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version 1.6, 2002/06/28 13:03:40

version 1.19, 2002/08/16 13:55:12

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<?xml version="1.0"?>

<!DOCTYPE archimedes [

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >

<info>

<author>Guidobaldo del Monte</author>

<title>Le Mechaniche</title>

<place>Venezia</place>

<locator>monte-it.xml</locator>

</info>

LE <lb/>MECHANICHE <lb/>DELL'ILLVSTRISS SIG.<lb/>GVIDO VBALDO <lb/>DE' MARCHESI DEL <lb/>MONTE: <lb/>TRADOTTE IN VOL GARE <lb/>DAL SIG. FILIPPO PIGAFETTA: <lb/>Nellequali &longs;i contiene la vera Dottrina di rutti gli I&longs;trumenti <lb/>principali da mouer pe&longs;i grandis&longs;imi con <lb/>picciola forza.

</s>

<emph type="italics"/>A beneficio di chi &longs;i diletta di que&longs;ta nobili&longs;&longs;ima scionza; & ma&longs;&longs;imamente <lb/>di Capitani di guerra, Ingegnieri, Architetti, & d'ogni <lb/>Artefice, che intenda per via di Machine <lb/>far opre marauiglio&longs;e, e qua&longs;i <lb/>&longs;opra naturali.<emph.end type="italics"/>

</s>

Et &longs;i dichiarano i vocaboli, & luoghi più difficili.

</s>

</figure>

<emph type="italics"/>In Venetia, Appre&longs;&longs;o France&longs;co di France&longs;chi Sane&longs;e.

</s>

MD LXXXI.<emph.end type="italics"/>

</s>

</section>

</figure>

ALL'ILLVSTRISSIMO <lb/>SIGNOR GIVLIO <lb/>SAVOR GNANO, <lb/>CONTE DI BELGRADO. &c.

</s>

Signore o&longs;&longs;eruandi&longs;&longs;imo.

</s>

</figure>

C<emph type="italics"/>onciosia co&longs;a, che la &longs;cienza delle Mecha-<lb/>niche gioui &longs;ommamente à molte, & importan-<lb/>ti attioni della no&longs;tra vita, à gran ragione fu ella <lb/>da i Filo&longs;ofi, & da i Rè antichi &longs;timata degna di <lb/>laudi &longs;ingularißime; & i Matematici vi han-<lb/>no impiegato lo &longs;tudio, & l'opera più che meza-<lb/>namente, & i Principi fauoriti gl'ingegnieri ec <lb/>cellenti, & arricchiti.

</s>

Ben è per certo di alti&longs;-<lb/>&longs;ima &longs;peculatione, & di &longs;ottile manifattura; imperoche tocca quella par-<lb/>te della Filo&longs;ofia, che tratta de gli elementi in vniuer&longs;ale, & del moto, & <lb/>della quiete de' corpi, &longs;econdo i luoghi &longs;uoi, a&longs;&longs;egnando la cagione in certo <lb/>modo de' loro mouimenti naturali; & anco sforzandoli, per via di machi-<lb/>ne à partir&longs;i da proprij &longs;iti, gli tra&longs;porta all'insù, & per ogni lato in mo-<lb/>uimenti contrari alla natura loro.<emph.end type="italics"/>

</s>

<emph type="italics"/>Mena ella ad effetto ambedue que&longs;te intentioni con le propo&longs;itioni che <lb/>na&longs;cono, & &longs;ono congiunte con la materia &longs;te&longs;&longs;a, & co' difici, & i&longs;trumen <lb/>ti, che forma artificialmente.

</s>

La onde egli è dibi&longs;ogno con&longs;iderare que&longs;ta<emph.end type="italics"/><pb id="p.0004" xlink:href="pagethumb-it/007.jpg" /><emph type="italics"/>dottrina in due manìere; l'vna ìn quanto và &longs;peculando, & con ragione <lb/>di&longs;correndo &longs;opra le co&longs;e, che s'hanno à &longs;are, &longs;eruendo&longs;i dell' Arithmetica, <lb/>della Geometria, dell' A&longs;trologia, & della Filo&longs;ofia naturale: & l'altra che <lb/>po&longs;cia le manda ad e&longs;ecutione, & haue nece&longs;sita dell'e&longs;&longs;ercitio, & lauoro <lb/>delle mani, v&longs;ando l'Architettura, la Pittura, il di&longs;egno, l'arte de' fabri, <lb/>de'legnaiuoli, de'muratori, & d'altri me&longs;tieri tali, per modo che ella vie-<lb/>ne ad e&longs;&longs;ere me&longs;colata, & in parte compo&longs;ta della naturale Filo&longs;ofia, delle <lb/>Matematiche, & delle arti manuali.

</s>

Per laqual co&longs;a chiunque &longs;i troua <lb/>dotato d'ingegno acuto, & da fanciullo hà incominciato ad apprendere le <lb/>già dette &longs;cienze, & &longs;a di&longs;egnare, & lauorare di &longs;ua mano, potrà nel vero <lb/>ottimo Mechanico, & <expan abbr="inu&emacr;tore">inuentore</expan>, & facitore di opere marauiglio&longs;e riu&longs;cire.<emph.end type="italics"/>

</s>

<emph type="italics"/>Infinite parti, & vtilißime à gli huomini comprende que&longs;la noti-<lb/>tia, & in guerra, & in pace, ne i commodi della città, della villa, & della <lb/>mercatantia, & in altri; peroche la Medicina toglie da lei i difici per ri-<lb/>porre le o&longs;&longs;a &longs;mo&longs;&longs;e, & rotte ne i &longs;iti &longs;uoi.

</s>

Onde pone Oriba&longs;io nel libro delle <lb/>Machine, diuer&longs;i i&longs;trumenti pre&longs;i dalla Mechanica, & <expan abbr="cõuertiti">conuertiti</expan> nell'v&longs;o del <lb/>la Medicina, come il Tri&longs;pa&longs;ton di Archimede: l'arte del nauigare ricono-<lb/>&longs;ce anco diuer&longs;i aiuti, come il timone, co'l quale, collocato di dietro, ouero <lb/>alle bande del nauilio ageuolmente lo moue, & dirizza, quantunque per <lb/>ri&longs;petto à tutto il corpo del va&longs;ello piccioli&longs;simo &longs;ia.

</s>

I remi, che à gui&longs;a di <lb/>leua lo &longs;pingono innanzi, & l'arbore, & la vela &longs;ono pur di &longs;ua inuentio <lb/>ne.

</s>

I molini, i quali &longs;i girano co'l vento, con l'acqua, & con la forza vi-<lb/>ua: & i pi&longs;trini, le carra, gli aratri, & altri ordigni di villa; il pe&longs;are con <lb/>la bilancia, & con la &longs;tadera; il cauare l'acqua da pozzi con le grù, ouero <lb/>cicogne, dette da latini to&longs;senoni, che &longs;ono come grandis&longs;ime bilancie, & <lb/>con le rote, & altre co&longs;e tali &longs;i riducono alla Mechanica.

</s>

La ragione pa-<lb/>rimente del condurre le acque, & da profondis&longs;ime valli in alto farle &longs;ur <lb/>gere uà &longs;otto lei.

</s>

Chiamarono gli antichi coloro Mechanici ancora, i quali <lb/>co'l fiato, ò vento, ouero acqua, ò corde, ò nerui faceuano vedere, & vdi <lb/>re effetti miracolo&longs;i; come &longs;uoni diuer&longs;i, & canti d'augelli, & fin ad e&longs;pri-<lb/>mere la voce humana in parole: & quelli che con horologi, i quali &longs;i mo-<lb/>uono da &longs;e &longs;tes&longs;i con rote, ò da acqua, ò da &longs;ole il tempo mi&longs;urarono, & di-<lb/>&longs;tin&longs;ero in hore.

</s>

Appartengono alla Mechanica gli facitori delle Sfere <lb/>compartite ne'&longs;uoi cieli, co'l mouimento de'Pianeti, & di tutti i corpi <lb/>cele&longs;tiali à &longs;embianza dell'vniuer&longs;o mondo, & ciò mediante il mouimen-<lb/>to eguale, & in giro, che loro daua l'acqua, di cui la fama &longs;uona e&longs;&longs;ere <lb/>&longs;tato Archimede Siracu&longs;ano il primo mae&longs;tro.

</s>

il mouere etiandio con poca<emph.end type="italics"/><pb id="p.0005" xlink:href="pagethumb-it/008.jpg" /><emph type="italics"/>forza pe&longs;i grandis&longs;imi con i&longs;trumenti, & ingegni diuer&longs;i è principale of-<lb/>ficio della Mechanica, come Bilancie, Stadere, Leue, Taglie, Cunei, Moli-<lb/>nelli, Rote co' denti & &longs;enza, Viti d'ogni &longs;orte, Argani, Mangani, Triuel <lb/>le, & altri molti, i quali da que&longs;ti &longs;i compongono: & &longs;econdo Ari&longs;totele <lb/>tutti &longs;iriducono alla Leua, & al cerchio, & alla machina ritonda, laquale <lb/>quanto è maggiore, tanto più velocemente &longs;i moue.

</s>

L'arte del fortificare <lb/>le piazze, & i &longs;iti, & del difendergli, laquale acconciamente &longs;i puote chia <lb/>mare Architettur a militare, è pro&longs;es&longs;ione Mechanica: peroche per via di <lb/>Cortine, & di Baloardi, & d'altri ripari, qua&longs;i con machine, & i&longs;trumen-<lb/>ti s'ingegna l'huomo con po hi &longs;oldati di ributtarne in dietro molti, & <lb/>mantener&longs;i con vantaggio.

</s>

Il fabricare, & adoprare oltre à ciò gli i&longs;tru <lb/>menti da guerra è proprio dono di que&longs;ta &longs;cienza, come Bali&longs;te, ò Bale&longs;tre, <lb/>Catapulte, Scorpioni, Fionde, & &longs;imili, che da lontano gittano foco, & &longs;aßi, <lb/>& ma&longs;&longs;e di ferro pe&longs;anti dugento cinquanta, & più libre, & Moli da <lb/>molino &longs;econdo Silio Italico, & Vitruuio, per di&longs;tanza di for&longs;e<emph.end type="italics"/> 300. <emph type="italics"/>pas&longs;i <lb/>à mi&longs;ura con ruin &longs;o colpo; & &longs;aette, & verettoni, & falariche grandi <lb/>à gui&longs;a di traui: & quelli che percoteudno con l'vrto da pre&longs;&longs;o, come Arie <lb/>ti, Onagri, Te&longs;tugini, & &longs;imili; & in altri v&longs;i, come <expan abbr="Sãbuche">Sambuche</expan>, Corui, Mani <lb/>di ferro, & gli altri maritimi, & Angoni, Monangoni, Tollenoni, &longs;cale &longs;no-<lb/>date, ponti, torri mobili, & &longs;imili difici antichi, i quali &longs;ono &longs;tati poi ri <lb/>fiutati, &longs;uccedendo in &longs;uo luogo le Artiglierie, da e&longs;&longs;ere anch'e&longs;&longs;e ordinate <lb/>nell' ampiezza della con&longs;ideratione Mechanica, facendo elle còn sì poca mæ <lb/>teria acce&longs;a, tanto horribile perco&longs;&longs;a.<emph.end type="italics"/>

</s>

<emph type="italics"/>Que&longs;ta &longs;cienza, che fuor di quanto &longs;i è detto, abbraccia innumerab ili <lb/>altri v&longs;i, & diletteuoli, & nece&longs;&longs;ari à mortali, in diuer&longs;i tempi hebbe in <lb/>&longs;orte vari &longs;tati, per ri&longs;petto à gli artefici, che la e&longs;ercitarono: peroche, <lb/>di là cominciando, ne gli antichis&longs;imi &longs;ecoli, che pa&longs;&longs;arono auanti la guer <lb/>ra di Troia vi&longs;&longs;e Dedalo Athenie&longs;e gran mae&longs;tro di Mechanica, ilquale <lb/>trouò il primiero la &longs;ega, l'a&longs;cia, il piombino da torre le diritture, la tri-<lb/>uella, l'albero, l'antenna, la vela, & altri or digni: di&longs;egnò in Creta poi <lb/>quell'intricato labirinto, & alla fine gli conuenne fabricare per &longs;e, & per <lb/>Icaro &longs;uo figlio due paia d'ali, & volar&longs;ene via per l'aere à gui&longs;a d'au-<lb/>gelli, come cantano i Poeti.<emph.end type="italics"/>

</s>

<emph type="italics"/>Nella fabrica del tempio di Salomone, che fu la maggiore per grandez <lb/>za, per mae&longs;tria d' Architettura, & ornamento, di quanie ne &longs;iano &longs;tate <lb/>fatte giamai; & delle piramidi, & di tanti altri difici di quei &longs;eco'i, che <lb/>hanno riempito il mondo di &longs;tupore, egli &longs;i può credere, che interueni&longs;&longs;ero<emph.end type="italics"/><pb id="p.0006" xlink:href="pagethumb-it/009.jpg" /><emph type="italics"/>eccellenti Mechanici, per leuare in alto le pietre &longs;mi&longs;urate, & per altre <lb/>opere, lequali à condurgli à fine &longs;i ricercauano.

</s>

Nacquero dapoi Eudo&longs; <lb/>&longs;o, & Archita Tarentino, ambidue valenti ingegnieri; & di Archita &longs;i <lb/>legge, che lauorò di legno vna colomba con tanta mae&longs;tria temperata, & <lb/>gonfiata, che da &longs;e volaua per l'aria à gui&longs;a di viua colomba.

</s>

Seguì co-<lb/>&longs;toro il Filo&longs;ofo Ari&longs;totele, ilquale certe poche, ma bellis&longs;ime que&longs;tioni Me-<lb/>chaniche, la&longs;ciò &longs;critte.

</s>

A lui venne appre&longs;&longs;o Demetrio Rè, nominato il <lb/>pigliatore, ò di&longs;truggitore delle città, peroche fabricaua machine, & difi-<lb/>ci, co' quali per di&longs;opra vi montaua, & &longs;e ne faceua padrone, lequali per <lb/>auentura furono &longs;imiglianti alla machina detta Cauallo, con cui li Greci <lb/>pre&longs;ero la famo&longs;a Troia; di che ragionando Pau&longs;ania nell' Attica, dice che <lb/>giudica e&longs;pre&longs;&longs;a mattezza il credere, che fo&longs;&longs;e vn cauallo, & non machina <lb/>bellico&longs;a per acco&longs;tare alle muraglie, & prenderle.

</s>

Que&longs;to Rè cominciò <lb/>ad aumentare la Mechanica in qualche honore.

</s>

Ma Archimede, che fù <lb/>il megliore artefice di quanti fecero giamai que&longs;ta profes&longs;ione innanzi, & <lb/>dopo lui, & qua&longs;i vn lume, che poi ha illu&longs;trato tutto il mondo, accrebbe <lb/>in colmo la riputatione della Mechanica, & di pouera arte, & vile, che pri <lb/>ma era, come vuole Plutarco nella vita di Marcello, nel numero delle arti <lb/>nobili, & pregiate alla militia pertinenti la ripo&longs;e.

</s>

Imperoche combat-<lb/>tendo Marcello Sir acu&longs;a patria &longs;ua per mare, & per terra con grande <lb/>ho&longs;te di Romani, egli co'&longs;uoi diuer&longs;i ingegni, & machine differenti, ribut-<lb/>tò &longs;empre gli sforzi, con graue lor danno, & vergogna; come Liuio, Plutar <lb/>co, & altri nominando i difici che v&longs;aua, diffu&longs;amente raccontano.

</s>

Per-<lb/>cioche quando Marcello s'auicinaua aile muraglie per conqui&longs;tar le con la <lb/>Sambuca, il buon Archimede co'l Tollenone, & con le mani di ferro la al-<lb/>zaua di pe&longs;o in aere, & poi &longs;nodando quegli vncini &longs;uoi, la faceua cadere <lb/>da alto, in mare &longs;ommergendola; il mede&longs;imo effetto adoprando eontra gli <lb/>altri nauili, sì fattamente, che gli conuenne allontanare l'armata ben to <lb/>&longs;to dalle mura.

</s>

Ne ce&longs;sò tuttauia d'infe&longs;tare il nemico: ma &longs;i come nota <lb/>Galeno nel terzo libro de' temper amenti, & Giouanni Zonara, & Tze&longs;es <lb/>confermano, allegando Diodoro, & Dione, compo&longs;e certi &longs;pecchi grandi <lb/>& concaui, &longs;econdo la proportione della di&longs;t anza di quei va&longs;elli dalla mu-<lb/>raglia, & opponendogli à raggi del Sole in diritta linea qua&longs;i per miraco-<lb/>lo, gli bru&longs;ciaua.

</s>

Dalla parte della terra &longs;imilmente offendeua gli aduer-<lb/>&longs;ari con arme diuer&longs;e da gittare.

</s>

Per laqual co&longs;a nè in mare, nè in terra <lb/>da gl'ingegni di quell'eccellente Mechanico &longs;i poteua egli &longs;chermire, nuoui <lb/>ripari, & horribili offe&longs;e apparecchiando &longs;empre.

</s>

Pappo Ale&longs;&longs;andrino<emph.end type="italics"/><pb id="p.0007" xlink:href="pagethumb-it/010.jpg" /><emph type="italics"/>allega il quar ante&longs;imo trouato di Archimede, per dichiarare, che almeno <lb/>i &longs;uoi difici al numero di quaranta a&longs;cendeuano.

</s>

La onde Marcello, veg-<lb/>gendo, che niuno profitto apportauano all'impre&longs;a gli a&longs;&longs;alti &longs;uoi, & che <lb/>erano vn mettere le genti ad euidente pericolo, per cagione di quel &longs;olo <lb/>valoro&longs;o vecchio, gli nacque vna tal opinione, & à tutto l'e&longs;ercito, che da <lb/>po&longs;&longs;anza diuina fo&longs;&longs;e gouernato in quella dife&longs;a, & mutò la ragione del <lb/>guerreggiare, dando&longs;i all'aßedio, & al vietare &longs;tret tißimamente le vitto-<lb/>uaglie a quella città.<emph.end type="italics"/>

</s>

<emph type="italics"/>Que&longs;te furono le cagioni, che la Mechanica &longs;alì in tanta gloria, & che <lb/>i Romani le a&longs;&longs;egnarono dapoi grado honoreuolißimo ne gli e&longs;erciti lo-<lb/>ro, come &longs;i legge nel primo libro della guerra ciuile, che Ce&longs;are &longs;e prigione <lb/>il Capitano de' fabri di Pompeio, nomato Magio Cremona, & Vitruuio fu <lb/>Capitano delle Bali&longs;te di Ce&longs;are Augu&longs;to, che &longs;arebbe nella militia moder-<lb/>na, come Capitano generale dell' artiglieria.

</s>

La qual gloria &longs;ucceßiua-<lb/>mente le fu mantenuta poi da molti dottißimi &longs;crittori, & mae&longs;tri di <lb/>Mechani a, come da Cte&longs;ibio Ale&longs;&longs;andrino, da Herone Ale&longs;&longs;andrino, da <lb/>un'altro Herone, da Ateneo, da Bione, da Pappo Ale&longs;&longs;andrino, che allega <lb/>Carpo di Antiochia, da Eliodoro, da Oriba&longs;io, & da altri Greci, i quali fio <lb/>rirono in diuer&longs;i tempi, in&longs;egnando la ragione, la mi&longs;ura, & l'v&longs;o de gli <lb/>i&longs;trumenti bellico&longs;i non &longs;olo, ma di tutti gli altri, che le pertengono.

</s>

Fra <lb/>Latini antichi Varrone &longs;cri&longs;&longs;e dell' Architettura, & per con&longs;eguente douet <lb/>te anco far mentione della Mechanica: & Vitruuio, & Vegetio, & qual-<lb/>che altro hanno fauellato d'intorno alla fabrica delle machine militari, <lb/>& da mouer pe&longs;i, & aiutato à con&longs;eruare fra gli huomini viua la digni-<lb/>tà della Mechanica.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ma ruinando l'Imperio di Romani, & &longs;uccedendo i barbari in Italia, <lb/>in Grecia, in Egitto, & in ogni contrada, oue &longs;i e&longs;er cita&longs;&longs;ero le buone lette <lb/>re, caddero mi&longs;erabilmente, & &longs;i perderono qua&longs;i del tutto le &longs;cienze, & in <lb/>&longs;pecialità re&longs;tò la Mechanica lunghißimo tempo negletta, non cono&longs;cen-<lb/>do&longs;i in guerra altri difici, che Bricole, Trabucchi, Mangani, Martinelli, & <lb/>certi i&longs;trumenti tali, finche &longs;ouragiun&longs;e l'artiglieria, laquale à poco à po-<lb/>co gli fe di&longs;u&longs;are à fatto: & di quella parte altre&longs;i della Mechanica, laqua <lb/>le s'adopra al mouer pe&longs;i, ben picciolo intendimento rima&longs;e.

</s>

Vera co&longs;a è, <lb/>che &longs;embra da vn tempo in quà le arti, & le dottrine più nobili, come le <lb/>belle lettere appellate humane, la Filo&longs;ofia, la Medicina, l'A&longs;trologia, l'A-<lb/>rithmetica con la Mu&longs;ica, la Geometria, l'Architettura, la Scoltura, la Pit <lb/>tura con molte altre: & &longs;pecialmente la Mechanica e&longs;&longs;ere dalle o&longs;cure te-<emph.end type="italics"/><pb id="p.0008" xlink:href="pagethumb-it/011.jpg" /><emph type="italics"/>nebre, oue giaceuano &longs;epolte, alla thiara luce ri&longs;u&longs;citate: Percioche ri-<lb/>&longs;tringendomi alle Mechaniche Giordano, che &longs;cri&longs;&longs;e de' pe&longs;i, la incominciò <lb/>à &longs;olleuare alquanto, & poi Leon Batti&longs;ta Alberti nella &longs;ua Architettu-<lb/>ra: il Tartaglia aper&longs;e anco la via à molte &longs;peculationi Mechaniche: Vitto<lb/>rio Fau&longs;to nell' Arzanà di Venetia mo&longs;trò d'e&longs;&longs;ere buon Mechanico: Mon-<lb/>&longs;ig. Reuerendi&longs;s. barbaro eletto d' Aquileia ne' Commentari del decimo di <lb/>Vitruuio nominò gli i&longs;trumenti da mouer pe&longs;i: Georgio Agricola nel &longs;e&longs;to <lb/>de' Metalli raccol&longs;e a&longs;&longs;ai machine da leuar pe&longs;i, & qualched'vn'altro: & <lb/>nuoua <expan abbr="m&etilde;te">mente</expan> l'Autoredi que&longs;t'opera, ilquale ben d'altra maniera in ciò pro <lb/>ce lette, che gli autori nominati, peroche con ordine ammir abile, & con <lb/>vere, & certe ragioni ha in&longs;egnato &longs;olo fra Latini ottimamente que&longs;tæ <lb/>&longs;cienza tutta da mouer pe&longs;i.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ma &longs;i come i moderni da me ricordati, & principalmente l'Autore del <lb/>pre&longs;ente libro hanno ornata & e&longs;altata la Mechanica con le parole, & co i <lb/>volumi; co&longs;i V. S. Illu&longs;triß.

</s>

l'hà celebrata, & magnificata co' di&longs;cor&longs;i, & <lb/>con le operationi i&longs;te&longs;&longs;e, & co' fattire&longs;a famigliare, & dome&longs;tica, diuer&longs;e <lb/>machine fabricando con profondißima dottrina, & facendone e&longs;perten-<lb/>ze nel mouere qualunque gran pe&longs;o, di cui &longs;i po&longs;&longs;a l'huomo in ogni bi&longs;ogno <lb/>&longs;eruire.

</s>

Talche ben &longs;i puote con verità affermare, che per vna parte e&longs;&longs;a, <lb/>& l'Autore di que&longs;ti trattati per l'altra, habbiate alla Mechanica il pri&longs;ti <lb/>no honore re&longs;tituito, che da i tempi antichi in quà le cra &longs;marrito.<emph.end type="italics"/>

</s>

<emph type="italics"/>Sono for&longs;e quaranta anni gia &longs;cor&longs;i, che per i&longs;cherzare con Nicolò Tar<lb/>taglia, per&longs;ona à &longs;uoi tempi molto &longs;timata in que&longs;ta profeßone, & che &longs;i <lb/>dilettaua di andare &longs;oluendo que&longs;tioni &longs;ottili di Mechanica, & di Mathe <lb/>matica, & ne' &longs;uoi dialoghi introduceua à fauellare per&longs;onaggi grandi: <lb/>& alcuna fiata gli faceua dire qualche co&longs;a, di cui eßi prendeuano onta, <lb/>V. S. Illu&longs;triß.

</s>

gliene propo&longs;e for&longs;e quaranta Mechaniche qua&longs;i tutte, & <lb/>difficili: alcune delle quali egli prouò di &longs;oluere, delle altre &longs;i &longs;cusò con di <lb/>re, che à cia&longs;cheduna di loro &longs;arebbe &longs;tato me&longs;tieri vn volume intero, co-<lb/>me &longs;i legge ne' &longs;uoi lib i &longs;tampati della noua &longs;cientia.<emph.end type="italics"/>

</s>

<emph type="italics"/>Hor non è punto di marauiglia, che ella habbia penetrato con l'inten-<lb/>dimento <expan abbr="tãto">tanto</expan> dentro, & &longs;aputo co&longs;i bene operare nelle Mechaniche, & &longs;ia <lb/>fatta padrona in tutto dell'arte del fortificare i &longs;iti, & d'ogni altra parte <lb/>della militia: peroche fu dall'ottimo &longs;uo padre alleuata in compagnia di <lb/>huomini &longs;cientiati, & d'alio affare, tra quali fu vn tempo Con&longs;tantino <lb/>La&longs;cari nobilißimo huomo Greco, & piono di dottrina, da cui &longs;ucceßi-<lb/>uamente imparò, oltra le altre lettere, Arithmetica, Geometria, A&longs;tro-<emph.end type="italics"/><pb id="p.0009" xlink:href="pagethumb-it/012.jpg" /><emph type="italics"/>logia, Geogra&longs;ia; à ài&longs;egnare, & lauorare manualmente in me&longs;tieri diuer-<lb/>&longs;i; à caualcare, à maneggiare le arme, à tirare d'archibugio, & d'artiglie <lb/>ria, & à <expan abbr="cõporre">comporre</expan> fochi artificiati, & l'arte per eccellenza detta del bom <lb/>bardiero; à viuere &longs;obriamente, & le fatiche rolerare al caldo, al freddo, <lb/>& ad ogni di&longs;agio, co&longs;e tutte, che di&longs;pongono l'animo, & indurano il corpo <lb/>alla militia.

</s>

Giunta poi all' età di &longs;edici anni, fu inutata con dodici caual <lb/>li qua&longs;i tutti Turchi, & con prouedimento conueneuole di denari à vede-<lb/>re tutta quella guerra, che pa&longs;sò in Italia dalla pre&longs;ura del Rè France&longs;co <lb/>Primo di Francia, fin alla pace generale, che &longs;eguì l'anno<emph.end type="italics"/> 1529. <emph type="italics"/>Nella-<lb/>quale interuennero qua&longs;i tutti i mouimenti militari, che &longs;i po&longs;&longs;ano ima-<lb/>ginare, sì per gli e&longs;erciti grandi, che erano à fronte l'vn contra l'altro, sì <lb/>per la qualità, & quantità delle impre&longs;e fatte, & per mille altri acciden <lb/>ti importantißimi, & &longs;tratagemi auenuti, & sì principalmente; percio-<lb/>che nell'vn campo, & l'altro in varie &longs;tagioni militarono i primi guer-<lb/>rieri del mondo, & in gran numero, i quali con prudenza, a&longs;tutia, & <lb/>brauura contendeuano à gara, & per honore di &longs;oura&longs;tare, & e&longs;&longs;ere vinci <lb/>tori.

</s>

Et veramente chi ben con&longs;idera, fin da i tempi antichi, rarißime vol <lb/>te è &longs;tato con numero maggiore di Capitani famo&longs;i, ò con più copia d'im-<lb/>pre&longs;e grandi guerreggiato, che in quegli anni: Peroche furono fatti prigio-<lb/>ni due de' maggiori Prencipi del mondo, &longs;i a&longs;&longs;ediò Milano, & per forza fu-<lb/>rono pre&longs;e tre città, Roma, Cremona, & Pauia; &longs;i videro più fatti d'ar-<lb/>me, & gli e&longs;erciti &longs;i andarono per&longs;eguitando da Milano à Roma; &longs;i che Pia <lb/>cenza, Parma, Bologna, & Fiorenza guardaròn&longs;i dalle armi nemiche.<emph.end type="italics"/>

</s>

<emph type="italics"/>Nello &longs;plendore dunque della &longs;cola del Duca France&longs;co Maria d'V rbino, <lb/>ilquale era Capitano generale della Lega, & di quegli altri valentißimi<lb/>Capitani, andaua V. S. Illu&longs;triß.

</s>

come di &longs;ua libertà, & benißimo à ca-<lb/>uallo, con chi le piaceua, & &longs;i trouaua à quelle fattioni, che volea, &longs;eguen <lb/>do le più volte il Sig.

</s>

Giouanni de' Medici, & Paulo Luzza&longs;co, che erano <lb/>&longs;empre de&longs;ti, & arditi, & come l'occhio dell'e&longs;ercito.

</s>

Quì non è mia in-<lb/>tentione di narrare gli auenimenti di quella guerra, ma &longs;i bene di auerti <lb/>re, che chi la vide, & appre&longs;e da buon &longs;enno i &longs;uoi moti; & &longs;eppe manda-<lb/>re à memoria quei &longs;atti marauiglio&longs;i, ben puote meritamente vantar&longs;i <lb/>di hauer mirato ca&longs;i memorabili, i quali nè anche in migliaia d'anni &longs;o-<lb/>gliono accadere; come ella, che e&longs;&longs;endo giouine di viuace &longs;pirito, & am-<lb/>mae&longs;trata nclle arti nece&longs;&longs;arie al&longs;oldato, & volentern&longs;ißima d'imparare, <lb/>hebbe opportuna occa&longs;ione di far&longs;i prattica dell'ordinare, dell'e&longs;ercitare, <lb/>del far marciare in battaglia, dell'alloggiare in campagna gli e&longs;erciti &longs;i-<emph.end type="italics"/><pb id="p.0010" xlink:href="pagethumb-it/013.jpg"/><emph type="italics"/>curamente: & del pre&longs;entare al nemico il fatto d'arme con vantaggio: <lb/>Del fortificare, & difendere i &longs;iti, & offenderli con le mine, con le trin-<lb/>cee, con le artiglierie, con gli a&longs;&longs;alts, & con tutti gli altri sforzi; & d'o-<lb/>gni parte della militare &longs;cienza.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ritornati in pace i Prencipi Chri&longs;tiani, &longs;i dedicò al &longs;eruigio de' Sereniß. <lb/>&longs;uoi Signori, oue ne i più importanti carichi, & maggiori, & in due guer <lb/>re haue e&longs;&longs;a aggiunto cinquanta anni di noua, & ottima &longs;eruitù all'an-<lb/>tica di qua&longs;i dugento anni, continua, & fedeli&longs;s.

</s>

fattagli da i &longs;uoi pre-<lb/>dece&longs;&longs;ori Sauorgnani, fabricando nello &longs;patio di que&longs;to tempo in diuer&longs;e pro<lb/>uincie de' &longs;uoi &longs;tati pre&longs;&longs;o che cinquanta Baloardi, con eccellentißima ra-<lb/>gione inte&longs;i, & con vero magi&longs;terio lauorati, & notabilißimo ri&longs;parmio <lb/>del publico danaro.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ma per tornare alle Mechaniche dico, che quando gli anni pa&longs;&longs;ati io <lb/>venni à vi&longs;it arla ad O&longs;opo &longs;ua fortezza, &longs;entì &longs;ommo piacere in &longs;corgere <lb/>quel monte, che circonda più d'un miglio, &longs;ituato alla foce del fiume Ta-<lb/>gliamento, oue dalle &longs;trettezze di quei gioghi s'allarga nelle pianure del <lb/>Friuli, d'ogn'intorno alto pre&longs;&longs;o che &longs;e&longs;&longs;anta paßi à mi&longs;ura, tutto di ma-<lb/>cigno duro, & di&longs;co&longs;ce&longs;e, & erto sì, che rende la &longs;alita impoßibile fornito <lb/>attorno di baloardi cauati nel &longs;a&longs;&longs;o, & di molti tagli, & canoniere per <lb/>ferire gli aduer&longs;ari, & di artiglierie, & d'arme d'ogni &longs;orte à &longs;u&longs;&longs;icienza, <lb/>da cui &longs;i hà vi&longs;ta di qua&longs;i tutto il Friuli, & è &longs;cudo, & riparo, come al-<lb/>tra volta fù, contra l'empito delle genti nemiche, lequali in Italia tenta&longs; <lb/>&longs;ero di &longs;oendere da quella parte; po&longs;to di co&longs;ta alla &longs;trada principale, che <lb/>conduce in Lamagna, per laqual vanno, & vengono Signori, & Principi, <lb/>& Amba&longs;ciadori, & infinite mercatantie; onde ella, che tiene &longs;empre le <lb/>guardie, & vedette sù quel monte, quando pa&longs;&longs;ano Signori principali, <lb/>hà per co&longs;tume di &longs;alutargli con le &longs;ue artiglterie, & conuitarg'i anco <lb/>nel &longs;uo alloggiamento d'O&longs;opo, oue tutto l'anno &longs;oggiorna, quantunque <lb/>habbia & Belgrado, & Aris, & Ca&longs;telnouo, & Sauorgnano, & villaggi <lb/>a&longs;&longs;ai: percioche l'aere vi è purißimo, & &longs;pende il &longs;uo tempo in ocio con ne <lb/>gocio, di continuo vi&longs;itata da Gentil'huomini, & Signori diuer&longs;i; ta che la <lb/>&longs;ua ca&longs;a viene ad e&longs;&longs;ere vn ridotto di per&longs;one virtuo&longs;e, & vn'albergo di &longs;ol <lb/>dati, & di dottori.

</s>

lui &longs;i caualca, tenendo ella vna &longs;talla piena di buoni&longs;-<lb/>&longs;imi caualli, &longs;i armeggia, &longs;i và alla caccia, & in ogni attione &longs;i e&longs;ercita vi-<lb/>ta cauallere&longs;ca.

</s>

Oltre à quanto hò diui&longs;ato, pre&longs;i anco diletto in vedere la <lb/>&longs;ua habitatione e&longs;&longs;ere à gui&longs;a d'vna bottega d'arme politamente à &longs;uoi <lb/>luoghi &longs;erbate: & vn magazino di machine bellico&longs;e, & da mouer pe&longs;i,<emph.end type="italics"/><pb id="p.0011" xlink:href="pagethumb-it/014.jpg"/><emph type="italics"/>hauendone ella fabricate di &longs;ua indu&longs;tria for&longs;e dodici di maniere differen <lb/>ti, parte da &longs;tra &longs;cinare, & parte da alzare con pochißima forza &longs;mi&longs;u-<lb/>rati pe&longs;i: come quella, che hà vna &longs;ola rota co' denti, & ali'erta tira cin-<lb/>que de' &longs;uoi canoni con la po&longs;&longs;anza di Grada&longs;&longs;o &longs;uo Nano: & quell'altra, la <lb/>quale con vna oncia di forza &longs;ola, po&longs;ta nel manico, che la volge, dà il me <lb/>to à quattordici mila libre di pe&longs;o: che &longs;e al detto manico &longs;i attribui&longs;ce <lb/>la forza, che comunalmente haue l'huomo con la mano, cioè libre cinquan <lb/>ta, egli è manife&longs;to la predetta machina hauere po&longs;&longs;anza di mouere, co&longs;a <lb/>incredibile, molto più di otto millioni di libre.

</s>

Que&longs;te machine portabi-<lb/>li da vn mulo, & alcune anche da vn'huomo &longs;ono à diuer&longs;i affari nece&longs;&longs;a-<lb/>rijßime, & maßimamente à maneggiare, & condurrei pezzi großi del-<lb/>l'artiglieria.

</s>

& per certo &longs;e l'anno<emph.end type="italics"/> 1529. <emph type="italics"/>il Conte di San Polo Capitano <lb/>France&longs;e nel ritirar&longs;i dall'a&longs;&longs;edio di Milano inuer&longs;o Piemonte con l'e&longs;er-<lb/>cito, & con l'artiglieria, haue&longs;&longs;e portato &longs;eco vno de' minimi i&longs;trumenti <lb/>d'O&longs;opo, non &longs;arcbbe &longs;cor&longs;o in quello &longs;tremo infortunio, percioche in mar <lb/>ciando fu da vn graue canone rotto il ponte, che trauer&longs;aua il &longs;o&longs;&longs;o della <lb/>&longs;trada, & il pezzo cadè nel fango.

</s>

Onde formoßi il campo per non la-<lb/>&longs;ciarlo à dietro, & non hauendo ingegno da cauarlo fuori, &longs;i con&longs;umò tan-<lb/>to tempo, che &longs;opragiun&longs;e Antonio da Leua con le &longs;ue genti, & ritrouan <lb/>do l'e&longs;&longs;ercito nemico &longs;eparato, & in quel di&longs;ordine, lo mi&longs;e in rotta, & fè <lb/>preda delle bagaglie, delle artiglierie, & del Capitano mede&longs;mo.

</s>

Non hà <lb/>troppo iempo, che il Duca France&longs;co di Gui&longs;a, allhor che di Francia guidò <lb/>l'e&longs;ercito in Abruzzo, douendo partire, volle &longs;piegare prima la fanteria, <lb/>& cauælleria &longs;ua in ordinanza à fronte del nemico, qua&longs;i à battaglia sfi-<lb/>dandolo; ma poi nel ritorno &longs;caualco&longs;si vn pezzo d'artiglieria, & s'arre-<lb/>&longs;tò tutta la ma&longs;&longs;a delle genti, & quei Prencipi France&longs;i &longs;montati da ca-<lb/>uallo, penarono buona pezza auanti, che lo ripone&longs;&longs;ero &longs;u le rote, con ri&longs;chio <lb/>di patir danno da gli aduer&longs;ari, che haue&longs;&longs;ero con quella occa&longs;ione &longs;pinto <lb/>innanzi.

</s>

Di quc&longs;ti e&longs;empi non mancano per l'hi&longs;torie.<emph.end type="italics"/>

</s>

<emph type="italics"/>Hora che è pace V. S. Illu&longs;triß. è andata inue&longs;tigando per &longs;uo diporto <lb/>molte, & varie &longs;orti di ordigni da mouer pe&longs;i, affine di valer&longs;ene nelle <lb/>fabriche, & nell'argine di pietre, che fa per ritenere l'impeto del Taglia-<lb/>mento, che non gua&longs;ti i colti di O&longs;opo, & per douer&longs;ene anco &longs;eruire, quan<lb/>do che &longs;ia in guerra.

</s>

Si come fece Archimede, ilquale, &longs;econdo Plutarco, &longs;tan<lb/>do in pace à petitione di Hierone Rè, compo&longs;e quelle <expan abbr="tãie">tanie</expan> Machine per giuo-<lb/>co, & i&longs;cherzo di Geometria, lequali poi &longs;oprauenendo la guerra, le &longs;eppe <expan abbr="cõ">com</expan> <lb/>uertire opportunamente contra Romani.

</s>

Et &longs;e egli, come te&longs;tificano diuer&longs;i<emph.end type="italics"/><pb id="p.0012" xlink:href="pagethumb-it/015.jpg"/><emph type="italics"/>autori, &longs;edendo con certa machina detta, &longs;econdo Oriba&longs;io, Tri&longs;pa&longs;ton, per <lb/>che &longs;i maneggiaua con tre cor de, tirò dal mare in terra quella gran naue <lb/>del Rè &longs;uo; & con la forza della mano &longs;ini&longs;tra mo&longs;&longs;e mediante l'i&longs;tru-<lb/>mento vn pe&longs;o di cinque mila &longs;taia ò moggia, sì fattamente che diputan-<lb/>do à cia&longs;cuno &longs;taio quarantacinque libre di pe&longs;o, a&longs;cenderebbono alla &longs;om-<lb/>ma di dugento venticinque mila libre; & pre&longs;umeua&longs;i di hauer potuto <lb/>mouere la terra, trouando doue fermar&longs;i con la leua, ò con quella &longs;ua ma-<lb/>china de&longs;critta da Pappo nell'ottauo libro delle raccolte matematiche, la <lb/>quale hauea cinque rote co' &longs;uoi as&longs;i, & vna vite perpetua co'l manico: Io <lb/>mi rendo certo, che ella s'ingegnerebbe di &longs;ormare i&longs;trumenti per adoprare <lb/>altretanto.<emph.end type="italics"/>

</s>

<emph type="italics"/>Hauendo io dunque veduti, & i&longs;perimentati que&longs;ti vari difici ad O&longs;o-<lb/>po; & es&longs;endomi &longs;tato da lei mo&longs;trato la prima volta il pre&longs;ente libro, & <lb/>commendato &longs;ommamente, mi propo&longs;i nell' animo, che vtile &longs;arebbe il ri <lb/>durlo in volgare, accioche coloro i quali &longs;ono atti per altro ad intenderlo, <lb/>ma non hanno cono&longs;cenza del Latino, pote&longs;sero, farne &longs;uo profitto.

</s>

Co&longs;i <lb/>compiuta l'opera, & fattala &longs;tampare, la mando à V. S. Illu&longs;tri&longs;s.

</s>

che po&longs; <lb/>&longs;ede e&longs;qui&longs;it amente que&longs;ta materia, & &longs;econda i &longs;tudi delle buone lette-<lb/>re, i quali, &longs;e dopo Iddio, non vengono fauoriti da i gran Signori, nulla va <lb/>gliono.

</s>

Che &longs;e in qualche parte haurò à gli amatori delle Mechaniche re-<lb/>cata ageuolezza, & vtilità con le mie fatiche, douranno eglino &longs;aper' à <lb/>lei buon grado, che di que&longs;ta fattura è &longs;tata cagione. <lb/>Di Venetia à<emph.end type="italics"/> 28. <emph type="italics"/>di Giugno<emph.end type="italics"/> 1581.

</s>

<emph type="italics"/>Di V. S. Illu&longs;tri&longs;s.<emph.end type="italics"/>

</s>

<emph type="italics"/>Affettionatiß.

</s>

&longs;cruidore <lb/>Filippo Pigafetta.<emph.end type="italics"/>

</s>

</section>

AI LETTORI

</s>

Il prefente libro contiene &longs;ei trattati, il primo de <lb/>quali è della Bilancia con la Stadera, l'altro della <lb/>Leua, il terzo della Taglia, il quarto dell' A&longs;&longs;e nel-<lb/>la rota, il quinto del Cuneo, & l'vltimo della Vite, <lb/>che tutti &longs;ono i&longs;trumenti Mechanici.

</s>

Intitula&longs;i le <lb/>Mechaniche.

</s>

Ma percioche que&longs;ta parola Mechaniche non ver <lb/>rà for &longs;e int e&longs;a da cia&longs;cheduno perlo &longs;uo vero &longs;ignificato, anzi <lb/>troueran&longs;i di quelli, che &longs;timeranno lei e&longs;&longs;ere voce d'ingiuria, <lb/>&longs;olendo&longs;i in molte parti d'Italia dire ad altrui Mechanico per <lb/>i&longs;cherno, & villania; & alcuni per e&longs;&longs;ere chiamati Ingegnieri &longs;i <lb/>prendono &longs;degno: non &longs;arà per auentura fuori di propo&longs;ito il <lb/>ricordare, che Mechanico è vocabolo honorati&longs;&longs;imo, dimo&longs;tran <lb/>te, &longs;econdo Plutarco, me&longs;tiero alla Militia pertinente, & conue <lb/>neuole ad huomo di alto affare, & che &longs;appia con le &longs;ue mani, <lb/>& co'l &longs;enno mandare ad e&longs;ecutione opre marauiglio&longs;e à &longs;ingu <lb/>lare vtilità, & diletto del viuere humano.

</s>

Fù, per nomiuarne alcuno tra molti Filo&longs;ofi, & Prencipi de' <lb/>preteriti &longs;ecoli, Archita Tarentino, & Eudo&longs;&longs;o <expan abbr="cõpagni">compagni</expan> di Pla-<lb/>tone, & valenti&longs;&longs;imi Ingegnieri, & Mechanici, che &longs;ono vna me <lb/>de&longs;ma co&longs;a, di cui fa Plutarco mentione nella vita di Marcello: <lb/>& Demetrio Rè, inuentore &longs;ottili&longs;&longs;imo di Machine bellico&longs;e, <lb/>& ne lauoraua di &longs;ua mano ancora: & fra Greci di Sicilia Me-<lb/>chanico, & Ingegniere famo&longs;is&longs;imo Archimede Siracu&longs;ano, il <lb/>quale era di <expan abbr="grã">gram</expan> legnaggio, & parente di Hierone Rè di Sicilia.

</s>

Et quantunque Plutarco nell'i&longs;te&longs;&longs;a vita affermi, che egli di <lb/>&longs;pregia&longs;&longs;e le Mechaniche, come bas&longs;i & vili, & materiali, nè di <lb/>loro degna&longs;&longs;e &longs;criuere giamai, & che non per opera principale, <lb/>ma per vn cotale &longs;ollazzo, & giuoco di Geometria impiegaua <lb/>la fatica nelle Mechaniche, pregato da quel Rè; sì leggiamo <lb/>noi tuttauia in altri autori, lui hauere dettato vn libro della mi <lb/>&longs;ura, & proportione d'ogni maniera di va&longs;ello, diui&longs;ando la for <lb/>ma della gran naue fabricata da Hierone, à cui nulla manca-<lb/>ua: & Pappo Ale&longs;&longs;andrino allega il libro della Bilancia di Ar-<lb/>chimede, che è pur Mechanico tutto: & l'i&longs;te&longs;&longs;o nell'ottauo del <lb/>le raccolte Matematiche pone vn'i&longs;trumento da mouer pe&longs;i, <pb id="p.0014" xlink:href="pagethumb-it/017.jpg"/>

mo&longs;trando e&longs;&longs;ere il quarante&longs;imo trouato d' Archimede, per cui <lb/>di&longs;&longs;e; Dami oue io mi fermi, ch'io mouerò la terra; & Carpo <lb/>Mechanico &longs;c ri&longs;&longs;e, che Archimede compo&longs;e vn libro del modo <lb/>del fare le Sfere, che è fattura Mechanica.

</s>

Ma più il mede&longs;imo <lb/>Archimede, non vna &longs;ola volta cita &longs;e &longs;te&longs;&longs;o, nel libro della Qua <lb/>dratura della Parabola, con parole tali.

</s>

Imperoche egli è dimo-<lb/>&longs;trato nelle Mechaniche; accennando alcune propo&longs;itioni del <lb/>&longs;uo libro delle co&longs;e, che egualmente pe&longs;ano, ilquale è tutto Me-<lb/>chanico.

</s>

Oltre à ciò vna parte del libro della Quadratura della <lb/>Parabola, & il &longs;econdo delle co&longs;e, che &longs;tanno &longs;opra l'acqua, oue-<lb/>ro à galla &longs;ono Mechanici.

</s>

Da que&longs;ti luoghi vede&longs;i e&longs;pre&longs;&longs;o, che <lb/>non &longs;olamente Archimede fece opre Mechaniche, ma ne &longs;cri&longs;&longs;e <lb/>anco molti trattati; & confe&longs;&longs;a Plutarco per niuna altra dottri-<lb/>na e&longs;&longs;ere tanto in riputatione &longs;alito Archimede, quanto per le <lb/>impre&longs;e Mechaniche; anzi veramente co'l mezo loro hauer&longs;i egli <lb/>all'hora procacciato fama non di &longs;cienza humana, ma di &longs;apien-<lb/>za diuina.

</s>

Per la qual co&longs;a egli è ben da con&longs;iderare, come Plu-<lb/>tarco &longs;i &longs;ia la&longs;ciato tra&longs;correr' à dire, che Archimede le Mechani <lb/>che di&longs;preggia&longs;&longs;e, nè di loro degna&longs;&longs;e &longs;criuere: & per certo egli <lb/>forte d'opinione &longs;arebbe&longs;i <expan abbr="ingãnato">ingannato</expan>, &longs;e haue&longs;&longs;e poco &longs;timata quel <lb/>la facultà, che lo fè guadagnare gloria di gran lunga maggio-<lb/>re, che qualunque altra &longs;cienza &longs;i po&longs;&longs;ede&longs;&longs;e.

</s>

Vitruuio de i <lb/>Latini fù buon Mechanico, & &longs;eruì per Capitano delle Bali&longs;te, <lb/>& delle altre machine da guerra Ottauiano Ce&longs;are, & gli intitu-<lb/>lò le &longs;ue fatiche dell' Architettura, & ne diuenne ricco.

</s>

L'e&longs;&longs;ere Mechanico dunque, & Ingegniero con l'e&longs;empio di <lb/>tanti valent'huomini, è officio da per&longs;ona degna, & &longs;ignorile: <lb/>& Mechanica è voce Greca &longs;ignificante co&longs;a fatta con artificio <lb/>da mouere, come per miracolo, & fuori dell'humana po&longs;&longs;anza <lb/>grandis&longs;imi pe&longs;i con picciola forza, & in generale comprende <lb/>cia&longs;cun Dificio, Ordigno, I&longs;trumento, Argano, Mangano, oue-<lb/>ro ingegno mae&longs;treuolmente ritrouato, & lauorato per cotali ef <lb/>fetti, & &longs;imili altri infiniti in qual &longs;i voglia &longs;cienza, arte, & e&longs;er-<lb/>citio.

</s>

Laquale hò de&longs;critta co&longs;i materialmente per darne vn cer <lb/>to &longs;aggio accommodato al gu&longs;to del più de gli huomini; trala-<lb/>&longs;ciando le accurate di&longs;&longs;initioni à miglior tempo.

</s>

Aggiunga&longs;i, che &longs;otto que&longs;to vniuer&longs;ali&longs;&longs;imo titolo &longs;i è con-<pb id="p.0015" xlink:href="pagethumb-it/018.jpg"/>

tentato l'Autore di manife&longs;tare per hora, & il primo de Latini <lb/>con dimo&longs;trationi ageuoli, & piane, in&longs;egnare &longs;olamente la ra-<lb/>gion dello intendere, & maneggiare gli &longs;ei predetti l&longs;trumenti <lb/>Mechanici; à quali &longs;i riducono tutti gli altri, come à &longs;uoi prin-<lb/>cipil, & fondamenti; & da'quali &longs;i po&longs;&longs;ono comporne diuer&longs;e ma <lb/>niere, accozzandone in&longs;ieme due, tre, & più, come l'A&longs;&longs;e nella <lb/>rota con la Taglia, la Vite co'l detto A&longs;&longs;e, & con la Leua, & &longs;uc-<lb/>ces&longs;iuamente de gli altri ad arbitrio di chiunque in varie opre &longs;e <lb/>ne sà con giudicio valere, come nota l'Autore nel fine di que&longs;to <lb/>volume.

</s>

Hor come che l'Autore con bella via, & chiara, & con ordine <lb/>ammirabile di que&longs;ti difici habbia ragionato, & la co&longs;a per &longs;e <lb/>molto o&longs;cura non &longs;ia ad intender&longs;i: nondimeno ben ricerca ella <lb/>tutto l'intelletto dell'huomo, & che con &longs;i&longs;&longs;a &longs;peculatione &longs;i leg-<lb/>gano attentis&longs;imamente più d'vna volta le dimo&longs;trationi.

</s>

Doue &longs;i vede in alcuni luoghi di que&longs;ti trattati cotale &longs;orte di <lb/>lettere picciole, differente dalle altre, come la pre&longs;ente; auer-<lb/>ta&longs;i che non vi &longs;ono co&longs;e dettate dall' Autore di que&longs;to libro di <lb/>Mechaniche, ma notate da colui che l'hà volgarizato, à fine di <lb/>chiarire qualche pa&longs;&longs;o difficile, & ageuolare l'intendimento à' <lb/>Lettori non co&longs;i prattichi nelle Scole de' Filo&longs;ofi.

</s>

Ponga&longs;i anco mente, che à carte 121. nel trattato della Vite, <lb/>è po&longs;to fra i detti dell' Autore il Problema di Pappo, ilquale do-<lb/>uea e&longs;&longs;ere &longs;tampato con lettere differenti dalle altre, ma per in-<lb/>auertenza è &longs;tato me&longs;&longs;o co' caratteri &longs;te&longs;&longs;i delle propo&longs;itioni del <lb/>l' Autore, che è difetto.

</s>

Non è &longs;tato pos&longs;ibile &longs;chluare alcuni <lb/>falli nello &longs;tampare.

</s>

Onde correggan&longs;i in que&longs;ta maniera.

</s>

Nel <lb/>la Lettera à carte 1. faccia 2. ver&longs;i 25. to&longs;&longs;enoni, leggi tollenoni. <lb/>car. 43. ver. 22. dell'angolo, all'angolo. carte 48. f. 2. nella po-<lb/>&longs;tilla, per la 2. di que&longs;to; della 2. di que&longs;to. carte 87. f. 2. <lb/>ver. 14. dalla, alla. carte 93. ver. 32. cni, cui. carte 115. ver. 20. <lb/>Hlici, Helici.

</s>

Gli altri errori di lettere meno importanti, & che <lb/>non mouono il &longs;en&longs;o alla, di&longs;cretione del giudicio&longs;o Lettore &longs;i ri <lb/>mettono.

</s>

</section>

TRATTATI IN QVEST'OPERA <lb/>CONTENVTI.</s>

I. <lb/>Della Bilancia, con la Stadera à carte 1<lb/>

</s>

II. <lb/>Della Leua. 35<lb/>

</s>

III. <lb/>Della Taglia. 56<lb/>

</s>

IIII. <lb/>Dell'A&longs;&longs;e nella Rota. 102<lb/>

</s>

V. <lb/>Del Cuneo. 107<lb/>

</s>

VI. <lb/>Della Vite. 115<lb/>

</s>

</section>

</front>

LIBRO DI <lb/>MECHANICHE, <lb/>DELL'ILLVSTRISSIMO <lb/>SIGNORE, <lb/>II. S. GVIDO VBALDO DE' MARCHESI <lb/>DEL MONTE.

</s>

</figure>

Diffinitioni.

</s>

Il centro della grauezza di cia&longs;cun corpo e vn <lb/>certo punto po&longs;to dentro, dal quale &longs;e con la <lb/>imaginatione s'intende e&longs;&longs;erui appe&longs;o il gra-<lb/>ue, mentre è portato &longs;ta fermo, & mantiene <lb/>quel &longs;ito, che egli hauea da principio, ne in <lb/>quel portamento &longs;i và riuolgendo.

</s>

<emph type="italics"/>Que&longs;ta diffinitione del centro della grauezza in&longs;egnò <lb/>Pappo Ale&longs;&longs;andrino nell'ottauo libro delle raccolte ma-<lb/>thematiche.

</s>

Ma Federico Comandino nel libro del cen-<lb/>tro della grauezza de' corpi &longs;olidi dichiarò l'i&longs;te&longs;&longs;o centro in questa maniera de&longs;cri-<lb/>uendolo.<emph.end type="italics"/>

</s>

Il centro della grauezza di cia&longs;cuna figura &longs;olida è quel punto po&longs;to <lb/>dentro, d'intorno alquale le parti di momenti eguali da ogni parte <lb/>&longs;i fermano.

</s>

Peroche &longs;e per tale centro &longs;arà condotto vn piano, che <lb/>&longs;eghi in qual &longs;i voglia modo la figura, &longs;empre la diuiderà in parti, <lb/>che pe&longs;eranno egualmente.

</s>

NOTITIE COMVNI.

</s>

</s>

Se da co&longs;e egualmente pe&longs;anti &longs;i leneranno co&longs;e, che pur egualmente <lb/>pe&longs;ino, le re&longs;tanti pe&longs;eranno egualmente.

</s>

II.

</s>

Se à co&longs;e egualmente pe&longs;anti &longs;i aggiungeranno co&longs;e, che pur <expan abbr="egualm&etilde;">egualmen</expan> <lb/>te pe&longs;ino, tutte in&longs;ieme pe&longs;eranno egualmente.

</s>

III.

</s>

Le co&longs;e, che all'i&longs;te&longs;&longs;o &longs;ono eguali in pe&longs;o, &longs;ono tra loro anco gra-<lb/>ui egualmente.

</s>

PRESVPPOSTE.

</s>

</s>

Di vno corpo è vn &longs;olo centro della grauezza.

</s>

II.

</s>

Il centro della grauezza di vn corpo è &longs;empre nel mede&longs;imo &longs;ito per <lb/>ri&longs;petto al &longs;uo corpo.

</s>

III.

</s>

I Pe&longs;i &longs;ono portati in giu &longs;econdo il centro della grauezza.

</s>

DIFFINITIONI.

</s>

La diffinitione è vn breue parlare, che manife&longs;ta, & inte-<lb/>ramente dichiara la co&longs;a propo&longs;ta, &longs;i fattamente che non &longs;i po&longs;&longs;a trouare condi-<lb/>tione, ouero accidente alcuno principale in e&longs;&longs;a co&longs;a, &longs;e la diffinitione è buona, <lb/>che non &longs;ia in virtù compre&longs;a, & detta da lui; come per e&longs;empio l'Autore qui di <lb/>&longs;opra da ad inten dere che &longs;ia il centro della grauezza con due diffinitioni.

</s>

Le Notitie comuni poi &longs;ono certe &longs;entenze manife&longs;te al &longs;en&longs;o comune de gli huomi-<lb/>ni, lequali pur che vi &longs;i ponga mente, &longs;ubito vdite, &longs;i intendono, & &longs;e le pre&longs;ta il <lb/>con&longs;entimento.

</s>

Ma la Pre&longs;uppo&longs;ta è diuer&longs;a, peroche mette per vero la co&longs;a co&longs;i e&longs;&longs;ere, come &longs;i pro-<lb/>pone &longs;enza altro di&longs;cor&longs;o per farla cono&longs;cere.

</s>

</chap>

DELLA BILANCIA

</s>

Avanti che &longs;i faccia mentione della Bilancia, accioche la <lb/>co&longs;a re&longs;ti più chiara, &longs;ia la Bilancia AB in linea diritta, & <lb/>CD la Truttina della Bilancia, laquale &longs;econdo la con&longs;uetu <lb/>dine comune &longs;tà &longs;empre à piombo dell'orizonte.

</s>

& il punto C im <lb/>mobile, d'intorno alquale &longs;i volge la Bilancia, &longs;i chiami il centro del <lb/>la bilancia, &longs;ia pur collo-<lb/>cato di &longs;opra della bilan <lb/>cia, ò di &longs;otto, benche <lb/>non propriamente, che <lb/>non fa nulla Ma il CA, <lb/>& il CB &longs;iano le di&longs;tan <lb/>ze, & braccia della Bilan <lb/>cia, co&longs;i nomate.

</s>

& &longs;e <lb/>dal centro della bilancia <lb/>collocato di &longs;opra, ò di <lb/>&longs;otto della Bilancia, &longs;arà <lb/>tirata vna linea à piom-<lb/>bo di AB, que&longs;ta &longs;i chia <lb/>merà perpendicolo, che <lb/>&longs;o&longs;terrà la Bilancia AB, <lb/>& &longs;empre &longs;tarà à piom-<lb/>bo di e&longs;&longs;a Bilancia, mo-<lb/>ua&longs;i ella in qual &longs;i voglia <lb/>modo.

</s>

</figure>

Concio&longs;ia che in que&longs;to trattato della Bilancia, & ne gli altri ancora l'Autore v&longs;i <lb/>alcune parole, lequali non &longs;i &longs;ono potute tra&longs;portare commodamente in v olga-<lb/>re, per non e&longs;&longs;ere e&longs;&longs;e anco &longs;tate accettate in que&longs;ta lingua, ne inte&longs;e da ognuno, <lb/>io le ho la&longs;ciate co&longs;i latine.

</s>

Ma accioche non facciano difficultà à coloro, i quali <lb/>non intendono il latino, le andrò per tutto à fuoi luoghi dichiarando.

</s>

Nel re&longs;to poi delle parole mi &longs;ono attenuto più al chiaro, & all'v&longs;ato, che &longs;ia pos&longs;i-<lb/>bile, & ho po&longs;to angolo retto, & linea retta in cambio di angolo diritto, & linea <lb/>diritta, & linea della direttione in lo co di linea della dirittura, & co&longs;i diretto per <lb/>diritto, & alcuna volta magnitudine in vece di grandezza, & angolo mi&longs;to per <lb/>me&longs;colato, & angolo curuilineo per di linee torte, & linea curua per torta, & &longs;oli-<lb/>do per &longs;odo, & for&longs;e qualche altro vocabolo poco v&longs;ato in que&longs;ta no&longs;tra fauella, <lb/>&longs;timando che cote&longs;te parole &longs;iano per dimo&longs;trare maggiormente la co&longs;a, & la in-<lb/>tentione dell' Autore: & etiandio de&longs;iderando, che &longs;i rendano famigliari, & dome <lb/>&longs;tiche in que&longs;ta &longs;cienza, talche ognuno le po&longs;&longs;a ageuolmente intendere.

</s>

Trutina è quella co&longs;a, che &longs;o&longs;tiene tutta la Bilancia, laquale Trutina pigli a il Perno, <lb/>ouero l'A&longs;&longs;etto, & noma&longs;i in que&longs;ti pae&longs;i Gioa, altroue Giouola, ouero l'o recchie <lb/>della Bilancia, & in altre contrade Scocca, talche non &longs;i troua &longs;in hora vocabolo, <pb id="2v" xlink:href="pagethumb-it/023.jpg"/>che in Italia communemente vi &longs;i confaccia, ne alcuno di qne&longs;ti &longs;arebbe inte&longs;o <lb/>per tutto.

</s>

Onde io ho &longs;critto co&longs;i la Trutina, &longs;perando, che &longs;i habbia à fare termi <lb/>ne, & parola generale à tutte le nationi d'Italia.

</s>

Perpendicolo vuol dire quella linea, che &longs;porge in fuori dal centro della Bilancia al <lb/>mezo di detta Bilancia, ilqual Perpendicolo è &longs;olamente nelle Bilancie, lequali han <lb/>no il centro di fuori della Bilancia, o &longs;ia di &longs;otto, ò &longs;ia di &longs;opra.

</s>

Ma quando il cen-<lb/>tro della Bilancia è nel mezo di e&longs;&longs;a, all'hora non vi è que&longs;to Perpendicolo per e&longs; <lb/>&longs;ere il centro della Bilancia, & il mezo di e&longs;&longs;a vn'i&longs;te&longs;&longs;o punto.

</s>

Et que&longs;to Perpen-<lb/>dicolo è co&longs;a imaginata dall' Autore &longs;olamente, & non da altri, per ageuolare al-<lb/>cune dimo&longs;trationi della Bilancia, che di nouo ha inue&longs;tigate: & non è la linguet-<lb/>ta, ne meno la linea della direttione, ò dirittura che &longs;i habbia à dire.

</s>

LEMMA.

</s>

Sia la linca AB à piombo dell'orizonte, & col diametro AB &longs;i de&longs;cri-<lb/>ua il cerchio AEBD, il cui centro &longs;ia C. Dico il punto B e&longs;&longs;ere <lb/>l'infimo luogo della circonferenza del cerchio AEBD, & il pun-<lb/>to A il piu alto, & quali &longs;i voglian punti, come DE, i quali &longs;iano <lb/>però egualmente di&longs;tanti da A e&longs;&longs;ere egualmente po&longs;ti di &longs;otto, & <lb/>quelli che &longs;tanno piu da pre&longs;&longs;o ad e&longs;&longs;o A, e&longs;&longs;ere più alti di quelli, che <lb/>&longs;ono più da lunge.

</s>

</figure>

<arrow.to.target n="note1"></arrow.to.target><emph type="italics"/>Allunghi&longs;i la linea AB fin al centro del mondo, <lb/>che &longs;ia F. Dapoi &longs;ia pre&longs;o nella circonferenza <lb/>del cerchio qual &longs;i voglia punto, come G, & &longs;i <lb/>congiungano le linee FG FD FE. Hor per-<lb/>cioche BF è la minima linea di tutte quelle, <lb/>che dal punto F &longs;ono tirate alla circonferenza <lb/>AEBD, &longs;arà la BF minore della FG. Per <lb/>laqual co&longs;a il punto B &longs;arà piu da pre&longs;&longs;o al pun-<lb/>to F, che il G. Et per cotesta ragione &longs;i dimo-<lb/>strerà, che il punto B &longs;ta più da pre&longs;&longs;o al centro <lb/>del mondo di qual &longs;i voglia altro punto della cir-<lb/>conferenza del cerchio AEBD. Sarà dunque <lb/>il punto B l'infimo luogo della circon&longs;erenza del <lb/>cerchio AEBD. Dapoi perche AF tirata <lb/>per lo centro è maggiore di GF, &longs;arà il punto A <lb/>più alto non &longs;olamente di G, ma etiandio di qual <lb/>&longs;i voglia altro punto della circon&longs;erenza del cer-<lb/>chio AEBD. Oltre à ciò perche DF, & FE <lb/>&longs;ono eguali, i punti DE &longs;aranno egualmente di <lb/>stanti dal centro del mondo.

</s>

Et e&longs;&longs;endo DF <lb/>maggiore di FG, &longs;arà il punto D, che è più da <lb/>pre&longs;&longs;o al punto A, più alto del punto G, lequali <lb/>co&longs;e tutte erano da mo&longs;trar&longs;i.<emph.end type="italics"/>

</s>

<margin.target id="note1"></margin.target><emph type="italics"/>Per la ottaua del terzo.<emph.end type="italics"/>

</s>

Que&longs;to vocabolo Lemma greco v&longs;ato da tutti i volgarizatori di Euclide, & da gli <lb/>altri Scrittori di Mathematica ancora, hò accettato anch'io.

</s>

Ma ben con tutto ciò <lb/>&longs;timo che egli habbia me&longs;tieri di vn poco di lume per e&longs;&longs;er inte&longs;o; & viene à dire, <lb/>&longs;i come nota Cicerone nel &longs;econdo della Diuinatione, co&longs;a che prima &longs;i prende <lb/>per render facile l'intendimento delle co&longs;e, lequali &longs;i hanno dapoi à mo&longs;trare, & <lb/><expan abbr="nõ">non</expan> è Pre&longs;uppo&longs;ta, perche ella <expan abbr="nõ">non</expan> &longs;i proua <expan abbr="cõ">com</expan> ragione, ma &longs;uppon&longs;i; ma il Lemma <lb/>&longs;i dimo&longs;tra, come in que&longs;to luogo, che prende il punto B e&longs;&longs;ere po&longs;to nell'infimo <lb/>&longs;ito della circonferenza del cerchio, & lo proua per douer&longs;ene valere nelle &longs;eguen <lb/>ti dimo&longs;trationi.

</s>

Doue in que&longs;to Lemma &longs;i dice, che la linea AB è à piombo dell'orizonte, intenda&longs;i <lb/>per orizonte il piano della campagna, & del terreno &longs;ottopo&longs;to, volendo dire ori <lb/>zonte parola greca vn cerchio, che termina la no&longs;tra veduta, & abbraccia & diui <lb/>de la metà della terra tutta.

</s>

Quando dunque &longs;i troua in que&longs;ti libri vna linea, oue-<lb/>ro altra quantità e&longs;&longs;ere à piombo, ouero egualmente di&longs;tante, ò inchinata all'ori-<lb/>zonte, intenda&longs;i per l'orizonte il piano della campagna, ò del terreno.

</s>

PROPOSITIONE I.

</s>

Se il pe&longs;o &longs;arà &longs;o&longs;tenuto nel centro della &longs;ua grauezza da linea diritta <lb/>non &longs;i fermerà giamai, &longs;e quella i&longs;te&longs;&longs;a linea non &longs;arà à piombo del <lb/>l'orizonte.

</s>

</figure>

<emph type="italics"/>Sia il pe&longs;o A, & il centro della &longs;ua <lb/>grauezza B, ilqual pe&longs;o venga &longs;o <lb/>&longs;tenuto dalla linea CB. Dico che <lb/>il pe&longs;o non è per fermar&longs;i giamai, <lb/>&longs;e CB non &longs;arà à piombo dell'o-<lb/>rizonte.

</s>

Sia il punto C immobi-<lb/>le, e&longs;&longs;endo co&longs;i nece&longs;&longs;ario, accio il <lb/>pe&longs;o &longs;ia &longs;o&longs;tenuto: & e&longs;&longs;endo il pun <lb/>to C immobile, &longs;e il pe&longs;o A de-<lb/>ue&longs;i mouere, il punto B de&longs;criuerà <lb/>la circonferenza di vn cerchio, il <lb/>cui mezo diametro &longs;arà CB. Per <lb/>laqual co&longs;a &longs;u'l centro A & con <lb/>lo &longs;patio BC &longs;i de&longs;criua il cerchio <lb/>BFDE. & &longs;ia di prima BC à <lb/>piombo dell'orizonte, & &longs;ia tirata <lb/>&longs;in à D, & il punto C &longs;tia di &longs;ot <lb/>to al punto B. Hor percioche il pe&longs;o A &longs;i moue in giù &longs;econdo il centro della gra-<emph.end type="italics"/> <arrow.to.target n="note2"></arrow.to.target><lb/><emph type="italics"/>uezza, il punto B &longs;i mouerà in giù, oue naturalmente inchina ver&longs;o il centro del mon <lb/>do per la linea diritta BD: tutto il pe&longs;o A dunque con B &longs;uo centro della gra-<lb/>uezza, grauerà &longs;opra la linea diritta BC, & concio&longs;ia che il pe&longs;o venga &longs;o&longs;tenuto <lb/>dalla linea CB, la linea CB &longs;o&longs;terrà tutto il pe&longs;o A, &longs;opra laquale non puote mo<emph.end type="italics"/><pb id="3v" xlink:href="pagethumb-it/025.jpg"/><emph type="italics"/>uer&longs;i in giù, e&longs;&longs;endogliene da e&longs;&longs;a <lb/>vietato.

</s>

Per la diffinitione dun-<lb/>que del centro della grauezza, il <lb/>punto B & il pe&longs;o A &longs;taranno <lb/>in que&longs;to &longs;ito.

</s>

& quantunque il <lb/>B &longs;ia piu alto di qual &longs;i voglia al-<lb/>tro punto del cerchio, tuttauia non <lb/>&longs;i mouerà in giù da que&longs;to &longs;ito per <lb/>la circonferenza del cerchio, pero-<lb/>che non &longs;i inchinerà più ver&longs;o lo F, <lb/>che ver&longs;o lo E, per e&longs;&longs;ere nell'vna <lb/>parte & nell'altra eguale la di&longs;ce-<lb/>&longs;a: ne il pe&longs;a A piu &longs;tà pendente <lb/>in vna parte che nell'altra, ilche <lb/>non auiene in qual &longs;i voglia altro <lb/>punto della circon&longs;erenza del cer-<lb/>chin, eccettuato il D. Sia il centro <lb/><arrow.to.target n="fig1"></arrow.to.target><lb/>della grauezza dell'i&longs;te&longs;&longs;o pe&longs;o, come in F, concio&longs;ia che la di&longs;ce&longs;a &longs;ia dal punto <lb/>F ver&longs;o il D, & la a&longs;ce&longs;a ver&longs;o il B, però il punto F mouera&longs;&longs;i in giù: & per-<lb/>cioche non &longs;i puote mouere al centro del mondo per linea diritta, per e&longs;&longs;ere impe-<lb/>dito dal punto C immobile per cau&longs;a della linea CF, ma ben &longs;i mouerà &longs;empre <lb/>in giù come richiede la &longs;ua natura: & e&longs;&longs;endo il D il luogo infimo, &longs;i mouerà per <lb/>la circonferenza FD finche peruenga in D, nelqual &longs;ito fermera&longs;&longs;i il pe&longs;o, & <lb/>re&longs;terà immobile, sì perche non &longs;i puote più mouere in giù per e&longs;&longs;ere attaccato al <lb/>punto C, sì anche percioche egli è &longs;o&longs;tenuto nel &longs;uo centro della grauezza.

</s>

Et <lb/>quando F &longs;arà in D, &longs;arà &longs;imilmente la FC in DC, & in&longs;ieme à piombo <lb/>dell'orizonte.

</s>

il pe&longs;o dunque non &longs;i fermerà giamai finche la linea CF non &longs;tia <lb/>à piombo dell'orizonte, che bi&longs;ognaua prouare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note2"></margin.target><emph type="italics"/>Per la terza pre&longs;upposta di questo.<emph.end type="italics"/>

</s>

Di quì &longs;i puote cauare, che il pe&longs;o &longs;ia pur &longs;o&longs;tenuto in vn dato punto <lb/>in qual &longs;i voglia modo, non &longs;tarà fermo giamai, &longs;e non quando la <lb/>linea tirata dal centro della grauezza del pe&longs;o à quel punto, &longs;tia à <lb/>piombo dell'orizonte.

</s>

<emph type="italics"/>Come, po&longs;te le co&longs;e i&longs;te&longs;&longs;e, &longs;ia &longs;o&longs;tenuto <lb/>il pe&longs;o dalle linee CG CH. Dico <lb/>che &longs;e la tirata linea BC &longs;arà à <lb/>piombo dell'orizonte, il pe&longs;o &longs;tarà <lb/>fermo: ma &longs;e la tirata linea CF <lb/>non &longs;arà à piombo dell'orizonte, il <lb/>punto F &longs;imouerà in giù fin al D, <lb/>nel qual &longs;ito &longs;tarà fermo il pe&longs;o, <lb/>& la tirata linea CD &longs;arà à piom-<lb/>bo dell'orizonte.

</s>

Le quali co&longs;e <lb/>tutte con laragione mede&longs;ima &longs;i pro-<lb/>uerebbono.<emph.end type="italics"/>

</s>

</figure>

PROPOSITIONE II.

</s>

La bilancia egualmente di&longs;tante dall'orizonte, il cui centro &longs;tia &longs;opra <lb/>la detta bilancia, & che habbia i pe&longs;i eguali nelle &longs;tremità, & egual-<lb/>mente di&longs;tanti dal perpendicolo, &longs;e da cotale &longs;ito &longs;arà mo&longs;&longs;a, & <lb/>nell'i&longs;te&longs;&longs;o di nuouo la&longs;ciata, ritornerà, & iui re&longs;terà.

</s>

</figure>

<emph type="italics"/>Sia la bilancia AB in <lb/>linea diritta egualmen <lb/>te di&longs;tante dall'orizon <lb/>te, il cui centro C &longs;ia <lb/>&longs;opra la bilancia, & <lb/>&longs;ia CD il perpendi-<lb/>colo, il quale &longs;arà à <lb/>piombo dell'orizonte: <lb/>& la di&longs;tanza DA <lb/>&longs;ia eguale alla di&longs;tan-<lb/>za DB: & &longs;iano i <lb/>pe&longs;i in AB eguali, <lb/>i centri della grauez-<lb/>za de' quali &longs;iano ne i <lb/>punti AB. Moua&longs;i <lb/>da que&longs;to &longs;ito la bi-<lb/>lancia AB come in EF, dapoi &longs;ia la&longs;ciata.

</s>

Dico che la bilancia EF ritor-<lb/>neràin AB di&longs;tante egualmente dall'orizonte, & iui rimanerà.

</s>

Hora percioche<emph.end type="italics"/><pb id="4v" xlink:href="pagethumb-it/027.jpg"/><emph type="italics"/>il punto C &longs;tà immobì <lb/>le mentre la bilancia &longs;i <lb/>moue, il punto D veni <lb/>rà à de&longs;criuere vna cir-<lb/>con&longs;erenza di cerchio, il <lb/>cui mezo diametro &longs;a-<lb/>rà CD. Per laqual <lb/>co&longs;a co'lcentro D, & <lb/>lo &longs;patio CD de&longs;cri-<lb/>ua&longs;i il cerchio DGH. <lb/>Et perche CD &longs;empre <lb/>&longs;tà à piombo della bi-<lb/>lancia, mentre la bilan <lb/>cia &longs;arà in EF, la li-<lb/>nea CD &longs;arà in CG <lb/>&longs;i fattamente, che CG <lb/><arrow.to.target n="fig2"></arrow.to.target><lb/>venga ad e&longs;&longs;ere à piombo di EF: & concio&longs;ia che AB &longs;ia diui&longs;a in due parti<emph.end type="italics"/><lb/><arrow.to.target n="note3"></arrow.to.target> <emph type="italics"/>eguali nel punto D, & i pe&longs;iin AB &longs;iano eguali, &longs;arà etiandio il centro della <lb/>grauezza della magnitudine compo&longs;ta di que&longs;ti due corpi AB nel mezo, cioè in <lb/>D: & quando la bilancia in&longs;ieme co i pe&longs;i &longs;arà in EF, &longs;arà parimente G il cen <lb/>tro della grauezza della magnitudine compo&longs;ta di e&longs;&longs;i AB: & percioche CG <lb/>non è à piombo dell'orizonte, la grandezza compo&longs;ta de i pe&longs;i EF non rimarrà<emph.end type="italics"/><lb/><arrow.to.target n="note4"></arrow.to.target> <emph type="italics"/>in questo &longs;ito, ma &longs;i mouerà in giù &longs;econdo il centro della grauezza &longs;ua, che è in <lb/>G, per la circonferenza GD, finche &longs;i faccia à piombo dell'orizonte, cioè finche <lb/>CG ritorni in CD. Et quando CG &longs;arà in CD, la linea EF (perche &longs;em-<lb/>pre &longs;tà ad angoli retti con CG) &longs;arà in AB, nelqual &longs;ito &longs;tarà &longs;erma.

</s>

La bi-<emph.end type="italics"/><lb/><arrow.to.target n="note5"></arrow.to.target> <emph type="italics"/>lancia dunque EF ritornerà in AB, laquale è di&longs;tante egualmente dall'orizon-<lb/>te, & iui rimarrà, che bi&longs;ognaua dimo&longs;trare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note3"></margin.target><emph type="italics"/>Per la quarta del primo di Archimede delle co&longs;e che pe&longs;ano egualmente.<emph.end type="italics"/>

</s>

<margin.target id="note4"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

<margin.target id="note5"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

PROPOSITIONE III.

</s>

La bilancia egualmente di&longs;tante dall'orizonte, che habbia nelle &longs;tre-<lb/>mità pe&longs;i eguali, & egualmente lontani dal perpendicolo, e&longs;&longs;endo <lb/>collocato il centro di &longs;otto, rimarrà in que&longs;to &longs;ito.

</s>

Ma &longs;e indi &longs;arà <lb/>mo&longs;&longs;a, & la&longs;ciata à ba&longs;&longs;o, &longs;i mouerà &longs;econdo la parte piu ba&longs;&longs;a.

</s>

</figure>

<emph type="italics"/>Sia la bilancia AB in <lb/>linea diritta, egual-<lb/>mente di&longs;tante dall'ori<lb/>zonte, il cui centro C <lb/>&longs;ia di &longs;otto alla bilan-<lb/>cia, & &longs;ia CD il per-<lb/>pendicolo, ilquale &longs;arà <lb/>à piombo dell'orizon-<lb/>te, & la di&longs;tanza AD <lb/>&longs;ia eguale alla distan-<lb/>za DB, & &longs;iano in <lb/>AB pe&longs;i eguali, i cen-<lb/>tri della grauezza de' <lb/>quali &longs;iano ne' punti <lb/>AB. Dico primiera-<lb/>mente che la bilancia <lb/>AB &longs;tarà &longs;erma in <lb/>que&longs;to &longs;ito.

</s>

Hor percioche AB &longs;i diuide in parti eguali nel punto D, & i <lb/>pe&longs;i po&longs;ti in AB &longs;ono eguali, &longs;egue, che il punto D &longs;ia il centro della grauez-<lb/>za della magnitudine compo&longs;ta di ambedue i corpi me&longs;&longs;i in AB; & il CD che<emph.end type="italics"/> <arrow.to.target n="note6"></arrow.to.target><lb/><emph type="italics"/>&longs;ostiene la bilancia &longs;tà à piombo dell'orizonte: Adunque la bilancia AB in <lb/>que&longs;to &longs;ito rimarrà ferma.

</s>

Ma da que&longs;to &longs;ito moua&longs;i la bilancia AB come in <lb/>EF, & la&longs;ci&longs;i dapoi.

</s>

Dico che la bilancia EF &longs;i mouerà dalla parte dello F. <lb/>Et percioche il CD &longs;tà &longs;empre à piombo della bilancia, mentre la bilancia &longs;arà <lb/>in EF verrà ad e&longs;&longs;ere anche il CD in CG à piombo di EF, & il punto<emph.end type="italics"/> <arrow.to.target n="note7"></arrow.to.target><lb/><emph type="italics"/>G della magnitudine composta di EF &longs;arà il centro della grauezza, ilquale men <lb/>tre &longs;i moue de&longs;criuerà la circonferenza del cerchio DGH, il cui mezo diametro <lb/>è CD, & il centro C. Ma perche CG non &longs;tà à piombo dell'orizonte, la <lb/>grandezza compo&longs;ta de i pe&longs;i EF non rimarrà in questo &longs;ito, ma &longs;econdo il cen-<lb/>tro della &longs;ua grauezza &longs;i mouerà in giù per la circonferenza GH. La bilancia <lb/>dunque EF &longs;i mouerà in giù dalla parte dello F, che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

<margin.target id="note6"></margin.target><emph type="italics"/>Per la quar ta del primo d' Archimede delle co&longs;e che pe&longs;ano <expan abbr="egualm&etilde;te">egualmente</expan>.<emph.end type="italics"/>

</s>

<margin.target id="note7"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

PROPOSITIONE IIII.

</s>

La bilancia egualmente di&longs;tante dall'orizonte, & che habbia nelle &longs;tre <lb/>mità pe&longs;i eguali, & egualmente di&longs;tanti dal centro collocato in e&longs;&longs;a <lb/>bilancia.

</s>

Se ella indi &longs;arà mo&longs;&longs;a, ò non, douunque ella &longs;arà la&longs;cia-<lb/>ta, rimarrà.

</s>

</figure>

<emph type="italics"/>Sia la bilancia nella linea <lb/>diritta AB egualmen <lb/>te di&longs;tante dall'orizon-<lb/>te, il cui centro C &longs;ia <lb/>nella i&longs;te&longs;&longs;a linea AB, <lb/>& la di&longs;tanza CA &longs;ia <lb/>eguale alla distanza <lb/>CB, & &longs;iano i pe&longs;i <lb/>AB eguali, i cui cen-<lb/>tri della grauezza &longs;tia <lb/>no ne i punti AB. Mo <lb/>ua&longs;i la bilancia come in <lb/>DE, & iui &longs;ia la&longs;cia-<lb/>ta.

</s>

Dico primamen-<lb/><arrow.to.target n="fig3"></arrow.to.target><lb/>te che la bilancia DE non &longs;i mouerà, & rimarrà in quel &longs;ito.

</s>

Hor percioche i <lb/>pe&longs;i AB &longs;ono eguali, &longs;arà il centro della grauezza della magnitudine compo&longs;ta <lb/>delli due pe&longs;i A & B in C. Per laqual co&longs;a l'i&longs;te&longs;&longs;o punto C &longs;arà il centro <lb/>della bilancia, & il centro della grauezza di tutto il pe&longs;o.

</s>

Et percioche il centro <lb/>della bilancia che è C, mentre la bilancia AB in&longs;ieme co'pe&longs;i &longs;i moue in DE, <lb/>rimane immobile, non &longs;i mouerà ne anche il centro della grauezza, che è l'i&longs;te&longs;&longs;o C. <lb/>Adunque ne anche la bilancia DE &longs;i mouerà per la diffinitione del centro della <lb/>grauezza, e&longs;&longs;endo in e&longs;&longs;o appiccata.

</s>

L'i&longs;te&longs;&longs;o accade parimente &longs;tando la bilancia <lb/>AB egualmente di&longs;tante dall'orizonte, ouero e&longs;&longs;endo in qual &longs;i voglia altro &longs;ito. <lb/>Rimarrà dunque la bilancia oue &longs;arà la&longs;ciata, che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

<emph type="italics"/>Benche habbiamo con&longs;iderato nelle co&longs;e predette le grauezze &longs;olamente delle magni-<lb/>tudini, le quali &longs;ono po&longs;te nelle &longs;tremità della bilancia, &longs;enza la grauezza della bi-<lb/>lancia; niente di manco per e&longs;&longs;ere anche le braccia della bilancia eguali, auenir à lo <lb/>i&longs;te&longs;&longs;o alla bilancia, con&longs;iderata la &longs;ua grauezza in&longs;ieme co' pe&longs;i, ouero &longs;enza pe&longs;i, <lb/>percioche il centro iste&longs;&longs;o della grauezza &longs;enza pe&longs;i &longs;arà anco centro della grauez-<lb/>za della bilancia &longs;ola.

</s>

Similmente &longs;e li pe&longs;i &longs;aranno appiccati nelle &longs;tremità del-<lb/>la bilancia, come &longs;uole far&longs;t, aùerrà l'iste&longs;&longs;o, purche le linee tirate da i punti oue &longs;o-<lb/>no attaccati i pe&longs;i ver&longs;o i centri delle grauezze, (moua&longs;i la bilancia in qual &longs;i vo-<lb/>gliamodo) vadano à concorrere nel centro del mondo, peroche doue &longs;ono attaccati <lb/>i pe&longs;i in questa maniera, iui grauano, come &longs;e in quegli &longs;te&longs;&longs;i punti baue&longs;&longs;ero i cen <lb/>tri delle grauezze.

</s>

Oltre à ciò poßiamo con&longs;iderare le co&longs;e che &longs;eguono in tut-<lb/>to al modo i&longs;te&longs;&longs;o.<emph.end type="italics"/>

</s>

<arrow.to.target n="note8"></arrow.to.target><emph type="italics"/>Ma percioche à que&longs;ta vltima conchiu&longs;ione molte co&longs;e dette da alcuni, che &longs;entono al-<lb/>tramente, paiono contra&longs;tare; però in cote&longs;ta parte egli &longs;arà bi&longs;ogno dimorare <lb/>alquanto, & &longs;econdo le mie forze non &longs;olo farò opra di difendere la propria <lb/>mia &longs;entenza, ma Archimede ancora, ilquale &longs;embra e&longs;&longs;ere &longs;tato in que&longs;to i&longs;te&longs;-<lb/>&longs;o parere.<emph.end type="italics"/>

</s>

<margin.target id="note8"></margin.target><emph type="italics"/>Giord.

</s>

de' pe&longs;i.

</s>

Il Car dano della &longs;ottigliezza.

</s>

Il Tartaglia de' que&longs;iti, & <expan abbr="inu&etilde;tioni">inuentioni</expan><emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Po&longs;te le co&longs;e i&longs;te&longs;&longs;e, &longs;ia <lb/>tirata la linea FCG <lb/>à piombo di AB, & <lb/>dell'orizonte: & col <lb/>centro C, & lo &longs;pa-<lb/>tio CA &longs;ia de&longs;crit-<lb/>to il cerchio ADFB <lb/>EG: &longs;aranno i punti <lb/>ADBE nella circon <lb/>ferenza del cerchio, <lb/>per e&longs;&longs;ere le braccia <lb/>della bilancia eguali. <lb/>& percioche conuen-<lb/>gono que&longs;ti autori in <lb/>vna &longs;entenza, affer-<lb/>mando, che la bilan-<lb/>cia DE non &longs;i moue <lb/>in FG, ne rimane in<emph.end type="italics"/><lb/><arrow.to.target n="fig4"></arrow.to.target><lb/><emph type="italics"/>DE, maritornanellalinea AB egualmente di&longs;tante dall'orizonte, mo&longs;trerò que <lb/>&longs;ta loro opinione non potere à modo alcuno &longs;tare.

</s>

Percioche &longs;e egli è vero quel <lb/>che dicono, ouero auenir à questo effetto per e&longs;&longs;ere il pe&longs;o D più graue del pe&longs;o E, <lb/>ouero &longs;e li pe&longs;i &longs;ono eguali, le di&longs;tanze nelle quali &longs;ono po&longs;ti, non &longs;aranno eguali, <lb/>cioè la CD non &longs;arà eguale alla CE, ma più grande.

</s>

Ma che i pe&longs;i col-<lb/>locati in DE &longs;iano eguali, & la di&longs;tanza CD &longs;ia eguale alla di&longs;tanza CE, è <lb/>chiaro dalla pre&longs;uppo&longs;ta.

</s>

Hor perche dicono che il pe&longs;o po&longs;to in D in quel &longs;i-<lb/>to è più graue del pe&longs;o po&longs;to in E nell altro &longs;ito da ba&longs;&longs;o: mentre i pe&longs;i &longs;ono in <lb/>DE, non &longs;arà il punto C piu centro della grauezza, imperoche non stanno fer-<lb/>mi &longs;e &longs;ono attaccati al C, ma &longs;arà nella linea CD per la terza del primo di At <lb/>chimede delle co&longs;e che pe&longs;ano egualmente.

</s>

Non &longs;arà già nella CE per e&longs;&longs;ere il <lb/>pe&longs;o D più graue del pe&longs;o E: &longs;ia dunque in H, nelquale &longs;e &longs;aranno attacca-<lb/>ti, rimarranno.

</s>

Et percioche il centro della grauezza de' pe&longs;i congiunti in AB <lb/>&longs;tà nel punto C: ma de' pe&longs;i po&longs;tiin DE il punto è H: mentre dunque i pe&longs;i <lb/>AB &longs;i muouono in DE, il centro della grauezza C moueraßi ver&longs;o D, & <lb/>s'appre&longs;&longs;er à più da vicino al D, ilche è impoßibile, per mantenere i pe&longs;i vname-<lb/>de&longs;ima di&longs;tanza fra loro: peroche il centro della grauezza di cia&longs;cun corpo &longs;tà &longs;em-<lb/>pre nel mede&longs;imo &longs;ito per ri&longs;petto al &longs;uo corpo.

</s>

Et quantunque il punto C &longs;ia il<emph.end type="italics"/> <arrow.to.target n="note9"></arrow.to.target><lb/><emph type="italics"/>centro della grauezza di due corpi A. & B, tuttauia per e&longs;&longs;ere mediante la bi-<lb/>lancia co&longs;i giunti in&longs;ieme, che &longs;empre &longs;i trouano nell'iste&longs;&longs;o modo; però il punto C<emph.end type="italics"/> <arrow.to.target n="note10"></arrow.to.target><lb/><emph type="italics"/>&longs;arà co&longs;i centro della grauezza loro, come &longs;e fo&longs;&longs;e vna &longs;ola magnitudine; percio-<lb/>che la bilancia in&longs;ieme co' pe&longs;i fa vn &longs;olo corpo continuo, il cui centro della grauez <lb/>za &longs;empre &longs;tarà nel mezo.

</s>

Non è dunque il pe&longs;o po&longs;to in D più graue del pe-<lb/>&longs;o po&longs;to in E. Che &longs;e dice&longs;&longs;ero il centro della grauezza non nella linea CD, ma<emph.end type="italics"/><pb id="6v" xlink:href="pagethumb-it/030.jpg"/><emph type="italics"/>nella CE douer e&longs;&longs;ere, auerrà l'i&longs;te&longs;&longs;o &longs;allo.<emph.end type="italics"/>

</s>

<margin.target id="note9"></margin.target><emph type="italics"/>Per la &longs;ecom da &longs;upposta di questo.<emph.end type="italics"/>

</s>

<margin.target id="note10"></margin.target><emph type="italics"/>Per la quar ta del primo di Archime de delle co&longs;e che pe&longs;ano egualmente.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Di più &longs;e il pe&longs;o D &longs;i mouer à in giù, mouer à il pe&longs;o E in sù.

</s>

Adunque vn pe&longs;o <lb/>più graue di E nel mede&longs;imo &longs;ito pe&longs;erà tanto quanto il pe&longs;o D, & auerr à che <lb/>co&longs;e graui di&longs;uguali, po&longs;te in eguale distanza pe&longs;eranno egualmente.

</s>

Aggiun-<lb/>ga&longs;i dunque al pe&longs;o E qualche co&longs;a graue, &longs;i &longs;attamente, che contrape&longs;i al D &longs;e <lb/>nel C &longs;aranno attac <lb/>cati.

</s>

Ma e&longs;&longs;endo &longs;ta-<lb/>to di &longs;opra mo&longs;trato <lb/>il punto C e&longs;&longs;ere il cè-<emph.end type="italics"/><lb/><arrow.to.target n="note11"></arrow.to.target> <emph type="italics"/>tro della grauezza di <lb/>pe&longs;i eguali po&longs;ti in <lb/>DE; &longs;e dunque il pe-<lb/>&longs;o.

</s>

E &longs;arà più graue <lb/>del pe&longs;o D, &longs;arà anche <lb/>il centro della grauez <lb/>za nella linea CE. <lb/>& &longs;ia que&longs;to centro <lb/>il<emph.end type="italics"/> K. <emph type="italics"/>Ma per la diffi-<lb/>nitione del centro del <lb/>la grauezza, &longs;e li pe&longs;i <lb/>&longs;aranno appiccati al<emph.end type="italics"/><lb/>K, <emph type="italics"/>staranno fermi. <lb/>Dunque &longs;e &longs;aranno<emph.end type="italics"/><lb/><arrow.to.target n="fig5"></arrow.to.target><lb/><emph type="italics"/>appiccati al C, non &longs;taranno fermi, che è contra la pre&longs;uppo&longs;ta: ma il pe&longs;o E &longs;i<emph.end type="italics"/><lb/><arrow.to.target n="note12"></arrow.to.target> <emph type="italics"/>mouer à in giù.

</s>

Che &longs;e appiccati al C pe&longs;a&longs;&longs;ero ancora egualmente, na&longs;cerebbe <lb/>che di vna magnitudine, due &longs;arebbono i centri della grauezza, che è impo&longs;&longs;ibile. <lb/>Adunque il pe&longs;o po&longs;to in E più graue di quello che è in D, non pe&longs;er à tanto <lb/>quanto il D attaccando&longs;i al punto C. I pe&longs;i dunque eguali po&longs;ti in DE, attac-<lb/>cati nel centro della loro grauezza pe&longs;eranno egualmente, & &longs;taranno immobili, <lb/>che &longs;u proposto di mo&longs;trare.<emph.end type="italics"/>

</s>

<margin.target id="note11"></margin.target><emph type="italics"/>Per laterza del primo di Archimede delle co&longs;e che pe&longs;ano egual mente.<emph.end type="italics"/>

</s>

<margin.target id="note12"></margin.target><emph type="italics"/>Per la prima &longs;upposta di questo.<emph.end type="italics"/>

</s>

<arrow.to.target n="note13"></arrow.to.target> <emph type="italics"/>A que&longs;ta vltima &longs;conueneuolezza ri&longs;pondono, dicendo e&longs;&longs;ere impo&longs;&longs;ibile aggiungere al <lb/>lo E &longs;i picciolo pe&longs;o, che in ogni modo &longs;e ben &longs;i appiccano al C, il pe&longs;o E non <lb/>&longs;i moua &longs;empre in giù ver&longs;o il G. La qual co&longs;a habbiamo noi pre&longs;uppo&longs;to poter&longs;i <lb/>fare, & credeuamo poter&longs;i fare: Peroche quel che è di più del pe&longs;o D &longs;opra <lb/>il pe&longs;o E, hauendo ragione, & parte di quantità, &longs;i imaginauamo non &longs;olamente <lb/>e&longs;&longs;ere minimo, ma ancora poter&longs;i diuidere in infinito, il che eßi per certo non &longs;ola-<lb/>mente minimo, ma ne anche e&longs;&longs;ere minimo, non potendo&longs;i ritrouare, &longs;i s&longs;orzano di <lb/>mo&longs;tr are in que&longs;ta maniera.<emph.end type="italics"/>

</s>

<margin.target id="note13"></margin.target><emph type="italics"/>Il Tartaglia nella &longs;esta propo&longs;itione del quate libre.<emph.end type="italics"/>

</s>

<emph type="italics"/>Pongan&longs;i le co&longs;e iste&longs;&longs;e <lb/>& da i punti DE <lb/>&longs;iano tirate le linee <lb/>DHE<emph.end type="italics"/>K <emph type="italics"/>à piombo <lb/>dell'orizonte, & &longs;ia <lb/>vn'altro cerchio L <lb/>DM, il cui centro <lb/>&longs;ia N, ilquale toc<emph.end type="italics"/> <arrow.to.target n="note14"></arrow.to.target><lb/><emph type="italics"/>chi FDG nel pun <lb/>to D, & &longs;ia eguale<emph.end type="italics"/> <arrow.to.target n="note15"></arrow.to.target><lb/><emph type="italics"/>ad FDG. Sarà <lb/>NC linea retta: & <lb/>perche l'angolo<emph.end type="italics"/> K <lb/><emph type="italics"/>EC è eguale all'an-<lb/>golo HDN, & <lb/>l'angolo CEG è pa <lb/>rimente eguale al-<lb/>l'angolo NDM,<emph.end type="italics"/><lb/><arrow.to.target n="fig6"></arrow.to.target><lb/><emph type="italics"/>peroche egli è contenuto da mezi diametri, & da circonferenze eguali: &longs;arà il re-<lb/>stante angolo & mi&longs;to<emph.end type="italics"/> K<emph type="italics"/>EG eguale al re&longs;tante angolo & mi&longs;to HDM. Et per-<lb/>cioche pre&longs;uppongono, che quanto è minore l'angolo contenuto dalla linea tirata à <lb/>piombo dell'orizonte, & dalla circonferenza, tanto in quel &longs;ito e&longs;&longs;ere anco più gra <lb/>ue il pe&longs;o.

</s>

Talche &longs;i come l'angolo contenuto da HD, & dalla circonferenza <lb/>DG, è minore dell'angolo<emph.end type="italics"/> K<emph type="italics"/>EG, cioè dell'angolo HDM, co&longs;i &longs;econdo que&longs;ta <lb/>proportione il pe&longs;o po&longs;to in D &longs;ia più graue di quello che &longs;tà in E. Mala pro-<lb/>portione dell'angolo MHD all'angolo HDG è minore di qual &longs;i voglia altra <lb/>proportione, che &longs;i troui tra la maggiore, & minore quantità: Adunque la pro-<lb/>portione de i pe&longs;i DE &longs;arà la minima di tutte le proportioni, anzinon &longs;arà qua&longs;i <lb/>ne anche proportione, e&longs;&longs;endo la minima di tutte le proportioni.

</s>

Che la propor-<lb/>tione di MDH ver&longs;o HDG &longs;ia di tutte la minima, mo&longs;trano con que&longs;ta ne-<lb/>ce&longs;&longs;aria ragione, peroche MHD &longs;upera HDG con angolo di linea curua, che <lb/>è MGD, ilquale angolo è il minimo di tutti gli angoli fatti di linee rette: ne po-<lb/>tendo&longs;i dare angolo minore di MGD &longs;arà la proportione di MDH ver&longs;o HDG <lb/>la minima di tutte le proportioni.

</s>

Laqual ragione pare e&longs;&longs;ere grandemente friuo-<lb/>la, peroche quantunque l'angolo MDG &longs;ia di tutti gli angoli fatti di linee rette <lb/>il minore, non perciò &longs;egue totalmente egli e&longs;&longs;ere di tutti gli angoli il minimo, im-<emph.end type="italics"/> <arrow.to.target n="note16"></arrow.to.target><lb/><emph type="italics"/>peroche &longs;ia dal punto D tirata la linea DO à piombo di NC, ambedue que-<lb/>ste toccberanno le circonferenze LDMFDG nel punto D. Ma percioche le <lb/>circonferenze &longs;ono eguali, &longs;arà l'angolo MDO misto eguale all'angolo ODG mi-<lb/>&longs;to.

</s>

L'vno de gli angoli dunque, cioè ODG &longs;arà minore di MDG, cioè minore<emph.end type="italics"/> <arrow.to.target n="note17"></arrow.to.target><lb/><emph type="italics"/>del minimo.

</s>

Dapoi l'angolo ODH &longs;arà minore dell'angolo MDH. Per laqual co&longs;a <lb/>ODH haurà proportione minore all'angolo HDG, che MDH all'i&longs;te&longs;&longs;o<emph.end type="italics"/><pb id="7v" xlink:href="pagethumb-it/033.jpg"/><emph type="italics"/>HDG. Dara&longs;&longs;i dunque la proportione anco minore della minima, laquale mostre-<lb/>remo dauantaggio in in&longs;inito minore in questo modo.

</s>

De&longs;criua&longs;i il cerchio DR, <lb/>il cui centro &longs;ia E, & il mezo diametro ED, la circonferentia DR tocche-<emph.end type="italics"/><lb/><arrow.to.target n="note18"></arrow.to.target> <emph type="italics"/>rà la circonferenza <lb/>DG nel punto D, <lb/>& la linea DO nel<emph.end type="italics"/><lb/><arrow.to.target n="note19"></arrow.to.target> <emph type="italics"/>punto D. Per laqual <lb/>co&longs;a minore &longs;arà l'an <lb/>golo RDG dell'an-<lb/>golo ODG, & &longs;i-<lb/>milmente l'angolo R <lb/>DH dell'angolo O <lb/>DH. Adunque ha-<lb/>uer à minore propor-<lb/>tione RDH ad HD <lb/>G di quel che haurà <lb/>ODH ad HDG. <lb/>Pigli&longs;i dapoi tra E <lb/>& C, come &longs;i vuo-<lb/>le, il punto P, dal <lb/>quale nella di&longs;tanza<emph.end type="italics"/><lb/><arrow.to.target n="fig7"></arrow.to.target><lb/><emph type="italics"/>di PD &longs;i de&longs;criua vn'altra circonferenza DQ, laquale toccherà la circonferen-<lb/>tia DR, & la circonferentia DG nel punto D, & l'angolo QDH &longs;arà mi <lb/>nore dell'angolo RDH. Adunque QDH haurà proportione minore ad HDG <lb/>che RDH ad HDG, & nell'i&longs;te&longs;&longs;o modo in tutto, &longs;e tra il C & il P &longs;i tor-<lb/>rà vn'altro punto, & tra que&longs;to, & il C vn'altro, & co&longs;i &longs;ucceßiuamente &longs;i de-<lb/>&longs;criueranno infinite circonferentie tra DO, & la circonferenza DG: dalle quali <lb/>troueremo &longs;empre la proportione minore in infinito: & co&longs;i &longs;egue, che la propor-<lb/>tione del pe&longs;o po&longs;to in D al pe&longs;o po&longs;to in E non &longs;ia tanto picciola, che non &longs;i <lb/>po&longs;&longs;a ritrouarla &longs;empre minore in infinito.

</s>

Et perche l'angolo MDG &longs;i puote <lb/>diuidere in infinito, &longs;i potrà anche diuidere quel più di grauezza che ha il D &longs;o-<lb/>pra lo E in infinito.<emph.end type="italics"/>

</s>

</figure>

</figure>

<margin.target id="note14"></margin.target><emph type="italics"/>Per la &longs;econda del terzo<emph.end type="italics"/>

</s>

<margin.target id="note15"></margin.target><emph type="italics"/>Per la vige&longs;imanona del primo.<emph.end type="italics"/>

</s>

<margin.target id="note16"></margin.target><emph type="italics"/>Per la decima ottaua del terzo.<emph.end type="italics"/>

</s>

<margin.target id="note17"></margin.target><emph type="italics"/>Per la ottaua del quinto.<emph.end type="italics"/>

</s>

<margin.target id="note18"></margin.target><emph type="italics"/>Per la vnde cima del terzo.<emph.end type="italics"/>

</s>

<margin.target id="note19"></margin.target><emph type="italics"/>Per la decima ottaua del terzo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ne bi&longs;ogna trala&longs;ciare, che <lb/>eglino hanno pre&longs;upp o&longs;to <lb/>nella demo&longs;tratione l'ango <lb/>lo<emph.end type="italics"/> K<emph type="italics"/>EG e&longs;&longs;er maggiore del <lb/>l'angolo HDC, come co <lb/>&longs;a nota: il che ben è vero &longs;e <lb/>DHE<emph.end type="italics"/>K <emph type="italics"/>&longs;ono fra loro e-<lb/>gualmente di&longs;tanti.

</s>

Ma <lb/>percioche, come eßi pari-<lb/>mente pre&longs;uppongono, le <lb/>linee DHE<emph.end type="italics"/>K <emph type="italics"/>&longs;i vanno à <lb/>trouare nel centro del mon <lb/>do, le linee DHE<emph.end type="italics"/>K <emph type="italics"/>non <lb/>&longs;aranno egualmente di&longs;tan <lb/>ti giamai, et <expan abbr="l'ãgolo">l'angolo</expan><emph.end type="italics"/> K<emph type="italics"/>EG <lb/>non &longs;olo non &longs;arà maggio-<lb/>re dall'angolo HDG, ma <lb/>minore.

</s>

Come per gra-<lb/>tia di e&longs;&longs;empio, &longs;ia tirata la <lb/>linea FG &longs;in al centro del <lb/>mondo, che &longs;ia S, & con <lb/>giungan&longs;i DS ES. Egli <lb/>è da mostrare l'angolo SE <lb/>G e&longs;&longs;ere minore dell'ango <lb/>lo SDG. Tiri&longs;i dal punto <lb/>E la linea ET, che toc-<lb/>chi il cerchio DGEF, & <lb/>dall'i&longs;te&longs;&longs;o punto &longs;ia tirata <lb/>la EV egualmente di&longs;tan<emph.end type="italics"/><lb/><arrow.to.target n="fig8"></arrow.to.target><lb/><emph type="italics"/>te da DS: Percioche dunque EVDS &longs;ono traloro egualmente di&longs;tanti, &longs;imil-<lb/>mente ET DO &longs;ono egualmente di&longs;tanti: &longs;arà l'angolo VET eguale all'ango-<lb/>lo SDO: & l'angolo TEG eguale all'angolo ODM, per e&longs;&longs;ere contenuto da <lb/>linee toccanti la circonferenza, & da circonferenze eguali.

</s>

Tutto l'angolo dun-<lb/>que VEG &longs;arà eguale all'angolo SDM. Leui&longs;i via dall'angolo SDM l'ango <lb/>lo di linee curue MDG: & dall'angolo VEG leui&longs;i via l'angolo VES, & <lb/>l'angolo VES fatto di linee rette è maggiore dell'angolo MDG fatto di linee <lb/>curue; &longs;arà il re&longs;tante angolo SEG minore dell'angolo SDG. Per laqual co&longs;a <lb/>dalle pre&longs;uppo&longs;te loro non &longs;olo il pe&longs;o posto in D &longs;arà più graue del pe&longs;o po&longs;to <lb/>in E, ma per lo contrario il pe&longs;o E &longs;arà più graue dell'i&longs;te&longs;&longs;o D.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Producono tutta via <lb/>ragioni con le quali <lb/>&longs;i sforzano di mo-<lb/>&longs;trare, che la bilan-<lb/>cia DE ritorna per <lb/>neceßità in AB e-<lb/>gualmente distante <lb/>dall'orizonte.

</s>

Pri-<lb/>ma dimo&longs;trano l'i-<lb/>&longs;te&longs;&longs;o pe&longs;o e&longs;&longs;ere più <lb/>graue in A, che <lb/>in altro &longs;ito, che <lb/>chiamano &longs;ito della <lb/>egualità, e&longs;&longs;endo la <lb/>linea AB egual-<lb/>mente di&longs;tante dal-<lb/>l'orizonte.

</s>

Da-<lb/>poi quanto è più da<emph.end type="italics"/><lb/><arrow.to.target n="fig9"></arrow.to.target><lb/><emph type="italics"/>pre&longs;&longs;o allo A, tanto e&longs;&longs;ere piu graue di qual &longs;i voglia altro più da lontano, cioè <lb/>il pe&longs;o po&longs;to in A e&longs;&longs;ere più graue, che in D; & in D, che in L: & &longs;imil-<lb/>mente in A più graue, che in N; & in N più graue, che in M. Con&longs;ide-<emph.end type="italics"/><lb/><arrow.to.target n="note20"></arrow.to.target> <emph type="italics"/>rando &longs;olamente vn pe&longs;o in vno delle braccia in sù, ouero in giù mo&longs;&longs;o.

</s>

Percio-<lb/>che dicono, po&longs;ta la trutina della bilancia in CF, il pe&longs;o me&longs;&longs;o in A è più lunge <lb/>dalla trutina che in D; & in D più lunge, che in L: peroche tirate le linee DO<emph.end type="italics"/><lb/><arrow.to.target n="note21"></arrow.to.target> <emph type="italics"/>LP à piombo di CF, la linea AC re&longs;ta maggiore di DO, & DO di e&longs;&longs;a LP, <lb/>& auiene l'i&longs;te&longs;&longs;o ne i punti NM.

</s>

Dapoi dicono da qual luogo il pe&longs;o &longs;i mo-<lb/>ue più velocemente, iui è più graue: ma egli &longs;i moue più velocemente dallo<emph.end type="italics"/><lb/><arrow.to.target n="note22"></arrow.to.target> <emph type="italics"/>A, che da altro &longs;ito; adunque egli è più graue nello A.

</s>

Con &longs;imile mo-<lb/>do, quanto più egli è da pre&longs;&longs;o allo A, tanto più velocemente &longs;i moue: <lb/>adunque nel D &longs;arà più graue, che in L. L'altra cagione poi che cauano dal mo-<emph.end type="italics"/><lb/><arrow.to.target n="note23"></arrow.to.target> <emph type="italics"/>uimento più diritto, & più torto è, che quanto il pe&longs;o di&longs;cende più diritto in archi <lb/>eguali, pare e&longs;&longs;er anco più graue; concio&longs;ia che il pe&longs;o e&longs;&longs;endo libero, & &longs;ciolto, &longs;i <lb/>moua di &longs;ua propria natura per lo diritto; ma in A egli di&longs;cende più dirittamen<emph.end type="italics"/><lb/><arrow.to.target n="note24"></arrow.to.target> <emph type="italics"/>te; dunque in A &longs;arà più graue, & dimo&longs;trano ciò pigliando l'arco AN egua-<lb/>le all'arco LD. & da i punti NL &longs;iano tirate le linee NRLQ egualmente di-<lb/>&longs;tanti dalla linea FG, laquale chiamano anche della direttione; & quelle altre &longs;e-<lb/>gheranno le linee ABDO in QR, & dal punto N &longs;ia tirata la NT à piombo <lb/>di FG: Dimo&longs;trano veramente LQ e&longs;&longs;ere eguale à PO, & NR ad e&longs;&longs;a CT, <lb/>& la linea NR e&longs;&longs;er maggiore di LQ.

</s>

Hor percioche la di&longs;ce&longs;a del pe&longs;o dallo A <lb/>fin ad N per la circonferentia di AN trapa&longs;&longs;a maggior parte della linea FG, <lb/>(che eßi chiamano pigliare di diritto) che la di&longs;ce&longs;a di L in D per la circonferenza <lb/>LD; concio&longs;ia che la di&longs;ce&longs;a AN trapaßi la linea CT, ma la di&longs;ce&longs;a LD la linea<emph.end type="italics"/><pb id="9" xlink:href="pagethumb-it/036.jpg"/><emph type="italics"/>PO, & CT è maggiore di PO, la di&longs;ce&longs;a di AN &longs;arà più diritta, che la di-<lb/>&longs;ce&longs;a di LD: &longs;arà dunque più graue il pe&longs;o po&longs;to in A, che in L, ouero in qual <lb/>&longs;i voglia altro &longs;ito, & nell'i&longs;te&longs;&longs;o modo dimo&longs;trano, che quanto il pe&longs;o è più vicino <lb/>allo A, è più graue; cioè &longs;iano le circonferenze LD DA traloro eguali, & <lb/>dal punto D &longs;ia tirata la linea DR à piombo di AB; &longs;arà la DR eguale al-<emph.end type="italics"/> <arrow.to.target n="note25"></arrow.to.target><lb/><emph type="italics"/>la CO. & dimo-<lb/>&longs;trano po&longs;cia, che <lb/>la linea DR è mag<lb/>giore della LQ, & <lb/>dicono che la &longs;ce&longs;a <lb/>di DA prende più <lb/>di &longs;ce&longs;a diritta, che <lb/>non fa LD, pe-<lb/>roche è maggiore <lb/>la linea CO, che <lb/>la OT: Per la-<lb/>qual co&longs;a il pe&longs;o &longs;a <lb/>rà più graue in D, <lb/>che in L, ilche pa<lb/>rimente auiene ne <lb/>punti NM. & <lb/>co&longs;i il pre&longs;uppo&longs;to, <lb/>per loquale dimo-<emph.end type="italics"/><lb/><arrow.to.target n="fig10"></arrow.to.target><lb/><emph type="italics"/>&longs;trano la bilancia DE ritornare in AB a&longs;fermano come noto, & manife&longs;to; cioè<emph.end type="italics"/> <arrow.to.target n="note26"></arrow.to.target><lb/><emph type="italics"/>che &longs;econdo il &longs;ito il pe&longs;o è tanto più graue, quanto nel mede&longs;imo &longs;ito manco tor-<lb/>ta è la &longs;ce&longs;a: & la cagione di cotal ritorno dicono e&longs;&longs;ere que&longs;ta; peroche la &longs;ce&longs;a del <lb/>pe&longs;o po&longs;to in D è più diritta della &longs;ce&longs;a del pe&longs;o po&longs;to in E, per pigliare il pe&longs;o<emph.end type="italics"/> <arrow.to.target n="note27"></arrow.to.target><lb/><emph type="italics"/>di E manco della direttione in de&longs;cendendo che non fa il pe&longs;o di D pur nel di&longs;cen <lb/>dere: Come &longs;e l'arco EV &longs;ia eguale à DA, & &longs;iano tirate VHET à piom<lb/>bo di FG; &longs;arà maggiore DR di TH. Per laqual co&longs;a per la pre&longs;uppo&longs;ta il pe<emph.end type="italics"/> <arrow.to.target n="note28"></arrow.to.target><lb/><emph type="italics"/>&longs;o me&longs;&longs;o in D per ri&longs;petto al &longs;ito &longs;arà più graue del pe&longs;o me&longs;&longs;o in E.

</s>

Adunque <lb/>il pe&longs;o me&longs;&longs;o in D e&longs;&longs;endo più graue &longs;i mouerà in giù, & il pe&longs;o po&longs;to in E in <lb/>&longs;u fin che la bilancia DE ritorni in AB.<emph.end type="italics"/>

</s>

</figure>

</figure>

<margin.target id="note20"></margin.target><emph type="italics"/>Il Cardano nel primo della &longs;ottigliezza.<emph.end type="italics"/>

</s>

<margin.target id="note21"></margin.target><emph type="italics"/>Giordano nella quarta propo&longs;itione<emph.end type="italics"/>

</s>

<margin.target id="note22"></margin.target><emph type="italics"/>Il Tartaglia nella quinta propo&longs;itione.<emph.end type="italics"/>

</s>

<margin.target id="note23"></margin.target><emph type="italics"/>Il Cardano.

</s>

Giordano al la propo&longs;itio ne quarta.<emph.end type="italics"/>

</s>

<margin.target id="note24"></margin.target><emph type="italics"/>Il Tartaglia alla pro po&longs;itione<emph.end type="italics"/> 5.

</s>

<margin.target id="note25"></margin.target><emph type="italics"/>Per la trige &longs;imaquarta del primo.<emph.end type="italics"/>

</s>

<margin.target id="note26"></margin.target><emph type="italics"/>Giordane nella quarta pre &longs;apoosta<emph.end type="italics"/>

</s>

<margin.target id="note27"></margin.target><emph type="italics"/>Giordano nella &longs;econda propo&longs;itione.<emph.end type="italics"/>

</s>

<margin.target id="note28"></margin.target><emph type="italics"/>Il Tartaglia nella quinta propo&longs;icione.<emph.end type="italics"/>

</s>

<emph type="italics"/>L'altra ragione ancora di que&longs;to ritorno è, che <expan abbr="quãdo">quando</expan> la trutina della bilancia è &longs;opra<emph.end type="italics"/> <arrow.to.target n="note29"></arrow.to.target><lb/><emph type="italics"/>dilei in CF; la linea CG è la meta: & percio che l'angolo GCD è maggiore <lb/>dell'angolo GCE, & l'angolo maggiore dalla meta rende più graue il pe&longs;o: adun-<lb/>que &longs;tando la trutina della bilancia di &longs;opra &longs;arà più graue il pe&longs;o in D, che in E, <lb/>& perciò il D ritorner à nello A, & lo E nel B.<emph.end type="italics"/>

</s>

<margin.target id="note29"></margin.target><emph type="italics"/>Il Cardano.<emph.end type="italics"/>

</s>

Meta è pur voce Latina co&longs;tumata da gli antichi ne i giuo chi, & conte&longs;e fatte ne i cer <lb/>chi murati, & ne i Theatri, percio che il principio, oue &longs;i dauano le mo&longs;&longs;e a' corri-<lb/>tori, &longs;i chiamaua Carcere, & il fine Meta; di modo, che meta viene à dire termine <lb/>& fine: & piu in altro &longs;ignificato il luogo piu ba&longs;&longs;o, & in&longs;imo.

</s>

Hor qui &longs;i puote <pb id="9v" xlink:href="pagethumb-it/037.jpg"/>intendere ad ambidue i modi, cioè che la linea CG &longs;ia la meta, cioè il termine <lb/>& fine, nelquale ha da peruenire il pe&longs;o collo cato nella bilancia; ouero il luogo <lb/>infimo della circonferenza, alquale capita il pe&longs;o per natura.

</s>

Doue &longs;criue l'Auto <lb/>re l'angolo maggiore dalla Meta, vuol dire l'angolo, che fa il braccio della bilan-<lb/>cia con la Meta CG.

</s>

<emph type="italics"/>Et co&longs;i <expan abbr="cõ">com</expan> que&longs;te ragioni &longs;i sforzano dimo&longs;trare la bilancia DE ritornare in AB; le <lb/>quali al parer mio &longs;i po&longs;&longs;ono ageuolmente &longs;oluere.<emph.end type="italics"/>

</s>

<emph type="italics"/>Primieramente dunque in quanto s'appartiene alle ragioni, che dicono il pe&longs;o me&longs;&longs;o <lb/>in A e&longs;&longs;ere piu graue, che in altro &longs;ito, lequali cauano dalla di&longs;tanza piu da lonta-<lb/>no, & piu da pre&longs;&longs;o della linea FG, & dal mouimento piu veloce, & piu diritto <lb/>dal punto A. In prima non dimo&longs;trano veramente perche il pe&longs;o &longs;i moua piu velo-<lb/>cemente dallo A, che da al tro &longs;ito.

</s>

ne perche &longs;ia maggiore CA di DO, & DO <lb/>di LP, per que&longs;to, come per vera cagione, &longs;egue il pe&longs;o po&longs;to in A e&longs;&longs;ere piu gra-<lb/>ue di quello, che è in D, & quello di D, di quel che &longs;tà in L, percioche non &longs;i queta <lb/>l'intelletto, &longs;e di ciò altra cagione non &longs;i dimo&longs;tra, parendo &longs;egno piu to&longs;to, che vera <lb/>cagione.

</s>

Quello ste&longs;&longs;o accade parimente all'altra ragione, laquale adducono dal <lb/>mouimento piu diritto, & piu torto.

</s>

Oltre à ciò tutte quelle co&longs;e, che per&longs;uadono <lb/>per via del <expan abbr="mouim&etilde;">mouimen</expan> <lb/>to piu veloce, & <lb/>piu tardo il pe&longs;o in <lb/>A e&longs;&longs;ere piu graue, <lb/>che in D, non per-<lb/>ciò dimo &longs;trano, che <lb/>il pe&longs;o in A, in <expan abbr="quã">quam</expan> <lb/>to è in A, &longs;ia piu <lb/>graue del pe&longs;o D, in <lb/>quanto è in D, ma <lb/>in quanto &longs;i parte <lb/>da i punti DA. <lb/>Onde, <expan abbr="auãti">auanti</expan> che piu <lb/>oltre &longs;i proceda, pri <lb/>ma dimo&longs;trerò, che <lb/>il pe&longs;o quanto egli <lb/>è piu da pre&longs;&longs;o ad <lb/>FG manco graua, <lb/>&longs;i in quanto egli &longs;tà <lb/>nel &longs;ito, oue &longs;i ritro<emph.end type="italics"/><lb/><arrow.to.target n="fig11"></arrow.to.target><lb/><emph type="italics"/>ua, come anche in quanto &longs;i parte da quello: & in&longs;ieme, che egli è fal&longs;o il pe&longs;o e&longs;&longs;ere <lb/>piu graue in A, che in altro &longs;ito.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Tiri&longs;i la FG fin al centro del mondo, che &longs;ia in S, & dal punto S tiri&longs;i anco vna linea, <lb/>che tocchi il cerchio AFBG. non potrà già questa linea tirata dal punto S toc-<lb/>care il cerchio nel punto A; imperoche tirata la linea AS, il triangolo ACS ver<emph.end type="italics"/><pb id="10" xlink:href="pagethumb-it/038.jpg"/><emph type="italics"/>rebbe ad hauere due angoli retti, cioè SAC, & ACS, che è impoßibile: ne me <lb/>no toccherà &longs;opra il punto A nella circonferenza AF; peroche &longs;egherebbe il cer-<emph.end type="italics"/> 2<arrow.to.target n="note30"></arrow.to.target><lb/><emph type="italics"/>chio.

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Toccherà dunque &longs;otto, & &longs;ia SO: &longs;iano dapoi congiunte le lince SD SL, <lb/>lequali &longs;eghino la circonferenza AOG ne' punti<emph.end type="italics"/> K<emph type="italics"/>H, & &longs;iano ancho congiunte le <lb/>linee C<emph.end type="italics"/>K <emph type="italics"/>CH. Et percioche il pe&longs;o, quanto egli è piu da pre&longs;&longs;o di F, tanto piu an-<lb/>co &longs;tà &longs;opra il centro; come il pe&longs;o in D preme, & &longs;tà piu &longs;opra il punto del volgi-<lb/>mento C, come à centro, cioè in D piu graua &longs;opra la linea CD, che &longs;e egli fo&longs;&longs;e in A <lb/>&longs;opra la linea CA: & dauantaggio piu in L &longs;opra la linea CL. imperoche e&longs;&longs;endo <lb/>li tre angoli di cia&longs;cun triangolo eguali à due angoli retti, & l'angolo DC<emph.end type="italics"/>K <emph type="italics"/>del <lb/>triangolo DC<emph.end type="italics"/>K, <emph type="italics"/>che è di due lati eguali &longs;ia <lb/>minore dell'angolo LCH del <expan abbr="triãgolo">triangolo</expan> LCH, <lb/>che è pur di due lati eguali: &longs;aranno gli altri <lb/>alla ba&longs;e, cioè CD<emph.end type="italics"/>K <emph type="italics"/>C<emph.end type="italics"/>K<emph type="italics"/>D in&longs;ieme pre&longs;i <lb/>maggiori de gli altri CLH CHL; & le <lb/>metà di que&longs;ti, cioè l'angolo CDS &longs;arà mag <lb/>giore dell'angolo CLS. E&longs;&longs;endo adunque <lb/>CLS minore, la linea CL piu &longs;i acco&longs;terà <lb/>al mouimento naturale del pe&longs;o me&longs;&longs;o in L <lb/>del tutto &longs;ciolto; cioè à dire alla linea LS, <lb/>che CD al mouimento DS: percioche il pe <lb/>&longs;o po&longs;to in L libero, & &longs;ciolto &longs;i mouerebbe <lb/>ver&longs;o il centro del mondo per LS, & il pe-<lb/>&longs;o po&longs;to in D per DS. Ma perche il pe&longs;o <lb/>me&longs;&longs;o in L graua tutto &longs;opra LS, & quello <lb/>che è in D &longs;opra DS, il pe&longs;o in L grauerà <lb/>pu &longs;opra la linea CL, che quello, che &longs;tà in <lb/>D &longs;opra la linea DC. Adunque la linea <lb/>CL &longs;o&longs;terrà piu il pe&longs;o, che lalinea CD, & <lb/>nel modo iste&longs;&longs;o quanto piu il pe&longs;o &longs;arà da <lb/>pre&longs;&longs;o ad F, &longs;i dimo strerà piu e&longs;&longs;er &longs;o&longs;tenuto <lb/>dalla linea CL per cotesta cagione, peroche <lb/>&longs;empre l'angolo CLS &longs;arebbe minore, la-<lb/>qual co&longs;a etiandio èmanife&longs;ta; perche &longs;e le li <lb/>nee CL, & LS s'incontra&longs;&longs;ero in vna li <lb/>nea, ilche auiene in FCS, all'hora la linea <lb/>CF &longs;o&longs;terrebbe tutto il pe&longs;o, che è in F, & <lb/>lo renderebbe immobile, nè haurebbe niuna <lb/>grauezza in tutto nella circonferenza del cer <lb/>chio.

</s>

Li&longs;te&longs;&longs;o pe&longs;o dunque per la diuer&longs;ità<emph.end type="italics"/><lb/><arrow.to.target n="fig12"></arrow.to.target><lb/><emph type="italics"/>de' &longs;iti &longs;arà piu graue, & piu lieue.

</s>

& que&longs;to non già percio che per ragione del &longs;ito <lb/>alcuna volta egli acqui&longs;ti veramente grauezza maggiore, & alcuna volta la perda, <lb/>e&longs;&longs;endo &longs;empre della i&longs;te&longs;&longs;a grauezza, troui&longs;i douunque &longs;i voglia: ma percioche egli<emph.end type="italics"/><pb id="10v" xlink:href="pagethumb-it/039.jpg"/><emph type="italics"/>graua piu, & meno nella circonferenza, come in D piu graua &longs;opra la circonferenza <lb/>DA, che in L &longs;opra la circonferenza LD: cioè &longs;e il pe&longs;o &longs;arà &longs;o&longs;tenuto dalle circon <lb/>ferenze, & dalle linee diritte; la circonferenza AD &longs;o&longs;terrà piu il pe&longs;o po&longs;to in D, <lb/>che la circonferenza DL, &longs;tando il pe&longs;o in L; peroche meno aiuta CD, che CL. <lb/>Oltre à ciò quando il pe&longs;o è in L, &longs;e egli fo&longs;&longs;e del tutto libero & &longs;ciolto, &longs;i mouerebbe <lb/>in giu per LS, &longs;e non gliene fu&longs;&longs;e vietato dalla linea CL, laquale sforza il pe&longs;o po&longs;to <lb/>in L à mouer&longs;i oltre la linea LS per la circonferenza LD, & lo caccia in certo mo <lb/>do, & in cacciandolo viene in parte à &longs;o&longs;tenerlo; percioche &longs;e non lo &longs;o&longs;tene&longs;&longs;e, & <lb/>gli face&longs;&longs;e re&longs;i&longs;tenza, &longs;i mouerebbe in giu per la linea LS, ma non già per la cir-<lb/>conferenza LD. Similmente la CD fa re&longs;i&longs;tenza al pe&longs;o po&longs;to in D, sforzan-<lb/>dolo à mouer&longs;i per la circonferenza DA. Nell'iste&longs;&longs;o modo &longs;tando il pe&longs;o in A, <lb/>la linea CA con&longs;tringerà il pe&longs;o à mouer&longs;i <lb/>oltre la linea AS per la circoferenza AO; <lb/>peroche l'angolo CAS è acuto, e&longs;&longs;endo lo <lb/>angolo ACS retto.

</s>

Adunque le linee <lb/>CA CD in qualche parte, ma non già e-<lb/>gualmente fanno re&longs;istenza al pe&longs;o.

</s>

& qua <lb/>lunque volta l'angolo, che è nella circonfe-<lb/>renza del cerchio fatto dalle linee che e&longs;cono <lb/>dal centro del monde S, & dal centro C &longs;a-<lb/>rà acuto, dimo&longs;treremo auenire l'i&longs;te&longs;&longs;o.

</s>

Hor <lb/>percioche l'angolo mi&longs;to CLD è eguale à <lb/>l'angolo CDA, per e&longs;&longs;ere conteuuto da <lb/>mezi diametri, & dall'i&longs;te&longs;&longs;a circonferenza; <lb/>& l'angolo CLS è minore dell'angolo <lb/>CDS; &longs;arà il reflante SLD maggiore <lb/>del re&longs;tante SDA. Per laqual co&longs;a la cir <lb/>conferenza DA, cioè la di&longs;ce&longs;a del pe&longs;o <lb/>in D &longs;ara piu da pre&longs;&longs;o al mouimento natu-<lb/>rale del pe&longs;o &longs;ciolto me&longs;&longs;o in D, cioè della li-<lb/>nea DS, che la circonferenza LD della <lb/>linea LS. Meno dunque farà re&longs;i&longs;tenza la <lb/>linea CD al pe&longs;o po&longs;to in D, che la linea <lb/>CL al pe&longs;o po&longs;to in L. Però la linea CD <lb/>&longs;o&longs;terrà meno, che CL, & il pe&longs;o &longs;arà <lb/>piu libero in D, che in L: mouendo&longs;i piu <lb/>naturalmente il pe&longs;o per DA, che per LD. <lb/>Per laqual co&longs;a piu graue &longs;arà in D, che in <lb/>L. Similmente dimo&longs;treremo, che CA man <lb/>co&longs;o&longs;tiene, che CD & che il pe&longs;o piu in A, <lb/>che in D è libero, & piu graue.

</s>

Dopo dalla<emph.end type="italics"/><lb/><arrow.to.target n="fig13"></arrow.to.target><lb/><emph type="italics"/>parte di &longs;otto per l'i&longs;te&longs;&longs;e cagioni, quanto il pe&longs;o &longs;arà piu da pre&longs;&longs;o al G, &longs;arà piu ri-<emph.end type="italics"/><pb id="11" xlink:href="pagethumb-it/040.jpg"/><emph type="italics"/>tenuto, come in H dalla linea CH, che in<emph.end type="italics"/> K <emph type="italics"/>dalla linea C<emph.end type="italics"/>K: <emph type="italics"/>percioche e&longs;&longs;en<emph.end type="italics"/> <arrow.to.target n="note31"></arrow.to.target><lb/><emph type="italics"/>do l'angolo CHS maggiore dell'angolo C<emph.end type="italics"/>K<emph type="italics"/>S, le linee CH HS, &longs;i acco&longs;te-<lb/>ranno piu alla direttione, che C<emph.end type="italics"/>K K<emph type="italics"/>S. & per que&longs;to &longs;arà piu ritenuto il pe&longs;o da <lb/>CH, che da C<emph.end type="italics"/>K; <emph type="italics"/>percioche &longs;e CH HS &longs;i incontra&longs;&longs;ero in vna linea, come auie-<lb/>ne &longs;tando il pe&longs;o in G, allbora la linea CG &longs;o&longs;terrebbe tutto il pe&longs;o in G, per <lb/>modo che &longs;tarebbe immobile.

</s>

Quanto minore dunque &longs;arà l'angolo contenuto dal <lb/>la linea CH, & dalla di&longs;ce&longs;a del pe&longs;o &longs;ciolto, cioè dalla linea HS, tanto meno <lb/>anco quella linea ritenirà il pe&longs;o, & doue &longs;arà manco ritenuto, iui &longs;arà piu libero, & <lb/>piu graue.

</s>

Oltre à ciò &longs;e il pe&longs;o fo&longs;&longs;e libero in K, & &longs;ciolto, &longs;i mouerebbe per la li-<lb/>nea KS, ma egli è impedito dalla linea CK, laquale sforza il pe&longs;o a mouer&longs;i di <lb/>qua dalla linea KS per la circonferenza KH; percio che lo ritira in certo modo, <lb/>& in ritirandolo viene a &longs;o&longs;tenerlo, peroche &longs;e non lo &longs;o&longs;tene&longs;&longs;e, &longs;i mouerebbe il pe-<lb/>&longs;o in giu per la linea diritta KS, ma non per la circonferenza KH.

</s>

Similmente <lb/>la CH ritiene il pe&longs;o, sforzandolo a mouer&longs;i per la circonferenza HG.

</s>

Et percio-<lb/>che l'angolo CHS è maggiore dell'angolo CKS, leuati via gli angoli eguali <lb/>CHG, C<emph.end type="italics"/>K<emph type="italics"/>H, &longs;arà il re&longs;tante SHG maggiore del re&longs;tante S<emph.end type="italics"/>K<emph type="italics"/>H.

</s>

Adunque <lb/>la circonferenza KH, cioè la di&longs;ce&longs;a del pe&longs;o po&longs;to in K &longs;arà piu da pre&longs;&longs;o al mo-<lb/>uimento naturale del pe&longs;o po&longs;to in K &longs;ciolto, cioè alla linea KS, che la circonfe-<lb/>renza HG alla linea HS.

</s>

Per laqual co&longs;a meno ritiene la linea CK, che CH, <lb/>mouend o&longs;i il pe&longs;o piu naturalmente per KH, che per HG, Con ragione &longs;imile <lb/>anco &longs;i mo&longs;trerà, che quanto minore &longs;arà l'angolo SKH, la linea CK &longs;o&longs;terrà <lb/>meno.

</s>

Stando dunque il pe&longs;o in O, percioche l'angolo SOC non &longs;olamente è <lb/>minore dell'angolo CKS, ma anco il minimo di tutti gli angoli, che e&longs;con da i pun <lb/>ti CS, & hanno la cima nella circonferenza OKG; &longs;arà l'angolo SOK il mi <lb/>nimo &longs;i dell'angolo SKH, come de tutti gli altri co&longs;i fatti.

</s>

Adunque la di&longs;ce&longs;a <lb/>del pe&longs;o po&longs;to in O &longs;arà piu da pre&longs;&longs;o al mouimento naturale di e&longs;&longs;o pe&longs;o &longs;ciolto in <lb/>O, che in altro &longs;ito della circonferenza OKG: & la linea CO meno &longs;o&longs;tenirà <lb/>il pe&longs;o, che &longs;e egli fo&longs;&longs;e in qual &longs;i voglia altro &longs;ito della i&longs;te&longs;&longs;a circonferenza OG.<lb/>

</s>

Similmente perche l'angolo del toccamento SOK è minore &longs;i dell'angolo SDA, <lb/>&longs;i dello SAO, & &longs;i di qual &longs;i voglia altro &longs;imile; &longs;arà la &longs;ce&longs;a del pe&longs;o me&longs;&longs;o in O <lb/>piu da pre&longs;&longs;o al mouimento naturale di e&longs;&longs;o pe&longs;o &longs;ciolto in O, che in altro &longs;ito del-<lb/>la <expan abbr="circõfer&etilde;za">circonferenza</expan> ODF.

</s>

Oltre a ciò perche la linea CO no puote &longs;pingere il pe&longs;o po&longs;to <lb/>in O mentre egli &longs;i moue in giu, per modo che egli &longs;i moua oltre la linea OS, per <lb/>cioche la linea OS non taglia il cerchio, ma lo tocca; & l'angolo SOC è retto <lb/>& non acuto, il pe&longs;o po&longs;to in O non grauerà niente &longs;opra la linea CO, ne &longs;tarà <lb/>&longs;opra il centro, come accaderebbe in qual &longs;i voglia altro punto &longs;opra l'O.

</s>

Sarà dun-<lb/>que il pe&longs;o po&longs;to in O per que&longs;te cagioni libero, & &longs;ciolto piu in que&longs;to &longs;ito, che in <lb/>qual &longs;i voglia altro della circonferenza FOG; & perciò in que&longs;to &longs;arà piu graue, <lb/>cioè a dire piu grauerà, che in altro &longs;ito.

</s>

Et quanto &longs;arà piu da pre&longs;&longs;o ad O, &longs;arà <lb/>piu graue di quello, che &longs;e fo&longs;&longs;e piu da lunge: & la linea CO &longs;arà egualmente di-<lb/>&longs;tante dall'orizonte: non pero all'orizonte del punto C (come &longs;timano e&longs;&longs;i) ma <lb/>del pe&longs;o po&longs;to in O, douendo&longs;i prendere l'orizonte dal centro della grauezza del pe <lb/>&longs;o.

</s>

Lequali co&longs;e tutte bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

</figure>

</figure>

<margin.target id="note30"></margin.target><emph type="italics"/>Per la decimaottaua del terzo<emph.end type="italics"/>

</s>

<margin.target id="note31"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 21. <emph type="italics"/>del prim.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ma &longs;e il braccio della bilancia fo&longs;&longs;e maggiore <lb/>di CO, come per la quantità di CD; <lb/>&longs;arà parimente il pe&longs;o me&longs;&longs;o in O piu gra-<lb/>ue.

</s>

De&longs;criua&longs;i il cerchio OH, il cui <lb/>centro &longs;ia D, & il mezo diametro DO. <lb/>il cerchio OH toccherà il cerchio FOG <lb/>nel punto O, & toccherà anche la linea<emph.end type="italics"/><lb/><arrow.to.target n="note32"></arrow.to.target> <emph type="italics"/>OS nel punto mede&longs;imo, laquale è la &longs;ce-<lb/>&longs;a naturale, & diritta del pe&longs;o po&longs;to in O.<emph.end type="italics"/><lb/><arrow.to.target n="note33"></arrow.to.target>

</s>

<emph type="italics"/>Et percioche l'angolo SOH è minore del <lb/>l'angolo SOG, &longs;arà la &longs;ce&longs;a del pe&longs;o po&longs;to <lb/>in O per la circonferenza OH piu dapre&longs; <lb/>&longs;o al mouimento naturale OS, che per la <lb/>circonferenza OG.

</s>

Piu libero dunque <lb/>& &longs;ciolto, & per con&longs;equente piu graue &longs;a-<lb/>ràin O, &longs;tante il centro della bilancia in <lb/>D, che in C.

</s>

Similmente &longs;i mo&longs;trerà, <lb/>che quanto piu grande &longs;arà il braccio DO, <lb/>il pe&longs;o po&longs;to in O &longs;arà d'auantaggio piu <lb/>graue.<emph.end type="italics"/>

</s>

<margin.target id="note32"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del terzo<emph.end type="italics"/>

</s>

<margin.target id="note33"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 18. <emph type="italics"/>del terzo.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Ma &longs;e l'iste&longs;&longs;o cerchio AFBG co'l &longs;uo centro R &longs;arà piu da pre&longs;&longs;o ad S centro <lb/>del mondo, & dal punto S &longs;ia tirata vna linea, che tocchi il cerchio ST, il pun-<lb/>to T, (doue il pe&longs;o è piu graue) &longs;arà piu lontano dal punto A, che il punto O: <lb/>percioche &longs;iano tirate da i punti OT le linee OMTN à piombo di CS, & <lb/>congiungan &longs;i RT, & &longs;ia il centro R nella linea CS, & la linea ARB &longs;ia <lb/>egualmente di&longs;tante ad ACB.

</s>

Percioche dunque i triangoli COS RTS &longs;ono<emph.end type="italics"/><lb/><arrow.to.target n="note34"></arrow.to.target> <emph type="italics"/>di angoli retti, &longs;arà SC à CO, come CO à CM.

</s>

<s id="id.2.1.171.1.2">Similmente SR ad<emph.end type="italics"/><lb/><arrow.to.target n="note35"></arrow.to.target> <emph type="italics"/>RT, come RT ad RN. E&longs;&longs;endo dunque RT eguale à CO, & SC mag <lb/>giore di RS: haurà proportione maggiore SC à CO, che SR ad RT. on<emph.end type="italics"/><lb/><arrow.to.target n="note36"></arrow.to.target> <emph type="italics"/>de baurà parimente proportione maggiore CO à CM, che RT ad RN. &longs;a <lb/>rà dunque minore CM, che RN.

</s>

Tagli&longs;i dunque RN in P &longs;i fattamen-<emph.end type="italics"/><pb id="12" xlink:href="pagethumb-it/042.jpg"/><emph type="italics"/>te, che RP &longs;ia eguale à CM; & dal <lb/><expan abbr="p&utilde;to">punto</expan> P &longs;ia tirata la linea PQ egual <lb/>mente di&longs;tante dalle linee MONT, <lb/>laquale tagli la <expan abbr="circõfer&etilde;za">circonferenza</expan> AT in Q, <lb/>& in fine <expan abbr="cõgiõgan&longs;i">congiongan&longs;i</expan> la RQ.

</s>

Hor per <lb/>cioche le due CO CM &longs;ono eguali à <lb/>le due RQ RP, & l'angolo CMO<emph.end type="italics"/> <arrow.to.target n="note37"></arrow.to.target><lb/><emph type="italics"/>è eguale all'angolo RPQ; &longs;arà an-<lb/>che l'angolo MCO eguale all'angolo <lb/>PRQ.

</s>

Ma l'angolo MCA retto <lb/>è eguale all'angolo PRA retto; a-<lb/>dunque il re&longs;tante OCA al restante<emph.end type="italics"/> <arrow.to.target n="note38"></arrow.to.target><lb/><emph type="italics"/>QRA &longs;arà eguale, & la circonferen-<lb/>za OA parimente eguale alla circon <lb/>ferenza QA.

</s>

Però il punto T per <lb/>e&longs;&longs;ere piu di&longs;tante dal punto A, che <lb/>Q, &longs;arà anco piu di&longs;tante dal punto <lb/>A, che il punto O.

</s>

Dimo&longs;trera&longs;&longs;i pa<lb/>rimente, che quanto piu il cerchio &longs;arà <lb/>vicino al centro del mondo, che egli &longs;a <lb/>rà anco piu lontano.

</s>

Et co&longs;i come pri-<lb/>ma dimo&longs;trera&longs;&longs;i il pe&longs;o nella cir confe-<lb/>renza TAF &longs;tar &longs;opra il centro R, <lb/>ma nella circonferenza TG e&longs;&longs;ere ri-<lb/>tenuto dalla linea, & ritrouar&longs;i piu gra<lb/>ue nel punto T.<emph.end type="italics"/>

</s>

<margin.target id="note34"></margin.target><emph type="italics"/>Per la ottaua del &longs;esto.<emph.end type="italics"/>

</s>

<margin.target id="note35"></margin.target><emph type="italics"/>Per la ottaua del quito<emph.end type="italics"/>

</s>

<margin.target id="note36"></margin.target><emph type="italics"/>Per la decima del quinto.<emph.end type="italics"/>

</s>

<margin.target id="note37"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del &longs;esto.<emph.end type="italics"/>

</s>

<margin.target id="note38"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 26. <emph type="italics"/>del terzo.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Che &longs;e il punto G fo&longs;&longs;e nel centro del mondo; allhora quanto piu il pe&longs;o &longs;arà da pre&longs;&longs;o al <lb/>G, &longs;arà piu graue: & douunque &longs;ia po&longs;to il pe&longs;o, fuor che nel G &longs;empre &longs;tarà &longs;opra <lb/>il centro C, come in<emph.end type="italics"/> K<emph type="italics"/>: Imperoche tirata la linea G<emph.end type="italics"/>K; <emph type="italics"/>que&longs;ta (&longs;e condo laqua <lb/>le &longs;i fa il mouimento naturale del pe&longs;o) in&longs;ieme co'l braccio della bilancia<emph.end type="italics"/> K<emph type="italics"/>C <lb/>farà vn'angolo acuto, peroche <lb/>gli angoli posti alla ba&longs;e in<emph.end type="italics"/> K <lb/><emph type="italics"/>& G del triangolo di due la <lb/>ti eguali C<emph.end type="italics"/>K<emph type="italics"/>G &longs;ono &longs;empre <lb/>acuti.

</s>

Hor &longs;iano paragonate <lb/>in&longs;ieme que&longs;te due co&longs;e, cioè il <lb/>pe&longs;o posto in<emph.end type="italics"/> K, <emph type="italics"/>& quello, <lb/>che è po&longs;to in D, &longs;arà il pe&longs;o <lb/>in K piu graue, che quello <lb/>in D; imperoche tirata la li-<lb/>nea DG, e&longs;&longs;endo che li tre an <lb/>goli di cia&longs;cuno triangolo &longs;iano <lb/>eguali à due angoli retti, & <lb/>l'angolo DCG del triangolo <lb/>CDG di due lati eguali &longs;ia <lb/>maggiore dell'angolo KCG <lb/>del triangolo CKG di due <lb/>lati eguali; &longs;aranno gli altri an <lb/>goli alla ba&longs;e DGC GDC <lb/>pre&longs;i in&longs;ieme minori de gli al-<lb/>tri KGC GKC pre&longs;i in&longs;ie<emph.end type="italics"/><lb/><arrow.to.target n="fig14"></arrow.to.target><lb/><emph type="italics"/>me; & la metà di questi, cioè l'angolo CDG &longs;arà minore dell'angolo CKG: <lb/>Per laqual co&longs;a mouendo&longs;i il pe&longs;o po&longs;to in K &longs;ciolto naturalmente per KG, & <lb/>il pe&longs;o po&longs;to in D per DG come per &longs;patij, per i quali &longs;ono portati nel centro del <lb/>mondo; la linea CD, cioè il braccio della bilancia &longs;i acco&longs;terà piu al mouimento <lb/>naturale del pe&longs;o po&longs;to in D <expan abbr="totalm&etilde;te">totalmente</expan> &longs;ciolto, alla linea cioè DG, che CK al <lb/>mouimento &longs;atto &longs;econdo KG.

</s>

So&longs;tenterà dunque piu la linea CD, che CK. <lb/>& perciò il pe&longs;o po&longs;to in K per le co&longs;e di &longs;opra dette &longs;arà piu graue, che in D.

</s>

Ol-<lb/>tre à ciò, perche &longs;e il pe&longs;o po&longs;to in K fo&longs;&longs;e del tutto libero, & &longs;ciolto, &longs;i mouerebbe <lb/>in giu per KG, &longs;e egli non fo&longs;&longs;e impedito dalla linea CK, laquale sforza il pe&longs;o <lb/>à mouer&longs;i oltra la linea KG per la circonferenza KH; la linea KG &longs;o&longs;tente-<lb/>rà il pe&longs;o in parte, & gli farà re&longs;istenza, sforzandolo à mouer&longs;i per la circonferenza <lb/>KH.

</s>

Et percioche l'angolo CDG è minore dell'angolo CKG, & l'angolo <lb/>CDK è eguale all'angolo CKH, &longs;arà l'angolo re&longs;tante GDK maggiore del re <lb/>&longs;tante GKH.

</s>

Dunque la circonferenza KH &longs;arà piu da pre&longs;&longs;o al mouimento <lb/>naturale del pe&longs;o &longs;ciolto po&longs;to in K, cioè alla linea KG, che la circonferenza <lb/>DK alla linea DG.

</s>

Per laqual co&longs;a la linea CD &longs;a piu re&longs;i&longs;tenza al pe&longs;o po&longs;to <lb/>in D, che la linea CK al pe&longs;o posto in K.

</s>

Adunque il pe&longs;o po&longs;to in K &longs;arà<emph.end type="italics"/><pb id="13" xlink:href="pagethumb-it/044.jpg"/><emph type="italics"/>piu graue, che in D.

</s>

Similmente mostrera&longs;&longs;i, che quanto il pe&longs;o &longs;arà piu da pre&longs;&longs;o <lb/>ad F, come in L manco grauerà; ma quanto piu da pre&longs;&longs;o &longs;i trouerà al G, co-<lb/>me in H, e&longs;&longs;ere piu graue.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Che &longs;e il centro del mondo fo&longs;&longs;e in S fra i punti CG;

</s>

Primieramente &longs;i mo&longs;trerà nel <lb/>modo i&longs;te&longs;&longs;o, che il pe&longs;o in qualunque luogo po&longs;to starà &longs;opra il centro C, come in <lb/>H: peroche tirate le li-<lb/>nee HG HS, l'angolo <lb/>che è alla ba&longs;e GHC del <lb/><expan abbr="triãgolo">triangolo</expan> di due lati eguali <lb/>CHG è &longs;empre acuto: <lb/>Perlaqual co&longs;a anco SHC <lb/>minor di lui &longs;arà parimen <lb/>te &longs;empre acuto.

</s>

ma &longs;ia ti <lb/>rata dal punto S la linea <lb/>SK à piombo di CS. <lb/>

</s>

Dico che il pe&longs;o è piu gra-<lb/>ue in<emph.end type="italics"/> K, <emph type="italics"/>che in alcun'al <lb/>tro &longs;ito della circonferen <lb/>za FKG; & quanto <lb/>piu da pre&longs;&longs;o &longs;arà allo F, <lb/>ouero al G meno graue-<lb/>rà.

</s>

Prendan&longs;i ver&longs;o lo <lb/>F i punti DL, & con <lb/><expan abbr="giungã&longs;i">giungan&longs;i</expan> le linee LC LS <lb/>DC DS, & &longs;iano al-<emph.end type="italics"/><lb/><arrow.to.target n="fig15"></arrow.to.target><lb/><emph type="italics"/>lungate le linee LS DS KS HS fin'alla <expan abbr="circõferenza">circonferenza</expan> del cerchio in EM NO; <lb/>& &longs;iano <expan abbr="cõgiunte">congiunte</expan> CE, CM, CN, CO.

</s>

Hor percioche LE DM &longs;i taglia-<lb/>no in&longs;ieme in S, &longs;arà il rettangolo LSE eguale al rettangolo DSM.

</s>

Onde &longs;i co<emph.end type="italics"/> <arrow.to.target n="note39"></arrow.to.target><lb/><emph type="italics"/>me è la LS ver&longs;o la DS, co&longs;i &longs;arà la SM ver&longs;ola SE; ma è maggior la LS <lb/>della DS; & la SM di e&longs;&longs;a SE.

</s>

Dunque LS SE pre&longs;e in&longs;ieme &longs;aranno mag-<emph.end type="italics"/> <arrow.to.target n="note40"></arrow.to.target><lb/><emph type="italics"/>giori delle DS SM. & per la ragion i&longs;te&longs;&longs;a &longs;i mo&longs;trerà la KN e&longs;&longs;er minore di DM. <lb/>

</s>

Di piu percioche il rettangolo OSH è eguale alrett'angolo KSN; per la mede&longs;i-<emph.end type="italics"/> <arrow.to.target n="note41"></arrow.to.target><lb/><emph type="italics"/>ma ragione la HO &longs;arà maggiore della KN. & nell'i&longs;te&longs;&longs;o modo in tutto la<emph.end type="italics"/> <arrow.to.target n="note42"></arrow.to.target><lb/><emph type="italics"/>KN &longs;i dimostrerà minore di tutte le altre linee, che pa&longs;&longs;ino per lo punto S.

</s>

Et <lb/>percioche de i triangoli di due lati eguali CLE DCM i lati LC CE &longs;ono e-<lb/>guali a i lati DC CM; & la ba&longs;e LE è maggiore di DM: &longs;arà l'angolo <lb/>LCE maggiore dell'angolo DCM.

</s>

Per laqual co&longs;a gli angoli CLE CEL po<emph.end type="italics"/> <arrow.to.target n="note43"></arrow.to.target><lb/><emph type="italics"/>sti alla ba&longs;e tolti in&longs;ieme &longs;aranno minori de gli angoli CDM CMD; & le me-<lb/>tà di que&longs;ti, cioè l'angolo CLS &longs;arà minore dell'angolo CDS. Dunque il pe&longs;o po <lb/>&longs;to in L &longs;opra la linea LC grauerà piu, che po&longs;to in D &longs;opra la DC; & piu <lb/>&longs;tarà &longs;opra il centro in L, che in D.

</s>

Similmente &longs;i mo&longs;trerà, che il pe&longs;o in D<emph.end type="italics"/><pb id="13v" xlink:href="pagethumb-it/045.jpg"/><emph type="italics"/>&longs;tarà piu &longs;opra il centro C, che in K. Adunque il pe&longs;o po&longs;to in K &longs;arà piu <lb/>graue, che in D, & in D, che in L. & con la mede&longs;ima ragione in tutto, pero-<lb/>che KN è minore di HO, &longs;arà l'angolo CKS maggiore dell'angolo CHS. <lb/>

</s>

Per laqual co&longs;a il pe&longs;o posto in H &longs;tarà piu &longs;opra il centro C, che in<emph.end type="italics"/> K; <emph type="italics"/>& in que-<lb/>&longs;ta maniera &longs;i mostrerà, che douunque &longs;ia il pe&longs;o nella circonferenza FDG, manco <lb/>starà &longs;opra il centro quando &longs;arà po&longs;to in K, che in altro &longs;ito: & quanto piu da <lb/>pre&longs;&longs;o egli &longs;arà ad F, ouero à G piu &longs;tarà &longs;opra.

</s>

Dopo percioche l'angolo CKS <lb/>è maggiore del CDS, & CDK è eguale à CKH: &longs;arà il re&longs;tante SKH mi-<lb/>nore del re&longs;tante SDK.

</s>

Per laqual co&longs;a la circonferenza KH &longs;arà piu da pre&longs;&longs;o <lb/>al mouimento naturale <lb/>diritto del pe&longs;o po&longs;to in <lb/>K &longs;ciolto, cioè alla li-<lb/>nea KS, che la circon <lb/>ferenza DK al moui-<lb/>mento DS.

</s>

& perciò <lb/>la linea CD &longs;a piu re&longs;i <lb/>&longs;tenza al pe&longs;o po&longs;to in D <lb/>che la CK al pe&longs;o me&longs;-<lb/>&longs;o in<emph.end type="italics"/> K.

</s>

<emph type="italics"/>& per que&longs;ta <lb/>ragione &longs;i mo&longs;trera l'an-<lb/>golo SHG e&longs;&longs;er mag-<lb/>giore dello SKH; & <lb/>per con&longs;equente la linea <lb/>CH &longs;are piu re&longs;i&longs;tenza <lb/>al pe&longs;o po&longs;to in H, che <lb/>CK al pe&longs;o me&longs;&longs;o in K. <lb/>

</s>

Similmente dimo&longs;trera&longs;&longs;i <lb/>che la linea CL piu &longs;o-<lb/>&longs;tenterà il pe&longs;o, che CD:<emph.end type="italics"/><lb/><arrow.to.target n="fig16"></arrow.to.target><lb/><emph type="italics"/>& per le cagioni i&longs;te&longs;&longs;e &longs;i prouerà, che il pe&longs;o me&longs;&longs;o in K grauerà meno &longs;opra la li-<lb/>nea CK, che in qual &longs;i voglia altro &longs;ito della circon&longs;erenza FDG: & quanto <lb/>piu da pre&longs;&longs;o &longs;arà ad F, ouero à G, manco grauerà.

</s>

dunque piu graue &longs;ara in K, <lb/>che in altro &longs;ito: & &longs;arà meno graue quanto piu da pre&longs;&longs;o &longs;tara ad F, ouero a G.<emph.end type="italics"/>

</s>

</figure>

</figure>

<margin.target id="note39"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 35. <emph type="italics"/>del terzo.<emph.end type="italics"/>

</s>

<margin.target id="note40"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del &longs;esto.<emph.end type="italics"/>

</s>

<margin.target id="note41"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 7. <emph type="italics"/>del terzo.<emph.end type="italics"/>

</s>

<margin.target id="note42"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 25. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<margin.target id="note43"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 25. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Se in fine il centro C fo&longs;&longs;e nel centro del mondo, egli è manife&longs;to, che il pe&longs;o po&longs;to doue<emph.end type="italics"/><lb/><arrow.to.target n="note44"></arrow.to.target> <emph type="italics"/>&longs;i voglia &longs;tarà fermo.

</s>

Come posto il pe&longs;o in D la linea CD &longs;o&longs;terrà tutto il pe&longs;o, <lb/>per e&longs;&longs;er a piombo dell'orizonte di e&longs;&longs;o pe&longs;o po&longs;to in D.

</s>

Dunque &longs;tarà fermo <lb/>il pe&longs;o.<emph.end type="italics"/>

</s>

<margin.target id="note44"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Hor percioche nelle co&longs;e, che fin qui &longs;ono &longs;tate dimostrate non habbiamo fatto mentio-<lb/>ne alcuna della grauezza del braccio della bilancia, però &longs;e vorremo anco con&longs;idera-<lb/>re la grauezza del detto braccio, &longs;i potrà ritrouare il centro della grauezza della ma<emph.end type="italics"/><pb id="14" xlink:href="pagethumb-it/046.jpg"/><emph type="italics"/>gnitudine fatta dal pe&longs;o, & dal braccio, & &longs;i <expan abbr="de&longs;criuerãno">de&longs;criueranno</expan> le circonferenze de' cerch; <lb/>&longs;econdo la di&longs;tanza dal centro della bilancia ad e&longs;&longs;o centro della grauezza, come &longs;e <lb/>in e&longs;&longs;o (come è veramente) fo&longs;&longs;e posto il pe&longs;o, Et le co&longs;e che &longs;enza la con&longs;ideratio <lb/>ne della grauezza del braccio della bilancia habbiamo trouato, tutte nell'i&longs;te&longs;&longs;o mo-<lb/>do con&longs;iderando ancora tal grauit à le ritrouaremo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Dalle co&longs;e dette dunque, <expan abbr="con&longs;iderãdo">con&longs;iderando</expan> la bilancia, <lb/>come ella è lontana dal centro del mondo <lb/>nel modo che e&longs;&longs;i hanno fatto, come etiandio <lb/>è in atto, appare la fal&longs;it à di coloro, che dico-<lb/>no il pe&longs;o po&longs;to in A e&longs;&longs;ere piu graue, che <lb/>in altro &longs;ito; & in&longs;ieme e&longs;&longs;er fal&longs;o, che quan-<lb/>to piu il pe&longs;o è lontano dalla linea FG, tan-<lb/>to e&longs;&longs;ere piu graue: imperoche il punto O <lb/>è piu da pre&longs;&longs;o alla FG, che il punto A; <lb/>percioche la linea tirata a piombo dal pun-<emph.end type="italics"/> <arrow.to.target n="note45"></arrow.to.target><lb/><emph type="italics"/>to O ad FG è minore della CA.

</s>

Da poi <lb/>egli è parimente fal&longs;o, che il pe&longs;o dal punto <lb/>A &longs;i moua piu velocemente, che da altro <lb/>&longs;ito.

</s>

peroche dal punto O &longs;i mouerà piu ve <lb/>locemente, che dal punto A, concio&longs;ia che <lb/>in O &longs;ia piu libero e &longs;ciolto, che in altro &longs;ito; <lb/>& la &longs;ce&longs;a dal punto O &longs;ia piu da pre&longs;&longs;o al <lb/>mouimento naturale diritto, che qual &longs;i vo-<lb/>glia altra di&longs;ce&longs;a.<emph.end type="italics"/>

</s>

<margin.target id="note45"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 15. <emph type="italics"/>del terzo.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Oltre a ciò quando mo&longs;trano per via della piu diritta, & della piu torta di&longs;ce&longs;a, che il pe-<lb/>&longs;o è piu graue in A, che in D, & in D, che in L.

</s>

Primieramente per certo e&longs;tima <lb/>no il fal&longs;o, che &longs;e alcun pe&longs;o &longs;arà collocato in qual &longs;i voglia &longs;ito della circonferenza, <lb/>come in D, la &longs;ua vera di&longs;ce&longs;a douer&longs;i fare per la linea diritta DR egualmente di-<lb/>&longs;tante da e&longs;&longs;a FG, come &longs;econdo il mouimento naturale, &longs;i come prima è &longs;tato det-<lb/>to.

</s>

Percioche in qual &longs;i voglia &longs;ito &longs;i collochi alcun pe&longs;o, &longs;e riguardiamo il mouimen <lb/>to &longs;uo naturale al proprio luogo, alquale &longs;i moue dirittamente per &longs;ua natura, pre&longs;up <lb/>po&longs;ta tutta la figura dell'vniuer&longs;o mondo, &longs;arà tale, che &longs;empre lo &longs;patio, per lo qua-<lb/>le &longs;i moue naturalmente, parerà hauere ragione di linea tirata dalla circonferenza al <lb/>centro.

</s>

Adunque le na <lb/>turali di&longs;ce&longs;e diritte di <lb/>qual &longs;i voglia pe&longs;o &longs;ciol <lb/>to non &longs;i po&longs;&longs;ono fare <lb/>per linee tra loro egual <lb/>mente di&longs;tanti, per an-<lb/>dar&longs;i à trouar tutte nel <lb/>centro del mondo.

</s>

pre <lb/>&longs;uppongono da poi, che <lb/>il pe&longs;o mo&longs;&longs;o da D in <lb/>A per linea diritta ver <lb/>&longs;o il centro del mondo <lb/>&longs;ia della <expan abbr="quãtità">quantità</expan> i&longs;te&longs;&longs;a, <lb/>come &longs;e egli fo&longs;&longs;e da O <lb/>in C &longs;i fattamente, <lb/>che il <expan abbr="p&utilde;to">punto</expan> A &longs;ia egual <lb/>mente di&longs;tante dal cen-<lb/>tro del mondo, come C; <lb/>ilche è parimente fal&longs;o:<emph.end type="italics"/><lb/><arrow.to.target n="fig17"></arrow.to.target><lb/><arrow.to.target n="note46"></arrow.to.target> <emph type="italics"/>

</s>

Imperoche il punto A è piu da lontano dal centro del mondo, che C: percioche <lb/>maggior è la linea tirata dal centro del mondo fin ad A, che quella del centro del <lb/>mondo fin a C, concio&longs;ia che vna linea dal centro del mondo fin ad A &longs;i di&longs;tenda <lb/>&longs;otto vn'angolo retto contenuto dalle linee AC, & dal punto C al centro del <lb/>mondo.

</s>

Dalle quali co&longs;e non &longs;olo rie&longs;ce vana quella pre&longs;uppo&longs;ta, laquale dimostra, <lb/>che la bilancia DE ritorna in AB, ma anco cadono tutte le loro dimo&longs;trationi; <lb/>&longs;e for&longs;e non dice&longs;&longs;ero, che que&longs;te co&longs;e tutte per la grandi&longs;&longs;ima di&longs;tanza, che è fra il cen <lb/>tro del mondo, & noi &longs;ono co&longs;i in&longs;en&longs;ibili, che per cagione di que&longs;ta in&longs;en&longs;ibilità, <lb/>&longs;i po&longs;&longs;ano pre&longs;upponere, come vere; concio&longs;ia, che tutti quelli, iquali hanno trattato <lb/>que&longs;te co&longs;e, le habbiano pre&longs;uppo&longs;te, come note; ma&longs;&longs;imamente, percioche quello <lb/>e&longs;&longs;ere in&longs;en&longs;ibile non fà, che la di&longs;ce&longs;a del pe&longs;o da L in D (per v&longs;are le loro paro-<lb/>le) non pigli meno del diretto, che la di&longs;ce&longs;a DA.

</s>

Similmente l'arco DA piglie-<lb/>rà piu del diretto, che la circon&longs;erenza EV. onde &longs;arà vera la pre&longs;uppo&longs;ta, & le <lb/>altre dimo&longs;trationi rimarranno nella &longs;ua &longs;ua forza.

</s>

Concediamo etiandio, che il pe<emph.end type="italics"/><pb id="15" xlink:href="pagethumb-it/048.jpg"/><emph type="italics"/>&longs;o po&longs;to in A &longs;ia piu graue, che in altro &longs;ito; & che la di&longs;ce&longs;a diritta del pe&longs;o &longs;i deb <lb/>ba fare per linea diritta egualmente di&longs;tante da FG, & quali&longs;i voglian punti pre&longs;i <lb/>nelle linee egualmente di&longs;tanti dall'orizonte e&longs;&longs;ere egualmente lontani dal centro <lb/>del mondo: non &longs;eguiter à gia per que&longs;to, che la loro dimostratione &longs;ia vera, con la-<lb/>quale vengono a dire, che il pe&longs;o posto in A è piu grane, che in altro &longs;ito, come in <lb/>L.

</s>

Percioche &longs;e egli fo&longs;&longs;e vero, che quanto piu il pe&longs;o in que&longs;ta maniera di&longs;cende <lb/>piu al diritto, iui fo&longs;&longs;e piu graue; &longs;eguirebbe etiandio, che quanto l'iste&longs;&longs;o pe&longs;o de-<lb/>&longs;cende&longs;&longs;e egualmente in archi eguali al diritto, che ne i luoghi mede&longs;imi haue&longs;&longs;e gra-<lb/>uezza eguale, ilche in que&longs;to modo e&longs;&longs;er fal&longs;o &longs;i dimo&longs;tra.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note46"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 18. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Siano le circonferenze AL AM tra loro eguali, & congiunga&longs;i LM, laquale ta-<lb/>gli AB in X; &longs;arà LM egualmente di&longs;tante da FG, & à piombo di AB,<emph.end type="italics"/> <arrow.to.target n="note47"></arrow.to.target><lb/><emph type="italics"/>& XM &longs;arà eguale ad XL.

</s>

Se dunque il pe&longs;o da L &longs;arà mo&longs;&longs;o in A per la cir-<lb/>conferenza LA, il mouimento &longs;uo diritto &longs;arà &longs;econdo la linea LX.

</s>

Ma &longs;e egli &longs;i <lb/>mouerà da A in M per la circonferenza AM, il &longs;uo mouimento &longs;arà &longs;econdo <lb/>la linea diritta XM.

</s>

Per laqual co&longs;a la &longs;ce&longs;a da L in A &longs;arà eguale alla &longs;ce&longs;a da <lb/>A in M, &longs;i per cau&longs;a delle circonferenze eguali, & &longs;i per le linee rette eguali, & à <lb/>piombo di e&longs;&longs;a AB.

</s>

Adunque il pe&longs;o mede&longs;imo po&longs;to in L grauerà egualmente, <lb/>come in A, ilche è fal&longs;o, concio&longs;ia, che egli è di gran lunga piu graue in A, che in L.<emph.end type="italics"/>

</s>

<margin.target id="note47"></margin.target><emph type="italics"/>Per la terza del terzo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Et benche AMLA prendano, &longs;econdo e&longs;&longs;i, egualmente del diretto, diranno for&longs;e, <lb/>nondimeno perche il principio della &longs;ce&longs;a da L, cioè LD piglia meno del diretto, che <lb/>il principio della &longs;ce&longs;a da A, cioè AN, il pe&longs;o in A &longs;arà piu graue, che in L. <lb/>

</s>

Imperoche e&longs;&longs;endo (come è &longs;tato di &longs;opra po&longs;to) la circonferenza AN eguale ad <lb/>LD, laquale (&longs;econdo eßi) piglia di diretto CT; ma LD piglia di diretto PO, <lb/>però il pe&longs;o &longs;arà piu graue in A, che in L.

</s>

ilche &longs;e fo&longs;&longs;e vero, &longs;eguirebbe, che l'i&longs;te&longs;-<lb/>&longs;o pe&longs;o nel mede&longs;imo &longs;ito, in diuer&longs;o modo &longs;olamente con&longs;iderato, ver&longs;o il mede&longs;imo <lb/>&longs;ito fo&longs;&longs;e & piu graue, & piu lieue; ilche è impo&longs;&longs;ibile.

</s>

cioè &longs;e con&longs;ideriamo la &longs;ce&longs;a <lb/>del pe&longs;o po&longs;to in L in quanto egli de&longs;cende da L in A &longs;arà piu graue, che &longs;e con&longs;ide <lb/>reremo la &longs;ce&longs;a del pe&longs;o i&longs;te&longs;&longs;o da L in D &longs;olamente.

</s>

ne po&longs;&longs;ono negare per i mede <lb/>&longs;imi detti &longs;uoi, che la di&longs;ce&longs;a del pe&longs;o da L in A non pigli del diretto LX, ouero PC. <lb/>

</s>

Et che &longs;imilmente la &longs;ce&longs;a AM non prenda di diretto XM: pigliando cßi ancora <lb/>à que&longs;to modo, & co&longs;i nece&longs;&longs;ario &longs;ia di pigliare.

</s>

percioche &longs;e vogliono dimo&longs;trare, <lb/>che la bilancia DE ritorni in AB paragonando la &longs;ce&longs;a del pe&longs;o po&longs;to in D con <lb/>la &longs;ce&longs;a del pe&longs;o posto in E, egli è nece&longs;&longs;ario, che mo&longs;trino, che la diritta &longs;ce&longs;a OC <lb/>ri&longs;pondente alla circonferenza DA &longs;ia maggiore della &longs;ce&longs;a diritta TH ri&longs;ponden-<lb/>te alla circonferenza EV. peroche &longs;e piglia&longs;&longs;ero &longs;olamente vna parte di tutta la &longs;ce <lb/>&longs;a da D in A, come D<emph.end type="italics"/>K, <emph type="italics"/>& dimo&longs;tra&longs;&longs;ero, che piu di diretto piglia la &longs;ce&longs;a D<emph.end type="italics"/>K, <lb/><emph type="italics"/>che la eguale portione della &longs;ce&longs;a dal punto E, &longs;eguirebbe il pe&longs;o po&longs;to in D, &longs;econ-<lb/>do eßi, e&longs;&longs;ere piu graue del pe&longs;o po&longs;to in E, & mouer&longs;i in giu fin al K &longs;olamente. <lb/>per modo che la bilancia &longs;ia mo&longs;&longs;a in KI.

</s>

Similmente &longs;e vogliono mo&longs;trare, che la <lb/>bilancia KI ritorni in AB pigliando vna portione della &longs;ce&longs;a da K in A, cioè KS, <lb/>& mo&longs;tra&longs;&longs;ero, che KS pigli piu di diretto, che la &longs;ce&longs;a eguale, che è dirimpetto dal <lb/>punto I: &longs;eguirebbe con &longs;imile modo il pe&longs;o po&longs;to in K e&longs;&longs;ere piu graue, che in I, &<emph.end type="italics"/><pb id="15v" xlink:href="pagethumb-it/049.jpg"/><emph type="italics"/>mouer&longs;i &longs;olamente fin ad S.

</s>

Et &longs;e di nouo mo&longs;tra&longs;&longs;ero vna portione della &longs;ce&longs;a da S <lb/>in A, & co&longs;i &longs;ucceßiuamente e&longs;&longs;ere piu diritta della &longs;ce&longs;a eguale del pe&longs;o oppo&longs;to; <lb/>&longs;empre &longs;eguirà, che la bilancia SI andarà piu da pre&longs;&longs;o ad AB, ma non <expan abbr="dimostre-<lb> rãno">dimostre-<lb/>ranno</expan> giamai che per <lb/>uenga in AB.

</s>

Se <lb/>dunque vogliono di <lb/>mo&longs;trare, che la <expan abbr="bilã">bilam</expan> <lb/>cia DE ritorni in <lb/>AB, egli è nece&longs;&longs;a-<lb/>rio, che pre&longs;upponga <lb/>no, che la &longs;ce&longs;a del <lb/>pe&longs;o da D in A <expan abbr="pr&etilde;">prem</expan> <lb/>da di diretto la quan <lb/>tità della linea tira-<lb/>ta dal punto D ad <lb/>AB ad angoli ret-<lb/>ti; & co&longs;i, &longs;e para-<lb/>goneremo le &longs;ce&longs;e e-<lb/>guali di DA AN <lb/>fra loro, lequali <expan abbr="pr&etilde;">prem</expan> <lb/>dono di diretto OC <lb/>CT, accaderà, che<emph.end type="italics"/><lb/><arrow.to.target n="fig18"></arrow.to.target><lb/><emph type="italics"/>il pe&longs;o i&longs;te&longs;&longs;o &longs;arà in D graue egualmente, come in A.

</s>

Ma &longs;e le portioni &longs;olamente <lb/>piglieremo da DA, &longs;arà piu graue in A, che in D.

</s>

Adunque dalla diuer&longs;ità &longs;o-<lb/>lamente del modo del con&longs;iderare, auerrà, che il pe&longs;o mede&longs;imo &longs;arà & piu graue, <lb/>& piu leggiero; & non per la natura della co&longs;a.

</s>

Di piu la pre&longs;uppo&longs;ta loro non <lb/>afferma, che il pe&longs;o &longs;econdo il &longs;ito &longs;ia piu graue, quanto nel &longs;ito mede&longs;imo il principio <lb/>della &longs;ua di&longs;ce&longs;a è meno obliquo.

</s>

La pre&longs;upposta dunque di &longs;opra addotta, cioè che <lb/>&longs;econdo il &longs;ito il pe&longs;o è piu graue quanto nell'i&longs;te&longs;&longs;o &longs;ito meno obliqua è la di&longs;ce&longs;a, non <lb/>&longs;olamente non &longs;i puote concedere à modo alcuno, per le co&longs;e, che habbiamo dette; <lb/>ma anco percioche non è co&longs;a difficile il dimo&longs;trare tutto l'oppo&longs;to, cioè il pe&longs;o mede&longs;i <lb/>mo in eguali circonferenze quanto meno obliqua è la di&longs;ce&longs;a, iui meno grauare.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Siano come prima le circonferenze AL AM tra loro eguali; & &longs;ia il punto L vici <lb/>no ad F, & congiunga&longs;i LM, la quale &longs;arà à piombo di AB & LX &longs;arà anco <lb/>eguale ad XM.

</s>

Dapoi pre&longs;&longs;o ad M tra M & G &longs;ia pre&longs;o come &longs;i vuole, il pun<emph.end type="italics"/><lb/><arrow.to.target n="note48"></arrow.to.target> <emph type="italics"/>to P, & &longs;ia fatta la circonferenza PO eguale alla circonferenza AM, &longs;arà il <lb/>punto O pre&longs;&longs;o ad A. & &longs;iano congiunte le linee CL, CO, CM, CP, OP.<emph.end type="italics"/><lb/><arrow.to.target n="note49"></arrow.to.target> <emph type="italics"/>& dal punto P tiri&longs;i la PN a piombo di OC. & percioche la circonferenza. <lb/>AM è eguale alla circonferentia OP; &longs;arà l'angolo ACM eguale all'angolo<emph.end type="italics"/><lb/><arrow.to.target n="note50"></arrow.to.target> <emph type="italics"/>OCP, & l'angolo CXM retto eguale al retto CNP, &longs;arà anco il re&longs;tante angolo <lb/>XMC del triangolo MXC eguale al re&longs;tante NPC del triangolo PCN.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ma il lato ancora CM è eguale al lato CP, dunque il triangolo MCX è egua <lb/>le al triangolo PCN, & il lato MX eguale al lato NP.

</s>

Onde la linea PN <lb/>&longs;arà eguale ad LX.

</s>

Tiri&longs;i oltre a ciò dal punto O la linea OT egualmente di-<lb/>&longs;tante da AC, laquale tagli NP in V. & &longs;ia anco tirata dal punto P vna <lb/>linea a piombo di OT, <lb/>la quale per certo non <lb/>puote cadere tra OV, <lb/>perche e&longs;&longs;endo l'angolo <lb/>ONV retto, &longs;arà acu<emph.end type="italics"/> <arrow.to.target n="note51"></arrow.to.target><lb/><emph type="italics"/>to lo OVN.

</s>

Per la <lb/>qualco&longs;a OVP &longs;arà <lb/>ottu&longs;o.

</s>

Non caderà <lb/>dunque la linea tirata <lb/>dal punto P tra OV <lb/>à piombo di OT: pe-<lb/>roche due angoli d'uno <lb/><expan abbr="triãgolo">triangolo</expan> &longs;arebbono l'u-<lb/>no retto, & l'altro ot-<lb/>tu&longs;o, che è impoßibile. <lb/>Caderà dun que nella li <lb/>nea OT nellaparte di <lb/>VT, et &longs;ia PT. &longs;arà &longs;e <lb/>condo e&longs;&longs;i, PT la di<emph.end type="italics"/><lb/><arrow.to.target n="fig19"></arrow.to.target><lb/><emph type="italics"/>ritta &longs;ce&longs;a della circonferenza OP.

</s>

Percioche dunque l'angolo ONV è retto,<emph.end type="italics"/> <arrow.to.target n="note52"></arrow.to.target><lb/><emph type="italics"/>&longs;arà la linea OV maggiore della ON.

</s>

Onde la OT &longs;arà parimente maggiore <lb/>della ON. & co&longs;i di&longs;tendendo&longs;i la linea OP &longs;otto gli angoli retti ONP, <lb/>OTP, &longs;arà il quadrato di OP eguale alli quadrati ON NP in&longs;ieme pre&longs;i, &longs;i<emph.end type="italics"/> <arrow.to.target n="note53"></arrow.to.target><lb/><emph type="italics"/>milmente eguale a i quadrati di OT TP in&longs;ieme.

</s>

per laqual co&longs;a li quadrati in&longs;ie-<lb/>me di ON NP &longs;aranno eguali a i quadrati in&longs;ieme di OT TP. Ma il quadrato <lb/>di OT è maggiore del quadrato di ON. per e&longs;&longs;ere maggiore la linea OT della <lb/>ON.

</s>

Adunque il quadrato di NP &longs;ara maggiore del quadrato TP & perciò la <lb/>linea TP &longs;arà minore della linea PN, & della linea LX.

</s>

Meno obliqua <lb/>dunque &longs;arà la &longs;ce&longs;a dell'arco LA, che dell'arco OP.

</s>

Dunque il pe&longs;o po-<lb/>sto in L, per i loro detti, &longs;arà piu graue, che in O, il che, per le co&longs;e, che di <lb/>&longs;opra habbiamo detto, è manife&longs;tamente fal&longs;o. concio&longs;ia, che il pe&longs;o po&longs;to in O <lb/>&longs;ia piu graue, che in L.

</s>

Non &longs;i puote dunque raccogliere dal piu diritto, & <lb/>piu torto mouimento in quel modo pigliato, e&longs;&longs;ere il pe&longs;o tanto piu graue &longs;econ-<lb/>do il &longs;ito, quanto nel mede&longs;imo &longs;ito è meno torta la &longs;ce&longs;a.

</s>

& quinci na&longs;ce tutto <lb/>qua&longs;i il &longs;uo errore & inganno in cote&longs;ta co&longs;a.

</s>

Imperoche quantunque per acciden-<lb/>te alle volte dalle co&longs;e fal&longs;e ne &longs;egua il vero, tutta via per &longs;e &longs;te&longs;&longs;e principalmente <lb/>dalle fal&longs;e ne &longs;egue il fal&longs;o, &longs;i come dalle vere &longs;empre il vero ne &longs;egue.

</s>

Non è pero <lb/>da mar auigliar&longs;i, &longs;e mentre e&longs;&longs;i prendono co&longs;e fal&longs;e, & &longs;tanno &longs;opra quelle, come ve<emph.end type="italics"/><pb id="16v" xlink:href="pagethumb-it/051.jpg"/><emph type="italics"/>ri&longs;&longs;ime, raccolgono, & conchiudono co&longs;e in tutto fal&longs;i&longs;&longs;ime.

</s>

&longs;ono oltre a ciò inganna-<lb/>ti, mentre pigliano a contemplare la bilancia &longs;emplicemente per via di matematica, <lb/>e&longs;&longs;endo la con&longs;ideratione &longs;ua mechanica affatto, ne di lei &longs;i po&longs;&longs;a ragionare a modo al <lb/>cuno &longs;enza il vero mouimento, & &longs;enza i pe&longs;i, che &longs;ono in tutto co&longs;e naturali, &longs;en-<lb/>za le quali non &longs;i po&longs;&longs;ono ritrouare per niuna maniera le vere cagioni di quelle co&longs;e, <lb/>che accadono alla bilancia.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note48"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 27. <emph type="italics"/>del terzo<emph.end type="italics"/>

</s>

<margin.target id="note49"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 32. <emph type="italics"/>del primo<emph.end type="italics"/>

</s>

<margin.target id="note50"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 26. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note51"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 13. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note52"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 19. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note53"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 47. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Oltre a ciò &longs;e anche con <lb/>cederemo la pre&longs;up-<lb/>po&longs;ta, &longs;i partono tut<lb/>tauia molto <expan abbr="l&utilde;ge">lunge</expan> dal <lb/>la <expan abbr="cõ&longs;ideratione">con&longs;ideratione</expan> della <lb/>bilancia, mentre di-<lb/>&longs;corrono; che in quel <lb/>la maniera debba la <lb/>bilancia DE ritor-<lb/>nare in AB: percio <lb/>che &longs;empre pigliano <lb/>vn di due pe&longs;i &longs;epara <lb/>tamente come D, <lb/>ouero E, come &longs;e hor <lb/>l'uno, hor l'altro fo&longs; <lb/>&longs;e po&longs;to nella bilan-<lb/>cia, non congiunti in <lb/>&longs;ieme ambidue in <lb/>modo veruno, e&longs;&longs;en-<emph.end type="italics"/><lb/><arrow.to.target n="fig20"></arrow.to.target><lb/><emph type="italics"/>doche nondimeno bi&longs;ogni fare tutto all'oppo&longs;ito di ciò, ne &longs;i puote con&longs;iderare dirit-<lb/>tamente l'uno &longs;enza l'altro, e&longs;&longs;endoche &longs;i ragiona di loro nella bilancia collocati. <lb/>

</s>

Concio&longs;ia che quando dicono la di&longs;ce&longs;a del pe&longs;o po&longs;to in D e&longs;&longs;ere meno torta, che <lb/>la di&longs;ce&longs;a del pe&longs;o po&longs;to in E, co&longs;i &longs;arà il pe&longs;o in D, per la pre&longs;uppo&longs;ta, piu graue <lb/>del pe&longs;o po&longs;to in E; onde per e&longs;&longs;ere piu graue, eglie nece&longs;&longs;ario, che &longs;i moua in giu, <lb/>& che la bilancia DE ritorni in AB: Cote&longs;to di&longs;cor&longs;o non è di momento alcu-<lb/>no.

</s>

Primieramente &longs;empre argomentano come &longs;e i pe&longs;i in DE debbano &longs;cende-<lb/>re, con&longs;iderando la &longs;ce&longs;a di vno &longs;olameute &longs;enza la compagnia, & congiungimen-<lb/>to dell'altro.

</s>

Vltimamente nondimeno e&longs;&longs;i per la comparatione delle di&longs;ce&longs;e de'pe-<lb/>&longs;i conchiudono il pe&longs;o posto in D mouer&longs;i in giu, & il po&longs;to in E in &longs;u, prenden-<lb/>do l'uno, & l'altro pe&longs;o congiunti in&longs;ieme fra loro nella bilancia.

</s>

Ma da &longs;uoi me-<lb/>de&longs;imi principij, i quali v&longs;ano, & dalle &longs;ue dimo&longs;trationi &longs;i puote cauare ageuoli&longs;&longs;i-<emph.end type="italics"/><lb/><arrow.to.target n="note54"></arrow.to.target> <emph type="italics"/>mamente l'oppo&longs;ito di quel che &longs;i faticano di difendere.

</s>

Imperoche &longs;e &longs;i paragona <lb/>la di&longs;ce&longs;a del pe&longs;o po&longs;to in D con la &longs;alita del pe&longs;o po&longs;to in E, come tirate le'linee <lb/>E<emph.end type="italics"/>K <emph type="italics"/>DH a piombo di AB, e&longs;&longs;endo l'angolo DCH eguale all'angolo ECK,<emph.end type="italics"/><lb/><arrow.to.target n="note55"></arrow.to.target> <emph type="italics"/>& l'angolo DHC retto eguale al retto E<emph.end type="italics"/>K<emph type="italics"/>C, & il lato DC eguale al lato <lb/>CE; &longs;arà il triangolo CDH eguale al triangolo CEK, & il lato DH egua<emph.end type="italics"/><pb id="17" xlink:href="pagethumb-it/052.jpg"/><emph type="italics"/>le al lato EK: & e&longs;&longs;endo l'angolo DCA eguale all'angolo ECB, &longs;arà anco <lb/>la circonferenza DA eguale alla circonferenza BE.

</s>

Mentre dunque il pe&longs;o po-<lb/>sto in D &longs;cende per la circonferenza DA, il pe&longs;o po&longs;to in E &longs;ale per la circon-<lb/>ferenza EB eguale a DA, & la &longs;ce&longs;a del pe&longs;o po&longs;to in D prenderà, (&longs;econdo <lb/>il co&longs;tume loro) di diretto DH: & la &longs;alita del pe&longs;o E prenderà di diretto EK <lb/>eguale a DH: &longs;arà dunque la &longs;ce&longs;a del pe&longs;o posto in D eguale alla &longs;alita del pe&longs;o <lb/>po&longs;to in E: & quale &longs;arà la inclinatione d'uno al mouimento in giù, tale &longs;arà etian <lb/>dio la re&longs;i&longs;tenza dell'altro al mouimento in sù, cioè la re&longs;istentia della violenza del <lb/>pe&longs;o po&longs;to in E nella a&longs;ce&longs;a, contra&longs;tando &longs;i oppone alla naturale po&longs;&longs;anza del pe-<lb/>&longs;o po&longs;to in D per e&longs;&longs;ere a lei eguale; percioche quanto il pe&longs;o po&longs;to in D per la na-<lb/>tural po&longs;&longs;anza de&longs;cende piu velocemente in giù, in tanto il pe&longs;o po&longs;to in E più tar-<lb/>do &longs;ale violentemente.

</s>

Per laqual co&longs;a niuno di loro due pe&longs;era piu dell'altro, non <lb/>procedendo attione da eguale.

</s>

il pe&longs;o po&longs;to in D dunque non mouerà il pe&longs;o po&longs;to <lb/>in E in &longs;u&longs;o, peroche &longs;e lo moue&longs;&longs;e, &longs;arebbe nece&longs;&longs;ario, che il pe&longs;o po&longs;to in D ha-<lb/>ue&longs;&longs;e virtu maggiore in di&longs;cendendo, che il pe&longs;o po&longs;to in E in &longs;alendo, ma que&longs;te co-<lb/>&longs;e &longs;ono eguali: adunque &longs;taranno &longs;ermi i pe&longs;i, & la grauezza del pe&longs;o po&longs;to in D &longs;a-<lb/>rà eguale alla grauezza del pe&longs;o po&longs;to in E.

</s>

Oltre a ciò perche pre&longs;uppongono, che <lb/>quanto il pe&longs;o è piu di&longs;tante dalla linea FG della dirittura, tanto e&longs;&longs;ere piu graue. <lb/>però tirate parimente da i punti DE le linee DO, EI apiombo di FG, con <lb/>modo &longs;imile &longs;i dimostrerà il triangolo CDO e&longs;&longs;ere eguale al triangolo CEI: & <lb/>la linea DO e&longs;&longs;ere eguale ad EI.

</s>

Tanto dunque è di&longs;tante il pe&longs;o po&longs;to in D <lb/>dalla linea FG, quanto il pe&longs;o po&longs;to in E.

</s>

Dalle ragioni loro dunque, & dalle &longs;ue <lb/>pre&longs;uppo&longs;te li pe&longs;i me&longs;&longs;i in DE &longs;ono graui egualmente.

</s>

Di piu, che vieta che non &longs;i di <lb/>mo&longs;tri la bi lancia DE mouer&longs;i per nece&longs;&longs;ità in FG con &longs;imile ragione?

</s>

Primie-<lb/>ramente &longs;i puote raccogliere dalle loro mede&longs;ime dimo&longs;trationi, la &longs;alita del pe&longs;o po-<lb/>&longs;to in E ver&longs;o il B e&longs;&longs;ere piu diritta della &longs;alita del pe&longs;o po&longs;to in D ver&longs;o lo F, <lb/>cioè manco prendere di diretto la &longs;alita del pe&longs;o po&longs;to in D in archi eguali, che la <lb/>&longs;alita del pe&longs;o po&longs;to in E.

</s>

Pre&longs;upponga&longs;i dunque, che il pe&longs;o &longs;ia piu leggiero &longs;econ-<lb/>do il &longs;ito tanto quanto nel &longs;ito mede&longs;imo meno diritta è la &longs;ua &longs;alita: Laqual pre-<lb/>&longs;upposta pare tanto manife&longs;ta, quanto l'altraloro.

</s>

percioche dunque la &longs;alita del <lb/>pe&longs;o po&longs;to in E è piu diritta della &longs;alita del pe&longs;o po&longs;to in D, per la pre&longs;uppo&longs;ta il <lb/>pe&longs;o po&longs;to in D &longs;arà piu leggiero del pe&longs;o po&longs;to in E.

</s>

Adunque il pe&longs;o po&longs;to in D <lb/>&longs;i mouerà in sù dal pe&longs;o po&longs;to in E, &longs;i &longs;attamente che la bilancia peruenga in FG, <lb/>& co&longs;i potra&longs;si dimo&longs;trare la bilancia DE mouer&longs;i in FG, laqual dimo&longs;tratio-<lb/>ne è del tutto veramente friuola, & pati&longs;ce le difficultà mede&longs;ime.

</s>

Percioche quan-<lb/>tunque &longs;i conceda, come vero, che il pe&longs;o po&longs;to in E &longs;alendo &longs;ia piu graue del pe&longs;o <lb/>in D &longs;imilmente &longs;alendo, non perciò da que&longs;to &longs;egue, che il pe&longs;o po&longs;to in E de-<lb/>&longs;cendendo &longs;ia piu graue del pe&longs;o posto in D &longs;alendo.

</s>

Niuna dunque di que&longs;te due <lb/>dimo&longs;trationi, che dicono la bilancia DE ritornare in AB, ouero mouer&longs;i in <lb/>FG, è vera.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note54"></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="note55"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 25. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Oltre a ciò &longs;e e&longs;amineremo la loro pre&longs;uppo&longs;ta, & la &longs;orza delle loro parole, vedremo <lb/>per certo che altro &longs;entimento hanno.

</s>

Imperoche e&longs;&longs;endo che &longs;empre lo &longs;patio per lo<emph.end type="italics"/><pb id="17v" xlink:href="pagethumb-it/053.jpg"/><emph type="italics"/>quale il pe&longs;o natur <expan abbr="alm&etilde;te">almente</expan> &longs;i moue, &longs;i deue prendere dal centro della grauezza di e&longs;-<lb/>&longs;o pe&longs;o ver&longs;o il centro del mondo à &longs;embianza di vna linea diritta tirata dal centro <lb/>della grauezza al centro del mondo, tanto &longs;i dir à que&longs;ta co&longs;i fatta di&longs;ce&longs;a del pe&longs;o <lb/>piu, & meno obliqua, quanto, &longs;econdo lo &longs;patio di&longs;&longs;egnato, a &longs;embianza della pre-<lb/>detta linea piu ò meno &longs;i mouerà, (andando pero &longs;empre a trouare il luogo &longs;uo natu <lb/>rale, & vie piu &longs;empre auicinandoui&longs;i.) talche tanto piu obliqua &longs;i dica la &longs;ce&longs;a <expan abbr="quã">quam</expan> <lb/>to &longs;i parte da cotale &longs;patio: & piu diritta quanto a lui &longs;i acco&longs;ta.

</s>

& in que&longs;to <lb/>&longs;entimento quella pre&longs;upposta non deue partorire difficulta ad alcuno, percioche co-<lb/>&longs;i è la verita &longs;ua chiara, & conforme alla ragione, che non pare hauer me&longs;tieri di e&longs;-<lb/>&longs;er &longs;atta in alcun modo manife&longs;ta.<emph.end type="italics"/>

</s>

<emph type="italics"/>Se dunque il pe&longs;o &longs;ciolto, collocato nel &longs;i-<lb/>to di D &longs;i deue mouere al luogo pro-<lb/>prio, &longs;enza dubbio, po&longs;to S centro del <lb/>mondo, &longs;i mouerà per la linea DS, <expan abbr="&longs;i-<lb> milm&etilde;te">&longs;i-<lb/>milmente</expan> il pe&longs;o po&longs;to in E &longs;ciolto &longs;i mo <lb/>uerà per la linea ES.

</s>

Per laqual co-<lb/>&longs;a &longs;e, (come è vero) la &longs;ce&longs;a del pe&longs;o &longs;i <lb/>dirà piu, ò meno obliqua, &longs;econdo lo al <lb/>lontanar&longs;i, ouero appre&longs;&longs;ar&longs;i a gli &longs;patij <lb/>di&longs;segnati per le linee DS ES, per ri <lb/>&longs;petto a'loro naturali mouimenti ver&longs;o <lb/>iproprij luoghi, egli è chiaro, che meno <lb/>obliqua è la &longs;ce&longs;a di E per EG, che <lb/>di D per DA, per e&longs;&longs;ere stato di <lb/>&longs;opra mo&longs;trato che l'angolo SEG è <lb/>minore dell'angolo SDA. Per laqual <lb/>co&longs;a piu grauer à il pe&longs;o in E, che in D, <lb/>il che totalmente è il contrario di quel-<lb/>lo, che e&longs;si &longs;i &longs;ono s&longs;orzati di prouare. <lb/>Leueran&longs;i per auuentura contra di noi <lb/>dicendo.

</s>

Se dundue il pe&longs;o po&longs;to in E è <lb/>piu graue del pe&longs;o po&longs;to in D, la bi-<lb/>lancia DE non &longs;tar à giamai in que-<lb/>&longs;to &longs;ito, laqual co&longs;a noi habbiamo pro-<lb/>po&longs;to di mantenere, ma &longs;i mouer à in F <lb/>G.

</s>

Allequali co&longs;e ri&longs;pondiamo. che im-<lb/>porta a&longs;&longs;ai, &longs;e noi con&longs;ideriamo i pe&longs;i o-<lb/>uero in quanto &longs;ono &longs;eparati l'uno dal-<lb/>l'altro, ouero in quanto &longs;ono traloro <lb/>congiunti: perche altra è la ragione del<emph.end type="italics"/><lb/><arrow.to.target n="fig21"></arrow.to.target><lb/><emph type="italics"/>pe&longs;o po&longs;to in E &longs;enza il congiungimento del pe&longs;o po&longs;to in D, & altra di lui con <lb/>l'altro pe&longs;o congiunto, &longs;i fattamente che l'uno &longs;enza l'altro non &longs;i po&longs;&longs;a mouere.

</s>

Im<emph.end type="italics"/><pb id="18" xlink:href="pagethumb-it/054.jpg"/><emph type="italics"/>peroche la diritta, & naturale di&longs;ce&longs;a dal pe&longs;o po&longs;to in E, inquanto egli è &longs;enza al-<lb/>tro congiungimento di pe&longs;o, &longs;i fa per la linea ES. ma inquanto egli è congiunto <lb/>col pe&longs;o D, la &longs;ua naturale di&longs;ce&longs;a non &longs;arà piu per la linea ES, ma per vna li-<lb/>nea egualmente di&longs;tante da CS. percioche la magnitudine compo&longs;ta de i pe&longs;i ED. <lb/>& della bilancia DE il cui centro della grauezza è C, &longs;e in ne&longs;&longs;un luogo non &longs;a-<lb/>rà &longs;o&longs;tenuta, &longs;i mouerà naturalmente in giu nel modo che &longs;i troua, &longs;econdo la gra-<lb/>uezza del centro per la linea diritta tirata dal centro della grauezza C al centro <lb/>del mondo S, finche il centro C peruenga nel centro S.

</s>

La bilancia dunque DE <lb/>in&longs;ieme co'pe&longs;i, in quella maniera, che &longs;i troua &longs;i mouerà in giu per modo tale, che il <lb/>punto C &longs;i moua per la linea CS, fin che C peruenga in S, & la bilancia <lb/>DE in HK; & habbia la bilancia in HK la po&longs;itione i&longs;te&longs;&longs;a, che prima hauea; <lb/>cio è, che la HK &longs;ia egualmente distante da DE.

</s>

Congiungan&longs;i dunque DH <lb/>EK. egli è manife&longs;to, che mentre la bilancia DE &longs;i moue in HK, mouer&longs;i an-<lb/>che ipunti DE per le linee DH EK, come quelle che &longs;ono & &longs;ra &longs;e, & ad<emph.end type="italics"/> <arrow.to.target n="note56"></arrow.to.target><lb/><emph type="italics"/>e&longs;&longs;a CS eguali, & egualmente di&longs;tanti.

</s>

Per la qual co&longs;a i pe&longs;i posti in DE, in <lb/>quanto &longs;ono &longs;ra loro congiunti, &longs;e riguarderemo il mouimento loro naturale &longs;imoue <lb/>ranno non &longs;econdo le linee DS, ES, ma &longs;econdo LDH MEK egualmente <lb/>di&longs;tanti da e&longs;&longs;a CS.

</s>

Ma la naturale inclinatione del pe&longs;o po&longs;to in E libero, & <lb/>&longs;ciolto &longs;arà per ES, & del pe&longs;o po&longs;to in D <expan abbr="&longs;imilm&etilde;te">&longs;imilmente</expan> &longs;ciolto &longs;arà per DS. & per-<lb/>cio non è &longs;conueneuole, che il pe&longs;o mede&longs;imo hora in E, hora in D, &longs;ia piu graue <lb/>in E, che in D.

</s>

Ma&longs;e i pe&longs;i po&longs;ti in ED &longs;ono l'un l'altro fra &longs;e congiunti, & gli <lb/>con&longs;idereremo in quanto &longs;ono congiunti, &longs;arà la naturale inclinatione del pe-<lb/>&longs;o po&longs;to in E per la linea MEK, percioche la grauezza dell'altro pe&longs;o po&longs;to <lb/>in D fa &longs;i, che il pe&longs;o po&longs;to in E non graui &longs;opra la linea ES, ma nella EK. <lb/>

</s>

Ilche fa parimente la grauezza del pe&longs;o po&longs;to in E, cioè, che il pe&longs;o po&longs;to in D <lb/>non graui per la linea retta DS, ma &longs;econdo DH, per impedir&longs;i ambedue l'uno <lb/>l'altro che non vadino à propri luoghi.

</s>

Concio&longs;ia dunque che la naturale &longs;ce&longs;a dirit-<lb/>ta de i pe&longs;i po&longs;ti in DE &longs;ia &longs;econdo LDH, MEK, &longs;arà &longs;imilmente la naturale <lb/>&longs;alita diritta loro &longs;econdo le i&longs;te&longs;&longs;e linee HDL KEM. & la naturale &longs;alita del <lb/>pe&longs;o po&longs;to in E &longs;i dirà più, & meno torta, quanto che &longs;econdo lo &longs;patio &longs;i mouerà <lb/>più, & meno pre&longs;&longs;o la linea MK. & a que&longs;to modo in tutto &longs;i ha da pigliare & la &longs;a <lb/>lita & la di&longs;ce&longs;a del pe&longs;o po&longs;to in D &longs;econdo la linea LH, &longs;e dunque il pe&longs;o po&longs;to <lb/>in E &longs;i moue&longs;&longs;e in giù per la linea EG, mouerebbe il pe&longs;o po&longs;to in D in sù per <lb/>DF. & percioche l'angolo CEK è eguale all'angolo CDL, & l'angolo CEG<emph.end type="italics"/> <arrow.to.target n="note57"></arrow.to.target><lb/><emph type="italics"/>è eguale all'angolo CDF; &longs;arà il <expan abbr="re&longs;tãte">re&longs;tante</expan> angolo GEK al re&longs;tante LDF egua <lb/>le.

</s>

& e&longs;&longs;endo quella pre&longs;uppo&longs;ta, che dice il pe&longs;o e&longs;&longs;er più graue &longs;econdo il &longs;ito, <lb/>quanto in quel mede&longs;imo &longs;ito la di&longs;ce&longs;a è meno obliqua per chiara, & manife&longs;ta ri-<lb/>ceuuta, &longs;arà anche da e&longs;&longs;ere accettata &longs;enza dubbio que&longs;t' altra, cioè, che il pe&longs;o &longs;arà <lb/>più graue &longs;econdo il &longs;ito, quanto nel &longs;ito mede&longs;imo meno obliqua &longs;arà la &longs;alita; per <lb/>non e&longs;&longs;ere manco manife&longs;ta, ne meno conforme alla ragione.

</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

<pb id="18v" xlink:href="pagethumb-it/055.jpg"/>&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/>

</s>

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.

</s>

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.

</s>

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>

</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"/>

</s>

<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>

<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>

<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/>il 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>

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 id="19" xlink:href="pagethumb-it/056.jpg"/>mente non è della grauez <lb/>za cagione?

</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>

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"/>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>

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>

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.

</s>

Ma &longs;ia &longs;o&longs;tenuta la trutina da due po&longs;&longs;anze in F cioè, & in G,<pb id="19v" xlink:href="pagethumb-it/057.jpg"/>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.

</s>

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

</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/>

</s>

Co&longs;i ne anche la bilancia <lb/>DE da que&longs;to &longs;ito per que <lb/>&longs;ta cagione &longs;i mouerà.

</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.

</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.

</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.

</s>

& quando <lb/>la trutina &longs;tà in CG, mouer&longs;i in FG.

</s>

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.

</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"/>

</s>

</figure>

</figure>

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

</s>

<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>

&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.

</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 terza di questo.<emph.end type="italics"/>

</s>

</figure>

</figure>

<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>

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>

<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>

</figure>

<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>

Adunque dalla parte di D la bilancia &longs;i mouerà in giu fin che ri-<lb/>torni in AB.

</s>

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.

</s>

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 id="21" xlink:href="pagethumb-it/060.jpg"/><emph type="italics"/>modo, il perpendicolo FG non diuiderà giamai la bilancia &longs;e non nel punto C, et <lb/>in parti eguali.

</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. 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/>

</s>

<s id="id.2.1.392.4.0">Dalla qual co&longs;a accade il <lb/>ritorno della bilancia ad <lb/>eguale di&longs;tanza dall'ori-<lb/>zonte.

</s>

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

</s>

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>

</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.

</s>

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/>

</s>

&longs;ia allungata prima la linea <lb/>CD fin'al centro del mon <lb/>do, che &longs;ia S.

</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.

</s>

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>

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.

</s>

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>

ma e&longs;&longs;endo EF eguale ad AB, &longs;arà la circonfe-<lb/>renza EAF eguale alla circonferenza AFB.

</s>

Onde tolta via la comune AF<emph.end type="italics"/><pb id="22" xlink:href="pagethumb-it/062.jpg"/><emph type="italics"/>&longs;arà la circonferenza EA eguale alla cir conferenza FB.

</s>

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.

</s>

Da quali &longs;e &longs;aranno leuati via gli angoli HFG HEK eguali, &longs;arà l'an <lb/>golo GFB maggiore dell'angolo KEA.

</s>

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.

</s>

Onde grauezza maggiore hauerà il pe&longs;o posto in E, <lb/>che il pe&longs;o po&longs;to in F.

</s>

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="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="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="note121"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 29. <emph type="italics"/>del primo.<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.

</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>

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"/>

</s>

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

</s>

<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.

</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>

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 id="22v" xlink:href="pagethumb-it/063.jpg"/><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.

</s>

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/>

</s>

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/>

</s>

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>

<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.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

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>

</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>

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

</s>

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

</s>

&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>

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

</s>

<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 dei 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>

<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"/>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 id="24" xlink:href="pagethumb-it/066.jpg"/><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>

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.

</s>

Ma <lb/>e&longs;&longs;endo HE eguale ad <lb/>HF, &longs;arà EN mag-<lb/>gior di NF.

</s>

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 di 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.

</s>

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="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="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"/>

</s>

<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"/>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.

</s>

Siano dai <lb/>punti EF tirate le linee EQ FR a piombo di OP.

</s>

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.

</s>

<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>

<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.

</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.

</s>

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.

</s>

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"/>

</s>

<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.

</s>

Adunque il pe&longs;o po&longs;to in E haurà grauezza maggiore del pe&longs;o po&longs;to in F.<lb/>

</s>

Dalle quali co&longs;e &longs;egue, che la bilancia EF &longs;i moue in giù dalla parte di E.<emph.end type="italics"/>

</s>

</figure>

<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>

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>

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.

</s>

Imperoche proponendo egli nella &longs;econda parte della que&longs;tione &longs;econda. <lb/>

</s>

“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/>

</s>

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"/>

</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>

& 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.

</s>

& accioche la bilancia AB &longs;i moua da que&longs;to &longs;ito, dice<emph.end type="italics"/><pb id="25" xlink:href="pagethumb-it/068.jpg"/><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/>dicemmo: 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>

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>

</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>

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>

<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/>

</s>

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>

&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.

</s>

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.

</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.

</s>

Dal por&longs;i dunque pe&longs;o maggiore ò minore in B, la <lb/>bilancia &longs;i inchinerà piu ò meno.

</s>

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"/>

</s>

</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.

</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"/>

</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"/>

</s>

<emph type="italics"/>Ma 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>

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 id="26" xlink:href="pagethumb-it/070.jpg"/><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>

</figure>

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

</s>

&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>

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>

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.

</s>

La qual co&longs;a hauerà &longs;empre, quan-<lb/>tunque &longs;i ponga vn minimo pe&longs;o in B.

</s>

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.

</s>

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.

</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"/><pb id="26v" xlink:href="pagethumb-it/071.jpg"/><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"/>

</s>

</figure>

<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.

</s>

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;">bilan</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.

</s>

& 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>

<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>

</figure>

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

</s>

<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 rimarrà.<emph.end type="italics"/>

</s>

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

</s>

</figure>

<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="fig49"></arrow.to.target><lb/><emph type="italics"/>

</s>

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

</s>

</figure>

<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.

</s>

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.

</s>

Moua&longs;i poi <lb/>la <expan abbr="bil&amacr;cia">bilancia</expan> da que&longs;to &longs;ito, come in ECF.<lb/>

</s>

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.

</s>

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="fig49b"></arrow.to.target><lb/><emph type="italics"/>te.

</s>

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

</s>

<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>

</figure>

</figure>

</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/>& la linea 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"/>

</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"/>

</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"/>

</s>

<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. 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>

&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"/>

</s>

</figure>

In que&longs;to luogo egli conuiene auertire, il che poteua&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. 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>

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.

</s>

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'orizonte.

</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. 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.

</s>

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>

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, finche la <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 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 bilancia 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.

</s>

Que<lb/>&longs;ti 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 id="29" xlink:href="pagethumb-it/076.jpg"/>to a&longs;&longs;ai, & &longs;in qui è &longs;tato &longs;eguito molto nella &longs;ua dottrina.

</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.

</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.

</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.

</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.

</s>

Con laquale &longs;pecu-<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>

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/>mente 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>

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>

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

</s>

Di&longs;&longs;e il Petrarcha.

</s>

PROPOSITIONE V.

</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.

</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.

</s>

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.

</s>

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.

</s>

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 Q.

</s>

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.

</s>

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.

</s>

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.

</s>

Per la qual co&longs;a per la pro <lb/>portione vguale come CH ad HB, co&longs;i F ad N.

</s>

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 id="30" xlink:href="pagethumb-it/078.jpg"/><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.

</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>

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.

</s>

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"/>

</s>

<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>

<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>

<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>

<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>

<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>

<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="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="note65"></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="note66"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 6. <emph type="italics"/>del primo di Archimede 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>.

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>.

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

</s>

</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.

</s>

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.

</s>

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.

</s>

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.

</s>

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"/>

</s>

<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>

<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.

</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"/>

</s>

<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"/>

</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.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

Ma per e&longs;&longs;ere ME traloro eguali, &longs;aran-<lb/>no anche NH tra &longs;e eguali.

</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.

</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.

</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>

& 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 id="31" xlink:href="pagethumb-it/080.jpg"/><emph type="italics"/>pe&longs;eranno egualmente.

</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.

</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>

& 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/>

</s>

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.

</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>

<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"/>

</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>

<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"/>

</s>

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

</s>

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

</s>

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

</s>

<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"/>notitia commune 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>

<margin.target id="note82"></margin.target><emph type="italics"/>Per la commune notitia 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>

</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.

</s>

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.

</s>

Ipe&longs;i LM pe&longs;eranno egualmente (come è detto <lb/>di &longs;opra) conlipe&longs;i EF appiccati in GB.

</s>

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.

</s>

In fine congiunga&longs;i GO, laquale tagli HP in R.

</s>

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.

</s>

Similmente percioche RP è egual<emph.end type="italics"/><pb id="31v" xlink:href="pagethumb-it/081.jpg"/><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.

</s>

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>

</s>

<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.

</s>

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.

</s>

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.

</s>

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:

</s>

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.

</s>

Sono dunque egual-<lb/>mente graui i pe&longs;i EF attaccati in GB, come attaccati in H.<emph.end type="italics"/>

</s>

</figure>

<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="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="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>

<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>

</figure>

</figure>

<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/>

</s>

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.

</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>

<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>

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.

</s>

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/>

</s>

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.

</s>

Tagli&longs;i DC in due parti eguali in H, & da H &longs;iano fatti pendere <lb/>ambidue i pe&longs;i EF.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

Adunque come BA ver&longs;o AC, così FG pe&longs;i al pe&longs;o L.

</s>

Per laqual<emph.end type="italics"/><pb id="32v" xlink:href="pagethumb-it/083.jpg"/><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.

</s>

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.

</s>

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"/>

</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"/>

</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"/>

</s>

<margin.target id="note89"></margin.target><emph type="italics"/>Per la con&longs;eguenza della quarta del 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>

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

</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/>

</s>

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.

</s>

Et percioche AD è eguale ad AB; i pe&longs;i FG pe&longs;eran <lb/>no egualmente, & hauranno la mede&longs;ima grauezza.

</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>

</figure>

Altramente.

</s>

<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 id="33" xlink:href="pagethumb-it/084.jpg"/><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/>

</s>

<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.

</s>

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.

</s>

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.

</s>

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 H attac<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"/>

</s>

<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.

</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.

</s>

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.

</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"/>

</s>

</figure>

COROLLARIO.

</s>

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.

</s>

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. del Purgatorio.

</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.

</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.

</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 corollarij, molti de i quali han-<lb/>no congiunta la &longs;ua dimo&longs;tratione.

</s>

<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.

</s>

Appicchi&longs;i in A il pe&longs;o D, che pe&longs;i egualmente col marco E appic-<lb/>cato in F.

</s>

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.

</s>

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/>

</s>

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.

</s>

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.

</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"/>

</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>

<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.

</s>

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.

</s>

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.

</s>

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"/>

</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>

PROPOSITIONE VII.

</s>

PROBLEMA.

</s>

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.

</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.

</s>

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

</s>

</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/>

</s>

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.

</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.

</s>

Dapoi diuida&longs;i anco BL in N, &longs;i che <lb/>LN ad NB &longs;ia come la grauezza del pe&longs;o G alla grauezza del pe&longs;o F.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

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

</s>

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

</s>

<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>

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>

<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>

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

</s>

</chap>

DELLA LEVA.

</s>

LEMMA.

</s>

</figure>

Siano quattro grandezze ABCD; & &longs;ia la A <lb/>maggiore della B, & C maggiore della D.

</s>

Dico, <lb/>che A ver&longs;o D hà proportione maggiore di quello <lb/>che hà B ver&longs;o C.

</s>

<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/>

</s>

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"/>

</s>

<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>

PROPOSITIONE I.

</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.

</s>

<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.

</s>

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 id="35v" xlink:href="pagethumb-it/089.jpg"/><arrow.to.target n="note99"></arrow.to.target> <emph type="italics"/>ver&longs;o la CB.

</s>

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.

</s>

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"/>

</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 Archimede delleco &longs;ache egual <expan abbr="m&etilde;te">mente</expan> pe&longs;ano.<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"/>

</s>

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.

</s>

<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.

</s>

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:

</s>

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.

</s>

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"/>

</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>

COROLLARIO.

</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.

</s>

PROPOSITIONE II.

</s>

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

</s>

<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.

</s>

Dico, che &longs;i come <lb/>BD à BA; co&longs;i è lapo&longs;&longs;anza di A' al pe&longs;o C.

</s>

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.

</s>

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.

</s>

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.

</s>

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 attaccato 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.

</s>

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.

</s>

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.

</s>

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>

</figure>

<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>

<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"/>

</s>

<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>

<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 Corollario della<emph.end type="italics"/> 4 <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, & 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.

</s>

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.

</s>

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.

</s>

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.

</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.

</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"/>

</s>

</figure>

COROLLARIO I.

</s>

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>

<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>

<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>

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.

</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.

</s>

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.

</s>

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"/>

</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>

<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>

PROPOSITIONE III.

</s>

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

</s>

<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.

</s>

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/>

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</s>

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.

</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>

<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>

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.

</s>

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.

</s>

& percioche AB è eguale à BE, & i pe&longs;i<emph.end type="italics"/> <pb id="38" xlink:href="pagethumb-it/093.jpg"/><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.

</s>

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>

& percioche i pe&longs;i FGC, & la po&longs;&longs;anza <lb/>in D pe&longs;ano egualmente, leuati via dunque i pe&longs;i FG, i quali pe&longs;ano egualmente, <lb/>i re&longs;tanti pe&longs;eranno egualmente, cioè la po&longs;&longs;anza in D co'l pe&longs;o C, cioè la po&longs;&longs;an <lb/>za in D &longs;o&longs;terrà il pe&longs;o C, talche la leua AB stia come prima.

</s>

& per e&longs;&longs;ere la <lb/>po&longs;&longs;anza in D eguale al pe&longs;o G, & il pe&longs;o C eguale al pe&longs;o, hauerà la po&longs;&longs;an <lb/>zaposta in D la proportione mede&longs;ima al pe&longs;o C, che EB, cioè AB à BD. <lb/>che bi&longs;ognaua mostrare.<emph.end type="italics"/>

</s>

</figure>

COROLLARIO I.

</s>

Da que&longs;to è chiaro ancora, come prima, che &longs;e &longs;arà po&longs;to il pe-<lb/>&longs;o più vicino al &longs;o&longs;tegno B, come in H, il pe&longs;o douer&longs;i &longs;o-<lb/>&longs;tenere da forza minore.

</s>

<emph type="italics"/>Percioche HB ha proportione minore à BD, che AB à BD. & quanto più<emph.end type="italics"/> <arrow.to.target n="note136"></arrow.to.target><lb/><emph type="italics"/>da vicino &longs;arà al &longs;o&longs;tegno, &longs;empre anco minore forza vi &longs;i ricercherà.<emph.end type="italics"/>

</s>

<margin.target id="note136"></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>

Egli è parimente manife&longs;to, che la po&longs;&longs;anza in D è &longs;empre <lb/>maggiore del pe&longs;o C.

</s>

<emph type="italics"/>Perche &longs;e tra AB &longs;i piglia qual &longs;i voglia punto, come D, &longs;empre AB &longs;arà mag<lb/>giore di BD.<emph.end type="italics"/>

</s>

<emph type="italics"/>El è da auertire, che que&longs;te dimo&longs;trationi lequali habbiamo prodotte in mezo, &longs;i po&longs;&longs;o-<lb/>no à tutte que&longs;te co&longs;e commodamente adattare non &longs;olamente e&longs;&longs;endo le leue egual-<lb/>mente distanti dall'orizonte, ma anche inchinate le dette leue all'orizonte.

</s>

ilche è <lb/>chiaro da quel che nella bilancia &longs;i è diui&longs;ato.<emph.end type="italics"/>

</s>

PROPOSITIONE IIII.

</s>

Se la po&longs;&longs;anza mouerà il pe&longs;o appiccato nella leua, &longs;arà lo &longs;patio <lb/>della po&longs;&longs;anza mo&longs;&longs;a allo &longs;patio del pe&longs;o mo&longs;&longs;o, come la di&longs;tan <lb/>za dal &longs;o&longs;tegno alla po&longs;&longs;anza, alla di&longs;tanza dall'i&longs;te&longs;&longs;o &longs;o&longs;tegno <lb/>fin allo appiccamento del pe&longs;o.

</s>

<emph type="italics"/>Sia la leua AB, il cui &longs;o&longs;tegno C, & &longs;ia il pe&longs;o D attaccato al punto B, & &longs;ia <lb/>la po&longs;&longs;anza in A mouente il pe&longs;o D conlaleua AB.

</s>

Dico lo &longs;patio della po&longs;-<lb/>&longs;anza in A allo &longs;patio del pe&longs;o e&longs;&longs;ere co&longs;i come CA à CB.

</s>

Moua&longs;i la leua <lb/>AB, & affine che il pe&longs;o D &longs;i moua in sù, bi&longs;ogna che B &longs;i moua in sù, & A in <lb/>giù.

</s>

& percioche C è punto immobile; però mentre A, & B &longs;i mouono, de-<lb/>&longs;criueranno circonferenze di cerchi.

</s>

Moua&longs;i dunque AB in EF; &longs;aranno AEBF <lb/>circonferenze di cerchi, i me-<lb/>zi diametri de' quali &longs;ono CA <lb/>CB. compi&longs;ca&longs;i tutta la cir-<lb/>conferenza AGE, & tut-<lb/>ta la BHF, & &longs;iano KH <lb/>i punti doue AB, & EF ta-<lb/>gliano il cerchio BHF.

</s>

Hor <lb/>percioche l'angolo BCF è<emph.end type="italics"/><lb/><arrow.to.target n="note137"></arrow.to.target> <emph type="italics"/>eguale all'angolo HCK, &longs;a-<lb/>rà la circonferenza KH egua<emph.end type="italics"/><lb/><arrow.to.target n="note138"></arrow.to.target> <emph type="italics"/>le alla circonferenza BF, & <lb/>concio&longs;ia, che le circonferen-<lb/>ze AEKH &longs;iano &longs;otto l'i-<lb/>&longs;te&longs;&longs;o angolo ACE, & la <lb/>circonferenza AE à tutta <lb/>la circonferenza AGE &longs;ia <lb/>come l'angolo ACE à quat <lb/>tro retti, & come l'i&longs;te&longs;&longs;o an-<lb/>golo HCK à quattro retti, <lb/>co&longs;i anche è la circonferenza <lb/>HK à tutta la circonferentia <lb/>HBK, &longs;arà la circonferentia<emph.end type="italics"/><lb/><arrow.to.target n="fig53"></arrow.to.target><lb/><emph type="italics"/>AE à tutta la circonferentia AGE, come la circonferentia KH à tutta la<emph.end type="italics"/><lb/><arrow.to.target n="note139"></arrow.to.target> <emph type="italics"/>KFH. & permutando come la circonferentia AE alla circonferenza KH, cioè <lb/>BF, co&longs;i tutta la circonferenza AGE à tutta la circonferenza BHF; ma tut-<emph.end type="italics"/><lb/><arrow.to.target n="note140"></arrow.to.target> <emph type="italics"/>ta la circonferenza AGE co&longs;i &longs;i ha à tutta la BHF, come il diametro del cer-<lb/>chio AEG al diametro del cerchio BHF. Come dunque la circonferenza AE<emph.end type="italics"/><pb id="39" xlink:href="pagethumb-it/096.jpg"/><emph type="italics"/>ver&longs;o la circonferenza BF, co&longs;i è il diametro del cerchio AGE al diametro del<emph.end type="italics"/> <arrow.to.target n="note141"></arrow.to.target><lb/><emph type="italics"/>cerchio BHF: ma come il diametro al diametro, co&longs;i è anche il mezo diametro al <lb/>mezo diametro, cioè CA à CB.

</s>

Per laqual co&longs;a come la circonferenza AE <lb/>alla circonferenza BF, co&longs;i CA à CB: ma la circonferenza AE è lo <lb/>&longs;patio della po&longs;&longs;anza mo&longs;&longs;a, & la circonferenza BF è eguale allo &longs;patio di D pe-<lb/>&longs;o mo&longs;&longs;o, peroche lo &longs;patio del mouimento del pe&longs;o D &longs;empre è eguale allo &longs;patio <lb/>del mouimento del punto B, per e&longs;&longs;ere attaccato in B.

</s>

Lo &longs;patio dunque della po&longs; <lb/>&longs;anza mo&longs;&longs;a allo &longs;patio del pe&longs;o mo&longs;&longs;o è come CA à CB; cioè come la di&longs;tan-<lb/>za dal &longs;o&longs;tegno alla po&longs;&longs;anza, alla distanza dall'i&longs;te&longs;&longs;o all'appiccamento del pe&longs;o. <lb/>che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note137"></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="note138"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 26. <emph type="italics"/>del terzo.<emph.end type="italics"/>

</s>

<margin.target id="note139"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 16. <emph type="italics"/>del<emph.end type="italics"/> 15.

</s>

<margin.target id="note140"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 23. <emph type="italics"/>del<emph.end type="italics"/> 8. <emph type="italics"/>di Pappo.<emph.end type="italics"/>

</s>

<margin.target id="note141"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 11. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

<emph type="italics"/>Ma &longs;ia la leua AB, il cui &longs;o&longs;tegno B, & la po&longs;&longs;anza mouente in A, & il pe&longs;o <lb/>in C.

</s>

Dico lo &longs;patio della po&longs;&longs;anza mo&longs;&longs;a allo &longs;patio del pe&longs;o tra&longs;portato co&longs;i e&longs;-<lb/>&longs;ere, come BA à BC.<lb/>

</s>

Moua&longs;i la leua, & accioche <lb/>il pe&longs;o &longs;ia alzato in sù, egli <lb/>è nece&longs;&longs;ario, che anche i pun <lb/>ti CA &longs;imouano in sù.<lb/>

</s>

Moua&longs;i dunque A in sù <lb/>fin'in D; & &longs;ia il mouimen <lb/>to della leua BD.

</s>

mo&longs;tre-<lb/>remo nel modo i&longs;te&longs;&longs;o, come <lb/>prima è detto, che i punti <lb/>CA de&longs;criuono circonferen <lb/>ze di cerchi, i cui mezi dia-<lb/>metri &longs;ono BA BC. & di-<lb/>mo&longs;treremo &longs;imilmente co&longs;i <lb/>e&longs;&longs;ere AD à CE, come il <lb/>mezo diametro AB al me-<lb/>zo diametro BC.<emph.end type="italics"/>

</s>

<emph type="italics"/>Et per la ragione i&longs;te&longs;&longs;a, &longs;e la <lb/>po&longs;&longs;anza fo&longs;&longs;e in C, & il <lb/>pe&longs;o in A &longs;i prouerà co&longs;i <lb/>e&longs;&longs;ere CE ver&longs;o AD, co-<emph.end type="italics"/><lb/><arrow.to.target n="fig54"></arrow.to.target><lb/><emph type="italics"/>me BC à BA, cioè la di&longs;tanza dal &longs;o&longs;tegno alla po&longs;&longs;anza; alla di&longs;tanza dal-<lb/>l'iste&longs;&longs;o allo attaccamento del pe&longs;o.

</s>

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

</s>

</figure>

COROLLARIO.

</s>

Da que&longs;te co&longs;e è manife&longs;to, che maggiore proportione ha lo &longs;pa <lb/>tio della po&longs;&longs;anza, che moue allo &longs;patio del pe&longs;o mo&longs;&longs;o, che il <lb/>pe&longs;o alla mede&longs;ima po&longs;&longs;anza.

</s>

<emph type="italics"/>Percioche lo &longs;patio della po&longs;&longs;anza allo &longs;patio del pe&longs;o ha la mede&longs;ima proportione, <lb/>che il pe&longs;o alla po&longs;&longs;anza, che &longs;o&longs;liene il detto pe&longs;o.

</s>

Ma la po&longs;&longs;anza, che &longs;ostie-<lb/>ne è minore della po&longs;&longs;anza che moue, però il pe&longs;o haurà proportione minore alla <lb/>po&longs;&longs;anza che lo moue, che alla po&longs;&longs;anza, che lo &longs;ostiene.

</s>

Lo &longs;patio dunque della<emph.end type="italics"/><lb/><arrow.to.target n="note142"></arrow.to.target> <emph type="italics"/>po&longs;&longs;anza che moue allo &longs;patio del pe&longs;o haur à proportione maggiore, che il pe&longs;o al-<lb/>l'i&longs;le&longs;&longs;a po&longs;&longs;anza.<emph.end type="italics"/>

</s>

<margin.target id="note142"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 8. <emph type="italics"/>del quinto.<emph.end type="italics"/>

</s>

PROPOSITIONE V.

</s>

La po&longs;&longs;anza che in qual &longs;i voglia modo &longs;o&longs;tenga il pe&longs;o con la le-<lb/>ua hauerà la proportione mede&longs;ima ad e&longs;&longs;o pe&longs;o, che la di&longs;tan <lb/>za frapo&longs;ta dal &longs;o&longs;tegno al punto, doue dal centro della gra-<lb/>uezza del pe&longs;o tirata vna linea à piombo all'orizonte tagli la <lb/>leua, alla di&longs;tanza che è fra il &longs;o&longs;tegno, & la po&longs;&longs;anza.

</s>

<emph type="italics"/>Sia la leua AB egualmente di&longs;tante dall'orizonte, col &longs;uo &longs;o&longs;tegno N. &longs;ia dopo il pe <lb/>&longs;o AC, il cui centro della grauezza &longs;ia D, ilquale &longs;ia prima &longs;otto la leua: ma <lb/>il pe&longs;o &longs;ia appiccato à i punti AO. & dal punto D &longs;ia tirata la linea DE à <lb/>piomho dell' orizonte, & di AB.

Che &longs;e vi &longs;aranno altre leue ancora AF AG, <lb/>i cui &longs;o-<lb/>stegni, <lb/>&longs;iano H <lb/>K, & il <lb/>pe&longs;o A <lb/>C &longs;ia ap<lb/>piccato <lb/>nella le-<lb/>ua AG <lb/>ne i pun <lb/>ti AQ, <lb/>& nella <lb/>leua A <lb/>F ne' <expan abbr="p&utilde;">pum</expan> <lb/>ti AP: <lb/>& la li-<lb/>nea DE <lb/>allunga-<emph.end type="italics"/><lb/><arrow.to.target n="fig55"></arrow.to.target><lb/><emph type="italics"/>ta tagli AF in L, & AC in M. Dico che la po&longs;&longs;anza in F &longs;o&longs;tenente il pe&longs;o AC <lb/>ha quella proportione ad e&longs;&longs;o pe&longs;o, che ha KL à KF; & la po&longs;&longs;anza in D ha quella <lb/>proportione al pe&longs;o, che ha NE ad NB; & la po&longs;&longs;anza in G al pe&longs;o quella, che ha <lb/>HM ad HG. Hor percioche DL &longs;tà à piombo dell' orizonte, il pe&longs;o AC venga ap-<emph.end type="italics"/><pb id="40" xlink:href="pagethumb-it/098.jpg"/><emph type="italics"/>piccato doue &longs;i voglia nella linea DL, rimarrà nel modo i&longs;te&longs;&longs;o che &longs;i troua.

</s>

Per la-<lb/>qual co&longs;a &longs;e nella leua AB &longs;i &longs;cioglieranno gli appiccamenti, che &longs;ono ad AO, il <lb/>pe&longs;o AC appiccato in E rimarr à nell'i&longs;te&longs;&longs;o modo, come hora rimane, cioè leuato via <lb/>il punto A, & la linea QO, nell'i&longs;te&longs;&longs;o modo il pe&longs;o appiccato in E rimarrà, come <lb/>era &longs;o&longs;tenuto da punti i&longs;te&longs;&longs;i AO, come &longs;i proua per lo commentario di Federico <lb/>Commandino nella &longs;esta propo&longs;itione di Archimede della quadratura della parabo <lb/>la, & dalla prima di que&longs;to della bilancia.

</s>

Co&longs;i percio che il pe&longs;o AC ha &longs;empre la <lb/>i&longs;te&longs;&longs;a di&longs;po&longs;itione ver&longs;o la bilancia, &longs;ia pur in AO &longs;ostentato, ouero pendente dal <lb/>punto E; la po&longs;&longs;anza mede&longs;ima in B &longs;o&longs;tenterà il pe&longs;o i&longs;te&longs;&longs;o AC pendente, ouero <lb/>da E, ouero da AO. ma la po&longs;&longs;anza in B &longs;o&longs;tenente il pe&longs;o AC appiccato in E co&longs;i <lb/>&longs;i hà ad e&longs;&longs;o pe&longs;o, come NE ad NB;

</s>

La po&longs;&longs;anza dunque in B &longs;o&longs;tenente il pe&longs;o <lb/>AC da punti AO pendente &longs;arà co&longs;i ad e&longs;&longs;o pe&longs;o, come NE ad NB. Non altra-<emph.end type="italics"/> <arrow.to.target n="note143"></arrow.to.target><lb/><emph type="italics"/>mente &longs;i mo&longs;trerà, che il pe&longs;o AC pendente dal punto L rimane, come &longs;e &longs;o&longs;&longs;e &longs;oste <lb/>nuto da punti AP; & la po&longs;&longs;anza in F ad e&longs;&longs;o pe&longs;o e&longs;&longs;ere co&longs;i come<emph.end type="italics"/> KL <emph type="italics"/>à KF.

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Ma <lb/>nella leua AG il pe&longs;o AC appiccato in M co&longs;i rimanere, come egli è &longs;o&longs;tenuto da <lb/>punti AQ; & la po&longs;&longs;anza di G co&longs;i e&longs;&longs;ere al pe&longs;o AC, come HM ad HG, cioè co-<lb/>me la di&longs;tanza dal &longs;o&longs;tegno al punto, doue la linea tirata à piombo dell' orizonte <lb/>dal centro della grauezza del pe&longs;o taglia la leua, alla di&longs;tanza dal &longs;o&longs;tegno alla po&longs;-<lb/>&longs;anza.

</s>

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

</s>

</figure>

<margin.target id="note143"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Che &longs;e FBG &longs;o&longs;&longs;ero i &longs;o&longs;tegni delle leue, & le po&longs;&longs;anze fo&longs;&longs;ero in KNH &longs;o&longs;tenenti il pe <lb/>&longs;o, con &longs;imile modo &longs;i mo&longs;trerà la po&longs;&longs;anza in H, co&longs;i e&longs;&longs;ere al pe&longs;o, come GM à GH, <lb/>et la <expan abbr="po&longs;s&amacr;za&imacr;">po&longs;sanzaim</expan> N al pe&longs;o, come BE à BN, et la <expan abbr="po&longs;s&amacr;za">po&longs;sanza</expan> <expan abbr="&imacr;">im</expan> K al pe&longs;o come FL ad FK.<emph.end type="italics"/>

</s>

<emph type="italics"/>Et &longs;e le leue AB AF AG haue&longs;&longs;ero i &longs;o&longs;legni in A, & il pe&longs;o fo&longs;&longs;e NO; poi dal <lb/>centro D del <lb/>la &longs;ua gra-<lb/>uezza fo&longs;&longs;e <lb/>tirata la li-<lb/>nea DME <lb/>L à piombo <lb/>di AB, & <lb/>dell' orizon <lb/>te, & fo&longs;&longs;e-<lb/>ro le po&longs;&longs;an <lb/>ze in FB <lb/>G; <expan abbr="&longs;imilm&etilde;">&longs;imilmen</expan> <lb/>re mo&longs;tre-<lb/>ra&longs;&longs;i la po&longs; <lb/>&longs;anza di G <lb/>&longs;o&longs;tenente <lb/>il pe&longs;o N<emph.end type="italics"/><lb/><arrow.to.target n="fig56"></arrow.to.target><lb/><emph type="italics"/>O co&longs;i e&longs;&longs;ere ad e&longs;&longs;o pe&longs;o, come AM ad AG, & la po&longs;&longs;anza in B come AE ad <lb/>AB; & la po&longs;&longs;anza in F come AL ad AF.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Sia dapoi la leua AB egualmente di&longs;tante dall'orizonte, il cui &longs;o&longs;tegno &longs;ia D, & &longs;ia <lb/>BE il pe&longs;o, il cui centro della grauezza &longs;ia F &longs;opra la leua; & dal punto F riri&longs;i la <lb/>linea FH à piombo, & dell' orizonte, & di e&longs;&longs;a AB; & &longs;ia &longs;o&longs;tenuto il pe&longs;o dal <lb/>punto B, & da PQ &longs;iano po&longs;cia altre leue BLBM, i cui &longs;o&longs;tegni &longs;iano NO; <lb/>& la linea FH allungatatagli BM in K, & BL in G; & venga &longs;o&longs;tenuto il pe&longs;o<emph.end type="italics"/><lb/><arrow.to.target n="fig57"></arrow.to.target><lb/><emph type="italics"/>nella leua BL ne'punti BP; & nella leua BM dal punto B, & PR.

</s>

Dico, che <lb/>la po&longs;&longs;anza in L &longs;o&longs;tenente il pe&longs;o BE nella leua BL ha quella proportione ad <lb/>e&longs;&longs;o pe&longs;o, che NG ad NL; & la po&longs;&longs;anza in A al pe&longs;o ha quella proportio-<lb/>ne, che DH à DA; & la po&longs;&longs;anza di M al pe&longs;o ha quella proportione, che <lb/>OK ad OM.

</s>

Hor percioche la linea KF tirata dal centro della grauezza F è<emph.end type="italics"/><lb/><arrow.to.target n="note144"></arrow.to.target> <emph type="italics"/>à piombo dell' orizonte, &longs;ia pur &longs;ostenuto il pe&longs;o da qual &longs;i voglia punto della linea <lb/>KF, egli rimarrà, come hora &longs;i troua.

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Se dunque &longs;arà &longs;ostenuto in H, rimarrà co <lb/>me prima, cioè leuato via il punto B, & PQ, i quali &longs;o&longs;tengono il pe&longs;o, rimarrà <lb/>il pe&longs;o BE nel modo che da e&longs;&longs;i era &longs;o&longs;tenuto.

</s>

Per la qual co&longs;a grauerà nella le-<lb/>ua AB in H, & haurà alla leua quella di&longs;po&longs;itione mede&longs;ima, che prima, & per-<lb/>ciò &longs;arà come &longs;e fo&longs;&longs;e appiccato in H. La mede&longs;ma po&longs;&longs;anza dunque &longs;o&longs;terrà il me <lb/>de&longs;imo pe&longs;o BE &longs;o&longs;tentato ouero in H, ouero in B & Q.

</s>

Ma la po&longs;&longs;anza in A<emph.end type="italics"/><lb/><arrow.to.target n="note145"></arrow.to.target> <emph type="italics"/>&longs;o&longs;tenente il pe&longs;o BE appiccato in H con la leua AB hal'i&longs;te&longs;&longs;a proportione ad e&longs;-<lb/>&longs;o pe&longs;o, che DH à DA; l'i&longs;te&longs;&longs;a po&longs;&longs;anza dunque in A &longs;o&longs;tenente il pe&longs;o BE ne' <lb/>punti BQ &longs;o&longs;tentato, &longs;arà ad e&longs;&longs;o pe&longs;o come DH à DA.

</s>

Similmente &longs;i mo&longs;trer à <lb/>il pe&longs;o BE, &longs;e in G &longs;arà &longs;o&longs;tenuto, rimanere come egliera &longs;o&longs;tenuto da punti BP: <lb/>& nel punto K, come dapunti BR.

</s>

Per la qual co&longs;a la po&longs;&longs;anza in L &longs;o&longs;tenente<emph.end type="italics"/><pb id="41" xlink:href="pagethumb-it/100.jpg"/><emph type="italics"/>il pe&longs;o BE ad e&longs;&longs;o pe&longs;o co&longs;i &longs;arà come NG ad NL.

</s>

ma la po&longs;&longs;anza in M al pe <lb/>&longs;o, come OK ad OM; cioè come la di&longs;tanza dal &longs;o&longs;tegno al punto, doue dal cen<lb/>tro della grauezza del pe&longs;o la linea tirata à piombo dell' orizonte taglia la leua, alla <lb/>di&longs;tanza dal &longs;o&longs;tegno alla po&longs;&longs;anza.

</s>

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

</s>

</figure>

<margin.target id="note144"></margin.target><emph type="italics"/>Per la prima di questo della bilancia.<emph.end type="italics"/>

</s>

<margin.target id="note145"></margin.target><emph type="italics"/>Per la prima di questo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Che &longs;e LAM fo&longs;&longs;ero i &longs;o&longs;tegni, & le po&longs;&longs;anze in NDO; &longs;imilmente mo&longs;trera&longs;&longs;i <lb/>la po&longs;&longs;anza in N co&longs;i e&longs;&longs;ere al pe&longs;o, come LG ad LN; & la po&longs;&longs;anza in D, <lb/>come AH ad AD, & la po&longs;&longs;anza in O come MK ad MO.<emph.end type="italics"/>

</s>

<emph type="italics"/>Et &longs;e le leue BA BL BM haue&longs;&longs;ero i &longs;o&longs;tegni in B, & il pe&longs;o fo&longs;&longs;e NO &longs;opra <lb/>la leua, & dal centro F della grauezza fo&longs;&longs;e tirata la linea FD EG à piombo <lb/>di AB, & dell' orizonte; & fo&longs;&longs;ero le po&longs;&longs;anze in LAM, &longs;imilmente proue-<emph.end type="italics"/><lb/><arrow.to.target n="fig58"></arrow.to.target><lb/><emph type="italics"/>ra&longs;&longs;i la po&longs;&longs;anza in L &longs;o&longs;tenente il pe&longs;o co&longs;i e&longs;&longs;ere ad e&longs;&longs;o pe&longs;o, come BD à BL; <lb/>& la po&longs;&longs;anza in A al pe&longs;o come BE à BA, & la po&longs;&longs;anza in M come BG <lb/>à BM.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Sia vltimamente la leua. AB egualmente di&longs;tante dall'orizonte, il cui &longs;ostegno &longs;ia <lb/>C, & il pe&longs;o DE habbia il centro della graueza F nella leua AB; & &longs;iano <lb/>alla fine altre leue GHKL, co i &longs;o&longs;tegni &longs;uoi MN; & il pe&longs;o nella leua GH <lb/>&longs;ia &longs;o&longs;tentato da i punti GO, & nella leua AB da punti AT, & nella leua <lb/>KL da punti KQ, & il centro F della grauezza &longs;ia parimente in amendue le le-<emph.end type="italics"/><lb/><arrow.to.target n="fig59"></arrow.to.target><lb/><emph type="italics"/>ue GH<emph.end type="italics"/> K<emph type="italics"/>L, & &longs;iano le po&longs;&longs;anze in HBL.

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Dico la po&longs;&longs;anza in H co&longs;i e&longs;&longs;ere al <lb/>pe&longs;o, come N<emph.end type="italics"/>F <emph type="italics"/>ad NH; & la po&longs;&longs;anza in B al pe&longs;o, come C<emph.end type="italics"/>F <emph type="italics"/>à CB, & la po&longs; <lb/>&longs;anza in L al pe&longs;o, come M<emph.end type="italics"/>F <emph type="italics"/>ad ML. Hor percioche F è il centro della grauez-<lb/>za del pe&longs;o DE, &longs;e dunque in<emph.end type="italics"/> F <emph type="italics"/>&longs;arà &longs;o&longs;tenuto, &longs;tarà il pe&longs;o DE come prima, per <lb/>la diffinitione del centro della grauezza; & &longs;arà come &longs;e egli fo&longs;&longs;e appiccato in<emph.end type="italics"/> F; <lb/><emph type="italics"/>& &longs;tarà nella leua in quel modo i&longs;te&longs;&longs;o, &longs;o&longs;tenga&longs;i pure ò da punti AP, ouero dal <lb/>punto<emph.end type="italics"/> F. <emph type="italics"/>ilche parimente auerrà nelle leue GH KL, cioè che il pe&longs;o re&longs;terà nel mo <lb/>do i&longs;te&longs;&longs;o, &longs;o&longs;tenti&longs;i pur ò in<emph.end type="italics"/> F, <emph type="italics"/>ouero in GO ouero in KQ.

</s>

La mede&longs;ma po&longs;&longs;anza <lb/>dunque in B &longs;o&longs;tenterà il pe&longs;o i&longs;te&longs;&longs;o DE appiccato, ouero in<emph.end type="italics"/> F, <emph type="italics"/>ouero in AP: & <lb/>quando egli è appiccato in<emph.end type="italics"/> F, <emph type="italics"/>è ad e&longs;&longs;o pe&longs;o come CF à CB, dunque la po&longs;&longs;anza &longs;o-<lb/>&longs;tenente il pe&longs;o DE appiccato ad AP &longs;arà ad e&longs;&longs;o pe&longs;o come C<emph.end type="italics"/>F <emph type="italics"/>à CB. & nel mo<lb/>do i&longs;te&longs;&longs;o la po&longs;&longs;anza in H &longs;arà al pe&longs;o appiccato in OG co&longs;i, come N<emph.end type="italics"/>F <emph type="italics"/>ad NH. & <lb/>la po&longs;&longs;anza in L &longs;arà al pe&longs;o appiccato in KQ, come M<emph.end type="italics"/>F <emph type="italics"/>ad ML. ilche anco bi&longs;o-<lb/>gnaua mo&longs;trare.<emph.end type="italics"/>

</s>

</figure>

<emph type="italics"/>Ma &longs;e li &longs;o&longs;tegni fo&longs;&longs;ero HBL, & le po&longs;&longs;anze fo&longs;&longs;ero in NCM; &longs;imilmente prouera&longs;&longs;i <lb/>la po&longs;&longs;anza in N co&longs;i e&longs;&longs;ere al pe&longs;o, come HF ad HN & la po&longs;&longs;anza in C come <lb/>BF à BC; & la po&longs;&longs;anza in M come LF ad LM.<emph.end type="italics"/>

</s>

<emph type="italics"/>Et &longs;e le leue BA BC BD haue&longs;&longs;ero i &longs;o&longs;tegni in B, & fo&longs;&longs;ero i pe&longs;i in EF GH <lb/>KL, di modo che i loro centri della grauezza MNO fo&longs;&longs;ero nelle leue, & le<emph.end type="italics"/><lb/><arrow.to.target n="fig60"></arrow.to.target><lb/><emph type="italics"/>po&longs;&longs;anze fo&longs;&longs;ero in CAD.

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Similmente prouera&longs;&longs;i, che la po&longs;&longs;anza in C co&longs;i è <lb/>al pe&longs;o EF, come BM à BC, & la po&longs;&longs;anza in A al pe&longs;o GH, come <lb/>BN à BA, & la po&longs;&longs;anza in D al pe&longs;o KL, come BO à BD.<emph.end type="italics"/>

</s>

</figure>

PROPOSITIONE VI.

</s>

Sia AB linea retta, ad angoli retti, dellaquale &longs;tia AD, la-<lb/>quale dalla parte di D &longs;ia allungata come &longs;i vuole fin'al C, <lb/>& &longs;ia congiunta la CB, laquale parimente allunghi&longs;i dalla <lb/>parte di B fin ad E.

</s>

Dapoi &longs;iano dal punto B tirate altre <lb/>linee, come &longs;i vuole BF BG eguali ad AB tra AB BE; <lb/>& da i punti FG &longs;iano tirate le linee FH GK à piombo <lb/>delle &longs;udette, lequali &longs;i facciano eguali fra loro, & ad e&longs;&longs;a A <lb/>D come &longs;e BA AD fo&longs;&longs;ero mo&longs;&longs;e in BF FH, & in BG <lb/>GH; & congiungan&longs;i CH CK, lequali taglino le linee BF <lb/>BG ne'punti MN.

</s>

Dico che BN è minore di BM, & <lb/>BM di e&longs;&longs;a BA.

</s>

<emph type="italics"/>Congiungan&longs;i BD BH B<emph.end type="italics"/>K, <emph type="italics"/>& percioche due linee DA AB &longs;ono eguali à due<emph.end type="italics"/><lb/><arrow.to.target n="note146"></arrow.to.target> <emph type="italics"/>HF FB, & l'angolo DAB retto è anco eguale al retto HFB; &longs;aranno i <lb/>re&longs;tanti angoli eguali à i re&longs;tanti angoli, & HB eguale ad e&longs;&longs;a DB.

</s>

Similmen-<lb/>te mo&longs;trera&longs;&longs;i il triangolo BKG e&longs;&longs;ere eguale al triangolo BHF.

</s>

Per laqual co <lb/>&longs;a co'l centro B, & con l'in <lb/>teruallo di vna di e&longs;&longs;e de&longs;cri-<lb/>ua&longs;i il cerchio DH<emph.end type="italics"/> K<emph type="italics"/>E, il <lb/>quale tagli le linee CH CK <lb/>ne' punti OP; & congiun-<lb/>gan&longs;i OB PB.

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Percioche <lb/>dunque il punto K è più vi-<lb/>cino ad E, che H; &longs;arà la<emph.end type="italics"/><lb/><arrow.to.target n="note147"></arrow.to.target> <emph type="italics"/>linea CK maggiore di CH, <lb/>& CP minore di CO: dun<lb/>que PK &longs;arà maggiore di <lb/>OH.

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Ma perche il triangolo <lb/>BKP di due lati eguali ha i <lb/>&longs;uoi lati BK BP eguali à i <lb/>lati BH BO del triangolo <lb/>BHO di due lati eguali, ma <lb/>ben la ba&longs;e KP maggiore <lb/>della ba&longs;e HO, &longs;arà l'ango-<lb/>lo KBP maggiore dell' an<emph.end type="italics"/><lb/><arrow.to.target n="note148"></arrow.to.target> <emph type="italics"/>golo HBO.

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dunque i restan<lb/>ti angoli alla ba&longs;e, cioè KPB <lb/>PKB pre&longs;i in&longs;ieme, i quali <lb/>tra loro &longs;ono eguali, &longs;aranno <lb/>minori de i re&longs;tanti angol i al-<lb/>la ba&longs;e po&longs;ti, cioè OHB <lb/>HOB, iquali etiandio tra lo <lb/>ro &longs;ono eguali e&longs;&longs;endo che tut <lb/>ti gli angoli di cia&longs;cuno trian<emph.end type="italics"/><lb/><arrow.to.target n="note149"></arrow.to.target> <emph type="italics"/>golo &longs;iano eguali à due angoli <lb/>retti.

</s>

Per laqual co&longs;a anche <lb/>le metà di que&longs;ti, cioè NKB <lb/>&longs;arà minore di MHB.

</s>

Et<emph.end type="italics"/><lb/><arrow.to.target n="note150"></arrow.to.target> <emph type="italics"/>concio&longs;ia, che l'angolo BKG<emph.end type="italics"/><lb/><arrow.to.target n="fig61"></arrow.to.target><lb/><emph type="italics"/>&longs;ia eguale all'angolo BHF, &longs;arà NKG maggiore di MHF.

</s>

Se dunque nel <lb/>punto K &longs;i &longs;accia l'angolo GKQ eguale ad FHM &longs;i &longs;arà il triangolo GKQ <lb/>eguale al triangolo FHM; Imperoche due angoli in FH divno &longs;ono eguali à <lb/>due in GK d'vn'altro, & il lato FH è eguale al lato GK, &longs;arà GQ eguale <lb/>ad FM. Adunque GN &longs;arà maggiore di FM.

</s>

& co&longs;i per e&longs;&longs;ere BG egua-<emph.end type="italics"/><pb id="43" xlink:href="pagethumb-it/104.jpg"/><emph type="italics"/>le à BF, &longs;arà BN minore di e&longs;&longs;a BM. ma che BM &longs;ia minore di e&longs;&longs;a BA <lb/>è manife&longs;to, percioche BM, è minore di e&longs;&longs;a BF, laquale è eguale à BA. che <lb/>bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

</s>

</figure>

<margin.target id="note146"></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="note147"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 8. <emph type="italics"/>del serzo.<emph.end type="italics"/>

</s>

<margin.target id="note148"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 25. <emph type="italics"/>del<emph.end type="italics"/> 5.

</s>

<margin.target id="note149"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 5. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<margin.target id="note150"></margin.target><emph type="italics"/>Per la<emph.end type="italics"/> 26. <emph type="italics"/>del primo.<emph.end type="italics"/>

</s>

<emph type="italics"/>Di più &longs;e tra BG BE &longs;i tiri à piacere vn'altra linea eguale à BG; & faccia&longs;i l'ope <lb/>ratione, come di &longs;opra è stato detto, prouera&longs;&longs;i &longs;imilmente la linea BR e&longs;&longs;er mi-<lb/>nore di BN. & quanto più da vicino &longs;arà ad e&longs;&longs;a BE, &longs;arà anche &longs;empre minore.<emph.end type="italics"/>

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Che &longs;e i triangoli eguali BFH BGK fo&longs;&longs;ero di &longs;otto fra BC <lb/>BA collocati; & fo&longs;&longs;ero congiunte le linee HC KC, le-<lb/>quali taglia&longs;&longs;ero le linee BF BG allungate dalla parte di FG <lb/>ne' punti MN, &longs;arà <lb/>la BN maggiore del <lb/>la BM, & la BM di <lb/>e&longs;&longs;a BA.

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<emph type="italics"/>Imperoche allunghi&longs;i CH CK <lb/>fin alla circonferenza in OP, <lb/>& congiungan&longs;i BO BP; <lb/>con &longs;imile modo mo&longs;trera&longs;&longs;i <lb/>la linea PK e&longs;&longs;ere maggiore <lb/>ai OH, & l'angolo PKB e&longs; <lb/>&longs;ere minore dell <expan abbr="ãgolo">angolo</expan> OHB. <lb/>& percioche l'angolo BHF <lb/>è eguale dell' angolo BKG, &longs;a <lb/>rà tutto l'angolo PKG mi-<lb/>nore dell' angolo OHF.

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Per <lb/>laqual co&longs;a il re&longs;tante GKN <lb/>&longs;arà maggiore del re&longs;tante <lb/>FHM.

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Se <expan abbr="d&utilde;que">dunque</expan> fara&longs;&longs;i l'an <lb/>golo GKQ eguale ad FHM <lb/>la linea KQ taglier à in modo <lb/>la GN, che GQ diuenterà <lb/>eguale ad FM.

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Per laqual <lb/>co&longs;a maggiore &longs;arà GN, che <lb/>FM; allequali &longs;e &longs;ar anno ag <lb/>giunte le eguali BF BG, &longs;a-<lb/>rà BN maggiore di BM. & <lb/>per e&longs;&longs;ere BM maggiore di <lb/>FB, &longs;arà anco maggiore di <lb/>BA. &longs;imilmente prouera&longs;&longs;i <lb/>che <expan abbr="quãto">quanto</expan> più da vicino &longs;arà <lb/>BG à BC, la linea BN &longs;em <lb/>pre &longs;arà maggiore.<emph.end type="italics"/>

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</figure>

PROPOSITIONE VII.

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Sia la linea retta AB, à cui &longs;tia à piombo AD, laquale allun-<lb/>ghi&longs;i dalla parte di D come pare &longs;in'à C, & congiunga&longs;i C <lb/>B, laquale etiandio &longs;i allunghi fin'ad E; & &longs;imilmente tra <lb/>AB BE &longs;iano, come pare, tirate BF BG eguali ad e&longs;&longs;a AB, <lb/>& da punti FG &longs;iano <lb/>tirate le linee FH GK <lb/>pur eguali ad e&longs;&longs;a AD, <lb/>& à piombo di BF BG, <lb/>come &longs;e BA AD fo&longs;-<lb/>&longs;ero mo&longs;&longs;e in BF FH <lb/>BG GK: & congiun-<lb/>gan&longs;i CH CK, lequali <lb/>taglino le linee allunga <lb/>te BF BG ne' punti <lb/>MN.

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Dico che BN è <lb/>maggiore di BM, & <lb/>BM di e&longs;&longs;a BA.

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</figure>

<emph type="italics"/>Congiungan&longs;i BD BH BK, & <lb/>co'l centro B, & conlo &longs;patio <lb/>BD de&longs;criua&longs;i il cerchio.

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&longs;imil-<lb/>mente come nella precedente, di-<lb/>mo&longs;treremo ipunti KHDOP <lb/>e&longs;&longs;ere nella circonferenza del cer <lb/>chio; & <expan abbr="itri&amacr;goli">itriangoli</expan> ABD FBH <lb/>GBK e&longs;&longs;ere tra loro eguali, & <lb/>la linea PK e&longs;&longs;ere maggiore <lb/>della OH, & l'angolo PKB <lb/>e&longs;&longs;ere minore dell'angolo OHB. <lb/>

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Percioche <expan abbr="d&utilde;que">dunque</expan> l'angolo BHF <lb/>è eguale all'angolo BKG, &longs;arà <lb/>tutto l'angolo PKG minore <lb/>dell'angolo OHF.

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Per laqual <lb/>co&longs;a il re&longs;tante G<emph.end type="italics"/>K<emph type="italics"/>N &longs;arà <lb/>maggiore del re&longs;tante FHM. <lb/>

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Se <expan abbr="d&utilde;que">dunque</expan> &longs;i &longs;arà l'angolo G<emph.end type="italics"/>K<emph type="italics"/>Q<emph.end type="italics"/><pb id="44" xlink:href="pagethumb-it/106.jpg"/><emph type="italics"/>eguale ad e&longs;&longs;o FHM, &longs;arà il triangolo GKQ eguale al triangolo FHM, & <lb/>il lato GQ al lato FM eguale; &longs;arà dunque maggiore GN di e&longs;&longs;a FM; & <lb/>perciò BN maggiore &longs;arà di BM. & BM &longs;arà maggiore di BA; impe-<lb/>roche BM èmaggiore di e&longs;&longs;ai BE.

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Che bi&longs;ognaua mo&longs;trare.<emph.end type="italics"/>

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<emph type="italics"/>Et nel modo i&longs;te&longs;&longs;o in tutto, quanto più da pre&longs;&longs;o &longs;arà BG ad e&longs;&longs;a BE, &longs;empre la li-<lb/>nea BN &longs;i dimo&longs;trerà e&longs;&longs;er maggiore.<emph.end type="italics"/>

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Che &longs;e &longs;aranno po&longs;ti di <lb/>&longs;otto i triangoli BF <lb/>HB GK tra AB <lb/>BC, & &longs;iano tiratele <lb/>linee CHO GKP, <lb/>lequali taglino le li-<lb/>nee BF BG ne' pun<lb/>ti MN: &longs;arà la linea <lb/>BN minore di e&longs;&longs;a <lb/>BM, & BM di e&longs;sa <lb/>BA.

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</figure>

<emph type="italics"/>Congiungan&longs;i BO BP. &longs;imilmen <lb/>te prouera&longs;&longs;i, che l'angolo P <lb/>KB è minore dell' angolo OH <lb/>B.

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Hor percioche l'angolo F <lb/>HB è eguale all'angolo GKB; <lb/>&longs;arà l'angolo GKN maggio-<lb/>re dell'angolo FHM: per la <lb/>qual co&longs;a la linea GN &longs;arà <lb/>maggiore di e&longs;&longs;a FM. & per-<lb/>ciò la linea BN &longs;arà minore <lb/>della linea BM. & concio-<lb/>&longs;ia che maggiore &longs;ia BF di <lb/>BM; &longs;arà BM minore di <lb/>BA. & con &longs;imile modo <lb/>proueraßi, che quanto più B <lb/>G &longs;arà dapre&longs;&longs;o ad e&longs;&longs;a BC, <lb/>la linea BN &longs;empre &longs;arà <lb/>minore.<emph.end type="italics"/>

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PROPOSITIONE VIII.

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La po&longs;&longs;anza &longs;o&longs;tenente il pe&longs;o che habbia il centro della grauez-<lb/>za fopra la leuà egualmente di&longs;tante dall'orizonte, quanto <lb/>più il pe&longs;o &longs;i inalzerà da que&longs;to &longs;ito con la leua &longs;empre haurà <lb/>bi&longs;ogno di po&longs;sanza minore per e&longs;sere &longs;o&longs;tenuto: ma &longs;e &longs;arà <lb/>abba&longs;sato di maggiore.

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<emph type="italics"/>Sia la leua AB egualmente di&longs;tante dall'orizonte, il cui &longs;o&longs;tegno &longs;ia C, & il pe&longs;o <lb/>BD il centro della grauezza delquale &longs;ia doue è H &longs;opra la leua; & &longs;ia la po&longs;&longs;an<emph.end type="italics"/><lb/><arrow.to.target n="fig62"></arrow.to.target><lb/><emph type="italics"/>za &longs;o&longs;tenente in A.

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Moua&longs;i dapoi la leua AB in EF, & &longs;ia il pe&longs;o mo&longs;&longs;o <lb/>in FG.

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Dico primieramente che minore po&longs;&longs;anza po&longs;ta in E &longs;o&longs;tenir à il pe&longs;o <lb/>FG con la leua EF, che la po&longs;&longs;anza in A il pe&longs;o BD con la leua AB. &longs;ia <lb/>il K il centro della grauezza del pe&longs;o FG.

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Dapoi &longs;iano tirate sì da H, come<emph.end type="italics"/><pb id="45" xlink:href="pagethumb-it/108.jpg"/><emph type="italics"/>da K le linee HL KM à piombo de'loro orizonti, lequali &longs;i andaranno à tro-<lb/>uare nel centro del mondo, & &longs;ia HL à piombo anche di e&longs;&longs;a AB.

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Dapoi &longs;ia <lb/>tirata la linea KN à piombo di EF, laquale &longs;arà eguile ad HL, & la CN <lb/>eguale ad e&longs;&longs;a CL.

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Hor percioche HL è à piombo dell'orizonte, la po&longs;&longs;anza <lb/>in A &longs;o&longs;tenente il pe&longs;o BD haurà quella proportione ad e&longs;&longs;o pe&longs;o, che CL à<emph.end type="italics"/> <arrow.to.target n="note151"></arrow.to.target><lb/><emph type="italics"/>CA.

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Di nuouo, percioche KM è à piombo dell'orizonte, la po&longs;&longs;anza in E &longs;o-<lb/>&longs;tenente il pe&longs;o FG co&longs;i &longs;arà al pe&longs;o come CM à CE. & per e&longs;&longs;ere CN NK <lb/>eguali ad e&longs;&longs;e CL LH, & contenere angoliretti, &longs;arà CM minore di e&longs;&longs;a CL;<emph.end type="italics"/> <arrow.to.target n="note152"></arrow.to.target><lb/><emph type="italics"/>

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Dunque CM à CA haurà proportione minore, che CL à CA; & CA <lb/>è eguale à CE, dunque haurà CM proportione minore à CE, che CL à<emph.end type="italics"/> <arrow.to.target n="note153"></arrow.to.target><lb/><emph type="italics"/>CA: & per e&longs;&longs;erei pe&longs;i BD FG eguali, però che è il pe&longs;o mede&longs;imo.

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Dun-<lb/>que &longs;arà minore proportione della po&longs;&longs;anza in E &longs;o&longs;tenente il pe&longs;o FG ad e&longs;&longs;o <lb/>pe&longs;o, che della po&longs;&longs;anza in A &longs;o&longs;tenente il pe&longs;o BD ad e&longs;&longs;o pe&longs;o.

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Per laqual <lb/>co&longs;a minore po&longs;&longs;anza po&longs;ta in E &longs;o&longs;tenterà il pe&longs;o FG, che la po&longs;&longs;anza in A<emph.end type="italics"/> <arrow.to.target n="note154"></arrow.to.target><lb/><emph type="italics"/>il pe&longs;o BD. & quanto più &longs;arà inalzato il pe&longs;o, &longs;empre &longs;i mo&longs;trerà po&longs;&longs;anza<emph.end type="italics"/> <arrow.to.target n="note155"></arrow.to.target><lb/><emph type="italics"/>anche minore douer &longs;o&longs;tenere il pe&longs;o, per e&longs;&longs;ere la linea PC minore della CM. <lb/>

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Sia dapoi la leua in QR, & il pe&longs;o in QS, il cui centro della grauezza &longs;ia O. <lb/>

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Dico che po&longs;&longs;anza maggiore &longs;i richiede in R per &longs;o&longs;tenere il pe&longs;o QS, che in <lb/>A per &longs;ostentare il pe&longs;o BD.

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Tiri&longs;i dal centro O della grauezza la linea OT <lb/>a piombo dell'orizonte.

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& percioche le linee HL OT &longs;e &longs;aranno allungate dal-<lb/>la parte di L, & di T &longs;i andranno à ritrouare nel centro del mondo, &longs;arà la CT mag <lb/>giore della CL: & è la CA eguale ad e&longs;&longs;a CR, dunque la TC haurà pro-<emph.end type="italics"/> <arrow.to.target n="note156"></arrow.to.target><lb/><emph type="italics"/>portione maggiore à CR, che LC à CA.

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Maggiore dunque &longs;arà la po&longs;&longs;an-<emph.end type="italics"/> <arrow.to.target n="note157"></arrow.to.target><lb/><emph type="italics"/>za in R &longs;o&longs;tenente il pe&longs;o QS, che in A &longs;o&longs;tenente il BD.

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Similmente mo-<lb/>&longs;trera&longs;&longs;i, che quanto la leua RQ abba&longs;&longs;ando&longs;i, &longs;arà più di&longs;tante dalla leua AB,<emph.end type="italics"/> <arrow.to.target n="note158"></arrow.to.target><lb/><emph type="italics"/>&longs;empre più &longs;i ricercherà po&longs;&longs;anza maggiore à &longs;o&longs;tenere il pe&longs;o: peroche la di&longs;tanza<emph.end type="italics"/> <arrow.to.target n="note159"></arrow.to.target><lb/><emph type="italics"/>CV è più lunga di CT.

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Quanto dunque il pe&longs;o &longs;i alzerà più dal &longs;ito egualmente <lb/>di&longs;tante dall'orizonte, &longs;arà &longs;empre &longs;o&longs;tenuto da po&longs;&longs;anza minore; & quanto più &longs;i <lb/>abba&longs;&longs;erà, di po&longs;&longs;anza maggiore haurà me&longs;tieri per e&longs;&longs;er &longs;o&longs;tentato.

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che bi&longs;ogna-<lb/>ua mo&longs;trare.<emph.end type="italics"/>

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</figure>