;equitur motus mixtus ex recto centri, & circulari <lb/>etbis; </s>

<s id="N26B91">Decimooctauò, cum ita proijcitur baculus, vt altera extremitas citíùs <lb/>moueatur quàm alia, &longs;equitur motus mixtus ex recto centri, & circulari <lb/>orbis; </s>

<s id="N26B99">quia &longs;cilicet illa pars, quæ maiorem impetum habet, qua&longs;i retrò <lb/>agitur ab alia, quæ minorem habet, non quidem motu purè circulari; <lb/>alioqui omninò retineretur ab alia extremitate, &longs;ed alio mixto, quia non <lb/>omninò retinetur. </s>

Line 16812

<s id="N26BF9"><lb/>3&degree;. </s>

<s id="N26BFD">hinc, &longs;i etiam per imum pedem directo ictu verberentur, plùs re&longs;i<lb/>&longs;tunt, quia minor e&longs;t vectis, 4&degree;. </s>

<s id="N26C02">hinc &longs;tatim à recta via globus deflectit, <lb/>5&degree;. </s>

<s id="N26C07">&longs;i obliquè globus feriat trunculum, qua&longs;i lambendo, parùm declinat <lb/>à &longs;uo cur&longs;u, q<gap/>inima e&longs;t re&longs;i&longs;tentia, quía obliquus ictus minimus <lb/>e&longs;t, vt con&longs;tat ex dictis &longs;æpiùs in &longs;uperioribus libris. </s>

<s id="N26C07">&longs;i obliquè globus feriat trunculum, qua&longs;i lambendo, parùm declinat <lb/>à &longs;uo cur&longs;u, quia minima e&longs;t re&longs;i&longs;tentia, quía obliquus ictus minimus <lb/>e&longs;t, vt con&longs;tat ex dictis &longs;æpiùs in &longs;uperioribus libris. </s>

<s id="N26C10">6. cum &longs;ic obliquè <lb/>decutitur trunculus, hic decu&longs;&longs;us deinde alios decutit; </s>

<s id="N26C16">quia ex obliquo <lb/>ictu cra&longs;&longs;ioris pedis agitur in vertiginem circa verticem ad in&longs;tar coni, <lb/>de quo &longs;uprà; & cum maiorem gyrum de&longs;cribit, vix vnquam accidit, vt <lb/>in &longs;atis frequenti &longs;ylua in alium trunculum non incidat, quem etiam <lb/>decutit. </s>

<s id="N26C22">7&degree;. </s>

Line 16849

<s id="N26CEB"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s>

<s id="N26CF9"><emph type="italics"/>Explicari po&longs;&longs;unt omnia ph&oelig;nomena turbinis &longs;en trocbi circumacti<emph.end type="italics"/>: </s>

<s id="N26CF9"><emph type="italics"/>Explicari po&longs;&longs;unt omnia ph&oelig;nomena turbinis &longs;en trochi circumacti<emph.end type="italics"/>: </s>

<s id="N26D02">Tur<lb/>binum puerilium duo &longs;unt genera: primum e&longs;t eorum, qui ferro mu<lb/>niuntur, qui certè diuer&longs;æ &longs;unt figuræ, &longs;phæricæ, conicæ &c. </s>

<s id="N26D0A">communi<lb/>ter tamen fiunt iuxta figuram cordis, vt vides in A. </s>

<s id="N26D10">Secundum e&longs;t eo<lb/>rum, qui ferro carent, quorum &longs;unt etiam diuer&longs;æ figuræ, communior e&longs;t <lb/>conois, vt vides in</s>

Line 16885

<s id="N26D92">&longs;ecundò motus centri, quia eadem lora ad in<lb/>&longs;tar fundæ qua&longs;i trochum explodunt; </s>

<s id="N26D98">&longs;ic plerumque accidit adhiberi lora, <lb/>vt longiùs ligneus orbis proijciatur; </s>

<s id="N26D9E">quippe dum explicantur lora, du<lb/>plex ille motus nece&longs;&longs;ariò imprimitur; </s>

<s id="N26DA4">primus quidem, quia expltcari <lb/>non po&longs;&longs;unt, ni&longs;i trochus circumagatur; </s>

<s id="N26DA4">primus quidem, quia explicari <lb/>non po&longs;&longs;unt, ni&longs;i trochus circumagatur; </s>

<s id="N26DAA">&longs;ecundus verò, quia explicari <lb/>lora non po&longs;&longs;unt ni&longs;i in aliquam partem ferantur, & trochum ip&longs;um tra<lb/>hant, vel &longs;altem impellant; </s>

<s id="N26DB2">adde quod diutiùs manet potentia applicata; <lb/>hinc maior effectus, analogiam habes in funda. </s>

<s id="N26DBA">Nonò, quando turbo ferro in&longs;tructus, cui funiculus aduolutus e&longs;t, re<lb/>tentâ alterà funiculi extremitate, & explicato eodem fudiculo circum<lb/>agitur; </s>

<s id="N26DBA">Nonò, quando turbo ferro in&longs;tructus, cui funiculus aduolutus e&longs;t, re<lb/>tentâ alterà funiculi extremitate, & explicato eodem funiculo circum<lb/>agitur; </s>

<s id="N26DC2">haud dubiè maiore vi pollet hic motus, <expan abbr="durat&qacute;ue">duratque</expan> diù, tùm quie <lb/>funiculus e&longs;t, longior, tùm quia maiore ni&longs;u qua&longs;i euibratur, tùm quia <lb/>diù manet potentia applicata; </s>

<s id="N26DCE">porrò duobus modis explicatur funiculus; </s>

<s id="N26DD2"><lb/>primò enim adducitur, &longs;eu retrahitur, ex quo accidit, vt motus centri <lb/>determinetur in <expan abbr="eãdem">eandem</expan> partem; </s>

Line 16903

<s id="N26DFC"><lb/>ratio e&longs;t, quia circularis axis determinatur à circulari orbis; igitur vter<lb/>que fit in <expan abbr="eãdem">eandem</expan> partem. </s>

<s id="N26E09">Vndecimò, diuer&longs;a &longs;cabrities plani in quo circumagitur turbo mul<lb/>tùm immutat turbinationis modum; tunc enim vel diuer&longs;a plani incli<lb/>natî ratio, vel diuer&longs;æ qua&longs;i fo&longs;&longs;ulæ, vel in&longs;en&longs;ibiles &longs;copuli turbinem eò <lb/>fæpe adigunt, quo impre&longs;&longs;i motus indoles minimè ferret. </s>

<s id="N26E09">Vndecimò, diuer&longs;a &longs;cabrities plani in quo circumagitur turbo mul<lb/>tùm immutat turbinationis modum; tunc enim vel diuer&longs;a plani incli<lb/>natî ratio, vel diuer&longs;æ qua&longs;i fo&longs;&longs;ulæ, vel in&longs;en&longs;ibiles &longs;copuli turbinem eò <lb/>&longs;æpe adigunt, quo impre&longs;&longs;i motus indoles minimè ferret. </s>

<s id="N26E13"><lb/>Duodecimò, licèt imprimatur motus rectus axi per adductionem, vel <lb/>emi&longs;&longs;ionem funiculi, non tamen mouetur axis motu recto; quia hic mo<lb/>tus rectus ab ip&longs;o motu orbis immutatur, ita vt ex vtroque motus fiat <lb/>mixtus, ip&longs;eque adeò axis motu qua&longs;i &longs;pirali, reliquæ verò partes inæ<lb/>quali motu circumagantur. </s>

Line 16918

<s id="N26E5E">&longs;it enim centrum circuli, qui circa alium immobilem conuertitur, <lb/>decurrat circulum duplò maiorem, de&longs;cribit lineam cordis, de qua &longs;uprà, <lb/>&longs;i maiorem duplo (eâ tamen lege vt centrum, & orbis æquali tempore <lb/>&longs;uum circulum decurrant) de&longs;cribitur linea, quæ accedit propiùs ad cir<lb/>culum; </s>

<s id="N26E6A">&longs;i verò circulus centri &longs;it æqualis circulo orbis, habes lineam in <lb/>&longs;uperiore &longs;chemate, quæ geminum <expan abbr="circul&utilde;">circulum</expan> imperfectum præfert, qui eò <lb/>propiùs ad &longs;e inuicem <expan abbr="acced&utilde;t">accedunt</expan>, quo circulus centri minor e&longs;t; </s>

<s id="N26E7A">cùm enim <lb/>nullus e&longs;t omninò <expan abbr="c&etilde;tri">centri</expan> circulus, tunc ambo circuli imperfecti in vnum <lb/><expan abbr="perfect&utilde;">perfectum</expan> coëunt; &longs;i verò circulus centri &longs;it minor duplò, &longs;ed maior æquali, <lb/>minor erit &longs;uperior illa figura EFA, &c. </s>

<s id="N26E8B">donec tandem vbi circulus cen<lb/>tri e&longs;t duplus circuh orbis vnica tantùm figura de&longs;cribatur, &longs;cilicet linea <lb/>cordis. </s>

<s id="N26E8B">donec tandem vbi circulus cen<lb/>tri e&longs;t duplus circuli orbis vnica tantùm figura de&longs;cribatur, &longs;cilicet linea <lb/>cordis. </s>

<s id="N26E92">Sed de his omnibus fusè &longs;uo loco; &longs;unt enim mirificæ harum <lb/>linearum proprietates. </s>

Line 16929

<s id="N26EB4">Decimo&longs;extò, antequam quie&longs;cat turbo, inclinatur, &longs;uo&longs;que orbes agit <lb/>inclinato qua&longs;i corpore, & obliquo axe; </s>

<s id="N26EBA">ratio e&longs;t, quia vel axis &longs;eu ferreus <lb/>mucro tantillùm abe&longs;t à grauitatis centro, vel aliquis plani &longs;eopulus, vel <lb/>decliuis plaga turbinem ip&longs;um inclinat; agit tamen adhuc aliquot obli<lb/>quos gyros propter vim prioris impetus, quæ &longs;en&longs;im à grauitatione tur<lb/>binis frangitur, & tandem omninò &longs;uperatur. </s>

<s id="N26EBA">ratio e&longs;t, quia vel axis &longs;eu ferreus <lb/>mucro tantillùm abe&longs;t à grauitatis centro, vel aliquis plani &longs;copulus, vel <lb/>decliuis plaga turbinem ip&longs;um inclinat; agit tamen adhuc aliquot obli<lb/>quos gyros propter vim prioris impetus, quæ &longs;en&longs;im à grauitatione tur<lb/>binis frangitur, & tandem omninò &longs;uperatur. </s>

<s id="N26EC8">Decimo&longs;eptimò, hinc, vbi terrarum tangit depre&longs;&longs;us turbo, ad in&longs;tar <lb/>rotæ deindæ rotatur; ratio e&longs;t, quia multus adhuc re<gap/>net impetus ad <lb/>motum orbis determinatus, qui vbi tangitur, &longs;olum trochum ip&longs;um cum <lb/>centro ad in&longs;tar rotæ præcipitem agit. </s>

<s id="N26EC8">Decimo&longs;eptimò, hinc, vbi terrarum tangit depre&longs;&longs;us turbo, ad in&longs;tar <lb/>rotæ deindæ rotatur; ratio e&longs;t, quia multus adhuc remanet impetus ad <lb/>motum orbis determinatus, qui vbi tangitur, &longs;olum trochum ip&longs;um cum <lb/>centro ad in&longs;tar rotæ præcipitem agit. </s>

<s id="N26ED6">Decimooctauò, hinc vides naturam maximè gaudere motu recto qui <lb/>paulò ante turbini erecto minimè concedebatur; cur enim in vnam po<lb/>tiùs partem, quàm in aliam? </s>

Line 16955

<s id="N26F24">&longs;it circulus ALK <lb/>M centro E; </s>

<s id="N26F2A">&longs;it alius excentricus ACOD centro B, circa quod mouea<lb/>tur punctum A v.g. motu orbis; </s>

<s id="N26F32">Primò, nulla erit inæqualitàs motus, &longs;ed <lb/>tantùm videbitur e&longs;&longs;e; </s>

<s id="N26F38">nam <expan abbr="punct&utilde;">punctum</expan> A, in quo &longs;it a&longs;trum po&longs;t decurfum <lb/>quadrantem; </s>

<s id="N26F38">nam <expan abbr="punct&utilde;">punctum</expan> A, in quo &longs;it a&longs;trum po&longs;t decur&longs;um <lb/>quadrantem; </s>

<s id="N26F42">videbitur in N; </s>

<s id="N26F46">igitur videbitur tantùm confeci&longs;&longs;e arcum A <lb/>N minorem quadrante; </s>

<s id="N26F4C">hinc motus ab A ad C indicabitur tardior; </s>

Line 16992

<s id="N26FBB"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s>

<s id="N26FC9"><emph type="italics"/>Po&longs;&longs;unt explicari omnia ph&oelig;uomena<emph.end type="italics"/> <emph type="italics"/>Epiclclorum.<emph.end type="italics"/></s>

<s id="N26FC9"><emph type="italics"/>Po&longs;&longs;unt explicari omnia ph&oelig;nomena<emph.end type="italics"/> <emph type="italics"/>Epiciclorum.<emph.end type="italics"/></s>

<s id="N26FD6"> Primò &longs;it circulus H <lb/>BCK centro A, &longs;it epicyclus LIQG, centro G; </s>

<s id="N26FDC">a&longs;&longs;umatur quodlibet <lb/>eius punctum, putà G, quod moueatur motu mixto id e&longs;t, motu centri, <lb/>& motu orbis: po&longs;&longs;unt a&longs;&longs;ignari omnia puncta lineæ huius motus, om<lb/>nes velocitatis proportiones, &c. </s>

Line 17034

<s id="N27080">&longs;imiliter inuenientur alia puncta, quod &longs;uffi<lb/>ciat indica&longs;&longs;e; </s>

<s id="N27086">e&longs;t autem hic motus maximè inæqualis propter ratio<lb/>nem, de qua &longs;uprà: </s>

<s id="N2708C">&longs;ed de his &longs;atis; </s>

<s id="N27090">immò certnm e&longs;t punctum F &longs;uo <lb/>motu prædicto de&longs;cribere perfectum circulum duplum circuli rota<lb/>ti, cuius centrum e&longs;t D crectum in A, nam DH, DF, DK &longs;unt æqua<lb/>les; </s>

<s id="N27090">immò certum e&longs;t punctum F &longs;uo <lb/>motu prædicto de&longs;cribere perfectum circulum duplum circuli rota<lb/>ti, cuius centrum e&longs;t D erectum in A, nam DH, DF, DK &longs;unt æqua<lb/>les; </s>

<s id="N2709A">&longs;i enim circulus tangat in M, punctum F erectum toto arcu FM, <lb/>re&longs;pondebit perpendiculariter puncto O, ita vt OM &longs;it æqualis PB, vel <lb/>HS, vel AN; erigatur autem OR, donec incubet perpendiculariter, <lb/>extat &longs;uper AD erecta in A tota QR, ita OQ &longs;it æqualis AD. </s>

<s id="N270AA">AO e&longs;t æquale quadratis AM, MO; igitur &longs;it quad. </s>

Line 17057

<s id="N270FA"><emph type="center"/>LIBER DECIMVS, <lb/><emph type="italics"/>DE DIVERSIS MOTIONVM, VEL <lb/>imprimendi motus rationibus.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N2710B">HACTENVS explicauimus natutam cau<lb/>&longs;æ formalis motus, ide&longs;t impetus in <lb/>libro primo: proprietates motus natu<lb/>ralis &longs;ecundo: tertio violenti affectio<lb/>nes; </s>

<s id="N2710B">HACTENVS explicauimus naturam cau<lb/>&longs;æ formalis motus, ide&longs;t impetus in <lb/>libro primo: proprietates motus natu<lb/>ralis &longs;ecundo: tertio violenti affectio<lb/>nes; </s>

<s id="N27117">quarto mixti ex pluribus rectis: </s>

<s id="N2711B"><lb/>quinto motum in diuer&longs;is planis con&longs;iderauimus; <lb/>&longs;exto reflexum; &longs;eptimo circularem; octauo fune<lb/>pendulorum vibrationes; nono mixtum ex circulari, <lb/>quæ omnia &longs;pectant, vel ad cau&longs;am formalem, vel <lb/>ad principium intrin&longs;ecum, vel ad modum etiam <lb/>intrin&longs;ecum, vel ad &longs;patium, &c. </s>

<s id="N2712A">iam verò con&longs;i<lb/>deramus diuer&longs;os modos, quibus impetus imprimi <lb/>pote&longs;t; pote&longs;t enim mobile proijci, pelli, trahi, percuti, <lb/>premi, &longs;u&longs;tineri, tornari, &c. </s>

Line 17195

<s id="N273C6">certè deor&longs;um tendunt, motu naturaliter <lb/>accelerato, vnde tandem organum ip&longs;um deor&longs;um &longs;ecum trahunt; &longs;ed <lb/>de his aliàs plura, cum de potentia progre&longs;&longs;iua. </s>

<s id="N273D0">Decimotertiò, quando pondus &longs;n&longs;tinetur à plano immobili, v. g. à <lb/>men&longs;a, non producitur in eo impetus &longs;ur&longs;um à men&longs;a; quia impetus <lb/>producitur tantùm ad extra ab alio impetu, per Th.42. l.1. &longs;ed nullus e&longs;t <lb/>impetus &longs;ur&longs;um in men&longs;a, vt patet. </s>

<s id="N273D0">Decimotertiò, quando pondus &longs;u&longs;tinetur à plano immobili, v. g. à <lb/>men&longs;a, non producitur in eo impetus &longs;ur&longs;um à men&longs;a; quia impetus <lb/>producitur tantùm ad extra ab alio impetu, per Th.42. l.1. &longs;ed nullus e&longs;t <lb/>impetus &longs;ur&longs;um in men&longs;a, vt patet. </s>

<s id="N273E0">Decimoquartò, pondus non producit impetum in ip&longs;a men&longs;a, ni&longs;i vel <lb/>tota men&longs;a, vel aliquæ eius partes moueantur, vel comprimantur, vel <lb/>dilatentur; </s>

Line 17250

<s id="N274DF">&longs;ecundò, qua&longs;i pellendo, nul<lb/>lus impetus producitur per &longs;e in mobili retento à retinente; </s>

<s id="N274E5">quod pro-<pb pagenum="381" xlink:href="026/01/415.jpg"/>batur eodem modo, quo &longs;uprà; </s>

<s id="N274EE">per accidens autem producitur propter <lb/><expan abbr="eãdem">eandem</expan> rationem vnde &longs;uprà; </s>

<s id="N274F7">&longs;uppono autem nullo modo vel trahi <lb/>&longs;ur&longs;um, vel pelli vtrimque: potrò retinetur ab æquali potentia, quod <lb/>iam alibi demon&longs;trauimus lib.5. in quo etiam fusè explicuimus diuer<lb/>&longs;as lineas, quibus potentia applicari pote&longs;t. </s>

<s id="N274F7">&longs;uppono autem nullo modo vel trahi <lb/>&longs;ur&longs;um, vel pelli vtrimque: porrò retinetur ab æquali potentia, quod <lb/>iam alibi demon&longs;trauimus lib.5. in quo etiam fusè explicuimus diuer<lb/>&longs;as lineas, quibus potentia applicari pote&longs;t. </s>

<s id="N27503"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/></s>

Line 17263

<s id="N27523">&longs;ic dum quis ambulat, pileum etiam, quo caput tegitur, mouet; &longs;ic <lb/>equus rapit, nauis vehit nautam, currus aurigam defert. </s>

<s id="N2752B">Sccundò, imprimitur impetus in vtroque; probatur facilè; quia <lb/>vtrumque mouetur cum eo tamen di&longs;crimine, quod lator in &longs;e producit <lb/>impetum, qui in mobili delato alium producit. </s>

<s id="N2752B">Secundò, imprimitur impetus in vtroque; probatur facilè; quia <lb/>vtrumque mouetur cum eo tamen di&longs;crimine, quod lator in &longs;e producit <lb/>impetum, qui in mobili delato alium producit. </s>

<s id="N27535">Tertiò, impetus latoris æqualis e&longs;t impetui delato, quia vtrique ine&longs;t <lb/>æqualis motus; igitur æqualis impetus. </s>

Line 17294

<s id="N275B2">Octauò, hinc quò velociùs corpus progredietur minoribu&longs;que, licèt, <pb pagenum="382" xlink:href="026/01/416.jpg"/>frequentioribus pa&longs;&longs;ibus, brachij motus accedit propiùs ad æquabilem; </s>

<s id="N275BB"><lb/>igitur minùs mutatur &longs;uperficies liquoris va&longs;e contenti; </s>

<s id="N275C0">hinc in naui, <lb/>quæ veloci&longs;&longs;imo motu fertur, ne tremit quidem fuperficies aquæ, quam <lb/>repo&longs;itam quis habet in va&longs;e; denique quò &longs;uperficies concaua orbis <lb/>&longs;eu va&longs;is e&longs;t maioris circuli faciliùs effunditur liquor, quia planum e&longs;t <lb/>minus decliue, & minus recedit ab horizontali, & contrà &longs;i e&longs;t minoris <lb/>&longs;phæræ &longs;eu circuli, hinc fortè tantus e&longs;t maris æ&longs;tus in Oceano, & mo<lb/>dicus valdè in Mediterraneo, &longs;ed de his alibi. </s>

<s id="N275C0">hinc in naui, <lb/>quæ veloci&longs;&longs;imo motu fertur, ne tremit quidem &longs;uperficies aquæ, quam <lb/>repo&longs;itam quis habet in va&longs;e; denique quò &longs;uperficies concaua orbis <lb/>&longs;eu va&longs;is e&longs;t maioris circuli faciliùs effunditur liquor, quia planum e&longs;t <lb/>minus decliue, & minus recedit ab horizontali, & contrà &longs;i e&longs;t minoris <lb/>&longs;phæræ &longs;eu circuli, hinc fortè tantus e&longs;t maris æ&longs;tus in Oceano, & mo<lb/>dicus valdè in Mediterraneo, &longs;ed de his alibi. </s>

<s id="N275D2">Nonò, his adde amphoras illas aqua, vel lacte ad &longs;ummum v&longs;que <lb/>marginem repletas, quas ru&longs;ticanæ f&oelig;minæ è &longs;ummo capite ita portant, <lb/>vt nihil penitus effundatur, quia &longs;cilicet ten&longs;o collo ambulant, vt capi<lb/>tis motus ad æquabilem propius accedat. </s>

Line 17303

<s id="N275DD">Decimò, non e&longs;t omittendum ille orbis gyrus cum &longs;cypho pleno; <lb/>quod vt melius intelligatur. </s>

<s id="N275E3">Sit orbis AFEG pendulus filo FA; </s>

<s id="N275E7">&longs;it <lb/>&longs;cyphus EDC plenus aqua vel alio liquore, puncto circuli E in&longs;idens, <lb/>tùm rotetur orbis circa centrum F; </s>

<s id="N275EF">haud dubiè, ne gutta quidem aquæ <lb/>effundetut; </s>

<s id="N275EF">haud dubiè, ne gutta quidem aquæ <lb/>effundetur; </s>

<s id="N275F5">ratio e&longs;t, cùm E &longs;it &longs;emper punctum oppo&longs;itum centro, mo<lb/>tus F & &longs;cyphus motu illo circulari maximè pellatur, prematurque ver<lb/>&longs;us E, aqua ip&longs;a etiam ver&longs;us E recipit impetum ver&longs;us fundum &longs;cyphi; </s>

<s id="N275FD"><lb/>qui cùm &longs;it inten&longs;ior natiuo propriæ grauitationis aquæ, non e&longs;t mirum <lb/>&longs;i præualeat, & nihil penitus effundatur in gyro, præ&longs;ertim cùm partes <lb/>omnes aquæ moueantur eo motu, quo in primo &longs;itu omninò relinquun<lb/>tur; </s>

<s id="N27608">adde quod licèt impetus innatus tantillùm obe&longs;&longs;et, impeditur ta<lb/>men ab illa vligine, quæ cum aqua commixta e&longs;t, de qua iam &longs;uprà; </s>

Line 17348

<s id="N276AC"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/></s>

<s id="N276BB"><emph type="italics"/>Aliquoâ mobile proiectum excipitur manu multis modis.<emph.end type="italics"/></s>

<s id="N276BB"><emph type="italics"/>Aliquotâ mobile proiectum excipitur manu multis modis.<emph.end type="italics"/></s>

<s id="N276C4">Primò, firma & fixa manu, in quam cadit eodem modo, quo caderet <lb/>in parietem, vt patet. </s>

Line 17377

<s id="N27723">Primò, trahitur mobile per productionem impetus; </s>

<s id="N27727">nec enim po<lb/>tentia motrix, quæ reuerâ cau&longs;a e&longs;t tractionis, quidquam aliud produce<lb/>re pote&longs;t; </s>

<s id="N2772F">præterca quod trahitur, verè mouetur; igitur per impetum, <lb/>&longs;ic differt tractio à mera detentione, de qua &longs;uprà. </s>

<s id="N2772F">præterea quod trahitur, verè mouetur; igitur per impetum, <lb/>&longs;ic differt tractio à mera detentione, de qua &longs;uprà. </s>

<s id="N27737">Secundò, hinc tractio e&longs;t actio potentiæ motricis, qua mobile ip&longs;um <lb/>propiùs accedit ad motorem; </s>

Line 17398

<s id="N2777C">immò non producitur in vna, ni&longs;i producatur in aliis; </s>

<s id="N27780"><lb/>alioquin fru&longs;trà e&longs;&longs;et ille impetus, cui nullus effectus re&longs;pon<lb/>deret; </s>

<s id="N27787">igitur &longs;i de&longs;truitur, quando fru&longs;trà e&longs;&longs;et, &longs;i con&longs;eruaretur; </s>

<s id="N2778B">ita <lb/>ctiam non producitur quando fru&longs;trà e&longs;&longs;et, &longs;i produceretur; e&longs;t enim <lb/>par vtrimque ratio. </s>

<s id="N2778B">ita <lb/>etiam non producitur quando fru&longs;trà e&longs;&longs;et, &longs;i produceretur; e&longs;t enim <lb/>par vtrimque ratio. </s>

<s id="N27795">Quartò, hinc licèt trahatur ingens rupes, non propterea mouetur, <lb/>quia non pote&longs;t impetus produci in omnibus illius partibus ab applica<lb/>ta potentia; igitut in nulla per Th.33.l.1. </s>

Line 17409

<s id="N277AB">Quintò, hinc vna pars tracta non &longs;equitur aliam vltrò; </s>

<s id="N277AF">&longs;i enim vltrò <lb/>&longs;equeretur minima potentia, &longs;ufficeret ad trahendum maximum pondus; <lb/>prærerea &longs;ingulæ partes mouentur per impetum. </s>

<s id="N277AF">&longs;i enim vltrò <lb/>&longs;equeretur minima potentia, &longs;ufficeret ad trahendum maximum pondus; <lb/>præterea &longs;ingulæ partes mouentur per impetum. </s>

<s id="N277B9">Diceret aliquis, impetus productus in vna parte producit impetum <lb/>in alia. </s>

Line 17418

<s id="N277C5">Dices, impetus vnius corporis producit impetum in alio, à quo eius <lb/>motus impeditur; igitur impetus vnius partis producit impetum in <lb/>alia, à qua eius motus impeditur. </s>

<s id="N277CD">Re&longs;p. impetum, qui reuerâ alicui <lb/>corpori ine&longs;t, hoc ip&longs;um præ&longs;tare; </s>

<s id="N277D3">at impetus non producitur in vna <lb/>parte mobilis, ni&longs;i fimul in aliis producatur; </s>

<s id="N277D3">at impetus non producitur in vna <lb/>parte mobilis, ni&longs;i &longs;imul in aliis producatur; </s>

<s id="N277D9">vel enim producitur in <lb/>omnibus, vel in nulla; </s>

<s id="N277DF">hinc colliges quantum ab&longs;urdum &longs;equerctur, <lb/>ni&longs;i hoc e&longs;&longs;et; </s>

<s id="N277DF">hinc colliges quantum ab&longs;urdum &longs;equeretur, <lb/>ni&longs;i hoc e&longs;&longs;et; </s>

<s id="N277E5">quia perpetua e&longs;&longs;et impetus productio, & minimus im<lb/>petus totam ip&longs;am terram moueret; </s>

<s id="N277EB">vide quæ diximus &longs;uper ea re toto <lb/>lib.1. nec enim totus impetus motoris producit totum &longs;uum effectum <lb/>in vnico puncto mobilis, quod ridiculum dictu e&longs;t; </s>

<s id="N277F3">alioquin produ<lb/>ceretur impetus inten&longs;i&longs;&longs;imus; </s>

Line 17443

<s id="N27831">Primò, &longs;i altera eius extre<lb/>mitas annulo, &longs;eu clauo immobili affixa &longs;it; </s>

<s id="N27837">alteri verò applicetur po<lb/>tentia, vel pondus; &longs;iue &longs;it in &longs;itu horizontali, &longs;iue in verticali. </s>

<s id="N2783D">Secundò, <lb/>&longs;i vtrique extremitati applicetur pondus vel alia potentia motrix. </s>

<s id="N27842"><lb/>Tertiò, &longs;i vtraque extremitas clauo immobiliter affigatur in &longs;ittu hori-<pb pagenum="385" xlink:href="026/01/419.jpg"/>zontali, admoueaturque pondus, &longs;eu potentia alicui chordæ puncto <lb/>deor&longs;um trahens: </s>

<s id="N27842"><lb/>Tertiò, &longs;i vtraque extremitas clauo immobiliter affigatur in &longs;itu hori-<pb pagenum="385" xlink:href="026/01/419.jpg"/>zontali, admoueaturque pondus, &longs;eu potentia alicui chordæ puncto <lb/>deor&longs;um trahens: </s>

<s id="N2784E">denique &longs;i ponticulo maximè attollatur, & tendatur <lb/>chorda po&longs;ita in priori &longs;itu; </s>

<s id="N27854">&longs;i primò, rumpetur chorda per &longs;e in ea ex<lb/>tremitate, quæ immobiliter clauo affigitur; </s>

<s id="N2785A">&longs;i tertio & quarto in ea <lb/>parte, in qua vel deprimitur, vel attollitur: dixi per &longs;e, quia per acci<lb/>dens &longs;ecus accidit, vt reuerâ &longs;æpè fit, vel propter inflexionem nodi, vel <lb/>aliquas partes debiliores, vel pre&longs;&longs;ionem maiorem cum ten&longs;ione con<lb/>iunctam &c. </s>

Line 17473

<s id="N278F5">Decimò, hinc facilè colligi pote&longs;t, quid dicendum &longs;it de pluribus equis <lb/>trahentibus currum; </s>

<s id="N278FB">qui certè ad currum iungi non po&longs;&longs;unt, ni&longs;i &longs;int <lb/>plures funes, qui tamen in communem &longs;eu funem &longs;eu temonem de&longs;i<lb/><gap/>unt; &longs;it autem pondus A, linea dicectionis GE. </s>

<s id="N278FB">qui certè ad currum iungi non po&longs;&longs;unt, ni&longs;i &longs;int <lb/>plures funes, qui tamen in communem &longs;eu funem &longs;eu temonem de&longs;i<lb/>nunt; &longs;it autem pondus A, linea directionis GE. </s>

<s id="N27904">Si &longs;it tantùm vnus <pb pagenum="386" xlink:href="026/01/420.jpg"/>equus, vel trahet duobus funibus BECE, vel vnico GE, addito axe <lb/>DF, & duobus funibus DHFH. </s>

<s id="N2790E">Hoc &longs;ecundo modo faciliùs trahet; <lb/>quia impetus meliùs deriuatur in pondus A per lineam EG, quæ per <lb/>centrum grauitatis ducitur. </s>

Line 17549

<s id="N27AAA">Primò ad lit<lb/>tus tendit cum trahitur vnco annullus immobilis, vt iam dictum e&longs;t. </s>

<s id="N27AAF">Se<lb/>cundò, &longs;i pellitur, vel fundum aquæ, vel aliud corpus immobile longio<lb/>ri ligno, & pede pellatur ip&longs;a nauis in aduer&longs;am partem, in cam ibit <lb/>propter <expan abbr="eãdem">eandem</expan> rationem; Tertiò &longs;i pellatur aqua remis fixo etiam pe<lb/>de vel crure contranitente in aduer&longs;am partem, idem &longs;equetur effectus. </s>

<s id="N27ABF"><lb/>Quartò, hinc quò remus latior e&longs;t, & longior erit, maior erit effectus, <pb pagenum="388" xlink:href="026/01/422.jpg"/>modò &longs;uppetant vires. </s>

<s id="N27AC8">Quintò, hinc latioris claui inflexione vertltur <lb/>nauis; </s>

<s id="N27AC8">Quintò, hinc latioris claui inflexione vertitur <lb/>nauis; </s>

<s id="N27ACE">Sextò, inflata ventis &longs;ecundis vela nauem agunt; </s>

<s id="N27AD2">ratio clari&longs;&longs;ima <lb/>e&longs;t, quia non po&longs;&longs;unt vela impelli, ni&longs;i alia nauis, cui &longs;unt coniuncta mo<lb/>ueatur; &longs;ed de re nautica agemus fusè &longs;uo loco, atque adeo de tota re <lb/>hydraulica. </s>

<s id="N27ADE">Decimo&longs;eptimò, denique ex dictis multa corollaria con&longs;equi po&longs;&longs;unt. </s>

<s id="N27AE1"><lb/>C<gap/>um e&longs;t. </s>

<s id="N27AE1"><lb/>Certum e&longs;t. </s>

<s id="N27AE7">1&degree;. </s>

<s id="N27AEA">pars tracta non &longs;equitur trahentem &longs;ua &longs;ponte 2.&degree;. </s>

<s id="N27AED">re&longs;i&longs;tit <lb/>alteri trahenti, 3&degree;. </s>

Line 17575

<s id="N27B28">1&degree;. </s>

<s id="N27B2B">extremitas funis fracti re&longs;ilit propter <lb/>præcedentem ten&longs;ionem. </s>

<s id="N27B30">11&degree;. </s>

<s id="N27B33">hinc cum di&longs;cerpitur charta vel tela edi<lb/>tur &longs;onus &longs;tridrulus, qui prouenit à motu extremorum filorum quæ re&longs;i<lb/>liunt. </s>

<s id="N27B33">hinc cum di&longs;cerpitur charta vel tela edi<lb/>tur &longs;onus &longs;tridulus, qui prouenit à motu extremorum filorum quæ re&longs;i<lb/>liunt. </s>

<s id="N27B3A">12&degree;. </s>

<s id="N27B3D">immò cum baculus frangitur, aliqua &longs;egmenta maxima vi eui<lb/>brantur, &longs;entiturque in manu qua&longs;i formicans dolor, propter illas tre<lb/>mulas &longs;uccu&longs;&longs;iones. </s>

<s id="N27B44">13&degree;. </s>

<s id="N27B47">cum trahitur cylindrus vtrimque in aduer&longs;as <lb/>partes à duobus contranitentibus æqualium virium, &longs;i minimè inflecti <lb/>po&longs;&longs;it, ille præualebit, cuius vtraque manus propiùs ad medium cylin<lb/>drrum accedit; </s>

<s id="N27B51">&longs;ecùs verò, &longs;i inflectatur; e&longs;t enim ad in&longs;tar gemini vectis. </s>

<s id="N27B55"><lb/>14&degree;. </s>

<s id="N27B59">cum trahitur cylindrus æqualiter vtrimque, qui neque flecti, ne<lb/>que tendi po&longs;&longs;it; </s>

Line 17617

<s id="N27BE4">producitur tamen <lb/>împetus in organo; probatur ex ni&longs;u; immò & compre&longs;&longs;ione molliorum <lb/>partium. </s>

<s id="N27BEC">9&degree;. </s>

<s id="N27BEF">quando duo &longs;e&longs;e mutuò, & æquali ni&longs;u pellunt, vterque in &longs;e <lb/>ip&longs;o, & in alio producit impetum; </s>

<s id="N27BF5">in &longs;e quidem, quia maximè euititur, <lb/>& defatigatur potentia motrix; in alio verò, in quo fit aliqua partium <lb/>compre&longs;&longs;io, quæ &longs;ine impetu <expan abbr="n&utilde;quam">nunquam</expan> fit. </s>

<s id="N27BF5">in &longs;e quidem, quia maximè euitetur, <lb/>& defatigatur potentia motrix; in alio verò, in quo fit aliqua partium <lb/>compre&longs;&longs;io, quæ &longs;ine impetu <expan abbr="n&utilde;quam">nunquam</expan> fit. </s>

<s id="N27C01">10&degree;. </s>

<s id="N27C04">&longs;i os pelleretos, &longs;eu corpus <lb/>durum aliud durum, natiua vi di&longs;tincta à grauitatione, in neutro pro<lb/>duceretur impetus; </s>

<s id="N27C0C">quia e&longs;&longs;et fru&longs;trà: vide quæ diximus &longs;uprà de tra<lb/>ctione. </s>

Line 17649

<s id="N27C95"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 9.<emph.end type="center"/></s>

<s id="N27CA3"><emph type="italics"/>Corpus<emph.end type="italics"/> 1&degree;. <emph type="italics"/>deprimitur per impetum infra medium granius, v. g. lignu&mtail; <lb/>infra aquam<emph.end type="italics"/>; ratio clara e&longs;t. </s>

<s id="N27CA3"><emph type="italics"/>Corpus<emph.end type="italics"/> 1&degree;. <emph type="italics"/>deprimitur per impetum infra medium grauius, v. g. lignu&mtail; <lb/>infra aquam<emph.end type="italics"/>; ratio clara e&longs;t. </s>

<s id="N27CB8">2&degree;. </s>

<s id="N27CBB">deprimitur, vel trahendo, vel impellen<lb/>do, vel calcando. </s>

<s id="N27CC0">3&degree;. </s>

<s id="N27CC3">trahimus &longs;æpè deor&longs;um, vt corpus attollatur &longs;ur<lb/>fum, vt in trochleis. </s>

<s id="N27CC3">trahimus &longs;æpè deor&longs;um, vt corpus attollatur &longs;ur<lb/>&longs;um, vt in trochleis. </s>

<s id="N27CC8">4&degree;. </s>

<s id="N27CCB">quò corpus maius e&longs;t, & leuius difficiliùs depri<lb/>mitur infra medium grauius, quia non pote&longs;t deprimi ni&longs;i plures medij <lb/>grauiores partes attollantur, vt clarum e&longs;t; exemplum habes in nauibus, <lb/>5&degree;. </s>

<s id="N27CD5">deprimimus aliquando corpora per ten&longs;ionem, vt ramos arborum, <lb/>&longs;eu per librationem, vt campanarum funes, &longs;eu extremos vectes. </s>

Line 17673

<s id="N27D08"><emph type="italics"/>Omnes gyrationum modi explicari, & demon&longs;trari po&longs;&longs;unt.<emph.end type="italics"/></s>

<s id="N27D11">Primò, vertitur baculus manu primo circa proprium axem, vt veru, <lb/>quia inflectitur eodem modo manus & inferior brachij portio: </s>

<s id="N27D11">Primò, vertitur baculus manu primo circa proprium axem, vt <expan abbr="veru">verum</expan>, <lb/>quia inflectitur eodem modo manus & inferior brachij portio: </s>

<s id="N27D17">&longs;ecundo <lb/>eirca alteram extremitatem quæ manu tenetur: tertio circa quodlibet <lb/>aliud punctum, ratio petitur tùm à tali brachij motu, tùm ab eo modo, <lb/>quo baculus tenetur, </s>

<s id="N27D17">&longs;ecundo <lb/>circa alteram extremitatem quæ manu tenetur: tertio circa quodlibet <lb/>aliud punctum, ratio petitur tùm à tali brachij motu, tùm ab eo modo, <lb/>quo baculus tenetur, </s>

<s id="N27D23">Secundò, circumagitur funis vel funda; </s>

Line 17686

<s id="N27D3C">quot enim habemus articulos, tot motus cir<lb/>cularis habemus centra; </s>

<s id="N27D42">hinc &longs;uæ apothecæ caput o&longs;&longs;is tam aptè in&longs;e<lb/>ritur, vt circa illam facilè moueatur; </s>

<s id="N27D48">exemplum habes in oculo, dum <lb/>infra &longs;uam thecam voluitur; </s>

<s id="N27D4E">&longs;ed de tota corporis fabrica, quatenus con<lb/>ducit ad motum, &longs;uo loco agemus; nec enim hi motus ad hunc tracta<lb/>ctum pertinent. </s>

<s id="N27D4E">&longs;ed de tota corporis fabrica, quatenus con<lb/>ducit ad motum, &longs;uo loco agemus; nec enim hi motus ad hunc tracta<lb/>tum pertinent. </s>

<s id="N27D58">Quartò, hinc reuoca deflexionem illam iacti globi, de qua &longs;uprà, quæ <lb/>familiaris e&longs;t trunculorum ludo, item gyros globi, quem, vel inter duas <lb/>volas circumagis, vel inter volam, & aliud planum, qui partim ad impul<lb/>&longs;um, partim ad tractum pertinent; &longs;ed neque hæc &longs;unt difficilia. </s>

Line 17697

<s id="N27D72">Ob&longs;eruabis vix po&longs;&longs;e vno Theoremate compræhendi omnia ph&oelig;no<lb/>mena percu&longs;&longs;ionis, cuius &longs;unt tria veluti prima genera, &longs;cilicet ictus, ca<lb/>&longs;us, iactus: ictum appello illam percu&longs;&longs;ionem, quæ infligitur pugno, ma<lb/>nu, calce, cornu, vel quolibet organo, cum potentia motrice coniuncto, <lb/>v.g. fu&longs;te, &longs;axo, flagello, &c. </s>

<s id="N27D80">ca&longs;us e&longs;t percu&longs;&longs;io à corpore graui deor&longs;um <lb/>cadente inflicta; iactus denique e&longs;t percu&longs;&longs;io, quæ aliquam emi&longs;&longs;ionem, <lb/>&longs;eu vibrationem &longs;upponit, lapidis, pilæ, &c. </s>

<s id="N27D88">itaque vt omnia percu&longs;&longs;io<lb/>nis ph&oelig;nomena di&longs;tinctiùs explicemus, &longs;ingulis Theorematis &longs;ingulos <lb/>percu&longs;&longs;ionis modos oxplicabimus. </s>

<s id="N27D91"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s>

Line 17712

<s id="N27DBC">vbi <lb/>autem F peruenit in G; </s>

<s id="N27DC2">a&longs;&longs;umatur GE æqualis FB: </s>

<s id="N27DC6">vbi verò F peruenit <lb/>in H; </s>

<s id="N27DCC">a&longs;&longs;umatur HD æqualis FB, & habebitur proportio motus extre<lb/>initatis F & capitis B; vides motum rectum FI mixtum ex duobus cir<lb/>cularibus circa centrum immobile A, & mobile B. </s>

<s id="N27DCC">a&longs;&longs;umatur HD æqualis FB, & habebitur proportio motus extre<lb/>mitatis F & capitis B; vides motum rectum FI mixtum ex duobus cir<lb/>cularibus circa centrum immobile A, & mobile B. </s>

<s id="N27DD6">Secundò, po&longs;&longs;et moueri per omnem lineam, v. g. FN, FM, <pb pagenum="391" xlink:href="026/01/425.jpg"/>immò, & per lineam perpendicularem &longs;ur&longs;um, vel deor&longs;um, & quò <lb/>plùs contrahetur brachium, motus rectus per horizontalem erit maior; </s>

Line 17791

<s id="N27F59">Vndecimò, breuiter indico ictum inflictum ab ip&longs;o cubiti capi<lb/>te retrò acto, &longs;atis grauem e&longs;&longs;e; </s>

<s id="N27F5F">tùm quia durior e&longs;t ille nodus; tùm <lb/>quia ad eius motum non modò &longs;uperius brachij &longs;egmentum, verùm <lb/>etim inferius concurrit. </s>

<s id="N27F5F">tùm quia durior e&longs;t ille nodus; tùm <lb/>quia ad eius motum non modò &longs;uperius brachij &longs;egmentum, verùm <lb/>etiam inferius concurrit. </s>

<s id="N27F69">Duodecimò, infligitur etiam grauis ictus calce, cuius e&longs;t eadem <lb/>ratio, quæ &longs;uprà; e&longs;t enim duplex centrum, duplex motus, &c. </s>

Line 17807

<s id="N27F9A">Decimotertiò, explo&longs;ione inten&longs;i digiti talitrum imprimitur, cuius <lb/>&longs;unt tres modi; primus e&longs;t, cum vngue medij, vel alterius digiti pul&longs;o <lb/>tanti&longs;per molliore &longs;ummi pollicis apice, inten&longs;us deinde digitus eo<lb/>dem vngue talitrum impingit. </s>

<s id="N27FA4">Secundum e&longs;t, cum retento &longs;ummo di<lb/>gito ab aliquo molliori corpore &longs;tatim dimittitur. </s>

<s id="N27FA9">Tertium e&longs;t, cum <lb/>mollior medij digiti, & pollicis apex po&longs;t aliquam pre&longs;&longs;ionem, non <lb/>&longs;ine aliquo &longs;trepitu exploditur; </s>

<s id="N27FB1">ratio primi e&longs;t, quia dum vnguis mol<lb/>liorem &longs;nb&longs;tantiam premit, auget impetum potentia motrix in illa <lb/>mora, neruu&longs;que maximè intenditur; </s>

<s id="N27FB1">ratio primi e&longs;t, quia dum vnguis mol<lb/>liorem &longs;ub&longs;tantiam premit, auget impetum potentia motrix in illa <lb/>mora, neruu&longs;que maximè intenditur; </s>

<s id="N27FB9">igitur maior e&longs;t ictus; </s>

<s id="N27FBD">eadem <lb/>ratio valet pro &longs;ecundo, & tertio modo; </s>

<s id="N27FC3">&longs;trepitus ille oritur à colli<lb/>&longs;ione, vel compre&longs;&longs;ione: </s>

Line 17820

<s id="N27FE0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s>

<s id="N27FEE"><emph type="italics"/>Explicari po&longs;&longs;unt omnes ictus, qui infliguntur impacto &longs;cilicet &longs;axo, fu&longs;te, <lb/>flagello, & alio quouis organo, cui &longs;emper potentia motrix couiuncta e&longs;t, nec <lb/>ab ea &longs;eparatur,<emph.end type="italics"/> excepto dumtaxat omni malleorum genere, gladiorum, <lb/>&c. </s>

<s id="N27FEE"><emph type="italics"/>Explicari po&longs;&longs;unt omnes ictus, qui infliguntur impacto &longs;cilicet &longs;axo, fu&longs;te, <lb/>flagello, & alio quouis organo, cui &longs;emper potentia motrix coniuncta e&longs;t, nec <lb/>ab ea &longs;eparatur,<emph.end type="italics"/> excepto dumtaxat omni malleorum genere, gladiorum, <lb/>&c. </s>

<s id="N27FFC">primò manus in&longs;tructa &longs;axo grauiorem ictum infligit; </s>

<s id="N28000">tùm quia <lb/>multus impetus imprimitur graui &longs;axo; </s>

<s id="N28006">tùm quia durior e&longs;t materia; </s>

Line 17837

<s id="N28037">Tertiò, cum punctim impingitur fu&longs;tis, quò hic maior e&longs;t, maiorem <lb/>incutit ictum; </s>

<s id="N2803D">præ&longs;ertim, &longs;i gemina manu intenditur; </s>

<s id="N28041">quia &longs;cilicet ma<lb/>jor impetus imprimitur; </s>

<s id="N28047">huc reuoca &longs;ari&longs;&longs;æ graui&longs;&longs;imum ictum, quo <lb/>ferrea larica perfodi pote&longs;t; </s>

<s id="N28047">huc reuoca &longs;ari&longs;&longs;æ graui&longs;&longs;imum ictum, quo <lb/>ferrea lorica perfodi pote&longs;t; </s>

<s id="N2804D">quia &longs;cilicet maior impetus imprimitur in<lb/>tentis priùs, & vibratis brachijs; </s>

<s id="N28053">multùm enim confert, tum illa bra<lb/>chiorum, atque adeò totius &longs;ari&longs;&longs;æ vibratio; </s>

<s id="N28059">tùm etiam neruorum ten<lb/>&longs;io, vt videmus in arcu; </s>

Line 17847

<s id="N28069">Quartò, longitudo &longs;ari&longs;&longs;æ compen&longs;ari pote&longs;t cra&longs;&longs;itie; </s>

<s id="N2806D">&longs;it enim <lb/>&longs;ari&longs;&longs;a 12. pedes alta pendens 12. libras; </s>

<s id="N28073">&longs;it alia 6. pedes alta pendens <pb pagenum="394" xlink:href="026/01/428.jpg"/>12. libras vtraque æquali ni&longs;u, & modo ab eadem potentia impacta æ<lb/>qualem ictum infligit; </s>

<s id="N2807E">probatur quia tantuindem impetus imprimitur <lb/>vni, quantum alteri; </s>

<s id="N2807E">probatur quia tantumdem impetus imprimitur <lb/>vni, quantum alteri; </s>

<s id="N28084">nam aëris re&longs;i&longs;tentia vix quidquam facit; </s>

<s id="N28088">licèt pau<lb/>lò plùs re&longs;i&longs;tat aër breuiori, cuius ba&longs;is latior e&longs;t in ratione dupla, quàm <lb/>longiori; hinc cra&longs;&longs;iori fu&longs;te licèt breuiore maximus ictus infringitur, <lb/>vt patet experientiâ. </s>

Line 17855

<s id="N28094">Diceret aliquis hæc repugnare omnibus experimentis, quibus &longs;cili<lb/>cet clari&longs;&longs;imè con&longs;tat minorem e&longs;&longs;e breuiorum &longs;ari&longs;&longs;arum vim. </s>

<s id="N2809B">Re&longs;p. hoc ip&longs;um accidere; quia brcuiores &longs;ari&longs;&longs;æ, quas habemus, vel <lb/>exiliores &longs;unt longioribus, vel &longs;altem non cra&longs;&longs;iores, cùm tamen cra&longs;&longs;io<lb/>res e&longs;&longs;e oporteat in eadem ratione, in qua illæ longiores &longs;unt vt æqualis <lb/>&longs;it ictus. </s>

<s id="N2809B">Re&longs;p. hoc ip&longs;um accidere; quia breuiores &longs;ari&longs;&longs;æ, quas habemus, vel <lb/>exiliores &longs;unt longioribus, vel &longs;altem non cra&longs;&longs;iores, cùm tamen cra&longs;&longs;io<lb/>res e&longs;&longs;e oporteat in eadem ratione, in qua illæ longiores &longs;unt vt æqualis <lb/>&longs;it ictus. </s>

<s id="N280A6">Quintò, cur verò maior fu&longs;tis maiorem impetum à brachiorum vi <lb/>recipiat; </s>

Line 17894

<s id="N28165">Ob&longs;eruabis autem primò ratione ponderis H, quod &longs;u&longs;ti&nacute;ctur, aliquid <lb/>impetus detrahendum e&longs;&longs;e. </s>

<s id="N28165">Ob&longs;eruabis autem primò ratione ponderis H, quod &longs;u&longs;ti&nacute;etur, aliquid <lb/>impetus detrahendum e&longs;&longs;e. </s>

<s id="N2816A">Secundò, vt accuratè procedatur vtrumque <lb/>fu&longs;tem funependulum e&longs;&longs;e po&longs;&longs;e. </s>

<s id="N2816F">Tertiò, ictus e&longs;&longs;e vt impetus; impetus <lb/>verò in ratione &longs;ubduplicata ponderum, hoc e&longs;t, vt radices quadratas. </s>

<s id="N28175"><lb/>v.g. fu&longs;tis maior pendit 36. libras, minor 4; </s>

Line 17923

<s id="N281E7">v. g. &longs;i &longs;egmentum CB &longs;eiunctum <lb/>e&longs;&longs;et à &longs;egmento BA; </s>

<s id="N281F1">haud dubiè punctum B perueniet citiùs in F, quàm <lb/>&longs;i vtrumque &longs;egmentum coniunctum e&longs;&longs;et, vt notum e&longs;t; </s>

<s id="N281F7">quia maior im<lb/>petus imprimitur B &longs;eiuncta; </s>

<s id="N281FD">atqui licèt CB &longs;it coniunctum BA, ab eo <lb/>tamen facilè, non quidem omninò &longs;eiungi, &longs;ed deflecti, dimoucri pote&longs;t <lb/>propter flexibilitatem materiæ; </s>

<s id="N281FD">atqui licèt CB &longs;it coniunctum BA, ab eo <lb/>tamen facilè, non quidem omninò &longs;eiungi, &longs;ed deflecti, dimoueri pote&longs;t <lb/>propter flexibilitatem materiæ; </s>

<s id="N28205">igitur B <gap/>linquet à tergo BA; </s>

<s id="N28205">igitur B relinquet à tergo BA; </s>

<s id="N2820B">igitur <lb/>fu&longs;tis inflectetur, & hæc e&longs;t vera ratio huius ph&oelig;nomeni: hinc virgulæ <lb/>&longs;ucco & humore plenæ, nerui bubuli latiores, canoncs, funiculi, lora, <lb/>en&longs;es, manubria Tudiculæ maioris, & alia huiu&longs;modi propter rationem <lb/>prædictam inflectuntur. </s>

<s id="N2820B">igitur <lb/>fu&longs;tis inflectetur, & hæc e&longs;t vera ratio huius ph&oelig;nomeni: hinc virgulæ <lb/>&longs;ucco & humore plenæ, nerui bubuli latiores, canones, funiculi, lora, <lb/>en&longs;es, manubria Tudiculæ maioris, & alia huiu&longs;modi propter rationem <lb/>prædictam inflectuntur. </s>

<s id="N28219">Nonò, extremitas fu&longs;tis inflexi, cum deinde redit, maiorem ictum in<lb/>fligit: </s>

Line 17933

<s id="N28225">quia maiorem <lb/>impetum habet; </s>

<s id="N2822B">nam præter impre&longs;&longs;um à potentia applicata in C, acce<lb/>dit alius ab ip&longs;a inflexione, cuius rationem afferemus tractatu &longs;equenti, <lb/>cum de compre&longs;&longs;ione, & ten&longs;ione corporum; </s>

<s id="N28233">e&longs;t enim quædam potentia <lb/>media inter potentiam grauitationis, & potentiam animatorum, quam <lb/>proinde mediam appellabimus; </s>

<s id="N2823B">quâ &longs;cilicet corpora &longs;e&longs;e re&longs;tituunt pri<lb/>&longs;tinæ exten&longs;ioni, cuius mirificos effectus habemus in arcu chordis pul-<pb pagenum="396" xlink:href="026/01/430.jpg"/>&longs;atis, va&longs;is pneumaticis, & hydraulicis, denique in tota re tormentoria; <lb/>hinc primò Tudiculæ maioris manubrium inflexum multùm auget ip&longs;am <lb/>vim ictus, de quo infrà. </s>

<s id="N2823B">quâ &longs;cilicet corpora &longs;e&longs;e re&longs;tituunt pri<lb/>&longs;tinæ exten&longs;ioni, cuius mirificos effectus habemus in arcu chordis pul-<pb pagenum="396" xlink:href="026/01/430.jpg"/>&longs;atis, va&longs;is pneumaticis, & hydraulicis, denique in tota re tormentaria; <lb/>hinc primò Tudiculæ maioris manubrium inflexum multùm auget ip&longs;am <lb/>vim ictus, de quo infrà. </s>

<s id="N2824A">Secundò, neruus bubulus, primò inflexus, tùm <lb/>&longs;tatim rediens &longs;capulas malè afficit. </s>

<s id="N2824F">Tertiò, flexibiles virgæ tran&longs;uer&longs;as <lb/>plagas cum tanto dolore infligunt inu&longs;tis vibicibus. </s>

<s id="N28254">Quartò, idem dico <lb/>de regula illa latiore, qua remigiorum præ&longs;ides, remiges tardos ca&longs;ti<lb/>gant &c. </s>

Line 17948

<s id="N2827D">ratio e&longs;t, quia cùm partes funis, quæ <lb/>propius ad manubrium accedunt, citiùs moueantur, & alias ponè relin <lb/>quant, i&longs;tæ deinde in &longs;uo motu plùs temporis ponunt; </s>

<s id="N28285">igitur, cùm &longs;it <lb/>motus acceleratus, maiorem induunt impetum, maioremque imprimunt: </s>

<s id="N2828B"><lb/>adde quòd, continuò arcum minoris circuli extremitas ip&longs;a de&longs;cribit, <lb/>quæ vltimò tantum applicatur: </s>

<s id="N28292">hinc nouus accelerationis modus, vt <lb/>clari&longs;&longs;imè vidctur in funiculo circa digitum, cui aduoluitur in gyros <lb/>acto: </s>

<s id="N28292">hinc nouus accelerationis modus, vt <lb/>clari&longs;&longs;imè videtur in funiculo circa digitum, cui aduoluitur in gyros <lb/>acto: </s>

<s id="N2829A">Quod &longs;pectat ad flagellum frumentarium, mouetur motu mixto <lb/>ex duobus circularibus; </s>

<s id="N282A0">con&longs;tat enim de gemino fu&longs;te, quorum alter <lb/>circa alterius extremitatem rotatur; </s>

<s id="N282A6">hic verò circa centrum humeri: </s>

Line 17958

<s id="N282BD">igitur maiorem impetum producit, ex quo &longs;equitur maior ictus; </s>

<s id="N282C1"><lb/>porrò vt vltima extremitas extremi fu&longs;tis qua&longs;i retroagitur; </s>

<s id="N282C6">quod &longs;cilicet <lb/>eius centrum antè producatur, &longs;eu porrigatur; </s>

<s id="N282CC">cùm enim attollitur fla<lb/>gellum illud plicatilc; haud dubiè extremitas deor&longs;um tendit proprio <lb/>ponderc, & producto in aduer&longs;am partem eius centro, vel altera extre<lb/>mitate, quid mirum &longs;i perficit circulum? </s>

<s id="N282CC">cùm enim attollitur fla<lb/>gellum illud plicatile; haud dubiè extremitas deor&longs;um tendit proprio <lb/>pondere, & producto in aduer&longs;am partem eius centro, vel altera extre<lb/>mitate, quid mirum &longs;i perficit circulum? </s>

<s id="N282D6">eius lineam de&longs;cribemus l.12. </s>

Line 17991

<s id="N28374">haud dubiè A tanget &longs;olum AB ex G, antequam B de&longs;cendat in B <lb/>ex H; </s>

<s id="N2837A">igitur attemperandus e&longs;t motus fu&longs;tis DA; </s>

<s id="N2837E">præterea pondus in <lb/>de&longs;cen&longs;u auget ictum, deinde B de&longs;cendit deor&longs;um motu orbis & motu <lb/>centri: </s>

<s id="N28386">præterea B pote&longs;t in a&longs;cen&longs;u maiorem arcum &longs;ui orbis decurre<lb/>re, quàm in de&longs;cen&longs;u, vel æqualem: denique maior e&longs;t ictus quando po<lb/>tentia toto ni&longs;u cuitente &longs;u&longs;tis AB plùs temporis ante ictum in &longs;uo mo<lb/>tu in&longs;umit. </s>

<s id="N28386">præterea B pote&longs;t in a&longs;cen&longs;u maiorem arcum &longs;ui orbis decurre<lb/>re, quàm in de&longs;cen&longs;u, vel æqualem: denique maior e&longs;t ictus quando po<lb/>tentia toto ni&longs;u euitente fu&longs;tis AB plùs temporis ante ictum in &longs;uo mo<lb/>tu in&longs;umit. </s>

<s id="N28392">Decimotertiò, e&longs;t etiam aliud flagelli genus pluribus catenulis ferreis <lb/>in&longs;tructi, ex quibus &longs;ingulis &longs;inguli ferrei globi aliquando &longs;piculis, & <lb/>clauis armati pendent, quorum graui&longs;&longs;imus e&longs;t ictus propter rationes <lb/>prædictas; </s>

Line 17999

<s id="N283A2">neque dee&longs;t ar<lb/>tificium; quo quis hoc armorum genere vtens etiam contra plures &longs;e&longs;e <lb/>tueri po&longs;&longs;it. </s>

<s id="N283AC">Decimoquartò, denique vulgare e&longs;t ph&oelig;nomenum illud funiculi, &longs;en <lb/>flagelli, quo &longs;cilicet inirio remouetur manubrij extremitas, mox &longs;tatim <lb/>adducitur, ex qua productione, & adductione per vndantem funem <lb/>propagatur impetus v&longs;que ad eiu&longs;dem extremitatem nodo vt plurimùm <lb/>ad&longs;trictam. </s>

<s id="N283AC">Decimoquartò, denique vulgare e&longs;t ph&oelig;nomenum illud funiculi, &longs;en <lb/>flagelli, quo &longs;cilicet initio remouetur manubrij extremitas, mox &longs;tatim <lb/>adducitur, ex qua productione, & adductione per vndantem funem <lb/>propagatur impetus v&longs;que ad eiu&longs;dem extremitatem nodo vt plurimùm <lb/>ad&longs;trictam. </s>

<s id="N283B7">Hinc primò &longs;trepitus ille aurigis familiarif&longs;imus; </s>

<s id="N283B7">Hinc primò &longs;trepitus ille aurigis familiari&longs;&longs;imus; </s>

<s id="N283BB">quippe <lb/>maxima fit aëris colli&longs;io in extremo fune; immo, & partium ten&longs;io, &longs;eu <lb/>di&longs;tractio propter motus illos contrarios productionis. </s>

<s id="N283C3">Secundò, hinc <lb/>di&longs;trahitur funis, & qua&longs;i laceratur, di&longs;tractis &longs;cilicet tenui&longs;&longs;imis illis <lb/>filamentis, ex quibus con&longs;tat. </s>

<s id="N283CA">Tertiò, hinc &longs;tringitur illa extremitas no<lb/>do, tùm vt acrior &longs;it ictus, tùm vt filamenta illa nodo illo contineantur. </s>

<s id="N283CF"><lb/>Quartò, duplex e&longs;t motus illius funis propter flexibilitatem; </s>

<s id="N283D4">hinc illæ <lb/>vndæ &longs;eu &longs;piræ; </s>

<s id="N283DA">nam remouetur caput funis, quod deinde &longs;equuntus <lb/>aliæ partes per &longs;inuo&longs;os flexus; &longs;ed mox vbi adducitur idem caput, maios <lb/>impetus producitur in aliis partibus. </s>

<s id="N283DA">nam remouetur caput funis, quod deinde &longs;equuntur <lb/>aliæ partes per &longs;inuo&longs;os flexus; &longs;ed mox vbi adducitur idem caput, maios <lb/>impetus producitur in aliis partibus. </s>

<s id="N283E2">Quintò, currentes vndæ &longs;eu flexus <lb/>adductionis, quæ fit maiore impetu, quàm productio, tandem in <lb/>primos flexus &longs;inuatos ab ip&longs;a productione incurrunt: hinc augetur <lb/>impetus, & motus extremitatis. </s>

<s id="N283EC">Sextò, adde quod licèt &longs;it tantùm, vel <lb/>productio, vel adductio flagelli, &longs;unt iidem &longs;erè effectus, &longs;ed minimè <lb/>æquales, quia augetur continuò motus flexuum; </s>

<s id="N283F4">tùm quia funis ver&longs;us <pb pagenum="398" xlink:href="026/01/432.jpg"/>extremitatem &longs;en&longs;im imminuitur; </s>

Line 18030

<s id="N28466">Primò, quò maior e&longs;t malleus eodem arcu impactus & manubrio, <lb/>maior e&longs;t ictus, quia tardiùs mouetur; </s>

<s id="N2846C">igitur potentia manet diutiùs <lb/>applicata; igitur maior e&longs;t ictus, vt con&longs;tar ex dictis. </s>

<s id="N2846C">igitur potentia manet diutiùs <lb/>applicata; igitur maior e&longs;t ictus, vt con&longs;tat ex dictis. </s>

<s id="N28474">Secundò, hinc ex hac hypothe&longs;i ictus &longs;unt in ratione &longs;ubduplicata <lb/>ponderum malleorum; con&longs;tat etiam, po&longs;ita &longs;cilicet eadem longitudine <lb/>manubrij. </s>

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