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annotate texts/archimedesOldCVSRepository/archimedes/raw/monte_mecha_02_it_1581.raw @ 19:d1dd35fc15df

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Yet another new version.
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Thu, 02 May 2013 12:23:20 +0200
parents 22d6a63640c6
children
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1 <pb id="p.0001">
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2 <HEAD>LE
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3 MECHANICHE
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4 DELL'ILLVSTRISS SIG.</HEAD>
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5 <HEAD>GVIDO VBALDO
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6 DE' MARCHESI DEL
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7 MONTE:
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8 TRADOTTE IN VOL GARE
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9 DAL SIG. FILIPPO PIGAFETTA:
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10 Nellequali $i contiene la vera Dottrina di rutti gli I$trumenti
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11 principali da mouer pe$i grandis$imi con
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12 picciola forza.</HEAD>
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13 <HEAD><I>A beneficio di chi $i diletta di que$ta nobili$$ima scionza; &amp; ma$$imamente
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14 di Capitani di guerra, Ingegnieri, Architetti, &amp; d'ogni
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15 Artefice, che intenda per via di Machine
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16 far opre marauiglio$e, e qua$i
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17 $opra naturali.</I></HEAD>
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18 <HEAD>Et $i dichiarano i vocaboli, &amp; luoghi pi&ugrave; difficili.</HEAD>
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19 <fig>
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20 <HEAD><I>In Venetia, Appre$$o France$co di France$chi Sane$e. MD LXXXI.</I></HEAD>
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21 <pb>
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22 <fig>
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23 <HEAD>ALL'ILLVSTRISSIMO
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24 SIGNOR GIVLIO
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25 SAVOR GNANO,
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26 CONTE DI BELGRADO. &amp;c.</HEAD>
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27 <HEAD>Signore o$$eruandi$$imo.</HEAD>
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28 <fig>
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29 <p>C<I>onciosia co$a, che la $cienza delle Mecha-
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30 niche gioui $ommamente &agrave; molte, &amp; importan-
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31 ti attioni della no$tra vita, &agrave; gran ragione fu ella
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32 da i Filo$ofi, &amp; da i R&egrave; antichi $timata degna di
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33 laudi $ingulari&szlig;ime; &amp; i Matematici vi han-
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34 no impiegato lo $tudio, &amp; l'opera pi&ugrave; che meza-
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35 namente, &amp; i Principi fauoriti gl'ingegnieri ec
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36 cellenti, &amp; arricchiti. Ben &egrave; per certo di alti$-
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37 $ima $peculatione, &amp; di $ottile manifattura; imperoche tocca quella par-
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38 te della Filo$ofia, che tratta de gli elementi in vniuer$ale, &amp; del moto, &amp;
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39 della quiete de' corpi, $econdo i luoghi $uoi, a$$egnando la cagione in certo
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40 modo de' loro mouimenti naturali; &amp; anco sforzandoli, per via di machi-
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41 ne &agrave; partir$i da proprij $iti, gli tra$porta all'ins&ugrave;, &amp; per ogni lato in mo-
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42 uimenti contrari alla natura loro.</I>
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43 <p><I>Mena ella ad effetto ambedue que$te intentioni con le propo$itioni che
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44 na$cono, &amp; $ono congiunte con la materia $te$$a, &amp; co' difici, &amp; i$trumen
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45 ti, che forma artificialmente. La onde egli &egrave; dibi$ogno con$iderare que$ta</I>
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46 <foot><I>a 2</I></foot>
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47 <pb>
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48 <I>dottrina in due man&igrave;ere; l'vna &igrave;n quanto v&agrave; $peculando, &amp; con ragione
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49 di$correndo $opra le co$e, che s'hanno &agrave; $are, $eruendo$i dell' Arithmetica,
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50 della Geometria, dell' A$trologia, &amp; della Filo$ofia naturale: &amp; l'altra che
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51 po$cia le manda ad e$ecutione, &amp; haue nece$sita dell'e$$ercitio, &amp; lauoro
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52 delle mani, v$ando l'Architettura, la Pittura, il di$egno, l'arte de' fabri,
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53 de'legnaiuoli, de'muratori, &amp; d'altri me$tieri tali, per modo che ella vie-
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54 ne ad e$$ere me$colata, &amp; in parte compo$ta della naturale Filo$ofia, delle
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55 Matematiche, &amp; delle arti manuali. Per laqual co$a chiunque $i troua
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56 dotato d'ingegno acuto, &amp; da fanciullo h&agrave; incominciato ad apprendere le
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57 gi&agrave; dette $cienze, &amp; $a di$egnare, &amp; lauorare di $ua mano, potr&agrave; nel vero
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58 ottimo Mechanico, &amp; inu&emacr;tore, &amp; facitore di opere marauiglio$e riu$cire.</I>
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59 <p><I>Infinite parti, &amp; vtili&szlig;ime &agrave; gli huomini comprende que$la noti-
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60 tia, &amp; in guerra, &amp; in pace, ne i commodi della citt&agrave;, della villa, &amp; della
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61 mercatantia, &amp; in altri; peroche la Medicina toglie da lei i difici per ri-
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62 porre le o$$a $mo$$e, &amp; rotte ne i $iti $uoi. Onde pone Oriba$io nel libro delle
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63 Machine, diuer$i i$trumenti pre$i dalla Mechanica, &amp; c&otilde;uertiti nell'v$o del
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64 la Medicina, come il Tri$pa$ton di Archimede: l'arte del nauigare ricono-
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65 $ce anco diuer$i aiuti, come il timone, co'l quale, collocato di dietro, ouero
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66 alle bande del nauilio ageuolmente lo moue, &amp; dirizza, quantunque per
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67 ri$petto &agrave; tutto il corpo del va$ello piccioli$simo $ia. I remi, che &agrave; gui$a di
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68 leua lo $pingono innanzi, &amp; l'arbore, &amp; la vela $ono pur di $ua inuentio
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69 ne. I molini, i quali $i girano co'l vento, con l'acqua, &amp; con la forza vi-
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70 ua: &amp; i pi$trini, le carra, gli aratri, &amp; altri ordigni di villa; il pe$are con
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71 la bilancia, &amp; con la $tadera; il cauare l'acqua da pozzi con le gr&ugrave;, ouero
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72 cicogne, dette da latini to$senoni, che $ono come grandis$ime bilancie, &amp;
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73 con le rote, &amp; altre co$e tali $i riducono alla Mechanica. La ragione pa-
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74 rimente del condurre le acque, &amp; da profondis$ime valli in alto farle $ur
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75 gere u&agrave; $otto lei. Chiamarono gli antichi coloro Mechanici ancora, i quali
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76 co'l fiato, &ograve; vento, ouero acqua, &ograve; corde, &ograve; nerui faceuano vedere, &amp; vdi
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77 re effetti miracolo$i; come $uoni diuer$i, &amp; canti d'augelli, &amp; fin ad e$pri-
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78 mere la voce humana in parole: &amp; quelli che con horologi, i quali $i mo-
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79 uono da $e $tes$i con rote, &ograve; da acqua, &ograve; da $ole il tempo mi$urarono, &amp; di-
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80 $tin$ero in hore. Appartengono alla Mechanica gli facitori delle Sfere
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81 compartite ne'$uoi cieli, co'l mouimento de'Pianeti, &amp; di tutti i corpi
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82 cele$tiali &agrave; $embianza dell'vniuer$o mondo, &amp; ci&ograve; mediante il mouimen-
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83 to eguale, &amp; in giro, che loro daua l'acqua, di cui la fama $uona e$$ere
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84 $tato Archimede Siracu$ano il primo mae$tro. il mouere etiandio con poca</I>
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85 <pb>
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86 <I>forza pe$i grandis$imi con i$trumenti, &amp; ingegni diuer$i &egrave; principale of-
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87 ficio della Mechanica, come Bilancie, Stadere, Leue, Taglie, Cunei, Moli-
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88 nelli, Rote co' denti &amp; $enza, Viti d'ogni $orte, Argani, Mangani, Triuel
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89 le, &amp; altri molti, i quali da que$ti $i compongono: &amp; $econdo Ari$totele
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90 tutti $iriducono alla Leua, &amp; al cerchio, &amp; alla machina ritonda, laquale
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91 quanto &egrave; maggiore, tanto pi&ugrave; velocemente $i moue. L'arte del fortificare
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92 le piazze, &amp; i $iti, &amp; del difendergli, laquale acconciamente $i puote chia
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93 mare Architettur a militare, &egrave; pro$es$ione Mechanica: peroche per via di
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94 Cortine, &amp; di Baloardi, &amp; d'altri ripari, qua$i con ma<*>hine, &amp; i$tr umen-
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95 ti s'ingegna l'huomo con po hi $oldati di ributtarne in dietro molti, &amp;
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96 mantener$i con vantaggio. Il fabricare, &amp; adoprare oltre &agrave; c<*>&ograve; gli i$tru
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97 menti da guerra &egrave; proprio dono di que$ta $cienza, come Bali$te, &ograve; Bale$tre,
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98 Catapulte, Scorpioni, Fionde, &amp; $imili, che da lontano gittano foco, &amp; $a&szlig;i,
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99 &amp; ma$$e di ferro pe$anti dugento cinquanta, &amp; pi&ugrave; libre, &amp; Moli da
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100 molino $econdo Silio Italico, &amp; Vitruuio, per di$tanza di for$e</I> 300. <I>pas$i
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101 &agrave; mi$ura con ruin $o colpo; &amp; $aette, &amp; verettoni, &amp; falariche grandi
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102 &agrave; gui$a di traui: &amp; quelli che percoteudno con l'vrto da pre$$o, come Arie
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103 ti, Onagri, Te$tugini, &amp; $imili; &amp; in altri v$i, come S&atilde;buche, Corui, Mani
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104 di ferro, &amp; gli altri maritimi, &amp; Angoni, Monangoni, Tollenoni, $cale $no-
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105 date, ponti, torri mobili, &amp; $imili difici antichi, i quali $ono $tati poi ri
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106 fiutati, $uccedendo in $uo luogo le Artiglierie, da e$$ere anch'e$$e ordinate
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107 nell' ampiezza della con$ideratione Mechanica, facendo elle c&ograve;n s&igrave; poca m&aelig;
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108 teria acce$a, tanto horribile perco$$a.</I>
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109 <p><I>Que$ta $cienza, che fuor di quanto $i &egrave; detto, abbraccia innumerab ili
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110 altri v$i, &amp; diletteuoli, &amp; nece$$ari &agrave; mortali, in diuer$i tempi hebbe in
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111 $orte vari $tati, per ri$petto &agrave; gli artefici, che la e$ercitarono: peroche,
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112 di l&agrave; cominciando, ne gli antichis$imi $ecoli, che pa$$arono auanti la guer
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113 ra di Troia vi$$e Dedalo Athenie$e gran mae$tro di Mechanica, ilquale
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114 trou&ograve; il primiero la $ega, l'a$cia, il piombino da torre le diritture, la tri-
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115 uella, l'albero, l'antenna, la vela, &amp; altri or digni: di$egn&ograve; in Creta poi
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116 quell'intricato labirinto, &amp; alla fine gli conuenne fabricare per $e, &amp; per
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117 Icaro $uo figlio due paia d'ali, &amp; volar$ene via per l'aere &agrave; gui$a d'au-
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118 gelli, come cantano i Poeti.</I>
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119 <p><I>Nella fabrica del tempio di Salomone, che fu la maggiore per grandez
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120 za, per mae$tria d' Architettura, &amp; ornamento, di quanie ne $iano $tate
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121 fatte giamai; &amp; delle piramidi, &amp; di tanti altri difici di quei $eco'i, che
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122 hanno riempito il mondo di $tupore, egli $i pu&ograve; credere, che interueni$$ero</I>
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123 <pb>
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124 <I>curamente: &amp; del pre$entare al nemico il fatto d'arme con vantaggio:
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125 Del fortificare, &amp; difendere i $iti, &amp; offenderli con le mine, con le trin-
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126 cee, con le artiglierie, con gli a$$alts, &amp; con tutti gli altri sforzi; &amp; d'o-
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127 gni parte della militare $cienza.</I>
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128 <p><I>Ritornati in pace i Prencipi Chri$tiani, $i dedic&ograve; al $eruigio de' Sereni&szlig;.
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129 $uoi Signori, oue ne i pi&ugrave; importanti carichi, &amp; maggiori, &amp; in due guer
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130 re haue e$$a aggiunto cinquanta anni di noua, &amp; ottima $eruit&ugrave; all'an-
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131 tica di qua$i dugento anni, continua, &amp; fedeli$s. fattagli da i $uoi pre-
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132 dece$$ori Sauorgnani, fabricando nello $patio di que$to tempo in diuc<*>$e pro
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133 uincie de' $uoi $tati pre$$o che cinquanta Baloardi, con eccellenti&szlig;ima ra-
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134 gione inte$i, &amp; con vero magi$terio lauorati, &amp; notabili&szlig;imo ri$parmio
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135 del publico danaro.</I>
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136 <p><I>Ma per tornare alle Mechaniche dico, che quando gli anni pa$$ati io
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137 venni &agrave; vi$it arla ad O$opo $ua fortezza, $ent&igrave; $ommo piacere in $corgere
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138 quel monte, che circonda pi&ugrave; d'un miglio, $ituato alla foce del fiume Ta-
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139 gliamento, oue dalle $trettezze di quei gioghi s'allarga nelle pianure del
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140 Friuli, d'ogn'intorno alto pre$$o che $e$$anta pa&szlig;i &agrave; mi$ura, tutto di ma-
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141 cigno duro, &amp; di$co$ce$e, &amp; erto s&igrave;, che rende la $alita impo&szlig;ibile fornito
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142 attorno di baloardi cauati nel $a$$o, &amp; di molti tagli, &amp; canoniere per
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143 ferire gli aduer$ari, &amp; di artiglierie, &amp; d'arme d'ogni $orte &agrave; $u$$icienza,
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144 da cui $i h&agrave; vi$ta di qua$i tutto il Friuli, &amp; &egrave; $<*>udo, &amp; riparo, come al-
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145 tra volta f&ugrave;, contra l'empito delle genti nemiche, lequali in Italia tenta$
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146 $ero di $oendere da quella parte; po$to di co$ta alla $trada principale, che
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147 conduce in Lamagna, per laqual vanno, &amp; vengono Signori, &amp; Principi,
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148 &amp; Amba$ciadori, &amp; infinite mercatantie; onde ella, che tiene $empre le
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149 guardie, &amp; vedette s&ugrave; quel monte, quando pa$$ano Signori principali,
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150 h&agrave; per co$tume di $alutargli con le $ue artiglterie, &amp; conuitarg'i anco
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151 <*>el $uo alloggiamento d'O$opo, oue tutto l'anno $oggiorna, quantunque
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152 habbia &amp; Belgrado, &amp; Aris, &amp; Ca$telnouo, &amp; Sauorgnano, &amp; villaggi
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153 a$$ai: percioche l'aere vi &egrave; puri&szlig;imo, &amp; $pende il $uo tempo in ocio con ne
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154 gocio, di continuo vi$itata da Gentil'huomini, &amp; Signori diuer$i; ta che la
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155 $ua ca$a viene ad e$$ere vn ridotto di per$one virtuo$e, &amp; vn'albergo di $ol
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156 dati, &amp; di dottori. lui $i caualca, tenendo ella vna $talla piena di buoni$-
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157 $imi caualli, $i armeggia, $i v&agrave; alla caccia, &amp; in ogni attione $i e$ercita vi-
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158 ta cauallere$ca. Oltre &agrave; quanto h&ograve; diui$ato, pre$i anco diletto in vedere la
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159 $ua habitatione e$$ere &agrave; gui$a d'vna bottega d'arme politamente &agrave; $uoi
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160 luoghi $erbate: &amp; vn magazino di machine bellico$e, &amp; da mouer pe$i,</I>
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161 <pb>
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162 <I>eccellenti Mechanici, per leuare in alto le pietre $mi$urate, &amp; per altre
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163 opere, lequali &agrave; condurgli &agrave; fine $i ricercauano. Nacquero dapoi Eudo$
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164 $o, &amp; Archita Tarentino, ambidue valenti ingegnieri; &amp; di Archita $i
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165 legge, che lauor&ograve; di legno vna colomba con tanta mae$tria temperata, &amp;
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166 gonfiata, che da $e volaua per l'aria &agrave; gui$a di viua colomba. Segu&igrave; co-
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167 $toro il Filo$ofo Ari$totele, ilquale certe poche, ma bellis$ime que$tioni Me-
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168 chaniche, la$ci&ograve; $critte. A lui venne appre$$o Demetrio R&egrave;, nominato il
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169 pigliatore, &ograve; di$truggitore delle citt&agrave;, peroche fabricaua machine, &amp; difi-
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170 ci, co' quali per di$opra vi montaua, &amp; $e ne faceua padrone, lequali per
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171 auentura furono $imiglianti alla machina detta Cauallo, con cui li Greci
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172 pre$ero la famo$a Troia; di che ragionando Pau$ania nell' Attica, dice che
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173 giudica e$pre$$a mattezza il credere, che fo$$e vn cauallo, &amp; non machina
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174 bellico$a per acco$tare alle muraglie, &amp; prenderle. Que$to R&egrave; cominci&ograve;
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175 ad aumentare la Mechanica in qualche honore. Ma Archimede, che f&ugrave;
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176 il megliore artefice di quanti fecero giamai que$ta profes$ione innanzi, &amp;
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177 dopo lui, &amp; qua$i vn lume, che poi ha illu$trato tutto il mondo, accrebbe
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178 in colmo la riputatione della Mechanica, &amp; di pouera arte, &amp; vile, che pri
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179 ma era, come vuole Plutarco nella vita di Marcello, nel numero delle arti
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180 nobili, &amp; pregiate alla militia pertinenti la ripo$e. Imperoche combat-
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181 tendo Marcello Sir acu$a patria $ua per mare, &amp; per terra con grande
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182 ho$te di Romani, egli co'$uoi diuer$i ingegni, &amp; machine differenti, ribut-
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183 t&ograve; $empre gli sforzi, con graue lor danno, &amp; vergogna; come Liuio, Plutar
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184 co, &amp; altri nominando i difici che v$aua, diffu$amente raccontano. Per-
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185 cioche quando Marcello s'auicinaua aile muraglie per conqui$tar le con la
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186 Sambuca, il buon Archimede co'l Tollenone, &amp; con le mani di ferro la al-
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187 zaua di pe$o in aere, &amp; poi $nodando quegli vncini $uoi, la faceua cadere
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188 da alto, in mare $ommergendola; il mede$imo effetto adoprando eontra gli
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189 altri nauili, s&igrave; fattamente, che gli conuenne allontanare l'armata ben to
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190 $to dalle mura. Ne ce$s&ograve; tuttauia d'infe$tare il nemico: ma $i come nota
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191 Galeno nel terzo libro de' temper amenti, &amp; Giouanni Zonara, &amp; Tze$es
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192 confermano, allegando Diodoro, &amp; Dione, compo$e certi $pecchi grandi
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193 &amp; concaui, $econdo la proportione della di$t anza di quei va$elli dalla mu-
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194 raglia, &amp; opponendogli &agrave; raggi del Sole in diritta linea qua$i per miraco-
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195 lo, gli bru$ciaua. Dalla parte della terra $imilmente offendeua gli aduer-
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196 $ari con arme diuer$e da gittare. Per laqual co$a n&egrave; in mare, n&egrave; in terra
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197 da gl'ingegni di quell'eccellente Mechanico $i poteua egli $chermire, nuoui
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198 ripari, &amp; horribili offe$e apparecchiando $empre. Pappo Ale$$andrino</I>
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199 <pb>
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200 <I>allega il quar ante$imo trouato <*> Archimode, per dichiarare, che almeno
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201 i $uoi difici al numero di quaranta a$cendeuano. La onde Marcello, veg-
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202 gendo, che niuno profitto apportauano all'impre$a gli a$$alti $uoi, &amp; che
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203 erano vn mettere le genti ad euidente pericolo, per cagione di quel $olo
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204 valoro$o vecchio, gli nacque vna tal opinione, &amp; &agrave; tutto l'e$ercito, che da
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205 po$$anza diuina fo$$e gouernato in quella dife$a, &amp; mut&ograve; la ragione del
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206 guerreggiare, dando$i all'a&szlig;edio, &amp; al vietare $tret ti&szlig;imamente le vitto-
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207 uaglie a quella citt&agrave;.</I>
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208 <p><I>Que$te furono le cagioni, che la Mechanica $al&igrave; in tanta gloria, &amp; che
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209 i Romani le a$$egnarono dapoi grado honoreuoli&szlig;imo ne gli e$erciti lo-
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210 ro, come $i legge nel primo libro della guerra ciuile, che Ce$are $e prigione
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211 il Capitano de' fabri di Pompeio, nomato Magio Cremona, &amp; Vitruuio fu
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212 Capitano delle Bali$te di Ce$are Augu$to, che $arebbe nella militia moder-
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213 na, come Capitano generale dell' artiglieria. La qual gloria $ucce&szlig;iua-
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214 mente le fu mantenuta poi da molti dotti&szlig;imi $crittori, &amp; mae$tri di
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215 Mechani a, come da Cte$ibio Ale$$andrino, da Herone Ale$$andrino, da
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216 un'altro Herone, da Ateneo, da Bione, da Pappo Ale$$andrino, che allega
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217 Carpo di Antiochia, da Eliodoro, da Oriba$io, &amp; da altri Greci, i quali fio
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218 rirono in diuer$i tempi, in$egnando la ragione, la mi$ura, &amp; l'v$o de gli
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219 i$trumenti bellico$i non $olo, ma di tutti gli altri, che le pertengono. Fra
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220 Latini antichi Varrone $cri$$e dell' Architettura, &amp; per con$eguente douet
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221 te anco far mentione della Mechanica: &amp; Vitruuio, &amp; Vegetio, &amp; qual-
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222 che altro hanno fauellato d'intorno alla fabrica delle machine militari,
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223 &amp; da mouer pe$i, &amp; aiutato &agrave; con$eruare fra gli huomini viua la digni-
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224 t&agrave; della Mechanica.</I>
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225 <p><I>Ma ruinando l'Imperio di Romani, &amp; $uccedendo i barbari in Italia,
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226 in Grecia, in Egitto, &amp; in ogni contrada, oue $i e$er cita$$ero le buone lette
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227 re, caddero mi$erabilmente, &amp; $i perderono qua$i del tutto le $cienze, &amp; in
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228 $pecialit&agrave; re$t&ograve; la Mechanica lunghi&szlig;imo tempo negletta, non cono$cen-
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229 do$i in guerra altri difici, che Bricole, Trabucchi, Mangani, Martinelli, &amp;
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230 certi i$trumenti tali, finche $ouragiun$e l'artiglieria, laquale &agrave; poco &agrave; po-
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231 co gli fe di$u$are &agrave; fatto: &amp; di quella parte altre$i della Mechanica, laqua
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232 le s'adopra al mouer pe$i, ben picciolo intendimento rima$e. Vera co$a &egrave;,
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233 che $embra da vn tempo in qu&agrave; le arti, &amp; le dottrine pi&ugrave; nobili, come le
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234 belle lettere appellate humane, la Filo$ofia, la Medicina, l'A$trologia, l'A-
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235 rithmetica con la Mu$ica, la Geometria, l'Architettura, la Scoltura, la Pit
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236 tura con molte altre: &amp; $pecialmente la Mechanica e$$ere dalle o$cure te-</I>
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237 <pb>
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238 <I>nebre, oue giaccudno $epolte, alla thiara luce ri$u$citate: Percioche ri-
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239 $tringendomi alle Mechaniche Giordano, che $<*>ri$$e de' pe$i, la incominci&ograve;
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240 &agrave; $olleuare alquanto, &amp; poi Leon Batti$ta Alberti nella $ua Architettu-
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241 ra: il Tartaglia aper$e anco la via &agrave; molte $peculationi Mechaniche: Vitto
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242 rio Fau$to nell' Arzan&agrave; di Vene<*>ia m<*>$tr&ograve; d'e$$ere buon Mechanico: Mon-
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243 $ig. Reuerendi$s. barbaro eletto d' Aquileia ne' Commentari del decimo di
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244 Vitruuio nomin&ograve; gli i$trumenti da mouer pe$i: Georgio Agricola nel $e$to
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245 de' Metalli raccol$e a$$ai machine da leuar pe$i, &amp; qualched'vn'altro: &amp;
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246 nuoua m&etilde;te l'Autoredi que$t'opera, ilquale ben d'altra maniera in ci&ograve; pro
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247 ce lette, che gli autori nominati, peroche con ordine ammir abile, &amp; con
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248 vere, &amp; certe ragioni ha in$egnato $olo fra Latini ottimamente que$t&aelig;
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249 $cienza tutta da mouer pe$i.</I>
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250 <p><I>Ma $i come i moderni da me ricordati, &amp; principalmente l'Autore del
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251 pre$ente libro hanno ornata &amp; e$altata la Mechanica con le parole, &amp; co i
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252 volumi; co$i V. S. Illu$tri&szlig;. l'h&agrave; celebrata, &amp; magnificata co' di$cor$i, &amp;
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253 con le operationi i$te$$e, &amp; co' fattire$a famigliare, &amp; dome$tica, diuer$e
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254 machine fabricando con profondi&szlig;ima dottrina, &amp; facendone e$perten-
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255 ze nel mouere qualunque gran pe$o, di cui $i po$$a l'huomo in ogni bi$ogno
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256 $eruire. Talche ben $i puote con verit&agrave; affermare, che per vna pa<*>te e$$a,
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257 &amp; l'Autore di que$ti trattati per l'altra, habbiate alla Mechanica il pri$ti
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258 no honore re$tituito, che da i tempi antichi in qu&agrave; le cra $marrito.</I>
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259 <p><I>S<*>no $or$e quaran a anni gia $cor$i, che per i$cherzare con Nicol&ograve; Tar
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260 taglia, per$ona &agrave; $uoi tempi molto $timata in que$ta profe&szlig;one, &amp; che $i
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261 dile ttaua di andare $oluendo que$tioni $ottili di Mechanica, &amp; di Mathe
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262 matica, &amp; ne' $uoi dialoghi introduceua &agrave; fauellare per$onaggi grandi:
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263 &amp; alcuna fiata gli faceua dire qualche co$a, di cui e&szlig;i prendeuano onta,
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264 V. S. Illu$tri&szlig;. gliene propo$e for$e quaranta Mechaniche qua$i tu<*>te, &amp;
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265 difficili: alcune delle quali egli prou&ograve; di $oluere, delle altre $i $cus&ograve; con di
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266 re, che &agrave; cia$cheduna di loro $arebbe $tato me$tieri vn volume intero, co-
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267 me $i legge ne' $uoi lib i $tampati della noua $cientia.</I>
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268 <p><I>Hor non &egrave; punto di marauiglia, che ella habbia penetrato con l'inten-
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269 dimento t&atilde;to dentro, &amp; $aputo co$i bene operare nelle Mechaniche, &amp; $ia
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270 fatta padrona in tut<*>o dell'arte del fortificare i $iti, &amp; d'ogni altra parte
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271 della militia: peroche fu dall'ottimo $uo padre alleuata in compagnia di
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272 huomini $cientiati, &amp; d'alio affare, tra quali fu vn tempo Con$tantino
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273 La$cari nobili&szlig;imo huomo Greco, &amp; piono di dottrina, da cui $ucce&szlig;i-
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274 uamente impar&ograve;, oltra le altre lettere, Arithmetica, Geometria, A$tro-</I>
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275 <pb>
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276 <I>logia, Geogra$ia; &agrave; &agrave;i$egnare, &amp; lauorare manualmente in me$tieri diuer-
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277 $i; &agrave; caualcare, &agrave; maneggiare le arme, &agrave; tirare d'archibugio, &amp; d'artiglie
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278 ria, &amp; &agrave; c&otilde;porre fochi artificiati, &amp; l'arte per eccellenza detta del bom
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279 bardiero; &agrave; viuere $obriamente, &amp; le fatiche rolerare al caldo, al freddo,
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280 &amp; ad ogni di$agio, co$e tutte, che di$pongono l'animo, &amp; indurano il corpo
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281 alla militia. Giunta poi all' et&agrave; di $edici anni, fu inutata con dodici caual
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282 li qua$i tutti Turchi, &amp; con prouedimento conuene<*>ole di denari &agrave; vede-
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283 re tutta quella guerra, che pa$s&ograve; in Italia dalla pre$ura del R&egrave; France$co
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284 Primo di Francia, fin alla pace generale, che $egu&igrave; l'anno</I> 1529. <I>Nella-
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285 quale interuennero qua$i tutti i mouimenti militari, che $i po$$ano ima-
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286 ginare, s&igrave; per gli e$erciti grandi, che erano &agrave; front<*> l'vn contra l'altro, s&igrave;
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287 per la qualit&agrave;, &amp; quantit&agrave; delle impre$e fatte, &amp; per mille altri acciden
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288 ti importanti&szlig;imi, &amp; $tratagemi auenuti, &amp; s&igrave; principalmente; percio-
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289 che nell'vn campo, &amp; l'altro in varie $tagioni militarono i primi guer-
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290 rieri del mondo, &amp; in gran numero, i quali con prudenza, a$tutia, &amp;
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291 brauura contendeuano &agrave; gara, &amp; per honore di $oura$tare, &amp; e$$ere vinci
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292 tori. Et veramente chi ben con$idera, fin da i tempi antichi, rari&szlig;ime vol
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293 te &egrave; $tato con numero maggiore di Capitani famo$i, &ograve; con pi&ugrave; copia d'im-
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294 pre$e grandi guerreggiato, che in quegli anni: Peroche furono fatti prigio-
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295 ni due de' maggiori Prencipi del mondo, $i a$$edi&ograve; Milano, &amp; per forza fu-
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296 rono pre$e tre citt&agrave;, Roma, Cremona, &amp; Pauia; $i videro pi&ugrave; fatti d'ar-
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297 me, &amp; gli e$erciti $i andarono per$eguitando da Milano &agrave; Roma; $i che Pia
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298 cenza, Parma, Bologna, &amp; Fiorenza guardar&ograve;n$i dalle armi nemiche.</I>
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299 <p><I>Nello $plendore dunque della $cola del Duca France$co Maria d'V rbino,
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300 ilquale era Capitano generale della Lega, &amp; di quegli altri valenti&szlig;im<*>
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301 Capitani, andaua V. S. Illu$tri&szlig;. come di $ua libert&agrave;, &amp; beni&szlig;imo &agrave; ca-
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302 uallo, con chi le piaceua, &amp; $i trouaua &agrave; quelle fattioni, che volea, $eguen
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303 do le pi&ugrave; volte il Sig. Giouanni de' Medici, &amp; Paulo Luzza$co, che erano
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304 $empre de$ti, &amp; arditi, &amp; come l'occhio dell'e$ercito. Qu&igrave; non &egrave; mia in-
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305 tentione di narrare gli auenimenti di quella guerra, ma $i bene di auerti
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306 re, che chi la vide, &amp; appre$e da buon $enno i $uoi moti; &amp; $eppe manda-
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307 re &agrave; memoria quei $atti marauiglio$i, ben puote meritamente vantar$i
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308 di hauer mirato ca$i memorabili, i quali n&egrave; anche in migliaia d'anni $o-
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309 gliono accadere; come ella, che e$$endo giouine di viuace $pirito, &amp; am-
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310 mae$trata nclle arti nece$$arie al$oldato, &amp; volentern$i&szlig;ima d'imparare,
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311 hebbe opportu<*>a occa$ione di far$i prattica d<*>ll'ordinare, de<*>'e$ercitare,
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312 del far marciare in battaglia, dell'alloggiare in campagna gli e$erciti $i-</I>
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313 <foot><I>b</I></foot>
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314 <pb>
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315 <I>hauendone ella fabricate di $ua indu$tria for$e dodici di maniere differen
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316 ti, parte da $tra $cinare, &amp; parte da alzare con pochi&szlig;ima forza $mi$u-
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317 rati pe$i: come quella, che h&agrave; vna $ola rota co' denti, &amp; ali'erta tira cin-
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318 que de' $uoi canoni con la po$$anza di Grada$$o $uo Nano: &amp; quell'altra, la
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319 quale con vna oncia di forza $ola, po$ta nel manico, che la volge, d&agrave; il me
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320 to &agrave; quattordici mila libre di pe$o: che $e al detto manico $i attribui$ce
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321 la forza, che comunalmente haue l'huomo con la mano, cio&egrave; libre cinquan
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322 ta, egli &egrave; manife$to la predetta machina hauere po$$anza di mouere, co$a
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323 incredibile, molto pi&ugrave; di otto millioni di libre. Que$te machine portabi-
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324 li da vn mulo, &amp; alcune anche da vn'huomo $ono &agrave; diuer$i affari nece$$a-
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325 rij&szlig;ime, &amp; ma&szlig;imamente &agrave; maneggiare, &amp; condurrei pezzi gro&szlig;i del-
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326 l'artiglieria. &amp; per certo $e l'anno</I> 1529. <I>il Conte di San Polo Capitano
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327 France$e nel ritirar$i dall'a$$edio di Milano inuer$o Piemonte con l'e$er-
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328 cito, &amp; con l'artiglieria, haue$$e portato $eco vno de' minimi i$trumenti
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329 d'O$opo, non $arcbbe $cor$o in quello $tremo infortunio, percioche in mar
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330 ciando fu da vn graue canone rotto il ponte, che trauer$aua il $o$$o della
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331 $trada, &amp; il pezzo cad&egrave; nel fango. Onde formo&szlig;i il campo per non la-
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332 $ciarlo &agrave; dietro, &amp; non hauendo ingegno da cauarlo fuori, $i con$um&ograve; tan-
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333 to tempo, che $opragiun$e Antonio da Leua con le $ue genti, &amp; ritrouan
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334 do l'e$$ercito nemico $eparato, &amp; in quel di$ordine, lo mi$e in rotta, &amp; f&egrave;
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335 preda delle bagaglie, delle artiglierie, &amp; del Capitano mede$mo. Non h&agrave;
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336 troppo iempo, che il Duca France$co di Gui$a, allhor che di Francia guid&ograve;
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337 l'e$ercito in Abruzzo, douendo partire, volle $piegare prima la fanteria,
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338 &amp; cau&aelig;lleria $ua in ordinanza &agrave; fronte del nemico, qua$i &agrave; battaglia sfi-
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339 dandolo; ma poi nel ritorno $caualco$si vn pezzo d'artiglieria, &amp; s'arre-
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340 $t&ograve; tutta la ma$$a delle genti, &amp; quei Prencipi France$i $montati da ca-
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341 uallo, penarono buona pezza auanti, che lo ripone$$ero $u le rote, con ri$chio
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342 di patir danno da gli aduer$ari, che haue$$ero con quella occa$ione $pinto
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343 innanzi. Di quc$ti e$empi non mancano per l'hi$torie.</I>
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344 <p><I>Hora che &egrave; pace V. S. Illu$tri&szlig;. &egrave; andata inue$tigando per $uo diporto
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345 molte, &amp; varie $orti di ordigni da mouer pe$i, affine di valer$ene nelle
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346 fabriche, &amp; nell'argine di pietre, che fa per ritenere l'impeto del Taglia-
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347 mento, che n<*>n gua$ti i colti di O$opo, &amp; per douer$ene anco $eruire, quan
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348 do che $ia in guerra. Si come fece Archimede, ilquale, $econdo Plutarco, $tan
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349 do in pace &agrave; petitione di Hierone R&egrave;, compo$e quelle t&atilde;ie Machine per giuo-
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350 co, &amp; i$ch<*>rzo di Geometria, l<*>quali poi $oprauenendo la guerra, le $eppe c&otilde;
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351 uertire opportunamente contra Romani. Et $e egli, come te$tificano diuer$i</I>
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352 <foot><I>b 2</I></foot>
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353 <pb>
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354 <I>autori, $edendo con certa machina detta, $econdo Oriba$io, Tri$pa$ton, per
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355 che $i maneggiaua con tre cor de, tir&ograve; dal mare in terra quella gran naue
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356 del R&egrave; $uo; &amp; con la forza della mano $ini$tra mo$$e mediante l'i$tru-
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357 mento vn pe$o di cinque mila $taia &ograve; moggia, s&igrave; fattamente che diputan-
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358 do &agrave; cia$cuno $taio quarantacinque libre di pe$o, a$cenderebbono alla $om-
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359 ma di dugento venticinque mila libre; &amp; pre$umeua$i di hauer potuto
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360 mouere la terra, trouando doue fermar$i con la leua, &ograve; con quella $ua ma-
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361 china de$critta da Pappo nell'ottauo libro delle raccolte matematiche, la
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362 quale hauea cinque rote co' $uoi as$i, &amp; vna vite perpetua co'l manico: Io
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363 mi rendo certo, che ella s'ingegnerebbe di $ormare i$trumenti per adoprare
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364 altretanto.</I>
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365 <p><I>Hauendo io dunque veduti, &amp; i$perimentati que$ti vari difici ad O$o-
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366 po; &amp; es$endomi $tato da lei mo$trato la prima volta il pre$ente libro, &amp;
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367 commendato $ommamente, mi propo$i nell' animo, che vtile $arebbe il ri
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368 durlo in volgare, accioche coloro i quali $ono atti per altro ad intenderlo,
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369 ma non hanno cono$<*>enza del Latino, pote$sero, farne $uo profitto. Co$i
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370 compiuta l'opera, &amp; fattala $tampare, la mando &agrave; V. S. Illu$tri$s. che po$
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371 $ede e$qui$it amente que$ta materia, &amp; $econda i $tudi delle buone lette-
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372 re, i quali, $e dopo Iddio, non vengono fauoriti da i gran Signori, nulla va
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373 gliono. Che $e in qualche parte haur&ograve; &agrave; gli amatori delle Mechani<*>he re-
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374 cata ageuolezza, &amp; vtilit&agrave; con le mie fatiche, douranno eglino $aper' &agrave;
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375 lei buon grado, che di que$ta fattura &egrave; $tata cagione.
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376 Di Venetia &agrave;</I> 28. <I>di Giugno</I> 1581.
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377 <p><I>Di V. S. Illu$tri$s.</I>
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378 <p><I>Affettionati&szlig;. $cruidore
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379 Filippo Pigafetta.</I>
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380 <pb>
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381 <HEAD>AI LETTORI</HEAD>
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382 <p>Il prefente libro contiene $ei trattati, il primo de
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383 quali &egrave; della Bilancia con la Stadera, l'altro della
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384 Leua, il terzo della Taglia, il quarto dell' A$$e nel-
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385 la rota, il quinto del Cuneo, &amp; l'vltimo della Vite,
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386 che tutti $ono i$trumenti Mechanici. Intitula$i le
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387 Mechaniche. Ma percioche que$ta parola Mechaniche non ver
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388 r&agrave; for $e int e$a da cia$cheduno perlo $uo vero $ignificato, anzi
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389 troueran$i di quelli, che $timeranno lei e$$ere voce d'ingiuria,
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390 $olendo$i in molte parti d'Italia dire ad altrui Mechanico per
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391 i$cherno, &amp; villania; &amp; alcuni per e$$ere chiamati Ingegnieri $i
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392 prendono $degno: non $ar&agrave; per auentura fuori di propo$ito il
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393 ricordare, che Mechanico &egrave; vocabolo honorati$$imo, dimo$tran
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394 te, $econdo Plutarco, me$tiero alla Militia pertinente, &amp; conue
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395 neuole ad huomo di alto affare, &amp; che $appia con le $ue mani,
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396 &amp; co'l $enno mandare ad e$ecutione opre marauiglio$e &agrave; $ingu
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397 lare vtilit&agrave;, &amp; diletto del viuere humano.
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398 <p>F&ugrave;, per nomiuarne alcuno tra molti Filo$ofi, &amp; Prencipi de'
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399 preteriti $ecoli, Archita Tarentino, &amp; Eudo$$o c&otilde;pagni di Pla-
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400 tone, &amp; valenti$$imi Ingegnieri, &amp; Mechanici, che $ono vna me
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401 de$ma co$a, di cui fa Plutarco mentione nella vita di Marcello:
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402 &amp; Demetrio R&egrave;, inuentore $ottili$$imo di Machine bellico$e,
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403 &amp; ne lauoraua di $ua mano ancora: &amp; fra Greci di Sicilia Me-
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404 chanico, &amp; Ingegniere famo$is$imo Archimede Siracu$ano, il
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405 quale era di gr&atilde; legnaggio, &amp; parente di Hierone R&egrave; di Sicilia.
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406 <p>Et quantunque Plutarco nell'i$te$$a vita affermi, che egli di
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407 $pregia$$e le Mechaniche, come bas$i &amp; vili, &amp; materiali, n&egrave; di
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408 loro degna$$e $criuere giamai, &amp; che non per opera principale,
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409 ma per vn cotale $ollazzo, &amp; giuoco di Geometria impiegaua
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410 la fatica nelle Mechaniche, pregato da quel R&egrave;; s&igrave; leggiamo
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411 noi tuttauia in altri autori, lui hauere dettato vn libro della mi
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412 $ura, &amp; proportione d'ogni maniera di va$ello, diui$ando la for
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413 ma della gran naue fabricata da Hierone, &agrave; cui nulla manca-
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414 ua: &amp; Pappo Ale$$andrino allega il libro della Bilancia di Ar-
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415 chimede, che &egrave; pur Mechanico tutto: &amp; l'i$te$$o nell'ottauo del
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416 le raccolte Matematiche pone vn'i$trumento da mouer pe$i,
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417 <pb>
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418 tentato l'Autore di manife$tare per hora, &amp; il primo de Latini
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419 con dimo$trationi ageuoli, &amp; piane, in$egnare $olamente la ra-
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420 gion dello intendere, &amp; maneggiare gli $ei predetti l$trumenti
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421 Mechanici; &agrave; quali $i riducono tutti gli altri, come &agrave; $uoi prin-
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422 cipil, &amp; fondamenti; &amp; da'quali $i po$$ono comporne diuer$e ma
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423 niere, accozzandone in$ieme due, tre, &amp; pi&ugrave;, come l'A$$e nella
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424 rota con la Taglia, la Vite co'l detto A$$e, &amp; con la Leua, &amp; $uc-
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425 ces$iuamente de gli altri ad arbitrio di chiunque in varie opre $e
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426 ne s&agrave; con giudicio valere, come nota l'Autore nel fine di que$to
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427 volume.
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428 <p>Hor come che l'Autore con bella via, &amp; chiara, &amp; con ordine
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429 ammirabile di que$ti difici habbia ragionato, &amp; la co$a per $e
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430 molto o$cura non $ia ad intender$i: nondimeno ben ricerca ella
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431 tutto l'intelletto dell'huomo, &amp; che con $i$$a $peculatione $i leg-
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432 gano attentis$imamente pi&ugrave; d'vna volta le dimo$trationi.
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433 <p>Doue $i vede in alcuni luoghi di que$ti trattati cotale $orte di
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434 lettere picciole, differente dalle altre, come la pre$ente; auer-
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435 ta$i che non vi $ono co$e dettate dall' Autore di que$to libro di
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436 Mechaniche, ma notate da colui che l'h&agrave; volgarizato, &agrave; fine di
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437 chiarire qualche pa$$o difficile, &amp; ageuolare l'intendimento &agrave;'
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438 Lettori non co$i prattichi nelle Scole de' Filo$ofi.
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439 <p>Ponga$i anco mente, che &agrave; carte 121. nel trattato della Vite,
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440 &egrave; po$to fra i detti dell' Autore il Problema di Pappo, ilquale do-
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441 uea e$$ere $tampato con lettere differenti dalle altre, ma per in-
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442 auertenza &egrave; $tato me$$o co' caratteri $te$$i delle propo$itioni del
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443 l' Autore, che &egrave; difetto. Non &egrave; $tato pos$ibile $chluare alcuni
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444 falli nello $tampare. Onde correggan$i in que$ta maniera. Nel
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445 la Lettera &agrave; carte 1. faccia 2. ver$i 25. to$$enoni, leggi tollenoni.
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446 car. 43. ver. 22. dell'angolo, all'angolo. carte 48. f. 2. nella po-
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447 $tilla, per la 2. di que$to; della 2. di que$to. carte 87. f. 2.
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448 ver. 14. dalla, alla. carte 93. ver. 32. cni, cui. carte 115. ver. 20.
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449 Hlici, Helici. Gli altri errori di lettere meno importanti, &amp; che
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450 non mouono il $en$o alla, di$cretione del giudicio$o Lettore $i ri
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451 mettono.
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452 <pb>
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453 <p>mo$trando e$$ere il quarante$imo trouato d' Archimede, per cui
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454 di$$e; Dami oue io mi fermi, ch'io mouer&ograve; la terra; &amp; Carpo
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455 Mechanico $c ri$$e, che Archimede compo$e vn libro del modo
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456 del fare le Sfere, che &egrave; fattura Mechanica. Ma pi&ugrave; il mede$imo
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457 Archimede, non vna $ola volta cita $e $te$$o, nel libro della Qua
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458 dratura della Parabola, con parole tali. Imperoche egli &egrave; dimo-
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459 $trato nelle Mechaniche; accennando alcune propo$itioni del
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460 $uo libro delle co$e, che egualmente pe$ano, ilquale &egrave; tutto Me-
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461 chanico. Oltre &agrave; ci&ograve; vna parte del libro della Quadratura della
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462 Parabola, &amp; il $econdo delle co$e, che $tanno $opra l'acqua, oue-
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463 ro &agrave; galla $ono Mechanici. Da que$ti luoghi vede$i e$pre$$o, che
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464 non $olamente Archimede fece opre Mechaniche, ma ne $cri$$e
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465 anco molti trattati; &amp; confe$$a Plutarco per niuna altra dottri-
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466 na e$$ere tanto in riputatione $alito Archimede, quanto per le
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467 impre$e Mechaniche; anzi veramente co'l mezo loro hauer$i egli
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468 all'hora procacciato fama non di $cienza humana, ma di $apien-
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469 za diuina. Per la qual co$a egli &egrave; ben da con$iderare, come Plu-
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470 tarco $i $ia la$ciato tra$correr' &agrave; dire, che Archimede le Mechani
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471 che di$preggia$$e, n&egrave; di loro degna$$e $criuere: &amp; per certo egli
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472 forte d'opinione $arebbe$i ing&atilde;nato, $e haue$$e poco $timata quel
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473 la facult&agrave;, che lo f&egrave; guadagnare gloria di gran lunga maggio-
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474 re, che qualunque altra $cienza $i po$$ede$$e. Vitruuio de i
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475 Latini f&ugrave; buon Mechanico, &amp; $eru&igrave; per Capitano delle Bali$te,
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476 &amp; delle altre machine da guerra Ottauiano Ce$are, &amp; gli intitu-
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477 l&ograve; le $ue fatiche dell' Architettura, &amp; ne diuenne ricco.
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478 <p>L'e$$ere Mechanico dunque, &amp; Ingegniero con l'e$empio di
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479 tanti valent'huomini, &egrave; officio da per$ona degna, &amp; $ignorile:
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480 &amp; Mechanica &egrave; voce Greca $ignificante co$a fatta con artificio
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481 da mouere, come per miracolo, &amp; fuori dell'humana po$$anza
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482 grandis$imi pe$i con picciola forza, &amp; in generale comprende
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483 cia$cun Dificio, Ordigno, I$trumento, Argano, Mangano, oue-
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484 ro ingegno mae$treuolmente ritrouato, &amp; lauorato per cotali ef
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485 fetti, &amp; $imili altri infiniti in qual $i voglia $cienza, arte, &amp; e$er-
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486 citio. Laquale h&ograve; de$critta co$i materialmente per darne vn cer
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487 to $aggio accommodato al gu$to del pi&ugrave; de gli huomini; trala-
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488 $ciando le accurate di$$initioni &agrave; miglior tempo.
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489 <p>Aggiunga$i, che $otto que$to vniuer$ali$$imo titolo $i &egrave; con-
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490 <pb n=1>
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491 <HEAD>LIBRODI
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492 MECHANICHE,
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493 DELL'ILLVSTRISSIMO
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494 SIGNORE,
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495 II. S. GVIDO VBALDO DE' MARCHESI
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496 DEL MONTE.</HEAD>
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497 <fig>
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498 <HEAD>Diffinitioni.</HEAD>
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499 <p>Il centro della grauezza di cia$cun corpo e vn
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500 certo punto po$to dentro, dal quale $e con la
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501 imaginatione s'intende e$$erui appe$o il gra-
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502 ue, mentre &egrave; portato $ta fermo, &amp; mantiene
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503 quel $ito, che egli hauea da principio, ne in
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504 quel portamento $i v&agrave; riuolgendo.
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505 <p><I>Que$ta diffinitione del centro della grauezza in$egn&ograve;
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506 Pappo Ale$$andrino nell'ottauo libro delle raccolte ma-
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507 thematiche. Ma Federico Comandino nel libro del cen-
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508 tro della grauezza de' corpi $olidi dichiar&ograve; l'i$te$$o centro in questa maniera de$cri-
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509 uendolo.</I>
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510 <p>Il centro della grauezza di cia$cuna figura $olida &egrave; quel punto po$to
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511 dentro, d'intorno alquale le parti di momenti eguali da ogni parte
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512 $i fermano. Peroche $e per tale centro $ar&agrave; condotto vn piano, che
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513 $eghi in qual $i voglia modo la figura, $empre la diuider&agrave; in parti,
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514 che pe$eranno egualmente.
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515 <foot>A</foot>
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516 <pb>
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517 <HEAD>NOTITIE COMVNI.</HEAD>
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518 <HEAD>I.</HEAD>
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519 <p>Se da co$e egualmente pe$anti $i leneranno co$e, che pur egualmente
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520 pe$ino, le re$tanti pe$eranno egualmente.
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521 <HEAD>II.</HEAD>
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522 <p>Se &agrave; co$e egualmente pe$anti $i aggiungeranno co$e, che pur egualm&etilde;
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523 te pe$ino, tutte in$ieme pe$eranno egualmente.
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524 <HEAD>III.</HEAD>
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525 <p>Le co$e, che all'i$te$$o $ono eguali in pe$o, $ono tra loro anco gra-
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526 ui egualmente.
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527 <HEAD>PRESVPPOSTE.</HEAD>
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528 <HEAD>I.</HEAD>
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529 <p>Di vno corpo &egrave; vn $olo centro della grauezza.
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530 <HEAD>II.</HEAD>
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531 <p>Il centro della grauezza di vn corpo &egrave; $empre nel mede$imo $ito per
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532 ri$petto al $uo corpo.
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533 <HEAD>III.</HEAD>
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534 <p>I Pe$i $ono portati in giu $econdo il centro della grauezza.
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535 <p>DIFFINITIONI. La diffinitione &egrave; vn breue parlare, che manife$ta, &amp; inte-
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536 ramente dichiara la co$a propo$ta, $i fattamente che non $i po$$a trouare condi-
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537 tione, ouero accidente alcuno principale in e$$a co$a, $e la diffinitione &egrave; buona,
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538 che non $ia in virt&ugrave; compre$a, &amp; detta da lui; come per e$empio l'Autore qui di
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539 $opra da ad inten dere che $ia il centro della grauezza con due diffinitioni.
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540 <p>Le Notitie comuni poi $ono certe $entenze manife$te al $en$o comune de gli huomi-
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541 ni, lequali pur che vi $i ponga mente, $ubito vdite, $i intendono, &amp; $e le pre$ta il
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542 con$entimento.
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543 <p>Ma la Pre$uppo$ta &egrave; diuer$a, peroche mette per vero la co$a co$i e$$ere, come $i pro-
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544 pone $enza altro di$cor$o per farla cono$cere.
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545 <pb>
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546 <HEAD>TRATTATI IN QVEST'OPERA
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547 CONTENVTI.</HEAD>
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548 <TABLE>
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549 <ROW><COL>I.</COL><COL>Della Bilancia, con la Stadera &agrave; carte</COL><COL>1</COL></ROW>
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550 <ROW><COL>II.</COL><COL>Della Leua.</COL><COL>35</COL></ROW>
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551 <ROW><COL>III.</COL><COL>Della Taglia.</COL><COL>56</COL></ROW>
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552 <ROW><COL>IIII.</COL><COL>Dell' A$$e nella Rota.</COL><COL>102</COL></ROW>
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553 <ROW><COL>V.</COL><COL>Del Cuneo.</COL><COL>107</COL></ROW>
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554 <ROW><COL>VI.</COL><COL>Della Vite.</COL><COL>115</COL></ROW>
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555 </TABLE>
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556 <pb n=2>
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557 <HEAD>DELLA BILANCIA</HEAD>
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558 <p>Avanti che $i faccia mentione della Bilancia, accioche la
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559 co$a re$ti pi&ugrave; chiara, $ia la Bilancia AB in linea diritta, &amp;
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560 CD la Truttina della Bilancia, laquale $econdo la con$uetu
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561 dine comune $t&agrave; $empre &agrave; piombo dell'orizonte. &amp; il punto C im
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562 mobile, d'intorno alquale $i volge la Bilancia, $i chiami il centro del
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563 la bilancia, $ia pur collo-
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564 cato di $opra della bilan
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565 cia, &ograve; di $otto, benche
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566 non propriamente, che
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567 non fa nulla Ma il CA,
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568 &amp; il CB $iano le di$tan
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569 ze, &amp; braccia della Bilan
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570 cia, co$i nomate. &amp; $e
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571 dal centro della bilancia
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572 collocato di $opra, &ograve; di
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573 $otto della Bilancia, $ar&agrave;
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574 tirata vna linea &agrave; piom-
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575 bo di AB, que$ta $i chia
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576 mer&agrave; perpendicolo, che
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577 $o$terr&agrave; la Bilancia AB,
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578 &amp; $empre $tar&agrave; &agrave; piom-
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579 bo di e$$a Bilancia, mo-
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580 ua$i ella in qual $i voglia
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581 modo.
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582 <fig>
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583 <p>Concio$ia che in que$to trattato della Bilancia, &amp; ne gli altri ancora l'Autore v$i
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584 alcune parole, lequali non $i $ono potute tra$portare commodamente in v olga-
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585 re, per non e$$ere e$$e anco $tate accettate in que$ta lingua, ne inte$e da ognuno,
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586 io le ho la$ciate co$i latine. Ma accioche non facciano difficult&agrave; &agrave; coloro, i quali
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587 non intendono il latino, le andr&ograve; per tutto &agrave; fuoi luoghi dichiarando.
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588 <p>Nel re$to poi delle parole mi $ono attenuto pi&ugrave; al chiaro, &amp; all'v$ato, che $ia pos$i-
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589 bile, &amp; ho po$to angolo retto, &amp; linea retta in cambio di angolo diritto, &amp; linea
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590 diritta, &amp; linea della direttione in lo co di linea della dirittura, &amp; co$i diretto per
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591 diritto, &amp; alcuna volta magnitudine in vece di grandezza, &amp; angolo mi$to per
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592 me$colato, &amp; angolo curuilineo per di linee torte, &amp; linea curua per torta, &amp; $oli-
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593 do per $odo, &amp; for$e qualche altro vocabolo poco v$ato in que$ta no$tra fauella,
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594 $timando che cote$te parole $iano per dimo$trare maggiormente la co$a, &amp; la in-
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595 tentione dell' Autore: &amp; etiandio de$iderando, che $i rendano famigliari, &amp; dome
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596 $tiche in que$ta $cienza, talche ognuno le po$$a ageuolmente intendere.
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597 <p>Trutina &egrave; quella co$a, che $o$tiene tutta la Bilancia, laquale Trutina pigli a il Perno,
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598 ouero l'A$$etto, &amp; noma$i in que$ti pae$i Gioa, altroue Giouola, ouero l'o recchie
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599 della Bilancia, &amp; in altre contrade Scocca, talche non $i troua $in hora vocabolo,
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600 <foot>A 2</foot>
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601 <pb>
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602 che in Italia communcmente vi $i confaccia, ne alcuno di qne$ti $arebbe inte$o
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603 per tutto. Onde io ho $critto co$i la Trutina, $perando, che $i habbia &agrave; fare termi
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604 ne, &amp; parola generale &agrave; tutte le nationi d'Italia.
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605 <p>Perpendicolo vuol dire quella linea, che $porge in fuori dal centro della Bilancia al
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606 mezo di detta Bilancia, ilqual Perpendicolo &egrave; $olamente nelle Bilancie, lequali han
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607 no il centro di fuori della Bilancia, o $ia di $otto, &ograve; $ia di $opra. Ma quando il cen-
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608 tro della Bilancia &egrave; nel mezo di e$$a, all'hora non vi &egrave; que$to Perpendicolo per e$
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609 $ere il centro della Bilancia, &amp; il mezo di e$$a vn'i$te$$o punto. Et que$to Perpen-
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610 dicolo &egrave; co$a imaginata dall' Autore $olamente, &amp; non da altri, per ageuolare al-
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611 cune dimo$trationi della Bilancia, che di nouo ha inue$tigate: &amp; non &egrave; la linguet-
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612 ta, ne meno la linea della direttione, &ograve; dirittura che $i habbia &agrave; dire.
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613 <HEAD>LEMMA.</HEAD>
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614 <p>Sia la linca AB &agrave; piombo dell'orizonte, &amp; col diametro AB $i de$cri-
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615 ua il cerchio AEBD, il cui centro $ia C. Dico il punto B e$$ere
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616 l'infimo luogo della circonferenza del cerchio AEBD, &amp; il pun-
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617 to A il piu alto, &amp; quali $i voglian punti, come DE, i quali $iano
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618 per&ograve; egualmente di$tanti da A e$$ere egualmente po$ti di $otto, &amp;
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619 quelli che $tanno piu da pre$$o ad e$$o A, e$$ere pi&ugrave; alti di quelli, che
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620 $ono pi&ugrave; da lunge.
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621 <p><marg><I>Per la ottaua del terzo.</I></marg><I>Allunghi$i la linea AB fin al centro del mondo,
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622 che $ia F. Dapoi $ia pre$o nella circonferenza
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623 del cerchio qual $i voglia punto, come G, &amp; $i
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624 congiungano le linee FG FD FE. Hor per-
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625 cioche BF &egrave; la minima linea di tutte quelle,
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626 che dal punto F $ono tirate alla circonferenza
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627 AEBD, $ar&agrave; la BF minore della FG. Per
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628 laqual co$a il punto B $ar&agrave; piu da pre$$o al pun-
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629 to F, che il G. Et per cotesta ragione $i dimo-
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630 strer&agrave;, che il punto B $ta pi&ugrave; da pre$$o al centro
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631 del mondo di qual $i voglia altro punto della cir-
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632 conferenza del cerchio AEBD. Sar&agrave; dunque
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633 il punto B l'infimo luogo della circon$erenza del
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634 cerchio AEBD. Dapoi perche AF tirata
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635 per lo centro &egrave; maggiore di GF, $ar&agrave; il punto A
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636 pi&ugrave; alto non $olamente di G, ma etiandio di qual
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637 $i voglia altro punto della circon$erenza del cer-
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638 chio AEBD. Oltre &agrave; ci&ograve; perche DF, &amp; FE
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639 $ono eguali, i punti DE $aranno egualmente di
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640 stanti dal centro del mondo. Et e$$endo DF
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641 maggiore di FG, $ar&agrave; il punto D, che &egrave; pi&ugrave; da
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642 pre$$o al punto A, pi&ugrave; alto del punto G, lequali
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643 co$e tutte erano da mo$trar$i.</I>
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644 <fig>
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645 <pb n=3>
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646 <p>Que$to vocabolo Lemma greco v$ato da tutti i volgarizatori di Euclide, &amp; da gli
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647 altri Scrittori di Mathematica ancora, h&ograve; accettato anch'io. Ma ben con tutto ci&ograve;
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648 $timo che egli habbia me$tieri di vn poco di lume per e$$er inte$o; &amp; viene &agrave; dire,
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649 $i come nota Cicerone nel $econdo della Diuinatione, co$a che prima $i prende
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650 per render facile l'intendimento delle co$e, lequali $i hanno dapoi &agrave; mo$trare, &amp;
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651 n&otilde; &egrave; Pre$uppo$ta, perche ella n&otilde; $i proua c&otilde; ragione, ma $uppon$i; ma il Lemma
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652 $i dimo$tra, come in que$to luogo, che prende il punto B e$$ere po$to nell'infimo
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653 $ito della circonferenza del cerchio, &amp; lo proua per douer$ene valere nelle $eguen
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654 ti dimo$trationi.
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655 <p>Doue in que$to Lemma $i dice, che la linea AB &egrave; &agrave; piombo dell'orizonte, intenda$i
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656 per orizonte il piano della campagna, &amp; del terreno $ottopo$to, volendo dire ori
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657 zonte parola greca vn cerchio, che termina la no$tra veduta, &amp; abbraccia &amp; diui
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658 de la met&agrave; della terra tutta. Quando dunque $i troua in que$ti libri vna linea, oue-
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659 ro altra quantit&agrave; e$$ere &agrave; piombo, ouero egualmente di$tante, &ograve; inchinata all'ori-
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660 zonte, intenda$i per l'orizonte il piano della campagna, &ograve; del terreno.
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661 <HEAD>PROPOSITIONE I.</HEAD>
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662 <p>Se il pe$o $ar&agrave; $o$tenuto nel centro della $ua grauezza da linea diritta
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663 non $i fermer&agrave; giamai, $e quella i$te$$a linea non $ar&agrave; &agrave; piombo del
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664 l'orizonte.
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665 <fig>
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666 <p><I>Sia il pe$o A, &amp; il centro della $ua
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667 grauezza B, ilqual pe$o venga $o
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668 $tenuto dalla linea CB. Dico che
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669 il pe$o non &egrave; per fermar$i giamai,
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670 $e CB non $ar&agrave; &agrave; piombo dell'o-
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671 rizonte. Sia il punto C immobi-
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672 le, e$$endo co$i nece$$ario, accio il
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673 pe$o $ia $o$tenuto: &amp; e$$endo il pun
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674 to C immobile, $e il pe$o A de-
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675 ue$i mouere, il punto B de$criuer&agrave;
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676 la circonferenza di vn cerchio, il
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677 cui mezo diametro $ar&agrave; CB. Per
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678 laqual co$a $u'l centro A &amp; con
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679 lo $patio BC $i de$criua il cerchio
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680 BFDE. &amp; $ia di prima BC &agrave;
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681 piombo dell'orizonte, &amp; $ia tirata
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682 $in &agrave; D, &amp; il punto C $tia di $ot
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683 to al punto B. Hor percioche il pe$o A $i moue in gi&ugrave; $econdo il centro della gra-</I> <marg><I>Per la terza pre$upposta di questo.</I></marg>
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684 <I>uezza, il punto B $i mouer&agrave; in gi&ugrave;, oue naturalmente inchina ver$o il centro del mon
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685 do per la linea diritta BD: tutto il pe$o A dunque con B $uo centro della gra-
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686 uezza, grauer&agrave; $opra la linea diritta BC, &amp; concio$ia che il pe$o venga $o$tenuto
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687 dalla linea CB, la linea CB $o$terr&agrave; tutto il pe$o A, $opra laquale non puote mo</I>
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688 <pb>
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689 <I>uer$i in gi&ugrave;, e$$endogliene da e$$a
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690 vietato. Per la diffinitione dun-
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691 que del centro della grauezza, il
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692 punto B &amp; il pe$o A $taranno
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693 in que$to $ito. &amp; quantunque <*>il
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694 B $ia piu alto di qual $i voglia al-
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695 tro punto del cerchio, t<*>tauia non
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696 $i mouer&agrave; in gi&ugrave; da que$to $ito per
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697 la circonferenza del cerchio, pero-
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698 che non $i inchiner&agrave; pi&ugrave; ver$o lo F,
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699 che ver$o lo E, per e$$ere nell'vna
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700 parte &amp; nell'altra eguale la di$ce-
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701 $a: ne il pe$a A piu $t&agrave; pendente
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702 in vna parte che nell'altra, ilche
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703 non auiene in qual $i voglia altro
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704 punto della circon$erenza del cer-
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705 chin, eccettuato il D. Sia il centro
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706 <fig>
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707 della grauezza dell'i$te$$o pe$o, come in F, concio$ia che la di$ce$a $ia dal punto
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708 F ver$o il D, &amp; la a$ce$a ver$o il B, per&ograve; il punto F mouera$$i in gi&ugrave;: &amp; per-
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709 cioche non $i puote mouere al centro del mondo per linea diritta, per e$$er<*> impe-
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710 dito dal punto C immobile per cau$a della linea CF, ma ben $i mouer&agrave; $empre
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711 in gi&ugrave; come richiede la $ua natura: &amp; e$$endo il D il luogo infimo, $i mouer&agrave; per
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712 la circonferenza FD finche peruenga in D, nelqual $ito fermera$$i il pe$o, &amp;
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713 re$ter&agrave; immobile, s&igrave; perche non $i puote pi&ugrave; mouere in gi&ugrave; per e$$ere attaccato al
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714 punto C, s&igrave; anche percioche egli &egrave; $o$tenuto nel $uo centro della grauezza. Et
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715 quando F $ar&agrave; in D, $ar&agrave; $imilmente la FC in DC, &amp; in$ieme &agrave; piombo
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716 dell'orizonte. il pe$o dunque non $i fermer&agrave; giamai finche la linea CF non $tia
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717 &agrave; piombo dell'orizonte, che bi$ognaua prouare.</I>
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718 <p>Di qu&igrave; $i puote cauare, che il pe$o $ia pur $o$tenuto in vn dato punto
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719 in qual $i voglia modo, non $tar&agrave; fermo giamai, $e non quando la
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720 linea tirata dal centro della grauezza del pe$o &agrave; quel punto, $tia &agrave;
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721 piombo dell'orizonte.
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722 <pb n=4>
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723 <p><I>Come, po$te le co$e i$te$$e, $ia $o$tenuto
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724 il pe$o dalle linee CG CH. Dico
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725 che $e la tirata linea BC $ar&agrave; &agrave;
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726 piombo dell'orizonte, il pe$o $tar&agrave;
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727 fermo: ma $e la tirata linea CF
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728 non $ar&agrave; &agrave; piombo dell'orizonte, il
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729 punto F $imouer&agrave; in gi&ugrave; fin al D,
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730 nel qual $ito $tar&agrave; fermo il pe$o,
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731 &amp; la tirata linea CD $ar&agrave; &agrave; piom-
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732 bo dell'orizonte. Le quali co$e
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733 tutte con laragione mede$ima $i pro-
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734 uerebbono.</I>
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735 <fig>
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736 <HEAD>PROPOSITIONE II.</HEAD>
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737 <p>La bilancia egualmente di$tante dall'orizonte, il cui centro $tia $opra
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738 la detta bilancia, &amp; che habbia i pe$i eguali nelle $tremit&agrave;, &amp; egual-
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739 mente di$tanti dal perpendicolo, $e da cotale $ito $ar&agrave; mo$$a, &amp;
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740 nell'i$te$$o di nuouo la$ciata, ritorner&agrave;, &amp; iui re$ter&agrave;.
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741 <fig>
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742 <p><I>Sia la bilancia AB in
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743 linea diritta egualmen
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744 te di$tante dall'orizon
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745 te, il cui centro C $ia
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746 $opra la bilancia, &amp;
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747 $ia CD il perpendi-
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748 colo, il quale $ar&agrave; &agrave;
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749 piombo dell'orizonte:
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750 &amp; la di$tanza DA
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751 $ia eguale alla di$tan-
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752 za DB: &amp; $iano i
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753 pe$i in AB eguali,
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754 i centri della grauez-
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755 za de' quali $iano ne i
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756 punti AB. Moua$i
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757 da que$to $ito la bi-
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758 lancia AB come in EF, dapoi $ia la$ciata. Dico che la bilancia EF ritor-
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759 ner&agrave;in AB di$tante egualmente dall'orizonte, &amp; iui rimaner&agrave;. Hora percioche</I>
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760 <pb>
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761 <I>il punto C $t&agrave; immob&igrave;
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762 le mentre la bilancia $i
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763 moue, il punto D veni
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764 r&agrave; &agrave; de$criuere vna cir-
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765 con$erenza di cerchio, il
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766 cui mezo diametro $a-
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767 r&agrave; CD. Per laqual
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parents:
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768 co$a co'lcentro D, &amp;
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769 lo $patio CD de$cri-
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770 ua$i il cerchio DGH.
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771 Et perche CD $empre
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parents:
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772 $t&agrave; &agrave; piombo della bi-
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773 lancia, mentre la bilan
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774 cia $ar&agrave; in EF, la li-
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parents:
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775 nea CD $ar&agrave; in CG
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776 $i fattamente, che CG
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777 <fig>
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778 venga ad e$$ere &agrave; piombo di EF: &amp; concio$ia che AB $ia diui$a in due parti</I>
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779 <marg><I>Per la quarta del primo di Archimede delle co$e che pe$ano egualmente.</I></marg> <I>eguali nel punto D, &amp; i pe$iin AB $iano eguali, $ar&agrave; etiandio il centro della
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780 grauezza della magnitudine compo$ta di que$ti due corpi AB nel mezo, cio&egrave; in
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781 D: &amp; quando la bilancia in$ieme co i pe$i $ar&agrave; in EF, $ar&agrave; parimente G il cen
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782 tro della grauezza della magnitudine compo$ta di e$$i AB: &amp; percioche CG
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783 non &egrave; &agrave; piombo dell'orizonte, la grandezza compo$ta de i pe$i EF non rimarr&agrave;</I>
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784 <marg><I>Per la prima di questo.</I></marg> <I>in questo $ito, ma $i mouer&agrave; in gi&ugrave; $econdo il centro della grauezza $ua, che &egrave; in
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785 G, per la circonferenza GD, finche $i faccia &agrave; piombo dell'orizonte, cio&egrave; finche
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786 CG ritorni in CD. Et quando CG $ar&agrave; in CD, la linea EF (perche $em-
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787 pre $t&agrave; ad angoli retti con CG) $ar&agrave; in AB, nelqual $ito $tar&agrave; $erma. La bi-</I>
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788 <marg><I>Per la prima di questo.</I></marg> <I>lancia dunque EF ritorner&agrave; in AB, laquale &egrave; di$tante egualmente dall'orizon-
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789 te, &amp; iui rimarr&agrave;, che bi$ognaua dimo$trare.</I>
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790 <HEAD>PROPOSITIONE III.</HEAD>
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791 <p>La bilancia egualmente di$tante dall'orizonte, che habbia nelle $tre-
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792 mit&agrave; pe$i eguali, &amp; egualmente lontani dal perpendicolo, e$$endo
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793 collocato il centro di $otto, rimarr&agrave; in que$to $ito. Ma $e indi $ar&agrave;
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794 mo$$a, &amp; la$ciata &agrave; ba$$o, $i mouer&agrave; $econdo la parte piu ba$$a.
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diff changeset
795 <pb n=5>
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796 <fig>
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797 <p><I>Sia la bilancia AB in
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798 linea diritta, egual-
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799 mente di$tante dall'ori
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800 zonte, il cui centro C
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801 $ia di $otto alla bilan-
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diff changeset
802 cia, &amp; $ia CD il per-
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diff changeset
803 pendicolo, ilquale $ar&agrave;
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804 &agrave; piombo dell'orizon-
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805 te, &amp; la di$tanza AD
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806 $ia eguale alla distan-
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807 za DB, &amp; $iano in
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808 AB pe$i eguali, i cen-
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809 tri della grauezza de'
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810 quali $iano ne' punti
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811 AB. Dico primiera-
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812 mente che la bilancia
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813 AB $tar&agrave; $erma in
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814 que$to $ito. Hor percioche AB $i diuide in parti eguali nel punto D, &amp; i
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815 pe$i po$ti in AB $ono eguali, $egue, che il punto D $ia il centro della grauez-
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816 za della magnitudine compo$ta di ambedue i corpi me$$i in AB; &amp; il CD che</I> <marg><I>Per la quar ta del primo d' Archimede delle co$e che pe$ano egualm&etilde;te.</I></marg>
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817 <I>$ostiene la bilancia $t&agrave; &agrave; piombo dell'orizonte: Adunque la bilancia AB in
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818 que$to $ito rimarr&agrave; ferma. Ma da que$to $ito moua$i la bilancia AB come in
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819 EF, &amp; la$<*>i$i dapoi. Dico che la bilancia EF $i mouer&agrave; dalla parte dello F.
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820 Et percioche il CD $t&agrave; $empre &agrave; piombo della bilancia, mentre la bilancia $ar&agrave;
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821 in EF verr&agrave; ad e$$ere anche il CD in CG &agrave; piombo di EF, &amp; il punto</I> <marg><I>Per la prima di questo.</I></marg>
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822 <I>G della magnitudine composta di EF $ar&agrave; il centro della grauezza, ilquale men
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823 tre $i moue de$criuer&agrave; la circonferenza del cerchio DGH, il cui mezo diametro
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824 &egrave; CD, &amp; il centro C. Ma perche CG non $t&agrave; &agrave; piombo dell'orizonte, la
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825 grandezza compo$ta de i pe$i EF non rimarr&agrave; in questo $ito, ma $econdo il cen-
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826 tro della $ua grauezza $i mouer&agrave; in gi&ugrave; per la circonferenza GH. La bilancia
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827 dunque EF $i mouer&agrave; in gi&ugrave; dalla parte dello F, che bi$ognaua mo$trare.</I>
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828 <HEAD>PROPOSITIONE IIII.</HEAD>
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829 <p>La bilancia egualmente di$tante dall'orizonte, &amp; che habbia nelle $tre
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830 mit&agrave; pe$i eguali, &amp; egualmente di$tanti dal centro collocato in e$$a
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831 bilancia. Se ella indi $ar&agrave; mo$$a, &ograve; non, douunque ella $ar&agrave; la$cia-
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832 ta, rimarr&agrave;.
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833 <foot><I>B</I></foot>
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834 <pb>
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835 <p><I>Sia la bilancia nella linea
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836 diritta AB egualmen
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837 te di$tante dall'orizon-
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838 te, il cui centro C $ia
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839 nella i$te$$a linea AB,
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840 &amp; la di$tanza CA $ia
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841 eguale alla distanza
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842 CB, &amp; $iano i pe$i
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843 AB eguali, i cui cen-
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844 tri della grauezza $tia
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845 no ne i punti AB. Mo
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846 ua$i la bilancia come in
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847 DE, &amp; iui $ia la$cia-
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848 ta. Dico primamen-
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849 <fig>
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850 te che la bilancia DE non $i mouer&agrave;, &amp; rimarr&agrave; in quel $ito. Hor percioche i
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851 pe$i AB $ono eguali, $ar&agrave; il centro della grauezza della magnitudine compo$ta
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852 delli due pe$i A &amp; B in C. Per laqual co$a l'i$te$$o punto C $ar&agrave; il centro
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853 della bilancia, &amp; il centro della grauezza di tutto il pe$o. Et percioche il centro
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854 della bilancia che &egrave; C, mentre la bilancia AB in$ieme co'pe$i $i moue in DE,
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855 rimane immobile, non $i mouer&agrave; ne anche il centro della grauezza, che &egrave; l'i$te$$o C.
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856 Adunque ne anche la bilancia DE $i mouer&agrave; per la diffinitione del centro della
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857 grauezza, e$$endo in e$$o appiccata. L'i$te$$o accade parimente $tando la bilancia
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858 AB egualmente di$tante dall'orizonte, ouero e$$endo in qual $i voglia altro $ito.
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859 Rimarr&agrave; dunque la bilancia oue $ar&agrave; la$ciata, che bi$ognaua mo$trare.</I>
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860 <p><I>Benche habbiamo con$iderato nelle co$e predette le grauezze $olamente delle magni-
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861 tudini, le quali $ono po$te nelle $tremit&agrave; della bilancia, $enza la grauezza della bi-
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862 lancia; niente di manco per e$$ere anche le braccia della bilancia eguali, auenir &agrave; lo
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863 i$te$$o alla bilancia, con$iderata la $ua grauezza in$ieme co' pe$i, ouero $enza pe$i,
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864 percioche il centro iste$$o della grauezza $enza pe$i $ar&agrave; anco centro della grauez-
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865 za della bilancia $ola. Similmente $e li pe$i $aranno appiccati nelle $tremit&agrave; del-
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866 la bilancia, come $uole far$t, a&ugrave;err&agrave; l'iste$$o, purche le linee tirate da i punti oue $o-
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867 no attaccati i pe$i ver$o i centri delle grauezze, (moua$i la bilancia in qual $i vo-
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868 gliamodo) vadano &agrave; concorrere nel centro del mondo, peroche doue $ono attaccati
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869 i pe$i in questa maniera, iui grauano, come $e in quegli $te$$i punti baue$$ero i cen
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870 tri delle grauezze. Oltre &agrave; ci&ograve; po&szlig;iamo con$iderare le co$e che $eguono in tut-
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871 to al modo i$te$$o.</I>
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872 <p><marg><I>Giord. de' pe$i. Il Car dano della $ottigliezza. Il Tartaglia de' que$iti, &amp; inu&etilde;tioni</I></marg><I>Ma percioche &agrave; que$ta vltima conchiu$ione molte co$e dette da alcuni, che $entono al-
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873 tramente, paiono contra$tare; per&ograve; in cote$ta parte egli $ar&agrave; bi$ogno dimorare
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874 alquanto, &amp; $econdo le mie forze non $olo far&ograve; opra di difendere la propria
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875 mia $entenza, ma Archimede ancora, ilquale $embra e$$ere $tato in que$to i$te$-
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876 $o parere.</I>
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877 <pb n=6>
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878 <p><I>Po$te le co$e i$te$$e, $ia
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879 tirata la linea FCG
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880 &agrave; piombo di AB, &amp;
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881 dell'orizonte: &amp; col
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882 centro C, &amp; lo $pa-
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883 tio CA $ia de$crit-
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884 to il cerchio ADFB
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885 EG: $aranno i punti
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886 ADBE nella circon
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887 ferenza del cerchio,
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888 per e$$ere le braccia
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889 della bilancia eguali.
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890 &amp; percioche conuen-
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891 gono que$ti autori in
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892 vna $entenza, affer-
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893 mando, che la bilan-
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894 cia DE non $i moue
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895 in FG, ne rimane in</I>
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896 <fig>
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897 <I>DE, maritornanellalinea AB egualmente di$tante dall'orizonte, mo$trer&ograve; que
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898 $ta loro opinione non potere &agrave; modo alcuno $tare. Percioche $e egli &egrave; vero quel
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899 che dicono, ouero auenir &agrave; questo effetto per e$$ere il pe$o D pi&ugrave; graue del pe$o E,
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900 ouero $e li pe$i $ono eguali, le di$tanze nelle quali $ono po$ti, non $aranno eguali,
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901 cio&egrave; la CD non $ar&agrave; eguale alla CE, ma pi&ugrave; grande. Ma che i pe$i col-
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902 locati in DE $iano eguali, &amp; la di$tanza CD $ia eguale alla di$tanza CE, &egrave;
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903 chiaro dalla pre$uppo$ta. Hor perche dicono che il pe$o po$to in D in quel $i-
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904 to &egrave; pi&ugrave; graue del pe$o po$to in E nell altro $ito da ba$$o: mentre i pe$i $ono in
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905 DE, non $ar&agrave; il punto C piu centro della grauezza, imperoche non stanno fer-
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906 mi $e $ono attaccati al C, ma $ar&agrave; nella linea CD per la terza del primo di At
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907 chimede delle co$e che pe$ano egualmente. Non $ar&agrave; gi&agrave; nella CE per e$$ere il
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908 pe$o D pi&ugrave; graue del pe$o E: $ia dunque in H, nelquale $e $aranno attacca-
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909 ti, rimarranno. Et percioche il centro della grauezza de' pe$i congiunti in AB
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910 $t&agrave; nel punto C: ma de' pe$i po$tiin DE il punto &egrave; H: mentre dunque i pe$i
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911 AB $i muouono in DE, il centro della grauezza C mouera&szlig;i ver$o D, &amp;
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912 s'appre$$er &agrave; pi&ugrave; da vicino al D, ilche &egrave; impo&szlig;ibile, per mantenere i pe$i vname-
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913 de$ima di$tanza fra loro: peroche il centro della grauezza di cia$cun corpo $t&agrave; $em-
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914 pre nel mede$imo $ito per ri$petto al $uo corpo. Et quantunque il punto C $ia il</I> <marg><I>Per la $ecom da $upposta di questo.</I></marg>
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915 <I>centro della grauezza di due corpi A. &amp; B, tuttauia per e$$ere mediante la bi-
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916 lancia co$i giunti in$ieme, che $empre $i trouano nell'iste$$o modo; per&ograve; il punto C</I> <marg><I>Per la quar ta del primo di Archime de delle co$e che pe$ano egualmente.</I></marg>
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917 <I>$ar&agrave; co$i centro della grauezza loro, come $e fo$$e vna $ola magnitudine; percio-
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918 che la bilancia in$ieme co' pe$i fa vn $olo corpo continuo, il cui centro della grauez
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919 za $empre $tar&agrave; nel mezo. Non &egrave; dunque il pe$o po$to in D pi&ugrave; graue del pe-
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920 $o po$to in E. Che $e dice$$ero il centro della grauezza non nella linea CD, ma</I>
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921 <foot><I>B</I> 2</foot>
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922 <pb>
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923 <I>nella CE douer e$$ere, auerr&agrave; l'i$te$$o $allo.</I>
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924 <p><I>Di pi&ugrave; $e il pe$o D $i mouer &agrave; in gi&ugrave;, mouer &agrave; il pe$o E in s&ugrave;. Adunque vn pe$o
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925 pi&ugrave; graue di E nel mede$imo $ito pe$er&agrave; tanto quanto il pe$o D, &amp; auerr &agrave; che
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926 co$e graui di$uguali, po$te in eguale distanza pe$eranno egualmente. Aggiun-
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927 ga$i dunque al pe$o E qualche co$a graue, $i $attamente, che contrape$i al D $e
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928 nel C $aranno attac
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929 cati. Ma e$$endo $ta-
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930 to di $opra mo$trato
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931 il punto C e$$ere il c&egrave;-</I>
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932 <marg><I>Per laterza del primo di Archimede delle co$e che pe$ano egual mente.</I></marg> <I>tro della grauezza di
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933 pe$i eguali po$ti in
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934 DE; $e dunque il pe-
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935 $o. E $ar&agrave; pi&ugrave; graue
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936 del pe$o D, $ar&agrave; anche
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937 il centro della grauez
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938 za nella linea CE.
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939 &amp; $ia que$to centro
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940 il</I> K. <I>Ma per la diffi-
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941 nitione del centro del
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942 la grauezza, $e li pe$i
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943 $aranno appiccati al</I>
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944 K, <I>staranno fermi.
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945 Dunque $e $aranno</I>
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946 <fig>
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947 <I>appiccati al C, non $taranno fermi, che &egrave; contra la pre$uppo$ta: ma il pe$o E $i</I>
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948 <marg><I>Per la prima $upposta di questo.</I></marg> <I>mouer &agrave; in gi&ugrave;. Che $e appiccati al C pe$a$$ero ancora egualmente, na$cerebbe
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949 che di vna magnitudine, due $arebbono i centri della grauezza, che &egrave; impo$$ibile.
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950 Adunque il pe$o po$to in E pi&ugrave; graue di quello che &egrave; in D, non pe$er &agrave; tanto
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951 quanto il D attaccando$i al punto C. I pe$i dunque eguali po$ti in DE, attac-
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952 cati nel centro della loro grauezza pe$eranno egualmente, &amp; $taranno immobili,
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953 che $u proposto di mo$trare.</I>
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954 <p><marg><I>Il Tartaglia nella $esta propo$itione del quate li bre.</I></marg> <I>A que$ta vltima $conueneuolezza ri$pondono, dicendo e$$ere impo$$ibile aggiungere al
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955 lo E $i picciolo pe$o, che in ogni modo $e ben $i appiccano al C, il pe$o E non
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956 $i moua $empre in gi&ugrave; ver$o il G. La qual co$a habbiamo noi pre$uppo$to poter$i
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957 fare, &amp; credeuamo poter$i fare: Peroche quel che &egrave; di pi&ugrave; del pe$o D $opra
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958 il pe$o E, hauendo ragione, &amp; parte di quantit&agrave;, $i imaginauamo non $olamente
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959 e$$ere minimo, ma ancora poter$i diuidere in infinito, il che e&szlig;i per certo non $ola-
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960 mente minimo, ma ne anche e$$ere minimo, non potendo$i ritrouare, $i s$orzano di
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961 mo$tr are in que$ta maniera.</I>
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962 <pb n=7>
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963 <p><I>Pongan$i le co$e iste$$e
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964 &amp; da<*>i punti DE
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965 $iano tirate le linee
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966 DHE</I>K <I>&agrave; piombo
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967 dell'orizonte, &amp; $ia
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968 vn'altro cerchio L
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969 DM, il cui centro
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970 $ia N, ilquale toc</I> <marg><I>Per la $ecen da del terzo</I></marg>
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971 <I>chi FDG nel pun
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972 to D, &amp; $ia eguale</I> <marg><I>Per la vige $imanona del prim<*>.</I></marg>
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973 <I>ad FDG. Sar&agrave;
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974 NC linea retta: &amp;
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975 perche l'angolo</I> K
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976 <I>EC &egrave; eguale all'an-
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977 golo HDN, &amp;
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978 l'angolo CEG &egrave; pa
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979 rimente eguale al-
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980 l'angolo NDM,</I>
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981 <fig>
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982 <I>peroche egli &egrave; contenuto da mezi diametri, &amp; da circonferenze eguali: $ar&agrave; il re-
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983 stante angolo &amp; mi$to</I> K<I>EG eguale al re$tante angolo &amp; mi$to HDM. Et per-
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984 cioche pre$uppongono, che quanto &egrave; minore l'angolo contenuto dalla linea tirata &agrave;
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985 piombo dell'orizonte, &amp; dalla circonferenza, tanto in quel $ito e$$ere anco pi&ugrave; gra
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986 ue il pe$o. Talche $i come l'angolo contenuto da HD, &amp; dalla circonferenza
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987 DG, &egrave; minore dell'angolo</I> K<I>EG, cio&egrave; dell'angolo HDM, co$i $econdo que$ta
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988 proportione il pe$o po$to in D $ia pi&ugrave; graue di quello che $t&agrave; in E. Mala pro-
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989 portione dell'angolo MHD all'angolo HDG &egrave; minore di qual $i voglia altra
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990 proportione, che $i troui tra la maggiore, &amp; minore quantit&agrave;: Adunque la pro-
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991 portione de i pe$i DE $ar&agrave; la minima di tutte le proportioni, anzinon $ar&agrave; qua$i
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992 ne anche proportione, e$$endo la minima di tutte le proportioni. Che la propor-
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993 tione di MDH ver$o HDG $ia di tutte la minima, mo$trano con que$ta ne-
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994 ce$$aria ragione, peroche MHD $upera HDG con angolo di linea curua, che
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995 &egrave; MGD, ilquale angolo &egrave; il minimo di tutti gli angoli fatti di linee rette: ne po-
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996 tendo$i dare angolo minore di MGD $ar&agrave; la proportione di MDH ver$o HDG
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997 la minima di tutte le proportioni. Laqual ragione pare e$$ere grandemente friuo-
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998 la, peroche quantunque l'angolo MDG $ia di tutti gli angoli fatti di linee rette
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999 il minore, non perci&ograve; $egue totalmente egli e$$ere di tutti gli angoli il minimo, im-</I> <marg><I>Per la decima ottaua del terzo.</I></marg>
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1000 <I>peroche $ia dal punto D tirata la linea DO &agrave; piombo di NC, ambedue que-
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1001 ste toccberanno le circonferenze LDMFDG nel punto D. Ma percioche le
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1002 circonferenze $ono eguali, $ar&agrave; l'angolo MDO misto eguale all'angolo ODG mi-
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1003 $to. L'vno de gli angoli dunque, cio&egrave; ODG $ar&agrave; minore di MDG, cio&egrave; minore</I> <marg><I>Per la ottaua del quinto.</I></marg>
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1004 <I>del minimo. Dapoi l'angolo ODH $ar&agrave; minore dell'angolo MDH. Per laqual co$a
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1005 ODH haur&agrave; proportione minore all'angolo HDG, che MDH all'i$te$$o</I>
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1006 <pb>
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1007 <I>HDG. Dara$$i dunque la proportione anco minore della minima, laquale mostre-
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1008 remo dauantaggio in in$inito minore in questo modo. De$criua$i il cerchio DR,
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1009 il cui centro $ia E, &amp; il mezo diametro ED, la circonferentia DR tocche-</I>
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1010 <marg><I>Per la vnde cima del ter zo.</I></marg> <I>r&agrave; la circonferenza
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1011 DG nel punto D,
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1012 &amp; la linea DO nel</I>
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1013 <marg><I>Per la decima ottaua del terzo.</I></marg> <I>punto D. Per laqual
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1014 co$a minore $ar&agrave; l'an
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1015 golo RDG dell'an-
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1016 golo ODG, &amp; $i-
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1017 milmente l'angolo R
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1018 DH dell'angolo O
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1019 DH. Adunque ha-
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1020 uer &agrave; minore propor-
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1021 tione RDH ad HD
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1022 G di quel che haur&agrave;
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1023 ODH ad HDG.
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1024 Pigli$i dapoi tra E
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1025 &amp; C, come $i vuo-
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1026 le, il punto P, dal
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1027 quale nella di$tanza</I>
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1028 <fig>
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1029 <I>di PD $i de$criua vn'altra circonferenza DQ, laquale toccher&agrave; la circonferen-
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1030 tia DR, &amp; la circonferentia DG nel punto D, &amp; l'angolo QDH $ar&agrave; mi
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1031 nore dell'angolo RDH. Adunque QDH haur&agrave; proportione minore ad HDG
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1032 che RDH ad HDG, &amp; nell'i$te$$o modo in tutto, $e tra il C &amp; il P $i tor-
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1033 r&agrave; vn'altro punto, &amp; tra que$to, &amp; il C vn'altro, &amp; co$i $ucce&szlig;iuamente $i de-
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1034 $criueranno infinite circonferentie tra DO, &amp; la circonferenza DG: dalle quali
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1035 troueremo $empre la proportione minore in infinito: &amp; co$i $egue, che la propor-
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1036 tione del pe$o po$to in D al pe$o po$to in E non $ia tanto picciola, che non $i
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1037 po$$a ritrouarla $empre minore in infinito. Et perche l'angolo MDG $i puote
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1038 diuidere in infinito, $i potr&agrave; anche diuidere quel pi&ugrave; di grauezza che ha il D $o-
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1039 pra lo E in infinito.</I>
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1040 <pb n=8>
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1041 <p><I>Ne bi$ogna trala$ciare, che
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1042 eglino hanno pre$upp o$to
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1043 nella demo$tratione l'ango
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1044 lo</I> K<I>EG e$$er maggiore del
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1045 l'angolo HDC, come co
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1046 $a nota: il che ben &egrave; vero $e
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1047 DHE</I>K <I>$ono fra loro e-
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1048 gualmente di$tanti. Ma
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1049 percioche, come e&szlig;i pari-
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1050 mente pre$uppongono, le
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1051 linee DHE</I>K <I>$i vanno &agrave;
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1052 trouare nel centro del mon
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1053 do, le linee DHE</I>K <I>non
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1054 $aranno egualmente di$tan
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1055 ti giamai, et l'&atilde;golo</I> K<I>EG
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1056 non $olo non $ar&agrave; maggio-
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1057 re dall'angolo HDG, ma
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1058 minore. Come per gra-
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1059 tia di e$$empio, $ia tirata la
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1060 linea FG $in al centro del
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1061 mondo, che $ia S, &amp; con
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1062 giungan$i DS ES. Egli
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1063 &egrave; da mostrare l'angolo SE
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1064 G e$$ere minore dell'ango
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1065 lo SDG. Tiri$i dal punto
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1066 E la linea ET, che toc-
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1067 chi il cerchio DGEF, &amp;
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1068 dall'i$te$$o punto $ia tirata
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1069 la EV egualmente di$tan</I>
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1070 <fig>
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1071 <I>te da DS: Percioche dunque EVDS $ono traloro egualmente di$tanti, $imil-
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1072 mente ET DO $ono egualmente di$tanti: $ar&agrave; l'angolo VET eguale all'ango-
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1073 lo SDO: &amp; l'angolo TEG eguale all'angolo ODM, per e$$ere contenuto da
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1074 linee toccanti la circonferenza, &amp; da circonferenze eguali. Tutto l'angolo dun-
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1075 que VEG $ar&agrave; eguale all'angolo SDM. Leui$i via dall'angolo SDM l'ango
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1076 lo di linee curue MDG: &amp; dall'angolo VEG leui$i via l'angolo VES, &amp;
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1077 l'angolo VES fatto di linee rette &egrave; maggiore dell'angolo MDG fatto di linee
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1078 curue; $ar&agrave; il re$tante angolo SEG minore dell'angolo SDG. Per laqual co$a
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1079 dalle pre$uppo$te loro non $olo il pe$o posto in D $ar&agrave; pi&ugrave; graue del pe$o po$to
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1080 in E, ma per lo contrario il pe$o E $ar&agrave; pi&ugrave; graue dell'i$te$$o D.</I>
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1081 <pb>
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1082 <p><I>Producono tutta via
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1083 ragioni con le quali
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1084 $i sforzano di mo-
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1085 $trare, che la bilan-
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1086 cia DE ritorna per
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1087 nece&szlig;it&agrave; in AB e-
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1088 gualmente distante
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1089 dall'orizonte. Pri-
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1090 ma dimo$trano l'i-
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1091 $te$$o pe$o e$$ere pi&ugrave;
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1092 graue in A, che
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1093 in altro $ito, che
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1094 chiamano $ito della
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1095 egualit&agrave;, e$$endo la
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1096 linea AB egual-
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1097 mente di$tante dal-
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1098 l'orizonte. Da-
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1099 poi quanto &egrave; pi&ugrave; da</I>
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1100 <fig>
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1101 <I>pre$$o allo A, tanto e$$ere piu graue di qual $i voglia altro pi&ugrave; da lontano, cio&egrave;
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1102 il pe$o po$to in A e$$ere pi&ugrave; graue, che in D; &amp; in D, che in L: &amp; $imil-
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1103 mente in A pi&ugrave; graue, che in N; &amp; in N pi&ugrave; graue, che in M. Con$ide-</I>
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1104 <marg><I>Il Cardano nel primo della $ottigliezza.</I></marg> <I>rando $olamente vn pe$o in vno delle braccia in s&ugrave;, ouero in gi&ugrave; mo$$o. Percio-
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1105 che dicono, po$ta la trutina della bilancia in CF, il pe$o me$$o in A &egrave; pi&ugrave; lunge
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1106 dalla trutina che in D; &amp; in D pi&ugrave; lunge, che in L: peroche tirate le linee DO</I>
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1107 <marg><I>Giordano nella quarta propo$itione</I></marg> <I>LP &agrave; piombo di CF, la linea AC re$ta maggiore di DO, &amp; DO di e$$a LP,
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1108 &amp; auiene l'i$te$$o ne i punti NM. Dapoi dicono da qual luogo il pe$o $i mo-
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1109 ue pi&ugrave; velocemente, iui &egrave; pi&ugrave; graue: ma egli $i moue pi&ugrave; velocemente dallo</I>
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1110 <marg><I>Il Tartaglia nella quinta propo$itione.</I></marg> <I>A, che da altro $ito; adunque egli &egrave; pi&ugrave; graue nello A. Con $imile mo-
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1111 do, quanto pi&ugrave; egli &egrave; da pre$$o allo A, tanto pi&ugrave; velocemente $i moue:
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1112 adunque nel D $ar&agrave; pi&ugrave; graue, che in L. L'altra cagione poi che cauano dal mo-</I>
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1113 <marg><I>Il Cardano. Giordano al la propo$itio ne quarta.</I></marg> <I>uimento pi&ugrave; diritto, &amp; pi&ugrave; torto &egrave;, che quanto il pe$o di$cende pi&ugrave; diritto in archi
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1114 eguali, pare e$$er anco pi&ugrave; graue; concio$ia che il pe$o e$$endo libero, &amp; $ciolto, $i
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1115 moua di $ua propria natura per lo diritto; ma in A egli di$cende pi&ugrave; dirittamen</I>
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1116 <marg><I>Il Tartaglia alla pro po$itione</I> 5.</marg> <I>te; dunque in A $ar&agrave; pi&ugrave; graue, &amp; dimo$trano ci&ograve; pigliando l'arco AN egua-
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1117 le all'arco LD. &amp; da i punti NL $iano tirate le linee NRLQ egualmente di-
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1118 $tanti dalla linea FG, laquale chiamano anche della direttione; &amp; quelle altre $e-
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1119 gheranno le linee ABDO in QR, &amp; dal punto N $ia tirata la NT &agrave; piombo
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1120 di FG: Dimo$trano veramente LQ e$$ere eguale &agrave; PO, &amp; NR ad e$$a CT,
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1121 &amp; la linea NR e$$er maggiore di LQ. Hor percioche la di$ce$a del pe$o dallo A
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1122 fin ad N per la circonferentia di AN trapa$$a maggior parte della linea FG,
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1123 (che e&szlig;i chiamano pigliare di diritto) che la di$ce$a di L in D per la circonferenza
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1124 LD; concio$ia che la di$ce$a AN trapa&szlig;i la linea CT, ma la di$ce$a LD la linea</I>
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1125 <pb n=9>
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1126 <I>PO, &amp; CT &egrave; maggiore di PO, la di$ce$a di AN $ar&agrave; pi&ugrave; diritta, che la di-
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1127 $ce$a di LD: $ar&agrave; dunque pi&ugrave; graue il pe$o po$to in A, che in L, ouero in qual
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1128 $i voglia altro $ito, &amp; nell'i$te$$o modo dimo$trano, che quanto il pe$o &egrave; pi&ugrave; vicino
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1129 allo A, &egrave; pi&ugrave; graue; cio&egrave; $iano le circonferenze LD DA traloro eguali, &amp;
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1130 dal punto D $ia tirata la linea DR &agrave; piombo di AB; $ar&agrave; la DR eguale al-</I> <marg><I>Per la trige $imaquarta del primo.</I></marg>
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1131 <I>la CO. &amp; dimo-
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1132 $trano po$cia, che
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1133 la linea DR &egrave; mag
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1134 giore della LQ, &amp;
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1135 dicono che la $ce$a
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1136 di DA prende pi&ugrave;
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1137 di $ce$a diritta, che
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1138 non fa LD, pe-
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1139 roche &egrave; maggiore
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1140 la linea CO, che
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1141 la OT<*> Per la-
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1142 qual co$a<*> pe$o $a
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1143 r&agrave; pi&ugrave; graue in D,
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1144 che in L, ilche pa
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1145 rimente auiene ne
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1146 punti NM. &amp;
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1147 co$i il pre$uppo$to,
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1148 per loquale dimo-</I>
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1149 <fig>
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1150 <I>$trano la bilancia DE ritornare in AB a$fermano come noto, &amp; manife$to; cio&egrave;</I> <marg><I>Giordane nella quarta pre $apoosta</I></marg>
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1151 <I>che $econdo il $ito il pe$o &egrave; tanto pi&ugrave; graue, quanto nel mede$imo $ito manco tor-
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1152 ta &egrave; la $ce$a: &amp; la cagione di cotal ritorno dicono e$$ere que$ta; peroche la $ce$a del
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1153 pe$o po$to in D &egrave; pi&ugrave; diritta della $ce$a del pe$o po$to in E, per pigliare il pe$o</I> <marg><I>Giordano nella $econda propo$iti<*> ne.</I></marg>
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1154 <I>di E manco della direttione in de$cendendo che non fa il pe$o di D pur nel di$cen
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1155 dere: Come $e l'arco EV $ia eguale &agrave; DA, &amp; $iano tirate VHET &agrave; piom
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1156 bo di FG; $ar&agrave; maggiore DR di TH. Per laqual co$a per la pre$uppo$ta il pe</I> <marg><I>Il Tartaglia nella quinta propo$icione.</I></marg>
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1157 <I>$o me$$o in D per ri$petto al $ito $ar&agrave; pi&ugrave; graue del pe$o me$$o in E. Adunque
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1158 il pe$o me$$o in D e$$endo pi&ugrave; graue $i mouer&agrave; in gi&ugrave;, &amp; il pe$o po$to in E in
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1159 $u fin che la bilancia DE ritorni in AB.</I>
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1160 <p><I>L'altra ragione ancora di que$to ritorno &egrave;, che qu&atilde;do la trutina della bilancia &egrave; $opra</I> <marg><I>Il Cardano.</I></marg>
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1161 <I>dilei in CF; la linea CG &egrave; la meta: &amp; percio che l'angolo GCD &egrave; maggiore
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1162 dell'angolo GCE, &amp; l'angolo maggiore dalla meta rende pi&ugrave; graue il pe$o: adun-
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1163 que $tando la trutina della bilancia di $opra $ar&agrave; pi&ugrave; graue il pe$o in D, che in E,
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1164 &amp; perci&ograve; il D ritorner &agrave; nello A, &amp; lo E nel B.</I>
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1165 <p>Meta &egrave; pur voce Latina co$tumata da gli antichi ne i giuo chi, &amp; conte$e fatte ne i cer
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1166 chi murati, &amp; ne i Theatri, percio che il principio, oue $i dauano le mo$$e a' corri-
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1167 tori, $i chiamaua Carcere, &amp; il fine Meta; di modo, che meta viene &agrave; dire termine
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1168 &amp; fine: &amp; piu in altro $ignificato il luogo piu ba$$o, &amp; in$imo. Hor qui $i puote
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1169 <foot><I>C</I></foot>
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1170 <pb>
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1171 intendere ad ambidue i modi, cio&egrave; che la linea CG $ia la meta, cio&egrave; il termine
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1172 &amp; fine, nelquale ha da peruenire il pe$o collo cato nella bilancia; ouero il luogo
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1173 infimo della circonferenza, alquale capita il pe$o per natura. Doue $criue l'Auto
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1174 re l'angolo maggiore dalla Meta, vuol dire l'angolo, che fa il braccio della bilan-
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1175 cia con la Meta CG.
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1176 <p><I>Et co$i c&otilde; que$te ragioni $i sforzano dimo$trare la bilancia DE ritornare in AB; le
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1177 quali al parer mio $i po$$ono ageuolmente $oluere.</I>
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1178 <p><I>Primieramente dunque in quanto s'appartiene alle ragioni, che dicono il pe$o me$$o
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1179 in A e$$ere piu graue, che in altro $ito, lequali cauano dalla di$tanza piu da lonta-
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1180 no, &amp; piu da pre$$o della linea FG, &amp; dal mouimento piu veloce, &amp; piu diritto
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1181 dal punto A. In prima non dimo$trano veramente perche il pe$o $i moua piu velo-
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1182 cemente dallo A, che da al tro $ito. ne perche $ia maggiore CA di DO, &amp; DO
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1183 di LP, per que$to, come per vera cagione, $egue il pe$o po$to in A e$$ere piu gra-
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1184 ue di quello, che &egrave; in D, &amp; quello di D, di quel che $t&agrave; in L, percioche non $i queta
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1185 l'intelletto, $e di ci&ograve; altra cagione non $i dimo$tra, parendo $egno piu to$to, che vera
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1186 cagione. Quello ste$$o accade parimente all'altra ragione, laquale adducono dal
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1187 mouimento piu diritto, &amp; piu torto. Oltre &agrave; ci&ograve; tutte quelle co$e, che per$uadono
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1188 per via del mouim&etilde;
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1189 to piu veloce, &amp;
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1190 piu tardo il pe$o in
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1191 A e$$ere piu graue,
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1192 che in D, non per-
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1193 ci&ograve; dimo $trano, che
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1194 il pe$o in A, in qu&atilde;
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1195 to &egrave; in A, $ia piu
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1196 graue del pe$o D, in
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1197 quanto &egrave; in D, ma
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1198 in quanto $i parte
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1199 da i punti DA.
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1200 Onde, au&atilde;ti che piu
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1201 oltre $i proceda, pri
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1202 ma dimo$trer&ograve;, che
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1203 il pe$o quanto egli
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1204 &egrave; piu da pre$$o ad
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1205 FG manco graua,
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1206 $i in quanto egli $t&agrave;
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1207 nel $ito, oue $i ritro</I>
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1208 <fig>
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1209 <I>ua, come anche in quanto $i parte da quello: &amp; in$ieme, che egli &egrave; fal$o il pe$o e$$ere
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1210 piu graue in A, che in altro $ito.</I>
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1211 <p><I>Tiri$i la FG fin al centro del mondo, che $ia in S, &amp; dal punto S tiri$i anco vna linea,
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1212 che tocchi il cerchio AFBG. non potr&agrave; gi&agrave; questa linea tirata dal punto S toc-
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1213 care il cerchio nel punto A; imperoche tirata la linea AS, il triangolo ACS ver</I>
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1214 <pb n=10>
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1215 <I>rebbe ad hauere due angoli retti, cio&egrave; SAC, &amp; ACS, che &egrave; impo&szlig;ibile: ne me
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1216 no toccher&agrave; $opra il punto A nella circonferenza AF; peroche $egherebbe il cer-</I> 2<marg><I>Per la deci ma ottau<*> del terzo</I></marg>
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1217 <I>chio. Toccher&agrave; dunque $otto, &amp; $ia SO: $iano dapoi congiunte le lince SD SL,
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1218 lequali $eghino la circonferenza AOG ne' punti</I> K<I>H, &amp; $iano ancho congiunte le
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1219 linee C</I>K <I>CH. Et percioche il pe$o, quanto egli &egrave; piu da pre$$o di F, tanto piu an-
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1220 co $t&agrave; $opra il centro; come il pe$o in D preme, &amp; $t&agrave; piu $opra il punto del volgi-
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1221 mento C, come &agrave; centro, cio&egrave; in D piu graua $opra la linea CD, che $e egli fo$$e in A
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1222 $opra la linea CA: &amp; dauantaggio piu in L $opra la linea CL. imperoche e$$endo
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1223 li tre angoli di cia$cun triangolo eguali &agrave; due angoli retti, &amp; l'angolo DC</I>K <I>del
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diff changeset
1224 triangolo DC</I>K, <I>che &egrave; di due lati eguali $ia
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1225 minore dell'angolo LCH del tri&atilde;golo LCH,
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1226 che &egrave; pur di due lati eguali: $aranno gli altri
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diff changeset
1227 alla ba$e, cio&egrave; CD</I>K <I>C</I>K<I>D in$ieme pre$i
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1228 maggiori de gli altri CLH CHL; &amp; le
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1229 met&agrave; di que$ti, cio&egrave; l'angolo CDS $ar&agrave; mag
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1230 giore dell'angolo CLS. E$$endo adunque
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1231 CLS minore, la linea CL piu $i acco$ter&agrave;
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1232 al mouimento naturale del pe$o me$$o in L
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1233 del tutto $ciolto; cio&egrave; &agrave; dire alla linea LS,
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1234 che CD al mouimento DS: percioche il pe
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1235 $o po$to in L libero, &amp; $ciolto $i mouerebbe
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1236 ver$o il centro del mondo per LS, &amp; il pe-
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diff changeset
1237 $o po$to in D per DS. Ma perche il pe$o
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1238 me$$o in L graua tutto $opra LS, &amp; quello
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diff changeset
1239 che &egrave; in D $opra DS, il pe$o in L grauer&agrave;
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1240 pu $opra la linea CL, che quello, che $t&agrave; in
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1241 D $opra la linea DC. Adunque la linea
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1242 CL $o$terr&agrave; piu il pe$o, che lalinea CD, &amp;
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1243 nel modo iste$$o quanto piu il pe$o $ar&agrave; da
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1244 pre$$o ad F, $i dimo strer&agrave; piu e$$er $o$tenuto
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1245 dalla linea CL per cotesta cagione, peroche
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1246 $empre l'angolo CLS $arebbe minore, la-
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1247 qual co$a etiandio &egrave;manife$ta; perche $e le li
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1248 nee CL, &amp; LS s'incontra$$ero in vna li
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1249 nea, ilche auiene in FCS, all'hora la linea
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1250 CF $o$terrebbe tutto il pe$o, che &egrave; in F, &amp;
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1251 lo renderebbe immobile, n&egrave; haurebbe niuna
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1252 grauezza in tutto nella circonferenza del cer
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1253 chio. Li$te$$o pe$o dunque per la diuer$it&agrave;</I>
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1254 <fig>
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1255 <I>de' $iti $ar&agrave; piu graue, &amp; piu lieue. &amp; que$to non gi&agrave; percio che per ragione del $ito
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1256 alcuna volta egli acqui$ti veramente grauezza maggiore, &amp; alcuna volta la perda,
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1257 e$$endo $empre della i$te$$a grauezza, troui$i douunque $i voglia: ma percioche egli</I>
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1258 <foot><I>C</I> 2</foot>
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1259 <pb>
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1260 <I>graua piu, &amp; meno nella circonferenza, come in D piu graua $opra la circonferenza
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1261 DA, che in L $opra la circonferenza LD: cio&egrave; $e il pe$o $ar&agrave; $o$tenuto dalle circon
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1262 ferenze, &amp; dalle linee diritte; la circonferenza AD $o$terr&agrave; piu il pe$o po$to in D,
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1263 che la circonferenza DL, $tando il pe$o in L; peroche meno aiuta CD, che CL.
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1264 Oltre &agrave; ci&ograve; quando il pe$o &egrave; in L, $e egli fo$$e del tutto libero &amp; $ciolto, $i mouerebbe
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1265 in giu per LS, $e non gliene fu$$e vietato dalla linea CL, laquale sforza il pe$o po$to
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1266 in L &agrave; mouer$i oltre la linea LS per la circonferenza LD, &amp; lo caccia in certo mo
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1267 do, &amp; in cacciandolo viene in parte &agrave; $o$tenerlo; percioche $e non lo $o$tene$$e, &amp;
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1268 gli face$$e re$i$tenza, $i mouerebbe in giu per la linea LS, ma non gi&agrave; per la cir-
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1269 conferenza LD. Similmente la CD fa re$i$tenza al pe$o po$to in D, sforzan-
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1270 dolo &agrave; mouer$i per la circonferenza DA. Nell'iste$$o modo $tando il pe$o in A,
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1271 la linea CA con$tringer&agrave; il pe$o &agrave; mouer$i
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1272 oltre la linea AS per la circoferenza AO;
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1273 peroche l'angolo CAS &egrave; acuto, e$$endo lo
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1274 angolo ACS retto. Adunque le linee
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1275 CA CD in qualche parte, ma non gi&agrave; e-
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1276 gualmente fanno re$istenza al pe$o. &amp; qua
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1277 lunque volta l'angolo, che &egrave; nella circonfe-
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1278 renza del cerchio fatto dalle linee che e$cono
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1279 dal centro del monde S, &amp; dal centro C $a-
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1280 r&agrave; acuto, dimo$treremo auenire l'i$te$$o. Hor
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1281 percioche l'angolo mi$to CLD &egrave; eguale &agrave;
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1282 l'angolo CDA, per e$$ere conteuuto da
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1283 mezi diametri, &amp; dall'i$te$$a circonferenza;
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1284 &amp; l'angolo CLS &egrave; minore dell'angolo
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1285 CDS; $ar&agrave; il reflante SLD maggiore
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1286 del re$tante SDA. Per laqual co$a la cir
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1287 conferenza DA, cio&egrave; la di$ce$a del pe$o
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1288 in D $ara piu da pre$$o al mouimento natu-
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1289 rale del pe$o $ciolto me$$o in D, cio&egrave; della li-
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1290 nea DS, che la circonferenza LD della
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1291 linea LS. Meno dunque far&agrave; re$i$tenza la
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1292 linea CD al pe$o po$to in D, che la linea
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1293 CL al pe$o po$to in L. Per&ograve; la linea CD
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1294 $o$terr&agrave; meno, che CL, &amp; il pe$o $ar&agrave;
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1295 piu libero in D, che in L: mouendo$i piu
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1296 naturalmente il pe$o per DA, che per LD.
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1297 Per laqual co$a piu graue $ar&agrave; in D, che in
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1298 L. Similmente dimo$treremo, che CA man
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1299 co$o$tiene, che CD &amp; che il pe$o piu in A,
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1300 che in D &egrave; libero, &amp; piu graue. Dopo dalla</I>
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1301 <fig>
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1302 <I>parte di $otto per l'i$te$$e cagioni, quanto il pe$o $ar&agrave; piu da pre$$o al G, $ar&agrave; piu ri-</I>
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1303 <pb n=11>
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1304 <I>tenuto, come in H dalla linea CH, che in</I> K <I>dalla linea C</I>K: <I>percioche e$$en</I> <marg><I>Per la</I> 21. <I>del prim.</I></marg>
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1305 <I>do l'angolo CHS maggiore dell'angolo C</I>K<I>S, le linee CH HS, $i acco$te-
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1306 ranno piu alla direttione, che C</I>K K<I>S. &amp; per que$to $ar&agrave; piu ritenuto il pe$o da
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1307 CH, che da C</I>K; <I>percioche $e CH HS $i incontra$$ero in vna linea, come auie-
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1308 ne $tando il pe$o in G, allbora la linea CG $o$terrebbe tutto il pe$o in G, per
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1309 modo che $tarebbe immobile. Quanto minore dunque $ar&agrave; l'angolo contenuto dal
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1310 la linea CH, &amp; dalla di$ce$a del pe$o $ciolto, cio&egrave; dalla linea HS, tanto meno
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1311 anco quella linea ritenir&agrave; il pe$o, &amp; doue $ar&agrave; manco ritenuto, iui $ar&agrave; piu libero, &amp;
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1312 piu graue. Oltre &agrave; ci&ograve; $e il pe$o fo$$e libero in K, &amp; $ciolto, $i mouerebbe per la li-
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1313 nea KS, ma egli &egrave; impedito dalla linea CK, laquale sforza il pe$o a mouer$i di
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1314 qua dalla linea KS per la circonferenza KH; percio che lo ritira in certo modo,
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1315 &amp; in ritirandolo viene a $o$tenerlo, peroche $e non lo $o$tene$$e, $i mouerebbe il pe-
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1316 $o in giu per la linea diritta KS, ma non per la circonferenza KH. Similmente
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1317 la CH ritiene il pe$o, sforzandolo a mouer$i per la circonferenza HG. Et percio-
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1318 che l'angolo CHS &egrave; maggiore dell'angolo CKS, leuati via gli angoli eguali
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1319 CHG, C</I>K<I>H, $ar&agrave; il re$tante SHG maggiore del re$tante S</I>K<I>H. Adunque
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1320 la circonferenza KH, cio&egrave; la di$ce$a del pe$o po$to in K $ar&agrave; piu da pre$$o al mo-
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1321 uimento naturale del pe$o po$to in K $ciolto, cio&egrave; alla linea KS, che la circonfe-
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1322 renza HG alla linea HS. Per laqual co$a meno ritiene la linea CK, che CH,
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1323 mouend o$i il pe$o piu naturalmente per KH, che per HG, Con ragione $imile
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1324 anco $i mo$trer&agrave;, che quanto minore $ar&agrave; l'angolo SKH, la linea CK $o$terr&agrave;
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1325 meno. Stando dunque il pe$o in O, percioche l'angolo SOC non $olamente &egrave;
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1326 minore dell'angolo CKS, ma anco il minimo di tutti gli angoli, che e$con da i pun
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1327 ti CS, &amp; hanno la cima nella circonferenza OKG; $ar&agrave; l'angolo SOK il mi
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1328 nimo $i dell'angolo SKH, come de tutti gli altri co$i fatti. Adunque la di$ce$a
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1329 del pe$o po$to in O $ar&agrave; piu da pre$$o al mouimento naturale di e$$o pe$o $ciolto in
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1330 O, che in altro $ito della circonferenza OKG: &amp; la linea CO meno $o$tenir&agrave;
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1331 il pe$o, che $e egli fo$$e in qual $i voglia altro $ito della i$te$$a circonferenza OG.
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1332 Similmente perche l'angolo del toccamento SOK &egrave; minore $i dell'angolo SDA,
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1333 $i dello SAO, &amp; $i di qual $i voglia altro $imile; $ar&agrave; la $ce$a del pe$o me$$o in O
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1334 piu da pre$$o al mouimento naturale di e$$o pe$o $ciolto in O, che in altro $ito del-
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1335 la circ&otilde;fer&etilde;za ODF. Oltre a ci&ograve; perche la linea CO no puote $pingere il pe$o po$to
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1336 in O mentre egli $i moue in giu, per modo che egli $i moua oltre la linea OS, per
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1337 cioche la linea OS non taglia il cerchio, ma lo tocca; &amp; l'angolo SOC &egrave; retto
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1338 &amp; non acuto, il pe$o po$to in O non grauer&agrave; niente $opra la linea CO, ne $tar&agrave;
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1339 $opra il centro, come accaderebbe in qual $i voglia altro punto $opra l'O. Sar&agrave; dun-
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1340 que il pe$o po$to in O per que$te cagioni libero, &amp; $ciolto piu in que$to $ito, che in
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1341 qual $i voglia altro della circonferenza FOG; &amp; perci&ograve; in que$to $ar&agrave; piu graue,
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1342 cio&egrave; a dire piu grauer&agrave;, che in altro $ito. Et quanto $ar&agrave; piu da pre$$o ad O, $ar&agrave;
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1343 piu graue di quello, che $e fo$$e piu da lunge: &amp; la linea CO $ar&agrave; egualmente di-
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1344 $tante dall'orizonte: non pero all'orizonte del punto C (come $timano e$$i) ma
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1345 del pe$o po$to in O, douendo$i prendere l'orizonte dal centro della grauezza del pe
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1346 $o. Lequali co$e tutte bi$ognaua mo$trare.</I>
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1347 <pb>
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1348 <p><I>Ma $e il braccio della bilancia fo$$e maggiore
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1349 di CO, come per la quantit&agrave; di CD;
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1350 $ar&agrave; parimente il pe$o me$$o in O piu gra-
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1351 ue. De$criua$i il cerchio OH, il cui
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1352 centro $ia D, &amp; il mezo diametro DO.
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1353 il cerchio OH toccher&agrave; il cerchio FOG
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1354 nel punto O, &amp; toccher&agrave; anche la linea</I>
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1355 <marg><I>Per la</I> 11. <I>del terzo</I></marg> <I>OS nel punto mede$imo, laquale &egrave; la $ce-
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1356 $a naturale, &amp; diritta del pe$o po$to in O.</I>
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1357 <marg><I>Per la</I> 18. <I>del terzo.</I></marg> <I>Et percioche l'angolo SOH &egrave; minore del
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1358 l'angolo SOG, $ar&agrave; la $ce$a del pe$o po$to
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1359 in O per la circonferenza OH piu dapre$
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1360 $o al mouimento naturale OS, che per la
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1361 circonferenza OG. Piu libero dunque
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1362 &amp; $ciolto, &amp; per con$equente piu graue $a-
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1363 r&agrave;in O, $tante il centro della bilancia in
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1364 D, che in C. Similmente $i mo$trer&agrave;,
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1365 che quanto piu grande $ar&agrave; il braccio DO,
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1366 il pe$o po$to in O $ar&agrave; d'auantaggio piu
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1367 graue.</I>
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1368 <fig>
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1369 <p><I>Ma $e l'iste$$o cerchio AFBG co'l $uo centro R $ar&agrave; piu da pre$$o ad S centro
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1370 del mondo, &amp; dal punto S $ia tirata vna linea, che tocchi il cerchio ST, il pun-
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1371 to T, (doue il pe$o &egrave; piu graue) $ar&agrave; piu lontano dal punto A, che il punto O:
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1372 percioche $iano tirate da i punti OT le linee OMTN &agrave; piombo di CS, &amp;
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1373 congiungan $i RT, &amp; $ia il centro R nella linea CS, &amp; la linea ARB $ia
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1374 egualmente di$tante ad ACB. Percioche dunque i triangoli COS RTS $ono</I>
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1375 <marg><I>Per la <*>ttaua del $esto.</I></marg> <I>di angoli retti, $ar&agrave; SC &agrave; CO, come CO &agrave; CM. Similmente SR ad</I>
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1376 <marg><I>Per la ottaua del quito</I></marg> <I>RT, come RT ad RN. E$$endo dunque RT eguale &agrave; CO, &amp; SC mag
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1377 giore di RS: haur&agrave; proportione maggiore SC &agrave; CO, che SR ad RT. on</I>
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1378 <marg><I>Per la decima del q<*> to.</I></marg> <I>de baur&agrave; parimente proportione maggiore CO &agrave; CM, che RT ad RN. $a
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1379 r&agrave; dunque minore CM, che RN. Tagli$i dunque RN in P $i fattamen-</I>
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1380 <pb n=12>
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1381 <I>te, che RP $ia eguale &agrave; CM; &amp; dal
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1382 p&utilde;to P $ia tirata la linea PQ egual
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1383 mente di$tante dalle linee MONT,
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1384 laquale tagli la circ&otilde;fer&etilde;za AT in Q,
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1385 &amp; in fine c&otilde;gi&otilde;gan$i la RQ. Hor per
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1386 cioche le due CO CM $ono eguali &agrave;
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1387 le due RQ RP, &amp; l'angolo CMO</I> <marg><I>Per la</I> 7. <I>del $esto.</I></marg>
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1388 <I>&egrave; eguale all'angolo RPQ; $ar&agrave; an-
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1389 che l'angolo MCO eguale all'angolo
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1390 PRQ. Ma l'angolo MCA retto
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1391 &egrave; eguale all'angolo PRA retto; a-
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1392 dunque il re$tante OCA al restante</I> <marg><I>Per la</I> 26. <I>del terzo.</I></marg>
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1393 <I>QRA $ar&agrave; eguale, &amp; la circonferen-
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1394 za OA parimente eguale alla circon
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1395 ferenza QA. Per&ograve; il punto T per
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1396 e$$ere piu di$tante dal punto A, che
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1397 Q, $ar&agrave; anco piu di$tante dal punto
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1398 A, che il punto O. Dimo$trera$$i pa
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1399 rimente, che quanto piu il cerchio $ar&agrave;
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1400 vicino al centro del mondo, che egli $a
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1401 r&agrave; anco piu lontano. Et co$i come pri-
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1402 ma dimo$trera$$i il pe$o nella cir confe-
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1403 renza TAF $tar $opra il centro R,
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1404 ma nella circonferenza TG e$$ere ri-
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1405 tenuto dalla linea, &amp; ritrouar$i piu gra
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1406 ue nel punto T.</I>
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1407 <fig>
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1408 <pb>
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1409 <p><I>Che $e il punto G fo$$e nel centro del mondo; allhora quanto piu il pe$o $ar&agrave; da pre$$o al
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1410 G, $ar&agrave; piu graue: &amp; douunque $ia po$to il pe$o, fuor che nel G $empre $tar&agrave; $opra
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1411 il centro C, come in</I> K<I>: Imperoche tirata la linea G</I>K; <I>que$ta ($e condo laqua
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1412 le $i fa il mouimento naturale del pe$o) in$ieme co'l braccio della bilancia</I> K<I>C
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1413 far&agrave; vn'angolo acuto, peroche
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1414 gli angoli posti alla ba$e in</I> K
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1415 <I>&amp; G del triangolo di due la
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1416 ti eguali C</I>K<I>G $ono $empre
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1417 acuti. Hor $iano paragonate
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1418 in$ieme que$te due co$e, cio&egrave; il
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1419 pe$o posto in</I> K, <I>&amp; quello,
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1420 che &egrave; po$to in D, $ar&agrave; il pe$o
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1421 in K piu graue, che quello
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1422 in D; imperoche tirata la li-
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1423 nea DG, e$$endo che li tre an
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1424 goli di cia$cuno triangolo $iano
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1425 eguali &agrave; due angoli retti, &amp;
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1426 l'angolo DCG del triangolo
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1427 CDG di due lati eguali $ia
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1428 maggiore dell'angolo KCG
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1429 del triangolo CKG di due
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1430 lati eguali; $aranno gli altri an
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1431 goli alla ba$e DGC GDC
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1432 pre$i in$ieme minori de gli al-
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1433 tri KGC GKC pre$i in$ie</I>
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1434 <fig>
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1435 <I>me; &amp; la met&agrave; di questi, cio&egrave; l'angolo CDG $ar&agrave; minore dell'angolo CKG:
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1436 Per laqual co$a mouendo$i il pe$o po$to in K $ciolto naturalmente per KG, &amp;
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1437 il pe$o po$to in D per DG come per $patij, per i quali $ono portati nel centro del
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1438 mondo; la linea CD, cio&egrave; il braccio della bilancia $i acco$ter&agrave; piu al mouimento
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1439 naturale del pe$o po$to in D totalm&etilde;te $ciolto, alla linea cio&egrave; DG, che CK al
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1440 mouimento $atto $econdo KG. So$tenter&agrave; dunque piu la linea CD, che CK.
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1441 &amp; perci&ograve; il pe$o po$to in K per le co$e di $opra dette $ar&agrave; piu graue, che in D. Ol-
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1442 tre &agrave; ci&ograve;, perche $e il pe$o po$to in K fo$$e del tutto libero, &amp; $ciolto, $i mouerebbe
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1443 in giu per KG, $e egli non fo$$e impedito dalla linea CK, laquale sforza il pe$o
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1444 &agrave; mouer$i oltra la linea KG per la circonferenza KH; la linea KG $o$tente-
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1445 r&agrave; il pe$o in parte, &amp; gli far&agrave; re$istenza, sforzandolo &agrave; mouer$i per la circonferenza
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1446 KH. Et percioche l'angolo CDG &egrave; minore dell'angolo CKG, &amp; l'angolo
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1447 CDK &egrave; eguale all'angolo CKH, $ar&agrave; l'angolo re$tante GDK maggiore del re
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1448 $tante GKH. Dunque la circonferenza KH $ar&agrave; piu da pre$$o al mouimento
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1449 naturale del pe$o $ciolto po$to in K, cio&egrave; alla linea KG, che la circonferenza
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1450 DK alla linea DG. Per laqual co$a la linea CD $a piu re$i$tenza al pe$o po$to
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1451 in D, che la linea CK al pe$o posto in K. Adunque il pe$o po$to in K $ar&agrave;</I>
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1452 <pb n=13>
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1453 <I>piu graue, che in D. Similmente mostrera$$i, che quanto il pe$o $ar&agrave; piu da pre$$o
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1454 ad F, come in L manco grauer&agrave;; ma quanto piu da pre$$o $i trouer&agrave; al G, co-
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1455 me in H, e$$ere piu graue.</I>
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1456 <p><I>Che $e il centro del mondo fo$$e in S fra i punti CG; Primieramente $i mo$trer&agrave; nel
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1457 modo i$te$$o, che il pe$o in qualunque luogo po$to star&agrave; $opra il centro C, come in
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1458 H: peroche tirate le li-
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1459 nee HG HS, l'angolo
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1460 che &egrave; alla ba$e GHC del
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1461 tri&atilde;golo di due lati eguali
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1462 CHG &egrave; $empre acuto:
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1463 Perlaqual co$a anco SHC
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1464 minor di lui $ar&agrave; parimen
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1465 te $empre acuto. ma $ia ti
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1466 rata dal punto S la linea
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1467 SK &agrave; piombo di CS.
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1468 Dico che il pe$o &egrave; piu gra-
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1469 ue in</I> K, <I>che in alcun'al
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1470 tro $ito della circonferen
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1471 za FKG; &amp; quanto
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1472 piu da pre$$o $ar&agrave; allo F,
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1473 ouero al G meno graue-
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1474 r&agrave;. Prendan$i ver$o lo
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1475 F i punti DL, &amp; con
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1476 giung&atilde;$i le linee LC LS
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1477 DC DS, &amp; $iano al-</I>
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1478 <fig>
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1479 <I>lungate le linee LS DS KS HS fin'alla circ&otilde;ferenza del cerchio in EM NO;
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1480 &amp; $iano c&otilde;giunte CE, CM, CN, CO. Hor percioche LE DM $i taglia-
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1481 <*>o in$ieme in S, $ar&agrave; il rettangolo LSE eguale al rettangolo DSM. Onde $i co</I> <marg><I>Per la</I> 35. <I>del terzo.</I></marg>
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1482 <I>me &egrave; la LS ver$o la DS, co$i $ar&agrave; la SM ver$ola SE; ma &egrave; maggior la LS
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diff changeset
1483 della DS; &amp; la SM di e$$a SE. Dunque LS SE pre$e in$ieme $aranno mag-</I> <marg><I>Per la</I> 16. <I>del $esto.</I></marg>
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1484 <I>giori delle DS SM. &amp; per la ragion i$te$$a $i mo$trer&agrave; la KN e$$er minore di DM.
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1485 Di piu percioche il rettangolo OSH &egrave; eguale alrett'angolo KSN; per la mede$i-</I> <marg><I>Per la</I> 7. <I>del terzo.</I></marg>
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1486 <I>ma ragione la HO $ar&agrave; maggiore della KN. &amp; nell'i$te$$o modo in tutto la</I> <marg><I>Per la</I> 25. <I>del quinte.</I></marg>
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diff changeset
1487 <I>KN $i dimostrer&agrave; minore di tutte le altre linee, che pa$$ino per lo punto S. Et
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1488 percioche de i triangoli di due lati eguali CLE DCM i lati LC CE $ono e-
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diff changeset
1489 guali a i lati DC CM; &amp; la ba$e LE &egrave; maggiore di DM: $ar&agrave; l'angolo
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diff changeset
1490 LCE maggiore dell'angolo DCM. Per laqual co$a gli angoli CLE CEL po</I> <marg><I>Per la</I> 25. <I>del primo.</I></marg>
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diff changeset
1491 <I>sti alla ba$e tolti in$ieme $aranno minori de gli angoli CDM CMD; &amp; le me-
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diff changeset
1492 t&agrave; di que$ti, cio&egrave; l'angolo CLS $ar&agrave; minore dell'angolo CDS. Dunque il pe$o po
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1493 $to in L $opra la linea LC grauer&agrave; piu, che po$to in D $opra la DC; &amp; piu
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1494 $tar&agrave; $opra il centro in L, che in D. Similmente $i mo$trer&agrave;, che il pe$o in D</I>
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1495 <foot><I>D</I></foot>
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1496 <pb>
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1497 <I>$tar&agrave; piu $opra il centro C, che in K. Adunque il pe$o po$to in K $ar&agrave; piu
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1498 graue, che in D, &amp; in D, che in L. &amp; con la mede$ima ragione in tutto, pero-
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1499 che KN &egrave; minore di HO, $ar&agrave; l'angolo CKS maggiore dell'angolo CHS.
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1500 Per laqual cofa il pe$o posto in H $tar&agrave; piu $opra il centro C, che in</I> K; <I>&amp; in que-
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diff changeset
1501 $ta maniera $i mostrer&agrave;, che douunque $ia il pe$o nella circonferenza FDG, manco
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diff changeset
1502 star&agrave; $opra il centro quando $ar&agrave; po$to in K, che in altro $ito: &amp; quanto piu da
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1503 pre$$o egli $ar&agrave; ad F, ouero &agrave; G piu $tar&agrave; $opra. Dopo percioche l'angolo CKS
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1504 &egrave; maggiore del CDS, &amp; CDK &egrave; eguale &agrave; CKH: $ar&agrave; il re$tante SKH mi-
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1505 nore del re$tante SDK. Per laqual co$a la circonferenza KH $ar&agrave; piu da pre$$o
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1506 al mouimento naturale
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1507 diritto del pe$o po$to in
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1508 K $ciolto, cio&egrave; alla li-
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1509 nea KS, che la circon
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1510 ferenza DK al moui-
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1511 mento DS. &amp; perci&ograve;
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1512 la linea CD $a piu re$i
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1513 $tenza al pe$o po$to in D
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1514 che la CK al pe$o me$-
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1515 $o in</I> K. <I>&amp; per que$ta
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1516 ragione $i mo$trera l'an-
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1517 golo SHG e$$er mag-
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1518 giore dello SKH; &amp;
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1519 per con$equente la linea
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1520 CH $are piu re$i$tenza
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1521 al pe$o po$to in H, che
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1522 CK al pe$o me$$o in K.
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1523 Similmente dimo$trera$$i
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1524 che la linea CL piu $o-
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1525 $tenter&agrave; il pe$o, che CD:</I>
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1526 <fig>
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1527 <I>&amp; per le, cagioni i$te$$e $i prouer&agrave;, che il pe$o me$$o in K grauer&agrave; meno $opra la li-
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1528 nea CK, che in qual $i voglia altro $ito della circon$erenza FDG: &amp; quanto
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1529 piu da pre$$o $ar&agrave; ad F, ouero &agrave; G, manco grauer&agrave;. dunque piu graue $ara in K,
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1530 che in altro $ito: &amp; $ar&agrave; meno graue quanto piu da pre$$o $tara ad F, ouero a G.</I>
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1531 <p><I>Se in fine il centro C fo$$e nel centro del mondo, egli &egrave; manife$to, che il pe$o po$to doue</I>
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1532 <marg><I>Per la pri<*>ua di questo.</I></marg> <I>$i voglia $tar&agrave; fermo. Come posto il pe$o in D la linea CD $o$terr&agrave; tutto il pe$o,
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1533 per e$$er a piombo dell'orizonte di e$$o pe$o po$to in D. Dunque $tar&agrave; fermo
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1534 il pe$o.</I>
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1535 <p><I>Hor percioche nelle co$e, che fin qui $ono $tate dimostrate non habbiamo fatto mentio-
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1536 ne alcuna della grauezza del braccio della bilancia, per&ograve; $e vorremo anco con$idera-
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1537 re la grauezza del detto braccio, $i potr&agrave; ritrouare il centro della grauezza della ma</I>
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1538 <pb n=14>
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1539 <I>gnitudine fatta dal pe$o, &amp; dal braccio, &amp; $i de$criuer&atilde;no le circonferenze de' cerch;
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1540 $econdo la di$tanza dal centro della bilancia ad e$$o centro della grauezza, come $e
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1541 in e$$o (come &egrave; veramente) fo$$e posto il pe$o, Et le co$e che $enza la con$ideratio
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1542 ne della grauezza del braccio della bilancia habbiamo trouato, tutte nell'i$te$$o mo-
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1543 do con$iderando ancora tal grauit &agrave; le ritrouaremo.</I>
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1544 <p><I>Dalle co$e dette dunque, con$ider&atilde;do la bilancia,
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1545 come ella &egrave; lontana dal centro del mondo
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1546 nel modo che e$$i hanno fatto, come etiandio
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1547 &egrave; in atto, appare la fal$it &agrave; di coloro, che dico-
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1548 no il pe$o po$to in A e$$ere piu graue, che
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1549 in altro $ito; &amp; in$ieme e$$er fal$o, che quan-
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1550 to piu il pe$o &egrave; lontano dalla linea FG, tan-
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1551 to e$$ere piu graue: imperoche il punto O
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1552 &egrave; piu da pre$$o alla FG, che il punto A;
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1553 percioche la linea tirata a piombo dal pun-</I> <marg><I>Per la</I> 15. <I>del terzo.</I></marg>
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1554 <I>to O ad FG &egrave; minore della CA. Da poi
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1555 egli &egrave; parimente fal$o, che il pe$o dal punto
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1556 A $i moua piu velocemente, che da altro
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1557 $ito. peroche dal punto O $i mouer&agrave; piu ve
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1558 locemente, che dal punto A, concio$ia che
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1559 in O $ia piu libero e $ciolto, che in altro $ito;
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1560 &amp; la $ce$a dal punto O $ia piu da pre$$o al
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1561 mouimento naturale diritto, che qual $i vo-
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1562 glia altra di$ce$a.</I>
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1563 <fig>
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1564 <foot><I>D</I> 2</foot>
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1565 <pb>
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1566 <p><I>Oltre a ci&ograve; quando mo$trano per via della piu diritta, &amp; della piu torta di$ce$a, che il pe-
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1567 $o &egrave; piu graue in A, che in D, &amp; in D, che in L. Primier amente per certo e$tima
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1568 no il fal$o, che $e alcun pe$o $ar&agrave; collocato in qual $i voglia $ito della circonferenza,
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1569 come in D, la $ua vera di$ce$a douer$i fare per la linea diritta DR egualmente di-
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1570 $tante da e$$a FG, come $econdo il mouimento naturale, $i come prima &egrave; $tato det-
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1571 to. Percioche in qual $i voglia $ito $i collochi alcun pe$o, $e riguardiamo il mouimen
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1572 to $uo naturale al proprio luogo, alquale $i moue dirittamente per $ua natura, pre$up
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1573 po$ta tutta la figura dell'vniuer$o mondo, $ar&agrave; tale, che $empre lo $patio, per lo qua-
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1574 le $i moue naturalmente, parer&agrave; hauere ragione di linea tirata dalla circonferenza al
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1575 centro. Adunque le na
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1576 turali di$ce$e diritte di
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1577 qual $i voglia pe$o $ciol
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1578 to non $i po$$ono fare
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1579 per linee tra loro egual
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1580 mente di$tanti, per an-
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1581 dar$i &agrave; trouar tutte nel
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1582 centro del mondo. pre
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1583 $uppongono da poi, che
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1584 il pe$o mo$$o da D in
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1585 A per linea diritta ver
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1586 $o il centro del mondo
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1587 $ia della qu&atilde;tit&agrave; i$te$$a,
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1588 come $e egli fo$$e da O
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1589 in C $i fattamente,
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1590 che il p&utilde;to A $ia egual
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1591 mente di$tante dal cen-
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1592 tro del mondo, come C;
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1593 ilche &egrave; parimente fal$o:</I>
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1594 <fig>
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1595 <marg><I>Per la</I> 18. <I>del primo.</I></marg> <I>Imperoche il punto A &egrave; piu da lontano dal centro del mondo, che C: percioche
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1596 maggior &egrave; la linea tirata dal centro del mondo fin ad A, che quella del centro del
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1597 mondo fin a C, concio$ia che vna linea dal centro del mondo fin ad A $i di$tenda
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1598 $otto vn'angolo retto contenuto dalle linee AC, &amp; dal punto C al centro del
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1599 mondo. Dalle quali co$e non $olo rie$ce vana quella pre$uppo$ta, laquale dimostra,
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1600 che la bilancia DE ritorna in AB, ma anco cadono tutte le loro dimo$trationi;
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1601 $e for$e non dice$$ero, che que$te co$e tutte per la grandi$$ima di$tanza, che &egrave; fra il cen
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1602 tro del mondo, &amp; noi $ono co$i in$en$ibili, che per cagione di que$ta in$en$ibilit&agrave;,
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1603 $i po$$ano pre$upponere, come vere; concio$ia, che tutti quelli, iquali hanno trattato
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1604 que$te co$e, le habbiano pre$uppo$te, come note; ma$$imamente, percioche quello
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1605 e$$ere in$en$ibile non f&agrave;, che la di$ce$a del pe$o da L in D (per v$are le loro paro-
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1606 le) non pigli meno del diretto, che la di$ce$a DA. Similmente l'arco DA piglie-
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1607 r&agrave; piu del diretto, che la circon$erenza EV. onde $ar&agrave; vera la pre$uppo$ta, &amp; le
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1608 altre dimo$trationi rimarranno nella $ua $ua forza. Concediamo etiandio, che il pe</I>
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1609 <pb n=15>
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1610 <I>$o po$to in A $ia piu graue, che in altro $ito; &amp; che la di$ce$a diritta del pe$o $i deb
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1611 ba fare per linea diritta egualmente di$tante da FG, &amp; quali$i voglian punti pre$i
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1612 nelle linee egualmente di$tanti dall'orizonte e$$ere egualmente lontani dal centro
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1613 del mondo: non $eguiter &agrave; gia per que$to, che la loro dimostratione $ia vera, con la-
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1614 quale vengono a dire, che il pe$o posto in A &egrave; piu grane, che in altro $ito, come in
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1615 L. Percioche $e egli fo$$e vero, che quanto piu il pe$o in que$ta maniera di$cende
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1616 piu al diritto, iui fo$$e piu graue; $eguirebbe etiandio, che quanto l'iste$$o pe$o de-
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1617 $cende$$e egualmente in archi eguali al diritto, che ne i luoghi mede$imi haue$$e gra-
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1618 uezza eguale, ilche in que$to modo e$$er fal$o $i dimo$tra.</I>
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1619 <p><I>Siano le circonferenze AL AM tra loro eguali, &amp; congiunga$i LM, laquale ta-
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1620 gli AB in X; $ar&agrave; LM egualmente di$tante da FG, &amp; &agrave; piombo di AB,</I> <marg><I>Per la terza del terzo.</I></marg>
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1621 <I>&amp; XM $ar&agrave; eguale ad XL. Se dunque il pe$o da L $ar&agrave; mo$$o in A per la cir-
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1622 conferenza LA, il mouimento $uo diritto $ar&agrave; $econdo la linea LX. Ma $e egli $i
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1623 mouer&agrave; da A in M per la circonferenza AM, il $uo mouimento $ar&agrave; $econdo
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1624 la linea diritta XM. Per laqual co$a la $ce$a da L in A $ar&agrave; eguale alla $ce$a da
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1625 A in M, $i per cau$a delle circonferenze eguali, &amp; $i per le linee rette eguali, &amp; &agrave;
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1626 piombo di e$$a AB. Adunque il pe$o mede$imo po$to in L grauer&agrave; egualmente,
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1627 come in A, ilche &egrave; fal$o, concio$ia, che egli &egrave; di gran lunga piu graue in A, che in L.</I>
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1628 <p><I>Et benche AMLA prendano, $econdo e$$i, egualmente del diretto, diranno for$e,
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1629 nondimeno perche il principio della $ce$a da L, cio&egrave; LD piglia meno del diretto, che
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1630 il principio della $ce$a da A, cio&egrave; AN, il pe$o in A $ar&agrave; piu graue, che in L.
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1631 Imperoche e$$endo (come &egrave; $tato di $opra po$to) la circonferenza AN eguale ad
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1632 LD, laquale ($econdo e&szlig;i) piglia di diretto CT; ma LD piglia di diretto PO,
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1633 per&ograve; il pe$o $ar&agrave; piu graue in A, che in L. ilche $e fo$$e vero, $eguirebbe, che l'i$te$-
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1634 $o pe$o nel mede$imo $ito, in diuer$o modo $olamente con$iderato, ver$o il mede$imo
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1635 $ito fo$$e &amp; piu graue, &amp; piu lieue; ilche &egrave; impo$$ibile. cio&egrave; $e con$ideriamo la $ce$a
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1636 del pe$o po$to in L in quanto egli de$cende da L in A $ar&agrave; piu graue, che $e con$ide
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1637 reremo la $ce$a del pe$o i$te$$o da L in D $olamente. ne po$$ono negare per i mede
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1638 $imi detti $uoi, che la di$ce$a del pe$o da L in A non pigli del diretto LX, ouero PC.
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1639 Et che $imilmente la $ce$a AM non prenda di diretto XM: pigliando c&szlig;i ancora
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1640 &agrave; que$to modo, &amp; co$i nece$$ario $ia di pigliare. percioche $e vogliono dimo$trare,
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1641 che la bilancia DE ritorni in AB paragonando la $ce$a del pe$o po$to in D con
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1642 la $ce$a del pe$o posto in E, egli &egrave; nece$$ario, che mo$trino, che la diritta $ce$a OC
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1643 ri$pondente alla circonferenza DA $ia maggiore della $ce$a diritta TH ri$ponden-
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1644 te alla circonferenza EV. peroche $e piglia$$ero $olamente vna parte di tutta la $ce
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1645 $a da D in A, come D</I>K, <I>&amp; dimo$tra$$ero, che piu di diretto piglia la $ce$a D</I>K,
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1646 <I>che la eguale portione della $ce$a dal punto E, $eguirebbe il pe$o po$to in D, $econ-
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1647 do e&szlig;i, e$$ere piu graue del pe$o po$to in E, &amp; mouer$i in giu fin al K $olamente.
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1648 per modo che la bilancia $ia mo$$a in KI. Similmente $e vogliono mo$trare, che la
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1649 bilancia KI ritorni in AB pigliando vna portione della $ce$a da K in A, cio&egrave; KS,
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1650 &amp; mo$tra$$ero, che KS pigli piu di diretto, che la $ce$a eguale, che &egrave; dirimpetto dal
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1651 punto I: $eguirebbe con $imile modo il pe$o po$to in K e$$ere piu graue, che in I, &amp;</I>
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1652 <pb>
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1653 <I>mouer$i $olamente fin ad S. Et $e di nouo mo$tra$$ero vna portione della $ce$a da S
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1654 in A, &amp; co$i $ucce&szlig;iuamente e$$ere piu diritta della $ce$a eguale del pe$o oppo$to;
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1655 $empre $eguir&agrave;, che la bilancia SI andar&agrave; piu da pre$$o ad AB, ma non dimostre-
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1656 r&atilde;no giamai che per
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1657 uenga in AB. Se
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1658 dunque vogliono di
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1659 mo$trare, che la bil&atilde;
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1660 cia DE ritorni in
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1661 AB, egli &egrave; nece$$a-
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1662 rio, che pre$upponga
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1663 no, che la $ce$a del
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1664 pe$o da D in A pr&etilde;
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1665 da di diretto la quan
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1666 tit&agrave; della linea tira-
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1667 ta dal punto D ad
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1668 AB ad angoli ret-
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1669 ti; &amp; co$i, $e para-
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1670 goneremo le $ce$e e-
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1671 guali di DA AN
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1672 fra loro, lequali pr&etilde;
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1673 dono di diretto OC
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1674 CT, accader&agrave;, che</I>
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1675 <fig>
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1676 <I>il pe$o i$te$$o $ar&agrave; in D graue egualmente, come in A. Ma $e le portioni $olamente
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1677 piglieremo da DA, $ar&agrave; piu graue in A, che in D. Adunque dalla diuer$it&agrave; $o-
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1678 lamente del modo del con$iderare, auerr&agrave;, che il pe$o mede$imo $ar&agrave; &amp; piu graue,
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1679 &amp; piu leggiero; &amp; non per la natura della co$a. Di piu la pre$uppo$ta loro non
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1680 afferma, che il pe$o $econdo il $ito $ia piu graue, quanto nel $ito mede$imo il principio
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1681 della $ua di$ce$a &egrave; meno obliquo. La pre$upposta dunque di $opra addotta, cio&egrave; che
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1682 $econdo il $ito il pe$o &egrave; piu graue quanto nell'i$te$$o $ito meno obliqua &egrave; la di$ce$a, non
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1683 $olamente non $i puote concedere &agrave; modo alcuno, per le co$e, che habbiamo dette;
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1684 ma anco percioche non &egrave; co$a difficile il dimo$trare tutto l'oppo$to, cio&egrave; il pe$o mede$i
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1685 mo in eguali circonferenze quanto meno obliqua &egrave; la di$ce$a, iui meno grauare.</I>
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1686 <p><I>Siano come prima le circonferenze AL AM tra loro eguali; &amp; $ia il punto L vici
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1687 no ad F, &amp; congiunga$i LM, la quale $ar&agrave; &agrave; piombo di AB &amp; LX $ar&agrave; anco
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1688 eguale ad XM. Dapoi pre$$o ad M tra M &amp; G $ia pre$o come $i vuole, il pun</I>
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1689 <marg><I>Per la</I> 27. <I>del terzo</I></marg> <I>to P, &amp; $ia fatta la circonferenza PO eguale alla circonferenza AM, $ar&agrave; il
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1690 punto O pre$$o ad A. &amp; $iano congiunte le linee CL, CO, CM, CP, OP.</I>
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1691 <marg><I>Per la</I> 32. <I>del primo</I></marg> <I>&amp; dal punto P tiri$i la PN a piombo di OC. &amp; percioche la circonferenza.
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1692 AM &egrave; eguale alla circonferentia OP; $ar&agrave; l'angolo ACM eguale all'angolo</I>
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1693 <marg><I>Per la</I> 26. <I>del primo.</I></marg> <I>OCP, &amp; l'angolo CXM retto eguale al retto CNP, $ar&agrave; anco il re$tante angolo
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1694 XMC del triangolo MXC eguale al re$tante NPC del triangolo PCN.</I>
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1695 <pb n=16>
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1696 <I>Ma il lato ancora CM &egrave; eguale al lato CP, dunque il triangolo MCX &egrave; egua
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1697 le al triangolo PCN, &amp; il lato MX eguale al lato NP. Onde la linea PN
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1698 $ar&agrave; eguale ad LX. Tiri$i oltre a ci&ograve; dal punto O la linea OT egualmente di-
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1699 $tante da AC, laquale tagli NP in V. &amp; $ia anco tirata dal punto P vna
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1700 linea a piombo di OT,
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1701 la quale per certo non
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1702 puote cadere tra OV,
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1703 perche e$$endo l'angolo
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1704 ONV retto, $ar&agrave; acu</I> <marg><I>Per la</I> 13. <I>del primo.</I></marg>
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1705 <I>to lo OVN. Per la
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1706 qualco$a OVP $ar&agrave;
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1707 ottu$o. Non cader&agrave;
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1708 dunque la linea tirata
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1709 dal punto P tra OV
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1710 &agrave; piombo di OT: pe-
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1711 roche due angoli d'uno
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1712 tri&atilde;golo $arebbono l'u-
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1713 no retto, &amp; l'altro ot-
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1714 tu$o, che &egrave; impo&szlig;ibile.
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1715 Cader&agrave; dun que nella li
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1716 nea OT nellaparte di
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1717 VT, et $ia PT. $ar&agrave; $e
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1718 condo e$$i, PT la di</I>
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1719 <fig>
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1720 <I>ritta $ce$a della circonferenza OP. Percioche dunque l'angolo ONV &egrave; retto,</I> <marg><I>Per la</I> 19. <I>del primo.</I></marg>
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1721 <I>$ar&agrave; la linea OV maggiore della ON. Onde la OT $ar&agrave; parimente maggiore
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1722 della ON. &amp; co$i di$tendendo$i la linea OP $otto gli angoli retti ONP,
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1723 OTP, $ar&agrave; il quadrato di OP eguale alli quadrati ON NP in$ieme pre$i, $i</I> <marg><I>Per la</I> 47. <I>del primo.</I></marg>
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1724 <I>milmente eguale a i quadrati di OT TP in$ieme. per laqual co$a li quadrati in$ie-
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1725 me di ON NP $aranno eguali a i quadrati in$ieme di OT TP. Ma il quadrato
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1726 di OT &egrave; maggiore del quadrato di ON. per e$$ere maggiore la linea OT della
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1727 ON. Adunque il quadrato di NP $ara maggiore del quadrato TP &amp; perci&ograve; la
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1728 linea TP $ar&agrave; minore della linea PN, &amp; della linea LX. Meno obliqua
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1729 dunque $ar&agrave; la $ce$a dell'arco LA, che dell'arco OP. Dunque il pe$o po-
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1730 sto in L, per i loro detti, $ar&agrave; piu graue, che in O, il che, per le co$e, che di
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1731 $opra habbiamo detto, &egrave; manife$tamente fal$o. concio$ia, che il pe$o po$to in O
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1732 $ia piu graue, che in L. Non $i puote dunque raccogliere dal piu diritto, &amp;
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1733 piu torto mouimento in quel modo pigliato, e$$ere il pe$o tanto piu graue $econ-
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1734 do il $ito, quanto nel mede$imo $ito &egrave; meno torta la $ce$a. &amp; quinci na$ce tutto
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1735 qua$i il $uo errore &amp; inganno in cote$ta co$a. Imperoche quantunque per acciden-
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1736 te alle volte dalle co$e fal$e ne $egua il vero, tutta via per $e $te$$e principalmente
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1737 dalle fal$e ne $egue il fal$o, $i come dalle vere $empre il vero ne $egue. Non &egrave; pero
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1738 da mar auigliar$i, $e mentre e$$i prendono co$e fal$e, &amp; $tanno $opra quelle, come ve</I>
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1739 <pb>
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1740 <I>ri$$ime, raccolgono, &amp; conchiudono co$e in tutto fal$i$$ime. $ono oltre a ci&ograve; inganna-
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1741 ti, mentre pigliano a contemplare la bilancia $emplicemente per via di matematica,
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1742 e$$endo la con$ideratione $ua mechanica affatto, ne di lei $i po$$a ragionare a modo al
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1743 cuno $enza il vero mouimento, &amp; $enza i pe$i, che $ono in tutto co$e naturali, $en-
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1744 za le quali non $i po$$ono ritrouare per niuna maniera le vere cagioni di quelle co$e,
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1745 che accadono alla bilancia.</I>
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1746 <p><I>Oltre a ci&ograve; $e anche con
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1747 cederemo la pre$up-
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1748 po$ta, $i partono tut
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1749 tauia molto l&utilde;ge dal
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1750 la c&otilde;$ideratione della
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1751 bilancia, mentre di-
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1752 $corrono; che in quel
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1753 la maniera debba la
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1754 bilancia DE ritor-
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1755 nare in AB: percio
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1756 che $empre pigliano
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1757 vn di due pe$i $epara
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1758 tamente come D,
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1759 ouero E, come $e hor
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1760 l'uno, hor l'altro fo$
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1761 $e po$to nella bilan-
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1762 cia, non congiunti in
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1763 $ieme ambidue in
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1764 modo veruno, e$$en-</I>
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1765 <fig>
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1766 <I>doche nondimeno bi$ogni fare tutto all'oppo$ito di ci&ograve;, ne $i puote con$iderare dirit-
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1767 tamente l'uno $enza l'altro, e$$endoche $i ragiona di loro nella bilancia collocati.
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1768 Concio$ia che quando dicono la di$ce$a del pe$o po$to in D e$$ere meno torta, che
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1769 la di$ce$a del pe$o po$to in E, co$i $ar&agrave; il pe$o in D, per la pre$uppo$ta, piu graue
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1770 del pe$o po$to in E; onde per e$$ere piu graue, eglie nece$$ario, che $i moua in giu,
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1771 &amp; che la bilancia DE ritorni in AB: Cote$to di$cor$o non &egrave; di momento alcu-
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1772 no. Primieramente $empre argomentano come $e i pe$i in DE debbano $cende-
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1773 re, con$iderando la $ce$a di vno $olameute $enza la compagnia, &amp; congiungimen-
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1774 to dell'altro. Vltimamente nondimeno e$$i per la comparatione delle di$ce$e de'pe-
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1775 $i conchiudono il pe$o posto in D mouer$i in giu, &amp; il po$to in E in $u, prenden-
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1776 do l'uno, &amp; l'altro pe$o congiunti in$ieme fra loro nella bilancia. Ma da $uoi me-
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1777 de$imi principij, i quali v$ano, &amp; dalle $ue dimo$trationi $i puote cauare ageuoli$$i-</I>
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1778 <marg><I>Per la</I> 15. <I>del primo.</I></marg> <I>mamente l'oppo$ito di quel che $i faticano di difendere. Imperoche $e $i paragona
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1779 la di$ce$a del pe$o po$to in D con la $alita del pe$o po$to in E, come tirate le'linee
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1780 E</I>K <I>DH a piombo di AB, e$$endo l'angolo DCH eguale all'angolo ECK,</I>
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1781 <marg><I>Per la</I> 25. <I>del primo.</I></marg> <I>&amp; l'angolo DHC retto eguale al retto E</I>K<I>C, &amp; il lato DC eguale al lato
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1782 CE; $ar&agrave; il triangolo CDH eguale al triangolo CEK, &amp; il lato DH egua</I>
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1783 <pb n=17>
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1784 <I>le al lato EK: &amp; e$$endo l'angolo DCA eguale all'angolo ECB, $ar&agrave; anco
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1785 la circonferenza DA eguale alla circonferenza BE. Mentre dunque il pe$o po-
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1786 sto in D $cende per la circonferenza DA, il pe$o po$to in E $ale per la circon-
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parents:
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1787 ferenza EB eguale a DA, &amp; la $ce$a del pe$o po$to in D prender&agrave;, ($econdo
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1788 il co$tume loro) di diretto DH: &amp; la $alita del pe$o E prender&agrave; di diretto EK
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1789 eguale a DH: $ar&agrave; dunque la $ce$a del pe$o posto in D eguale alla $alita del pe$o
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1790 po$to in E: &amp; quale $ar&agrave; la inclinatione d'uno al mouimento in gi&ugrave;, tale $ar&agrave; etian
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1791 dio la re$i$tenza dell'altro al mouimento in s&ugrave;, cio&egrave; la re$istentia della violenza del
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1792 pe$o po$to in E nella a$ce$a, contra$tando $i oppone alla naturale po$$anza del pe-
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1793 $o po$to in D per e$$ere a lei eguale; percioche quanto il pe$o po$to in D per la na-
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1794 tural po$$anza de$cende piu velocemente in gi&ugrave;, in tanto il pe$o po$to in E pi&ugrave; tar-
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1795 do $ale violentemente. Per laqual co$a niuno di loro due pe$era piu dell'altro, non
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1796 procedendo attione da eguale. il pe$o po$to in D dunque non mouer&agrave; il pe$o po$to
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1797 in E in $u$o, peroche $e lo moue$$e, $arebbe nece$$ario, che il pe$o po$to in D ha-
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1798 ue$$e virtu maggiore in di$cendendo, che il pe$o po$to in E in $alendo, ma que$te co-
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1799 $e $ono eguali: adunque $taranno $ermi i pe$i, &amp; la grauezza del pe$o po$to in D $a-
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1800 r&agrave; eguale alla grauezza del pe$o po$to in E. Oltre a ci&ograve; perche pre$uppongono, che
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1801 quanto il pe$o &egrave; piu di$tante dalla linea FG della dirittura, tanto e$$ere piu graue.
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1802 per&ograve; tirate parimente da i punti DE le linee DO, EI apiombo di FG, con
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1803 modo $imile $i dimostrer&agrave; il triangolo CDO e$$ere eguale al triangolo CEI: &amp;
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1804 la linea DO e$$ere eguale ad EI. Tanto dunque &egrave; di$tante il pe$o po$to in D
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1805 dalla linea FG, quanto il pe$o po$to in E. Dalle ragioni loro dunque, &amp; dalle $ue
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1806 pre$uppo$te li pe$i me$$i in DE $ono graui egualmente. Di piu, che vieta che non $i di
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1807 mo$tri la bi lancia DE mouer$i per nece$$it&agrave; in FG con $imile ragione? Primie-
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1808 ramente $i puote raccogliere dalle loro mede$ime dimo$trationi, la $alita del pe$o po-
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1809 $to in E ver$o il B e$$ere piu diritta della $alita del pe$o po$to in D ver$o lo F,
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1810 cio&egrave; manco prendere di diretto la $alita del pe$o po$to in D in archi eguali, che la
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1811 $alita del pe$o po$to in E. Pre$upponga$i dunque, che il pe$o $ia piu leggiero $econ-
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1812 do il $ito tanto quanto nel $ito mede$imo meno diritta &egrave; la $ua $alita: Laqual pre-
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1813 $upposta pare tanto manife$ta, quanto l'altraloro. percioche dunque la $alita del
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1814 pe$o po$to in E &egrave; piu diritta della $alita del pe$o po$to in D, per la pre$uppo$ta il
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1815 pe$o po$to in D $ar&agrave; piu leggiero del pe$o po$to in E. Adunque il pe$o po$to in D
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1816 $i mouer&agrave; in s&ugrave; dal pe$o po$to in E, $i $attamente che la bilancia peruenga in FG,
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1817 &amp; co$i potra$si dimo$trare la bilancia DE mouer$i in FG, laqual dimo$tratio-
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1818 ne &egrave; del tutto veramente friuola, &amp; pati$ce le difficult&agrave; mede$ime. Percioche quan-
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1819 tunque $i conceda, come vero, che il pe$o po$to in E $alendo $ia piu graue del pe$o
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1820 in D $imilmente $alendo, non perci&ograve; da que$to $egue, che il pe$o po$to in E de-
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1821 $cendendo $ia piu graue del pe$o posto in D $alendo. Niuna dunque di que$te due
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1822 dimo$trationi, che dicono la bilancia DE ritornare in AB, ouero mouer$i in
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1823 FG, &egrave; vera.</I>
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1824 <p><I>Oltre a ci&ograve; $e e$amineremo la loro pre$uppo$ta, &amp; la $orza delle loro parole, vedremo
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1825 per certo che altro $entimento hanno. Imperoche e$$endo che $empre lo $patio per lo</I>
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1826 <foot><I>E</I></foot>
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1827 <pb>
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1828 <I>quale il pe$o natur alm&etilde;te $i moue, $i deue prendere dal centro della grauezza di e$-
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diff changeset
1829 $o pe$o ver$o il centro del mondo &agrave; $embianza di vna linea diritta tirata dal centro
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1830 della grauezza al centro del mondo, tanto $i dir &agrave; que$ta co$i fatta di$ce$a del pe$o
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1831 piu, &amp; meno obliqua, quanto, $econdo lo $patio di$$egnato, a $embianza della pre-
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1832 detta linea piu &ograve; meno $i mouer&agrave;, (andando pero $empre a trouare il luogo $uo natu
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1833 rale, &amp; vie piu $empre auicinandoui$i.) talche tanto piu obliqua $i dica la $ce$a qu&atilde;
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1834 to $i parte da cotale $patio: &amp; piu diritta quanto a lui $i acco$ta. &amp; in que$to
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1835 $entimento quella pre$upposta non deue partorire difficulta ad alcuno, percioche co-
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1836 $i &egrave; la verita $ua chiara, &amp; conforme alla ragione, che non pare hauer me$tieri di e$-
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1837 $er $atta in alcun modo manife$ta.</I>
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1838 <p><I><*>e dunque il pe$o $ciolto, collocato nel $i-
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1839 to di D $i deue mouere al luogo pro-
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1840 prio, $enza dubbio, po$to S centro del
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1841 mondo, $i mouer&agrave; per la linea DS, $i-
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1842 milm&etilde;te il pe$o po$to in E $ciolto $i mo
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1843 uer&agrave; per la linea ES. Per laqual co-
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1844 $a $e, (come &egrave; vero) la $ce$a del pe$o $i
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1845 dir&agrave; piu, &ograve; meno obliqua, $econdo lo al
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1846 lontanar$i, ouero appre$$ar$i a gli $patij
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1847 di$segnati per le linee DS ES, per ri
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1848 $petto a'loro naturali mouimenti ver$o
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1849 iproprij luoghi, egli &egrave; chiaro, che meno
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1850 obliqua &egrave; la $ce$a di E per EG, che
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1851 di D per DA, per e$$ere stato di
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1852 $opra mo$trato che l'angolo SEG &egrave;
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1853 minore dell'angolo SDA. Per laqual
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1854 co$a piu grauer &agrave; il pe$o in E, che in D,
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1855 il che totalmente &egrave; il contrario di quel-
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1856 lo, che e$si $i $ono s$orzati di prouare.
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1857 Leueran$i per auuentura contra di noi
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1858 dicendo. Se dundue il pe$o po$to in E &egrave;
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1859 piu graue del pe$o po$to in D, la bi-
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1860 lancia DE non $tar &agrave; giamai in que-
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1861 $to $ito, laqual co$a noi habbiamo pro-
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1862 po$to di mantenere, ma $i mouer &agrave; in F
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1863 G. Allequali co$e ri$pondiamo. che im-
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1864 porta a$$ai, $e noi con$ideriamo i pe$i o-
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1865 uero in quanto $ono $eparati l'uno dal-
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1866 l'altro, ouero in quanto $ono traloro
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1867 congiunti: perche altra &egrave; la ragione del</I>
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1868 <fig>
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1869 <I>pe$o po$to in E $enza il congiungimento del pe$o po$to in D, &amp; altra di lui con
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1870 l'altro pe$o congiunto, $i fattamente che l'uno $enza l'altro non $i po$$a mouere. Im</I>
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1871 <pb n=18>
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1872 <I>peroche la diritta, &amp; naturale di$ce$a dal pe$o po$to in E, inquanto egli &egrave; $enza al-
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1873 tro congiungimento di pe$o, $i fa per la linea ES. ma inquanto egli &egrave; congiunto
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1874 col pe$o D, la $ua naturale di$ce$a non $ar&agrave; piu per la linea ES, ma per vna li-
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1875 nea egualmente di$tante da CS. percioche la magnitudine compo$ta de i pe$i ED.
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1876 &amp; della bilancia DE il cui centro della grauezza &egrave; C, $e in ne$$un luogo non $a-
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1877 r&agrave; $o$tenuta, $i mouer&agrave; naturalmente in giu nel modo che $i troua, $econdo la gra-
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1878 uezza del centro per la linea diritta tirata dal centro della grauezza C al centro
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1879 del mondo S, finche il centro C peruenga nel centro S. La bilancia dunque DE
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1880 in$ieme co'pe$i, in quella maniera, che $i troua $i mouer&agrave; in giu per modo tale, che il
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1881 punto C $i moua per la linea CS, fin che C peruenga in S, &amp; la bilancia
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1882 DE in HK; &amp; habbia la bilancia in HK la po$itione i$te$$a, che prima hauea;
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1883 cio &egrave;, che la HK $ia egualmente distante da DE. Congiungan$i dunque DH
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1884 EK. egli &egrave; manife$to, che mentre la bilancia DE $i moue in HK, mouer$i an-
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1885 che ipunti DE per le linee DH EK, come quelle che $ono &amp; $ra $e, &amp; ad</I> <marg><I>Per la</I> 35. <I>del primo.</I></marg>
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1886 <I>e$$a CS eguali, &amp; egualmente di$tanti. Per la qual co$a i pe$i posti in DE, in
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1887 quanto $ono $ra loro congiunti, $e riguarderemo il mouimento loro naturale $imoue
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1888 ranno non $econdo le linee DS, ES, ma $econdo LDH MEK egualmente
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1889 di$tanti da e$$a CS. Ma la naturale inclinatione del pe$o po$to in E libero, &amp;
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1890 $ciolto $ar&agrave; per ES, &amp; del pe$o po$to in D $imilm&etilde;te $ciolto $ar&agrave; per DS. &amp; per-
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1891 cio non &egrave; $conueneuole, che il pe$o mede$imo hora in E, hora in D, $ia piu graue
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1892 in E, che in D. Ma$e i pe$i po$ti in ED $ono l'un l'altro fra $e congiunti, &amp; gli
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1893 con$idereremo in quanto $ono congiunti, $ar&agrave; la naturale inclinatione del pe-
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1894 $o po$to in E per la linea MEK, percioche la grauezza dell'altro pe$o po$to
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1895 in D fa $i, che il pe$o po$to in E non graui $opra la linea ES, ma nella EK.
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1896 Ilche fa parimente la grauezza del pe$o po$to in E, cio&egrave;, che il pe$o po$to in D
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1897 non graui per la linea retta DS, ma $econdo DH, per impedir$i ambedue l'uno
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1898 l'altro che non vadino &agrave; propri luoghi. Concio$ia dunque che la naturale $ce$a dirit-
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1899 ta de i pe$i po$ti in DE $ia $econdo LDH, MEK, $ar&agrave; $imilmente la naturale
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1900 $alita diritta loro $econdo le i$te$$e linee HDL KEM. &amp; la naturale $alita del
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1901 pe$o po$to in E $i dir&agrave; pi&ugrave;, &amp; meno torta, quanto che $econdo lo $patio $i mouer&agrave;
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1902 pi&ugrave;, &amp; meno pre$$o la linea MK. &amp; a que$to modo in tutto $i ha da pigliare &amp; la $a
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1903 lita &amp; la di$ce$a del pe$o po$to in D $econdo la linea LH, $e dunque il pe$o po$to
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1904 in E $i moue$$e in gi&ugrave; per la linea EG, mouerebbe il pe$o po$to in D in s&ugrave; per
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1905 DF. &amp; percioche l'angolo CEK &egrave; eguale all'angolo CDL, &amp; l'angolo CEG</I> <marg><I>Per la</I> 29. <I>del primo.</I></marg>
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1906 <I>&egrave; eguale all'angolo CDF; $ar&agrave; il re$t&atilde;te angolo GEK al re$tante LDF egua
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1907 le. &amp; e$$endo quella pre$uppo$ta, che dice il pe$o e$$er pi&ugrave; graue $econdo il $ito,
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1908 quanto in quel mede$imo $ito la di$ce$a &egrave; meno obliqua per chiara, &amp; manife$ta ri-
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1909 ceuuta, $ar&agrave; anche da e$$ere accettata $enza dubbio que$t' altra, cio&egrave;, che il pe$o $ar&agrave;
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1910 pi&ugrave; graue $econdo il $ito, quanto nel $ito mede$imo meno obliqua $ar&agrave; la $alita; per
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1911 non e$$ere manco manife$ta, ne meno conforme alla ragione. $ar&agrave; dunque eguale
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1912 la $ce$a del pe$o po$to in E alla $alita del pe$o po$to in D, percioche la $ce$a del pe
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1913 $o po$to in E tiene tanto di obliquo, quanto la $alita del pe$o po$to in D. &amp; quale</I>
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1914 <foot><I>E</I> 2</foot>
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1915 <pb>
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1916 <HEAD>PROPOSITIONE V.</HEAD>
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1917 <p>Due pe$i attaccati nella bilancia, $e la bilancia $ar&agrave; tra loro in modo
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1918 diui$a, chele parti ri$pondano $cambieuolmente &agrave; pe$i; pe$eranno
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1919 tanto ne'punti doue $ono attaccati, quanto $el'uno &amp; l'altro fo$$e
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1920 pendente dal punto della diui$ione.
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1921 <fig>
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1922 <p><I>Siala bilancia AB, il cui centro $ia C, &amp; $iano due pe$i EF pendenti da' punti
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1923 BG: &amp; diuida$i BG in H, $i fattamente, che BH ad HG habbia la pro-
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1924 portione iste$$a, che h&agrave; il pe$o E al pe$o F. Dico ipe$i EF pe$are tanto in BG,
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1925 quanto $e amendue pende$$ero dal punto H. faccia$i AC eguale &agrave; CH. &amp; $i
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1926 come AC &agrave; CG, co$i $accia$i il pe$o E al pe$o L. $imilmente come AC &agrave;
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1927 CB, co$i faccia$i il pe$o F al pe$o M. &amp; $iano attaccati ipe$i LM al punto
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1928 A. Horpercioche AC &egrave; eguale &agrave; CH, $ar&agrave; BC ver$o CH come il pe$o
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1929 M alpe$o F. &amp; percioche piu grande &egrave; BC di CH; $ar&agrave; anche il pe$o M</I>
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1930 <marg><I>Per la</I> 17. <I>del quinto.</I></marg> <I>maggiore di F. Diuida$i dunque il pe$o M in due parti QR, &amp; $iala parte di</I>
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1931 <marg><I>Per la con- $egu&etilde;za del la</I> 4. <I>del</I> 5.</marg> <I>Q eguale ad F; $ar&agrave; BC &agrave; CH, come RQ &agrave; Q: &amp; diuidendo, come BH
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1932 ad HC, co$i R &agrave; Q. Dapoi conuertendo, come CH ad HB, co$i Q ad</I>
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1933 <marg><I>Per la</I> 17. <I>del quinto.</I></marg> <I>R. Oltre &agrave; ci&ograve; perche CH &egrave; eguale &agrave; CA, $ar&agrave; HC ver$o CG come il pe$o
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1934 E al pe$o L: ma&egrave; piu grande HC di CG, per&ograve; $ar&agrave; anche il pe$o E maggio-</I>
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1935 <marg><I>Per la con$e gu&etilde;za della</I> 4. <I>del</I> 5.</marg> <I>re del pe$o L. Onde diuida$i il pe$o E in due parti NO, $i fattamente, che la
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1936 parte di O $ia eguale ad L, $ar&agrave; HC &agrave; CG come tutto lo NO ad O; &amp;
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1937 diuidendo, come HG &agrave; GC, co$i N ad O. &amp; conuertendo, come CG &agrave;</I>
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1938 <marg><I>Per la</I> 18. <I>del quinto.</I></marg> <I>GH, co$i O ad N. &amp; di nuouo componendo, come CH ad HG, co$i ON</I>
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1939 <marg><I>Per la</I> 16. <I>del quinto.</I></marg> <I>ad N. &amp; come GH ad HB, co$i &egrave; F ad ON. Per la qual co$a per la pro
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1940 portione vguale come CH ad HB, co$i F ad N. Ma come CH ad HB</I>
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1941 <marg><I>Per la</I> 11. <I>del quinto.</I></marg> <I>co$i &egrave; Q ad R: $ar&agrave; dunque Q ad R come F ad N. &amp; permutando co-
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1942 me Q ad F; co$i R ad N. ma la parte di Q &egrave; egual ad e$$o F. per la qual</I>
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1943 <marg><I>Per la</I> 16. <I>del quinto.</I></marg> <I>co$a la parte di R ancora $ar&agrave; eguale ad N. e$$endo dunque il pe$o L eguale</I>
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1944 <pb n=30>
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1945 <I>ad O, &amp; il pe$o F eguale parimente al Q, &amp; la parte di R eguale ad N; $a
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1946 ranno ipe$i LM eguali a i pe$i EF. &amp; percioche $i come AC ver$o CG, co</I> <marg><I>Perla</I> 6. <I>del primo di<*>r chimede del le co$e che pe $ano egualmente.</I></marg>
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1947 <I>$i &egrave; il pe$o E al pe$o L, ipe$i EL pe$eranno egualmente. $imilmente percioche
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1948 $i come AC &egrave; ver$o CB, co$i il pe$o F &egrave; alpe$o M, i pe$i FM pe$eranno
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1949 anco egualmente. i pe$i dunque LM pe$eranuo egualmente co'pe$i EF attacca-
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1950 ti in BG. &amp; e$$endo la di$tanza CA eguale alla di$tanza CH, $e dunque am
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1951 bidue i pe$i EF $ar anno attaccati in H, i pe$i LM pe$er anno egualmente co'</I> <marg><I>Per lo</I> 2. <I>c&otilde;. della not di questo.</I></marg>
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1952 <I>pe$i EF attaccati in H. Ma LM pe$a ancora egualmente con EF in GB.
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1953 Adunque $ar anno egualmente graui i pe$i EF in GB attaccati come in H. pe</I> <marg><I>Per la</I> 3. <I>c&otilde;. della not ai questo.</I></marg>
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1954 <I>$eranno dunque tanto in BG quanto attaccati in H.</I>
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1955 <fig>
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1956 <p><I>Ma $iano i pe$i EF attaccati in CB; &amp; $ia C il centro della bilancia, &amp; diuida$i
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1957 CB in H, per modo che CH ver$o HB $ia come il pe$o F al pe$o E. Dico
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1958 che i pe$i EF pe$er anno tanto in CB quanto nel punto H. faccia$i CA egua
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1959 le &agrave; CH, &amp; come CA ver$o CB; co$i faccia$i il pe$o F ver$o vn'altro, che
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1960 $ia D, ilquale $i appicchi in A. Hor percioche CH &egrave; eguale &agrave; CA, $ar&agrave; CH
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1961 ver$o CB, come F &agrave; D; &amp; ben &egrave; maggiore CB di CH, per&ograve; il pe$o D $a
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1962 r&agrave; maggiore del pe$o F. Diuida$i dunque il D in due parti GK, &amp; $ia il G</I> <marg><I>Per la</I> 17. <I>del quinto.</I></marg>
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1963 <I>eguale allo F; $ar&agrave; BC &agrave; CH come GK ver$o il G; et diuidendo, come BH
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1964 ad HC, co$i K ver$o G; &amp; conuertendo come CH ad HB, co$i G ver-</I> <marg><I>Per la con$e gu&etilde;za della</I> 4. <I>del</I> 5.</marg>
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1965 <I>$o K. &amp; come CH ad HB, co$i &egrave; F ver$o E. Dunque come G ver-
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1966 $o K co$i &egrave; F ad E. &amp; permutando come G ad F, co$i K ad E. &amp; per-</I> <marg><I>Per la</I> 11. <I>del quinto.</I></marg>
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1967 <I>che GF $ono eguali, $aranno anche KE tra loro eguali. Concio$ia dunque che
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1968 la parte G $ia eguale ad F, &amp; il K ad e$$o E; $ar&agrave; tutto il GK eguale a i pe</I> <marg><I>Per la</I> 16. <I>del quinto.</I></marg>
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1969 <I>$i EF. &amp; percioche AC &egrave; eguale &agrave; CH; $e dunque i pe$i EF $aranno penden
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1970 ti dal punto H, il pe$o D pe$er&agrave; egualmente co'pe$i EF attaccati in H. Ma
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1971 pe$a anche egualmente con e&szlig;i in CB, cio&egrave; F in B, &amp; E in C; per e$$ere
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1972 come AC ver$o CB, co$i F ver$o D: percioche il pe$o E pendente da C.
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1973 centro della bilancia non &egrave; cau$a, che la bilancia $i moua in alcuna delle due parti.
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1974 tanto $aranno dunque graui i pe$i EF in CB, quanto in H appicati.</I>
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1975 <foot><I>H</I> 2</foot>
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1976 <pb>
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1977 <fig>
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1978 <p><I>Sia finalm&etilde;te la bil&atilde;cia AB, &amp; da i p&utilde;ti AB $iano p&etilde;denti ipe$i EF, &amp; $idil centro
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1979 della bilancia C fra ipe$i, &amp; diuida$i la AB in D, talche AD ver$o DB
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1980 $ia come il pe$o F alpe$o E. Dico che i pe$i EF pe$ano tanto in AB, quan
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parents:
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1981 to $e ambidue $o$$ero pendenti dal punto D. faccia$i CG eguale &agrave; CD; &amp; co-
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1982 me DC &agrave; CA, co$i faccia$i il pe$o E ad vn'altro pe$o H, ilquale $ia attac
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1983 cato in D. &amp; come GC ver$o CB, co$i faccia$i il pe$o F ad vn'altro che
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1984 $ia K, &amp; attachi$i K in G. Horpercioche, come il BC &egrave; ver$o il CG, cio&egrave;
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1985 ver$o il CD, co$i il pe$o K ad F; $ar&agrave; il K maggiore del pe$o F. Per laqual
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1986 co$a diuida$i il pe$o K in L &amp; in MN, &amp; $accia$i la parte L eguale ad F,</I>
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parents:
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1987 <marg><I>Per la</I> 17. <I>del quinto.</I></marg> <I>$ar&agrave; come BC &agrave; CD, co$i tutto LMN ad L; &amp; diuidendo, come BD</I>
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1988 <marg><I>Per la</I> 23. <I>del quinto.</I></marg> <I>ver$o DC, co$i la parte MN alla parte L. come dunque BD &agrave; DC, co$i
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parents:
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1989 la parte MN ad F. &amp; come AD &agrave; DB, co$i F ad E. Per laqual co$a</I>
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1990 <marg><I>Per la</I> 17. <I>del quinto.</I></marg> <I>per la egual proportione, come AD ver$o DC, co$i MN ad E. &amp; e$$endo AD</I>
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1991 <marg><I>Corollario della quarta del quinto.</I></marg> <I>maggiore di CD; $ar&agrave; anco la parte MN maggiore del pe$o E. Diuida$i dun
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parents:
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1992 que MN in due parti MN, &amp; $ia M eguale ad E. $ar&agrave; come AD &agrave;</I>
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parents:
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1993 <marg>11. <I>del</I> 5.</marg> <I>DC, co$i NM ad M; &amp; diuidendo, come AC ver$o CD, co$i N ad M:</I>
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parents:
diff changeset
1994 <marg>16. <I>del</I> 5.</marg> <I>&amp; conuertendo, come DC ver$o CA, co$i M ad N. &amp; come DC &agrave;</I>
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parents:
diff changeset
1995 <marg><I>Per la</I> 6. <I>del</I> 1. <I>di Archi mede delle co fa che egual m&etilde;te pe$ano.</I></marg> <I>CA, co$i &egrave; E ad H; $ar&agrave; dunque M ad N come E ad H; &amp; permutan
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parents:
diff changeset
1996 do come M ad E, co$i N ad H. Ma per e$$ere ME traloro eguali, $aran-
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parents:
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1997 no anche NH tra $e eguali. &amp; percioche co$i &egrave; AC ver$o CD, come H
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parents:
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1998 ad E: i pe$i HE pe$eranno egualmente. $imilmente percioche, come &egrave; GC &agrave; CB,
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parents:
diff changeset
1999 co$i F ver$o K, i pe$i etiandio KF pe$eranno egualmente. Adunque i pe$i</I>
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parents:
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2000 <marg><I>Per la</I> 2. <I>no titia commu ne di que$io.</I></marg> <I>EK HF nella bilancia AB, il cui centro $ia C pe$eranno egualmente. &amp; con
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2001 cio$ia che GC $ia eguale &agrave; CD, &amp; il pe$o H $ia pur eguale ad N, ipe$i NH</I>
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2002 <pb n=31>
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2003 <I>pe$eranno egualmente. &amp; percioche tutti pe$ano egualmente, tolti via i pe$i HN,
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parents:
diff changeset
2004 iquali pe$ano egualmente, i re$tanti pe$eranno egualmente; cio&egrave; i pe$i EF, &amp; il pe</I> <marg><I>Per la commune notitia di questo.</I></marg>
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parents:
diff changeset
2005 <I>$o LM pendenti dal centro C della bilancia. Ma percioche la parte L &egrave; egua-
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parents:
diff changeset
2006 le ad F, &amp; la parte M &egrave; eguale alla parte E; $ar&agrave; tutto LM eguale a i pe$i
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parents:
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2007 FE in$ieme pre$i. &amp; e$$endo CG eguale &agrave; CD, $e i pe$i EF $aranno $atti
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parents:
diff changeset
2008 pendenti dal punto D, ipe$i EF appiccati in D pe$eranno egualm&etilde;te con LM.
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parents:
diff changeset
2009 Per laqual co$a LM pe$er&agrave; egualm&emacr;te t&amacr;to ad e&szlig;i EF appiccati in AB, qu&amacr;-
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parents:
diff changeset
2010 to $e fo$$ero appiccati nel punto D; peroche la bilancia rimane $empre nell'i$te$$o</I> <marg><I>Per la com munenotitia di questo.</I></marg>
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parents:
diff changeset
2011 <I>modo. Adunque i pe$i EF pe$eranno tanto in AB quanto nel punto D; che
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parents:
diff changeset
2012 bi$ognaua mo$trare.</I>
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diff changeset
2013 <p>Ma que$te co$e tutte dimo$treremo in altra maniera, &amp; piu Mechani
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parents:
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2014 camente.
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parents:
diff changeset
2015 <fig>
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parents:
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2016 <p><I>Sia la bilancia AB, &amp; il $uo centro C, &amp; $iano, come nel primo ca$o, due pe$i EF
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parents:
diff changeset
2017 pendenti da i punti BG: &amp; $ia GH ad HB, come il pe$o F al pe$o E. Di-
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parents:
diff changeset
2018 co che ipe$i EF pe$eranno tanto in GB, quanto $e ambidue $te$$ero pendenti
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parents:
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2019 dal punto H della diui$ione. Siano di$po$te le mede$ime co$e, cio&egrave; faccia$i AC
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parents:
diff changeset
2020 eguale &agrave; CH, &amp; dal punto A $iano appe$i due pe$i LM, per modo che il pe
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diff changeset
2021 $o E ver$o il pe$o L $ia come CA ver$o CG; &amp; come CB ver$o CA, co
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parents:
diff changeset
2022 $i $ia il pe$o M ver$o il pe$o F. Ipe$i LM pe$eranno egualmente (come &egrave; detto
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parents:
diff changeset
2023 di $opra) conlipe$i EF appiccati in GB. Siano dapoi due punti NO li centri
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parents:
diff changeset
2024 della grauezza de' pe$i EF; &amp; $iano congiunte le linee GN BO; &amp; $ia con-
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parents:
diff changeset
2025 giunta NO, laquale $ar&agrave; come bilancia; laquale etiandio faccia s&igrave;, che le linee
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parents:
diff changeset
2026 GN BO $iano traloro egualmente di$tanti; &amp; dal punto H $ia tirata la HP
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parents:
diff changeset
2027 &agrave; piombo dell'orizonte, laquale tagli NO nel P, &amp; $ia egualmente distante dal
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parents:
diff changeset
2028 le linee GN BO. In fine congiunga$i GO, laquale tagli HP in R. Percio</I> <marg><I>Per la $ecom da del $esta.</I></marg>
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parents:
diff changeset
2029 <I>che dunque HR &egrave; egualmente di$tante dal lato BO del triangolo GBO; $ar&agrave;
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parents:
diff changeset
2030 la GH ver$ola HB, come GR ad RO. Similmente percioche RP &egrave; egual</I>
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parents:
diff changeset
2031 <pb>
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parents:
diff changeset
2032 <fig>
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parents:
diff changeset
2033 <I>mente di$tante dal lato GN del triangolo OGN; $ar&agrave; GR ver$o RO, come
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parents:
diff changeset
2034 NP ver$o PO. Per laqual co$a come GH ad HB, cos&igrave; &egrave; NP ver$o PO.</I>
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parents:
diff changeset
2035 <marg><I>Per la</I> 11. <I>del quinto</I></marg> <I>Ma come GH ver$o HB, cos&igrave; &egrave; il pe$o F ver$o il pe$o E; adunque come NP
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parents:
diff changeset
2036 ver$o PO, cos&igrave; &egrave; il pe$o F ver$o il pe$o E. Dunque il punto P $ar&agrave; il centro</I>
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parents:
diff changeset
2037 <marg><I>Per la $esta del primo di Archimede d'lle co$e, che pe$ano egual mente.</I></marg> <I>della grauezza della magnitudine compo$ta di ambidue i pe$i EF. Intendan$i
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parents:
diff changeset
2038 dunque i pe$i EF e$$ere in maniera dalla bilancia NO annodati, come $e fo$$e vna
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parents:
diff changeset
2039 grandezza $ola d'ambidue ipe$i EF composta, &amp; attacata ne i punti BG, $e dun-
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parents:
diff changeset
2040 que $ar anno $cioltii legamenti BG de' pe$i; rimarr anno i pe$i EF p&etilde;denti da HP;
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parents:
diff changeset
2041 $i come prima $tauane in GB. Ma i pe$i EF appiccati in GB pe$ano egualmente
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parents:
diff changeset
2042 co'ipe$i LM, &amp; ipe$i EF pendenti dal punto H hanno l'i$te$$a di$po$itione ver</I>
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parents:
diff changeset
2043 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>$o la bilancia AB, come $e $o$$ero appiccati in BG: Gli iste&szlig;i pe$i dunque EF
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parents:
diff changeset
2044 pendenti da H pe$aranno egualmente con gli i$te$$i pe$i LM. Sono dunque egual-
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diff changeset
2045 mente graui i pe$i EF attaccati in GB, come attaccati in H.</I>
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2046 <fig>
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diff changeset
2047 <pb n=32>
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2048 <p><I>Similmente dimo$trera&szlig;i, che i pe$i EF pe$eranno tanto appiccati in qual $i voglia al-
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2049 tro punto, quanto $e l'vno, &amp; l'altro $o$$e pendente dal punto H della diui$ione.
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2050 Percioche$e, come di $opra habbiamo in$egnato, $i troueranno ipe$i nella bilancia, &agrave;
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2051 i quali i pe$i EF pe$ino egualmente; gliiste&szlig;i pe$i EF pendenti da H pe$eranno
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2052 egualmente co' mede$imi pe$i trouati; per e$$ere il punto P $empre il centro della
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2053 grauezzaloro; &amp; la HP a piombo dell'orizonte.</I>
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2054 <HEAD>PROPOSITIONE VI.</HEAD>
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2055 <p>I pe$i eguali nella bilancia appiccati hanno in grauezza quella pro-
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diff changeset
2056 portione, che hanno le di$tanze, dalle quali $tanno pendenti.
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diff changeset
2057 <fig>
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diff changeset
2058 <p><I>Sia la bilancia BAC $o$pe$a nel punto A; &amp; $ia $egata la AC, come pare in D. &amp;
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diff changeset
2059 da i punti DC $iano attaccati EF pe$i eguali. Dico, che il pe$o F ver$o il pe$o E ba
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diff changeset
2060 quella proportione in grauezza, che hala di$tanza CA alla di$tanza AD. Per-
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diff changeset
2061 cioche faccia$i come CA ver$o AD, co$i il pe$o F ver$o vn'altro pe$o, che $ia G.
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diff changeset
2062 Dico primai p $i GF pendenti dal punto C tanto pe$are, quanto i pe$i EF penden
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diff changeset
2063 ti da punti DC. Tagli$i DC in due parti eguali in H, &amp; da H $iano fatti pendere
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diff changeset
2064 ambidue i pe$i EF. Pe$eranno EF pre$i in$ieme in quel $ito tanto quanto pe$ano</I> <marg><I>Per la</I> 5. <I>di questo.</I></marg>
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diff changeset
2065 <I>in DC. Ponga$i BA eguale ad AH, &amp; $itagli BA in K, di modo, che KA
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diff changeset
2066 $ia eguale ad AD: dapoi dal punto B $ia $atto pendente il pe$o L, ilquale $ia il dop
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diff changeset
2067 pio del pe$o F, cio&egrave; eguale a i due pe$i EF, ilqual pe$er&agrave; egualmente co'pe$i EF ap
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parents:
diff changeset
2068 piccati in H, cio&egrave; appiccati in DC. Percioche dunque, come CA ver$o AD, cos&igrave; &egrave;
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diff changeset
2069 ilpe$o F ver$o il pe$o G, $ar&agrave; componendo come CA AD ver$o AD, cio&egrave; come
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diff changeset
2070 CK ver$o AD, cos&igrave; ipe$i FG ver$o il pe$o G. Ma per e$$er come CA ver$o AD,</I> <marg><I>Per la</I> 18. <I>del quinto.</I></marg>
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diff changeset
2071 <I>cos&igrave; il pe$o F al pe$o G, $ar&agrave; anche conuertendo, come DA ver$o AC, cos&igrave; il pe$o
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diff changeset
2072 G ver$o il pe$o F; &amp; i doppi de icon$eguenti, come DA alla doppia di e$$a AC,
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diff changeset
2073 cos&igrave; il pe$o G al doppio del pe$o F, cio&egrave; al pe$o L. Per laqual co$a come CK ver$o</I> <marg><I>Per la con$e guenza della quartadel quinto.</I></marg>
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diff changeset
2074 <I>DA, cos&igrave; ipe$i FG al pe$o G; &amp; come AD alla doppia di AC, cos&igrave; il pe$o G al
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diff changeset
2075 pe$o L, adunque dalla egual proportione come CK alla doppia di AC, cos&igrave; ipe$i FG
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2076 al pe$o L. Ma come CK alla doppia di AC, cos&igrave; la met&agrave; di CK, cio&egrave; AH, cio&egrave;</I> <marg><I>Per la</I> 22. <I>del quinto.</I></marg>
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diff changeset
2077 <I>BA ver$o AC. Adunque come BA ver$o AC, cos&igrave; FG pe$i al pe$o L. Per laqual</I>
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diff changeset
2078 <pb>
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diff changeset
2079 <I>co$a per la $e$ta dell'i$te$$o primo di Archimede, i due pe$i FG pendenti dal punto C</I>
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diff changeset
2080 <marg><I>Per la $ettima del</I> 5.</marg> <I>pe$eranno tanto, quanto il pe$o L pendente dal B; cio&egrave; quanto i pe$i EF pen-
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diff changeset
2081 denti da i punti DC. Cos&igrave; percioche i pe$i FG tanto pe$ano quanto ipe$i EF,
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diff changeset
2082 leuato via il pe$o comune F, tanto pe$er &agrave; il pe$o G appicato in C, quanto il pe</I>
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diff changeset
2083 <fig>
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diff changeset
2084 <I>$o E in D. Et perci&ograve; il pe$o F al pe$o E h&agrave; quella proportione in grauezza,
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2085 che h&agrave; al pe$o G. Ma il pe$o F ver$o il G era come CA ver$o AD. adun
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2086 que il pe$o F ancora ver$o il pe$o E hauer&agrave; quella proportione in grauczza, che
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2087 ha CA ver$o AD che bi$ognaua mo$trare.</I>
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2088 <p><I>Ma $e nella bilancia BAC $i faranno pendenti da i punti BC, i pe$i EF eguali;
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diff changeset
2089 Dico $imilmente, che il pe$o E ver$o il pe$o F h&agrave; quella proportione in grauezza,
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2090 che ha la di$tanza
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2091 CA alla di$tanza
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2092 AB. faccia$i AD
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2093 eguale ad AB, &amp;
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2094 dal punto D $ia
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2095 fatto p&emacr;dente il pe
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2096 $o G eguale al pe
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2097 $o F, ilquale eti&amacr;-</I>
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2098 <fig>
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2099 <I>dio $ar&agrave; eguale ad E. Et percioche AD &egrave; eguale ad AB; i pe$i FG pe$eran
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2100 no egualmente, &amp; hauranno la mede$ima grauezza. Et concio$ia, che la grauezza
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2101 del pe$o E ver$o la grauezza del pe$o G $ia come CA ad AD; $ar&agrave; la gra-
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2102 uezza del pe$o E ver$o la grauezza del pe$o F, come CA ad AD, cio&egrave; CA
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2103 ad AB, che parimente era da mo$trare.</I>
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2104 <HEAD>Altramente.</HEAD>
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2105 <p><I>Sia la bilancia BAC, col$uo centro A: &amp; ne i punti BC $iano appiccati pe$i
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2106 eguali GF, &amp; $ia prima il centro A, come $i vuole, fra B, &amp; C. Dico, che
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2107 il pe$o F ver$o il pe$o G h&agrave; quella proportione in grauezza, che ha la di$tanza
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2108 CA alla di$tanza AB. Faccia$i come BA ver$o AC, co$i il pe$o F ad vn-</I>
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2109 <pb n=33>
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2110 <I>altro H, ilquale $ia appiccato in B: i pe$i HF pe$eranno egualmente de A.</I> <marg><I>Per la</I> 6. <I>del prime di Ar chimede del le co$e che pe $ano egualmente.</I></marg>
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2111 <I>Ma e$$endo i pe$i FG eguali, haur&agrave; il pe$o H ver$o il pe$o G la proportione me
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2112 de$ima, che ha ad F. Come dunque CA ver$o AB, co$i &egrave; H ver$o G: &amp;
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parents:
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2113 come H ver$o G, co$i &egrave; lagrauezza di H alla grauezza di G, per e$$ere attac
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parents:
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2114 cati nell i$te$$o punto B. Per laqual co$a come CA ad AB, co$i la grauezza
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2115 del pe$o H alla grauezza del pe$o G. Et concio$ia che la grauezza del pe$o F
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2116 attacato in G $ia</I> <marg><I>Per la</I> 7. <I>del quinto.</I></marg>
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2117 <I>eguale alla grauez-
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parents:
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2118 za del pe$o Hattac
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2119 cato in B, $ar&agrave; la
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2120 grauezza del pe$o F
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2121 ver$o la grauezza
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2122 del pe$o G, come
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2123 CA ver$o AB,
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2124 cio&egrave; come la di$tan-
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2125 za alla di$tanza, che
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2126 bi$ognaua mostrare.</I>
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2127 <fig>
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2128 <p><I>Ma $e la bilancia BAC fo$$e tagliata, come $i vuole in D, &amp; appicchin$i in DC
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2129 i pe$i EF eguali. Dico $imilmente co$i e$$ere la grauezza del pe$o F alla gra-
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2130 uezza del pe$o E, come la di$tanza CA alla di$tanza AD. Faccia$i AB
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2131 eguale ad AD
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2132 &amp; $ia appicca-
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2133 to in B il pe$o
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2134 G eguale al pe
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2135 $o E, &amp; alpe
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2136 $o F. Hor
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2137 percioche AB
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2138 &egrave; eguale ad A
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2139 D; ipe$i GE</I>
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2140 <fig>
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2141 <I>pe$eranno egualmente. Ma per e$$ere la grauezza del pe$o F ver$o la grauezza
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2142 del pe$o G, come CA ad AB, &amp; la grauezza del pe$o E $ia eguale alla
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diff changeset
2143 grauezza del pe$o G; $ar&agrave; la grauezza del pe$o F ver$o la grauezza del pe$o E,
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diff changeset
2144 come CA ad AB, cio&egrave; CA ad AD, che bi$ognaua mo$trare.</I>
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diff changeset
2145 <HEAD>COROLLARIO.</HEAD>
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diff changeset
2146 <p>Da que$to &egrave; manife$to, che quanto il pe$o &egrave; piu di$tante dal centro
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diff changeset
2147 della bilancia, tanto egli &egrave; anco piu graue, &amp; per con$eguente mo-
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diff changeset
2148 uer$i piu velocemente.
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diff changeset
2149 <p>Quinci oltre &agrave; ci&ograve; $i mo$trer&agrave; facilmente anche la ragione della Sta-
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diff changeset
2150 dera.
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diff changeset
2151 <foot><I>I</I></foot>
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diff changeset
2152 <pb>
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diff changeset
2153 <p>Corollario vocabolo Latino co$tumato da tutti gli altri Scrittori Italiani in cotal ma
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diff changeset
2154 teria, n&egrave; di$piacque &agrave; Dante nel 28. cap. del Purgatorio. &ldquo;Dirotti vn corollario an-
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diff changeset
2155 co per gratia.&rdquo; vuol dire, $econdo Varrone nel primo libro della lingua Latina,
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diff changeset
2156 quella giunta, &amp; quel $opra piu, che $i d&agrave; oltre al pagamento, quando $i comp era
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diff changeset
2157 qualche co$a. Al tempo antico allhor che i recitatori di Tragedie, Comedie, &amp;
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diff changeset
2158 altri Poemi nelle $cene $i portauano bene, &amp; piaceuano &agrave; gli vditori, era loro do-
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2159 nato oltra al prezzo a$$egnato, vn corollario per cia$cuno, cio&egrave; vna piccola coro
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2160 na per douer$ene ornare le tempie per giunta, &amp; $opra piu delle $ue mercedi. Co$i
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2161 nelle $cienze matematiche v$a$i di aggiungere certe co$e, oltra le propo$itioni,
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2162 qua$i giunte &amp; con$equenze, le quali na$cono dalle co$e primieramente dimo$tra-
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diff changeset
2163 te, &amp; $ono loro corri$pondenti, &amp; non $ono per&ograve; n&egrave; propo$itioni, n&egrave; problemi,
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2164 n&egrave; lemmi, ma alla $embianza predetta chiaman$i coro llarij, molti de i quali han-
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2165 no congiunta la $ua dimo$tratione.
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2166 <p><I>Hor $ia AB il fusto della Stadera, la cui trutina $ia in C; &amp; $ia il marco della $ta</I>
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2167 <marg><I>Ragione del la stadera.</I></marg> <I>dera E. Appicchi$i in A il pe$o D, che pe$i egualmente col marco E appic-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2168 cato in F. Appicchi$i parimente vn'altro pe$o G in A, ilqual anco pe$i egual-
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2169 mente col marco E appiccato in B. Dico, la grauezza del pe$o D ver$o la gra-
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2170 uezza del
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2171 G e$$ere co
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2172 $i, come CF
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2173 ver$o CB.
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2174 Hor per-
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2175 cioche la
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diff changeset
2176 grauezza
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2177 del pe$o D
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2178 &egrave; eguale al
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2179 la grauez-
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2180 za del pe-
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2181 $o E at-
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2182 taccato in
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2183 F, &amp; la</I>
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2184 <fig>
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2185 <I>grauezza del pe$o G &egrave; eguale alla grauezza del pe$o E po$to in B; $ar&agrave; la grauez-
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2186 za del pe$o D alla grauezza del pe$o E po$to in F, come la grauezza del pe$o G alla
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2187 grauezza del pe$o E po$to in B; &amp; permutando come la grauezza del pe$o D alla
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2188 grauezza del pe$o G, co$i la grauezza di E po$to in F alla grauezza di E po$to in B;
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2189 ma la grauezza del pe$o E in F alla grauezza di E in B po$to &egrave; come CF
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2190 ver$o CB; come dunque la grauezza del pe$o D alla grauezza del pe$o G, co$i
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2191 &egrave; CF ver$o CB. Se dunque la parte del fu$to CB diuidera$$i in parti eguali, po
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2192 $to $olo il pe$o E &amp; piu da pre$$o, &amp; piu da lontano dal punto C; le grauezze de
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2193 pe$i, lequali$tanno pendenti dal punto A $aranno traloro manife$te &amp; note. Co-
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2194 me$e la di$tanza CB $ar&agrave; tripla della di$tanza CF, $ar&agrave; parimente la grauezza
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2195 di e$$o G tripla della grauezza di D, che bi$ognaua mo$trare.</I>
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2196 <pb n=34>
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2197 <p>In altro modo po$$iamo anco v$are la $tadera, affine che le grauezze
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2198 de ipe$i $i facciano note.
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2199 <p><I>Sia il fu$to della stadera AB, la cui trutina $ia in C, &amp; $ia il marco della stadera
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2200 E, ilquale $ia appiccato in A; &amp; $iano i pe$i DG di$uguali, le proportioni delle
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2201 grauezze de quali cerchia-
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2202 mo: $ia appiccato il pe$o D
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2203 in B talche pe$i egual-
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2204 mente con E. Similmente
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2205 appicchi$i il pe$o G in F,
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2206 ilquale pe$i egualmente con
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2207 l'i$te$$o pe$o E. Dico D
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2208 ver$o G co$i e$$ere; come</I> <marg><I>Per la $esta del primo di Archimede d'lle co$e, che pe$ano egual mente.</I></marg>
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2209 <I>CF ver$o CB. Hor perche
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2210 i pe$i DE pe$ano egualm&emacr;</I>
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2211 <fig>
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2212 <I>te, $ar&agrave; D ad E, come CA &agrave; CB. &amp; concio$ia, che anche i pe$i GE pe$i-
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2213 no egualmente, $ar&agrave; il pe$o E ver$o il pe$o G, come FC &agrave; CA; Per laqual
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2214 co$a per la proportion eguale il pe$o D al pe$o G, co$i $ar&agrave;, come CF &agrave; CB.
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2215 che parimente bi$ognaua mo$trare.</I> <marg><I>Per la</I> 23. <I>del quinto</I></marg>
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2216 <HEAD>PROPOSITIONE VII.</HEAD>
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2217 <HEAD>PROBLEMA.</HEAD>
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2218 <p>Dati quanti $i vogliano pe$i nella bilancia, appiccati in qualluogo $i
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2219 $ia, ritrouare il centro della bilancia, dal quale $e $ar&agrave; fatta penden-
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2220 te la bilancia, i dati pe$i $taranno fermi.
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2221 <p>PROBLEMA. Sotto il nome di Propo$itione $i contiene il Problema ancora vo-
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2222 cabolo greco; ma il Problema ha dauantaggio della Propo$itione in particolare,
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2223 che ordina, &amp; in$egna ad operare qualche effetto; doue la Propo$itione $uole $ta
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2224 re nella nuda $peculatione $olamente. Et que$ta &egrave; la differenza tra la Propo$itio-
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2225 ne, &amp; il Problema.
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2226 <foot><I>I</I> 2</foot>
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2227 <pb>
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2228 <fig>
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2229 <p><I>Sia la bilancia AB, &amp; $iano dati quanti $i vogliano pe$i CDEFG prendan$i nel
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2230 la bilancia, a piacere i punti AHKLB, da quali $ian fatti pendenti i dati pe$i.
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diff changeset
2231 Bi$ogna ritrouar il centro della bilancia, dal quale $e $i far &agrave; l'appiccamento, rim anga
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diff changeset
2232 no i dati pe$i. Diuida$i AH in M, $i che HM ad MA $ia come la grauezza
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diff changeset
2233 del pe$o C alla grauezza del pe$o D. Dapoi diuida$i anco BL in N, $i che
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diff changeset
2234 LN ad NB $ia come la grauez <*> pe$o G alla grauezza del pe$o F. Et di-
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diff changeset
2235 uida$i MN in O, $i che MO ver$o ON $ia come la grauezza de pe$i FG
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diff changeset
2236 alla grauezza de'pe$i CD. Et in fine diuida$i KO in P, $i che KP ver$o PO
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diff changeset
2237 $ia come la grauezza de'pe$i CD FG alla grauezza del pe$o E. Hor percio-</I>
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diff changeset
2238 <marg><I>Per la</I> 5. <I>di questo.</I></marg> <I>che i pe$i CDFG tanto pe$ano in O, quanto CD in M, &amp; FG in N;
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diff changeset
2239 pe$eranno egualmente i pe$i CD in M, &amp; FG in N, &amp; il pe$o E in K,
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diff changeset
2240 $e $aranno $o$pe$i nel punto P. Et concio$ia, che ipe$i CD tanto pe$ino in M,
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diff changeset
2241 quanto in AH, &amp; FG in N quanto in LB; ipe$i CDFG pendenti da'
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diff changeset
2242 punti AHLB, &amp; il pe$o E da K, $e da P $aranno $o$pe$i, pe$eranno egual-
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diff changeset
2243 mente, &amp; rimarranno. egli &egrave; dunque trouato il P centro della bilancia, dalquale
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diff changeset
2244 rimangono i pe$i dati. Che bi$ogna operare.</I>
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diff changeset
2245 <HEAD>COROLLARIO.</HEAD>
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diff changeset
2246 <p>Da que$to &egrave; chiaro, che $ei centri della grauezza de' pe$i CDEFG
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2247 fo$$ero ne' punti AHKLB, $arebbe il punto P il centro della
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diff changeset
2248 grauezza della magnitudine compo$ta di tutti i pe$i CDEFG.
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diff changeset
2249 <p><I>Que$to &egrave; manife$to dalla diffinitione del centro della grauezza, concio$ia che i pe$i ri-
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2250 mangano, $e $ono $o$tenuti dal punto P.</I>
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2251 <HEAD><I>Il fine della Bilancia.</I></HEAD>
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2252 <pb n=35>
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2253 <HEAD>DELLA LEVA.</HEAD>
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2254 <fig>
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2255 <HEAD>LEMMA.</HEAD>
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2256 <p>Siano quattro grandezze ABCD; &amp; $ia la A
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2257 maggiore della B, &amp; C maggiore della D. Dico,
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2258 che A ver$o D h&agrave; proportione maggiore di quello
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2259 che h&agrave; B ver$o C.
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2260 <p><I>Hor percioche A ver$o C h&agrave; proportion maggio-
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diff changeset
2261 re, che B ver$o C; &amp; A parimente ver$o D</I> <marg><I>Per la</I> 8. <I>del quinto.</I></marg>
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2262 <I>h&agrave; proportion maggiore di quel che ha ver$o C:
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2263 Dunque A ver$o D l'hauer &agrave; maggiore, che B
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2264 ver$o C, Che bi$ognaua mostrare.</I>
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2265 <fig>
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2266 <HEAD>PROPOSITIONE I.</HEAD>
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2267 <p>La po$$anza, che $o$tiene il pe$o attaccato alla Leua, ha la proportio
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2268 ne mede$ima al detto pe$o, che ha la di$tanza della Leua fra il $o$te
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2269 gno po$ta, &amp; lo attaccamento del pe$o, alla di$tanza, che &egrave; dal $o$te
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2270 gno alla po$$anza.
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2271 <p><I>Sia la leua AB, il cui $oftegno $ia C; &amp; $iail pe$o D pendente da A con AH,
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2272 $i che AH $ia $empre &agrave; piombo dell'orizonte: &amp; $ia la po$$anza $oftenente il pe-</I>
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2273 <fig>
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2274 <I>$o in B. Dico che la po$$anza posta in B ver$o il pe$o D $ta co$i, come la CA</I>
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2275 <pb>
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2276 <marg><I>Per la</I> 6. <I>del</I> 1. <I>di Archi mede delleco $ache egual m&etilde;te pe$ano.</I></marg> <I>ver$o la CB. Faccia$i come la BC alla CA, co$i il pe$o D ad vn'altro pe$o
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2277 E, talche $e egli in B $ar&agrave; appiccato, pe$er&agrave; egualm&etilde;te con D, per e$$er il C cen
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2278 tro della grauezza di ambidue. Per laqual co$a vna po$$anza eguale ad e$$o E po
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2279 $ta nel
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2280 mede$i
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2281 mo lo
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2282 go pe-
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2283 $er&agrave; e-
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2284 gual-
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2285 mente
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2286 con e$-</I>
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2287 <fig>
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2288 <I>$o D, nella leua AB, collocando il $o$tegno $uo in C, cio&egrave; impedir&agrave;, che il pe-</I>
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2289 <marg><I>Per la</I> 7. <I>del quinto.</I></marg> <I>$o D non inchini in giu$o, $i come impedi$ce il pe$o E. Ma la po$$anza di B al
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2290 pe$o D h&agrave;la mede$ima proportione, che il pe$o E ha all'iste$$o D: adunque la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2291 po$$anza di B ver$o il pe$o D $ar&agrave; come CA ver$o CB; cio&egrave; la di$tanza del-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2292 la leua dal $ostegno al $o$tenimento del pe$o, alla di$tanza dal $ostegno alla po$$an-
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2293 za, che bi$o gnaua mo$trare.</I>
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2294 <p>Di qu&igrave; ageuolmente $i puote mo$trare, che qu&atilde;to il $o$tegno $ar&agrave; piu
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2295 vicino al pe$o, tanto minor po$$anza $i ricerca &agrave; $o$tenere il detto
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2296 pe$o.
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2297 <p><I>Poste le co$e mede$ime $ia il $o$tegno in F piu da pre$$o ad A, che C; &amp; faccia$i
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2298 come BF ad FA, co$i il pe$o D ad vn'altro pe$o G, ilquale $e in B $ia ap-</I>
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2299 <marg><I>Per la mede $ima $esta.</I></marg> <I>piccato; i pe$i DG dal $o$tegno F pe$eranno egualmente. Hor percioche BF
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2300 &egrave; mag-
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2301 giore di
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2302 BC, &amp;
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2303 CA</I>
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2304 <marg><I>Per lo Lemma.</I></marg> <I>maggio
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2305 re di AF;
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2306 la
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2307 propor-
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2308 tione di</I>
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2309 <fig>
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2310 <I>BF ver$o FA $ar&agrave; maggiore, che di BC ver$o CA: &amp; perci&ograve; maggiore anco
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2311 $ar&agrave; la proportione del pe$o D alpe$o G, che de l'iste$$o D ad E: Dunque il</I>
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2312 <marg><I>Per la</I> 10. <I>del quinto</I></marg> <I>pe$o G $ar&agrave; minore del pe$o E. &amp; concio$ia che la po$$anza po$ta in B eguale &agrave;
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2313 G pe$i egualmente con D, auerr&agrave;, che minore po$$anza di quella, laquale &egrave; eguale
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2314 al pe$o E $o$tenter &agrave; il pe$o D; e$$endo la leua AB, &amp; il $o$tegno $uo doue &egrave; F,
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2315 che $e egli $o$$e doue &egrave; C. Similmente anche mo$trera$$i, che quanto piu dapre$$o $a
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2316 r&agrave; il $o$tegno al pe$o D, $empre vi $i ricercher&agrave; anco po$$anza minore per $o$tentare
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2317 il detto pe$o D.</I>
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2318 <pb n=36>
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2319 <HEAD>COROLLARIO.</HEAD>
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2320 <p>Onde $i puote raccogliere chiaramente, che e$$endo AF minore di
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2321 FB, minor po$$anza anco $i ricerca in B per $o$tenere il pe$o D.
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2322 &amp; e$$endo eguale, eguale: &amp; maggiore, maggiore.
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2323 <HEAD>PROPOSITIONE II.</HEAD>
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2324 <p>In altra maniera po$$iamo v$are la Leua.
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2325 <p><I>Sia la leua AB, il cui $o$tegno $ia B, &amp; il pe$o C $ia attaccato, come $i vuole, in D</I> <marg><I>Nella $esta di questo de la bilancia.</I></marg>
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2326 <I>fra AB; &amp; $ia la po$$anza in A che $ostiene il pe$o C. Dico, che $i come
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2327 BD &agrave; BA; co$i &egrave; lapo$$anza di A' al pe$o C. Appicchi$i in A il pe$o E
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2328 eguale al C; &amp; come AB ver$o BD, co$i faccia$i il pe$o E ver$o vn'altro pe$o,</I> <marg><I>Dalla</I> 11. <I>del quinto.</I></marg>
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2329 <I>come F. Et percioche i pe$i CE $ono tra$e eguali, $ar&agrave; il pe$o C ver$o il pe$o F
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2330 come AB ver$o BD. Attacchi$i parimente il pe$o F in A. &amp; percioche il</I> <marg><I>Per la $esta della bil&amacr;cia</I></marg>
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2331 <I>pe$o E al pe$o F
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2332 &egrave; come la grauez
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2333 za del pe$o di E
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2334 alla grauezza di
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2335 F; &amp; il pe$o E
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2336 ad F &egrave; come AB
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2337 &agrave; BD; come d&utilde;
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2338 que la grauezza
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2339 del pe$o E alla</I> <marg><I>Per la</I> 29. <I>del quinto.</I></marg>
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2340 <fig>
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2341 <I>grauezza del pe$o F, co$i &egrave; AB ver$o BD. ma come AB &agrave; BD, co$i &egrave; la
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2342 grauezza del pe$o E alla grauezza del pe$o C: Per laqual co$a la grauezza del
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2343 pe$o E alla grauezza del pe$o F co$i $ar&agrave;, come la grauezza del pe$o E alla gra-
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2344 uezza del pe$o C. I pe$i dunque CF hanno la mede$ima grauezza: $i che pon-
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2345 ga$i la po$$anza di A che $o$tenga il pe$o F, $ar&agrave; la po$$anza di A eguale al pe$o
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2346 F. &amp; percioche il pe$o E attaccat<*> in A &egrave; graue egualmente, come il C appicca-</I> <marg><I>Per la $ettima del</I> 5.</marg>
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2347 <I>to in D; hauer &agrave; la proportione i$te$$a la po$$anza di A ver$o la grauezza del pe$o
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2348 F appiccato in A, che ha alla grauezza del pe$o C appiccato in D. Mala po$$an
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2349 za di A eguale ad F $o$tiene il pe$o F; dunque la po$$anza di A $o$tenter&agrave; anco
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2350 il pe$o C. Et co$i per e$$ere la po$$anza di A eguale al pe$o F, &amp; il pe$o C ver$o
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2351 il pe$o F $ia come AB &agrave; BD; $ar&agrave; il pe$o C ver$o la po$$anza po$ta in A come
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2352 AB &agrave; BD. &amp; conuertendo, come BD &agrave; BA, co$i la po$$anza po$ta in A ver
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2353 $o il pe$o C. Dunque la po$$anza ver$o il pe$o co$i $ar&agrave;, come la di$tanza, che &egrave; fra</I> <marg><I>Per lo Corol lario della</I> 4 <I>del quinto.</I></marg>
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2354 <I>il $o$tegno, &amp; l'appiccamento del pe$o alla di$tanza, che &egrave; dal $o$tegno alla po$$an-
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2355 za, che bi$ognaua mo$trare.</I>
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2356 <pb>
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2357 <HEAD>Altramente.</HEAD>
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2358 <p><I>Sia la leua AB, il cui $o$tegno $ia B, &amp; il pe$o E $ia pendente dal punto C, &amp;
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2359 $ia in A la forza, che $ostiene l pe$o E. Dico, che $i come BC &agrave; BA, co$i &egrave;</I>
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2360 <fig>
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2361 <I>anco la po$$anza di A ver$o il pe$o E. Allunghi$i AB in D, &amp; faccia$i
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2362 BD eguale &agrave; BC; &amp; appicchi$i il pe$o F al punto D, che $ia eguale al pe$o E;
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2363 &amp; parimente dal punto A $i faccia pendere il punto G in modo, che il pe$o F hab
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2364 bia la proportione i$te$$a ver$o il pe$o G, che ha AB &agrave; BD. ipe$i FG verranno
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2365 &agrave; pe$ar egualmente: &amp; concio$ia che CB $ia eguale &agrave; BD, anco i pe$i FE egua
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2366 li pe$eranno egualmente. Ma ipe$i FEG nella bilancia, ouero nella leua DBA
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2367 appiccati, il cui $o$tegno &egrave; B, non pe$eranno egualmente, ma inchineranno &agrave; ba$$o
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2368 dalla parte di A. Per laqual co$a ponga$i in A tanta forza, che ipe$i FEG pe$i-
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2369 no egualmente, $ar&agrave; la po$$anza in A eguale al pe$o G; peroche i pe$i FE pe$a-
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2370 no egualmente, &amp; la forza in A niente altro deue fare, che $o$tenere il pe$o G, ac-
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2371 cio che non de$cenda. Et percio che i pe$i FEG, &amp; la po$$anza in A pe$ano egual
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2372 mente, leuati dunque via i pe$i FG, i quali pe$ano egualmente, i re$tanti pe$eran-
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2373 no pur egualmente, cio&egrave; la po$$anza in A co'l pe$o E, cio&egrave; la po$$anza in A $o-
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2374 sterra ilpe$o E, $i che la leua AB rimanga, come era prima. Et per e$$ere la
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2375 po$$anza in A eguale al pe$o G, &amp; il pe$o E eguale al pe$o F, haur&agrave; la po$$anza
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2376 in A la proportione iste$$a al pe$o E, che h&agrave; BD, cio&egrave; BC &agrave; BA, che bi$ogna
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2377 ua mo$trare.</I>
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2378 <HEAD>COROLLARIO I.</HEAD>
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2379 <p>Da que$to etiandio, come prima, puote e$$ere manife$to, che $eil pe$o
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2380 E $ar&agrave; po$to piu vicino al $o$tegno B, come in H, minore
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2381 po$$anza po$ta in A puote $o$tener il detto pe$o.
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2382 <p><I>Percioche minor proportione ha HB &agrave; BA, che CB &agrave; BA. &amp; quanto piu da</I>
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2383 <marg><I>Per la</I> 8. <I>del quinto.</I></marg> <I>vicino il pe$o $ar&agrave; al $o$tegno, $empre anco $i mo$trer&agrave; $imilmente minor po$$anza
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2384 poter $o$tener il pe$o E.</I>
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2385 <HEAD>COROLLARIO II.</HEAD>
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2386 <p>Segue etiandio, che la po$$anza in A $empre &egrave; minore del pe$o E:
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2387 <pb n=37>
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2388 <p><I>Percioche pigli$i tra A &amp; B qual punto $i voglia, come C, $empre BC $ar&agrave;
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2389 minore di BA.</I>
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2390 <HEAD>COROLLARIO III.</HEAD>
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2391 <p>Da que$to parimente $i puote cauare, che $e due $aranno le po$$anze,
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2392 l'vna in A, &amp; l'altra in B, &amp; ambedue $o$tentino il pe$o E, la po$-
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2393 $anza in A ver$o la po$$anza in B &egrave; come BC ver$o CA.
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2394 <p><I>Percioche la leua BA fal'officio di due leue, &amp; AB $ono come due $o$tegni, cio&egrave;
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2395 quando AB &egrave; leua, &amp; la forza che $o$tiene &egrave; in A, $ar&agrave; il $uo $o$tegno B. Ma
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2396 quando BA &egrave; leua, &amp; la po$$anza $ta in B, il $o$tegno $ar&agrave; A, &amp; il pe$o
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2397 $empre rimane appicca-
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2398 to in C. Et percio che la
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2399 po$$anza in A ver$o il
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2400 pe$o E &egrave; come BC &agrave;</I> <marg><I>Per la</I> 22. <I>del primo.</I></marg>
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2401 <I>BA, &amp; come il pe$o
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diff changeset
2402 E alla po$$anza, che &egrave;
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diff changeset
2403 in B, co$i &egrave; BA ad
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diff changeset
2404 AC, $ar&agrave; per la propor</I>
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diff changeset
2405 <fig>
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diff changeset
2406 <I>tion eguale la po$$anza in A alla po$$anza in B come BC &agrave; CA, &amp; &agrave; que
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diff changeset
2407 $to modo facilmente ancora potremo cono$cere la proportione, laquale &egrave; po$ta de
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diff changeset
2408 Ari$totele nelle que$tioni Mecaniche alla que$tione 29.</I>
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diff changeset
2409 <HEAD>COROLLARIO IIII.</HEAD>
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diff changeset
2410 <p>E manife$to etiandio, che ambedue le po$$anze in A, &amp; in B
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diff changeset
2411 pre$e in$ieme, $ono eguali al pe$o E.
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parents:
diff changeset
2412 <p><I>Percioche il pe$o E alla po$$anza in A &egrave; come BA &agrave; BC, &amp; l'i$te$$o pe$o E
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diff changeset
2413 ver$o la po$$anza in B &egrave; come BA ad AC; Per laqual co$a il pe$o E ver-
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diff changeset
2414 $o l'vna, &amp; l'altra po$$anzain A, &amp; in B pre$e in$ieme, &egrave; come AB ver$o
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diff changeset
2415 BC, &amp; CA in$ieme, cio&egrave; ver$o BA. il pe$o dunque E &egrave; eguale ad amen-
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diff changeset
2416 due le po$$anze pre$e in$ieme.</I>
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diff changeset
2417 <HEAD>PROPOSITIONE III.</HEAD>
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diff changeset
2418 <p>In altro modo ancora po$$iamo v$are la Leua.
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diff changeset
2419 <foot><I>K</I></foot>
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diff changeset
2420 <pb>
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diff changeset
2421 <p><I>Sia la leua AB, il cui $o$tegno $ia B. &amp; $ia il pe$o C appiccato al punto A,
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diff changeset
2422 &amp; $ia la po$$anza in D, comunque $i voglia tra AB, $o$tenente il pe$o C. Di-
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diff changeset
2423 co che come AB &agrave; BD, co$i &egrave; la po$$anza in D al pe$o C. Appicchi$i al
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diff changeset
2424 punto D il pe$o E eguale &agrave; C; &amp; come BD &agrave; BA, co$i $accia$i il pe$o
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diff changeset
2425 E ad vn'altro pe$o, come F: &amp; per e$$ere i pe$i CE traloro eguali, $ar&agrave; an-
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diff changeset
2426 co il pe$o C al
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parents:
diff changeset
2427 pe$o F, come
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diff changeset
2428 BD &agrave; BA.
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diff changeset
2429 Appicchi$i $imil
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diff changeset
2430 mente il pe$o F
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2431 in D. &amp; per-
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diff changeset
2432 che il pe$o E ad
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diff changeset
2433 F &egrave; come la gra
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diff changeset
2434 uezza del pe$o
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diff changeset
2435 E alla grauez-
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diff changeset
2436 za del pe$o F;
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diff changeset
2437 &amp; il pe$o E al</I>
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parents:
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2438 <fig>
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diff changeset
2439 <marg><I>Per la</I> 6. <I>di questo della bilancia.</I></marg> <I>pe$o F &egrave; come BD &agrave; BA. Come dunque la grauezza del pe$o E alla gra-
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parents:
diff changeset
2440 uezza del pe$o F, co$i &egrave; BD &agrave; BA. Ma come BD &agrave; BA, co$i &egrave; la gra-
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diff changeset
2441 uezza del pe$o E alla grauezza del pe$o C. Per laqual co$a la grauezza del</I>
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diff changeset
2442 <marg><I>Per la</I> 6. <I>di questo della bilancia.</I></marg> <I>pe$o E alla grauezza del pe$o F ha la proportione mede$ima, che ha alla gra-
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diff changeset
2443 uezza del pe$o C. i pe$i dunque CF hanno la grauezza mede$ma. Sia dunque</I>
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diff changeset
2444 <marg><I>Per la</I> 9. <I>del quinto.</I></marg> <I>la po$$anza in D $o$tenente il pe$o F, che verr&agrave; ad e$$ere la detta po$$anza in
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2445 D eguals al pe$o F. &amp; percioche il pe$o F posto in D &egrave; graue egualmente
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2446 come il pe$o C po$to in A; haur &agrave; la po$$anza in D la proportione mede$ima
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2447 ver$o la grauezza del pe$o F, che ha alla grauezza del pe$o C. Ma la po$$anza
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2448 in D $o$tiene il pe$o F, dunque la po$$anza in D $o$tenter&agrave; anco il pe$o C; &amp;
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diff changeset
2449 il pe$o C alla po$$anza in D $ar&agrave; co$i come il pe$o C al pe$o F; &amp; C ad F</I>
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2450 <marg><I>Per la</I> 7. <I>del quinto.</I></marg> <I>&egrave; come BD &agrave; BA, $ar&agrave; dunque il pe$o C alla po$$anza in D, come BD &agrave;
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2451 BA: &amp; conuertendo come AB &agrave; BD, co$i la po$$anza in D al pe$o C. La
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2452 po$$anza dunque al pe$o, &egrave; come la di$tanza dal $ostegno allo appiccamento del pe-
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2453 $o alla distanza dal $o$tegno alla po$$anza. che bi$ognaua mostrare.</I>
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2454 <HEAD>Altramente.</HEAD>
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2455 <p><I>Sia la leua AB, il cui $o$tegno $ia B. &amp; dal punto A $ia fatto pendente il pe$o
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2456 C, &amp; $ia la po$$anza in D $o$tenente il pe$o C. Dico, che come AB &agrave; BD,
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2457 co$i &egrave; la po$$anza in D al pe$o C. allunghi$ila AB in E, &amp; faccia$i BE egua-
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2458 le &agrave; BA, &amp; al punto E $ia appiccato il pe$o F eguale al pe$o C; &amp; come BD &agrave;
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2459 BE co$i faccia$i il pe$o F ad vn'altro pe$o G, ilquale $ia appiccato al punto D,
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2460 i pe$i FG pe$eranno egualmente. &amp; percioche AB &egrave; eguale &agrave; BE, &amp; i pe$i</I>
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2461 <foot><I>FC</I></foot>
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2462 <pb n=19>
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2463 <I>mente non &egrave; della grauez
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parents:
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2464 za cagione? Di questo ef
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2465 fetto mostrano di produ-
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parents:
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2466 cere in mezo que$ta cagio
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2467 ne, perche CG &egrave; la m&eacute;-
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parents:
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2468 ta, &amp; CF la trutina;
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parents:
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2469 $e (dicono e$$i) CG fo$
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parents:
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2470 $e la trutina, &amp; CF la
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parents:
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2471 m&eacute;ta, all'hora l'angolo
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2472 FCE $arebbe cagione
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2473 della grauezza, ma non
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2474 gi&agrave; il DCG ad e$$o e-
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2475 guale laquale ragione &egrave; al
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2476 tutto fatta con la imagi-
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2477 natione, &amp; di voglia pro
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parents:
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2478 pria. Peroche, che puote
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parents:
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2479 importare che la trutina
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parents:
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2480 $ia ouero in CF, ouero
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2481 in CG, e$$endo la bilan
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parents:
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2482 cia DE $empre $o$ten-
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2483 tata nell'i$te$$o punto C? Ma affine che l'inganno loro re$ti pi&ugrave; chiaro.</I>
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2484 <fig>
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2485 <p><I>Sia la mede$ima bilancia AB, il cui mezo C. dapoitutta la FG $ia la trutina,
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2486 laquale $tia immobile, &amp; $o$tenga la bilancia AB nel punto C. &amp; moua$i la
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2487 bilancia in DE. &amp; per-
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parents:
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2488 cioche la trutina &egrave; $opra, &amp;
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2489 $otto la bilancia, quale ango
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diff changeset
2490 lo $ar&agrave; cagione della grauez
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2491 za, e$$endo $o$tenuta la bi-
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2492 lancia DE $empre nel pun
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2493 to mede$imo? Diranno for-
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diff changeset
2494 $e $e la trutina $ar&agrave; $o$tenu-
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2495 ta dalla po$$anza po$ta in
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2496 F, allhora CG $ar&agrave; tan-
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2497 to quanto la m&eacute;ta, &amp; l'an-
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2498 golo DCG $ar&agrave; della gra
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2499 uezza cagione. Ma$e</I>
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2500 <fig>
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diff changeset
2501 <I>egli $ar&agrave; $ostenuto in G, allhora FCE $ar&agrave; cagione della grauezza, &amp; la CF
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diff changeset
2502 $ar&agrave; tanto quanto la m&eacute;ta. della qual co$a niuna cagione pare poter$i addurre,
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diff changeset
2503 $e n&otilde; imaginata; peroche la m&eacute;ta (che dicono) non pare hauere &agrave; modo veruno nien
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2504 te di virt&ugrave; che tiri dalla parte dell'angolo maggiore alcuna volta, &amp; alcuna dalla
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diff changeset
2505 parte del minore. Ma $ia $o$tenuta la trutina da due po$$anze in F cio&egrave;, &amp; in G,
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2506 <pb>
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diff changeset
2507 $ar&agrave; la inclinatione dell'vno al moui-
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2508 mento in gi&ugrave;, tale parimente $ar&agrave; la re
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diff changeset
2509 $istenza dell'altro al mouimento in s&ugrave;.
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2510 Adunque il pe$o po$to in E non mo-
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2511 uer&agrave; in s&ugrave; il pe$o po$to in D: ne il pe$o
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2512 po$to in D: $i mouer&agrave; in gi&ugrave; $i fatta-
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2513 mente, che moua in s&ugrave; il pe$o po$to in
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2514 E. imperoche e$$endo l'angolo CEB
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2515 egualea CDA, &amp; l'angolo CEM
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2516 $ia eguale all'angolo CDH; $ar&agrave; il
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2517 re$tante MEB eguale al re$tante</I>
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2518 <marg><I>Per la</I> 29. <I>del prime.</I></marg> <I>HDA. La $ce$a dunque del pe$o po-
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2519 $to in D $ar&agrave; eguale alla $alita del pe-
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diff changeset
2520 $o po$to in E. Adunque il pe$o po$to
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2521 in D non mouer&agrave; in s&ugrave; il pe$o po$to
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2522 in E. Dalle quali co$e $egue che i pe$i
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2523 po$ti in DE, in quanto tra loro $o-
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2524 no congiunti, $ono egualmente graui.</I>
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2525 <fig>
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2526 <p><I>L'altra ragione po$cia, con laquale vorrebbono mo$trare, che $imilmente la bilancia
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parents:
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2527 DE ritorna in AB, con dire, che e$$endo la trutina della bilancia CF, la m&eacute;ta
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2528 viene ad e$$er CG. &amp; percioche l'angolo DCG &egrave; maggiore dell'angolo ECG,
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2529 <*> pe$o po$to in D $ar&agrave; pi&ugrave; graue del po$to in E; dunque la bilancia DE ritorne
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2530 ra in AB; non conchiude nulla al parer mio; &amp; que$ta fintione della trutina, &amp;
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parents:
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2531 della m&eacute;ta &egrave; pi&ugrave; to$to da trala$ciare, &amp; pa$$arla con $ilentio, che farne pur vna paro
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2532 la per confonderla, e$$endo del tutto co$a volontaria, percioche la nece$$aria ragione
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parents:
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2533 per laquale il pe$o po$to in D dall' angolo maggiore $ia pi&ugrave; graue, &amp; perche il mag
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2534 giore angolo $ia cagione di grauezzamaggiore non appare in niun loco. che $e gli
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2535 angoli $aranno tra loro paragonati, e$$endo l'angolo GCD eguale all'angolo
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2536 FCE; $e l'angolo GCD &egrave; cau$a della grauezza, perche l'angolo FCE $imil-
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2537 <pb>
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parents:
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2538 ilche $i puote fare per nece$$it&agrave;, come $e la po$$anza posta in F $o$$e tanto debile,
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2539 che per $e $te$$a pote$$e $o$tentare $olamente la met&agrave; del pe$o &amp; $ia la po$$anza
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2540 posta in G eguale alla po$$anza po$ta in F, &amp; ambedue in$ieme co' pe$i $o$tenga-
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2541 no la bilancia. all'hora quale angolo $ar&agrave; cagione della grauezza? non gia
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parents:
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2542 FCE, peroche la trutina &egrave;
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2543 in CF, &amp; &egrave; $o$tentata in
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2544 F: ne meno il DCG, e$$en
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parents:
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2545 do la trutina in CG, &amp; pa
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parents:
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2546 rimente $o$tentata in G.
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parents:
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2547 Non $aranno dunque gli an
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parents:
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2548 goli della grauezza cagione.
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2549 Co$i ne anche la bilancia
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2550 DE da que$to $ito per que
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2551 $ta cagione $i mouer&agrave;. Ma</I>
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2552 <marg><I>il Cardano.</I></marg> <I>que$ta loro $entenza pare
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2553 e$$ere confermata da e$$i in
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2554 due modi. Primieramente</I>
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2555 <fig>
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2556 <I>dicono Ari$totele nelle que$tioni mecaniche hauere propo$to que$te due que$tioni $o
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parents:
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2557 lamente, &amp; le $ue dimo$trationi e$$ere fondate $i nel maggiore, &amp; nel minore
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parents:
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2558 angolo, &amp; $i nella giacitura della trutina della bilancia. Affermano dapoi que$to
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2559 iste$$o in$egnare la e$perientia ancora, cio&egrave;, che la bilancia DE, $tando la $ua
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parents:
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2560 trutina in CF, ritorna in AB egualmente di$tante dall'orizonte. &amp; quando
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2561 la trutina $t&agrave; in CG, mouer$i in FG. Mane Ari$totele, ne la e$perienza fauo-
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2562 ri$cono que$ta loro opinione, anzi pi&ugrave; to$to le $ono contrarij. Peroche in quan-
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2563 to appartiene alla e$perienza $i ingannano, e$$endo mani$e$to ci&ograve; per e$perienza
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2564 accadere, all'hor che il centro ancora della bilancia $ar&agrave; collocato &ograve; $opra, &ograve; $ot-
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2565 to della bilancia, ma non gi&agrave; auenire que$to stando la trutina &ograve; $opra $olamente,
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2566 &egrave; $otto.</I>
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parents:
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2567 <pb n=20>
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2568 <p><I>Imperoche $e la bilancia A
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2569 B haue$$e il centro C
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parents:
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2570 $opra la bilancia, &amp; fo$-
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parents:
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2571 $e la trutina CD $otto
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parents:
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2572 la bilancia, &amp; $i moue$-
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parents:
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2573 $e la bilancia in EF, al
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parents:
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2574 lhora EF di nouo ri-
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parents:
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2575 torner&agrave; in AB. egual-
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parents:
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2576 mente di$tante dall'o-
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parents:
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2577 rizonte. $imilmente $e la
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parents:
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2578 bilancia haue$$e il cen-
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parents:
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2579 tro C $otto la bilancia,
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parents:
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2580 &amp; $o$$e la trutina CD
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2581 $opra la bilancia, et $i mo
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diff changeset
2582 ue$$e la bilancia in EF,</I> <marg><I>Per la terz<*> di questo.</I></marg>
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diff changeset
2583 <I>egli &egrave; manife$to, che la bi
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diff changeset
2584 lancia $i mouer&agrave; in giu
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2585 dalla parte di F, $tan-
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diff changeset
2586 do la trutina $opra la bi-
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diff changeset
2587 lancia. &amp; in qual $i vo-
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2588 glia altro $ito che $ia la
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diff changeset
2589 trutina, auerr&agrave; $empre il
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diff changeset
2590 mede$imo. Adunque n&otilde;
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2591 &egrave; la trutina, ma il centro
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diff changeset
2592 della bilancia cagione di
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diff changeset
2593 cotali diuer$i effetti.</I>
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diff changeset
2594 <fig>
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parents:
diff changeset
2595 <p><I>Egli &egrave; pero d'auertire in que$ta parte che con di$$icult&agrave; $i puote lauora re vna bilancia
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diff changeset
2596 materiale, che in vno punto $olamente $ia $o$tenuta, $i come con la mente la imagi-
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diff changeset
2597 niamo, &amp; habbia le braccia dal centro co$i eguali non $olamente in lunghezza, ma
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diff changeset
2598 in larghezza, &amp; in profundit&agrave;, &ograve; gro$$ezza, che tutte le parti di qu&agrave;, &amp; di l&agrave; pe$i-
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2599 no a punto egualmente. percio che la materia di$$icili$$imam ente pati$ce cotale giu-
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diff changeset
2600 $ta mi$ura. Per laqual co$a $e con$idereremo il centro e$$ere in e$$a bilancia, non bi-
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diff changeset
2601 $ogna ricorrere al $en$o, concio$ia, che le co$e artificiate non $i po$$ano ridurre a quel
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2602 fommo grado di per$ettione. Ma nelle altre co$e la e$perienza veramente potr&agrave; in$e
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2603 gnare le co$e che appaiono percioche qu&atilde;tunque ilcentro della bil&atilde;cia $empre $ia vn
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diff changeset
2604 punto, nondimeno quando egli $ar&agrave; $opra la bilancia, poco importa, $e ben la bilancia
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diff changeset
2605 non $ara $o$tenuta in quel punto co$i puntalmente per&ograve; che per e$$ere $empre $opra la
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diff changeset
2606 bilancia auerr&agrave; $empre il mede$imo. Con $imile modo, quando egli anco &egrave; $otto la bi-
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diff changeset
2607 lancia, ilche tuttauia non accade stando il centro in e$$a bilancia, per che $e egli non
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diff changeset
2608 $ar&agrave; $o$tenuto $empre in quel mezo accuratamente, $ara differenza, e$$endo co$a faci
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diff changeset
2609 li$$ima, che quel centro, muti il proprio $ito, mentre $i moue la bilancia.</I>
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diff changeset
2610 <pb>
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diff changeset
2611 <p><I>Ma che Ari$totele habbia
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2612 propo$to due que$tioni $o
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2613 lamente, cio&egrave; perche la
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2614 trutina $tando $opra, $e
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2615 la bilancia n&otilde; $ar&agrave; egual
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2616 mente di$tante dall'ori-
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2617 zonte in equilibrio, cio&egrave;
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2618 egualmente di$tante dal
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2619 orizonte ritorna, ma $e la
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2620 trutina $ara po$ta $otto
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2621 non ritorna, ma di piu $i
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2622 moue $ec&otilde;do la parte ba$
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2623 $a: egli &egrave; ver&ograve; per certo.
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2624 Ma non gi&agrave; per que$to le
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2625 dimo$trationi $ue $ono
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2626 $ondate nell'angolo mag
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2627 giore, &ograve; minore, &amp; nella
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parents:
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2628 giacitura della trutina,
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2629 come e$$i dicono: per cio-
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parents:
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2630 che in questo non com-
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parents:
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2631 prendono la m&etilde;te del filo
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parents:
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2632 $ofo, che a$$egna la ragio
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2633 ne de gli effetti diuer$i
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parents:
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2634 de'mouimenti della bilan
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2635 cia. peroche tanto &egrave; lon-
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parents:
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2636 tano, che il filo$o$o attri
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2637 bui$ca que$ti diuer$i effet</I>
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2638 <fig>
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parents:
diff changeset
2639 <I>ti &agrave; gli angoli, che piu to$to dica e$$ere cagione l'ecce$$o, &amp; quel $opra pi&ugrave; della gran
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parents:
diff changeset
2640 dezza che &egrave; dal perpendicolo dell'uno delle braccia della bilancia hor dall'una parte,
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parents:
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2641 hora dall'altra.</I>
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2642 <p><I>Come stando la trutina $opra in CF, il perpendicolo $ar&agrave; FCG, il quale $em-
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parents:
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2643 pre inchina, $econdo lui, ver$o il centro del mondo, il quale anco diuide la bilancia mo$
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2644 $a in DE in parti di$uguali: &amp; la parte maggiore &egrave; ver$o il D, &amp; quel che &egrave; piu,
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2645 inchina in giu. Adunque dalla parte di D la bilancia $i mouer&agrave; in giu fin che ri-
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parents:
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2646 torni in AB. Ma $e la trutina $ar&agrave; in CG di $otto, $ar&agrave; GCF il perpendico-
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parents:
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2647 lo, ilquale diuider&agrave; parimente la bilancia DE in parte di$uguali, &amp; la parte mag
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parents:
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2648 giore $ar&agrave; ver$o E; Per laqual co$a la bilancia $i mouer&agrave; in giu dalla parte di E.
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parents:
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2649 &amp; accioche que$to $ia dirittamente compre$o, $appia$i, che quando la trutina &egrave; $o-
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parents:
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2650 pra la bilancia, $i ha da intendere, che anche il centro della bilancia $ia $opra la bi-
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parents:
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2651 lancia, &amp; $e di $otto, anche il centro deue $tare di $otto, come piu a ba$$o manife$te-
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2652 ra$$i, Altramente la dimo$tratione di Ari$totele non conchiuderebbe nulla, pero
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parents:
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2653 che stando il centro in e$$a bilancia, come in C moua$i la bilancia in qual $i voglia</I>
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2654 <pb n=21>
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2655 <I>modo, il perpendicolo FG non diuider&agrave; giamai la bilancia $e non nel punto C, et
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parents:
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2656 in parti eguali. Onde la $entenza di Ari$totele non $olamente non gli $auori$ce, ma
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parents:
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2657 gli fa anche grandi$sima
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2658 mente contra. il che
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parents:
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2659 non $olamente &egrave; chiaro
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parents:
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2660 dalla $econda &amp; terza
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parents:
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2661 propo$itione di que$to li
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parents:
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2662 bro, ma anco percioche
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parents:
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2663 $tando il centro $opra
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parents:
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2664 la bilancia, il pe$o alzato
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parents:
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2665 acqui$ta grauezza mag
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parents:
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2666 giore per cau$a del $ito.
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parents:
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2667 Dalla qual co$a accade il
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parents:
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2668 ritorno della bilancia ad
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2669 eguale di$tanza dall'ori-
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parents:
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2670 zonte. Ma per lo con-
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parents:
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2671 trario auiene quando il
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2672 centro &egrave; $otto la bilan-
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2673 cia. Le quali co$e tutte
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parents:
diff changeset
2674 $i dimo$treranno in que-
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diff changeset
2675 $ta maniera, pre$uppo-
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diff changeset
2676 nendo le co$e, che di $o-</I>
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diff changeset
2677 <fig>
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parents:
diff changeset
2678 <I>pra furono dechiarate, cio&egrave; il pe$o $ar$i pi&ugrave; graue da quelloco dal quale $cende piu
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parents:
diff changeset
2679 dirittamente, &amp; da quello che egli $ale piu dirittamente far$i parimente piu
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parents:
diff changeset
2680 graue.</I>
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parents:
diff changeset
2681 <foot><I>F</I></foot>
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parents:
diff changeset
2682 <pb>
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parents:
diff changeset
2683 <p><I>Sia la bilancia AB egualmente di$tante dall'orizonte, il cui centro C $ia $opra la
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parents:
diff changeset
2684 bilancia, &amp; $ia il perpendicolo CD: &amp; $iano i centri della grauezza di pe$i eguali
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parents:
diff changeset
2685 po$ti in AB: &amp; la bilancia $ia mo$$a in EF. Dico, che il pe$o posto in E ha
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parents:
diff changeset
2686 grauezzamaggiore, che il
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parents:
diff changeset
2687 pe$o posto in F. &amp; per-
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parents:
diff changeset
2688 ci&ograve; la bilancia EF e$$e-
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parents:
diff changeset
2689 re per ritornare in AB.
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parents:
diff changeset
2690 $ia allungata prima la linea
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parents:
diff changeset
2691 CD fin'al centro del mon
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parents:
diff changeset
2692 do, che $ia S. Dapoi $ia-
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2693 no congiunte le linee AC,
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parents:
diff changeset
2694 CB, EC, CF, HS;
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parents:
diff changeset
2695 &amp; dai punti EF $iano ti-
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parents:
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2696 rate le linee EKGFL egual
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parents:
diff changeset
2697 m&etilde;te di$tanti da HS. Per-
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parents:
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2698 cioche dunque la di$ce$a na
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parents:
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2699 turale diritta di tutta la
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parents:
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2700 grandezza, cio&egrave; della bilan
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parents:
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2701 cia EF co$i di$po$ta in$ie
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2702 me co'pe$i &egrave; $econdo la gra-
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parents:
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2703 uezza del centro H per la
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parents:
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2704 dirittalinea HS; $ar&agrave; pa
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parents:
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2705 rim&etilde;te la di$ce$a de'pe$ime$
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parents:
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2706 $i in EF co$i di$po$ti $econ
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parents:
diff changeset
2707 do le linee diritte E</I>K
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parents:
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2708 <I>FL egualmente distanti
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parents:
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2709 da HS, $i come di $opra
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parents:
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2710 habbiamo dimo$trato. La
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parents:
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2711 di$ce$a dunque, &amp; la $ali-
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parents:
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2712 ta de i pe$i po$ti in EF $i
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parents:
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2713 dir&agrave; pi&ugrave;, &amp; meno obliqua
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parents:
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2714 $econdo la vicinanza, &ograve; lon
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parents:
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2715 tananza diputata $econdo</I>
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diff changeset
2716 <marg><I>Per la</I> 4. <I>del primo.</I></marg> <I>le linee EK FL. &amp; per-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2717 cioche li due lati AD DC
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parents:
diff changeset
2718 $ono eguali a i due lati BD</I>
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parents:
diff changeset
2719 <fig>
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parents:
diff changeset
2720 <I>DC; &amp; gli angoli al D $ono retti, $ar&agrave; il lato AC eguale al lato CB. &amp; e$-
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parents:
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2721 $endo il punto C immobile; mentre, che i punti AB $imoueranno, de $criueran-
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parents:
diff changeset
2722 no la circonferenza di vno cerchio, il cui mezo diametro $ar&agrave; AC. Per laqual co</I>
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parents:
diff changeset
2723 <marg><I>Per la</I> 28. <I>del terzo.</I></marg> <I>$a co'l centro C $ia de$critto il cerchio AE BF, i punti AB E</I>F <I>$aranno nel
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parents:
diff changeset
2724 la circonferenza del cerchio. ma e$$endo EF eguale ad AB, $ar&agrave; la circonfe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2725 renza EAF eguale alla circonferenza AFB. Onde tolta via la comune AF</I>
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parents:
diff changeset
2726 <pb n=22>
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parents:
diff changeset
2727 <I>$ar&agrave; la circonferenza EA eguale alla cir conferenza FB. Hor percioche l'ango-
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parents:
diff changeset
2728 lo mi$to CEA &egrave; eguale al mi$to CFB, &amp; HFB &egrave; maggiore di CFB, &amp;</I> <marg><I>Per la</I> <*>. <I>del printo.</I></marg>
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parents:
diff changeset
2729 <I>l'angolo HEA &egrave; minore di CEA; $ar&agrave; l'angolo HFB maggiore dell'angolo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2730 HEA. Da quali $e $aranno leuati via gli angoli HFG HEK eguali, $ar&agrave; l'an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2731 golo GFB maggiore dell'angolo KEA. Adunque la di$ce$a del pe$o po$to in
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parents:
diff changeset
2732 E $ar&agrave; meno obliqua della $alita del pe$o po$to in F. &amp; qu&amacr;tunque il pe$o po$to in E
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parents:
diff changeset
2733 de$cendendo, &amp; il pe$o po$to in F $alendo $i mouino per eguali circonferenze, nondi
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parents:
diff changeset
2734 meno percioche il pe$o po$to in E da que$to luogo di$cende piu dirittamente di quel
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parents:
diff changeset
2735 che il pe$o F a$c&etilde;de:pero la naturale po$$anza del pe$o po$to in E $uperer&agrave; la re$i$t&etilde;
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parents:
diff changeset
2736 za della violentia del pe$o F. Onde grauezza maggiore hauer&agrave; il pe$o posto in E,
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casties
parents:
diff changeset
2737 che il pe$o po$to in F. Adunque il pe$o po$to in E $i mouer&agrave; in gi&ugrave; &amp; il pe$o po$to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2738 in F in s&ugrave;, fin che la bilancia EF ritorni in AB, che bi$ognaua mo$trare.</I>
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parents:
diff changeset
2739 <p><I>La ragione di que$to effetto po$ta da Ari$totele qui $i puote vedere manife$ta. Percio-</I> <marg><I>Ragione de Aristotele.</I></marg>
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parents:
diff changeset
2740 <I>che $ia il punto N doue le linee CS EF $i tagliano in$ieme. &amp; percioche HE
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2741 &egrave; eguale ad HF; $ar&agrave; NE maggiore di NF. adunque la linea CS, che no-
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parents:
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2742 ma perpendicolo, diuider&agrave; la bilancia EF in parti di$uguali. concio$ia dunque, che
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parents:
diff changeset
2743 la parte della bilancia NE $ia maggiore della NF, &amp; quel che &egrave; di pi&ugrave; bi$o-
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parents:
diff changeset
2744 gni, che $ia portato in gi&ugrave;, la bilancia EF dalla parte di E $i mouer&agrave; in giu finche
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parents:
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2745 ritorni in AB.</I>
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parents:
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2746 <p><I>Oltre &agrave; cio da quelle co$e, che
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parents:
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2747 fin hora $ono $tate dette,
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parents:
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2748 $i puote affermare, la bilan
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casties
parents:
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2749 cia EF da quel $ito mo-
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parents:
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2750 uer$i piu velocemente in
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parents:
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2751 AB; d'onde la linea EF
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casties
parents:
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2752 allungata a dirittura per-
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casties
parents:
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2753 uenga nel centro del mon-
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casties
parents:
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2754 do. come $ia EFS vna
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casties
parents:
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2755 linea diritta. &amp; percioche
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parents:
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2756 CD CK $ono tra loro
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parents:
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2757 eguali. $e dunque col cen-
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casties
parents:
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2758 tro C, &amp; con lo $patio
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casties
parents:
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2759 CD $i de$criuer&agrave; il cerchio
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casties
parents:
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2760 DHM, $aranno i punti
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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2761 DH nella circonferenza
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casties
parents:
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2762 del cerchio. Ma perche la
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casties
parents:
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2763 CH &egrave; &agrave; piombo di EF,
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parents:
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2764 toccher&agrave; la EHS il cer-
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parents:
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2765 chio DHM nel punto
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casties
parents:
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2766 H. il pe$o dunque po$to in
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parents:
diff changeset
2767 H, ($i come di $opra hab
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diff changeset
2768 biamo prouato) $ar&agrave; piu</I>
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parents:
diff changeset
2769 <fig>
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parents:
diff changeset
2770 <foot><I>F</I> 2</foot>
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parents:
diff changeset
2771 <pb>
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casties
parents:
diff changeset
2772 <I>graue che in verun altro $ito del cerchio DHM. Adunque la grandezza fatta de'
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parents:
diff changeset
2773 pe$i EF, &amp; della bilancia EF, il cui centro della grauczza sta in H, in cote$to
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parents:
diff changeset
2774 $ito grauer&agrave; pi&ugrave;, che in qual $i voglia altro $ito del cerchio $i troui il punto H. Da
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parents:
diff changeset
2775 que$to $ito adunque $i mouera piu velocemente che da qualunque altro. &amp; $e lo H
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parents:
diff changeset
2776 $ar&agrave; piu da pre$$o al D
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parents:
diff changeset
2777 manco grauer&agrave;, &amp; me-
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parents:
diff changeset
2778 no $i mouer&agrave; da quel $ito;
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parents:
diff changeset
2779 peroche $empre&egrave; piu torta
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parents:
diff changeset
2780 la $ce$a, &amp; meno diritta.
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parents:
diff changeset
2781 La bilancia dunque EF
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casties
parents:
diff changeset
2782 $i mouer&agrave; pi&ugrave; velocemen-
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parents:
diff changeset
2783 te da que$to $ito, che da
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parents:
diff changeset
2784 altro $ito, &amp; $e piu dapre$
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parents:
diff changeset
2785 $o acco$tera&szlig;i ad AB,
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parents:
diff changeset
2786 d'indi $i mouer&agrave; meno poi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2787 quanto piu da lunge $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2788 di$tante il punto H dal
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2789 punto C $i mouer&agrave; pi&ugrave; ve
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2790 locemente, il che non $olo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2791 da Ari$totele nel principio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2792 delle que$tioni mecaniche,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2793 &amp; dai detti di $opra &egrave; ma
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2794 nife$to, ma ancora da quel
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parents:
diff changeset
2795 le co$e, che di $otto nella
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parents:
diff changeset
2796 $e$ta propo$itione $iamo
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parents:
diff changeset
2797 per dire, apparer&agrave; chiaro.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2798 La bilancia dunque EF
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parents:
diff changeset
2799 quanto pi&ugrave; $ar&agrave; lontana
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2800 dal $uo centro, $i mouer&agrave; anche piu velocemente.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2801 <fig>
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parents:
diff changeset
2802 <pb n=23>
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casties
parents:
diff changeset
2803 <p><I>Sia poi labilancia AB, il cui centro C stia $otto la bilancia, &amp; $iano in AB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2804 pe$i eguali, &amp; $ia mo$$a la bilancia in EF. Dico che il pe$o ha grauezza maggio-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2805 re in F, che in E. &amp;
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casties
parents:
diff changeset
2806 perci&ograve; la bilancia EF
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2807 e$$ere per mouer$i in gi&ugrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2808 dalla parte di F. $ia allun
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2809 gata la linea DC dall'una
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2810 parte, &amp; dall'altra fin
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2811 nel centro del mondo S,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2812 &amp; fin ad O, &amp; $ia tira
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2813 tala linea HS, alla qua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2814 le dai punti EF $iano ti
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2815 rate le linee GEK FL
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2816 egualmente di$tanti, &amp;
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casties
parents:
diff changeset
2817 $iano congiunte le CE
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casties
parents:
diff changeset
2818 CF: &amp; dal centro C c&otilde;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2819 lo $patio CE de$criua$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2820 il cerchio AEO BF.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2821 $i dimo$trer&agrave; $imilmente
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2822 i punti AB EF e$$e-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2823 re nella circonferenza del
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parents:
diff changeset
2824 cerchio, &amp; che la di$ce$a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2825 della bilancia EF in$ie-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2826 me co'pe$i $i f&agrave; diritta $e
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2827 condo la linea HS: &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2828 de ipe$i po$ti in EF $e-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2829 condo le linee GK FL
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2830 egualmente di$tanti da
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2831 HS. Et percioche l'ango
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2832 lo CFP &egrave; eguale all'an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2833 golo CEO $ar&agrave; l'ango-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2834 lo HFP maggiore del-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2835 l'angolo HEO. ma l'an</I> <marg><I>Per la</I> 29. <I>del primo.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2836 <I>golo HFL &egrave; eguale al-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2837 l'angolo HEG. Da qua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2838 li $e $aranno leuati via
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2839 gli angoli HFP HEO,</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2840 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2841 <I>$ar&agrave; l'angolo LFP minore dell' angolo GEO. Per laqual co$a la $ce$a del pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2842 po$to in F $ar&agrave; piu diritta della a$ce$a del pe$o po$to in E. Adunque la po$$anza
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2843 naturale del pe$o po$to in F $uperer&agrave; la re$i$tenza della violentia del pe$o po$to in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2844 E. &amp; percio hauer&agrave; maggior grauezza il pe$o di F, che il pe$o di E. Adunque
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2845 il pe$o di F $imouer &agrave; in gi&ugrave;, &amp; il pe$o di E $i mouer&agrave; in s&ugrave;.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2846 <pb>
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casties
parents:
diff changeset
2847 <p><marg><I>Ragione di Aristotele.</I></marg><I>La ragione di Ari$totele parimente qui &egrave; cbiara. Percioche $ia il punto N doue le
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2848 linee CO EF $i tagliano in$ieme. $ar&agrave; la NF maggiore della NE. &amp; perche
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2849 il perpendicolo CO, $e-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2850 condo lui, diuide in parti
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2851 di$uguali la bilancia, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2852 la parte maggiore &egrave; ver$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2853 F, cio&egrave; NF; la bilan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2854 cia EF $i mouer&agrave; in gi&ugrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2855 dalla parte di F, concio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2856 $ia che quel che &egrave; di piu
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2857 venga portato &agrave; ba$$o.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2858 <p><I>Similmente dalle co$e dette
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casties
parents:
diff changeset
2859 caueremo, che qu&amacr;to piu
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2860 la bilancia EF tenente
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2861 il centro $otto la bilancia,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2862 $ar&agrave; l&otilde;tana dal $ito AB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2863 $i mouer&agrave; piu velocemen
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diff changeset
2864 te, percioche il centro del
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diff changeset
2865 la grauezza H, quanto
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diff changeset
2866 piu &egrave; di$tante dal punto
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diff changeset
2867 D, tanto piu velocemen
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diff changeset
2868 te il pe$o compo$to de<*> pe
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parents:
diff changeset
2869 $i EF, &amp; della bilancia
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parents:
diff changeset
2870 EF $i mouer&agrave;, finche
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parents:
diff changeset
2871 l'angolo CHS diuenga
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parents:
diff changeset
2872 retto. &amp; dauantaggio $i
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parents:
diff changeset
2873 mouer&agrave; anche piu veloce
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parents:
diff changeset
2874 mente quanto la bilancia
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parents:
diff changeset
2875 $ar&agrave; piu lontana dal cen-
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parents:
diff changeset
2876 tro C.</I>
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parents:
diff changeset
2877 <p><I>Oltre &agrave; ci&ograve; ne piace dalle $ue
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parents:
diff changeset
2878 ragioni, &amp; fal$e pre$uppo
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parents:
diff changeset
2879 $te manife$tare, &amp; pro
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parents:
diff changeset
2880 durre gli effetti, &amp; i moti
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parents:
diff changeset
2881 gi&agrave; dichiarati della bilan
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parents:
diff changeset
2882 cia, affine che appaia qu&amacr;
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parents:
diff changeset
2883 ta $ia la efficacia della ve-
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parents:
diff changeset
2884 rit&agrave;, come quella, che dalle co$e fal$e ancora $i sforza di ri$plendere.</I>
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diff changeset
2885 <fig>
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parents:
diff changeset
2886 <p><I>Pongan$i le co$e iste$$e, cio&egrave; $iail cerchio AE BF, &amp; la bilancia AB, il cui cen-
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diff changeset
2887 tro C $ia $opra la bilancia, moua$i in EF. Dico che il pe$o po$to in E h&agrave; iui
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parents:
diff changeset
2888 grauezza maggiore, che il pe$o po$to in F; &amp; che la bil&amacr;cia EF ritorner&agrave; in AB</I>
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parents:
diff changeset
2889 <pb n=42>
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parents:
diff changeset
2890 <I>$iano tirate dai punti EF le linee EL FM &agrave; piombo di AB, le quali $aran-</I> <marg><I>Per la</I> 28. <I>d l primo.</I></marg>
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parents:
diff changeset
2891 <I>no tra loro egualmente di$tanti, &amp; $ia il punto N doue la AB, &amp; la EF $i
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parents:
diff changeset
2892 tagliano fra loro. Percioche dunque l'angolo FNM &egrave; eguale all'angolo ENL,</I> <marg><I>Per la</I> 15. <I>del primo.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2893 <I>&amp; l'angolo FMN ret
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parents:
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2894 to &egrave; eguale ad ELN
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parents:
diff changeset
2895 retto, &amp; il re$tante
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parents:
diff changeset
2896 NFM al re$tante</I> <marg><I>Per la</I> 29. <I>del primo.</I></marg>
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parents:
diff changeset
2897 <I>NEL &egrave; etiandio egua-
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parents:
diff changeset
2898 le; $ar&agrave; il triangolo NLE
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2899 $imile al triangolo NMF.</I> <marg><I>Per la</I> 4.<I>del $esto.</I></marg>
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parents:
diff changeset
2900 <I>Si come dunque &egrave; la NE
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parents:
diff changeset
2901 ver$o la EL, co$i NF</I> <marg><I>Per la</I> 16. <I>del quinto.</I></marg>
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parents:
diff changeset
2902 <I>ad FM; &amp; permut an-
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parents:
diff changeset
2903 do, $i come EN ad NF,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2904 co$i EL ad FM. Ma
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2905 e$$endo HE eguale ad
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parents:
diff changeset
2906 HF, $ar&agrave; EN mag-
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parents:
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2907 gior di NF. Per laqual
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parents:
diff changeset
2908 co$a anco EL $ar&agrave; mag</I>
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parents:
diff changeset
2909 <fig>
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parents:
diff changeset
2910 <I>giore <*>i FM. &amp; percioche mentre il pe$o po$to in E de$cende per la circonferen-
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parents:
diff changeset
2911 za EA, il pe$o po$to in F $ale per la circon$erenza FB eguale alla circonferen-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2912 za EA, &amp; la di$ce$a del pe$o po$to in E piglia (come e$$i dicono) di diretto EL:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2913 &amp; la $alita del pe$o po$to in F piglia di diretto FM, meno di diretto verr&agrave; a pi-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2914 gliare la $alita del pe$o po$to in F, che la di$ce$a del pe$o po$to in E. Dunque il pe
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parents:
diff changeset
2915 $o po$to in E haur&agrave; grauezza maggiore, che il pe$o po$to in F.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2916 <p><I>Sia allungata la linea CD dall una parte, &amp; dall'altra in OP, laquale tagli la linea
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parents:
diff changeset
2917 EF nel punto S. &amp; percioche (come dicono) quanto piu &egrave; lontano il pe$o dalla
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parents:
diff changeset
2918 linea della direttione OP, tanto $i fa piu graue; per&ograve; con que$to mezo ancora pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2919 uera$$i il pe$o po$to in E hauer grauezza maggiore del pe$o po$to in F. Siano dai
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2920 punti EF tirate le linee EQ FR a piombo di OP. Con $imile ragione mo$tre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2921 ra$$i, che il triangolo QES &egrave; $imile al triangolo RFS; &amp; che la linea EQ &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2922 maggiore di RF. &amp; co$i il pe$o po$to in E $ar&agrave; piu lontano dalla linea OP, che
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parents:
diff changeset
2923 il pe$o po$to in F; &amp; per ci&ograve; il pe$o po$to in E hauer&agrave; grauezza maggiore del pe
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2924 $o po$to in</I> F. <I>Dallequali co$e appare euidente il ritorno della bilancia E</I>F <I>in AB.</I>
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parents:
diff changeset
2925 <pb>
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parents:
diff changeset
2926 <p><I>Ma $e il centro della bilancia $ar&agrave; $otto la bilancia, allhora $i mo$trer&agrave; con gli i$te$$i me
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2927 zi, che il pe$o abba$$ato hauer&agrave; grauezza maggiore dall'alzato. $iano tirate dapun-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2928 ti EF le linee EL FM
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2929 a piombo di AB. $imil
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2930 mente$i prouer&agrave; EL e$
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parents:
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2931 $ere maggiore di FM; et
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2932 perci&ograve; la $ce$a del pe$o po
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parents:
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2933 sto in F prender&agrave; meno
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parents:
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2934 di dirittura, che la $alita
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2935 del pe$o po$to in E. On-
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parents:
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2936 de la re$i$tenza della vio-
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parents:
diff changeset
2937 lentia del pe$o po$to in E
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parents:
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2938 $uperer&agrave; la naturale incli-
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parents:
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2939 natione del pe$o po$to in
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parents:
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2940 F. Adunque il pe$o po$to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2941 in E $ar&agrave; piu graue del
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parents:
diff changeset
2942 pe$o posto in F.</I>
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parents:
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2943 <p><I>Sia all&umacr;gata etiandio la CD
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2944 dall'una parte &amp; l'altra</I>
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2945 <fig>
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parents:
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2946 <I>in OP, &amp; $iano tirate dai punti EF le linee EQ FR &agrave; piombo dilei. $i pro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2947 ver&agrave; con l'i$te$$o modo in tutto, che la linea EQ &egrave; maggiore di FR. &amp; percio il
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2948 pe$o po$to in E $ar&agrave; piu lontano dalla linea della dirittura OP, che il pe$o po$to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2949 in F. Adunque il pe$o po$to in E haur&agrave; grauezza maggiore del pe$o po$to in F.
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parents:
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2950 Dalle quali co$e $egue, che la bilancia EF $i moue in gi&ugrave; dalla parte di E.</I>
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parents:
diff changeset
2951 <p><I>Si che Aristotele propo$e que$te due que$tioni $olamente, &amp; la$ci&ograve; la terza, cio&egrave; quando
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parents:
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2952 il centro della bilancia $t&agrave; nella bilancia i$te$$a. Que$ta per&ograve; trala$ci&ograve; egli, co-
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parents:
diff changeset
2953 me nota, $i come egli $ole trala$ciare le co$e molto note. Imperoche &agrave; chi puote
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parents:
diff changeset
2954 far dubbio, che $e il pe$o $ar&agrave; $o$tentato nel centro della grauezza$ua, che non i$tia
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parents:
diff changeset
2955 fermo? Mapotrebbe for$e alcuno riprendere quelle co$e che per $ua $ententia hab-
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parents:
diff changeset
2956 biamo propo$to, affermando noi non hauere prodotto in mezo tutta la intera $enten
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parents:
diff changeset
2957 za $ua. Imperoche proponendo egli nella $econda parte della que$tione $econda.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2958 &ldquo;Perche la bilancia e$$endo posta la trutina di $otto, quando, portato il pe$o in giu, al
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parents:
diff changeset
2959 cuno lo rimoue, non a$cende, ma rimane?&rdquo; non afferma perci&ograve; la bilancia mouer$i in
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parents:
diff changeset
2960 gi&ugrave;, ma rimanere, il che pare $imilmente hauere nella vltima conclu$ione raccolto.
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parents:
diff changeset
2961 Ma que$to non $o larnente non ci $a contra, ma$e egli &egrave; ben' inte$o grandi$$imamen-
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parents:
diff changeset
2962 te aiuta.</I>
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parents:
diff changeset
2963 <p><I>Percioche $ia la bilancia AB egualmente di$tante dall'orizonte, il cui centro E $ia
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parents:
diff changeset
2964 $otto la bilancia. &amp; perche Ari$totele con$idera la bilancia come ella &egrave; in fatto, per&ograve;
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parents:
diff changeset
2965 egli &egrave; nece$$ario collocare la trutina, ouero qualche altra co$a $otto il centro E, co-
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parents:
diff changeset
2966 me EF, che in ogni modo $ar&agrave; trutina, per modo, che $o$tengail centro E. &amp; $ia
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parents:
diff changeset
2967 ECD il perpendicolo. &amp; accioche la bilancia AB $i moua da que$to $ito, dice</I>
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parents:
diff changeset
2968 <pb n=25>
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parents:
diff changeset
2969 <I>Ari$totele, ponga$i il pe$o in B, ilquale e$$endo graue mouer&agrave; la bilancia dalla par-
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parents:
diff changeset
2970 te B in gi&ugrave;, come in G, talche per l'impedimento non potr&agrave; egli piu mouer$i in
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parents:
diff changeset
2971 giu, ma non dice gia Ari$totele, che $i moua la bilancia in giu dalla parte di B fin
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parents:
diff changeset
2972 tanto che parer&agrave;, da
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parents:
diff changeset
2973 poi $i la$ci, come noi
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casties
parents:
diff changeset
2974 di cemmo<*>ma ordina
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parents:
diff changeset
2975 che $ia posto il pe$o
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parents:
diff changeset
2976 in B, il quale di $ua
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parents:
diff changeset
2977 natura $i mouera
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parents:
diff changeset
2978 $empre in gi&ugrave; finche
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parents:
diff changeset
2979 la bilancia $i appog-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2980 gi alla trutina, ouer&ograve;
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parents:
diff changeset
2981 a qualche altra co$a.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2982 &amp; quando il B $a-
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parents:
diff changeset
2983 r&agrave; nel G, la bilan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2984 cia $ar&agrave; in GH, nel
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casties
parents:
diff changeset
2985 qual $ite leuato via
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parents:
diff changeset
2986 il pe$o, rimarr&agrave;: per
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parents:
diff changeset
2987 e$$ere la maggior par
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2988 te della bilancia dal
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casties
parents:
diff changeset
2989 perpendicolo uer$o il</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2990 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2991 <I>G, che &egrave; DG, che DH. ne piu mouera$$i in giu, imperoche la bilancia $tar &agrave; $opra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2992 la trutina, ouero qualche altra co$a, che $o$tenga il centro della bilancia. peroche $e a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2993 cote$ta non $i appoggia$$e, verrebbe la bilancia &agrave; mouer$i, $econdo la $ua opinione,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2994 in gi&ugrave; dalla parte di G, concio$ia, che quello che &egrave; di piu, cio&egrave; DG debba e$$ere
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2995 per nece$$it&agrave; in giu portato.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2996 <p><I>Ma potrebbe dauantagio dire alcuno, $e in B $ar&agrave; collocato vn pe$o picciolo, $i mo-
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parents:
diff changeset
2997 uer&agrave; ben la bilancia in giu, ma non gia fin al G; nel qual $ito, $econdo Aristo-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2998 tele, leuato via il pe$o, deue remanere. ilche &egrave; manife$to per la e$perientia, inchi-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2999 nando$i la bil&atilde;cia pi&ugrave;, &amp; meno, quando in vna e$tremita della bilancia $olamente
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parents:
diff changeset
3000 vi &egrave; po$to il pe$o, che $ia &ograve; maggiore, &ograve; minore. ilche &egrave; veri$$imo allhora che il centro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3001 &egrave; collocato $opra la bilancia, ma non gi&agrave; $otto, ne in e$$a bilancia, come per gratia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3002 di e$empio.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3003 <pb>
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parents:
diff changeset
3004 <p><I>Sia la bilancia AB egualmente di$tante dall'orizonte, il cui centro C $ia $opra la bi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3005 lancia, &amp; il perpendicolo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3006 CD a piombo dell' ori-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3007 zonte, il quale da la par-
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parents:
diff changeset
3008 te D $ia allungato in H.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3009 Hor percioche con$idera
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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3010 ta la grauezza della bi-
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parents:
diff changeset
3011 lancia, $ar&agrave; il punto D
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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3012 il centro della grauezza
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parents:
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3013 della bilancia. $e dunque
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parents:
diff changeset
3014 vn piccolo pe$o $ar&agrave; po-
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parents:
diff changeset
3015 $to nel B, il cui centro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3016 della grauezza $ia nel p&utilde;
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parents:
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3017 to B; gia piu non $ar&agrave;
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parents:
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3018 il centro della grauezza
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parents:
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3019 D della magnitudine</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3020 <marg><I>Per la</I> 6. <I>del primo. di. drch. del le co$e cgual m&etilde;se pes&amacr;ti.</I></marg> <I>compo$ta della bilancia</I>
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parents:
diff changeset
3021 <fig>
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parents:
diff changeset
3022 <I>AB, &amp; del pe$o po$to in B, ma $ar&agrave; nella linea DB, come in K: per modo
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parents:
diff changeset
3023 che DE ad EB $ia come il pe$o po$to in B alla grauezza della bilancia AB.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3024 congiunga$i la CE. &amp; percioche il punto C &egrave; immobile, mentre la bilancia $i
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parents:
diff changeset
3025 moue, il punto E de$criuer&agrave; la circonferenza del cerchio EFG, il cui mezo dia-
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parents:
diff changeset
3026 metro &egrave; CE, &amp; il centro C. Ma perche CD $t&agrave; a piombo dell' orizonte, la li
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parents:
diff changeset
3027 nea CE non $ar&agrave; gia ella &agrave; piombo dell' orizonte. Per laqual co$a la grandez-
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parents:
diff changeset
3028 za composta di AB, &amp; del pe$o po$to in B non rimarr&agrave; in questo $ito; ma $i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3029 mouer&agrave; in giu $econdo il centro E della $ua grauezza per la circonferenza EFG,</I>
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parents:
diff changeset
3030 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>finche CE diuenti a piombo dell' orizonte, cio&egrave; finche la CE peruenga in CDF.
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parents:
diff changeset
3031 &amp; allhora la bilancia AB $ar&agrave; mo$$ain KL, nel qual $ito la bilancia rimarr&agrave;
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casties
parents:
diff changeset
3032 in$ieme co'l pe$o, ne d'auantaggio $i mouer&agrave; in gi&ugrave;. che $e in B $ar&agrave; po$to vn pe$o
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parents:
diff changeset
3033 piu graue, il centro'della grauezza di tutta la magnitudine $ar&agrave; piu dappre$$o al B,
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parents:
diff changeset
3034 come in M. &amp; allhora la bilancia $i mouer&agrave; in giu, finche la congiunta linea CM
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parents:
diff changeset
3035 peruenga nella linea CDH. Dal por$i dunque pe$o maggiore &ograve; minore in B, la
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casties
parents:
diff changeset
3036 bilancia $i inchiner&agrave; piu &ograve; meno. Da che $egue che il pe$o B de$criuer&agrave; $empre vna
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casties
parents:
diff changeset
3037 circonferenza minore della quarta parte d'un cerchio, per e$$ere l'angolo FCE $em
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casties
parents:
diff changeset
3038 pre acuto:ne il punto B peruenir&agrave; gia mai fin alla linea CH, percioche $empre il
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parents:
diff changeset
3039 centro della grauezza del pe$o, &amp; dalla bilancia in$ieme $ar&agrave; fra BD. tuttauia qu&amacr;
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casties
parents:
diff changeset
3040 to $ar&agrave; il pe$o po$to in B piu graue, de$criuer&agrave; anche circonferenza maggiore, ve-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3041 nendo$i per que$to il punto B ad acco$tare piu alla linea CH.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3042 <p><I>Mi habbia la bilancia AB il centro C nella i$te$$a bilancia, &amp; nel $uo mezo,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3043 $ar&agrave; il C centro ancora della grauezza della bilancia, dal quale $ia tirata la li-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3044 nea FCG a piombo di e$$a AB, &amp; dell' orizonte. Ponga$i dapoi in B qual
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3045 pe$o $i voglia; $ar&agrave; il centro di tutta la grauezza, come in E; $i fattamente che
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3046 la CE ver$o EB $ia come il pe$o po$to in B alla grauezza della bilancia. &amp; per</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3047 <pb n=26>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3048 <I>cioche la CE non &egrave; a piombo dell' orizonte, la bilancia AB, &amp; il pe$o po$to in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3049 B non rimaranno in que-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3050 $to $ito gia mai; ma $i mo-
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casties
parents:
diff changeset
3051 ueranno in giu dalla par-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3052 te di B, fin che CE $i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3053 $accia &agrave; piombo dell' ori-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3054 zonte; cio&egrave; fin che la bilan-
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casties
parents:
diff changeset
3055 cia AB peruenga in FG.
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casties
parents:
diff changeset
3056 Onde &egrave; chiaro, che cia$cun
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3057 pe$o po$to in B, $empre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3058 de$criue la quarta parte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3059 d'un cerchio.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3060 <fig>
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casties
parents:
diff changeset
3061 <p><I>Ma $ia il centro C $otto la bilancia AB, &amp; $ia DCE il perpendicolo. $imilmente
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3062 per e$$er il pe$o posto in B, $ar&agrave; il centro della grauezza della magnitudine compe
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3063 $ta di AB bilancia, &amp; del pe$o po$to in B nella linea DB, come in F; $i fattam&emacr;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3064 te che come DF $i ha ver$o FB co$i $ia il pe$o po$to in B al pe$o della bilan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3065 cia. congiunga$i CF. &amp;
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casties
parents:
diff changeset
3066 percioche CD &egrave; a piombo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3067 dell' orizonte, non $ar&agrave; gia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3068 la linea CF a piombo del
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3069 l'orizonte. Per laqual co$a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3070 la magnitudine compo$ta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3071 della bilancia AB, &amp; del
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3072 pe$o po$to in B in que$to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3073 $ito non $tar&agrave; mai ferma;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3074 ma in giu mouera$$i $e alcu
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3075 na co$a non la impedi$ce,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3076 finche CF peruenga in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3077 DCE, nel qual $ito la bi-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3078 lancia rimarr&agrave; in$ieme co'l</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3079 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3080 <I>pe$o. &amp; il punto B $ar&agrave; come in G, &amp; il punto A in H, &amp; la bilancia GH
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3081 non hauer&agrave; piu il centro di $otto, ma $opra e$$a. La qual co$a hauer&agrave; $empre, quan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3082 tunque $i ponga vn minimo pe$o in B. Auanti che dunque il B peruenga al G,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3083 egli &egrave; nece$$ario, che la bilancia incontri la trutina po$ta di $otto, ouero alcuna altra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3084 co$a, che $o$tenti il centro C, &amp; iui s'appoggi. Da que$to $egue, che il pe$o B $em
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3085 pre $i moue oltre la linea DK, &amp; de$criue $empre vna circonferenza maggiore del
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3086 la quarta parte del cerchio, per e$$ere l'angolo FCE $empre ottu$o, &amp; l'angolo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3087 DCF $empre acuto. &amp; quanto il pe$o posto in B $ar&agrave; piu leggiero, de$criuer&agrave; tut-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3088 tauia anche circonferenza maggiore. Imperoche quanto il pe$o po$to in G $ar&agrave; piu
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3089 leggiero, tanto piu il pe$o detto posto in G $i alzer&agrave;; &amp; la bilancia GA s'acco$te</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3090 <foot><I>G</I> 2</foot>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3091 <pb n=27>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3092 <p><I>Ma $ia il centro della bilancia AB $opra il C in F; &amp; $ia FC &agrave; piombo di AB,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3093 &amp; dell' orizonte: &amp; $e
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3094 la bilancia $ar&agrave; mo$$a in</I> <marg><I>Per la prima di questo.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3095 <I>DE, la linea CF $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3096 mo$$a in FG, la quale
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3097 per non e$$ere &agrave; piombo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3098 dell' orizonte, la bilancia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3099 DE $imouer&agrave; in giu dalla
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3100 parte di D, finche FG
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3101 ritorni in FC: &amp; allho
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3102 ra la bilancia DE $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3103 in AB, nel qual $ito an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3104 che rim<*>r&agrave;.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3105 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3106 <p><I>Che $e il centro F della bi-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3107 lancia $ar&agrave; $otto la bil&emacr;-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3108 cia, &amp; $iala bilancia mo$</I> <marg><I>Per la prima di questo.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3109 <I>$a in DE primier amen
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3110 te egli &egrave; manife$to che la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3111 bilancia rimarr&agrave; in AB:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3112 &amp; in DE mouera$$i in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3113 giu dalla parte di E, per
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3114 non e$$ere la linea FG
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3115 &agrave; piombo dell' orizonte.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3116 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3117 <I>r&agrave; piu pre$$o al $ito egualmente di$tante dall'orizonte. Le quali co$e tutte re$tano ma
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3118 ni$e$te da quelle che di $opra $ono $tate dette.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3119 <p><I>Prouate que$te co$e, egli &egrave; chia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3120 ro, che il centro della bilan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3121 cia &egrave; cagione de gli effetti di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3122 uer$i della bilancia. &amp; $i ve
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3123 de ancora che tutte le pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3124 po$itioni di Archimede del
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3125 le co$e, che egualmente pe$a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3126 no, a ci&ograve; pertinenti, in ogni
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3127 $ito $ono vere. cio&egrave;, $ia pur
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3128 la bilancia di$tante egualm&etilde;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3129 te dall'orizonte, ouero non,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3130 pur che il centro della bilan
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3131 cia $ia collocato in e$$a bil&amacr;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3132 cia, $i come egli la con$ide-</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3133 <fig>
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casties
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diff changeset
3134 <I>r&agrave;. &amp; quantunque la bilancia habbia difuguali le braccia, auerrd tutt auia l'i$te$$o, &amp;
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diff changeset
3135 $i dimo$trer&agrave; co'l modo i$te$$o in tutto, che il centro della bilancia collocato in diuer
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parents:
diff changeset
3136 $e maniere produrr&agrave; vari effetti.</I>
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parents:
diff changeset
3137 <p><I>Percioche $ia la bilancia
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parents:
diff changeset
3138 AB egualmente di$tan
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parents:
diff changeset
3139 te dall'orizonte; &amp; $iano
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parents:
diff changeset
3140 in AB pe$i di$uguali, il
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3141 centro della grauezza
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parents:
diff changeset
3142 dei quali $ia in C, &amp;
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parents:
diff changeset
3143 $ia attacata la bilancia
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parents:
diff changeset
3144 nell'i$te$$o punto di C,
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parents:
diff changeset
3145 &amp; moua$i la bilancia in</I>
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parents:
diff changeset
3146 <marg><I>Per la diffi ni ione del centro della grauezza.</I></marg> <I>DE; egli&egrave; manife$to,
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parents:
diff changeset
3147 che la bilancia rimarr&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3148 non $olamente in DE,
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parents:
diff changeset
3149 ma in qual $i voglia altre
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parents:
diff changeset
3150 $ito.</I>
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parents:
diff changeset
3151 <fig>
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parents:
diff changeset
3152 <p><I>Da que$te co$e co$i terminate, $e la bilancia fo$$e inarcata, ouero, che le braccia della bi
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parents:
diff changeset
3153 lancia forma$$ero vn'angolo, &amp; $i di$pone&szlig;e il centro diuer$amente, (ben che que-
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parents:
diff changeset
3154 $ta propriamente non $arebbe bilancia,) potremo nondimeno anche dimo$trare di lei
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parents:
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3155 vary effetti. Come $ia la bilancia ACB, il cui centro, d'intorno al quale $i volge,
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parents:
diff changeset
3156 $i a C, &amp; tiratala linea AB, $ia
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parents:
diff changeset
3157 l'arco ouer&ograve; l'angolo ACB $opra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3158 la linea AB; &amp; pongan$i in AB
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parents:
diff changeset
3159 icentri della grauezza de'pe$i, i quali
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parents:
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3160 rimangano in que$to $ito. Moua$i poi
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parents:
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3161 la bil&amacr;cia da que$to $ito, come in ECF.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3162 Dico che la bilancia ECF ritorner&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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3163 in ACB. Ritroui$i il centro della
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parents:
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3164 grauczza di tutta la magnitudine D,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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3165 &amp; $ia congiunta la CD. Hor percio</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3166 <marg><I>Per la prima di questo.</I></marg> <I>che i pe$i AB stanno fermi, lali-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3167 nea CD $ar&agrave; &agrave; piombo dell' orizon-</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3168 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3169 <I>ie. Quando dunque la bilancia $ar&agrave; in ECF, la linea CD $ar&agrave; come in CG;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3170 la quale per non e$$ere &agrave; piombo dell' orizonte, la bilancia ECF ritorner&agrave; in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3171 ACB. ilche parimente auenir &agrave;, $e il centro C $ar&agrave; me$$o $opra la bilancia, co-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3172 me in H.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3173 <p><I>Che $e l'arco, ouero l'angolo ACB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3174 $ar&agrave; $otto la linea AB, nel
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3175 modo i$te$$o mo$treremo, la bi-
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parents:
diff changeset
3176 lancia ECF, il cui centro $ia
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parents:
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3177 ouero in C, ouero in H, do-
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parents:
diff changeset
3178 uer$i mouere in giu dalla parte
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parents:
diff changeset
3179 di F.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3180 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3181 <pb n=28>
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parents:
diff changeset
3182 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3183 <p><I>Et $e l'angolo ACB fo$$e $oprala linea AB, &amp; il centro della bilancia H; &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3184 &amp; lalinea CH $o$tene$$e la bilancia; &amp; $imoue$$e la bilancia in EKF; la bilan
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3185 cia EKF ritorner&agrave; in ACB.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3186 <p><I>Ma $e il centro della bilancia $ar&agrave; D, moua$i in qualunque modo la bilancia, doue $i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3187 la$cier&agrave;, iui rimarr&agrave;.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3188 <p><I>Se poi il punto H $ar&agrave; $otto la linea AB; allhora la bilancia EKF $i mouer&agrave; in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3189 giu dalla parte di F.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3190 <p><I>Et con $imile ragione in tutto, $e l'ango-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3191 lo ACB $ar&agrave; $otto la linea AB;
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parents:
diff changeset
3192 &amp; $ia il centro della bilancia H, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3193 $ia la bilancia $o$tentata dalla linea
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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3194 CH; $e la bilancia mouera&szlig;i da que$to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3195 $ito, $i mouer&agrave; in giu dalla parte del pe
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parents:
diff changeset
3196 $o pi&ugrave; ba$$o. &amp; $e il centro della bilan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3197 cia $ia D; rimarr&agrave; doue $i la$cier&agrave;. che
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parents:
diff changeset
3198 $e $ar&agrave; in K; &amp; da cotale $ito $i mo
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parents:
diff changeset
3199 uer&agrave;, ritorner&agrave; ad ogni modo nello i$te$
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parents:
diff changeset
3200 $o. Le quali co$e tutte da quel che in</I>
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parents:
diff changeset
3201 <fig>
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parents:
diff changeset
3202 <I>principio dicemmo $ono mani$este. $imilmente $e il centro della bilancia $ar&agrave; po$to
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parents:
diff changeset
3203 in vno della bracia della bilancia, &ograve; dentro, &ograve; $uori, &ograve; in qual $i voglia modo trouere
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parents:
diff changeset
3204 mo le co$e i$te$$e.</I>
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parents:
diff changeset
3205 <p>In que$to luogo egli conuiene auertire, il che potcua$i anco fare di $opra &agrave; carte cin
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parents:
diff changeset
3206 que pre$$o la fine della $econda faccia oue &egrave; $critto. oltre &agrave; ci&ograve; po$siamo con$ide-
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parents:
diff changeset
3207 rare le co$e che $eguono in tutto al modo i$te$$o. Che que$to autore &egrave; $tato il
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parents:
diff changeset
3208 primo &agrave; con$iderare e$qui$itamente la bilancia, &amp; intenderla dalla natura, &amp; dal
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parents:
diff changeset
3209 vero e$$er $uo; pero che egli il primiero di tutti ha manife$tato chia ramente il mo
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parents:
diff changeset
3210 do del trattarla, &amp; in$egnarla, con proporre tre centri da e$$ere con$iderati in que
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parents:
diff changeset
3211 $ta $peculatione; l'uno &egrave; il centro del mondo, l'altro il centro della bilancia, &amp; il
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parents:
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3212 terzo il centro della grauezza della bilancia, che in e$$a era vn na$co$to $ecreto di
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3213 natura. Senza que$ti tre centri, chiara co$a &egrave;, che non $i puote ve nire in cono$ci-
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parents:
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3214 mento per$etto, ne dimo$trare gli effetti varij della bilancia, i quali na$cono dalla
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parents:
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3215 diuer$it&agrave; del collo care il centro della bilancia in tre modi, cio&egrave; quando il
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parents:
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3216 centro della bilancia $ta $opra il centro della grauezza di e$$a, ouero quando &egrave;
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parents:
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3217 di $otto, o pure allhorche il centro della bilancia &egrave; nell'i$te$$o centro della gra-
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parents:
diff changeset
3218 uezza di lei; $i come l'autore in$egna nella tre precedenti dimo$trationi, cio&egrave;
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parents:
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3219 nella $ec&otilde;da, nella terza, &amp; nella quarta propo$itione: peroche nella $econda mo-
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parents:
diff changeset
3220 $tra quando la bilancia torna $empre egualmente di$tante dall'orizonte; nella ter-
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parents:
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3221 za quando non $olo non ritorna, ma $i moue al contrario; nella quarta, che
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parents:
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3222 e$$endo la bilancia $o$tenuta nel $uo centro dalla grauezza $ta ferma douunque el
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3223 la $i troua, il quale effetto in particolare non &egrave; piu $tato tocco, ne veduto, ne man
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diff changeset
3224 co da niuno manife$tato, fuor che dall'autore: anzi fin hora tenuto fal$o, &amp; impo$
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parents:
diff changeset
3225 $ibile da tutti gli prede ce$$ori no$tri; i quali con molte ragioni $i $ono sforzati di
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parents:
diff changeset
3226 prouare non $olamente il contrario, ma hanno etiandio affermato per certo, che
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parents:
diff changeset
3227 la $per&iacute;enza mo$tra la bilancia non dimorare gia mai ferma $e non quando ella &egrave;
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diff changeset
3228 egualmente di$tante dall'oritonte. Laqual co$a in tutto &egrave; contraria alla ragione
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parents:
diff changeset
3229 prima, per e$$ere la dimo$tratione della $udetta quarta propo$itione tanto chiara,
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parents:
diff changeset
3230 facile, &amp; vera, che non s&ograve;, come $e le po$$a in modo alcuno contradire: &amp; poial-
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diff changeset
3231 l'e$perienza concio$ia che l'autore habbia fatto $ottili$simamente lauorare bilan-
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parents:
diff changeset
3232 cie giu$te a po$ta per chiarire que$ta verit&agrave;, vna delle quali h&ograve; io veduto in mano
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diff changeset
3233 dell'Illu$tre Signor Gio. Vicenzo Pinello, mandatagli dall'i$te$$o autore, la quale
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parents:
diff changeset
3234 per e$$ere $o$tenuta nel centro della $u a grauezza, mo$$a douunque $i vuole, &amp; poi
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parents:
diff changeset
3235 la$ciata, $t&agrave; ferma in ogni $ito doue ella vien la$ciata. Ben &egrave; egli vero, che non bi
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parents:
diff changeset
3236 $ogna, nel fare cote$ta e$perienza, correr co$i a furia, per e$$ere co$a oltra modo
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parents:
diff changeset
3237 difficile, come dice l'&aacute;utore di $opra, il fare vna bilancia, la quale $ia nel mezo del
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parents:
diff changeset
3238 le $ue braccia $o$tenuta &agrave; punto, &amp; nel centro proprio della $ua grauezza. Per la
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parents:
diff changeset
3239 qual co$a egli &egrave; da por m&etilde;te, che qual'hora alcuno $i mette$$e &agrave; far cotale e$perien
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parents:
diff changeset
3240 ra, &amp; non gli riu$ci$$e, non perci&ograve; $i deue $gomentare, anzi dica pur fermamente
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parents:
diff changeset
3241 di non hauer bene operato, &amp; vn'altra volta ritorni &agrave; farne la $perienza, fin chela
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parents:
diff changeset
3242 bilancia $ia giu$ta, &amp; eguale, &amp; venga $o$tenuta &agrave; punto nel centro della grauez-
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parents:
diff changeset
3243 za $ua. Et benche da altri $iano $tate to cche le altre due predette $peculationi, cio&egrave;
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parents:
diff changeset
3244 quando la bilancia ritorna $empre egualmente di$tante dall'orizonte, &amp; quando
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parents:
diff changeset
3245 $i moue al contrario di que$to $ito, tuttauia non $i &egrave; piu inte$a que$ta verit&agrave; gia
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parents:
diff changeset
3246 mai apertamente, $e non dall'autore no$tro; peroche gli altri non hanno co'l $en-
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parents:
diff changeset
3247 no penetrato in ci&ograve; tanto auanti, che habbiano $aputo con di$tintione con$idera
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parents:
diff changeset
3248 re il centro della bila ncia in tre modi, come h&ograve; narrato. Che $e hanno pur diui$a
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parents:
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3249 to qualche co$a d'intorno &agrave; que$to, l'hanno fatto confu$i$simamente, &amp; con ma
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parents:
diff changeset
3250 le dimo$trationi, dalle quali non $i puote cauare ferma c&otilde;chiufione, &amp; chiara. Que
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parents:
diff changeset
3251 <*> predece$$ori no$tri han$i da intendere i moderni $crittori di cotal materia alle-
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parents:
diff changeset
3252 gati in diuer$i luoghi dall'autore, fra quali Giordano, che $cri$$e de'pe$i f&ugrave; riputa-
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diff changeset
3253 <pb n=29>
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parents:
diff changeset
3254 to a$$ai, &amp; $in qui &egrave; $tato $eguito molto nella $ua dottrina. Hor l'autore no$tro h&agrave;
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parents:
diff changeset
3255 procurato con ogni $tudi o di caminare per la via de' buoni Greci antichi,
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parents:
diff changeset
3256 mae$tri delle $cienze, &amp; in particolare di Archimede Sira cu$ano prencipe delle ma
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parents:
diff changeset
3257 thematiche famo $i$simo, &amp; di Pappo Ale$$andrino, come egli dice, leggendogli
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parents:
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3258 nella $ua propria fauella, non tradotti; peroche il piu delle volte $ono co$i mal
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parents:
diff changeset
3259 trattati, che &agrave; gran pen a'$i puote trarre da loro frutto veruno. &amp; affine che que$ta
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parents:
diff changeset
3260 noua opinion $ua, dimo$trata &agrave; pien o nella predetta quarta propo$itione, re$ti to-
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parents:
diff changeset
3261 talmente chiara, non $i &egrave; gia cont&etilde;tato egli d'hauerla dimo$trata con viue ragioni,
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parents:
diff changeset
3262 &amp; certe $olamente, ma come buon filo$ofo, procedente con via di reale dottrina,
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parents:
diff changeset
3263 &amp; di fon data $cienza, (imitando Ari$totele, ilqual ne' principii de $uoi libri, inue-
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parents:
diff changeset
3264 $tigando dottrina migliore, h&agrave; datto contra la opinione de gli antichi, $oluendo
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parents:
diff changeset
3265 le ragioni addotte da loro:) h&agrave; ben voluto, e$$endo la verit&agrave; vna $ola, proporre le
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parents:
diff changeset
3266 opinioni de'$uoi predece$$ori, &amp; e$aminare le loro ragioni, lequali $embrano pro
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parents:
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3267 uar il contrario, &amp; $oluerle, la loro fallenza dimo$tr&atilde;do co'l pre$ente di$cor$o, che
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parents:
diff changeset
3268 incomincia, come &egrave; detto &agrave; carte cinque nella faccia $econda, &amp; qui fini$ce ilqua
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parents:
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3269 le di$cor$o $eruir&agrave; in que$ta materia, $econdo che $i $uole dire per la opinione de
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parents:
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3270 gli antichi. Et percio che egli contiene co$e di alti$sima $peculatione, ma$simamen-
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parents:
diff changeset
3271 te d'intorno al con$iderare doue $ia piu graue vn pe$o $olo po$to in vno braccio
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parents:
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3272 della bilancia, bi$ogna in ogni modo, per bene intendere, leggerlo, &amp; i$tudiarlo
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parents:
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3273 con accurati$sima diligenza. Ma per certo l'autore &egrave; $tato non $olo il primo &agrave; tro
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parents:
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3274 uare que$ta verit&agrave;, ma il primo etiandio a dim o$trare in qual maniera $ia me$tieri
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parents:
diff changeset
3275 con$iderare, &amp; $peculare interamente la pre$ente materia tutta. Con laquale $p ecu-
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parents:
diff changeset
3276 latione proua di nouo, &amp; confermai varij effetti, &amp; accidenti della bilancia gi&agrave; di
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parents:
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3277 mo$trati nelle pro$sime tre propo$itioni; mo$trando ancora, come $in qui cote$te
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parents:
diff changeset
3278 co$e $iano da gli altri $tate malamente con$iderate, &amp; con principij fal$i. Anzi di
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parents:
diff changeset
3279 piu per confermatione della verit&agrave; $oggiunge, che que$ti tali non hanno $aputo fa
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parents:
diff changeset
3280 re le loro demo$trationi; poi che co'l proprio modo di $peculare v$ato da loro,
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parents:
diff changeset
3281 &amp; con le loro mede$ime ragioni proua la $ua intentione, &amp; $entenza e$$ere veri$si
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parents:
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3282 ma, appoggiando $i alla dottrina di Ari$totele $empre, &amp; facendo toccar con ma-
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parents:
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3283 no, che egli con e$$o lui &egrave; d'accordo nelle que$tioni mechaniche. In trattando
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parents:
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3284 que$ta materia moue l'autore alcuni dubbi molto belli, &amp; curio$i, &amp; poi chiara-
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parents:
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3285 ment e gli $olue. In vltimo, accioche non manca$$e nulla al compiuto cono$cimen
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parents:
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3286 to di que$to $oggetto, egli h&agrave; trattato delle bilancie, che hanno le braccia di$ugua
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parents:
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3287 li, &amp; di quelle che hanno le dette braccia piegate, &amp; torte. In $omma $i pu&ograve; ben
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parents:
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3288 affermare, che in cote$to di$cor$o $iano compre$e tutte quelle co$e, che po$$ono e$
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parents:
diff changeset
3289 $ere diui$ate d'intorno &agrave; materia tale. Le quali $ono di belli$s ima &amp; $ottili$sima $pe
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parents:
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3290 culatione, &amp; &agrave; chiunque $i diletta, &amp; attende &agrave; que$ti no bili $tudi nece$$arij $sime,
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parents:
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3291 &amp; da e$$ere, come h&ograve; ricordato piu d'una volta, con molta attentione vedute, &amp;
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parents:
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3292 con$iderate.
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parents:
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3293 <p>Doue $i legge que$to vocabolo latino Equilibrio, intenda$i per eguale contrape$o,
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parents:
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3294 cio &egrave; che pe$a tanto da vna banda, quanto dallaltra in pari lance, &ograve; libra, &ograve; bilancia
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parents:
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3295 che $i dica.
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parents:
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3296 <p><I>Librar congiu$te lance.</I>
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parents:
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3297 <p>Di$$e il Petrarcha.
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parents:
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3298 <foot><I>H</I></foot>
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parents:
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3299 <pb n=38>
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parents:
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3300 <p><I>FC $ono eguali, $imilmente i pe$i FC pe$eranno egualmente, ma i pe$i FGC ap-
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parents:
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3301 piccati nella leua EBA, il cui $o$tegno &egrave; in B non pe$eranno egualmente; ma in-
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parents:
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3302 chineranno in giu$o dalla parte di A. Ponga$i dunque in D tanta forza, che i
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parents:
diff changeset
3303 pe$i FGC pe$ino egualmente; $ar&agrave; la po$$anza in D eguale al pe$o G; peroche</I>
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3304 <fig>
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diff changeset
3305 <I>i pe$i FG pe$ano egualmente, &amp; la po$$anza in D niente altro deue fare, che
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3306 $o$tenere il pe$o G che non di$cenda. &amp; percioche i pe$i FGC, &amp; la po$$anza
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3307 in D pe$ano egualmente, leuati via dunque i pe$i FG, i quali pe$ano egualmente,
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3308 i re$tanti pe$eranno egualmente, cio&egrave; la po$$anza in D co'l pe$o C, cio&egrave; la po$$an
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3309 za in D $o$terr&agrave; il pe$o C, talche la leua AB stia come prima. &amp; per e$$ere la
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diff changeset
3310 po$$anza in D eguale al pe$o G, &amp; il pe$o C eguale al pe$o, hauer&agrave; la po$$an
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diff changeset
3311 zaposta in D la proportione mede$ima al pe$o C, che EB, cio&egrave; AB &agrave; BD.
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diff changeset
3312 che bi$ognaua mostrare.</I>
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diff changeset
3313 <HEAD>COROLLARIO I.</HEAD>
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3314 <p>Da que$to &egrave; chiaro ancora, come prima, che $e $ar&agrave; po$to il pe-
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diff changeset
3315 $o pi&ugrave; vicino al $o$tegno B, come in H, il pe$o douer$i $o-
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diff changeset
3316 $tenere da forza minore.
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diff changeset
3317 <p><I>Percioche HB ha proportione minore &agrave; BD, che AB &agrave; BD. &amp; quanto pi&ugrave;</I> <marg><I>Per la</I> 8. <I>del quinto.</I></marg>
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diff changeset
3318 <I>da vicino $ar&agrave; al $o$tegno, $empre anco minore forza vi $i ricercher&agrave;.</I>
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diff changeset
3319 <HEAD>COROLLARIO II.</HEAD>
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diff changeset
3320 <p>Egli &egrave; parimente manife$to, che la po$$anza in D &egrave; $empre
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3321 maggiore del pe$o C.
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diff changeset
3322 <p><I>Perche $e tra AB $i piglia qual $i voglia punto, come D, $empre AB $ar&agrave; mag
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3323 giore di BD.</I>
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diff changeset
3324 <p><I>El &egrave; da auertire, che que$te dimo$trationi lequali habbiamo prodotte in mezo, $i po$$o-
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3325 no &agrave; tutte que$te co$e commodamente adattare non $olamente e$$endo le leue egual-
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3326 mente distanti dall'orizonte, ma anche inchinate le dette leue all'orizonte. ilche &egrave;
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3327 chiaro da quel che nella bilancia $i &egrave; diui$ato.</I>
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3328 <foot>K 2</foot>
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3329 <pb>
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3330 <HEAD>PROPOSITIONE IIII.</HEAD>
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3331 <p>Se la po$$anza mouer&agrave; il pe$o appiccato nella leua, $ar&agrave; lo $patio
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3332 della po$$anza mo$$a allo $patio del pe$o mo$$o, come la di$tan
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3333 za dal $o$tegno alla po$$anza, alla di$tanza dall'i$te$$o $o$tegno
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3334 fin allo appiccamento del pe$o.
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3335 <p><I>Sia la leua AB, il cui $o$tegno C, &amp; $ia il pe$o D attaccato al punto B, &amp; $ia
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3336 la po$$anza in A mouente il pe$o D conlaleua AB. Dico lo $patio della po$-
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3337 $anza in A allo $patio del pe$o e$$ere co$i come CA &agrave; CB. Moua$i la leua
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3338 AB, &amp; affine che il pe$o D $i moua in s&ugrave;, bi$ogna che B $i moua in s&ugrave;, &amp; A in
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3339 gi&ugrave;. &amp; percioche C &egrave; punto immobile; per&ograve; mentre A, &amp; B $i mouono, de-
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3340 $criueranno circonferenze di cerchi. Moua$i dunque AB in EF; $aranno AEBF
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3341 circonferenze di cerchi, i me-
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3342 zi diametri de' quali $ono CA
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3343 CB. compi$ca$i tutta la cir-
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3344 conferenza AGE, &amp; tut-
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3345 ta la BHF, &amp; $iano KH
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3346 i punti doue AB, &amp; EF ta-
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3347 gliano il cerchio BHF. Hor
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3348 percioche l'angolo BCF &egrave;</I>
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3349 <marg><I>Per la</I> 15. <I>del primo.</I></marg> <I>eguale all'ango<*> HCK, $a-
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3350 r&agrave; la circonferenza KH egua</I>
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3351 <marg><I>Per la</I> 26. <I>del terzo.</I></marg> <I>le alla circonferenza BF, &amp;
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3352 concio$ia, che le circonferen-
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3353 ze AEKH $iano $otto l'i-
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3354 $te$$o angolo ACE, &amp; la
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3355 circonferenza AE &agrave; tutta
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3356 la circonferenza AGE $ia
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3357 come l'angolo ACE &agrave; quat
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3358 tro retti, &amp; come l'i$te$$o an-
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3359 golo HCK &agrave; quattro retti,
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3360 co$i anche &egrave; la circonferenza
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3361 HK &agrave; tutta la circonferentia
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3362 HBK, $ar&agrave; la circonferentia</I>
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3363 <fig>
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3364 <I>AE &agrave; tutta la circonferentia AGE, come la circonferentia KH &agrave; tutta la</I>
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3365 <marg><I>Per la</I> 16. <I>del</I> 15.</marg> <I>KFH. &amp; permutando come la circonferentia AE alla circonferenza KH, cio&egrave;
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3366 BF, co$i tutta la circonferenza AGE &agrave; tutta la circonferenza BHF; ma tut-</I>
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3367 <marg><I>Per la</I> 23. <I>del</I> 8. <I>di Pap po.</I></marg> <I>ta la circonferenza AGE co$i $i ha &agrave; tutta la BHF, come il diametro del cer-
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3368 chio AEG al diametro del cerchio BHF. Come dunque la circonferenza AE</I>
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3369 <pb n=39>
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parents:
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3370 <I>ver$o la circonferenza BF, co$i &egrave; il diametro del cerchio AGE al diametro del</I> <marg><I>Per la</I> 11. <I>del quinto.</I></marg>
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parents:
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3371 <I>cerchio BHF: ma come il diametro al diametro, co$i &egrave; anche il mezo diametro al
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parents:
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3372 mezo diametro, cio&egrave; CA &agrave; CB. Per laqual co$a come la circonferenza AE
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3373 alla circonferenza BF, co$i CA &agrave; CB: ma la circonferenza AE &egrave; lo
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diff changeset
3374 $patio della po$$anza mo$$a, &amp; la circonferenza BF &egrave; eguale allo $patio di D pe-
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parents:
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3375 $o mo$$o, peroche lo $patio del mouimento del pe$o D $empre &egrave; eguale allo $patio
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parents:
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3376 del mouimento del punto B, per e$$ere attaccato in B. Lo $patio dunque della po$
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parents:
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3377 $anza mo$$a allo $patio del pe$o mo$$o &egrave; come CA &agrave; CB; cio&egrave; come la di$tan-
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3378 za dal $o$tegno alla po$$anza, alla distanza dall'i$te$$o all'appiccamento del pe$o.
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3379 che bi$ognaua mo$trare.</I>
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3380 <p><I>Ma $ia la leua AB, il cui $o$tegno B, &amp; la po$$anza mouente in A, &amp; il pe$o
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3381 in C. Dico lo $patio della po$$anza mo$$a allo $patio del pe$o tra$portato co$i e$-
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parents:
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3382 $ere, come BA &agrave; BC.
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parents:
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3383 Moua$i la leua, &amp; accioche
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3384 il pe$o $ia alzato in s&ugrave;, egli
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3385 &egrave; nece$$ario, che anche i pun
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3386 ti CA $imouano in s&ugrave;.
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3387 Moua$i dunque A in s&ugrave;
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3388 fin'in D; &amp; $ia il mouimen
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3389 to della leua BD. mo$tre-
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3390 remo nel modo i$te$$o, come
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3391 prima &egrave; detto, che i punti
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diff changeset
3392 CA de$criuono circonferen
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3393 ze di cerchi, i cui mezi dia-
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3394 metri $ono BA BC. &amp; di-
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diff changeset
3395 mo$treremo $imilmente co$i
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3396 e$$ere AD &agrave; CE, come il
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diff changeset
3397 mezo diametro AB al me-
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diff changeset
3398 zo diametro BC.</I>
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3399 <p><I>Et per la ragione i$te$$a, $e la
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diff changeset
3400 po$$anza fo$$e in C, &amp; il
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diff changeset
3401 pe$o in A $i prouer&agrave; co$i
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3402 e$$ere CE ver$o AD, co-</I>
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diff changeset
3403 <fig>
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diff changeset
3404 <I>me BC &agrave; BA, cio&egrave; la di$tanza dal $o$tegno alla po$$anza; alla di$tanza dal-
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diff changeset
3405 l'iste$$o allo attaccamento del pe$o. che bi$ognaua mo$trare.</I>
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diff changeset
3406 <HEAD>COROLLARIO.</HEAD>
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diff changeset
3407 <p>Da que$te co$e &egrave; manife$to, che maggiore proportione ha lo $pa
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diff changeset
3408 tio della po$$anza, che moue allo $patio del pe$o mo$$o, che il
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diff changeset
3409 pe$o alla mede$ima po$$anza.
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diff changeset
3410 <p><I>Percioche lo $patio della po$$anza allo $patio del pe$o ha la mede$ima proportione,
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diff changeset
3411 che il pe$o alla po$$anza, che $o$liene il detto pe$o. Ma la po$$anza, che $ostie-
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diff changeset
3412 ne &egrave; minore della po$$anza che moue, per&ograve; il pe$o haur&agrave; proportione minore alla
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diff changeset
3413 po$$anza che lo moue, che alla po$$anza, che lo $ostiene. Lo $patio dunque della</I>
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diff changeset
3414 <marg><I>Per la</I> 8. <I>del quinto.</I></marg> <I>po$$anza che moue allo $patio del pe$o haur &agrave; proportione maggiore, che il pe$o al-
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diff changeset
3415 l'i$le$$a po$$anza.</I>
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diff changeset
3416 <HEAD>PROPOSITIONE V.</HEAD>
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diff changeset
3417 <p>La po$$anza che in qual $i voglia modo $o$tenga il pe$o con la le-
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3418 ua hauer&agrave; la proportione mede$ima ad e$$o pe$o, che la di$tan
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3419 za frapo$ta dal $o$tegno al punto, doue dal centro della gra-
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diff changeset
3420 uezza del pe$o tirata vna linea &agrave; piombo all'orizonte tagli la
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diff changeset
3421 leua, alla di$tanza che &egrave; fra il $o$tegno, &amp; la po$$anza.
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3422 <p><I>Sia la leua AB egualmente di$tante dall'orizonte, col $uo $o$tegno N. $ia dopo il pe
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3423 $o AC, il cui centro della grauezza $ia D, ilquale $ia prima $otto la leua: ma
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3424 il pe$o $ia appiccato &agrave; i punti AO. &amp; dal punto D $ia tirata la linea DE &agrave;
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diff changeset
3425 piomho dell' orizonte, &amp; di AB. Che $e vi $aranno altre leue ancora AF AG,
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parents:
diff changeset
3426 i cui $o-
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parents:
diff changeset
3427 stegni,
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parents:
diff changeset
3428 $iano H
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parents:
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3429 K, &amp; il
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parents:
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3430 pe$o A
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3431 C $ia ap
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3432 piccato
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parents:
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3433 nella le-
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parents:
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3434 ua AG
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parents:
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3435 ne i pun
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parents:
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3436 ti AQ,
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parents:
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3437 &amp; nella
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parents:
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3438 leua A
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parents:
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3439 F ne' p&utilde;
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parents:
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3440 ti AP:
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parents:
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3441 &amp; la li-
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parents:
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3442 nea DE
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parents:
diff changeset
3443 allunga-</I>
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parents:
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3444 <fig>
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parents:
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3445 <I>ta tagli AF in L, &amp; AC in M. Dico che la po$$anza in F $o$tenente il pe$o AC
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3446 ha quella proportione ad e$$o pe$o, che ha KL &agrave; KF; &amp; la po$$anza in D ha quella
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3447 proportione al pe$o, che ha NE ad NB; &amp; la po$$anza in G al pe$o quella, che ha
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3448 HM ad HG. Hor percioche DL $t&agrave; &agrave; piombo dell' orizonte, il pe$o AC venga ap-</I>
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3449 <pb n=40>
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parents:
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3450 <I>piccato doue $i voglia nella linea DL, rimarr&agrave; nel modo i$te$$o che $i troua. Per la-
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parents:
diff changeset
3451 qual co$a $e nella leua AB $i $cioglieranno gli appiccamenti, che $ono ad AO, il
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parents:
diff changeset
3452 pe$o AC appiccato in E rimarr &agrave; nell'i$te$$o modo, come hora rimane, cio&egrave; leuato via
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3453 il punto A, &amp; la linea QO, nell'i$te$$o modo il pe$o appiccato in E rimarr&agrave;, come
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parents:
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3454 era $o$tenuto da punti i$te$$i AO, come $i proua per lo commentario di Federico
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parents:
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3455 Commandino nella $esta propo$itione di Archimede della quadratura della parabo
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parents:
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3456 la, &amp; dalla prima di que$to della bilancia. Co$i percio che il pe$o AC ha $empre la
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parents:
diff changeset
3457 i$te$$a di$po$itione ver$o la bilancia, $ia pur in AO $ostentato, ouero pendente dal
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parents:
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3458 punto E; la po$$anza mede$ima in B $o$tenter&agrave; il pe$o i$te$$o AC pendente, ouero
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parents:
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3459 da E, ouero da AO. ma la po$$anza in B $o$tenente il pe$o AC appiccato in E co$i
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parents:
diff changeset
3460 $i h&agrave; ad e$$o pe$o, come NE ad NB; La po$$anza dunque in B $o$tenente il pe$o
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parents:
diff changeset
3461 AC da punti AO pendente $ar&agrave; co$i ad e$$o pe$o, come NE ad NB. Non altra-</I> <marg><I>Per la prima di questo.</I></marg>
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parents:
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3462 <I>mente $i mo$trer&agrave;, che il pe$o AC pendente dal punto L rimane, come $e $o$$e $oste
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parents:
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3463 nuto da punti AP; &amp; la po$$anza in F ad e$$o pe$o e$$ere co$i come</I> KL <I>&agrave; KF. Ma
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3464 nella leua AG il pe$o AC appiccato in M co$i rimanere, come egli &egrave; $o$tenuto da
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3465 punti AQ; &amp; la po$$anza di G co$i e$$ere al pe$o AC, come HM ad HG, cio&egrave; co-
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parents:
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3466 me la di$tanza dal $o$tegno al punto, doue la linea tirata &agrave; piombo dell' orizonte
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parents:
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3467 dal centro della grauezza del pe$o taglia la leua, alla di$tanza dal $o$tegno alla po$-
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parents:
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3468 $anza. che bi$ognaua mo$trare.</I>
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3469 <p><I>Che $e FBG $o$$ero i $o$tegni delle leue, &amp; le po$$anze fo$$ero in KNH $o$tenenti il pe
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parents:
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3470 $o, con $imile modo $i mo$trer&agrave; la po$$anza in H, co$i e$$ere al pe$o, come GM &agrave; GH,
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parents:
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3471 et la po$s&amacr;za&imacr; N al pe$o, come BE &agrave; BN, et la po$s&amacr;za &imacr; K al pe$o come FL ad FK.</I>
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3472 <p><I>Et $e le leue AB AF AG haue$$ero i $o$legni in A, &amp; il pe$o fo$$e NO; poi dal
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3473 centro D del
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parents:
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3474 la $ua gra-
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parents:
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3475 uezza fo$$e
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parents:
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3476 tirata la li-
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parents:
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3477 nea DME
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parents:
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3478 L &agrave; piombo
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3479 di AB, &amp;
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diff changeset
3480 dell' orizon
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diff changeset
3481 te, &amp; fo$$e-
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diff changeset
3482 ro le po$$an
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diff changeset
3483 ze in FB
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diff changeset
3484 G; $imilm&etilde;
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diff changeset
3485 re mo$tre-
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diff changeset
3486 ra$$i la po$
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diff changeset
3487 $anza di G
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diff changeset
3488 $o$tenente
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diff changeset
3489 il pe$o N</I>
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diff changeset
3490 <fig>
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diff changeset
3491 <I>O co$i e$$ere ad e$$o pe$o, come AM ad AG, &amp; la po$$anza in B come AE ad
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diff changeset
3492 AB; &amp; la po$$anza in F come AL ad AF.</I>
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parents:
diff changeset
3493 <p><I>Sia dapoi la leua AB egualmente di$tante dall'orizonte, il cui $o$tegno $ia D, &amp; $ia
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diff changeset
3494 BE il pe$o, il cui centro della grauezza $ia F $opra la leua; &amp; dal punto F riri$i la
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parents:
diff changeset
3495 linea FH &agrave; piombo, &amp; dell' orizonte, &amp; di e$$a AB; &amp; $ia $o$tenuto il pe$o dal
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diff changeset
3496 punto B, &amp; da PQ. $iano po$cia altre leue BLBM, i cui $o$tegni $iano NO;
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diff changeset
3497 &amp; la linea FH allungatatagli BM in K, &amp; BL in G; &amp; venga $o$tenuto il pe$o</I>
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diff changeset
3498 <fig>
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diff changeset
3499 <I>nella leua BL ne'punti BP; &amp; nella leua BM dal punto B, &amp; PR. Dico, che
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parents:
diff changeset
3500 la po$$anza in L $o$tenente il pe$o BE nella leua BL ha quella proportione ad
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parents:
diff changeset
3501 e$$o pe$o, che NG ad NL; &amp; la po$$anza in A al pe$o ha quella proportio-
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parents:
diff changeset
3502 ne, che DH &agrave; DA; &amp; la po$$anza di M al pe$o ha quella proportione, che
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parents:
diff changeset
3503 OK ad OM. Hor percioche la linea KF tirata dal centro della grauezza F &egrave;</I>
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diff changeset
3504 <marg><I>Per la prima di questo della bilancia.</I></marg> <I>&agrave; piombo dell' orizonte, $ia pur $ostenuto il pe$o da qual $i voglia punto della linea
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parents:
diff changeset
3505 KF, egli rimarr&agrave;, come hora $i troua. Se dunque $ar&agrave; $ostenuto in H, rimarr&agrave; co
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parents:
diff changeset
3506 me prima, cio&egrave; leuato via il punto B, &amp; PQ, i quali $o$tengono il pe$o, rimarr&agrave;
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parents:
diff changeset
3507 il pe$o BE nel modo che da e$$i era $o$tenuto. Per la qual co$a grauer&agrave; nella le-
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parents:
diff changeset
3508 ua AB in H, &amp; haur&agrave; alla leua quella di$po$itione mede$ima, che prima, &amp; per-
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parents:
diff changeset
3509 ci&ograve; $ar&agrave; come $e fo$$e appiccato in H. La mede$ma po$$anza dunque $o$terr&agrave; il me
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parents:
diff changeset
3510 de$imo pe$o BE $o$tentato ouero in H, ouero in B &amp; Q. Ma la po$$anza in A</I>
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parents:
diff changeset
3511 <marg><I>Per la prima di questo.</I></marg> <I>$o$tenente il pe$o BE appiccato in H con la leua AB hal'i$te$$a proportione ad e$-
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parents:
diff changeset
3512 $o pe$o, che DH &agrave; DA; l'i$te$$a po$$anza dunque in A $o$tenente il pe$o BE ne'
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parents:
diff changeset
3513 punti BQ $o$tentato, $ar&agrave; ad e$$o pe$o come DH &agrave; DA. Similmente $i mo$trer &agrave;
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parents:
diff changeset
3514 il pe$o BE, $e in G $ar&agrave; $o$tenuto, rimanere come egliera $o$tenuto da punti BP:
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diff changeset
3515 &amp; nel punto K, come dapunti BR. Per la qual co$a la po$$anza in L $o$tenente</I>
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diff changeset
3516 <pb n=41>
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diff changeset
3517 <I>il pe$o BE ad e$$o pe$o co$i $ar&agrave; come NG ad NL. ma la po$$anza in M al pe
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diff changeset
3518 $o, come OK ad OM; cio&egrave; come la di$tanza dal $o$tegno al punto, doue dal cen
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parents:
diff changeset
3519 tro della grauezza del pe$o la linea tirata &agrave; piombo dell' orizonte taglia la leua, alla
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parents:
diff changeset
3520 di$tanza dal $o$tegno alla po$$anza. che bi$ognaua mo$trare.</I>
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parents:
diff changeset
3521 <p><I>Che $e LAM fo$$ero i $o$tegni, &amp; le po$$anze in NDO; $imilmente mo$trera$$i
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parents:
diff changeset
3522 la po$$anza in N co$i e$$ere al pe$o, come LG ad LN; &amp; la po$$anza in D,
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parents:
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3523 come AH ad AD, &amp; la po$$anza in O come MK ad MO.</I>
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parents:
diff changeset
3524 <p><I>Et $e le leue BA BL BM haue$$ero i $o$tegni in B, &amp; il pe$o fo$$e NO $opra
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parents:
diff changeset
3525 la leua, &amp; dal centro F della grauezza fo$$e tirata la linea FD EG &agrave; piombo
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parents:
diff changeset
3526 di AB, &amp; dell' orizonte; &amp; fo$$ero le po$$anze in LAM, $imilmente proue-</I>
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parents:
diff changeset
3527 <fig>
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diff changeset
3528 <I>ra$$i la po$$anza in L $o$tenente il pe$o co$i e$$ere ad e$$o pe$o, come BD &agrave; BL;
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parents:
diff changeset
3529 &amp; la po$$anza in A al pe$o come BE &agrave; BA, &amp; la po$$anza in M come BG
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parents:
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3530 &agrave; BM.</I>
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parents:
diff changeset
3531 <foot><I>L</I></foot>
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3532 <pb>
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parents:
diff changeset
3533 <p><I>Sia vltimamente la leua. AB egualmente di$tante dall'orizonte, il cui $ostegno $ia
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parents:
diff changeset
3534 C, &amp; il pe$o DE habb<*>a il centro della graueza F nella leua AB; &amp; $iano
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parents:
diff changeset
3535 alla fine altre leue GHKL, co i $o$tegni $uoi MN; &amp; il pe$o nella leua GH
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parents:
diff changeset
3536 $ia $o$tentato da i punti GO, &amp; nella leua AB da punti AT, &amp; nella leua
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parents:
diff changeset
3537 KL da punti KQ, &amp; il centro F della grauezza $ia parimente in amendue le le-</I>
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3538 <fig>
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parents:
diff changeset
3539 <I>ue GH</I> K<I>L, &amp; $iano le po$$anze in HBL. Dico la po$$anza in H co$i e$$ere al
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parents:
diff changeset
3540 pe$o, come N</I>F <I>ad NH; &amp; la po$$anza in B alpe$o, come C</I>F <I>&agrave; CB, &amp; la po$
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parents:
diff changeset
3541 $anza in L alpe$o, come M</I>F <I>ad ML. Hor percioche F &egrave; il centro della grauez-
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parents:
diff changeset
3542 za del pe$o DE, $e dunque in</I> F <I>$ar&agrave; $o$tenuto, $tar&agrave; il pe$o DE come prima, per
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parents:
diff changeset
3543 la diffinitione del centro della grauezza; &amp; $ar&agrave; come $e egli fo$$e appiccato in</I> F;
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parents:
diff changeset
3544 <I>&amp; $tar&agrave; nella leua in quel modo i$te$$o, $o$tenga$i pure &ograve; da punti AP, ouero dal
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diff changeset
3545 punto</I> F. <I>ilche parimente auerr&agrave; nelle leue GH KL, cio&egrave; che il pe$o re$ter&agrave; nel mo
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parents:
diff changeset
3546 do i$te$$o, $o$tenti$i pur &ograve; in</I> F, <I>ouero in GO ouero in KQ. La mede$ma po$$anza
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parents:
diff changeset
3547 dunque in B $o$tenter&agrave; il pe$o i$te$$o DE appiccato, ouero in</I> F, <I>ouero in AP: &amp;
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parents:
diff changeset
3548 quando egli &egrave; appiccato in</I> F, <I>&egrave; ad e$$o pe$o come CF &agrave; CB, dunque la po$$anza $o-
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parents:
diff changeset
3549 $tenente il pe$o DE appiccato ad AP $ar&agrave; ad e$$o pe$o come C</I>F <I>&agrave; CB. &amp; nel mo
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diff changeset
3550 do i$te$$o l&atilde; po$$anza in H $ar&agrave; al pe$o appiccato in OG co$i, come N</I>F <I>ad NH. &amp;
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diff changeset
3551 la po$$anza in L $ar&agrave; al pe$o appiccato in KQ, come M</I>F <I>ad ML. ilche anco bi$o-
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diff changeset
3552 gnaua mo$trare.</I>
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3553 <p><I>Ma $e li $o$tegni fo$$ero HBL, &amp; le po$$anze fo$$ero in NCM; $imilmente prouera$$i
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3554 la po$$anza in N co$i e$$ere al pe$o, come HF ad HN &amp; la po$$anza in C come
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diff changeset
3555 BF &agrave; BC; &amp; la po$$anza in M come LF ad LM.</I>
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3556 <pb n=42>
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3557 <p><I>Et $e le leue BA BC BD haue$$ero i $o$tegni in B, &amp; fo$$ero i pe$i in EF GH
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3558 KL, di modo che i loro centri della grauezza MNO fo$$ero nelle leue, &amp; le</I>
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3559 <fig>
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3560 <I>po$$anze fo$$ero in CAD. Similmente prouera$$i, che la po$$anza in C co$i &egrave;
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3561 al pe$o EF, come BM &agrave; BC, &amp; la po$$anza in A al pe$o GH, come
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parents:
diff changeset
3562 BN &agrave; BA, &amp; la po$$anza in D al pe$o KL, come BO &agrave; BD.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3563 <HEAD>PROPOSITIONE VI.</HEAD>
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casties
parents:
diff changeset
3564 <p>Sia AB linea retta, ad angoli retti, dellaquale $tia AD, la-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3565 quale dalla parte di D $ia allungata come $i vuole fin'al C,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3566 &amp; $ia congiunta la CB, laquale parimente allunghi$i dalla
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3567 parte di B fin ad E. Dapoi $iano dal punto B tirate altre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3568 linee, come $i vuole BF BG eguali ad AB tra AB BE;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3569 &amp; da i punti FG $iano tirate le linee FH GK &agrave; piombo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3570 delle $udette, lequali $i facciano eguali fra loro, &amp; ad e$$a A
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3571 D come $e BA AD fo$$ero mo$$e in BF FH, &amp; in BG
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3572 GH; &amp; congiungan$i CH CK, lequali taglino le linee BF
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3573 BG ne'punti MN. Dico che BN &egrave; minore di BM, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3574 BM di e$$a BA.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3575 <foot><I>L</I> 2</foot>
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casties
parents:
diff changeset
3576 <pb>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3577 <p><I>Congiungan$i BD BH B</I>K, <I>&amp; percioche due linee DA AB $ono eguali &agrave; due</I>
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casties
parents:
diff changeset
3578 <marg><I>Per la</I> 4. <I>del primo.</I></marg> <I>HF FB, &amp; l'angolo DAB retto &egrave; anco eguale al retto HFB; $aranno i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3579 re$tanti angoli eguali &agrave; i re$tanti angoli, &amp; HB eguale ad e$$a DB. Similmen-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3580 te mo$trera$$i il triangolo BKG e$$ere eguale al triangolo BHF. Per laqual co
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3581 $a co'l centro B, &amp; con l'in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3582 teruallo di vna di e$$e de$cri-
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casties
parents:
diff changeset
3583 ua$i il cerchio DH</I> K<I>E, il
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casties
parents:
diff changeset
3584 quale tagli le linee CH CK
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3585 ne' punti OP; &amp; congiun-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3586 gan$i OB PB. Percioche
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casties
parents:
diff changeset
3587 dunque il punto K &egrave; pi&ugrave; vi-
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casties
parents:
diff changeset
3588 cino ad E, che H; $ar&agrave; la</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3589 <marg><I>Per la</I> 8. <I>del serzo.</I></marg> <I>linea CK maggiore di CH,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3590 &amp; CP minore di CO: dun
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3591 que PK $ar&agrave; maggiore di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3592 OH. Ma perche il triangolo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3593 BKP di due lati eguali ha i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3594 $uoi lati BK BP eguali &agrave; i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3595 lati BH BO del triangolo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3596 BHO di due lati eguali, ma
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3597 ben la ba$e KP maggiore
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3598 della ba$e HO, $ar&agrave; l'ango-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3599 lo KBP maggiore dell' an</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3600 <marg><I>Per la</I> 25. <I>del</I> 5.</marg> <I>golo HBO. dunque i restan
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3601 ti angoli alla ba$e, cio&egrave; KPB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3602 PKB pre$i in$ieme, i quali
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3603 tra loro $ono eguali, $aranno
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3604 minori de i re$tanti angol i al-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3605 la ba$e po$ti, cio&egrave; OHB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3606 HOB, iquali etiandio tra lo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3607 ro $ono eguali e$$endo che tut
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3608 ti gli angoli di cia$cuno trian</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3609 <marg><I>Per la</I> 5. <I>del primo.</I></marg> <I>golo $iano eguali &agrave; due angoli
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3610 retti. Per laqual co$a anche
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3611 le met&agrave; di que$ti, cio&egrave; NKB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3612 $ar&agrave; minore di MHB. Et</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3613 <marg><I>Per la</I> 26. <I>del primo.</I></marg> <I>concio$ia, che l'angolo BKG</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3614 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3615 <I>$ia eguale all'angolo BHF, $ar&agrave; NKG maggiore di MHF. Se dunque nel
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3616 punto K $i $accia l'angolo GKQ eguale ad FHM $i $ar&agrave; il triangolo GKQ
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3617 eguale al triangolo FHM; Imperoche due angoli in FH divno $ono eguali &agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3618 due in GK d'vn'altro, &amp; il lato FH &egrave; eguale al lato GK, $ar&agrave; GQ eguale
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3619 ad FM. Adunque GN $ar&agrave; maggiore di FM. &amp; co$i per e$$ere BG egua-</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3620 <pb n=43>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3621 <I>le &agrave; BF, $ar&agrave; BN minore di e$$a BM. ma che BM $ia minore di e$$a BA
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3622 &egrave; manife$to, percioche BM, &egrave; minore di e$$a BF, laquale &egrave; eguale &agrave; BA. che
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3623 bi$ognaua mo$trare.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3624 <p><I>Di pi&ugrave; $e tra BG BE $i tiri &agrave; piacere vn'altra linea eguale &agrave; BG; &amp; faccia$i l'ope
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3625 ratione, come di $opra &egrave; stato detto, prouera$$i $imilmente la linea BR e$$er mi-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3626 nore di BN. &amp; quanto pi&ugrave; da vicino $ar&agrave; ad e$$a BE, $ar&agrave; anche $empre minore.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3627 <p>Che $e i triangoli eguali BFH BGK fo$$ero di $otto fra BC
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3628 BA collocati; &amp; fo$$ero congiunte le linee HC KC, le-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3629 quali taglia$$ero le linee BF BG allungate dalla parte di FG
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3630 ne' punti MN, $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3631 la BN maggiore del
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3632 la BM, &amp; la BM di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3633 e$$a BA.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3634 <p><I>Imperoche allunghi$i CH CK
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3635 fin alla circonferenza in OP,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3636 &amp; congiungan$i BO BP;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3637 con $imile modo mo$trera$$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3638 la linea PK e$$ere maggiore
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3639 ai OH, &amp; l'angolo PKB e$
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3640 $ere minore dell &atilde;golo OHB.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3641 &amp; percioche l'angolo BHF
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3642 &egrave; eguale dell' angolo BKG, $a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3643 r&agrave; tutto l'angolo PKG mi-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3644 nore dell' angolo OHF. Per
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3645 laqual co$a il re$tante GKN
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3646 $ar&agrave; maggiore del re$tante
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3647 FHM. Se d&utilde;que fara$$i l'an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3648 golo GKQ eguale ad FHM
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3649 la linea KQ taglier &agrave; in modo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3650 la GN, che GQ diuenter&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3651 eguale ad FM. Per laqual
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3652 co$a maggiore $ar&agrave; GN, che
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3653 FM; allequali $e $ar anno ag
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3654 giunte le eguali BF BG, $a-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3655 r&agrave; BN maggiore di BM. &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3656 per e$$ere BM maggiore di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3657 FB, $ar&agrave; anco maggiore di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3658 BA. $imilmente prouera$$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3659 che qu&atilde;to pi&ugrave; da vicino $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3660 BG &agrave; BC, la linea BN $em
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3661 pre $ar&agrave; maggiore.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3662 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3663 <HEAD>PROPOSITIONE VII.</HEAD>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3664 <p>Sia la linea retta AB, &agrave; cui $tia &agrave; piombo AD, laquale allun-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3665 ghi$i dalla parte di D come pare $in'&agrave; C, &amp; congiunga$i C
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3666 B, laquale etiandio $i allunghi fin'ad E; &amp; $imilmente tra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3667 AB BE $iano, come pare, tirate BF BG eguali ad e$$a AB,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3668 &amp; da punti FG $iano
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3669 tirate le linee FH GK
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3670 pur eguali ad e$$a AD,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3671 &amp; &agrave; piombo di BF BG,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3672 come $e BA AD fo$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3673 $ero mo$$e in BF FH
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3674 BG GK: &amp; congiun-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3675 gan$i CH CK, lequali
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3676 taglino le linee allunga
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3677 te BF BG ne' punti
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3678 MN. Dico che BN &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3679 maggiore di BM, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3680 BM di e$$a BA.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3681 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3682 <p><I>Congiungan$i BD BH BK, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3683 co'l centro B, &amp; conlo $patio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3684 BD de$criua$i it cerchio. $imil-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3685 mente come nella precedente, di-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3686 mo$treremo ipunti KHDOP
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3687 e$$ere nella circonferenza del cer
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3688 chio; &amp; itri&amacr;goli ABD FBH
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3689 GBK e$$ere tra loro eguali, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3690 la linea PK e$$ere maggiore
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3691 della OH, &amp; l'angolo PKB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3692 e$$ere minore dell'angolo OHB.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3693 Percioche d&utilde;que l'angolo BHF
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3694 &egrave; eguale all'angolo BKG, $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3695 tutto l'angolo PKG minore
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3696 dell'angolo OHF. Per laqual
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3697 co$a il re$tante G</I>K<I>N $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3698 maggiore del re$tante FHM.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3699 Se d&utilde;que $i $ar&agrave; l'angolo G</I>K<I>Q</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3700 <pb n=44>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3701 <I>eguale ad e$$o FHM, $ar&agrave; il triangolo GKQ eguale al triangolo FHM, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3702 illato GQ al lato FM eguale; $ar&agrave; dunque maggiore GN di e$$a FM; &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3703 perci&ograve; BN maggiore $ar&agrave; di BM. &amp; BM $ar&agrave; maggiore di BA; impe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3704 roche BM &egrave;maggiore di e$$ai BE. Che bi$ognaua mo$trare.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3705 <p><I>Et nel modo i$te$$o in tutto, quanto pi&ugrave; da pre$$o $ar&agrave; BG ad e$$a BE, $empre la li-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3706 nea BN $i dimo$trer&agrave; e$$er maggiore.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3707 <p>Che $e $aranno po$ti di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3708 $otto i triangoli BF
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3709 HB GK tra AB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3710 BC, &amp; $iano tiratele
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3711 linee CHO GKP,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3712 lequali taglino le li-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3713 nee BF BG ne' pun
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3714 ti MN: $ar&agrave; la linea
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3715 BN minore di e$$a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3716 BM, &amp; BM di e$sa
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3717 BA.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3718 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3719 <p><I>Congiungan$i BO BP. $imilmen
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3720 te prouera$$i, che l'angolo P
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3721 KB &egrave; minore dell' angolo OH
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3722 B. Hor percioche l'angolo F
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3723 HB &egrave; eguale all'angolo GKB;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3724 $ar&agrave; l'angolo GKN maggio-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3725 re dell'angolo FHM: per la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3726 qual co$a la linea GN $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3727 maggiore di e$$a FM. &amp; per-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3728 ci&ograve; la linea BN $ar&agrave; minore
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3729 della linea BM. &amp; concio-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3730 $ia che maggiore $ia BF di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3731 BM; $ar&agrave; BM minore di
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3732 BA. &amp; con $imile modo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3733 prouera&szlig;i, che quanto pi&ugrave; B
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3734 G $ar&agrave; dapre$$o ad e$$a BC,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3735 la linea BN $empre $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3736 minore.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3737 <HEAD>PROPOSITIONE VIII.</HEAD>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3738 <p>La po$$anza $o$tenente il pe$o che habbia il centro della grauez-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3739 za fopra la leu&agrave; egualmente di$tante dall'orizonte, quanto
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3740 pi&ugrave; il pe$o $i inalzer&agrave; da que$to $ito con la leua $empre haur&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3741 bi$ogno di po$sanza minore per e$sere $o$tenuto: ma $e $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3742 abba$sato di maggiore.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3743 <p><I>Sia la leua AB egualmente di$tante dall'orizonte, il cui $o$tegno $ia C, &amp; il pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3744 BD il centro della grauezza delquale $ia doue &egrave; H $opra la leua; &amp; $ia la po$$an</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3745 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3746 <I>za $o$tenente in A. Moua$i dapoi la leua AB in EF, &amp; $ia il pe$o mo$$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3747 in FG. Dico primieramente che minore po$$anza po$ta in E $o$tenir &agrave; il pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3748 FG con la leua EF, che la po$$anza in A il pe$o BD con la leua AB. $ia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3749 il K il centro della grauezza del pe$o FG. Dapoi $iano tirate s&igrave; da H, come</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3750 <pb n=45>
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diff changeset
3751 <I>da K le linee HL KM &agrave; piombo de'loro orizonti, lequali $i andaranno &agrave; tro-
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diff changeset
3752 uare nel tentro del mondo, &amp; $ia HL &agrave; piom<*>o anche di e$$a AB. Dapoi $ia
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diff changeset
3753 tirata la linea KN &agrave; piom<*>, di EF, laquale $ar&agrave; eguile ad HL, &amp; la CN
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diff changeset
3754 eguale ad e$$a CL. Hor percioche HL &egrave; &agrave; piombo dell'orizonte, la po$$anza
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diff changeset
3755 in A $o$tenente il pe$o BD haur&agrave; quella proportione ad e$$o pe$o, che CL &agrave;</I> <marg><I>Per la quin ta di questo.</I></marg>
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diff changeset
3756 <I>CA. Di nuouo, percioche KM &egrave; &agrave; piombo dell'orizonte, la po$$anza in E $o-
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diff changeset
3757 $tenente il pe$o FG co$i $ar&agrave; al pe$o come CM &agrave; CE. &amp; per e$$ere CN NK
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diff changeset
3758 eguali ad e$$e CL LH, &amp; contenere angoliretti, $ar&agrave; CM minore di e$$a CL;</I> <marg><I>Per la</I> 6. <I>di questo.</I></marg>
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diff changeset
3759 <I>Dunque CM &agrave; CA haur&agrave; proportione minore, che CL &agrave; CA; &amp; CA
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diff changeset
3760 &egrave; eguale &agrave; CE, dunque haur&agrave; CM proportione minore &agrave; CE, che CL &agrave;</I> <marg><I>Per la otta ua del quinto.</I></marg>
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diff changeset
3761 <I>CA: &amp; per e$$erei pe$i BD FG eguali, per&ograve; che &egrave; il pe$o mede$imo. Dun-
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diff changeset
3762 que $ar&agrave; minore proportione della po$$anza in E $o$tenente il pe$o FG ad e$$o
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diff changeset
3763 pe$o, che della po$$anza in A $o$tenente il pe$o BD ad e$$o pe$o. Per laqual
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diff changeset
3764 co$a minore po$$anza po$ta in E $o$tenter&agrave; il pe$o FG, che la po$$anza in A</I> <marg><I>Per la</I> 10. <I>del quinto.</I></marg>
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diff changeset
3765 <I>il pe$o BD. &amp; quanto pi&ugrave; $ar&agrave; inalzato il pe$o, $empre $i mo$trer&agrave; po$$anza</I> <marg><I>Per la</I> 6. <I>di questo.</I></marg>
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diff changeset
3766 <I>anche minore douer $o$tenere il pe$o, per e$$ere la linea PC minore della CM.
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diff changeset
3767 Sia dapoi la leua in QR, &amp; il pe$o in QS, il cui centro della grauezza $ia O.
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diff changeset
3768 Dico che po$$anza maggiore $i richiede in R per $o$tenere il pe$o QS, che in
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diff changeset
3769 A per $ostentare il pe$o BD. Tiri$i dal centro O della grauezza la linea OT
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3770 a piombo dell'orizonte. &amp; percioche le linee HL OT $e $aranno allungate dal-
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3771 la parte di L, &amp; di T $i andranno &agrave; ritrouare nel centro del mondo, $ar&agrave; la CT mag
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diff changeset
3772 giore della CL: &amp; &egrave; la CA eguale ad e$$a CR, dunque la TC haur&agrave; pro-</I> <marg><I>Per la</I> 6. <I>di questo.</I></marg>
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diff changeset
3773 <I>portione maggiore &agrave; CR, che LC &agrave; CA. Maggiore dunque $ar&agrave; la po$$an-</I> <marg><I>Per la otta ua del</I> 5.</marg>
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diff changeset
3774 <I>za in R $o$tenente il pe$o QS, che in A $o$tenente il BD. Similmente mo-
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diff changeset
3775 $trera$$i, che quanto la leua RQ abba$$ando$i, $ar&agrave; pi&ugrave; di$tante dalla leua AB,</I> <marg><I>Per la</I> 10. <I>del quinto.</I></marg>
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diff changeset
3776 <I>$empre pi&ugrave; $i ricercher&agrave; po$$anza mag giore &agrave; $o$tenere il pe$o: peroche la di$tanza</I> <marg><I>Per la</I> 6. <I>di questo.</I></marg>
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diff changeset
3777 <I>CV &egrave; pi&ugrave; lunga di CT. Quanto dunque il pe$o $i alzer&agrave; pi&ugrave; dal $ito egualmente
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3778 di$tante dall'orizonte, $ar&agrave; $empre $o$tenuto da po$$anza minore; &amp; quanto pi&ugrave; $i
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3779 ab<*>a$$er&agrave;, di po$$anza maggiore haur&agrave; me$tieri per e$$er $o$tentato. che bi$ogna-
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3780 ua mo$trare.</I>
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diff changeset
3781 <p>Quinci facilmente $i caua, che la pos$anza in A alla po$sanza
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3782 in E co$i &egrave;, come CL &agrave; CM.
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3783 <p><I>Imperoche co$i&egrave; LC &agrave; CA, come la po$$anza in A al pe$o; &amp; come CA,
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diff changeset
3784 cio&egrave; CE &agrave; CM, co$i &egrave; il pe$o alla po$$anza in E; Per laqual co$a per la pro-</I> <marg><I>Per la</I> 22. <I>del quinto.</I></marg>
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diff changeset
3785 <I>portion eguale, la po$$anza in A alla po$$anza in E $ar&agrave; come CL &agrave; CM.</I>
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3786 <p><I>Con $imile ragione mo$trera&szlig;i non $olamente che la po$$anza in A co$i &egrave; alla po$-
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3787 $anza in R, come CL &agrave; CT, ma che la po$$anza in E ancora alla po$$anza
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3788 in R &egrave; co$i, come CM &agrave; CT, &amp; co$i nel re$to.</I>
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3789 <foot><I>M</I></foot>
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3790 <pb>
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3791 <p><I>Sia poila leua AB egualmente di$tante dall'orizonte, il cui $o$tegno $ia B, &amp; il
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3792 centro H della grauezza del pe$o CD $ia $opra la leua; &amp; moua$i la leua in
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3793 BE, &amp; il pe$o in FG. Dico che minore po$$anza po$ta in E $o$tiene il pe$o FG
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3794 con la leua EB, che la po$$anza in A il pe$o CD con la leua AB. Sia K
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3795 il centro della grauezza del pe$o FG, &amp; da i centri delle grauezze HK $iano</I>
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3796 <fig>
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3797 <marg><I>Per la</I> 6. <I>di questo.</I></marg> <I>tirate le linee HL</I> K<I>M &agrave; piombo de'loro orizonti. Hor percioche dalle co$e
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3798 di $opra mo$trate BM &egrave; minore di BL, &amp; BE &egrave; eguale &agrave; BA, haur&agrave; pro-</I>
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3799 <marg><I>Per la</I> 8. <I>del quinto.</I></marg> <I>portione minore BM &agrave; BE, che BL &agrave; BA: ma come BM &agrave; BE, co$i</I>
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3800 <marg><I>Per la</I> 5. <I>di questo.</I></marg> <I>&egrave; la po$$anza in E $o$tenente il pe$o FG ad e$$o pe$o, &amp; come BL a BA,
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3801 co$i la po$$anza in A al pe$o CD; la po$$anza in E al pe$o FG haur &agrave; propor-</I>
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3802 <marg><I>Per la</I> 10. <I>del quinto.</I></marg> <I>tione minore, che la po$$anza in A al pe$o CD. Dunque la po$$anza in E $a-
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3803 r&agrave; minore della po$$anza in A. Similmente mo$trera$$i quanto pi&ugrave; il pe$o $i alze-
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3804 r&agrave;, $empre minore po$$anza $o$tenere il pe$o, ma $ia la leua in BO, &amp; il pe$o in
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3805 BQ, il cui centro della grauezza $ia R. Dico, che maggior po$$anza $i ricerca
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3806 in O per $o$tenere il pe$o PQ con la leua BO, che per $o$tenere il pe$o CD con
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3807 la leua BA. Sia tirata dal punto R la linea RS &agrave; piombo dell'orizonte. &amp;</I>
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3808 <marg><I>Per la</I> 6. <I>di questo.</I></marg> <I>percioche BS &egrave; maggiore di BL, haur&agrave; BS proportione maggiore &agrave; BO, che
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3809 BL &agrave; BA; Per laqual co$a la po$$anza in O $o$tenente il pe$o PQ $ar&agrave; maggio
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3810 re della po$$anza in A $o$tenente il pe$o CD. &amp; &agrave; que$to modo $i mo$trer&agrave; an-
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3811 cora che quanto la leua BO abba$$an lo$i, $ar&agrave; pi&ugrave; di$tante dalla leua AB $em-
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3812 pre vi vorr&agrave; po$$anza maggiore &agrave; $o$iener il pe$o.</I>
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3813 <p><I>Di qui parimente, come di $opra &egrave; mani$e$to, che la po$$anza in A &egrave; alla po$$anza in</I>
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3814 <pb n=46>
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3815 <I>B, come BL &agrave; BM: &amp; la po$$anza in A alla po$$anza in O, come BL &agrave; BS. &amp;
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3816 la po$$anza in E alla po$$anza in O, come BM &agrave; BS.</I>
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3817 <p><I>Oltre &agrave; ci&ograve; $e $i intender&agrave; vn'altra po$$anza in B, per modo che due $iano le po$$an-
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3818 ze, che $o$tentino il pe$o, minore $ar&agrave; la po$$anza in B, che $o$tiene il pe$o PQ
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3819 con la leua BO, che il pe$o CD con la leua BA. ma per lo contrario $i ri-
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3820 cerca po$$anza maggiore in B per $o$tenere il pe$o FG con la leua BE, che
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3821 il pe$o CD con la leua AB: percioche tirata la linea KN &agrave; piombo di EB,
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3822 $ar&agrave; EN eguale ad AL: Per laqual co$a EM $ar&agrave; maggiore di LA. Dun</I> <marg><I>Per la</I> 8. <I>del quinto.</I></marg>
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3823 <I>que EM haur&agrave; proportione maggiore ad EB, che LA ad AB, &amp; LA
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3824 maggiore ad AB, che SO ad OB, lequali $ono proportioni della po$$anza</I> <marg><I>Per la</I> 5. <I>di questo.</I></marg>
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diff changeset
3825 <I>al p&euml;$o.</I>
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parents:
diff changeset
3826 <p><I>Similmente prouera$$i, che la po$$anza in B $o$tenente il pe$o con la leua AB &egrave; al-
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parents:
diff changeset
3827 la po$$anza $o$tenente po$ta nell'i$te$$o punto B con la leua EB, come LA
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parents:
diff changeset
3828 ad EM; &amp; co$i e$$ere anche alla po$$anza di B $o$tenente il pe$o con la leua OB,
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parents:
diff changeset
3829 come AL ad OS. Ma quelle po$$anze che $o$tengono con le leue EB OB
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parents:
diff changeset
3830 $ono co$itraloro come EM ad OS.</I>
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casties
parents:
diff changeset
3831 <p><I>Dapoi mo$treremo come nelle co$e che di $opra $ono $tate dette, che la po$$anza in B
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parents:
diff changeset
3832 ha quella proportione alla po$$anza in E, che EM ad MB; &amp; la po$$anza</I> <marg><I>Per il</I> 3. <I>ce roll ario.</I></marg>
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parents:
diff changeset
3833 <I>in B co$i e$$ere alla po$$anza in A, come AL ad LB, &amp; la po$$anza in B
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parents:
diff changeset
3834 alla po$$anza in O, come OS ad SB.</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
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parents:
diff changeset
3835 <p><I>Ma $ia la leua AB e-
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parents:
diff changeset
3836 gualmente di$tante
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parents:
diff changeset
3837 dall'orizonte, il cui
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parents:
diff changeset
3838 $o$tegno $ia B, &amp;
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parents:
diff changeset
3839 il centro H della
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parents:
diff changeset
3840 grauezza del pe$o
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parents:
diff changeset
3841 AC $ia $opra la
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parents:
diff changeset
3842 leua: &amp; moua$i la
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parents:
diff changeset
3843 leua in BE, &amp; il
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parents:
diff changeset
3844 pe$o in EF, &amp; la
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parents:
diff changeset
3845 po$$anza in G. di
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parents:
diff changeset
3846 mo$trera$$i parimen
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parents:
diff changeset
3847 te, come di $opra, che
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parents:
diff changeset
3848 la po$$anza in G $o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3849 $tenente il pe$o EF
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parents:
diff changeset
3850 &egrave; minore della po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3851 $anza in D $o$te-</I>
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parents:
diff changeset
3852 <fig>
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casties
parents:
diff changeset
3853 <I>nente il pe$o AC. percioche e$$endo minore BM di BL haur&agrave; minore pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3854 portione MB &agrave; BG, che LB &agrave; BD. &amp; &agrave; que$to modo prouera&szlig;i, che quan
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3855 to il pe$o pi&ugrave; $i alzer&agrave; con la leua, $empre minore po$$anza $i ricerca &agrave; $o$tenere</I>
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parents:
diff changeset
3856 <foot><I>M</I> 2</foot>
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parents:
diff changeset
3857 <pb>
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parents:
diff changeset
3858 <I>il detto pe$o. $imilmente $e la leua $i moue in BO, &amp; la po$$anza $o$tenente $ia
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parents:
diff changeset
3859 in N, $i mo$trer&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3860 la po$$anza in N e$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3861 $ere maggiore della
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parents:
diff changeset
3862 po$$anza in D. pe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3863 roche SB ha pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3864 portione maggiore
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
3865 &agrave; BN che LB
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3866 &agrave; BD. Mo$tre-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3867 ra&szlig;i ancora, che
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parents:
diff changeset
3868 quanto il pe$o pi&ugrave;
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parents:
diff changeset
3869 s'abb a$$er&agrave;, $empre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3870 ricercar$i po$$anza
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3871 maggiore &agrave; $o$tene-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3872 re il pe$o. che bi$o-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3873 gnaua mo$trare.</I>
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parents:
diff changeset
3874 <fig>
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parents:
diff changeset
3875 <p><I>Di qu&igrave; parim&emacr;te &egrave; chia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3876 ro, che le po$$anze
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3877 in GDN co$itraloro $ono, come BM &agrave; BL, &amp; come BL &agrave; BS, &amp; vlti-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3878 mamente come BM &agrave; BS.</I>
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parents:
diff changeset
3879 <HEAD>COROLLARIO</HEAD>
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parents:
diff changeset
3880 <p>Da que$te co$e &egrave; manife$to, che $e la po$sanza con la leua moue
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3881 r&agrave; in s&ugrave; il pe$o, il cui centro della grauezza $ia $opra la leua,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3882 quanto pi&ugrave; $ar&agrave; alzato il pe$o, $empre vi vorr&agrave; po$sanza mi-
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parents:
diff changeset
3883 nore per mouere il pe$o.
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parents:
diff changeset
3884 <p><I>Percioche doue la po$$anza $o$tenente il pe$o &egrave; $empre minore, $ar&agrave; parimente la po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3885 $anza, che lo moue $empre minore.</I>
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parents:
diff changeset
3886 <p><I>Da que$te co$e dimo$trera&szlig;i etiandio, $ia pur il centro della grauezza del pe$o mede$i-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3887 mo &ograve; pi&ugrave; da pre$$o, &ograve; pi&ugrave; da lunge della leua AB egualmente di$tante dall' ori-
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parents:
diff changeset
3888 zonte, che la po$$anza mede$ima in A $o$terr&agrave; nondimeno il pe$o: come $e il cen
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parents:
diff changeset
3889 tro H della grauezza del pe$o BD $ia pi&ugrave; da lunge dalla leua BA, che il cen-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3890 tro N della grauezza del pe$o PV, pur che la linea HL tirata dal punto H
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3891 &agrave; piombo dell'orizonte, &amp; della leua AB pa&szlig;i per N, &amp; $ia il pe$o PV
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3892 eguale al pe$o BD; $ar&agrave; s&igrave; il pe$o BD, &amp; s&igrave; il pe$o PV come $e ambidue $o$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3893 $ero appiccati ad L; &amp; $ono eguali per e$$ere pre$i in luogo di vn pe$o $olo, dun-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3894 que la i$te$$a po$$anza in A $o$ienente il pe$o BD $o$terr&agrave; anche il pe$o PV.</I>
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parents:
diff changeset
3895 <pb n=47>
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parents:
diff changeset
3896 <I>Ma nella leua EF quanto il centro della grauezza $ar&agrave; pi&ugrave; da lunge dalla leua.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3897 tanto pi&ugrave; egualmente la po$$anza $o$tenter &agrave; il pe$o mede$imo, come $e il centro K
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3898 della grauezza del pe$o FG $o$$e pi&ugrave; da lunge dalla leua EF, che il centro X
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3899 dalla grauezza del pe$o <G>*u</G>Z; in modo per&ograve;, che la lineatirata dal punto</I> K <I>&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3900 piombo della leua FE pa&szlig;i per X; &amp; $ia il pe$o FG eguale al pe$o <G>*u</G>Z;
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parents:
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3901 &amp; da punti KX $iano tirate le linee KM X<36> &agrave; piombo de loro orizonti; $a-</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3902 <fig>
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parents:
diff changeset
3903 <I>r&agrave; la C<36> maggiore di CM; &amp; perci&ograve; il pe$o FG $ar&agrave; nella leua co$i come
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3904 $e fo$$e appiccato in M, &amp; il pe$o <G>*u</G>Z come fo$$e appiccato in <36>. Hor per-</I> <marg><I>Per la</I> 8. <I>del quinto.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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3905 <I>cioche C<36> ha proportione maggiore &agrave; CE, che CM &agrave; CE, maggiore
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parents:
diff changeset
3906 $ar&agrave; la po$$anza po$ta in E, che $o$terr&agrave; il pe$o <G>*u</G>Z, che FG. Manella leua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3907 QR per lo contrario $i dimo$trer&agrave;, cio&egrave; che quanto il centro della grauezza del pe
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parents:
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3908 $o mede$imo &egrave; pi&ugrave; da lunge dalla leua, tanto pi&ugrave; anche maggiore &egrave; la po$$anza che
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parents:
diff changeset
3909 $o$tiene il pe$o. peroche maggiore &egrave; CT di CI, &amp; perci&ograve; CT hauer&agrave; proportio-
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parents:
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3910 ne maggiore &agrave; CR, che CI &agrave; CR. $imilmente dimo$trera&szlig;i, $e il pe$o $ar&agrave; col
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parents:
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3911 locato fra la po$$anza, &amp; il $o$tegno, ouero la po$$anza po$ta fra il $o$tegno, &amp; il
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parents:
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3912 pe$o, il che mede$imamente auuenir&agrave; alla po$$anz&agrave; che moue peroche doue po$$anza
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parents:
diff changeset
3913 minore $o$tiene il pe$o, iui po$$anza minore lo mouer&agrave;: &amp; doue $iricerca po$$anza
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diff changeset
3914 maggiore in $o$tenere, iui anche maggiore vi vuole in mouere.</I>
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diff changeset
3915 <HEAD>PROPOSITIONE IX.</HEAD>
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diff changeset
3916 <p>La po$$anza $o$tenente il pe$o, che habbia il centro della $ua gra
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diff changeset
3917 uezza $otto la leua egualmente di$tante dall'orizonte, quanto
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parents:
diff changeset
3918 pi&ugrave; il pe$o $ar&agrave; alzato da que$to $ito con la leua, haur&agrave; egli $em
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parents:
diff changeset
3919 preanco me$tieri di po$$anza maggiore ad e$$ere $o$tenuto;
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diff changeset
3920 Ma $e abba$$ato, di minore.
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parents:
diff changeset
3921 <p><I>Sia la leua AB egualmente di$t&amacr;te dall'orizonte, il cui $o$tegno $ia C, &amp; $ia il pe$o AD,
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diff changeset
3922 il cui centro L della grauezza $ia $otto la leua, &amp; $ia in B la po$$anza $o$tenen-
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diff changeset
3923 te il pe$o AD: moua$i dopo la leua in FG, &amp; il pe$o in FH. Dico prima,
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parents:
diff changeset
3924 che po$$anza maggiore $i ricerca in G per $o$tenere il pe$o FH con la leua FG,
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parents:
diff changeset
3925 di quel che $iala po$$anza in B e$$endo il pe$o AD, ma con la leua AB. $ia</I>
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parents:
diff changeset
3926 <fig>
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parents:
diff changeset
3927 <I>M il centro della grauezza del pe$o FH, &amp; da punti LM $iano tirate le linee</I>
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parents:
diff changeset
3928 <marg><I>Per la</I> 7. <I>di qu sto.</I></marg> <I>LK MN &agrave; piombo de'loro orizonti; &amp; $iatirata la linea MS &agrave; piombo di FG,
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parents:
diff changeset
3929 che $ar&agrave; eguale ad LK, &amp; CK $ar&agrave; etiandio eguale ad e$$a CS. Percioche dun</I>
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parents:
diff changeset
3930 <marg><I>Per la</I> 8. <I>del quinto.</I></marg> <I>que CN &egrave; maggiore di CK haur&agrave; NC proportione maggiore &agrave; CG, che CK
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parents:
diff changeset
3931 &agrave; CB; &amp; la po$$anza in B al pe$o AD ha la mede$ma proportione, che KC</I>
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parents:
diff changeset
3932 <marg><I>Per la</I> 5. <I>di questo.</I></marg> <I>&agrave; CB: &amp; come la po$$anza in G al pe$o FH, co$i &egrave; NC &agrave; CG; dunque la</I>
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parents:
diff changeset
3933 <marg><I>Per la</I> 10. <I>del quinto.</I></marg> <I>po$$anza in G hauer &agrave; maggiore proportione al pe$o FH, che la po$$anza in B
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parents:
diff changeset
3934 al pe$o AD. Maggiore dunque &egrave; la po$$anza in G della po$$anza in B. che$e</I>
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parents:
diff changeset
3935 <pb n=48>
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parents:
diff changeset
3936 <I>la leua $ar&agrave; in OP, &amp; il pe$o in OQ; $ar&agrave; la po$$anza po$ta in B maggiore,
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parents:
diff changeset
3937 che in P: percioche $i dimo$trer&agrave; nell'i$te$$o modo CR e$$ere minore di CK, &amp;
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parents:
diff changeset
3938 CR hauere proportione minore a CP, che CK a CB; &amp; perci&ograve; la po$$anza
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parents:
diff changeset
3939 po$ta in B e$$ere maggiore della po$$anza po$ta in P. &amp; a que$to modo mo$tre-
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parents:
diff changeset
3940 ra$$i che quanto pi&ugrave; il pe$o $i alzer&agrave; dal $ito AB, $empre vi vorr&agrave; po$$anza mag-
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parents:
diff changeset
3941 giore &agrave; $o$tenerlo. ma per lo contrario accader&agrave; $e egli $ar&agrave; abba$$ato. che bi$o-
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parents:
diff changeset
3942 gnaua mo$trare.</I>
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parents:
diff changeset
3943 <p><I>Di qu&agrave; ancora $i puote ageuolmente cauare, che le po$$anze po$te in PBG $ono in
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parents:
diff changeset
3944 modo di$po$te fraloro, come CR &agrave; CK; &amp; come CK &agrave; CN, &amp; come CN
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parents:
diff changeset
3945 &agrave; CR.</I>
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parents:
diff changeset
3946 <p><I>Sia dopo la leua AB egualmente di$tante dall'orizonte, co'l $uo $o$tegno B; &amp; il
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parents:
diff changeset
3947 pe$o CD habbia il centro O della grauezza $otto la leua, &amp; $ia in A la po$-
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parents:
diff changeset
3948 $anza $o$tenente il pe$o CD. Moua$i dapoi la leua in BE, &amp; BF, &amp; $i tra-
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diff changeset
3949 $porti il pe$o in GH KL. Dico, che maggiore po$$anza per $o$tenere il pe$o $i</I>
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parents:
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3950 <fig>
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parents:
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3951 <I>ricerca in E, che in A; &amp; maggiore in A che in F $iano tirate da i centri
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parents:
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3952 delle grauezze le linee NM OP QR &agrave; piombo de gli orizonti, lequali allun
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parents:
diff changeset
3953 gate da la parte di NOQ $i andranno &agrave; trouare nel centro del mondo. Mo$tre-
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parents:
diff changeset
3954 ra$$i parimente come di $opra, che BM &egrave; maggiore di BP, &amp; BP maggio-</I> <marg><I>Per la</I> 7. <I>di questo.</I></marg>
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3955 <I>re di BR; &amp; che BM ha proportione maggiore &agrave; BE, che BP &agrave; BA; &amp;
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parents:
diff changeset
3956 BP &agrave; BA maggiore che BR &agrave; BF: &amp; per que$to la po$$anza in E mag-
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parents:
diff changeset
3957 giore &egrave; della po$$anza in A; &amp; la po$$anza in A maggiore della po$$anza in</I>
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3958 F. <I>&amp; quanto la leua $i alzer&agrave; pi&ugrave; dal $ito AB, mo$trera$$i $empre, che mag-
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parents:
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3959 <pb>
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parents:
diff changeset
3960 giore po$$anza vi vuole &agrave; $o$tenere il pe$o: ma $e abba$$era&szlig;i, minore.</I>
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parents:
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3961 <p><I>Di qu&igrave; &egrave; chiaro etiandio che le po$$anze po$te in EAF co$itraloro $ono, come BM
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parents:
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3962 &agrave; BP, &amp; come BP &agrave; BR, &amp; come BM &agrave; BR.</I>
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parents:
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3963 <p><I>Di pi&ugrave; $e in B $ar&agrave; vn'altra po$$anza, per modo, che due po$$anze $iano quelle che
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parents:
diff changeset
3964 $o$tengano il pe$o. Di maggiore po$$anza &egrave; bi$ogno in B per $o$tenere il pe$o KL
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parents:
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3965 con la leua BF, che per $o$tenere il pe$o CD con la leua AB. &amp; dauan-</I>
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parents:
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3966 <fig>
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parents:
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3967 <I>taggio anco maggiore con la leua AB, che con la leua BE: peroche RF ha
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parents:
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3968 proportione maggiore ad FB, che PA ad AB; &amp; PA ad AB mag-
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parents:
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3969 giore, che EM ad EB.</I>
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parents:
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3970 <p><I>Similmente mo$trera&szlig;i, che le po$$anze in B $o$tenenti il pe$o con le leue traloro co$i
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parents:
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3971 e$$ere, come EM ad AP, &amp; come AP ad FR, &amp; come EM ad FR.</I>
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parents:
diff changeset
3972 <p><marg><I>Per lo</I> 3. <I>co<*>llario.</I></marg> <I>Oltre &agrave; ci&ograve; la po$$anza in B co$i $ar&agrave; alla po$$anza in F, come RF ad RB; &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
3973 la po$$anza in B alla po$$anza in A come PA &agrave; PB, &amp; la po$$anza in B al-</I>
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parents:
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3974 <marg><I><*>er la</I> 2. <I>di <*>esto.</I></marg> <I>la po$$anza in E come EM ad MB.</I>
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parents:
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3975 <pb n=49>
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parents:
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3976 <p><I>Ma$ia la leua AB egualmente di$tante dall'oriz&otilde;te, col $uo $o$tegno B, &amp; il pe$o AC,
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parents:
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3977 il cui centro della
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parents:
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3978 grauezza $ia $ot-
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parents:
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3979 to la leua, &amp; $ia
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parents:
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3980 la po$$anza $o$te-
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parents:
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3981 n&emacr;ce il pe$o in D,
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parents:
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3982 &amp; moua$i la le-
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parents:
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3983 ua in BE BF,
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parents:
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3984 &amp; la po$$anza
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parents:
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3985 in GH; $imil-
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parents:
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3986 mente mo$trera$
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parents:
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3987 $i, che la po$$an-
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parents:
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3988 za in G &egrave; mag
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parents:
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3989 giore della po$$an
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3990 za in D, &amp; la
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3991 po$$anza in D
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3992 maggiore della</I>
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3993 <fig>
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3994 <I>po$$anza in H. percioche KB ha proportione maggiore &agrave; BG, che BL &agrave; BD,
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3995 &amp; BL &agrave; BD maggiore che MB &agrave; BH. &amp; &agrave; questa maniera mo$trera$$i che
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parents:
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3996 quanto la leua pi&ugrave; $i alzer&agrave; dal $ito AB, dauantaggio douere $empre e$$ere mag
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3997 gior la po$$anza per $o$tenere il pe$o: &amp; quanto pi&ugrave; s'abba$$a, minore. che dimo
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diff changeset
3998 $trare era me$tieri.</I>
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diff changeset
3999 <p><I>Similmente in que$te, le po$$anze poste in GDH co$itraloro $aranno, come BK &agrave;
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diff changeset
4000 BL, &amp; come BL &agrave; BM, &amp; alla $ine come BK &agrave; BM.</I>
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diff changeset
4001 <HEAD>COROLLARIO.</HEAD>
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diff changeset
4002 <p>Da que$te co$e etiandio &egrave; pale$e, che $e la po$$anza mouer&agrave; con
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diff changeset
4003 la leua in s&ugrave; vn pe$o, che habbia il centro della grauezza $otto
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diff changeset
4004 la leua; Quanto pi&ugrave; il pe$o $ar&agrave; alzato, $empre vi vorr&agrave; po$-
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diff changeset
4005 $anza maggiore per mouere il pe$o.
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parents:
diff changeset
4006 <p><I>Imperoche $e la po$$anza $o$tenente il pe$o &egrave; $empre maggiore, $ar&agrave; parimente la
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diff changeset
4007 po$$anza che moue il pe$o $empre maggiore.</I>
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diff changeset
4008 <foot><I>N</I></foot>
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parents:
diff changeset
4009 <pb>
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diff changeset
4010 <p><I>Da que$te co$e anco $i cauer&agrave; facilmente $e $ar&agrave; il centro della grauezza dell'i$te$$o pe
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parents:
diff changeset
4011 $o &ograve; pi&ugrave; da pre$$o, &ograve; pi&ugrave; da lunge dalla leua AB egualmente di$tante dall'orizon
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parents:
diff changeset
4012 te, che la po$$anza mede$ima po$ta in B $o$terr&agrave; il pe$o. come $e il centro L della
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diff changeset
4013 grauezza del pe$o AD fo$$e pi&ugrave; da lunge dalla leua BA, che il centro N
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parents:
diff changeset
4014 della grauezza del pe$o PV, pur che la linea LK tirata dal punto L &agrave; piom
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parents:
diff changeset
4015 bo dell orizonte, &amp; della leua AB pa$$i per N: $imilmente come nella prece-</I>
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diff changeset
4016 <fig>
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parents:
diff changeset
4017 <I>dente $i mo$trer&agrave;, che la po$$anza mede$ima in B $ostiene &amp; il pe$o AD, &amp;
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4018 il pe$o PV. Ma nella leua EF quanto il centro della grauezza $ar&agrave; pi&ugrave; da lun
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parents:
diff changeset
4019 ge dalla leua, tanto haur &agrave; me$tieri di po$$anza maggiore per $ostenere il pe$o. co-
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parents:
diff changeset
4020 me il centro M della grauezza del pe$o FH $ia pi&ugrave; da lunge dalla leua EF, che
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parents:
diff changeset
4021 il centro S della grauezza del pe$o XZ. $iano tirate da i punti MS le linee
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parents:
diff changeset
4022 MI SG &agrave; piombo de gli orizonti; $ar&agrave; CI maggiore di CG: &amp; perci&ograve; la po$$an
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parents:
diff changeset
4023 za di E deue e$$ere maggiore $o$tenendo il pe$o FH, che il pe$o XZ. Maper
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parents:
diff changeset
4024 lo contrario $i mo$trer&agrave; nella leua OR, cio&egrave; che quanto il centro della grauezza
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parents:
diff changeset
4025 dell'i$te$$o pe$o &egrave; pi&ugrave; dalunge dalla leua, il pe$o viene $o$tentato da po$$anza mino
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parents:
diff changeset
4026 re. peroche minore &egrave; C<G>*u</G> de CT. &amp; in modo $imile demo$trara&szlig;i ancora $tan
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parents:
diff changeset
4027 do il pe$o fra la po$$anza, &amp; il $o$tegno, ouero la po$$anzatra il $ostegno, &amp; il</I>
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parents:
diff changeset
4028 <pb n=50>
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parents:
diff changeset
4029 <I>pe$o, ilche parimente auerr&agrave; alla po$$anza che moue; peroche doue po$$anza mino-
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parents:
diff changeset
4030 re $o$tien il pe$o, iui minore po$$anza lo mouer&agrave;. &amp; doue vuole po$$anza maggio-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4031 re in $o$tentare, iui anco ella $ar&agrave; maggiore in mouere.</I>
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parents:
diff changeset
4032 <HEAD>PROPOSITIO NE X.</HEAD>
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parents:
diff changeset
4033 <p>La po$$anza $o$tenente il pe$o che habbia il centro della grauez-
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parents:
diff changeset
4034 za nella i$te$$a leua, $ia pure in qual $i voglia modo tra$porta-
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parents:
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4035 to il pe$o con la leua; vi $ar&agrave; $empre me$tieri della po$$anza
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parents:
diff changeset
4036 i$te$$a, acci&ograve; $ia $o$tenuto.
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parents:
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4037 <p><I>Sia la leua AB egualmente di$tante dall'orizonte, co'l luo $o$tegno C, &amp; E cen-
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parents:
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4038 tro della grauezza del pe$o $ia in e$$a leua. Moua$i dapoi la leua in FG, &amp; HK,</I>
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4039 <fig>
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4040 <I>&amp; il centro della grauezza in LM. Dico che la mede$ima po$$anza di KBG $em-</I> <marg><I>Per la</I> 5. <I>di questo.</I></marg>
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4041 <I>pre $o$terr&agrave; l'iste$$o pe$o. Hor percioche il pe$o nella leua AB &egrave; $i fattamen-
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parents:
diff changeset
4042 te di$po$to, come $e egli fo$$e appiccato in E; &amp; nella leua GF come $e eglifo$
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parents:
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4043 $e appiccato in L; &amp; nella leua HK, come $e egli fo$$e appiccato in M; &amp; le</I>
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parents:
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4044 <foot><I>N</I> 2</foot>
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parents:
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4045 <pb>
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parents:
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4046 <I>distanze CL CE CM $ono traloro eguali; &amp; parimente CK CB CG pur
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parents:
diff changeset
4047 tra loro eguali; $ar&agrave; la po$$anza in B al pe$o, come CE &agrave; CB; &amp; la po$$an-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4048 za in K al pe$o, come CM &agrave; CK, &amp; la po$$anza in G al pe$o, come CL</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4049 <fig>
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parents:
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4050 <I>&agrave; CG. La po$$anza mede$ma dunque in KBG $osterr&agrave; il pe$o mede$mo tra$por
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parents:
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4051 tato in vari $iti. che bi$ognaua mo$trare.</I>
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parents:
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4052 <p><I>Similmente prouera$$i, $e il pe$o fo$$e tra la po$$anza, &amp; il $o$tegno; ouero la po$-
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parents:
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4053 $anza tra il $o$tegno, &amp; il pe$o, che il mede$imo auerr&agrave; alla po$$anza, che moue.</I>
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4054 <HEAD>PROPOSITIONE XI.</HEAD>
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parents:
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4055 <p>Se la di$tanza della leua tra il $o$tegno, &amp; la po$$anza haur&agrave; pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4056 portione maggiore alla di$tanza trapo$ta dal $o$tegno al pun-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4057 to, doue dal centro della grauezza del pe$o tirata vna linea &agrave;
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parents:
diff changeset
4058 piombo dell'orizonte taglia la leua che non ha il pe$o alla po$
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parents:
diff changeset
4059 $anza; il pe$o veramente $ar&agrave; mo$$o dalla po$$anza.
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parents:
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4060 <p><I>Sia la leua AB, &amp; dal punto A appicchi$i il pe$o C; cio&egrave; il punto A $empre
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parents:
diff changeset
4061 $ia quel punto, doue la linea tirata &agrave; piombo dal centro della grauezza del pe$o ta-
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parents:
diff changeset
4062 gli la leua; &amp; $ia la po$$anza in B, &amp; il $ostegno D; &amp; DB habbia &agrave; DA</I>
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parents:
diff changeset
4063 <pb n=51>
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parents:
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4064 <I>proportione maggiore, che il pe$o C alla po$$anza in B. Dico che il pe$o C $a-
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parents:
diff changeset
4065 r&agrave; mo$$o dalla po$$anza in B. Faccia$i come BD &agrave; DA, co$i il pe$o E alla</I> <marg><I>Per la prima di questo.</I></marg>
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parents:
diff changeset
4066 <I>po$$anza in B; &amp; appicchi$i parimente il pe$o E in A: egli&egrave; chiaro che la po$-
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parents:
diff changeset
4067 $anza in B pe-
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parents:
diff changeset
4068 $a egualm&emacr;te c&otilde;
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parents:
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4069 e$$o E; cio&egrave; che
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parents:
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4070 $o$tiene il detto
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parents:
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4071 pe$o E. &amp; per-
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parents:
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4072 cioche BD ha
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parents:
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4073 proportion mag
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parents:
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4074 giore &agrave; DA che
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parents:
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4075 C alla po$$anza
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parents:
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4076 in B. &amp; come
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parents:
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4077 BD &agrave; DA, co$i</I>
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parents:
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4078 <fig>
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parents:
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4079 <I>&egrave; il pe$o F. alla po$$anza: adunque E haur&agrave; proportione maggiore alla po$$an-</I> <marg><I>Per la</I> 10. <I>del quinto.</I></marg>
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parents:
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4080 <I>za, che il pe$o C alla po$$anza i$te$$a. Per laqual co$a il pe$o E $ar&agrave; maggiore
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parents:
diff changeset
4081 del pe$o C. &amp; perche la po$$anza pe$a egualmente cone$$o E; dunque la po$$an
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parents:
diff changeset
4082 za non pe$er&agrave; egualmente cone$$o C, ma per la forza $ua inchiner&agrave; al ba$$o. &agrave;un
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parents:
diff changeset
4083 que il pe$o C $ar&agrave; mo$$o dalla po$$anza in B con la leua AB, il cui $o$tegno
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parents:
diff changeset
4084 &egrave; in D.</I>
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parents:
diff changeset
4085 <p><I>Ma $e la leua fo$$e AB, &amp; il $o$tegno A, &amp; il pe$o C appiccato in D, &amp; la
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parents:
diff changeset
4086 po$$anza in B, &amp; BA haue$$e proportione maggiore ad AD, che il pe$o C
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parents:
diff changeset
4087 alla po$$anza in B. Dico che il pe$o C mouera$$i dalla po$$anza in B. faccia$i co</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
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parents:
diff changeset
4088 <I>me BA ad AD, co$i il pe-
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parents:
diff changeset
4089 $o E alla po$$anza in B: &amp;
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parents:
diff changeset
4090 $e E $ar&agrave; appiccato in D, la
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diff changeset
4091 po$$anza in B $o$tenter&agrave; il pe-
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parents:
diff changeset
4092 $o E. Ma per hauere BA pro-
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parents:
diff changeset
4093 portione maggiore ad AD,
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parents:
diff changeset
4094 che il pe$o C alla po$$anza in
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parents:
diff changeset
4095 B; &amp; come BA ad AD,
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parents:
diff changeset
4096 co$i &egrave; il pe$o E alla po$$anza in
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diff changeset
4097 B; dunque il pe$o E haur&agrave; pro
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diff changeset
4098 portione maggiore alla po$$an</I> <marg><I>Per la</I> 10. <I>del quinto.</I></marg>
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diff changeset
4099 <fig>
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parents:
diff changeset
4100 <I>za che &egrave; in B, che il pe$o C all'i$te$$a po$$anza: &amp; perci&ograve; il pe$o E $ar&agrave; maggio
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parents:
diff changeset
4101 re del pe$o C; &amp; la po$$anza in B $o$tiene il pe$o E; dunque la po$$anza in B
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diff changeset
4102 con la leua AB mouer&agrave; il pe$o C minore del pe$o E appiccato in D, il cui $o-
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parents:
diff changeset
4103 stegno &egrave; A.</I>
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parents:
diff changeset
4104 <p><I>Sia da capo la leua AB, &amp; il $uo $o$tegno A, &amp; il pe$o C $ia appiccato in B,
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diff changeset
4105 &amp; $ia la po$$anza in D: &amp; DA habbia proportione maggiore ad AB, che
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parents:
diff changeset
4106 il pe$o C al-
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parents:
diff changeset
4107 la po$$anza,
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parents:
diff changeset
4108 che &egrave; in D. Di
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parents:
diff changeset
4109 co che il pe$o C
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parents:
diff changeset
4110 $ar&agrave; mo$$o dal
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parents:
diff changeset
4111 la po&szlig;&amacr;za che
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parents:
diff changeset
4112 &egrave; in D. Fac-
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parents:
diff changeset
4113 cia$i come D
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parents:
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4114 A ad AB,
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parents:
diff changeset
4115 co$i il pe$o E
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4116 alla po$$anza,</I>
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diff changeset
4117 <fig>
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parents:
diff changeset
4118 <I>che &egrave; in D; &amp; $ia il pe$o E pendente dal punto B: la po$$anza in D $o$ter-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4119 r&agrave; il pe$o E. Ma DA tiene proportione maggiore ad AB, che C alla po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4120 $anza in D. &amp; come DA ad AB, co$i &egrave; il pe$o E alla po$$anza in D;
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parents:
diff changeset
4121 dunque il pe$o E haur&agrave; proportione maggiore alla po$$anza che &egrave; in D, che il
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4122 pe$o C alla i$te$$a po$$anza. Per laqual co$a il pe$o E &egrave; maggiore del pe$o C.
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4123 Et percioche la po$$anza in D $o$tiene il pe$o E, dunque la detta po$$anza in
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4124 D mouer&agrave; il pe$o C appiccato in B con la leua AB, il cui $o$tegno &egrave; A. che
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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4125 bi$ognaua prouare.</I>
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4126 <HEAD>Altramente.</HEAD>
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4127 <p><I>Sia la leua AB, &amp; il pe$o C appiccato in A, &amp; la po$$anza in B, &amp; $ia il
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diff changeset
4128 $o$tegno D; &amp; DB habbia proportione maggiore &agrave; DA, che il pe$o C alla
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parents:
diff changeset
4129 po$$anza in B.
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4130 Dico che il pe-
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4131 $o C $ar&agrave; mo$
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4132 $o dalla po$$an-
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parents:
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4133 za in B. Fac-
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parents:
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4134 cia$i BE ad
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parents:
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4135 EA, come il</I>
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parents:
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4136 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4137 <I>pe$o C $i ha inuer$o la po$$anza, $ar&agrave; il punto E tra BD: percioche egli &egrave; me-</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4138 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>$tieri che BE habbia proportione minore ad EA, che DB &agrave; DA; &amp; per&ograve;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4139 BE $ar&agrave; minore di BD. &amp; percioche la po$$anza in B $o$tiene il pe$o C ap-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4140 piccato in A con la leua AB, che h&agrave; il $o$tegno E; dunque minore po$$an-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4141 za po$ta in B, che la data $o$terr&agrave; il pe$o mede$imo nel $o$tegno D. La po$$an-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4142 za data dunque po$ta in B mouer&agrave; il pe$o C con la leua AB, che ha il $o$te-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
4143 gno in D.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4144 <pb n=52>
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parents:
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4145 <p><I>Sia dapoila leua AB, &amp; il $uo $o$tegno in A, &amp; il pe$o C appiccato in D, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4146 $iala po$$anza in B; &amp; AB habbia proportione maggiore ad AD, che il
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parents:
diff changeset
4147 pe$o C alla po$$anza in B. Di
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parents:
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4148 co che il pe$o C $i mouer&agrave; dalla
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parents:
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4149 po$$anza in B. Faccia$i AB ad
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parents:
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4150 AE, come il pe$o C alla po$
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4151 $anza; $ar&agrave; $imilmente il punto E
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4152 tra BD, percioche egli &egrave; nece$$a-</I> <marg><I>Per la otta ua del</I> 5.</marg>
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parents:
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4153 <I>rio che AE $ia maggiore di A
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4154 D. &amp; $e il pe$o C fo$$e appicca</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
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4155 <fig>
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4156 <I>to in E, la po$$anza in B lo $o$tentarebbe. ma po$$anza minore po$ta in B,
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4157 che la data $o$tiene il pe$o C appiccato in D; dunque la data po$$anza in B mo-</I> <marg><I>Per il</I> 1. <I>corollario del la</I> 2. <I>di que sto.</I></marg>
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parents:
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4158 <I>uer&agrave; il pe$o C appiccato in D con la leua AB, che ha il $uo $o$tegno A.</I>
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parents:
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4159 <p><I>Sia da capo la leua AB co'l $o$tegno $uo A; &amp; il pe$o C $ia appiccato in B, &amp;
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4160 $ia la po$$anza in D. &amp; DA habbia proportione maggiore ad AB, che il pe
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4161 $o C alla po$$anza in
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4162 D. Dico che il pe$o C</I> <marg><I>Per la</I> 8. <I>del quinto.</I></marg>
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4163 <I>$ar&agrave; mo$$o dalla po$$an-
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parents:
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4164 za in D. faccia$i come
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4165 il pe$o C a'la po$$anza,
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4166 co$i DA $ia ad AE;</I> <marg><I>Per la</I> 3. <I>di questo.</I></marg>
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4167 <I>$ar&agrave; AE maggiore di</I>
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4168 <fig>
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4169 <I>AB; per e$$ere proportione maggiore da DA ad AB, che da DA ad AE.</I> <marg><I>Per il</I> 1. <I>corollario del la</I> 3. <I>di que sto.</I></marg>
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4170 <I>Che $e il pe$o C $ar&agrave; appiccato in E, egli &egrave; chiaro, che la po$$anza in D $o$ter-
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diff changeset
4171 r&agrave; il pe$o C appiccato in E. Ma po$$anza minore che la data $o$tiene l'i$te$$o pe
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diff changeset
4172 $o C in B; dunque la data po$$anza in D mouer&agrave; il pe$o C appiccato in B, con
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diff changeset
4173 la leua AB che h&agrave; il $o$tegno $uo A. come bi$ognaua mo$trare.</I>
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diff changeset
4174 <HEAD>PROPOSITIONE XII.</HEAD>
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diff changeset
4175 <HEAD>PROBLEMA.</HEAD>
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4176 <p>Fare che vna data po$$anza, moua vn pe$o dato con vna data le-
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diff changeset
4177 ua.
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diff changeset
4178 <p><I>Sia il pe$o A come cento, &amp; la po$$anza che ha da mouere $ia come diece; &amp; $ia
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diff changeset
4179 la data leua BC. Egli &egrave; bi$ogno che la po$$anza, che &egrave; diece moua il pe$o A, che
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diff changeset
4180 &egrave; cento, con la leua BC. Diuida$i BC in D con $i fatta maniera che CD hab
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4181 bia la propor tione mede$ima &agrave; DB, che ha cento &agrave; diece, cio&egrave; diece ad vno; per-</I>
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4182 <fig>
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diff changeset
4183 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>cioche $e D $i face$$e $o$tegno, egli &egrave; mani$e$to, che la po$$anza in C come diece
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diff changeset
4184 pe$er&agrave; egualmente co'l pe$o A appiccato in B, cio&egrave; che $o$terr&agrave; il pe$o A. Pren</I>
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4185 <marg><I>Per lo lein ma di questo.</I></marg> <I>da$i tra BD qual $i voglia punto, come E, &amp; faccia$i E il $o$tegno. Hor per-
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diff changeset
4186 cioche maggiore &egrave; la proportione di CE ad EB, che di CD &agrave; DB; CE haur&agrave;
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4187 proportione maggiore ad EB, che il pe$o A alla po$$anza di diece po$ta in C;
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4188 dunque la po$$anza di diece po$ta in C mouer &agrave; il pe$o A, che &egrave; cento, appiccato</I>
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4189 <marg><I>Per la</I> 11. <I>di questo.</I></marg> <I>in B con la leua BC, che ha il $uo $o$tegno E.</I>
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4190 <p><I>Ma $e la leua fo$$e BC, &amp; il $o$tegno B. diuida$i CB in D per $i fatta maniera,
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4191 che CB habbia la proportione i$te$$a &agrave; BD, che ha cento &agrave; diece: &amp; $e il pe$o
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4192 A $ar&agrave; appic
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4193 cato in D, &amp;
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4194 la po$$anza in
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4195 C, la po$$an-</I>
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4196 <marg><I>Per la</I> 2. <I>di questo.</I></marg> <I>za in C come
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4197 diece $o$terr&agrave;
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4198 anco il pe$o
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4199 A appiccato</I>
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4200 <fig>
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4201 <I>in D. Prenda$i qual $i uoglia punto tra DB, come E, &amp; ponga$i il pe$o A in</I>
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4202 <marg><I>Per la ottaua del quinto.</I></marg> <I>E; &amp; per e$$ere proportione maggiore da CB &agrave; BE, che da BC &agrave; BD; CB
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4203 haur&agrave; proportione maggiore &agrave; BE, che il pe$o A di cento alla po$$anza di diece.
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4204 Dunque la po$$anza d<*> diece po$ta in C mouer&agrave; il pe$o A di cento appiccato in E</I>
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4205 <marg><I>Per la</I> 11. <I>di questo.</I></marg> <I>con la leua BC, che ha il $o$tegno $uo B. che bi$ognaua menar ad effetto.</I>
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4206 <p><I>Ma ci&ograve; non $i puote mandar' ad e$ecutione con la leua BC, che habbia il $o$tegno $uo
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4207 in B, &amp; il pe$o A di cento $ia appiccato in C. Percioche ponga$i la po$$anza
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4208 $o$tenente il pe$o A comunque $i $ia tra BC, come in D; $empre la po$$anza
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4209 $ar&agrave; maggiore del pe$o A. Per laqual co$a egli &egrave; me$tieri che $empre la data po$-</I>
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4210 <pb n=53>
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4211 <I>$anza $ia maggiore del pe$o A. Sia dunque la po$$anza data, come cento cin-</I> <marg><I>Per il</I> 2. <I>corollario della</I> 3. <I>di questo.</I></marg>
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4212 <I>quanta. Diuida$i BC in D $i fattamente che CB $ia &agrave; BD come cento cin-
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4213 quanta &agrave; cento, cio&egrave; tre &agrave; due: &amp; $e la po$$anza $ar&agrave; po$ta in D, egli &egrave; chiaro,
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4214 che la po$$anza in D $o$ter-
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4215 r&agrave; il pe$o A appiccato i<*> C.</I> <marg><I>Per la</I> 3. <I>di questo.</I></marg>
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4216 <I>&amp; co$i prenda$i tra DC
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4217 qual $i voglia punto, come
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4218 E, &amp; ponga$i la po$$aaza
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4219 mouente in E, &amp; per e$$ere
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4220 proportion maggiore da EB
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4221 &agrave; BC, che da DB &agrave; BC;
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4222 haur&agrave; EB proportione mag
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4223 giore &agrave; BC, che il pe$o A</I> <marg><I>Per la</I> 8. <I>del quinto.</I></marg>
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4224 <fig>
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4225 <I>alla po$$anza in E. Dunque la po$$anza di cento cinquanta po$ta in E mouer&agrave; il
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4226 pe$o A di cento appiccato in C con la leua BC che h&agrave; il $o$tegno B. come bi-</I> <marg><I>Per la</I> 11. <I>di questo.</I></marg>
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4227 <I>$ognaua oprare.</I>
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4228 <HEAD>COROLLARIO.</HEAD>
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4229 <p>Di qui &egrave; manife$to, $e la data po$$anza $ar&agrave; maggiore del dato
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4230 pe$o, que$to poter$i fare, ouero $tando in maniera la leua,
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4231 che il $o$tegno $uo $ia fra il pe$o, &amp; la po$$anza; ouero che el-
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4232 la habbia il pe$o fra il $o$tegno, &amp; la po$$anza; ouero alla fine
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4233 e$$endo po$ta la po$$anza fra il pe$o, &amp; il $o$tegno.
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4234 <p>Ma $e la data po$$anza $ar&agrave; minore, ouero eguale al dato pe$o,
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4235 egli &egrave; parimente chiaro, che il mede$imo $i puote mandare ad
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4236 e$ecutione $olamente $tando la leua in maniera, che il $o$te-
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4237 gno $uo $ia tra il pe$o, &amp; la po$$anza; ouero che ella habbia il
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4238 pe$o fra il $o$tegno, &amp; la po$$anza.
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4239 <HEAD>PROPOSITIONE XIII.</HEAD>
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4240 <HEAD>PROBLEMA.</HEAD>
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4241 <p>Dati quanti $i vogli&atilde; pe$i appiccati douunque $i $iano nella leua
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4242 il cui $o$tegno parimente $ia dato, ritrouare vna po$$anza la
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4243 quale $o$tenga i dati pe$i in vn punto dato.
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4244 <foot><I>O</I></foot>
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4245 <pb>
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4246 <p><I>Siano i dati pe$i ABC nella leua DE, &amp; il $o$tegno $uo F, douunque ne' pun-
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4247 ti DGH $iano appiccati, &amp; habbia$i &agrave; collocare la po$$anza nel punto E. egli
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4248 &egrave; me$tieri trouare la po$$anza, laquale $o$tenga in E i dati pe$i ABC con la le
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4249 ua DE. diuida$i DG in K $i fattamente, che DK $ia &agrave; KG come il pe-
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4250 $o B al pe$o A; dapoi diuida$i KH in L $i fattamente, che KL $ia ad LH
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4251 come il pe$o C &agrave; i pe$i BA, &amp; come FE ad FL, co$i $accian$i i pe$i ABC</I>
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4252 <fig>
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4253 <I>tutti in$ieme alla po$$anza, laquale ponga$i in E. dico, che la po$$anza in E. $o-</I>
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4254 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>$tenter&agrave; i dati pe$i ABC appiccati in DGH con la leua DE che ha il $o$te-</I>
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4255 <marg><I>Per la</I> 5. <I>di questo della bilancia.</I></marg> <I>gno $uo F. Hor percioche $e i pe$i ABC $o$$ero appiccati in$ieme in L, la po$
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4256 $anza in E $o$terrebbe i dati pe$i appiccati in L; ma i pe$i ABC pe$ano tan-
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4257 to in L, quanto $e C in H, &amp; BA in$ieme $o$$ero appiccati in K; &amp; AB</I>
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4258 <marg><I>Per la</I> 2. <I>di questo.</I></marg> <I>nel K tanto pe$ano, quanto $e A in D, &amp; B in G fo$$ero appiccati; dun-
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4259 qu&egrave; la po$$anza in E $o$tenter&agrave; i dati pe$i ABC appiccati in DGH con la
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4260 leua DE che ha il $o$tegno F. Che $e la po$$anza haue$$e ad e$$ere po$ta in qual
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4261 $i voglia altro punto dalla leua DE fuor che in F, come in K; faccia$i come
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4262 FK ad FL, co$ii pe$i ABC $iano alla po$$anza: $imilmente dimo$treremo,
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4263 che la po$$anza in K $o$terr&agrave; i pe$i ABC ne' punti DGH appiccati. come
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4264 bi$ognaua fare.</I>
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4265 <p><I>Da que$ta, &amp; dalla quinta di que$to, $e i pe$i ABC $aranno po$ti in qual $i voglia
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4266 modo nella leua DE, &amp; che bi$ogni ritrouare la po$$anza, la quale debba $o$te-
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4267 nere in E i dati pe$i $iano tirate da i centri delle grauezze de i pe$i le linee AB
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4268 C &agrave; piombo de gli orizonti, lequali taglino la leua DE ne' punti DGH; &amp;</I>
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4269 <pb n=54>
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4270 <I>$i operino le altre co$e nell'i$te$$o modo: egli &egrave; manife$to, che la po$$anza in E,</I>
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4271 <fig>
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4272 <I>ouero in K $o$tenter&agrave; i dati pe$i, percioche egli &egrave; l'i$te$$o come $e i pe$i fo$$ero
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4273 appiccati in DGH.</I>
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4274 <HEAD>PROPOSITIONE XIIII.</HEAD>
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4275 <HEAD>PROBLEMA.</HEAD>
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4276 <p>Fare che vna data po$$anza moua quanti pe$i $i vogliano, po$ti
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4277 douunque, &amp; in qualunque modo $i $ia in vna data leua.
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4278 <p><I>Sia la data leua DE, &amp; $iano i dati pe$i, come &egrave; po$to nel precedente corollario, &amp;
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4279 $ia A come cento, B come cinquanta, &amp; C come trenta; &amp; la data po$$an-
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4280 za $ia come trenta. $iano po$te le co$e mede$ime, &amp; ritroui$i il punto L; dapoi</I>
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4281 <fig>
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4282 <I>diuida$i LE in F, $i $attamente che FE ad FL $ia come cento ottanta &agrave;
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4283 trenta, cio&egrave; $ei ad vno, &amp; $e F $i face$$e $o$tegno, la po$$anza come trenta</I>
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4284 <foot><I>O</I> 2</foot>
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4285 <pb>
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4286 <marg><I>Per la</I> 13. <I>di questo.</I></marg> <I>in E $o$terrebbe i pe$i ABC. pigli$i dunque tra LF qualunque punto come
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4287 M, &amp; faccia$i M il $o$tegno: egli &egrave; manife$to, che la po$$anza po$ta in E co-</I>
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4288 <fig>
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4289 <marg><I>Per la</I> 11. <I>di questo.</I></marg> <I>me trenta mouer&agrave;i pe$i ABC come cento ottanta con la leua DE. che bi$o-
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4290 gnaua mo$trare.</I>
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4291 <p><I>Ma ci&ograve; non potremo gi&agrave; vniuer$almente menare ad ef$etto, $e il $o$tegno $o$$e nelle
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4292 $tremit&agrave; della leua, come in D; peroche la proportione di DE &agrave; DL, cio&egrave; la
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4293 proportione de' pe$i ABC alla po$$anza, laquale ha da $o$tenere i pe$i $empre
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4294 &egrave; data. Laqual co$a molto meno anco $i potrebbe fare, $e la po$$anza $i haue$$e
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4295 &agrave; porre tra DL.</I>
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4296 <HEAD>PROPOSITIONE XV.</HEAD>
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4297 <HEAD>PROBLEMA.</HEAD>
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4298 <p>Ma percioche mentre i pe$i $i mouono con la leua, ha la leua an-
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4299 cora grauezza, della quale infin qui non $i &egrave; fatto mentione
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4300 alcuna: per&ograve; dimo$triamo primieramente in che modo $i tro
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4301 ui la po$$anza, la quale $o$tenga nel dato punto la leua data, il
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4302 cui $o$tegno $ia parimente dato.
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4303 <p><I>Sia la leua data AB, il cui $o$tegno C $ia dato: &amp; $ia il punto D nelquale $i hab
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4304 bia &agrave; collocare la po$$anza, che debba $o$tentare la leua AB, $i $attamente che
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4305 re$ti immobile. $ia dal punto C tirata la linea CE &agrave; piombo dell'orizonte la
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4306 quale diuida la leua AB in due parti AE EF; &amp; della parte AE $ia il
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4307 centro G della grauezza, &amp; della parte EF il centro del'a grauezza $ia H,
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4308 &amp; dai punti GH $iano tirate le linee GK HL &agrave; piombo de gli orizonti, le</I>
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4309 <pb n=55>
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4310 <I>quali taglino la linea AF ne' punti KL. Hor percioche la leua AB &egrave; diui-
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4311 $a dalla linea CE in due parti, cio&egrave; AE EF; per&ograve; la leua AB, niente altro
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4312 $ar&agrave;, che due pe$i AE EF nella leua, ouero bilancia AF po$ti; il cui appicca
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4313 mento, ouero $o$tegno &egrave; C. Per laqual co$a i pe$i AE EF $aranno co$i po$ti,</I>
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4314 <fig>
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4315 <I>come $e fo$$ero appiccati in KL. Diuida$i dunque KL in M, $i fattamente,
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4316 che KM $ia ad ML come la grauezza della parte EF alla grauezza della
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4317 parte AE; &amp; come CA &agrave; CM, co$i $accia$i la grauezza di tutta la leua
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4318 AB alla po$$anza, laquale $e in D $ar&agrave; collocata (pur che DA $ia &agrave; piombo</I> <marg><I>Per la</I> 13. <I>di questo.</I></marg>
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4319 <I>dell'orizonte) pe$er&agrave; egualmente con la leua; cio&egrave; $o$terr&agrave; la leua AB premendo
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4320 in gi&ugrave;, che bi$ognaua trouare.</I>
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4321 <p><I>Che $e la po$$anza $i haue$$e &agrave; porre nel punto B. Faccia$i come CF &agrave; CM,
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4322 co$i il pe$o AB alla po$$anza. Con $imile modo prouera$$i che la po$$anza in
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4323 B $o$terr&agrave; la leua AB. &amp; l'i$te$$o d mo$trera$$i in qualunque altro $ito s'haue$-
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4324 $e &agrave; porre la po$$anza, (fuor che in E) come in N. peroche faccia$i CO &agrave;
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4325 CM come AB alla po$$anza, laquale $e $i porr&agrave; in N $o$tenter&agrave; la leua AB.</I>
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4326 <p>Ma aggiunga $i il pe$o appiccato, ouero po$to nella leua; come,
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4327 po$te le co$e i$te$fe, fia il pe$o P appiccato in A; &amp; la po$-
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4328 $anza s'habbia &agrave; porre in B, $i fattamente che $o$tenghi la le
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4329 ua AB in$ieme col pe$o P.
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4330 <p><I>Diuida$i AM in Q, $i $attamente, che AQ $ia &agrave; QM, come la grauezza</I> <marg><I>Per la</I> 13 <I>di questo.</I></marg>
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4331 <I>della leua AB alla grauezza del pe$o P; dapoi come CF &agrave; CQ, co$i fac-</I> <marg><I>Per la</I> 6. <I><*> Archirnc<*> dells col che egual meiue pe$e no.</I></marg>
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4332 <I>cia$i la grauezza AB, &amp; P in$ieme alla po$$anza, la quale ponga$i in B: e<*>li
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4333 &egrave; manife$to, che la po$$anza in B $o$terr&agrave; la leua AB in$ieme co'l pe$o P. Che
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4334 $e fo$$e CA &agrave; CM, come AB &agrave; P; $arebbe il punto C il loro centro della
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diff changeset
4335 grauezza, &amp; perci&ograve; la leua AB in$ieme co'l pe$o P $enza la po$$anza po$ta in
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4336 <pb>
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diff changeset
4337 B $tar&agrave; $erma. Ma $e il centro della grauezza de' pe$i fo$$e tra CF, come in
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diff changeset
4338 O. Faccia$i come CF &agrave; CO, co$i AB &amp; P in$ieme alla po$$anza, laqua-
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diff changeset
4339 le in B $o$tenter&agrave; s&igrave; la leua AB come il pe$o P.</I>
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diff changeset
4340 <fig>
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diff changeset
4341 <p><I>Similmente mo$trera$$i il mede$imo $e fo$$ero pi&ugrave; pe$i nella leua AB douunque,
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4342 &amp; in qual modo $i $ia di$po$ti.</I>
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4343 <p><I>Oltre &agrave; ci&ograve; da que$te co$e $i puote cono$cere, come nella decimaquarta propo$itione di
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diff changeset
4344 que$to habbiamo in$egnato, in che modo cio&egrave; po$$iamo mouere i dati pe$i po$ti do
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diff changeset
4345 uunque $i voglia nella leua, con vna data po$$anza, e con vna data leua, ilche po$-
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diff changeset
4346 $iamo fare nell'i$te$$o modo non $olamente con$iderando la grauezza della leua; ma
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diff changeset
4347 anco gli altri accidenti, iquali $ono $tati di $opra mo$trati $enza la grauezza del-
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diff changeset
4348 la leua; con $imile modo con$iderata la grauezza della leua in$ieme co' pe$i, ouero
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diff changeset
4349 $enza pe$i $i mo$treranno.</I>
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4350 <HEAD>IL FINE DELLA LEVA.</HEAD>
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4351 <pb n=56>
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4352 <fig>
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4353 <HEAD>DELLA TAGLIA.</HEAD>
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4354 <fig>
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4355 <p>Con l'in$trumento della Taglia $i pu&ograve; mouere il pe
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4356 $o in molti modi: ma percioche in tutti &egrave; la ragio-
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4357 ne mede$ima: per&ograve; affine che la co$a re$ti pi&ugrave; chia-
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diff changeset
4358 ra, intenda$i in quello che $i ha da dire, che il pe-
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4359 $o $empre $i habbia da mouere all'ins&ugrave; ad angoli
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diff changeset
4360 retti al piano dell'orizonte in que$to modo.
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4361 <p><I>Sia il pe$o A ilquale $i habbia ad alzare in s&ugrave; ad angoli retti al piano dell'orizonte:
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4362 &amp; come $i co$tuma di fare: $ia
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4363 aitaccata di $opra vna taglia,
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4364 che habbia due girelle, gli a$$etti
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4365 de<*>lequali $iano in BC: &amp; $ia
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4366 anche legata vn'altra taglia al
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4367 pe$o, laquale $imilmente habbia
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4368 due girelle, gli a$$etti delle qua-
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4369 li $<*>no in DE: &amp; per tutte
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4370 le girelle d'ambedue le taglie $ia
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4371 condo<*>a intorno la corda, la-
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4372 quale in vno de i capi, come in
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4373 F deue e$$ere legata. Ponga$i
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4374 ancorala po$$anza che moue in
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4375 G, laquale mentre di$cende, il
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4376 pe$o A per lo contrario $ar&agrave; le-
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4377 uato in $u$o, $i come afferma Pa
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4378 po nell'ottauo libro delle rac-
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parents:
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4379 colte matematiche, &amp; Vitruuio
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4380 nel decimo dell'architettura, &amp;
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4381 altri.</I>
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4382 <fig>
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4383 <p>Hor in che modo que$to
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4384 in$trumento della ta-
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4385 glia $i riduca alla leua,
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4386 &amp; perche vn pe$o gran-
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4387 de $i moua da piccola
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4388 forza, &amp; in qual modo,
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4389 &amp; in quanto tempo; &amp;
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parents:
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4390 perche la corda debba
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4391 e$$ere legata da vn ca-
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4392 po: &amp; quale debba e$-
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4393 $ere l'officio della ta-
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4394 glia, che &egrave; po$ta di $ot-
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4395 to, &amp; quale di quella,
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4396 che $t&agrave; di $opra, &amp; in
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4397 che modo $i po$$a tro-
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4398 uare ogni proportio-
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4399 ne data ne i numeri tra la po$$anza, &amp; il pe$o, diciamo.
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4400 <pb n=57>
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4401 <HEAD>LEMMA.</HEAD>
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4402 <p>Siano due linee rette AB CD egualmente di$tanti, lequali
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4403 tocchino il cerchio ACE ne' punti AC, il centro delqual
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4404 cerchio $ia F, &amp; $i congiunghino FA &amp; FC. dico chela
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parents:
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4405 linea AFC &egrave; retta.
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4406 <p><I>Tiri$i la linea FE egualmente di$tante dal-</I> <marg><I>Per la</I> 18. <I>del terzo.</I></marg>
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4407 <I>le linee AB CD. Et percioche AB
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4408 &amp; FE $ono egualmente di$tanti, &amp;</I> <marg><I>Per la</I> 29. <I>del primo.</I></marg>
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4409 <I>l'angolo BAF &egrave;retto: $ar&agrave; anco A
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4410 FE retto, &amp; all'ifte$$o modo CFE $a</I> <marg><I>Per la</I> 14. <I>del primo.</I></marg>
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4411 <I>r&agrave; retto: adunque la linea AFC &egrave;ret-
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4412 ta, ilche s'hauea &agrave; dimo$trare.</I>
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4413 <fig>
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4414 <HEAD>PROPOSITIONE I.</HEAD>
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4415 <p>Se la corda $i condurr&agrave; intorno alla girella della taglia, che $ia
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4416 attaccata di $opra, &amp; che vno delli $uoi capi $i leghi al pe$o, &amp;
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4417 l'altro tratanto $ia pre$o dalla po$sanza, che $o$tiene il detto
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4418 pe$o; la po$sanza $ar&agrave; eguale al pe$o.
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4419 <foot><I>P</I></foot>
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4420 <pb>
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4421 <p><I>Sia il pe$o A alquale venga legata la corda &agrave; B: &amp; la taglia, che habbia la girella
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4422 CEF il cui centro D appicchi$i di $opra: &amp; $ia parimente D il centro dell'a$
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4423 $etto, &amp; d'intorno alla girella volga$i la corda BCEFG: &amp; $ia in G la po$-
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4424 $anza, che $o$tiene il pe$o A. Dico la po$$anza po$tain G e$$ere eguale al pe-
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parents:
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4425 $o A. $ia FG
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4426 egualmente di-
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parents:
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4427 $tante da CB.
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parents:
diff changeset
4428 Percioche d&umacr;-
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4429 que il pe$o A
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diff changeset
4430 $ta fermo, $a-</I>
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4431 <marg><I>Per la</I> 8. <I>di questo della bilancia.</I></marg> <I>r&agrave; CB &agrave; piom
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diff changeset
4432 bo del piano
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4433 dell'orizonte.</I>
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diff changeset
4434 <marg><I>Per la <*>ta <*>a dell'vndecimo.</I></marg> <I>onde FG $a-
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diff changeset
4435 r&agrave; al piano
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diff changeset
4436 i$te$$o &agrave; piom-
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diff changeset
4437 bo. Siano i
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diff changeset
4438 punti CF nel-
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diff changeset
4439 la girella, da
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diff changeset
4440 quali le corde
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diff changeset
4441 CB FG $cen
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diff changeset
4442 dano nel pia-
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diff changeset
4443 no dell'orizon
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4444 te ad angoli
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parents:
diff changeset
4445 retti, tocche-
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parents:
diff changeset
4446 ranno le dette
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diff changeset
4447 corde BC FG
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diff changeset
4448 la girella CE</I>
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diff changeset
4449 <fig>
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diff changeset
4450 <I>F ne'punti CF peroche non po$$ono $egare la girella. Siano congiunte le li-</I>
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diff changeset
4451 <marg><I>Per la</I> 18. <I>del terzo.</I></marg> <I>nee DC DF. $ar&agrave; retta la linea CF &amp; $aranno anche retti gli ang oli DCB
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4452 DFG. Ma percioche BC $ta &agrave; piombo s&igrave; all'orizonte, come ad e$$a CF $ar&agrave;</I>
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4453 <marg><I>Per la</I> 28. <I>del primo.</I></marg> <I>la detta CF egualmente di$tante dall'orizonte. &amp; concio$ia che il pe$o $ia attac-
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4454 cato in CB &amp; la po$$anza $ia in G ch'&egrave; il mede$imo, come $e ella fo$$e in F:</I>
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4455 <marg><I>Per la</I> 1. <I>del</I> 1. <I>d'Archimede delle co$e che pe$ano egual mem<*>:.</I></marg> <I>$ar&agrave; CF tanto quanto vna bilancia, ouero vna leua, il cui centro, ouero $o$tegno
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4456 $ar&agrave; D, imperoche la girella &egrave; $o$tenuta nell'a$$etto, &amp; il punto D per e$$ere
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4457 centro dell'a$$etto, &amp; della girellarimane immobile, $eben l'vno, &amp; l'altro $ivol
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4458 gono intorno. Per laqual co$a e$$endo la di$tanza DC eguale alla di$tanza DF,
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4459 &amp; la po$$anza che &egrave; in F contrape$i egualmente al pe$o A attaccato in C $o-
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diff changeset
4460 $tenendo il pe$o in modo, che non cala al ba$$o, $ar&agrave; la po$$anza a$$egnata in F oue
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4461 ro in G che &egrave; tutt'vno, eguale al pe$o A: percioche po$ta in G fal'i$te$$o effet
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4462 to che $e nel mede$imo G $o$$e appiccato vn'altro pe$o eguale al pe$o A, liquali
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parents:
diff changeset
4463 pe$i attaccati in CF contrape$erann<*> egualmente. Oltre &agrave; ci&ograve; non facendo$i moto</I>
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4464 <pb n=58>
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4465 <I>in niuna delle parti, $ar&agrave; l'i$te$$o e$$endo circondata in que$to modo la girella intor-
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parents:
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4466 no con vna corda $ola BC e FG come $e $u$$ero due corde BC FG legate
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4467 alla leua, ouero alla bilancia CF.</I>
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4468 <HEAD>COROLLARIO.</HEAD>
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parents:
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4469 <p>Da que$to pu&ograve; e$$ere manife$to, che il mede$imo pe$o dalla i$te$-
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4470 $a po$$anza puote e$$ere tuttauia $o$tenuto $enza anche alcu-
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parents:
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4471 no aiuto di que$ta taglia.
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parents:
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4472 <p><I>Percioche $ia il pe$o H eguale al pe$o A &agrave; cui $ia legata la corda KL &amp; $iala
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4473 po$$anza, che $o$tiene il pe$o H in L. Hor concio$ia che volendo $o$tenere al-
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4474 cun pe$o $enza aiuto veruno vi bi$ogni tanta forza, quanta $ia eguale al pe$o; la
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4475 po$$anza che &egrave; in L $ar&agrave; eguale al
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4476 pe$o H, ma il pe$o H &egrave; po$to
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4477 eguale al pe$o A, alquale &egrave; anco
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4478 eguale la po$$anza G. $ar&agrave; dun-
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4479 que la po$$anza in G eguale alla
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4480 po$$anza in L che &egrave; l'i$te$$o, come $e
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4481 la i$te$$a po$$anza $o$tene$$e il pe$o
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4482 mede$imo. Oltre &agrave; ci&ograve; $e le po$$an
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4483 ze, lequali $ono in G &amp; in L $o$
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4484 $ero eguali fra loro, &amp; poi $epara-
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4485 tamente dai pe$i minori, &egrave; co$a chia
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parents:
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4486 ra, che le dette po$$anze non $areb
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4487 bono $ufficienti &agrave; $o$tenere quei pe$i
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4488 che $e que$te po$$anze $aranno mag
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parents:
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4489 giori, egli &egrave; manife$to, che e$$e mo-
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parents:
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4490 ueranno i pe$i. &amp; co$i la po$$anza
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4491 in L col pe$o H venir&agrave; ad e$$e-
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4492 re nella proportione mede$ima, co-
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parents:
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4493 me la po$$anza in G col pe$o A.</I>
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4494 <fig>
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parents:
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4495 <p><I>Ma perche nella dimo$tratione &egrave; $tato
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4496 pre$uppo$to che l'a$$etto $i volga in
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4497 torno, ilquale il pi&ugrave; delle volte $t&agrave;
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4498 immobile, per&ograve; $tando anche immobile il detto a$$etto dimo$tri$i li$te$$o.</I>
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parents:
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4499 <foot><I>P</I> 2</foot>
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4500 <pb>
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4501 <p><I>Sia la girella della taglia CEF, il cui centro $ia D, &amp; $ia l'a$$etto GHK, il cen-
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parents:
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4502 tro delquale $ia mede$imamenie D: Tiri$i il diametro CGDKF egualmente
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parents:
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4503 di$tante dall'orizonte. et percioche m&emacr;
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4504 tre la girella $i volge, la circonferenza
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4505 del cerchio CEF $empre va egual-
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4506 mente di$tante alla circonferenza del-
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4507 l'a$$etto GHK: percioche ella $i
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4508 volge intorno &agrave; l'a$$etto, &amp; le circonfe
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4509 renze de' cerchi egualmente di$tanti
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4510 hanno il centro mede$imo, $ar&agrave; il pun-
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4511 to D $empre centro &amp; della girella,
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4512 &amp; dell'a$$etto. Per laqual co$a e$$en-
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4513 do DC eguale &agrave; DF &amp; DG ad
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4514 e$$o DK, $ar&agrave; GC ad e$$o KF egua
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4515 le. Se dunque nella leua, ouero bilan-
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4516 cia CF $i attaccheranno pe$i eguali,
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parents:
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4517 contrape$eranno egualmente, peroche
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4518 la di$tanza CG &egrave; eguale alla di$tan-
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parents:
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4519 za KF, &amp; l'a$$etto GHK immobi
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diff changeset
4520 le $erue per centro, ouero per $o$tegno. Stando dunque immobile l'a$$etto, $e la
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diff changeset
4521 po$$anza $i metter&agrave; in F che $o$tenga il pe$o appiccato in C, $ar&agrave; la po$$anza
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diff changeset
4522 in F ad e$$o pe$o eguale, ilche era da mo$trare.</I>
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diff changeset
4523 <fig>
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diff changeset
4524 <p><I>Et concio$ia che del tutto $ia il mede$imo, che l'a$$etto ouero $i volga intorno, &ograve; non
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diff changeset
4525 $i volga: per&ograve; $ialecito nelle co$e, che $i hanno &agrave; dire, prendere in loco dello a$$etto
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diff changeset
4526 il centro $olamente.</I>
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diff changeset
4527 <HEAD>PROPOSITIONE II.</HEAD>
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diff changeset
4528 <p>Se la corda $i condurr&agrave; intorno alla girella della taglia, che $ia
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diff changeset
4529 legata al pe$o, legando l'vn de' capi $uoi in qualche loco, &amp;
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diff changeset
4530 l'altro $ia pre$o dalla po$$anza, che $o$tiene il pe$o, $ar&agrave; la po$-
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diff changeset
4531 $anza la met&agrave; meno del pe$o.
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diff changeset
4532 <p><I>Sia il pe$o A. $ia BCD la girella della taglia legata al pe$o, il cui centro $ia E,
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diff changeset
4533 $ia dapoi inuolta d'intorno la girella la corda FBCDG, &amp; legata in F, &amp; $ia
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diff changeset
4534 la po$$anza in G che $o$tiene il pe$o A. Dico che la po$$anza in G &egrave; la met&agrave;
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diff changeset
4535 meno del pe$o A. Siano le corde FB GD perpendicolari all' orizonte del pun</I>
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diff changeset
4536 <marg><I>Per la $esta dell'vndecimo.</I></marg> <I>to E, lequali $aranno fra loro egualmente di$tanti: &amp; tocchino le dette corde
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diff changeset
4537 FBGD, il cerchio BCD ne i punti BD: congiunga$i la linea BD ella pa$-</I>
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diff changeset
4538 <pb n=59>
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diff changeset
4539 <I>$er&agrave; per E centro, &amp; $ar&agrave; egualmente di$tante dall'or&igrave;zonte di e$$o centro, &amp;</I> <marg><I>Per la procedense.</I></marg>
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diff changeset
4540 <I>concio$ia che la G po$$anza debba $o$tenere il pe$o A con la taglia; bi$ogna,
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diff changeset
4541 che la corda $ia legata dal'vno de' capi, come in</I> F, <I>$i fattamente, che F fac-
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4542 cia re$i$tenza egualmente almeno alla po$$anza, ch'&egrave; in G, altramente e$$a po$$an
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diff changeset
4543 zain G non potrebbe &agrave; modo alcuno $o$tenere il pe$o. Et perche la po$$anza</I>
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diff changeset
4544 <fig>
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diff changeset
4545 <I>$o$tiene la girella mediante la corda, &amp; la girella $o$tiene la parte re$tante della
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4546 taglia mediante l'a$$etto, allaqual taglia il pe$o &egrave; appiccato, pe$er&agrave; que$ta parte del-
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4547 la taglia nell'a$$etto, cio&egrave; nel centro E: onde il pe$o A pe$er&agrave; $imilmente nel me
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diff changeset
4548 de$imo centro E, come $e egli fo$$e appiccato in E. Po$ta dunque la po$$auza
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4549 che st&agrave; in G doue &egrave; D (perche egli &egrave; totalmente il mede$imo) $ar&agrave; BD come
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parents:
diff changeset
4550 vna l&egrave;ua, il cui $o$tegno $ar&agrave; B, &amp; il pe$o attaccato in E, &amp; la po$$anzain D:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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4551 &amp; e$$endo la corda FB immobile, conueneuolmente il B puote $eruire per $o-
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diff changeset
4552 $tegno. Ma ci&ograve; pi&ugrave; chiaramente apparer&agrave; dapoi. Hora percioche la po$$anza al</I> <marg><I>Per la</I> 8. <I><*> questo nella leua.</I></marg>
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4553 <I>pe$o ha la proportione mede$ima, che h&agrave; BE &agrave; BD, &amp; BE in proportione
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4554 &egrave; la met&agrave; manco di BD: dunque la po$$anza che &egrave; in G $ar&agrave; la met&agrave; meno del
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diff changeset
4555 pe$o A. Che bi$ognaua dimo$trare.</I>
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4556 <p><I>Que$to dunque $t&agrave; nell'i$te$$o modo con vna corda $ola FBCDG condotta intor-
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diff changeset
4557 no alla girella, come $e $o$$ero due corde BF GD legate alla leua BD, il cui</I>
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4558 <fig>
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4559 <I>$o$tegno $ar&agrave; B, &amp; il pe$o fo$$e attaccato in E &amp; la po$$anza, che lo $o$tiene
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diff changeset
4560 $o$$e in D, ouero in G che &egrave; l'iste$$o.</I>
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4561 <HEAD>COROLLARIO I.</HEAD>
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4562 <p>Da que$to dunque &egrave; manife$to, che il pe$o &egrave; $o$tenuto &agrave; que$to
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4563 modo da po$$anza minore in proportlone della met&agrave; meno,
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4564 di quel che $arebbe $enza aiuto veruno di cotale taglia.
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4565 <pb n=60>
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4566 <p><I>Come $ia il pe$o H eguale al
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4567 pe$o A, alquale $ia lega-
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parents:
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4568 tala corda KL, &amp; la po$-
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diff changeset
4569 $anza, che &egrave; in L $o$ten-
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parents:
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4570 gail pe$o H, $ar&agrave; la po$-
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parents:
diff changeset
4571 $anza in L $eparatamente
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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4572 eguale al pe$o H, &amp; al
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parents:
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4573 pe$o A; ma la po$$an-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4574 za, che &egrave; in G in propor-
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4575 tione &egrave; la met&agrave; manco del
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4576 pe$o A. Per laqual co$a
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parents:
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4577 la po$$anzache &egrave; in G $a-
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4578 r&agrave; la met&agrave; meno in propor-
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parents:
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4579 tione della po$$anza, che &egrave;
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4580 in L, &amp; in que$to modo
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4581 ne gli altri tutti di que$ta
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parents:
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4582 maniera $i potr&agrave; ritrouare
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4583 la proportione.</I>
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4584 <fig>
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4585 <HEAD>COROLLARIO II.</HEAD>
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4586 <p>Egli &egrave; manife$to ancora, $e $aranno due po$$anze l'vna in G &amp;
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4587 l'altra in F, lequali $o$tengano il pe$o A, che l'vna, &amp; l'al-
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4588 tra in$ieme $aranno eguali al pe$o A, &amp; cia$cheduna di loro
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parents:
diff changeset
4589 $o$terr&agrave; la met&agrave; del pe$o A.
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4590 <p><I>Et que$to &egrave; mani$e$to dal terzo &amp; dal quarto corollario del $econdo di que$tonel trat.
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4591 tato della leua.</I>
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4592 <HEAD>COROLLARIO III.</HEAD>
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4593 <p>Oltre &agrave; ci&ograve; que$to parimente $i fa noto, perche cio&egrave; la corda
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4594 debba e$$ere legata nell'vno de' capi.
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4595 <HEAD>PROPOSITIONE III.</HEAD>
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4596 <p>Se &agrave; cia$cuna dell'vna, &amp; l'altra girella delle due taglie, l'vna del
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4597 le quali $ia po$ta di $opra, &amp; l'altra di $otto, &amp; que$ta $ia lega-
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4598 ta al pe$o; $ar&agrave; condotta intorno la corda: legando l'vno de'
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4599 capi in qualche loco, &amp; l'altro $ia tenuto dalla po$$anza, che
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4600 $o$tiene il pe$o, $ar&agrave; la po$$anza la met&agrave; meno del pe$o.
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4601 <p><I>Sia il pe$o A, $ia BCD la girella della
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4602 taglia, che $ia legata al pe$o A, il cui
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4603 centro $ia K, &amp; EFG $ia la girella
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4604 della taglia appiccata di opra, il cui cen-
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4605 tro $ia H, dapoi $ia condotta intorno
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diff changeset
4606 le girelle la corda LBCDMEFGN
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4607 laquale $ia legata in L, &amp; $ia la po$-
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diff changeset
4608 $anza, che $o$tiene il pe$o A in N.
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diff changeset
4609 Dico la po$$anza, che $ta in N e$$e-
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4610 re la met&agrave; meno del pe$o A. Percio-
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diff changeset
4611 che $e la po$$anza, che $o$tiene il pe$o</I>
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diff changeset
4612 <marg><I>Per la</I> 8. <I>di questo.</I></marg> <I>A fo$$e collocata doue $ta M, $areb-
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diff changeset
4613 be per certo la po$$anza in M la met&agrave;</I>
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diff changeset
4614 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>meno del pe$o A: &amp; alla po$$anza in
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diff changeset
4615 M &egrave; eguale la forza di N, percioche
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diff changeset
4616 egli &egrave; come $e la po$$anza in M $o$te-
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diff changeset
4617 ne$$e la met&agrave; del pe$o A $enza taglia,
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diff changeset
4618 alquale egualmente contrape$a il pe$o che
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diff changeset
4619 &egrave; in N per e$$ere eguale alla met&agrave; del
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diff changeset
4620 pe$o A. Per laqual co$ala forza in N
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diff changeset
4621 che &egrave; alla met&agrave; del pe$o A eguale, $o-
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diff changeset
4622 $tenir&agrave; e$$o A. La po$$anza dunque in
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diff changeset
4623 N che $o$tiene il pe$o A, &egrave; la met&agrave;
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diff changeset
4624 meno di e$$o A. che bi$ognaua mo.
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diff changeset
4625 <*>rare.</I>
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4626 <fig>
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diff changeset
4627 <pb n=61>
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diff changeset
4628 <p><I>Ma $e, come nella $econda figura, la cor
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4629 da BCDEFGHKL $ar&agrave; inuolta
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diff changeset
4630 d'intorno &agrave; le girelle, &amp; legata in
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4631 B: &amp; la po$$anza in L $o$tenga il
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4632 pe$o A, $ar&agrave; $imilmente la po$$an
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diff changeset
4633 za in L la met&agrave; meno del pe$o:
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4634 Peroche la girella della taglia di $o-
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4635 pra, &amp; la taglia i$te$$a $ono del tut-
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4636 to inutili: &amp; &egrave; il mede$imo, come $e
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diff changeset
4637 la corda fo$$e legata in F, &amp; che
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diff changeset
4638 la po$$anza in L $o$tene$$e il pe$o
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4639 con la $ola taglia legata al pe$o, la
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diff changeset
4640 qual po$$anza &egrave; $tata dimo$trata e$-
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diff changeset
4641 $ere la met&agrave; meno del pe$o A.</I>
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4642 <fig>
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4643 <HEAD>COROLLARIO.</HEAD>
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4644 <p>Seguita da que$te co$e, che $e $aranno due po$$anze in BL, am-
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4645 bedue tra loro $aranno eguali.
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4646 <p><I>Perciocheogn'vna di loro da per $e &egrave; la met&agrave;meno di e$$o A.</I>
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4647 <foot><I>Q</I></foot>
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4648 <pb>
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4649 <HEAD>PROPOSITIONE IIII.</HEAD>
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4650 <p>Sia la leua AB, il cui $o$tegno $ia A, laqual leua $ia diui$a in
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4651 due parti eguali in D, &amp; $ia il pe$o C appiccato in D, &amp;
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4652 $iano due po$$anze eguali in BD, che $o$tengano il pe$o C.
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4653 Dico, che ogn'vna di que$te po$$anze po$te in BD &egrave; vn ter-
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4654 zo del pe$o C.
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4655 <p><I>Hor percioche vna delle due po$$anze &egrave; collocata in D, &amp; il pe$o C $t&agrave; appiccato
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4656 all'i$te$$o punto D. La po$$anza in D $o$ienir&agrave; la parte del pe$o C, che $ar&agrave;
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4657 eguale ad e$$a po$$an-
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4658 za D. Per laqual co
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4659 $ala po$$anza in B $o
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parents:
diff changeset
4660 $tenir&agrave; l'altra parte re
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4661 $tante, laqual parte $a
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4662 r&agrave; il doppio t&amacr;to, quan
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4663 to &egrave; la po$$anza di B,
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4664 e$$endo che il pe$o ver
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4665 $o la po$$anza ha la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4666 proportione i$te$$a, che</I>
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parents:
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4667 <fig>
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parents:
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4668 <I>ha AB ad AD: &amp; le po$$anze po$te in BD $ono eguali, adunque la po$-
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parents:
diff changeset
4669 $anza, che &egrave; in B $o$tenir&agrave; il doppio pi&ugrave; di quello, che $o$tenir&agrave; la po$$anza, che &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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4670 in D. Diuida$i dunque il pe$o C in due parti, l'vna delle quali $ia il doppio del-
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parents:
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4671 l'altra: ilche $i far&agrave;, $e lo diuideremo in tre parti eguali EFG, &amp; all'hora FG
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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4672 $ar&agrave; il doppio di E. Co$i la po$$anzain D $o$tenir&agrave; la parte E, &amp; la po$$anza
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4673 in B le altre due parti FG. Ambedue dunque le po$$anze po$te in BD tra
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4674 loro eguali $o$terr&atilde;no in$ieme tutto il pe$o C. &amp; perche la po$$anza in D $o$tie-
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4675 ne la parte E, laquale &egrave; la terza parte del pe$o C, &amp; ad e$$o &egrave; eguale, $ar&agrave; la po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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4676 $anza in D vn terzo del pe$o C: &amp; concio$ia che la po$$anza di B $o$tenga le
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4677 parti FG, la po$$anza dellequali po$ta in B &egrave; la met&agrave; meno: $ar&agrave; la po$$anza
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4678 in B all'vna delle parti FG, come alla G eguale. &amp; il G &egrave; la terza parte
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4679 del pe$o C. La po$$anza dunque in B $ar&agrave; il terzo del pe$o C. Cia$cuna delle
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4680 po$$anze dunque in BD &egrave; vnterzo del pe$o C, che bi$ognaua dimo$trare.</I>
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diff changeset
4681 <pb n=62>
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4682 <p><I>Et $e fo$$ero due leue AB EF diui$e in due parti eguali in GD, i $o$tegni delle-
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4683 quali fo$$ero AF, &amp; il pe$o C fo$$e appiccato all'vna, &amp; l'altra leua in DG</I>
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4684 <fig>
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4685 <I>$i fattamente, per&ograve; che pe$a$$e egualmente nell'vna, &amp; l'altra: &amp; $o$$ero due po$-
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4686 $anze eguali in BG. Si dimo$trer&agrave; con ragione in tutto mede$ima, che ogn'vna
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parents:
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4687 delle po$$anze po$tein B &amp; G &egrave; vn terzo del pe$o C.</I>
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4688 <HEAD>PROPOSITIONE V.</HEAD>
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4689 <p>Se all'vna &amp; l'altra, di cia$cuna girella di due taglie, l'vna delle
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4690 quali $ia po$ta di $opra, &amp; l'altra di $otto, &amp; legata al pe$o; $a-
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parents:
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4691 r&agrave; condotta intorn&ograve; la corda, legando vno de'$uoi capi alla
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parents:
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4692 taglia di $otto, &amp; l'altro $ia tenuto dalla po$$anza, che $o$tie-
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parents:
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4693 ne il pe$o: $ar&agrave; la po$$anza vn terzo del pe$o.
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diff changeset
4694 <foot><I>Q</I> 2</foot>
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4695 <pb>
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diff changeset
4696 <p><I>Sia il pe$o A, $ia BCD la girella della taglia legata al pe$o A, il cui centro $ia
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diff changeset
4697 E, &amp; $ia FGH l'altra girella della taglia appiccata di $opra, il cui centro $ia
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diff changeset
4698 K: $ia condotta intorno alle girelle la corda LFGHBCDM, laquale $ia lega
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diff changeset
4699 ta alla taglia di $otto in L; &amp; la po$
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diff changeset
4700 $anza, che $o$tiene il pe$o A $ia in
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diff changeset
4701 M. Dico che la po$$anza in M &egrave; vn
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4702 terzo del pe$o A. Siano tirate le li-
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4703 nee FH BD per li centri KE egual
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diff changeset
4704 mente di$tanti dall'orizonte, $i come
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diff changeset
4705 nelle precedenti &egrave; detto. Hor percio-
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diff changeset
4706 che la corda FL $o$tiene la taglia di
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diff changeset
4707 $otto, laquale $o$tiene la girella nel $uo
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diff changeset
4708 centro E: $ar&agrave; la corda di L come
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diff changeset
4709 po$$anza che $o$tiene la girella, tanto
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diff changeset
4710 quanto $e fo$$e in e$$o E centro: &amp;
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diff changeset
4711 la po$$anza di M &egrave; come $e $te$$e in</I>
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diff changeset
4712 <marg><I>Per la</I> 2. <I>di questo</I></marg> <I>D; $i far&agrave; dunque DB come leua, il
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diff changeset
4713 cui $o$tegno $ar&agrave; B: ma il pe$o A,
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diff changeset
4714 come di $opra f&ugrave; dimo$trato, appicca-
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diff changeset
4715 to in E viene $o$tenuto da due po$-
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diff changeset
4716 $anze, l'vna po$ta in D, &amp; l'altra in
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diff changeset
4717 E. &amp; concio$ia, che nel $o$tenere i
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diff changeset
4718 pe$i $tiano le leue FH BD immobi-
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diff changeset
4719 li, $e li pe$i $aranno appiccati alle cor-</I>
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4720 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>de FL HB $aranno que$ti i$te$$i egua
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diff changeset
4721 li, per hauere laleua FH il $o$tegno
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4722 nel mezo; altramente dall'vna delle
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diff changeset
4723 parti $i farebbe il mouimento &agrave; ba$$o,
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4724 co$a che tuttauia non accade; Adun-
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diff changeset
4725 que tanto $o$tiene la corda FL, quan
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4726 to la HB. Di pi&ugrave; percioche dal me-
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4727 zo della leua BD il pe$o pende at-
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diff changeset
4728 taccato, per&ograve; $e fo$$ero due po$$anze
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4729 in BD che $o$tene$$ero il pe$o, $areb-
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4730 bon fra loro eguali: &amp; benche la cor-</I>
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4731 <marg><I>Per la</I> 3. <I>co rollario di questo.</I></marg> <I>da FL $o$tenga e$$a ancora il pe$o,
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diff changeset
4732 poiche ella $ta in loc<*> de la po$$anza</I>
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diff changeset
4733 <marg><I>Per la</I> 2. <I>di questo della leua.</I></marg> <I>E, nondimeno percioche $o$tiene da
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4734 quel mede$imo punto, doue &egrave; appicca-
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4735 to il pe$o, non far&agrave; per&ograve; che le po$-</I>
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diff changeset
4736 <fig>
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4737 <I>$anze, lequali $ono in BD non $iano traloro eguali, peroche aiuta tanto all'v-
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4738 na, quanto all'altra. Ma le po$$anze che $ono in BD $ono le i$te$$e, come $<*></I>
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4739 <pb n=63>
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4740 <I>fu$$ero in HM. Per laqual co$a tanto $o$terr&agrave; la corda MD quanto la HB: ma
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4741 co$i $o$tiene HB come FL; adunque la corda MD co$i $o$tenir&agrave;, come FL,
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4742 cio&egrave; come $e in D &amp; in L fo$$ero appiccati pe$i eguali. Concio$ia co$a dunque,
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4743 che pe$i eguali $ian $o$tenuti da po$$anze vguali, le po$$anze in ML $aranno egua
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4744 li, delle quali &egrave; in tutto vna ragione iste$$a, come $e ambedue fo$$ero in DE.
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diff changeset
4745 Onde, e$$endo che il pe$o A $tia attaccato nel mezo della leua BD, &amp; che due
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4746 po$$anze po$te in DE $o$tenente il pe$o $iano eguali: $ar&agrave; B il $o$tegno, &amp;
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parents:
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4747 cia$cheduna po$$anza po$ta in DE ouero in ML $ar&agrave; vn terzo del pe$o A.
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diff changeset
4748 Adunquela po$$anza in M $o$tenente il pe$o $ar&agrave; vn terzo del pe$o A. che</I> <marg><I>Per la</I> 4. <I>di questo.</I></marg>
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4749 <I>bi$ognaua mo$trare.</I>
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4750 <HEAD>COROLLARIO.</HEAD>
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4751 <p>Da que$to &egrave; manife$to, che ogn'vna delle corde MD FL HB
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4752 $o$tiene la terza parte del pe$o A.
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4753 <p><I>Oltre &agrave; ci&ograve; $e da M $ar &agrave; la corda portata intor-
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4754 no ad vn'altra girella po$ta pi&ugrave; $u nella ta-
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parents:
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4755 glia, che $imilmente $ia attaccata di $opra, il
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4756 cui centro $ia N $i fattamente che peruen
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4757 gain O, &amp; iui $ia tenuta dalla po$$anza; $a
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parents:
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4758 r&agrave; la po$$anza che in O $o$tiene il pe$o A
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4759 parimente vn terzo del pe$o. Percioche la
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parents:
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4760 corda MD $o$tiene tanto di pe$o, come $e in
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parents:
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4761 D fo$$e appiccato il pe$o eguale alla terza</I>
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4762 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>parte del pe$o A, alla quale &egrave; pari la po$-
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4763 $anza in O ad e$$a eguale, cio&egrave; vnterzo del
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4764 pe$o A. La po$$anza dunque in O &egrave; vn
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4765 terzo del pe$o A.</I>
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4766 <p><I>Et accioche non $i ritorni &agrave; dire $pe$$e volte il
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4767 mede$imo, egli f&agrave; me$tiero $apere, che lapo$
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parents:
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4768 $anza in O &egrave; $empre eguale &agrave; quella, che
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4769 $tain M. come $arebbe &agrave; dire, $e la po$$an-
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4770 zain M fo$$e vn quarto, ouero vn quinto,
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4771 &ograve; $imile co$a di e$$o pe$o, la po$$anza parimen
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4772 te in O $ar&agrave; vn quarto, ouero vn quinto,
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4773 &amp; co$i di mano in mano dell'i$te$$o pe$o, nel
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4774 modo che &egrave; di$po$ta la po$$anza di M.</I>
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4775 <fig>
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4776 <p>Potrebbbe for$e alcuno dubitare in alcune dimo$trationi delle taglie come in que$ta
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4777 quinta p<*>opo$itione, tolta da me per e$$empio per e$$ere piu $chietta delle altre,
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4778 che in fatto con la e$perientia non riu$ci$$ero in proportione le forze a' pe$i, co-
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4779 <pb n=64>
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4780 mela ragione dimo$tra; peroche pre$up ponendo $i nelle dimo$trationi matemati
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4781 che le linee $enza larghezza, &amp; profondit&agrave;, &amp; co$i le altre co$e imaginando $i $e-
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4782 parate dalla materia, ageuolmente $i per$uadiamo e$$ere vere come dicono. Ma
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diff changeset
4783 la e$perientia poi molte volte mo$tra diuer$it&agrave;, &amp; $i trouiamo ingannati, facendo
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4784 la materia gran demente variare le co$e. In que$ta propo$itione $i narra, che rauol
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diff changeset
4785 gendo d'intorno &agrave; due girelle di due taglie vna corda, &amp; quel che $egue, la forza
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diff changeset
4786 $ar&agrave; vn terzo del pe$o, cio&egrave; $e il pe$o $ara trecento, egli verr&agrave; $o$tenuto dalla po$
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diff changeset
4787 $anza di cento. Direbbe alcuno ci&ograve; e$$ere dubbio$o, peroche le girelle, gli a$$etti
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diff changeset
4788 $uoi, le funi, &amp; il pe$o della taglia di $otto fanno re$i$tenza alla forza, &amp; grauano
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diff changeset
4789 s&igrave;, che ella non potr&agrave; $o$tenere il pe$o. Si ri$ponde che que$te co$e ben farebbo-
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4790 no re$i$tenza nel mouere il pe$o, ma non gi&agrave; nel $o$tentarlo: &amp; bi$ogna notaro
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4791 con diligenza che l'autore in que$te dimo$trationi parla $empre del $o$tenere $o-
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diff changeset
4792 lamente con le forze i pe$i che non calino al ba$$o, non del mouere. Per&ograve; con-
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diff changeset
4793 $ideri$i, che quando li pe$i $i hanno da far mouere con le po$$anze, allhora le gi-
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diff changeset
4794 relle, &amp; gli altri impedimenti faranno re$i$tenza; ma quando $i ha da far $olamen-
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diff changeset
4795 te che il pe$o $tia fermo, &amp; habbia il $uo contrape$o $emplicemente $enza porre
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4796 in con$ideratione altri ri$petti, che &egrave; officio della po$$anza $o$tenente; all'horz
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diff changeset
4797 n&egrave; le girelle, n&egrave; altro danno re$i$tenza veruna, &amp; la proua fondata $u la ragione
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4798 torna $empre per eccellentia, anzi pare che quanto piu re$i$tenza vi $ia, tanto piu
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diff changeset
4799 facilmente la forza $o$tenga. Auertendo con tutto ci&ograve;, che nel fare la e$perienza
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diff changeset
4800 bi$ogna hauere riguardo alla taglia di $otto, &amp; alla corda, lequali hanno la $ua
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4801 grauezza $i fattamente, che $e il pe$o come nell'e$$empio propo$to, $ar&agrave; trecento
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4802 libre, &amp; la forza cento, &amp; la taglia di $otto con la $ua fune quattordici, &egrave; me$tieri
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diff changeset
4803 che alla po$$anza di M $i aggiungano quattro libre, &amp; due terzi di forza, ac-
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diff changeset
4804 cioche po$$a $o$tenere tutto il pe$o, &amp; co$i verr&agrave; ad e$$ere in M po$$anza vn ter-
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4805 zo giu$tamente del pe$o. Ma per $apere quanta forza bi$ogni aggiungere alla po$
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diff changeset
4806 $anza, accioche per ri$petto alla taglia di $otto, &amp; alla fune, $o$tenghi il pe$o tut-
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diff changeset
4807 to, faccia$i que$ta ragione. La taglia di $otto con parte della fune, per gratia di
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4808 e$$empio, &egrave; quattordici libre, il pe$o &egrave; trecento, &amp; la po$$anza cento. Hor per
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4809 la regola detta del tre. Se trecento danno cento, che daranno quattordici? Tro-
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parents:
diff changeset
4810 ueran$i quattro libre, &amp; due terzi da e$$ere aggiunte alla po$$anza di M, per
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parents:
diff changeset
4811 $o$tenere il pe$o A. &ldquo;Laqual co$a tocca in $o$tanza l'auttore pi&ugrave; &agrave; ba$$o
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parents:
diff changeset
4812 dicendo.$rdquo; &amp; $i come habbiamo ci&ograve; con$iderato nella decimaquinta, &amp; quel,
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parents:
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4813 che $egue. ilqual loco bi$ogna intendere in que$ta maniera, che le taglie non
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parents:
diff changeset
4814 $i deuono pigliare ad vn'i$te$$o modo $empre, ma diuer$amente, come graua-
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4815 no, ilche na$ce dall'e$$ere in vari luoghi, &amp; le po$$anze, &amp; i pe$i collocati, &amp; fer-
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4816 mate le taglie. Hor nella $econda propo$itione di que$to trattato has$i da inten-
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4817 dere la po$$anza e$$ere la meta meno del pe$o, prendendo perlo pe$o, &amp; il pe$o,
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4818 &amp; la taglia di $otto in$ieme, &agrave; cui $t&agrave; attaccato, come $i vede chiaro nella dimo$tra
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parents:
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4819 tione della detta $econda propo$itione, doue $i proua che la po$$anza $o$tiene la gi
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4820 rella, laquale $o$tiene anche il re$to della taglia nell'a$$etto, alla qual taglia &egrave; attac-
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parents:
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4821 cato il pe$o, oue $i cono$ce e$pre$$o, che la taglia, &amp; il pe$o s'hanno &agrave; pigliare
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4822 per tutto il pe$o. Per la qual co$a, $e in quel ca$o il pe$o in$ieme con la taglia pe-
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4823 $eranno vinti, la po$$anza che gli $o$tenter&agrave; $ar&agrave; dieci. Et per vn'altro e$$empio
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4824 nella nona propo$<*>ione di que$to nel primo ca$o, $e il pe$o con la taglia di $otto
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parents:
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4825 pe$eranno vinticinque, la po$$anza $o$tenente $ar&agrave; cinque. &amp; co$i egli &egrave; me$t<*>eri
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parents:
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4826 hauer con$ideratione nelle altre, cio&egrave; di$tinguere doue &egrave; la grauezza della taglia,
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parents:
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4827 quando graua di $otto $olamente, come nelle allegate propo$itioni, &amp; $imili: &amp;
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parents:
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4828 quando $olamente di $opra, come nelle propo$itioni 17. &amp; 18. &amp; $imili: &amp; quan
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parents:
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4829 do ambedue le taglie grauano di $opra, &amp; di $otto, come nelle propo$itioni 20.
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4830 22. &amp; 23. &amp; $imili: &amp; quando anche nel'vna taglia, ne l'altra grauano, come nella
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parents:
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4831 prima propo$itione &amp; nella 19. anzi in e$$a 19. la taglia di $otto aiuta la po$s&atilde;za ad
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parents:
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4832 e$$ere piu leggiera: &amp; nel $econdo ca$o dopo il corollario della 16. propo$itione,
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parents:
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4833 &amp; $imili. &amp; oltre &agrave; ci&ograve; deue$i por mente alle corde ancora, la grauezza delle qua-
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parents:
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4834 li non h&agrave; $empre da e$$ere con$iderata, peroche grauano nelle propo$itioni 15. 17.
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parents:
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4835 ma non grauano gi&agrave; nella 19.
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parents:
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4836 <p>Ne parmi etiandio che $i habbia ad hauere punto di riguardo alla picciolezza, &amp;
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parents:
diff changeset
4837 grandezza delle girelle po$te nelle taglie, &amp; de gli a$$etti $uoi, credendo che per
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parents:
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4838 neces$it&agrave; habbiano da e$$ere lauorati con mi$ura tale, &amp; proportione co$i ac<*>u-
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parents:
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4839 rata, che mancando da quella non rie$cano le dimo$trationi alla e$perientia; per
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parents:
diff changeset
4840 roche, $i come nota l'autore poco appre$$o, ba$ta che con certa conueneuole mi$n
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parents:
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4841 ra, &amp; proportione le girelle nelle taglie $iano maggiori l'vna dell'altra $i fattamen
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parents:
diff changeset
4842 te, che le corde non $i to cchino, &amp; freghino fra loro, &amp; co$i vengano ad impedi
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parents:
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4843 re i mouimenti delle po$$anze, &amp; de' pe$i.
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parents:
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4844 <HEAD>PROPOSITIONE VI.</HEAD>
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parents:
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4845 <p>Siano due leue AB CD diui$e in due parti eguali in EF, li
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parents:
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4846 $o$tegni delle quali $iano in BD; &amp; $ia il pe$o G in EF ap
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parents:
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4847 piccato all'vna, &amp; l'altra leua $i fattamente, che pe$i dall'vna,
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4848 &amp; dall'altra egualmente: &amp; $iano due po$$anze in AC egua-
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parents:
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4849 li, che $o$tengano il pe$o. Dico, che ogn'vna delle po$$anze
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parents:
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4850 in AC &egrave; vn quarto del pe$o G.
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4851 <p><marg><I>Per la</I> 2. <I>di questo nella leua.</I></marg> <I>Concio$ia che le po$$anze po-
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parents:
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4852 $te in AC $o$tengano tut
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4853 to il pe$o G, &amp; la po$$an-
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4854 za di A ver$ola parte del
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parents:
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4855 pe$o, che $o$tiene, $ia come
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parents:
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4856 BE &agrave; BA, &amp; la po$$an-
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parents:
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4857 zain C alla parte di e$$o
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parents:
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4858 G pe$o $o$tenuto da lei $ia
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4859 co$i, come DF &agrave; DC, &amp;
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4860 come BE &agrave; BA, co$i &egrave;
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parents:
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4861 DF &agrave; DC: $ar &agrave; lapo$$an
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4862 za po$ta in A ver$o la par
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4863 te del pe$o, che $o$tiene, co-</I>
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4864 <fig>
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4865 <I>me la po$$anza di C ver$o la parte di e$$o pe$o, che $o$tiene: &amp; le po$$anze po$ie
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4866 in AC $ono eguali; $aranno dunque le parti del pe$o G eguali, lequali $ono $o-</I>
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4867 <pb n=65>
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4868 <I>$tenute dalle po$$anze. Per laqual co$a cia$cuna po$$anza po$ta in AC $o$terr&agrave;
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4869 la met&agrave; del pe$o G. Mala po$$anza in A &egrave; la met&agrave; meno del pe$o, che $o$tie-
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4870 ne; adunque la po$$anza in A $ar&agrave; per lo mezo della met&agrave;, cio&egrave; eguale alla quar
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4871 ta portione del pe$o G; &amp; per&ograve; $ar&agrave; il quarto del pe$o G, n&egrave; altramente $i di-
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4872 mo$trer&agrave; la po$$anza in C e$$ere vn quarto dell'i$te$$o pe$o G. che bi$ognaua
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4873 mo$trare.</I>
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4874 <p><I>Ma $e $aranno tre leue AB
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4875 CD EF diui$e in due
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4876 parti eguali in GHK, li
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4877 $o$tegni delle quali $iano
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4878 BDF, &amp; il pe$o L $ia
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4879 nell'i$te$$o modo appicca-
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4880 to in GHK: &amp; $iano
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4881 tre po$$anze in ACE
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4882 eguali, che $o$tengano il
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4883 pe$o: $i mo$trer&agrave; $imil-
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4884 mente cia$cuna po$$anza
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4885 e$$ere vn $e$to del pe$o
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4886 L: &amp; con questo ordi-
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4887 ne $e fo$$ero quattro le-
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4888 ue, &amp; quattro po$$anze,
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4889 cia$cuna po$$anza $ar&agrave;
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4890 la ottaua parte del pe$o, &amp; co$i di mano in mano in infinito.</I>
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4891 <fig>
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4892 <HEAD>PROPOSITIONE VII.</HEAD>
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4893 <p>Se &agrave; tre girelle di due taglie, l'vna delle quali po$ta di $opra hab
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4894 bia vna $ola girella, &amp; l'altra di $otto ne habbia due, &amp; $ia lega
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4895 ta al pe$o; $ia po$ta d'intorno la corda; legando l'vn de' capi
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4896 $uoi in qualche loco, &amp; l'altro $ia tenuto dalla po$$anza, che
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4897 $o$tiene il pe$o. La po$$anza $ar&agrave; vn quarto del pe$o.
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4898 <foot><I>R</I></foot>
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4899 <pb>
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4900 <p><I>Sia il pe$o A: $iano le tre girelle, il centro dellequali $ia BCD: &amp; la girella, il
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4901 cui centro &egrave; D, $ia della taglia appiccata di
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parents:
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4902 $opra: ma quelle girelle, il cui centro &egrave; in B
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4903 C $iano della taglia legata al pe$o A: &amp;
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4904 la corda EFGHKLNOP $ia condotta
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4905 intorno &agrave; tutte le girelle, &amp; legata in E: &amp;
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4906 $ia la forza che $o$tiene il pe$o A in P.
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4907 Dicola po$$anza in P e$$ere vn quarto del
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4908 pe$o A. Siano tirate le linee KL GF ON
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4909 per li centri delle girelle, $i che $iano egual-
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4910 mente di$tanti dall'orizonte; le quali per le co
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4911 $e, che gi&agrave; $ono dette, $aranno come leue. &amp;
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4912 percioche per cagione della leua, ouero bilan-
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4913 cia KL, il cui $o$tegno, ouero centro &egrave; nel</I>
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4914 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>mezo, tanto $o$tiene la corda KG, quanto
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4915 la NL non $i $acendo mouimento in niu-
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4916 na delle parti: Di pi&ugrave; per cau$a della leua
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4917 GF dal cui mezo, come $o$pe$o dipende il
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4918 pe$o; $e fo$$ero due po$$anze in GF, oue-</I>
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4919 <marg><I>Per il</I> 2. <I>co rollario della</I> 2. <I>di questo.</I></marg> <I>ro in HE, (percioche $i come &egrave; $tato pi&ugrave;
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parents:
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4920 volte detto, la ragione dell'vno, &amp; dell'al-
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4921 tro $ito &egrave; pari) $arebbono per certo que$te
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parents:
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4922 tali po$$anze eguali fraloro. Onde co$i $o-
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parents:
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4923 $tiene la corda HG, come EF: $imilmen
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4924 te $imo$trer&agrave; tanto $o$tenere la corda PO,
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4925 quanto la NL. Per laqual co$a le corde
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4926 PO KG EF LN $o$tengono egualmen-
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parents:
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4927 te. Adunque $o$tiene egualmente s&igrave; la cor-
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parents:
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4928 da PO, come la KG. Se dunque s'inten-
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parents:
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4929 de$$ero e$$ere due po$$anze in OG, ouero in
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4930 PH, che &egrave; il mede$imo, lequali tuttauia $o-
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parents:
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4931 $tenghino il pe$o, come $o$tengono le corde,
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4932 $arebbono per certo eguali: &amp; GF ON
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parents:
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4933 baurebbono le $orze di due leue, il $o$tegno
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4934 delle quali $aranno FN &amp; il pe$o A $a
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4935 r&agrave; appiccato in BC, che &egrave; il mezo delle le-
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4936 ue. &amp; percioche tutte le corde $o$tengo-
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4937 no egualmente, tanto $o$teniranno le due</I>
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4938 <fig>
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4939 <I>PO LN quanto le due KG EF. tanto dunque $o$terr&agrave; la leua ON, quan-</I>
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4940 <marg><I>Per la</I> 6. <I>di questo.</I></marg> <I>to la leua GF. Onde nell'vna, &amp; l'altra leua ON GF pe$er&agrave; egualmente il
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4941 pe$o. $ar&agrave; dunque ogni po$$anza che &egrave; in PH vn quarto del pe$o A. &amp; e$$en</I>
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4942 <pb n=66>
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4943 <I>do, che la corda KG $i prenda in loco di po$$anza, come quella, che non $o$tiene
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4944 altramente di quel che faccia PO, $ar&agrave; la po$$anza di P, che $o$tiene il pe$o A
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4945 vn quarto di e$$o pe$o. che bi$ognaua mo$trare.</I>
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4946 <HEAD>COROLLARIO I.</HEAD>
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4947 <p>Di qui &egrave; manife$to, che cia$cuna corda EF GK LN OP $o-
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4948 $tiene la quarta parte del pe$o A.
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4949 <HEAD>COROLLARIO II.</HEAD>
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4950 <p>E chiaro ancora, che non meno $o$tiene la girella il cui centro
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4951 &egrave; C, di quello che faccia la girella, il centro dellaquale &egrave; B.
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4952 <foot><I>R</I> 2</foot>
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4953 <pb>
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4954 <HEAD>Altramente.</HEAD>
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4955 <p><I>Po$te ancora le co$e mede$ime, $e fo$$ero
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diff changeset
4956 due po$$anze eguali, che $o$tene$$ero</I>
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diff changeset
4957 <marg><I>Per la</I> 4. <I>di questo.</I></marg> <I>il pe$o A, l'vna in O, &amp; l'altrain
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4958 C: $arebbe cia$cuna delle dette po$$in-
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diff changeset
4959 ze vnterzo del pe$o A. Ma perche
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parents:
diff changeset
4960 la leua GF, il cui $o$tegno &egrave; F, &egrave;
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diff changeset
4961 diui$a in due parti eguali nel C. $e dun
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parents:
diff changeset
4962 que $i porr&agrave; la po$$anza in G che $o-
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parents:
diff changeset
4963 $tenga l'i$te$$o pe$o, come la po$$anza
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parents:
diff changeset
4964 di C, $ar&agrave; la po$$anza di G la met&agrave;
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parents:
diff changeset
4965 della po$$anza, che fo$$e in C; per-
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parents:
diff changeset
4966 cioche $e la po$$anza di C per $e $te$$a
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parents:
diff changeset
4967 $o$tene$$e il pe$o, che &egrave; appiccato in C,
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diff changeset
4968 $arebbe per certo eguale ad e$$o pe$o; et
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parents:
diff changeset
4969 $e l'i$te$$o pe$o fo$$e $o$tenuto dalla po$
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parents:
diff changeset
4970 $anza di G, $arebbe il doppio di e$$a G
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diff changeset
4971 po$$anza, &amp; la po$$anza di C $areb-</I>
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parents:
diff changeset
4972 <marg><I>Per la</I> 3. <I>di questo della leua.</I></marg> <I>be vn terzo del pe$o A; dunque la
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diff changeset
4973 po$$anza di G $arebbe vn $e$to della
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diff changeset
4974 po$$anza del pe$o A. Per laqual co
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parents:
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4975 $a, e$$endo, che la po$$anza di O $ia vn
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diff changeset
4976 terzo del pe$o A, &amp; la po$$anza di
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parents:
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4977 G vn $e$to: $ara l'vna, &amp; l'altra po$-
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diff changeset
4978 $anza in$ieme po$te in OG la met&agrave;
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4979 del pe$o A, percioche la terza par-
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4980 te con la $e$ta $&agrave; la met&agrave;. Ma per-
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4981 cioche la po$$anza di OG, ouero di
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4982 PH, (come prima &egrave; detto) $ono fra
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4983 loro eguali, &amp; l'vna, &amp; l'altra in$ie-
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4984 me $ono la met&agrave; del pe$o A, $ar&agrave;
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parents:
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4985 ogn'vna delle po$$anze po$te in PH
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4986 vn quarto di e$$o A. Adunque la
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4987 po$$anza di P che $o$tiene il pe$o A
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4988 $ar&agrave; vn quarto di e$$o pe$o A. che era
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4989 da mo$trare.</I>
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4990 <fig>
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diff changeset
4991 <pb n=67>
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4992 <p><I>Ma $e'la corda
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4993 $ar&agrave; legata in
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4994 E, &amp; $ia
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parents:
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4995 dauantaggio
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parents:
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4996 inuolta intor
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parents:
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4997 no &agrave; quattro
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4998 girelle, et per
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4999 uenga in P,
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5000 $imo$trer&agrave; $i
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parents:
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5001 milm&emacr;te, che
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parents:
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5002 la po$$anza
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parents:
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5003 di P $ar&agrave;
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parents:
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5004 vn quarto
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parents:
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5005 del pe$o A;
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parents:
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5006 peroche egli
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parents:
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5007 &egrave; il mede$i-
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5008 mo, come $e
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5009 la corda fo$-
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parents:
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5010 $e legata in
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parents:
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5011 L, &amp; che la
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5012 po$$anza $o-
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parents:
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5013 $tene$$e il pe
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parents:
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5014 $o con la cor-
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parents:
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5015 da inuolta in
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parents:
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5016 torno &agrave; tre gi
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parents:
diff changeset
5017 relle $olamen
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parents:
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5018 te, i centri
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parents:
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5019 delle quali fo$
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parents:
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5020 $ero BCQ,
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parents:
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5021 percioche la
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parents:
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5022 girella, il cui
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parents:
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5023 centro &egrave; D,
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parents:
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5024 del tutto &egrave;
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parents:
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5025 inutile.</I>
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parents:
diff changeset
5026 <fig>
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parents:
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5027 <HEAD>PROPOSITIONE VIII.</HEAD>
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parents:
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5028 <p>Siano due leue AB CD diui$e in due parti eguali EF, i $o-
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parents:
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5029 $tegni delle quali $iano AC, &amp; $ia appiccato il pe$o G ne'
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parents:
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5030 punti EF all'vna, &amp; l'altra leua, $i fattamente, che dall'vno,
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parents:
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5031 &amp; l'altro pe$i egualmente: &amp; $iano tre po$$anze eguali in BD
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parents:
diff changeset
5032 E che $o$tenghino il pe$o G. Dico, che cia$cuna delle det-
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parents:
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5033 te po$$anze $eparatamente &egrave; vn quinto del pe$o G.
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parents:
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5034 <p><I>Percioche il pe$o G $ta appiccato in EF, &amp; $ono le tre po$$anze in EBD egua-
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parents:
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5035 li: per&ograve; la po$$anza di E $o$terr&agrave; la parte $olamente del pe$o G, che $ar&agrave; eguale
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parents:
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5036 ad e$$a po$$anza di E, ma
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parents:
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5037 le po$$anze di BD $o$terran
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parents:
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5038 no la parte re$tante, &amp; la</I>
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5039 <marg><I>Per la</I> 4. <I>di questa nella leua.</I></marg> <I>parte, che &egrave; da B $o$tenu-
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parents:
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5040 ta, $ar&agrave; il doppio di e$$o: ma
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parents:
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5041 la parte $o$tenuta da D $a-
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parents:
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5042 r&agrave; $imilmente il doppio di e$
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parents:
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5043 $o D per cau$a della pro-
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parents:
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5044 portione di BA ver$o AE,
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parents:
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5045 &amp; di DC ver$o CF. Con
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parents:
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5046 cio$ia dunque, che le po$$an-</I>
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5047 <marg><I>Per la</I> 6. <I>di questo.</I></marg> <I>ze di BD $iano eguali, $a-
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parents:
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5048 ranno anche (per quel che di
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parents:
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5049 $opra &egrave; detto) le parti del pe</I>
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parents:
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5050 <fig>
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parents:
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5051 <I>$o G, lequali $ono $o$tenute dalle po$$anze di BD, $ra loro eguali, &amp; ogni vna
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parents:
diff changeset
5052 $ar &agrave; il doppio di quella tal parte, che &egrave; $o$tenuta dalla po$$anza di E. Diuida$i
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diff changeset
5053 dunque il pe$o G in tre parti, delle quali due $iano fra loro eguali, &amp; di pi&ugrave; ogni
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parents:
diff changeset
5054 vna di loro $eparatamente $ia il doppio dell'altra terza parte, ilche accader&agrave;, $e
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parents:
diff changeset
5055 in cinque parti eguali HKLMN $ar&agrave; diui$o: percioche la parte compo$ta di due
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parents:
diff changeset
5056 parti KL &egrave; il doppio della parte H, &amp; la parte ancora di MN &egrave; $imilmen-
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parents:
diff changeset
5057 te il doppio della parte i$te$$a H. Per laqual co$a anche la parte KL $ar&agrave; egua-
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parents:
diff changeset
5058 le alla parte MN. Ma $o$tenga la po$$anza di E la parte di H; &amp; la po$$an
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parents:
diff changeset
5059 za di B le parti di KL: &amp; la po$$anza di D le parti MN; adunque le tre
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parents:
diff changeset
5060 po$$anze eguali po$te in BDE $o$terranno tutto il pe$o G: &amp; ogn'vna delle
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parents:
diff changeset
5061 po$$anze di BD $o$terr&agrave; il doppio di quel che $o$tiene la po$$anza di E. Per&ograve;
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parents:
diff changeset
5062 e$$endo che la po$$anza di E $o$tenga la parte di H, laquale &egrave; la quinta parte del
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parents:
diff changeset
5063 pe$o G, &amp; $ia ad e$$o eguale, $ar&agrave; la po$$anza di E vn quinto del pe$o G. &amp;
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parents:
diff changeset
5064 percioche la po$$anza di B $o$tiene le parti di KL, lequali $ono il doppio &amp; del-</I>
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diff changeset
5065 <pb n=68>
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parents:
diff changeset
5066 <I>la po$$anza di B, &amp; della parte di H, $ar&agrave; ancora la po$$anza di B ad e$$o H
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parents:
diff changeset
5067 eguale. Per laqual co$a $ar&agrave; vn quinto del pe$o G. Ne altrimente $i dimo$tre-
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parents:
diff changeset
5068 r&agrave;, che la po$$anza di D &egrave; vn quinto del pe$o G. cia$cuna po$$anza dunque in
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parents:
diff changeset
5069 BDE &egrave; vn quinto del pe$o G. che bi$ognaua dimo$trare.</I>
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diff changeset
5070 <fig>
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parents:
diff changeset
5071 <p><I>Che $e $aranno tre leue AB
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parents:
diff changeset
5072 CD EF diui$e in due
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parents:
diff changeset
5073 parti eguali in GHK, i
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parents:
diff changeset
5074 $o$tegni dellequali $iano A
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parents:
diff changeset
5075 CE, &amp; il pe$o L nel mo
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parents:
diff changeset
5076 do i$te$$o $ia appiccato in
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parents:
diff changeset
5077 GHK, &amp; $iano quattro
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parents:
diff changeset
5078 po$$anze eguali in BD
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parents:
diff changeset
5079 FG che $o$tengano il pe-
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parents:
diff changeset
5080 $o L; $i mo$trer&agrave; con $imi-
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parents:
diff changeset
5081 gliante modo, che cia$cuna
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parents:
diff changeset
5082 po$$anza in BD FG $a-
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parents:
diff changeset
5083 r&agrave; vn $ettimo del pe$o L:
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parents:
diff changeset
5084 &amp; $e quattro fo$$ero le le-
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parents:
diff changeset
5085 ue, &amp; cinque le po$$anze
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parents:
diff changeset
5086 eguali $o$tenenti il pe$o; con l'i$te$$o modo ancora $i mo$trerebbe che ogni vna del-
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parents:
diff changeset
5087 le po$$anze $arebbe vn nono del pe$o, &amp; co$i di mano in mano $ucce$$iuamente.</I>
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5088 <HEAD>PROPOSITIONE IX.</HEAD>
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parents:
diff changeset
5089 <p>Se &agrave; quattro girelle di due taglie, l'vna delle quali $ia po$ta di
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parents:
diff changeset
5090 $opra, &amp; l'altra di $otto legata al pe$o, $ia condotta intorno
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parents:
diff changeset
5091 la corda, legando l'vno de'$uoi capi alla taglia di $otto, &amp; l'al-
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parents:
diff changeset
5092 tro $ia ritenuto dalla po$$anza, che $o$tiene il pe$o. $ar&agrave; la po$-
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parents:
diff changeset
5093 $anza vn quinto del pe$o.
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parents:
diff changeset
5094 <p><I>Sia il pe$o A, alquale $ia legata
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parents:
diff changeset
5095 la taglia, che habbia due girel-
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parents:
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5096 le, i cui centri $iano BC: &amp;
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parents:
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5097 $ia la taglia appiccata di $opra,
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parents:
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5098 che habbia due altre girelle, i
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parents:
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5099 cui centri $iano DE, &amp; la
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parents:
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5100 corda $ia tirata intorno &agrave; tutte
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parents:
diff changeset
5101 le girelle, laquale $ia legata al-
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parents:
diff changeset
5102 la taglia di $otto in F: &amp; $ia
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parents:
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5103 la po$$anza in G che $o$tiene
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5104 il pe$o A. Dico che la po$$an
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parents:
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5105 za di G &egrave; vn quinto del pe$o
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parents:
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5106 A. Siano tirate le linee HK
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parents:
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5107 LM per li centri BC egual-
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parents:
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5108 mente di$tanti dall'orizonte, le
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parents:
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5109 quali nel modo i$te$$o, che di
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parents:
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5110 $opra &egrave; $tato detto, dimo$trere-
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parents:
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5111 mo e$$ere come leue, i $o$tegni
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parents:
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5112 delle quali $ono KM, &amp; il pe
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parents:
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5113 $o A pende attaccato nel me-
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parents:
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5114 zo BC dell'vna, &amp; l'altra le-
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parents:
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5115 ua, &amp; le tre po$$anze LHC, che
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5116 $o$tengono il pe$o, lequali con
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parents:
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5117 $imile modo mo$treremo e$$ere
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parents:
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5118 eguali: percioche le corde fanno
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parents:
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5119 l'i$ie$$o officio, come $e fo$$ero
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parents:
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5120 po$$anze: &amp; percioche il pe$o
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parents:
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5121 dall'vna, &amp; l'altra leua HK
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parents:
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5122 LM pe$a egualmente, ilche $i
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5123 dimo$trer&agrave; ancora, come nelle
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parents:
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5124 precedenti &egrave; $tato dimo$trato:</I>
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5125 <marg><I>Per la</I> 8. <I>di questo.</I></marg> <I>$ar&agrave; ogni po$$anza po$ta s&igrave; in L
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5126 ouero in G, che &egrave; il mede$imo;
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5127 &amp; s&igrave; in H &amp; in C, cio&egrave; in F
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parents:
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5128 vn quinto del pe$o A. La po$
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5129 $anza dunque di G, che $o$tie-
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parents:
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5130 ne il pe$o A. $ar&agrave; vn quinto
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parents:
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5131 di e$$o pe$o A. che bi$ognaua
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5132 mo$trare.</I>
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parents:
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5133 <fig>
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parents:
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5134 <pb n=69>
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parents:
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5135 <p><I>Che $e dauantaggio $i traporter&agrave; la cor-
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parents:
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5136 da in F d'intorno ad vn'altra girella,
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parents:
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5137 il cui centro $ia N, &amp; $ia legata
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parents:
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5138 in O, $i prouer&agrave; $imilmente per due
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parents:
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5139 ragioni, come nella $ettima propo$i-
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parents:
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5140 tione di que$to, che la po$$anza di G
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5141 che $o$tiene il pe$o A, &egrave; vn $e$to</I> <marg><I>Per la</I> 6. <I>di questo</I></marg>
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5142 <I>di e$$o pe$o A. Percioche prima dal
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parents:
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5143 le treleue LM HK FP licui $o-
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parents:
diff changeset
5144 stegni $ono in KP, &amp; il pe$o &egrave; ap-
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5145 piccato nel mezo delle leue, &amp; le tre
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5146 po$$anze po$te in LHF che $o$ten-</I> <marg><I>Per la</I> 8. <I>di questo.</I></marg>
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5147 <I>gono il pe$o $ono eguali: poi dalle po$
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5148 $anze di LHN cia$cuna delle quali
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5149 $arebbe vn quinto del pe$o A, per-
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5150 cioche ambedue le po$$anze in$ieme
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5151 po$te in LH $arebbono $otto doppie $e$
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5152 quialtere al pe$o, &amp; la po$$anza di F
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5153 $arebbe vn decimo, e$$endo la met&agrave; di
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5154 e$$a N. Ma due quinte parti con
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5155 vna decima parte fanno la met&agrave;, la
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diff changeset
5156 qual met&agrave; $e $ar&agrave; diui$a per tre, ri-
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diff changeset
5157 $ponder&agrave; la $e$ta parte del pe$o &agrave; cia-
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diff changeset
5158 $cuna delle po$$anze po$te in LHF.
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diff changeset
5159 Dalle quali co$e &egrave; manife$to la po$$an-
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diff changeset
5160 za di G e$$ere vn $e$to del pe$o A;
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5161 &amp; $i dimo$trer&agrave; $imilmente che cia-
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5162 $cuna girella $o$tiene eguale portione
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5163 del pe$o.</I>
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5164 <fig>
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diff changeset
5165 <foot>S</foot>
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5166 <pb>
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diff changeset
5167 <p>In que$to trattato della taglia, $i come in tutti gli altri an cora, l'autore pre$uppone,
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5168 che qualunque per$ona $i mette &agrave; leggere il $uo libro delle Mechaniche $ia inten-
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5169 dente di numeri, &amp; di Geometria, &amp; per&ograve; ha $empre mantenuto quello accurato
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diff changeset
5170 $tile, &amp; dimo $tratiuo co$tumato da buoni Matematici, v$ando i vocaboli proprij
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5171 della $cienza, alcuni de' quali io h&ograve; ben potuto volgarizare facilmente, $i che
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5172 ogn'vno gli po$$a intendere, come per e$$empio, nelle proportioni duplum, tri-
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diff changeset
5173 plum, quadruplum, &amp; gli altri $imili, ponendo in vece loro due volte tanto, tre
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5174 volte tanto, &amp; quattro volte tanto: &amp; co$i per 'oppo$ito $ub duplum, $ubtriplu,
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diff changeset
5175 &amp; $ub quadruplum, la met&agrave;, vn terzo, &amp; vn quarto: &amp; parimente $e$quialterum,
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5176 $e$quitertium, &amp; $e$quiquartum, &amp; gli altri $imili, che vogliono dire vna volta &amp;
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5177 meza, vna volta, &amp; vn terzo, &amp; vna volta &amp; vn quarto. Que$ti dico s'hanno po
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5178 tuto ben dire, &amp; facilmente nella no$tra lingua. Ma nell'ampiezza delle propor-
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5179 tioni trouando$i altri vocaboli a$$ai, i quali non &egrave; pos$ibile co$i adattare alla no-
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diff changeset
5180 $tra lingua, tra quali alcuni $i trouano po$ti dall'autore in que$to trattato della ta
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diff changeset
5181 glia, &amp; io $ono $tato sforzato &agrave; la$ciargli co$i, come erano, per mancamento di pa
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diff changeset
5182 role, che nella no$tra fauella gli po$$ano e$primere; h&ograve; giudicato douer e$$ere co
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parents:
diff changeset
5183 $a vtile il dichiarare tuttii predetti vocaboli pertinenti alle proportioni, che ha il
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parents:
diff changeset
5184 pe$o alla po$$anza, &amp; la po$$anza al pe$o $critti dall'autore in que$to trattato della
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parents:
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5185 taglia, accio che quelle per$one lequali non po$$edono que$ti termini, non habbia
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parents:
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5186 no fatica di andare $tudiando iloro $ignificati.
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diff changeset
5187 <p>Dico dunque vna quantit&agrave; poter$i paragonare, &amp; hauere proportione con vn'altra
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parents:
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5188 in tre modi principali, la$ciando hora le pi&ugrave; $ottili di$tintioni. Primieramente
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5189 come maggiore ver$o la minore, dapoi come minore ver$o la maggiore, &amp; in fi-
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5190 ne come eguale ver$o la eguale. Tutta la dottrina delle'proportioni, con$i$te in
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diff changeset
5191 que$ti riguardi, cio&egrave; dal maggiore al minore, dal min ore al maggiore, &amp; dall'e-
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parents:
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5192 quale all'equale. Hor quando vna quantit&agrave;, che $ia maggiore &egrave; paragonata con
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diff changeset
5193 vn'altra, che $ia minore, che $i dice proportione di maggiore di$uguaglianza, na-
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parents:
diff changeset
5194 $cono cinque generi di proportioni, l'vno &egrave; il moltiphce $chietto, il $econdo &egrave; il
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5195 $opraparticolare, il rerzo il $o prapartiente, il quarto il moltiplice $opraparticola-
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5196 re, &amp; il quinto &amp; vltimo il moltiplice $oprapartiente. Ma quando $i fa compara-
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parents:
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5197 tione della minore quantit&agrave; ver$o la maggiore, all'hora $i producono cinque altri
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parents:
diff changeset
5198 generi oppo$ti apunto &agrave; i predetti cinque, &amp; $i dicono di minore di$uguaglian-
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parents:
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5199 za, &agrave; i quali per fargli differenti da loro $i aggiunge da Latini il $ub, cio&egrave; $otto,
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parents:
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5200 $criuendo$t $otto moltiplice, $otto$opra particolare, $otto $oprapartiente, $otto
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parents:
diff changeset
5201 moltiplice $opra particolare, &amp; $otto moltiplice $oprapartiente. Tutte le propor-
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parents:
diff changeset
5202 tioni dunque $ono compre$e in vniuer$ale da que$ti diece generi oppo$ti fra $e
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parents:
diff changeset
5203 l'vn l'altro, cia$cheduno de quali poi ha le $ue $petie differenti di proportioni. Ma
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5204 io non h&ograve; qui intentione di numerarle, n&egrave; dichiarare diffu$amente que$ta materia
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parents:
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5205 delle proportioni, ma $olamente li vocaboli po$ti dall'autore nel pre$ente libro
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parents:
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5206 della taglia, ba$tando mi hauerne dato in generale vna rozza cognitione. Ma chi
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parents:
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5207 di ci&ograve; de$idera hauere intero cono$cimento legga tra i $crittori della lingua Ita-
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parents:
diff changeset
5208 liana Fra Luca dal Borgo, il Tartaglia ne i libri della Arithmetica, &amp; il dottis$imo
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parents:
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5209 Zarlino nella prima parte delle In$titutioni Harmoniche. Dice l'autore in que$to
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parents:
diff changeset
5210 loco. Percio che $arebbono ambedue le po$$anze infieme in LH $otto doppie
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parents:
diff changeset
5211 $e$quialtere di e$$o pe$o. Cio&egrave; le due po$$anze po$te in LH haurebbono quella
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5212 proportione ver$o il pe$o, che ha 2. &agrave; 5. cio&egrave; $e il pe$o fo$$e come cinque, le po$-
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parents:
diff changeset
5213 $anze larebbono come 2. che &egrave; la proportione $otto dop pia $e$quialtera. Segue
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parents:
diff changeset
5214 <pb n=70>
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parents:
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5215 poi, Ma due quinte con vna decima fanno la me
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parents:
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5216 t&agrave;, cio&egrave; &agrave; $ommare in$ieme due quinti, &amp; vn
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parents:
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5217 decimo fanno la met&agrave; di cinque, pero che li
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parents:
diff changeset
5218 due quinti $ono due parti del cinque, &amp; la deci
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parents:
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5219 ma parte &egrave; la met&agrave; di vn quinto, tanto che met-
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parents:
diff changeset
5220 tono in$ieme due, &amp; mezo, che $ono la met&agrave; di
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parents:
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5221 cin que. Che $e que$ta met&agrave; poi $ar&agrave; diui$a per
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parents:
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5222 <*>re, ne riu$cir&agrave; la $e$ta parte da e$$ere attribuita &agrave;
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parents:
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5223 cia$cheduna delle tre po$$anze po$te in LHF.
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parents:
diff changeset
5224 Il modo del diuidere la met&agrave; per tre &egrave; facile, &amp;
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parents:
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5225 fas$i in que$ta maniera ponendo tre di $opra, &amp;
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parents:
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5226 vno di $otto; &amp; vno di $opra, &amp; due di $otto c&otilde;
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parents:
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5227 la $ua linea nel mezo, come $i co$tuma, &amp; mol-
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parents:
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5228 tiplicando il tre intero co'l due denominatore
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parents:
diff changeset
5229 della met&agrave;, ne viene 6, alquale di $opra $i ag-
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diff changeset
5230 giunge vno, &amp; &egrave; vn $e$to.
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5231 <p><I>Che $e come nella terza figura la corda $i allunghe
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diff changeset
5232 r&agrave; in O, &amp; $i condarr&agrave; intorno ad vn'altra gi-
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5233 rella, il cui centro $ia Q, la qual corda poi $i
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5234 leghi in R alla taglia di $otto; $ar&agrave; la po$$an-
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5235 za di G vn $ettimo del pe$o. &amp; co$i proceden
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diff changeset
5236 do in in$inito, la proportione della po$$anza al pe</I> <marg><I>Per la</I> 8. <I>di questo.</I></marg>
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5237 <I>$o, quanto $i voglia $otto moltiplice ver$o il pe-
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5238 $o $i potr&agrave; trouare. Dapoi $i mo$trer&agrave; $empre,
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5239 come nelle precedenti, che $e la po$$anza, la-
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diff changeset
5240 quale $o$tiene il pe$o $ar&agrave; vn quarto, ouero vn
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diff changeset
5241 quinto, ouero in qual $i voglia altro modo $ar&agrave;
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diff changeset
5242 di$po$ta ver$o il pe$o, che $imilmente cia$cuna
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diff changeset
5243 corda $o$terr&agrave; la quarta, &ograve; la quinta, ouero qual
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diff changeset
5244 $i voglia altra parte del pe$o, $i come la i$te$$a
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5245 po$$anza: peroche le corde fanno il mede$imo,
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5246 come $e fo$$ero tante po$$anze: &amp; le girelle co-
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diff changeset
5247 me $e fo$$ero tante leue.</I>
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5248 <p>Sotto moltiplice. Que$to &egrave; il primo genere delle
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5249 proportioni, che $i riguardano dal minore al
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5250 maggiore, detto di minore di$uguaglianza, il
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5251 quale $otto di $e tiene a$$ais$ime $petie, &amp; &egrave; op-
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5252 po$to come ho ricordato, al moltiplice. Dice
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5253 l'autore: &amp; co$i procedendo in infinito $i potr&agrave;
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diff changeset
5254 ritrouare qual $i voglia proportione $otto mol
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diff changeset
5255 tiplice. Percio che la po$$anza &egrave; minore del pe
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diff changeset
5256 $o, &amp; per&ograve; ver$o lui ha proportione $otto mol
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diff changeset
5257 tiplice, come di vno ver$o due, &amp; di due ver-
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5258 $o quattro per darne e$$empio, &amp; co$i de gli al-
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diff changeset
5259 tri numeri tali.
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5260 <fig>
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5261 <foot>S 2</foot>
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5262 <pb>
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5263 <HEAD>COROLLARIO</HEAD>
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5264 <p>Di qui &egrave; manife$to, che le girelle della taglia, allaquale &egrave; legato
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5265 il pe$o, fanno s&igrave;, che il pe$o &egrave; $o$tenuto da po$$anza minore,
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5266 di quel che $ia e$$o pe$o, co$a che veramente non fanno le gi-
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5267 relle della taglia di $opra.
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5268 <p><I>Egli nondimeno conuiene $apere, che come $uole $ar$i, la girella della taglia di $otto,
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5269 il cui centro &egrave; N, deue e$$ere minore di quella girella, il cui centro &egrave; C, &amp; que
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5270 $ta anche minore di quella, che ha il centro in B: &amp; in $omma $e $aranno pi&ugrave; gi
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5271 relle nella taglia di $otto legata al pe$o, $empre quella girella deue e$$ere maggiore
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5272 delle altre, che &egrave; pi&ugrave; vicina al pe$o attaccato: ma al contrario hanno &agrave; di$por$i le
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5273 girelle nella taglia di $opra, ilche $i co$tuma di fare, acci&ograve; che le corde fra loro non
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5274 $i intrichino; peroche in quanto alle girelle, $iano &ograve; grandi, &ograve; picciole, non importa
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5275 nulla, $eguendone $empre l'i$te$$o.</I>
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5276 <p><I>Di pi&ugrave; &egrave; da notare, ilche etiandio dalle co$e dette facilmente appare, che grandi$$ima
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5277 differenza na$ce trala po$$anza, &amp; il pe$o dal legare la corda ouero in R della ta
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5278 glia di $otto, ouero in S, percioche $e $i legher&agrave; in S, la po$$anza di G $ar&agrave; vn
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5279 $e$to del pe$o; ma $e in R vn $ettimo, co$a che non accade alla taglia di $opra:
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5280 percioche leghi$i la corda, come nella precedente figura, ouero in T, ouero in O,
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5281 $empre la po$$anza di G $ar&agrave; vn $e$to di e$$o pe$o.</I>
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parents:
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5282 <p><I>Dopo que$te co$e egli &egrave; da con$iderare in che modo la forza moua il pe$o, &amp; di pi&ugrave; lo
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diff changeset
5283 $patio, &amp; il tempo della po$$anza, che moue, &amp; del pe$o che &egrave; mo$$o.</I>
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diff changeset
5284 <p>&ldquo;Di piu egli &egrave; da notare ilche etiandio &egrave; manife$to dalle co$e dette &amp;c. Qui potreb-
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5285 be for$e ad alcuno parere difficile in che modo po$$a e$$ere, che dal legare la cor-
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5286 da in R, ouero in S, come $i vede in que$ta figura, na$ca tanta differenza. Onde
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5287 noti$i che legando la corda in S, la girella Q re$ta del tutto inutile, &amp; &egrave; come
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5288 $e ella non vifo$$e; &amp; la corda per non e$$ere attaccata in R alla taglia di $otto,
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5289 ma in S fuori non $o$tiene la taglia, talche la forza di G viene ad e$$ere $olamen
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5290 te vn $e$to del pe$o. $oggiunge poi ilche non auiene alla taglia di $opra.&rdquo; Doue
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5291 auerta$i che mentre $i ha tenuto propo$ito delle lettere S &amp; R, ha bi$ognato guar
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5292 dare nella qui $opra$critta figura, ma in parlando di TO, egli &egrave; me$tieri per in-
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5293 tendere que$to loco mirare nella figura precedente, che &egrave; la $econda della nona
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5294 propo$itione, peroche iui$ono le lettere TO. La ragione per la quale non na$ca
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parents:
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5295 differenza nella po$$anza &agrave; legare la corda in T ouero in O, ma $ia tutto vno,
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5296 &egrave; che la taglia di $opra $ta $empre ferma, per modo, che non importa nulla il le-
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5297 gare la corda in O nella taglia di $opra, ouero in T fuori di e$$a, poiche am-
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5298 bidue i luoghi $ono immobili, &amp; iui la corda $ta ferma. Lequali tutte co$e l'auto
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5299 re h&agrave; toccato breuis$imamente per e$$ere que$to trattato della taglia lungo, la-
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5300 $ciando al lettore ancora qualche co$a da $peculare per $e mede$imo.
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5301 <pb n=71>
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5302 <HEAD>PROPOSITIONE X.</HEAD>
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5303 <p>Se la corda $ar&agrave; inuolta intorno alla girella della taglia applcca-
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5304 ta di $opra, all'vno de'capi, dellaqual corda $ia attaccato il pe
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5305 $o, &amp; all'altro po$ta la po$$anza, che moue. La detta po$$anza mo
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5306 uer&agrave; con la leua $empre egualmente di$tante dall'orizonte.
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5307 <p><I>Sia il pe$o A. $ia la girella della taglia appiccata di $opra, che habbia il centro K.
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5308 Sia dapoi la corda HB CDEF legata al pe$o A in H, &amp; $ia inuolta d'intor
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5309 no alla girella; &amp; $ia la taglia per modo appiccata
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5310 in L, che non habbia alcun altro mouimento $uor
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5311 che il volgimento libero della girella d'intorno al
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5312 $uo a$$etto, &amp; $ia la po$$anza in F che moua il
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5313 pe$o A. Dico, che la po$$anza di F mouer&agrave;
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5314 $empre il pe$o A con la leua egualmente di$tan-
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5315 te dall'orizonte. $ia tirata la linea BKE egual-
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parents:
diff changeset
5316 mente di$tante dall'orizonte, &amp; $iano i punti BE</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
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parents:
diff changeset
5317 <I>doue le corde BH &amp; EF toccano il cerchio:
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parents:
diff changeset
5318 $ar&agrave; BKE la leua, il $o$tegno dellaquale &egrave; nel
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parents:
diff changeset
5319 $uo mezo, che &egrave; K, come di $opra &egrave; detto. Men-
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parents:
diff changeset
5320 tre che dunque la forza di F inchina al ba$$o ver
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parents:
diff changeset
5321 $o M, la leua EB $i mouer&agrave;, mouendo$i tut-
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parents:
diff changeset
5322 ta la girella, cio&egrave; volgendo$i attorno. Mentre
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parents:
diff changeset
5323 che dunque F $ta in M $ia il punto E della
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parents:
diff changeset
5324 leua mo$$o fin ad I, &amp; il B $in'al C, di mo-
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parents:
diff changeset
5325 do, che la leua $ia in CI. Dapoi $i faccia la li
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parents:
diff changeset
5326 nea NM eguale ad e$$a FE: &amp; quando il
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parents:
diff changeset
5327 punto E, $ar&agrave; in I all'hora il punto della cor
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parents:
diff changeset
5328 da, ilquale era in E $ar&agrave; in N, &amp; quello,</I>
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casties
parents:
diff changeset
5329 <fig>
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casties
parents:
diff changeset
5330 <I>che era in B $ar&agrave; in C di modo, che tirata la linea CI pa$$er&agrave; per lo centro
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parents:
diff changeset
5331 K. Hormentre il B $ta in C $ia il punto H in G, &amp; $ar&agrave; BH al CBG
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parents:
diff changeset
5332 eguale, e$$endo la mede$ima corda. &amp; percioche mentre EF inchina in MN
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parents:
diff changeset
5333 rimane pur $empre EFM &agrave; piombo dell'orizonte, &amp; tocca il cerchio nel punto
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parents:
diff changeset
5334 E di modo, che la linea tirata dal punto E per lo centro K $ia $empre egualmen
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parents:
diff changeset
5335 te di$tante dall'orizonte, ilche mede$imamente auiene alla corda BG &amp; al pun-
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parents:
diff changeset
5336 <pb>
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parents:
diff changeset
5337 to B. Mentre dunque il cerchio, ouero la girella $i volge intorno, $empre $i mo-
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parents:
diff changeset
5338 ue la leua EB, &amp; $em-
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parents:
diff changeset
5339 pre ancora rimane vn'al-
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parents:
diff changeset
5340 tra leua in EB, e$$endo
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parents:
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5341 che per natura di e$$a gi-
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parents:
diff changeset
5342 rella, nellaquale $empre,
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parents:
diff changeset
5343 mentre $i moue, re$ti il
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parents:
diff changeset
5344 diametro da B in E,
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casties
parents:
diff changeset
5345 (ilquale &egrave; in loco di le-
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casties
parents:
diff changeset
5346 ua) auuiene che parten
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parents:
diff changeset
5347 do$ene vna, $ucceda
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parents:
diff changeset
5348 l'altra $empre, durando
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parents:
diff changeset
5349 per&ograve; cotale aggiramen-
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parents:
diff changeset
5350 to; &amp; co$i accade, che
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parents:
diff changeset
5351 la po$$anza moua il pe
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parents:
diff changeset
5352 $o $empre con la leua
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casties
parents:
diff changeset
5353 EB egualmente di$tan
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casties
parents:
diff changeset
5354 te dall'orizonte, ilche
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parents:
diff changeset
5355 bi$ognaua mo$trare.</I>
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casties
parents:
diff changeset
5356 <fig>
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casties
parents:
diff changeset
5357 <p>Po$te le co$e i$te$$e, lo $patio della po$$anza, che moue il pe$o, &egrave;
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parents:
diff changeset
5358 eguale allo $patio dello i$te$$o pe$o, che &egrave; mo$$o.
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parents:
diff changeset
5359 <p><I>Percioche egli &egrave; $tato dimo$trato, che mentre F $t&agrave; in M, il pe$o A, cio&egrave; il punto
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parents:
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5360 H &egrave; in G: &amp; concio$ia che la corda HBCDEF $ia eguale alla GBCDEN
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casties
parents:
diff changeset
5361 FM per e$$ere la corda i$te$$a: leuata via dunque la commune GBCDENF
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parents:
diff changeset
5362 $ar&agrave; la HG alla FM eguale, &amp; $imilmente $i mo$trer&agrave; la di$ce$a di F e$$ere
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parents:
diff changeset
5363 $empre eguale alla $alita di H. Adunque lo $patio della po$$anza &egrave; eguale allo
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parents:
diff changeset
5364 $patio del pe$o. che era da dimo$trare.</I>
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parents:
diff changeset
5365 <p>Oltre &agrave; ci&ograve; la po$$anza moue il pe$o i$te$$o per i$patio eguale in
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parents:
diff changeset
5366 tempo eguale, tanto con la corda inuolta intorno alla girella
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parents:
diff changeset
5367 della taglia appiccata di $opra, quanto $enza taglia, pur che li
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casties
parents:
diff changeset
5368 mouimenti di e$$a po$$anza in velocit&agrave; $iano eguali.
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parents:
diff changeset
5369 <pb n=72>
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casties
parents:
diff changeset
5370 <p><I>Stando le co$e i$te$$e, $ia vn'altro pe$o P eguale al pe$o A, alquale $ia legata la cor
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casties
parents:
diff changeset
5371 da TQ &agrave; piombo dell'orizonte: &amp; $ia TQ eguale ad e$$a HB: &amp; muoua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5372 la po$$anza di Q il
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casties
parents:
diff changeset
5373 pe$o P all'ins&ugrave; ad
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casties
parents:
diff changeset
5374 angoli retti all'orizon
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casties
parents:
diff changeset
5375 te, come $i moue il pe
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parents:
diff changeset
5376 $o A. Dico, che per
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parents:
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5377 eguale $patio, &amp; in
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casties
parents:
diff changeset
5378 vno i$te$$o tempo la
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casties
parents:
diff changeset
5379 po$$anza di Q. mo-
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casties
parents:
diff changeset
5380 ue il pe$o P, &amp; la
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casties
parents:
diff changeset
5381 po$$anza di</I> F <I>il pe-
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casties
parents:
diff changeset
5382 $o A: ilche &egrave; il me-
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casties
parents:
diff changeset
5383 de$imo, come $e l'i-
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casties
parents:
diff changeset
5384 $te$$o pe$o fo$$e mo$-
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casties
parents:
diff changeset
5385 $o in tempo eguale,
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casties
parents:
diff changeset
5386 $econdo che habbia-
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casties
parents:
diff changeset
5387 mo propo$to. Sia
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casties
parents:
diff changeset
5388 allungata la EF in
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casties
parents:
diff changeset
5389 S, &amp; la TQ in R,
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casties
parents:
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5390 &amp; $iano le QRFS
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casties
parents:
diff changeset
5391 fatte eguali non $olo
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casties
parents:
diff changeset
5392 fra $e, ma etiandio
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casties
parents:
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5393 ad e$$a BH. Hor
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casties
parents:
diff changeset
5394 concio$ia che le TQ
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casties
parents:
diff changeset
5395 QR $iano eguali ad
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casties
parents:
diff changeset
5396 e$$e HB FS, &amp;
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casties
parents:
diff changeset
5397 la $orza di Q mo-
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casties
parents:
diff changeset
5398 ua il pe$o P per
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casties
parents:
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5399 la linea retta TQ
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casties
parents:
diff changeset
5400 R: &amp; dall'altro</I>
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casties
parents:
diff changeset
5401 <fig>
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casties
parents:
diff changeset
5402 <I>canto la forza di F moua A per la retta HB, &amp; le velocit&agrave; de i mouimenti
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casties
parents:
diff changeset
5403 dell'una, &amp; l'altra po$$anza $iano eguali, all'hor che nell'i$te$$o tempo la po$$anza di
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casties
parents:
diff changeset
5404 Q $ar&agrave; in R, &amp; la po$$anza di F $ar&agrave; in S, e$$endo gli $patij eguali: &amp; men
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casties
parents:
diff changeset
5405 tre la po$$anza di Q &egrave; in R, il pe$o P, cio&egrave; il punto T $ar&agrave; in Q, per e$$e-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5406 rela TQ eguale ad e$$a QR, &amp; mentre che la po$$anza di F $ta in S, il pe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5407 $o A, cio&egrave; il punto H $ar&agrave; in B; ma lo $patio TQ &egrave; eguale allo $patio HB:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5408 adunque le po$$anze di FQ mo$$e egualmente moueranno i pe$i PA eguali
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5409 per eguali $patij in tempo eguale. che era da mo$trare.</I>
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5410 <HEAD>PROPOSITIONE XI.</HEAD>
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5411 <p>Se la corda $ar&agrave; inuolta intorno alla girella della taglia legata al
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5412 pe$o, laqual corda con vno de' $uoi capi $ia legata in qualche
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5413 luogo, &amp; con l'altro pre$a dalla po$$anza che moue il pe$o; La
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diff changeset
5414 po$$anza mouer&agrave; $empre con la leua egualmente di$tante dal
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5415 l'orizonte.
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5416 <p><I>Sia il pe$o A: $ia la girella CED
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5417 della taglia legata al pe$o A,
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5418 da KH, &amp; $ia KH ad ango-
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5419 li retti dell'orizonte, di modo
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5420 the il pe$o $egua $empre il mo-
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5421 uimento della taglia, $ia pur fat-
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5422 to all'ins&ugrave;, ouero all'ingi&ugrave;, &amp;
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5423 $ia il centro della girella K, &amp;
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diff changeset
5424 la corda inuolta intorno alla gi-
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5425 rella $ia BCDEF, la quale
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5426 $ia legata in B, di modo che
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5427 $tia immobile in B<*> &amp; $ia in F
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5428 la po$$anza, che moue il pe$o A.
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5429 Dico che la po$$anza di F mo-
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5430 ue $empre il pe$o A con la le-
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5431 ua egualmente di$tante dall'ori-
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5432 zonte. Siano BC EF egual
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5433 mente di$tanti s&igrave; fra loro, come
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5434 ad e$$a KH, &amp; &agrave; piombo al-</I>
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5435 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>l'orizonte della i$te$$a KH, &amp;
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5436 toccanti il cerchio CED ne i
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5437 punti EC, &amp; $ia congiunta la
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5438 EC laquale pa$$er&agrave; per lo cen
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5439 tro K, &amp; $ar&agrave; egualmente di
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5440 $tante dall'orizonte, $i come pri-
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5441 ma &egrave; detto. Hor percioche la
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5442 girella CED $i volge d'intor-
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5443 no K $uo centro, per&ograve; mentre
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5444 la forza di F tira s&ugrave; il punto E
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5445 dourebbe di$cendere il punto C
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5446 &amp; tirare in gi&ugrave; B: mala cor-
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5447 da po$ta in B &egrave; immobile, on-
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5448 de BC non pu&ograve; di$cendere.
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5449 Per laqual co$a mentre la po$-</I>
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5450 <fig>
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5451 <pb n=73>
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5452 <I>$anza di F tira s&ugrave;lo E, tutta la girella $i mouer&agrave; in s&ugrave;, &amp; per con$equenza tut-
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5453 ta la taglia, &amp; il pe$o; &amp; EKC $ar&agrave; come leua, il cui $o$tegno $ar&agrave; C: pero-</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
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5454 <I>che il punto C per cau$a di BC qua$i &egrave; immobile, ma la po$$anza che moue la
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5455 leua &egrave; in F con la corda EF, &amp; il pe$o $ta appiccato in K. Che $e il punto
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5456 C fo$$e del tutto immobile, &amp; $i moua la leua EC in NC, &amp; $i diuida NC
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5457 in due parti eguali in L: $aranno CL LN eguali ad e$$e CK KE. Per la
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5458 qual co$a $e la leua EC fo$$e in CN, il punto K $arebbe in L: &amp; $e $i con
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5459 duce$$e la linea LM &agrave; piombo dell'orizonte, laquale $ia anche eguale alla KH,
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5460 $arebbe il pe$o A, cio&egrave; il punto H in M. Ma percioche la po$$anza di F men
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5461 tre v&agrave; in $u$o mouendo la girella $empre $i moue $opra la linea retta EFG, laquale
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5462 &egrave; anco egualmente di$tante $empre da BC, $ar&agrave; nece$$ario, che la girella della ta-
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5463 glia $empre $i trouitra le linee EG BC, &amp; il centro K $tando nel mezo, $i mo-
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diff changeset
5464 uer&agrave; $empre $opra la linea retta HKT. Sia condotta adunque per L la linea
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5465 PT LQ egualmente di$tante s&igrave; dall orizonte, come dalla EC, laquale $eghi la
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5466 HK allu<*>gatain T, &amp; co'l centro T, &amp; lo $patio TQ $i formi il cerchio QR
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5467 PS, ilquale $ar&agrave; eguale al cerchio CED; &amp; li punti PQ toccheranno le cor-
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5468 de FE BC ne i punti PQ. Peroche il rettangolo PECQ &amp; la PT &amp; la
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5469 TQ $ono eguali ad e$$e EK KC. Dapoi per T $ia tirato RTS diametro
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5470 del cerchio PQS egualmente di$tante ad e$$a NC, &amp; $ia fatta TO eguale</I> <marg><I>Per la</I> 34. <I>del pri<*>o.</I></marg>
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5471 <I>alla KH. Hor mentre il centro K $ar&agrave; mo$$o fin alla linea PQ all'hora il cen-
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parents:
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5472 tro K $ar&agrave; in T. Maegli&egrave; $tato dimo$trato, che il centro della girella $i moue
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5473 $empre per la linearetta HT. Onde accioche il centro K $ia nella linea PQ egual-
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5474 mente di$tante ad e$$a EC, egli &egrave; nece$$ario, che e$$o $ia in T: &amp; accioche an-
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5475 chora la leua EC $i alzinell'angolo ECN egli &egrave; nece$$ario, che $ia in RS &amp;
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parents:
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5476 non in CN percioche l'angolo RSE all'angolo NCE &egrave; eguale &amp; co$i il $o-</I> <marg><I>Per la</I> 29. <I><*></I></marg>
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5477 <I>$tegno C non &egrave; del tutto immobile, mouendo$i tutta la girella all'ins&ugrave;, &amp; tutta
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5478 mutt'il luogo: nondimeno il C ha ragione di $o$tegno, peroche meno $i moue C
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5479 di quel che f&agrave; K &amp; E, percioche $i moue il punto E fin ad R, &amp; il K fin al T,
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5480 ma il punto C fin ad S $olamente. Per laqual co$a mentre il centro K $i troua
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5481 in T, il $ito della girella $ar&agrave; QRPS: &amp; il pe$o A, cio&egrave; il punto H $ar&agrave;
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5482 in O, e$$endo TO eguale &agrave; KH; ma il $ito di EC, cio&egrave; della leua mo$$a, $ar&agrave;
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5483 RS: &amp; la po$$anza di F $ar&agrave; mo$$a in $u$o per la rettalinea EFG: ma nel-
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5484 <*>i$te$$o tempo, che K $ar&agrave; in T, $ia la po$$anza in G; &amp; mentre la leua EC in
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5485 que$to modo $i moue, rimangono pur $empre GPBQ fraloro egua mente di-
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5486 $tanti, &amp; &agrave; piombo dell'orizonte, talche doue toccano la girella, come ne' punti
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5487 PQ, $empre la linea PQ $ar&agrave; il diametro della girella &amp; come leua egualmen-
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5488 te di$tante dall'orizonte. Mentre dunque la girella $i moue, &amp; v&agrave; attorno, $em
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5489 pre anche $i moue la leua EC, &amp; $empre rimane vn'altra leua nellagirella egual
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5490 mente di$tante dall'orizonte, come PQ, per modo, che la po$$anza di F <*>ona
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5491 il pe$o, $tando la leua egualmente di$tante all'orizonte, il cui $o$tegno $ac&agrave; $e<*>pre
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parents:
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5492 nellalinea CB, &amp; il pe$o nel mezo della leua appiccato: &amp; la po$$anza nella li-
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5493 nea EG, che era da mo$trare.</I>
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diff changeset
5494 <foot><I>T</I></foot>
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5495 <pb>
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diff changeset
5496 <p>Stando le co$e i$te$$e. Lo $patio della po$$anza, che moue il pe-
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diff changeset
5497 $o &egrave; il doppio dello $patio dell'i$te$$o pe$o mo$$o.
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5498 <p><I>E$$endo $tato dimo$trato, che mentre il K $t&agrave; nel T, il pe$o A cio&egrave; il punto H
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diff changeset
5499 e$$ere in O: &amp; nell'i$te$$o tempo ancora la po$$anza di F e$$ere in G: &amp; per-
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diff changeset
5500 cioche la corda BCDEF eguale &egrave; alla corda EQSPG, peroche &egrave; la mede$ima
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diff changeset
5501 corda: &amp; la corda che &egrave; inuolta intorno al mezo cerchio CDE eguale &egrave; alla cor-
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5502 da, che $ta d'intorno al mezo cerchio QSP: tolti via dunque li due pezzi di cor
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diff changeset
5503 da communi BQ, &amp; FP: $ar&agrave; il re$lante della corda FG eguale ad e$$i due
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diff changeset
5504 pezzi di corda rima$i CQ &amp; EP in$ieme pre$i. Ma EP eguale &egrave; al TK,
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5505 &amp; il CQ $ar&agrave; anche eguale ad e$$o TK, peroche $ono PK &amp; TC parallelo-
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parents:
diff changeset
5506 grammi rettangoli. Per laqual co$a le linee EPCQ in$ieme $ono due volte tan
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diff changeset
5507 to, quanto &egrave; TK. Adunque la corda FC $ar&agrave; due volte tanto quanto la TK.
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diff changeset
5508 &amp; percioche la KH &egrave; eguale alla TO, leuando via la corda commune KO $a
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diff changeset
5509 r&agrave; la KT eguale ad e$$a KO. Per laqual co$a la corda FG $ar&agrave; due volte tan-
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5510 to quanto e$$a HO: cio&egrave; lo $patio d'lla po$$anza due volte tanto quanto lo $pa-
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diff changeset
5511 tio del pe$o, che era da mo$tra<*>e.</I>
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diff changeset
5512 <p>&ldquo;Parallelogrammi rettangoli. Vuol dire $igure di linee egualmente diftanti fra loro,
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5513 lequali formino angoli retti &agrave; differenza di altre figure, che $e ben $ono di linee
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5514 egualmente di$tanti, non formano tuttauia angoli retti.
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diff changeset
5515 <p>Dapoi la po$$anza mouer&agrave; il pe$o i$te$$o in tempo eguale per la
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5516 met&agrave; dello $patio, con la corda inuolta d'intorno alla girella
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5517 della taglia legata al pe$o, che $enza taglia; pur che le veloci-
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diff changeset
5518 t&agrave; de' mouimenti di e$$a po$$anza $iano eguali.
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diff changeset
5519 <pb n=74>
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5520 <p><I>Peroche $ia, $tando le co$e i$te$$e, vn'altro pe$o V eguale al pe$o A al quale $ia
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5521 legata la corda <36>X &amp; $ia in X la po$$anza, che moue il pe$o V, Dico, $e le ve
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5522 locit&agrave; de' mouimenti dell'vna, &amp; l'altra po$$anza $aranno eguali, che la po$$anza</I>
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5523 <fig>
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diff changeset
5524 <I>di</I> F <I>mouer&agrave; il pe$o A nell'i$te$$o tempo per la met&agrave; dello $patio, per lo quale
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5525 il pe$o V $ar&agrave; mo$$o dalla po$$anza di X, che &egrave; il mede$imo, come $el'i$te$$o pe-
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diff changeset
5526 $o in tempo eguale fo$$e mo$$o. Moua la po$$anza di X il pe$o V, &amp; la po$$an-
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parents:
diff changeset
5527 za peruenga in <G>*u</G>; &amp; $ia X<G>*u</G> eguale ad e$$a FG: &amp; $i faccia <G>*u</G>Z eguale
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diff changeset
5528 &agrave; X<36>, talche quando la po$$anza di X $ar&agrave; in <G>*u</G>, $ia il pe$o V cio&egrave; il punto <36></I>
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5529 <foot><I>T</I> 2</foot>
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5530 <pb>
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5531 <I>in Z; ma <36>Z &egrave; eguale ad FG, e$$endo eguale ad X<G>*u</G>: dunque <36>Z $ar&agrave; due
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5532 volte tanto, quanto OH. Per laqual co$a mentre le po$$anze $aranno in G<G>*u</G>, i
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5533 pe$i AV $aranno in OZ. Hor nell'i$te$$o tempo $aranuo le po$$anze in G<G>*u</G>,
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parents:
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5534 peroche le vetocit&agrave; de mouimenti $ono eguali: onde la forza di F mouer&agrave; il pe-
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5535 $o A nel mede$imo tempo per la met&agrave; di quello $patio, per loquale il pe$o V $a</I>
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5536 <fig>
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5537 <I>r&agrave; mo$$o dalla po$$anza di X: &amp; li pe$i $ono eguali, adunque la po$$anza moue-
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parents:
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5538 r&agrave; il pe$o i$l e$$o in tempo eguale per la met&agrave; dello $patio, con la corda, &amp; la taglia
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5539 legata in que$to modo al pe$o, che $enza taglia; purche le velocit&agrave; della po$$anza
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5540 de'mouimenti $iano eguali, che era da mo$trar$i.</I>
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5541 <pb n=75>
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5542 <HEAD>PROPOSITIONE XII.</HEAD>
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5543 <p>Se la corda $ar&agrave; riuolta d'intorno &agrave; pi&ugrave; girelle, legando l'vno de'
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parents:
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5544 capi $uoi in qualche loco, &amp; l'altro $ia tenuto dalla po$$anza,
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5545 che moue il pe$o: La po$$anza mouer&agrave; con le leue $empre
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5546 egualmente di$tanti dall'orizonte.
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5547 <p><I>Siail pe$o A. $ia la girella CED della
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5548 taglia legata al pe$o da KS ad angoli ret
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5549 ti all'orizonte; di modo, che il pe$o $egua
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5550 $empre il $uo mouimento &ograve; $u$o, &ograve; giu$o,
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5551 che $ia fatto. Sia dapoi la girella intorno
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5552 al centro L della taglia appiccata di $opra;
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5553 &amp; $iala corda BCDEHMNO riuol-
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5554 ta d'intorno alle girelle, laquale $ia legata
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5555 in B; &amp; $ia in O la forza mouente il
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5556 pe$o A, mouendo$i al ba$$o per OP. Di-
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5557 co che la po$$anza di O mouer&agrave; $empre il
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5558 pe$o A con le leue $empre egualmente
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5559 di$tanti dall'orizonte. $ia tirata la linea
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5560 NH per lo centro L egualmente di$tan-
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5561 te dall'orizonte, che $ar&agrave; la leua della girel-</I> <marg><I>Per la</I> 1. <I>&amp;</I> 10. <I>di questo.</I></marg>
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5562 <I>la, il cui centro &egrave; L: $ia tirata da poi la
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5563 EC per lo centro K, $imilmente di$tan-</I> <marg><I>Per la</I> 11. <I>di questo.</I></marg>
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5564 <I>te egualmente dall'orizonte, la quale $ar&agrave;
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5565 anche la leua della girella, il cui centro &egrave;</I> <marg><I>Par la</I> 10. <I>di questo.</I></marg>
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5566 <I>K. Moua$i la po$$anza di O in giu$o, la
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5567 quale mentre in giu$o $i moue, mouer&agrave; la
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5568 leua NH, &amp; mentre la leua $i moue, la
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5569 N $i mouer&agrave; in giu$o, &amp; la H in $u$o,
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5570 come &egrave; detto di $opra. Mamentre la H
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5571 $i moue in $u$o, moue etiandio in $u$o la E,
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5572 &amp; la leua EC, il cui $o$tegno &egrave; C, ma
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5573 il $o$tegno C non puote mouere in giu$o
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5574 il B; per&ograve; la girella il cui centro &egrave; K mo
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5575 uera$$i in $u$o, &amp; per con$equenza la ta-
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5576 glia, &amp; il pe$o A, come nella preceden-
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5577 te &egrave; stato detto. &amp; perche per la mede$i-
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5578 ma cau$a, che &egrave; stata a$$egnata nelle pre-
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parents:
diff changeset
5579 cedenti, rimangono $empre le leue egual-
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parents:
diff changeset
5580 mente distanti dall'orizonte in HN, &amp;</I>
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casties
parents:
diff changeset
5581 <fig>
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casties
parents:
diff changeset
5582 <I>in EC, la po$$anza dun-
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parents:
diff changeset
5583 que mouente il pe$o A
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casties
parents:
diff changeset
5584 lo mouer&agrave; $empre $tando
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casties
parents:
diff changeset
5585 le leue egualmente distan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5586 ti dall'orizonte; che erada
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5587 mo$trar$i.</I>
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casties
parents:
diff changeset
5588 <p><I>Et $e la corda $ar&agrave; riuolta d'in
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parents:
diff changeset
5589 torno &agrave; pi&ugrave; girelle; $imil-
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parents:
diff changeset
5590 mente $i dimo$trer&agrave; la po$-
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casties
parents:
diff changeset
5591 $anza mouere il pe$o con
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casties
parents:
diff changeset
5592 le leue $empre egualmente
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casties
parents:
diff changeset
5593 di$tanti dall'orizonte: &amp;
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casties
parents:
diff changeset
5594 le leue delle girelle della ta
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casties
parents:
diff changeset
5595 glia di $opra $empre e$$e-
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casties
parents:
diff changeset
5596 re come HN, i $o$tegni
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parents:
diff changeset
5597 delle quali $aranno $empre
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casties
parents:
diff changeset
5598 nel mezo: ma le leue delle
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parents:
diff changeset
5599 girelle della taglia di $otto
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casties
parents:
diff changeset
5600 $empre e$$ere, come EC;
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casties
parents:
diff changeset
5601 li cui $o$tegni $aranno nel-
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parents:
diff changeset
5602 le $tremit&agrave; delle leue.</I>
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parents:
diff changeset
5603 <p>Stando le co$e i$te$$e,
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parents:
diff changeset
5604 lo $patio della po$-
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casties
parents:
diff changeset
5605 $anza, &egrave; il doppio
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parents:
diff changeset
5606 dello $patio del pe-
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casties
parents:
diff changeset
5607 $o.
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casties
parents:
diff changeset
5608 <fig>
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casties
parents:
diff changeset
5609 <p><I>Sia mo$$o il centro K fin al centro R; &amp; $ia la girella FTG: poi $ia per lo cen-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5610 tro R condotta la linea GF egualmente di$tante da e$$a EC: le corde EH
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parents:
diff changeset
5611 CB toccheranno la girella ne i punti GF. Faccia$i alla fine RQ eguale &agrave;
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parents:
diff changeset
5612 KS. Mentre dunque K $ar&agrave; in R, il pe$o A, cio&egrave; il punto S $ar&agrave; in Q,</I>
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parents:
diff changeset
5613 <pb n=76>
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casties
parents:
diff changeset
5614 <I>&amp; mentre il centro della girella &egrave; in R, $ia la po$$anza di O mo$$a in P. &amp;
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parents:
diff changeset
5615 percioche la corda BCDEHMNO eguale &egrave; alla corda BFTGHMNP
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parents:
diff changeset
5616 per e$$er la corda iste$$a, &amp; FTG &egrave; eguale &agrave; CDE; leuate via dunque le com-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5617 muni BF &amp; GHMNO, $ar&agrave; la re$tante OP eguale ad e$$e FC EG pre-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5618 $e in$ieme: &amp; per con$equenza due volte tanto, quanto &egrave; KR, &amp; QS. &amp; e$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5619 $endo OP lo $patio della po$$anza mo$$a, &amp; SQ lo $patio del pe$o mo$$o;
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casties
parents:
diff changeset
5620 $ar&agrave; lo $patio della po$$anza due volte tanto quanto lo $patio del pe$o. che era
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5621 da mostrar$i.</I>
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casties
parents:
diff changeset
5622 <p>Oltre &agrave; ci&ograve; la po$$anza mouer&agrave; il pe$o i$te$$o in tempo eguale
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parents:
diff changeset
5623 per la met&agrave; dello $patio, con vna corda riuolta d'intorno &agrave;
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parents:
diff changeset
5624 due girelle, l'una delle quali $ia della taglia di $opra, &amp; l'altra
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parents:
diff changeset
5625 $ia della taglia legata al pe$o; che $enza taglie: pur che i mo-
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casties
parents:
diff changeset
5626 uimenti di e$$a po$$anza $iano egualmente veloci.
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parents:
diff changeset
5627 <p><I>Percioche $tando le co-
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parents:
diff changeset
5628 $e i$te$$e, $ia il pe$o
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parents:
diff changeset
5629 V eguale ad e$$o A,
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parents:
diff changeset
5630 alquale $ia legata la
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casties
parents:
diff changeset
5631 corda X<36>; &amp; $ia
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casties
parents:
diff changeset
5632 la po$$anza in X che
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parents:
diff changeset
5633 moue il pe$o V; la
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parents:
diff changeset
5634 quale mentre moue
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casties
parents:
diff changeset
5635 il pe$o, peruenga in
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casties
parents:
diff changeset
5636 <G>*u</G>: &amp; $iano fatte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5637 X<G>*u</G> Z<36> eguali ad
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parents:
diff changeset
5638 e$$a OP; $ar&agrave; Z<36>
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casties
parents:
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5639 due volte tanto qua-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5640 to QS. &amp; $e le
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5641 velocit&agrave; de' moui-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5642 menti dell'vna, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5643 l'altra po$$anza $a-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5644 ranno eguali; egli &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5645 manife$to, che il pe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5646 $o V trapa$$a due
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5647 volte tanto $patio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5648 nell'i$te$$o tempo, di
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parents:
diff changeset
5649 quel che trapa$$i il
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casties
parents:
diff changeset
5650 pe$o A: percioche
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casties
parents:
diff changeset
5651 nel tempo mede$imo
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casties
parents:
diff changeset
5652 la po$$anza di X per-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5653 uiene ad <G>*u</G>, &amp; la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5654 po$$anza di O &agrave; P;
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casties
parents:
diff changeset
5655 &amp; li pe$i $imilmen-
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casties
parents:
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5656 te in ZQ. che era
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5657 da mo$trar$i.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5658 <fig>
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parents:
diff changeset
5659 <HEAD>PROPOSITIONE XIII.</HEAD>
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casties
parents:
diff changeset
5660 <p>Riuolgendo la corda d'intorno &agrave; due girelle di due taglie, I'vna
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5661 dellequali $ia di $opra, &amp; l'altra di $otto, &amp; legata al pe$o; e$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5662 $endo anche l'vno de' capi di detta corda legato alla taglia di
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parents:
diff changeset
5663 $otto, &amp; l'altro tenuto dalla po$$anza che moue; $ar&agrave; lo $patio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5664 cor$o della po$$anza, che tira, tre volte tanto quanto lo $pati
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casties
parents:
diff changeset
5665 del pe$o mo$$o.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5666 <pb n=77>
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casties
parents:
diff changeset
5667 <p><I>Sia il pe$o A; $ia BCD la girel-
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casties
parents:
diff changeset
5668 la della taglia legata al pe$o A,
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casties
parents:
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5669 attaccato da EQ, &amp; $ia E il
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5670 centro della girella; $ia dapoi F
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5671 GH la girella della taglia appic-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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5672 cata di $opra, il cui centro K; &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5673 $ia la corda LFGHDBCM ri-
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casties
parents:
diff changeset
5674 uolta intorno &agrave; tutte le girelle, &amp;
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casties
parents:
diff changeset
5675 legata alla taglia di $otto in L:
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casties
parents:
diff changeset
5676 &amp; $ia in M la po$$anza, che
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casties
parents:
diff changeset
5677 moue. Dico lo $patio cor$o dalla
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parents:
diff changeset
5678 po$$anza di M, mentre moue il
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casties
parents:
diff changeset
5679 pe$o, e$$ere triplo dello $patio del
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casties
parents:
diff changeset
5680 pe$o mo$$o A. Moua$i la po$$an
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casties
parents:
diff changeset
5681 za di M fin ad N; &amp; il centro
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casties
parents:
diff changeset
5682 E $ia mo$$o fin ad O; &amp; L fin
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casties
parents:
diff changeset
5683 &agrave; P; &amp; il pe$o A, cio&egrave; il pun-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5684 to Q fin ad R; &amp; la girella
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5685 mo$$a $ia TSV. Siano condot-
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casties
parents:
diff changeset
5686 te per EO le linee ST BD
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5687 egualmente di$tanti dall'orizonte,
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casties
parents:
diff changeset
5688 lequali $aranno anche tra loro e-
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casties
parents:
diff changeset
5689 gualmente di$tanti. Ma percio-
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casties
parents:
diff changeset
5690 che mentre E $ta in O, il pun-
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casties
parents:
diff changeset
5691 to Q $ta in R; $ar&agrave; EQ egua
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casties
parents:
diff changeset
5692 le ad OR, &amp; EO ade$$o QR
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5693 eguale; $imilmente LQ $ar&agrave;
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casties
parents:
diff changeset
5694 eguale &agrave; PR, &amp; LP ad e$$o
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casties
parents:
diff changeset
5695 QR eguale. Adunque le tre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5696 QR EO LP fra loro $aranno
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5697 eguali; &agrave; cui $ono etiandio eguali
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5698 BS DT. Et percioche la corda
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5699 LFGHDCBM &egrave; eguale alla
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casties
parents:
diff changeset
5700 corda PFGHTVSN e$$en-
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casties
parents:
diff changeset
5701 do vna corda i$te$$a, &amp; la corda,
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casties
parents:
diff changeset
5702 che &egrave; intorno al mezo cerchio
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casties
parents:
diff changeset
5703 TVS &egrave; eguale alla corda, che &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5704 intorno al mezo cerchio BCD;
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casties
parents:
diff changeset
5705 tolte via dunque le communi PF
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casties
parents:
diff changeset
5706 GHT, &amp; SM; $ar&agrave; la re$tan-
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casties
parents:
diff changeset
5707 te MN eguale alle tre BS
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5708 LP DT pre$e in$ieme. ma BS LP DT in$ieme $ono tre volte tanto, quanto</I>
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parents:
diff changeset
5709 <fig>
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casties
parents:
diff changeset
5710 <foot><I>V</I></foot>
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parents:
diff changeset
5711 <pb>
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casties
parents:
diff changeset
5712 <I>EQ, &amp; per con$e-
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casties
parents:
diff changeset
5713 quenza QR. Lo
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casties
parents:
diff changeset
5714 $patio dunque MN
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casties
parents:
diff changeset
5715 della traportata po$
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casties
parents:
diff changeset
5716 $anza &egrave; tre volt<17>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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5717 tanto, quanto lo $pa
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casties
parents:
diff changeset
5718 tio QR del pe$o
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casties
parents:
diff changeset
5719 mo$$o. che era da
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casties
parents:
diff changeset
5720 mo$trar$i.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5721 <p><I>Il tempo ancora di que
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casties
parents:
diff changeset
5722 sto mouimento &egrave;
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parents:
diff changeset
5723 mani$e$to, percio-
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casties
parents:
diff changeset
5724 che la po$$anza i$te$
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5725 $a in tempo eguale
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casties
parents:
diff changeset
5726 mouer&agrave; l'i$te$$o pe-
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parents:
diff changeset
5727 $o in i$patio tre co-
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casties
parents:
diff changeset
5728 tanto maggiore $en-
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casties
parents:
diff changeset
5729 za tali taglie, di
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casties
parents:
diff changeset
5730 quel che $arebbe
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casties
parents:
diff changeset
5731 con e$$e taglie &agrave; que
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casties
parents:
diff changeset
5732 $to modo commoda
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casties
parents:
diff changeset
5733 te. Lo $patio del
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casties
parents:
diff changeset
5734 pe$o mo$$o $enza le
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casties
parents:
diff changeset
5735 taglie &egrave; eguale allo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5736 $patio della po$$an-
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casties
parents:
diff changeset
5737 za. &amp; in que$to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5738 modo ritrouaremo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5739 in tutte il tempo.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5740 <fig>
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casties
parents:
diff changeset
5741 <pb n=78>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5742 <HEAD>PROPOSITIONE XIIII.</HEAD>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5743 <p>Legando la corda d'intorno &agrave; tre girelle di due taglie, l'vna del-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5744 lequali $ia di $opra, &amp; habbia vna $ola girella, &amp; l'altra di $ot-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5745 to, &amp; ne habbia due, &amp; $ia lega
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5746 ta al pe$o; laqual corda $ia le-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5747 gata con l'vno de' capi $uoi in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5748 qualche loco, &amp; l'altro tenu-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5749 to dalla po$$anza, che moue il
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5750 pe$o: $ar&agrave; lo $patio cor$o dal-
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casties
parents:
diff changeset
5751 la po$$anza, che tira, quattro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5752 volte tanto, quanto &egrave; lo $patio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5753 del pe$o mo$$o.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5754 <p><I>Sia il pe$o A, $iano le due girelle, i cui cen
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casties
parents:
diff changeset
5755 tri</I> K <I>I della taglia legata al pe$o con
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5756 K<G>a</G>; dimodo, che il pe$o $empre $egua il
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5757 mouimento della taglia in $u$o, ouero in
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casties
parents:
diff changeset
5758 giu$o: $ia dapoi la girella il cui centro L
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5759 della taglia appe$a di $opra in <G>d</G>; &amp; $ia la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5760 corda BCDEFGHZMNO riuolta
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5761 intorno &agrave; tutte le girelle, &amp; legata in B;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5762 &amp; $ia in O la po$$anza, che moue il pe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5763 $o A. Dico lo $patio, ilquale la po$$an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5764 za di O mouendo trapa$$a, e$$ere quat-
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casties
parents:
diff changeset
5765 tro volte tanto, quanto lo $patio del pe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5766 $o A mo$$o. Mouan$i le girelle della
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casties
parents:
diff changeset
5767 taglia legata al pe$o; &amp; mentre il centro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5768 K &egrave; in R, il centro I $ia in S, &amp; il
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5769 pe$o A, cio&egrave; il punto <G>a</G> in <G>b</G>: $aranno
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5770 IS KR <G>ab</G> tra $e eguali, &amp; parimen-
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casties
parents:
diff changeset
5771 te KI ad e$$a RS eguale: percioche le
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casties
parents:
diff changeset
5772 girelle mantengono fra $e la di$tanza me
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5773 de$ima $empre; &amp; K<G>a</G> $ar&agrave; eguale ad e$
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5774 $a R<G>b</G>. $iano condotte per li centri delle
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5775 girelle le linee FHQTECVXNZ
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diff changeset
5776 egualmente distanti dall orizonte, lequa
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parents:
diff changeset
5777 li tocchino le corde ne i puntl FH QT</I>
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parents:
diff changeset
5778 <fig>
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parents:
diff changeset
5779 <foot><I>V</I> 2</foot>
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diff changeset
5780 <pb>
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parents:
diff changeset
5781 <I>EC VX NZ che parimente $aranno
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parents:
diff changeset
5782 fra loro egualmente di$tanti: &amp; EQ CT
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parents:
diff changeset
5783 VN XZ non $olamente fra $e, ma
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parents:
diff changeset
5784 ancora ad e$$e IS KR <G>ab</G> $aranno e-
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diff changeset
5785 guali: &amp; mentre li centri KI $ono in
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parents:
diff changeset
5786 RS, la po$$anza di O $ia mo$$a in P.
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parents:
diff changeset
5787 Et percioche la corda BCDEFGHZ
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parents:
diff changeset
5788 MNO &egrave; eguale alla corda BT<36>QF
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parents:
diff changeset
5789 GHX<G>*u</G>VP e$$endo vna corda mede-
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parents:
diff changeset
5790 $ima, &amp; le corde d'intorno &agrave; mezi cerchi
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parents:
diff changeset
5791 T<36>Q X<G>*u</G>V $ono eguali alle corde, che
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parents:
diff changeset
5792 $ono d'intorno &agrave; CDE ZMN; tolte
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parents:
diff changeset
5793 via dunque le communi BT, QFGHX,
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parents:
diff changeset
5794 &amp; VO; $ar&agrave; OP eguale ad e$$e VN
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parents:
diff changeset
5795 XZ CT QE pre$e tutte in$ieme. male
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parents:
diff changeset
5796 quattro VN ZX CT QE $ono tra$e
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parents:
diff changeset
5797 eguali, &amp; in$ieme quattro volte tanto
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parents:
diff changeset
5798 quanto KR &amp; <G>ab</G>. Per laqual co$a OP
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parents:
diff changeset
5799 $ar&agrave; quattro volte tanto quanto &egrave; e$$a
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parents:
diff changeset
5800 <G>ab</G>. Adunque lo $patio della po$$anza
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parents:
diff changeset
5801 &egrave; quattro volte tanto quanto &egrave; lo $palio
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parents:
diff changeset
5802 del pe$o. che era da mo$trare.</I>
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parents:
diff changeset
5803 <p><I>Et $e la corda in P $ar&agrave; dauantaggio ri-
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parents:
diff changeset
5804 uolta d'intorno ad vn'altra girella ver$o il
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parents:
diff changeset
5805 <G>d</G>, &amp; la po$$anza mouendo$i in gi&ugrave; mo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5806 ua in s&ugrave; il pe$o: $imilmente $i mo$trer&agrave;
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parents:
diff changeset
5807 lo $patio della po$$anza e$$ere quattro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5808 volte tanto quanto lo $patio del pe$o.</I>
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parents:
diff changeset
5809 <fig>
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casties
parents:
diff changeset
5810 <p><I>Ma$e la corda in B $i riuolger&agrave; d'intorno ad
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parents:
diff changeset
5811 vn'altra girella, laqual corda $ilegbi da</I>
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parents:
diff changeset
5812 <marg><I>Per la</I> 9. <I>di questo.</I></marg> <I>poi alla taglia di $otto; $ar&agrave; la po$$anza
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parents:
diff changeset
5813 di O, che $o$tiene il pe$o A vn quinto
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parents:
diff changeset
5814 dal pe$o. &amp; $e in O $ar&agrave; la po$$anza,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5815 che moua il pe$o A; $imilm&egrave;te $i dimo$tre
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5816 r&agrave; lo $patio della po$$anza po$ta in O e$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5817 $ere cinque volte tanto quanto lo $patio del pe$o A.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5818 <p><I>Et $e la corda $i adatter&agrave; in modo d'intorno alle girelle, che la po$$anza di O $o$tenen
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parents:
diff changeset
5819 te il pe$o $ia vn $e$to del pe$o; &amp; in loco della po$$anza $o$tenente il pe$o, $i met-
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parents:
diff changeset
5820 ta in O la po$$anza, che lo moua; nell'i$te$$o modo $i mo$trer&agrave; lo $patio della po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5821 $anza e$$ere $ei volte tanto quanto lo $patio del pe$o mo$$o. &amp; co$i procedendo in</I>
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parents:
diff changeset
5822 <pb n=79>
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casties
parents:
diff changeset
5823 <I>infinito $i troueranno le proportioni dello $patio della po$$anza allo $patio del pe-
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parents:
diff changeset
5824 $o mo$$o quanto $i vogliano moltiplici.</I>
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parents:
diff changeset
5825 <p>Et co$i procedendo in infinito $i troueranno le proportioni dello $patio della po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5826 $anza allo $patio del pe$o mo$$o quanto $i vorr&agrave; moltiplici. Gi&agrave; &egrave; detto che mol
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5827 tiplice &egrave; il primo genere delle proportioni nelle quantit&agrave; paragonate dal mag-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5828 giore al minore, per&ograve; qui vuol dire, che con tale regola $i ritroueranno le pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5829 portioni dello $patio del pe$o allo $patio della po$$anza in infinito, dou&etilde;do e$$ere
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5830 lo $patio della po$$anza mouente moltiplice, cio&egrave; molte volte maggiore dello
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5831 $patio del pe$o mo$$o, come appare nel pre$ente e$$empio, che &egrave; $ei volte pi&ugrave;,
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parents:
diff changeset
5832 come $ei ad vno; &amp; que$to &egrave; il $ignifi cato di moltiplice.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5833 <HEAD>COROLLARIO I.</HEAD>
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parents:
diff changeset
5834 <p>Da que$te co$e &egrave; manife$to, co$i hauer$i il pe$o ver$o la po$$an-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5835 za, che lo $o$tiene, come lo $patio della po$$anza che moue al-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5836 lo $patio del pe$o mo$$o.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5837 <p><I>Come $e il pe$o A $ar&agrave; cinque volte tanto quanto la po$$anza di O, che $o$tiene
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5838 il detto pe$o A; $ar&agrave; anche lo $patio OP della po$$anza mouente il pe$o cin-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5839 que volte tanto quanto lo $patio <G>a b</G> del pe$o mo$$o.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5840 <HEAD>COROLLARIO II.</HEAD>
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parents:
diff changeset
5841 <p>E manife$to ancora per le co$e dette, che le girelle della taglia,
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parents:
diff changeset
5842 laquale &egrave; legata al pe$o, fanno s&igrave;, che minore $patio &egrave; quello,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5843 ilquale &egrave; de$critto dal pe$o mo$$o, che dalla po$$anza che tira;
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parents:
diff changeset
5844 &amp; che in tempo maggiore $i de$criua vn dato $patio eguale,
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parents:
diff changeset
5845 che $enza loro: ilche veramente non fanno le girelle della ta-
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parents:
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5846 glia di $opra.
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casties
parents:
diff changeset
5847 <p><I>Mo$trata la proportione moltiplice, che ha il pe$o ver$o la po$$anza, hora $i mo$triper
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parents:
diff changeset
5848 lo contrario la proportione moltiplice, che haue la po$$anza ver$o il pe$o.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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5849 <HEAD>PROPOSITIONE XV.</HEAD>
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parents:
diff changeset
5850 <p>Se la corda $ar&agrave; inuolta d'intorno alla girella della taglia tenu-
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parents:
diff changeset
5851 ta di $opra dalla po$$anza; l'vn capo dellaquale $ia legato in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5852 qualche loco, ma all'altro $ia appiccato il pe$o, $ar&agrave; la po$$an-
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parents:
diff changeset
5853 za due volte tanto quanto il pe$o.
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casties
parents:
diff changeset
5854 <p><I>Sia la taglia, che habbia la girella co'l $uo centro A; &amp; $ia il pe$o B legato alla
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parents:
diff changeset
5855 corda CDEFG, laquale $ia in uol-
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parents:
diff changeset
5856 ta d'intorno alla girella, &amp; alla fine
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parents:
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5857 legata in G; &amp; $ia la po$$anza, che
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parents:
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5858 $o$tiene il pe$o in H. Dico, che la
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parents:
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5859 po$$anza di H &egrave; due volte tanto quan
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parents:
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5860 to il pe$o B. Sia condotta la linea
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parents:
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5861 DF per lo centro A egualmente di
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parents:
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5862 $tante dall'orizonte. Percioche dun-
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parents:
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5863 que la po$$anza di H $o$tiene la ta-
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parents:
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5864 glia, laquale $o$tiene la girella nel $uo
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parents:
diff changeset
5865 centro A, laqual girella $o$liene il pe
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diff changeset
5866 $o; $ar&agrave; la po$$anza, che $o$tiene la gi-
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diff changeset
5867 rella, come $e fo$$e po$ta in A; $tan-
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parents:
diff changeset
5868 do dunque e$$a in A, &amp; il pe$o ap-
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parents:
diff changeset
5869 piccato in D, &amp; legato alla corda
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parents:
diff changeset
5870 CD; $ar&agrave; la DF come leua, il cui
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parents:
diff changeset
5871 $o$tegno $ar&agrave; F, il pe$o in D &amp; la</I>
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parents:
diff changeset
5872 <marg><I>Per la</I> 3. <I>di questo nella leua.</I></marg> <I>po$$anza in A. Ma la po$$anza ver-
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parents:
diff changeset
5873 $o il pe$o &egrave; come DF ad FA, &amp;
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parents:
diff changeset
5874 DF &egrave; il doppio di FA: adunque la
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parents:
diff changeset
5875 po$$anza di A ouero di H, che &egrave;
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parents:
diff changeset
5876 l'i$te$$o, $ar&agrave; due volte tanto, quanto il
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parents:
diff changeset
5877 pe$o B. che bi$ognaua mo$trare.</I>
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parents:
diff changeset
5878 <fig>
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casties
parents:
diff changeset
5879 <p><I>Oltre &agrave; ci&ograve; occorre &agrave; con$iderare, $tando ferme tutte que$te co$e, che egli &egrave; l'i$te$$o, e$-
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parents:
diff changeset
5880 $endo vna corda $ola CDEFG in que$to modo inuolta d'intorno alla girella, co-
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parents:
diff changeset
5881 me $e fo$$ero due corde CDFG legate nella leua, ouero nella bilancia DF.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5882 <HEAD>Altramente.</HEAD>
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parents:
diff changeset
5883 <p><I>Stando le mede$ime co$e, $e in G $o$$e appiccato un pe$o K eguale al pe$o B, li pe$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5884 BK pe$erebbono egualmente nella bilancia DF, il cui centro A. Ma la po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5885 $anza di H, laquale $o$tiene i pe$i BK &egrave; eguale ad ambidue pre$i in$ieme, &amp; i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5886 pe$i BK $ono due volte tanto quanto &egrave; e$$o B. Adunque la po$$anza di H $a-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5887 r&agrave; due volte tanto quanto &egrave; il B. &amp; percioche la corda legata in G non fa al-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5888 tro niente, $e non che $o$tiene il pe$o B, che non di$cenda, laqual co$a parimente
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5889 f&agrave; il pe$o K appiccato in G: la po$$anza dunque di H, che $o$tiene il pe$o B,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5890 e$$endo la corda legata in G, &egrave; due volte tanto quanto il pe$o B. che bi$ognaua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5891 mostrare.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5892 <pb n=80>
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parents:
diff changeset
5893 <HEAD>PROPOSITIONE XVI.</HEAD>
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parents:
diff changeset
5894 <p>Po$te le co$e i$te$$e, $e in H $ar&agrave; la po$$anza che moue il pe$o,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5895 mouer&agrave; ella con la leua egualmente di$tante dall'orizonte.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5896 <p><I>Que$to etiandio $i mo$trer&agrave;, co-
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parents:
diff changeset
5897 me &egrave; detto di $opra. Moua$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5898 la girella in s&ugrave;, &amp; habbia il
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parents:
diff changeset
5899 $ito di MNO, il cui centro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5900 L: &amp; per L $ia condotta la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5901 linea MLO egualmente di-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5902 $tante da e$$a DF, &amp; dall'o
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parents:
diff changeset
5903 rizonte. &amp; percioche le cor-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5904 de toccano il cerchio MON
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5905 ne i punti MO; per&ograve; e$$en-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5906 do che la po$$anza di A, oue
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5907 ro di H, che &egrave; l'i$te$$o, mo-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5908 ua il pe$o B appiccato in D
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5909 con la leua DF, il cui $o$te-
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parents:
diff changeset
5910 gno &egrave; F; $empre rimarr&agrave; da
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5911 uantaggio vn'altra leua, co-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5912 me MO egualmente di$tan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5913 te dall'orizonte, di modo che
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parents:
diff changeset
5914 $empre la po$$anza moua il pe
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5915 $o, $tando la leua egualmente
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5916 di$tante dall'orizonte, il cui
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parents:
diff changeset
5917 $o$tegno $empre &egrave; nella linea
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parents:
diff changeset
5918 OG, &amp; il pe$o in MC, &amp;
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parents:
diff changeset
5919 la po$$anza nel centro della
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5920 girella.</I>
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parents:
diff changeset
5921 <fig>
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parents:
diff changeset
5922 <p>Po$te le co$e mede$ime, lo $patio del pe$o mo$$o &egrave; due volte tan
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parents:
diff changeset
5923 to quanto lo $patio della po$$anza, che moue.
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parents:
diff changeset
5924 <p><I>Sia mo$$a la girella dal centro A fin al centro L; &amp; il pe$o B, cio&egrave; il punto e,
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parents:
diff changeset
5925 nell'i$te$$o tempo $ia mo$$o nel P; &amp; la po$$anza di H fin in K; far&agrave; AH
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parents:
diff changeset
5926 ad e$$a LK eguale, &amp;
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parents:
diff changeset
5927 AL ad e$$a HK: &amp;
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casties
parents:
diff changeset
5928 percioche le corda CDE
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5929 FG eguale &egrave; alla corda
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5930 PMNOG, peroche &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5931 vna corda i$te$$a, &amp; la
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parents:
diff changeset
5932 corda d'intorno al mezo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5933 cerchio MNO eguale &egrave;
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parents:
diff changeset
5934 alla corda d'intorno al me
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5935 zo cerchio DEF: tolte
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parents:
diff changeset
5936 via dunque le communi
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parents:
diff changeset
5937 corde DP FG, $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5938 PC eguale &agrave; DM FO
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
5939 pre$e in$ieme, lequali cor-
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parents:
diff changeset
5940 de $ono due volte tanto
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parents:
diff changeset
5941 quanto &egrave; e$$a AL &amp; per
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5942 con$eguenza e$$a HK.
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parents:
diff changeset
5943 Lo $patio dunque del pe-
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parents:
diff changeset
5944 $o mo$$o CP &egrave; due vol-
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parents:
diff changeset
5945 te tanto, quanto &egrave; lo $pa-
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parents:
diff changeset
5946 tio della po$$anza HK.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5947 che bi$ognaua mostrare.</I>
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parents:
diff changeset
5948 <fig>
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parents:
diff changeset
5949 <HEAD>COROLLARIO</HEAD>
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parents:
diff changeset
5950 <p>Da que$to &egrave; manife$to, l'i$te$$o pe$o e$$ere tirato dalla i$te$$a po$
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5951 $anza in tempo eguale per due volte tanto $patio con la taglia
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parents:
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5952 in que$to modo accommodata, che $enza taglia; pur che i
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parents:
diff changeset
5953 mouimenti di e$$a po$$anza $iano eguali in velocit&agrave;.
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parents:
diff changeset
5954 <p><I>Percioche lo $patio del pe$o mo$$o $enza taglia &egrave; vguale allo $patio della po$$anza.</I>
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parents:
diff changeset
5955 <pb n=81>
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parents:
diff changeset
5956 <p><I>Che $e la corda $ar&agrave; in G riuolta d'intorno ad vn'altra girella, il cia centro K; &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5957 $ia la taglia di cotale girella attaccata di $otto, laquale non habbia alcuno altro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
5958 mouimento, $e non il libero riuolgimento della girella d'intorno all'a$$etto $uo; &amp;
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parents:
diff changeset
5959 la corda $i leghi in M; $ar&agrave;
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parents:
diff changeset
5960 la po$$anza di H che $o$tiene
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parents:
diff changeset
5961 il pe$o B. $imilmente due vol
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parents:
diff changeset
5962 te tanto, quanto &egrave; e$$o pe$o. il
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parents:
diff changeset
5963 che per certo &egrave; manife$to, con-
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parents:
diff changeset
5964 cio$ia, che egli $ia in tutto vna
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parents:
diff changeset
5965 co$a i$te$$a, $e ouero la corda $ia
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parents:
diff changeset
5966 in M ouero in G legata, per-
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parents:
diff changeset
5967 cioche la girella del centro K
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parents:
diff changeset
5968 non f&agrave; nulla, &amp; &egrave; totalmente
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parents:
diff changeset
5969 inutile.</I>
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parents:
diff changeset
5970 <p><I>Ma $e la po$$anza che $o$tiene il
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parents:
diff changeset
5971 pe$o B $ar&agrave; in M, &amp; la ta
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parents:
diff changeset
5972 glia di $opra $ia appiccata in
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parents:
diff changeset
5973 s&ugrave;; $ar&agrave; la po$$anza di M e-
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parents:
diff changeset
5974 guale al pe$o B.</I>
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parents:
diff changeset
5975 <p><I>Percioche la po$$anza di G, che</I> <marg><I>Per la</I> 1. <I>di questo.</I></marg>
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parents:
diff changeset
5976 <I>$o$tiene il pe$o B &egrave; eguale al
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parents:
diff changeset
5977 pe$o B; &amp; ad e$$a po$$anza
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parents:
diff changeset
5978 di G &egrave; eguale la po$$anza di
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parents:
diff changeset
5979 L; percioche GL &egrave; leua, il
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parents:
diff changeset
5980 cui $o$iegno &egrave; K; &amp; la di-
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parents:
diff changeset
5981 $tanza GK &egrave; eguale alla di$tan
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parents:
diff changeset
5982 za KL; $ar&agrave; dunque la po$-
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parents:
diff changeset
5983 $anza di L, ouero (che &egrave; il me
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parents:
diff changeset
5984 de$imo,) di M eguale al pe$o B.</I>
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diff changeset
5985 <fig>
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parents:
diff changeset
5986 <p><I>Que$to tale mouimento $i f&agrave; nel-
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parents:
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5987 le leue DF LG i cui $o$tegni
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parents:
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5988 $ono KA, &amp; il pe$o in D, &amp; la po$$anza in F; ma nella leua LG la po$$an
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parents:
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5989 za $t&agrave; in L, &amp; il pe$o come $e fu$$e in G.</I>
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parents:
diff changeset
5990 <p><I>Se poi $ar&agrave; in M la po$$anza, che moue il pe$o, &amp; $i tra$porti, la po$$anza in N
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parents:
diff changeset
5991 &amp; il pe$o $ia mo$$o fin ad O; $ar&agrave; lo $patio MN della po$$anza eguale allo $patio
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parents:
diff changeset
5992 di CO pe$o; percioche e$$endo la corda MLGFDC eguale alla corda NLG
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parents:
diff changeset
5993 FDO, peroche &egrave; vna i$te$$a corda; leuata via la commune MLGFDO, $ar&agrave; lo
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parents:
diff changeset
5994 $patio MN della po$$anza eguale allo $patio CO del pe$o.</I>
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parents:
diff changeset
5995 <p><I>Et $e la corda in M $ar&agrave; inuolta intorno &agrave; pi&ugrave; girelle, $empre la po$$anza, che in vno
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parents:
diff changeset
5996 delli $uoi e$tremi $o$terr&agrave; il pe$o $ar&agrave; eguale ad e$$o pe$o: &amp; gli $patij del pe$o, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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5997 della po$$anza che moue $empre $i mo$treranno e$$ere eguali.</I>
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parents:
diff changeset
5998 <foot><I>X</I></foot>
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parents:
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5999 <pb>
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parents:
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6000 <HEAD>PROPOSITIONE XVII.</HEAD>
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parents:
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6001 <p>Se &agrave; cia$cuna delle due girelle di due taglie, l'vna delle quali $ia
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parents:
diff changeset
6002 $o $tenuta di $opra dalla po$$anza, &amp; l'altra $ia po$ta di $otto, &amp;
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parents:
diff changeset
6003 iui attaccata, $i condurr&agrave; intorno la corda; con l'vno de' $uoi
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parents:
diff changeset
6004 capi legato alla taglia di $opra, &amp; l'altro appiccato al pe$o; la
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parents:
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6005 po$$anza $ar&agrave; tre volte tanto quanto il pe$o.
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parents:
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6006 <p><I>Sia la girella co'l centro A della
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parents:
diff changeset
6007 taglia all accaia di $otto; &amp; $ia la
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parents:
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6008 corda BCDEFG inuolta intor
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parents:
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6009 no non $olamente &agrave; cote$ta girel
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parents:
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6010 la, ma etiandio alla girella della
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parents:
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6011 taglia di $opra, che ha il centro K;
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parents:
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6012 &amp; $ia la cordalegata in B della
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parents:
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6013 taglia di $opra; &amp; in G $ia at-
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parents:
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6014 taccato il pe$o H; &amp; la po$$an-
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parents:
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6015 zain L $o$tenga il pe$o H. Di-
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parents:
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6016 co che la po$$anza in L &egrave;tre vol
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parents:
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6017 te tanto quanto il pe$o H, per-
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parents:
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6018 cioche $e fo$$ero due po$$anze, che
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parents:
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6019 $o$tenne$$ero il pe$o H vna in K,
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parents:
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6020 &amp; l'altra in B, $arebbono ambe-
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parents:
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6021 due in$ieme tre volte tanto quan-</I>
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6022 <marg><I>Per la</I> 15. <I>di questo. Nella prece dente.</I></marg> <I>to il pe$o H: percioche la po$$an
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parents:
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6023 za in K &egrave; due volte tanto quan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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6024 to il pe$o H, &amp; la po$$anza in
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parents:
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6025 B &egrave; eguale ad e$$o pe$o. &amp; per
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parents:
diff changeset
6026 cioche la $ola po$$anza in L &egrave;
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parents:
diff changeset
6027 eguale ad ambedue le po$$anze in
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parents:
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6028 KB, peroche la po$$anza in L $o-
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parents:
diff changeset
6029 $tiene s&igrave; la po$$anza po$ta in K,
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parents:
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6030 come la po$$anza po$ta in B; &amp;
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parents:
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6031 la detta po$$anza in L fa l'i$te$$o,
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parents:
diff changeset
6032 come $e fu$$ero due po$$anze, l'v-
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parents:
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6033 na in K &amp; l'altra in B. Sar&agrave;
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parents:
diff changeset
6034 dunque tre volte tanto la po$$an-
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parents:
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6035 za in L quanto il pe$o H. Che
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parents:
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6036 bi$ognaua mo$trare.</I>
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parents:
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6037 <fig>
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parents:
diff changeset
6038 <pb n=82>
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parents:
diff changeset
6039 <p>Ma $e in L $ar&agrave; la po$$anza, che moue il pe$o. Dico lo $patio
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parents:
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6040 del pe$o mo$$o e$$ere tre volte tanto, quanto lo $patio della
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parents:
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6041 po$$anza mo$$a.
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parents:
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6042 <p><I>Moua$i il centro della girella
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casties
parents:
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6043 K fin ad M, lo $patio
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parents:
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6044 delquale mouimento &egrave; ve-
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parents:
diff changeset
6045 ramente eguale allo $patio
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parents:
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6046 della po$$anza mo$$a, co-
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parents:
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6047 me &egrave; detto di $opra: &amp;</I> <marg><I>Nella precede<*>e.</I></marg>
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parents:
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6048 <I>quando K $ar&agrave; in M, B
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parents:
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6049 $ar&agrave; in N, &amp; NB $a
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casties
parents:
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6050 r&agrave; eguale ad MK; &amp;
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parents:
diff changeset
6051 mentre K &egrave; in M, fia il
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diff changeset
6052 pe$o H, cio&egrave; il punto G
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diff changeset
6053 mo$$o in O; &amp; per MK
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6054 $iano condotte le linee EF
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diff changeset
6055 PQ egualmente di$tanti
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6056 dall'orizonte; $ar&agrave; cia$cu-
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diff changeset
6057 na delle EP BN FQ
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diff changeset
6058 eguale ad e$$a KM. Et
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parents:
diff changeset
6059 perciochela co da BCD
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diff changeset
6060 EFG eguale &egrave; alla corda
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diff changeset
6061 NCDPQO; e$$endo
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diff changeset
6062 vna mede$ima corda; &amp;
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6063 la corda po$ta intorno al
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6064 mezo cerchio ERF e-
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diff changeset
6065 guale &egrave; alla corda po$ta in
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diff changeset
6066 torno al mezo cerchio
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parents:
diff changeset
6067 PSQ; tolte via dunque
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6068 le corde communi BC
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diff changeset
6069 DE, &amp; FO, $ar&agrave; OG
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6070 eguale alle tre corde QF
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6071 NB PE pre$e in$ieme.
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6072 ma QF NB PE in-
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diff changeset
6073 $ieme $ono tre volte tanto
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6074 quanto MK, cio&egrave; lo $pa-
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6075 tio della po$$anza mo$$a;
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parents:
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6076 lo $patio dunque GO del
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parents:
diff changeset
6077 pe$o H mo$$o, &egrave; tre vol-
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6078 te tanto quanto &egrave; lo $pa-
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diff changeset
6079 tio della po$$anza mo$$a.
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6080 che bi$egn<*>a mo$trare.</I>
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diff changeset
6081 <fig>
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parents:
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6082 <foot><I>X</I> 2</foot>
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6083 <pb>
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6084 <HEAD>PROPOSITIONE XVIII.</HEAD>
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6085 <p>Se ad ambedue le girelle delle due taglie: l'vna delle quali $ia $o
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6086 $tenuta di $opra dalla po$$anza, &amp; l'altra $ia po$ta di $otto, &amp;
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parents:
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6087 iui attaccata, $ar&agrave; inuolta intorno la corda; con l'vno de' ca-
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6088 pi $uoi in qualche luogo legato, ma non gi&agrave; nella taglia di $o-
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6089 pra, &amp; all'altro $ia appiccato il pe$o; la po$$anza $ar&agrave; quattro
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6090 volte tanto quanto il pe$o.
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parents:
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6091 <p><I>Sia la taglia di $otto, che habbia due gi-
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parents:
diff changeset
6092 relle con li centri $uoi AB; &amp; $ia
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6093 la taglia di $opra, che $imilmente hab-
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parents:
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6094 bia due girelle con li centri $uoi CD:
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parents:
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6095 &amp; $ia la corda EFGHKLMNOP
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parents:
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6096 riuolta d'intorno &agrave; tutte le girelle, che
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6097 $ia legata poi in E, &amp; $ia appicca-
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6098 to in P il pe$o Q: &amp; $ia la po$$an-
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6099 za in R. Dico la po$$anza di R e$-
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6100 $ere quattro volte tanto quanto il pe-
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6101 $o Q: concio$ia che $e $i intenderan-</I>
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6102 <marg><I>Per la</I> 16. <I>di questo.</I></marg> <I>no due po$$anze, l'vnain K &amp; l'al-
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6103 train D, la po$$anza in K che $o
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6104 $tiene il pe$o Q con la corda KLM
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6105 NOP $ar&agrave; eguale al pe$o; &amp; $aran
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6106 no le due po$$anze in$ieme l'vna in D
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6107 &amp; l'altra in K $ostenenti il pe$o Q
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6108 tre volte tanto quanto l'i$te$$o pe$o.
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6109 Ma la po$$anza di C &egrave; due volte tan
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6110 to quanto la po$$anza di K, &amp; per con</I>
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6111 <marg><I>Per la</I> 15. <I>di questo.</I></marg> <I>$equenza del pe$o Q; peroche egli &egrave;
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parents:
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6112 la me de$ima co$a, come $e in K fo$$e
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6113 appiccato vn pe$o eguale al pe$o Q,
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6114 delquale &egrave; due volte tanto la po$$anza
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parents:
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6115 di C. Adunque due po$$anze po$te
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6116 in DC $ono quattro volte tanto quan
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parents:
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6117 to &egrave; il pe$o Q. &amp; concio$ia, che la
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6118 po$$anza di R $o$tenga con le girelle
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parents:
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6119 il pe$o Q, $ar&agrave; la po$$anza di R co-
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diff changeset
6120 me $e fo$$ero due po$$anze l'vna in D</I>
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diff changeset
6121 <fig>
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parents:
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6122 <pb n=83>
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parents:
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6123 <I>&amp; l'altra in C: &amp; l'vna, &amp; l'altra in$ieme $o$tene$$e il pe$o Q. La po$$anza
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parents:
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6124 dunque di R &egrave; quattro volte tanto quanto il pe$o Q. che bi$ognaua dimo$trare.</I>
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parents:
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6125 <HEAD>COROLLARIO</HEAD>
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parents:
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6126 <p>Dalla qual co$a &egrave; manife$to, che $e la corda $ar&agrave; legata in G, &amp;
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parents:
diff changeset
6127 riuolta d'intorno alle girelle, i cui centri $ono BCD; $ar&agrave;
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parents:
diff changeset
6128 la po$$anza di R che $o$tiene quat
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parents:
diff changeset
6129 tro volte tanto, $imilmente quan-
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parents:
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6130 to il pe$o Q. Percioche la girel-
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parents:
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6131 la il cui centro &egrave; A non f&agrave; nulla.
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parents:
diff changeset
6132 <p>Che $e la po$$anza mou&egrave;nte il pe$o $a
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parents:
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6133 r&agrave; in R. Dico lo $patio del pe$o
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casties
parents:
diff changeset
6134 mo$$o e$$ere quattro volte tanto
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parents:
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6135 quanto lo $patio della po$$anza.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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6136 <fig>
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parents:
diff changeset
6137 <p><I>Siano mo$$i i centri CD delle girelle fin ad ST;
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parents:
diff changeset
6138 $aranno per le co$e di $opra dette CS DT
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casties
parents:
diff changeset
6139 eguali allo $patio della po$$anza; &amp; per SDT
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casties
parents:
diff changeset
6140 $iano condotte le linee HK VX NO <G>*u</G>Z
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parents:
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6141 egualmente di$tanti dall'orizonte; &amp; mentre
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parents:
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6142 li centri CD $ono in ST, $ia il pe$o Q,
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casties
parents:
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6143 cio&egrave; il punto P mo$$o in <36>. &amp; percioche
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parents:
diff changeset
6144 la corda EFGHKLMNOP eguale &egrave; al
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parents:
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6145 la corda EFGVXLM<G>*u</G>Z<36>; e$$endo vna
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parents:
diff changeset
6146 mede$ima corda: &amp; le corde po$te d'intorno &agrave;
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casties
parents:
diff changeset
6147 mezi cerchi NIOH<G>a</G>K $iano egua i alle cor
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casties
parents:
diff changeset
6148 de, lequali $ono intorno &agrave; i mezi cerchi <G>*ud</G>Z
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casties
parents:
diff changeset
6149 V<G>b</G>X; tolte via dunque le communi EFGH
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casties
parents:
diff changeset
6150 KLMN &amp; O<36>; $ar&agrave; P<36> eguale ad e$$e
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6151 N<G>*u</G> ZO VH XK in$ieme pre$e, ma le quat
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parents:
diff changeset
6152 tro N<G>*u</G> ZO VH XK tutte in$ieme $ono
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casties
parents:
diff changeset
6153 quattro volte tanto quanto DT cio&egrave; lo $pa-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6154 tio della po$$anza. Lo $patio dunque PQ del
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casties
parents:
diff changeset
6155 pe$o &egrave; quattro volte tanto quanto lo $patio
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casties
parents:
diff changeset
6156 della po$$anza. che era da mo$trar$i.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6157 <p><I>Ma $e la corda $a
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casties
parents:
diff changeset
6158 r&agrave; rilegata in
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casties
parents:
diff changeset
6159 E della taglia
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casties
parents:
diff changeset
6160 di $opra, &amp; la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6161 po$$anza di R
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casties
parents:
diff changeset
6162 $o$tenga il pe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6163 $o Q; $ar&agrave; la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6164 po$$anza di R
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casties
parents:
diff changeset
6165 cinque volte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6166 tanto quanto
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6167 il pe$o Q. &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6168 $e in R $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6169 la po$$anza,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6170 che moue il pe
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casties
parents:
diff changeset
6171 $o $ar&agrave; lo $pa
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6172 tio del pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6173 mo$$o cinque
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casties
parents:
diff changeset
6174 volte tanto,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6175 quanto lo $pa-
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casties
parents:
diff changeset
6176 tio della po$-
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casties
parents:
diff changeset
6177 $anza. Lequa-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6178 li co$e tutte $i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6179 dimo$trer anno
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casties
parents:
diff changeset
6180 con modo $imi
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casties
parents:
diff changeset
6181 le, come nelle
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casties
parents:
diff changeset
6182 precedenti &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6183 $tato fatto.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6184 <fig>
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casties
parents:
diff changeset
6185 <pb n=84>
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casties
parents:
diff changeset
6186 <p><I>Ma $e la po$$anza di R $o-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6187 $tene$$e il pe$o Q hauen-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6188 do la taglia tre girelle, i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6189 cui centri $iano ABC; &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6190 $ia vn'altra taglia di $otto,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6191 che habbia due, &ograve; tre girel-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6192 le, i cui centri $iano DEF;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6193 &amp; $ia la corda riuolta d'in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6194 torno &agrave; tutte le girelle, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6195 $ia legatain G ouero in H;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6196 $imilmente mo$trera$$i la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6197 po$$anza di R e$$ere $ei
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6198 volte tanto quanto il pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6199 Q. &amp; $e in R $ar&agrave; la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6200 forza mouente il pe$o, $i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6201 mo$trer<*> lo $patio del pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6202 mo$$o e$$ere $ei volte tan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6203 to quanto lo $patio della
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6204 po$$anza.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6205 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6206 <p><I>Et $e la corda $ar&agrave; legata in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6207 K della taglia di $opra, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6208 in R $ia la po$$anza che
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6209 $o$tiene il pe$o; con modo
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casties
parents:
diff changeset
6210 $imile $i prouer&agrave; la po$$an-
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casties
parents:
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6211 za di R e$$ere $ette volte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6212 tanto quanto il pe$o Q.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6213 <p><I>Et $e in R $ar&agrave; la po$$anza
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6214 che moue, $i mo$trer&agrave; lo $pa
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6215 tio del pe$o Q e$$ere $ette
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casties
parents:
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6216 volte tanto quanto lo $pa-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6217 tio della po$$anza. &amp; co$t
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6218 in infinito ogni proportio-
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casties
parents:
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6219 ne molteplice della po$$an-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6220 za ver$o il pe$o potra$$i
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casties
parents:
diff changeset
6221 trouare. &amp; $i mo$trer&agrave;
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casties
parents:
diff changeset
6222 $empre, co$i e$$ere il pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6223 ver$o la po$$anza che lo $o-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6224 $tiene, come lo $patio della
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6225 po$$anza che moue il pe$o,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6226 allo $patio del pe$o mo$$o.</I>
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casties
parents:
diff changeset
6227 <p><I>Hor il mouimento
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casties
parents:
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6228 delle leue delle gi
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casties
parents:
diff changeset
6229 relle in que$te $i f&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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6230 in cotal modo,
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casties
parents:
diff changeset
6231 cio&egrave; le leue delle
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casties
parents:
diff changeset
6232 girelle della taglia
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6233 di $opra $i mouo-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6234 no, come &egrave; detto,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6235 nella decima$e$ta
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casties
parents:
diff changeset
6236 di que$to; cio&egrave; han
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casties
parents:
diff changeset
6237 no il $o$tegno nel-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6238 le $tremit&agrave;, la po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6239 $anza nel mezo,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6240 &amp; il pe$o nell'al-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6241 tra $tremit&agrave; ap-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6242 piccato. Ma le
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6243 leue della taglia di
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casties
parents:
diff changeset
6244 $otto hanno il $o-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6245 $tegno nel mezo,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6246 &amp; il pe$o, &amp; la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6247 po$$anzanelle $tro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6248 mit&agrave;.</I>
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6249 <fig>
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diff changeset
6250 <pb n=85>
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diff changeset
6251 <HEAD>COROLLARIO</HEAD>
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6252 <p>In que$te co$e &egrave; manife$to, che le girelle della taglia di $opra $o-
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diff changeset
6253 no cagione, che il pe$o $i moua da po$$anza maggio re di e$$o
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diff changeset
6254 pe$o, &amp; per maggiore $patio di quel che &egrave; lo $patio di e$$a po$
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diff changeset
6255 $anza, &amp; per eguale in manco tempo: co$a che veramente
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6256 non fanno le girelle della taglia di $otto.
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diff changeset
6257 <p><I>In altro modo ancora po$$iamo ritrouare que$ta proportione moltiplice della po$$an-
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diff changeset
6258 za ver$o il pe$o.</I>
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diff changeset
6259 <HEAD>PROPOSITIONE XIX.</HEAD>
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diff changeset
6260 <p>Se &agrave; cia$cuna delle girelle dell'vna, &amp; l'altra delle due taglic, l'v-
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diff changeset
6261 na delle quali $ia appiccata di $opra, &amp; l'altra di $otto ritenu-
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diff changeset
6262 ta dalla po$$anza, che $o$tiene, $i riuolga intorno la corda; con
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diff changeset
6263 l'vno de' capi $uoi legato in qualche loco, &amp; con l'altro attac-
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diff changeset
6264 cato al pe$o: la po$$anza $ar&agrave; due volte tanto quanto il pe$o.
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diff changeset
6265 <foot><I>Y</I></foot>
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diff changeset
6266 <pb>
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diff changeset
6267 <p><I>Sia la girella della taglia appiccata di $opra, il cui centro $ia A; &amp; BCD $ia del-
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diff changeset
6268 la taglia di $otto; $ia dapoi la corda EBCDFGHL rilegata in E; &amp; in L $ia
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diff changeset
6269 appiccato il pe$o M; &amp; $ia la po$
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6270 $anza che $ostiene il pe$o M po$ta in
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diff changeset
6271 N. Dico la po$$anza di N e$$ere</I>
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6272 <marg><I>Per la</I> 3. <I>di questo.</I></marg> <I>due volte tanto quanto il pe$o M. Per
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6273 cioche e$$endo $tato di $opra mo$trato
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6274 la po$$anza di L, laquale per gratia
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6275 di e$$empio, $o$teaga il pe$o O ap-
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6276 piccato in N, e$$ere la met&agrave; meno di
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6277 e$$o pe$o; adunque la po$$anza di N,
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6278 che &egrave; eguale al pe$o O $o$tenir&agrave; il pe-
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diff changeset
6279 $o M, che &egrave; eguale alla po$$anza di L;
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6280 &amp; $ar&agrave; detta po$$anza due volte tan-
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diff changeset
6281 to quanto il pe$o M. che bi$ognaua
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6282 mo$trare.</I>
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6283 <fig>
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6284 <HEAD>Altramente.</HEAD>
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6285 <p><I>Po$te le co$e i$te$$e. Percioche la po$$an-
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6286 za di F, ouero di D, che &egrave; l'i$te$$o,</I>
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6287 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>&egrave; eguale al pe$o M: &amp; BD &egrave; vna
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6288 leua, il cui $o$tegno &egrave; B, &amp; la po$-
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6289 $anza di N &egrave; come $e ella fo$$e nel
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6290 mezo della leua, &amp; il pe$o eguale ad
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6291 e$$o M $t&agrave; come $e egli fu$$e in D
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6292 per cau$a della corda FD, che &egrave; l'i-
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6293 $te$$o, come $e BCD fo$$e la girella
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6294 della taglia di $opra, &amp; il pe$o fo$$e
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6295 appiccato nella corda DF, $i come
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6296 nella decimaquinta, &amp; nella decima-
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6297 $e$ta &egrave; detto. La po$$anza dunque di
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6298 N &egrave; due volte tanto, quanto il pe$o
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6299 M. che era da mo$trar$i.</I>
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6300 <p><I>Ma $e in N $ar&agrave; la po$$anza, che moue
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6301 il pe$o M, $ar&agrave; lo $patio del pe$o M
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6302 due volte tanto quanto la po$$anza po$ta in N, ilche &egrave; mani$e$to dalla duodecima
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6303 di que$to; percioche lo $patio del punto L che inchina in giu$o, &egrave; due volte tanto
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6304 quanto lo $patio di N che v&agrave; in $u$o; $ar&agrave; dunque per lo contrario lo $patio del-
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6305 la po$$anza di N che inchina in gi&ugrave; la met&agrave; meno dello $patio del pe$o M mo$-
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6306 $a all'in s&ugrave;.</I>
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6307 <p><I>Hor $i come dalla terza, dalla quinta, &amp; dalla $ettima di que$to &amp;c. $i po$$ono rac-</I>
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6308 <pb n=86>
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6309 <I>cogliere le ragioni del pe$o O, $iano quanto $i voglia molteplici ad e$$a po$$anza
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6310 po$ta in L, con l'i$te$$o modo parimente $i potranno mo$trare le ragioni quanto
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6311 $i voglia molteplici della po$$anza po$ta in N, che $o$tiene il pe$o M. &amp; co$i
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6312 dalla decnnaterza, &amp; dalla decimaquarta $i mo$treranno le ragioni quanto $i voglia
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diff changeset
6313 molteplici allo $patio del pe$o M, allo $patio della po$$anza po$ta in N.</I>
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6314 <p><I>Si potr&agrave; ancora dalla decima$ettima, &amp; dalla decimaottaua di que$to ritrouare la
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6315 proportione molteplice, laquale ha la po$$anza, che $o$tiene il pe$o ver$o l'i$te$$o
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6316 pe$o, $i come la proportione della po$$anza di N al pe$o M $i dimo$traua nel-
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6317 la propo$itione decimaquinta, &amp; decima$e$ta: &amp; $i trouer&agrave; co$i e$$ere il pe$o
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6318 alla po$$anza, che $o$tiene il pe$o; come lo $patio della po$$anza, che moue allo
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6319 $patio del pe$o.</I>
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6320 <p><I>Li mouimenti delle leue in que$te $i f&agrave; in cotal modo, cio&egrave; le leue delle girelle della ta-
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6321 glia di $otto $i mouono, come della leua BD, laquale $i moue, come $e B fo$$e il
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6322 $o$tegno, &amp; il pe$o $te$$e in D, &amp; la po$$anza nel mezo. Ma le leue delle girel-
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6323 le della taglia di $opra $i mouono, come FH, il cui $o$tegno &egrave; nel mezo, il pe$o in
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6324 H &amp; la po$$anza in F.</I>
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6325 <HEAD>COROLLARIO.</HEAD>
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6326 <p>Da que$to &egrave; manife$to, che le girelle della taglia di $otto in que-
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6327 $te fanno effetto tale, che il pe$o vien mo$$o da po$$anza mag-
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parents:
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6328 giore, di quel che $ia e$$o pe$o, &amp; per maggiore $patio dello
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6329 $patio di e$$a po$$anza, &amp; per eguale in manco tempo. Co$a
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6330 che non fanno gi&agrave; le girelle della taglia di $opra.
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6331 <p><I>Cono$ciute le proportioni molteplici, hor egli &egrave; da accostar$i alle $opra particolari.</I>
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6332 <p>Cono$ciute le proportioni molteplici, gi&agrave; egli &egrave; da venire alle $opraparticolari. Il
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6333 genere $opraparticolare &egrave; il $econdo propo$to di $opra, quando cio &egrave; $i paragona
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6334 vna quantit&agrave; maggiore ver$o vna minore $i fattamente, che e$$a maggiore con-
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diff changeset
6335 tenga la minore vna &ograve; piu volte, &amp; di piu parte di e$$a, che la pos$i numerare in-
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diff changeset
6336 teramente: come per e$$empio, il tre contiene il due vna volta, &amp; pi&ugrave; la met&agrave; di
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parents:
diff changeset
6337 e$$o due, cio&egrave; vno, ilquale puote numerare il tre. Intende dunque l'autore d'in-
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parents:
diff changeset
6338 ue$t&imacr;gare la proportione $opraparticolare, che h&agrave; il pe$o alla po$$anza.
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diff changeset
6339 <foot><I>Y</I> 2</foot>
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diff changeset
6340 <pb>
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6341 <HEAD>PROPOSITIONE XX.</HEAD>
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6342 <p>Se &agrave; cia$cuna delle girelle dell'vna &amp; l'altra delle due taglie, l'v-
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6343 na delle quali $ia $o$tenuta di $opra dalla po$$anza, &amp; di $otto
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6344 $ia po$ta, &amp; legata al pe$o, $ar&agrave; inuolta d'intorno la corda;
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parents:
diff changeset
6345 con l'vno de' $uoi capi legato in qualche loco, &amp; l'altro attac-
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parents:
diff changeset
6346 cato alla taglia di $otto; il pe$o $ar&agrave; vna volta &amp; meza tanto
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6347 quanto la po$$anza.
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parents:
diff changeset
6348 <p><I>Sia ABC la girella della taglia di $opra, &amp; DEF
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diff changeset
6349 quella della taglia di $otto legata al pe$o G; &amp;
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diff changeset
6350 $ia la corda HABCDEFK inuolta d'intorno
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parents:
diff changeset
6351 alle, girellel aqual corda $ia legata in K, &amp; in H
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6352 alla taglia di $otto; &amp; $ia in L la po$$anza che
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diff changeset
6353 $o$tiene il pe$o G. Dico, che il pe$o &egrave; vna volta
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6354 &amp; meza tanto quanto la po$$anza. Hor percio-</I>
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diff changeset
6355 <marg><I>Per il corol lario della</I> 5. <I>di que$io.</I></marg> <I>che l'vna, &amp; l'altra corda CD AH $o$tiene la
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6356 terza parte del pe$o G; $ar&agrave; ogn'vna delle po$-
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6357 $anze po$te in DH vn terzo del pe$o G; alle
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diff changeset
6358 quali tutte pre$e in$ieme &egrave; eguale la po$$anza di</I>
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diff changeset
6359 <marg><I>Per la</I> 15. <I>di questo.</I></marg> <I>L: peroche la detta po$$anza di L &egrave; due volte
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6360 tanto quanto &egrave; la po$$anza di D, &amp; di quella
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6361 che $ta in H. Per laqual co$a la po$$anza di L
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parents:
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6362 viene ad e$$ere $otto $e$quialtera del pe$o G.
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6363 Adunque il pe$o G ver$o la po$$anza di L &egrave; co-
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parents:
diff changeset
6364 me tre &agrave; due. cio&egrave; vna volta &amp; meza. che bi$o-
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parents:
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6365 gnaua mo$trare.</I>
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diff changeset
6366 <fig>
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parents:
diff changeset
6367 <p>&ldquo;Per laqual co$a la po$$anza di L &egrave; $otto $e$quialtera del pe$o G. H&ograve; detto, che il
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parents:
diff changeset
6368 $opraparticolare &egrave; il $econdo genere de'moltiplici, la prima $petie del quale &egrave;
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parents:
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6369 tre &agrave; due, che &egrave; $e$quialtera, cio&egrave; vna volta &amp; meza. Hor chi f&agrave; comparatione
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parents:
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6370 al contrario di due &agrave; tre na$ce la $otto $e$quialtera, hauendo forza quella voce
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parents:
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6371 $otto di paragonare la minore quantita con la maggiore. La po$$anza dunque di
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parents:
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6372 L $ar&agrave; in proportione co'l pe$o G come due&agrave; tre, &amp; in que$ta gui$a deue$i in-
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parents:
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6373 tendere $empre tale vocabolo.
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6374 <pb n=87>
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6375 <p>Ma $e la po$$anza che moue il pe$o $ar&agrave; in L: Dico lo $patio
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6376 della po$$anza e$$ere vna volta &amp; meza tanto, quanto lo $pa-
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parents:
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6377 tio del pe$o.
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parents:
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6378 <p><I>Stando le co$e ifle$$e, peruenga la girella
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parents:
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6379 ABC fin ad MNO, &amp; la girella
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parents:
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6380 DEF fin &agrave; PQR; &amp; H in S;
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6381 &amp; il pe$o G fin in T. Et perche la
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6382 corda HABCDEFK &egrave; eguale alla
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parents:
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6383 corda SMNOPQRK e$$endo la
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parents:
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6384 corda i$te$$a; &amp; le corde che $ono d'in-
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parents:
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6385 torno &agrave; mezi cerchi ABCMNO $o
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parents:
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6386 no tra loro eguali, &amp; quelle, che $ono
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parents:
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6387 d'intorno alli mezi cerchi DEF PQR
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parents:
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6388 $imilmente $ono tra loro eguali; tolte
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parents:
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6389 via dunque le corde AS CP RK
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parents:
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6390 communi, $aranno le due CO MA e-
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parents:
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6391 guali alle tre DP HS FR. ma l'v-
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parents:
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6392 na, &amp; l'altra di CO AM $eparata-
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parents:
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6393 mente &egrave; eguale allo $patio della po$$an-
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6394 za mo$$a. Per laqual co$a le due CO
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parents:
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6395 MA in$ieme $aranno due volte tanto
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parents:
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6396 quanto lo $patio della po$$anza; &amp; le
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parents:
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6397 tre DP HS FR in$ieme con $imile
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parents:
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6398 modo $aranno tre volte tanto quanto
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6399 lo $patio del pe$o mo$$o. Ma la met&agrave;,
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parents:
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6400 cio&egrave; lo $patio della po$$anza mo$$a, al-
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parents:
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6401 la terza parte, cio&egrave; allo $patio del pe$o
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parents:
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6402 mo$$o, ha proportione tale quale &egrave; dal
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parents:
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6403 doppio della met&agrave; al doppio del terzo,
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6404 cio&egrave; come il tutto &agrave; duo terzi, che &egrave; come
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parents:
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6405 tre &agrave; due. Lo $patio dunque della po$$an
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parents:
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6406 za po$ta in L &egrave; vna volta &amp; meza tan
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6407 to quanto lo $patio del pe$o G mo$$o.
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6408 che bi$ognaua mo$trare.</I>
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6409 <fig>
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6410 <HEAD>PROPOSITIONE XXI.</HEAD>
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6411 <p>Se &agrave; tre girelle di due taglie, l vna delle quali $ia $o$tenuta dalla
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6412 po$$anza di $opra con vna $ola girella, &amp; l'altra con due girel-
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parents:
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6413 le $ia po$ta di $otto, &amp; legata al pe$o, $ar&agrave; inuolta d'intorno
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parents:
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6414 la corda, con l'vno de' $uoi capi legato in qualche luogo, &amp;
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parents:
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6415 l'altro legato nella taglia di $opra; il pe$o $ar&agrave; vna volta, &amp; vn
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parents:
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6416 terzo tanto quanto la po$$anza.
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parents:
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6417 <p><I>Sia il pe$o A legato alla taglia di
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parents:
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6418 $otto, laquale habbia due girelle, i
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parents:
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6419 cui centri $iano BC, &amp; la taglia
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parents:
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6420 di $opra habbia la girella co'l centro
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parents:
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6421 D; &amp; $ia la corda EFGHKL
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parents:
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6422 MN riuolta d'intorno &agrave; tuttele gi-
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parents:
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6423 relle, laquale $ia legata in N, &amp;
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parents:
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6424 in E dalla taglia di $opra; &amp; $ia
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parents:
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6425 la po$$anza in O, che $o$tenga il pe
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casties
parents:
diff changeset
6426 $o A. Dico che il pe$o &egrave; vna volta
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diff changeset
6427 &amp; vn terzo tanto quanto &egrave; la po$$an
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parents:
diff changeset
6428 za. Et percioche cia$cheduna delle</I>
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parents:
diff changeset
6429 <marg><I>Per il</I> 1. <I>co volario della</I> V. <I>di que$to.</I></marg> <I>corde NM HG EF KL $o$tie-
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parents:
diff changeset
6430 ne la quarta parte del pe$o A; &amp;
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diff changeset
6431 tutte in$ieme $o$tengono tutto il pe-
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parents:
diff changeset
6432 $o; le tre HG EF KL in$ieme
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parents:
diff changeset
6433 $o$ierranno le tre parti del pe$o A.
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parents:
diff changeset
6434 Per laqual co$a il pe$o A ver$o tut
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parents:
diff changeset
6435 te que$te in$ieme $ar&agrave; come quattro
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diff changeset
6436 &agrave; tre: &amp; concio$ia che la po$$anza di
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parents:
diff changeset
6437 O faccia il mede$imo, che $anno le
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parents:
diff changeset
6438 corde HG EF KL tutte in$ie-
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parents:
diff changeset
6439 me; peroche le $o$tiene tutte; $ar&agrave; la
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parents:
diff changeset
6440 po$$anza di O eguale &agrave; le tre HG
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parents:
diff changeset
6441 EF KL in$ieme; &amp; perci&ograve; il pe$o
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parents:
diff changeset
6442 A ver$o la po$$anza di O $ar&agrave; co-
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parents:
diff changeset
6443 me quattro &agrave; tre, cio&egrave; vna volta, &amp;
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parents:
diff changeset
6444 vn cerzo. che bi$ognaua mo$trare.</I>
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diff changeset
6445 <fig>
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parents:
diff changeset
6446 <pb n=88>
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parents:
diff changeset
6447 <p>Ma $e in O $ar&agrave; la po$$an-
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parents:
diff changeset
6448 za che moua il pe$o A.
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parents:
diff changeset
6449 Dico lo $patio cor$o dal-
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parents:
diff changeset
6450 la po$$anza di O e$$ere
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6451 vna volta &amp; vn terzo tan-
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parents:
diff changeset
6452 to quanto &egrave; lo $patio del
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parents:
diff changeset
6453 pe$o A mo$$o.
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parents:
diff changeset
6454 <p><I>Stando le co$e mede$ime, $ia il centro
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parents:
diff changeset
6455 B mo$$o in P; &amp; C fin in Q;
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parents:
diff changeset
6456 &amp; D in R; &amp; E in S nel-
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diff changeset
6457 l'i$te$$o tempo: &amp; $iano per li cen-
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parents:
diff changeset
6458 tri condotte le linee ML<36>ZFG
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parents:
diff changeset
6459 TV HK X<G>*u</G> egualmente di$tan
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parents:
diff changeset
6460 ti, &amp; dall' orizonte, &amp; fra $e $te$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6461 $e: $imilmente, come nella prece-
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parents:
diff changeset
6462 dente $i dimo$trer&agrave;, le tre corde
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parents:
diff changeset
6463 XH SE <G>*u</G>K e$$ere eguali alle
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parents:
diff changeset
6464 quattro TG VF ZL <36>M. &amp;
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parents:
diff changeset
6465 percioche le tre XH SE <G>*u</G>K $o-
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parents:
diff changeset
6466 no in$ieme tre volte tanto quanto
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parents:
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6467 lo $patio della po$$anza: ma le
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parents:
diff changeset
6468 quattro TG VF ZL <36>M in-
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parents:
diff changeset
6469 $ieme $ono quattro volte t&amacr;to quan
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parents:
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6470 to lo $patio del pe$o mo$$o; $ar&agrave; lo
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parents:
diff changeset
6471 $patio della po$$anza ver$o lo $pa-
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parents:
diff changeset
6472 tio del pe$o, come la terza parte
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parents:
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6473 alla quarta parte. Ma la terza
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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6474 parte ver$o la quarta parte &egrave; come
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parents:
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6475 tre terzi &agrave; tre quarti, cio&egrave; come il
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parents:
diff changeset
6476 tutto ver$o tre quarti, che &egrave; come
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6477 quattro ver$o tre. Lo $patio dun-
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parents:
diff changeset
6478 que della po$$anza allo $patio del
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parents:
diff changeset
6479 pe$o mo$$o h&agrave; proportione di vna
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parents:
diff changeset
6480 volta &amp; vn terzo. che era damo-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6481 $trar$i.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6482 <fig>
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parents:
diff changeset
6483 <p><I>Ma $e la corda in E $ar&agrave; inuolta d'in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6484 torno vn'altra girella, laqual cor-</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6485 <pb n=89>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6486 <HEAD>PROPOSITIONE XXII.</HEAD>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6487 <p>Se all'vna &amp; l'altra di cia$cuna girella delle due taglie, l'vna del-
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parents:
diff changeset
6488 le quali $ia $o$tenuta di $opra dalla po$$anza, &amp; l'altra po$ta di
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parents:
diff changeset
6489 $otto, &amp; legata al pe$o, $ar&agrave; condotta d'intorno la corda; con
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6490 l'vno de $uoi capi legato in qualche luogo, &amp; l'altro attaccato
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6491 alla taglia di $opra. $ar&agrave; la po$$anza vna volta &amp; meza tanto
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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6492 quanto il pe$o.
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parents:
diff changeset
6493 <p><I>Sia la girella ABC della taglia legata
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casties
parents:
diff changeset
6494 al pe$o D; &amp; EFG la girella del-
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parents:
diff changeset
6495 la taglia di $opra, il cui centro $ia H;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6496 $ia dapoi la corda KABCEFGL ri-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6497 uolta d'intorno alle girelle, &amp; legata
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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6498 in L &amp; in K alla taglia di $opra; &amp;
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parents:
diff changeset
6499 $ia in M la po$$anza, che $o$tiene il</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
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parents:
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6500 <I>pe$o D. Dico che la po$$anza &egrave; vna
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parents:
diff changeset
6501 volta &amp; meza quanto &egrave; il pe$o. Hor</I> <marg><I>Per la</I> 15. <I>di questo.</I></marg>
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parents:
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6502 <I>percioche la po$$anza di E $o$tenente
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casties
parents:
diff changeset
6503 il pe$o D &egrave; la met&agrave; meno del pe$o D;</I> <marg><I>Per il</I> 2. <I>co rollario del la</I> 2. <I>di questo.</I></marg>
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parents:
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6504 <I>&amp; la po$$anza di H &egrave; due volte quan
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parents:
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6505 to la po$$anza po$ta in E; $ar&agrave; la po$-
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parents:
diff changeset
6506 $anza di H eguale al pe$o D; &amp; con
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parents:
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6507 cio$ia, che la po$$anza di K $ia la me-
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casties
parents:
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6508 t&agrave; meno del pe$o D; $aranno ambe-
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casties
parents:
diff changeset
6509 due le po$$anze in$ieme po$te in HK
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parents:
diff changeset
6510 vna volta &amp; meza quanto il pe$o D.
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parents:
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6511 e$$endo adunque la po$$anza di M egua-
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casties
parents:
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6512 le &agrave; due po$$anze in HK pre$e in$ie-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
6513 me, $i come di $opra &egrave; $tato dichiarato;
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parents:
diff changeset
6514 $ar&agrave; la po$$anza di M vna volta &amp;
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parents:
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6515 meza quanto il pe$o D. che bi$ogna-
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casties
parents:
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6516 ua mo$trare.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
6517 <fig>
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parents:
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6518 <p><I>Ma $e la po$$anza che moue il pe$o $ar&agrave; in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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6519 M, $i mo$trer&agrave; $imilmente, come nelle
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casties
parents:
diff changeset
6520 precedenti, lo $patio del pe$o e$$ere vna
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diff changeset
6521 volta &amp; meza tanto quanto lo $patio
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6522 della po$$anza.</I>
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diff changeset
6523 <foot><I>Z</I></foot>
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6524 <pb>
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diff changeset
6525 <p><I>Et $e la corda in K $ar&agrave; inuolta d'interno ad vn'altra girella, il cui centro $ia N;
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diff changeset
6526 laquale dapoi $ta rilegata alla taglia di $otto in O; &amp; la po$$anza di M $o$ten-
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6527 ga il pe$o D. Dico la proportione
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6528 della po$$anza al pe$o e$$ere vna
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diff changeset
6529 volta, &amp; vn terzo.</I>
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diff changeset
6530 <p><I>Hor percioche la po$$anza di E che</I>
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6531 <marg><I>Per la</I> 5. <I>di questo.</I></marg> <I>$o$tiene il pe$o D conla corda EC
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diff changeset
6532 BAKPO &egrave; vn terzo di e$$o D,</I>
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diff changeset
6533 <marg><I>Dalla</I> 15. <I>di questo.</I></marg> <I>&amp; la po$$anza di H &egrave; due volte
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6534 tanto quanto e$$o E; $ar&agrave; la po$-
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diff changeset
6535 $anza di H $otto $e$quialtera al pe-
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diff changeset
6536 $o D. &amp; nel modo iste$$o, per-
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6537 cioche la po$$anza di O, laquale
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6538 &egrave; come $e fo$$e nel centro della gi-
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diff changeset
6539 rella ABC &egrave; vn terzo del pe$o</I>
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6540 <marg><I>Per la</I> 3. <I>&amp;</I> 15. <I>di questo.</I></marg> <I>D, &amp; la po$$anza di N &egrave; due
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6541 volte tanto quanto &egrave; e$$o O. $ar&agrave;
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diff changeset
6542 parimente la po$$anza di N $otto
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diff changeset
6543 $e$quialtera al pe$o D. Per laqual
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6544 co$a due po$$anze in$ieme po$te in
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6545 HN $uperano il pe$o D d'vna
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6546 terza parte, &amp; $ono ver$o il detto
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6547 D in ragione di vna volta &amp; vn
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6548 terzo. &amp; concio$ia, che la po$$an-
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6549 za di M $ia eguale alle due po$$an
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6550 ze di HN pre$e in$ieme, $upere-
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6551 ra mede$imamente la detta po$$an-
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6552 za di M il pe$o D di vn terzo.
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6553 Adunque la proportione della po$-
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6554 $anza po$ta in M ver$o il pe$o D
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6555 &egrave; vna volta, &amp; vn terzo. che bi-
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diff changeset
6556 $ognaua mo$trare.</I>
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6557 <fig>
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6558 <p><I>Che $e la po$$anza mouente il pe$o $a-
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6559 r&agrave; in M, con modo $imile proue-
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6560 ra$$i lo $patio del pe$o D e$$ere vna
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6561 volta &amp; vn terzo tanto quanto la
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6562 po$$anza di M.</I>
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6563 <p><I>Et $e la corda in O $ar&agrave; inuolta d'in-
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6564 torno ad vn'altra girella, laquale dapoi $ia legata alla taglia di $opra; nell'i$te$$o
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6565 modo dimo$treremo la proportione della po$$anza M, che $o$tiene il pe$o e$$ere
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6566 vna volta &amp; vn quarto tanto quanto il pe$o. &amp; $e in M $ar&agrave; la po$$anza che
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6567 moue, $imilmente mo$trera&szlig;ilo $patio del pe$o e$$ere vna volta &amp; vn quarto tan</I>
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6568 <pb n=90>
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6569 <I>to quanto lo $patio della po$$anza. &amp; co$i procedendo in infinito ritrouereme
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6570 qual $i voglia proportione $opraparticolare della po$$anza al pe$o, &amp; $empre
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6571 mostreremo la po$$anza, che $o$tiene il pe$o co$i e$$ere ver$o il pe$o, come lo $pa-
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6572 tio del pe$o allo $patio della po$$anza, che moue il pe$o.</I>
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6573 <p><I>Ma il mouimento della leua EG &egrave; come $e G $o$$e il $o$tegno, e$$endo la corda legata
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6574 in L, &amp; il pe$o, come $e fo$$e appiccato in E, &amp; la po$$anza nel mezo. Ma
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parents:
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6575 della leua CA il $o$tegno &egrave; A, il pe$o nelmezo, &amp; la po$$anza in C. &amp; il
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6576 K &egrave; il $o$tegno della leua PK, il pe$o in P, &amp; la po$$anza nel mezo. Le qua-
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6577 li co$e tutte $i dimo$treranno, come nelle precedenti.</I>
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6578 <HEAD>PROPOSITIONE XXIII.</HEAD>
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6579 <p>Se all'vna, &amp; l'altra delle due girelle di due taglie, l'vna dellequa
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6580 li $ia $o$tenuta di $opra dalla po$$anza, &amp; l'altra po$ta &agrave; ba$$o,
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6581 &amp; legata al pe$o, $ia menata intorno la corda, legando am-
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6582 bidue li $uoi capi in qualche luogo, non gi&agrave; nelle taglie; la
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6583 po$$anza $ar&agrave; eguale al pe$o.
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6584 <foot><I>Z</I> 2</foot>
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6585 <pb>
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6586 <p><I>Sia la girella della taglia di $o
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parents:
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6587 pra ABC, il cui centro D;
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6588 &amp; la girella della taglia le-
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parents:
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6589 gata al pe$o H $ia EFG; il
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6590 cui centro K; &amp; $ia la cor
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6591 da LEFGABCM ri-
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parents:
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6592 uolta d'intorno alle girelle
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6593 &amp; legatain LM; &amp; $ia
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6594 in N la po$$anza che $o-
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6595 $tiene il pe$o H. Dico che
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6596 la po$$anza di N &egrave; egua-
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6597 le al pe$o H. Prenda$i
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6598 il punto O douunque $i
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6599 $ia nella corda AG. Hor
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6600 percioche $e la po$$anza,
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6601 che $o$tiene il pe$o H fo$</I>
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6602 <marg><I>Per la</I> 2. <I>di questo.</I></marg> <I>$e in O, $arebbe la met&agrave;
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6603 meno del pe$o H, &amp; la</I>
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6604 <marg><I>Per la</I> 15. <I>di questo.</I></marg> <I>po$$anza po$ta in D &egrave; due
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6605 volte quanto &egrave; quella di O,
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6606 ouero (che &egrave; l'i$te$$o) di N;
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6607 $ar&agrave; la po$$anza di N e-
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6608 guale al pe$o H. che bi-
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6609 $ognaua mo$trare.</I>
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6610 <fig>
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6611 <p>Et $e in N $ar&agrave; la po$
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6612 $anza, che moue il
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6613 pe$o. Dico, che lo
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6614 $patio della po$$an-
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6615 za po$ta in N &egrave; e-
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6616 guale allo $patio del
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6617 pe$o H mo$$o.
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6618 <p><marg><I>Per la</I> 11. <I>di questo.</I></marg> <I>Percio che lo $patio del punto O mo$$o &egrave; due volte tanto quanto &egrave; lo $patio s&igrave; del pe</I>
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6619 <marg><I>Per la</I> 16. <I>di questo.</I></marg> <I>$o H mo$$o, come della po$$anza N mo$$a; $ar&agrave; lo $patio della po$$anza N
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6620 allo $patio del pe$o H eguale.</I>
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diff changeset
6621 <pb n=91>
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6622 <HEAD>Altramente.</HEAD>
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6623 <p><I>Stando le co$e i$te$$e. $ia tra-
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6624 portato il centro della gi-
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6625 rella ABC fin &agrave; P; &amp;
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6626 la girella habbia il $ito in
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parents:
diff changeset
6627 QRS. Dapoi nell'i$te$$o
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parents:
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6628 tempo la girella EFG $ia
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parents:
diff changeset
6629 in TVX, il cui centro
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diff changeset
6630 $ia <G>*u</G>, &amp; il pe$o $ia per
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parents:
diff changeset
6631 uenuto in Z. $iano tira-
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6632 te per i centri delle girel-
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parents:
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6633 le le linee GETX AC
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parents:
diff changeset
6634 QS egualmente di$tanti
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parents:
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6635 dall' orizonte. &amp; $i come
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6636 nelle altre fu dimo$trato,
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6637 le due corde AQ CS $a
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parents:
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6638 ranno eguali alle due cor-
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parents:
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6639 de XG TE; ma AQ
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diff changeset
6640 CS in$ieme $ono due vol
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parents:
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6641 te tanto quanto lo $patio
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parents:
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6642 della po$$anza mo$$a; &amp;
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6643 le due XG TE in$ieme
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6644 $imilmente $ono due vol-
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parents:
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6645 te tanto quanto lo $patio
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6646 del pe$o; $ar&agrave; dunque lo
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diff changeset
6647 $patio della po$$anza egua
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6648 le allo $patio del pe$o. che
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6649 bi$ognaua mostrare.</I>
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6650 <fig>
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6651 <p><I>Che $e l'vna, &amp; l'altra taglia haur&agrave; etiandio due girelle, i cui centri $iano ABCD,
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6652 &amp; la corda $ia inuolta d'intorno &agrave; tutte, la quale $ia rilegata in LM; $imilmen-
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6653 te $i mo$trer&agrave;, che la po$$an-
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6654 za di N &egrave; eguale al pe$o H.
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parents:
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6655 Peroche cia$cuna po$$anza
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6656 po$ta in EF $o$tenente il
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6657 pe$o &egrave; vn quarto del pe$o; &amp;
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6658 le po$$anze di CD $ono due
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6659 volte tanto quanto quelle,
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6660 che $ono in EF; $ar&agrave; cia-
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6661 $cuna po$$anza di CD la
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parents:
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6662 met&agrave; del pe$o H. Per la-
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6663 qual co$a le po$$anze di CD
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6664 pre$e in$ieme $aranno eguali
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6665 al pe$o H. Et percioche la
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6666 po$$anza di N &egrave; eguale &agrave;
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6667 due po$$anze po$te in CD;
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parents:
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6668 $ar&agrave; la po$$anza di N egua
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6669 le al pe$o H.</I>
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6670 <fig>
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6671 <p><I>Et $e la po$$anza che moue $a-
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parents:
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6672 r&agrave; in N, con modo $imile
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parents:
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6673 $i mo$trer&agrave; lo $patio della po$
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parents:
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6674 $anza e$$ere eguale allo $pa-
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parents:
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6675 tio del pe$o.</I>
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parents:
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6676 <p><I>Ma $e l'vna &amp; l'altra taglia ha-
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parents:
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6677 uer&agrave; tre, &ograve; quattro, oue-
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parents:
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6678 ro quante $i voglia girelle,
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parents:
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6679 $empre $i dimostrer&agrave; la po$-
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parents:
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6680 $anza di N e$$ere eguale al
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parents:
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6681 pe$o H; &amp; lo $patio della
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parents:
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6682 po$$anza mouente il pe$o e$-
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parents:
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6683 $ere eguale allo $patio del pe
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parents:
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6684 $o mo$$o.</I>
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parents:
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6685 <p><I>Ma i mouimenti delle leue in
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parents:
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6686 que$ta maniera $ono di$po$ti,
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parents:
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6687 che il $o$tegno delle girelle
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parents:
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6688 della taglia di $opra, come
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parents:
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6689 AC della figura preceden-
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parents:
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6690 te &egrave; in C, il pe$o appiccato in A, &amp; la po$$anza nel mezo in D. ma le leue
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parents:
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6691 delle girelle della taglia di $otto co$i $i mouono, che di e$$o GE il $o$tegno $ia E,
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6692 il pe$o appiccato nel mezo, &amp; la po$$anza in G.</I>
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parents:
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6693 <pb n=92>
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6694 <HEAD>PROPOSITIONE XXIIII.</HEAD>
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parents:
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6695 <p>Se &agrave; tre girelle di due taglie, l'vna delle quali, che habbia vna gi
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parents:
diff changeset
6696 rella $olamente $ia $o$tenuta di $opra dalla po$$anza, &amp; l'altra
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parents:
diff changeset
6697 po$ta di $otto con due girelle, &amp; legata al pe$o, $ar&agrave; girata in-
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parents:
diff changeset
6698 torno la corda: e$$endo li due $uoi capi legat in qualche luo
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parents:
diff changeset
6699 go, ma non gi&agrave; nella taglia di $opra: il pe$o $ar&agrave; il doppio del
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parents:
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6700 la po$$anza.
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parents:
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6701 <p><I>Siano AB i centri delle girelle della
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parents:
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6702 taglia legata al pe$o C: &amp; il D
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parents:
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6703 $ia il centro della girella di $opra;
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parents:
diff changeset
6704 $ia dapoi la corda riuolta d'intorno
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parents:
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6705 &agrave; tutte le girelle, &amp; rilegata in EF;
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parents:
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6706 &amp; $ia in G la po$$anza, che $o-
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parents:
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6707 $tiene il pe$o C. Dico, che il pe$o
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parents:
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6708 C &egrave; due volte tanto quanto la
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parents:
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6709 po$$anza G. Hor percioche $e in
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parents:
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6710 HK fo$$ero due po$$anze, che $o-
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6711 $tene$$ero il pe$o con due corde ri-
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6712 uolte d'intorno alle girelle $olamen
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6713 te della taglia di $otto, $arebbe per
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diff changeset
6714 certo l'vna &amp; l'altra po$$anza po-</I> <marg><I>Dalla</I> 7. <I>di questo.</I></marg>
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6715 <I>$ta in KH vn quarto del pe$o C;
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6716 Mala po$$anza di G &egrave; eguale alle
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diff changeset
6717 po$$anze di HK pre$e in$ieme:</I> <marg><I>Dalla</I> 15. <I>di questo.</I></marg>
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6718 <I>percioche &egrave; due volte tanto quan-
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6719 to cia$cuna delle po$$anze di H,
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6720 &amp; K; $ar&agrave; la po$$anza di G la
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6721 met&agrave; del pe$o C. il pe$o dunque
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6722 $ar&agrave; il doppio della po$$anza. che
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6723 bi$ognaua mo$trare.</I>
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6724 <fig>
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6725 <p>Et $e in G $ar&agrave; la po$$anza
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6726 mouente il pe$o. Dico
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6727 che lo $patio della po$$an
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6728 za &egrave; il doppio dello $pa-
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6729 tio del pe$o.
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6730 <fig>
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diff changeset
6731 <p><I>Stando le co$e i$te$$e. $iano mo$$e le gi
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6732 relle; $i dimo$trer&agrave; $imilmente am-
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6733 bedue quelle corde LM NO e$-
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diff changeset
6734 $ere eguali alle quattro PQ RS
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diff changeset
6735 TV X<G>*u</G>. Ma LM NO in-
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6736 $ieme $ono il doppio dello $patio
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6737 della po$$anza di G mo$$a; &amp;
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6738 le quattro PQ RS TV X<G>*u</G>
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6739 in$ieme $ono quattro volte tanto
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6740 quanto lo $patio del pe$o mo$$o.
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6741 Lo $patio dunque della po$$anza
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6742 ver$o lo $patio del pe$o &egrave; come la
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6743 met&agrave; ad vn quarto. Sar&agrave; dunque
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6744 lo $patio della po$$anza allo $patio
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6745 del pe$o il doppi&ograve;.</I>
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6746 <pb n=93>
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diff changeset
6747 <p><I>Di qui egli &egrave; da con$iderare
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6748 in che modo $i faccia il mo
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6749 uimento; percioche e$$en-
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6750 do legata la corda in F,
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6751 la leua NO nella prima
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6752 figura haur&agrave; il $o$tegno in
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6753 O, il pe$o nel mezo, &amp; la
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6754 po$$anza in N. $rmil.
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6755 mente percioche la corda
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6756 &egrave; rilegata in E, la leua
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6757 PQ haur&agrave; il $o$tegno in
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6758 P, &amp; il pe$o ne, nezo,
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6759 &amp; la po$$anza in Q. On
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6760 de le parti delle girelle di
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6761 N &amp; Q $i moueranno
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6762 in s&ugrave;; adunque le girelle
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6763 $i moueranno non ad vna
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6764 parte, ma in contrarie par
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6765 ti, cio&egrave; vna alla de$tra, &amp;
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6766 l'altra alla $ini$tra. &amp;
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6767 percioche le po$$anze di
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6768 NQ $on<*>le i$te$$e, che
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6769 $ono in LM; le po$$an-
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6770 ze dunque di LM e$$en-
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6771 do eguali $i moueranno
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6772 in s&ugrave;. La leua dunque
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6773 LM non $i mouer&agrave; in
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6774 niuna delle parti. Per la
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6775 qual co$a no anche la gi-
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6776 rella $i girer&agrave; intorno.
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6777 Co$i LM $ar&agrave; come bi-
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6778 lancia, il cni centro D,
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6779 &amp; li pe$i appiccati in LM
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6780 $aranno eguali alla quar-</I>
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6781 <fig>
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parents:
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6782 <I>ta parte del pe$o C; peroche cia$cheduna corda in LN MQ $o$tiene la quar
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6783 ta parte del pe$o C; $i mouer&agrave; dunque tuttala girella, il cui centro &egrave; D in s&ugrave;,
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parents:
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6784 ma non gi&agrave; voltera$$i intorno.</I>
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6785 <foot><I>A a</I></foot>
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6786 <pb>
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parents:
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6787 <p><I>Et $e la corda po$ta in F $iriuolger&agrave;
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6788 d'intorno &agrave; due altre girelle, i cui
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6789 centri $iano HK l'aquale dapoi $ia
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6790 rilegata in L; $ar&agrave; la proportione
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6791 del pe$o alla po$$anza vna volta &amp;
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6792 meza.</I>
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6793 <p><marg><I>Per la</I> 9. <I>di questo.</I></marg> <I>Percioche $e fo$$ero quattro po$$anze in
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6794 MNOI, cia$cheduna di loro $areb
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6795 be vn $e$to del pe$o C. Per laqual
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parents:
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6796 co$a quattro po$$anze in$ieme in MN
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6797 OI $aranno quattro $e$ti del pe$o C.
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6798 &amp; percioche due po$$anze in$ieme po
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6799 $te in HD $ono eguali &agrave; quattro po$
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6800 $anze po$te in MNOI; &amp; la po$-
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6801 $anza di G &egrave; eguale alle po$$anze di
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parents:
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6802 DH; $ar&agrave; la po$$anza di G egua-
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parents:
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6803 le &agrave; quattro po$$anze in$ieme po$te
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parents:
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6804 in MNOI; &amp; perci&ograve; $ar&agrave; quat-
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parents:
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6805 tro $e$ti del pe$o C. La proportio-
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parents:
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6806 ne dunque del pe$o C alla po$$anza
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parents:
diff changeset
6807 di G &egrave; vna volta &amp; meza.</I>
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diff changeset
6808 <fig>
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6809 <p><I>Et $e in G $ar&agrave; la po$$anza, che moue,
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6810 con modo $imile $i mo$trer&agrave; lo $patio
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diff changeset
6811 della po$$anza e$$ere vna volta &amp;
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diff changeset
6812 meza tanto quanto lo $patio del pe$o.</I>
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diff changeset
6813 <p><I>Et $e la corda di L $ar&agrave; dauantaggio
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diff changeset
6814 riuolta d'intorno due altre girelle, $i-
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6815 milmente $i dimo $trer&agrave; la proportio-
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diff changeset
6816 ne del pe$o alla po$$anza e$$ere vna
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diff changeset
6817 volta, &amp; vn terzo. Che $e in G
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diff changeset
6818 $ar&agrave; la po$$anza che moue, $i mo$tre-
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diff changeset
6819 r&agrave; lo $patio della po$$anza e$$ere vna
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diff changeset
6820 volta, &amp; vn terzo quanto lo $patio
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diff changeset
6821 del pe$o, &amp; co$i di mano in mano
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diff changeset
6822 procedendo in infinito ritroueremo
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diff changeset
6823 qual $i voglia proportione $oprapar-
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diff changeset
6824 ticolare del pe$o alla po$$anza. &amp;
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diff changeset
6825 $empre ritroueremo co$i e$$ere il pe$o
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6826 ver$o la po$$anza che lo $o$tiene, co-
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diff changeset
6827 me lo $patio della po$$anza che moue
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diff changeset
6828 allo $patio del pe$o mo$$o dalla po$-
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diff changeset
6829 $anza.</I>
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diff changeset
6830 <pb n=94>
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diff changeset
6831 <p><I>Il mouimento delle leue $i fa in que$to modo, la leua <G>*u</G> Z, e$$endo la corda legata in
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diff changeset
6832 E ha il $o$tegno in <G>*u</G>, il pe$o attaccato in B nel mezo, &amp; la po$$anza in Z.
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diff changeset
6833 &amp; la leua PQ hail $ostegno in P, la po$$anza nel mezo, &amp; il pe$o in Q.
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diff changeset
6834 Percioche bi$ogna, che le girelle, i cui centri $ono BD, $i mouano nella parte
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parents:
diff changeset
6835 i$te$$a, cio&egrave; che QZ $i mouano all'insu. &amp; percioche la corda &egrave; rilegata in L,
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diff changeset
6836 $ara il T il $o$iegno della leua ST, che hail pe$o nel mezo, &amp; la po$$anza in
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diff changeset
6837 S; &amp; percioche S $i moue all'ins&ugrave;, &egrave; co$a nece$$aria, che R anchora $i moua
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diff changeset
6838 all'ins&ugrave;; &amp; per&ograve;, F $ar&agrave; il $o$tegno della leua FR, &amp; il pe$o $ar&agrave; in R, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
6839 la po$$anza nel mezo. Le girelle dunque, i cui centri $ono HK $i mouono in
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diff changeset
6840 parti contrarie di quelle, le quali hanno i centri BD; Per laqual co$a le parti del-
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diff changeset
6841 le girelle PF nelle girelle inchineranno al ba$$o, cio&egrave; ver$o XV. La leua dun
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diff changeset
6842 que VX non $i mouer&agrave; n&egrave; in vna, n&egrave; in altra parte, mouendo$i P &amp; F al
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parents:
diff changeset
6843 ba$$o; &amp; VX $ar&agrave; come leua, nel cui mezo $ia appiccato il pe$o, &amp; in VX
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parents:
diff changeset
6844 due po$$anze eguali alla $e$ta parte del pe$o C. Percioche le po$$anze di MO,
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diff changeset
6845 cio&egrave; le corde PV FX $o$tengono la $e$ta parte del pe$o C. Adunque tutta
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diff changeset
6846 la girella, il cui centro &egrave; A $i mouer&agrave; in s&ugrave; in$ieme con la taglia, ma non gi&agrave; $i
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6847 volger&agrave; intorno.</I>
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6848 <HEAD>PROPOSITIONE XXV.</HEAD>
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6849 <p>Se &agrave; tre girelle di due taglie, l'vna delle quali habbia due girel-
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parents:
diff changeset
6850 le, &amp; $ia tenuta di $opra dalla po$$anza; &amp; l'altra habbia vna $o
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parents:
diff changeset
6851 la girella, &amp; $ia po$ta di $otto, &amp; legata al pe$o, $ar&agrave; inuolta in
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parents:
diff changeset
6852 torno la corda: e$$endo legato l'vn &amp; l'altro de'$uoi capi in
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parents:
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6853 qualche luogo, ma non gi&agrave; nella taglia di $otto. La pos$anza
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parents:
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6854 $ar&agrave; due volte tanto quanto il pe$o.
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diff changeset
6855 <foot><I>A a</I> 2</foot>
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6856 <pb>
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parents:
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6857 <p><I>Sia il pe$o A legato alla taglia di $otto, laquale habbia la girella $u&auml; co'l centro B;
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parents:
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6858 ma la taglia di $opra habbia due girelle, i cui centri $iano CD, &amp; $ia la corda
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parents:
diff changeset
6859 inuolta d'intorno &agrave; tutte le girelle, &amp; rilegata in EF; &amp; la po$$anza che fo$tie-
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parents:
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6860 ne il pe$o $ia in G. Di-
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parents:
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6861 co la po$$anza di G e$$e-
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parents:
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6862 re due volte tanto quanto</I>
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6863 <marg><I>Per il</I> 2. <I>co rollario del la</I> 2. <I>di questo.</I></marg> <I>il pe$o. A. Percioche $e
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6864 in HK $o$$ero due po$$an
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6865 ze, che $o$tene$$ero il pe-
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parents:
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6866 $o, l'vna &amp; l'altra $areb-</I>
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6867 <marg><I>Per la</I> 15. <I>di questo.</I></marg> <I>be la met&agrave; del pe$o A:
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parents:
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6868 ma la po$$anza di D &egrave; due
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parents:
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6869 volte tanto quanto la po$-
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parents:
diff changeset
6870 $anza di H, &amp; la po$$an
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parents:
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6871 za di C &egrave; due volte tanto
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parents:
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6872 quanto la po$$anza di K;
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parents:
diff changeset
6873 Per laqual co$a due po$-
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parents:
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6874 $anze in$ieme po$te in CD
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parents:
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6875 $aranno il doppio di ambe-
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parents:
diff changeset
6876 due le po$$anze di HK pre
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parents:
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6877 $e in$ieme. Male po$$an-
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parents:
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6878 ze di HK $ono eguali al
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parents:
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6879 pe$o A &amp; le po$$anze di
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parents:
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6880 CD $ono etiandio eguali
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parents:
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6881 ad e$$a po$$anza di G; la
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parents:
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6882 po$$anza dunque di G $a-
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parents:
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6883 r&agrave; il doppio del pe$o A,
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6884 che bi$ognaua mo$trare.</I>
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6885 <fig>
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parents:
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6886 <p><I>Ma $e in G $ar&agrave; la po$$anza
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parents:
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6887 mouente il pe$o, $imilmen
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6888 te $i mo$trer&agrave;, come nella
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6889 precedente lo $patio del
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parents:
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6890 pe$o e$$ere il doppio dello
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6891 $patio della po$$anza.</I>
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6892 <p><I>Qui parmente &egrave; da con$ide-
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6893 rare, che la leua PQ non $i moue, peroche la leua LM h&agrave; il $o$tegno in L, la
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6894 po$$anza nel mezo, &amp; il pe$o in M. Mala leua NO h&agrave; il $o$tegno in O, la po$
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6895 $anza nel mezo, &amp; il pe$o in N. Per laqual co$a M, &amp; N $i moueranno all'in
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6896 s&ugrave;. Le girelle dunque, lequali hanno i centri CD $i mouono in parti contrarie.
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parents:
diff changeset
6897 Onde la leua PQ non $i mouer&agrave; n&egrave; all'vna, n&egrave; all'altra parte; &amp; $ar&agrave; come $e
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diff changeset
6898 fo$$e appiccato il pe$o nel mezo, &amp; in PQ due po$$anze fu$$ero eguali alla met&agrave;
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diff changeset
6899 del pe$o A. Peroche l'vna &amp; l'altra po$$anza di HK &egrave; la met&agrave; del pe$o A.</I>
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6900 <pb n=95>
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diff changeset
6901 <I>Tutta la girella dunque il cui centro &egrave; B $i mouer&agrave; all'ins&ugrave;, ma non gi&agrave; $i volge-
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diff changeset
6902 r&agrave; intorno.</I>
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diff changeset
6903 <p>Et $e la corda di F $i volge$$e
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diff changeset
6904 ancora d'intorno &agrave; due al-
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diff changeset
6905 tre girelle, i cui centri $o$-
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diff changeset
6906 $ero HK, laqual corda
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diff changeset
6907 poi $ia legata in L; $ar&agrave; la
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diff changeset
6908 proportione della po$$an-
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diff changeset
6909 za po$ta in G vna volta
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6910 &amp; meza quanto il pe$o A.
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6911 <fig>
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diff changeset
6912 <p><I>Percioche $e in MN OP fo$$ero quat
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diff changeset
6913 tro po$$anze $o$tenenti il pe$o, cia-</I> <marg><I>Per la</I> 7. <I><*> questo.</I></marg>
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diff changeset
6914 <I>$cheduna di loro $arebbe il quarto del
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diff changeset
6915 pe$o A: ma concio$ia che la po$$an</I> <marg><I>Per la</I> 15. <I><*> questo.</I></marg>
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diff changeset
6916 <I>za di K $ia il doppio della po$$anza
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diff changeset
6917 di N; $ar&agrave; la po$$anza di K vn
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diff changeset
6918 quarto del pe$o A. &amp; percioche
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6919 la po$$anza po$ta in D &egrave; eguale al
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diff changeset
6920 le due po$$anze MO; $ar&agrave; ancho-
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6921 rala po$$anza di D vn quarto del
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diff changeset
6922 pe$o A. Et di pi&ugrave; e$$endo la po$-
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6923 $anza di C vn quarto della po$$an-
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6924 za di P, $ar&agrave; $imilmente la po$$an
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parents:
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6925 za di C vn quarto del pe$o A.
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diff changeset
6926 Tre po$$anze dunque po$te in CDK
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diff changeset
6927 $ono eguali &agrave; tre met&agrave; del pe$o A.
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6928 Ma percioche la po$$anza di G &egrave;
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6929 eguale alle po$$anze di CDK, $a-
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diff changeset
6930 r&agrave; la po$$anza di G eguale alle tre
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6931 met&agrave; del pe$o A. La proportio-
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6932 ne dunque della po$$anza al pe$o &egrave;
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6933 vna volta, &amp; meza.</I>
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6934 <p><I>Che $e in G $ar&agrave; la po$$anza, che mo-
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diff changeset
6935 ue, $ar&agrave; lo $patio del pe$o vna volta
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6936 &amp; meza tanto quanto lo $patio del-
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diff changeset
6937 la po$$anza.</I>
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parents:
diff changeset
6938 <p><I>Et $e la eorda in L $ar&agrave; inuolta da<*>an-
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6939 <pb>
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parents:
diff changeset
6940 tag gio d'intorno &agrave; due altre girelle,
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6941 $imilmente $i mostrer&agrave; la proportio-
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6942 ne della po$$anza al pe$o e$$ere vna
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parents:
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6943 volta &amp; vn terzo. &amp; co$i in infini
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6944 to ritroueremo tutte le proportioni
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6945 $opraparticolari della po$$anza al pe
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6946 $o. &amp; mo$treremo la po$$anza che
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6947 $o$tiene il pe$o e$$ere co$i ver$o il pe-
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6948 $o, come lo $patio d l pe$o mo$$o
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6949 allo $patio della po$$anza che mo-
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6950 ue il pe$o.</I>
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6951 <fig>
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parents:
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6952 <p><I>Il mouimento delle leue $i far&agrave; in que-
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6953 $to modo, cio&egrave; il Q $ar&agrave; il $o$tegn<*>
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6954 della leua QR, la po$$anza nel me
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6955 zo, il pe$o in R; &amp; della leua Z <36>
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6956 il $o$tegno $ar&agrave; il Z, il pe$o nel
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diff changeset
6957 mezo, &amp; la po$$anza in <36>. $imil-
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6958 mente lo X $ar&agrave; il $o$tegno della le
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6959 ua VX, la po$$anza nel mezo, &amp;
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6960 il pe$o in V. &amp; percioche lo V
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diff changeset
6961 $i moue all'ins&ugrave;, $i mouer&agrave; all in s&ugrave; lo
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parents:
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6962 <G>*u</G> ancora, &amp; della leua <G>*u</G> F il $o-
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diff changeset
6963 $tegno $ar&agrave; F. Per laqual co$a F
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6964 &amp; Z nelle girelle $i moueranno in
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6965 gi&ugrave;. &amp; perci&ograve; la leua ST non $i
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6966 mouer&agrave; n&egrave; in vna, n&egrave; in altna par-
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6967 te; &amp; ST $ar&agrave; come bilancia, il
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6968 cui centro $ar&agrave; D, &amp; i pe$i po$ti
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parents:
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6969 in ST $aranno eguali alla quarta
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6970 parte del pe$o A. Peroche cia$cu-
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6971 na corda SZ TF $o$tiene la quar-
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parents:
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6972 ta parte del pe$o A. La girell&aacute;
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6973 dunque del centro D $i moner&agrave; al-
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6974 l'ins&ugrave;, ma non $i volger&agrave; intorno.</I>
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6975 <p><I>Fin qui, $ono $tate dichiarate le propor
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parents:
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6976 tioni molteplici, &amp; $otto molteplici
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6977 che ha il pe$o alla po$$anza; &amp; da-
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parents:
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6978 poi le proportioni $opraparticolari,
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6979 &amp; $otto $opraparticolari. Hora re-
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parents:
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6980 $ta, che $i manife$tino le proportio-</I>
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6981 <pb n=96>
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parents:
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6982 <I>ni tra il pe$o, &amp; la po$$anza $oprapartienti, &amp; molteplici $opraparticolari, &amp;
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6983 molteplici $oprapartienti.</I>
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parents:
diff changeset
6984 <p>Et dapoi le $opraparticolari, &amp; le $otto $opraparticolari furono dichiarate. &ldquo;Dal co
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parents:
diff changeset
6985 no$cimento del $opraparticolare $i intende ageuolmente il $otto $opraparticolare
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parents:
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6986 che gli &egrave; oppo$to; pero che paragonando come &egrave; detto il 3. co'l 2. na$ce il $o-
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parents:
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6987 praparticolare, &amp; per lo contrario il 2. co'l 3. $i produce il $otto $opraparticolare
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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6988 per la forza di quella voce $otto.
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parents:
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6989 <p>Hora re$ta &amp;c. &ldquo;Qui propone di trattare delle proportioni, che il pe$o h&agrave; con la po$
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parents:
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6990 $anza nel genere $oprapartiente, &amp; nel genere compo$to del molteplice $oprapar
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diff changeset
6991 ticolare, &amp; del molteplice $oprapa<*>tiente. il genere $o prapartiente &egrave; diuer$o dal
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diff changeset
6992 $opraparticolare, che doue nel $opraparticolare vna quantit&agrave; contiene l'altra vna
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parents:
diff changeset
6993 &ograve; pi&ugrave; volte, &amp; pi&ugrave; parte, che pu&ograve; interamente numerare &amp; l'vna, &amp; l'altra: nel
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diff changeset
6994 $oprapartiente contiene vna, &ograve; pi&ugrave;<*>volte, &amp; dauantaggio parte che non le puo-
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parents:
diff changeset
6995 te numerare, &amp; mi$urare perfettamente, come il cinque contiene il 3. vna volta,
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diff changeset
6996 &amp; piu parte di e$$o, che &egrave; il 2. il quale non &egrave; mi$ura commune di ambidue loro,
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diff changeset
6997 &amp; $i denomina $oprabipartiente terze, pero che contiene vna volta, &amp; piu due
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parents:
diff changeset
6998 terze parti del contenuto.
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diff changeset
6999 <p>Segue poi. Et le molteplici $opraparti<*>olari, che h&ograve; di $opra mo$trato. &ldquo;Componen
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diff changeset
7000 do due generi in$ieme il molteplice, &amp; il $o praparticolare na$ce que$to moltepli-
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parents:
diff changeset
7001 ce $o praparticolare, nelquale vna quantit&agrave; contiene l'altra molte volte, &amp; pi&ugrave; par
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parents:
diff changeset
7002 te di e$$a, che &egrave; mi$ura commune di<*>ambedue. La primiera $ua $petie &egrave; il 5. pa-
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parents:
diff changeset
7003 ragonato co'l due, che lo contiene due volte, &amp; piu la met&agrave; di lui, cio&egrave; vno, mi-
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parents:
diff changeset
7004 $ura di ambedue. Chiama$i que$ta proportione doppia $e$quialtera. Mettendo
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parents:
diff changeset
7005 parimente in$ieme il genere molteplice co'l $oprapartiente, $i fa il molteplice $o-
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parents:
diff changeset
7006 prapartiente, il quale &egrave; differente dal $o pradetto per ri$petto che in lui la maggior
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parents:
diff changeset
7007 quantit&agrave; contiene la minore molte volte, &amp; piu parte di e$$a, che non puote e$$e-
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parents:
diff changeset
7008 re loro mi$ura commune; la prima $petie del qual genere &egrave; come 8. &agrave; 3. peroche
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parents:
diff changeset
7009 l'otto contiene il 3. due volte, &amp; piu parte di e$$o 3. cio&egrave; 2. che non gli puo mi$u
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parents:
diff changeset
7010 rare ambidue, concio$ia che il 2. non puo mi$urare il 3. come f&agrave; l'otto per e$$ere
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parents:
diff changeset
7011 que$ti due numeri 8. &amp; 3. tra $e primi. &amp; chiama$i proportione doppia $oprabi-
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parents:
diff changeset
7012 partiente. Vuole dunque l'autore andar inue$tigando le proportioni fra il pe$o,
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parents:
diff changeset
7013 &amp; la po$$anza ne i predetti generi an cora, come h&agrave; fatto ne gli altri.
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parents:
diff changeset
7014 <p>Da que$te poche co$e, lequali h&ograve; qui narrato per ageuolare l'int&eacute;dimento de i voca-
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parents:
diff changeset
7015 boli pertinenti alle proportioni po$te da l'autore, $i potr&agrave; facilmente con qual-
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parents:
diff changeset
7016 che $tudio comprendere tutta la $omma delle vltime dimo $trationi della taglia,
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parents:
diff changeset
7017 nelle quali $ono que$ti vocaboli di proportioni, quantunque in ogni loco qua$i
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parents:
diff changeset
7018 con gli e$$empi $tes$i de' numeri $iano dall'autore manife$tate.
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parents:
diff changeset
7019 <HEAD>PROPOSITIONE XXVI.</HEAD>
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parents:
diff changeset
7020 <HEAD>PROBLEMA.</HEAD>
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parents:
diff changeset
7021 <p>Se vogliamo trouare la proportione $oprapartiente, come $e la
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parents:
diff changeset
7022 proportione, laquale h&agrave; il pe$o alla po$$anza che $o$tiene il pe
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parents:
diff changeset
7023 $o $ar&agrave; $oprabipartiente, come il cin que &agrave; tre.
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parents:
diff changeset
7024 <p><marg><I>Per la</I> 9. <I>di questo.</I></marg> <I>Ponga$i la po$$anza in A, the $o-
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parents:
diff changeset
7025 $tenga il pe$o B, &amp; il pe$o B
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parents:
diff changeset
7026 habbia proportione alla po$$an-
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parents:
diff changeset
7027 za A, come cinque ad vno;
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parents:
diff changeset
7028 cio&egrave; $ia la po$$anza di A vn quin
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parents:
diff changeset
7029 to del pe$o B: dapoiriuolgendo
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parents:
diff changeset
7030 la corda i$te$$a d'intorno ad altre</I>
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parents:
diff changeset
7031 <marg><I>Per la</I> 17. <I>di questo.</I></marg> <I>girelle, ritroui$i la po$$anza di C,
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parents:
diff changeset
7032 laquale $ia tre volte tanto quan-
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parents:
diff changeset
7033 to la po$$anza di A. Et percio
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parents:
diff changeset
7034 che il pe$o B alla po$$anza po-
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parents:
diff changeset
7035 $ta in A &egrave; come cinque ad vno;
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parents:
diff changeset
7036 &amp; la po$$anza di A alla po$$an
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parents:
diff changeset
7037 za di C &egrave; come vno ver$o tre, $a
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parents:
diff changeset
7038 r&agrave; il pe$o B ver$o la po$$anza
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parents:
diff changeset
7039 di C come cinque &agrave; tre, cio&egrave; $o-
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parents:
diff changeset
7040 prabipartiente.</I>
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parents:
diff changeset
7041 <fig>
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parents:
diff changeset
7042 <p><I>Et &agrave; que$to modo tutte le proportio-
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parents:
diff changeset
7043 ni $oprapartienti del pe$o alla po$
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parents:
diff changeset
7044 $anza $i troueranno; come $e la
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parents:
diff changeset
7045 proportione $opratrepartiente vor
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parents:
diff changeset
7046 r&agrave; alcuno trouare, proceda con
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parents:
diff changeset
7047 l'ordine iste$$o: cio&egrave; $accia$i che la
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parents:
diff changeset
7048 po$$anza di A $ostenente il pe-
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parents:
diff changeset
7049 $o B $ia vn $ettimo del pe$o B;
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parents:
diff changeset
7050 Dapoi $i faccia, che la po$$anza
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parents:
diff changeset
7051 di C $ia quattro volte tanto quan
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parents:
diff changeset
7052 to &egrave; quella di A; $ar&agrave; il pe$o B
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parents:
diff changeset
7053 ver$o la po$$anza di C, come $et
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parents:
diff changeset
7054 te &agrave; quattro; cio&egrave; $opratrepar-
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parents:
diff changeset
7055 tiente.</I>
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parents:
diff changeset
7056 <p>Ma $e in C $ar&agrave; la po$$an-
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parents:
diff changeset
7057 za mouente il pe$o, $ar&agrave;
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parents:
diff changeset
7058 lo $patio della po$$anza
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parents:
diff changeset
7059 $oprabipartiente allo $pa
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parents:
diff changeset
7060 tio del pe$o.
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parents:
diff changeset
7061 <p><marg><I>Per la</I> 17. <I>di questo.</I></marg> <I>Per cioche lo $patio della po$$anza
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parents:
diff changeset
7062 po$ta in C &egrave; la terza parte della
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parents:
diff changeset
7063 $patio della po$$anza po$ta in A,</I>
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parents:
diff changeset
7064 <pb n=97>
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parents:
diff changeset
7065 <I>cio&egrave;, che co$i $ono tra loro, come il cinque al quindici: &amp; lo $patio della po$$anza</I> <marg><I>Per la</I> 14. <I>di questo.</I></marg>
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casties
parents:
diff changeset
7066 <I>di A &egrave; cinque volte tanto quanto lo $patio del pe$o B, cio&egrave; come quindici &agrave; tre.
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parents:
diff changeset
7067 $ar&agrave; dunque lo $patio della po$$anza posta in C ver$o lo $patio del pe$o B come
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parents:
diff changeset
7068 cinque &agrave; tre; cio&egrave; $oprabipartiente: &amp; $empre dimostreremo, co$i e$$ere lo $patio
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parents:
diff changeset
7069 della po$$anza che moue allo $patio del pe$o; come il pe$o alla po$$anza che lo $o-
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parents:
diff changeset
7070 $tiene.</I>
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parents:
diff changeset
7071 <p><I>Et con ragione del tutto $imile ritroueremo la proportione $oprapartiente della po$$an
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parents:
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7072 za al pe$o. Peroche $e C fo$$e di $otto, &amp; in e$$o fo$$e appiccato il pe$o; &amp; il
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parents:
diff changeset
7073 B di $opra, nelquale fo$$e la po$$anza che in C $o$tiene il pe$o, $arebbe la po$-
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parents:
diff changeset
7074 $anza di B $oprabipartiente al pe$o appiccato in C: e$$endo il B allo A come</I> <marg><I>Per la</I> 18. <I>&amp; per la</I> 5. <I>di questo.</I></marg>
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parents:
diff changeset
7075 <I>cinque ad vno; ma A al C come l'vno al tre.</I>
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parents:
diff changeset
7076 <p>Ma $e vorremo trouare la proportione molteplice $oprapartico-
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diff changeset
7077 lare; come $e la proportione, laquale ha il pe$o alla po$$anza,
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diff changeset
7078 che lo $o$tiene $ia doppia $e$quialtera, come cinque &agrave; due.
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parents:
diff changeset
7079 <p><I>Nell'i$te$$o modo, co'l quale ritrouiamo le $oprapartienti, ritroueremo ancora tutte que
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parents:
diff changeset
7080 ste molteplici $opraparticolari. Come faccia$i il pe$o po$to in B alla po$$anza di A,</I> <marg><I>Per la</I> 9. <I>di questo.</I></marg>
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parents:
diff changeset
7081 <I>come il cinque all'vno; &amp; la po$$anza di C alla po$$anza di A come il due all'vno;
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parents:
diff changeset
7082 co$a che $i far&agrave;, $ela corda $ar&agrave; rilegata in D, ouero in E; ma non gi&agrave; alla ta-</I> <marg><I>Per la</I> 15. <I>&amp;</I> 16. <I>di questo.</I></marg>
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parents:
diff changeset
7083 <I>glia di $opra; $ar&agrave; il pe$o B alla po$$anza di C, come il cinque al due, cio&egrave; dop-
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parents:
diff changeset
7084 pio $e$quialtero.</I>
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parents:
diff changeset
7085 <p><I>Et per lo contrario ritrouaremo la proportione molteplice $opraparticolare della po$-
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parents:
diff changeset
7086 $anza al pe$o; &amp; come nelle altre $i mo$trer&agrave; co$i e$$ere lo $patio della po$$anza
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parents:
diff changeset
7087 che moue allo $patio del pe$o, come il pe$o alla po$$anza, che lo $o&sacute;tiene.</I>
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parents:
diff changeset
7088 <p>Con l'i$te$$o modo ritrouaremo ancora ogni proportione $opra-
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parents:
diff changeset
7089 partiente; come $e la proportione, laquale ha la po$$anza co'l
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7090 pe$o, $ar&agrave; doppia $oprabipartiente, come l'otto al tre.
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casties
parents:
diff changeset
7091 <p><I>Faccia$i la po$$anza po$ta in A $o$tenente il pe$o B vn'ottauo del pe$o B, &amp;</I> <marg><I>Per la</I> 9. <I>di questo.</I></marg>
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parents:
diff changeset
7092 <I>la po$$anza di C $ia vn terzo della po$$anza di A; $ar&agrave; il pe$o B alla po$$an
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parents:
diff changeset
7093 za di C, come l'otto al tre. &amp; per lo contrario ritroueremo ogni proportione mol</I> <marg><I>Per la</I> 17. <I>di questo.</I></marg>
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parents:
diff changeset
7094 <foot><I>B b</I></foot>
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parents:
diff changeset
7095 <pb>
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casties
parents:
diff changeset
7096 <I>replice $oprapartiente della po$$anza al pe$o. &amp; come nelle altre ritrouaremo co$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7097 e$$ere il pe$o alla po$$anza che lo $o$tiene, come lo $patio della po$$anza che moue
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7098 allo $patio del pe$o.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7099 <p><I>Ma egli &egrave; da notare, che benche pi&ugrave; volte $ia $tato detto nelle demo$irationi prece-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7100 denti, la po$$anza $o$tenente il pe$o e$$ere due volte tanto quanto e$$o pe$o, &ograve; tre,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7101 &amp; co$i di mano in mano, come nella decimaquinta di questo &egrave; $tato mo$trato; non-
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parents:
diff changeset
7102 dimeno percioche la po$$anza $o$liene non $olamente il pe$o, ma la taglia ancora,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7103 per&ograve; egli pare, che $ia me$tieri porre la po$$anza di molto maggiore virt&ugrave;, &amp; di pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7104 portione maggiore ver$o il pe$o. ilche &egrave; vero, $<*> vogliamo con$iderare etiandio la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7105 grauezza della taglia. Ma percioche cerchiamo la proportione che &egrave; fra la po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7106 $anza &amp; il pe$o, per&ograve; habbiamo trala$ciato cote$ta grauezza della taglia, laquale
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parents:
diff changeset
7107 $e alcuno vorr&agrave; anche con$iderare, alla po$$anza potr&agrave; aggiungere $orza che $ia
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parents:
diff changeset
7108 eguale alla taglia. ilche mede$imamente $i potr&agrave; o$$eruare nella corda. &amp; $i co-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7109 me habbiamo <*>&ograve; con$iderato nella decimaquinta, l'i$te$$o parimente nelle altre po-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7110 tremo con$iderare.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7111 <pb n=98>
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parents:
diff changeset
7112 <p><I>Egli &egrave; me$tieri $apere etiandio, che $i come tut-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7113 te le proportioni tra la po$$anza, &amp; il pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7114 $ono $tate ritrouate con vna $ola corda: co$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7115 ancora potranno$i le i$te$$e ritrouare con pi&ugrave;
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parents:
diff changeset
7116 corde, &amp; con pi&ugrave; taglie. come $e vorremo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7117 ritrouare la proportione molteplice $oprapar
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7118 ticolare con pi&ugrave; corde, cio&egrave; $e la proportio-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7119 ne, laquale h&agrave; il pe$o alla po$$anza che lo $o
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parents:
diff changeset
7120 $tiene $ar&agrave; doppia $e$quialtera, come cinque
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parents:
diff changeset
7121 &agrave; due; bi$ogna comporre que$ta proportione
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parents:
diff changeset
7122 da pi&ugrave; proportioni come per gratia di e$$em-
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parents:
diff changeset
7123 pio dalla proportione $e$quiquarta, che &egrave; il
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parents:
diff changeset
7124 cinque al quattro, &amp; dalla doppia, che &egrave; il
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parents:
diff changeset
7125 quattro al due. Ponga$i dunque la po$$an-</I> <marg><I>Per la</I> 21. <I>di questo.</I></marg>
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parents:
diff changeset
7126 <I>za di A che $o$tenga il pe$o B, alla qua-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7127 le il pe$o habbia la proportione di vna volta
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parents:
diff changeset
7128 &amp; vn quarto, come cinque &agrave; quattro: da</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7129 <I>poi con vn'altra corda $i troui la po$$anza
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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7130 di C, della quale $ia doppia la po$$anza di
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parents:
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7131 A. &amp; percioche il B all' A &egrave; come cin-
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parents:
diff changeset
7132 que &agrave; quattro: &amp; l' A. al C come il quat-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7133 tro al due: $ar&agrave; la po$$anza di B alla po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7134 $anza di C come il cinque al due; cio&egrave; ha-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7135 ur&agrave; la proportione doppia $e$quialtera.</I>
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parents:
diff changeset
7136 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7137 <p><I>Et &egrave; da &szlig;otare pote $i trouar' anche que$ta pro-
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parents:
diff changeset
7138 portione, $e comporremo la proportione di
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parents:
diff changeset
7139 cinque &agrave; due da pi&ugrave;, come cinque &agrave; quindici,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7140 &amp; il quindici al venti, &amp; il venti al due. Et
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7141 in que$to modo ritroueremo non $olo ogni al-
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parents:
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7142 tra proportione, ma qualunque $i $ia in mol-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7143 ti, &amp; in$initi modi ritroueremo. percioche
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parents:
diff changeset
7144 ogni proportione $i pu&ograve; comporre di propor-
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parents:
diff changeset
7145 tioni in$inite. come &egrave; manife$to nel commen-
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parents:
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7146 tario di Eutocio nella quarta propo$itione del
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parents:
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7147 $econdo libro di Archimede della s$era, &amp;
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parents:
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7148 Cilindro.</I>
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parents:
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7149 <p>Po$$iamo ancora v$are pi&ugrave; corde: &amp;
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parents:
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7150 adoperare le taglie di $otto $ola-
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parents:
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7151 mente, ouero quelle di $opra.
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parents:
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7152 <foot>B b 2</foot>
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parents:
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7153 <pb n=99>
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parents:
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7154 <p><I>Sia poi il pe$o A legato alla fune, la-
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parents:
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7155 quale $ia inuolta d'intorno alla girel-
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parents:
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7156 la della taglia di $opra, &amp; rilegata in
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parents:
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7157 B, &amp; $ia la po$$anza di C che $o
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parents:
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7158 $tenga il pe$o A; $ar&agrave; la po$$anza
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7159 di C due volte tanto quanto il pe$o</I> <marg><I>Per la</I> 15. <I>di questo.</I></marg>
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parents:
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7160 <I>A: dapoi C $ia rilegata ad vn'al-
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parents:
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7161 tra fune, laquale $ia rinuolta d'intor
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parents:
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7162 no la girella d'vn'altra taglia, &amp; ri-
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7163 legata in D; $ar&agrave; la po$$anza di E</I> <marg><I>Per la isse$ $a.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
7164 <I>due volte tanto quanto la po$$anza
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7165 di C. Per laqual co$a la po$$anza
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parents:
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7166 di E $ar&agrave; quattro volte tanto quan-
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parents:
diff changeset
7167 to il pe$o A. Et $e dauantaggio
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parents:
diff changeset
7168 lo E $i rilegher&agrave; ad vn'altra fune,
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parents:
diff changeset
7169 laquale $ia inuolta dintorno' alla gi-
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parents:
diff changeset
7170 rella d'vn'altra taglia ancora, &amp; $ia
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diff changeset
7171 rilegata in F; $ar&agrave; la po$$anza di G
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parents:
diff changeset
7172 due volte tanto quanto la po$$anza
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parents:
diff changeset
7173 di E. Adunque la po$$anza po$ta
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parents:
diff changeset
7174 in G &egrave; otto volte tanto quanto il pe
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7175 $o A; &amp; co$i in in$inito ritrouere-
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parents:
diff changeset
7176 mo $empre la po$$anza e$$ere due vol
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parents:
diff changeset
7177 te tanto quanto la po$$anza prece-
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parents:
diff changeset
7178 dente.</I>
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casties
parents:
diff changeset
7179 <fig>
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parents:
diff changeset
7180 <p><I>Ma $e in G fo$$e la po$$anza che moue,
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parents:
diff changeset
7181 $ar&agrave; lo $patio del pe$o otto volte tan
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parents:
diff changeset
7182 to quanto lo $patio della po$$anza po
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parents:
diff changeset
7183 $tain G: percioche lo $patio del pe-</I> <marg><I>Per la</I> 16. <I>di questo.</I></marg>
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parents:
diff changeset
7184 <I>$o A &egrave; due volte tanto quanto lo
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parents:
diff changeset
7185 $patio della po$$anza posta in C, &amp;
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diff changeset
7186 il C &egrave; due volte tanto quanto &egrave; lo
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diff changeset
7187 $patio di e$$o E. Per laqual co$a lo
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diff changeset
7188 $patio del pe$o A $ar&agrave; quattro vol
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parents:
diff changeset
7189 te tanto quanto lo $patio della po$$an
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parents:
diff changeset
7190 za di E. $imilmente percioche lo
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parents:
diff changeset
7191 $patio di E &egrave; due volte tanto quan-
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diff changeset
7192 to &egrave; lo $patio della po$$anza po$ta in
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parents:
diff changeset
7193 G; $ar&agrave; dunque lo $patio del pe$o A
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parents:
diff changeset
7194 otto volte tanto quanto lo $patio della
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parents:
diff changeset
7195 po$$anza po$ta in G.</I>
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parents:
diff changeset
7196 <HEAD>COROLLARIO.</HEAD>
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parents:
diff changeset
7197 <p>Da que$te co$e &egrave; manife$to, che $empre lo $patio della po$$anza
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7198 che moue ha proportione maggiore ver$o lo $patio del pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7199 mo$$o, di quel che ha il pe$o ver$o la mede$ima po$$anza.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7200 <p><I>Que$to &egrave; chiaro da quelle co$e lequali $ono $tate dette nel corollario della quarta pro-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7201 po$itione di que$to nella leua.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7202 <HEAD>PROPOSITIONE XXVII.</HEAD>
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parents:
diff changeset
7203 <HEAD>PROBLEMA.</HEAD>
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casties
parents:
diff changeset
7204 <p>Che $i moua vn pe$o dato da vna po$$anza data con le taglie.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7205 <p><I>La po$$anza data &ograve; che ella &egrave; maggiore, ouero eguale, &ograve; pure minore del pe$o dato.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7206 <p><I>Se &egrave; maggiore, all'hora la po$-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7207 $anza, $enza altro $tromen-
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parents:
diff changeset
7208 to, &ograve; fune inuolta d'intor-
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parents:
diff changeset
7209 no alla girella della taglia</I>
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parents:
diff changeset
7210 <marg><I>Per la</I> 1. <I>di questo.</I></marg> <I>appiccata di $opra, mouer&agrave;
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parents:
diff changeset
7211 il pe$o dato. percio che po$
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parents:
diff changeset
7212 $anza minore della data pe
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parents:
diff changeset
7213 $a tanto quanto il pe$o,
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parents:
diff changeset
7214 adunque la data, che &egrave; mag
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parents:
diff changeset
7215 giore mouer&agrave;. L'i$te$$o $i
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parents:
diff changeset
7216 pu&ograve; fare in tutte le propo-
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parents:
diff changeset
7217 $itioni nelle quali la po$$an-
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parents:
diff changeset
7218 za, che $o$tiene il pe$o &egrave; $ta
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parents:
diff changeset
7219 ta dimo$trata &ograve; eguale, &ograve;
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parents:
diff changeset
7220 minore del pe$o.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7221 <fig>
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casties
parents:
diff changeset
7222 <pb n=100>
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casties
parents:
diff changeset
7223 <p><I>Ma $e eguale mouer&agrave; il
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parents:
diff changeset
7224 pe$o e$$endo la fune
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casties
parents:
diff changeset
7225 inuolta d'intorno al
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casties
parents:
diff changeset
7226 la girella della ta-
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casties
parents:
diff changeset
7227 glia legata al pe$o,</I> <marg><I>Per la</I> 2. <I>di questo.</I></marg>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7228 <I>percio che la po$$an-
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parents:
diff changeset
7229 za che $o$tiene il pe
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casties
parents:
diff changeset
7230 $o &egrave; la met&agrave; del pe-
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casties
parents:
diff changeset
7231 $o. la po$$anza dun-
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casties
parents:
diff changeset
7232 que eguale al. pe$o
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casties
parents:
diff changeset
7233 mouer&agrave; il pe$o da-
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casties
parents:
diff changeset
7234 to. ilche parimen-
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casties
parents:
diff changeset
7235 te $i puote fare $e-
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parents:
diff changeset
7236 condo le propo$itio-
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casties
parents:
diff changeset
7237 ni, nellequali $i &egrave;
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casties
parents:
diff changeset
7238 mo$trato la po$$an-
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casties
parents:
diff changeset
7239 za e$$ere minore del
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casties
parents:
diff changeset
7240 pe$o.</I>
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parents:
diff changeset
7241 <fig>
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casties
parents:
diff changeset
7242 <p><I>Che $e &egrave; minore, $ia il pe$o
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casties
parents:
diff changeset
7243 dato come $e$$anta, &amp; la
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casties
parents:
diff changeset
7244 po$$anza che moue $ia da-
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casties
parents:
diff changeset
7245 ta come tredici. Troui$i
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7246 la po$$anza di A, che $o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7247 $tenga il pe$o B, laquale</I>
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casties
parents:
diff changeset
7248 <marg><I>Per la</I> 9. <I>di questo.</I></marg> <I>$ia vn quinto del pe$o B.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7249 &amp; percioche la po$$anza
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7250 di A che $o$tiene il pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7251 &egrave; come dodici; adunque
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7252 po$$anza maggiore di do-
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casties
parents:
diff changeset
7253 dici po$ta in A mouer&agrave;
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casties
parents:
diff changeset
7254 il pe$o B. Per laqual c<*>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7255 $ala po$$anza come tredi-
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casties
parents:
diff changeset
7256 ci po$ta in A mouer&agrave; il
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7257 pe$o B. che bi$ognaua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
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7258 fare.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7259 <fig>
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parents:
diff changeset
7260 <p><I>Egli &egrave; parimente da auerti-
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diff changeset
7261 re nel mouere i pe$i, che
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diff changeset
7262 la po$$anza alcuna volta
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diff changeset
7263 meglio for$e moue mouen-
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diff changeset
7264 do$i in gi&ugrave;, che mouendo$i
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diff changeset
7265 in s&ugrave;. come volga$i dauan
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diff changeset
7266 taggio la fune d'intorno ad
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diff changeset
7267 vn'altra girella della ta-
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parents:
diff changeset
7268 glia di $opra, il cui centro
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parents:
diff changeset
7269 $ia C, &amp; la fune per-
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parents:
diff changeset
7270 uenga in D; $ar&agrave; la po$-</I>
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diff changeset
7271 <marg><I>Per la</I> 5. <I>di questo.</I></marg> <I>$anza di D $o$tenente il
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diff changeset
7272 pe$o B $imilmente dodi-
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parents:
diff changeset
7273 ci, $i come ella erain A.
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diff changeset
7274 Per&ograve; la po$$anza di tredici
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diff changeset
7275 po$ta in D mouer&agrave; il pe-
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diff changeset
7276 $o B. &amp; percioche $i
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parents:
diff changeset
7277 moue in gi&ugrave;, for$e tirer&agrave;
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parents:
diff changeset
7278 pi&ugrave; facilmente, che $e fo$-
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diff changeset
7279 $e po$ta in A, ma il tem
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7280 po &egrave; l'i$te$$o, $i come egli
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diff changeset
7281 era etiandio in A.</I>
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diff changeset
7282 <pb n=101>
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7283 <HEAD>PROPOSITIONE XXVIII.</HEAD>
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7284 <HEAD>PROBLEMA.</HEAD>
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7285 <p>Sia propo$to &agrave; noi il fare, che la po$$anza mouente il pe$o, &amp; il
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diff changeset
7286 pe$o $i mouano per gli
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parents:
diff changeset
7287 $patij dati, i quali $ia-
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parents:
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7288 no fra loro commen-
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parents:
diff changeset
7289 $urabili.
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parents:
diff changeset
7290 <p><I>Sia dato lo $patio della po$$anza</I> <marg><I>Per la.</I> 22. <I>di questo.</I></marg>
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7291 <I>come tre, &amp; del pe$o come
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parents:
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7292 quattro. ritroui$i la po$$anza
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7293 di A $o$tenente il pe$o B, la
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diff changeset
7294 quale $ia vna volta, &amp; vn ter-
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7295 zo quanto il pe$o, come quat-
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parents:
diff changeset
7296 tro &agrave; tre. Se dunque in A</I> <marg><I>Per <*>istof-fa.</I></marg>
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diff changeset
7297 <I>fo$$e la po$$anza mouente il
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7298 pe$o; $arebbe lo $patio del pe-
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parents:
diff changeset
7299 $o vna volta, &amp; vn terzo
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parents:
diff changeset
7300 quanto lo $patio della po$$an-
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parents:
diff changeset
7301 za, cio&egrave; come quattro &agrave; tre;
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diff changeset
7302 che bi$ognaua fare.</I>
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parents:
diff changeset
7303 <fig>
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parents:
diff changeset
7304 <p><I>Ci&ograve; po$$iamo menar ad effetto con
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7305 vna $ola fune per le co$e det-
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7306 te nella vige$ima $econda, &amp;
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7307 nella vige$ima quinta di que-
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parents:
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7308 $to. che $e ci&ograve; vorremo fare
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parents:
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7309 con pi&ugrave; funi, potremo porlo
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parents:
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7310 in opra non $olo con molti,
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parents:
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7311 ma con modi infiniti, come di
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parents:
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7312 $opra &egrave; detto. Per laqual co-
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parents:
diff changeset
7313 $a ci&ograve; ben po$siamo affermare,</I> <marg><I>Nella</I> 26. <I>di questo.</I></marg>
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parents:
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7314 <I>che pare co$a marauiglio$a,
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parents:
diff changeset
7315 cio&egrave;.</I>
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diff changeset
7316 <HEAD>CROLLARIO I.</HEAD>
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7317 <p>Da que$te co$e e$$ere manife$to, Qualunque data proportione
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parents:
diff changeset
7318 ne i numeri tra il pe$o, &amp; la po$$anza; &amp; tra lo $patio del pe$o
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parents:
diff changeset
7319 mo$$o, &amp; lo $patio della po$$anza mo$$a; poter$i trouare con
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parents:
diff changeset
7320 le taglie in modi infiniti.
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parents:
diff changeset
7321 <HEAD>COROLLARIO II.</HEAD>
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parents:
diff changeset
7322 <p>Dalle co$e dette &egrave; manife$to etiandio che quanto pi&ugrave; facilmen-
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parents:
diff changeset
7323 te $i moue il pe$o, tanto maggiore e$$ere etiandio il tempo;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7324 ma quanto pi&ugrave; difficilmente, tanto minore e$$ere: &amp; co$i per
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parents:
diff changeset
7325 lo contrario.
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parents:
diff changeset
7326 <HEAD>IL FINE DELLA TAGLIA.</HEAD>
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parents:
diff changeset
7327 <pb n=102>
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parents:
diff changeset
7328 <HEAD>DELL'ASSE</HEAD>
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parents:
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7329 <HEAD>NELLA ROTA.</HEAD>
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parents:
diff changeset
7330 <fig>
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parents:
diff changeset
7331 <p>La fabrica, &amp; compo$itione di que$to i$trumento
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parents:
diff changeset
7332 in$egna Pappo nell'ottauo libro delle raccolte ma-
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parents:
diff changeset
7333 tematiche: &amp; chiama a$$e AB, &amp; timpano CD
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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7334 d'intorno al centro mede$imo (che noi diremo ro-
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parents:
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7335 ta) &amp; noma$citale quei ba$toni i quali $ono fic-
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parents:
diff changeset
7336 cati ne'buchi della rota notate per EFGH, &amp; le altre $uc-
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7337 ce$$iuamente, che noi pur diremo raggi. talche la po$$anza,
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parents:
diff changeset
7338 <foot><I>Cc</I> 2</foot>
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7339 <pb>
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parents:
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7340 laquale &egrave; $empre ne i raggi, come in F, mentre ella volge
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parents:
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7341 intorno la rota, &amp; l'a$$e, moua anco in s&ugrave; il pe$o K appicca-
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parents:
diff changeset
7342 to all'a$$e con la corda LM riuolta d'intorno all'a$$e. A noi
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7343 re$ta dunque, di mo$trare, perche i gran pe$i da piccola forza,
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parents:
diff changeset
7344 <fig>
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parents:
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7345 &amp; in che modo etiandio $i mouano con que$to i$trumento:
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7346 &amp; di pi&ugrave; manife$tare la ragione del tempo, &amp; dello $patio del-
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parents:
diff changeset
7347 la po$$anza mouente, &amp; del pe$o mo$$o fra loro, &amp; ridurre l'v-
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parents:
diff changeset
7348 $o di cote$to i$trumento alla leua.
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parents:
diff changeset
7349 <pb n=103>
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7350 <HEAD>PROPOSITIONE I.</HEAD>
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parents:
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7351 <p>La po$$anza $o$tenente il pe$o con l'a$$e nella rota, ha la propor-
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parents:
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7352 tione mede$ima al pe$o, che il mezo diametro dell'a$$e al me-
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parents:
diff changeset
7353 zo diametro della rota in$ieme co'l raggio.
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parents:
diff changeset
7354 <fig>
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casties
parents:
diff changeset
7355 <p><I>Sia il diametro dell'a$$e AB, &amp; il $uo centro C; $ia il diametro della rota DCE
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diff changeset
7356 d'intorno al centro mede$imo; &amp; $iano AB DE nell i$te$$a linea retta; $iano
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7357 dopo li raggi eguali tra loro, &amp; egualmente di$tanti DF GH, &amp; gli altri ne' bu-
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7358 chi della rota; &amp; $ia FE egualmente di$tante dall'orizonte, &amp; il pe$o K $ia
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7359 <pb>
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diff changeset
7360 appiccato alla corda BL volubile d'intorno all'a$$e. &amp; la po$$anza po$ta in F
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7361 $o$tenga il pe$o K. Dico che la po$$anza in F co$i $i h&agrave; al pe$o K, come CB
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7362 &agrave; CF. Faccia$i come CF &agrave; CB, co$i il pe$o K ad vn altro pe$o come M, il
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7363 quale $ia appi<*>ato in F. &amp; percioche i pe$i MK $ono appiccati in - FB; $ar&agrave;
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7364 FB come leua, ouero bilancia; ma percioche il C &egrave; punto immobile, d'intorno</I>
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diff changeset
7365 <fig>
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diff changeset
7366 <marg><I>Per la</I> 6. <I>del</I> 1. <I>d' Ar chimede del le co$e che pe$anoegual mense.</I></marg> <I>alquale l'a$$e, &amp; la rota $i riuolgono; $ar&agrave; C il $o$tegno della leua FB, ouero il
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7367 centro della bilancia. &amp; per e$$ere co$i CF &agrave; CB come K ad M, i pe$i KM
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diff changeset
7368 pe$eranno egualmente. La po$$anza dunque di F $o$tenente il pe$o K contra-
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diff changeset
7369 pe$er&agrave; egualmente con e$$o pe$o K accioche egli non chini al ba$$o, &amp; $ar&agrave; eguale
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7370 ad M. Percioche la po$$anza opera il mede$imo che il pe$o M. dunque il pe$o K</I>
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diff changeset
7371 <pb n=104>
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diff changeset
7372 <I>$ar&agrave; alla po$$anza di F, come CF &agrave; CB, &amp; conuertendo la po$$anza $ar&agrave; al
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diff changeset
7373 pe$o, come CB &agrave; CF, cio&egrave; il mezo diametro dell'a$$e al mezo diametro della rota</I> <marg><I>Per lo corol lario della</I> 4. <I>del</I> 5.</marg>
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diff changeset
7374 <I>in$ieme co'l raggio DF. $imilmente mo$trera$$i anco, che $e la po$$anza $o$tenente
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7375 il pe$o fo$$e in Q, all'hora $o$terrebbe con la leua CQ; &amp; haurebbe quella pro-</I> <marg><I>Per la</I> 2. <I>di questo della leua.</I></marg>
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7376 <I>portione al pe$o, che CB haue &agrave; CQ; cio&egrave; il mezo diametro dell'a$$e al mezo dia-
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7377 metro della rota in$ieme co'l raggio EQ, che bi$ognaua dimo$trare.</I>
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7378 <HEAD>COROLLARIO.</HEAD>
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7379 <p>Egli &egrave; manife$to che la po$$anza $empre &egrave; minore del pe$o.
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7380 <p><I>Percio che il mezo diametro dell'a$$e $empre &egrave; minore del mezo diametro della rota.
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7381 &amp; la po$$anza in tanto &egrave; minore del pe$o, in quanto il mezo diametro dell'a$$e &egrave; mi
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7382 nore del mezo diametro della rota in$ieme co'l raggio. Per laqual co$a quanto &egrave; pi&ugrave;
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7383 lungo CF, ouero CQ; &amp; quanto &egrave; pi&ugrave; corto CB, tanto anco $empre minore po$$an
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7384 za po$ta in F, ouero in Q, $o$tenter&agrave; il pe$o K. percioche quanto minore &egrave; CB,
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7385 tanto il mezo diametro dell'a$$e, haur&agrave; proportione minore al mezo diametro della
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7386 rota in$ieme co'l raggio.</I>
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7387 <p><I>In que$to loco occorre da e$$ere con$iderato, che $e il pe$o $ar&agrave; appiccato in vn'altro
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7388 raggio, come in T, che $o$tenga il pe$o K, in modo cio&egrave;, che il pe$o appiccato in
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7389 T, &amp; il pe$o K po$to d'intorno all'a$$e rimangano; $ar&agrave; il pe$o in T pi&ugrave; graue del
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7390 pe$o M appiccato in F. Percioche $ia congiunta TB, &amp; dal punto C $ia
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7391 tirata la CI &agrave; piombo dell'orizonte, laquale tagli la TB in I; &amp; alla fine con
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7392 giunga$i TC, laquale $ar&agrave; eguale &agrave; CF. Et percioche i pe$i $ono appiccati in
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7393 TB $i haueranno in modo come $e haue$$ero i centri delle grauezze loro in TB,
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7394 come dianzi fu detto. &amp; percbe rimangono, $ar&agrave; il punto I per la prima di que-
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diff changeset
7395 $to della bilancia, il centro della grauezza di ambidue in$ieme, per e$$ere CI &agrave; piom</I> <marg><I>Per la</I> 29. <I>del primo.</I></marg>
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7396 <I>bo dell'orizonte. Ma percioche l'angolo BCI &egrave; retto, $ara BIC acuto, &amp; la
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7397 linea BI $ar&agrave; maggiore di e$$a BC. Per laqual co$a l'angolo CIT $ar&agrave; ottu$o,</I> <marg><I>Per la</I> 13. <I>del primo.</I></marg>
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7398 <I>&amp; perci&ograve; la linea CT $ar&agrave; maggiore di TI. Et concio$ia che CT $ia maggiore
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7399 di TI, &amp; IB maggiore di BC; haur&agrave; TC proportione maggiore &agrave; CB,
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7400 che TI ad IB; &amp; conuertendo BC haur&agrave; proportione minore &agrave; CT, cio&egrave;
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7401 &agrave; CF, che BI ad IT, come per la vige$ima$e$ta del quinto de gli elementi;
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7402 ($econdo il Commandino) &egrave; mani$e$to. Ma percioche il punto I &egrave; centro della
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7403 grauezza de' pe$i $tanti in TB, $ar&agrave; il pe$o po$to in T al pe$o po$to in B, come</I> <marg><I>Per la</I> 6. <I>del</I> 1. <I>di Ar chimede del le co$e che pe$ano egual mente.</I></marg>
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7404 <I>BI ad IT. ma il pe$o in F $i h&agrave; al pe$o mede$imo in B, come BC &agrave; CF;
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7405 dunque il pe$o in T haur&agrave; proportione maggiore al pe$o in B, che il pe$o in F
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7406 a'li$te$$o pe$o in B. adunque $ar&agrave; pi&ugrave; graue il pe$o in T, che il pe$o in F.</I>
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7407 <p><I>Che $e in loco del pe$o in T $i porr&agrave; vna po$$anza animata, che $o$tenga il pe$o K,
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7408 laquale in maniera $i inchini, come $e vole$$e andare al centro del mondo, come di</I> <marg><I>Per la</I> 10. <I>del</I> 5.</marg>
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7409 <I>$ua propria natura $&agrave; il pe$o appiccato in T; $ar&agrave; que$ta $te$$a eguale al pe$o ap-
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7410 <pb>
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7411 piccato in T, altramente non $o$tentarebbe, laquale veramente $ar&agrave; maggiore
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7412 della po$$anza collocata in F. percioche $i come $i ha il pe$o di T al pe$o di F,
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7413 co$i ha$$i anco la po$$anza di T alla po$$anza di F, per e$$ere le po$$anze eguali
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7414 a' pe$i. Ma $e cia$cheduna po$$anza pre$a $eparatamente $o$tenente il pe$o tanto
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7415 in T quanto in F, $econdo la circonferenza THFN, $i vole$$e mouere, come
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7416 $e il raggio fo$$e pre$o con vna mano; all'hora la mede$ima po$$anza po$ta in F,
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7417 ouero in T, potr&agrave; $o$tenere l'i$te$$o pe$o K; concio$ia, che ponga$i pure nella $tre
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7418 mit&agrave; di qual $i voglia raggio, $empre verr&agrave; ad e$$ere egualmente di$tante dall'i$te$-
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7419 $o centro C, &amp; ad hauere la $ua inclinatione $econdo la circon$erenza i$te$$a egual
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7420 mente di$tante $empre dal centro mede$imo. ne come fa il pe$o di $ua propria na-
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7421 tura pi&ugrave; de$idera e$$ere portata nel centro, che mouer$i in cerchio: percioche riguar-
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7422 da l'vno, &amp; l'altro, ouero qual $i voglia altro mouimento $enza veruna differenza
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7423 in tutto. Per laqual co$a non i$ta il fatto nel modo i$te$$o, $e ouero i pe$i, ouero le
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7424 po$$anze animate $aranno po$te ne' luoghi mede$imi per far l'i$te$$o officio.</I>
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7425 <p><I>Mala po$$anza moue il pe$o con la leua FB, cio&egrave; mentre la po$$anza di F volge in-
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7426 torno la rota, gira intorno anche l'a$$e, &amp; FB $i f&agrave; come leua, il cui $o$tegno &egrave; C;
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7427 la po$$anza mouente in F, &amp; il pe$o &egrave; appiccato in B: &amp; mentre il punto F
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7428 peruiene in N il punto H $ar&agrave; in F, &amp; il punto B $ar&agrave; in O; per modo che
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7429 la tirata linea NO pa$$i per C; &amp; nell'i$te$$o tempo il pe$o K $ar&agrave; mo$$o in P,
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7430 per modo che OBP $ia eguale ad e$$o BL, e$$endo la i$te$$a corda.</I>
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7431 <p><I>Dapoi dalla quarta di que$to della leua ageuolmente caueremo co$i e$$ere lo $patio del
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diff changeset
7432 la po$$anza che moue allo $patio del pe$o mo$$o, come il mezo diametro della rota
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diff changeset
7433 in$ieme co'l raggio al mezo diametro dell'a$$e, cio&egrave; come CF &agrave; CB; per e$$ere</I>
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diff changeset
7434 <marg><I>Per la</I> 4. <I>di questo della leua.</I></marg> <I>la circonferenza FN ver$o BO, come CF &agrave; CB. Et percioche BL &egrave; egua
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diff changeset
7435 le ad OBP, leuata via la commune BP, $ar&agrave; OB eguale ad e$$a PL. Per la qual
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diff changeset
7436 co$a FN che &egrave; lo $patio della po$$anza ver$o PL $patio del pe$o, $ar&agrave; come CF
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7437 &agrave; CB, cio&egrave; il mezo diametro della rota in$ieme co'l raggio al mezo diametro del-
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diff changeset
7438 <*>a$$e. Laqual co$a parimente mo$trera$$i, $tando la po$$anza in Q, ouero in qual $i
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diff changeset
7439 voglia altro raggio, come in S. concio$ia, che e$$endo li raggi fra lcro eguali, &amp;
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diff changeset
7440 egualmente di$tanti; $ia doue $i voglia la po$$anza mo$$a con velocit&agrave; eguale, tra-
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diff changeset
7441 pa$$er&agrave; $empre in tempo eguale $patio eguale, cio&egrave; da Q in R, ouero da S in T
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diff changeset
7442 $i mouer&agrave; nel mede$imo tempo, che da F in N. ma in quel tempo che la po$$anza
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diff changeset
7443 $i moue da F in N, nel mede$imo in tutto anco il pe$o K da L $i moue in P.
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diff changeset
7444 adunque $ia doue $i voglia la po$$anza, $ar&agrave; lo $patio della po$$anza allo $patio del
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diff changeset
7445 pe$o mo$$o, come CF &agrave; CB, cio&egrave; come il mezo diametro della rota co'l raggio al
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diff changeset
7446 mezo diametro dell'a$$e.</I>
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diff changeset
7447 <pb n=105>
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diff changeset
7448 <HEAD>COROLLARIO I.</HEAD>
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7449 <p>Da que$te co$e &egrave; manife$to, che co$i &egrave; il pe$o alla po$$anza $o$te-
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diff changeset
7450 nente il pe$o, come lo $patio della po$$anza mouente allo $pa
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7451 tio del pe$o mo$$o.
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diff changeset
7452 <fig>
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diff changeset
7453 <HEAD>COROLLARIO II.</HEAD>
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7454 <p>Egli &egrave; manife$to etiandio, che lo $patio della po$$anza mouen-
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7455 te h&agrave; $empre maggiore proportione allo $patio del pe$o mo$-
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diff changeset
7456 $o, che il pe$o alla $te$$a po$$anza.
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7457 <foot><I>Dd</I></foot>
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7458 <pb>
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diff changeset
7459 <p><I>Oltre &agrave; ci&ograve; quanto il cerchio FHN d'intorno &agrave; i raggi &egrave; pi&ugrave; grande, tanto anco $i
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7460 con$umer&agrave; pi&ugrave; tempo in mouere il pe$o, pur che la po$$anza $i moua con eguale ve-</I>
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diff changeset
7461 <marg><I>Per la</I> 23. <I>dell'estano li bre di Pappe.</I></marg> <I>locit&agrave;; &amp; il tempo tanto $ar&agrave; maggiore quanto il diametro dell'vno $ar&agrave; maggiore
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7462 del diametro dell'altro; percioche le circonferenze de'cerchi $i hanno come i diame
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7463 tri. &amp; concio$ia, che per la trige$ima $e$ta del quarto libro di Pappo delle raccolte</I>
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7464 <fig>
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7465 <I>matematiche po$$iamo ritrouare le circonferenze eguali di due cerchi di$uguali; per-
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7466 ci&ograve; ritroueremo anche il tempo &agrave; que$to modo delle portioni di$uguali de' cerchi. Ma
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7467 per lo contrario quanto $ar&agrave; maggiore la circonferenza dell'a$$e, il pe$o mouera$$i
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7468 pi&ugrave; pre$to in s&ugrave;, percioche maggior parte della corda BL in vno giro compiuto, $i
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7469 riuolge d'intorno al cerchio ABO, che $e fo$$e minore, per e$$ere la corda inuolta
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7470 eguale alla circonferenza del cerchio, d'intorno alquale $i riuolge.</I>
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7471 <pb n=106>
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7472 <HEAD>COROLLARIO.</HEAD>
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7473 <p>Da que$te co$e &egrave; manife$to, che quanto pi&ugrave; ageuolmente $i mo
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7474 ue il pe$o, tanto il tempo &egrave; anco maggiore; &amp; quanto pi&ugrave; ma-
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7475 lageuolmente, tanto il tempo e$$ere minore. &amp; co$i per lo
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7476 contrario.
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7477 <HEAD>PROPOSITIONE II.</HEAD>
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7478 <HEAD>PROBLEMA.</HEAD>
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7479 <p>Far che $i moua vn dato pe$o, con l'a$$e nella rota da vna data
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7480 po$$anza.
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7481 <p><I>Sia il dato pe$o $e$$anta, &amp; la po$$anza come dieci. Faccia$i vna linea retta AB, laquale
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7482 $i diuida in C, $i fattamente che AC habbia la proportione i$te$$a &agrave; CB, che ha
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7483 $e$$anta &agrave; diece. &amp; $e CB
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7484 fo$$e il mezo diametro del-
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7485 l'a$$e, &amp; CA il mezo dia</I> <marg><I>Per la prece dente.</I></marg>
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7486 <I>metro della rota co'raggi;
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7487 egli &egrave; chiaro, che la po$$an-
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7488 za come dieci po$ta in A</I> <marg><I>Per il lemma nella pri ma di questo della leua.</I></marg>
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7489 <I>pe$erebbe egualmente co'l</I>
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7490 <fig>
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7491 <I>pe$o $e$$anta po$to in B. ma pigli$i tra BC qual $i voglia punto, &amp; $ia D; &amp;
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7492 faccia$i BD il mezo diametro dell'a$$e, &amp; DA il mezo diametro della rota co'rag
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7493 gi, &amp; ponga$i il pe$o $e$$anta in B con vna corda inuolta d'intorno all'a$$e, &amp; la po$</I> <marg><I>Per la</I> 11. <I>di questo della leua.,</I></marg>
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7494 <I>$anza in A. Hor percioche AD ha proportione maggiore &agrave; DB, che AC &agrave;
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7495 CB: haur &agrave; proportione maggiore AD &agrave; DB, che il pe$o $e$$anta appiccato in
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7496 B alla po$$anza di dieci posta in A. Per laqual co$a la po$$anza di A mouer&agrave; il
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7497 pe$o di $e$$anta con l'a$$e nella rota, il mezo diametro delquale &egrave; BD, &amp; DA &egrave;
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7498 il mezo diametro della rota co'raggi. ilche era da far$i.</I>
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7499 <foot><I>Dd</I> 2</foot>
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7500 <pb>
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7501 <HEAD>Altramente.</HEAD>
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7502 <p>Ma Mecanicamente meglio $ar&agrave; in que$to modo.
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7503 <p><I>Ponga$i l'a$$e, il cui mezo diametro $ia BD, &amp; il centro $uo C, ilquale a$$e $ta-
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7504 tuiremo maggiore, &ograve; minore, come la grandezza, &amp; grauezza del pe$o ricerca.
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7505 Allunghi$i po$cia la li-
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7506 nea BD fin ad A; &amp;
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7507 faccia$i BC &agrave; CA, co
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7508 me diece &agrave; $e$$anta., &amp;
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7509 $e CA fo$$e il mezo dia
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7510 metro della rota co'rag
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7511 gi, la po$$anza di diece</I>
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7512 <fig>
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7513 <I>po$ta in A pe$erebbe egualmente co'l pe$o di $e$$anta po$to in B. Ma allunghi$i,
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7514 BA dalla parte di A, &amp; in que$ta allungata linea prenda$i qual $i voglia punto
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7515 come E, &amp; faccia$i CE il mezo diametro della rota co'raggi; &amp; pong a$i la po$-
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7516 $anza di diece in E; haur&agrave; EC a CB proportione maggiore, che il pe$o $e$$anta
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diff changeset
7517 po$to in B alla po$$anza di diece po$ta in E. Dunque la po$$anza di diece po$ta in
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diff changeset
7518 E mouer&agrave; il pe$o $e$$anta appiccato in B, con la corda inuolta d'intorno all'a$$e, il
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diff changeset
7519 cui mezo diametro &egrave; CB, &amp; CE &egrave; il mezo diametro della rota co i raggi. che bi-
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diff changeset
7520 $ognaua fare.</I>
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diff changeset
7521 <p>Sotto que$ta $orte d'i$trumento $ono gli argani, i molinelli, le tri
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diff changeset
7522 uelle, i timpani, &ograve; rote co' $uoi a$$i, &ograve; $iano dentate, &ograve; n&ograve;, &amp;
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diff changeset
7523 $imili.
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diff changeset
7524 <p><I>Ma la triuella tiene anco non $o che della vite; pero che mentre moue il pe$o, cio&egrave; men-
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diff changeset
7525 tre fora, per $ua qua$i natura $empre trapa$$a vi&egrave; pi&ugrave; oltre: percioche ha qua$i le
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diff changeset
7526 helici de$critte come d'intorno ad vn cono. ma perche ella ha la cima acuta, $i puo-
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diff changeset
7527 te anche ridurre commodamente alla ragione del cuneo.</I>
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diff changeset
7528 <pb n=107>
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diff changeset
7529 <fig>
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diff changeset
7530 <p>L'Autore h&agrave; qui me$$o que$te cinque figure, lequali rappre$entano cinque i$trumen
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diff changeset
7531 ti da mouer pe$i, iquali $i riducono $otto que$ta facult&agrave;, accio che $i vegga es$i e$-
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parents:
diff changeset
7532 $er vna co$a mede$ima con l'i$trumento dell'a$$e nella rota gi&agrave; dichiarato; &amp; vi
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diff changeset
7533 h&agrave; po$to le lettere ABC con le $ue linee, per dar ad intendere, che il pe$o h&agrave; la
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parents:
diff changeset
7534 proportione mede$ima alla po$$anza, che lo $o$tiene, che h&agrave; AC &agrave; CB, &amp; $e
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diff changeset
7535 $ar&agrave; mo$$o il pe$o da vna po$$anza mouente, lo $patio della po$$anza $ar&agrave; $imil-
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diff changeset
7536 mente allo $patio del pe$o, come AC &agrave; CB; laqual po$$anza deue$i intendere
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parents:
diff changeset
7537 po$ta in cima de i manichi delle $tanghette di$co$to dal centro tanto quanto &egrave;
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diff changeset
7538 CA. Il pe$o has$i poi da intendere legato ad vna corda, che $ia auolta d'intorno
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parents:
diff changeset
7539 all'a$$e, ilquale $ar&agrave; lontano dal centro tanto quanto &egrave; CB: &amp; co$i per le co$e
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diff changeset
7540 dette in que$to Trattato, la po$$anza che $o$tien haur&agrave; quella proportione al pe$o,
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diff changeset
7541 <*>e ha CB &agrave; CA. Con $imile modo s'ha da intendere la figura, che h&agrave; il timpano,
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7542 con$iderando che $e la forza fo$$e nella $tremit&agrave; del timpano, &amp; il pe$o $arebbe
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parents:
diff changeset
7543 auolto d'intorno all'a$$e. Quanto alla triuella, &ograve; $ucchiello che $i nomi, per e$-
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diff changeset
7544 $ore vn'i$trumento fatto non per $o$tenere, ma per mouere, egli &egrave; bi$ogno, che
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7545 la po$$anza habbia proportione maggiore al pe$o di quel che ha CB &agrave; CA per
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7546 la vndecima propo$itione di que$to nella leua.
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7547 <HEAD>IL FINE DE LL'ASSE NELLA ROTA.</HEAD>
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parents:
diff changeset
7548 <HEAD>DEL CVNEO.</HEAD>
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diff changeset
7549 <fig>
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parents:
diff changeset
7550 <p>Aristotele nelle que$tioni mecaniche
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7551 nella que$tione 17. afferma, che il cuneo nel
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7552 fendere vn pe$o fa l'officio totalmente di due le
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7553 ue contrarie l'vna all'altra fra loro in que$to
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7554 modo.
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parents:
diff changeset
7555 <p><I>Sia il cuneo ABC, &amp; la $ua cima B, &amp; $ia AB eguale &agrave; BC, &amp; quel che s'ha
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parents:
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7556 da fendere $ia DE
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parents:
diff changeset
7557 FG; &amp; $ia la par
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parents:
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7558 te del cuneo HBK
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7559 fra DE FG, &amp;
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7560 HB $ia eguale ad
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parents:
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7561 e$$a BK. Percuo-
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parents:
diff changeset
7562 ta$i, come $uol far$i,
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parents:
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7563 il cuneo in AC,
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7564 mentre il cuneo vi&egrave;
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parents:
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7565 perco$$o in AC, $i
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parents:
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7566 f&agrave; AB leua, il cui
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parents:
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7567 $o$tegno &egrave; in H, &amp;
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parents:
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7568 il pe$o in B. &amp; nel
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parents:
diff changeset
7569 modo i$te$$o CB $i
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parents:
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7570 fa leua, il cui $o$te-
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parents:
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7571 gno &egrave; K, &amp; il pe-
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parents:
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7572 $o $imilmente in B.
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parents:
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7573 Ma mentre il cu-
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parents:
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7574 neo &egrave; perco$$o, egli
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parents:
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7575 entra in e$$o DE</I>
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parents:
diff changeset
7576 <fig>
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parents:
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7577 <I>FG anco con portione di $e maggiore di quel che fo$$e prima: &amp; $ia questa por-
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parents:
diff changeset
7578 tione MBL; &amp; $ia MB eguale ad e$$a BL. &amp; per e$$ere MB, &amp; BL mag-
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parents:
diff changeset
7579 giori di HB BK, $ar&agrave; anco ML maggiore di HK. Mentre dunque ML $ar&agrave;
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parents:
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7580 nel $ito di HK; egli &egrave; me$tieri che la fe$$a $i faccia maggiore; &amp; che D $i moua</I>
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parents:
diff changeset
7581 <pb n=108>
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parents:
diff changeset
7582 <I>ver$o O, &amp; G ver$o N; &amp; quanto maggior parte del cuneo entra fra DEFG,
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parents:
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7583 tanto maggior fe$$a $i $accia; &amp; DG $empre pi&ugrave; $aranno cacciati ver$o ON.
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parents:
diff changeset
7584 dunque la parte KG che $i fende mouera$$i dalla leua AB, ilcui $o$tegno &egrave; in H,
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parents:
diff changeset
7585 &amp; il pe$o in B; $iche il punto B di e$$a leua AB cacci la parte KG: &amp; la parte
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parents:
diff changeset
7586 HD mouera$$i dalla leua CB, il cui $o$tegno &egrave; K, $i che B con la leua CB cacci
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parents:
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7587 la parte HD.</I>
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diff changeset
7588 <p>Ma trouando$i tre maniere di leue, come &egrave; $tato di $opra mo-
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parents:
diff changeset
7589 $trato. per&ograve; $ar&agrave; for$e pi&ugrave; conueneuole con$iderare il cuneo
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parents:
diff changeset
7590 in que$to modo.
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parents:
diff changeset
7591 <p><I>Po$te le co$e iste$$e, intenda$i la leua AB, &amp; il $o$tegno $uo B, &amp; il pe$o in H, come
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parents:
diff changeset
7592 nella $econda di questo nella leua dicemmo. $imilmente $ia la leua CB co'l $uo
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parents:
diff changeset
7593 $o$tegno B, &amp; il pe$o in K; $iche la parte HD $i moua dalla leua AB, il
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parents:
diff changeset
7594 cui $o$tegno &egrave; B, &amp; il pe$o in H; $iche il punto H di e$$a leua AB cacci la
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parents:
diff changeset
7595 parte HD. &amp; con modo $imile la parte KG moua$i dalla leua CB, il cut $o$te-
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parents:
diff changeset
7596 gno &egrave; B, &amp; il pe$o in K, $iche il K di e$$a leua CB mouala parte KG. ilche
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parents:
diff changeset
7597 $ar&agrave; $or$e pi&ugrave; conforme alla ragione.</I>
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parents:
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7598 <p><I>Percioche $ia il cuneo ABC; &amp; $iano due pe$i $eparati DEFG, &amp; HIKL, fra
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parents:
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7599 quali $ia la parte DBH del cuneo, la cui cima B tenga il mezo tral'vno, &amp; l'al-
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parents:
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7600 tro $ito. Percota$i il cu
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parents:
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7601 neo in modo, che anche
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parents:
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7602 dauantaggio pi&ugrave; $ia cac
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parents:
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7603 ciato fra i pe$i, come pri
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parents:
diff changeset
7604 ma&egrave; stato detto; per-
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parents:
diff changeset
7605 cioche $ono que$ti pe$i
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diff changeset
7606 come $e $o$$ero vno con-
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parents:
diff changeset
7607 tinuo $olamente GF
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parents:
diff changeset
7608 KL, che bi$ogna$$e fen
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parents:
diff changeset
7609 dere: percioche nel mo-
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parents:
diff changeset
7610 do iste$$o la parte DG
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parents:
diff changeset
7611 mentre il cuneo &egrave; pi&ugrave; ol
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parents:
diff changeset
7612 tre cacciato, $i mouer&agrave;
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parents:
diff changeset
7613 ver$o M, &amp; la parte
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parents:
diff changeset
7614 HL ver$o N. Moua$i
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parents:
diff changeset
7615 dunque la parte DG
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parents:
diff changeset
7616 ver$o M, &amp; la parte
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parents:
diff changeset
7617 HL ver$o N; &amp; il B</I>
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parents:
diff changeset
7618 <fig>
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parents:
diff changeset
7619 <I>mentre trapa$$a pi&ugrave; oltre, $empre rimanga nel mezo tra l'vn pe$o, &amp; l'altro. Hor
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parents:
diff changeset
7620 mentre D G &egrave; mo$$o dal cuneo in uer$o M; egli &egrave; manife$to, che B non moue la
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parents:
diff changeset
7621 parte DG inuer$o M con la leua CB, il cui $o$tegno &egrave; H, perche il punto B non
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parents:
diff changeset
7622 tocca il pe$o; ma DG mouera&szlig;i dal punto D della leua con e$$a leua AB, che ha
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parents:
diff changeset
7623 per $o$tegno B; pereche il punto D tocca il pe$o. &amp; gli i$trumenti mouono per
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parents:
diff changeset
7624 toccamento. $imilmente HL mouera&szlig;i da H con la leua CB, che ha per $o$te-
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parents:
diff changeset
7625 gno B; &amp; ambedue le leue $i fanno re$i$tenza l'vna all'altra fra loro in B, talche
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parents:
diff changeset
7626 B faccia pi&ugrave; tosto officio di $o$tegno, che di mouere il pe$o. laqual co$a anco ma-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7627 nife$tera&szlig;i in que$ta maniera.</I>
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parents:
diff changeset
7628 <pb n=109>
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parents:
diff changeset
7629 <p><I>Sia quel che s'ha da fendere vnparallelo grammo rettangolo ABCD; &amp; $iano due
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parents:
diff changeset
7630 leue eguali EF GF, &amp; le parti delle leue HF KF $iano tra AB CD; &amp; $ia
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parents:
diff changeset
7631 HF eguale ad FK, &amp; $ia HA
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parents:
diff changeset
7632 eguale &agrave; KB. &amp; faccia me$tieri
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parents:
diff changeset
7633 con le leue EF FG fendere AB
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parents:
diff changeset
7634 CD $enza perco$$a, cio&egrave; $iano le
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parents:
diff changeset
7635 po$$anze mouenti in EG eguali.
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parents:
diff changeset
7636 Ma per e$$ere fe$$a AB CD, egli
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parents:
diff changeset
7637 &egrave; me$tieri che la parte HA $i mo
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parents:
diff changeset
7638 ua ver$o M; &amp; KB ver$o N:
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parents:
diff changeset
7639 ma mentre le leue $i mouono, co-
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parents:
diff changeset
7640 me per e$$empio l'vna in M, &amp;
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parents:
diff changeset
7641 l'altrain N; egli &egrave; nece$$ario,
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parents:
diff changeset
7642 che il punto F rimanga immobi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7643 le, perche in e$$o $i fa l'incontro del
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parents:
diff changeset
7644 le leue. Per laqual co$a F $ar&agrave; il
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parents:
diff changeset
7645 $o$tegno dell'vna, &amp; l'altra leua;
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parents:
diff changeset
7646 &amp; FG mouer&agrave; la parte KB, il</I>
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parents:
diff changeset
7647 <fig>
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casties
parents:
diff changeset
7648 <I>cui $o$tegno $ar&agrave; F, &amp; la po$$anza mouente in G; &amp; il pe$o in K. $imilmente
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7649 la parte HA mouera&szlig;i dalla leua EF, il cui $o$tegno &egrave; F, &amp; la po$$anza in E,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7650 &amp; il pe$o in H.</I>
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parents:
diff changeset
7651 <p><I>Che $e KH fo$$ero i $o$tegni immobili, &amp; i pe$i in F; mentre la leua FG $i sforza di
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parents:
diff changeset
7652 mouere il pe$o po$to in F, all'hora le fa re$i$tenza la leua EF, laquale parimente
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parents:
diff changeset
7653 $i sforza di mouere il pe$o po$to in F in uer$o la parte oppo$ta; ma percioche le po$-
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parents:
diff changeset
7654 $anze $ono eguali, &amp; le altre co$e eguali: dunque non $i far&agrave; mouimento in F;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7655 percioche l'eguale non moue l'eguale. Egli &egrave; dunque pale$e, che in F $i f&agrave; grandi&szlig;ima
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7656 re$i$tenza dalle leue, che iui fra loro $i incontrano, talche F viene ad e$$ere vn cer-
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parents:
diff changeset
7657 to che immobile. Per laqual co$a con$iderando il cuneo come moue con le leue fra
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parents:
diff changeset
7658 loro contrarie, egli per auentura le v$a pi&ugrave; to$to &agrave; que$to $econdo modo, che al
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parents:
diff changeset
7659 primo.</I>
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casties
parents:
diff changeset
7660 <p>Ma percioche tutto il cuneo $i moue nel fendere, per&ograve; po$$iamo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7661 con$iderarlo anche in vn'altro modo, cio&egrave; mentre che entra
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parents:
diff changeset
7662 in quel che viene fe$$o, niente altro e$$ere, che vn mouere vn
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parents:
diff changeset
7663 pe$o $opra vn piano inchinato all'orizonte.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7664 <foot><I>Ee</I></foot>
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parents:
diff changeset
7665 <pb>
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casties
parents:
diff changeset
7666 <p><I>Sia il piano egualmente di$tante dall'orizonte, che pa&szlig;i per AB; $ia anco il cuneo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7667 CDB; &amp; $ia CD eguale ad e$$a DB: &amp; il lato del cuneo DB $ia $empre nel
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7668 $ottopo$to piano. $ia dopo il pe$o AEFG immobile in A; &amp; $ia la parte del
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casties
parents:
diff changeset
7669 cuneo EDH $otto AEFG. Hor percioche mentre il cuneo &egrave; perco$$o in CB,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7670 maggior parte del detto cuneo entra $otto AEFG, di quel che $ia EDH; $ia</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7671 <fig>
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casties
parents:
diff changeset
7672 <I>que$ta parte IDH. &amp; perche illato del cuneo DB &egrave; $empre nel piano $ottopo-
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parents:
diff changeset
7673 $to tirato per AB egualmente di$tante dall'orizonte, allhora quando la parte del
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parents:
diff changeset
7674 cuneo KDI $ar&agrave; $otto AEFG; $ar&agrave; il punto K in H, &amp; I $otto E, ma IK
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parents:
diff changeset
7675 &egrave; maggiore di HE: dunque il punto E $ar&agrave; mo$$o in s&ugrave;. &amp; mentre il cuneo entra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7676 $otto AEFG, il punto E $i mouer&agrave; in s&ugrave; $opra il lato EI del cuneo; &amp; nel mo
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casties
parents:
diff changeset
7677 do i$te$$o, $e il cuneo trapa$$er&agrave; pi&ugrave; oltre, il punto E mouera&szlig;i $empre $opra il la-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7678 to DC del cuneo; dunque il punto E del pe$o $i mouer&agrave; $opra il piano DC in-
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parents:
diff changeset
7679 chinato all orizonte, la cui inclinatione &egrave; l'angolo BDC. che bi$ognaua mo$trare.</I>
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parents:
diff changeset
7680 <p><I>In que$to e$$empio con$iderand<*> il cuneo, che moue &agrave; $embianza dileua, egli &egrave; manife$to
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parents:
diff changeset
7681 che il cuneo BCD moue il pe$o AEFG conla leua CD: $i che D $ia il $o$te-
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casties
parents:
diff changeset
7682 gno, &amp; il pe$o po$to in E: ma non gi&agrave; con la leua BD, il cui $o$tegno $ia H, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7683 il pe$o po$to in D.</I>
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casties
parents:
diff changeset
7684 <pb n=110>
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casties
parents:
diff changeset
7685 <p>Ma accioche la co$a re$ti pi&ugrave; chiara v$iamo altro e$$empio.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7686 <p><I>Sia vn piano egualmente di$tante dall'orizonte, che pa&szlig;i per AB: $ia ilcuneo CAB,
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casties
parents:
diff changeset
7687 il cui lato AB $ia $empre nel $ottopo$to piano; &amp; $ia il pe$o AEFG, che non
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casties
parents:
diff changeset
7688 habbia verun'altro moto $e non in s&ugrave;, &amp; in gi&ugrave; ad ang oli retti all'orizonte: talcbe</I>
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casties
parents:
diff changeset
7689 <fig>
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casties
parents:
diff changeset
7690 <I>tirata la linea IGK &agrave; piombo del piano $ottopo$to, &amp; di e$$a AB, il punto G
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7691 venga ad e$$ere $empre nella linea IGK. &amp; percio che mentre il cuneo &egrave; perco$$o
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diff changeset
7692 in CB, egli trapa$$a tutto pi&ugrave; oltre $opra AB; il pe$o AEFG $i leuer&agrave;, come
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diff changeset
7693 per le co$e predette $i &egrave; mo$trato. Moua$i il cuneo in modo, che E alla fine peruen
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diff changeset
7694 ga in C, &amp; la giacitura del cuneo ABC venga ad e$$ere MNO, &amp; la giaci-
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diff changeset
7695 tura del pe$o AEFG $ia PMQI, &amp; G $ia in I. co$i perche mentre il cuneo
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diff changeset
7696 $i moue $opra la linea BO, il pe$o AEFG $i moue in s&ugrave; dalla linea AC. &amp;
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parents:
diff changeset
7697 mentre il cuneo ABC trapa$$a pi&ugrave; oltre, il pe$o AEFG $empre pi&ugrave; dal lato del
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diff changeset
7698 cuneo AC $i leua: dunque il pe$o AEFG $i mouer&agrave; $opra il piano del cuneo
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diff changeset
7699 AC; ilche veramente altro non &egrave;, $e non vn piano inchinato all'orizonte, la cui
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diff changeset
7700 inclinatione &egrave; l'angolo BAC.</I>
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parents:
diff changeset
7701 <p><I>Que$to mouimento $i riduce ageuolmente alla bilancia, &amp; alla leua; percioche quel
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parents:
diff changeset
7702 che $i moue $opra il piano inchinato all'orizonte, $i riduce alla bilancia per la nona
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parents:
diff changeset
7703 propo$itione di Pappo dell'ottauo libro delle raccolte matematiche. percioche &egrave; vna
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parents:
diff changeset
7704 i$te$$a ragione, che ouero $tando fermo il cuneo, il pe$o $i moua $opra il lato del cu-
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parents:
diff changeset
7705 neo; ouero che e$$endo egli mo$$o, $i moua anco il pe$o $opra il $uo lato, come $o-
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diff changeset
7706 pra vn piano inchinato all'orizonte.</I>
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parents:
diff changeset
7707 <p>La propo$itione di Pappo allegata qui dall'Autore, &amp; in altri luoghi di que$to li-
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parents:
diff changeset
7708 bro, h&ograve; ripo$ta in loco conueneuole nel Trattato della Vite, $timando, che per
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parents:
diff changeset
7709 auentura ella $ia per tornare pi&ugrave; al propo$ito della Vite, &amp; $eruirle in pi&ugrave; chiarez-
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parents:
diff changeset
7710 <*>a, che al Cuneo. Laquale pro po$itione mi f&ugrave; man data dall'Autore, &amp; io $e ben
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parents:
diff changeset
7711 non le manca nulla, la h&ograve; rincontrata accuratamente co'l Pappo Greco del Sig.
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parents:
diff changeset
7712 Pinello, per modo che $i haur&agrave; perfettis$ima ad vtile, &amp; diletto di coloro, i qua-
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parents:
diff changeset
7713 li niuna co$a di Pappo $crittore marauiglio$o di Mecaniche hanno n&egrave; veduto, n&egrave;
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parents:
diff changeset
7714 letto giamai.
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parents:
diff changeset
7715 <foot><I>Ee</I> 2</foot>
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parents:
diff changeset
7716 <pb>
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parents:
diff changeset
7717 <p>Hora mo$triamo in che modo, quelle co$e lequali $ono fe$$e, $i
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parents:
diff changeset
7718 mouano come $opra piani inchinati all'orizonte.
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parents:
diff changeset
7719 <p><I>Sia il cuneo ABC, &amp; AB $ia eguale ad e$$a BC. Diuida$i AC in due partii<*>
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parents:
diff changeset
7720 D, &amp; $ia congiunta BD. $ia dopo la linea EF, per laquale pa&szlig;i il piano egual-
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parents:
diff changeset
7721 mente di$tante dall'orizonte, &amp; $ia BD nella mede$ima linea EF; &amp; mentre il</I>
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parents:
diff changeset
7722 <fig>
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parents:
diff changeset
7723 <I>cuneo &egrave; perco$$o, &amp; mentre $i moue in ver$o E, $empre BD $ia nella linea EF.
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parents:
diff changeset
7724 &amp; quel che $i hada fendere $ia GHLM, dentro alquale $ia la parte del cuneo
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parents:
diff changeset
7725 KBI: egli &egrave; mani$e$to, che mentre il cuneo $i moue in ver$o E, la parte KG mo-
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parents:
diff changeset
7726 uer$i in ver$o N; &amp; la parte HI in ver$o O. percota$i il cuneo per modo che la
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parents:
diff changeset
7727 linea AC $ia nella linea NO; allhora K $ar&agrave; in A, &amp; I in C: &amp; K perle
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parents:
diff changeset
7728 co$e $udette $ar&agrave; mo$$o $opra KA, &amp; I $opra IC. Per laqual co$a mentre $i mo
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parents:
diff changeset
7729 ue il cuneo, la parte KG $i mouer&agrave; $opra il lato BA del cuneo, &amp; la parte IH
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diff changeset
7730 $opra il lato BC. La parte dunque KG $i mouer&agrave; $opra il piano inchinato all'o-
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parents:
diff changeset
7731 rizonte, la cui inclinatione &egrave; l'angolo FBA. $imilmente IH $i moue $opra il
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parents:
diff changeset
7732 piano BC nell'angolo FBC. le parti dunque di quel che $i $ende moueran$i $o-
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parents:
diff changeset
7733 pra piani inchinati all'orizonte. &amp; quantun que il piano BC $ia $otto l'orizonte;
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parents:
diff changeset
7734 tutta via la parte IH $i moue $opra IC, come $e BC $o$$e $opra l'orizonte nel-
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parents:
diff changeset
7735 l'angolo DBC: percioche le parti di quel che $i fende $i mouono nel tempo me-
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parents:
diff changeset
7736 de$imo dall'i$te$$a po$$anza. $ar&agrave; dunque la mede$ima ragione del mouimento della
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parents:
diff changeset
7737 parte IH, &amp; della parte KG. $imilmente &egrave; l'i$te$$a ragione $e EF &egrave; egualmente
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parents:
diff changeset
7738 di$tante dall'orizonte, ouero $e &egrave; &agrave; piombo dell'orizonte, ouero in altro modo: pe
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parents:
diff changeset
7739 roche egli &egrave; nece$$ario, che la po$$anza, laquale moue il cuneo, $ia la mede$ima, re-
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parents:
diff changeset
7740 $tando le altre co$e le mede$ime. $ar&agrave; dunque la $te$$a ragione.</I>
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7741 <pb n=111>
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parents:
diff changeset
7742 <p><I>Dopo que$te co$e egli &egrave; da con$iderare, quali $iano quelle co$e, lequali fanno s&igrave;, che pi&ugrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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7743 ageuolmente alcuna co$a $i moua, ouero $i $enda, lequali $ono due.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7744 <p>Primieramente quel che opera in modo, che alcuna co$a pi&ugrave;
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parents:
diff changeset
7745 ageuolmente $ia fe$$a. ilche pi&ugrave; appartiene etiandio alla e$-
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parents:
diff changeset
7746 $enza del cuneo, &egrave; l'angolo po$to alla cima del cuneo: pero che
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parents:
diff changeset
7747 quanto minore &egrave; l'angolo, tanto pi&ugrave; ageuolmente moue, &amp;
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parents:
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7748 fende.
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parents:
diff changeset
7749 <p><I>Siano due cunei ABC DEF, &amp; l'angolo ABC po$to alla cima $ia minore dell'an
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parents:
diff changeset
7750 golo DEF. Dico che alcuna co$a pi&ugrave; ageuolmente $i moue, &ograve; fende dal cuneo
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parents:
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7751 ABC, che da DEF. Diuidan$i AC DF in due parti eguali ne'punti GH;
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parents:
diff changeset
7752 &amp; $iano congiunte BG &amp; EH. Hor
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parents:
diff changeset
7753 percioche le parti di quello, che $i fen
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parents:
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7754 de dal cuneo ABC $i mouono $opra
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parents:
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7755 il piano inchinato all'orizonte, la cui
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parents:
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7756 inclinatione &egrave; GBA; &amp; quelle che
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parents:
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7757 dal cuneo DEF $i mouono $opra il
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parents:
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7758 piano inchinato all'orizonte, la cui
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parents:
diff changeset
7759 inclinatione &egrave; HED, &amp; l'angolo
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parents:
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7760 GBA &egrave; minore dell'angolo HED;
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parents:
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7761 per e$$ere GBA minore di DEF:
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casties
parents:
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7762 &amp; per la nona di Pappo dell'ottauo
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casties
parents:
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7763 libro delle raccolte matematiche, quel
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parents:
diff changeset
7764 che $i moue $opra il piano AB, $i mo
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parents:
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7765 uer&agrave; pi&ugrave; facilmente, &amp; da po$$anza
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parents:
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7766 minore, che $opra ED. Quel che $i
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parents:
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7767 $ende dunque dal cuneo ABC pi&ugrave;</I>
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parents:
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7768 <fig>
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parents:
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7769 <I>ageuolmente, &amp; da po$$anza minore $i fende, che dal cuneo DEF. $imilmente
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casties
parents:
diff changeset
7770 mo$trera$$i, che quanto pi&ugrave; acuto $ar&agrave; l'angolo po$to alla cima del cuneo, tanto pi&ugrave;
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parents:
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7771 ageuolmente mouera$$i, &amp; fendera$$i alcuna co$a. che bi$ognaua mo$trare.</I>
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parents:
diff changeset
7772 <p>Pos$iamo dimo$trare que$to etiandio con altra ragione, con$i-
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parents:
diff changeset
7773 derando il cuneo come egli moue con le leue contrarie l'vna
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parents:
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7774 all'altra fra loro, fi come nel $econdo modo f&ugrave; detto. ma bi$o
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parents:
diff changeset
7775 gna prima dimo$trare que$to.
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casties
parents:
diff changeset
7776 <p><I>Sia la leua AB, che habbia il $uo $o$tegno B immobile, &amp; quel che s'ha da mouere
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casties
parents:
diff changeset
7777 $ia CD EF rettangolo, co$i di$po$to, che non po$$a mouer$i in gi&ugrave; dalla parte di
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casties
parents:
diff changeset
7778 FE; &amp; il punto E $ia immobile, &amp; come centro; $iche il punto D $i moua per
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casties
parents:
diff changeset
7779 la circonferenza del cerchio
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casties
parents:
diff changeset
7780 DH, il cui centro $ia E. &amp;
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casties
parents:
diff changeset
7781 C per la circonferenza CL,
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casties
parents:
diff changeset
7782 $i che la linea congiunta CE
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casties
parents:
diff changeset
7783 $ia il $uo mezo diametro.
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casties
parents:
diff changeset
7784 di pi&ugrave; CDEF tocchi la le
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casties
parents:
diff changeset
7785 ua AB in C, &amp; la leua
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casties
parents:
diff changeset
7786 AB moua il pe$o CDEF,
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casties
parents:
diff changeset
7787 &amp; la po$$anza mouente $ia
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casties
parents:
diff changeset
7788 in A, il $o$tegno in B, &amp;
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casties
parents:
diff changeset
7789 il pe$o in C. $ia dapoi vn'al
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casties
parents:
diff changeset
7790 traleua MCN, laquale
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7791 etiandio moua CD EF, il
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casties
parents:
diff changeset
7792 cui $o$tegno immobile $ia
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casties
parents:
diff changeset
7793 N; la po$$anza mouente in
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casties
parents:
diff changeset
7794 M, &amp; il pe$o $imilmente in
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casties
parents:
diff changeset
7795 C; &amp; $ia CN eguale ad</I>
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casties
parents:
diff changeset
7796 <fig>
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casties
parents:
diff changeset
7797 <I>e$$a CB, &amp; CM ad e$$a CA; &amp; moua$i alternamente il pe$o CDEF con le
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7798 leue AB MN. Dico che CDEF pi&ugrave; ageuolmente $i mouer&agrave; dall'i$te$$a po$$an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7799 za con la leua AB, che con la leua MN.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7800 <p><I>Faccia$i il centro B, &amp; con lo $patio BC de$criua$i la circonferenza CO. $imilmen-
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casties
parents:
diff changeset
7801 te co'l centro N, &amp; lo $patio NC de$criua$i la circonferenza CP. Hor percio-
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casties
parents:
diff changeset
7802 che mentre la leua AB moue CD EF, il punto della leua C $i moue $opra la
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7803 circonferenza CO, per e$$ere B $o$tegno, &amp; centro immobile. $imilmente men-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7804 tre la leua MN moue CD EF, il punto C $i moue per la circonferenza CP:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7805 mentre dunque la leua AB moue CD EF, $i s$orza mouere il punto C del pe$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7806 $opra la circonferenza CO; ilche non pu&ograve; gi&agrave; fare, perche C $i moue $opra la cir-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7807 conferenza CL. Per laqual co$a nel mouimento della leua AB $econdo la parte</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7808 <pb n=112>
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casties
parents:
diff changeset
7809 <I>che le ri$ponde, &amp; nel mouimento del pe$o fatto $econdo C, ne na$ce vn certo con-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7810 tra$to: percioche $i mouono in diuer$e parti. $imilmente mentre la leua MN mo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7811 ue CD EF, $i sforza mouere il C $opra la circonferenza CP: &amp; per&ograve; in que$to
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7812 ancora na$ce in ambidue i mouimenti vn $imile contra$to. Et perche la circon$eren
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7813 za CO &egrave; pi&ugrave; da pre$$o alla circonferenza CL, che non &egrave; CP, cio&egrave; pi&ugrave; da pre$$o
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7814 al mouimento, che fa il punto C del pe$o; per&ograve; il contra$to tra il mouimento della le
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7815 ua AB, &amp; il mouimento del pe$o C $ar&agrave; minore, che tra il mouimento della leua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7816 MN, &amp; il mouimento dell'i$te$$o C, ilche etiandio &egrave; chiaro, $e $i intenda che CF
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7817 $ia &agrave; piombo dell'orizonte; percioche all'hora la circonferenza CP pi&ugrave; inchina al
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casties
parents:
diff changeset
7818 ba$$o, che CO: &amp; CL v&agrave; in s&ugrave;. &amp; perci&ograve; $i fa contra$to minore tra la leua
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7819 AB, &amp; il mouimento C, che fra la leua MN, &amp; il mouimento C. Ma doue
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7820 &egrave; conte$a minore, iui &egrave; pi&ugrave; ageuolezza. Dunque $i mouer&agrave; pi&ugrave; facilmente CDEF
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7821 con la leua AB, che con la leua MN. che bi$ognaua mo$trare.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7822 <HEAD>COROLLARIO</HEAD>
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casties
parents:
diff changeset
7823 <p>Da que$to &egrave; chiaro, che quanto minore &egrave; l'angolo contenuto
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7824 dalla linea CF, ouero CE, ouero CD; cio&egrave; quanto
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7825 minore &egrave; l'angolo BCF, ouero BCE, ouero anche BCD;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7826 tanto pi&ugrave; ageuolmente il pe$o &egrave; mo$$o. ilche mo$treras$i nel-
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casties
parents:
diff changeset
7827 l'i$te$$o modo.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7828 <p><I>Siano li cunei ABC DEF, &amp; l'angolo ABC $ia minore dell'angolo DEF, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7829 AB BC DE EF $iano tra loro eguali. $iano dapoi quattro pe$i eguali GH IL
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7830 NO QR rettangoli; &amp; $iano LM KH nella mede$ima linea retta. $imilmente</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7831 <marg><I>Per la</I> 28. <I>del primo.</I></marg> <I>RS PO in linea retta; $aranno GK IM egualmente di$tanti, &amp; NP QS an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7832 co egualmente di$tanti. $ia IBG la parte del cuneo fraipe$i GH IL; &amp; la par
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7833 te del cuneo QEN fra i pe$i NOQR; &amp; $iano IB BG QE EN traloro
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7834 eguali. Dico che i pe$i GH IL pi&ugrave; ageuolmente $aranno dalla po$$anza i$te$$a co'l
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7835 cuneo ABC mo$si, che i pe$i NO QR dal cuneo DEF.</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7836 <p><I>Diuidan$i AC DF in due parti eguali in TV, &amp; congiungan$i TBVE, $aranno
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casties
parents:
diff changeset
7837 gli angoli po$ti al T, &amp; V retti. congiunga$i IG, laquale tagli BT in X. Hor</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7838 <fig>
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casties
parents:
diff changeset
7839 <marg><I>Per la</I> 2. <I>del $esto.</I></marg> <I>percioche IB &egrave; eguale &agrave; BG, &amp; BA eguale &agrave; BC: $ar&agrave; IA eguale ad e$$a</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7840 <marg><I>Per la</I> 9. <I>del primo.</I></marg> <I>GC. Per laqual co$a BI ad IA &egrave; co$i, come BG &agrave; GC; dunque IG &egrave; egualmen
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7841 te di$tante ad e$$a AC: &amp; perci&ograve; gli angoli ad X $ono retti; ma gli angoli XGK</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7842 <marg><I>Per la</I> 28. <I>del primo.</I></marg> <I>XIM $ono retti, peroche GM &egrave; rettangolo. Per laqual co$a TB &egrave; egualmente di-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7843 $tante da GKIM. dunque l'angolo TBC &egrave; eguale all'angolo BGK, &amp; TBA &egrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7844 eguale ad e$$o BIM. $imilm&emacr;te mo$treremo che l'angolo VEF &egrave; eguale ad ENP,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7845 &amp; VED eguale ad EQS. &amp; per e$$ere l'angolo ABC minore dell'angolo DEF;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7846 $ar&agrave; anco l'angolo TBC minore di VEN. Per laqual co$a BGK $ar&agrave; anche mi-
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casties
parents:
diff changeset
7847 nore di ENP. con $imile modo BIM &egrave; minore di EQS. Hor percioche il cuneo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7848 ABC moue con due leue AB BC, che hanno i $o$tegni $uoi in B, &amp; i pe$i in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7849 GI. $imilmente il cuneo DEF moue con due altre leue DE EF, i cui $o$tegni $o-
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casties
parents:
diff changeset
7850 no in E; &amp; i pe$i in NQ: per la precedente i pe$i GH IL $i moueranno pi&ugrave; ageuol
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7851 mente con le leue AB BC, che i pe$i NO QR conle leue DE EF. i pe$i dunque
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7852 GH IL, $i moueranno pi&ugrave; ageuolmente co'lcuneo ABC, che i pe$i NO QR co'l</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7853 <pb n=113>
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casties
parents:
diff changeset
7854 <I>euneo DEF. &amp; perche &egrave; la ragione i$le$$a nel mouere &amp; nel fendere; per&ograve; pi&ugrave; age
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7855 uolmente $i fender&agrave; alcuna co$a co'l cuneo ABC, che co'l cuneo DE</I>F. <I>Et dimo-
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casties
parents:
diff changeset
7856 $trera$$i mede$imamente che quanto minore &egrave; l'angolo po$to alla cima del cuneo, tan
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casties
parents:
diff changeset
7857 to pi&ugrave; ageuolmente $i moue alcuna co$a, ouero $i fende, che bi$ognaua mostrare.</I>
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casties
parents:
diff changeset
7858 <p><I>Oltre &agrave; ci&ograve; quelle co$e, lequali $ono mo$$e dal cuneo DEF, $i mouono per maggiori
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casties
parents:
diff changeset
7859 $patij che quelle che $ono mo$$e dal cuneo ABC. Imperoche affine che D</I>F <I>$ia
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casties
parents:
diff changeset
7860 tra QN, &amp; affine che AC $ia tr&agrave; IG, egli &egrave; nece$$ario che QN $i mouano per
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casties
parents:
diff changeset
7861 maggiori $patij, cio&egrave; l'vno alla de$tra, l'alrro alla $ini$tra, che IG, per e$$ere D</I>F
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casties
parents:
diff changeset
7862 <I>maggiore di AC: pur che tutto il cuneo entri fra i pe$i. Ma dalla po$$anza pi&ugrave;
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casties
parents:
diff changeset
7863 facilmente $i moue per minor $patio alcuna co$a nel mede$imo tempo, che per mag-
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casties
parents:
diff changeset
7864 giore: pur che le altre co$e con le quali $i f&agrave; il mouimento $iano eguali: $e dunque
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casties
parents:
diff changeset
7865 AC D</I>F <I>peruerranno nell'i$te$$o tempo in IG QN, e$$endo A I CG DQ</I>F<I>N
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casties
parents:
diff changeset
7866 tra loro eguali; pi&ugrave; facilmente dalla po$$anza $imoueranno GI co'l cuneo ABC,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7867 che QN co'l cuneo DE</I>F. <I>per laqual co$a i pe$i GHIL $i moueranno pi&ugrave; facil-
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casties
parents:
diff changeset
7868 mente dalla po$$anza co'l cuneo ABC, che i pe$i NO QR co'l cuneo DE</I>F.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7869 <I>&amp; $imilmente $i mostrer&agrave;, che quanto l'angolo po$to alla cima del cuneo $ar&agrave; mino
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casties
parents:
diff changeset
7870 re, tanto pi&ugrave; ageuolmente $i moueranno i pe$i, ouero $i fenderanno.</I>
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casties
parents:
diff changeset
7871 <p>La $econda co$a laquale &egrave; cagione, che alcuna co$a $i fenda pi&ugrave;
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casties
parents:
diff changeset
7872 ageuolmente &egrave; la perco$$a, mediante laquale &egrave; mo$$o il cuneo
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casties
parents:
diff changeset
7873 &amp; moue, cio&egrave; vien perco$$o, &amp; fende.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7874 <foot><I>Ff</I></foot>
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casties
parents:
diff changeset
7875 <pb>
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casties
parents:
diff changeset
7876 <p><I>Sia il cuneo A, quel
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casties
parents:
diff changeset
7877 che s'hada fendere
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casties
parents:
diff changeset
7878 B, &amp; quel che per
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casties
parents:
diff changeset
7879 cuote C; ilquale
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casties
parents:
diff changeset
7880 ouero da $e $te$$o
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casties
parents:
diff changeset
7881 percuote, &amp; moue;
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casties
parents:
diff changeset
7882 ouero dalla po$$an-
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casties
parents:
diff changeset
7883 za che lo regge, &amp;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7884 moue. che $e da $e
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casties
parents:
diff changeset
7885 $te$$o, prima s ha da
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casties
parents:
diff changeset
7886 auertire, che quan-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7887 to pi&ugrave; $ar&agrave; graue,
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casties
parents:
diff changeset
7888 tanto $i far&agrave; la per
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parents:
diff changeset
7889 co$$a maggiore. &amp;
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casties
parents:
diff changeset
7890 oltre &agrave; ci&ograve; quanto
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casties
parents:
diff changeset
7891 pi&ugrave; $ar&agrave; lunga la di-
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casties
parents:
diff changeset
7892 stanzatra AC, fa
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7893 ra&szlig;i parimente mag
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casties
parents:
diff changeset
7894 giore perco$$a: pe-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7895 roche cia$cuna co$a
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casties
parents:
diff changeset
7896 graue, mentre $i mo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7897 ue, prende pi&ugrave; di gra
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7898 uezza mo$$a, che
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casties
parents:
diff changeset
7899 $tando ferma, &amp;
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casties
parents:
diff changeset
7900 dauantaggio anco
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casties
parents:
diff changeset
7901 pi&ugrave;, quanto pi&ugrave; da
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parents:
diff changeset
7902 lontano &egrave; mo$$a.</I>
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casties
parents:
diff changeset
7903 <fig>
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casties
parents:
diff changeset
7904 <p><I>Che $e C $ar&agrave; mo$$o da qualche po$$anza,
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parents:
diff changeset
7905 come per lo manico DE $ia mo$$o. Pri
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casties
parents:
diff changeset
7906 ma quanto C $ar&agrave; pi&ugrave; graue; dapoi
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7907 quanto $ar&agrave; pi&ugrave; lungo DE, tanto la
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casties
parents:
diff changeset
7908 perco$$a fara&szlig;imaggiore: percioche $e
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7909 la po$$anza mouente $ar&agrave; posta in E,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7910 $ar&agrave; il C pi&ugrave; di$tante dal centro, &amp; pe
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casties
parents:
diff changeset
7911 r&ograve; mouera&szlig;i pi&ugrave; tosto, come Ari$to-
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casties
parents:
diff changeset
7912 tele dimostra nelle questioni mecani-
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casties
parents:
diff changeset
7913 che; &amp; puote e$$ere anco chiaro da
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casties
parents:
diff changeset
7914 quelle co$e, che furono dette nel trat-
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casties
parents:
diff changeset
7915 tato della bilancia, che quanto pi&ugrave; il</I>
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casties
parents:
diff changeset
7916 <fig>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7917 <pb n=114>
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casties
parents:
diff changeset
7918 <I>pe$o C &egrave; di$tante dal centro, tanto pi&ugrave; far$i graue, &amp; vrter&agrave; etiandio con pi&ugrave; ga-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7919 gliard'empito, e$$endo la forza in E pi&ugrave; po$$ente.</I>
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casties
parents:
diff changeset
7920 <p><I>Ma que$ta &egrave; la $ec&otilde;da co$a, laqual &egrave; cagione che con que$to i$trumento $imouano gran
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7921 pe$i, &amp; $i fendano. Percioche la perco$$a &egrave; vna forza gagliardi&szlig;ima, come &egrave; ma-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7922 nife$to da la decimanona delle questioni
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casties
parents:
diff changeset
7923 mec aniche di Ari$totele: peroche $e $o-
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casties
parents:
diff changeset
7924 pra il cuneo $i imporr&agrave; vn pe$o grandi&szlig;i-
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casties
parents:
diff changeset
7925 mo, allhora il cuneo non far&agrave; nulla &agrave; pa-
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casties
parents:
diff changeset
7926 ragone $petialmente della perco$$a. che $e
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casties
parents:
diff changeset
7927 anco $i adatta$$e al cuneo vna leua, ouero
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casties
parents:
diff changeset
7928 vna vite, &ograve; qualche altro tale $tromento
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casties
parents:
diff changeset
7929 per cacciare il cuneo pi&ugrave; &agrave; dentro nel pe$o,
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casties
parents:
diff changeset
7930 non auenir &agrave; effetto qua$i di momento niu
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casties
parents:
diff changeset
7931 no, ri$petto alla perco$$a. della qual co$a
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casties
parents:
diff changeset
7932 puote e$$ere inditio, che $e fo$$e il corpo A
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casties
parents:
diff changeset
7933 di pietra, da cui alcuno vole$$e leuar via</I>
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casties
parents:
diff changeset
7934 <fig>
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casties
parents:
diff changeset
7935 <I>qualche parte, come vn pezzo dell'angolo B, allhora potrebbe rompere ageuolmen
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casties
parents:
diff changeset
7936 te con vno martello di ferro, $enza altro $tromento, percotendo in B, qualche pezzo
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7937 dell'angolo B: ilche non potr&agrave; fare con ne$$uno altro $tromento, che $ia priuo di per-
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casties
parents:
diff changeset
7938 co$$a, $e non con difficult&agrave; grandi&szlig;ima, $ia &ograve; leua, &ograve; vite, &ograve; qual $i voglia altra co$a
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casties
parents:
diff changeset
7939 tale. La onde la perco$$a &egrave; cagione, che $i fendano i gran pe$i. &amp; hauendo la per-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
7940 co$$a co$i gran forza, $e le ag giungeremo qualche $tromento accommodato &agrave; moue-
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casties
parents:
diff changeset
7941 re, &amp; fendere, vedremo per certo co$e marauiglio$e. Cote$to $tromento &egrave; il cuneo,
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casties
parents:
diff changeset
7942 nel quale due co$e, inquanto s'ap
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casties
parents:
diff changeset
7943 partiene alla $ua forma, occor-
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casties
parents:
diff changeset
7944 rono ad e$$ere con$iderate: L'v-
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casties
parents:
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7945 na, che il cuneo &egrave; atti&szlig;imo &agrave; ri-
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casties
parents:
diff changeset
7946 ceuere, &amp; $o$tenere la perco$$a:
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casties
parents:
diff changeset
7947 l'altra &egrave;, che per la $ua $ottigliez
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casties
parents:
diff changeset
7948 za nell vna delle parti facilm&emacr;te
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casties
parents:
diff changeset
7949 entra ne'corpi, come e$pre$$a-
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diff changeset
7950 mente $i vede. Il cuneo dunque
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diff changeset
7951 opera$i con la $ua perco$$a, che
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diff changeset
7952 vediamo qua$i miracoli nel fen-
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diff changeset
7953 dere i corpi.</I>
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casties
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diff changeset
7954 <fig>
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parents:
diff changeset
7955 <foot><I>Ff</I> 2</foot>
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parents:
diff changeset
7956 <pb>
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parents:
diff changeset
7957 <p><I>Alla facolt&agrave; di cotale $tromento $i po$$ono etiandio ridurre commodamente quelle co
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diff changeset
7958 $e tutte, lequali con perco$$a, ouero $pinta tagliano, diuidono, $orano, &amp; fanno al
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parents:
diff changeset
7959 tri cotali e$fetti, come $pade, punte, coltelli, $curi, &amp; $imili. La $ega ancora $i
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parents:
diff changeset
7960 ridurr&agrave; &agrave; que$to: peroche i $uoi denti percotono, &amp; $ono &agrave; $emb ianza di cuneo.</I>
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parents:
diff changeset
7961 <HEAD>IL FINE DEL CVNEO.</HEAD>
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parents:
diff changeset
7962 <pb n=115>
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parents:
diff changeset
7963 <HEAD>DELLA VITE.</HEAD>
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parents:
diff changeset
7964 <fig>
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parents:
diff changeset
7965 <p>Pappo nell'i$te$$o ottauo libro trattando mol-
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parents:
diff changeset
7966 te co$e della vite, in$egna come ella $i deue fa-
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parents:
diff changeset
7967 bricare; &amp; come con cotale $tromento $i moua-
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parents:
diff changeset
7968 no grandi pe$i: &amp; di pi&ugrave; mette altre $peculatio-
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parents:
diff changeset
7969 ni molto vtili alla cognitione di lei. Ma per-
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parents:
diff changeset
7970 cioche tra le altre co$e egli promette di voler mo$trare la vi-
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parents:
diff changeset
7971 te niente altro e$$ere, che vn cuneo pre$o $enza la perco$$a, il
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parents:
diff changeset
7972 quale faccia il mouimento $uo con la leua. &amp; que$to in lui $i
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parents:
diff changeset
7973 de$idera: per&ograve; noi $i sforzeremo di mo$trare ci&ograve;. &amp; di pi&ugrave;
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parents:
diff changeset
7974 ridurre la detta vite alla leua, &amp; alla bilancia, accioche alla fi-
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parents:
diff changeset
7975 ne $e n'habbia compiuta cognitione.
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parents:
diff changeset
7976 <p>H&ograve; ritonuto nel tradurre le parole Cilindro, &amp; Helice i vocaboli i$tes$i, come l'Au-
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parents:
diff changeset
7977 tore gli ha po$ti, percioche la no$tra lingua pouera ancora di que$te voci, non ne
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parents:
diff changeset
7978 h&agrave; fin hora approuata alcuna per buona, &amp; communemente in te$a in tutta Italia
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parents:
diff changeset
7979 per $ignificare le predette due co$e Cilindro, &amp; Helice. Per&ograve; io, affine di dome-
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casties
parents:
diff changeset
7980 $ticarle, h&ograve; voluto farne e$perientia, la$ciandole co$i, $e per auentura pote$$ero
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parents:
diff changeset
7981 e$$er accettate. Cilindro, voce Greca, &egrave; quel ba$tone lauorato al torno, nel quale
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parents:
diff changeset
7982 $i intagliano quei rileui co' $uoi concaui, che vanno montando in $u$o &agrave; lumaca,
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parents:
diff changeset
7983 &ograve; chio cciola, &amp; $i dicono vite, ouero in qualche contrada d'Italia vermi, &ograve; chioc
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parents:
diff changeset
7984 ciole, &amp; l'Autore qui noma Hlici. Ba$ta che la co$a re$ti chiara, non que$tionan-
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parents:
diff changeset
7985 do de' nomi, &amp; $i intenda che voglia dire Cilindro, &amp; Helice. La Vite in latino
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
7986 $i chiama Cochlea &agrave; $imiglianza cied'io dell'animale che $i m&atilde;gia detto lumaca, &ograve;
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casties
parents:
diff changeset
7987 bouolo, &ograve; chiocciola, che &egrave; pi&ugrave; $imile &agrave; Cochlea latino, talche la vite, $tando s&ugrave;
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parents:
diff changeset
7988 inomi, viene ad hauere pre$o il nome da quell'animale, che nella ca$a, la quale $em
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parents:
diff changeset
7989 pre porta $eco $i ra$$embra, mas$imamente nel fondo di e$$a, in certo modo al rile
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parents:
diff changeset
7990 uo, &ograve; verme, ouero helice della vite. Onde ben $i potrebbe con ragione dire
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parents:
diff changeset
7991 chiocciola alla vite, volgarizando il vocabolo latino cochlea, come $i appellane
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parents:
diff changeset
7992 chiocciole le $cale che a$cendono &agrave; vite.
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parents:
diff changeset
7993 <p><I>Sia il cuneo ABC, ilquale $iriuolga d'intorno al Cilindro DE, &amp; $ia IGH il cu-
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parents:
diff changeset
7994 neo riuolto d'intorno al cilindro, la cui cima $ia I. $ia dapoi il cilindro in$ieme co'lcu
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parents:
diff changeset
7995 neo po$toui d'intorno accomm o dato in modo, che $enza alcuno impedimento $ipo$$a
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parents:
diff changeset
7996 volgere intorno co'l manico KF attaccato all'a$$e: &amp; $ia LMNO quel che s'ha
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parents:
diff changeset
7997 da fendere, ilquale etiandio dalla parte di MN $ia immobile, $i come $uole far$i
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parents:
diff changeset
7998 in quelle co$e, che $i fendono. &amp; $ia la cima I'tra RS. Volga$i intorno KF, &amp;</I>
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casties
parents:
diff changeset
7999 <fig>
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parents:
diff changeset
8000 <I>peruenga &agrave; KP; &amp; mentre che KF $i volge intorno, tutto il cilindro DE anc<*>
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parents:
diff changeset
8001 ra $i volge intorno, &amp; il cuneo IGH. per laqual co$a mentre KF $ar&agrave; in KP,
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parents:
diff changeset
8002 la cima I non $ar&agrave; pi&ugrave; tra RS, ma altr a parte del cuneo, come TV: ma TV &egrave;
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parents:
diff changeset
8003 maggiore di RS; peroche la parte del cuneo, laquale &egrave; pi&ugrave; di$tante dalla cima, $em-
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parents:
diff changeset
8004 pre &egrave; mag giore di quella, che &egrave; pi&ugrave; ad e$$a vicina. accioche dunque TV $ia tra RS,
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parents:
diff changeset
8005 bi$ogna che R ceda, &amp; $i moua ver$o X, &amp; S in ver$o Z, come fanno le co$e, che
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parents:
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8006 $i fendono. tutto dunque LMNO $i fender&agrave;. Similmente dimo$treremo, che men
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parents:
diff changeset
8007 tre il manico KP $ar&agrave; in KQ, allhora GH $ar&agrave; fra RS: &amp; mentre GH $ar&agrave;
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parents:
diff changeset
8008 tra RS, egli &egrave; nece$$ario che R $ia in X, &amp; S in Z. talche XZ $ia eguale &agrave; GH;
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parents:
diff changeset
8009 &amp; $empre LM NO $i fender&agrave; dauantaggio. co$i dunque &egrave; manife$to, che mentre
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parents:
diff changeset
8010 KF $i volge intorno, $empre R $i moue in ver$o X, &amp; S in ver$o Z: &amp; R mo-
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parents:
diff changeset
8011 <*>er$i $empre $opra ITG, &amp; S $opra IVH, cio&egrave; $opra i lati del cuneo volti
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parents:
diff changeset
8012 d'intorno al cilindro.</I>
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parents:
diff changeset
8013 <pb n=116>
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parents:
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8014 <HEAD>PROPOSITIONE I.</HEAD>
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parents:
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8015 <p>Il cuneo accommodato in que$to modo d'intorno al cilindro,
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parents:
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8016 niente altro &egrave;, che la vite, laquale habbia due helici congiun
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parents:
diff changeset
8017 te fra loro in vno punto.
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casties
parents:
diff changeset
8018 <p><I>Sia il cuneo ABC; &amp; AB $ia eguale &agrave; BC. diuida$i AC in due parti in D,
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parents:
diff changeset
8019 &amp; congiunga$i BD; $ar&agrave; BD &agrave; piombo di AC: &amp; AD eguale &agrave; DC, &amp; il
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parents:
diff changeset
8020 triangolo ABD eguale al triangolo CBD. Faccia$i dapoi i triangoli rettangoli
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parents:
diff changeset
8021 EFG HIK non $olo tra loro eguali, ma etiandio eguali ad ambidue i triang oli</I>
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parents:
diff changeset
8022 <fig>
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parents:
diff changeset
8023 <I>ADB, &amp; CDB. &amp; $ia il cilindro LMNO, la cui linea che lo circonda detto
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casties
parents:
diff changeset
8024 Perimetro $ia eguale ad ambedue FGKI: &amp; LMNO $ia parallelo gram-
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casties
parents:
diff changeset
8025 mo per l'a$$e. &amp; faccia$i MP eguale ad FE, &amp; PN eguale ad HI. &amp; pon
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parents:
diff changeset
8026 ga$i HI in NP, &amp; inuolga$i il triangolo HIK d'intorno al cilindro; &amp; $ia de
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parents:
diff changeset
8027 $critta la helice NQR $econdo KH, come in$egna anche Pappo nell'ottauo libro
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parents:
diff changeset
8028 alla propo$itione vige$ima quarta. &amp; $imilmente ponga$i EF in MP, &amp; in-
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parents:
diff changeset
8029 uolga$i il triangolo EFG d'intorno al cilindro, &amp; de$criua$i per EG la helice
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casties
parents:
diff changeset
8030 PRM. &amp; co$i per e$$ere PM PN eguali ad EF HI, $ar&agrave; MN eguale ad
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casties
parents:
diff changeset
8031 e$$a AC, &amp; per e$$ere le helici PRM PQN eguali alle linee EG HK; $a-</I>
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casties
parents:
diff changeset
8032 <p><I>Similm ente $e la vite
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parents:
diff changeset
8033 haur&agrave; pi&ugrave; helici co-
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diff changeset
8034 me nella $econda $i-
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diff changeset
8035 gura, il pe$o A, men
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parents:
diff changeset
8036 tre la vite $i volge
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parents:
diff changeset
8037 intorno, $empre $i
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parents:
diff changeset
8038 mouer&agrave; $opr a le he-
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parents:
diff changeset
8039 lici BCD EFG;
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casties
parents:
diff changeset
8040 pur che il pe$o A
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parents:
diff changeset
8041 in modo $i adatti,
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diff changeset
8042 che non po$$a mo-
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parents:
diff changeset
8043 uer$i $e non $opra la
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parents:
diff changeset
8044 retta linea HI e-
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parents:
diff changeset
8045 gualmente di$tante
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diff changeset
8046 da e$$o cilindro. Per
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parents:
diff changeset
8047 cioche nell'i$te$$o mo
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parents:
diff changeset
8048 do, che $i moue $o-
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diff changeset
8049 pra la prima helice,
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parents:
diff changeset
8050 $i moue etiandio $o-
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parents:
diff changeset
8051 pra la $econda, &amp; $o
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parents:
diff changeset
8052 pra la terza, et $opra
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casties
parents:
diff changeset
8053 le altre. Percioche
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casties
parents:
diff changeset
8054 quante $i vogli&amacr;heli
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parents:
diff changeset
8055 ci che $iano, non $on
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parents:
diff changeset
8056 altro niente, che vn
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parents:
diff changeset
8057 lato del cuneo inuol-
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parents:
diff changeset
8058 to d'intorno all'i$te$-</I>
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parents:
diff changeset
8059 <fig>
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parents:
diff changeset
8060 <I>$o cilindro vna, &amp; pi&ugrave; volte. et $ia la vite ouero &agrave; piombo dell'orizonte, ouero egual
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parents:
diff changeset
8061 mente di$tante dall orizonte, ouero in altro modo collocata, nonimporta nulla; per-
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parents:
diff changeset
8062 cioche $empre valer&agrave; l'i$te$$a ragione.</I>
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parents:
diff changeset
8063 <pb n=117>
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parents:
diff changeset
8064 <p><I>che non po$$ano mouer$i $e non $opra la diritta linea LO, laquale $ia egualmente
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parents:
diff changeset
8065 di$tante dail'a$$e del cilindro; &amp; $iano MN pre$$o la cima I del cuneo. Volga$i
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parents:
diff changeset
8066 intorno KF, &amp; peruenga in KP: &amp; mentre KF $ar&agrave; in KP, allhora TV $a
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parents:
diff changeset
8067 r&agrave; fra i pe$i MN, $i come di $opra habbiamo detto. dunque M $i mouer&agrave; ver$o</I>
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parents:
diff changeset
8068 <fig>
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parents:
diff changeset
8069 <I>L, &amp; N ver$o O. Similmente mo$trera$$i, che mentre KP $ar&agrave; in KQ, allho-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
8070 ra GH $ar&agrave; tra i pe$i MN; &amp; M $ar&agrave; in X, &amp; N in Z; $i che XZ $ar&agrave;
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
8071 eguale <*> GH. Per laqual co$a mentre KF $i volge intorno, $empre il pe$o N $i
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parents:
diff changeset
8072 moue in ver$o O, &amp; $opra la helice IRS; &amp; M $opra l'altra helice.</I>
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parents:
diff changeset
8073 <foot><I>Gg</I></foot>
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parents:
diff changeset
8074 <pb>
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parents:
diff changeset
8075 <p><I>ranno dunque le dette helici eguali ad e$$e AB BC. dunque il cuneo. ABC $ar&agrave;
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parents:
diff changeset
8076 tutto inuolt<G>q</G> d'intorno al cilindro LMNO. Siano tagliate da poile helici, come
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parents:
diff changeset
8077 in$egna Pappo, $econdo la larghezza del cuneo; &amp; &agrave; que$lo modo il cuneo in$ieme</I>
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parents:
diff changeset
8078 <fig>
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parents:
diff changeset
8079 <I>co'l cilindro niente altro $ar&agrave;, che la vite, laquale habbia due helici PRM PQN
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parents:
diff changeset
8080 congiunte fra loro d'intorno al cilindro LN in vno $olo punto. che bi$ognaua
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parents:
diff changeset
8081 mo$trare.</I>
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casties
parents:
diff changeset
8082 <HEAD>COROLLARIO.</HEAD>
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parents:
diff changeset
8083 <p>Di qui puote e$$ere manife$to, come $i po$$ano de$criuere le he
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parents:
diff changeset
8084 lici nella vite.
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casties
parents:
diff changeset
8085 <p>Hora dimo$triamo, come $i mouano i pe$i $opra le helici della
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parents:
diff changeset
8086 vite.
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casties
parents:
diff changeset
8087 <p><I>Sia come prima il cuneo IGH inuolto d'intorno al cilindro DE, la cui cima $ia I, &amp;
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parents:
diff changeset
8088 $i adatti il ciliadro in modo, che $i po$$a volgere liberamente con l'a$$e $uo. &amp; $ia-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
8089 no due pe$i MN di qualunque figura vogliamo, commodati nondimeno in modo</I>
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parents:
diff changeset
8090 <pb n=118>
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casties
parents:
diff changeset
8091 <p><I>Che $e come nella terza figura, $i imporr&agrave; alcuna co$a $opra la vite, come B, che &egrave; no
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
8092 mata Tilo di$po$to in modo, che dalla parte di $otto egli habbia le helici concaue
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
8093 adattate <*>olto acconciamente ad e$$a vite. egli potr&agrave; e$$ere a$$ai chiaro, che e$$o B,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
8094 mentre la vite $i volge intorno, mouera$$i &agrave; quel modo in tutto $opra le helici della</I>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
8095 <fig>
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casties
parents:
diff changeset
8096 <I>vite, come $i moueua il pe$o $econdo la prima figura; purche il tilo $i accommo-
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parents:
diff changeset
8097 di, come in$egna Pappo nell'ottauo libro, in maniera cio&egrave;, che egli $i moua egual-
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
8098 mente di$tante dall'a$$e del cilindro auanti, ouero indietro $olamente.</I>
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casties
parents:
diff changeset
8099 <foot><I>Gf</I> 2</foot>
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casties
parents:
diff changeset
8100 <pb>
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casties
parents:
diff changeset
8101 <p><I>Et $e in luogo del tilo, che h&agrave; le helici concaue nella parte di $otto, $i ponga, come nel
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
8102 la quarta figura il cilindro concauo, come D, &amp; nella $ua concaua $uperficie $i de-
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parents:
diff changeset
8103 $criuano le helici, &amp; $i taglino in modo, che acconciamente $i adattino alla vite;
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parents:
diff changeset
8104 (percioche nel mede$imo modo $i de$criueranno le helici nella $uperficie concaua del
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casties
parents:
diff changeset
8105 cilindro, come $i f&agrave; nella conue$$a) $e la vite poi $ar&agrave; $ermata ne' poli $uoi, cio&egrave; nel</I>
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parents:
diff changeset
8106 <fig>
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parents:
diff changeset
8107 <I>$uo a$$e, &amp; volga$i intorno, egli &egrave; manife$to, che D $i mouer&agrave; al mouimento del
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parents:
diff changeset
8108 giro della vite, come $a il tilo. &amp; di pi&ugrave; $e D $i $ermer&agrave; in EF, $i che rimanga im
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parents:
diff changeset
8109 mobile, mentre la vite $i volge intorno, mouera$$i $opra le helici del cilindro D $e-
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parents:
diff changeset
8110 condo il mouimento del giro $uo, fatto alla de$tra, ouero alla $ini$tra, s&igrave; all'innan-
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parents:
diff changeset
8111 zi, come all'indtetro, &amp; il cilindro D in que$ta maniera accommedato, $i chiama
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parents:
diff changeset
8112 volgarmente la madre, ouero la femina della vite.</I>
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diff changeset
8113 <pb n=119>
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parents:
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8114 <p><I>Che $e alla vite (come nella quinta figura) $ar&agrave; po$ta la rota C co' dent&igrave;torti, come
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parents:
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8115 in$egna Pappo nel mede$imo ottauo libro, ouero anche diritti; ma in modo $atti,
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parents:
diff changeset
8116 che $i adattino facilmente con la vite. egli &egrave; $imilmente manife$to, che al mo uimen</I>
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parents:
diff changeset
8117 <fig>
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parents:
diff changeset
8118 <I>to della vite mouera&szlig;i etiandio intorno la rota C. &amp; nell'i$te$$a maniera $i moue-
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parents:
diff changeset
8119 rannoi denti della rota C $opra le helici della vite. &amp; que$ta $i dice vite perpetua,
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parents:
diff changeset
8120 percioche s&igrave; la vite, come la rota mentre $i riuolgono $tanno $empre nel modo
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parents:
diff changeset
8121 i$te$$o.</I>
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8122 <p><I>Que$te co$e habbiamo detto, accioche $ia pale$e, che la vite nel mouere il pe$o f&agrave; l'officio
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8123 del cuneo $enza perco$$a. percio che lo rimoue dal luogo oue era, $i come il cuneo
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8124 rimoue quelle co$e che moue, &amp; $ende. &amp; que$ie co$e tutte $i mouono dalla vite
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8125 come il pe$o A nella $econda figura, &amp; lo M nella prima.</I>
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8126 <p><I>Hor percioche habbiamo dimo$trato poter$i con$iderare con due ragioni il cuneo, che
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8127 moue, cio&egrave; come moue con le leue, ouero come &egrave; vn piano inchinato all' orizonie,
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8128 per&ograve; con$ideraremo anco la vite in due modi.</I>
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8129 <p><I>Et prima come ella moue conle leue; come nella prima figura. giri$i intorno KF, &amp;</I>
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8130 <fig>
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8131 <I>peruenga in KP, allhora, $i come &egrave; detto, TV $ar&agrave; fra pe$i MN. &amp; $i come
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8132 con$ideriamo le leue nel cuneo, co$i le po$siamo parimente con$ider are nella vite in
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8133 que$ta maniera, cio&egrave; $ar&agrave; IVH la leua co'l $o$tegno $uo I, &amp; il pe$o po$to in
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8134 V. $imilmente ITG la leua co'l $o$tegno $uo I, &amp; il pe$o in T. &amp; le po$$an-
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diff changeset
8135 ze mouenti dourebbono e$$ere in GH; ma $i come nel cuneo la po$$anza mouen
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diff changeset
8136 te &egrave; la perco$$a, laquale moue il cuneo; per&ograve; $ar&agrave; doue la po$$anza moue la vite, co-
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8137 me in P colmanico KP; peroche la vite $i moue $enza perco$$a. Ma que$ta con
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8138 $ideratione parer&agrave; for$e impropria per cau$a delle leue piegate. Onde $e $i inten-
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diff changeset
8139 der&agrave;, quello che &egrave; mo$$o dalla vite, e$$ere mo$$o $opra vn piano inchinato all' oriz&otilde;te;
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8140 per certo cotale con$ideratione $ar&agrave; pi&ugrave; conforme alla figura di e$$a vite, ma$sima-
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8141 mente conuenendo anche al cuneo.</I>
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8142 <pb n=120>
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8143 <HEAD>PROPOSITIONE II.</HEAD>
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8144 <p>Se $ar&agrave; la vite AB, c'habbia le helici CDEFG eguali: Di-
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8145 co che e$$e non $ono altro niente, che vn piano inchinato al-
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8146 l'orizonte, riuolto d'intorno al cilindro.
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8147 <p><I>Sia la vite AB &agrave; piombo dell'orizonte, che habbia due helici CDEFG. Ponga$i
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8148 HI eguale &agrave; GC, laquale diuida$i in due parti in K. $aranno HK KI non $o-
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8149 lamente fra loro, ma etiandio ad e$$e GEEC eguali, &amp; tiri$i ad e$$a HI la li-</I>
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8150 <fig>
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8151 <I>nea LI ad angoliretti; &amp; intenda$i per LI vn piano egualmente di$tante dall'o-
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8152 rizonte: &amp; $ia LI due volte tanto quanto la linea che gira intorno al cilindro
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8153 AB che dice$i Perimetro, laquale diuida$i in due parti eguali in M; $ar anno IM
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8154 ML eguali al Perimetro del cilindro. Congiunga$i HL, &amp; da punto M $ia ti-
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8155 <pb>
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8156 rata la linea MN egualmente di$tante da HI, &amp; congiunga$i KN. Hor per-
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8157 cioche i triangoli HIL NML $ono $imili fra loro, per e$$ere NM egualmen-</I>
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8158 <marg><I>Per la</I> 4. <I><*> questo.</I></marg> <I>te di$tante da HI; $ar&agrave; LI ad IH, come LM ad MN: &amp; permutando co-
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8159 me IL ad LM, co$i HI ad NM. Ma IL &egrave; due volte tanto quanto LM; dun
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8160 que anco HI $ar&agrave; il doppio di MN. ma ella &egrave; il doppio anche di KI; per laqual</I>
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8161 <fig>
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8162 <I>co$a KI NM $ono tra $e eguali. &amp; percioche gli angoli po$ti ad MI $ono retti,
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8163 $ar &agrave; KM vn parallel&ograve; grammo rettangolo, &amp; KN $ar&agrave; eguale ad IM. Per la-
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8164 q<*> al co$a KN $ar&agrave; eguale al Perimetro del cilindro AB. Co$i ponga$i HI in
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8165 GC <*> HK in GE. Volga$i in giro dapoi il triangolo HKN d'intorno al ci-
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8166 lind. o AP, de$criuer&agrave; HN la helice GFE; per e$$ere NK eguale al Perime-
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8167 tro del cilindro, &amp; il punto N $ar&agrave; in E &amp; MN in CE. &amp; percioche ML &egrave;
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8168 eguale al Perimetro del cilindro. Vo ga$i di nuouo in giro il triangolo NML d'in
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8169 torno al cilindro AB NI, de$criuer&agrave; la he ice EDC. Per laqual co$a tutta la LH
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8170 de$cr uer&agrave; due helici CDEFG. egli &egrave; dunque chiaro che que$te helici della vite
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8171 niente altro $ono $e non il piano inchinato all'orizonte, la cui inclinatione &egrave; l'ango
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8172 lo HLI inuolto intorno al cilindro, $opra ilquale moue$i il pe$o. che bi$ognaua
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8173 mo$trare.</I>
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8174 <pb n=121>
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8175 <p><I>Ma in che maniera ci&ograve; $i riduca alla bilancia &egrave; manife$to per la nona dell ottauo libre
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8176 dell'i$te$$o Pappo.</I>
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8177 <p>Ma in che maniera ci&ograve; $i riduca alla bilancia. &amp;c.
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8178 <p>L'Autore in tutti que$ti $uoi libri delle Mechaniche non h&agrave; voluto trappore co$a al-
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8179 cuna detta da altri, &amp; che non $ia to talmente $ua, per&ograve; h&agrave; la$ciata la propo$itio-
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8180 ne di Pappo qu&igrave; allegata da lui, laquale facendo mirabilmente al propo$ito per
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8181 dichiarare dauantaggio quanto egli in que$to luogo propone, h&ograve; giudicato
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8182 e$$ere conueneuole l'aggiungeruela.
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8183 <HEAD>PROBLEMA DI PAPPO ALESSANDRINO
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8184 nell'ottauo libro delle raccolte Mathematiche.</HEAD>
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8185 <p><*>o$$o vn dato pe$o da vna po$$anza in vn piano egualmente di-
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8186 $tante dall'orizonte, &amp; dato vn'altro piano inchinato, ilquale
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8187 faccia vn'angolo dato co'l $ottopo$to piano; trouar vna po$
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8188 $anza, dallaquale $ia mo$$o il dato pe$o nel piano inchinato.
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8189 <p><I>Pa$$i il $ottoposto piano egualmente di$tante dall'orizonte per la linea MN. ma per
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8190 KM pa$si il piano inchinato &agrave; que$to nel dato angolo KMN. &amp; $ia il pe$o A
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8191 mo$$o dalla po$$anza C nel $ottopo$to piano. &amp; in vece di A intenda$i vna s$e-</I>
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8192 <fig>
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8193 <I>ra egualmente graue intorno al centro E; laqual $i collochi nel piano por MK, &amp;
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8194 lo tocchi in L. la linea dunque tirata EL &egrave; &agrave; piombo al piano, $i come &egrave; $tato di-
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8195 mo$trato nel quarto teorema de i Sferici. et per&ograve; ella &egrave; perpendicolare alla linea KM.
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8196 Tiri$i EH equidi$iante alla MN. &amp; dal punto L $i tiri ad EH la perpendico-
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8197 lare LF. Hor percioche l'angolo EHL &egrave; dato per e$$er eguale al dato angolo acu
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8198 to KMN; $ar&agrave; ancora l'angolo ELF dato, cio&egrave; eguale all'angolo EHL e$$en</I>
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8199 <foot><I>Hh</I></foot>
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8200 <pb>
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8201 <I>do che il triangolo ELF $ia equiangolo al triangolo EHL. adunque il triangolo
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8202 ELF &egrave; dato in $pecie; &amp; la proportione di EL, cio&egrave; di EG ad EF &egrave; data. per
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8203 laqual co$a, &amp; la proportion della restante FG ad EF $ar&agrave; data. Faccia$i come
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8204 GF ad FE, co$i il pe$o A al pe$o B; &amp; la po$$anza C alla po$$anza D. Ma
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8205 la po$$anza del pe$o A &egrave; C; adunque la po$$anza del pe$o B nel mede$imo piano
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8206 $ar&agrave; D. &amp; perche co$i &egrave; laretta linea GF ad FE, come il pe$o A al pe$o B:</I>
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8207 <fig>
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8208 <I>$e li pe$i AB $aranno po$ti ne i centri EG appiccati nel punto F, pe$eranno egual
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8209 mente; come $ostentati dalla ba$e LF, laquale &egrave; &agrave; piombo all'orizonte. Ma &egrave; po
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8210 $to il pe$o A intorno al centro E. percioche in $uo luogo &egrave; la s$era. dunque il pe-
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8211 $o B posto intorn'al G, pe$er&agrave; egualmente; di modo che la s$era per la inclinatio-
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8212 ne del piano non de$cender &agrave; al ba$$o; ma$tar&agrave; $erma, come $e ella fo$$e nel $ottopo-
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8213 $to piano. &amp; perche nel $ottopo$to piano ella $arebbe mo$$a dalla po$$anza C; adun-
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8214 que nel piano inclinato $ar&agrave; mo$$a dall'vna el'altra, cio&egrave; dalla po$$anza C, &amp; dal
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8215 la po$$anza del pe$o B, cio&egrave; dalla po$$anza D. &amp; la po$$anza D &egrave; data.</I>
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8216 <p><I>La ri$olutione adunque del problema &egrave; $tata geometricamente dimo$trata. ma accioche
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8217 con vn e$empio facciamo &amp; la con$trutione, &amp; la dimostratione. $ia il pe$o A, per e-
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8218 $empio, di ducento talenti, condotto nel piano equidi$tante all'orizonte dalla po$$anza
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8219 C mouente; cio&egrave; $iano quaranta huomini, che lo mouano. ma l'angolo KMN,
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8220 cio&egrave; EHL $ia due terzi di vn retto: $ar&agrave; ilre$tante FLH vn terzo d'vn retto.
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8221 ma l'angolo ELH &egrave;retto, adunque &amp; lo ELF &egrave; due terzi d'vn retto. &amp; di quali
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8222 parti quattro retti contengono</I> 360. <I>di tali l'angolo ELF, ne contiene</I> 60. <I>ma di
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8223 quali due retti contengono</I> 360. <I>di tali l'angolo ELF ne contiene</I> 120. <I>per laqual
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8224 co$a de$critto vn cerchio intorn' al triangolo rettangolo ELF; $ar&agrave; la circon$eren-
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8225 za, allaquale &egrave; $ottoposta la retta linea EF,</I> 120. <I>di quelle parti, delle quali tutto</I>
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8226 <pb n=122>
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8227 <I>il cerchio &egrave;</I> 360. <I>&amp; la retta linea EF &egrave; qua$i</I> 104. <I>di quelle parti, dellequali EL
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8228 diametro del cerchio &egrave;</I> 120. <I>Si come que$te $ono co$e chiare dalla tauola delle linee
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8229 rette, che $i de$criuono nel cerchio, appre$$o Tolomeo nel primo libro delle co$e Ma-
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8230 tematiche. La proportione adunque della retta imea EL, cio&egrave; di EG ad EF &egrave; quel-
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8231 la, che ha</I> 120. <I>&agrave;</I> 104. <I>&amp; per&ograve; la proportione della re$tante GF ad FE &egrave; quella
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8232 che h&agrave;</I> 16. <I>&agrave;</I> 104. <I>Mala mede$ima &egrave; del pe$o A al pe$o B, &amp; della po$$anza C
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8233 alla po$$anza D. Ma il pe$o A &egrave; di</I> 200. <I>talenti, &amp; la po$$anza C, che lo moue, &egrave;
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8234 di</I> 40. <I>huomini; adunque il pe$o B $ar&agrave; di mille, e trecento talenti. mala po$$an-
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8235 za D di ducento &amp; $e$$anta huomini. percioche come</I> 16. <I>&agrave;</I> 104. <I>co$i &egrave;</I> 200. <I>&agrave;</I>
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8236 1300 <I>&amp;</I> 40. <I>&agrave;</I> 260. <I>$i che e$$endo che primamente il pe$o di ducento talenti $ia
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8237 mo$$o da quaranta huomini nel piano egualmente distante dall'orizonte: $ar&agrave; mo$-
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8238 $o l'i$te$$o pe$o da gli huomini gia detti; cio&egrave; da trecent'huomininel piano inchina-
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8239 to all'orizonte $econdo l'angolo KMN. ilquale &egrave; po$to e$$er due terzi di vn
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8240 retto.</I>
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8241 <p><I>Poiche habbiamo veduto in che modo $i mouono i pe$i con que$to istrumento; hora
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8242 egli &egrave; da con$iderare quali $iano quelle co$e, lequali operano s&igrave;, che ipe$i $i mouano fa-
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8243 cilmente, &amp; que$te $ono due.</I>
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8244 <foot><I>Hh</I> 2</foot>
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8245 <pb>
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8246 <p>Primieramente quel che fa s&igrave; che pi&ugrave; facilmente il pe$o $i moue,
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8247 &amp; che pi&ugrave; appartiene etiandio alla e$$entia della vite, &egrave; la he-
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8248 lice po$ta d'intorno alla vite. Come $e d'intorno alla data vi-
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8249 te AB $aranno due helici di$pari CDAEFG, &amp; $ia AC
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8250 minore di EG. Dico che il pe$o mede$imo $i mouer&agrave; pi&ugrave; fa
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8251 cilmente $opra la helice CDA, che $opra EFG
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8252 <p><I>Compia$i il cuneo AD CHI, cio&egrave; de$criua$i la helice CHI eguale &agrave; CDA, &amp; $ia
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8253 la cima del cuneo C. $imilmente compia$i il cuneo GFEKL, la cui cima $ia E. pon</I>
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8254 <fig>
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8255 <I>ga$i dapoi la linea retta MN, laquale $ia eguale ad AC, &agrave; piombo dellaquale $ia</I>
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8256 <marg><I>Per la</I> 1. <I>di <*>esto.</I></marg> <I>tirata la liuea NP, che $ia eguale al Perimetro del cilindro AB: &amp; congiun-
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8257 ga$i PM; $ar&agrave; PM perle co$e dette, eguale ad e$$a CDA. Allunghi$i po$cia</I>
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8258 <marg><I>Per la</I> 1. <I>di <*>esto.</I></marg> <I>MN in O, et $accia$i ON eguale ad MN, et congiunga$i OP; $ar&agrave; il cuneo
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8259 OPM eguale al cuneo ADCHI. &amp; $imilmente faccia$i il cuneo STQ eguale</I>
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8260 <pb n=123>
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8261 <I>ai cuneo GFEKL; $ar&agrave; TR eguale ad e$$a PN, &amp; al Perimetro del cilindro
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8262 &amp; QR eguale &agrave; GE. &amp; pere$$ere GE maggiore di AC, $ar&agrave; anco RQ mag
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8263 giore di MN. tagli$i RQ in V, &amp; $accia$i RV eguale ad e$$a MN, &amp; con-
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8264 giunga$i TV: $ar&agrave; il triangolo TVR eguale al triangolo MPN; percioche le
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8265 due linee TRRV $ono eguali alle due PN NM, &amp; gli angoli i quali conten-
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8266 gono $ono eguali, cio&egrave; retti. dunque l'angolo RTV $ar&agrave; eguale all'angolo NPM.</I> <marg><I>Per la</I> 4. <I>del primo.</I></marg>
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8267 <I>Per laqual co$a l'angolo MPN &egrave; minore dell'angolo QTR; &amp; i doppi di que$ti,
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8268 cio&egrave; l'angolo MPO &egrave; minore dell'angolo QTS. Horpercioche il cuneo, ilquale h&agrave;
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8269 l'angolo alla cima minore pi&ugrave; facilmente moue, &amp; fende, che quello che l'hamaggio
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8270 re. dunque il cuneo MPO pi&ugrave; facilmente mouer&agrave;, che QTS. piu facilmente dun
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8271 que $ar&agrave; mo$$o il pe$o dal cuneo ADCHI, che dal cuneo GFEKL. dunque il
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8272 pe$o pi&ugrave; $acilmente $ar&agrave; mo$$o $oprala helice CDA, che $opra la EFG. &amp; nel
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8273 modo i$te$$o prouera$$i, che quanto minore $ar&agrave; AC tanto pi&ugrave; ageuolmente $i mo
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8274 uer&agrave; il pe$o. il che bi$ogncua mo$trare.</I>
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8275 <HEAD>Altramente.</HEAD>
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8276 <p><I>Sia data la vite AB, che habbia due helici eguali CDEFG; $ia dapoi vn'altro ci-
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8277 lindro <G>a b</G> eguale ad e$$o AB, nel quale prenda$i OP eguale &agrave; CG; &amp; diuida$i
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8278 OP in tre parti eguali OR RT TP; &amp; de$criuan$i tre helici OQ RS TV P;
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8279 $ar&agrave; cia$cuna delle OR RT TP minore di CE, &amp; di EG; percioche la terza</I>
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8280 <fig>
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8281 <I>parte &egrave; minore della met&agrave;. dico, che il pe$o mede$imo $i mouer&agrave; pi&ugrave; facilmente $o-
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8282 prale helici OQRS TVP, che $opra CDEFG. faccia$i HIL triangolo di an
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8283 goli retti, in modo che HI $ia eguale &agrave; CG, &amp; IL $ia eguale al doppio del Peri-
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8284 metro del cilindro AB, &amp; per LI $i intenda vn piano egualmente di$tante dall'o-</I>
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8285 <marg><I>Per la</I> 2. <I>di<*>esto.</I></marg> <I>rizonte; $ar&agrave; HL eguale &agrave; CDEFG, &amp; HLI $ar&agrave; l'angolo della inclinatione.
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8286 faccia$i $imilmente il triangolo X<G>*u</G>Z di angoli retti, in modo che XZ $ia egualc</I>
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8287 <pb n=124>
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8288 <I>ad e$$a OP, laquale $ar&agrave; etiandio eguale &agrave; CG, &amp; ad HI; &amp; $ia Z<G>*u</G> tre volte
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8289 tanto quanto &egrave; il Perimetro del cilindro: $ar&agrave; X<G>*u</G> eguale ad OQRSTVP. di-
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diff changeset
8290 uida$i Z<G>*u</G> in tre parti eguali in <G>g d</G>, $ar&agrave; cia$cuna delle linee Z <G>g g d d *u</G> egua-
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8291 le al Perimetro del cilindro <G>a b</G>, lequali etiandio $aranno eguali al Perimetro del
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8292 cilindro AB; &amp; per con$eguente ad e$$e IM, &amp; ML. congiunga$i X <G>d</G>. &amp;
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8293 percioche le due linee HI IL $ono eguali alle due XZ Z<G>d</G>, &amp; l'angolo HIL ret
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8294 to &egrave; eguale all'angolo XZ<G>d</G> retto; $ar&agrave; il triangolo HIL eguale al triangolo XZ<G>d</G>;
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8295 &amp; l'angolo HLI eguale all'angolo X<G>d</G>Z; &amp; X<G>d</G> eguale ad HL. ma perche
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diff changeset
8296 l'angolo X <G>d</G> Z &egrave; maggiore dell'angolo X<G>*u</G>Z; $ar&agrave; l'angolo HLI maggiore del-</I> <marg><I>Per la</I> 21. <I>del prime.</I></marg>
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8297 <I>l'angolo X <G>*u</G>Z. &amp; perci&ograve; il piano HL pi&ugrave; inchina all'orizonte, che X <G>*u</G>. Per la
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8298 qual co$a il pe$o mede$imo da po$$anza minore $opra il piano X<G>*u</G> $ar&agrave; mo$$o, che $o
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8299 pra il piano HL; come anco facilmente $i caua dalla $te$$a nona di Pappo. &amp; per
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8300 non e$$ere nient'altro le helici OQRSTVP, che il piano X<G>*u</G> inchinato all' ori-
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8301 zonte nell'angolo X <G>*u</G> Z d'intorno al cilindro <G>a b</G> inuolto; &amp; $imilmente per non
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8302 e$$ere niente altro le helici CDEFG, che il piano HL inchinato all'orizonte nel-
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8303 l'angolo HLI d'intorno al cilindro AB inuolto; dunque pi&ugrave; facilmente mouera$$i
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8304 il pe$o $opra le helici OQRS TVP, che $opra le helici CDEFG.</I>
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8305 <p><I>Che $e OP diuidera$$i in quattro parti eguali, &amp; $i de$criueranno d'intorno <G>a b</G> quat-
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8306 tro helici, $i mouer&agrave; anco pi&ugrave; facilmente il pe$o $opra queste quattro, che $opra le
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8307 tre OQRS TVP, &amp; quanto pi&ugrave; helici $aranno, tanto pi&ugrave; facilmente $i mouer&agrave;
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8308 il pe$o. ilche bi$ognaua mostrare.</I>
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8309 <p><I>Ma il tempo di que$to mouimento facilmente $i fa chiaro, perochele helici CDEFG
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8310 $ono eguali ad HL: &amp; le helici OQRS TVP $ono eguali ad X<G>*u</G>; ma X<G>*u</G> &egrave;
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8311 maggiore di HL; per&ograve; $accia$i <G>*u c</G> eguale ad HL: $e dunque due pe$i $i moueran</I> <marg><I>Per la</I> 18. <I>del primo.</I></marg>
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8312 <I>no $oprale linee LH <G>*u</G>X, &amp; le velocit&agrave; de' mouimenti $iano eguali, pi&ugrave; to$to pa$
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8313 $er &agrave; quel che $i moue $opra LH, di quel che $i moue $opra <G>*u</G>X: peroche nel tempo</I> <marg><I>Per la</I> 48. <I>del primo.</I></marg>
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8314 <I>i$te$$o $aranno in H<G>e</G>. Per laqual co$a il tempo di quel che $i moue $opra le helici</I> <marg><I>Per la prima delle da te. &amp; per la</I> 6. <I>del</I> 1. <I>del Monteregie de i tri<*> goli.</I></marg>
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8315 <I>OQRSTVP $ar&agrave;maggiore di quello che &egrave; mi$ura di quello che moue$i $opra CD
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8316 EFG, &amp; quanto pi&ugrave; helici $aranno, tanto maggiore $ar&agrave; il tempo. &amp; e$$endo date
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8317 le linee HI XZ, &amp; IL Z<G>*u</G>; percioche gi&agrave; $ono date le viti AB <G>a b</G>, &amp; dati
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8318 gli angoli ad IZ retti, $ar&agrave; data HL. $imilmente anco X<G>*u</G> $ar&agrave; data. Per la-
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8319 qual co$a $ar&agrave; data anco la loro proportione. La proportione dunque de' tempi
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8320 delle co$e lequali $ono mo$$e $opra le helici, $ar&agrave; data.</I>
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8321 <p>L'altra co$a, la quale &egrave; cagione che i pe$i ageuolmente $i muouo-
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8322 no $ono le $tanghe, ouero i manichi, co' quali $i volge intorno
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8323 la vite.
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parents:
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8324 <p><I>Sia la vite che habbia le helici ABCD, &amp; habbia anche le $tanghe EF GH po$te
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parents:
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8325 ne'buchi della vite. $ia $otto le helici il cilindro MN nel quale non $iano intaglia
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8326 te le belici; &amp; d'intorno al cilindro volga$i la corda, che tiri il pe$o O, ilquale $i mo
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8327 ua $econdo il mouimento delle $tanghe EF GH, come $e fo$$e tirato con lo $tro-
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parents:
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8328 mento dell'argano. $ia tirata (per quelle co$e, che prima $ono $tate dette dell'a$$e</I>
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8329 <fig>
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parents:
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8330 <I>nella rota) la linea LK eguale alla $tanga, &amp; &agrave; piombo dell'a$$e del cilindro, &amp;
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parents:
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8331 che lo tagli in I: egli &egrave; manife$to, che quanto $ar&agrave; pi&ugrave; lunga LI, &amp; quanto pi&ugrave; cor
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parents:
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8332 ta IK, che il pe$o O pi&ugrave; facilmente $i mouer&agrave;. ma egli &egrave; da auertire che mentre
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parents:
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8333 la vite moue il pe$o, $e $i imaginer&agrave;, che in luogo di tirare il pe$o O con la corda, ella
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8334 moua il detto pe$o $opra le helici ABCD, mouer&agrave; etiandio il pe$o in K, ilquale</I>
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8335 <marg><I><*>l corolla <*>.</I></marg> <I>$ia R pi&ugrave; ageuolmente $opra le helici. percioche LK &egrave; leua, il cui $o$tegno &egrave; I; e$
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parents:
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8336 $endo che $i volga la vite d'intorno all'a$$e, &amp; la po$$anza mouente $ia in L, &amp; il</I>
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parents:
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8337 <marg><I>Per la</I> 1. <I>di<*>sto del <*>ua.</I></marg> <I>pe$o in K; peroche $imoue pi&ugrave; facilmente il pe$o con la leua LK, che $enza la le-
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parents:
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8338 ua; percioche LI $empre &egrave; maggiore di IK. Onde intenda$i, che $tando $erma la</I>
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parents:
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8339 <pb n=125>
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parents:
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8340 <I>vite $i moua il pe$o R dalla po$$anza di L con la leua LK $opra la helice CK, oue
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parents:
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8341 ro che &egrave; il mede$imo, $i come anco di $opra dicemmo, $e il pe$o R $ar&agrave; in maniera ac-
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parents:
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8342 commodato, che non po$$a mouer$i $e non $opra la linearetta PQ egualmente di-
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parents:
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8343 $tante dall'a$$e del cilindro: &amp; $ia riuolta intorno la vite, $tando la po$$anza in L:
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parents:
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8344 mouera$$i il pe$o R $opra la helice CD nell'i$te$$o modo, come $e fo$$e mo$$a dalla
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parents:
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8345 leua LK. percioche egli &egrave; il mede$imo, che ouero $tando $erma la vite il pe$o $imo
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parents:
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8346 ua $opra la helice, ouero che la helice $i volga intorno, in modo che il pe$o $i moua $o
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parents:
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8347 pra lei per e$$ere mo$$o dall'i$te$$a po$$anza di L. $imilmente mo$trera&szlig;i, che quan-</I> <marg><I>Per la</I> 1. <I>di questo della leua.</I></marg>
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parents:
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8348 <I>to pi&ugrave; lunga &egrave; LI, dauantaggio anco mouer$i $empre piu $acilmente il pe$o, pero-
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parents:
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8349 che $i mouerebbe da po$$anza minore. che era il propo$ito.</I>
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8350 <p><I><*>tempo di que$to moto parimente &egrave; mani$e$to, percioche quanto &egrave; pi&ugrave; longa LI tanto
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8351 il tempo $ar&agrave; maggiore, pur che le po$$anze de i mouimenti $iano eguali in velocit&agrave;,
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8352 $i come &egrave; detto dell'a$$e nella rota.</I>
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8353 <HEAD>COROLLARIO.</HEAD>
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8354 <p>Da que$te co$e &egrave; manife$to, che quante pi&ugrave; helici $ono, &amp; quan
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parents:
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8355 to pi&ugrave; $ono lunghe le $tanghe, ouero i manichi, il pe$o ben pi&ugrave;
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8356 facilmente $i moue, ma pi&ugrave; tardo.
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parents:
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8357 <p>Et alla fine di qui $i far&agrave; manife$ta la virt&ugrave; della po$$anza che mo
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diff changeset
8358 ue, che &egrave; po$ta nelle $tanghe.
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8359 <foot><I>Ii</I></foot>
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8360 <pb>
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8361 <p><I>Sia dato il pe$o A come cento, $ia CD vn piano inchinato all'orizonte nell'angolo
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8362 DCE. Troui$i per la i$te$$a nona di Pappo con quanta $orza il pe$o A $i moue $o
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diff changeset
8363 pra CD, che $ia diece. Faccia$i la vite LM, che habbia le helici GHIK &amp; le
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diff changeset
8364 altre nell'angolo ECD per le co$e che $ono dette, la po$$anza di diece mouer&agrave; il
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diff changeset
8365 pe$o A $opra le helici GHIK. Ma $e con que$ta vite vogliamo mouere il pe$o A,</I>
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8366 <fig>
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diff changeset
8367 <I>&amp; la po$$anza mouente $ia come due. Tiri$i la linea NP &agrave; piombo dell'a$$e della</I>
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diff changeset
8368 <marg><I>Per la</I> 1. <I>di<*>esto del<*>.</I></marg> <I>vite, che tagli quell a$$e in O; &amp; faccia$i PO ad ON, come vno &agrave; cinque, cio&egrave;
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8369 due &agrave; diece. Hor percioche la po$$anza che moue il pe$o A in P, cio&egrave; $opra le he-
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diff changeset
8370 lic, &egrave; come diece, allaquale po$$anza re$iste, &amp; &egrave; eguale la po$$anza di N, come
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diff changeset
8371 due, percioche NP &egrave; vnaleua, il cui $o$tegno &egrave; O. dunque la po$$anza come
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8372 due po$ta in N mouer&agrave; il pe$o A $oprale helici della vite. Faccian$i dunque che
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8373 le $tanghe, ouero i manichi peruengano fin ad N. egli &egrave; mani$e$to, che la po$$an-
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diff changeset
8374 za di due in que$te mouer&agrave;'l pe$o di cento con la vite LM.</I>
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8375 <p><I>Se dunque $ar&agrave; la vite QR, che habbia le helici nell'angolo DCE, &amp; d'intorno ad</I>
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8376 <pb n=126>
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8377 <I>e$$a $ia la $ua madre S, laquale $e pe$er&agrave; cento, aggiunga$i ST che $ia certo mani
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diff changeset
8378 co, &ograve; $tanga, di modo che T $ia di$tante dall'a$$e del cilindro nella proportione
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diff changeset
8379 i$te$$a, che &egrave; NOP; egli &egrave; manife$to, che la po$$anza di due in T moue S $opra
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diff changeset
8380 le helici della vite; peroche niente altro &egrave; S che il pe$o mo$$o $oprale helici della vi
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parents:
diff changeset
8381 te, $imilmente $e S $ar&agrave; immobile volti$i intorno la vite co'l manico, ouero con la
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8382 $tanga QX fatta nella proportione mede$ima; &amp; $e $ar&agrave; la vite cento di pe$o, (la
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8383 quale ben da $e $te$$a, ouero co'l pe$o V attaccato alla vite, ouero co'l pe$o <G>*u</G> po$to
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diff changeset
8384 $opra la vite pe$er&agrave; cento) egli &egrave; manife$to, che la po$$anza di due in X mouer&agrave; la
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diff changeset
8385 vite QR $opra le helici intagliate nella madre della vite. &amp; co$i nelle altre co$e,
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diff changeset
8386 lequali co'l d<*>ficio della vite $i mouono, ritroueremo la proportione del pe$o alla po$-
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8387 $anza.</I>
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8388 <HEAD>COROLLARIO.</HEAD>
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8389 <p>Da que$to &egrave; chiaro come vn dato pe$o $i moua da vna data po$-
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8390 $anza con la vite.
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8391 <foot><I>Ii</I> 2</foot>
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8392 <pb>
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8393 <p><I>Oltre &agrave; ci&ograve; parimente in que$to luogo occorre ad e$$ere o$$eruato, che quanto pi&ugrave; heli-
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8394 ci $aranno nella madre della vite, tanto meno pati$ce la vite nel mouere i pe$i, che
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8395 $e la madre haur&agrave; vn'helice $ola, allhora il pe$o di cento $ar&agrave; $o$tenuto da vna $ola
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8396 helice della vite, ma $e pi&ugrave; $ar&agrave; anco compartita la grauezza del pe$o in pi&ugrave;, &amp; in</I>
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8397 <fig>
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8398 <I>tante quante $aranno le helici della vite; come $e conterr&agrave; quattro helici, allhora
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8399 quattro helici della vite, l'vna aiutando l'altra fra loro pre$teranno l'opera &agrave; $o$te-
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8400 nere tutto il pe$o; percioche cia$cuna di loro $o$tenter&agrave; la quarta parte del pe$o tut
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8401 to. che $e dauantaggio contenir&agrave; pi&ugrave; helici, $i compartir&agrave; an<*>o in pi&ugrave; portioni, &amp;
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8402 perci&ograve; minori, tuttala grauezza del pe$o.</I>
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8403 <p>Egli &egrave; $tato dunque dimo$trato, che il pe$o $i moue dalla vite,
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8404 come da cuneo $enza perco$$a: peroche ella in vece di perco$
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8405 $a moue con la leua, cio&egrave; con la $tanga, ouero manico.
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8406 <pb n=127>
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8407 <p>Dimo$trate cote$te co$e, egli&egrave; manife$to in qual modo $i po$$a
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parents:
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8408 mouere vn dato pe$o da vna data po$$anza. che $e con la leua
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parents:
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8409 ci&ograve; vogliamo menar ad effetto; po$$iamo &amp; con vna data leua
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parents:
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8410 mouere vn dato pe$o con vna data po$$anza. La qual co$a
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parents:
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8411 non $i puote gi&agrave; fare del tutto da ne$$uno de gli altri di$ici,
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8412 $ia ouero la vite, ouero l'a$$e nella rota, &ograve; pur la taglia, per-
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8413 cioche n&egrave; con le taglie date, n&egrave; con vn dato a$$e nella rota, n&egrave;
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8414 meno con vna data vite, $i puote mouere vn pe$o dato da
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8415 vna po$$anza data; per e$$ere in loro $empre determinata la
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8416 po$$anza. Se dunque la po$$anza, che habbia &agrave; mouere il pe-
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8417 $o, $ar&agrave; data minore di que$ta, non mouer&agrave; il pe$o giamai.
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8418 nondimeno po$$iamo dato l'a$$e, &amp; la rota $enza i raggi moue
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8419 re vn pe$o dato con vna data po$$anza: potendo noi adattare
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8420 i raggi in modo, che il mezo diametro della rota data in$ieme
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8421 con la lunghezza del raggio habbia al mezo diametro dell'a$-
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8422 $e la proportione data. la qual co$a i$te$$a puote accadere alla
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8423 vite ancora; cio&egrave; mouere vn dato pe$o con vna data vite $en-
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8424 za il manico, &ograve; $tanga con vna data po$$anza. percioche cono
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8425 $ciuta la po$$anza, la quale habbia da mouere il pe$o $opra le he
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8426 lici, po$$iamo di$porre in maniera il manico, &ograve; $tanga, che la
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8427 data po$$anza nella $tanga habbia la forza mede$ima, che la
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8428 po$$anza mouente il pe$o $opra le helici. &amp; concio$ia, che que
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8429 $to non po$$a per niun modo auenire alle date taglie; tuttauia
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8430 po$$iamo mouere vn dato pe$o con le date taglie, &amp; con la da
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8431 ta po$$anza in modi in finiti. Ma con lo $tromento del cuneo
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8432 egli pare e$$ere chiaro che non $i puote gi&agrave; mouere vn pe$o
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8433 dato con vna data po$$anza: percioche vna data po$$anza non
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8434 puote mouere vn dato pe$o $opra vn piano inchinato all'ori-
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8435 zonte: n&egrave; da vna po$$anza data $i mouer&agrave; vn dato pe$o con le
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8436 leue contrarie fra loro, $i come $ono nel cuneo; concio$ia che
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8437 non $i po$$a nelle leue del cuneo manten<*>re la propria, &amp; ve-
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8438 ra proportione della leua: percioche i $o<*> gni delle leue non
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8439 $ono immobili per mouer$i tutto il cunco.
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8440 <pb>
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8441 <p>Potr&agrave; dapoi cia$cuno fabricare machine, &amp; comporle di pi&ugrave; $or
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8442 ti, come di taglie, &amp; molinelli, &ograve; di argani, ouero di pi&ugrave; rote
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8443 co' denti, ouero in qual $i voglia altro modo; &amp; da quelle co-
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8444 $e che habbiamo detto ageuolmente ritrouare la proportio-
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8445 ne tra il pe$o, &amp; la po$$anza.
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8446 <p>In que$to loco &egrave; da por mente, che $e l'Autore non h&agrave; $eruato il modo di con$ide-
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8447 rare que$ti due vltimi i$trumenti, cio&egrave; il cuneo, &amp; la vite, come h&agrave; fatto la leua,
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8448 la taglia, &amp; l'a$$e nella rota, ne'quali puntalmente h&agrave; dimo$trato la proportione
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8449 della forza co'l pe$o; che ci&ograve; h&agrave; egli fatto per e$$ere que$ti due i$trumenti, cio&egrave;
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8450 il cuneo, &amp; la vite per $e $tes$i non atti ad e$$ere con$iderati in quanto $o$tengo-
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8451 no il pe$o, ma ben in quanto lo mouono. Percioche e$$endo, che le po$$anze lo
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8452 quali mouono po$$ano e$$ere infinite, non $ene puo a$$egnare ferma regola, co-
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8453 me $i farebbe della po$$anza, che $o$tiene, laquale &egrave; vna $ola, &amp; determinata. Hor
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8454 che il cuneo non $ia atto ad e$$ere con$iderato in quanto $o$tiene, que$to &egrave; chia-
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8455 ro per $e $te$$o: $imilmente che la vite non $ia atta ad e$$ere con$iderata in quan-
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8456 to $o$tiene, ci&ograve; pur $i vede manife$to nelle viti ordinarie da mouer pe$i. Come per
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8457 e$empio nella figura po$ta qu&igrave; di $opra, imaginiamoci che la madre <*> della det-
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8458 ta vite QR $tia ferma; poi $ia il pe$o V attaccato alla vite di che grauezza $i vo-
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8459 glia, &amp; hora maggiore, &amp; hora minore, con tutto ci&ograve; il pe$o V non far&agrave; giamai
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8460 s&igrave;, che la vite QK <*>ali al <*>a$$o volgendo$i nella madre. Doue e$pre$$amente $i
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8461 vede, che non $i pu&ograve; fare il pe$o V di tal $orte, &amp; grandezza che la vite $tia ferma,
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8462 talche per ogni minima aggiunta che $i face$$e al pe$o ella an da$$e al ba$$o; percio
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8463 che, $i come &egrave; detto, $empre re$terebbe ferma. L'Autore dunque h&agrave; trattato de i
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8464 due predetti vltimi $tromenti per quanto comportaua la natura loro, $i come pa-
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8465 ragonando in$ieme tutti cinque gli $trumenti da mouere pe$i per conclu$i one
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8466 dell'o pera, dice. &ldquo;Dimo$trate que$te co$e egli re$ta chiaro, &amp; quel che $egue $in'al
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8467 $ine.
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8468 <HEAD>IL FINE.</HEAD>