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version 1.9, 2002/07/23 15:32:10

version 1.13, 2002/07/23 17:08:56

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<info>

Line 1528

Line 1924

</s>

&longs;arà dunque eguale <lb/>la &longs;ce&longs;a del pe&longs;o po&longs;to in E alla &longs;alita del pe&longs;o po&longs;to in D, percioche la &longs;ce&longs;a del pe <lb/>&longs;o po&longs;to in E tiene tanto di obliquo, quanto la &longs;alita del pe&longs;o po&longs;to in D. & quale<emph.end type="italics"/>

<pb/>&longs;arà la inclinatione dell'vno al moui-<lb/>mento in giù, tale parimente &longs;arà la re <lb/>&longs;istenza dell'altro al mouimento in sù. <lb/>Adunque il pe&longs;o po&longs;to in E non mo-<lb/>uerà in sù il pe&longs;o po&longs;to in D: ne il pe&longs;o <lb/>po&longs;to in D: &longs;i mouerà in giù &longs;i fatta-<lb/>mente, che moua in sù il pe&longs;o po&longs;to in <lb/>E. imperoche e&longs;&longs;endo l'angolo CEB <lb/>egualea CDA, & l'angolo CEM <lb/>&longs;ia eguale all'angolo CDH; &longs;arà il <lb/>re&longs;tante MEB eguale al re&longs;tante<emph.end type="italics"/><lb/><arrow.to.target n="note116"></arrow.to.target> <emph type="italics"/>HDA. La &longs;ce&longs;a dunque del pe&longs;o po-<lb/>&longs;to in D &longs;arà eguale alla &longs;alita del pe-<lb/>&longs;o po&longs;to in E. Adunque il pe&longs;o po&longs;to <lb/>in D non mouerà in sù il pe&longs;o po&longs;to <lb/>in E. Dalle quali co&longs;e &longs;egue che i pe&longs;i <lb/>po&longs;ti in DE, in quanto tra loro &longs;o-<lb/>no congiunti, &longs;ono egualmente graui.<emph.end type="italics"/>

</s>

<pb/>

</figure>

<margin.target id="note56"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 35. <emph type="italics"/>del primo.<emph.end type="italics"/>

<margin.target id="note116"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del prime.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note57"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del primo.<emph.end type="italics"/>

<emph type="italics"/>L'altra ragione po&longs;cia, con laquale vorrebbono mo&longs;trare, che &longs;imilmente la bilancia <lb/>DE ritorna in AB, con dire, che e&longs;&longs;endo la trutina della bilancia CF, la méta <lb/>viene ad e&longs;&longs;er CG. & percioche l'angolo DCG è maggiore dell'angolo ECG, <lb/><*> pe&longs;o po&longs;to in D &longs;arà più graue del po&longs;to in E; dunque la bilancia DE ritorne <lb/>ra in AB; non conchiude nulla al parer mio; & que&longs;ta fintione della trutina, & <lb/>della méta è più to&longs;to da trala&longs;ciare, & pa&longs;&longs;arla con &longs;ilentio, che farne pur vna paro <lb/>la per confonderla, e&longs;&longs;endo del tutto co&longs;a volontaria, percioche la nece&longs;&longs;aria ragione <lb/>per laquale il pe&longs;o po&longs;to in D dall' angolo maggiore &longs;ia più graue, & perche il mag <lb/>giore angolo &longs;ia cagione di grauezzamaggiore non appare in niun loco.

</s>

PROPOSITIONE V.

</s>

Di questo ef <lb/>fetto mostrano di produ-<lb/>cere in mezo que&longs;ta cagio <lb/>ne, perche CG è la mé-<lb/>ta, & CF la trutina; <lb/>&longs;e (dicono e&longs;&longs;i) CG fo&longs; <lb/>&longs;e la trutina, & CF la <lb/>méta, all'hora l'angolo <lb/>FCE &longs;arebbe cagione <lb/>della grauezza, ma non <lb/>già il DCG ad e&longs;&longs;o e-<lb/>guale laquale ragione è al <lb/>tutto fatta con la imagi-<lb/>natione, & di voglia pro <lb/>pria.

</s>

Due pe&longs;i attaccati nella bilancia, &longs;e la bilancia &longs;arà tra loro in modo <lb/>diui&longs;a, chele parti ri&longs;pondano &longs;cambieuolmente à pe&longs;i; pe&longs;eranno <lb/>tanto ne'punti doue &longs;ono attaccati, quanto &longs;el'uno & l'altro fo&longs;&longs;e <lb/>pendente dal punto della diui&longs;ione.

Peroche, che puote <lb/>importare che la trutina <lb/>&longs;ia ouero in CF, ouero <lb/>in CG, e&longs;&longs;endo la bilan <lb/>cia DE &longs;empre &longs;o&longs;ten-<lb/>tata nell'i&longs;te&longs;&longs;o punto C? Ma affine che l'inganno loro re&longs;ti più chiaro.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Siala bilancia AB, il cui centro &longs;ia C, & &longs;iano due pe&longs;i EF pendenti da' punti <lb/>BG: & diuida&longs;i BG in H, &longs;i fattamente, che BH ad HG habbia la pro-<lb/>portione iste&longs;&longs;a, che hà il pe&longs;o E al pe&longs;o F. Dico ipe&longs;i EF pe&longs;are tanto in BG, <lb/>quanto &longs;e amendue pende&longs;&longs;ero dal punto H. faccia&longs;i AC eguale à CH. & &longs;i <lb/>come AC à CG, co&longs;i &longs;accia&longs;i il pe&longs;o E al pe&longs;o L. &longs;imilmente come AC à <lb/>CB, co&longs;i faccia&longs;i il pe&longs;o F al pe&longs;o M. & &longs;iano attaccati ipe&longs;i LM al punto <lb/>A. Horpercioche AC è eguale à CH, &longs;arà BC ver&longs;o CH come il pe&longs;o <lb/>M alpe&longs;o F. & percioche piu grande è BC di CH; &longs;arà anche il pe&longs;o M<emph.end type="italics"/><lb/><arrow.to.target n="note58"></arrow.to.target> <emph type="italics"/>maggiore di F. Diuida&longs;i dunque il pe&longs;o M in due parti QR, & &longs;iala parte di<emph.end type="italics"/><lb/><arrow.to.target n="note59"></arrow.to.target> <emph type="italics"/>Q eguale ad F; &longs;arà BC à CH, come RQ à Q: & diuidendo, come BH <lb/>ad HC, co&longs;i R à <expan abbr="q.">que</expan> Dapoi conuertendo, come CH ad HB, co&longs;i Q ad<emph.end type="italics"/><lb/><arrow.to.target n="note60"></arrow.to.target> <emph type="italics"/>R. Oltre à ciò perche CH è eguale à CA, &longs;arà HC ver&longs;o CG come il pe&longs;o <lb/>E al pe&longs;o L: maè piu grande HC di CG, però &longs;arà anche il pe&longs;o E maggio-<emph.end type="italics"/><lb/><arrow.to.target n="note61"></arrow.to.target> <emph type="italics"/>re del pe&longs;o L. Onde diuida&longs;i il pe&longs;o E in due parti NO, &longs;i fattamente, che la <lb/>parte di O &longs;ia eguale ad L, &longs;arà HC à CG come tutto lo NO ad O; & <lb/>diuidendo, come HG à GC, co&longs;i N ad O. & conuertendo, come CG à<emph.end type="italics"/><lb/><arrow.to.target n="note62"></arrow.to.target> <emph type="italics"/>GH, co&longs;i O ad N. & di nuouo componendo, come CH ad HG, co&longs;i ON<emph.end type="italics"/><lb/><arrow.to.target n="note63"></arrow.to.target> <emph type="italics"/>ad N. & come GH ad HB, co&longs;i è F ad ON. Per la qual co&longs;a per la pro <lb/>portione vguale come CH ad HB, co&longs;i F ad N. Ma come CH ad HB<emph.end type="italics"/><lb/><arrow.to.target n="note64"></arrow.to.target> <emph type="italics"/>co&longs;i è Q ad R: &longs;arà dunque Q ad R come F ad N. & permutando co-<lb/>me Q ad F; co&longs;i R ad N. ma la parte di Q è egual ad e&longs;&longs;o F. per la qual<emph.end type="italics"/><lb/><arrow.to.target n="note65"></arrow.to.target> <emph type="italics"/>co&longs;a la parte di R ancora &longs;arà eguale ad N. e&longs;&longs;endo dunque il pe&longs;o L eguale<emph.end type="italics"/><pb n="30"/><emph type="italics"/>ad O, & il pe&longs;o F eguale parimente al Q, & la parte di R eguale ad N; &longs;a <lb/>ranno ipe&longs;i LM eguali a i pe&longs;i EF. & percioche &longs;i come AC ver&longs;o CG, co<emph.end type="italics"/> <arrow.to.target n="note66"></arrow.to.target><lb/><emph type="italics"/>&longs;i è il pe&longs;o E al pe&longs;o L, ipe&longs;i EL pe&longs;eranno egualmente.

<emph type="italics"/>Sia la mede&longs;ima bilancia AB, il cui mezo C. dapoitutta la FG &longs;ia la trutina, <lb/>laquale &longs;tia immobile, & &longs;o&longs;tenga la bilancia AB nel punto C. & moua&longs;i la <lb/>bilancia in DE. & per-<lb/>cioche la trutina è &longs;opra, & <lb/>&longs;otto la bilancia, quale ango <lb/>lo &longs;arà cagione della grauez <lb/>za, e&longs;&longs;endo &longs;o&longs;tenuta la bi-<lb/>lancia DE &longs;empre nel pun <lb/>to mede&longs;imo?

</s>

&longs;imilmente percioche <lb/>&longs;i come AC è ver&longs;o CB, co&longs;i il pe&longs;o F è alpe&longs;o M, i pe&longs;i FM pe&longs;eranno <lb/>anco egualmente.

Diranno for-<lb/>&longs;e &longs;e la trutina &longs;arà &longs;o&longs;tenu-<lb/>ta dalla po&longs;&longs;anza po&longs;ta in <lb/>F, allhora CG &longs;arà tan-<lb/>to quanto la méta, & l'an-<lb/>golo DCG &longs;arà della gra <lb/>uezza cagione.

</s>

i pe&longs;i dunque LM pe&longs;eranuo egualmente co'pe&longs;i EF attacca-<lb/>ti in BG. & e&longs;&longs;endo la di&longs;tanza CA eguale alla di&longs;tanza CH, &longs;e dunque am <lb/>bidue i pe&longs;i EF &longs;ar anno attaccati in H, i pe&longs;i LM pe&longs;er anno egualmente co'<emph.end type="italics"/> <arrow.to.target n="note67"></arrow.to.target><lb/><emph type="italics"/>pe&longs;i EF attaccati in H. Ma LM pe&longs;a ancora egualmente con EF in GB. <lb/>Adunque &longs;ar anno egualmente graui i pe&longs;i EF in GB attaccati come in H. pe<emph.end type="italics"/> <arrow.to.target n="note68"></arrow.to.target><lb/><emph type="italics"/>&longs;eranno dunque tanto in BG quanto attaccati in H.<emph.end type="italics"/>

Ma&longs;e<emph.end type="italics"/><lb/><arrow.to.target n="fig35"></arrow.to.target><lb/><emph type="italics"/>egli &longs;arà &longs;ostenuto in G, allhora FCE &longs;arà cagione della grauezza, & la CF <lb/>&longs;arà tanto quanto la méta.

</s>

della qual co&longs;a niuna cagione pare poter&longs;i addurre, <lb/>&longs;e <expan abbr="nõ">non</expan> imaginata; peroche la méta (che dicono) non pare hauere à modo veruno nien <lb/>te di virtù che tiri dalla parte dell'angolo maggiore alcuna volta, & alcuna dalla <lb/>parte del minore.

<margin.target id="note58"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Ma &longs;ia &longs;o&longs;tenuta la trutina da due po&longs;&longs;anze in F cioè, & in G,<pb/>ilche &longs;i puote fare per nece&longs;&longs;ità, come &longs;e la po&longs;&longs;anza posta in F &longs;o&longs;&longs;e tanto debile, <lb/>che per &longs;e &longs;te&longs;&longs;a pote&longs;&longs;e &longs;o&longs;tentare &longs;olamente la metà del pe&longs;o & &longs;ia la po&longs;&longs;anza <lb/>posta in G eguale alla po&longs;&longs;anza po&longs;ta in F, & ambedue in&longs;ieme co' pe&longs;i &longs;o&longs;tenga-<lb/>no la bilancia.

<margin.target id="note59"></margin.target><emph type="italics"/>Per la con-<expan abbr="&longs;egu&etilde;za">&longs;eguenza</expan> del la<emph.end type="italics"/> 4. <emph type="italics"/>del<emph.end type="italics"/> 5.

</s>

all'hora quale angolo &longs;arà cagione della grauezza?

<margin.target id="note60"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

non gia <lb/>FCE, peroche la trutina è <lb/>in CF, & è &longs;o&longs;tentata in <lb/>F: ne meno il DCG, e&longs;&longs;en <lb/>do la trutina in CG, & pa <lb/>rimente &longs;o&longs;tentata in G. <lb/>Non &longs;aranno dunque gli an <lb/>goli della grauezza cagione. <lb/>Co&longs;i ne anche la bilancia <lb/>DE da que&longs;to &longs;ito per que <lb/>&longs;ta cagione &longs;i mouerà.

<margin.target id="note61"></margin.target><emph type="italics"/>Per la con&longs;e <expan abbr="gu&etilde;za">guenza</expan> della<emph.end type="italics"/> 4. <emph type="italics"/>del<emph.end type="italics"/> 5.

</s>

Ma<emph.end type="italics"/><lb/><arrow.to.target n="note117"></arrow.to.target> <emph type="italics"/>que&longs;ta loro &longs;entenza pare <lb/>e&longs;&longs;ere confermata da e&longs;&longs;i in <lb/>due modi.

<margin.target id="note62"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 18. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Primieramente<emph.end type="italics"/><lb/><arrow.to.target n="fig36"></arrow.to.target><lb/><emph type="italics"/>dicono Ari&longs;totele nelle que&longs;tioni mecaniche hauere propo&longs;to que&longs;te due que&longs;tioni &longs;o <lb/>lamente, & le &longs;ue dimo&longs;trationi e&longs;&longs;ere fondate &longs;i nel maggiore, & nel minore <lb/>angolo, & &longs;i nella giacitura della trutina della bilancia.

<margin.target id="note63"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Affermano dapoi que&longs;to <lb/>iste&longs;&longs;o in&longs;egnare la e&longs;perientia ancora, cioè, che la bilancia DE, &longs;tando la &longs;ua <lb/>trutina in CF, ritorna in AB egualmente di&longs;tante dall'orizonte.

<margin.target id="note64"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

& quando <lb/>la trutina &longs;tà in CG, mouer&longs;i in FG. Mane Ari&longs;totele, ne la e&longs;perienza fauo-<lb/>ri&longs;cono que&longs;ta loro opinione, anzi più to&longs;to le &longs;ono contrarij.

<margin.target id="note65"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Peroche in quan-<lb/>to appartiene alla e&longs;perienza &longs;i ingannano, e&longs;&longs;endo mani&longs;e&longs;to ciò per e&longs;perienza <lb/>accadere, all'hor che il centro ancora della bilancia &longs;arà collocato ò &longs;opra, ò &longs;ot-<lb/>to della bilancia, ma non già auenire que&longs;to stando la trutina ò &longs;opra &longs;olamente, <lb/>è &longs;otto.<emph.end type="italics"/>

<margin.target id="note66"></margin.target><emph type="italics"/>Perla<emph.end type="italics"/> 6. <emph type="italics"/>del primo di<*>r chimede del le co&longs;e che pe &longs;ano egualmente.<emph.end type="italics"/>

</s>

<margin.target id="note67"></margin.target><emph type="italics"/>Per lo<emph.end type="italics"/> 2. <emph type="italics"/><expan abbr="cõ">com</expan>.

</figure>

</s>

della not di questo.<emph.end type="italics"/>

<margin.target id="note117"></margin.target><emph type="italics"/>il Cardano.<emph.end type="italics"/>

</s>

<margin.target id="note68"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 3. <emph type="italics"/><expan abbr="cõ">com</expan>.

<emph type="italics"/>Imperoche &longs;e la bilancia A <lb/>B haue&longs;&longs;e il centro C <lb/>&longs;opra la bilancia, & fo&longs;-<lb/>&longs;e la trutina CD &longs;otto <lb/>la bilancia, & &longs;i moue&longs;-<lb/>&longs;e la bilancia in EF, al <lb/>lhora EF di nouo ri-<lb/>tornerà in AB. egual-<lb/>mente di&longs;tante dall'o-<lb/>rizonte.

</s>

della not ai questo.<emph.end type="italics"/>

&longs;imilmente &longs;e la <lb/>bilancia haue&longs;&longs;e il cen-<lb/>tro C &longs;otto la bilancia, <lb/>& &longs;o&longs;&longs;e la trutina CD <lb/>&longs;opra la bilancia, et &longs;i mo <lb/>ue&longs;&longs;e la bilancia in EF,<emph.end type="italics"/> <arrow.to.target n="note118"></arrow.to.target><lb/><emph type="italics"/>egli è manife&longs;to, che la bi <lb/>lancia &longs;i mouerà in giu <lb/>dalla parte di F, &longs;tan-<lb/>do la trutina &longs;opra la bi-<lb/>lancia.

</s>

& in qual &longs;i vo-<lb/>glia altro &longs;ito che &longs;ia la <lb/>trutina, auerrà &longs;empre il <lb/>mede&longs;imo.

</figure>

<emph type="italics"/>Ma &longs;iano i pe&longs;i EF attaccati in CB; & &longs;ia C il centro della bilancia, & diuida&longs;i <lb/>CB in H, per modo che CH ver&longs;o HB &longs;ia come il pe&longs;o F al pe&longs;o E. Dico <lb/>che i pe&longs;i EF pe&longs;er anno tanto in CB quanto nel punto H. faccia&longs;i CA egua <lb/>le à CH, & come CA ver&longs;o CB; co&longs;i faccia&longs;i il pe&longs;o F ver&longs;o vn'altro, che <lb/>&longs;ia D, ilquale &longs;i appicchi in A. Hor percioche CH è eguale à CA, &longs;arà CH <lb/>ver&longs;o CB, come F à D; & ben è maggiore CB di CH, però il pe&longs;o D &longs;a <lb/>rà maggiore del pe&longs;o F. Diuida&longs;i dunque il D in due parti GK, & &longs;ia il G<emph.end type="italics"/> <arrow.to.target n="note69"></arrow.to.target><lb/><emph type="italics"/>eguale allo F; &longs;arà BC à CH come GK ver&longs;o il G; et diuidendo, come BH <lb/>ad HC, co&longs;i K ver&longs;o G; & conuertendo come CH ad HB, co&longs;i G ver-<emph.end type="italics"/> <arrow.to.target n="note70"></arrow.to.target><lb/><emph type="italics"/>&longs;o K. & come CH ad HB, co&longs;i è F ver&longs;o E. Dunque come G ver-<lb/>&longs;o K co&longs;i è F ad E. & permutando come G ad F, co&longs;i K ad E. & per-<emph.end type="italics"/> <arrow.to.target n="note71"></arrow.to.target><lb/><emph type="italics"/>che GF &longs;ono eguali, &longs;aranno anche KE tra loro eguali.

</s>

Concio&longs;ia dunque che <lb/>la parte G &longs;ia eguale ad F, & il K ad e&longs;&longs;o E; &longs;arà tutto il GK eguale a i pe<emph.end type="italics"/> <arrow.to.target n="note72"></arrow.to.target><lb/><emph type="italics"/>&longs;i EF. & percioche AC è eguale à CH; &longs;e dunque i pe&longs;i EF &longs;aranno penden <lb/>ti dal punto H, il pe&longs;o D pe&longs;erà egualmente co'pe&longs;i EF attaccati in H. Ma <lb/>pe&longs;a anche egualmente con eßi in CB, cioè F in B, & E in C; per e&longs;&longs;ere <lb/>come AC ver&longs;o CB, co&longs;i F ver&longs;o D: percioche il pe&longs;o E pendente da C. <lb/>centro della bilancia non è cau&longs;a, che la bilancia &longs;i moua in alcuna delle due parti. <lb/>tanto &longs;aranno dunque graui i pe&longs;i EF in CB, quanto in H appicati.<emph.end type="italics"/>

Adunque <expan abbr="nõ">non</expan> <lb/>è la trutina, ma il centro <lb/>della bilancia cagione di <lb/>cotali diuer&longs;i effetti.<emph.end type="italics"/>

</s>

<pb/>

<margin.target id="note118"></margin.target><emph type="italics"/>Per la terz<*> di questo.<emph.end type="italics"/>

<margin.target id="note69"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note70"></margin.target><emph type="italics"/>Per la con&longs;e <expan abbr="gu&etilde;za">guenza</expan> della<emph.end type="italics"/> 4. <emph type="italics"/>del<emph.end type="italics"/> 5.

<emph type="italics"/>Egli è pero d'auertire in que&longs;ta parte che con di&longs;&longs;icultà &longs;i puote lauora re vna bilancia <lb/>materiale, che in vno punto &longs;olamente &longs;ia &longs;o&longs;tenuta, &longs;i come con la mente la imagi-<lb/>niamo, & habbia le braccia dal centro co&longs;i eguali non &longs;olamente in lunghezza, ma <lb/>in larghezza, & in profundità, ò gro&longs;&longs;ezza, che tutte le parti di quà, & di là pe&longs;i-<lb/>no a punto egualmente.

</s>

percio che la materia di&longs;&longs;icili&longs;&longs;imam ente pati&longs;ce cotale giu-<lb/>&longs;ta mi&longs;ura.

</s>

<margin.target id="note71"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del quinto.<emph.end type="italics"/>

Per laqual co&longs;a &longs;e con&longs;idereremo il centro e&longs;&longs;ere in e&longs;&longs;a bilancia, non bi-<lb/>&longs;ogna ricorrere al &longs;en&longs;o, concio&longs;ia, che le co&longs;e artificiate non &longs;i po&longs;&longs;ano ridurre a quel <lb/>fommo grado di per&longs;ettione.

</s>

Ma nelle altre co&longs;e la e&longs;perienza veramente potrà in&longs;e <lb/>gnare le co&longs;e che appaiono percioche <expan abbr="quãtunque">quantunque</expan> ilcentro della <expan abbr="bilãcia">bilancia</expan> &longs;empre &longs;ia vn <lb/>punto, nondimeno quando egli &longs;arà &longs;opra la bilancia, poco importa, &longs;e ben la bilancia <lb/>non &longs;ara &longs;o&longs;tenuta in quel punto co&longs;i puntalmente però che per e&longs;&longs;ere &longs;empre &longs;opra la <lb/>bilancia auerrà &longs;empre il mede&longs;imo.

</s>

Con &longs;imile modo, quando egli anco è &longs;otto la bi-<lb/>lancia, ilche tuttauia non accade stando il centro in e&longs;&longs;a bilancia, per che &longs;e egli non <lb/>&longs;arà &longs;o&longs;tenuto &longs;empre in quel mezo accuratamente, &longs;ara differenza, e&longs;&longs;endo co&longs;a faci <lb/>li&longs;&longs;ima, che quel centro, muti il proprio &longs;ito, mentre &longs;i moue la bilancia.<emph.end type="italics"/>

</s>

<pb/>

<margin.target id="note72"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<emph type="italics"/>Ma che Ari&longs;totele habbia <lb/>propo&longs;to due que&longs;tioni &longs;o <lb/>lamente, cioè perche la <lb/>trutina &longs;tando &longs;opra, &longs;e <lb/>la bilancia <expan abbr="nõ">non</expan> &longs;arà egual <lb/>mente di&longs;tante dall'ori-<lb/>zonte in equilibrio, cioè <lb/>egualmente di&longs;tante dal <lb/>orizonte ritorna, ma &longs;e la <lb/>trutina &longs;ara po&longs;ta &longs;otto <lb/>non ritorna, ma di piu &longs;i <lb/>moue <expan abbr="&longs;ecõdo">&longs;econdo</expan> la parte ba&longs; <lb/>&longs;a: egli è verò per certo. <lb/>Ma non già per que&longs;to le <lb/>dimo&longs;trationi &longs;ue &longs;ono <lb/>&longs;ondate nell'angolo mag <lb/>giore, ò minore, & nella <lb/>giacitura della trutina, <lb/>come e&longs;&longs;i dicono: per cio-<lb/>che in questo non com-<lb/>prendono la <expan abbr="m&etilde;te">mente</expan> del filo <lb/>&longs;ofo, che a&longs;&longs;egna la ragio <lb/>ne de gli effetti diuer&longs;i <lb/>de'mouimenti della bilan <lb/>cia.

</s>

peroche tanto è lon-<lb/>tano, che il filo&longs;o&longs;o attri <lb/>bui&longs;ca que&longs;ti diuer&longs;i effet<emph.end type="italics"/><lb/><arrow.to.target n="fig37"></arrow.to.target><lb/><emph type="italics"/>ti à gli angoli, che piu to&longs;to dica e&longs;&longs;ere cagione l'ecce&longs;&longs;o, & quel &longs;opra più della gran <lb/>dezza che è dal perpendicolo dell'uno delle braccia della bilancia hor dall'una parte, <lb/>hora dall'altra.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Sia <expan abbr="finalm&etilde;te">finalmente</expan> la <expan abbr="bilãcia">bilancia</expan> AB, & da i <expan abbr="p&utilde;ti">punti</expan> AB &longs;iano <expan abbr="p&etilde;denti">pendenti</expan> ipe&longs;i EF, & &longs;idil centro <lb/>della bilancia C fra ipe&longs;i, & diuida&longs;i la AB in D, talche AD ver&longs;o DB <lb/>&longs;ia come il pe&longs;o F alpe&longs;o E. Dico che i pe&longs;i EF pe&longs;ano tanto in AB, quan <lb/>to &longs;e ambidue &longs;o&longs;&longs;ero pendenti dal punto D. faccia&longs;i CG eguale à CD; & co-<lb/>me DC à CA, co&longs;i faccia&longs;i il pe&longs;o E ad vn'altro pe&longs;o H, ilquale &longs;ia attac <lb/>cato in D. & come GC ver&longs;o CB, co&longs;i faccia&longs;i il pe&longs;o F ad vn'altro che <lb/>&longs;ia K, & attachi&longs;i K in G. Horpercioche, come il BC è ver&longs;o il CG, cioè <lb/>ver&longs;o il CD, co&longs;i il pe&longs;o K ad F; &longs;arà il K maggiore del pe&longs;o F. Per laqual <lb/>co&longs;a diuida&longs;i il pe&longs;o K in L & in MN, & &longs;accia&longs;i la parte L eguale ad F,<emph.end type="italics"/><lb/><arrow.to.target n="note73"></arrow.to.target> <emph type="italics"/>&longs;arà come BC à CD, co&longs;i tutto LMN ad L; & diuidendo, come BD<emph.end type="italics"/><lb/><arrow.to.target n="note74"></arrow.to.target> <emph type="italics"/>ver&longs;o DC, co&longs;i la parte MN alla parte L. come dunque BD à DC, co&longs;i <lb/>la parte MN ad F. & come AD à DB, co&longs;i F ad E. Per laqual co&longs;a<emph.end type="italics"/><lb/><arrow.to.target n="note75"></arrow.to.target> <emph type="italics"/>per la egual proportione, come AD ver&longs;o DC, co&longs;i MN ad E. & e&longs;&longs;endo AD<emph.end type="italics"/><lb/><arrow.to.target n="note76"></arrow.to.target> <emph type="italics"/>maggiore di CD; &longs;arà anco la parte MN maggiore del pe&longs;o E. Diuida&longs;i dun <lb/>que MN in due parti MN, & &longs;ia M eguale ad E. &longs;arà come AD à<emph.end type="italics"/><lb/><arrow.to.target n="note77"></arrow.to.target> <emph type="italics"/>DC, co&longs;i NM ad M; & diuidendo, come AC ver&longs;o CD, co&longs;i N ad M:<emph.end type="italics"/><lb/><arrow.to.target n="note78"></arrow.to.target> <emph type="italics"/>& conuertendo, come DC ver&longs;o CA, co&longs;i M ad N. & come DC à<emph.end type="italics"/><lb/><arrow.to.target n="note79"></arrow.to.target> <emph type="italics"/>CA, co&longs;i è E ad H; &longs;arà dunque M ad N come E ad H; & permutan <lb/>do come M ad E, co&longs;i N ad H. Ma per e&longs;&longs;ere ME traloro eguali, &longs;aran-<lb/>no anche NH tra &longs;e eguali.

<emph type="italics"/>Come stando la trutina &longs;opra in CF, il perpendicolo &longs;arà FCG, il quale &longs;em-<lb/>pre inchina, &longs;econdo lui, ver&longs;o il centro del mondo, il quale anco diuide la bilancia mo&longs; <lb/>&longs;a in DE in parti di&longs;uguali: & la parte maggiore è ver&longs;o il D, & quel che è piu, <lb/>inchina in giu.

</s>

& percioche co&longs;i è AC ver&longs;o CD, come H <lb/>ad E: i pe&longs;i HE pe&longs;eranno egualmente.

Adunque dalla parte di D la bilancia &longs;i mouerà in giu fin che ri-<lb/>torni in AB. Ma &longs;e la trutina &longs;arà in CG di &longs;otto, &longs;arà GCF il perpendico-<lb/>lo, ilquale diuiderà parimente la bilancia DE in parte di&longs;uguali, & la parte mag <lb/>giore &longs;arà ver&longs;o E; Per laqual co&longs;a la bilancia &longs;i mouerà in giu dalla parte di E. <lb/>& accioche que&longs;to &longs;ia dirittamente compre&longs;o, &longs;appia&longs;i, che quando la trutina è &longs;o-<lb/>pra la bilancia, &longs;i ha da intendere, che anche il centro della bilancia &longs;ia &longs;opra la bi-<lb/>lancia, & &longs;e di &longs;otto, anche il centro deue &longs;tare di &longs;otto, come piu a ba&longs;&longs;o manife&longs;te-<lb/>ra&longs;&longs;i, Altramente la dimo&longs;tratione di Ari&longs;totele non conchiuderebbe nulla, pero <lb/>che stando il centro in e&longs;&longs;a bilancia, come in C moua&longs;i la bilancia in qual &longs;i voglia<emph.end type="italics"/><pb n="21"/><emph type="italics"/>modo, il perpendicolo FG non diuiderà giamai la bilancia &longs;e non nel punto C, et <lb/>in parti eguali.

</s>

&longs;imilmente percioche, come è GC à CB, <lb/>co&longs;i F ver&longs;o K, i pe&longs;i etiandio KF pe&longs;eranno egualmente.

Onde la &longs;entenza di Ari&longs;totele non &longs;olamente non gli &longs;auori&longs;ce, ma <lb/>gli fa anche grandi&longs;sima <lb/>mente contra.

</s>

Adunque i pe&longs;i<emph.end type="italics"/><lb/><arrow.to.target n="note80"></arrow.to.target> <emph type="italics"/>EK HF nella bilancia AB, il cui centro &longs;ia C pe&longs;eranno egualmente.

il che <lb/>non &longs;olamente è chiaro <lb/>dalla &longs;econda & terza <lb/>propo&longs;itione di que&longs;to li <lb/>bro, ma anco percioche <lb/>&longs;tando il centro &longs;opra <lb/>la bilancia, il pe&longs;o alzato <lb/>acqui&longs;ta grauezza mag <lb/>giore per cau&longs;a del &longs;ito. <lb/>Dalla qual co&longs;a accade il <lb/>ritorno della bilancia ad <lb/>eguale di&longs;tanza dall'ori-<lb/>zonte.

</s>

& con <lb/>cio&longs;ia che GC &longs;ia eguale à CD, & il pe&longs;o H &longs;ia pur eguale ad N, ipe&longs;i NH<emph.end type="italics"/><pb n="31"/><emph type="italics"/>pe&longs;eranno egualmente.

Ma per lo con-<lb/>trario auiene quando il <lb/>centro è &longs;otto la bilan-<lb/>cia.

</s>

& percioche tutti pe&longs;ano egualmente, tolti via i pe&longs;i HN, <lb/>iquali pe&longs;ano egualmente, i re&longs;tanti pe&longs;eranno egualmente; cioè i pe&longs;i EF, & il pe<emph.end type="italics"/> <arrow.to.target n="note81"></arrow.to.target><lb/><emph type="italics"/>&longs;o LM pendenti dal centro C della bilancia.

Le quali co&longs;e tutte <lb/>&longs;i dimo&longs;treranno in que-<lb/>&longs;ta maniera, pre&longs;uppo-<lb/>nendo le co&longs;e, che di &longs;o-<emph.end type="italics"/><lb/><arrow.to.target n="fig38"></arrow.to.target><lb/><emph type="italics"/>pra furono dechiarate, cioè il pe&longs;o &longs;ar&longs;i più graue da quelloco dal quale &longs;cende piu <lb/>dirittamente, & da quello che egli &longs;ale piu dirittamente far&longs;i parimente piu <lb/>graue.<emph.end type="italics"/>

</s>

Ma percioche la parte L è egua-<lb/>le ad F, & la parte M è eguale alla parte E; &longs;arà tutto LM eguale a i pe&longs;i <lb/>FE in&longs;ieme pre&longs;i.

<pb/>

</figure>

<emph type="italics"/>Sia la bilancia AB egualmente di&longs;tante dall'orizonte, il cui centro C &longs;ia &longs;opra la <lb/>bilancia, & &longs;ia il perpendicolo CD: & &longs;iano i centri della grauezza di pe&longs;i eguali <lb/>po&longs;ti in AB: & la bilancia &longs;ia mo&longs;&longs;a in EF. Dico, che il pe&longs;o posto in E ha <lb/>grauezzamaggiore, che il <lb/>pe&longs;o posto in F. & per-<lb/>ciò la bilancia EF e&longs;&longs;e-<lb/>re per ritornare in AB. <lb/>&longs;ia allungata prima la linea <lb/>CD fin'al centro del mon <lb/>do, che &longs;ia S. Dapoi &longs;ia-<lb/>no congiunte le linee AC, <lb/>CB, EC, CF, HS; <lb/>& dai punti EF &longs;iano ti-<lb/>rate le linee EKGFL egual <lb/><expan abbr="m&etilde;te">mente</expan> di&longs;tanti da HS. Per-<lb/>cioche dunque la di&longs;ce&longs;a na <lb/>turale diritta di tutta la <lb/>grandezza, cioè della bilan <lb/>cia EF co&longs;i di&longs;po&longs;ta in&longs;ie <lb/>me co'pe&longs;i è &longs;econdo la gra-<lb/>uezza del centro H per la <lb/>dirittalinea HS; &longs;arà pa <lb/><expan abbr="rim&etilde;te">rimente</expan> la di&longs;ce&longs;a de'pe&longs;ime&longs; <lb/>&longs;i in EF co&longs;i di&longs;po&longs;ti &longs;econ <lb/>do le linee diritte E<emph.end type="italics"/>K <lb/><emph type="italics"/>FL egualmente distanti <lb/>da HS, &longs;i come di &longs;opra <lb/>habbiamo dimo&longs;trato.

</s>

& e&longs;&longs;endo CG eguale à CD, &longs;e i pe&longs;i EF &longs;aranno &longs;atti <lb/>pendenti dal punto D, ipe&longs;i EF appiccati in D pe&longs;eranno <expan abbr="egualm&etilde;te">egualmente</expan> con LM. <lb/>Per laqual co&longs;a LM pe&longs;erà <expan abbr="egualm&emacr;te">egualmente</expan> <expan abbr="t&amacr;to">tanto</expan> ad eßi EF appiccati in AB, <expan abbr="qu&amacr;-<lb> to">quan-<lb/>to</expan> &longs;e fo&longs;&longs;ero appiccati nel punto D; peroche la bilancia rimane &longs;empre nell'i&longs;te&longs;&longs;o<emph.end type="italics"/> <arrow.to.target n="note82"></arrow.to.target><lb/><emph type="italics"/>modo.

La <lb/>di&longs;ce&longs;a dunque, & la &longs;ali-<lb/>ta de i pe&longs;i po&longs;ti in EF &longs;i <lb/>dirà più, & meno obliqua <lb/>&longs;econdo la vicinanza, ò lon <lb/>tananza diputata &longs;econdo<emph.end type="italics"/><lb/><arrow.to.target n="note119"></arrow.to.target> <emph type="italics"/>le linee EK FL. & per-<lb/>cioche li due lati AD DC <lb/>&longs;ono eguali a i due lati BD<emph.end type="italics"/><lb/><arrow.to.target n="fig39"></arrow.to.target><lb/><emph type="italics"/>DC; & gli angoli al D &longs;ono retti, &longs;arà il lato AC eguale al lato CB. & e&longs;-<lb/>&longs;endo il punto C immobile; mentre, che i punti AB &longs;imoueranno, de &longs;criueran-<lb/>no la circonferenza di vno cerchio, il cui mezo diametro &longs;arà AC. Per laqual co<emph.end type="italics"/><lb/><arrow.to.target n="note120"></arrow.to.target> <emph type="italics"/>&longs;a co'l centro C &longs;ia de&longs;critto il cerchio AE BF, i punti AB E<emph.end type="italics"/>F <emph type="italics"/>&longs;aranno nel <lb/>la circonferenza del cerchio.

</s>

Adunque i pe&longs;i EF pe&longs;eranno tanto in AB quanto nel punto D; che <lb/>bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

ma e&longs;&longs;endo EF eguale ad AB, &longs;arà la circonfe-<lb/>renza EAF eguale alla circonferenza AFB. Onde tolta via la comune AF<emph.end type="italics"/><pb n="22"/><emph type="italics"/>&longs;arà la circonferenza EA eguale alla cir conferenza FB. Hor percioche l'ango-<lb/>lo mi&longs;to CEA è eguale al mi&longs;to CFB, & HFB è maggiore di CFB, &<emph.end type="italics"/> <arrow.to.target n="note121"></arrow.to.target><lb/><emph type="italics"/>l'angolo HEA è minore di CEA; &longs;arà l'angolo HFB maggiore dell'angolo <lb/>HEA. Da quali &longs;e &longs;aranno leuati via gli angoli HFG HEK eguali, &longs;arà l'an <lb/>golo GFB maggiore dell'angolo KEA. Adunque la di&longs;ce&longs;a del pe&longs;o po&longs;to in <lb/>E &longs;arà meno obliqua della &longs;alita del pe&longs;o po&longs;to in F. & <expan abbr="qu&amacr;tunque">quantunque</expan> il pe&longs;o po&longs;to in E <lb/>de&longs;cendendo, & il pe&longs;o po&longs;to in F &longs;alendo &longs;i mouino per eguali circonferenze, nondi <lb/>meno percioche il pe&longs;o po&longs;to in E da que&longs;to luogo di&longs;cende piu dirittamente di quel <lb/>che il pe&longs;o F <expan abbr="a&longs;c&etilde;de">a&longs;cende</expan>:pero la naturale po&longs;&longs;anza del pe&longs;o po&longs;to in E &longs;upererà la <expan abbr="re&longs;i&longs;t&etilde;">re&longs;i&longs;tem</expan> <lb/>za della violentia del pe&longs;o F. Onde grauezza maggiore hauerà il pe&longs;o posto in E, <lb/>che il pe&longs;o po&longs;to in F. Adunque il pe&longs;o po&longs;to in E &longs;i mouerà in giù & il pe&longs;o po&longs;to <lb/>in F in sù, fin che la bilancia EF ritorni in AB, che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note73"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note119"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 4. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note74"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 23. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note120"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 28. <emph type="italics"/>del terzo.<emph.end type="italics"/>

</s>

<margin.target id="note75"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note121"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> <*>. <emph type="italics"/>del printo.<emph.end type="italics"/>

</s>

<margin.target id="note76"></margin.target><emph type="italics"/>Corollario della quarta del quinto.<emph.end type="italics"/>

<emph type="italics"/>La ragione di que&longs;to effetto po&longs;ta da Ari&longs;totele qui &longs;i puote vedere manife&longs;ta.

</s>

Percio-<emph.end type="italics"/> <arrow.to.target n="note122"></arrow.to.target><lb/><emph type="italics"/>che &longs;ia il punto N doue le linee CS EF &longs;i tagliano in&longs;ieme.

<margin.target id="note77"></margin.target>11. <emph type="italics"/>del<emph.end type="italics"/> 5.

</s>

& percioche HE <lb/>è eguale ad HF; &longs;arà NE maggiore di NF. adunque la linea CS, che no-<lb/>ma perpendicolo, diuiderà la bilancia EF in parti di&longs;uguali.

<margin.target id="note78"></margin.target>16. <emph type="italics"/>del<emph.end type="italics"/> 5.

</s>

concio&longs;ia dunque, che <lb/>la parte della bilancia NE &longs;ia maggiore della NF, & quel che è di più bi&longs;o-<lb/>gni, che &longs;ia portato in giù, la bilancia EF dalla parte di E &longs;i mouerà in giu finche <lb/>ritorni in AB.<emph.end type="italics"/>

<margin.target id="note79"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>del<emph.end type="italics"/> 1. <emph type="italics"/>di Archi mede delle co fa che egual <expan abbr="m&etilde;te">mente</expan> pe&longs;ano.<emph.end type="italics"/>

</s>

<margin.target id="note80"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 2. <emph type="italics"/>no titia commu ne di que&longs;io.<emph.end type="italics"/>

<margin.target id="note122"></margin.target><emph type="italics"/>Ragione de Aristotele.<emph.end type="italics"/>

</s>

<margin.target id="note81"></margin.target><emph type="italics"/>Per la commune notitia di questo.<emph.end type="italics"/>

<emph type="italics"/>Oltre à cio da quelle co&longs;e, che <lb/>fin hora &longs;ono &longs;tate dette, <lb/>&longs;i puote affermare, la bilan <lb/>cia EF da quel &longs;ito mo-<lb/>uer&longs;i piu velocemente in <lb/>AB; d'onde la linea EF <lb/>allungata a dirittura per-<lb/>uenga nel centro del mon-<lb/>do.

</s>

come &longs;ia EFS vna <lb/>linea diritta.

<margin.target id="note82"></margin.target><emph type="italics"/>Per la com munenotitia di questo.<emph.end type="italics"/>

</s>

& percioche <lb/>CD CK &longs;ono tra loro <lb/>eguali.

Ma que&longs;te co&longs;e tutte dimo&longs;treremo in altra maniera, & piu Mechani <lb/>camente.

</s>

&longs;e dunque col cen-<lb/>tro C, & con lo &longs;patio <lb/>CD &longs;i de&longs;criuerà il cerchio <lb/>DHM, &longs;aranno i punti <lb/>DH nella circonferenza <lb/>del cerchio.

</figure>

<emph type="italics"/>Sia la bilancia AB, & il &longs;uo centro C, & &longs;iano, come nel primo ca&longs;o, due pe&longs;i EF <lb/>pendenti da i punti BG: & &longs;ia GH ad HB, come il pe&longs;o F al pe&longs;o E. Di-<lb/>co che ipe&longs;i EF pe&longs;eranno tanto in GB, quanto &longs;e ambidue &longs;te&longs;&longs;ero pendenti <lb/>dal punto H della diui&longs;ione.

</s>

Siano di&longs;po&longs;te le mede&longs;ime co&longs;e, cioè faccia&longs;i AC <lb/>eguale à CH, & dal punto A &longs;iano appe&longs;i due pe&longs;i LM, per modo che il pe <lb/>&longs;o E ver&longs;o il pe&longs;o L &longs;ia come CA ver&longs;o CG; & come CB ver&longs;o CA, co <lb/>&longs;i &longs;ia il pe&longs;o M ver&longs;o il pe&longs;o F. Ipe&longs;i LM pe&longs;eranno egualmente (come è detto <lb/>di &longs;opra) conlipe&longs;i EF appiccati in GB. Siano dapoi due punti NO li centri <lb/>della grauezza de' pe&longs;i EF; & &longs;iano congiunte le linee GN BO; & &longs;ia con-<lb/>giunta NO, laquale &longs;arà come bilancia; laquale etiandio faccia sì, che le linee <lb/>GN BO &longs;iano traloro egualmente di&longs;tanti; & dal punto H &longs;ia tirata la HP <lb/>à piombo dell'orizonte, laquale tagli NO nel P, & &longs;ia egualmente distante dal <lb/>le linee GN BO. In fine congiunga&longs;i GO, laquale tagli HP in R. Percio<emph.end type="italics"/> <arrow.to.target n="note83"></arrow.to.target><lb/><emph type="italics"/>che dunque HR è egualmente di&longs;tante dal lato BO del triangolo GBO; &longs;arà <lb/>la GH ver&longs;ola HB, come GR ad RO. Similmente percioche RP è egual<emph.end type="italics"/><pb/><arrow.to.target n="fig22"></arrow.to.target><lb/><emph type="italics"/>mente di&longs;tante dal lato GN del triangolo OGN; &longs;arà GR ver&longs;o RO, come <lb/>NP ver&longs;o PO. Per laqual co&longs;a come GH ad HB, così è NP ver&longs;o PO.<emph.end type="italics"/><lb/><arrow.to.target n="note84"></arrow.to.target> <emph type="italics"/>Ma come GH ver&longs;o HB, così è il pe&longs;o F ver&longs;o il pe&longs;o E; adunque come NP <lb/>ver&longs;o PO, così è il pe&longs;o F ver&longs;o il pe&longs;o E. Dunque il punto P &longs;arà il centro<emph.end type="italics"/><lb/><arrow.to.target n="note85"></arrow.to.target> <emph type="italics"/>della grauezza della magnitudine compo&longs;ta di ambidue i pe&longs;i EF. Intendan&longs;i <lb/>dunque i pe&longs;i EF e&longs;&longs;ere in maniera dalla bilancia NO annodati, come &longs;e fo&longs;&longs;e vna <lb/>grandezza &longs;ola d'ambidue ipe&longs;i EF composta, & attacata ne i punti BG, &longs;e dun-<lb/>que &longs;ar anno &longs;cioltii legamenti BG de' pe&longs;i; rimarr anno i pe&longs;i EF <expan abbr="p&etilde;denti">pendenti</expan> da HP; <lb/>&longs;i come prima &longs;tauane in GB. Ma i pe&longs;i EF appiccati in GB pe&longs;ano egualmente <lb/>co'ipe&longs;i LM, & ipe&longs;i EF pendenti dal punto H hanno l'i&longs;te&longs;&longs;a di&longs;po&longs;itione ver<emph.end type="italics"/><lb/><arrow.to.target n="note86"></arrow.to.target> <emph type="italics"/>&longs;o la bilancia AB, come &longs;e &longs;o&longs;&longs;ero appiccati in BG: Gli isteßi pe&longs;i dunque EF <lb/>pendenti da H pe&longs;aranno egualmente con gli i&longs;te&longs;&longs;i pe&longs;i LM. Sono dunque egual-<lb/>mente graui i pe&longs;i EF attaccati in GB, come attaccati in H.<emph.end type="italics"/>

Ma perche la <lb/>CH è à piombo di EF, <lb/>toccherà la EHS il cer-<lb/>chio DHM nel punto <lb/>H. il pe&longs;o dunque po&longs;to in <lb/>H, (&longs;i come di &longs;opra hab <lb/>biamo prouato) &longs;arà piu<emph.end type="italics"/><lb/><arrow.to.target n="fig40"></arrow.to.target><pb/><emph type="italics"/>graue che in verun altro &longs;ito del cerchio DHM. Adunque la grandezza fatta de' <lb/>pe&longs;i EF, & della bilancia EF, il cui centro della grauczza sta in H, in cote&longs;to <lb/>&longs;ito grauerà più, che in qual &longs;i voglia altro &longs;ito del cerchio &longs;i troui il punto H. Da <lb/>que&longs;to &longs;ito adunque &longs;i mouera piu velocemente che da qualunque altro.

</s>

& &longs;e lo H <lb/>&longs;arà piu da pre&longs;&longs;o al D <lb/>manco grauerà, & me-<lb/>no &longs;i mouerà da quel &longs;ito; <lb/>peroche &longs;empreè piu torta <lb/>la &longs;ce&longs;a, & meno diritta. <lb/>La bilancia dunque EF <lb/>&longs;i mouerà più velocemen-<lb/>te da que&longs;to &longs;ito, che da <lb/>altro &longs;ito, & &longs;e piu dapre&longs; <lb/>&longs;o acco&longs;teraßi ad AB, <lb/>d'indi &longs;i mouerà meno poi <lb/>quanto piu da lunge &longs;arà <lb/>di&longs;tante il punto H dal <lb/>punto C &longs;i mouerà più ve <lb/>locemente, il che non &longs;olo <lb/>da Ari&longs;totele nel principio <lb/>delle que&longs;tioni mecaniche, <lb/>& dai detti di &longs;opra è ma <lb/>nife&longs;to, ma ancora da quel <lb/>le co&longs;e, che di &longs;otto nella <lb/>&longs;e&longs;ta propo&longs;itione &longs;iamo <lb/>per dire, apparerà chiaro. <lb/>La bilancia dunque EF <lb/>quanto più &longs;arà lontana <lb/>dal &longs;uo centro, &longs;i mouerà anche piu velocemente.<emph.end type="italics"/>

</s>

</figure>

</figure>

<margin.target id="note83"></margin.target><emph type="italics"/>Per la &longs;ecom da del &longs;esta.<emph.end type="italics"/>

<emph type="italics"/>Sia poi labilancia AB, il cui centro C stia &longs;otto la bilancia, & &longs;iano in AB <lb/>pe&longs;i eguali, & &longs;ia mo&longs;&longs;a la bilancia in EF. Dico che il pe&longs;o ha grauezza maggio-<lb/>re in F, che in E. & <lb/>perciò la bilancia EF <lb/>e&longs;&longs;ere per mouer&longs;i in giù <lb/>dalla parte di F. &longs;ia allun <lb/>gata la linea DC dall'una <lb/>parte, & dall'altra fin <lb/>nel centro del mondo S, <lb/>& fin ad O, & &longs;ia tira <lb/>tala linea HS, alla qua <lb/>le dai punti EF &longs;iano ti <lb/>rate le linee GEK FL <lb/>egualmente di&longs;tanti, & <lb/>&longs;iano congiunte le CE <lb/>CF: & dal centro C <expan abbr="cõ">com</expan> <lb/>lo &longs;patio CE de&longs;criua&longs;i <lb/>il cerchio AEO BF. <lb/>&longs;i dimo&longs;trerà &longs;imilmente <lb/>i punti AB EF e&longs;&longs;e-<lb/>re nella circonferenza del <lb/>cerchio, & che la di&longs;ce&longs;a <lb/>della bilancia EF in&longs;ie-<lb/>me co'pe&longs;i &longs;i fà diritta &longs;e <lb/>condo la linea HS: & <lb/>de ipe&longs;i po&longs;ti in EF &longs;e-<lb/>condo le linee GK FL <lb/>egualmente di&longs;tanti da <lb/>HS. Et percioche l'ango <lb/>lo CFP è eguale all'an <lb/>golo CEO &longs;arà l'ango-<lb/>lo HFP maggiore del-<lb/>l'angolo HEO. ma l'an<emph.end type="italics"/> <arrow.to.target n="note123"></arrow.to.target><lb/><emph type="italics"/>golo HFL è eguale al-<lb/>l'angolo HEG. Da qua <lb/>li &longs;e &longs;aranno leuati via <lb/>gli angoli HFP HEO,<emph.end type="italics"/><lb/><arrow.to.target n="fig41"></arrow.to.target><lb/><emph type="italics"/>&longs;arà l'angolo LFP minore dell' angolo GEO. Per laqual co&longs;a la &longs;ce&longs;a del pe&longs;o <lb/>po&longs;to in F &longs;arà piu diritta della a&longs;ce&longs;a del pe&longs;o po&longs;to in E. Adunque la po&longs;&longs;anza <lb/>naturale del pe&longs;o po&longs;to in F &longs;upererà la re&longs;i&longs;tenza della violentia del pe&longs;o po&longs;to in <lb/>E. & percio hauerà maggior grauezza il pe&longs;o di F, che il pe&longs;o di E. Adunque <lb/>il pe&longs;o di F &longs;imouer à in giù, & il pe&longs;o di E &longs;i mouerà in sù.<emph.end type="italics"/>

</s>

<pb/>

<margin.target id="note84"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del quinto<emph.end type="italics"/>

</figure>

<margin.target id="note123"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note85"></margin.target><emph type="italics"/>Per la &longs;esta del primo di Archimede d'lle co&longs;e, che pe&longs;ano egual mente.<emph.end type="italics"/>

<arrow.to.target n="note124"></arrow.to.target><emph type="italics"/>La ragione di Ari&longs;totele parimente qui è cbiara.

</s>

Percioche &longs;ia il punto N doue le <lb/>linee CO EF &longs;i tagliano in&longs;ieme.

</s>

<margin.target id="note86"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 1. <emph type="italics"/>di questo.<emph.end type="italics"/>

&longs;arà la NF maggiore della NE. & perche <lb/>il perpendicolo CO, &longs;e-<lb/>condo lui, diuide in parti <lb/>di&longs;uguali la bilancia, & <lb/>la parte maggiore è ver&longs;o <lb/>F, cioè NF; la bilan-<lb/>cia EF &longs;i mouerà in giù <lb/>dalla parte di F, concio <lb/>&longs;ia che quel che è di piu <lb/>venga portato à ba&longs;&longs;o.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note124"></margin.target><emph type="italics"/>Ragione di Aristotele.<emph.end type="italics"/>

<emph type="italics"/>Similmente dimo&longs;treraßi, che i pe&longs;i EF pe&longs;eranno tanto appiccati in qual &longs;i voglia al-<lb/>tro punto, quanto &longs;e l'vno, & l'altro &longs;o&longs;&longs;e pendente dal punto H della diui&longs;ione. <lb/>Percioche&longs;e, come di &longs;opra habbiamo in&longs;egnato, &longs;i troueranno ipe&longs;i nella bilancia, à <lb/>i quali i pe&longs;i EF pe&longs;ino egualmente; gliisteßi pe&longs;i EF pendenti da H pe&longs;eranno <lb/>egualmente co' mede&longs;imi pe&longs;i trouati; per e&longs;&longs;ere il punto P &longs;empre il centro della <lb/>grauezzaloro; & la HP a piombo dell'orizonte.<emph.end type="italics"/>

</s>

PROPOSITIONE VI.

<emph type="italics"/>Similmente dalle co&longs;e dette <lb/>caueremo, che <expan abbr="qu&amacr;to">quanto</expan> piu <lb/>la bilancia EF tenente <lb/>il centro &longs;otto la bilancia, <lb/>&longs;arà <expan abbr="lõtana">lontana</expan> dal &longs;ito AB <lb/>&longs;i mouerà piu velocemen <lb/>te, percioche il centro del <lb/>la grauezza H, quanto <lb/>piu è di&longs;tante dal punto <lb/>D, tanto piu velocemen <lb/>te il pe&longs;o compo&longs;to de<*> pe <lb/>&longs;i EF, & della bilancia <lb/>EF &longs;i mouerà, finche <lb/>l'angolo CHS diuenga <lb/>retto.

</s>

& dauantaggio &longs;i <lb/>mouerà anche piu veloce <lb/>mente quanto la bilancia <lb/>&longs;arà piu lontana dal cen-<lb/>tro C.<emph.end type="italics"/>

</s>

I pe&longs;i eguali nella bilancia appiccati hanno in grauezza quella pro-<lb/>portione, che hanno le di&longs;tanze, dalle quali &longs;tanno pendenti.

<emph type="italics"/>Oltre à ciò ne piace dalle &longs;ue <lb/>ragioni, & fal&longs;e pre&longs;uppo <lb/>&longs;te manife&longs;tare, & pro <lb/>durre gli effetti, & i moti <lb/>già dichiarati della bilan <lb/>cia, affine che appaia <expan abbr="qu&amacr;">quam</expan> <lb/>ta &longs;ia la efficacia della ve-<lb/>rità, come quella, che dalle co&longs;e fal&longs;e ancora &longs;i sforza di ri&longs;plendere.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Sia la bilancia BAC &longs;o&longs;pe&longs;a nel punto A; & &longs;ia &longs;egata la AC, come pare in D. & <lb/>da i punti DC &longs;iano attaccati EF pe&longs;i eguali.

<emph type="italics"/>Pongan&longs;i le co&longs;e iste&longs;&longs;e, cioè &longs;iail cerchio AE BF, & la bilancia AB, il cui cen-<lb/>tro C &longs;ia &longs;opra la bilancia, moua&longs;i in EF. Dico che il pe&longs;o po&longs;to in E hà iui <lb/>grauezza maggiore, che il pe&longs;o po&longs;to in F; & che la <expan abbr="bil&amacr;cia">bilancia</expan> EF ritornerà in AB<emph.end type="italics"/><pb n="42"/><emph type="italics"/>&longs;iano tirate dai punti EF le linee EL FM à piombo di AB, le quali &longs;aran-<emph.end type="italics"/> <arrow.to.target n="note125"></arrow.to.target><lb/><emph type="italics"/>no tra loro egualmente di&longs;tanti, & &longs;ia il punto N doue la AB, & la EF &longs;i <lb/>tagliano fra loro.

</s>

Dico, che il pe&longs;o F ver&longs;o il pe&longs;o E ba <lb/>quella proportione in grauezza, che hala di&longs;tanza CA alla di&longs;tanza AD. Per-<lb/>cioche faccia&longs;i come CA ver&longs;o AD, co&longs;i il pe&longs;o F ver&longs;o vn'altro pe&longs;o, che &longs;ia G. <lb/>Dico primai p &longs;i GF pendenti dal punto C tanto pe&longs;are, quanto i pe&longs;i EF penden <lb/>ti da punti DC. Tagli&longs;i DC in due parti eguali in H, & da H &longs;iano fatti pendere <lb/>ambidue i pe&longs;i EF. Pe&longs;eranno EF pre&longs;i in&longs;ieme in quel &longs;ito tanto quanto pe&longs;ano<emph.end type="italics"/> <arrow.to.target n="note87"></arrow.to.target><lb/><emph type="italics"/>in DC. Ponga&longs;i BA eguale ad AH, & &longs;itagli BA in K, di modo, che KA <lb/>&longs;ia eguale ad AD: dapoi dal punto B &longs;ia &longs;atto pendente il pe&longs;o L, ilquale &longs;ia il dop <lb/>pio del pe&longs;o F, cioè eguale a i due pe&longs;i EF, ilqual pe&longs;erà egualmente co'pe&longs;i EF ap <lb/>piccati in H, cioè appiccati in DC. Percioche dunque, come CA ver&longs;o AD, così è <lb/>ilpe&longs;o F ver&longs;o il pe&longs;o G, &longs;arà componendo come CA AD ver&longs;o AD, cioè come <lb/>CK ver&longs;o AD, così ipe&longs;i FG ver&longs;o il pe&longs;o G. Ma per e&longs;&longs;er come CA ver&longs;o AD,<emph.end type="italics"/> <arrow.to.target n="note88"></arrow.to.target><lb/><emph type="italics"/>così il pe&longs;o F al pe&longs;o G, &longs;arà anche conuertendo, come DA ver&longs;o AC, così il pe&longs;o <lb/>G ver&longs;o il pe&longs;o F; & i doppi de icon&longs;eguenti, come DA alla doppia di e&longs;&longs;a AC, <lb/>così il pe&longs;o G al doppio del pe&longs;o F, cioè al pe&longs;o L. Per laqual co&longs;a come CK ver&longs;o<emph.end type="italics"/> <arrow.to.target n="note89"></arrow.to.target><lb/><emph type="italics"/>DA, così ipe&longs;i FG al pe&longs;o G; & come AD alla doppia di AC, così il pe&longs;o G al <lb/>pe&longs;o L, adunque dalla egual proportione come CK alla doppia di AC, così ipe&longs;i FG <lb/>al pe&longs;o L. Ma come CK alla doppia di AC, così la metà di CK, cioè AH, cioè<emph.end type="italics"/> <arrow.to.target n="note90"></arrow.to.target><lb/><emph type="italics"/>BA ver&longs;o AC. Adunque come BA ver&longs;o AC, così FG pe&longs;i al pe&longs;o L. Per laqual<emph.end type="italics"/><pb/><emph type="italics"/>co&longs;a per la &longs;e&longs;ta dell'i&longs;te&longs;&longs;o primo di Archimede, i due pe&longs;i FG pendenti dal punto C<emph.end type="italics"/><lb/><arrow.to.target n="note91"></arrow.to.target> <emph type="italics"/>pe&longs;eranno tanto, quanto il pe&longs;o L pendente dal B; cioè quanto i pe&longs;i EF pen-<lb/>denti da i punti DC. Così percioche i pe&longs;i FG tanto pe&longs;ano quanto ipe&longs;i EF, <lb/>leuato via il pe&longs;o comune F, tanto pe&longs;er à il pe&longs;o G appicato in C, quanto il pe<emph.end type="italics"/><lb/><arrow.to.target n="fig23"></arrow.to.target><lb/><emph type="italics"/>&longs;o E in D. Et perciò il pe&longs;o F al pe&longs;o E hà quella proportione in grauezza, <lb/>che hà al pe&longs;o G. Ma il pe&longs;o F ver&longs;o il G era come CA ver&longs;o AD. adun <lb/>que il pe&longs;o F ancora ver&longs;o il pe&longs;o E hauerà quella proportione in grauczza, che <lb/>ha CA ver&longs;o AD che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

Percioche dunque l'angolo FNM è eguale all'angolo ENL,<emph.end type="italics"/> <arrow.to.target n="note126"></arrow.to.target><lb/><emph type="italics"/>& l'angolo FMN ret <lb/>to è eguale ad ELN <lb/>retto, & il re&longs;tante <lb/>NFM al re&longs;tante<emph.end type="italics"/> <arrow.to.target n="note127"></arrow.to.target><lb/><emph type="italics"/>NEL è etiandio egua-<lb/>le; &longs;arà il triangolo NLE <lb/>&longs;imile al triangolo NMF.<emph.end type="italics"/> <arrow.to.target n="note128"></arrow.to.target><lb/><emph type="italics"/>Si come dunque è la NE <lb/>ver&longs;o la EL, co&longs;i NF<emph.end type="italics"/> <arrow.to.target n="note129"></arrow.to.target><lb/><emph type="italics"/>ad FM; & permut an-<lb/>do, &longs;i come EN ad NF, <lb/>co&longs;i EL ad FM. Ma <lb/>e&longs;&longs;endo HE eguale ad <lb/>HF, &longs;arà EN mag-<lb/>gior di NF. Per laqual <lb/>co&longs;a anco EL &longs;arà mag<emph.end type="italics"/><lb/><arrow.to.target n="fig42"></arrow.to.target><lb/><emph type="italics"/>giore <*>i FM. & percioche mentre il pe&longs;o po&longs;to in E de&longs;cende per la circonferen-<lb/>za EA, il pe&longs;o po&longs;to in F &longs;ale per la circon&longs;erenza FB eguale alla circonferen-<lb/>za EA, & la di&longs;ce&longs;a del pe&longs;o po&longs;to in E piglia (come e&longs;&longs;i dicono) di diretto EL: <lb/>& la &longs;alita del pe&longs;o po&longs;to in F piglia di diretto FM, meno di diretto verrà a pi-<lb/>gliare la &longs;alita del pe&longs;o po&longs;to in F, che la di&longs;ce&longs;a del pe&longs;o po&longs;to in E. Dunque il pe <lb/>&longs;o po&longs;to in E haurà grauezza maggiore, che il pe&longs;o po&longs;to in F.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note87"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 5. <emph type="italics"/>di questo.<emph.end type="italics"/>

<margin.target id="note125"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 28. <emph type="italics"/>d l primo.<emph.end type="italics"/>

</s>

<margin.target id="note88"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 18. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note126"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 15. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note89"></margin.target><emph type="italics"/>Per la con&longs;e guenza della quartadel quinto.<emph.end type="italics"/>

<margin.target id="note127"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note90"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 22. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note128"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 4.<emph type="italics"/>del &longs;esto.<emph.end type="italics"/>

</s>

<margin.target id="note91"></margin.target><emph type="italics"/>Per la &longs;ettima del<emph.end type="italics"/> 5.

<margin.target id="note129"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ma &longs;e nella bilancia BAC &longs;i faranno pendenti da i punti BC, i pe&longs;i EF eguali; <lb/>Dico &longs;imilmente, che il pe&longs;o E ver&longs;o il pe&longs;o F hà quella proportione in grauezza, <lb/>che ha la di&longs;tanza <lb/>CA alla di&longs;tanza <lb/>AB. faccia&longs;i AD <lb/>eguale ad AB, & <lb/>dal punto D &longs;ia <lb/>fatto <expan abbr="p&emacr;dente">pendente</expan> il pe <lb/>&longs;o G eguale al pe <lb/>&longs;o F, ilquale <expan abbr="eti&amacr;-">etian-</expan><emph.end type="italics"/><lb/><arrow.to.target n="fig24"></arrow.to.target><lb/><emph type="italics"/>dio &longs;arà eguale ad E. Et percioche AD è eguale ad AB; i pe&longs;i FG pe&longs;eran <lb/>no egualmente, & hauranno la mede&longs;ima grauezza.

<emph type="italics"/>Sia allungata la linea CD dall una parte, & dall'altra in OP, laquale tagli la linea <lb/>EF nel punto S. & percioche (come dicono) quanto piu è lontano il pe&longs;o dalla <lb/>linea della direttione OP, tanto &longs;i fa piu graue; però con que&longs;to mezo ancora pro-<lb/>uera&longs;&longs;i il pe&longs;o po&longs;to in E hauer grauezza maggiore del pe&longs;o po&longs;to in F. Siano dai <lb/>punti EF tirate le linee EQ FR a piombo di OP. Con &longs;imile ragione mo&longs;tre <lb/>ra&longs;&longs;i, che il triangolo QES è &longs;imile al triangolo RFS; & che la linea EQ è <lb/>maggiore di RF. & co&longs;i il pe&longs;o po&longs;to in E &longs;arà piu lontano dalla linea OP, che <lb/>il pe&longs;o po&longs;to in F; & per ciò il pe&longs;o po&longs;to in E hauerà grauezza maggiore del pe <lb/>&longs;o po&longs;to in<emph.end type="italics"/> F. <emph type="italics"/>Dallequali co&longs;e appare euidente il ritorno della bilancia E<emph.end type="italics"/>F <emph type="italics"/>in AB.<emph.end type="italics"/>

</s>

Et concio&longs;ia, che la grauezza <lb/>del pe&longs;o E ver&longs;o la grauezza del pe&longs;o G &longs;ia come CA ad AD; &longs;arà la gra-<lb/>uezza del pe&longs;o E ver&longs;o la grauezza del pe&longs;o F, come CA ad AD, cioè CA <lb/>ad AB, che parimente era da mo&longs;trare.<emph.end type="italics"/>

</s>

<pb/>

</figure>

<emph type="italics"/>Ma &longs;e il centro della bilancia &longs;arà &longs;otto la bilancia, allhora &longs;i mo&longs;trerà con gli i&longs;te&longs;&longs;i me <lb/>zi, che il pe&longs;o abba&longs;&longs;ato hauerà grauezza maggiore dall'alzato.

Altramente.

</s>

&longs;iano tirate dapun-<lb/>ti EF le linee EL FM <lb/>a piombo di AB. &longs;imil <lb/>mente&longs;i prouerà EL e&longs; <lb/>&longs;ere maggiore di FM; et <lb/>perciò la &longs;ce&longs;a del pe&longs;o po <lb/>sto in F prenderà meno <lb/>di dirittura, che la &longs;alita <lb/>del pe&longs;o po&longs;to in E. On-<lb/>de la re&longs;i&longs;tenza della vio-<lb/>lentia del pe&longs;o po&longs;to in E <lb/>&longs;upererà la naturale incli-<lb/>natione del pe&longs;o po&longs;to in <lb/>F. Adunque il pe&longs;o po&longs;to <lb/>in E &longs;arà piu graue del <lb/>pe&longs;o posto in F.<emph.end type="italics"/>

<emph type="italics"/>Sia la bilancia BAC, col&longs;uo centro A: & ne i punti BC &longs;iano appiccati pe&longs;i <lb/>eguali GF, & &longs;ia prima il centro A, come &longs;i vuole, fra B, & C. Dico, che <lb/>il pe&longs;o F ver&longs;o il pe&longs;o G hà quella proportione in grauezza, che ha la di&longs;tanza <lb/>CA alla di&longs;tanza AB. Faccia&longs;i come BA ver&longs;o AC, co&longs;i il pe&longs;o F ad vn-<emph.end type="italics"/><pb n="33"/><emph type="italics"/>altro H, ilquale &longs;ia appiccato in B: i pe&longs;i HF pe&longs;eranno egualmente de A.<emph.end type="italics"/> <arrow.to.target n="note92"></arrow.to.target><lb/><emph type="italics"/>Ma e&longs;&longs;endo i pe&longs;i FG eguali, haurà il pe&longs;o H ver&longs;o il pe&longs;o G la proportione me <lb/>de&longs;ima, che ha ad F. Come dunque CA ver&longs;o AB, co&longs;i è H ver&longs;o G: & <lb/>come H ver&longs;o G, co&longs;i è lagrauezza di H alla grauezza di G, per e&longs;&longs;ere attac <lb/>cati nell i&longs;te&longs;&longs;o punto B. Per laqual co&longs;a come CA ad AB, co&longs;i la grauezza <lb/>del pe&longs;o H alla grauezza del pe&longs;o G. Et concio&longs;ia che la grauezza del pe&longs;o F <lb/>attacato in G &longs;ia<emph.end type="italics"/> <arrow.to.target n="note93"></arrow.to.target><lb/><emph type="italics"/>eguale alla grauez-<lb/>za del pe&longs;o Hattac <lb/>cato in B, &longs;arà la <lb/>grauezza del pe&longs;o F <lb/>ver&longs;o la grauezza <lb/>del pe&longs;o G, come <lb/>CA ver&longs;o AB, <lb/>cioè come la di&longs;tan-<lb/>za alla di&longs;tanza, che <lb/>bi&longs;ognaua mostrare.<emph.end type="italics"/>

</s>

<margin.target id="note92"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>del prime di Ar chimede del le co&longs;e che pe &longs;ano egualmente.<emph.end type="italics"/>

<emph type="italics"/>Sia <expan abbr="all&umacr;gata">allungata</expan> etiandio la CD <lb/>dall'una parte & l'altra<emph.end type="italics"/><lb/><arrow.to.target n="fig43"></arrow.to.target><lb/><emph type="italics"/>in OP, & &longs;iano tirate dai punti EF le linee EQ FR à piombo dilei.

</s>

&longs;i pro <lb/>verà con l'i&longs;te&longs;&longs;o modo in tutto, che la linea EQ è maggiore di FR. & percio il <lb/>pe&longs;o po&longs;to in E &longs;arà piu lontano dalla linea della dirittura OP, che il pe&longs;o po&longs;to <lb/>in F. Adunque il pe&longs;o po&longs;to in E haurà grauezza maggiore del pe&longs;o po&longs;to in F. <lb/>Dalle quali co&longs;e &longs;egue, che la bilancia EF &longs;i moue in giù dalla parte di E.<emph.end type="italics"/>

<margin.target id="note93"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Ma &longs;e la bilancia BAC fo&longs;&longs;e tagliata, come &longs;i vuole in D, & appicchin&longs;i in DC <lb/>i pe&longs;i EF eguali.

<emph type="italics"/>Si che Aristotele propo&longs;e que&longs;te due que&longs;tioni &longs;olamente, & la&longs;ciò la terza, cioè quando <lb/>il centro della bilancia &longs;tà nella bilancia i&longs;te&longs;&longs;a.

</s>

Dico &longs;imilmente co&longs;i e&longs;&longs;ere la grauezza del pe&longs;o F alla gra-<lb/>uezza del pe&longs;o E, come la di&longs;tanza CA alla di&longs;tanza AD. Faccia&longs;i AB <lb/>eguale ad AD <lb/>& &longs;ia appicca-<lb/>to in B il pe&longs;o <lb/>G eguale al pe <lb/>&longs;o E, & alpe <lb/>&longs;o F. Hor <lb/>percioche AB <lb/>è eguale ad A <lb/>D; ipe&longs;i GE<emph.end type="italics"/><lb/><arrow.to.target n="fig25"></arrow.to.target><lb/><emph type="italics"/>pe&longs;eranno egualmente.

Que&longs;ta però trala&longs;ciò egli, co-<lb/>me nota, &longs;i come egli &longs;ole trala&longs;ciare le co&longs;e molto note.

</s>

Ma per e&longs;&longs;ere la grauezza del pe&longs;o F ver&longs;o la grauezza <lb/>del pe&longs;o G, come CA ad AB, & la grauezza del pe&longs;o E &longs;ia eguale alla <lb/>grauezza del pe&longs;o G; &longs;arà la grauezza del pe&longs;o F ver&longs;o la grauezza del pe&longs;o E, <lb/>come CA ad AB, cioè CA ad AD, che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

Imperoche à chi puote <lb/>far dubbio, che &longs;e il pe&longs;o &longs;arà &longs;o&longs;tentato nel centro della grauezza&longs;ua, che non i&longs;tia <lb/>fermo?

</s>

Mapotrebbe for&longs;e alcuno riprendere quelle co&longs;e che per &longs;ua &longs;ententia hab-<lb/>biamo propo&longs;to, affermando noi non hauere prodotto in mezo tutta la intera &longs;enten <lb/>za &longs;ua.

</figure>

COROLLARIO.

</s>

Imperoche proponendo egli nella &longs;econda parte della que&longs;tione &longs;econda. <lb/>“Perche la bilancia e&longs;&longs;endo posta la trutina di &longs;otto, quando, portato il pe&longs;o in giu, al <lb/>cuno lo rimoue, non a&longs;cende, ma rimane?” non afferma perciò la bilancia mouer&longs;i in <lb/>giù, ma rimanere, il che pare &longs;imilmente hauere nella vltima conclu&longs;ione raccolto. <lb/>Ma que&longs;to non &longs;o larnente non ci &longs;a contra, ma&longs;e egli è ben' inte&longs;o grandi&longs;&longs;imamen-<lb/>te aiuta.<emph.end type="italics"/>

Da que&longs;to è manife&longs;to, che quanto il pe&longs;o è piu di&longs;tante dal centro <lb/>della bilancia, tanto egli è anco piu graue, & per con&longs;eguente mo-<lb/>uer&longs;i piu velocemente.

</s>

Quinci oltre à ciò &longs;i mo&longs;trerà facilmente anche la ragione della Sta-<lb/>dera.

<emph type="italics"/>Percioche &longs;ia la bilancia AB egualmente di&longs;tante dall'orizonte, il cui centro E &longs;ia <lb/>&longs;otto la bilancia.

</s>

<pb/>

& perche Ari&longs;totele con&longs;idera la bilancia come ella è in fatto, però <lb/>egli è nece&longs;&longs;ario collocare la trutina, ouero qualche altra co&longs;a &longs;otto il centro E, co-<lb/>me EF, che in ogni modo &longs;arà trutina, per modo, che &longs;o&longs;tengail centro E. & &longs;ia <lb/>ECD il perpendicolo.

Corollario vocabolo Latino co&longs;tumato da tutti gli altri Scrittori Italiani in cotal ma <lb/>teria, nè di&longs;piacque à Dante nel 28. cap.

</s>

del Purgatorio.

& accioche la bilancia AB &longs;i moua da que&longs;to &longs;ito, dice<emph.end type="italics"/><pb n="25"/><emph type="italics"/>Ari&longs;totele, ponga&longs;i il pe&longs;o in B, ilquale e&longs;&longs;endo graue mouerà la bilancia dalla par-<lb/>te B in giù, come in G, talche per l'impedimento non potrà egli piu mouer&longs;i in <lb/>giu, ma non dice gia Ari&longs;totele, che &longs;i moua la bilancia in giu dalla parte di B fin <lb/>tanto che parerà, da <lb/>poi &longs;i la&longs;ci, come noi <lb/>di cemmo<*>ma ordina <lb/>che &longs;ia posto il pe&longs;o <lb/>in B, il quale di &longs;ua <lb/>natura &longs;i mouera <lb/>&longs;empre in giù finche <lb/>la bilancia &longs;i appog-<lb/>gi alla trutina, ouerò <lb/>a qualche altra co&longs;a. <lb/>& quando il B &longs;a-<lb/>rà nel G, la bilan-<lb/>cia &longs;arà in GH, nel <lb/>qual &longs;ite leuato via <lb/>il pe&longs;o, rimarrà: per <lb/>e&longs;&longs;ere la maggior par <lb/>te della bilancia dal <lb/>perpendicolo uer&longs;o il<emph.end type="italics"/><lb/><arrow.to.target n="fig44"></arrow.to.target><lb/><emph type="italics"/>G, che è DG, che DH. ne piu mouera&longs;&longs;i in giu, imperoche la bilancia &longs;tar à &longs;opra <lb/>la trutina, ouero qualche altra co&longs;a, che &longs;o&longs;tenga il centro della bilancia.

</s>

“Dirotti vn corollario an-<lb/>co per gratia.” vuol dire, &longs;econdo Varrone nel primo libro della lingua Latina, <lb/>quella giunta, & quel &longs;opra piu, che &longs;i dà oltre al pagamento, quando &longs;i comp era <lb/>qualche co&longs;a.

peroche &longs;e a <lb/>cote&longs;ta non &longs;i appoggia&longs;&longs;e, verrebbe la bilancia à mouer&longs;i, &longs;econdo la &longs;ua opinione, <lb/>in giù dalla parte di G, concio&longs;ia, che quello che è di piu, cioè DG debba e&longs;&longs;ere <lb/>per nece&longs;&longs;ità in giu portato.<emph.end type="italics"/>

</s>

Al tempo antico allhor che i recitatori di Tragedie, Comedie, & <lb/>altri Poemi nelle &longs;cene &longs;i portauano bene, & piaceuano à gli vditori, era loro do-<lb/>nato oltra al prezzo a&longs;&longs;egnato, vn corollario per cia&longs;cuno, cioè vna piccola coro <lb/>na per douer&longs;ene ornare le tempie per giunta, & &longs;opra piu delle &longs;ue mercedi.

</figure>

<emph type="italics"/>Ma potrebbe dauantagio dire alcuno, &longs;e in B &longs;arà collocato vn pe&longs;o picciolo, &longs;i mo-<lb/>uerà ben la bilancia in giu, ma non gia fin al G; nel qual &longs;ito, &longs;econdo Aristo-<lb/>tele, leuato via il pe&longs;o, deue remanere.

</s>

Co&longs;i <lb/>nelle &longs;cienze matematiche v&longs;a&longs;i di aggiungere certe co&longs;e, oltra le propo&longs;itioni, <lb/>qua&longs;i giunte & con&longs;equenze, le quali na&longs;cono dalle co&longs;e primieramente dimo&longs;tra-<lb/>te, & &longs;ono loro corri&longs;pondenti, & non &longs;ono però nè propo&longs;itioni, nè problemi, <lb/>nè lemmi, ma alla &longs;embianza predetta chiaman&longs;i coro llarij, molti de i quali han-<lb/>no congiunta la &longs;ua dimo&longs;tratione.

ilche è manife&longs;to per la e&longs;perientia, inchi-<lb/>nando&longs;i la <expan abbr="bilãcia">bilancia</expan> più, & meno, quando in vna e&longs;tremita della bilancia &longs;olamente <lb/>vi è po&longs;to il pe&longs;o, che &longs;ia ò maggiore, ò minore.

</s>

ilche è veri&longs;&longs;imo allhora che il centro <lb/>è collocato &longs;opra la bilancia, ma non già &longs;otto, ne in e&longs;&longs;a bilancia, come per gratia <lb/>di e&longs;empio.<emph.end type="italics"/>

</s>

<pb/>

<emph type="italics"/>Hor &longs;ia AB il fusto della Stadera, la cui trutina &longs;ia in C; & &longs;ia il marco della &longs;ta<emph.end type="italics"/><lb/><arrow.to.target n="note94"></arrow.to.target> <emph type="italics"/>dera E. Appicchi&longs;i in A il pe&longs;o D, che pe&longs;i egualmente col marco E appic-<lb/>cato in F. Appicchi&longs;i parimente vn'altro pe&longs;o G in A, ilqual anco pe&longs;i egual-<lb/>mente col marco E appiccato in B. Dico, la grauezza del pe&longs;o D ver&longs;o la gra-<lb/>uezza del <lb/>G e&longs;&longs;ere co <lb/>&longs;i, come CF <lb/>ver&longs;o CB. <lb/>Hor per-<lb/>cioche la <lb/>grauezza <lb/>del pe&longs;o D <lb/>è eguale al <lb/>la grauez-<lb/>za del pe-<lb/>&longs;o E at-<lb/>taccato in <lb/>F, & la<emph.end type="italics"/><lb/><arrow.to.target n="fig26"></arrow.to.target><lb/><emph type="italics"/>grauezza del pe&longs;o G è eguale alla grauezza del pe&longs;o E po&longs;to in B; &longs;arà la grauez-<lb/>za del pe&longs;o D alla grauezza del pe&longs;o E po&longs;to in F, come la grauezza del pe&longs;o G alla <lb/>grauezza del pe&longs;o E po&longs;to in B; & permutando come la grauezza del pe&longs;o D alla <lb/>grauezza del pe&longs;o G, co&longs;i la grauezza di E po&longs;to in F alla grauezza di E po&longs;to in B; <lb/>ma la grauezza del pe&longs;o E in F alla grauezza di E in B po&longs;to è come CF <lb/>ver&longs;o CB; come dunque la grauezza del pe&longs;o D alla grauezza del pe&longs;o G, co&longs;i <lb/>è CF ver&longs;o CB. Se dunque la parte del fu&longs;to CB diuidera&longs;&longs;i in parti eguali, po <lb/>&longs;to &longs;olo il pe&longs;o E & piu da pre&longs;&longs;o, & piu da lontano dal punto C; le grauezze de <lb/>pe&longs;i, lequali&longs;tanno pendenti dal punto A &longs;aranno traloro manife&longs;te & note.

<emph type="italics"/>Sia la bilancia AB egualmente di&longs;tante dall'orizonte, il cui centro C &longs;ia &longs;opra la bi <lb/>lancia, & il perpendicolo <lb/>CD a piombo dell' ori-<lb/>zonte, il quale da la par-<lb/>te D &longs;ia allungato in H. <lb/>Hor percioche con&longs;idera <lb/>ta la grauezza della bi-<lb/>lancia, &longs;arà il punto D <lb/>il centro della grauezza <lb/>della bilancia.

</s>

Co-<lb/>me&longs;e la di&longs;tanza CB &longs;arà tripla della di&longs;tanza CF, &longs;arà parimente la grauezza <lb/>di e&longs;&longs;o G tripla della grauezza di D, che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

&longs;e dunque <lb/>vn piccolo pe&longs;o &longs;arà po-<lb/>&longs;to nel B, il cui centro <lb/>della grauezza &longs;ia nel <expan abbr="p&utilde;">pum</expan> <lb/>to B; gia piu non &longs;arà <lb/>il centro della grauezza <lb/>D della magnitudine<emph.end type="italics"/><lb/><arrow.to.target n="note130"></arrow.to.target> <emph type="italics"/>compo&longs;ta della bilancia<emph.end type="italics"/><lb/><arrow.to.target n="fig45"></arrow.to.target><lb/><emph type="italics"/>AB, & del pe&longs;o po&longs;to in B, ma &longs;arà nella linea DB, come in K: per modo <lb/>che DE ad EB &longs;ia come il pe&longs;o po&longs;to in B alla grauezza della bilancia AB. <lb/>congiunga&longs;i la CE. & percioche il punto C è immobile, mentre la bilancia &longs;i <lb/>moue, il punto E de&longs;criuerà la circonferenza del cerchio EFG, il cui mezo dia-<lb/>metro è CE, & il centro C. Ma perche CD &longs;tà a piombo dell' orizonte, la li <lb/>nea CE non &longs;arà gia ella à piombo dell' orizonte.

</s>

Per laqual co&longs;a la grandez-<lb/>za composta di AB, & del pe&longs;o po&longs;to in B non rimarrà in questo &longs;ito; ma &longs;i <lb/>mouerà in giu &longs;econdo il centro E della &longs;ua grauezza per la circonferenza EFG,<emph.end type="italics"/><lb/><arrow.to.target n="note131"></arrow.to.target> <emph type="italics"/>finche CE diuenti a piombo dell' orizonte, cioè finche la CE peruenga in CDF. <lb/>& allhora la bilancia AB &longs;arà mo&longs;&longs;ain KL, nel qual &longs;ito la bilancia rimarrà <lb/>in&longs;ieme co'l pe&longs;o, ne d'auantaggio &longs;i mouerà in giù.

</figure>

<margin.target id="note94"></margin.target><emph type="italics"/>Ragione del la stadera.<emph.end type="italics"/>

</s>

che &longs;e in B &longs;arà po&longs;to vn pe&longs;o <lb/>piu graue, il centro'della grauezza di tutta la magnitudine &longs;arà piu dappre&longs;&longs;o al B, <lb/>come in M. & allhora la bilancia &longs;i mouerà in giu, finche la congiunta linea CM <lb/>peruenga nella linea CDH. Dal por&longs;i dunque pe&longs;o maggiore ò minore in B, la <lb/>bilancia &longs;i inchinerà piu ò meno.

In altro modo po&longs;&longs;iamo anco v&longs;are la &longs;tadera, affine che le grauezze <lb/>de ipe&longs;i &longs;i facciano note.

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Da che &longs;egue che il pe&longs;o B de&longs;criuerà &longs;empre vna <lb/>circonferenza minore della quarta parte d'un cerchio, per e&longs;&longs;ere l'angolo FCE &longs;em <lb/>pre acuto:ne il punto B peruenirà gia mai fin alla linea CH, percioche &longs;empre il <lb/>centro della grauezza del pe&longs;o, & dalla bilancia in&longs;ieme &longs;arà fra BD. tuttauia <expan abbr="qu&amacr;">quam</expan> <lb/>to &longs;arà il pe&longs;o po&longs;to in B piu graue, de&longs;criuerà anche circonferenza maggiore, ve-<lb/>nendo&longs;i per que&longs;to il punto B ad acco&longs;tare piu alla linea CH.<emph.end type="italics"/>

<emph type="italics"/>Sia il fu&longs;to della stadera AB, la cui trutina &longs;ia in C, & &longs;ia il marco della stadera <lb/>E, ilquale &longs;ia appiccato in A; & &longs;iano i pe&longs;i DG di&longs;uguali, le proportioni delle <lb/>grauezze de quali cerchia-<lb/>mo: &longs;ia appiccato il pe&longs;o D <lb/>in B talche pe&longs;i egual-<lb/>mente con E. Similmente <lb/>appicchi&longs;i il pe&longs;o G in F, <lb/>ilquale pe&longs;i egualmente con <lb/>l'i&longs;te&longs;&longs;o pe&longs;o E. Dico D <lb/>ver&longs;o G co&longs;i e&longs;&longs;ere; come<emph.end type="italics"/> <arrow.to.target n="note95"></arrow.to.target><lb/><emph type="italics"/>CF ver&longs;o CB. Hor perche <lb/>i pe&longs;i DE pe&longs;ano <expan abbr="egualm&emacr;">egualmen</expan><emph.end type="italics"/><lb/><arrow.to.target n="fig27"></arrow.to.target><lb/><emph type="italics"/>te, &longs;arà D ad E, come CA à CB. & concio&longs;ia, che anche i pe&longs;i GE pe&longs;i-<lb/>no egualmente, &longs;arà il pe&longs;o E ver&longs;o il pe&longs;o G, come FC à CA; Per laqual <lb/>co&longs;a per la proportion eguale il pe&longs;o D al pe&longs;o G, co&longs;i &longs;arà, come CF à CB. <lb/>che parimente bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/> <arrow.to.target n="note96"></arrow.to.target>

</s>

</figure>

<margin.target id="note95"></margin.target><emph type="italics"/>Per la &longs;esta del primo di Archimede d'lle co&longs;e, che pe&longs;ano egual mente.<emph.end type="italics"/>

<margin.target id="note130"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>del primo.

</s>

di.

<margin.target id="note96"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 23. <emph type="italics"/>del quinto<emph.end type="italics"/>

</s>

drch.

PROPOSITIONE VII.

</s>

del le co&longs;e cgual <expan abbr="m&etilde;se">mense</expan> <expan abbr="pes&amacr;ti">pesanti</expan>.<emph.end type="italics"/>

PROBLEMA.

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Dati quanti &longs;i vogliano pe&longs;i nella bilancia, appiccati in qualluogo &longs;i <lb/>&longs;ia, ritrouare il centro della bilancia, dal quale &longs;e &longs;arà fatta penden-<lb/>te la bilancia, i dati pe&longs;i &longs;taranno fermi.

<margin.target id="note131"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 1. <emph type="italics"/>di questo.<emph.end type="italics"/>

</s>

PROBLEMA. Sotto il nome di Propo&longs;itione &longs;i contiene il Problema ancora vo-<lb/>cabolo greco; ma il Problema ha dauantaggio della Propo&longs;itione in particolare, <lb/>che ordina, & in&longs;egna ad operare qualche effetto; doue la Propo&longs;itione &longs;uole &longs;ta <lb/>re nella nuda &longs;peculatione &longs;olamente.

<emph type="italics"/>Mi habbia la bilancia AB il centro C nella i&longs;te&longs;&longs;a bilancia, & nel &longs;uo mezo, <lb/>&longs;arà il C centro ancora della grauezza della bilancia, dal quale &longs;ia tirata la li-<lb/>nea FCG a piombo di e&longs;&longs;a AB, & dell' orizonte.

</s>

Et que&longs;ta è la differenza tra la Propo&longs;itio-<lb/>ne, & il Problema.

Ponga&longs;i dapoi in B qual <lb/>pe&longs;o &longs;i voglia; &longs;arà il centro di tutta la grauezza, come in E; &longs;i fattamente che <lb/>la CE ver&longs;o EB &longs;ia come il pe&longs;o po&longs;to in B alla grauezza della bilancia.

</s>

& per<emph.end type="italics"/><pb n="26"/><emph type="italics"/>cioche la CE non è a piombo dell' orizonte, la bilancia AB, & il pe&longs;o po&longs;to in <lb/>B non rimaranno in que-<lb/>&longs;to &longs;ito gia mai; ma &longs;i mo-<lb/>ueranno in giu dalla par-<lb/>te di B, fin che CE &longs;i <lb/>&longs;accia à piombo dell' ori-<lb/>zonte; cioè fin che la bilan-<lb/>cia AB peruenga in FG. <lb/>Onde è chiaro, che cia&longs;cun <lb/>pe&longs;o po&longs;to in B, &longs;empre <lb/>de&longs;criue la quarta parte <lb/>d'un cerchio.<emph.end type="italics"/>

</s>

<pb/>

</figure>

<emph type="italics"/>Sia la bilancia AB, & &longs;iano dati quanti &longs;i vogliano pe&longs;i CDEFG prendan&longs;i nel <lb/>la bilancia, a piacere i punti AHKLB, da quali &longs;ian fatti pendenti i dati pe&longs;i. <lb/>Bi&longs;ogna ritrouar il centro della bilancia, dal quale &longs;e &longs;i far à l'appiccamento, rim anga <lb/>no i dati pe&longs;i.

<emph type="italics"/>Ma &longs;ia il centro C &longs;otto la bilancia AB, & &longs;ia DCE il perpendicolo.

</s>

Diuida&longs;i AH in M, &longs;i che HM ad MA &longs;ia come la grauezza <lb/>del pe&longs;o C alla grauezza del pe&longs;o D. Dapoi diuida&longs;i anco BL in N, &longs;i che <lb/>LN ad NB &longs;ia come la grauez <*> pe&longs;o G alla grauezza del pe&longs;o F. Et di-<lb/>uida&longs;i MN in O, &longs;i che MO ver&longs;o ON &longs;ia come la grauezza de pe&longs;i FG <lb/>alla grauezza de'pe&longs;i CD. Et in fine diuida&longs;i KO in P, &longs;i che KP ver&longs;o PO <lb/>&longs;ia come la grauezza de'pe&longs;i CD FG alla grauezza del pe&longs;o E. Hor percio-<emph.end type="italics"/><lb/><arrow.to.target n="note97"></arrow.to.target> <emph type="italics"/>che i pe&longs;i CDFG tanto pe&longs;ano in O, quanto CD in M, & FG in N; <lb/>pe&longs;eranno egualmente i pe&longs;i CD in M, & FG in N, & il pe&longs;o E in K, <lb/>&longs;e &longs;aranno &longs;o&longs;pe&longs;i nel punto P. Et concio&longs;ia, che ipe&longs;i CD tanto pe&longs;ino in M, <lb/>quanto in AH, & FG in N quanto in LB; ipe&longs;i CDFG pendenti da' <lb/>punti AHLB, & il pe&longs;o E da K, &longs;e da P &longs;aranno &longs;o&longs;pe&longs;i, pe&longs;eranno egual-<lb/>mente, & rimarranno.

&longs;imilmente <lb/>per e&longs;&longs;er il pe&longs;o posto in B, &longs;arà il centro della grauezza della magnitudine compe <lb/>&longs;ta di AB bilancia, & del pe&longs;o po&longs;to in B nella linea DB, come in F; &longs;i <expan abbr="fattam&emacr;">fattamen</expan> <lb/>te che come DF &longs;i ha ver&longs;o FB co&longs;i &longs;ia il pe&longs;o po&longs;to in B al pe&longs;o della bilan-<lb/>cia.

</s>

egli è dunque trouato il P centro della bilancia, dalquale <lb/>rimangono i pe&longs;i dati.

congiunga&longs;i CF. & <lb/>percioche CD è a piombo <lb/>dell' orizonte, non &longs;arà gia <lb/>la linea CF a piombo del <lb/>l'orizonte.

</s>

Che bi&longs;ogna operare.<emph.end type="italics"/>

Per laqual co&longs;a <lb/>la magnitudine compo&longs;ta <lb/>della bilancia AB, & del <lb/>pe&longs;o po&longs;to in B in que&longs;to <lb/>&longs;ito non &longs;tarà mai ferma; <lb/>ma in giu mouera&longs;&longs;i &longs;e alcu <lb/>na co&longs;a non la impedi&longs;ce, <lb/>finche CF peruenga in <lb/>DCE, nel qual &longs;ito la bi-<lb/>lancia rimarrà in&longs;ieme co'l<emph.end type="italics"/><lb/><arrow.to.target n="fig46"></arrow.to.target><lb/><emph type="italics"/>pe&longs;o.

</s>

& il punto B &longs;arà come in G, & il punto A in H, & la bilancia GH <lb/>non hauerà piu il centro di &longs;otto, ma &longs;opra e&longs;&longs;a.

<margin.target id="note97"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 5. <emph type="italics"/>di questo.<emph.end type="italics"/>

</s>

La qual co&longs;a hauerà &longs;empre, quan-<lb/>tunque &longs;i ponga vn minimo pe&longs;o in B. Auanti che dunque il B peruenga al G, <lb/>egli è nece&longs;&longs;ario, che la bilancia incontri la trutina po&longs;ta di &longs;otto, ouero alcuna altra <lb/>co&longs;a, che &longs;o&longs;tenti il centro C, & iui s'appoggi.

COROLLARIO.

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Da que&longs;to &longs;egue, che il pe&longs;o B &longs;em <lb/>pre &longs;i moue oltre la linea DK, & de&longs;criue &longs;empre vna circonferenza maggiore del <lb/>la quarta parte del cerchio, per e&longs;&longs;ere l'angolo FCE &longs;empre ottu&longs;o, & l'angolo <lb/>DCF &longs;empre acuto.

Da que&longs;to è chiaro, che &longs;ei centri della grauezza de' pe&longs;i CDEFG <lb/>fo&longs;&longs;ero ne' punti AHKLB, &longs;arebbe il punto P il centro della <lb/>grauezza della magnitudine compo&longs;ta di tutti i pe&longs;i CDEFG.

</s>

& quanto il pe&longs;o posto in B &longs;arà piu leggiero, de&longs;criuerà tut-<lb/>tauia anche circonferenza maggiore.

<emph type="italics"/>Que&longs;to è manife&longs;to dalla diffinitione del centro della grauezza, concio&longs;ia che i pe&longs;i ri-<lb/>mangano, &longs;e &longs;ono &longs;o&longs;tenuti dal punto P.<emph.end type="italics"/>

</s>

Imperoche quanto il pe&longs;o po&longs;to in G &longs;arà piu <lb/>leggiero, tanto piu il pe&longs;o detto posto in G &longs;i alzerà; & la bilancia GA s'acco&longs;te<emph.end type="italics"/>

<emph type="italics"/>Il fine della Bilancia.<emph.end type="italics"/>

</s>

DELLA LEVA.

</s>

</figure>

LEMMA.

<emph type="italics"/>Ma &longs;ia il centro della bilancia AB &longs;opra il C in F; & &longs;ia FC à piombo di AB, <lb/>& dell' orizonte: & &longs;e <lb/>la bilancia &longs;arà mo&longs;&longs;a in<emph.end type="italics"/> <arrow.to.target n="note132"></arrow.to.target><lb/><emph type="italics"/>DE, la linea CF &longs;arà <lb/>mo&longs;&longs;a in FG, la quale <lb/>per non e&longs;&longs;ere à piombo <lb/>dell' orizonte, la bilancia <lb/>DE &longs;imouerà in giu dalla <lb/>parte di D, finche FG <lb/>ritorni in FC: & allho <lb/>ra la bilancia DE &longs;arà <lb/>in AB, nel qual &longs;ito an <lb/>che rim<*>rà.<emph.end type="italics"/>

</s>

Siano quattro grandezze ABCD; & &longs;ia la A <lb/>maggiore della B, & C maggiore della D. Dico, <lb/>che A ver&longs;o D hà proportione maggiore di quello <lb/>che hà B ver&longs;o C.

<margin.target id="note132"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Hor percioche A ver&longs;o C hà proportion maggio-<lb/>re, che B ver&longs;o C; & A parimente ver&longs;o D<emph.end type="italics"/> <arrow.to.target n="note98"></arrow.to.target><lb/><emph type="italics"/>hà proportion maggiore di quel che ha ver&longs;o C: <lb/>Dunque A ver&longs;o D l'hauer à maggiore, che B <lb/>ver&longs;o C, Che bi&longs;ognaua mostrare.<emph.end type="italics"/>

<emph type="italics"/>Che &longs;e il centro F della bi-<lb/>lancia &longs;arà &longs;otto la <expan abbr="bil&emacr;-<lb> cia">bilen-<lb/>cia</expan>, & &longs;iala bilancia mo&longs;<emph.end type="italics"/> <arrow.to.target n="note133"></arrow.to.target><lb/><emph type="italics"/>&longs;a in DE primier amen <lb/>te egli è manife&longs;to che la <lb/>bilancia rimarrà in AB: <lb/>& in DE mouera&longs;&longs;i in <lb/>giu dalla parte di E, per <lb/>non e&longs;&longs;ere la linea FG <lb/>à piombo dell' orizonte.<emph.end type="italics"/><lb/><arrow.to.target n="fig47"></arrow.to.target><lb/><emph type="italics"/>rà piu pre&longs;&longs;o al &longs;ito egualmente di&longs;tante dall'orizonte.

</s>

Le quali co&longs;e tutte re&longs;tano ma <lb/>ni&longs;e&longs;te da quelle che di &longs;opra &longs;ono &longs;tate dette.<emph.end type="italics"/>

<margin.target id="note98"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 8. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

PROPOSITIONE I.

<margin.target id="note133"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

La po&longs;&longs;anza, che &longs;o&longs;tiene il pe&longs;o attaccato alla Leua, ha la proportio <lb/>ne mede&longs;ima al detto pe&longs;o, che ha la di&longs;tanza della Leua fra il &longs;o&longs;te <lb/>gno po&longs;ta, & lo attaccamento del pe&longs;o, alla di&longs;tanza, che è dal &longs;o&longs;te <lb/>gno alla po&longs;&longs;anza.

<emph type="italics"/>Prouate que&longs;te co&longs;e, egli è chia <lb/>ro, che il centro della bilan-<lb/>cia è cagione de gli effetti di <lb/>uer&longs;i della bilancia.

</s>

& &longs;i ve <lb/>de ancora che tutte le pro-<lb/>po&longs;itioni di Archimede del <lb/>le co&longs;e, che egualmente pe&longs;a <lb/>no, a ciò pertinenti, in ogni <lb/>&longs;ito &longs;ono vere.

<emph type="italics"/>Sia la leua AB, il cui &longs;oftegno &longs;ia C; & &longs;iail pe&longs;o D pendente da A con AH, <lb/>&longs;i che AH &longs;ia &longs;empre à piombo dell'orizonte: & &longs;ia la po&longs;&longs;anza &longs;oftenente il pe-<emph.end type="italics"/><lb/><arrow.to.target n="fig28"></arrow.to.target><lb/><emph type="italics"/>&longs;o in B. Dico che la po&longs;&longs;anza posta in B ver&longs;o il pe&longs;o D &longs;ta co&longs;i, come la CA<emph.end type="italics"/><pb/><arrow.to.target n="note99"></arrow.to.target> <emph type="italics"/>ver&longs;o la CB. Faccia&longs;i come la BC alla CA, co&longs;i il pe&longs;o D ad vn'altro pe&longs;o <lb/>E, talche &longs;e egli in B &longs;arà appiccato, pe&longs;erà <expan abbr="egualm&etilde;te">egualmente</expan> con D, per e&longs;&longs;er il C cen <lb/>tro della grauezza di ambidue.

</s>

Per laqual co&longs;a vna po&longs;&longs;anza eguale ad e&longs;&longs;o E po <lb/>&longs;ta nel <lb/>mede&longs;i <lb/>mo lo <lb/>go pe-<lb/>&longs;erà e-<lb/>gual-<lb/>mente <lb/>con e&longs;-<emph.end type="italics"/><lb/><arrow.to.target n="fig29"></arrow.to.target><lb/><emph type="italics"/>&longs;o D, nella leua AB, collocando il &longs;o&longs;tegno &longs;uo in C, cioè impedirà, che il pe-<emph.end type="italics"/><lb/><arrow.to.target n="note100"></arrow.to.target> <emph type="italics"/>&longs;o D non inchini in giu&longs;o, &longs;i come impedi&longs;ce il pe&longs;o E. Ma la po&longs;&longs;anza di B al <lb/>pe&longs;o D hàla mede&longs;ima proportione, che il pe&longs;o E ha all'iste&longs;&longs;o D: adunque la <lb/>po&longs;&longs;anza di B ver&longs;o il pe&longs;o D &longs;arà come CA ver&longs;o CB; cioè la di&longs;tanza del-<lb/>la leua dal &longs;ostegno al &longs;o&longs;tenimento del pe&longs;o, alla di&longs;tanza dal &longs;ostegno alla po&longs;&longs;an-<lb/>za, che bi&longs;o gnaua mo&longs;trare.<emph.end type="italics"/>

cioè, &longs;ia pur <lb/>la bilancia di&longs;tante <expan abbr="egualm&etilde;">egualmen</expan> <lb/>te dall'orizonte, ouero non, <lb/>pur che il centro della bilan <lb/>cia &longs;ia collocato in e&longs;&longs;a <expan abbr="bil&amacr;">bilam</expan> <lb/>cia, &longs;i come egli la con&longs;ide-<emph.end type="italics"/><lb/><arrow.to.target n="fig48"></arrow.to.target><lb/><emph type="italics"/>rà.

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& quantunque la bilancia habbia difuguali le braccia, auerrd tutt auia l'i&longs;te&longs;&longs;o, & <lb/>&longs;i dimo&longs;trerà co'l modo i&longs;te&longs;&longs;o in tutto, che il centro della bilancia collocato in diuer <lb/>&longs;e maniere produrrà vari effetti.<emph.end type="italics"/>

</s>

</figure>

</figure>

<margin.target id="note99"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>del<emph.end type="italics"/> 1. <emph type="italics"/>di Archi mede delleco &longs;ache egual <expan abbr="m&etilde;te">mente</expan> pe&longs;ano.<emph.end type="italics"/>

<emph type="italics"/>Percioche &longs;ia la bilancia <lb/>AB egualmente di&longs;tan <lb/>te dall'orizonte; & &longs;iano <lb/>in AB pe&longs;i di&longs;uguali, il <lb/>centro della grauezza <lb/>dei quali &longs;ia in C, & <lb/>&longs;ia attacata la bilancia <lb/>nell'i&longs;te&longs;&longs;o punto di C, <lb/>& moua&longs;i la bilancia in<emph.end type="italics"/><lb/><arrow.to.target n="note134"></arrow.to.target> <emph type="italics"/>DE; egliè manife&longs;to, <lb/>che la bilancia rimarrà <lb/>non &longs;olamente in DE, <lb/>ma in qual &longs;i voglia altre <lb/>&longs;ito.<emph.end type="italics"/>

</s>

<margin.target id="note100"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note134"></margin.target><emph type="italics"/>Per la diffi ni ione del centro della grauezza.<emph.end type="italics"/>

</s>

</figure>

Di quì ageuolmente &longs;i puote mo&longs;trare, che <expan abbr="quãto">quanto</expan> il &longs;o&longs;tegno &longs;arà piu <lb/>vicino al pe&longs;o, tanto minor po&longs;&longs;anza &longs;i ricerca à &longs;o&longs;tenere il detto <lb/>pe&longs;o.

<emph type="italics"/>Da que&longs;te co&longs;e co&longs;i terminate, &longs;e la bilancia fo&longs;&longs;e inarcata, ouero, che le braccia della bi <lb/>lancia forma&longs;&longs;ero vn'angolo, & &longs;i di&longs;poneße il centro diuer&longs;amente, (ben che que-<lb/>&longs;ta propriamente non &longs;arebbe bilancia,) potremo nondimeno anche dimo&longs;trare di lei <lb/>vary effetti.

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Come &longs;ia la bilancia ACB, il cui centro, d'intorno al quale &longs;i volge, <lb/>&longs;i a C, & tiratala linea AB, &longs;ia <lb/>l'arco ouerò l'angolo ACB &longs;opra <lb/>la linea AB; & pongan&longs;i in AB <lb/>icentri della grauezza de'pe&longs;i, i quali <lb/>rimangano in que&longs;to &longs;ito.

<emph type="italics"/>Poste le co&longs;e mede&longs;ime &longs;ia il &longs;o&longs;tegno in F piu da pre&longs;&longs;o ad A, che C; & faccia&longs;i <lb/>come BF ad FA, co&longs;i il pe&longs;o D ad vn'altro pe&longs;o G, ilquale &longs;e in B &longs;ia ap-<emph.end type="italics"/><lb/><arrow.to.target n="note101"></arrow.to.target> <emph type="italics"/>piccato; i pe&longs;i DG dal &longs;o&longs;tegno F pe&longs;eranno egualmente.

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Hor percioche BF <lb/>è mag-<lb/>giore di <lb/>BC, & <lb/>CA<emph.end type="italics"/><lb/><arrow.to.target n="note102"></arrow.to.target> <emph type="italics"/>maggio <lb/>re di AF; <lb/>la <lb/>propor-<lb/>tione di<emph.end type="italics"/><lb/><arrow.to.target n="fig30"></arrow.to.target><lb/><emph type="italics"/>BF ver&longs;o FA &longs;arà maggiore, che di BC ver&longs;o CA: & perciò maggiore anco <lb/>&longs;arà la proportione del pe&longs;o D alpe&longs;o G, che de l'iste&longs;&longs;o D ad E: Dunque il<emph.end type="italics"/><lb/><arrow.to.target n="note103"></arrow.to.target> <emph type="italics"/>pe&longs;o G &longs;arà minore del pe&longs;o E. & concio&longs;ia che la po&longs;&longs;anza po&longs;ta in B eguale à <lb/>G pe&longs;i egualmente con D, auerrà, che minore po&longs;&longs;anza di quella, laquale è eguale <lb/>al pe&longs;o E &longs;o&longs;tenter à il pe&longs;o D; e&longs;&longs;endo la leua AB, & il &longs;o&longs;tegno &longs;uo doue è F, <lb/>che &longs;e egli &longs;o&longs;&longs;e doue è C. Similmente anche mo&longs;trera&longs;&longs;i, che quanto piu dapre&longs;&longs;o &longs;a <lb/>rà il &longs;o&longs;tegno al pe&longs;o D, &longs;empre vi &longs;i ricercherà anco po&longs;&longs;anza minore per &longs;o&longs;tentare <lb/>il detto pe&longs;o D.<emph.end type="italics"/>

Moua&longs;i poi <lb/>la <expan abbr="bil&amacr;cia">bilancia</expan> da que&longs;to &longs;ito, come in ECF. <lb/>Dico che la bilancia ECF ritornerà <lb/>in ACB. Ritroui&longs;i il centro della <lb/>grauczza di tutta la magnitudine D, <lb/>& &longs;ia congiunta la CD. Hor percio<emph.end type="italics"/><lb/><arrow.to.target n="note135"></arrow.to.target> <emph type="italics"/>che i pe&longs;i AB stanno fermi, lali-<lb/>nea CD &longs;arà à piombo dell' orizon-<emph.end type="italics"/><lb/><arrow.to.target n="fig49"></arrow.to.target><lb/><emph type="italics"/>ie.

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Quando dunque la bilancia &longs;arà in ECF, la linea CD &longs;arà come in CG; <lb/>la quale per non e&longs;&longs;ere à piombo dell' orizonte, la bilancia ECF ritornerà in <lb/>ACB. ilche parimente auenir à, &longs;e il centro C &longs;arà me&longs;&longs;o &longs;opra la bilancia, co-<lb/>me in H.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note101"></margin.target><emph type="italics"/>Per la mede &longs;ima &longs;esta.<emph.end type="italics"/>

<margin.target id="note135"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

<margin.target id="note102"></margin.target><emph type="italics"/>Per lo Lemma.<emph.end type="italics"/>

<emph type="italics"/>Che &longs;e l'arco, ouero l'angolo ACB <lb/>&longs;arà &longs;otto la linea AB, nel <lb/>modo i&longs;te&longs;&longs;o mo&longs;treremo, la bi-<lb/>lancia ECF, il cui centro &longs;ia <lb/>ouero in C, ouero in H, do-<lb/>uer&longs;i mouere in giu dalla parte <lb/>di F.<emph.end type="italics"/><lb/><arrow.to.target n="fig50"></arrow.to.target>

</s>

<margin.target id="note103"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 10. <emph type="italics"/>del quinto<emph.end type="italics"/>

</figure>

</figure>

<emph type="italics"/>Et &longs;e l'angolo ACB fo&longs;&longs;e &longs;oprala linea AB, & il centro della bilancia H; & <lb/>& lalinea CH &longs;o&longs;tene&longs;&longs;e la bilancia; & &longs;imoue&longs;&longs;e la bilancia in EKF; la bilan <lb/>cia EKF ritornerà in ACB.<emph.end type="italics"/>

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COROLLARIO.

<emph type="italics"/>Ma &longs;e il centro della bilancia &longs;arà D, moua&longs;i in qualunque modo la bilancia, doue &longs;i <lb/>la&longs;cierà, iui rimarrà.<emph.end type="italics"/>

</s>

Onde &longs;i puote raccogliere chiaramente, che e&longs;&longs;endo AF minore di <lb/>FB, minor po&longs;&longs;anza anco &longs;i ricerca in B per &longs;o&longs;tenere il pe&longs;o D. <lb/>& e&longs;&longs;endo eguale, eguale: & maggiore, maggiore.

<emph type="italics"/>Se poi il punto H &longs;arà &longs;otto la linea AB; allhora la bilancia EKF &longs;i mouerà in <lb/>giu dalla parte di F.<emph.end type="italics"/>

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PROPOSITIONE II.

<emph type="italics"/>Et con &longs;imile ragione in tutto, &longs;e l'ango-<lb/>lo ACB &longs;arà &longs;otto la linea AB; <lb/>& &longs;ia il centro della bilancia H, & <lb/>&longs;ia la bilancia &longs;o&longs;tentata dalla linea <lb/>CH; &longs;e la bilancia moueraßi da que&longs;to <lb/>&longs;ito, &longs;i mouerà in giu dalla parte del pe <lb/>&longs;o più ba&longs;&longs;o.

</s>

& &longs;e il centro della bilan-<lb/>cia &longs;ia D; rimarrà doue &longs;i la&longs;cierà.

In altra maniera po&longs;&longs;iamo v&longs;are la Leua.

</s>

che <lb/>&longs;e &longs;arà in K; & da cotale &longs;ito &longs;i mo <lb/>uerà, ritornerà ad ogni modo nello i&longs;te&longs; <lb/>&longs;o.

<emph type="italics"/>Sia la leua AB, il cui &longs;o&longs;tegno &longs;ia B, & il pe&longs;o C &longs;ia attaccato, come &longs;i vuole, in D<emph.end type="italics"/> <arrow.to.target n="note104"></arrow.to.target><lb/><emph type="italics"/>fra AB; & &longs;ia la po&longs;&longs;anza in A che &longs;ostiene il pe&longs;o C. Dico, che &longs;i come <lb/>BD à BA; co&longs;i è lapo&longs;&longs;anza di A' al pe&longs;o C. Appicchi&longs;i in A il pe&longs;o E <lb/>eguale al C; & come AB ver&longs;o BD, co&longs;i faccia&longs;i il pe&longs;o E ver&longs;o vn'altro pe&longs;o,<emph.end type="italics"/> <arrow.to.target n="note105"></arrow.to.target><lb/><emph type="italics"/>come F. Et percioche i pe&longs;i CE &longs;ono tra&longs;e eguali, &longs;arà il pe&longs;o C ver&longs;o il pe&longs;o F <lb/>come AB ver&longs;o BD. Attacchi&longs;i parimente il pe&longs;o F in A. & percioche il<emph.end type="italics"/> <arrow.to.target n="note106"></arrow.to.target><lb/><emph type="italics"/>pe&longs;o E al pe&longs;o F <lb/>è come la grauez <lb/>za del pe&longs;o di E <lb/>alla grauezza di <lb/>F; & il pe&longs;o E <lb/>ad F è come AB <lb/>à BD; come <expan abbr="d&utilde;">dum</expan> <lb/>que la grauezza <lb/>del pe&longs;o E alla<emph.end type="italics"/> <arrow.to.target n="note107"></arrow.to.target><lb/><arrow.to.target n="fig31"></arrow.to.target><lb/><emph type="italics"/>grauezza del pe&longs;o F, co&longs;i è AB ver&longs;o BD. ma come AB à BD, co&longs;i è la <lb/>grauezza del pe&longs;o E alla grauezza del pe&longs;o C: Per laqual co&longs;a la grauezza del <lb/>pe&longs;o E alla grauezza del pe&longs;o F co&longs;i &longs;arà, come la grauezza del pe&longs;o E alla gra-<lb/>uezza del pe&longs;o C. I pe&longs;i dunque CF hanno la mede&longs;ima grauezza: &longs;i che pon-<lb/>ga&longs;i la po&longs;&longs;anza di A che &longs;o&longs;tenga il pe&longs;o F, &longs;arà la po&longs;&longs;anza di A eguale al pe&longs;o <lb/>F. & percioche il pe&longs;o E attaccat<*> in A è graue egualmente, come il C appicca-<emph.end type="italics"/> <arrow.to.target n="note108"></arrow.to.target><lb/><emph type="italics"/>to in D; hauer à la proportione i&longs;te&longs;&longs;a la po&longs;&longs;anza di A ver&longs;o la grauezza del pe&longs;o <lb/>F appiccato in A, che ha alla grauezza del pe&longs;o C appiccato in D. Mala po&longs;&longs;an <lb/>za di A eguale ad F &longs;o&longs;tiene il pe&longs;o F; dunque la po&longs;&longs;anza di A &longs;o&longs;tenterà anco <lb/>il pe&longs;o C. Et co&longs;i per e&longs;&longs;ere la po&longs;&longs;anza di A eguale al pe&longs;o F, & il pe&longs;o C ver&longs;o <lb/>il pe&longs;o F &longs;ia come AB à BD; &longs;arà il pe&longs;o C ver&longs;o la po&longs;&longs;anza po&longs;ta in A come <lb/>AB à BD. & conuertendo, come BD à BA, co&longs;i la po&longs;&longs;anza po&longs;ta in A ver <lb/>&longs;o il pe&longs;o C. Dunque la po&longs;&longs;anza ver&longs;o il pe&longs;o co&longs;i &longs;arà, come la di&longs;tanza, che è fra<emph.end type="italics"/> <arrow.to.target n="note109"></arrow.to.target><lb/><emph type="italics"/>il &longs;o&longs;tegno, & l'appiccamento del pe&longs;o alla di&longs;tanza, che è dal &longs;o&longs;tegno alla po&longs;&longs;an-<lb/>za, che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

<pb/>

Le quali co&longs;e tutte da quel che in<emph.end type="italics"/><lb/><arrow.to.target n="fig51"></arrow.to.target><lb/><emph type="italics"/>principio dicemmo &longs;ono mani&longs;este.

</figure>

<margin.target id="note104"></margin.target><emph type="italics"/>Nella &longs;esta di questo de la bilancia.<emph.end type="italics"/>

</s>

&longs;imilmente &longs;e il centro della bilancia &longs;arà po&longs;to <lb/>in vno della bracia della bilancia, ò dentro, ò &longs;uori, ò in qual &longs;i voglia modo trouere <lb/>mo le co&longs;e i&longs;te&longs;&longs;e.<emph.end type="italics"/>

<margin.target id="note105"></margin.target><emph type="italics"/>Dalla<emph.end type="italics"/> 11. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note106"></margin.target><emph type="italics"/>Per la &longs;esta della <expan abbr="bil&amacr;cia">bilancia</expan><emph.end type="italics"/>

In que&longs;to luogo egli conuiene auertire, il che potcua&longs;i anco fare di &longs;opra à carte cin <lb/>que pre&longs;&longs;o la fine della &longs;econda faccia oue è &longs;critto.

</s>

oltre à ciò po&longs;siamo con&longs;ide-<lb/>rare le co&longs;e che &longs;eguono in tutto al modo i&longs;te&longs;&longs;o.

<margin.target id="note107"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Che que&longs;to autore è &longs;tato il <lb/>primo à con&longs;iderare e&longs;qui&longs;itamente la bilancia, & intenderla dalla natura, & dal <lb/>vero e&longs;&longs;er &longs;uo; pero che egli il primiero di tutti ha manife&longs;tato chia ramente il mo <lb/>do del trattarla, & in&longs;egnarla, con proporre tre centri da e&longs;&longs;ere con&longs;iderati in que <lb/>&longs;ta &longs;peculatione; l'uno è il centro del mondo, l'altro il centro della bilancia, & il <lb/>terzo il centro della grauezza della bilancia, che in e&longs;&longs;a era vn na&longs;co&longs;to &longs;ecreto di <lb/>natura.

<margin.target id="note108"></margin.target><emph type="italics"/>Per la &longs;ettima del<emph.end type="italics"/> 5.

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Senza que&longs;ti tre centri, chiara co&longs;a è, che non &longs;i puote ve nire in cono&longs;ci-<lb/>mento per&longs;etto, ne dimo&longs;trare gli effetti varij della bilancia, i quali na&longs;cono dalla <lb/>diuer&longs;ità del collo care il centro della bilancia in tre modi, cioè quando il <lb/>centro della bilancia &longs;ta &longs;opra il centro della grauezza di e&longs;&longs;a, ouero quando è <lb/>di &longs;otto, o pure allhorche il centro della bilancia è nell'i&longs;te&longs;&longs;o centro della gra-<lb/>uezza di lei; &longs;i come l'autore in&longs;egna nella tre precedenti dimo&longs;trationi, cioè <lb/>nella <expan abbr="&longs;ecõda">&longs;econda</expan>, nella terza, & nella quarta propo&longs;itione: peroche nella &longs;econda mo-<lb/>&longs;tra quando la bilancia torna &longs;empre egualmente di&longs;tante dall'orizonte; nella ter-<lb/>za quando non &longs;olo non ritorna, ma &longs;i moue al contrario; nella quarta, che <lb/>e&longs;&longs;endo la bilancia &longs;o&longs;tenuta nel &longs;uo centro dalla grauezza &longs;ta ferma douunque el <lb/>la &longs;i troua, il quale effetto in particolare non è piu &longs;tato tocco, ne veduto, ne man <lb/>co da niuno manife&longs;tato, fuor che dall'autore: anzi fin hora tenuto fal&longs;o, & impo&longs; <lb/>&longs;ibile da tutti gli prede ce&longs;&longs;ori no&longs;tri; i quali con molte ragioni &longs;i &longs;ono sforzati di <lb/>prouare non &longs;olamente il contrario, ma hanno etiandio affermato per certo, che <lb/>la &longs;períenza mo&longs;tra la bilancia non dimorare gia mai ferma &longs;e non quando ella è <lb/>egualmente di&longs;tante dall'oritonte.

<margin.target id="note109"></margin.target><emph type="italics"/>Per lo Corol lario della<emph.end type="italics"/> 4 <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Laqual co&longs;a in tutto è contraria alla ragione <lb/>prima, per e&longs;&longs;ere la dimo&longs;tratione della &longs;udetta quarta propo&longs;itione tanto chiara, <lb/>facile, & vera, che non sò, come &longs;e le po&longs;&longs;a in modo alcuno contradire: & poial-<lb/>l'e&longs;perienza concio&longs;ia che l'autore habbia fatto &longs;ottili&longs;simamente lauorare bilan-<lb/>cie giu&longs;te a po&longs;ta per chiarire que&longs;ta verità, vna delle quali hò io veduto in mano <lb/>dell'Illu&longs;tre Signor Gio.

Altramente.

</s>

Vicenzo Pinello, mandatagli dall'i&longs;te&longs;&longs;o autore, la quale <lb/>per e&longs;&longs;ere &longs;o&longs;tenuta nel centro della &longs;u a grauezza, mo&longs;&longs;a douunque &longs;i vuole, & poi <lb/>la&longs;ciata, &longs;tà ferma in ogni &longs;ito doue ella vien la&longs;ciata.

<emph type="italics"/>Sia la leua AB, il cui &longs;o&longs;tegno &longs;ia B, & il pe&longs;o E &longs;ia pendente dal punto C, & <lb/>&longs;ia in A la forza, che &longs;ostiene l pe&longs;o E. Dico, che &longs;i come BC à BA, co&longs;i è<emph.end type="italics"/><lb/><arrow.to.target n="fig32"></arrow.to.target><lb/><emph type="italics"/>anco la po&longs;&longs;anza di A ver&longs;o il pe&longs;o E. Allunghi&longs;i AB in D, & faccia&longs;i <lb/>BD eguale à BC; & appicchi&longs;i il pe&longs;o F al punto D, che &longs;ia eguale al pe&longs;o E; <lb/>& parimente dal punto A &longs;i faccia pendere il punto G in modo, che il pe&longs;o F hab <lb/>bia la proportione i&longs;te&longs;&longs;a ver&longs;o il pe&longs;o G, che ha AB à BD. ipe&longs;i FG verranno <lb/>à pe&longs;ar egualmente: & concio&longs;ia che CB &longs;ia eguale à BD, anco i pe&longs;i FE egua <lb/>li pe&longs;eranno egualmente.

</s>

Ma ipe&longs;i FEG nella bilancia, ouero nella leua DBA <lb/>appiccati, il cui &longs;o&longs;tegno è B, non pe&longs;eranno egualmente, ma inchineranno à ba&longs;&longs;o <lb/>dalla parte di A. Per laqual co&longs;a ponga&longs;i in A tanta forza, che ipe&longs;i FEG pe&longs;i-<lb/>no egualmente, &longs;arà la po&longs;&longs;anza in A eguale al pe&longs;o G; peroche i pe&longs;i FE pe&longs;a-<lb/>no egualmente, & la forza in A niente altro deue fare, che &longs;o&longs;tenere il pe&longs;o G, ac-<lb/>cio che non de&longs;cenda.

Ben è egli vero, che non bi <lb/>&longs;ogna, nel fare cote&longs;ta e&longs;perienza, correr co&longs;i a furia, per e&longs;&longs;ere co&longs;a oltra modo <lb/>difficile, come dice l'áutore di &longs;opra, il fare vna bilancia, la quale &longs;ia nel mezo del <lb/>le &longs;ue braccia &longs;o&longs;tenuta à punto, & nel centro proprio della &longs;ua grauezza.

</s>

Et percio che i pe&longs;i FEG, & la po&longs;&longs;anza in A pe&longs;ano egual <lb/>mente, leuati dunque via i pe&longs;i FG, i quali pe&longs;ano egualmente, i re&longs;tanti pe&longs;eran-<lb/>no pur egualmente, cioè la po&longs;&longs;anza in A co'l pe&longs;o E, cioè la po&longs;&longs;anza in A &longs;o-<lb/>sterra ilpe&longs;o E, &longs;i che la leua AB rimanga, come era prima.

Per la <lb/>qual co&longs;a egli è da por <expan abbr="m&etilde;te">mente</expan>, che qual'hora alcuno &longs;i mette&longs;&longs;e à far cotale e&longs;perien <lb/>ra, & non gli riu&longs;ci&longs;&longs;e, non perciò &longs;i deue &longs;gomentare, anzi dica pur fermamente <lb/>di non hauer bene operato, & vn'altra volta ritorni à farne la &longs;perienza, fin chela <lb/>bilancia &longs;ia giu&longs;ta, & eguale, & venga &longs;o&longs;tenuta à punto nel centro della grauez-<lb/>za &longs;ua.

</s>

Et per e&longs;&longs;ere la <lb/>po&longs;&longs;anza in A eguale al pe&longs;o G, & il pe&longs;o E eguale al pe&longs;o F, haurà la po&longs;&longs;anza <lb/>in A la proportione iste&longs;&longs;a al pe&longs;o E, che hà BD, cioè BC à BA, che bi&longs;ogna <lb/>ua mo&longs;trare.<emph.end type="italics"/>

Et benche da altri &longs;iano &longs;tate to cche le altre due predette &longs;peculationi, cioè <lb/>quando la bilancia ritorna &longs;empre egualmente di&longs;tante dall'orizonte, & quando <lb/>&longs;i moue al contrario di que&longs;to &longs;ito, tuttauia non &longs;i è piu inte&longs;a que&longs;ta verità gia <lb/>mai apertamente, &longs;e non dall'autore no&longs;tro; peroche gli altri non hanno co'l &longs;en-<lb/>no penetrato in ciò tanto auanti, che habbiano &longs;aputo con di&longs;tintione con&longs;idera <lb/>re il centro della bila ncia in tre modi, come hò narrato.

</s>

Che &longs;e hanno pur diui&longs;a <lb/>to qualche co&longs;a d'intorno à que&longs;to, l'hanno fatto confu&longs;i&longs;simamente, & con ma <lb/>le dimo&longs;trationi, dalle quali non &longs;i puote cauare ferma <expan abbr="cõchiufione">conchiufione</expan>, & chiara.

</figure>

COROLLARIO I.

</s>

Que <lb/><*> predece&longs;&longs;ori no&longs;tri han&longs;i da intendere i moderni &longs;crittori di cotal materia alle-<lb/>gati in diuer&longs;i luoghi dall'autore, fra quali Giordano, che &longs;cri&longs;&longs;e de'pe&longs;i fù riputa-<pb n="29"/>to a&longs;&longs;ai, & &longs;in qui è &longs;tato &longs;eguito molto nella &longs;ua dottrina.

Da que&longs;to etiandio, come prima, puote e&longs;&longs;ere manife&longs;to, che &longs;eil pe&longs;o <lb/>E &longs;arà po&longs;to piu vicino al &longs;o&longs;tegno B, come in H, minore <lb/>po&longs;&longs;anza po&longs;ta in A puote &longs;o&longs;tener il detto pe&longs;o.

</s>

Hor l'autore no&longs;tro hà <lb/>procurato con ogni &longs;tudi o di caminare per la via de' buoni Greci antichi, <lb/>mae&longs;tri delle &longs;cienze, & in particolare di Archimede Sira cu&longs;ano prencipe delle ma <lb/>thematiche famo &longs;i&longs;simo, & di Pappo Ale&longs;&longs;andrino, come egli dice, leggendogli <lb/>nella &longs;ua propria fauella, non tradotti; peroche il piu delle volte &longs;ono co&longs;i mal <lb/>trattati, che à gran pen a'&longs;i puote trarre da loro frutto veruno.

<emph type="italics"/>Percioche minor proportione ha HB à BA, che CB à BA. & quanto piu da<emph.end type="italics"/><lb/><arrow.to.target n="note110"></arrow.to.target> <emph type="italics"/>vicino il pe&longs;o &longs;arà al &longs;o&longs;tegno, &longs;empre anco &longs;i mo&longs;trerà &longs;imilmente minor po&longs;&longs;anza <lb/>poter &longs;o&longs;tener il pe&longs;o E.<emph.end type="italics"/>

</s>

& affine che que&longs;ta <lb/>noua opinion &longs;ua, dimo&longs;trata à pien o nella predetta quarta propo&longs;itione, re&longs;ti to-<lb/>talmente chiara, non &longs;i è gia <expan abbr="cont&etilde;tato">contentato</expan> egli d'hauerla dimo&longs;trata con viue ragioni, <lb/>& certe &longs;olamente, ma come buon filo&longs;ofo, procedente con via di reale dottrina, <lb/>& di fon data &longs;cienza, (imitando Ari&longs;totele, ilqual ne' principii de &longs;uoi libri, inue-<lb/>&longs;tigando dottrina migliore, hà datto contra la opinione de gli antichi, &longs;oluendo <lb/>le ragioni addotte da loro:) hà ben voluto, e&longs;&longs;endo la verità vna &longs;ola, proporre le <lb/>opinioni de'&longs;uoi predece&longs;&longs;ori, & e&longs;aminare le loro ragioni, lequali &longs;embrano pro <lb/>uar il contrario, & &longs;oluerle, la loro fallenza <expan abbr="dimo&longs;trãdo">dimo&longs;trando</expan> co'l pre&longs;ente di&longs;cor&longs;o, che <lb/>incomincia, come è detto à carte cinque nella faccia &longs;econda, & qui fini&longs;ce ilqua <lb/>le di&longs;cor&longs;o &longs;eruirà in que&longs;ta materia, &longs;econdo che &longs;i &longs;uole dire per la opinione de <lb/>gli antichi.

<margin.target id="note110"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 8. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Et percio che egli contiene co&longs;e di alti&longs;sima &longs;peculatione, ma&longs;simamen-<lb/>te d'intorno al con&longs;iderare doue &longs;ia piu graue vn pe&longs;o &longs;olo po&longs;to in vno braccio <lb/>della bilancia, bi&longs;ogna in ogni modo, per bene intendere, leggerlo, & i&longs;tudiarlo <lb/>con accurati&longs;sima diligenza.

COROLLARIO II.

</s>

Ma per certo l'autore è &longs;tato non &longs;olo il primo à tro <lb/>uare que&longs;ta verità, ma il primo etiandio a dim o&longs;trare in qual maniera &longs;ia me&longs;tieri <lb/>con&longs;iderare, & &longs;peculare interamente la pre&longs;ente materia tutta.

Segue etiandio, che la po&longs;&longs;anza in A &longs;empre è minore del pe&longs;o E:

</s>

Con laquale &longs;p ecu-<lb/>latione proua di nouo, & confermai varij effetti, & accidenti della bilancia già di <lb/>mo&longs;trati nelle pro&longs;sime tre propo&longs;itioni; mo&longs;trando ancora, come &longs;in qui cote&longs;te <lb/>co&longs;e &longs;iano da gli altri &longs;tate malamente con&longs;iderate, & con principij fal&longs;i.

</s>

<emph type="italics"/>Percioche pigli&longs;i tra A & B qual punto &longs;i voglia, come C, &longs;empre BC &longs;arà <lb/>minore di BA.<emph.end type="italics"/>

Anzi di <lb/>piu per confermatione della verità &longs;oggiunge, che que&longs;ti tali non hanno &longs;aputo fa <lb/>re le loro demo&longs;trationi; poi che co'l proprio modo di &longs;peculare v&longs;ato da loro, <lb/>& con le loro mede&longs;ime ragioni proua la &longs;ua intentione, & &longs;entenza e&longs;&longs;ere veri&longs;si <lb/>ma, appoggiando &longs;i alla dottrina di Ari&longs;totele &longs;empre, & facendo toccar con ma-<lb/>no, che egli con e&longs;&longs;o lui è d'accordo nelle que&longs;tioni mechaniche.

</s>

In trattando <lb/>que&longs;ta materia moue l'autore alcuni dubbi molto belli, & curio&longs;i, & poi chiara-<lb/>ment e gli &longs;olue.

</s>

In vltimo, accioche non manca&longs;&longs;e nulla al compiuto cono&longs;cimen <lb/>to di que&longs;to &longs;oggetto, egli hà trattato delle bilancie, che hanno le braccia di&longs;ugua <lb/>li, & di quelle che hanno le dette braccia piegate, & torte.

</s>

In &longs;omma &longs;i può ben <lb/>affermare, che in cote&longs;to di&longs;cor&longs;o &longs;iano compre&longs;e tutte quelle co&longs;e, che po&longs;&longs;ono e&longs; <lb/>&longs;ere diui&longs;ate d'intorno à materia tale.

</s>

Le quali &longs;ono di belli&longs;s ima & &longs;ottili&longs;sima &longs;pe <lb/>culatione, & à chiunque &longs;i diletta, & attende à que&longs;ti no bili &longs;tudi nece&longs;&longs;arij &longs;sime, <lb/>& da e&longs;&longs;ere, come hò ricordato piu d'una volta, con molta attentione vedute, & <lb/>con&longs;iderate.

</s>

COROLLARIO III.

Doue &longs;i legge que&longs;to vocabolo latino Equilibrio, intenda&longs;i per eguale contrape&longs;o, <lb/>cio è che pe&longs;a tanto da vna banda, quanto dallaltra in pari lance, ò libra, ò bilancia <lb/>che &longs;i dica.

</s>

Da que&longs;to parimente &longs;i puote cauare, che &longs;e due &longs;aranno le po&longs;&longs;anze, <lb/>l'vna in A, & l'altra in B, & ambedue &longs;o&longs;tentino il pe&longs;o E, la po&longs;-<lb/>&longs;anza in A ver&longs;o la po&longs;&longs;anza in B è come BC ver&longs;o CA.

<emph type="italics"/>Librar congiu&longs;te lance.<emph.end type="italics"/>

</s>

<emph type="italics"/>Percioche la leua BA fal'officio di due leue, & AB &longs;ono come due &longs;o&longs;tegni, cioè <lb/>quando AB è leua, & la forza che &longs;o&longs;tiene è in A, &longs;arà il &longs;uo &longs;o&longs;tegno B. Ma <lb/>quando BA è leua, & la po&longs;&longs;anza &longs;ta in B, il &longs;o&longs;tegno &longs;arà A, & il pe&longs;o <lb/>&longs;empre rimane appicca-<lb/>to in C. Et percio che la <lb/>po&longs;&longs;anza in A ver&longs;o il <lb/>pe&longs;o E è come BC à<emph.end type="italics"/> <arrow.to.target n="note111"></arrow.to.target><lb/><emph type="italics"/>BA, & come il pe&longs;o <lb/>E alla po&longs;&longs;anza, che è <lb/>in B, co&longs;i è BA ad <lb/>AC, &longs;arà per la propor<emph.end type="italics"/><lb/><arrow.to.target n="fig33"></arrow.to.target><lb/><emph type="italics"/>tion eguale la po&longs;&longs;anza in A alla po&longs;&longs;anza in B come BC à CA, & à que <lb/>&longs;to modo facilmente ancora potremo cono&longs;cere la proportione, laquale è po&longs;ta de <lb/>Ari&longs;totele nelle que&longs;tioni Mecaniche alla que&longs;tione 29.<emph.end type="italics"/>

Di&longs;&longs;e il Petrarcha.

</s>

<pb/>

</figure>

<margin.target id="note111"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 22. <emph type="italics"/>del primo.<emph.end type="italics"/>

<margin.target id="note56"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 35. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

COROLLARIO IIII.

<margin.target id="note57"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

E manife&longs;to etiandio, che ambedue le po&longs;&longs;anze in A, & in B <lb/>pre&longs;e in&longs;ieme, &longs;ono eguali al pe&longs;o E.

PROPOSITIONE V.

</s>

<emph type="italics"/>Percioche il pe&longs;o E alla po&longs;&longs;anza in A è come BA à BC, & l'i&longs;te&longs;&longs;o pe&longs;o E <lb/>ver&longs;o la po&longs;&longs;anza in B è come BA ad AC; Per laqual co&longs;a il pe&longs;o E ver-<lb/>&longs;o l'vna, & l'altra po&longs;&longs;anzain A, & in B pre&longs;e in&longs;ieme, è come AB ver&longs;o <lb/>BC, & CA in&longs;ieme, cioè ver&longs;o BA. il pe&longs;o dunque E è eguale ad amen-<lb/>due le po&longs;&longs;anze pre&longs;e in&longs;ieme.<emph.end type="italics"/>

</s>

</figure>

PROPOSITIONE III.

</s>

&longs;imilmente percioche <lb/>&longs;i come AC è ver&longs;o CB, co&longs;i il pe&longs;o F è alpe&longs;o M, i pe&longs;i FM pe&longs;eranno <lb/>anco egualmente.

</s>

</s>

In altro modo ancora po&longs;&longs;iamo v&longs;are la Leua.

<margin.target id="note58"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<pb/>

<emph type="italics"/>Sia la leua AB, il cui &longs;o&longs;tegno &longs;ia B. & &longs;ia il pe&longs;o C appiccato al punto A, <lb/>& &longs;ia la po&longs;&longs;anza in D, comunque &longs;i voglia tra AB, &longs;o&longs;tenente il pe&longs;o C. Di-<lb/>co che come AB à BD, co&longs;i è la po&longs;&longs;anza in D al pe&longs;o C. Appicchi&longs;i al <lb/>punto D il pe&longs;o E eguale à C; & come BD à BA, co&longs;i &longs;accia&longs;i il pe&longs;o <lb/>E ad vn'altro pe&longs;o, come F: & per e&longs;&longs;ere i pe&longs;i CE traloro eguali, &longs;arà an-<lb/>co il pe&longs;o C al <lb/>pe&longs;o F, come <lb/>BD à BA. <lb/>Appicchi&longs;i &longs;imil <lb/>mente il pe&longs;o F <lb/>in D. & per-<lb/>che il pe&longs;o E ad <lb/>F è come la gra <lb/>uezza del pe&longs;o <lb/>E alla grauez-<lb/>za del pe&longs;o F; <lb/>& il pe&longs;o E al<emph.end type="italics"/><lb/><arrow.to.target n="fig34"></arrow.to.target><lb/><arrow.to.target n="note112"></arrow.to.target> <emph type="italics"/>pe&longs;o F è come BD à BA. Come dunque la grauezza del pe&longs;o E alla gra-<lb/>uezza del pe&longs;o F, co&longs;i è BD à BA. Ma come BD à BA, co&longs;i è la gra-<lb/>uezza del pe&longs;o E alla grauezza del pe&longs;o C. Per laqual co&longs;a la grauezza del<emph.end type="italics"/><lb/><arrow.to.target n="note113"></arrow.to.target> <emph type="italics"/>pe&longs;o E alla grauezza del pe&longs;o F ha la proportione mede&longs;ima, che ha alla gra-<lb/>uezza del pe&longs;o C. i pe&longs;i dunque CF hanno la grauezza mede&longs;ma.

</s>

Sia dunque<emph.end type="italics"/><lb/><arrow.to.target n="note114"></arrow.to.target> <emph type="italics"/>la po&longs;&longs;anza in D &longs;o&longs;tenente il pe&longs;o F, che verrà ad e&longs;&longs;ere la detta po&longs;&longs;anza in <lb/>D eguals al pe&longs;o F. & percioche il pe&longs;o F posto in D è graue egualmente <lb/>come il pe&longs;o C po&longs;to in A; haur à la po&longs;&longs;anza in D la proportione mede&longs;ima <lb/>ver&longs;o la grauezza del pe&longs;o F, che ha alla grauezza del pe&longs;o C. Ma la po&longs;&longs;anza <lb/>in D &longs;o&longs;tiene il pe&longs;o F, dunque la po&longs;&longs;anza in D &longs;o&longs;tenterà anco il pe&longs;o C; & <lb/>il pe&longs;o C alla po&longs;&longs;anza in D &longs;arà co&longs;i come il pe&longs;o C al pe&longs;o F; & C ad F<emph.end type="italics"/><lb/><arrow.to.target n="note115"></arrow.to.target> <emph type="italics"/>è come BD à BA, &longs;arà dunque il pe&longs;o C alla po&longs;&longs;anza in D, come BD à <lb/>BA: & conuertendo come AB à BD, co&longs;i la po&longs;&longs;anza in D al pe&longs;o C. La <lb/>po&longs;&longs;anza dunque al pe&longs;o, è come la di&longs;tanza dal &longs;ostegno allo appiccamento del pe-<lb/>&longs;o alla distanza dal &longs;o&longs;tegno alla po&longs;&longs;anza.

<margin.target id="note60"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

che bi&longs;ognaua mostrare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note62"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 18. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note112"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>di questo della bilancia.<emph.end type="italics"/>

</s>

<margin.target id="note113"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>di questo della bilancia.<emph.end type="italics"/>

<margin.target id="note63"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<margin.target id="note114"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 9. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note64"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<margin.target id="note115"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note65"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Altramente.

</s>

<emph type="italics"/>Sia la leua AB, il cui &longs;o&longs;tegno &longs;ia B. & dal punto A &longs;ia fatto pendente il pe&longs;o <lb/>C, & &longs;ia la po&longs;&longs;anza in D &longs;o&longs;tenente il pe&longs;o C. Dico, che come AB à BD, <lb/>co&longs;i è la po&longs;&longs;anza in D al pe&longs;o C. allunghi&longs;ila AB in E, & faccia&longs;i BE egua-<lb/>le à BA, & al punto E &longs;ia appiccato il pe&longs;o F eguale al pe&longs;o C; & come BD à <lb/>BE co&longs;i faccia&longs;i il pe&longs;o F ad vn'altro pe&longs;o G, ilquale &longs;ia appiccato al punto D, <lb/>i pe&longs;i FG pe&longs;eranno egualmente.

<margin.target id="note67"></margin.target><emph type="italics"/>Per lo<emph.end type="italics"/> 2. <emph type="italics"/><expan abbr="cõ">com</expan>.

</s>

& percioche AB è eguale à BE, & i pe&longs;i<emph.end type="italics"/><pb n="19"/><emph type="italics"/>mente non è della grauez <lb/>za cagione?

della not di questo.<emph.end type="italics"/>

</s>

<margin.target id="note68"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 3. <emph type="italics"/><expan abbr="cõ">com</expan>.

</s>

della not ai questo.<emph.end type="italics"/>

</s>

</figure>

</s>

</s>

<pb/>

<margin.target id="note69"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</s>

Ma &longs;ia &longs;o&longs;tenuta la trutina da due po&longs;&longs;anze in F cioè, & in G, <pb/>&longs;arà la inclinatione dell'vno al moui-<lb/>mento in giù, tale parimente &longs;arà la re <lb/>&longs;istenza dell'altro al mouimento in sù. <lb/>Adunque il pe&longs;o po&longs;to in E non mo-<lb/>uerà in sù il pe&longs;o po&longs;to in D: ne il pe&longs;o <lb/>po&longs;to in D: &longs;i mouerà in giù &longs;i fatta-<lb/>mente, che moua in sù il pe&longs;o po&longs;to in <lb/>E. imperoche e&longs;&longs;endo l'angolo CEB <lb/>egualea CDA, & l'angolo CEM <lb/>&longs;ia eguale all'angolo CDH; &longs;arà il <lb/>re&longs;tante MEB eguale al re&longs;tante<emph.end type="italics"/><lb/><arrow.to.target n="note116"></arrow.to.target> <emph type="italics"/>HDA. La &longs;ce&longs;a dunque del pe&longs;o po-<lb/>&longs;to in D &longs;arà eguale alla &longs;alita del pe-<lb/>&longs;o po&longs;to in E. Adunque il pe&longs;o po&longs;to <lb/>in D non mouerà in sù il pe&longs;o po&longs;to <lb/>in E. Dalle quali co&longs;e &longs;egue che i pe&longs;i <lb/>po&longs;ti in DE, in quanto tra loro &longs;o-<lb/>no congiunti, &longs;ono egualmente graui.<emph.end type="italics"/>

<margin.target id="note71"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note72"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note116"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del prime.<emph.end type="italics"/>

</s>

</figure>

</s>

che &longs;e gli <lb/>angoli &longs;aranno tra loro paragonati, e&longs;&longs;endo l'angolo GCD eguale all'angolo <lb/>FCE; &longs;e l'angolo GCD è cau&longs;a della grauezza, perche l'angolo FCE &longs;imil-<pb/>ilche &longs;i puote fare per nece&longs;&longs;ità, come &longs;e la po&longs;&longs;anza posta in F &longs;o&longs;&longs;e tanto debile, <lb/>che per &longs;e &longs;te&longs;&longs;a pote&longs;&longs;e &longs;o&longs;tentare &longs;olamente la metà del pe&longs;o & &longs;ia la po&longs;&longs;anza <lb/>posta in G eguale alla po&longs;&longs;anza po&longs;ta in F, & ambedue in&longs;ieme co' pe&longs;i &longs;o&longs;tenga-<lb/>no la bilancia.

& percioche co&longs;i è AC ver&longs;o CD, come H <lb/>ad E: i pe&longs;i HE pe&longs;eranno egualmente.

</s>

all'hora quale angolo &longs;arà cagione della grauezza?

&longs;imilmente percioche, come è GC à CB, <lb/>co&longs;i F ver&longs;o K, i pe&longs;i etiandio KF pe&longs;eranno egualmente.

</s>

Adunque i pe&longs;i<emph.end type="italics"/><lb/><arrow.to.target n="note80"></arrow.to.target> <emph type="italics"/>EK HF nella bilancia AB, il cui centro &longs;ia C pe&longs;eranno egualmente.

</s>

</s>

</s>

Ma percioche la parte L è egua-<lb/>le ad F, & la parte M è eguale alla parte E; &longs;arà tutto LM eguale a i pe&longs;i <lb/>FE in&longs;ieme pre&longs;i.

</s>

</s>

Adunque i pe&longs;i EF pe&longs;eranno tanto in AB quanto nel punto D; che <lb/>bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note73"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<margin.target id="note117"></margin.target><emph type="italics"/>il Cardano.<emph.end type="italics"/>

</s>

<margin.target id="note74"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 23. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</s>

<margin.target id="note75"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 17. <emph type="italics"/>del quinto.<emph.end type="italics"/>

& in qual &longs;i vo-<lb/>glia altro &longs;ito che &longs;ia la <lb/>trutina, auerrà &longs;empre il <lb/>mede&longs;imo.

</s>

Adunque <expan abbr="nõ">non</expan> <lb/>è la trutina, ma il centro <lb/>della bilancia cagione di <lb/>cotali diuer&longs;i effetti.<emph.end type="italics"/>

</s>

<margin.target id="note118"></margin.target><emph type="italics"/>Per la terz<*> di questo.<emph.end type="italics"/>

<margin.target id="note76"></margin.target><emph type="italics"/>Corollario della quarta del quinto.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note77"></margin.target>11. <emph type="italics"/>del<emph.end type="italics"/> 5.

</s>

percio che la materia di&longs;&longs;icili&longs;&longs;imam ente pati&longs;ce cotale giu-<lb/>&longs;ta mi&longs;ura.

</s>

</s>

</s>

</s>

<pb/>

<margin.target id="note78"></margin.target>16. <emph type="italics"/>del<emph.end type="italics"/> 5.

</s>

</s>

</figure>

</s>

</s>

Onde la &longs;entenza di Ari&longs;totele non &longs;olamente non gli &longs;auori&longs;ce, ma <lb/>gli fa anche grandi&longs;sima <lb/>mente contra.

<margin.target id="note80"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 2. <emph type="italics"/>no titia commu ne di que&longs;io.<emph.end type="italics"/>

</s>

<margin.target id="note81"></margin.target><emph type="italics"/>Per la commune notitia di questo.<emph.end type="italics"/>

</s>

Ma per lo con-<lb/>trario auiene quando il <lb/>centro è &longs;otto la bilan-<lb/>cia.

<margin.target id="note82"></margin.target><emph type="italics"/>Per la com munenotitia di questo.<emph.end type="italics"/>

</s>

Ma que&longs;te co&longs;e tutte dimo&longs;treremo in altra maniera, & piu Mechani <lb/>camente.

</s>

<pb/>

</figure>

</s>

</s>

</s>

</figure>

<margin.target id="note119"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 4. <emph type="italics"/>del primo.<emph.end type="italics"/>

<margin.target id="note83"></margin.target><emph type="italics"/>Per la &longs;ecom da del &longs;esta.<emph.end type="italics"/>

</s>

<margin.target id="note120"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 28. <emph type="italics"/>del terzo.<emph.end type="italics"/>

<margin.target id="note84"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del quinto<emph.end type="italics"/>

</s>

<margin.target id="note121"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> <*>. <emph type="italics"/>del printo.<emph.end type="italics"/>

<margin.target id="note85"></margin.target><emph type="italics"/>Per la &longs;esta del primo di Archimede d'lle co&longs;e, che pe&longs;ano egual mente.<emph.end type="italics"/>

</s>

<emph type="italics"/>La ragione di que&longs;to effetto po&longs;ta da Ari&longs;totele qui &longs;i puote vedere manife&longs;ta.

<margin.target id="note86"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 1. <emph type="italics"/>di questo.<emph.end type="italics"/>

</s>

Percio-<emph.end type="italics"/> <arrow.to.target n="note122"></arrow.to.target><lb/><emph type="italics"/>che &longs;ia il punto N doue le linee CS EF &longs;i tagliano in&longs;ieme.

</s>

& percioche HE <lb/>è eguale ad HF; &longs;arà NE maggiore di NF. adunque la linea CS, che no-<lb/>ma perpendicolo, diuiderà la bilancia EF in parti di&longs;uguali.

</s>

</s>

</figure>

<margin.target id="note122"></margin.target><emph type="italics"/>Ragione de Aristotele.<emph.end type="italics"/>

</s>

PROPOSITIONE VI.

</s>

come &longs;ia EFS vna <lb/>linea diritta.

</s>

& percioche <lb/>CD CK &longs;ono tra loro <lb/>eguali.

</s>

&longs;e dunque col cen-<lb/>tro C, & con lo &longs;patio <lb/>CD &longs;i de&longs;criuerà il cerchio <lb/>DHM, &longs;aranno i punti <lb/>DH nella circonferenza <lb/>del cerchio.

</s>

</s>

I pe&longs;i eguali nella bilancia appiccati hanno in grauezza quella pro-<lb/>portione, che hanno le di&longs;tanze, dalle quali &longs;tanno pendenti.

</s>

</figure>

</figure>

<emph type="italics"/>Sia la bilancia BAC &longs;o&longs;pe&longs;a nel punto A; & &longs;ia &longs;egata la AC, come pare in D. & <lb/>da i punti DC &longs;iano attaccati EF pe&longs;i eguali.

</s>

</s>

<pb/>

</figure>

<margin.target id="note123"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del primo.<emph.end type="italics"/>

<margin.target id="note87"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 5. <emph type="italics"/>di questo.<emph.end type="italics"/>

</s>

<arrow.to.target n="note124"></arrow.to.target><emph type="italics"/>La ragione di Ari&longs;totele parimente qui è cbiara.

<margin.target id="note88"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 18. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Percioche &longs;ia il punto N doue le <lb/>linee CO EF &longs;i tagliano in&longs;ieme.

</s>

</s>

<margin.target id="note124"></margin.target><emph type="italics"/>Ragione di Aristotele.<emph.end type="italics"/>

<margin.target id="note89"></margin.target><emph type="italics"/>Per la con&longs;e guenza della quartadel quinto.<emph.end type="italics"/>

</s>

<margin.target id="note90"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 22. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

& dauantaggio &longs;i <lb/>mouerà anche piu veloce <lb/>mente quanto la bilancia <lb/>&longs;arà piu lontana dal cen-<lb/>tro C.<emph.end type="italics"/>

</s>

<margin.target id="note91"></margin.target><emph type="italics"/>Per la &longs;ettima del<emph.end type="italics"/> 5.

</s>

</figure>

</s>

</s>

</figure>

<margin.target id="note125"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 28. <emph type="italics"/>d l primo.<emph.end type="italics"/>

Altramente.

</s>

<margin.target id="note126"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 15. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note127"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note128"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 4.<emph type="italics"/>del &longs;esto.<emph.end type="italics"/>

<margin.target id="note93"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note129"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del quinto.<emph.end type="italics"/>

<emph type="italics"/>Ma &longs;e la bilancia BAC fo&longs;&longs;e tagliata, come &longs;i vuole in D, & appicchin&longs;i in DC <lb/>i pe&longs;i EF eguali.

</s>

</s>

<pb/>

</s>

</figure>

COROLLARIO.

</s>

</s>

Quinci oltre à ciò &longs;i mo&longs;trerà facilmente anche la ragione della Sta-<lb/>dera.

</s>

<pb/>

</figure>

Corollario vocabolo Latino co&longs;tumato da tutti gli altri Scrittori Italiani in cotal ma <lb/>teria, nè di&longs;piacque à Dante nel 28. cap.

</s>

Que&longs;ta però trala&longs;ciò egli, co-<lb/>me nota, &longs;i come egli &longs;ole trala&longs;ciare le co&longs;e molto note.

del Purgatorio.

</s>

Imperoche à chi puote <lb/>far dubbio, che &longs;e il pe&longs;o &longs;arà &longs;o&longs;tentato nel centro della grauezza&longs;ua, che non i&longs;tia <lb/>fermo?

</s>

</s>

</s>

<emph type="italics"/>Percioche &longs;ia la bilancia AB egualmente di&longs;tante dall'orizonte, il cui centro E &longs;ia <lb/>&longs;otto la bilancia.

</s>

</s>

</figure>

<margin.target id="note94"></margin.target><emph type="italics"/>Ragione del la stadera.<emph.end type="italics"/>

</s>

In altro modo po&longs;&longs;iamo anco v&longs;are la &longs;tadera, affine che le grauezze <lb/>de ipe&longs;i &longs;i facciano note.

</s>

</figure>

</s>

</figure>

<margin.target id="note95"></margin.target><emph type="italics"/>Per la &longs;esta del primo di Archimede d'lle co&longs;e, che pe&longs;ano egual mente.<emph.end type="italics"/>

</s>

<margin.target id="note96"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 23. <emph type="italics"/>del quinto<emph.end type="italics"/>

</s>

<pb/>

PROPOSITIONE VII.

</s>

PROBLEMA.

</s>

</s>

</s>

Et que&longs;ta è la differenza tra la Propo&longs;itio-<lb/>ne, & il Problema.

</s>

<pb/>

</figure>

<margin.target id="note130"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>del primo.

</s>

di.

</s>

drch.

egli è dunque trouato il P centro della bilancia, dalquale <lb/>rimangono i pe&longs;i dati.

</s>

del le co&longs;e cgual <expan abbr="m&etilde;se">mense</expan> <expan abbr="pes&amacr;ti">pesanti</expan>.<emph.end type="italics"/>

Che bi&longs;ogna operare.<emph.end type="italics"/>

</s>

<margin.target id="note131"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 1. <emph type="italics"/>di questo.<emph.end type="italics"/>

<margin.target id="note97"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 5. <emph type="italics"/>di questo.<emph.end type="italics"/>

</s>

COROLLARIO.

</s>

</s>

</s>

</figure>

<emph type="italics"/>Ma &longs;ia il centro C &longs;otto la bilancia AB, & &longs;ia DCE il perpendicolo.

</s>

</s>

congiunga&longs;i CF. & <lb/>percioche CD è a piombo <lb/>dell' orizonte, non &longs;arà gia <lb/>la linea CF a piombo del <lb/>l'orizonte.

</s>

<emph type="italics"/>Il fine della Bilancia.<emph.end type="italics"/>

</s>

& il punto B &longs;arà come in G, & il punto A in H, & la bilancia GH <lb/>non hauerà piu il centro di &longs;otto, ma &longs;opra e&longs;&longs;a.

DELLA LEVA.

</s>

</figure>

LEMMA.

</s>

Siano quattro grandezze ABCD; & &longs;ia la A <lb/>maggiore della B, & C maggiore della D. Dico, <lb/>che A ver&longs;o D hà proportione maggiore di quello <lb/>che hà B ver&longs;o C.

</s>

& quanto il pe&longs;o posto in B &longs;arà piu leggiero, de&longs;criuerà tut-<lb/>tauia anche circonferenza maggiore.

</s>

Imperoche quanto il pe&longs;o po&longs;to in G &longs;arà piu <lb/>leggiero, tanto piu il pe&longs;o detto posto in G &longs;i alzerà; & la bilancia GA s'acco&longs;te<emph.end type="italics"/>

<margin.target id="note98"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 8. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

PROPOSITIONE I.

</s>

<margin.target id="note132"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

</figure>

</s>

Le quali co&longs;e tutte re&longs;tano ma <lb/>ni&longs;e&longs;te da quelle che di &longs;opra &longs;ono &longs;tate dette.<emph.end type="italics"/>

</s>

</figure>

</figure>

<margin.target id="note133"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Prouate que&longs;te co&longs;e, egli è chia <lb/>ro, che il centro della bilan-<lb/>cia è cagione de gli effetti di <lb/>uer&longs;i della bilancia.

<margin.target id="note100"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

& &longs;i ve <lb/>de ancora che tutte le pro-<lb/>po&longs;itioni di Archimede del <lb/>le co&longs;e, che egualmente pe&longs;a <lb/>no, a ciò pertinenti, in ogni <lb/>&longs;ito &longs;ono vere.

</s>

</s>

</s>

</figure>

<margin.target id="note101"></margin.target><emph type="italics"/>Per la mede &longs;ima &longs;esta.<emph.end type="italics"/>

</s>

<margin.target id="note102"></margin.target><emph type="italics"/>Per lo Lemma.<emph.end type="italics"/>

</s>

<margin.target id="note103"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 10. <emph type="italics"/>del quinto<emph.end type="italics"/>

</s>

<margin.target id="note134"></margin.target><emph type="italics"/>Per la diffi ni ione del centro della grauezza.<emph.end type="italics"/>

COROLLARIO.

</s>

</figure>

</s>

PROPOSITIONE II.

</s>

In altra maniera po&longs;&longs;iamo v&longs;are la Leua.

</s>

</s>

<pb/>

</figure>

<margin.target id="note135"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

<margin.target id="note104"></margin.target><emph type="italics"/>Nella &longs;esta di questo de la bilancia.<emph.end type="italics"/>

</s>

<margin.target id="note105"></margin.target><emph type="italics"/>Dalla<emph.end type="italics"/> 11. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note106"></margin.target><emph type="italics"/>Per la &longs;esta della <expan abbr="bil&amacr;cia">bilancia</expan><emph.end type="italics"/>

</figure>

</s>

<emph type="italics"/>Ma &longs;e il centro della bilancia &longs;arà D, moua&longs;i in qualunque modo la bilancia, doue &longs;i <lb/>la&longs;cierà, iui rimarrà.<emph.end type="italics"/>

<margin.target id="note107"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<emph type="italics"/>Se poi il punto H &longs;arà &longs;otto la linea AB; allhora la bilancia EKF &longs;i mouerà in <lb/>giu dalla parte di F.<emph.end type="italics"/>

<margin.target id="note108"></margin.target><emph type="italics"/>Per la &longs;ettima del<emph.end type="italics"/> 5.

</s>

<margin.target id="note109"></margin.target><emph type="italics"/>Per lo Corol lario della<emph.end type="italics"/> 4 <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

& &longs;e il centro della bilan-<lb/>cia &longs;ia D; rimarrà doue &longs;i la&longs;cierà.

Altramente.

</s>

che <lb/>&longs;e &longs;arà in K; & da cotale &longs;ito &longs;i mo <lb/>uerà, ritornerà ad ogni modo nello i&longs;te&longs; <lb/>&longs;o.

</s>

Le quali co&longs;e tutte da quel che in<emph.end type="italics"/><lb/><arrow.to.target n="fig51"></arrow.to.target><lb/><emph type="italics"/>principio dicemmo &longs;ono mani&longs;este.

</s>

</s>

</s>

</figure>

In que&longs;to luogo egli conuiene auertire, il che potcua&longs;i anco fare di &longs;opra à carte cin <lb/>que pre&longs;&longs;o la fine della &longs;econda faccia oue è &longs;critto.

COROLLARIO I.

</s>

oltre à ciò po&longs;siamo con&longs;ide-<lb/>rare le co&longs;e che &longs;eguono in tutto al modo i&longs;te&longs;&longs;o.

</s>

</s>

<margin.target id="note110"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 8. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

COROLLARIO II.

</s>

Segue etiandio, che la po&longs;&longs;anza in A &longs;empre è minore del pe&longs;o E:

</s>

<emph type="italics"/>Percioche pigli&longs;i tra A & B qual punto &longs;i voglia, come C, &longs;empre BC &longs;arà <lb/>minore di BA.<emph.end type="italics"/>

</s>

COROLLARIO III.

</s>

</s>

</s>

</figure>

<margin.target id="note111"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 22. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

COROLLARIO IIII.

</s>

E manife&longs;to etiandio, che ambedue le po&longs;&longs;anze in A, & in B <lb/>pre&longs;e in&longs;ieme, &longs;ono eguali al pe&longs;o E.

</s>

</s>

PROPOSITIONE III.

</s>

In altro modo ancora po&longs;&longs;iamo v&longs;are la Leua.

</s>

<pb/>

</s>

In trattando <lb/>que&longs;ta materia moue l'autore alcuni dubbi molto belli, & curio&longs;i, & poi chiara-<lb/>ment e gli &longs;olue.

</s>

che bi&longs;ognaua mostrare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note112"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>di questo della bilancia.<emph.end type="italics"/>

</s>

<margin.target id="note113"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>di questo della bilancia.<emph.end type="italics"/>

</s>

<margin.target id="note114"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 9. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<emph type="italics"/>Librar congiu&longs;te lance.<emph.end type="italics"/>

<margin.target id="note115"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

Di&longs;&longs;e il Petrarcha.

Altramente.

</s>

</s>

& percioche AB è eguale à BE, & i pe&longs;i<emph.end type="italics"/>

<emph type="italics"/>FC &longs;ono eguali, &longs;imilmente i pe&longs;i FC pe&longs;eranno egualmente, ma i pe&longs;i FGC ap-<lb/>piccati nella leua EBA, il cui &longs;o&longs;tegno è in B non pe&longs;eranno egualmente; ma in-<lb/>chineranno in giu&longs;o dalla parte di A. Ponga&longs;i dunque in D tanta forza, che i <lb/>pe&longs;i FGC pe&longs;ino egualmente; &longs;arà la po&longs;&longs;anza in D eguale al pe&longs;o G; peroche<emph.end type="italics"/><lb/><arrow.to.target n="fig52"></arrow.to.target><lb/><emph type="italics"/>i pe&longs;i FG pe&longs;ano egualmente, & la po&longs;&longs;anza in D niente altro deue fare, che <lb/>&longs;o&longs;tenere il pe&longs;o G che non di&longs;cenda.

</s>

Line 8069

Line 8462

</back>

</text>

</archimedes>

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