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New Special Instructions
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 30 Jul 2014 15:58:21 +0200 |
| parents | 22d6a63640c6 |
| children |
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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Tartaglia, Niccolo</author> <title>Quesiti et Inventione Diverse</title> <date>1554</date> <place>Napoli</place> <translator/> <lang>it</lang> <cvs_file>tarta_quesi_042_la_1554.xml</cvs_file> <cvs_version>1.8</cvs_version> <locator>042.xml</locator> </info> <text> <front> </front> <body> <chap><subchap1> <pb id="p.0001" xlink:href="042/01/001.jpg"/> <p type="head"> <s id="s.000001">QVESITI ET INVEN<lb/><emph type="italics"/>TIONI DIVERSE <emph.end type="italics"/><lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000002">DI NOVO RESTAMPATI CON VNA <lb/>GIONTA AL SESTO LIBRO, NULLA <lb/><emph type="italics"/>quale &longs;i mo&longs;tra duoi modi di redur una Citta ine&longs;pugnabile.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000003">LA DIVISIONE ET CONTINENTIA DI TVTTA <lb/>l'opra nel &longs;eguente foglio &longs;i trouara notata.</s> </p> <p type="head"> <s id="s.000004">CON PRIVILEGIO</s> </p> <figure id="id.042.01.001.1.jpg" xlink:href="042/01/001/1.jpg"/> <p type="head"> <s id="s.000005">APPRE<emph type="italics"/>SS<emph.end type="italics"/>O DE L'AVTTORE <lb/>MD LIIII.<!-- KEEP S--></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/002.jpg"/> <p type="head"> <s id="s.000006">LA PRESENTE OPERA E DI­<lb/><emph type="italics"/>ui&longs;a in noue libri, la continentia di cia&longs;cun di loro <lb/>&longs;ummariamente di &longs;otto &longs;i narra.<emph.end type="italics"/><lb/><emph type="italics"/>Nel primo libro &longs;i tratta, delli tiri & effetti delle artegliarie, &longs;econdo le &longs;ue va-<lb/> rie elleuationi, & &longs;econdo la uaria po&longs;ition delle mire con altri &longs;uoi &longs;trani <lb/> accidenti. a car. </s> <s id="s.000007">5 <lb/>Nel &longs;econdo &longs;i manife&longs;ta la differentia, che occorre fra li tiri, & effetti fatti con balle di <lb/> piombo, di ferro, ouer di pietra, con altre &longs;otilita circa la proportion pe&longs;o & mi&longs;ura <lb/> delle dette balle. a car. </s> <s id="s.000008">32 <lb/>Nel tertio &longs;e notifica le &longs;pecie di &longs;alnitri, & le uarie compo&longs;itioni delle poluere u&longs;ata da <lb/> no&longs;tri antichi & moderni &longs;perimentatori. a car. </s> <s id="s.000009">73 <lb/>Nel quarto &longs;i da el modo di &longs;aper ordinar li e&longs;&longs;erciti in battaglia &longs;otto uarie & diuer&longs;e <lb/> forme, con un modo di faper tramutar in un &longs;ubito una ordinanza in forma quadra di <lb/> gente, in una forma cunea &longs;enza de&longs;ordinar la prima ordinanza & altre. </s> <s id="s.000010">a char. </s> <s id="s.000011">43 <lb/>Nel quinto libro &longs;e in&longs;egna il modo di mettere rettamente il di&longs;egno con el Bo&longs;&longs;olo, li &longs;iti, <lb/> Pae&longs;i, & le piante delle Città, con el modo de fabicar il detto Bo&longs;&longs;olo in dui modi. <lb/> a carte. </s> <s id="s.000012">55 <lb/>Nel &longs;e&longs;to libro &longs;i narra, il modo, che &longs;i doueria o&longs;&longs;eruar nel fortificar le Città a que&longs;ti tem<lb/>pi per ouiar alli uigoro&longs;i colpi delle artegliarie per uigor della forma. a car. </s> <s id="s.000013">64 <lb/>Nella gionta del detto &longs;e&longs;to libro &longs;i mo&longs;tra dui modi de fortificar una Città, luno di quali <lb/> per &longs;e la redu&longs;&longs;e ine&longs;pugnabile, et che non potra e&longs;&longs;er battuta ne daneggiata da nemici <lb/> <expan abbr="cõ">com</expan> le artegliarie, ne potra e&longs;&longs;er minata, ne ìpite le fo&longs;&longs;e, et l'altro &longs;ara tale, che <expan abbr="ruuinã">ruuinam</expan> <lb/> dogli le mura &longs;i fara qua&longs;i piu forte che con le mura, <expan abbr="cõ">com</expan> altre particolarita. a car. </s> <s id="s.000014">71 <lb/>Nel &longs;ettimo libro &longs;i manife&longs;ta alcuni dubbij, che mouer &longs;i po&longs;&longs;eno &longs;opra li principij delle <lb/> que&longs;tioni Mecanice de Ari&longs;totile, per acuir li pelegrini in gegni. </s> <s id="s.000015">a car. </s> <s id="s.000016">78 <lb/>Nel ottauo libro &longs;i tratta della &longs;cientia di Pe&longs;i demo&longs;tratiuamente, per mezzo della qual <lb/> &longs;cientia non &longs;olamente &longs;i puo cono&longs;cere & &longs;apere la forza de l'huomo, ma anchora <lb/> trouar modo, di augumentar quella con artificio&longs;i i&longs;trumenti in infinito. </s> <s id="s.000017">a car. </s> <s id="s.000018">83 <lb/>Nel nono libro &longs;i da regola & modo di &longs;aper ri&longs;oluere uarij & diuer&longs;i ca&longs;i, ouer que­<lb/>&longs;tioni in Arithmetica, in Geometria, & in la Pratica &longs;peculatiua de l'arte Magna, <lb/> detta Algebra & almucabala, uolgarmente detta la Regola della co&longs;a, & maßime <lb/> &longs;opra le Regole de co&longs;e e cubi eguali a numero, dal pre&longs;ente Autor ritrouate, & &longs;imel <lb/> mente de cen&longs;i e cubi & altri &longs;uoi edderenti, li quali da &longs;apienti erano giudicati im­<lb/>poßibili. a car.<emph.end type="italics"/> 98 </s> </p> </subchap1><subchap1> <pb xlink:href="042/01/003.jpg"/> <p type="head"> <s id="s.000019"><emph type="italics"/>TAVOLA DE CIO CHE <emph.end type="italics"/><lb/>SI CONTIEN PARTICOLARMEN­<lb/>TEIN CIASCVNLIBRO.</s> </p> <p type="head"> <s id="s.000020"><emph type="italics"/>El &longs;oggetto delli Que&longs;iti del primo libro.<emph.end type="italics"/><lb/>Di <emph type="italics"/>che &longs;o&longs;tantia &longs;ia la notitia della proportione delli tiri lontani e propinqui. </s> <s id="s.000021">a car­<lb/>te. </s> <s id="s.000022">5. al Que&longs;ito primo <lb/>Come che una artegliaria fara maggior effetto nelli tiri elleuati che nelli aliueliati. </s> <s id="s.000023">a car­<lb/>te. </s> <s id="s.000024">7. al Que&longs;ito &longs;econdo <lb/>Come the una balla tirata da una artegliaria mai ua per linea retta eccetto che rettamente <lb/> in &longs;u&longs;o uer&longs;o el cielo, ouer rettam&ebreve;te in zo&longs;o uer&longs;o el centro del <expan abbr="mõdo">mondo</expan>. </s> <s id="s.000025">a car.<emph.end type="italics"/> 11. <expan abbr="q.">que</expan> 3 <lb/>C<emph type="italics"/>ome che tirando un pezzo due uolte luna drieto l'altra in un mede&longs;imo uer&longs;o, tirara <lb/> piu alla &longs;econda uolta che alla prima. a carte. </s> <s id="s.000026">23. al Que&longs;ito. <!-- REMOVE S-->4 <lb/><expan abbr="Cõe">Cone</expan> che a tirar molte uolte <expan abbr="cõtinue">continue</expan> un pezzo al fine tirara men <expan abbr="lõtano">lontano</expan>. </s> <s id="s.000027">a car. </s> <s id="s.000028">13. al<emph.end type="italics"/> <expan abbr="q.">que</expan> 5 <lb/>D<emph type="italics"/>onde procede che da gando piu poluer a un pezzo dara piu alto da quel &longs;egno doue con <lb/> men poluere ue tiraua rettamente de mira. </s> <s id="s.000029">a car. </s> <s id="s.000030">14. al Que&longs;ito. <!-- REMOVE S-->6. <lb/>De tutti li effetti, ouer botte cha puo occorrere nel tirar de mira quando che la mira da­<lb/>uanti del pezzo e egualmente alta a quella da drio, o ueramente piu alta o ueramente <lb/> piu ba&longs;&longs;a del &longs;uo douere. a carte. </s> <s id="s.000031">14. al Que&longs;ito. <!-- REMOVE S-->7. <lb/>De tutti li effetti, ouer botte che puo occorrere nel tirar de mira quando che la mira dauan<lb/>ti non e tanto piu corta di quella de drio quanto bi&longs;ognaria. a car. </s> <s id="s.000032">16. al<emph.end type="italics"/> <expan abbr="q.">que</expan> 8. <lb/>D<emph type="italics"/>e tutti li effetti, ouer botte che puo occorrere nel tirar de mira quando che la mira dauan<lb/>ti ha la &longs;ua conueniente ba&longs;&longs;ezza re&longs;petto a quella de drio. </s> <s id="s.000033">a car. </s> <s id="s.000034">17. al Que&longs;ito. <!-- REMOVE S-->9. <lb/>Donde puo proceder la cau&longs;a quando che un pezzo da molto co&longs;tero nel tirar de mira. <lb/> a carte. </s> <s id="s.000035">17. al Que&longs;ito. <!-- REMOVE S-->10. <lb/>Come che el non e generale que&longs;ta regola che quanto che un pezzo e piu longo di canna <lb/> tanto piu tiri lontano, & come che nel far colobrine molto longhe è un error troppo <lb/> manife&longs;to & di molto danno. a car. </s> <s id="s.000036">18. al Que&longs;ito. <!-- REMOVE S-->11. <lb/>Della longhezza de tutte le &longs;pecie de pezzi, & della quantita del metallo, che <expan abbr="cõmunam&ebreve;-">communam&ebreve;­<lb/></expan> te ue intra in cadauno de loro, et delli animali, che ui uol a <expan abbr="cõdurli">condurli</expan>. </s> <s id="s.000037">a. <!-- REMOVE S-->c. <!-- REMOVE S-->19. al<emph.end type="italics"/> <expan abbr="q.">que</expan> 11. <lb/>D<emph type="italics"/>i quanta longhezza doueria e&longs;&longs;er la canna de cadaun pezzo a douer e&longs;&longs;er ben propor<lb/>tionata la longhezza. a car. </s> <s id="s.000038">20. al Que&longs;ito. <!-- REMOVE S-->22. <lb/>Come de nece&longs;sita eglie un certo termine, ouer mi&longs;ura nel dar della poluere nel qual <lb/> daendo piu, ouer men poluer al pezzo di quella tal mi&longs;ura &longs;empre tal pezzo tirara <lb/> manco. a car. </s> <s id="s.000039">20. al Que&longs;ito. <!-- REMOVE S-->13. <lb/>Qual &longs;ia meglio calcar benißimo la poluer nel pezzo ouer la&longs;&longs;arla alquanto rara. </s> <s id="s.000040">a car­<lb/>te. </s> <s id="s.000041">22. al Que&longs;ito. <!-- REMOVE S-->14. <lb/>Qual è la cau&longs;a che con un &longs;chioppo &longs;e tiri piu lontan de mira che non &longs;i fa con un ar­<lb/>chibu&longs;o & tamen lo archibu&longs;o fara maggior pa&longs;&longs;ata in un comun tramite del &longs;chiop-<emph.end type="italics"/><pb xlink:href="042/01/004.jpg"/> <emph type="italics"/>po. </s> <s id="s.000042">a car. </s> <s id="s.000043">22. al Que&longs;ito. <!-- REMOVE S-->15. <lb/>Donde procede che una artegliaria non fa tanto effetto percotendo in una naue ouer ga­<lb/>lia in mare quanto faria percottendo in una muraglia. </s> <s id="s.000044">a car. </s> <s id="s.000045">22. al Que&longs;ito. <!-- REMOVE S-->16. <lb/>Come &longs;e potria di&longs;chiodare al improui&longs;o una multitudine de artegliarie che fu&longs;&longs;eno &longs;tate <lb/> inchiodate. a car. </s> <s id="s.000046">23. al Que&longs;ito. <!-- REMOVE S-->17. <lb/>Doue na&longs;ce la cau&longs;a che una artegliaria fa manco effetto nella co&longs;a doue &longs;e tira, a &longs;tarui <lb/> molto propinquo che a &longs;tarui alquanto di lontano. </s> <s id="s.000047">a car. </s> <s id="s.000048">23. al Que&longs;ito. <!-- REMOVE S-->18. <lb/>In quanta di&longs;tantia una artegliaria faria el maggior effetto, che far po&longs;&longs;a. </s> <s id="s.000049">a carte. </s> <s id="s.000050">24. <lb/> al Que&longs;ito. <!-- REMOVE S-->29. <lb/>Perche cau&longs;a &longs;e mette quelli &longs;troppaioni di fieno, ouer di &longs;toppa auanti alla balla & da <lb/> poi. a car. </s> <s id="s.000051">24. al Que&longs;ito. <!-- REMOVE S-->20 <lb/>La cau&longs;a d'un certo ca&longs;o rediculo&longs;o di una artegliaria che &longs;orbete dentro nella canna un <lb/> cagnolino. a car. </s> <s id="s.000052">24. al Que&longs;ito. <!-- REMOVE S-->21. <lb/><expan abbr="Dõde">Donde</expan> procede che de tutte le artegliarie che creppano, creppano la maggior parte de drio, <lb/> ouer nella bocca, & rare uolte nel mezzo. a carte. </s> <s id="s.000053">25. al Que&longs;ito. <!-- REMOVE S-->22 <lb/>Come &longs;e potria cono&longs;cere &longs;e una artegliaria tirara li &longs;uoi tiri retti &longs;enza tirarla altra­<lb/>mente. a carte. </s> <s id="s.000054">26. al Que&longs;ito. <!-- REMOVE S-->23. <lb/>La cau&longs;a d'un'altro accidente di una artegliaria che &longs;orbette &longs;u&longs;o gran quantita di &longs;abbia <lb/> a Lio. a car. </s> <s id="s.000055">27. al Que&longs;ito. <!-- REMOVE S-->24. <lb/>Come che quelle mire che &longs;eruono per tirar in piano, non &longs;eruono co&longs;i preci&longs;amente per <lb/> tirar a l'alta, ouer al ba&longs;&longs;o. a car. </s> <s id="s.000056">27. al Que&longs;ito. <!-- REMOVE S-->25 &. </s> <s id="s.000057">26. <lb/>Come che quelle mire che fanno dar la botta di &longs;opra dal &longs;egno in maggior di&longs;tantia la <lb/> faranno dar molto piu di &longs;opra dal &longs;egno. a car. </s> <s id="s.000058">28. al Que&longs;ito. <!-- REMOVE S-->27. <lb/>Come che quelle mire che fanno dar la botta de &longs;otto dal &longs;egno in maggior di&longs;tantia puo <lb/> far uarij effetti. a car. </s> <s id="s.000059">28. al Que&longs;ito. <!-- REMOVE S-->28. <lb/>Donde procede che ogni Schioppettero, & anche Bombardero, generalmente quanto <lb/> che e piu propinquo al &longs;egno tolto de mira tanto piu è atto a far piu bella botta. <lb/> a car. </s> <s id="s.000060">29. al Que&longs;ito. <!-- REMOVE S-->29. <lb/>Donde procede che<gap/>urando de continuo a un &longs;e gno de mira con un mede&longs;imo &longs;chioppo alle <lb/> uolte &longs;e da molto di &longs;opra, alle uolte molto di &longs;otto, alle uolte molto costero del &longs;egno <lb/> tolto de mira & alle uolte nel &longs;egno. a car. </s> <s id="s.000061">31. al Que&longs;ito.<emph.end type="italics"/> 30 </s> </p> <p type="head"> <s id="s.000062"><emph type="italics"/>El&longs;oggetto delli Que&longs;iti del Secondo libro.<emph.end type="italics"/><lb/>Q<emph type="italics"/>ual andara piu lontaro (& quanto) una balla di Piombo, ouer di Ferro, ouer di Pie­<lb/>tra, & prima con equal quantita di Poluere, & da poi con la &longs;ua poluere ordinaria. <lb/> a car. </s> <s id="s.000063">32. al Que&longs;ito. <!-- REMOVE S-->1. 2. 3. &. </s> <s id="s.000064">4. <lb/>Qual fara maggior effetto in una di&longs;tantia comuna, una balla di Piombo, ouer di Ferro, <lb/> ouer di Pietra, & prima con equal quantita di poluere, & dapoi con la &longs;ua poluere <lb/> ordinaria. a car. </s> <s id="s.000065">33. al Que&longs;ito. <!-- REMOVE S-->5. &. </s> <s id="s.000066">6. <lb/>Donde procede che e&longs;&longs;endo tirato ad alcuni gua&longs;tadori in Rodi, alla prima uolta la balla <pb xlink:href="042/01/005.jpg"/> ziffolana molto forte per aere, & alle altri tiri la balla ui ueniua tacita & quieta. <lb/> a car. </s> <s id="s.000067">33. al Que&longs;ito. <!-- REMOVE S-->7. <lb/>Qual andara piu lontano una balla graue, ouer legera. </s> <s id="s.000068">a car. </s> <s id="s.000069">34. al Que&longs;ito. <!-- REMOVE S-->8. <lb/>Certe regole, che per la notitia del diometro & pe&longs;o di una balla &longs;e puol determinare el <lb/> pe&longs;o, ouer el diametro di qualunque altra. </s> <s id="s.000070">a car. </s> <s id="s.000071">34. al Que&longs;ito. <!-- REMOVE S-->9. & 10. <lb/>La determinatione del diametro de piu &longs;orte balle per linea ritrouati geometrice per la no <lb/> titia d'un diametro dato. a car. </s> <s id="s.000072">35. al Que&longs;ito. <!-- REMOVE S-->11. &<emph.end type="italics"/> 12. </s> </p> <p type="head"> <s id="s.000073"><emph type="italics"/>El&longs;uggetto delli Que&longs;iti del Terzo libro.<emph.end type="italics"/><lb/>Q<emph type="italics"/>ualmente la notitia del Salnitrio & la natura &longs;ua è antiquißima & come ne &longs;ono de ua­<lb/>rie &longs;pecie. a car. </s> <s id="s.000074">37. al Que&longs;ito. <!-- REMOVE S-->1. & 2. <lb/>Perche cau&longs;a li antiqui non &longs;epeno componer la poluere delle artegliarie. </s> <s id="s.000075">a carte 38. <lb/> al Que&longs;ito. <!-- REMOVE S-->3. <lb/>Che uirtu, ouer officio particolare ha cadauno di tre &longs;implici, ouer materiali, cioe Salnitrio, <lb/> Solphere et Carbone nella compo&longs;itione della poluere. </s> <s id="s.000076">a car. </s> <s id="s.000077">38. al Que&longs;ito. <!-- REMOVE S-->4. <lb/>Chi fu inuentor della poluere, & con che ragione fu determinata la proportione della quan <lb/> tita de cadauno de detti tre materiali. a car. </s> <s id="s.000078">39. al Que&longs;ito. <!-- REMOVE S-->5. <lb/>Delli uarij ordeni &longs;i antiqui come moderni u&longs;itadi nella compo&longs;itione delle poluere gro&longs;&longs;e <lb/> & fine. a car. </s> <s id="s.000079">39. al Que&longs;ito. <!-- REMOVE S-->5. <lb/>Come &longs;e puol cono&longs;cere una poluere e&longs;&longs;er piu potente de un'altra. </s> <s id="s.000080">a car. </s> <s id="s.000081">41. al Que&longs;ito. <!-- REMOVE S-->6. <lb/>Come &longs;i puo augumentar la poluere in uirtu, ouer potentia. </s> <s id="s.000082">a car. </s> <s id="s.000083">41. al Que&longs;ito. <!-- REMOVE S-->7. <lb/>Se egli è nece&longs;&longs;ario a limitar la compo&longs;itione della poluere delle artegliarie gro&longs;&longs;e da quel <lb/> la delle &longs;otile & da quella delli archibu&longs;i & Schioppi. </s> <s id="s.000084">a car. </s> <s id="s.000085">42. al Que&longs;ito. <!-- REMOVE S-->8. <lb/>Perche cau&longs;a &longs;i da la grana alla poluere delli archibu&longs;i, & non a quella delle artegliarie. <lb/> a car. </s> <s id="s.000086">42. al Que&longs;ito. <!-- REMOVE S-->9. &<emph.end type="italics"/> 10. </s> </p> <p type="head"> <s id="s.000087"><emph type="italics"/>El&longs;uggetto delli Que&longs;iti del Quarto libro.<emph.end type="italics"/><lb/>C<emph type="italics"/>ome &longs;i de procedere, a uoler redure una quantità de fanti, ouer un e&longs;&longs;ercito in Batta­<lb/>glia quadra di gente & a quanti per fila &longs;i debbono far caminar per uiaggio, ouer ca­<lb/>mino accio che occorrendo el bi&longs;ogno con facilità &longs;i pote&longs;&longs;eno mettere &longs;ubito in orde­<lb/>nanza. a car. </s> <s id="s.000088">43. al Que&longs;ito. <!-- REMOVE S-->1. &. </s> <s id="s.000089">2. <lb/>Come &longs;e debbe procedere a uoler far una ordinanza &longs;imile a una data in ogni quantità <lb/> de fanti. a car. </s> <s id="s.000090">46. al Que&longs;ito. <!-- REMOVE S-->3. <lb/>Come &longs;i de procedere uolendo redur una quantità de fanti, ouer un e&longs;&longs;ercito in una Batta­<lb/>glia quadra di terreno. a car. </s> <s id="s.000091">47. al Que&longs;ito 4. <lb/>Come &longs;i de procedere de una quantita de fanti a uolerne formar el cuneo, ouer la forfice. <lb/> a car. </s> <s id="s.000092">47. al Que&longs;ito. <!-- REMOVE S-->5. & 6. <lb/>Di che auantaggio &longs;aria un'e&longs;&longs;ercito formato in forma cunea, quando che li nemici non <lb/> &longs;ape&longs;&longs;eno con&longs;tituir la for&longs;ice. a car. </s> <s id="s.000093">48. al Que&longs;ito. <!-- REMOVE S-->7. <lb/>Come &longs;e doueria procedere uolendo de una quantità de fanti formar la Serra, ouer Segha. <lb/> a car. </s> <s id="s.000094">49. al Que&longs;ito.<emph.end type="italics"/> 8. <pb xlink:href="042/01/006.jpg"/>C<emph type="italics"/>ome &longs;e doueria procedere uolendo redur una quantita de fanti in figura Rhombica di <lb/> gente. a car. </s> <s id="s.000095">49. al Que&longs;ito. <!-- REMOVE S-->9. <lb/>Come &longs;e poteria ordinar una quantita de fanti, ouer un e&longs;&longs;ercito in una battaglia cor­<lb/>nuta. a car. </s> <s id="s.000096">50. al Que&longs;ito. <!-- REMOVE S-->10. <lb/>Come non e licito uno e&longs;&longs;ercito offe&longs;o dalle artegliarie nemiche, a re&longs;tringer&longs;i in&longs;ieme, ne <lb/> manco a caminare &longs;econdo che &longs;i troua. a car. </s> <s id="s.000097">52. al Que&longs;ito. <!-- REMOVE S-->11. <lb/>Come &longs;e doueria procedere uolendo in un &longs;ubito ridure una ordinanza in forma quadra <lb/> di gente, in una forma cunea &longs;enza de&longs;ordinare la prima ordinanza. a carte. </s> <s id="s.000098">52. <lb/> al Que&longs;ito. <!-- REMOVE S-->22. <lb/>Con ragion &longs;e approua come che eglie poßibile a ritrouar col frequente &longs;tudio modi di <lb/> ordinar un e&longs;&longs;ercito qua&longs;i di che fattion, ouer autorita &longs;i uoglia. </s> <s id="s.000099">a car. </s> <s id="s.000100">53. &.<emph.end type="italics"/> 54. </s> </p> <p type="head"> <s id="s.000101"><emph type="italics"/>El&longs;oggetto delli Que&longs;iti del quinto libro.<emph.end type="italics"/><lb/>C<emph type="italics"/>ome ua fabricato il Bo&longs;&longs;olo per tor in di&longs;egno li &longs;iti pae&longs;i & le piante delle Città. <lb/> a carte. </s> <s id="s.000102">55. al Que&longs;ito primo <lb/>Come &longs;e de proceder a, uoler tor in di&longs;egno un &longs;ito, ouer pae&longs;e contenuto da linee rette. <lb/> a carte. </s> <s id="s.000103">56. al Que&longs;ito &longs;econdo <lb/>Come &longs;e de procedere uolendo tor in di&longs;egno un pae&longs;e contenuto da linee corue & rette. <lb/> a carte. </s> <s id="s.000104">79. &. </s> <s id="s.000105">60. al Que&longs;ito. <!-- REMOVE S-->3. &. </s> <s id="s.000106">4. <lb/>Come &longs;i de procedere uolendo tor in di&longs;egno la pianta de una Città. <!-- KEEP S--></s> <s id="s.000107">a car. </s> <s id="s.000108">61. al<emph.end type="italics"/> <expan abbr="q.">que</expan> 5. <lb/>C<emph type="italics"/>ome &longs;e de procedere uolendo formar un Bo&longs;&longs;olo per &longs;e mede&longs;imo & con puoco artefi­<lb/>cio & &longs;pe&longs;a. a carte. </s> <s id="s.000109">61. al Que&longs;ito.<emph.end type="italics"/> 6. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.000110">ALLI LETTORI.</s> </p> <p type="main"> <s id="s.000111">C<emph type="italics"/>hi Brama di ueder noue inuentioni, <lb/>Non tolte da Platon, ne da Plotino, <lb/>Ne d'alcun altro Greco, ouer Latino, <lb/>Ma &longs;ol da Larte, mi&longs;ura, e Ragioni.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000112">L<emph type="italics"/>ega di que&longs;to le interrogationi, <lb/>Fatte da Pietro, Pol, Zuann', e Martino<emph.end type="italics"/><lb/>(S<emph type="italics"/>i come, l'occorea &longs;era, e Matino<emph.end type="italics"/>) <lb/>E<emph type="italics"/>t &longs;imelmente, le re&longs;pon&longs;ioni.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000113">Q<emph type="italics"/>ui dentr'intendara, sè non m'inganno, <lb/>De molti effetti a&longs;&longs;ai &longs;peculatiui, <lb/>La cau&longs;a propinqua del &longs;uo danno,<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000114">A<emph type="italics"/>nchor de molti atti operatiui, <lb/>Se uedera e&longs;&longs;equir con puoc'affanno<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000115"><emph type="italics"/>Nell'arte della guerra Profittiui. <lb/></s> <s id="s.000116">Et molto defen&longs;ui.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000117">C<emph type="italics"/>on altre co&longs;e di magno ualore,<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000118">E<emph type="italics"/>t inuentioni nell'arte maggiore.<emph.end type="italics"/></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/007.jpg"/> <p type="head"> <s id="s.000119"><emph type="italics"/>AL CLEMENTISSIMO, ET <emph.end type="italics"/><lb/>INVITTISSIMO HENRICO, OTTAVO, <lb/>PERLA DIO GRATIA RE DE ANGLIA, DE <lb/>FRANCIA, ET DE HIB ERNIA, ETC.</s> </p> <figure id="id.042.01.007.1.jpg" xlink:href="042/01/007/1.jpg"/> <p type="head"> <s id="s.000120"><emph type="italics"/>NICOLO TARTAGLIA.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000121">Le <emph type="italics"/>Dimande, Que&longs;iti, ouer Interrogationi Mae&longs;tà <lb/>Serenißima, & Illu&longs;trißima, fatte da Saui, & <lb/>Prudenti Domandatori, fanno molte uolte con&longs;i­<lb/>derare allo interrogato molte co&longs;e, & anchora co­<lb/>no&longs;cerne molte altre, le quale &longs;enza e&longs;&longs;erne adi­<lb/>mandato giamai harebbe cono&longs;ciute, ne con&longs;iderate. <lb/></s> <s id="s.000122">Que&longs;to dico per me, qual mai feci profeßione, <lb/>ouer dilettai de tirare di alcuna &longs;orte, Arteglia­<lb/>ria, Archibu&longs;o, Bombarda, ne Schioppo, (ne <lb/>manco tirar intendo) & un &longs;ol que&longs;ito fattomi da <lb/>un perito Bombardero, l'anno<emph.end type="italics"/> MDXXXI. <lb/><emph type="italics"/>in Verona, mi fece à quel tempo con&longs;iderare, & inue&longs;tigare &longs;peculatiuamente l'ordine, <lb/>& proportione di tiri propinqui, & lontani, &longs;econdo le uarie elleuationi de tale ma­<lb/>chine tormentarie, alle qual co&longs;e giamai haueria po&longs;to cura, &longs;e tal Bombardero, con <lb/>tal &longs;uo que&longs;ito non mi haue&longs;&longs;e in tal materia &longs;ueggiato. </s> <s id="s.000123">Ma piu &longs;entendo io l'anno <emph.end type="italics"/><lb/>MDXXXVII. <emph type="italics"/>con quanto gran preparamente &longs;i moueua Soliman Impera­<lb/>tor de Turchi, per infe&longs;tare la no&longs;tra Chri&longs;tiana Religione, Compoßi con gran celeri­<lb/>tà &longs;opra à tal materia una operina, & quella publicai. </s> <s id="s.000124">Accioche tai mie particolar in­<lb/>uentioni &longs;i haue&longs;&longs;eno à &longs;perimentare, uedere, & con&longs;iderare &longs;e di quelle &longs;i poteua caua­<lb/>re qualche buon co&longs;trutto in beneficio & difen&longs;ion di quella, & quantunque di tal co&longs;a <lb/>non ne &longs;eguita&longs;&longs;e altro (per uari accidenti, ne manco io me ne curai, perche tal guerra <lb/>in fummo &longs;i ri&longs;ol&longs;e,) nondimeno tal mia operina, ha prouocato uarie qualità di per&longs;o­<lb/>ne, & maggior parte non uolgare, ma di &longs;upremo, & alto ingegno) à trouagliarmi <lb/>di nouo con altri uarij Que&longs;iti, ouer interrogationi, & non &longs;olamente &longs;opra à tal ma­<lb/>teria di Artegliarie, Balle, Salnitrio, & Poluere. </s> <s id="s.000125">Ma anchora &longs;opra di nouo me han­<lb/>no fatto non &longs;olamente con&longs;iderare tai particolarità da loro adimandate, ma anchora co­<lb/>no&longs;cerne, & ritrouarne (com'e detto) molte altre, lequale &longs;enza tai &longs;uoi Que&longs;iti, <lb/>ouer interrogationi, for&longs;i giamai haueria cono&longs;ciute, ne con&longs;iderate. </s> <s id="s.000126">Dapoi fra me <lb/>pen&longs;ando, che non puoco bia&longs;ino merita quel huomo, qual, ouer per &longs;cientia, ouer per &longs;ua <lb/>indu&longs;tria, ouer per &longs;orte ritroua qualche notabil particolarità, & chi &longs;olamente lui &longs;olo<emph.end type="italics"/><pb xlink:href="042/01/008.jpg"/><emph type="italics"/>ne uoglia e&longs;&longs;er po&longs;&longs;e&longs;&longs;ore, perche &longs;e tutti li no&longs;tri anciani il mede&longs;imo haue&longs;&longs;eno o&longs;&longs;er­<lb/>uato, poco dalli animali irrationali al pre&longs;ente &longs;areßimo differenti adunque per non in­<lb/>correre in que&longs;to bia&longs;imo. </s> <s id="s.000127">Ho deliberato di uolere tai mei que&longs;iti, ouer inuentioni man­<lb/>dar al tutto in luce, & per dar principio ad e&longs;&longs;equire tal mio bon uolere, ne ho raccolto <lb/>per al pre&longs;ente una parte da un mio memoriale nel qual &longs;empre per bona memoria tutti <lb/>li notabili, che me ueneuan &longs;atti de mia man notaua, & que&longs;ta parte la ho di&longs;tribuita in <lb/>nuoue libri di&longs;tinti &longs;econdo la qualità delle materie conforme de tai Que&longs;iti. </s> <s id="s.000128">Dapoi ue­<lb/>nendomi ad aricordare, che ragionando un giorno, con el no&longs;tro honorando compare, <lb/>me&longs;&longs;er Ricardo Ventuorth, gentil'huomo di uo&longs;tra Sacra Mae&longs;tà, elqual predicandomi <lb/>della Magnificentia, Magnanimità, Liberalità, Genero&longs;ità, Humanità, & Clemen­<lb/>tia di uo&longs;tra Altezza, mi di&longs;&longs;e anchora, qualmente uo&longs;tra Cel&longs;itudine &longs;i dilettaua gran­<lb/>damente di tutte le co&longs;e alla guerra pertinente. </s> <s id="s.000129">Il che pen&longs;ando, ini ha datto ardire<emph.end type="italics"/><lb/>( Q<emph type="italics"/>uantunque in me non &longs;ia quella eloquentia, & ornato dire, che &longs;e rechiederia al­<lb/>l'udito di uo&longs;tra Serenità) di douere tai mei Que&longs;iti, ouer interrogationi, con le &longs;ue ri­<lb/>&longs;olute ri&longs;po&longs;te à quella offerire, & dedicare, non come co&longs;a conueniente à uo&longs;tra Subli­<lb/>mità (perche in uero le co&longs;e di profondißima dottrina, narrate, & e&longs;plicate con elle­<lb/>gante, & ter&longs;o &longs;tile, non potriano aggiungere al primo grado di uo&longs;tra altezza, non <lb/>che que&longs;te no&longs;tre, che &longs;ono co&longs;e Mechanice, e plebee, & &longs;imilmente dette. </s> <s id="s.000130">& prononcia­<lb/>te con rozzo & ba&longs;&longs;o &longs;tile.) Ma &longs;olamente come co&longs;e nuoue à quella le offeri&longs;co, & de­<lb/>dico, come &longs;i co&longs;tuma à fare delli primi frutti, che al principio di &longs;ua &longs;tagione uengono <lb/>ritrouati, liquait (anchor che &longs;iano alquanto immatturi, & di puoca &longs;o&longs;tantia, & men <lb/>&longs;apore) &longs;empre &longs;e &longs;ogliono appre&longs;entare à per&longs;one Magnifiche & &longs;ignorile, non per <lb/>la qualita della materia, ma per la nouità di quella, perche le co&longs;e nuoue naturalmente &longs;o­<lb/>ghono aggradire al intelletto humano, & cio mi ha dato à credere, tai no&longs;tre inuentioni <lb/>non douere à uo&longs;tra Clementia in tutto di&longs;piacere anzi aggradirli alquanto, il che e&longs;&longs;en­<lb/>do (come de&longs;idero) mi darà animo di douere per l'auenire piu oltra tentare, alli piedi <lb/>della quale, pro&longs;trato in terra con le man gionte, & capo chino humilmente mi racco­<lb/>mando.<emph.end type="italics"/></s> </p> </subchap1><subchap1> <pb pagenum="5" xlink:href="042/01/009.jpg"/> <p type="head"> <s id="s.000131">IL PRIMO LIBRO DELLI <lb/>QVESITI, ET INVENTIONI DIVERSE <lb/>DE NICOLO TARTAGLIA, <lb/>SOPRA GLI TIRI DELLE ARTIGLIERIE, <lb/>ET ALTRI SVOI VARII <lb/>ACCIDENTI.</s> </p> <figure id="id.042.01.009.1.jpg" xlink:href="042/01/009/1.jpg"/> <p type="head"> <s id="s.000132">QVESITO PRIMO FATTO DALL'ILLVSTRISS. <lb/>S<emph type="italics"/>ignor France&longs;co Maria Duca Eccellentißimo di Vrbino.<emph.end type="italics"/><lb/>L'A<emph type="italics"/>nno.<emph.end type="italics"/> M. D. XXXVIII. <lb/>IN VENETIA.</s> </p> <p type="main"> <s id="s.000133">Dvca. </s> <s id="s.000134">C<emph type="italics"/>he ragioni&longs;ono quelle che dicete hauer trouato, nel uo­<lb/>&longs;tro libro à me intitolato, &longs;opra al tirare delle artiglierie.<emph.end type="italics"/> NI­<lb/>COLO. L<emph type="italics"/>a proportione, & ordine de i tiri lontani, & pro­<lb/>pinqui di qual &longs;i uoglia pezzo, & con qual &longs;iuoglia &longs;orte di balla.<emph.end type="italics"/><lb/>S. D. I<emph type="italics"/>o non u'intendo parlatemi piu chiaro, & datemi un'eßem <lb/>pio.<emph.end type="italics"/> N. V<emph type="italics"/>olendo e&longs;&longs;emplificar que&longs;ta no&longs;tra inuentione à uo­<lb/>stra Eccellentia, &longs;ono astretto à parlar prima di quello istrumen­<lb/>to materiale, da noi ritrouato, figurato nel principio del detto no&longs;tro libretto à quella <lb/>intitolato: il qual i&longs;trumento è una &longs;quadra di legno, ouer di alcun mettallo fatta con di<lb/>ligentia, alla &longs;imilitudine della &longs;otto &longs;critta figura. </s> <s id="s.000135">b. <!-- REMOVE S-->a. <!-- REMOVE S-->c. <!-- REMOVE S-->la quale ha interchiu&longs;o uno <lb/>quadrante, cioè una quarta parte di un cerchio, alla &longs;imiliuudine della figura. </s> <s id="s.000136">h. <!-- REMOVE S-->i. <!-- REMOVE S-->g. <!-- REMOVE S-->k. <lb/>la qual figura, ouer quadrante. </s> <s id="s.000137">h. <!-- REMOVE S-->i. <!-- REMOVE S-->g. <!-- REMOVE S-->k. <!-- REMOVE S-->&longs;i de&longs;criue con un compa&longs;&longs;o &longs;opra il centro. </s> <s id="s.000138">h. <lb/><!-- REMOVE S-->cioè ponendo il pede immobile del detto compa&longs;&longs;o, in el detto ponto. </s> <s id="s.000139">h. (angolo intrin­<lb/>&longs;tco di tal &longs;quadra, & l'altro piede mobile girandolo per. </s> <s id="s.000140">i. <!-- REMOVE S-->g.<emph.end type="italics"/> k. <emph type="italics"/>formando il detto la­<lb/>to curuo. </s> <s id="s.000141">i. <!-- REMOVE S-->g.<emph.end type="italics"/> k. <emph type="italics"/>del detto quadrante, & dapoi re&longs;tringere alquanto el detto compaßo, <lb/>& de&longs;criuere un'altra linea curua, equidi&longs;tante alla prima, quale &longs;ia la linea. </s> <s id="s.000142">e. <!-- REMOVE S-->f. <!-- REMOVE S-->et tut <lb/>to quel &longs;patio, che è fra que&longs;te due linee curue, cioè fra el lato curuo. </s> <s id="s.000143">i. <!-- REMOVE S-->g.<emph.end type="italics"/> k. <emph type="italics"/>et la curua <lb/>e. <!-- REMOVE S-->f. <!-- REMOVE S-->uuol e&longs;&longs;er diui&longs;o, prima in dodici parte equali, le quai diui&longs;ioni uogliono e&longs;&longs;er tirate <lb/>con una rega, che uenga dal ponto. </s> <s id="s.000144">h. (centro del quadrante) à cia&longs;cheduna di dette di <lb/>ui&longs;ioni, accioche cia&longs;cheduna diui&longs;ione ri&longs;guardi il detto centro. </s> <s id="s.000145">h. <!-- REMOVE S-->come in la figura <lb/>appare, & que&longs;te dodici parte le chiameremo ponti.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/010.jpg"/> <figure id="id.042.01.010.1.jpg" xlink:href="042/01/010/1.jpg"/> <p type="main"> <s id="s.000146">An<emph type="italics"/>chora cadauna di queste tai parti, ouero ponti uuol e&longs;&longs;er anchora diui&longs;a in'al­<lb/>tre dodici parti equali, con il mede&longs;imo ordine, le qual diui&longs;ioni non ho uoluto <lb/>tirare in que&longs;ta figura piccola, perche generarebbeno confu&longs;ione, ma in una &longs;qua­<lb/>dra di commune grandezza, co&longs;i, come ho detto, uuol e&longs;&longs;er diui&longs;a, tal che tutto il det­<lb/>to quadrante. </s> <s id="s.000147">e. <!-- REMOVE S-->f. <!-- REMOVE S-->i. <!-- REMOVE S-->g.<emph.end type="italics"/> k. <emph type="italics"/>nenira à e&longs;&longs;er diui&longs;o in. </s> <s id="s.000148">144. parti equali, le qual parti chia­<lb/>meremo minuti, & questi minuti &longs;e &longs;egnano con lineette alquanto piu corte di quel­<lb/>le delli ponti, perche &longs;ono poi piu facili da e&longs;&longs;er numerati per mezzo de i ponti (con <lb/>maggior lince depinti) per &longs;aper gia che ogni ponto contiene. </s> <s id="s.000149">12. minuti. </s> <s id="s.000150">Fatto que­<lb/>sto bi&longs;ogna ficcare un pironcino di ferro, ouero di ottone preci&longs;amente in ponto. </s> <s id="s.000151">h. <lb/>(centro del quadrante) & à quel tal pironcino attaccarui uno perpendicolo girabi­<lb/>le, cioè uno fil di &longs;eta (ò d'altro) con uno piombino dacapo alla &longs;imilitudine del per­<lb/>pendicolo. </s> <s id="s.000152">h. <!-- REMOVE S-->g. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.000153">& co&longs;i con tal i&longs;trumento habbiamo con&longs;iderato tutte le uarie po&longs;i­<lb/>tioni, ouero elleuationi, che occorrer po&longs;&longs;a in qual &longs;i uoglia pezzo di artiglieria. </s> <s id="s.000154">Et <lb/>la prima po&longs;itione di cadauno pezzo &longs;e intende quando, che quello è aliuello, cioè tal­<lb/>mente a&longs;&longs;ettato, che ponendoui la gamba piu longa della detta no&longs;tra &longs;quadra in boc­<lb/>ca di&longs;te&longs;a rettamente per el fondo del uacuo della canna, el per pendicolo ca&longs;chi preci­<lb/>&longs;amente &longs;opra ellato. </s> <s id="s.000155">h. <!-- REMOVE S-->f.<emph.end type="italics"/> k. <emph type="italics"/>del quadrante, come di &longs;otto appare nella prima figura, <lb/>Et &longs;imilmente uno pezzo &longs;e intende e&longs;&longs;er elleuato un ponto quando che quello &longs;ia tal­<lb/>mente a&longs;&longs;ettato, che ponendoui la detta gamba piu longa della detta no&longs;tra &longs;quadra <lb/>in bocca di&longs;te&longs;a rettamente per el fondo del uacuo della canna (come prima) el per­<lb/>pendicolo <expan abbr="ca&longs;chipreci&longs;am&etilde;te">ca&longs;chi preci&longs;amente</expan> &longs;u la diui&longs;ione del primo ponto, come di &longs;otto appar nel­<lb/>la &longs;econda figura: Et co&longs;i un pezzo &longs;e intende e&longs;&longs;ere elleuato due ponti, quando che el <lb/>detto perpendicolo ca&longs;chi preci&longs;amente &longs;opra la diui&longs;ione del detto &longs;econdo ponto, & <lb/>co&longs;i al terzo quando ca&longs;cara &longs;opra la div&longs;ion del terzo, el mede&longs;imo &longs;e intende del <lb/>quarto, quinto, & &longs;e&longs;to. </s> <s id="s.000156">Et quando che uno pezzo è elleuato al &longs;e&longs;to ponto (cioè co-<emph.end type="italics"/><pb pagenum="6" xlink:href="042/01/011.jpg"/><emph type="italics"/>me di &longs;otto appare nella terza figura) &longs;e intende alla maggiore elleuatione, che elleuar <lb/>&longs;i po&longs;&longs;a.<emph.end type="italics"/> (D<emph type="italics"/>ico un pezzo d'artigliaria perche li mortari poi &longs;e po&longs;&longs;ono elleuare in <lb/>tutti li altri &longs;eguenti per fin al duodecimo ponto.<emph.end type="italics"/>) E<emph type="italics"/>t que&longs;to che habbiamo detto de i <lb/>ponti, &longs;e debbe anchora intendere de i minuti, cioè, che quando, che uno pezzo &longs;ia tal <lb/>mente elleuato, che el perpendicolo ca&longs;chi preci&longs;amente &longs;opra la diui&longs;ione del pri­<lb/>mo minuto, cioè &longs;opra la duodecima parte del primo ponto, tal pezzo s'intende e&longs;­<lb/>&longs;er elleuato uno minuto, & quando ca&longs;chara &longs;opra alli due minuti, s'intendera e&longs;&longs;ere <lb/>elleuato duoi minuti, il medefimo s'intendera de tutti li altri, per fin alla maggior el­<lb/>leuatione cioè alla elleuatione del &longs;e&longs;to <expan abbr="põto">ponto</expan>, ouero &longs;ettantadue minuti, come nella det­<lb/>ta terza figura appare: Li altri minuti che &longs;eguita per fino in capo, &longs;ono per le elle­<lb/>uationi di mortari.<emph.end type="italics"/><lb/><figure id="id.042.01.011.1.jpg" xlink:href="042/01/011/1.jpg"/><lb/><figure id="id.042.01.011.2.jpg" xlink:href="042/01/011/2.jpg"/></s> </p> <pb xlink:href="042/01/012.jpg"/> <figure id="id.042.01.012.1.jpg" xlink:href="042/01/012/1.jpg"/> <p type="main"> <s id="s.000157">S. DVCA. C<emph type="italics"/>he uolete inferir per que&longs;to.<emph.end type="italics"/> N. P<emph type="italics"/>rimamente uoglio inferir que <lb/>&longs;to, che tirando un pezzo alla elleuatione del primo ponto, tir ara molto piu lontano di <lb/>quello che fara &longs;tando aliuello, & tirandolo alla elleuatione del &longs;econdo ponto, tirara <lb/>molto piu lontano di quello, che fara alla elleuatione del primo ponto, & co&longs;i alla elle­<lb/>uatione del terzo ponto tirara piu lontano, che alla elleuatione del &longs;econdo, & co&longs;i alla <lb/>elleuation del quarto tirara anchora a&longs;&longs;ai piu lontano di quello, che fara alla elleuatio­<lb/>ne del terzo, & &longs;imilmente alla elleuatione del quinto tirara alquanto piu, che alla elle <lb/>uatione del quarto, & co&longs;i alla ultima elleuatione, cioè al &longs;e&longs;to ponto, con balla di piom<lb/>bo tirara alquanto piu, che alla elleuation del quinto, ma poco piu, per che la ragion ne <lb/>dimostra, che que&longs;ti que tiri, cioè tirati al quinto, & &longs;e&longs;to ponto &longs;ono tanto uicini, o­<lb/>uer tanto poco differenti, che ogni poco d'auantaggio, che &longs;i troua&longs;&longs;e nel quinto, ò per <lb/>uigor di poluere, ouer per altro, al detto quinto, &longs;e tiraria <expan abbr="tãto">tanto</expan>, quanto al &longs;e&longs;to, et for&longs;i <lb/>piu. </s> <s id="s.000158">Et chi pote&longs;&longs;e elleuar tal pezzo come &longs;e fanno li mortari, cioè al &longs;ettimo ponto, <lb/>&longs;enza dubbio al detto &longs;ettimo ponto tirara alquanto manco, che al detto &longs;e&longs;to, & co&longs;i <lb/>all'ottauo pento tirara a&longs;&longs;ai manco, che al detto &longs;ettimo, & &longs;imilmente, al nono tirara <lb/>molto manco, che all'ottauo, & co&longs;i al decimo tirara molto manco, che al nono, et co&longs;i <emph.end type="italics"/><pb pagenum="7" xlink:href="042/01/013.jpg"/><emph type="italics"/>al undecimo, tirara molto manco, che al decimo, & &longs;imelmente al duodecimo, cioc al <lb/>ultimo ponto tirara molto e molto manco che al undecimo anci in tal ultima elleuatio­<lb/>ne per ra&longs;on naturale la balla doueria retornar a dare preci&longs;amente nella bocca di tal <lb/>pezzo, ma per molti <expan abbr="accidti&etilde;">accidtiem</expan> che ui puo occorrere nel di&longs;ca<gap/>agar&longs;i, tal balla <expan abbr="nõ">non</expan> ui ritor <lb/>nara co&longs;i preci&longs;e, ma bennon andara a dare molto lontana dal detto pezzo.<emph.end type="italics"/> S. D. <lb/>E<emph type="italics"/>glie co&longs;a con&longs;onante qua&longs;i tutto quello che haueti detto, ma che uoleti inferire per <lb/>que&longs;to.<emph.end type="italics"/> N. V<emph type="italics"/>oglio &longs;econdariamente inferir que&longs;to, che noi habbiamo ritrouato in <lb/>che &longs;pecie di proportione, ouer ordine uanno augumentando li detti tiri in ogni elleua­<lb/>tione, & non &longs;olamente a ponto per ponto della detta nostra &longs;quadra, ma anchora a mi <lb/>nuto per m<gap/>uto per fin alla elleuatione del &longs;e&longs;to ponto, ouer di. </s> <s id="s.000159">72. minuti, & in ogni <lb/>&longs;orte balla, cioe di piombo, ferro, ouer di pietra. </s> <s id="s.000160">Et &longs;imelmente chi pote&longs;&longs;e elleuare li <lb/>pezzi oltra al detto &longs;esto ponto (come &longs;e fanno li mortari) hauemo anchora ritrouato <lb/>in che proportione andaranno calando li &longs;uoi tiri, & non &longs;olamente a ponto per pon­<lb/>to, ma anchora (come detto) a minuto per minuto per fin al fine di tutta la &longs;quadra, <lb/>cioe per fin in capo de tutti li 12. ponti, ouer. </s> <s id="s.000161">144. minuti.<emph.end type="italics"/> S.D. Q<emph type="italics"/>ue co&longs;trutto &longs;e <lb/>puo cauar de tal uo&longs;tra inuentione.<emph.end type="italics"/> N. E<emph type="italics"/>l co&longs;trutto de tal inuentione è questo, che <lb/>per la notitia de un&longs;ol tiro di qual &longs;i uoglia pezzo, po&longs;&longs;o formar una tauola de tutti li <lb/>tiri che tirara quel tal pezzo in ogni elleuatione, cioe a ponto per ponto, et a minutop <lb/>minuto della no&longs;tra&longs;quadra, la qual tauola &longs;ara di tal <expan abbr="&longs;o&longs;tãtia">&longs;o&longs;tantia</expan>, ouer proprieta, che qua <lb/><expan abbr="lũque">lunque</expan> p&longs;ona la hauera a pre&longs;&longs;o di&longs;e, <expan abbr="nõ">non</expan> <expan abbr="&longs;olam&etilde;te">&longs;olamente</expan> &longs;apra tirare, ma &longs;apra far tirare ogni <lb/>gro&longs;&longs;o bombardero con tal &longs;orte pezzi di lontano quanti pa&longs;&longs;a li parira (pur che non <lb/>&longs;la piu lontano del maggior tiro di tal pezzo) & che non hauera la detta no&longs;tra tauo­<lb/>la, non potra imparare alcuna particolarita di tal inuentione, ma tal &longs;ecreto re&longs;tara &longs;o <lb/>lamente a pre&longs;&longs;o di colui che hauera tal tauola, & non ad altri.<emph.end type="italics"/> S.D. M<emph type="italics"/>o &longs;i colui che <lb/>hauera tal uo&longs;tra tauola non uora tirare lui mede&longs;imo, ma uora far tirare a un'altra <lb/>&longs;econda per&longs;ond, non &longs;ara nece&longs;&longs;ario che tal &longs;econda per&longs;ona impari tal &longs;ecreto.<emph.end type="italics"/> N. <lb/>N<emph type="italics"/>on Signor Eccellentißimo, anci tal &longs;econda per&longs;ona re&longs;tara come restano li garzo­<lb/>ni di &longs;peciari de medicine, li quali <expan abbr="continuam&etilde;te">continuamente</expan> <expan abbr="cõponeno">componeno</expan> medicine, <expan abbr="&longs;ecõdo">&longs;econdo</expan> che gli uen <lb/>gono or dinate dalli medici, & tamen mai imparano a &longs;aper medicare.<emph.end type="italics"/> S.D. Q<emph type="italics"/>ue&longs;ta <lb/>mi pare una co&longs;a molto dura da credere, & tanto piu che nel no&longs;tro libretto (a me inti­<lb/>tulato) uoi diceti che mai tira&longs;ti di artegliaria, ne di &longs;chioppo, & colui che &longs;a un giudi <lb/>cio di una co&longs;a, della quale non habbia ui&longs;to lo effetto, ouer i&longs;perientia, lamaggior par­<lb/>te delle uolte &longs;e inganna, perche &longs;olamente l'occhio è quello che ne rende uera testimo­<lb/>nianza delle co&longs;e immaginate.<emph.end type="italics"/> N. E<emph type="italics"/>glie benuero che il &longs;en&longs;o i&longs;teriore, ne dice la ue­<lb/>rita nelle co&longs;e particolare, ma non nelle uniuer&longs;ale, perche le co&longs;e uniuer&longs;ale &longs;ono &longs;ot­<lb/>topo&longs;te &longs;olamente al intelletto, & non ad alcun &longs;en&longs;o.<emph.end type="italics"/> S.D. B<emph type="italics"/>a&longs;ta &longs;e me fareti ueder <lb/>que&longs;to (co&longs;a che non credo) el me parera un miracolo.<emph.end type="italics"/> N. T<emph type="italics"/>utte le co&longs;e che accade­<lb/>no per natura, ouer per arte pareno de grande ammiratione, quando che di quelle non <lb/>&longs;i &longs;ala cau&longs;a, mapre&longs;to uo&longs;tra Eccellentia &longs;e ne potrachiarire, facendone far lai&longs;pe­<lb/>rientia con un pezzo.<emph.end type="italics"/> S.D. V<emph type="italics"/>oglio andare per fina à Pe&longs;aro, &longs;ubito che &longs;ia ritor­<lb/>nato, certo la uoglio uedere.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/014.jpg"/> <p type="head"> <s id="s.000162">QVESITO SECONDO FATTO <lb/><emph type="italics"/>dal mede&longs;imo Illust. <!-- REMOVE S-->Sig. <!-- REMOVE S-->Duca con&longs;equentemente <lb/>al precedente.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000163">DVCA. M<emph type="italics"/>a ditemi un poco per qual uer&longs;o credete uoi che una <lb/>Artegliaria <lb/>fara maggior effetto, ouer pa&longs;&longs;ata nella co&longs;a doue &longs;e tira, tirandoui con quel­<lb/>la aliuellata, ouer elleuata <expan abbr="dauãti">dauanti</expan>.<emph.end type="italics"/> N. <!-- KEEP S--></s> <s id="s.000164">A <emph type="italics"/>uoler re&longs;oluere que&longs;to que&longs;ito &longs;enza repren<lb/>&longs;ione, egliè nece&longs;&longs;ario, che uo&longs;tra Eccellentia, me proponga tal que&longs;ito per e&longs;&longs;empio, <lb/>ouer figura, con la quantita della di&longs;tantia de tal Artegliaria, & la qualita del luoco <lb/>doue &longs;e tira.<emph.end type="italics"/> S.D. P<emph type="italics"/>ongo per <expan abbr="eß&etilde;pio">eßempio</expan>, che il mi occorre&longs;&longs;e di far battere una fortez­<lb/>za che fu&longs;&longs;e in cima di una colina, ouer monticello, alto pa&longs;&longs;a. </s> <s id="s.000165">60. & che lontano pa&longs;­<lb/>&longs;a. </s> <s id="s.000166">100. da quella tal colina, ouer monticello, ui fu&longs;&longs;e un'altra còlina, ouer monticel­<lb/>lo, alto alla equalita di detta fortezza, cioè pur pa&longs;&longs;a. </s> <s id="s.000167">60. (come di &longs;otto appare in <lb/>figura) & poniamo che &longs;opra la cima di que&longs;to &longs;econdo monticello, ui &longs;e pote&longs;&longs;e sta­<lb/>re commodamente con la artegliaria à battere que&longs;ta tal fortezza, la quale arteglia­<lb/>ria in tal luoco ueneria à tirare in quella retto tramite, cioè con la detta artegliaria <lb/>aliuellata (come di &longs;otto appare in figura) & poniamo anchora che tal fortezza, &longs;l <lb/>pote&longs;&longs;e commodamente battere &longs;tando con la artegliaria nel piano (cioè &longs;tando da <lb/>banda nel pie del detto &longs;econdo monticello in quella mede&longs;ima di&longs;tantia) cioè &longs;tando <lb/>lontano dal pie del monte, doue è la fortezza pur pa&longs;&longs;a. </s> <s id="s.000168">100. nel qual luoco, la detta <lb/>artegliaria uerria à tirare in quella stante molto elleuata dauanti, cioè tiraria in quel­<lb/>la di &longs;otto in &longs;u&longs;o (come di &longs;otto appare in figura.) Hor ue adimando, in qual luoco <lb/>pen&longs;ati che tale artegliaria faria maggiore effetto, ouer pa&longs;&longs;ata in detta fortezza,<emph.end type="italics"/><lb/><figure id="id.042.01.014.1.jpg" xlink:href="042/01/014/1.jpg"/><pb pagenum="8" xlink:href="042/01/015.jpg"/><emph type="italics"/>eioè &longs;tando in cima del detto monticello, ouer &longs;tando iui da banda nel pie di quello.<emph.end type="italics"/><lb/>N. S<emph type="italics"/>enza dubbio, che &longs;tando nel piano, cioè nel pie del monte, faria mag­<lb/>giore effetto, ouer pa&longs;&longs;ata in detta fortezza, di quello faria &longs;tando nella &longs;ommita del <lb/>monte.<emph.end type="italics"/> S.D. E<emph type="italics"/>t lo giudicarei, & giudico e&longs;&longs;er tutto al <expan abbr="cõtrario">contrario</expan>, perche quelle che ti­<lb/>rar anno dalla &longs;ommita del monte &longs;aranno molto piu propinque alle muraglie di quel­<lb/>la tal fortezza, di quello che &longs;aranno quelle che tirar anno dal pie del monte, & quan­<lb/>to che la co&longs;a doue &longs;e tira è piu propinqua alla artegliaria, per ragion naturale, la <lb/>balla douria far maggiore effetto in lei.<emph.end type="italics"/> N. Q<emph type="italics"/><expan abbr="uãdo">uando</expan> che un'artegliaria tira&longs;&longs;e egual­<lb/>mente per ogni uer&longs;o &longs;egueria quello, che dice uo&longs;tra Eccellentia. </s> <s id="s.000169">Ma per efficace ra­<lb/>gioni ritrouo tutto all'oppo&longs;ito, cioè che ogni &longs;orte di artegliaria nece&longs;&longs;ariamente ti­<lb/>rara manco per line a retta, &longs;tante aliuellata di quello faria in qualunque altro modo <lb/>a&longs;&longs;ettata, o per dir meglio, che ogni &longs;orte di artegliaria nece&longs;&longs;ariamente tirara pile <lb/>per linea retta &longs;tante alquanto elleuata dauanti di quello fara &longs;tante quella à liuello, <lb/>& quanto piu &longs;tara elleuata tanto piu tirara per retta linea, il mede&longs;imo &longs;i debbe in­<lb/>tendere e&longs;&longs;endo abba&longs;&longs;ata, cioè che molto piu tir ara per linea retta &longs;tante quella al­<lb/>quanto abba&longs;&longs;ata dauanti, di quello fara &longs;tante à liuello, & quanto piu &longs;tara abba&longs;­<lb/>&longs;ata, <expan abbr="tãto">tanto</expan> piu tirara per linea retta.<emph.end type="italics"/> S.D. Q<emph type="italics"/>ue&longs;to che uoi dite, me pare una co&longs;a mol­<lb/>to &longs;trania da credere, cioè à dire, che una mede&longs;ima quantita, e po&longs;&longs;anza di poluere, <lb/>debbia &longs;pingere piu uigoro&longs;amente una mede&longs;ima grauita di balla, per un uer&longs;o, che <lb/>per un'altro, e pero haria à caro, che uoi me aßigna&longs;ti la ragione, e cau&longs;a di questa uo­<lb/>&longs;tra openione.<emph.end type="italics"/> N. L<emph type="italics"/>a ragion di questo lo dimo&longs;tr amo (per li accidenti accadenti nelli <lb/>&longs;uoi tiri) nella ultima propo&longs;itione del Secondo libro della no&longs;tra nuoua &longs;cientia, ue­<lb/>ro è, che in tal dimo&longs;tratione, non &longs;e a&longs;&longs;egna la cau&longs;a propinqua di tale effetto, la qual <lb/>co&longs;a in tal luoco pretermeßi, per non fa&longs;tidiar uostra Eccellentia, perche tal cau&longs;a <lb/>propinqua, &longs;e dimo&longs;tra con la &longs;cientia di pe&longs;i, la quale è una &longs;cientia di non poca &longs;pe­<lb/>culatione, per e&longs;&longs;er quella &longs;ubalternata, &longs;i dalla Geometria, come dalla natural Filo­<lb/>&longs;ophia. </s> <s id="s.000170">Ma quando non &longs;ia graue à quella lo a&longs;coltarme, io mi sforzaro di dimostrar­<lb/>la al pre&longs;ente.<emph.end type="italics"/> S.D. S<emph type="italics"/>eguitatipur, ma &longs;otto breuita.<emph.end type="italics"/> N. P<emph type="italics"/>er dimo&longs;trar que&longs;ta co&longs;a <lb/>rettamente &longs;ono astretto uolendo e&longs;&longs;ere inte&longs;o à <expan abbr="mãdare">mandare</expan> auanti la diffinitione de alcu­<lb/>ni termini opportuni, etiam alcune &longs;uppo&longs;itioni, come &longs;i co&longs;tuma in cia&longs;cuna &longs;cientia, <lb/>& perche tutte le co&longs;e meglio &longs;e apprendono per e&longs;&longs;empio, che per parole. </s> <s id="s.000171">Pongo <lb/>per e&longs;&longs;empio la libra, ouer bilanza.a.b. </s> <s id="s.000172">con li dui brazzi.a.c. </s> <s id="s.000173">&.c.b. </s> <s id="s.000174">eguali, & il <lb/>centro, &longs;opra del qual lei gira, &longs;ia il detto ponto.c.& nelle e&longs;tremita di detti dui braz­<lb/>zi &longs;lano congionti dui corpi egualmente graui, li quali nominaremo dalle mede&longs;ime <lb/>lettere, cioè.a.&.b. </s> <s id="s.000175">li quali dui corpi, per e&longs;&longs;ere eguali in grauita, dal pre&longs;uppo&longs;ito, <lb/>& appe&longs;i in longhezze eguali, cioè à gli detti dui brazzi.a.c.&.c.b. </s> <s id="s.000176">della propo­<lb/>&longs;ta libra, qual &longs;ouo &longs;ta &longs;uppo&longs;ti e&longs;&longs;ere egualmente longhi, per la prima petitione adut­<lb/>ta da Archimede, nel libro che fa del centro della grauita, quelli inclinar anno egual­<lb/>mente, cioè che &longs;taranno in equilibra, come di &longs;otto appare in figura.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/016.jpg"/> <figure id="id.042.01.016.1.jpg" xlink:href="042/01/016/1.jpg"/> <p type="main"> <s id="s.000177">An<emph type="italics"/>chora &longs;ta de&longs;critto &longs;opra il centro.c.un cerchio, &longs;econdo la quantita dell'u­<lb/>no di brazzi della libra, ouer bilanza qual &longs;la il cerchio.e.a.f.b. </s> <s id="s.000178">la circonfe­<lb/>rentia del quale &longs;upponeremo per il uiaggio che fariano li centri di detti corpi, gi­<lb/>rando à torno la detta bilanza &longs;opra il &longs;uo centro.c.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000179">D<emph type="italics"/>iffinitione Prima.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000180">S<emph type="italics"/>tando adunque li detti dui corpi in equilibra, come in figura appare, in tal luoco <lb/>li detti dui corpi, &longs;e dicono e&longs;&longs;er nel &longs;ito della equalita.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000181">D<emph type="italics"/>iffinitione Seconda.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000182">A<emph type="italics"/>nchor tirando dalla &longs;ommita una perpendicolare pa&longs;&longs;ante per il centro. </s> <s id="s.000183">c. <lb/>(quala &longs;ia la linea.e.c.f.) tal linea uien detta la linea della direttione.<emph.end type="italics"/></s> </p> <figure id="id.042.01.016.2.jpg" xlink:href="042/01/016/2.jpg"/> <p type="head"> <s id="s.000184">S<emph type="italics"/>uppo&longs;itione Prima.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000185">An<emph type="italics"/>chora bi&longs;ogna notare qualmente un corpo graue &longs;e &longs;uppone e&longs;&longs;er tanto piu <lb/>graue, nel luoco doue &longs;e ritroua quanto che il di&longs;cender di quello è manco obli­<lb/>quo, cicè manco curuo, in el mede&longs;imo &longs;ito, ouer luoco. </s> <s id="s.000186">Lo e&longs;&longs;empto di que&longs;ta &longs;uppo­<lb/>&longs;itione &longs;e adura nella &longs;eguente figuratione.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000187">S<emph type="italics"/>uppo&longs;itione Seconda.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000188">E<emph type="italics"/>t il di&longs;cender d'un corpo graue, &longs;e &longs;uppone e&longs;&longs;er tanto piu obliquo, quanto che <lb/>nel &longs;uo di&longs;cender capi&longs;&longs;e manco del diretto, in mede&longs;ima quantita, cioe che capi&longs;&longs;e man <lb/>co parte della linea della direttione, ouer di una altra a quella equidi&longs;tante, in la mede­<lb/>&longs;ima quanlita, cioe in mede&longs;ima quantita di cir conferentia del cerchio doue gira, ouer <lb/>ua, & que&longs;to nella figuration &longs;equente meglio &longs;e intendera.<emph.end type="italics"/></s> </p> <pb pagenum="9" xlink:href="042/01/017.jpg"/> <p type="main"> <s id="s.000189">Sv<emph type="italics"/>pposte adunque le &longs;opradette &longs;uppo&longs;itione, adduco questa propo&longs;itione, & dico <lb/>che ogni librato pe&longs;o partendo&longs;l dal &longs;ito, ouer luoco della equalita, quel &longs;i fa piu le <lb/>ue, & tanto piu quanto piu &longs;ara lontano dal detto luoco della equalita. </s> <s id="s.000190">Et per e&longs;&longs;eme <lb/>pio di questa propo&longs;itione &longs;ia la libra.a.b. (della figura precedente) girabile &longs;opra el <lb/>detto centro.c. </s> <s id="s.000191">con li dui mede&longs;imi corpi.a.&.b. (equali) appe&longs;i, ouer congionti alle <lb/>due e&longs;tremita di ambi dui li brazzi della detta libra, & &longs;tiano nel mede&longs;imo &longs;ito della <lb/>equalita (come di &longs;opra fu &longs;uppo&longs;to) hor dico, che remouando l'uno, & l'altro de detti <lb/>corpi dal detto &longs;ito della equalita (cioè arba&longs;&longs;andone uno, & elleuando l'altro) l'uno, <lb/>e l'altro de quelli &longs;ara fatto piu leue &longs;econdo el luoco, & tanto piu leui, quanto che piu <lb/>&longs;aranno allontanati dal detto luoco della equalita. </s> <s id="s.000192">Et per dimo&longs;trar que&longs;to &longs;ia arba&longs;&longs;a <lb/>to el corpo.a. (della detta figura precedente) per fina al <expan abbr="põto">ponto</expan>.u. (come nella &longs;otto &longs;crit<lb/>ta figura appare, & l'altro &longs;uo oppo&longs;ito (cioè el corpo.b.) uerra à e&longs;&longs;er&longs;e elleuato per <lb/>in fina al ponto.i.& &longs;ia diui&longs;o l'uno, e l'altro di dui archi.a.u.&.i.b. </s> <s id="s.000193">in quante parti <lb/>&longs;i uoglia, equale hor poniamo l'uno, e l'altro in trei parti equali in li ponti. </s> <s id="s.000194">l.n.et.q.&longs;. <lb/><!-- REMOVE S-->& dalli trei ponti.n.l.i.&longs;iano tirate le tre linee.n.o.l.m.&.i.<emph.end type="italics"/>k <emph type="italics"/>equidi&longs;tante al diame­<lb/>tro.b.a.le quale &longs;egarano la linea.e.f.della direttione nelli trei ponti.z.y.x.&longs;imelmen <lb/>te dalli trei ponti.q.s.u. </s> <s id="s.000195">&longs;iano tirate le tre linee.q.p.s.r. </s> <s id="s.000196">&.u.t.pur equidi&longs;tante alla <lb/>medema linea.a.b. </s> <s id="s.000197">le quale &longs;egarano la medema linea della direttione nelli tre ponti, <lb/>&.<36><gap/>. </s> <s id="s.000198">Onde per queste co&longs;e co&longs;i de&longs;po&longs;ite ueniremo ad hauer diui&longs;o tutto el decen&longs;o <lb/>a.u.fatto dal detto corpo.a.nel di&longs;cender in ponto.u.in trei decen&longs;i, ouer parti equa­<lb/>li, le quale &longs;ono.a.q.q.s.&.s.u. </s> <s id="s.000199">Et &longs;imelmente tutto el decen&longs;o.i.b. </s> <s id="s.000200">qual faria el detto <lb/>corpo.b. <!-- REMOVE S-->nel di&longs;cendere, ouer ritornare al &longs;uo primo luoco (cioè in ponto.b.) uerra à e&longs; <lb/>&longs;er diui&longs;o in trei decen&longs;i, ouer in tre parti equali, le quali &longs;ono.i.l.l.n.&.n.b.& cadau <lb/>no de que&longs;ti tre, & tre partiai decen&longs;i capi&longs;&longs;e una parte della linea della direttione, <lb/>cioè el decen&longs;o dal.a.al.q. </s> <s id="s.000201">piglia, ouer capi&longs;&longs;e dalla linea della direttione la parte.c.&. <lb/></s> <s id="s.000202">lo decen&longs;o.q.s.piglia, ouer capi&longs;&longs;e la parte, &.<36>. </s> <s id="s.000203">& lo decen&longs;o.s.u. </s> <s id="s.000204">capi&longs;&longs;e la parte <36>. <lb/><gap/>.& perche la parte.c.&. </s> <s id="s.000205">emaggiore della parte.&.<36>. (come facilmente geometri <lb/>ce &longs;e puo prouare) onde (per la &longs;econda &longs;uppo&longs;itione) el decen&longs;o.q.s. </s> <s id="s.000206">uerra à e&longs;&longs;er piu <lb/>obliquo del decen&longs;o.a.q. </s> <s id="s.000207">onde piu leue &longs;ara el detto corpo.a. (per la &longs;uppo&longs;itione) &longs;tan <lb/>te quello in ponto. </s> <s id="s.000208">q di quello &longs;ara, &longs;tante quello in ponto.a. </s> <s id="s.000209">Simelmente perche la par <lb/>te.<36>.<gap/>. (della linea della direttione) è menore della parte. </s> <s id="s.000210">&.<36>. </s> <s id="s.000211">el decen&longs;o.s.u. (per la <lb/>mede&longs;ima &longs;econda &longs;uppo&longs;itione &longs;ara piu obliquo del decen&longs;o.q.s.& con&longs;equentemen­<lb/>te) per la prima &longs;uppo&longs;itione piu leue &longs;ara el detto corpo.a &longs;tante quello in ponto.s. </s> <s id="s.000212">di <lb/>quello &longs;ara&longs;tante in ponto.q. </s> <s id="s.000213">Et tutto que&longs;to, & per li mede&longs;imi modi &longs;e demo&longs;trara <lb/>nella oppo&longs;ita parte del corpo.b. <!-- REMOVE S-->cioè chel decen&longs;o di quello dal ponto.i. </s> <s id="s.000214">al ponto. </s> <s id="s.000215">l. <!-- REMOVE S-->è <lb/>piu obliquo di quello, che è dal ponto.l. </s> <s id="s.000216">al ponto.n. (per la detta &longs;econda &longs;uppo&longs;itione) <lb/>perche la parte.x.y. </s> <s id="s.000217">che capi&longs;&longs;e della linea della direttione, è menore della parte y.z. <lb/><!-- REMOVE S-->onde per la detta prima &longs;uppo&longs;itione piu leue &longs;ara el detto corpo &longs;tante quello in pon­<lb/>to.i.di quello &longs;ara &longs;tante quello in ponto.l. </s> <s id="s.000218">& per le mede&longs;ime ragioni piu leue &longs;ara <lb/>&longs;tante quello in ponto.l.di quello &longs;ara &longs;tante in ponto.n. </s> <s id="s.000219">& &longs;imelmente piu leue &longs;ara <lb/><expan abbr="stãte">stante</expan> in <expan abbr="põto">ponto</expan>.n. </s> <s id="s.000220">di quello &longs;ara &longs;tante in <expan abbr="põto">ponto</expan>.b. (&longs;ito della equalita) che è il propo&longs;ito.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/018.jpg"/> <figure id="id.042.01.018.1.jpg" xlink:href="042/01/018/1.jpg"/> <p type="main"> <s id="s.000221">S. DVCA. C<emph type="italics"/>he uoleti inferir per que&longs;to.<emph.end type="italics"/> N. V<emph type="italics"/>oglio inferir que&longs;to, che ogni arti <lb/>gliaria e&longs;&longs;endo aliuellata, la &longs;e intende e&longs;&longs;er nel &longs;ito della equalita, & la balla tirata da <lb/>quella, in tal &longs;ito u&longs;ci&longs;&longs;e del pezzo piu graue, che in qualunque altro modo elleuata, <lb/>ouer &longs;eparata da quel &longs;ito della equalita (per le ragioni di &longs;opra adutte) e pero in tal <lb/>&longs;ito la balla ua con piu difficultà, & molto piu pre&longs;to comincia à declinar al ba&longs;&longs;o, cioè <lb/>uer&longs;o terra, & in maggior quantita lei ua declinando, che in qualunque altro modo el <lb/>leuata, cioè che lei ua (come fra bombardieri&longs;e dice) molto manco per linea retta, che <lb/>in qualunque altro modo elleuata, e pero li effetti di tiri fatti in tal &longs;ito &longs;aranno men ui <lb/>goro&longs;i, ouer di menor effetto, che in qualunque altro uer&longs;o. </s> <s id="s.000222">Vero è, che uo&longs;tra Eccellen<lb/>tia potria dire, & ragioneuolmente, per que&longs;te tue ragioni &longs;on chiaro, che in di&longs;tantia <lb/>equale lei fara <expan abbr="mãco">manco</expan> effetto, ma in distantie inequale re&longs;to dubbio&longs;o, perche nel no&longs;tro <lb/>Que&longs;ito &longs;i uede, che quelle artegliarie, che &longs;ono nel piano, ouer nel pie del monte, &longs;ono <lb/>molto piu di&longs;tante, dalla fortezza, di quelle, che &longs;on nella &longs;ommita del monte, talmente <lb/>che tal differentia potria e&longs;&longs;er molto maggiore della differentia del &longs;uo tirar per li­<lb/>nea retta, ouer della differentia de &longs;uoi effetti in di&longs;tantie equale, & e&longs;&longs;endo co&longs;i quelle <lb/>de la &longs;ommita del monte, uerriano à far maggior effetto, di quelle po&longs;te in piano, cir­<lb/>ca al qual dubbio ri&longs;pondo, che gliè ben uero, che la di&longs;tantia di quelle, che &longs;tano in pia <lb/>no, potria e&longs;&longs;er alle uolte tanto grandemente differente da quella, di quelle, che &longs;ono ne <lb/>la &longs;ommita del monte, che &longs;eguiria quello, che di &longs;opra hauemo detto, ouer dubitato.<emph.end type="italics"/><lb/>S.D. D<emph type="italics"/>atime <expan abbr="un'eß&etilde;pio">un'eßempio</expan> in figura, &longs;e uoleti, che ue intenda.<emph.end type="italics"/> N. P<emph type="italics"/>er uoler e&longs;&longs;emplifi <lb/>care figuralmente que&longs;ta co&longs;a &longs;upponeremo una colobrina da lire. </s> <s id="s.000223">20. di balla, laqual <lb/>colobrina (per quella &longs;perientia, che fu fatta à Verona, narrata nel principio della no <lb/>&longs;tra noua &longs;cientia à uo&longs;tra Eccellentia) io trouo, che tal colobrina nel &longs;ito della equali­<lb/>ta (cioè &longs;tando aliuellata) tirara de mira, ouer per linea retta circa pa&longs;&longs;a. </s> <s id="s.000224">200. & alla <lb/>elleuatione de. </s> <s id="s.000225">45. gradi, cioè al &longs;e&longs;to ponto, ouer alli. </s> <s id="s.000226">72. minuti della no&longs;tra &longs;quadra <lb/>tal colobrina (per le ragioni adutte nella ultima propo&longs;itione del <expan abbr="&longs;ecõdo">&longs;econdo</expan> libro della no <lb/>stra noua &longs;cientia) tirara de mira, ouer per linea retta, in quel uer&longs;o, circa pa&longs;&longs;a.<emph.end type="italics"/> 800. <lb/>S.D A<emph type="italics"/>dunque <expan abbr="tirãdo">tirando</expan> la detta colobrina à tal elleuatione tirara circa pa&longs;&longs;a. </s> <s id="s.000227">800. per <lb/>linea retta, & tirandola poi aliuellata, non tirara &longs;aluo che circa pa&longs;&longs;a.<emph.end type="italics"/> 200 N. C<emph type="italics"/>o <lb/>&longs;i ne afferma la ragione.<emph.end type="italics"/> S.D. L<emph type="italics"/>a me pare una grah differentia.<emph.end type="italics"/> N. Q<emph type="italics"/>uesto pro­<lb/>cede per e&longs;&longs;er anchora tal ellcuatione molto differente dal &longs;ito della equalita, perche &longs;e<emph.end type="italics"/><pb pagenum="10" xlink:href="042/01/019.jpg"/><emph type="italics"/>condo che la &longs;i ua elleuando de minuto in minuto, co&longs;i de minuto in minuto lei ua ancho <lb/>ra augumentando il &longs;uo tirar per linea retta, il mede&longs;imo fara etiam nelli ponti, & in <lb/>maggior quantita, cioè, che elleuata al primo ponto della &longs;quadra tirara molto piu <lb/>per linea retta, di quello fara nel &longs;ito della equalita, cioè aliuellata, & elleuata poi al &longs;e <lb/>condo ponto di detta &longs;quadra, molto piu tirara per linea retta, di quello fara elleuata al <lb/>primo ponto, & co&longs;i elleuata al terzo ponto, tirara piu pur per linea retta, di quello <lb/>fara al &longs;econdo, & co&longs;i &longs;ucceßiuamente al quarto, tirara piu, che al terzo & al quin­<lb/>to piu che al quarto, & al &longs;e&longs;to (detto di &longs;opra) tirara piu che al quinto, & &longs;e piu ol­<lb/>tra la &longs;i pote&longs;&longs;e elleuare gradatamante andaria augumentando il &longs;uo tirare per linea <lb/>retta, cioè, che al. <!-- REMOVE S-->7. ponto, tirara piu per linea retta, che al. <!-- REMOVE S-->6. & al. <!-- REMOVE S-->8. piu che al. <!-- REMOVE S-->7. <lb/>& al. <!-- REMOVE S-->9. piu che al. <!-- KEEP S--></s> <s id="s.000228">8. & al. <!-- REMOVE S-->10. piu che al. <!-- REMOVE S-->9. & al. <!-- REMOVE S-->11. piu che al. <!-- REMOVE S-->10. & al. <!-- REMOVE S-->12. piu che <lb/>al. <!-- REMOVE S-->11. & à que&longs;to. </s> <s id="s.000229">12. tutto il &longs;uo tiro &longs;ara per linea retta, perche &longs;ara perpendicola­<lb/>re &longs;opra all'orizonte, & que&longs;to tale &longs;ara piu perfettamente retto de cadauno delli an­<lb/>teditti, perche in uero il tran&longs;ito, ouer moto uiolente d'un corpo egualmente graue, <lb/>che &longs;ia fora della perpendicolar del orizonte, mai pol hauere alcuna parte, che &longs;ia per <lb/>fettamente retta (come fu detto &longs;opra la &longs;econda &longs;uppo&longs;itione del &longs;econdo libro della <lb/>no&longs;tra noua &longs;cientia.<emph.end type="italics"/> S.D. P<emph type="italics"/>erche diceti adunque per linea retta, non e&longs;&longs;endo per­<lb/>fettamente retta.<emph.end type="italics"/> N. P<emph type="italics"/>er e&longs;&longs;er inte&longs;o dal uolgo, perche quella parte, che è qua&longs;i in­<lb/>&longs;en&longs;ibelmente curua, la chiamamo retta, & quella che è euidentamente curua, li dico­<lb/>no curua.<emph.end type="italics"/> S.D. S<emph type="italics"/>eguitati.<emph.end type="italics"/> N. H<emph type="italics"/>or per ritornare al no&longs;tro propo&longs;ito, dico adun­<lb/>que, che &longs;e la altezza della predetta &longs;ortezza fo&longs;&longs;e tanta, che da quella à le arteglia­<lb/>rie, che fu&longs;&longs;eno nel piano del monte, fu&longs;&longs;e. </s> <s id="s.000230">760. pa&longs;&longs;a, & che dalla medema fortezza <lb/>à quelle artegliarie, che fu&longs;&longs;eno nella &longs;ummita del monte, fu&longs;&longs;e &longs;olamente pa&longs;&longs;a. </s> <s id="s.000231">130. in <lb/>questo ca&longs;o dico, che la &longs;opra detta colobrina faria mazzor effetto nelle muraglie di <lb/>detta fortezza, stante quella ne la &longs;ommita del monte, di quello faria, &longs;tante nel pie dil <lb/>monte. </s> <s id="s.000232">La cau&longs;a è, perche la detta colobrina (&longs;tante aliuellata) tira circa pa&longs;&longs;a. </s> <s id="s.000233">200. <lb/>per linea retta (come di &longs;opra fu detto) E&longs;&longs;endo adunque da quella à la muraglia pa&longs;­<lb/>&longs;a. </s> <s id="s.000234">130. (come fu &longs;upposto) lei ueneria à percuotere ne la detta muraglia circa per. </s> <s id="s.000235">70. <lb/>pa&longs;&longs;a auanti al termine dil &longs;uo andar per linea retta: Ma &longs;tante quella nel pie dil mon­<lb/>te (dal qual luoco alla detta muraglia è &longs;ta &longs;uppo&longs;to e&longs;&longs;er diametralmente pa&longs;&longs;a. </s> <s id="s.000236">760.) <lb/>& elleuandola alla elleuatione de. </s> <s id="s.000237">45. gradi (cioè al. <!-- REMOVE S-->6. ponto della no&longs;tra &longs;quadra) ti­<lb/>rara circa pa&longs;&longs;a. </s> <s id="s.000238">800. per linea retta (come di &longs;oprafu detto) onde lei ueneria à per­<lb/>cuotere nella detta muraglia &longs;olamente circa per pa&longs;&longs;a. </s> <s id="s.000239">40. auanti il termine del &longs;uo <lb/>andar per linea retta, cioè auanti la &longs;ua &longs;en&longs;ibil declinatione. </s> <s id="s.000240">Et perche quella balla che <lb/>nel &longs;uo percotere hauera à tran&longs;ire per piu longo &longs;patio (non trouando re&longs;i&longs;tcntta) fa <lb/>ra maggior effetto in tal re&longs;istente (per le ragioni adutte &longs;opra la. </s> <s id="s.000241">4. propo&longs;itione del <lb/>primo libro della no&longs;tra noua &longs;cientia) perche adunque la halla tirata da la &longs;ommita <lb/>del monte nel &longs;uo percottere haueria anchora à andare pa&longs;&longs;a. </s> <s id="s.000242">70. per linea retta. </s> <s id="s.000243">Et <lb/>quella tirata dal piano, nel &longs;uo percottere haueria à procedere &longs;olamente pa&longs;&longs;a. </s> <s id="s.000244">40. <lb/>per linea retta, & per que&longs;te ragiom &longs;e <expan abbr="cõchiuderia">conchiuderia</expan> in tal ca&longs;o, che maggior effetto fa <lb/>ria la detta colobrina in detta muraglia, &longs;tante quella ne la &longs;ommita del monte di quel­<lb/>lo faria &longs;tante nel piano, ouero pie dil monte alla elleuatione del detto. </s> <s id="s.000245">6 ponto della<emph.end type="italics"/><pb xlink:href="042/01/020.jpg"/><emph type="italics"/>no&longs;tra &longs;quadra), & &longs;e alla detta elleuatione dil. </s> <s id="s.000246">6. ponto lei fara manco effetto, molto <lb/>meno lei lo faria ad alcuna altra piu ba&longs;&longs;a elleuatione. </s> <s id="s.000247">Ma &longs;e per ca&longs;o la distantia de <lb/>detta fortezza alle artegliarie, che fu&longs;&longs;eno nel piano fu&longs;&longs;e pa&longs;&longs;a. </s> <s id="s.000248">600. cioè diametral­<lb/>mente, & che dalla medema à quelle che fu&longs;&longs;eno nella &longs;ommita del monte fu&longs;&longs;e pa&longs;&longs;a <lb/>150. in tal ca&longs;o dico, che la detta colobrina fara molto maggiore effetto nella detta mu <lb/>raglia stante nel piano (ouer pie dil monte alla elleuatione del detto. </s> <s id="s.000249">6. ponto.) di quel­<lb/>lo faria &longs;tante nella &longs;ommita del monte, perche stante nel piano le balle tirate da quel­<lb/>ia ueniranno à percuottere nella detta muraglia circa à pa&longs;&longs;a. </s> <s id="s.000250">200. auanti il termine <lb/>dil &longs;uo procedere per linea retta, Et quelle tirate dalla &longs;ommita del monte ueneriano <lb/>à percuotere &longs;olamente à pa&longs;&longs;a. </s> <s id="s.000251">50. auanti al termine del &longs;uo andar per linea retta, & <lb/>perche la differentia de detti effetti, cioè dalli. </s> <s id="s.000252">50. pa&longs;&longs;a, alli. </s> <s id="s.000253">200. (che feri&longs;cono <expan abbr="auã">auam</expan> <lb/>ti la &longs;ua &longs;en&longs;ibel declinatione) è circa pa&longs;&longs;a. </s> <s id="s.000254">150. e per tanto la detta colobrina non &longs;o­<lb/>lamente alla elleuatione del &longs;e&longs;to ponto della no&longs;tra &longs;quadra ma anchora alla elleuatio­<lb/>ne del quinto ponto, fara maggior el detto effetto: ma di que&longs;to non uoglio star à far­<lb/>ne dimo&longs;tratione, perche &longs;o che ueneria in fa&longs;tidio à quella. </s> <s id="s.000255">Adunque, &longs;e in una co&longs;t <lb/>grande altezza (quala in que&longs;to ultimo ca&longs;o hauemo &longs;uppo&longs;ta) la detta colobrina fa­<lb/>ria maggior effetto (stante quella nel piano alla elleuatione del. <!-- REMOVE S-->6. & etiam del. <!-- REMOVE S-->5. pon­<lb/>to) di quello faria &longs;tante la medema nella &longs;ommita del monte, molto piu euidentamen­<lb/>te &longs;eguiria tal effetto nel primo ca&longs;o propo&longs;to da<emph.end type="italics"/> V. E<emph type="italics"/>c. <!-- REMOVE S-->nel quale fu &longs;uppo&longs;to il <expan abbr="mõte">monte</expan>, <lb/>et etiam la fortezza, e&longs;&longs;ere egualmente alti &longs;olamente pa&longs;&longs;a. </s> <s id="s.000256">60. & la di&longs;tantia delle <lb/>radice delli dui monti, ouer le cime de quelli e&longs;&longs;er pa&longs;&longs;a. </s> <s id="s.000257">100. onde la linea diametrale, <lb/>ouer diagonale, cioè la distantia de detta fortezza al luoco à co&longs;to alla radice del mon <lb/>te, doue &longs;e &longs;uppone el &longs;tar delle artegliarie in piano, per la penultima del primo di Eu­<lb/>clide &longs;ara circa pa&longs;&longs;a. </s> <s id="s.000258">116. (la&longs;&longs;ando li rotti) è per tanto, le balle tirate dalla detta no­<lb/>&longs;tra colobrina, &longs;tante quella nella &longs;ommita del monte, ueriano à percuottere nella det­<lb/>ta muraglia circa à pa&longs;&longs;a. </s> <s id="s.000259">140. auanti al termine del &longs;uo procedere per linea retta, & <lb/>quelle tirate dalla mede&longs;ima &longs;tante quella nel piano alla elleuatione del. <!-- REMOVE S-->6. ponto uene­<lb/>riano à percottere nella detta mur aglia, circapa&longs;&longs;a. </s> <s id="s.000260">684. auanti al termine del &longs;uo an <lb/>dar per linea retta, & perche tal differentia è grandißima, cioè da. </s> <s id="s.000261">140. pa&longs;&longs;a à. </s> <s id="s.000262">684. <lb/>pa&longs;&longs;a, che feri&longs;cono auanti al termine del &longs;uo andar per linea retta. </s> <s id="s.000263">Eglie co&longs;a euiden­<lb/>te, e chiara, in que&longs;to ca&longs;o, che non &longs;olamente alla elleuatione del. <!-- REMOVE S-->6. ponto, la detta colo <lb/>brina &longs;tante nel pie del monte, fara maggior effetto in detta fortezza di quello faria <lb/>&longs;tante nella &longs;ommita. </s> <s id="s.000264">Ma anchora alla elleuatione di qual &longs;iuoglia ponto, che &longs;ia elleua <lb/>ta, che è il propo&longs;ito.<emph.end type="italics"/> S.D. M<emph type="italics"/>e haueti ri&longs;olto a&longs;&longs;ai bene que&longs;to Que&longs;ito.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000265">QVESITO TERZO FATTO DAL MEDESIMO <lb/>I<emph type="italics"/>llu&longs;trißimo Signor Duca con&longs;equentemente.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000266">DVCA. M<emph type="italics"/>a nel uo&longs;tro arguire me haueti reduto in un'altra maggior <lb/>difficul­<lb/>ta, ouer dubitatione <21>che &longs;e <expan abbr="b&etilde;">bem</expan> ui aricordati, haueti detto, che la balla sboccata <lb/>che &longs;ia d'un pezzo maiua parte alcuna del &longs;uo motto <21> linea retta, &longs;aluo che <expan abbr="tirãdola">tirandola</expan> <lb/><expan abbr="rettam&etilde;te">rettamente</expan> in &longs;u&longs;o uer&longs;o il cielo.<emph.end type="italics"/> N. O<emph type="italics"/>uer <expan abbr="rettam&etilde;te">rettamente</expan> in zo&longs;o uer&longs;o il centro dil <expan abbr="mõdo">mondo</expan>?<emph.end type="italics"/><pb pagenum="11" xlink:href="042/01/021.jpg"/>S.D. Q<emph type="italics"/>ue&longs;to ui <expan abbr="cõcedo">concedo</expan> ben, cioe che <expan abbr="tirãdo">tirando</expan> o <expan abbr="rettam&etilde;te">rettamente</expan> in &longs;u&longs;o uer&longs;o il cielo, ouer retta <lb/>mente in zo&longs;o uer&longs;o il centro del mondo, che il tran&longs;ito, ouer moto di tal balla, &longs;ia total <lb/>mente retto, & anchora ui concedo che in tai dui uer&longs;i tal balla uada molto piu per li­<lb/>nea retta che in qual &longs;iuoglia altra elleuatione, ouer in qual &longs;i uoglia altro uer&longs;o. </s> <s id="s.000267">Ma <lb/>che in ogni altro uer&longs;o delli detti dui in fuora la non uada parte alcuna del &longs;uo moto ret <lb/>tamente, cioe per retta lunea, la non mi pare co&longs;a da credere, ne io la credo, perche &longs;e <lb/>ben ue aricordati di &longs;opra dice&longs;ti che per quelli dui tiri a Verona tirati, uoi troua&longs;ti <lb/>che la detta colobrina da lire. </s> <s id="s.000268">20. tiraua de mira, cioe per retta linea in quanto al &longs;en­<lb/>&longs;o, circa pa&longs;&longs;a. </s> <s id="s.000269">200. e&longs;&longs;endo aliuellata, hor &longs;e tal tramito de pa&longs;&longs;a. </s> <s id="s.000270">200. uoi trouati <lb/>poi con ragione non e&longs;&longs;er totalmente retto, cioe totalmente per linea retta, io uel cre­<lb/>do, et uel concedo. </s> <s id="s.000271">Ma &longs;e tal pezzo non puol tirare per retta linea li detti pa&longs;&longs;a. </s> <s id="s.000272">200. <lb/>non uoleti concedere che una tal machina ne tiri al manco la mita, cioe pa&longs;&longs;a. </s> <s id="s.000273">100. & <lb/>&longs;e non. </s> <s id="s.000274">100. al men.<emph.end type="italics"/> 50. N. N<emph type="italics"/>on &longs;olamente la non tirara li detti pa&longs;&longs;a. </s> <s id="s.000275">50. per linea <lb/>perfettamente retta, ma la non tirara un pa&longs;&longs;o &longs;olo.<emph.end type="italics"/> S.D. E<emph type="italics"/>glie una pacia la uo&longs;tra.<emph.end type="italics"/><lb/>N. L<emph type="italics"/>a ragione è quella che acquieta lo intelletto delli huomini, per che quella, ne di­<lb/>&longs;cerne il uero dal fal&longs;o.<emph.end type="italics"/> S.D. E<emph type="italics"/>glie il uero.<emph.end type="italics"/> N. D<emph type="italics"/>apoi adunque che la opinione di <lb/>uo&longs;tra Eccellentia è che la balla tirata da tal colobrina aliuellata, debbia andare una <lb/>parte del &longs;uo tran&longs;ito, ouer moto uiolente per linea retta, & il re&longs;tante poi per linea <lb/>curua &longs;tante che que&longs;to fu&longs;&longs;e il uero, uoria &longs;apere da quella, qual è la cau&longs;a propria <lb/>che tal balla uada co&longs;i per linea retta, in quella parte, doue che quella &longs;uppone che uada <lb/>co&longs;i rettamente, & quala &longs;ia mede&longs;imamente la cau&longs;a che lei uada co&longs;i per linea curua, <lb/>in quella parte, doue &longs;uppone uostra Eccellentia che uada co&longs;i curuamente.<emph.end type="italics"/> S.D. L<emph type="italics"/>a <lb/>grandißima uelocita che &longs;e ritroua nel moto di tal balla, nel u&longs;cir della bocca del pez­<lb/>zo è la propria cau&longs;a che tal balla per un poco di tempo, ouer &longs;pacio uada rettamen­<lb/>te per aere, ma dapoi mancando alquanto in quella il uigore, & la uelocita comincia <lb/>pói ad alentar&longs;e & ad abba&longs;&longs;ar&longs;e &longs;ucceßiuamente uer&longs;o terra, & co&longs;i ua continuando <lb/>per fin che percuote &longs;opra quella.<emph.end type="italics"/> N. C<emph type="italics"/>ertamente uo&longs;tra Eccellentia non potea ri­<lb/>&longs;ponder meglio di quello ha ri&longs;po&longs;to, cioe a dire che la gran uelocita è la propria cau­<lb/>&longs;a, di redure il moto di tal balla (&longs;e poßibil è) alla rettitudine, & &longs;imilmente, il mancar <lb/>della uelocita in quella, e la propria cau&longs;a di farla tendere & declinare nel &longs;uo moto <lb/>curuamente uer&longs;o terra, & quanto piu ua mancando in quella la detta uelocita, tanto <lb/>piu fa maggiore la &longs;ua declinatione, ouer curuita, & tutto que&longs;to procede, perche ogni <lb/>corpo graue &longs;pinto uiolentemente per acre, quanto piu ua ueloce, tanto piu in tal mo­<lb/>to &longs;e fa men graue, e pero ua piu rettamente per aere, perche lo aere piu facilmente &longs;o­<lb/>stenta un corpo quanto piu eglie leue, tamen nel far di &longs;uoi effetti in tal moto a&longs;&longs;um­<lb/>me molto maggior grauita della &longs;ua propria, e pero quanto piu un corpo graue ua ue­<lb/>loce (nel moto uiolente) tanto maggior effetto fa in ogni re&longs;i&longs;tente. </s> <s id="s.000276">Similmente quan­<lb/>to piu ua mancando in quello la uelocita, tanto piu in tal moto gli ua cre&longs;cendo la gra­<lb/>uita, la qual grauita, continuamente lo ua &longs;timulando, & tirando uer&longs;o terra. </s> <s id="s.000277">Ma nel <lb/>far de &longs;uoi effetti in tal moto a&longs;&longs;umme maggior leuita, ouer minor grauita, e pero fa <lb/>minor effetto.<emph.end type="italics"/> S.D. Q<emph type="italics"/>ue&longs;to uo&longs;tro di&longs;cor&longs;o non me di&longs;piace, e pero &longs;eguitate.<emph.end type="italics"/> N. <lb/>D<emph type="italics"/>ico adunque che da que&longs;te co&longs;e dette, & per ragion naturale approbate, na&longs;ce que-<pb xlink:href="042/01/022.jpg"/>&longs;ta conclu&longs;ione, che doue è maggior uelocita nella balla tir ata uio lentemente per aere, <lb/>in quella è manco grauita, & econuer&longs;o, cioe che doue che in quella è menor uelocita iui<lb/>è maggior grauita in quella.<emph.end type="italics"/> S. D. E<emph type="italics"/>glie il uero.<emph.end type="italics"/> N. A<emph type="italics"/>nchor dico, che doue che in <lb/>quella è maggior grauita, iui è maggior &longs;timulatione di quella in tirare la detta balla <lb/>uer&longs;o il centro del mondo, cioe uer&longs;o la terra.<emph.end type="italics"/> S. D. E<emph type="italics"/>glie co&longs;a credibile.<emph.end type="italics"/> N. H<emph type="italics"/>or <lb/>per conchiuder il nostro'propo&longs;ito, &longs;up poneremo che tutto il tran&longs;ito, ouer uiaggio che <lb/>debbia far, ouer che habbia fatto la balla tirata dalla &longs;opradetta colobrina &longs;ia tutta la <lb/>linea. </s> <s id="s.000278">a. <!-- REMOVE S-->b. <!-- REMOVE S-->c. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.000279">& &longs;e poßibil è che in quello &longs;ia alcuna parte che &longs;ia per&longs;ettamente retta, <lb/>poniamo che quella &longs;ia tutta la parte. </s> <s id="s.000280">a. <!-- REMOVE S-->b. <!-- REMOVE S-->la qual &longs;ia diui&longs;a in due parti eguali in ponto <lb/>e. <!-- REMOVE S-->& perche la balla tran&longs;ira piu ueloce per il &longs;pacio. </s> <s id="s.000281">a. <!-- REMOVE S-->e. (per la terza propo&longs;itione <lb/>del primo, della no&longs;tra nuoua &longs;cientia) di quello fara per il &longs;pacio. </s> <s id="s.000282">e. <!-- REMOVE S-->b. <!-- KEEP S--></s> <s id="s.000283">Adunque la det­<lb/>ta balla andara piu rettamente, per le ragioni di &longs;opra adutte, per il &longs;pacio. </s> <s id="s.000284">a. <!-- REMOVE S-->e. <!-- REMOVE S-->di quel <lb/>lo fara per il &longs;pacio. </s> <s id="s.000285">e. <!-- REMOVE S-->b. <!-- REMOVE S-->onde la linea. </s> <s id="s.000286">a. <!-- REMOVE S-->e. <!-- REMOVE S-->&longs;aria piu retta della. </s> <s id="s.000287">e. <!-- REMOVE S-->b. <!-- REMOVE S-->la qual co&longs;a è impo&longs; <lb/>&longs;ibile, perche &longs;e tutta la. </s> <s id="s.000288">a. <!-- REMOVE S-->b. <!-- REMOVE S-->è &longs;uppo&longs;ta e&longs;&longs;er perfettamente retta, la mitade di quella <lb/>non puol e&longs;&longs;er ne piu ne men retta dell'altra mitade, & &longs;e pur l'una mitade &longs;ara piu ret­<lb/>ta dell'altra &longs;eguita nece&longs;&longs;ariamente quell'altra mitade non e&longs;&longs;er retta, e pero &longs;egui­<lb/>ta de neceßita, la parte. </s> <s id="s.000289">e. <!-- REMOVE S-->b. <!-- REMOVE S-->non e&longs;&longs;er perfettamente retta.<emph.end type="italics"/></s> </p> <figure id="id.042.01.022.1.jpg" xlink:href="042/01/022/1.jpg"/> <p type="main"> <s id="s.000290">E<emph type="italics"/>t &longs;e pur alcuno haue&longs;&longs;e anchora opinione che la parte. </s> <s id="s.000291">a. <!-- REMOVE S-->e. <!-- REMOVE S-->fu&longs;&longs;e pur <21> <expan abbr="fettam&etilde;te">fettamente</expan> retta, <lb/>tal opinione &longs;e reprobara per fal&longs;a, per li mede&longs;imi modi, e uie, cioe diuidendo la detta <lb/>parte. </s> <s id="s.000292">a. <!-- REMOVE S-->e. <!-- REMOVE S-->pur in due parti eguali in ponto. </s> <s id="s.000293">f. <!-- REMOVE S-->& per le mede&longs;ime ragioni di &longs;opra adut­<lb/>te, &longs;era manife&longs;to la parte. </s> <s id="s.000294">a. <!-- REMOVE S-->f. <!-- REMOVE S-->e&longs;&longs;er piu retta della parte. </s> <s id="s.000295">f. <!-- REMOVE S-->e. <!-- REMOVE S-->adunque la detta parte. </s> <s id="s.000296">f. <lb/><!-- REMOVE S-->e. <!-- REMOVE S-->de neceßita non &longs;ara perfettamente retta, &longs;imilmente che diuide&longs;&longs;e anchora la. </s> <s id="s.000297">a. <!-- REMOVE S-->f. <lb/>in due parti eguali, con le mede&longs;ime ragioni &longs;e manife&longs;ta la mita di quella uer&longs;o. </s> <s id="s.000298">a. <!-- REMOVE S-->e&longs;&longs;er <lb/>piu retta di quella che uer&longs;o. </s> <s id="s.000299">f. <!-- REMOVE S-->& co&longs;i chi diuide&longs;&longs;e quella mita pur in altre due parti <lb/>eguali il mede&longs;imo &longs;eguira, cioe la parte terminante in a. <!-- REMOVE S-->e&longs;&longs;er piu retta dell'altra, & <lb/>perche que&longs;to procedere è infinito &longs;eguita di neceßita che non &longs;olamente tutta la. </s> <s id="s.000300">a. <!-- REMOVE S-->b. <lb/>non è perfettamente retta, ma che alcuna minima parte di quella non puo e&longs;&longs;er perfet­<lb/>tamente retta, che è il propo&longs;ito. </s> <s id="s.000301">Si uede adunque qualmente la balla tirata da detta co <lb/>lobrina in tal uer&longs;o non ua alcuna minima parte del &longs;uo moto, ouer tran&longs;ito per linea <lb/>perfettamente retta (u&longs;ci&longs;ca pur con qual grandißima uelocita &longs;i uoglia) perche la ue­<lb/>locita (per granda che la &longs;ia) mai è &longs;ufficiente, in &longs;imili uer&longs;i, a farla andar per linea <lb/>retta, uero è che quanto piu ua ueloce in &longs;imili uer&longs;i tanto piu col moto &longs;uo &longs;e appro­<lb/>pinqua al moto retto, cioe all'andar per retta linea, tamen mai puo arriuar a tal &longs;egno, <lb/>e pero piu conueniente è a dire in &longs;imil ca&longs;o, che quanto piu la detta balla ua ueloce, fa<emph.end type="italics"/><pb pagenum="12" xlink:href="042/01/023.jpg"/><emph type="italics"/>il moto &longs;uo men curuo.<emph.end type="italics"/> S. D. D<emph type="italics"/>oue procede adunque che molte uolte &longs;e ui&longs;to per­<lb/>cuotere uno preci&longs;amente nel luoco tolto de mira, la qual co&longs;a non potria occorrere &longs;e <lb/>tal balla non fu&longs;&longs;e andata rettamente.<emph.end type="italics"/> N. S<emph type="italics"/>ignor que&longs;to non ne fa certi che la balla <lb/>uada rettamente, perche anchora molte uolte &longs;e ui&longs;to percuotere di &longs;opra dal &longs;egno <lb/>tolto de mira, la qual co&longs;a, e&longs;&longs;endo le mire eguale, è impoßibile, cioe che la balla &longs;eghi <lb/>la linea ui&longs;uale equidi&longs;tante alla canna di tal pezzo, ma tai effetti non procedeno, per­<lb/>che la balla uada rettamente, ne perche quella a&longs;cenda oltra la rettitudine, ma proce­<lb/>dano totalmente dalle mire, ouer dal tra&longs;guardante. </s> <s id="s.000302">Eglie ben uero, che chi pote&longs;&longs;e ue­<lb/>der la balla, nel moto &longs;uo &longs;enza dubbio giudicarebbe tal balla per un commun &longs;pacio <lb/>e&longs;&longs;er andata rettißima, perche il no&longs;tro &longs;en&longs;o non è atto, ne &longs;ufficiente a di&longs;cerner tale <lb/>obliquita, &longs;i come occorre, guardando l'acqua del mare quando è quieto, la quale per <lb/>una gran di&longs;tantia ne pare perfettamente piana, & nondimeno, per meggio della ra­<lb/>gione &longs;apemo e&longs;&longs;er all oppo&longs;ito, cioe &longs;pherica, e pero nelli giudici fatti &longs;econdo il &longs;en&longs;o <lb/>del uedere, molte uolte &longs;e ingannamo.<emph.end type="italics"/> S. D. L<emph type="italics"/>e ragioni uo&longs;tre &longs;on buone certo, pur <lb/>mi pare molto distranio a dire, che una balla tirata da una tal machina, & con tanta <lb/>uehementia, non uada alquanto per linea retta, ma pur con&longs;ider ando anchor che in tal <lb/>obliquo uer&longs;o la grauita della balla è molto piu atta a far declinar, ouer a tirare la det <lb/>ta balla uer&longs;o terra, che in ogni altra elleuatione, mi fa credere che uoi diciate il uero. <lb/></s> <s id="s.000303">Ma tir ando quella alquanto elleuata dauanti, pen&longs;o & tengo per fermo che quella deb <lb/>ba andar per alquanto rettamente per aere, perche la grauita di tal balla tirandola in <lb/>&longs;imei uer&longs;i elleuati è manco atta a far declinar la balla uer&longs;o terra di quello che è tiran <lb/>dola a liuello.<emph.end type="italics"/> N. V<emph type="italics"/>o&longs;tra Eccellentia dice ben il uero, che la grauita della balla non è <lb/>tanto atta a ouiar il moto di quella, nelli tiri elleuati, quanto che nelli tiri equidi&longs;tanti <lb/>all'orizonte, cioe aliuellati, ouer de ponto in bianco (come dicono li bombarderi) per <lb/>due cau&longs;e, l'una perche in tal&longs;ito (come nel principio fu approuato) ui è maggior graui <lb/>ta, l'altra perche la detta grauita tira la balla perpendicolarmente &longs;opra il moto, ouer <lb/>tran&longs;ito di quella uer&longs;o terra, il qual modo da tirare è piu uigoro&longs;o, e gagliardo, che <lb/>in ogni altra elleuatione, perche elleuandola gradatamente, etiam gradatamente la det <lb/>ta grauita, &longs;i ua accostando uer&longs;o il &longs;uo tran&longs;ito, cioe che non ui cade co&longs;i perpendico­<lb/>lare &longs;opra il detto moto, ouer tran&longs;ito, anci &longs;empre &longs;i ua piu restringendo uer&longs;o quello: <lb/>ilche la fa men uigoro&longs;a, ouer men gagliarda a tirar detta balla fuora del uiaggio, ouer <lb/>moto &longs;uo, & oltra di que&longs;to (come in principio fu dimo&longs;trato) quanto piu &longs;i ua elleuan <lb/>do tanto piu lí tiri &longs;uoi&longs;ono ben men curui, tamen mai ponno e&longs;&longs;er per alcuna &longs;ua par­<lb/>te perfettamente retti, eccetto nelli &longs;opradetti duoi uer&longs;i, cioe rettamente in &longs;u&longs;o uer&longs;o <lb/>il cielo, ouer rettamente in gio&longs;o uer&longs;o il centro del mondo, <21> che in ogni uer&longs;o ui é alc<gap/><lb/>na parte de grauita quala &longs;empre tira la detta balla fuora del &longs;uo uiaggio, ouer fuora <lb/>del &longs;uo tran&longs;ito, ouer moto, eccetto che nelli predetti dui uer&longs;i, cioe rettamente uer&longs;o il <lb/>cielo, ouer <expan abbr="rettam&etilde;te">rettamente</expan> in giu&longs;o uer&longs;o il <expan abbr="c&etilde;tro">centro</expan> del <expan abbr="mõdo">mondo</expan>, nelli quali dui uer&longs;i la detta graui <lb/>ta (&longs;e pur <gap/> è grauita) uien a tirare la detta balla <expan abbr="rettam&etilde;te">rettamente</expan> <expan abbr="&longs;ecõdo">&longs;econdo</expan> l'or dine del &longs;uo uiag <lb/>gio, ouer moto, et <expan abbr="nõ">non</expan> fuora di quello, come <21> la &longs;otto&longs;critta figura <expan abbr="facilm&etilde;te">facilmente</expan> &longs;enza altra <lb/><expan abbr="lõga">longa</expan> dimostratione &longs;i puo <expan abbr="cõpr&etilde;dere">comprendere</expan>, et co&longs;i nelli tiri abba&longs;&longs;ati, come nelli elleuati, <expan abbr="&longs;up-pen&etilde;do">&longs;up­<lb/>penendo</expan>. </s> <s id="s.000304">a. <!-- REMOVE S-->la bocca del pezzo, doue &longs;ia u&longs;cita la balla. </s> <s id="s.000305">b. <!-- REMOVE S-->et la grauita di tal balla. </s> <s id="s.000306">b. <!-- REMOVE S-->la &longs;up <pb xlink:href="042/01/024.jpg"/>poneremo in forma del <21> <expan abbr="p&etilde;dicolo">pendicolo</expan>. </s> <s id="s.000307">c. <!-- REMOVE S-->il <expan abbr="&qtilde;l">qual</expan> <expan abbr="<21>p&etilde;dicolo"><21>pendicolo</expan>, ouer gra<lb/>uita. </s> <s id="s.000308">c. <!-- REMOVE S-->in ogni uer&longs;o &longs;empre <expan abbr="uatirãdo">uatirando</expan> la detta balla uer&longs;o il <expan abbr="c&etilde;">cem</expan> <lb/>tro del <expan abbr="mõdo">mondo</expan>, cioe <21> <expan abbr="p&etilde;dicolarm&etilde;te">pendicolarmente</expan> uer&longs;o terra, onde <expan abbr="argum&etilde;">argumen</expan> <lb/><expan abbr="tãdo">tando</expan>, come nel tiro aliuellato &longs;u fatto, &longs;ara manife&longs;to <expan abbr="qualm&etilde;">qualmen</expan> <lb/>te in nullo altro uer&longs;o che nelli dui &longs;opra detti, la balla tirata <lb/>da detta colobrina, ouer d'altro pezzo, non puo andare alcu <lb/>na minima parte del &longs;uo moto per linea perfettamente retta, <lb/>che è il propo&longs;ito.<emph.end type="italics"/> S. D. V<emph type="italics"/>oi haueti ben dife&longs;a la uo&longs;tra ra­<lb/>gione, & questo ba&longs;ta per hoggi, come &longs;ia ritornato da Pe&longs;a­<lb/>ro uoro che &longs;i faccia la i&longs;perientia di que&longs;te uo&longs;tre inuentioni.<emph.end type="italics"/></s> </p> <figure id="id.042.01.024.1.jpg" xlink:href="042/01/024/1.jpg"/> <p type="head"> <s id="s.000309">QVESITO QVARTO FATTO DAL SIGNOR <lb/>G<emph type="italics"/>abriel Tadino da Martinengo Cauallier de Rodi, <lb/>& Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000310">PRIORE. T<emph type="italics"/>irando un pezzo di artegliaria due uolte l'una drieto a l'altra, <lb/>a <lb/>una mede&longs;ima elleuatione, & uer&longs;o uno mede&longs;imo luoco, et cargato &longs;empre egual <lb/>mente, domando &longs;e que&longs;ti dui tiri &longs;ar anno eguali.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio &longs;aranno in eguali, <lb/>perche tirara piu lontano alla &longs;econda uolta che alla prima.<emph.end type="italics"/> P. P<emph type="italics"/>erche ragione.<emph.end type="italics"/> N. <lb/>P<emph type="italics"/>er due ragioni, la prima è que&longs;ta, che al primo tiro la balla ritrouara l'aere quieto, et <lb/>nel &longs;econdo lo ritrouara non &longs;olamente tutto commo&longs;&longs;o dalla balla tirata dal primo ti­<lb/>vo, ma anchora molto tendente, ouer &longs;corrente uer&longs;o al luoco doue &longs;e tira. </s> <s id="s.000311">Et perche <lb/>eglie piu facile a mouere etiam a penetrare una co&longs;a gia commo&longs;&longs;a & penetrata, che <lb/>una che &longs;tia ripo&longs;ata & quieta. </s> <s id="s.000312">Seguita che la balla tirata alla &longs;econda uolta (per ritro <lb/>uare men ostacolo nel &longs;uo moto della prima) andara molto piu lontano di quella tirata <lb/>alla prima uolta. </s> <s id="s.000313">La &longs;econda ragione è que&longs;ta, che al primo tiro la poluere po&longs;ta nel <lb/>pezzo, &longs;pe&longs;&longs;e uolte ritroua la canna alquanto humida, maßime quando che quel tal pez <lb/>zo non fu&longs;&longs;e &longs;tato tirato gia alquanti giorni, per la qual co&longs;a, la detta poluere non bru<lb/>&longs;ara co&longs;i pre&longs;to, come faria trouando tal luoco arido, & alquanto caldo d'una calidita <lb/>temperata: la qual calidita &longs;uga alquanto la poluere de ogni humidita che in lei fu&longs;&longs;e: il­<lb/>che la fa piu pre&longs;ta, e potente nell'abbru&longs;iare, & per tanto non operara co&longs;i uigoro&longs;a­<lb/>mente nel primo tiro, come fara nel &longs;econdo, &longs;i che anchora per questa &longs;econda ra­<lb/>gione alla &longs;econda uolta douera tirar piu lontano che alla prima.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;te uo&longs;tre <lb/>ragioni molto mi piaceno, & uoglio che ba&longs;ti per que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000314">QVESITO QVINTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo. </s> <s id="s.000315">Sig. <!-- REMOVE S-->Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000316">PRIORE. H<emph type="italics"/>ier&longs;era uoi conclude&longs;ti, & con buone ragioni naturali <lb/>approua­<lb/>sti, che tirando un pezzo due uolte l'una drieto l'altra a una mede&longs;ima elleua­<lb/>tione, & uer&longs;o uno mede&longs;imo luoco, & etiam egualmente cargato, molto piu tirara la <lb/>&longs;econda uolta, che la prima, hor ue adimando, che continua&longs;&longs;e per longo tempo a tira-<emph.end type="italics"/><pb pagenum="13" xlink:href="042/01/025.jpg"/><emph type="italics"/>re ìl detto pezzo à tal elleuatione, & uer&longs;o il mede&longs;imo luoco, &longs;e contìnuamente anda <lb/>ria augmentando li &longs;uoi tiri.<emph.end type="italics"/> N. N<emph type="italics"/>on &longs;ignore, chel non &longs;eguiria que&longs;to.<emph.end type="italics"/> P. M<emph type="italics"/>o <lb/>perche uoi dice&longs;ti pur hier&longs;era, che per trouare lo aere commo&longs;&longs;o, & alquanto &longs;cor­<lb/>rente uer&longs;o el luoco doue &longs;e tira, etiam perche la poluere posta nel pezzo, troua el <lb/>luoco piu arido, & &longs;utto, & alquanto caldo, che alla &longs;econda uolta tiraria piu, che alla <lb/>prima, e per tanto quanto piu &longs;i ua <expan abbr="tirarãdo">tirarando</expan>, tanto piu la balla uien à ritrouare l'aere <lb/>piu commo&longs;&longs;o, e penetrato, etiam piu &longs;corrente uer&longs;o al luoco doue &longs;e tira (per cau&longs;a <lb/>delli tiri anciani) & &longs;imelmente la poluere, che &longs;e ua recargando, ouer remettendo nel <lb/>pezzo, continuamente ua ritrouando il luoco (cioè la canna del pezzo) continuamen­<lb/>te piu arida, & &longs;utta, & piu calda, la qual calidita (come uoi dice&longs;ti hier&longs;era) &longs;uga la <lb/>poluere de ogni humidita, che in lei fu&longs;&longs;e, per il che tal poluere &longs;i fa piu pre&longs;ta nel ab­<lb/>bru&longs;iare: la qual pre&longs;tezza la uien à far piu potente del &longs;olito.<emph.end type="italics"/> N. E<emph type="italics"/>glie ben uero <lb/>tutto quello, che dice uostra Signoria, ma ui occorre un'altro accidente molto contra­<lb/>rio, el quale è questo: che per el continuo tirare el pezzo continuamente piu &longs;e ua &longs;cal­<lb/>dando, & quanto piu è caldo, tanto piu la canna di quello &longs;i fa attrattiua, cioè, &longs;i come <lb/>una uento&longs;a, quando è&longs;caldata per la &longs;toppa abbru&longs;iata dentro in quella, & perche la <lb/>balla non è &longs;pul&longs;ata, ouer &longs;pinta da altro, che dalla e&longs;&longs;alatione aerea, ouer uento&longs;a, cau­<lb/>&longs;ata dal &longs;alnitrio, onde facendo&longs;i tal pezzo continuamente piu attrattiuo, come ho det <lb/>to, per el maggior caldo, quel medemo uiene à &longs;orbere, & à retenere, & continuamen <lb/>te piu di quella uento&longs;ita, che doueria &longs;eruire al &longs;pingere la balla, e pero &longs;cemando (& <lb/>continuamente piu) la uirtu e&longs;pul&longs;iua nel detto pezzo, ra&longs;oneuolmente la balla conti­<lb/>nuamente debbe u&longs;cire men ueloce, ouer piu debile, & con&longs;equentemente andar conti­<lb/>nuamente men lontano.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;ta uo&longs;tra ragione mi con&longs;ona molto<emph.end type="italics"/>: <emph type="italics"/>ma chi &longs;a, che <lb/>quelli dui accidenti primi, che dano fauore, & aiuto al moto della balla, cioe la gran <lb/>combu&longs;tione, ouer &longs;correntia del aere uer&longs;o al luoco doue continuamente &longs;e tira, & lo <lb/>uigore, che &longs;e augumenta nella poluere, per cau&longs;a del caldo, non &longs;iano &longs;officienti à &longs;up­<lb/>plire à quel difetto attratiuo cau&longs;ato dalla gran calidita del pezzo et for&longs;i piu, la qual <lb/>co&longs;a e&longs;&longs;endo co&longs;i, &longs;eguiria, che el detto pezzo tira&longs;&longs;e &longs;empre à uno mede&longs;imo modo e&longs;­<lb/>&longs;endo tanto quello, che ui aggionge&longs;&longs;e li detti dui primi accidenti, quanto quello, che ui <lb/>roba&longs;&longs;e el terzo, oueramente che tira&longs;&longs;e continuamente piu, e&longs;&longs;endo piu la augmenta­<lb/>tione di ditti dui primi accidenti, della detrattione del terzo.<emph.end type="italics"/> N. C<emph type="italics"/>ertamente el non <lb/>&longs;i puo negare, che quelli dui primi accidenti (cioe el rompimento dell'aere, & quel ui­<lb/>gor che accre&longs;&longs;e nella poluere) non diano grande aiuto e &longs;ußidio al moto della balla, el <lb/>qual aiuto, e &longs;ußidio, eglie da credere, che per alquanto tempo &longs;uppli&longs;ca (& &longs;or&longs;i da­<lb/>uantaggio) per quella uirtu expul&longs;iua, che continuamente ua robando, ouer &longs;orbendo <lb/>el pezzo, &longs;econdo che fi ua &longs;caldando, talmente che for&longs;i el terzo, & quarto tiro &longs;aran <lb/>no qua&longs;i pari in bilancia, con el &longs;econdo, ouer poco differenti, nondimeno à longo anda­<lb/>re, eglie da tenere, che li detti dui accidenti non potranno &longs;upplire al difetto del terzo <lb/>accidente, per la augmentatione del grandißimo caldo, che continuamente &longs;i ua cau&longs;an <lb/>do in quel tal pezzo, per il che el detto pezzo, come di &longs;opra è detto, &longs;i fa continua­<lb/>mente piu attrattiuo, e pero continuamente ua robando, ouero &longs;orbendo piu di quella <lb/>e&longs;&longs;alatione, che doueria &longs;pingere la balla, & per tanto que&longs;to terzo accidente à longo<emph.end type="italics"/><pb xlink:href="042/01/026.jpg"/><emph type="italics"/>andare uien à re&longs;tar &longs;uperiore alli detti dui primi, et per que&longs;to à longo andar talpez <lb/>zo uien à tirare molto manco del &longs;olito.<emph.end type="italics"/> P. M<emph type="italics"/>o chi reffredda&longs;&longs;e tal pezzo, con ac­<lb/>qua (cioè gettandoui dell'acqua nella canna) non credeti chel tiraraue piu uer&longs;o il me­<lb/>de&longs;imo luoco.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubio che tiraraue piu, quando che tal pezzo re&longs;ta&longs;&longs;e per­<lb/>fettamente fredo, & a&longs;ciuto, ma raffredandolo co&longs;i con acqua, el metallo che è caldo, <lb/>&longs;orbe di quella acqua, & &longs;orbendola la ri&longs;olue in uapore aereo, el qual uapore non po­<lb/>tendo stare nella canna è sforzato à u&longs;cir di quella pian piano, el qual uapore, quando <lb/>chel non porta&longs;&longs;e con &longs;eco alcuna humidita, & chel pezzo resta&longs;&longs;e di dentro ben a&longs;ciu <lb/>to, tal uapore doueria piu pre&longs;to augumentar il tiro in tal pezzo, che &longs;cemarlo: per­<lb/>che de attrattiuo, che era tal pezzo, per lo continuo u&longs;cire di tal uapore &longs;aria fatto <lb/>e&longs;pul&longs;iuo, ma perche tal uapore è tutto humidità, onde recargando tal pezzo, quan­<lb/>tunque para a&longs;ciuto nel metterui la poluere, el non puo e&longs;&longs;ere che tal uapore humido, <lb/>non humidi&longs;ca alquanto la poluere, per il che non fara <expan abbr="tãto">tanto</expan> uigoro&longs;o il &longs;uo effetto, <expan abbr="quã">quam</expan> <lb/>to faria &longs;e tal pezzo &longs;i la&longs;&longs;aße raffredare per &longs;e &longs;te&longs;&longs;o &longs;enza metterui acqua.<emph.end type="italics"/> P. V<emph type="italics"/>oi <lb/>me haueti molto &longs;atisfatto que&longs;ta &longs;era, ma <21> e&longs;&longs;er hora tarda, uoglio, che questo ba&longs;ti.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000317">QVESITO SESTO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000318">PRIORE. Q<emph type="italics"/>ual è la cau&longs;a, che dando&longs;i piu quantita di poluere del <lb/>&longs;olito à un <lb/>pezzo di artegliaria quella percuottera piu alto del &longs;egno, doue che prima con <lb/>men poluere ui tiraua rettamente de mira.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to procede, che il moto, ouero <lb/>tran&longs;ito di tal balla tirata con piu poluere, è manco curuo, che quel di quella tirata con <lb/>men poluere, & la differentia di que&longs;te due curuita piu &longs;e dimo&longs;tra, ouer che piu &longs;i fa <lb/>apparente nel fin del moto, che in ogni altro luoco, pero che quel tran&longs;ito, ouer moto, <lb/>che è men curuo, &longs;empre &longs;e i&longs;tende, & procede di &longs;opra à quello, che è piu curuo, & <lb/>quanto piu è longo el tiro, tanto piu la percußione del <expan abbr="m&etilde;">men</expan> curuo &longs;ara piu alta di quella <lb/>del piu curuo, perche il tran&longs;ito, ouer moto men curuo piu &longs;i accosta al tran&longs;ito, ouero <lb/>moto retto, di quello. </s> <s id="s.000319">che fa lo piu curuo, & perche el tramito, ouer tran&longs;ito retto, <lb/>cioe quello, che &longs;e i&longs;tende rettamente &longs;econdo la rettitudine della canna del pezzo in <lb/>qual &longs;i uoglia uer&longs;o, è&longs;empre &longs;uperiore à tutti li moti, ouer tran&longs;iti obliqui di qual &longs;i <lb/>uoglia balla, che uiolentemente u&longs;ci&longs;ca di quel pezzo in qual &longs;i uoglia uer&longs;o.<emph.end type="italics"/> E <emph type="italics"/>pero <lb/>quel moto, ouer tran&longs;ito, che piu &longs;i acco&longs;ta al detto retto, &longs;empre uien à e&longs;&longs;er &longs;uperiore <lb/>à quello, che men ui &longs;i acco&longs;ta, & perche la balla tirata con piu poluere u&longs;ci&longs;&longs;e, & ua <lb/>piu ueloce di quella tirata con men poluere, e pero fa el moto &longs;uo piu retto, ouer men <lb/>curuo di l'altra, e per tanto la &longs;ua percußione è &longs;uperiore à quella di l'altra.<emph.end type="italics"/> P. I<emph type="italics"/>o <lb/><expan abbr="nõ">non</expan> bene <expan abbr="int&etilde;do">intendo</expan> que&longs;to che uoi diceti, che el tiro fatto con piu poluere ua men curuo di <lb/>quello fatto con men poluere. </s> <s id="s.000320">Non uoleti uoi, che una balla tirata con un pezzo car­<lb/>gato con la &longs;ua debita, & con&longs;ueta mi&longs;ura di poluere uada rettamente al luoco, ouer &longs;e <lb/>gno tolto de mira, in una mediocre di&longs;tantia.<emph.end type="italics"/> N. A<emph type="italics"/>nci que&longs;to il nego, cioe, che tal <lb/>balla uada per linea retta al&longs;egno tolto de mira, & que&longs;to medemo pa&longs;&longs;o fu da me di­<lb/>&longs;putato un'altra uolta auanti della buona memoria della Eccellentia del Duca di Vrbi-<emph.end type="italics"/><pb pagenum="14" xlink:href="042/01/027.jpg"/><emph type="italics"/>no padre di questo, cioe, che una balla tirata con qual &longs;i uoglia pezzo di artegliaria, <lb/>& per qual &longs;i uoglia uer&longs;o mai ua, ne puo andare alcuna minima parte del &longs;uo moto, <lb/>ouer tran&longs;ito per linea perfettamente retta, &longs;aluo che non la tira&longs;&longs;e rettamente uer&longs;o <lb/>el cielo, ouer rettamente uer&longs;o el centro del mondo.<emph.end type="italics"/> P. C<emph type="italics"/>omprendo, che uoi diti la <lb/>uerita, perche &longs;e quella anda&longs;&longs;e alla prima rettamente al &longs;egno, per darui poi piu quan <lb/>tita di poluere, ra&longs;oneuolmente non doueria dar de &longs;opra del &longs;egno, anzi doueria pur <lb/>dar nel mede&longs;imo loco, doue che prima con men poluere percuoteua, & per que&longs;to ui <lb/>ho fatto lo pre&longs;ente Que&longs;ito, perche mi pareua di &longs;tranio, che per darui piu poluere <lb/>la balla doue&longs;&longs;e a&longs;cendere di &longs;opra alla rettitudine, nondimeno doman di &longs;era uoro che <lb/>di&longs;putamo meglio que&longs;ta materia, perche la me piace.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000321">QVESITO SETTIMO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000322">PRIORE. H<emph type="italics"/>ier&longs;era uoi concludesti, & con buone ragioni naturale uoi dimo <lb/>&longs;tra&longs;ti qualmente una balla tirata da una artegliaria, mai ua per linea retta in <lb/>parte alcuna, &longs;aluo che rettamente uer&longs;o il cielo, ouer rettamente uer&longs;o il centro del <lb/>mondo. </s> <s id="s.000323">Hor ue dimando donde procede, che tirando&longs;e ad alcun &longs;egno de mira, alcuna <lb/>fiata &longs;i da preci&longs;amente in brocca, cioe nel &longs;egno tolto de mira, alcun'altra fiata &longs;i da di <lb/>&longs;otto, & alcun'altra di &longs;opra dal &longs;egno.<emph.end type="italics"/> N. T<emph type="italics"/>utto que&longs;to procede dalle mire, perche <lb/>&longs;e la mira dauanti é preci&longs;amente tanto alta, quanto quella de drio, cioe, che l'una, & <lb/>l'altra &longs;iano egualmente lontane dal fondo del uacuo della canna di tal pezzo, & che <lb/>colui, che uol tirare ad alcun &longs;egno, incontri col &longs;uo occhio preci&longs;amente el detto &longs;egno <lb/>con le due mire, cioe con le i&longs;tremita di quelle &longs;empre in tal ca&longs;o dara alquanto di &longs;otto <lb/>dal &longs;egno, & quanto piu il detto &longs;egno &longs;ara lontano, tanto piu ba&longs;&longs;a &longs;ara la botta, & é <lb/>conuer&longs;o, cioé, che quanto piu &longs;ara propinquo il detto &longs;egno, tanto men ba&longs;&longs;a &longs;ara la <lb/>detta botta. </s> <s id="s.000324">Que&longs;to mede&longs;imo, & con maggior differentia, &longs;eguiria quando che la mi <lb/>ra de drio fu&longs;&longs;e piu ba&longs;&longs;a, ouero piu corta di quella dauanti, dico piu corta in re&longs;petto <lb/>al fondo del uacuo della canna del pezzo.<emph.end type="italics"/> P. N<emph type="italics"/>on ue intendo.<emph.end type="italics"/> N. A<emph type="italics"/>ccio meglio <lb/>me intendiati uoglio ponere figuralmente la &longs;otto&longs;critta artegliaria con le due mire <lb/>e. <!-- REMOVE S-->&. </s> <s id="s.000325">d. <!-- KEEP S--></s> <s id="s.000326">le qual due mire poniamo in que&longs;to ca&longs;o, che &longs;iano equale, cioe, che le due istre­<lb/>mita di quelle (cioe. </s> <s id="s.000327">c. <!-- REMOVE S-->&. </s> <s id="s.000328">d.) &longs;iano egualmente di&longs;tante dal fondo del uacuo della can­<lb/>na, & con que&longs;te due mire &longs;ia incontrato el ponto. </s> <s id="s.000329">e. <!-- REMOVE S-->cioe &longs;upponemo, chel ponto. </s> <s id="s.000330">e. <!-- REMOVE S-->&longs;ia <lb/>el &longs;egno, che hauemo tolto de mira per tirarui, hor dico in que&longs;to ca&longs;o, che nece&longs;&longs;a­<lb/>riamente &longs;empre &longs;e dara alquanto piu ba&longs;&longs;o del &longs;egno, & &longs;ia tal &longs;egno lontano, ouero <lb/>propinquo quanto &longs;i uoglia. </s> <s id="s.000331">Perche la no&longs;tra linea ui&longs;uale (qual &longs;ia la. </s> <s id="s.000332">c. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.000333">e.) <lb/>&longs;empre procedera, ouero &longs;e e&longs;tendera egualmente di&longs;tante al uacuo della canna, o­<lb/>uero alla linea, che &longs;ia protratta rettamente in longo, &longs;econdo l'ordine del uacuo <lb/>della canna, ouero centro di quella, la quale in que&longs;to ca&longs;o pongo &longs;ia la linea. </s> <s id="s.000334">f. <!-- REMOVE S-->g. <lb/>et perche il ponto. </s> <s id="s.000335">g. <!-- REMOVE S-->é nece&longs;&longs;ario e&longs;&longs;er piu ba&longs;&longs;o del ponto. </s> <s id="s.000336">e. <!-- REMOVE S-->per tanto quanto che é dal <lb/>ponto. </s> <s id="s.000337">d al centro della canna, &longs;i uede adunque, che &longs;e la balla anda&longs;&longs;e perfettamente <lb/>per linea retta, in que&longs;to ca&longs;o lei percuotteria de &longs;otto dal &longs;egno, cioe in ponto. </s> <s id="s.000338">g. <!-- REMOVE S-->ma<emph.end type="italics"/><pb xlink:href="042/01/028.jpg"/><emph type="italics"/>per e&longs;&longs;er &longs;tato dimo&longs;trato, che in &longs;imei tiri la balla mai ua per linea perfettamenteret <lb/>ta, ma &longs;empre per obliqua, ouer curua &longs;eguita di neceßita, che tal balla dia, ouer dara <lb/>di &longs;otto dal ponto. </s> <s id="s.000339">g. <!-- REMOVE S-->come &longs;aria à dire in ponto. </s> <s id="s.000340">i. <!-- REMOVE S-->& perche ogni commune intelletto, <lb/>&longs;enza altra dimostratione, confirmara in que&longs;to ca&longs;o, che quanto piu &longs;ara lontano el <lb/>detto &longs;egno. </s> <s id="s.000341">e. <!-- REMOVE S-->tanto piu ba&longs;&longs;o &longs;ara el ponto. </s> <s id="s.000342">i. <!-- REMOVE S-->perche el tran&longs;ito, ouer moto curuo con <lb/>tinuamente &longs;i ua piu curuando uer&longs;o terra, che è il primo propo&longs;ito.<emph.end type="italics"/></s> </p> <figure id="id.042.01.028.1.jpg" xlink:href="042/01/028/1.jpg"/> <p type="main"> <s id="s.000343">E<emph type="italics"/>l &longs;econdo propo&longs;ito (cioè, che &longs;e la mira dauanti &longs;ara piu alta, che quella de drio, <lb/>che &longs;imelmente la botta &longs;empre dara piu ba&longs;&longs;a del &longs;egno, & in ogni uer&longs;o, & molto <lb/>piu ba&longs;&longs;o di quello faria con le mire eguale, & que&longs;to &longs;enza altra dimo&longs;tratione è ma <lb/>nife&longs;to, come per la figura &longs;otto&longs;critta &longs;en&longs;ibelmente &longs;i uede, e pero &longs;opra di cio non di <lb/>ro altro, &longs;aluo che que&longs;ti dui e&longs;&longs;empi, quantunque &longs;iano dati nel tirar aliuello &longs;i debbe <lb/>intendere il mede&longs;imo &longs;uccedere in ogni altro uer&longs;o.<emph.end type="italics"/></s> </p> <figure id="id.042.01.028.2.jpg" xlink:href="042/01/028/2.jpg"/> <p type="main"> <s id="s.000344">PRIORE. Q<emph type="italics"/>ue&longs;ti dui uo&longs;tri e&longs;&longs;empi, gli ho inte&longs;o benißimo, &longs;i che uegnamo <lb/>pur all'altra parte, cioè doue na&longs;ce, che molte uolte &longs;i da in brocca, & alcuna fiata di <lb/>&longs;otto dal &longs;egno.<emph.end type="italics"/> N. D<emph type="italics"/>etta la conditione, & qualita delle botte, che occorre, quando <lb/>che le due mire &longs;ono eguale, & etiam quando, che la mira dauanti è piu alta di quella <lb/>de drio (cioè, che in l'una, & l'altra &longs;empre de neceßita &longs;i da di &longs;oto dal &longs;egno.) Hor <lb/>re&longs;ta &longs;olamente à narrare le conditione, & qualita delle botte, che puo occorrere <expan abbr="quã">quam</expan> <lb/>do che la mira dauanti &longs;ia alquanto piu ba&longs;&longs;a, cioè alquanto piu corta di quella de drio, <lb/>& questo piu ba&longs;&longs;a, ouer piu corta &longs;i debbe intendere &longs;empre (come di &longs;opra fu detto) <lb/>in ri&longs;petto al fundo del uacuo della canna del detto pezzo. </s> <s id="s.000345">Dico adunque, che quando <lb/>la mira dauanti &longs;ara alquanto piu ba&longs;&longs;a di quella de drio in tal ca&longs;o puo occorrere, che <lb/>alcuna fiata &longs;e dia in brocca, & alcun'altra, che &longs;e dia di &longs;opra, & alcun'altra di &longs;otto <lb/>dal &longs;egno.<emph.end type="italics"/> P. P<emph type="italics"/>erche ragione.<emph.end type="italics"/> N. L<emph type="italics"/>a ragione è que&longs;ta, che ogni uolta, che la mi­<lb/>ra dauanti &longs;ia alquanto piu ba&longs;&longs;a di quella de drio (per la quinta petitione di Eucli­<lb/>de) la nostra linea ui&longs;uale è nece&longs;&longs;ario concorrere con la linea retta, che procede<emph.end type="italics"/><pb pagenum="15" xlink:href="042/01/029.jpg"/><emph type="italics"/>qettamente &longs;econdo lo aßis del uacuo della canna, & perche il tran&longs;ito, ouer viaggio, <lb/>qual debbe far la balla (quantunque il non &longs;ia retto, ne che uada realmente per la detta <lb/>linea che procede rettamente &longs;econdo l'ordine del aßis del uacuo della canna del pez­<lb/>zo) tamen per molto &longs;pacio ua quafi contiguo con quella, ouer poco lontano da quella.<emph.end type="italics"/><lb/>E <emph type="italics"/>per tanto tal &longs;egamento puo e&longs;&longs;er in tal luoco che la mede&longs;ima linea ui&longs;uale &longs;eghera <lb/>anchora il tran&longs;ito, ouer uiaggio qual debbe far la balla. (Et que&longs;to accadera quando <lb/>che la mira dauanti &longs;ara piu ba&longs;&longs;a del douere ri&longs;petto a quella de drio) & puo anchora <lb/>e&longs;&longs;er in tal luoco, che non &longs;olamente la detta linea ui&longs;uale non &longs;eghera il detto tran&longs;ito, <lb/>ouer uiaggio, ma anchora non lo toccata, & questo accadera quando che la mira da­<lb/>uanti non &longs;ara a &longs;ufficientia piu ba&longs;&longs;a di quella de drio. </s> <s id="s.000346">Anchora puo e&longs;&longs;er in tal luoco <lb/>che tal linea ui&longs;uale &longs;ara contingente con il detto tran&longs;ito, ouer uiaggio qual debbe far <lb/>la balla, & que&longs;to occorrera quando che la mira dauanti hauera la &longs;ua debita & conue <lb/>niente ba&longs;&longs;ezza ri&longs;petto alla mira de drio, &longs;e per &longs;orte adunque la no&longs;tra linea ui&longs;ua­<lb/>le &longs;eghera il detto tran&longs;ito, ouer uiaggio qual debbe far la balla, & che per &longs;orte an­<lb/>chora il &longs;egno che &longs;e tuol de mira, &longs;ia preci&longs;amente nel ponto di tal inter&longs;ecatione &longs;en­<lb/>za dubbio la balla dara preci&longs;amente in brocca, ma &longs;e per ca&longs;o il detto &longs;egno &longs;ara di den <lb/>tro da tal inter&longs;eccatione, cioe piu in uer&longs;o il pezzo, tal balla dara &longs;empre alquanto di <lb/>&longs;otto dal &longs;egno, cioe dalla brocca di quello, & quanto piu il detto &longs;egno &longs;ara remoto, <lb/>ouer lontano datal inter&longs;eccatione, cioe piu uer&longs;o il pezzo, tanto piu ba&longs;&longs;o dal &longs;egno, <lb/>ouer dalla brocca di quello, dara la detta balla. </s> <s id="s.000347">Ma &longs;e per ca&longs;o il detto &longs;egno &longs;ara alquan <lb/>to fuora della detta inter&longs;eccatione, cioe alquanto piu alta de tal inter&longs;eccatione, tal <lb/>balla dara di &longs;opra dal detto &longs;egno, & quanto piu &longs;ara da quello lontano (per un certo <lb/>&longs;pacio) tanto piu dara di &longs;opra da quello.<emph.end type="italics"/> P. N<emph type="italics"/>on ue intendo troppo bene.<emph.end type="italics"/> N. P<emph type="italics"/>o­<lb/>niamo per figura la &longs;otto&longs;critta artegliaria, & le due mire di quella &longs;iano. </s> <s id="s.000348">c. <!-- REMOVE S-->&. </s> <s id="s.000349">d. <!-- KEEP S--></s> <s id="s.000350">& <lb/>&longs;ta la mira. </s> <s id="s.000351">d. <!-- KEEP S--></s> <s id="s.000352">piu ba&longs;&longs;a della mira. </s> <s id="s.000353">c. <!-- REMOVE S-->& &longs;ia la linea che procede rettamente &longs;econdo l'or <lb/>dine del aßis del uacuo della canna, la. </s> <s id="s.000354">f. <!-- REMOVE S-->g. <!-- REMOVE S-->& il tran&longs;ito, ouer uiaggio qual debbe far la <lb/>balla la linea. </s> <s id="s.000355">h. <!-- REMOVE S-->i. <!-- REMOVE S-->& la no&longs;tra linea ui&longs;uale quella che procede rettamente &longs;econdo l'or­<lb/>dine delle due i&longs;treme ponte delle due mire. </s> <s id="s.000356">c. <!-- REMOVE S-->&. </s> <s id="s.000357">d. <!-- KEEP S--></s> <s id="s.000358">la quale nece&longs;&longs;ariamente (come è det <lb/>to) &longs;eghera la linea. </s> <s id="s.000359">f. <!-- REMOVE S-->g. <!-- REMOVE S-->& per tanto poniamo anchor che quella &longs;eghi la detta linea. </s> <s id="s.000360">h. <lb/><!-- REMOVE S-->i. <!-- REMOVE S-->in ponto.<emph.end type="italics"/> k. <emph type="italics"/>(come di &longs;otto appar in figura) hor dico, che &longs;e il &longs;egno che &longs;e tuol de mi­<lb/>ra &longs;ara preci&longs;amente in ponto.<emph.end type="italics"/> k. <emph type="italics"/>tal balladara preci&longs;amente in brocca, & &longs;e per ca&longs;o il <lb/>detto &longs;egno fu&longs;&longs;e di dentro di tal inter&longs;eccatione, cioe in uer&longs;o del pezzo, come &longs;aria a <lb/>dire in ponto. </s> <s id="s.000361">m. <!-- REMOVE S-->tal balla dara &longs;empre alquanto di &longs;otto dalla brocca del detto &longs;egno, <lb/>perche per tutto tal luoco, ouer &longs;pacio il tran&longs;ito della balla pa&longs;&longs;a &longs;empre di &longs;otto dalla <lb/>no&longs;tra linea ui&longs;uale, & quanto piu remoto &longs;ara il detto &longs;egno dal ponto.<emph.end type="italics"/> k. <emph type="italics"/>cioe quanto <lb/>piu &longs;ara uer&longs;o il pezzo, tanto piu ba&longs;&longs;a &longs;ara la detta no&longs;tra botta, niente dimeno tal <lb/>ba&longs;&longs;ezza in un &longs;imil ca&longs;o mai puo e&longs;&longs;er eguale alla differentia, che è dalla i&longs;tremita della <lb/>mira dinanti, cioe dal ponto. </s> <s id="s.000362">d. <!-- KEEP S--></s> <s id="s.000363">al centro del foro del pezzo, ouer uacuo della canna, la <lb/>qual differentia è circa alla mita della gro&longs;&longs;ezza del pezzo nella parte de drio, cioe <lb/>nella culatta, e per tanto, e&longs;&longs;endo il &longs;egno doue &longs;e tira de mira di qua da tal inter&longs;ecca­<lb/>tione, il bombardiero è &longs;oggietto a poco errore (per conto delle mire.) Ma quando tal <lb/>&longs;egno fu&longs;&longs;e alquanto fuora da tal inter&longs;eccatione, come &longs;aria a dire in ponto. </s> <s id="s.000364">l. <!-- REMOVE S-->tal balla <pb xlink:href="042/01/030.jpg"/>dara di &longs;opra dal &longs;egno, per che per un longo tramito, ouer &longs;pacio, il tran&longs;ito della balla <lb/>pa&longs;&longs;a di &longs;opra dalla linea ui&longs;uale, e pero quanto piu lontano &longs;ara il detto &longs;egno dal pon­<lb/>to.<emph.end type="italics"/> k. <emph type="italics"/>per un longo &longs;pacio, tanto piu alta &longs;ara la botta, uero è, che à longo andare la bal­<lb/>la con il tran&longs;ito &longs;uo curuo, ouer naturale ritornera à &longs;egare un'altra uolta la no&longs;tra li <lb/>nea ui&longs;uale, perche la no&longs;tra linea ui&longs;uale. </s> <s id="s.000365">c. <!-- REMOVE S-->d.<emph.end type="italics"/> k. <emph type="italics"/>l. <!-- REMOVE S-->procede in infinito rettamente, & la <lb/>balla per il tran&longs;ito. </s> <s id="s.000366">h.<emph.end type="italics"/> k. <emph type="italics"/>i. <!-- REMOVE S-->non procede in infinito, anci con tempo ua mancando, & &longs;i <lb/>ua curuando uer&longs;o il centro del mondo, & finalmente &longs;e redrizza rettamente di moto <lb/>naturale (non trouando re&longs;istentia) uer&longs;o il detto centro del mondo, e pero eglie nece&longs;­<lb/>&longs;ario che a longo andare che la ritorni con il tran&longs;ito &longs;uo à inter&longs;eccar&longs;e un'altra uolta <lb/>con la nostra linea ui&longs;uale, e pero &longs;e il detto &longs;egno fu&longs;&longs;e tanto, & tanto lontano, cioe tan <lb/>to oltra la prima inter&longs;eccatione fatta in ponto.<emph.end type="italics"/> k. <emph type="italics"/>& che per &longs;orte fu&longs;&longs;e anchora pre­<lb/>ci&longs;amente in quella altra &longs;econda inter&longs;eccatione, &longs;enza dubbio in tal luoco co&longs;i lontano <lb/>&longs;e daria preci&longs;amente in brocca, perche ogni uolta che la no&longs;tra linea ui&longs;uale &longs;eghi il <lb/>tran&longs;ito della balla, eglie nece&longs;&longs;ario che la &longs;eghi quello in dui lochi, l'uno de quali, cioe il <lb/>primo, non puo e&longs;&longs;er molto lontano, ma l'altro, cioe il &longs;econdo è nece&longs;&longs;ario che &longs;ia mol­<lb/>to, e molto lontano, cioe qua&longs;i in fine del &longs;uo moto uiolente, & tal hora potria e&longs;&longs;er nel <lb/>&longs;uo moto, ouer tran&longs;ito naturale, e pero in tal ca&longs;o e&longs;&longs;endo il &longs;egno che &longs;e tuol de mira, <lb/>in qual &longs;i uoglia de que&longs;ti dui lochi, ouer iter&longs;eccationi, <expan abbr="nece&longs;&longs;ariam&etilde;te">nece&longs;&longs;ariamente</expan> &longs;e daria i brocca.<emph.end type="italics"/></s> </p> <figure id="id.042.01.030.1.jpg" xlink:href="042/01/030/1.jpg"/> <p type="main"> <s id="s.000367">PRIORE. Q<emph type="italics"/>ue&longs;ta Speculatione molto mi piace, & è molto bella, ma non ho trop­<lb/>po ben inte&longs;a questa ultima particularita che mi haueti detta, cioe che in dui &longs;egni po&longs;ti <lb/>in dui diuer&longs;i luoghi, ui &longs;i po&longs;&longs;a tirar, & dar de mira, e pero datime un'e&longs;&longs;empio &longs;e po&longs; <lb/>&longs;i<gap/>il è in figura, perche à mi me pare che tal co&longs;a non &longs;ia poßibile.<emph.end type="italics"/> N. S<emph type="italics"/>ia e&longs;&longs;em pi <lb/>gratia la &longs;otto&longs;critta artegliaria con le due mire. </s> <s id="s.000368">c. <!-- REMOVE S-->&. </s> <s id="s.000369">d. <!-- KEEP S--></s> <s id="s.000370">&longs;econdo il propo&longs;ito, cioe <lb/>che la mira. </s> <s id="s.000371">d. <!-- KEEP S--></s> <s id="s.000372">&longs;ia talmente piu ba&longs;&longs;a della mira. </s> <s id="s.000373">c. <!-- REMOVE S-->che la no&longs;tra linea ui&longs;uale &longs;eghi il <expan abbr="trã">tram</expan> <lb/>&longs;ito, ouer uiaggio qual debbe far la balla, & &longs;ia tutto il tran&longs;ito, ouer uiaggio che hab­<lb/>bia fatto, ouer che faria la balla (non trouando re&longs;istentia) di moto uiolente tutta la li­<lb/>nea. </s> <s id="s.000374">h. <!-- REMOVE S-->i.<emph.end type="italics"/> k. <emph type="italics"/>l. <!-- REMOVE S-->m. <!-- REMOVE S-->& la linea. </s> <s id="s.000375">m. <!-- REMOVE S-->n. <!-- REMOVE S-->&longs;ia parte del tran&longs;ito, ouer uiaggio che quella habbia <lb/>fatto, ouer faria de moto naturale, hor dico, che &longs;e la no&longs;tra linea ui&longs;uale (procedente <lb/>per le i&longs;tremita delle due mire. </s> <s id="s.000376">c. <!-- REMOVE S-->&. </s> <s id="s.000377">d.) Seghara il detto tran&longs;ito, ouer uiaggio. </s> <s id="s.000378">h. <!-- REMOVE S-->i.<emph.end type="italics"/> k. <emph type="italics"/>l. <lb/><!-- REMOVE S-->m. <!-- REMOVE S-->n. <!-- REMOVE S-->et quella procedendo rettamente in in infinito (per le ragion di &longs;opra aditte) eglie <lb/>nece&longs;&longs;ario che la inter&longs;eghi tal tran&longs;ito, ouer uiaggio in dui lochi, cioe uno nella parte <lb/>retta (ouer men curua.) h. <!-- REMOVE S-->i.<emph.end type="italics"/> k. <emph type="italics"/>& l'altro nella parte curua.<emph.end type="italics"/> k. <emph type="italics"/>l. <!-- REMOVE S-->m. <!-- REMOVE S-->ouer nel tran&longs;ito na <lb/>turale. </s> <s id="s.000379">m. <!-- REMOVE S-->n. <!-- REMOVE S-->hor &longs;upponamo che nella parte retta. </s> <s id="s.000380">h. <!-- REMOVE S-->i.<emph.end type="italics"/> k. <emph type="italics"/>la la &longs;eghi in ponto. </s> <s id="s.000381">i. <!-- REMOVE S-->& nella <lb/>curua in ponto, l. (come nella figura appare) conchiudo adunque che &longs;e il &longs;egno tolto de<emph.end type="italics"/><pb pagenum="16" xlink:href="042/01/031.jpg"/><emph type="italics"/>mira, &longs;ara in qual &longs;i uoglia delle dette due inter&longs;eccationi, cioe in ponto. </s> <s id="s.000382">i. <!-- REMOVE S-->ouer in pon <lb/>to. </s> <s id="s.000383">l. <!-- KEEP S--></s> <s id="s.000384">nece&longs;&longs;ariamente la balla dara preci&longs;amente in brocca, & quando che il detto &longs;egno <lb/>&longs;ara piu in fuora della prima inter&longs;eccatione, cioe dal ponto. </s> <s id="s.000385">i. <!-- REMOVE S-->per fin al ponto.<emph.end type="italics"/> k. <emph type="italics"/>tan­<lb/>to piu alta &longs;ara la detta botta, ma quanto piu oltra al detto ponto.<emph.end type="italics"/> k. <emph type="italics"/>per fin al ponto. </s> <s id="s.000386">l. <lb/><!-- KEEP S--></s> <s id="s.000387">&longs;ara il detto &longs;egno tanto men alta &longs;ara la detta botta, ma quando che il detto &longs;egno fu&longs;&longs;e <lb/>per alquanto oltra al ponto. </s> <s id="s.000388">l. <!-- KEEP S--></s> <s id="s.000389">tal botta nece&longs;&longs;ariamente dara di &longs;otto dal &longs;egno, & <expan abbr="quã">quam</expan> <lb/>do tal &longs;egno &longs;ara molto oltra al ponto. </s> <s id="s.000390">l. <!-- KEEP S--></s> <s id="s.000391">la detta balla non potra arriuare al &longs;egno, co­<lb/>me (per ragion naturale) credo, che quella po&longs;&longs;a facilmente comprendere.<emph.end type="italics"/> P. C<emph type="italics"/>om­<lb/>prendo che eglie troppo il uero. </s> <s id="s.000392">Et <expan abbr="certam&etilde;te">certamente</expan> questa è &longs;tata una bella Speculatione, e pe <lb/>ro non uoglio che piu ue affaticati per que&longs;ta &longs;era, diman de &longs;era direti poi il restante.<emph.end type="italics"/></s> </p> <figure id="id.042.01.031.1.jpg" xlink:href="042/01/031/1.jpg"/> <p type="head"> <s id="s.000393">QVESITO OTTAVO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> S. P<emph type="italics"/>rior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000394">PRIORE. H<emph type="italics"/>or &longs;eguitamo la materia de hier&longs;era.<emph.end type="italics"/> N. H<emph type="italics"/>ier&longs;era (&longs;e ben mi ari <lb/>cordo) fu detto tutti gli effetti, ouer botte che puo occorrere, quando che per la <lb/>molta cortezza, ouer ba&longs;&longs;ezza della mira denanti ri&longs;petto à quella de drio, la nostra <lb/>linea ui&longs;uale &longs;eghera il tran&longs;ito, ouer uiaggio qual debbe far la balla. </s> <s id="s.000395">Et que&longs;ta &longs;era uo­<lb/>glio dichiarire tutti gli effetti, ouer botte, che puo occorrere, quando che la detta mi­<lb/>ra de nanti non è talmente piu corta, ouer ba&longs;&longs;a della mira de drio, quanto ui &longs;i conue­<lb/>gneria, per la qual cau&longs;a, la no&longs;tra linea ui&longs;uale non procede tanto al ba&longs;&longs;o che &longs;i po&longs;&longs;a <lb/>congiongere con il tran&longs;ito, ouer uiaggio qual debbe far la balla, e pero in &longs;imil ca&longs;o, <lb/>&longs;empre la balla dara di &longs;otto dal &longs;egno, perche per tutto tal luoco, ouer &longs;pacio, il tran­<lb/>&longs;ito della balla pa&longs;&longs;a di &longs;otto della no&longs;tra linea ui&longs;uale, uero è, che ui è un certo luoco, nel <lb/>quale la no&longs;tra linea ui&longs;uale piu &longs;e appropinqua al detto tran&longs;ito della balla che in ogni <lb/>altro luoco, e per tanto, &longs;e per ca&longs;o il &longs;egno doue &longs;e tira de mira &longs;ara nel detto luoco, a <lb/>ben che la balla dara di &longs;otto da quello pur ui dara piu propinquo che in ogni altro luo <lb/>co e&longs;&longs;empi gratia &longs;ia per figura lo &longs;otto&longs;critto pezzo di artegliaria: le due mire delqua <lb/>le fiamo. </s> <s id="s.000396">c. <!-- REMOVE S-->&. </s> <s id="s.000397">d. <!-- KEEP S--></s> <s id="s.000398">& &longs;ia il tran&longs;ito della balla la linea. </s> <s id="s.000399">h. <!-- REMOVE S-->i.<emph.end type="italics"/> k. <emph type="italics"/>& &longs;ia pur la mira denanti, <lb/>cioe la. </s> <s id="s.000400">d. <!-- KEEP S--></s> <s id="s.000401">alquanto piu corta, ouer piu ba&longs;&longs;a della. </s> <s id="s.000402">c. <!-- REMOVE S-->ma in tanta poca quantita che la li­<lb/>nea ui&longs;uale che <expan abbr="trã&longs;tra">tran&longs;tra</expan> p le i&longs;tremita di quelle (quala &longs;ia la linea. </s> <s id="s.000403">c. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.000404">m. <!-- REMOVE S-->l.) non tocchi lo <lb/>detto <expan abbr="trã&longs;ito">tran&longs;ito</expan>. </s> <s id="s.000405">h. <!-- REMOVE S-->i.<emph.end type="italics"/> k. <emph type="italics"/>et &longs;ia il <expan abbr="põto">ponto</expan>. </s> <s id="s.000406">m. <!-- REMOVE S-->il luoco di tal linea piu propinquo al detto <expan abbr="trã&longs;ito">tran&longs;ito</expan> di <pb xlink:href="042/01/032.jpg"/>qualunque altro, hor dico, che &longs;e per ca&longs;o il &longs;egno che &longs;e tuol de mira &longs;ara in ponto. </s> <s id="s.000407">m. <lb/><!-- REMOVE S-->la balla dara pur di &longs;otto dal &longs;egno, cioe daria in ponto. </s> <s id="s.000408">n. <!-- REMOVE S-->ma pur ui dara piu propin­<lb/>quo che in qualunque altro luoco, perche &longs;e tal &longs;egno fu&longs;&longs;e piu de la dal ponto. </s> <s id="s.000409">m. (come <lb/>&longs;aria a dire in ponto. </s> <s id="s.000410">l.) ouer di qua (come &longs;aria a dire in ponto. </s> <s id="s.000411">o.) &longs;empre dara piu <lb/>ba&longs;&longs;o, uero è che eglie &longs;uggetto a maggior errore di la, che di qua dal detto ponto. </s> <s id="s.000412">m. <lb/>(come dì &longs;otto nella figura appare.)<emph.end type="italics"/> P. N<emph type="italics"/>on piu che ue ho inte&longs;o benißimo, circa a <lb/>que&longs;ta parte.<emph.end type="italics"/></s> </p> <figure id="id.042.01.032.1.jpg" xlink:href="042/01/032/1.jpg"/> <p type="head"> <s id="s.000413">QVESITO NONO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> S. P<emph type="italics"/>rior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000414">PRIORE. H<emph type="italics"/>or &longs;eguitati la ultima parte di que&longs;ta propo&longs;ta materia, cioe <expan abbr="quã">quam</expan> <lb/>do che la mira dauanti hauera la &longs;ua conueniente cortezza, ouer ba&longs;&longs;ezza ri­<lb/>&longs;petto a quella de drio.<emph.end type="italics"/> N. Q<emph type="italics"/>uando che la mira dauanti &longs;ara talmente piu &longs;car&longs;etta, <lb/>ouer piu ba&longs;&longs;a di quella de drio, che la no&longs;tra linea ui&longs;uale che tran&longs;ira per le i&longs;tremita <lb/>delle ponte di quelle, nel tuor la mira delle co&longs;e, uada &longs;olamente a toccare, e non &longs;egare <lb/>il tran&longs;ito, ouer uiaggio qual debbe far la balla (come nella &longs;otto&longs;critta figura appare <lb/>in ponto. </s> <s id="s.000415">m.) & tutta la di&longs;tantia che &longs;ara dalla bocca de tal pezzo al ponto de tal toc <lb/>camento che nella &longs;otto&longs;critta figura &longs;aria la linea. </s> <s id="s.000416">h. <!-- REMOVE S-->m. <!-- REMOVE S-->tanto &longs;e potra dire con ragio­<lb/>ne, che tal pezzo tiri de mira, perche &longs;e per ca&longs;o il &longs;egno che &longs;e tuol de mira &longs;e trouara <lb/>à e&longs;&longs;ere nel ponto di tal toccamento, la balla dara preci&longs;amente in brocca, ma e&longs;&longs;endo <lb/>fuora di tal toccamento, cioe fuora del ponto. </s> <s id="s.000417">m. <!-- REMOVE S-->la balla &longs;empre dara alquanto di &longs;otto <lb/>di tal &longs;egno, cioe di &longs;otto dalla brocca di quello, & tanto piu quanto piu &longs;ara remoto il <lb/>detto &longs;egno dal detto ponto del toccamento. </s> <s id="s.000418">o. <!-- REMOVE S-->&longs;ia de là, ouer de quà da quello. </s> <s id="s.000419">Vero è, <lb/>che e&longs;&longs;endo de quà, cioe uer&longs;o il pezzo, tal balla non puo dar molto ba&longs;&longs;a, perche tal <lb/>ba&longs;&longs;ezzamai &longs;e puo agguagliare alla altezza della mira de drio, che puo e&longs;&longs;ere circa <lb/>allamita della gro&longs;&longs;ezza del pezzo nella culattade drio (come fu detto anchora in fi­<lb/>ne del Settimo que&longs;ito) e pero in tal ca&longs;o &longs;e è &longs;uggetto à poco errore in ri&longs;petto à quello <lb/>che potria occorrer quando che il &longs;egno fu&longs;&longs;e de la dal ponto del detto toccamento, co­<lb/>me ogni commun intelletto puo con&longs;iderare.<emph.end type="italics"/> P. P<emph type="italics"/>erche uoleti co&longs;i attribuire alla di­<lb/>&longs;tanua del &longs;opradetto ponto del toccamento che &longs;ia il tirar de mira di tal pezzo, et non <lb/>alla di&longs;tantia del ponto della inter&longs;eccatione, nel quale e&longs;&longs;endoui il &longs;egno, la balla da me <lb/>de&longs;imamente in brocca, &longs;i come fa nel ponto del toccamento, come fu dimo&longs;trato nel <lb/>Settimo que&longs;ito.<emph.end type="italics"/> N. P<emph type="italics"/>erche il ponto della inter&longs;eccatione non ha luoco determinato,<emph.end type="italics"/><pb pagenum="17" xlink:href="042/01/033.jpg"/><emph type="italics"/>ma puo occorrere in infiniti luochi, &longs;econdo li infiniti modi, che la mira dauanti puo e&longs; <lb/>&longs;er di &longs;operchio piu corta di quella de drio, ma el ponto del toccamento non puo occor <lb/>rere, &longs;aluo che in un luoco &longs;olo, el qual luoco è il piu lontano della bocca del pezzo de <lb/>qual &longs;i uoglia altro, doue concorrer po&longs;&longs;a la no&longs;tra linea ui&longs;uale con el tran&longs;ito, ouer <lb/>uiaggio qual debbe far la balla, e&longs;&longs;endo adunque el piu lontano concor&longs;o de cadauno de <lb/>li altri concor&longs;i, che &longs;e inter&longs;ecano, & el manco uariabile: per tale ragioni à mi me pa <lb/>re, che piu meritamente à quel &longs;i debbia atribuire tal dignita, che ad alcuno di ponti <lb/>delle inter&longs;ecationi.<emph.end type="italics"/> P. V<emph type="italics"/>oi hauetiragione, & que&longs;ta con le due pa&longs;&longs;ate &longs;ono state <lb/>tre belle lettioni.<emph.end type="italics"/></s> </p> <figure id="id.042.01.033.1.jpg" xlink:href="042/01/033/1.jpg"/> <p type="head"> <s id="s.000420">QVESITO DECIMO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000421">PRIORE. F<emph type="italics"/>in qua me haueti fatto chiaro, donde procede la cau&longs;a, <expan abbr="quãdo">quando</expan> che <lb/>uno tirando de mira à uno &longs;egno alle uolte da in brocca, alle uolte di &longs;opra, et alle <lb/>uolte di &longs;otto del detto &longs;egno, hor uoria &longs;apere da che procede, che alcune uolte da mol <lb/>to costero dal detto &longs;egno tolto de mira.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to puo procedere per due cau&longs;e, l'u­<lb/>na è per le mire, le quale alle uolte l'una, ouer ambe due non &longs;ara preci&longs;amente nella <lb/>mezzara del pezzo, cioè nel mezzo della parte &longs;uperiore del pezzo, per il che tal <lb/>pezzo èsforzato à percuottere co&longs;tero, perche &longs;e la mira de drio &longs;ara fora del detto <lb/>ponto di mezzo: poniamo uer&longs;o la no&longs;tra man de&longs;tra, etiam el detto pezzo dara co&longs;te <lb/>ro alla mede&longs;ima banda de&longs;tra del &longs;egno, che &longs;e tol de mira, & &longs;e la detta mira de drio <lb/>&longs;ara fora del ponto di me<emph.end type="italics"/>zz<emph type="italics"/>o, & uer&longs;o la man &longs;ini&longs;tra, etiam el detto pe<emph.end type="italics"/>zz<emph type="italics"/>o percuote <lb/>ra co&longs;tero, & uer&longs;o la mede&longs;ima parte &longs;ini&longs;tra.<emph.end type="italics"/> P. <!-- KEEP S--></s> <s id="s.000422">A <emph type="italics"/>me pare, che doueria e&longs;&longs;er al <lb/>contrario di quello che haueti detto, cioè che &longs;e la mira de drio &longs;ia fora del ponto di <lb/>me<emph.end type="italics"/>zz<emph type="italics"/>o, & uer&longs;o la banda destra, che il detto pe<emph.end type="italics"/>zz<emph type="italics"/>o ueria tirar costero uer&longs;o la ban­<lb/>da &longs;ini&longs;tra.<emph.end type="italics"/> N. N<emph type="italics"/>on Signore, anci eglie, come hauemo detto, & accioche quella <lb/>per ragione ne &longs;ia certa, poniamo eßempi gratia, lo &longs;otto &longs;critto pe<emph.end type="italics"/>zz<emph type="italics"/>o, che la mira de <lb/>drio. </s> <s id="s.000423">c. <!-- REMOVE S-->&longs;ia alquanto fora del ponto di me<emph.end type="italics"/>zz<emph type="italics"/>o, & uer&longs;o man de&longs;tra, & che la mira. </s> <s id="s.000424">d. <lb/><!-- KEEP S--></s> <s id="s.000425">dauanti &longs;ia iu&longs;tamente nel ponto de me<emph.end type="italics"/>zz<emph type="italics"/>o, & il &longs;egno incontrato, ouer tolto de mira <lb/>con le dette due mire, poniamo &longs;ia el ponto. </s> <s id="s.000426">e. <!-- REMOVE S-->el qual ponto. </s> <s id="s.000427">e. <!-- REMOVE S-->eglie nece&longs;&longs;ario, che &longs;ia <lb/>di&longs;crepante, ouer di&longs;co&longs;to dal uiaggio, che debbe far la balla, & uer&longs;o la banda &longs;ini­<lb/>stra, come di &longs;otto in figura appare, &longs;upponendo che la linea f. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;ia el uiaggio, che de <lb/>ue far la balla. </s> <s id="s.000428">E&longs;&longs;endo adunque el&longs;egno. </s> <s id="s.000429">e. <!-- REMOVE S-->di&longs;co&longs;to à <expan abbr="bãda">banda</expan> &longs;inistra del uiaggio, che de-<emph.end type="italics"/><pb xlink:href="042/01/034.jpg"/><emph type="italics"/>ue far la balla, &longs;eguita chel uiaggio che deue far la detta balla paßi di&longs;co&longs;to dal detto <lb/>&longs;egno, & uer&longs;o la banda destra di quello, come nello &longs;otto &longs;critto e&longs;&longs;empio &longs;i puo uede <lb/>re, & molto piu &longs;eguiria tal effetto &longs;e la mira. </s> <s id="s.000430">d. <!-- KEEP S--></s> <s id="s.000431">dauanti fu&longs;&longs;e anchora lei fuora del det <lb/>to ponto di mezzo, ma uer&longs;o l'altra banda, cioe uer&longs;o la banda &longs;inistra.<emph.end type="italics"/></s> </p> <figure id="id.042.01.034.1.jpg" xlink:href="042/01/034/1.jpg"/> <p type="main"> <s id="s.000432">LA<emph type="italics"/>&longs;econda cau&longs;a, che puo cau&longs;ar tal effetto, ouer inconueniente puo procedere <lb/>del uacuo della canna, el quale molte uolte non è triuellato, ouer gettato dretta­<lb/>mente nel me<emph.end type="italics"/>zz<emph type="italics"/>o del mettallo, cioe, che tal foro non è perfettamente nel mezzo del <lb/>mettallo, anci da una banda ui è piu &longs;ottile, ouer piu gro&longs;&longs;o, che non è dall'altra, talmen <lb/>te, che &longs;e ben le due mire fu&longs;&longs;eno collocate, & a&longs;&longs;ettate perfettamente nelli ponti di <lb/>me<emph.end type="italics"/>zz<emph type="italics"/>o di la parte &longs;uperiore del mettallo, tal pe<emph.end type="italics"/>zz<emph type="italics"/>o nece&longs;&longs;ariamente tirara co&longs;tero, <lb/>perche &longs;e ben le mire &longs;ono nelli ponti del me<emph.end type="italics"/>zz<emph type="italics"/>o del &longs;uperior mettallo non &longs;ono &longs;opra <lb/>la me<emph.end type="italics"/>zz<emph type="italics"/>ara del foro, & per que&longs;ta cau&longs;a da co&longs;tero, onde per remediar à tal inconue <lb/>niente, eglie nece&longs;&longs;ario <expan abbr="cõ">com</expan> indu&longs;tria ritrouare doue batte la mezzara del foro &longs;i de drio <lb/>come dauanti, & iui a&longs;&longs;ettaruile mire: & leuaraßi tal inconueniente al detto pezzo, <lb/>per trouar la me<emph.end type="italics"/>zz<emph type="italics"/>aria del detto foro, li bombardieri co&longs;tumano à retrouarla (per <lb/>quanto ho inte&longs;o da alcuni) con due li&longs;te, ouer cantinelle egualmente larghe, & rettißi <lb/>me, & una ne cazano nel pezzo rettamente per ilfondo della canna, & l'altra di fo­<lb/>ra &longs;opra il pe<emph.end type="italics"/>zz<emph type="italics"/>o, & incontrano una parte di quella di &longs;opra el pezzo <expan abbr="cõ">com</expan> quella par <lb/>te, che auanza fora della bocca del pezzo di quella, che ua per dentro el pe<emph.end type="italics"/>zz<emph type="italics"/>o, & <lb/>co&longs;i doue batte el mezzo di quella di fora&longs;opra il pezzo &longs;i de drio, come dauanti ui <lb/>pongono l'una, & l'altra mira, el qual modo per e&longs;&longs;er a&longs;&longs;ai &longs;pediente, & di poco artifi <lb/>cio, non è da bia&longs;mare, quantunque per altre uie &longs;e potriano inue&longs;tigare.<emph.end type="italics"/> P. N<emph type="italics"/>on &longs;e <lb/>potria truouare el mo do di agiu&longs;tar le dette mire &longs;enza altra indu&longs;tria de dette li&longs;te, <lb/>ma&longs;olamente nel tirar continuamente el pezzo.<emph.end type="italics"/> N. S<emph type="italics"/>e potria &longs;i, cioe &longs;el pezzo de&longs; <lb/>&longs;e co&longs;tero, poniamo uer&longs;o la banda de&longs;tra del &longs;egno, &longs;pingendo la mira de drio alquan­<lb/>to uer&longs;o la parte &longs;ini&longs;tra, & &longs;e per ca&longs;o lui percote&longs;&longs;e co&longs;tero uer&longs;o la banda &longs;inistra <lb/>del &longs;egno, &longs;pingere alquanto la detta mira de drio uer&longs;o la banda de&longs;tra, & co&longs;i andar <lb/><expan abbr="fac&etilde;do">facendo</expan>, tanto che &longs;e ritroui il perfetto luoco di tal mira, & ritrouato che &longs;ia far in tal <lb/>luoco un &longs;egno &longs;tabile (&longs;e tal mira fu&longs;&longs;e co&longs;a mobile) accioche un'altra uolta non &longs;i hab <lb/>bia cau&longs;a à ricercar tal luoco.<emph.end type="italics"/> P. V<emph type="italics"/>e ho inte&longs;o benißimo, & basta per que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000433">QVESITO VNDECIMO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000434">PRIORE. P<emph type="italics"/>erche cau&longs;a uno pezzo di artegliaria quanto è piu <expan abbr="lõgo">longo</expan> di <expan abbr="cãna">canna</expan>,<emph.end type="italics"/><pb pagenum="18" xlink:href="042/01/035.jpg"/><emph type="italics"/>tanto piu tira lontano.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;ta uo&longs;tra propo&longs;itione non è generale, cioe che <expan abbr="quã">quam</expan> <lb/>to piu è longo di canna un pezzo tanto piu tiri lontano. </s> <s id="s.000435">Anci è da credere, & da te­<lb/>ner per fermo, che ogni &longs;pecie di pezzo, ui &longs;ia una &longs;ua certa, & determinata longhez <lb/>za, co&longs;i debitamente proportionata alla poluere, & balla che porta quello tal pezzo, <lb/>la quale ogni uolta che &longs;ia preterita (in qual modo &longs;i uoglia) tal pezzo &longs;empre deb­<lb/>bia tirar manco, e per tanto dico, che pote&longs;&longs;e hauer perfetta cognitione di que&longs;ta &longs;ua <lb/>proportionata longhezza in ogni &longs;pecie di pe<emph.end type="italics"/>zz<emph type="italics"/>o non accaderia à fare pezzi <expan abbr="lõghi">longhi</expan>, <lb/>& pezzi corti di canna (&longs;aluo per neceßità) perche ogni uolta che una &longs;pecie di pez­<lb/>zo fu&longs;&longs;e fatto piu <expan abbr="lõgo">longo</expan> di quella &longs;ua proportionata <expan abbr="lõghe">longhe</expan><emph.end type="italics"/>zz<emph type="italics"/>a, ouer piu corto tal pez <lb/>zo &longs;empre tirariamanco (dico con una mede&longs;ima quantita di poluere.<emph.end type="italics"/> P. C<emph type="italics"/>redo che <lb/>uoi diciati el uero, perche uedo che à tutte le &longs;pecie de canoni, & altri pezzi corti, per <lb/>tirarli ordinariamente ui danno di poluere li dui terzi di quello, che pe&longs;a la balla. </s> <s id="s.000436">Ma <lb/>à tutte le &longs;pecie di colobrine, per e&longs;&longs;er pezzi piu longhi di canna à cadauna ordinaria <lb/>mente per tirarla ui danno li quatro quinti di quello pe&longs;a la balla, & tutto questo cre­<lb/>do chel facciano, perche daendoli &longs;olamente li dui terzi, come &longs;i co&longs;tuma dar alli cano­<lb/>ni for&longs;i che la non tiraria tanto, come fanno li canoni.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to è una co&longs;a certa­<lb/>mente, che io non &longs;apeua, & e&longs;&longs;endo co&longs;i ho molto à caro hauerla inte&longs;a.<emph.end type="italics"/> P. A<emph type="italics"/>nci <lb/>que&longs;ta è una co&longs;a, che è notißima ad ogni minimo bombardiero.<emph.end type="italics"/> N. C<emph type="italics"/>redo, che e&longs;&longs;en <lb/>do co&longs;i ui debbia e&longs;&longs;er nota à cadauno di loro. </s> <s id="s.000437">Ma io non &longs;o che materia &longs;ia que&longs;ta, & <lb/>molto mi marauiglio di Principi, che fanno gettar tai pezzi con uno difetto tanto eui <lb/>dente per uoler poi medicar quel tal effetto con &longs;uo gran <expan abbr="di&longs;cõmodo">di&longs;commodo</expan>, & &longs;pe&longs;a.<emph.end type="italics"/> P. M<emph type="italics"/>a <lb/>&longs;e ben que&longs;te colobrine ui&longs;i da piu poluere di quello, che &longs;e fa alli canoni, tirano poi an <lb/>chora piu di quello fanno li canoni.<emph.end type="italics"/> N. N<emph type="italics"/>e ha mai fatto far i&longs;perientia uo&longs;tra Signo­<lb/>ria di que&longs;to.<emph.end type="italics"/> P. I<emph type="italics"/>o non ho mai fatto far que&longs;ta &longs;perientia, nondimeno io ho per fer­<lb/>mo, che &longs;ia co&longs;i, perche etiam tutti li <expan abbr="bõbardieri">bombardieri</expan> <expan abbr="hãno">hanno</expan> <expan abbr="uniuer&longs;alm&etilde;te">uniuer&longs;almente</expan> que&longs;ta opinione, <lb/>& non puo e&longs;&longs;er altramente, perche e&longs;&longs;endo la colobrina piu <expan abbr="lõga">longa</expan> di canna del canone, <lb/>& daendoli poi anchor piu poluere di quello &longs;i fa al canone, el <expan abbr="nõ">non</expan> puo e&longs;&longs;er altramen­<lb/>te, che la non tiri a&longs;&longs;ai piu di quello che fa il canone, & la &longs;pe&longs;a <expan abbr="nõ">non</expan> è tanto grande, come <lb/>uoi la fati, perche in uno canone da libre. </s> <s id="s.000438">20. di balla ui &longs;i da ordinariamente per ti­<lb/>rarlo libre. </s> <s id="s.000439">13. onze. </s> <s id="s.000440">4. di poluere, & alla colobrina pur da libre. </s> <s id="s.000441">20. di balla ui &longs;i da <lb/>ordinariamente per tirarla lire. </s> <s id="s.000442">16. di poluere, che &longs;aria &longs;olamente lire. </s> <s id="s.000443">2. onze.<emph.end type="italics"/> S. <emph type="italics"/>de <lb/>piu, &longs;i che que&longs;ta &longs;pe&longs;a de lire. </s> <s id="s.000444">2. onze. </s> <s id="s.000445">8. de poluere de piu è una mi&longs;eria.<emph.end type="italics"/> N. I<emph type="italics"/>o <expan abbr="nõ">non</expan> uo <lb/>glio affermare, che la colobrina debbia tirar piu, ouer meno del &longs;uo canone <21> <expan abbr="nõ">non</expan> e&longs;&longs;er <lb/>tal co&longs;a molto chiara, <21> <expan abbr="nõ">non</expan> hauer&longs;i perfetta notitia della &longs;ua proportionata <expan abbr="lõghezza">longhezza</expan> <lb/>(detta di &longs;opra) ma &longs;e eglie il uero, che la colobrina <expan abbr="cargãdola">cargandola</expan> &longs;olamente con tanta pol <lb/>uere, quanta &longs;i da al &longs;uo canone, la non tiritanto quanto fa el &longs;uo canone, io &longs;on certißi <lb/>mo, che à uoler che la tiri preci&longs;amente tanto, <expan abbr="quãto">quanto</expan> fa el &longs;uo canone, eglie nece&longs;&longs;ario à <lb/>porui <expan abbr="d&etilde;tro">dentro</expan> piu poluere di quello &longs;i fa al canone, & tanto piu poluere ui uora, quanto <lb/>maggior &longs;ara la <expan abbr="differ&etilde;tia">differentia</expan> di dui tiri fatti <expan abbr="cõ">com</expan> egual <expan abbr="quãtita">quantita</expan> di poluere, et <21> <expan abbr="tãto">tanto</expan> <expan abbr="cõchiu">conchiu</expan> <lb/>do chel potria e&longs;&longs;er <expan abbr="facilm&etilde;te">facilmente</expan>, che <expan abbr="tirãdo">tirando</expan> la &longs;opra detta colobrina da. </s> <s id="s.000446">20. <expan abbr="cõ">com</expan> la poluere <lb/>che <expan abbr="ordinariam&etilde;te">ordinariamente</expan> ui &longs;i da de piu del canone, che quella tal poluere <expan abbr="nõ">non</expan> &longs;ara for&longs;i <expan abbr="&longs;offi-&etilde;te">&longs;offi­<lb/>ente</expan> à farla arriuare à quel &longs;egno, che tira el canone, uero è chel potria e&longs;&longs;er anchora<emph.end type="italics"/><pb xlink:href="042/01/036.jpg"/><emph type="italics"/>che da quelli primi, che determinorono, che ui &longs;e doue&longs;&longs;e dare li detti quattro quinli di <lb/>quello, che pe&longs;a la balla, ui la proportionarono for&longs;i talmente con la i&longs;perientia, che la <lb/>tira&longs;&longs;e tanto, quanto &longs;a el &longs;uo canone, & for&longs;i piu, ma tal co&longs;a non &longs;i potria affermare, <lb/>ne negare &longs;enza qualche particolar i&longs;perientia, nondimeno &longs;ia come &longs;i uoglia &longs;e la det <lb/>ta colobrina, con la mede&longs;ima poluere, che &longs;i da al canone non tira tanto, quanto fa el <lb/>&longs;uo canone. </s> <s id="s.000447">Eglie un'error euidentißimo, & è una co&longs;a rediculo&longs;a, à dir poi di uoler re <lb/>mediare à tal errore con dire: metteremo, ouer daremo alquanto piu quantita de polue <lb/>re alla detta colobrina, accioche la tiri tanto, quanto fa detto &longs;uo canone, ouer piu di <lb/>quello, la qual poluere, che ui &longs;i da di piu, che la de&longs;&longs;e mede&longs;imamente al detto canone <lb/>for&longs;i che tiraria molto piu della detta colobrina. </s> <s id="s.000448">Circa alla &longs;pe&longs;a, che ui ua de piu, qua­<lb/>la uostra Signoria dice e&longs;&longs;er una mi&longs;eria. </s> <s id="s.000449">Dico e&longs;&longs;er molto maggiore di quello, che uo <lb/>&longs;tra Signoria &longs;i pen&longs;a: perche, &longs;e non me inganno, facendo&longs;i le dette colobrine piu lon­<lb/>ghe delli canom, la ragion uole, che &longs;i facciano anchor piu gro&longs;&longs;e di metallo. </s> <s id="s.000450">Il che e&longs;­<lb/>&longs;endo, ui intra molto piu metallo, che in uno canone, & con&longs;equentemente debbeno e&longs;­<lb/>&longs;er molto piu graue delli &longs;uoi canoni, et e&longs;&longs;endo piu graue, uogliono anchora (per con <lb/>durle) piu numero de buoui, ouer caualli, di quello uoleno li canoni, & maggior molti­<lb/>tudine de huomini, che gouerni quelli, & maggior quantita di uettouaglia &longs;i per li ani <lb/>mali, come per li huomini, che gouernan quelli oltra il <expan abbr="&longs;tip&etilde;dio">&longs;tipendio</expan>, che à quelli ui &longs;i da per <lb/>ordinario ò dal principe, ouer da quelli communi, che li manda per comandamento del <lb/>principe, &longs;i uede adunque da un picciolo errore fatto nel principio quanti ne &longs;eguita <lb/>nel fine, & &longs;e tali errori &longs;ono a&longs;&longs;ai in una colobrina da lire. </s> <s id="s.000451">20. di balla, molto piu &longs;e <lb/>trouara occorrere in quelle di. </s> <s id="s.000452">30. 40. 50. &. </s> <s id="s.000453">60. lire di balla, come ho inte&longs;o da bom <lb/>bardieri, che &longs;e co&longs;tumano.<emph.end type="italics"/> P. S<emph type="italics"/>enza dubbio, che piu metallo intra in le colobrine, <lb/>che nelli canoni, & con&longs;equentamente per condurle, ui ua piu animali, & di que&longs;to ne <lb/>azzo una notta in un mio memoriale &longs;i del mettallo che ui intra, & della &longs;ua longhez­<lb/>za di cadauna &longs;orte pezzo, come delli animali, che gliua à condurle.<emph.end type="italics"/> N. D<emph type="italics"/>i gratia <lb/>uo&longs;tra &longs;ignoria me ne dia la coppia, perche di que&longs;te particolarita ne potria for&longs;i ca­<lb/>uar con tempo qualche co&longs;trutto.<emph.end type="italics"/> P. M<emph type="italics"/>olto uolentieri, portame qua quel mio me­<lb/>moriale, che è in la mia ca&longs;&longs;a.<emph.end type="italics"/> SERVO. E<emph type="italics"/>ccolo Signore.<emph.end type="italics"/> P. H<emph type="italics"/>or &longs;criueti co&longs;i. <lb/></s> <s id="s.000454">Vn falconetto da lire tre di balla di piombo ua longo piedi cinque e meggio, & di met­<lb/>tallo ui intra com munamente lire quatrocento, & à condurlo ui uuol caualli pa­<lb/>ra uno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000455">V<emph type="italics"/>n falcon da lire. </s> <s id="s.000456">6. ua longo piedi. </s> <s id="s.000457">7. & uuol lire. </s> <s id="s.000458">890. di mettallo, & per condur­<lb/>lo caualli para.<emph.end type="italics"/> 2. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000459">A<emph type="italics"/>&longs;pidi da lire. </s> <s id="s.000460">12. de longhezza de pie. </s> <s id="s.000461">5. e meggio, uuol di mettallo lire. </s> <s id="s.000462">1300. & per <lb/>condurli caualli para.<emph.end type="italics"/> 3. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000463">S<emph type="italics"/>acri da lire. </s> <s id="s.000464">12. de longhezza de pie.<emph.end type="italics"/> S. <emph type="italics"/>uuol di mettallo lire. </s> <s id="s.000465">1400. & per condurli <lb/>caualli para.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000466">S<emph type="italics"/>acri la lire. </s> <s id="s.000467">12. de longhezza de pie. </s> <s id="s.000468">9. uuol di mettallo lire. </s> <s id="s.000469">2150. & per condurli <lb/>caualli para.<emph.end type="italics"/> 5. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000470">S<emph type="italics"/>acri da lire. </s> <s id="s.000471">10. de longhezza de pie. </s> <s id="s.000472">8. uuol di mettallo iire. </s> <s id="s.000473">1300. & per condurli <lb/>caualli para.<emph.end type="italics"/> 3. <!-- KEEP S--></s> </p> <pb pagenum="19" xlink:href="042/01/037.jpg"/> <p type="main"> <s id="s.000474">C<emph type="italics"/>olobrina da lire. </s> <s id="s.000475">16. di balla di ferro de longhezza de piedi. </s> <s id="s.000476">7. e meggio, uol di metal­<lb/>lo lire. </s> <s id="s.000477">1750. & per condur la caualli para. </s> <s id="s.000478">4. in.<emph.end type="italics"/> 5. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000479">P<emph type="italics"/>a&longs;&longs;auolante da lire. </s> <s id="s.000480">16. di longhezza piedi. </s> <s id="s.000481">12. uol di metallo lire. </s> <s id="s.000482">2740. & per con­<lb/>durlo buoui para.<emph.end type="italics"/> 5. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000483">C<emph type="italics"/>olobrina da lire. </s> <s id="s.000484">14. di longhezza piedi. </s> <s id="s.000485">8. e meggio, uol di metallo lire. </s> <s id="s.000486">2233. & <lb/>per condurla buoui para.<emph.end type="italics"/> 5. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000487">C<emph type="italics"/>olubrina da lire. </s> <s id="s.000488">20. di longhezza piedi. </s> <s id="s.000489">10. uol di metallo lire. </s> <s id="s.000490">4300. & per con­<lb/>durla buoui para.<emph.end type="italics"/> 7. </s> </p> <p type="main"> <s id="s.000491">V<emph type="italics"/>n canon da lire. </s> <s id="s.000492">20. di longhezza piedi. </s> <s id="s.000493">7. uol di metallo lire. </s> <s id="s.000494">2200. & per con­<lb/>durlo buoui para.<emph.end type="italics"/> 5. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000495">V<emph type="italics"/>n canon da lire. </s> <s id="s.000496">20. di longhezza piedi. </s> <s id="s.000497">8. uol di metallo lire. </s> <s id="s.000498">2500. & per condur­<lb/>lo buoui para. </s> <s id="s.000499">5. in. </s> <s id="s.000500">6. <lb/>Vna colobrina da lire. </s> <s id="s.000501">30. di longhezza piedi uol di metallo lire & <lb/> per condurla buoui para. </s> <s id="s.000502">8. <lb/>Vn canon da lire. </s> <s id="s.000503">30. di longhezza piedi uol di metallo lire & per <lb/> condurlo buoui para.<emph.end type="italics"/> 6. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000504">V<emph type="italics"/>na colobrina da lire. </s> <s id="s.000505">50. da piedi. </s> <s id="s.000506">10. e meggio, di <expan abbr="lõghezza">longhezza</expan> uol di metallo lire. </s> <s id="s.000507">5387. <lb/>& per condurla buoui para.<emph.end type="italics"/> 12. </s> </p> <p type="main"> <s id="s.000508">E<emph type="italics"/>t una colobrina pur da lire. </s> <s id="s.000509">50. di longhezza de piedi. </s> <s id="s.000510">12. uol di metallo lire. </s> <s id="s.000511">6600. <lb/>& per condurla buoui para.<emph.end type="italics"/> 14. </s> </p> <p type="main"> <s id="s.000512">V<emph type="italics"/>n canon da lire. </s> <s id="s.000513">50. di longhezza de piedi. </s> <s id="s.000514">8. e meggio, uol di metallo lire. </s> <s id="s.000515">4000. & <lb/>per condurlo para. </s> <s id="s.000516">9. de buoui.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000517">V<emph type="italics"/>n canon da lire. </s> <s id="s.000518">100. di longhezza de piedi. </s> <s id="s.000519">9. e meggio, uol di metallo lire. </s> <s id="s.000520">8800. <lb/>& per condurlo buoui para.<emph.end type="italics"/> 18. </s> </p> <p type="main"> <s id="s.000521">C<emph type="italics"/>anoni da lire. </s> <s id="s.000522">120. di longhezza piedi. </s> <s id="s.000523">10. uol di metallo lire. </s> <s id="s.000524">12459. & per con­<lb/>durli buoui para.<emph.end type="italics"/> 25. </s> </p> <p type="main"> <s id="s.000525">C<emph type="italics"/>olobrine da lire. </s> <s id="s.000526">120. di longhezza de piedi. </s> <s id="s.000527">15. uol di metallo lire. </s> <s id="s.000528">13000. & per <lb/>condurle buoui para.<emph.end type="italics"/> 28. </s> </p> <p type="main"> <s id="s.000529">N. V<emph type="italics"/>o&longs;tra Signorla non me ne dica piu, perche mi bastaua della mita di questi che ho <lb/>notati.<emph.end type="italics"/> P. M<emph type="italics"/>e ne resta de dirui &longs;olamente &longs;ei altri, e pero compiteli, cioe ui &longs;ono an­<lb/>chora bombarde de lire. </s> <s id="s.000530">250. di balla di pietra, di longhezza piedi. </s> <s id="s.000531">10. e meggio, che <lb/>uol di metallo lire. </s> <s id="s.000532">8900. & per condurle para. </s> <s id="s.000533">18. in. </s> <s id="s.000534">19. de buoui.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000535">A<emph type="italics"/>ltre da lire. </s> <s id="s.000536">150. longhe piedi. </s> <s id="s.000537">10. che uol di metallo lire. </s> <s id="s.000538">6146. & per condurle buo­<lb/>ui para.<emph.end type="italics"/> 12. </s> </p> <p type="main"> <s id="s.000539">A<emph type="italics"/>ltre da lire. </s> <s id="s.000540">100. longhe pur piedi. </s> <s id="s.000541">10. che uol di metallo lire. </s> <s id="s.000542">5500. & per condurle <lb/>buoui para.<emph.end type="italics"/> 11. </s> </p> <p type="main"> <s id="s.000543">A<emph type="italics"/>ltre pur da lire. </s> <s id="s.000544">100. longhe &longs;olamente piedi. </s> <s id="s.000545">8. e meggio, che uol di metallo lire. <lb/></s> <s id="s.000546">4500. & per condurle buoui para.<emph.end type="italics"/> 9. </s> </p> <p type="main"> <s id="s.000547">A<emph type="italics"/>nchora ui &longs;ono cortaldi da lire. </s> <s id="s.000548">45. longhi piedi. </s> <s id="s.000549">7. che uoleno di metallo lire. </s> <s id="s.000550">2740. <lb/>& per condurli buoui para.<emph.end type="italics"/> 5. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000551">V<emph type="italics"/>n'altra &longs;orte de cortaldi da lire. </s> <s id="s.000552">30. longhi piedi. </s> <s id="s.000553">7. e meggio, uoleno di metallo lire. <lb/></s> <s id="s.000554">1600. & per condurli buoui para. </s> <s id="s.000555">3. & co&longs;i faremo fine.<emph.end type="italics"/><pb xlink:href="042/01/038.jpg"/>N. L<emph type="italics"/>e &longs;opra annotate lire &longs;ono alla &longs;ottile, ouer alla gro&longs;&longs;a, & &longs;imilmente li piedi &longs;o­<lb/>no piedi alia mi&longs;ura di Venetia, ouer maggiore, ouer menore di quella.<emph.end type="italics"/> P. L<emph type="italics"/>e lire cre <lb/>do &longs;tano tutte alla &longs;ottile, delli piedi non uel &longs;aprei dire, ma perche que&longs;ta nota mi fu da <lb/>ta à Barletta, potria e&longs;&longs;er che fu&longs;&longs;eno piedi à mi&longs;ura di quelle bande, pur credo &longs;iano <lb/>egualt à questi.<emph.end type="italics"/> N. H<emph type="italics"/>or non importa hauer la co&longs;a tanto per &longs;ottile, ma me ba&longs;ta ha <lb/>uer inie&longs;o che in un canone da. </s> <s id="s.000556">50. longo piedi. </s> <s id="s.000557">8. e meggio, uol di metallo lire. </s> <s id="s.000558">4000. <lb/>Et le colc brine pur da. </s> <s id="s.000559">50. ui ne una &longs;orte longa piedi. </s> <s id="s.000560">12. che uol di metallo lire. </s> <s id="s.000561">6600. <lb/>che &longs;arian lire. </s> <s id="s.000562">2600. di metallo piu del canone, & questa uol para. </s> <s id="s.000563">5. de buoui di piu <lb/>di quello uol il canone, & li detti cinque para de buoui credo uorranno cinque huomini <lb/>che li gouerni, hor guardati &longs;e que&longs;to importa à longo andare, oltra la &longs;pe&longs;a della pol­<lb/>uere che uole de piu à ogni colpo che la &longs;e tira.<emph.end type="italics"/> P. L<emph type="italics"/>a importa &longs;i in una, ma molto <lb/>piu importa in molte, & certamente &longs;e fu&longs;&longs;e &longs;ano ne uorria ueder la i&longs;perientia per e&longs;­<lb/>&longs;er co&longs;a molto importante.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000564">QVESITO DVODECIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> S. P<emph type="italics"/>rior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000565">PRIORE. H<emph type="italics"/>ier&longs;era fu a&longs;&longs;ai di&longs;putato qualmente à ogni artegliaria lo e&longs;&longs;er <lb/>troppo longa di canna, & etiam lo e&longs;&longs;er troppo cortanoce alli tiri di quella, hor <lb/>uorria &longs;apere di quanta longhezza &longs;e potria con ragion naturale determinare che do­<lb/>ue&longs;&longs;e e&longs;&longs;er la &longs;ua canna, à douer e&longs;&longs;er debitamente proportionata alla &longs;ua conueniente <lb/>mi&longs;ura di poluere, & balla.<emph.end type="italics"/> N. L<emph type="italics"/>a &longs;ua longhezza uorria e&longs;&longs;er tanta che in quello <lb/>i&longs;tante che tutta la poluere compi&longs;&longs;e di e&longs;&longs;er ri&longs;olta in fuoco, in quello mede&longs;imo la bal <lb/>la &longs;e ritroui e&longs;&longs;er peruenuta preci&longs;amente nella i&longs;tremita della canna, cioe preci&longs;amente <lb/>alla bocca del pezzo, perche in tal i&longs;tante tutta la uirtu i&longs;pul&longs;iua della poluere uiene à <lb/>operare nella balla nel colmo della &longs;ua furia, ouer po&longs;&longs;anza, & dapoi che tal uirtu ha <lb/>operato nella detta balla, la detta balla non ritroua co&longs;a alcuna, che ui impedi&longs;ca, ouer <lb/>che gli interrompa il moto eccetto che l'aere, e pero debbe andar piu in tal longhezza, <lb/>che &longs;e tal canna fu&longs;&longs;e piu longa, ouer piu corta, perche &longs;e la canna fu&longs;&longs;e piu corta, la bal <lb/>la u&longs;ci&longs;&longs;e della bocca del pezzo auanti che &longs;ia compita di e&longs;&longs;er ri&longs;olta in fuoco tutta la <lb/>poluere, e pero tutta la uirtu i&longs;pul&longs;iua della poluere non uiene à operare nella balla, an <lb/>ci parte di quella re&longs;ta una, & puo accadere facilmente, che molta poluere u&longs;ci&longs;ca &longs;a­<lb/>na fuora del pezzo in&longs;ieme con la balla, cioe poluere non tocca dal fuoco. </s> <s id="s.000566">Ma quando <lb/>poi che la detta canna fu&longs;&longs;e piu longa, in quello i&longs;tante che compi&longs;&longs;e da e&longs;&longs;er ri&longs;olta in <lb/>&longs;uoco tutta la poluere, la balla in quel mede&longs;imo non &longs;i troua co&longs;i preci&longs;amente alla boc <lb/>ca del pezzo, ma alquanto piu in dentro, e per tanto la detta balla nel colmo della &longs;ua ue <lb/>locita, &longs;correndo per quella poca parte di canna che ui re&longs;taua à compire, la detta can­<lb/>na grandemente ue interrompe il &longs;uo moto, perche ogni uolta che un corpo immobile <lb/>tocchi alcun corpo che &longs;i moua &longs;empre ui interrompe il moto, & tanto piu, quanto che <lb/>maggior parte, ouer per maggior tempo ua toccando quello.<emph.end type="italics"/> P. V<emph type="italics"/>e ho inte&longs;o beni&longs;­<lb/>&longs;imo, & que&longs;te uo&longs;tre ragioni me piaceno molto, ne uoglio che procedemo in altro per <lb/>que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <pb pagenum="20" xlink:href="042/01/039.jpg"/> <p type="head"> <s id="s.000567">QVESITO DECIMOTERTIO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di <lb/>Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000568">PRIORE. H<emph type="italics"/>ier&longs;era uoi dimo&longs;tra&longs;ti con buone ragioni di quanta longhezza &longs;e <lb/>potria con ragione determinare che doue&longs;&longs;e e&longs;&longs;er la longhezza della canna d'un <lb/>pezzo di Artegliaria ad e&longs;&longs;ere debitamente proportionata alla conueniente mi&longs;ura <lb/>della poluere, & balla che &longs;i co&longs;tuma à dare à un tal pezzo, la qual mi&longs;ura conueniente <lb/>il &longs;e &longs;uppone che &longs;ia li dui terzi di quello che pe&longs;a la balla. </s> <s id="s.000569">Hor &longs;e il fu&longs;&longs;e uno pezzo <lb/>(poniamo uno canon da. </s> <s id="s.000570">20.) che per &longs;orte haue&longs;&longs;e quella &longs;ua debita & proportiona­<lb/>ta longhezza che ui &longs;i conuiene alli dui terzi poluere di quello pe&longs;a la balla, che gli de&longs; <lb/>&longs;e poi piu poluere, cioe piu delli detti dui terzi di quello che pe&longs;a la balla, ue adimando <lb/>&longs;e tal pezzo tirara piu del &longs;olito.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio che lui tirara alquanto piu del&longs;o <lb/>lito.<emph.end type="italics"/> P. Q<emph type="italics"/>uesto &longs;aria contra alle ragioni da uoi hier&longs;era adutte, perche in que&longs;to ca&longs;o <lb/>la balla &longs;ara u&longs;cita della bocca del pezzo auanti che tutta la detta poluere &longs;ia compita di <lb/>ri&longs;oluer&longs;i in fuoco, e pero quella parte de uigore, che &longs;ara cau&longs;ato da quella tal parte de <lb/>poluere di piu, dapoi che &longs;ara u&longs;cita la balla della bocca del pezzo &longs;ara fru&longs;ta è uana, <lb/>e pero tal pezzo non doueria tirar piu, per tal poluer dataui de piu (re&longs;tando il uigor <lb/>di quella in tutto uano è fru&longs;to) anci doueria tirare &longs;olamente &longs;econdo il &longs;olito.<emph.end type="italics"/> N. <lb/>Q<emph type="italics"/>uel uigore uento&longs;o, che generara quella parte di poluer dataui de piu (dapoi che la <lb/>balla &longs;ara u&longs;cita dalla bocca del pezzo) à benche lui non potra operare nella detta balla <lb/>mentre che quella &longs;ara dentro della canna del pezzo, il non re&longs;tara pero da operare <lb/>in quella, dapoi che &longs;ara u&longs;cita dalla bocca del pezzo, cioe in aere, perche tutto quel <lb/>uento che uien cau&longs;ato dalla poluere nella detta canna &longs;empre &longs;eguita per alquanto uni­<lb/>tamente la balla, anchor che la balla &longs;ia u&longs;cita per alquanto fuora della bocca del pez­<lb/>zo, e pero ui augumenta alquanto il moto, uero è che tal uigor uento&longs;o non operara <lb/>tanto nel &longs;pingere la detta balla (per trouarla co&longs;i fuora della detta canna) come faria <lb/>&longs;e la troua&longs;&longs;e dentro nella canna, cioe che tal &longs;uo operare non &longs;ara proportionale à <lb/>quella quantita di poluere po&longs;taui di piu, anei &longs;ara molto lontano di tal proportione.<emph.end type="italics"/><lb/>P. I<emph type="italics"/>o non intendo que&longs;to operar poportionale.<emph.end type="italics"/> N. O<emph type="italics"/>perar proportionale &longs;e in­<lb/>tende in que&longs;to modo, poniamo e&longs;&longs;empi gratia che que&longs;to no&longs;tro canon da lire uenti, ti­<lb/>randolo à una data elleuatione con li dui terzi poluere di quello pe&longs;a la balla, tiri pa&longs;&longs;a <lb/>1000. tirandolo poi con tanta poluere quanto pe&longs;a la balla, la qual poluere ueneria à <lb/>e&longs;&longs;ere un tanto è meggio di quello era prima (cioe dalli dui terzi) hor dico, che &longs;e que­<lb/>&longs;ta poluere che ui fu&longs;&longs;e aggionta de piu opera&longs;&longs;e proportionalmente nella balla, tal <lb/>pezzo doueria lirare alla mede&longs;ima elleuatione preci&longs;amente pa&longs;&longs;a. </s> <s id="s.000571">1500. cioe un tan <lb/>to è meggio di quello fece con li dui terzi poluere. </s> <s id="s.000572">Et io dico, che il pezzo in &longs;imil ca­<lb/>&longs;o non &longs;olamente il non tiraria li detti pa&longs;&longs;a. </s> <s id="s.000573">500. de piu, ma for&longs;i che il non tiraria <lb/>manco la mita di piu, cioe pa&longs;&longs;a. </s> <s id="s.000574">250. Ma &longs;upponemo che lui tira&longs;&longs;e li detti pa&longs;&longs;a. <lb/></s> <s id="s.000575">250. de piu (che in &longs;umma &longs;aria pa&longs;&longs;a. </s> <s id="s.000576">1250.) Anchora dico, che tira&longs;&longs;e il me­<lb/>de&longs;imo canone con uno altro terzo di poluere de piu, cioe con tanta poluere quan­<lb/>to pe&longs;a la balla, & un terzo piu, che &longs;aria quattro terzi que&longs;to &longs;econdo terzo non <pb xlink:href="042/01/040.jpg"/>accre&longs;ceria il detto tiro tanto quanto fece il primo terzo, cioe chel non accre&longs;cera quel <lb/>li pa&longs;&longs;a. </s> <s id="s.000577">250. che fu &longs;uppo&longs;to che face&longs;&longs;e il primo terzo, ma cre&longs;ceria molto manco de <lb/>dettipa&longs;&longs;a. </s> <s id="s.000578">250. & &longs;imilmente, che ui aggionge&longs;&longs;e anchora un'altro terzo di poluere di <lb/>piu que&longs;t'altro terzo accre&longs;ceria pur il tiro, ma molto manco di quello hauera fatto lo <lb/>&longs;econdo terzo, che fu aggionto, &longs;i che ogni accre&longs;cimento di poluere andaria per fina à <lb/>un certo termine &longs;empre accre&longs;cendo alquanto il tiro, ma tal cre&longs;cere andaria &longs;empre <lb/>&longs;minuendo del &longs;uo anciano per fina al detto termine, ma da quello termine in &longs;u&longs;o che ui <lb/>aggionge&longs;&longs;e piu poluere non faria accre&longs;cere piuil detto tiro, anci potria e&longs;&longs;er tanto lo <lb/>accre&longs;cimento della poluere che non &longs;olamente la non faria cre&longs;cere, ma faria calare a&longs; <lb/>&longs;ai il detto tiro.<emph.end type="italics"/> P. V<emph type="italics"/>oi diceti una co&longs;a, che non mi con&longs;ona molto, cioe à dire che ui &longs;e <lb/>potria aggiongere, ouer accre&longs;cerui tanta poluere oltra à un certo termine, che non &longs;o <lb/>lamente la non faria accre&longs;cere il tiro à tal pe<emph.end type="italics"/>zz<emph type="italics"/>o, ma che lo faria callare, la qual co&longs;a <lb/>me pare molto fuora diragione.<emph.end type="italics"/> N. A<emph type="italics"/>nci è ragioneuole per commun prouerbio: qual <lb/>dice, che ogni &longs;uperchio rompe il coperchio, & per chiarire ben que&longs;to dubbio bi&longs;o­<lb/>gna uenir alli e&longs;tremi. </s> <s id="s.000579">Et per tanto dico, che chicarga&longs;&longs;e que&longs;to tal pe<emph.end type="italics"/>zz<emph type="italics"/>o con tanta <lb/>poluere quanto puo tener la canna, la&longs;&longs;andoui &longs;olamente nella i&longs;tremita di detta canna <lb/>tanto diuacuo quanto è il diametro della balla, cioe tanto che ui &longs;t pote&longs;&longs;e mettere la bal <lb/>la à pena, & tir arlo poi in tal modo cargato, adimando à uo&longs;tra Signoria, &longs;e quella cre <lb/>de, che quello tiraria piu, ouer meno di quello faria à cargarlo &longs;econdo l'ordinario, cioe <lb/>con dui terzi poluere di quello pe&longs;a la balla.<emph.end type="italics"/> P. I<emph type="italics"/>o credo che chi il tira&longs;&longs;e in tal modo <lb/>cargato che tal pezzo crepparia, & che uer amente il &longs;uperchio di detta poluere, rom <lb/>peria il coperchio (come dice il uo&longs;tro prouerbio) cioe che romperia il detto pezzo.<emph.end type="italics"/><lb/>N. N<emph type="italics"/>on uoglio &longs;tare à di&longs;putare che in un tal ca&longs;o, tal pezzo doue&longs;&longs;e ragioneuolmen <lb/>te creppare, ouer non creppare, perche longa &longs;aria tal di&longs;putta, ma &longs;uppo&ngrave;iamo pur, <lb/>che tal pezzo non creppa&longs;&longs;e.<emph.end type="italics"/> P. I<emph type="italics"/>n que&longs;to ca&longs;o che gli pone&longs;&longs;e una balla che ui entra&longs; <lb/>&longs;e talmente &longs;tretta, che fu&longs;&longs;e nece&longs;&longs;ario à farla entrar per forza di ma<emph.end type="italics"/>zz<emph type="italics"/>ate. </s> <s id="s.000580">Io ten­<lb/>go per fermo che tiraria molto lontano.<emph.end type="italics"/> N. I<emph type="italics"/>n tutte le co&longs;e che &longs;ono &longs;tate dette, et che <lb/>&longs;e hanno da dire, circa alle co&longs;e di tiri delle artegliarie, &longs;empre &longs;e &longs;uppone (non &longs;pecifi­<lb/>cando altro) che le balle &longs;iano, eguale &longs;i in grandezza, come di pe&longs;o, etiam che &longs;iano <lb/>egualmente rotonde, perche cia&longs;cuno di questi accidenti fanno uarìar li tiri.<emph.end type="italics"/> E <emph type="italics"/>per tan­<lb/>to in que&longs;to no&longs;tro ca&longs;o dico, che &longs;e debbe intendere, che la balla che &longs;e ha datir are conla <lb/>canna piena di poluer &longs;ia di quella mede&longs;ima qualita di pe&longs;o, mi&longs;ura, & rotondita, che <lb/>quella che &longs;e ha da tirare &longs;econdo l'ordinario, cioe con li dui terzi poluere di quello pe <lb/>&longs;a la balla.<emph.end type="italics"/> P. P<emph type="italics"/>igliandola per il modo che uoi diceti, in effetto la co&longs;a è dubbio&longs;a.<emph.end type="italics"/> N. <lb/>N<emph type="italics"/>on ui è dubbio alcuno, anci è co&longs;a certa che tirandola conla canna piena di poluere ti <lb/>rara molto, & molto manco di quello faria con la poluere ordinaria.<emph.end type="italics"/> P. P<emph type="italics"/>erche ra­<lb/>gione.<emph.end type="italics"/> N. L<emph type="italics"/>aragion è que&longs;ta, che ognipoluere (per fina che la &longs;ia) abbru&longs;a in tem­<lb/>po, cioe che prima abbru&longs;a quella che &longs;e ritroua nel luoco doue ui &longs;e da fuoco, di quella <lb/>che è alquanto remota dal detto luoco, & quella, che è piu propinqua al detto luoco &longs;e <lb/>abbru&longs;a alquanto auanti di quella, che ui è men propinqua, ouer che ui è piu remota, <lb/>&longs;tante adunque que&longs;ta propo&longs;itione, eglie manife&longs;to che qual &longs;i uoglia parte di quella tal <lb/>poluere, che &longs;e ritroua nella canna del detto pezzo, che &longs;ia piu propinqua al foro doue<emph.end type="italics"/><pb pagenum="21" xlink:href="042/01/041.jpg"/><emph type="italics"/>&longs;e gli da el fuoco, &longs;e abbru&longs;a auanti di quella, che glie piu remota, & per e&longs;&longs;er me­<lb/>glio inte&longs;o, diuidamo con la mente tutta la longhezza della poluere, che &longs;e ritroua in <lb/>detta canna in quattro parti equali. </s> <s id="s.000581">Dico adunque, che quella quarta parte, che termi <lb/>na al bu&longs;o, doue che ui &longs;tda el fuoco, &longs;e abbru&longs;a auanti dell' altra con&longs;e quente parte, & <lb/>bru&longs;iando genera tanta gran quantita di e&longs;&longs;alation uento&longs;a, che diece luochi equali al <lb/>luoco della poluere abbru&longs;ata non &longs;ariano capaci per la detta e&longs;&longs;alatione, & per tan­<lb/>to &longs;econdo che la detta e&longs;&longs;alatione continuamente &longs;e ua cau&longs;ando, per la poluere, che <lb/>continuamente &longs;e ua abbru&longs;ando. </s> <s id="s.000582">Anchora eglie nece&longs;&longs;ario à quella tal e&longs;&longs;alatione con <lb/>tinuamente andar&longs;e acqui&longs;tando per forza luoco maggiore a&longs;&longs;ai, di quello della polue <lb/>re, da che eglie cau&longs;ata, & questo luoco la nol puol acqui&longs;tare, &longs;aluo che per due uie. <lb/></s> <s id="s.000583">La prima è &longs;pingendo per forza auanti il re&longs;tante della poluere, non abbru&longs;ata, che è <lb/>uer&longs;o la bocca del pezzo in&longs;teme con la balla, oueramente far crepare il pezzo, & <lb/>perche eglie da credere, che piu facil ui &longs;ia à &longs;pingere fuora la detta poluere in&longs;ieme <expan abbr="cõ">com</expan> <lb/>la balla, che à far creppar il pezzo, & maßime per e&longs;&longs;er la balla nella i&longs;tremita della <lb/>canna, diremo adunque, che la prima quarta parte de ditta no&longs;tra poluere, che prima <lb/>&longs;e abbru&longs;a, bru&longs;ando continuamente ua &longs;pingendo auanti l'altra poluere, che &longs;i ua tro­<lb/>uando auanti di &longs;e, & con&longs;equentemente quella &longs;penge la balla, et per e&longs;&longs;er la balla co&longs;i <lb/>propinquißima all'u&longs;cita alla prima, & minima urtata, che nel principio &longs;ente, quella <lb/>u&longs;ci&longs;&longs;e del pezzo &longs;ubito, &longs;pinta &longs;olamente dalla poluer &longs;ana (come detto) & non dalla <lb/>propria e&longs;&longs;alatione della poluere abbru&longs;ata, lo qual &longs;pengimento (per e&longs;&longs;er fatto co&longs;i <lb/>nel principio) non puo e&longs;&longs;er &longs;e non dabole nella balla, dico debole ri&longs;petto à quello che <lb/>&longs;aria, <expan abbr="quãdo">quando</expan> che quella fu&longs;&longs;e &longs;pinta dalla propria e&longs;&longs;alatione uento&longs;a, et nel colmo della <lb/>gran furia di quella<emph.end type="italics"/>: E<emph type="italics"/>t oltra di que&longs;to, la balla nell'u&longs;cire del pezzo è &longs;eguitata (per <lb/>alquanto) dalla poluere &longs;ana, la qual poluere dali à un puoco cade in terra, la qual pol <lb/>uere nel andar per aere, & poi nel cader in terra, molto interrompe el moto di quel­<lb/>la e&longs;&longs;alatione uento&longs;a, che dapoi&longs;eguita la balla, il che non poco nuoce al moto di quel­<lb/>la Si che per que&longs;te ragionital balla (in &longs;imel ca&longs;o) non andara molto da lontano: ma <lb/>che ricarga&longs;&longs;e tal pezzo con alquanto men poluer &longs;enza dubbio lui tirar aue a&longs;&longs;ai piu <lb/>di quello faria, e&longs;&longs;endo co&longs;i piena la canna, perche &longs;e in que&longs;to &longs;econdo modo ui manca&longs; <lb/>&longs;e à impire tutta la canna dui diametri di balla, cargato che &longs;ia la balla, non &longs;e ritroua­<lb/>ra co&longs;i nella istremita della bocca del pezzo, ma piu in dentro, & pero quella non u&longs;ci <lb/>ra co&longs;i della bocca del pezzo alla prima, & minima urtata dalla poluere, anci re&longs;i&longs;te­<lb/>ra per un poco piu dell'altra, nel qual tempo, molto piu poluere &longs;ara abbru&longs;ata, et con <lb/>&longs;equentemente maggior quantita de e&longs;&longs;alatione uento&longs;a &longs;ara cau&longs;ata, & tal balla da <lb/>maggior impeto, ouer furore &longs;ara urtata, & &longs;pinta, dico urtata, & &longs;pinta pur dalla <lb/>poluere, & non dalla propria e&longs;&longs;alatione uento&longs;a, &longs;i come dell'altro tiro fu detto, & co <lb/>&longs;i per tale euidente ragioni, in questo &longs;econdo tiro con men poluere, conchiudemo che <lb/>tirara piu lontano di quello, faria al primo con qua&longs;itutta la canna piena di poluere, et <lb/>&longs;imelmente, che recarga&longs;&longs;e tal pezzo anchor con men poluere, cioè poniamo con tan­<lb/>ta poluere, che ui manca&longs;&longs;e à impire tutta la canna tre diametri di balla, dico che in tal <lb/>ca&longs;o lui tiraria piu di quello faria cargandolo, &longs;econdo che di &longs;opra fu detto, cioè &longs;ola­<lb/>mente per dui diametri manco, & co&longs;i chel carga&longs;&longs;e per quattro diametri manco tira<emph.end type="italics"/><pb xlink:href="042/01/042.jpg"/><emph type="italics"/>ra piu che <expan abbr="cõ">com</expan> li tre manco, et co&longs;i con cinque manco tirara piu che con quattro <expan abbr="mãco">manco</expan>, et <lb/>co&longs;i andaria <expan abbr="proced&etilde;do">procedendo</expan> per fin à un certo termine medio fra que&longs;ti dui e&longs;tremi, el qual <lb/>termine <expan abbr="giõto">gionto</expan> che ui &longs;e fu&longs;&longs;e haueria que&longs;ta dignita in &longs;e, che chi carga&longs;&longs;e poi tal pez­<lb/>zo <expan abbr="cõ">com</expan> <expan abbr="m&etilde;">men</expan> poluere lui tir araue <expan abbr="mãco">manco</expan>, et <expan abbr="&longs;imelm&etilde;te">&longs;imelmente</expan> che ui daße piu poluere, anchora ti­<lb/>rar aue <expan abbr="mãco">manco</expan>.<emph.end type="italics"/> P. C<emph type="italics"/><expan abbr="ertam&etilde;te">ertamente</expan> questa è una bella &longs;peculatione, et molto mi piace, per­<lb/>che in uero cono&longs;co, che fra dui i&longs;tremi diuer&longs;i in proprieta eglie nece&longs;&longs;ario e&longs;&longs;erui un <lb/>per&longs;etto me<emph.end type="italics"/>zz<emph type="italics"/>o.<emph.end type="italics"/> SERVO. S<emph type="italics"/>ignor el pa&longs;&longs;a l'hora da cena.<emph.end type="italics"/> P. H<emph type="italics"/>or&longs;u chel &longs;e ceni.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000584">QVESITO DECIMO QVARTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000585">PRIORE. Q<emph type="italics"/>ual credeti &longs;ia meglio à calcar benißimo la poluere in un pe<emph.end type="italics"/>zz<emph type="italics"/>o <lb/>ouer à la&longs;&longs;arla alquanto di&longs;per&longs;a, erara.<emph.end type="italics"/> N. I<emph type="italics"/>n tutti gli i&longs;tremi contrari bi&longs;o <lb/>gna fondar&longs;e &longs;ul me<emph.end type="italics"/>zz<emph type="italics"/>o, cioè, che la non uuol e&longs;&longs;er molto calcata, ne molto di&longs;per&longs;a, <lb/>perche la poluere molto, e molto calcata fa maggior re&longs;i&longs;tentia al ingre&longs;&longs;o del fuoco, <lb/>di quello faria e&longs;&longs;endo alquanto rara, & per tanto la poluere molto, e molto calcata <lb/>pena piu tempo ad e&longs;&longs;er con&longs;umata dal fuoco, di quello faria, &longs;e quella fu&longs;&longs;e <expan abbr="alquãto">alquanto</expan> ra <lb/>ra, & quanto piu tempo pena una poluere ad e&longs;&longs;er con&longs;umata dal fuoco, tanto piu de­<lb/>boli &longs;egue li &longs;uoi effetti, & é conuer&longs;o, cioe, che quanto piu pre&longs;to uien ri&longs;olta in fuoco <lb/>tanto piu uigoro&longs;amente &longs;pinge la balla, perche la &longs;ua uirtu, ouer po&longs;&longs;anza piu unita­<lb/>mente opera. </s> <s id="s.000586">Il mede&longs;imo qua&longs;i &longs;eguita, e&longs;&longs;endo molto di&longs;per&longs;a, & rara, & maßime in <lb/>forma longa, come &longs;i uede &longs;eguir nelle &longs;ementelle, che &longs;i co&longs;tumano per uoler dar fuoco <lb/>à qualche co&longs;a &longs;tando da lontano, delle qual &longs;ementelle prima abbru&longs;a quella parte, <lb/>che &longs;e ritroua nel capo di tal &longs;ementalla doue ui &longs;i da fuoco, & &longs;ucceßiuamente ua con­<lb/>tinuando, cioè abbru&longs;ando di mano in mano, per fin chel fuoco aggionge all'altro ca­<lb/>po, & quanto piu è longa tal &longs;ementella, tanto piu tempo pena tal poluere ad e&longs;&longs;er to <lb/>talmente con&longs;umata dal fuoco. </s> <s id="s.000587">Il mede&longs;imo uoglio inferire delle artegliarie, che quan­<lb/>to piu &longs;e la&longs;&longs;a la poluere di&longs;per&longs;a, & rara quella occupa piu della canna, cioè tal for­<lb/>ma di poluere uien à e&longs;&longs;er piu longa, e pero piu tempo ui uuol ad e&longs;&longs;er totalmente con­<lb/>&longs;umata dal fuoco, e per tanto li &longs;uoi effetti non &longs;aranno co&longs;i uigoro&longs;i. </s> <s id="s.000588">Conclude&longs;i adun <lb/>que, che la poluere molto e molto calcata nel pezzo, ouer molto di&longs;per&longs;a e rara inde­<lb/>bili&longs;&longs;e gli effetti di tel pezzo, e pero bi&longs;ogna fondar&longs;e nel termine di mezzo (come di <lb/>&longs;opra e detto) & non nelli i&longs;tremi, cioe, che quella &longs;ia non molto colcata, ne molto ra­<lb/>ra.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;ta uostra openione molto mi con&longs;ona.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000589">QVESITO DECIMO QVINTO FATTO DAL <lb/><emph type="italics"/>detto Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000590">PRIORE. Q<emph type="italics"/>ual è la cau&longs;a che con un &longs;chioppo &longs;e tira piu rettamente, & piu <lb/>lontano de mira, che non &longs;e fa con uno archibu&longs;o, et <expan abbr="tam&etilde;">tamen</expan> lo archibu&longs;o fara mag <lb/>gior effetto, ouer pa&longs;&longs;ata m un commun tramite del &longs;ehioppo.<emph.end type="italics"/> N. Q<emph type="italics"/>uesto procede, <lb/>che le balle delli ar chibu&longs;i debbono e&longs;&longs;er for&longs;i piu gro&longs;&longs;e di quelle di &longs;chioppi, & la<emph.end type="italics"/><pb pagenum="22" xlink:href="042/01/043.jpg"/><emph type="italics"/>grauita della balla offende a&longs;&longs;ai piu della uelocita di quella, e&longs;&longs;enipi gratia e&longs;&longs;endo un <lb/>&longs;chioppo, che tiri di lontano retto tramite pa&longs;&longs;a. </s> <s id="s.000591">400. con una balla di pe&longs;o di mezza <lb/>onza, & un archibu&longs;o, che retto tramite tiri &longs;olamente pa&longs;&longs;a. </s> <s id="s.000592">300. ma con una balla, <lb/>che pe&longs;iuna onza, hor dico, che in un tramite di. </s> <s id="s.000593">100. ouer. </s> <s id="s.000594">150. pa&longs;&longs;a, lo archibu&longs;o fa­<lb/>ra maggior pa&longs;&longs;ata del &longs;chioppo, quantunque in tal luoco la balla del &longs;chioppo uada <lb/>piu ueloce per le ragioni adutte nella quarta propo&longs;itione del primo libro della no&longs;tra <lb/>noua &longs;cientia, di quella del archibu&longs;o. </s> <s id="s.000595">Et pero e&longs;&longs;endo, come dice uo&longs;tra &longs;ignoria, di ra <lb/>gione la balla dello archibu&longs;o debbeno e&longs;&longs;e piu gro&longs;&longs;e, che quelle de &longs;chioppi.<emph.end type="italics"/> P. S<emph type="italics"/>en <lb/>za dubbio, che gli archibu&longs;t portano generalmente maggior balla de &longs;chioppi, uero è, <lb/>che &longs;ono alcune &longs;orte de &longs;chioppi, che portano balle alla equalita de alcuni archibu&longs;t.<emph.end type="italics"/><lb/>N. M<emph type="italics"/>a quando fu&longs;&longs;e un &longs;chioppo, che porta&longs;&longs;e tanta balla, quanto che face&longs;&longs;e un ar­<lb/>chibu&longs;o, & che tal &longs;chioppo tira&longs;&longs;e piu rettamente, ouer piu lontano di mira, di quello <lb/>tal archibu&longs;o, &longs;enza dubbio in <expan abbr="di&longs;tãtie">di&longs;tantie</expan> equale, lo &longs;chioppo fara maggior pa&longs;&longs;ata del ar <lb/>chibu&longs;o.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;to è co&longs;ara&longs;oneuole, & basta per que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000596">QVESITO DECIMOSESTO FATTO DAL <lb/><emph type="italics"/>detto Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000597">PRIORE. D<emph type="italics"/>onde procede la cau&longs;a, che percuotendo con una artegliaria in <lb/>unanaue, ouer galia in mare, el pare che tal artegliaria faccia puoco effetto, o­<lb/>uer pa&longs;&longs;ata re&longs;petto à quello che &longs;olita à far <expan abbr="tirãdo">tirando</expan> in una mur aglia, perche e&longs;&longs;endo co <lb/>me &longs;i &longs;ame &longs;i &longs;a ogni naue, ouer galia di tabule di legname onde e&longs;&longs;endo due, ouer tre <lb/>naue uni appre&longs;&longs;o laltra, el pare, che tirando un pezzo gro&longs;&longs;o in quelle, re&longs;petto à <lb/>quello, che faria tal pezzo in una gro&longs;&longs;a muraglia, ragioneuolmente le doueria pene <lb/>trar tutte tre dabanda à banda con tutte le bagaglie che ritroua&longs;&longs;e per quelle, per e&longs;­<lb/>&longs;er ognico&longs;a di legname, & tamen rare uolte accade, che ne po&longs;&longs;a penetr ar una &longs;ola da <lb/>banda à banda, anci la maggior parte delle uolte le balle re&longs;tano nellanaue, ouer galia.<emph.end type="italics"/><lb/>N. E<emph type="italics"/>glie manife&longs;to per ragion naturale, che quella co&longs;a, che piu impedi&longs;ce il moto, <lb/>piu uien &longs;penta, urtata, ouer offe&longs;a dalla co&longs;a mobile, ouer percotente per e&longs;&longs;er adun­<lb/>que la muraglia una co&longs;a &longs;tabile, & &longs;oda, & che piu impedi&longs;&longs;e el moto della balla del­<lb/>la artegliaria di quello fa una naue, ouer galia e&longs;&longs;endo quella in el mare, mobile, la qual <lb/>mobilita fa che la detta naue ouer galia con&longs;ente alquanto al moto, ouer alla percußio <lb/>ne della balla, per il che la balla non fa quel uigoro&longs;o effecto, ouer pa&longs;&longs;ata, che faria &longs;e <lb/>tal naue, ouer galia fu&longs;&longs;e ben a&longs;&longs;ettata in terra ferma, &longs;i come &longs;ono le muraglie. </s> <s id="s.000598">Si che <lb/>per tal ragione, piu gagliardo effetto fauna artegliaria in una muraglia, ouer in una <lb/>altra co&longs;a ferma e &longs;i&longs;&longs;a in terra &longs;oda, che non fa in una naue, ouer galia, nel mare mobi­<lb/>le. </s> <s id="s.000599">Ma molto maggior effetto fara la detta artegliaria in una naue, ouer galia, che gli <lb/>uegna alincontro, di quello faria in una, che gli fuggi&longs;&longs;e dauanti, perche quella, che gli <lb/>uien alincontro uien contra al moto della balla, & pero la ballo debbe far maggior ef <lb/>fetto in quella, che non farta &longs;tando quella ferma in mare. </s> <s id="s.000600">Et quella, che gli fuggie da­<lb/>uanti, molto piu ua con&longs;entendo alla percußion della balla, di quello faria, &longs;e quella &longs;t<gap/>&longs; <lb/>&longs;e in mare &longs;erma, & quteta.<emph.end type="italics"/> P. V<emph type="italics"/>e ho inte&longs;o benißimo.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/044.jpg"/> <p type="head"> <s id="s.000601">QVESITO DECIMOSETTIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000602">PRIORE. D<emph type="italics"/>iteme un poco, &longs;e per ca&longs;o in qualche improui&longs;o a&longs;&longs;alto ne &longs;u&longs;&longs;e <lb/>inchiodate le artegliarie, &longs;aria poßibile à ritrouar un modo, che fu&longs;&longs;e &longs;pediente <lb/>& pre&longs;to di poter ip&longs;o facto, cioe de &longs;ubito di&longs;chiodar le dette artegliarie, dico de &longs;ubi <lb/>co, perche moliti dicono &longs;aper far, & fanno certa acqua, ouer olio, qual ponendolo &longs;o­<lb/>pra el &longs;oro inchiodato corode quel ferro talmente, che di&longs;chiodano quel tal pezzo. <lb/></s> <s id="s.000603">Alcuni altri ho inte&longs;o, che fanno el mede&longs;imo con un trappano, cioe per el modo che u­<lb/>&longs;ano à farui il primo bu&longs;o, nondimeno cadauno di que&longs;ti modi uoleno tempo a&longs;&longs;ai, & <lb/>maßime e&longs;&longs;endoui molto numero de pe<emph.end type="italics"/>zz<emph type="italics"/>i da de&longs;chiodare, & io uoria ritrouar un mo <lb/>do, &longs;e poßit el fu&longs;&longs;e, di poterle di&longs;chiodar con cellerita, & pre&longs;tezza.<emph.end type="italics"/> N. <!-- KEEP S--></s> <s id="s.000604">A <emph type="italics"/>me mi <lb/>pare, che tal co&longs;a &longs;e potria fare (&longs;e non me inganno) à recargare tutte le dette arteglia <lb/>ria, con balle alquanto &longs;car&longs;ette, cioe, che non uadano molto &longs;errate nel pezzo, & da <lb/>poi che &longs;ono cargate, metterle à &longs;egno uer&longs;o al luoco doue potria occorrer il bi&longs;ogno, <lb/>cioe come proprio &longs;e faria, quando che loro non fu&longs;&longs;eno inchiodate, & dapoi farui una <lb/>&longs;ementella di poluere nel fondo della <expan abbr="cãna">canna</expan>, che uada dalla bocca del pezzo, per fin alla <lb/>balla di cadauna artegliaria, & per non tirarle fru&longs;tamente a&longs;pettar la occa&longs;tione, & <lb/>occorrendo la occa&longs;ione da tirarle, darui il &longs;uoco per la bocca, onde oltra che faranno <lb/>li &longs;uoi effetti ordinarij, tutte nel di&longs;cargar&longs;e pen&longs;o &longs;e di&longs;chioderanno, & getteranno <lb/>fuora quel chiodo, ouer ponta di ferro con che furono inchiodate: & co&longs;i facendo de <lb/>tal inchiodatura &longs;e uenira à non patirne alcun &longs;enistro ouer di&longs;conzo.<emph.end type="italics"/> P. C<emph type="italics"/>erto que <lb/>sto è bello, e molto &longs;pediente, & non credo, che &longs;i pote&longs;&longs;e ritrouar modo meglio di que <lb/>&longs;to, domente che nel di&longs;cargar&longs;e facciano questo effetto, che haueti detto di gettarne <lb/>quel chiodo, ouer ponta di ferro, con che furno inchiodate.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio lo git­<lb/>taranno.<emph.end type="italics"/> P. E<emph type="italics"/>t &longs;e per ca&longs;o alcuna non lo getta&longs;&longs;e, per e&longs;&longs;crui for&longs;i piu fi&longs;&longs;amente po­<lb/>sto delle altre, che rimedio ui &longs;i potria aggiongere.<emph.end type="italics"/> N. C<emph type="italics"/>argarla, & tirarla un'al­<lb/>tra uolta per el mede&longs;imo modo, uero è che ui getta&longs;&longs;e &longs;opra la inchiodatura un poco <lb/>di oglio caldißimo &longs;caldando anchora prima el luoco doue è la inchiodatura con car­<lb/>bon acce&longs;o, poi con creda farui &longs;opra un ua&longs;etto attorno el bu&longs;o, che ritenga quello olio <lb/>caldo, che ui &longs;i ponera, il che facendo el buco con quel ferro interpo&longs;to, per la &longs;ua cali­<lb/>dita, &longs;orbiranno quello olio caldo, la qual co&longs;a fara quel tal ferro piu lubrico&longs;o ad u&longs;ci <lb/>re. </s> <s id="s.000605">Anchora &longs;e dapoi che &longs;i hauera po&longs;ta, & a&longs;&longs;ettata la poluere nel mezzo (innanti <lb/>che ui &longs;e ponga la balla) &longs;ara fatto uno bu&longs;o con una a&longs;ta nella detta poluere, el quale <lb/>penetri per fin in fondo della canna del ditto pe<emph.end type="italics"/>zz<emph type="italics"/>o, cioe che uada à referire appre&longs;­<lb/>&longs;o al detto bu&longs;o inchiodato, tal cautella <expan abbr="nõ">non</expan> &longs;ara fora di propo&longs;ito in questo ca&longs;o: Et cre <lb/>do, che <34>&longs;ta &longs;upplira &longs;enza operar <expan abbr="altram&etilde;te">altramente</expan> olio caldo.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;to credo anchora <lb/>mi, perche nel di&longs;cargar&longs;e, la furia del fuoco troua tutte le comi&longs;&longs;ure mal come&longs;&longs;e, & <lb/>pero non credo che ui&longs;ta debi&longs;ogno à preparar la materia con olio caldo, ne fredo, al­<lb/>tramente. </s> <s id="s.000606">Et perche credo &longs;ta hora da'cena, non uoglio proccdiamo piu oltra, et pla­<lb/>uenire, <expan abbr="nõ">non</expan> uoglio che piu parlamo della artegliaria, ma che intramo in qual che altra in <lb/>genio&longs;a materia, perche circa alle co&longs;e della artegliaria, io non &longs;o piu che <expan abbr="adimãdarui">adimandarui</expan>.<emph.end type="italics"/></s> </p> <pb pagenum="23" xlink:href="042/01/045.jpg"/> <p type="head"> <s id="s.000607">QVESITO DECIM'OTTAVO FATTOMI <lb/><emph type="italics"/>dal Signor Iacomo de Achaial' Anno.<emph.end type="italics"/> 1542.</s> </p> <p type="head"> <s id="s.000608">I<emph type="italics"/>n Venetia qual ui <expan abbr="u&etilde;ne">uenne</expan> alla Sen&longs;a.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000609">SIGNOR IACOMO. I<emph type="italics"/>o ho ui&longs;to per i&longs;perientia che tirando con una Arte­<lb/>gliaria in una muraglia standoui molto propinquo non ui fa co&longs;i gagliardo effet­<lb/>to, ouer pa&longs;&longs;ata quanto fa à starui alquanto piu di lontano, et per leragioni da uoi aduc<lb/>te nella uo&longs;tra nuoua &longs;cientia, doueria &longs;eguir tutto al contrario, perche la balla tirata <lb/>da ogni artegliaria quanto piu &longs;e allontana dalla bocca del pezzo tanto piu &longs;e allenta di <lb/>uelocita, come uoi approuate, cioe che quella ua men ueloce, & doue ua men ueloce, iui <lb/>fa menor effetto. </s> <s id="s.000610">Adunque quanto piu &longs;i sta propinquo al luoco doue &longs;e tira tanto mag <lb/>gior effetto doueria far tal balla nel luoco doue percuote, di quello faria &longs;tandoui piu <lb/>lontano, perche tal balla feri&longs;&longs;e di moto piu ueloce, & tamen, come di&longs;opra ho detto. <lb/></s> <s id="s.000611">Io trouo con la i&longs;perientia riu&longs;cir tutto al contrario, è per tanto ui adimando la cau&longs;a <lb/>di que&longs;to inconueniente.<emph.end type="italics"/> N. P<emph type="italics"/>er ben ri&longs;oluere que&longs;to dubbio bi&longs;ogna notare qual­<lb/>mente ogni co&longs;a mo&longs;&longs;a moue &longs;empre qualche altra co&longs;a. </s> <s id="s.000612">Et pero quando che la balla <lb/>uien moue&longs;ta da quella uento&longs;ita cau&longs;ata dal &longs;alnitrio, la mede&longs;ima balla in&longs;teme con la <lb/>mede&longs;ima uento&longs;ita, moue anchora in quel mede&longs;imo i&longs;tante quel aere à &longs;e conterminale <lb/>nella canna, & quel mede&longs;imo aere moue & &longs;pinge l'altro aere à &longs;e con&longs;equentemente <lb/>conterminale, & co&longs;i l'altro &longs;pinge l'altro talmente che la detta balla uien à &longs;pingere, <lb/>& à mandare auanti di &longs;e una gran quantita di aere di forma molto longa, la qual for­<lb/>ma, quantunque la &longs;ia de aere, per uigor del moto, tal aere &longs;umme grauita in &longs;e talmen­<lb/>te, che per un certo poco ditempo ua penetrando l'altro aere che per iluiaggio &longs;uo ri­<lb/>troua, come &longs;e fu&longs;&longs;e qua&longs;i un trauo di legno, ma tal &longs;uo penetrar non procede molto <expan abbr="lõ">lom</expan> <lb/>tano, perche tal figura aerea, per un poco di tempo, ouer &longs;pacio procede auanti della <lb/>balla, ma perche la balla è di materia graue piu facilmente penetra lo aere, di quello fa <lb/>la detta figura aerea, & pero la balla uien a e&longs;&longs;er di moto molto piu uelocißima della <lb/>detta figura aerea, & per tanto in breuißimo tempo la detta balla uien à la&longs;ciar&longs;e de <lb/>drio da &longs;e quella tal fignra aerea (che prima andaua auanti di&longs;e) hor per tornare al no <lb/>&longs;tro primo propo&longs;ito, quando che con una artegliaria&longs;e tira in una co&longs;a, che ki&longs;ia mol­<lb/>to propinquißima, quella figura aerea, che è &longs;pinta auanti della balla detta di &longs;opra) <lb/>per cuotera prima in quella co&longs;a doue &longs;e tira, dellaballa, & per non e&longs;&longs;er tal figura ae­<lb/>rea atta à penetrar quella co&longs;a, eglie nece&longs;&longs;ario, che quella prima, & i&longs;trema parte di <lb/>tal figura, che prima percuote, à refflettere, & ritornar in drio, in contra alla mede­<lb/>&longs;ima figura, & alla balla, che &longs;eguita (maßime quando tal tiro &longs;ia tirato con il pezzo <lb/>aliuellato) la qual reffleßione (continua) nell'aggiongere della balla con il re&longs;iduo di tal <lb/>figura aerea che è contigua alla balla fanno uno contra&longs;to grandißimo, cioe il re&longs;iduo <lb/>della figura aereauol proceder auanti, & non puo parte, per non e&longs;&longs;er atto (come di <lb/>&longs;opra è detto) à penetrar quella co&longs;a doue &longs;e tira, & parte par cau&longs;a di quell'altra par <lb/>te che è sforzata à ritornar in drio, la qual combustione da un grande impedimento al <lb/>moto della balla, talmente che la balla non puo far sutto quello effetto, che doueria fa­<lb/>re. </s> <s id="s.000613">Ma quando che il luoco doue &longs;e tira è d'una mediocre di&longs;tantia, la bala per la &longs;ua <pb xlink:href="042/01/046.jpg"/>uelocita la&longs;&longs;a de drio da&longs;e la detta figura aerea, & &longs;e non tutta almeno la maggior par <lb/>te, talmente che in tal luoco di mediocre distantia la balla ui fara maggior effetto di <lb/>quello faria nel luoco piu propinquo, perche tal balla nel fare il &longs;uo effetto non ritroua <lb/>tanto impedimento di reffleßione ne combu&longs;tion di aere.<emph.end type="italics"/> S. IACO MO. Q<emph type="italics"/>ue&longs;tauo <lb/>straragione ne con&longs;ona molto, & comprendo che non puo procedere da altra co&longs;a.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000614">QVESITO DECIMONONO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Iacomo <lb/>de Achaia.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000615">SIGNOR IACOMO. M<emph type="italics"/>a un'altro dubbio uorria che me chiare&longs;ti, il qual <lb/>è que&longs;to, &longs;e per &longs;tar troppo propinquo con la artegliaria alla co&longs;a doue &longs;e tira, gli <lb/>effetti di tal artegliaria, non &longs;ono co&longs;i uigoro&longs;i quanto &longs;ariano in una mediocre di&longs;tan­<lb/>tia, per le ragioni per uoi adutte, è per le &longs;perientie per me fatte, &longs;imilmente per &longs;tar­<lb/>ui troppo di lontano (per commune opinione) &longs;eguitail mede&longs;imo, cioe che per &longs;tarui <lb/>molto di lontano non fa co&longs;i gagliardo effetto, nella co&longs;a doue percuote quanto faria <lb/>in una mediocre di&longs;tantia, hor ui adimando doue &longs;e potria con ragione determinare il <lb/>luoco doue che la balla di tal artegliaria faria il piu gagliardo, ouer uigoro&longs;o effetto, <lb/>che far pote&longs;&longs;e in tutto il tran&longs;ito, ouer uiaggio che far debbe, ouer che faria, quella tal <lb/>balla, non trouando alcuno impedimento.<emph.end type="italics"/> N. I<emph type="italics"/>n quello i&longs;tante che la balla peruiene, <lb/>ouer aggionge nella i&longs;trema parte di quella figura aerea (detta nel precedente que&longs;i­<lb/>to) trouando in tal luoco un re&longs;istente, in quel tal luoco ui faria maggiore, ouer pue <lb/>uigoro&longs;o effetto, che in qualunque altro luoco, perche &longs;e tal re&longs;i&longs;tente fu&longs;&longs;e piu in uer­<lb/>&longs;o la bocca del pe<emph.end type="italics"/>zz<emph type="italics"/>o, in quel tale re&longs;i&longs;tente prima ui percuoteria la detta figura aerea <lb/>che la balla (come nel precedente que&longs;ito fu detto) & dapoi la per cußione immediate <lb/>refflettaria in drio incontra alla mede&longs;ima figura aerea, & alla balla, ouiando alquan­<lb/>to il moto di quella (come fu detto nel precedente que&longs;ito.) Et &longs;e tal re&longs;i&longs;tente &longs;ara piu <lb/>lontano di tal luoco, &longs;ubito che la balla u&longs;ci&longs;&longs;e totalmente di quella figura aerea, cioe la <lb/>&longs;ciando quella de drio da &longs;e immediate ritroua lo aere qua&longs;i quieto, onde tal balla uiene <lb/>ad hauer alquanto piu difficulta à penetr ar tal aere quieto, che non haueua à penetra­<lb/>re quello della detta figura aerea, per e&longs;&longs;er quello di detta figura mede&longs;imamente in <lb/>cor&longs;o, & uer&longs;o il mede&longs;imo luoco doue ua la balla. </s> <s id="s.000616">Et per tanto u&longs;cita la balla di tal fi­<lb/>gura continuamente ui andara mancando il uigore, & tanto piu quanto piu &longs;e andara <lb/>allontanando, e pero con&longs;equentemente tanto piu deboli fara li &longs;uoi affetti &longs;i che per <lb/>que&longs;te due ragioni, la detta balla doueria far piu gagliardo effetto in un re&longs;itente tro­<lb/>uando quello preci&longs;amente nello u&longs;cire della i&longs;tremita della &longs;opradetta figura aerea, <lb/>che in qualunque altro luoco piu lontano, ouer propinquo.<emph.end type="italics"/> S.I. E<emph type="italics"/>glie da credere che <lb/>&longs;ia co&longs;i, perche in effetto comprendo che in tal luoco la balla feri&longs;&longs;e &longs;enza impedimen­<lb/>to dire&longs;&longs;leßione de aere, ne per fina allhora non è stata impedita da aere quieto, come <lb/>&longs;aria impedita per lo auenire &longs;e procede&longs;&longs;e piu oltra.<emph.end type="italics"/></s> </p> <pb pagenum="24" xlink:href="042/01/047.jpg"/> <p type="head"> <s id="s.000617">QVESITO VIGESIMO FATTO DA VNO <lb/>C<emph type="italics"/>apo de Bombardieri.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000618">BOMBARDIERO. P<emph type="italics"/>erche cau&longs;a credete uoiche &longs;i metta quelli dui &longs;trope <lb/>paioni de &longs;ieno, ouer de &longs;toppa, ogni uolta che &longs;i carga una artegliaria, cioe uno <lb/>dapoi che ui &longs;e ha po&longs;ta la poluere, cioe auanti che ui &longs;i metta la balla, & l'altro dapoi <lb/>che ui &longs;i ha po&longs;ta la detta balla.<emph.end type="italics"/> N. C<emph type="italics"/>ertamente che io non &longs;apeua que&longs;ta co&longs;a, che uoi <lb/>me haueti detto, cioe che auanti che &longs;i metta la balla nel pe<emph.end type="italics"/>zz<emph type="italics"/>o ui &longs;i metta uno &longs;trop­<lb/>paion de fieno, ouer de &longs;toppa, & co&longs;i un'altro dapoi che ui &longs;e ha po&longs;ta la balla, ma e&longs;­<lb/>&longs;endo co&longs;i (come al pre&longs;ente credo) à me mi pare, che piu &longs;e conuegnaria che io ui adi­<lb/>manda&longs;&longs;e à uoi la cau&longs;a di tal cautella, cha che uoi l'adimanda&longs;ti à me, perche &longs;e uoi u&longs;a <lb/>ti di far tal co&longs;a ogniuolta che uoi cargati un pezzo, uoi douere&longs;ti pur &longs;apere à che fin <lb/>il fati, perche l'arte bi&longs;ogna che la imiti lanatura in questo, che tutte le co&longs;e, che quella <lb/>fa, le faccia à qualche fine.<emph.end type="italics"/> B. M<emph type="italics"/>aue dirò, io non ho grammatica, & &longs;e pur u&longs;o di far <lb/>que&longs;ta co&longs;a, lo faccio, perche ho ui&longs;to che tutti glialtrilo fanno.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to &longs;i co&longs;tu­<lb/>ma in molti, & in molte arte, &longs;i mecanice come liberale, e pero non me mar auiglio di <lb/>uoi, ne manco uibia&longs;imo, anci ue laudo à ricercar la cau&longs;a di quelle co&longs;e che &longs;i co&longs;tuma <lb/>difare nell'arte uostra, ilche doueria far ogniuno, perche il &longs;apere non è altro che co­<lb/>no&longs;cere la co&longs;a per la cau&longs;a, hor tornando al no&longs;tro propo&longs;ito, il primo &longs;troppaione, <lb/>cioe quello che diceti che &longs;i mette drio alla poluere, auanti che ui &longs;e metta la balla, non <lb/>po&longs;&longs;o pen&longs;are che ui &longs;i metta per altro, &longs;aluo che per &longs;pazzar, & condure tutta quella <lb/>poluere (che nel cargare il pezzo fu&longs;&longs;e rimasta per la canna) in&longs;ieme con l'altra, & à <lb/>tenerla dapoi unita al &longs;uo luoco, dou'è &longs;tata a&longs;&longs;ettata. </s> <s id="s.000619">Ma il &longs;econdo &longs;troppaione, cioe <lb/>quello che uoi diceti che metteti drio alla balla, bi&longs;ogna pen&longs;are, che colui, che prima co <lb/>mincio à porui tal stroppaione fu a&longs;tretto da qualche neceßita, la qual neceßita non ui <lb/>puo e&longs;&longs;er occor&longs;a, &longs;aluo che lui doueua e&longs;&longs;ere in qualche luoco doue gli conuenia tirare <lb/>alba&longs;&longs;o, cioe tirar de &longs;u&longs;o in giu&longs;o, la qual co&longs;a <expan abbr="uol&etilde;dola">uolendola</expan> e&longs;&longs;equire &longs;enza porui tal &longs;trop­<lb/>paione, nell'abba&longs;&longs;are il pe<emph.end type="italics"/>zz<emph type="italics"/>o dauanti per metterlo à &longs;egno, la balla &longs;aria u&longs;cita del <lb/>pezzo, e pero accio che tal balla non u&longs;cide&longs;&longs;e, fu sforzato à porui tal &longs;troppione.<emph.end type="italics"/> B. <lb/>Q<emph type="italics"/>ue&longs;te uo&longs;tre ragioni &longs;ono bonißime, ma e uedo che tal stroppaione uc lo ponemo an­<lb/>chora quando che uolemo tirare all'alta, cioe di giu&longs;o in &longs;u&longs;o, doue non è quel pericolo <lb/>che diceti, cioe che la balla u&longs;ci&longs;ca del pe<emph.end type="italics"/>zz<emph type="italics"/>o nel metterlo à &longs;egno, e pero uorria &longs;apere <lb/>la cau&longs;a di questo.<emph.end type="italics"/> N. L<emph type="italics"/>a cau&longs;a di que&longs;to è la ignorantia, perche &longs;e uoi &longs;ape&longs;ti la cau&longs;a <lb/>di tal attione, uoi non ui ponere&longs;ti tal &longs;troppaione, &longs;aluo quando che la neceßita, accio <lb/>ue a&longs;tringe&longs;&longs;e.<emph.end type="italics"/> B. C<emph type="italics"/>ertamente comprendo che uoi diceti troppo il uero.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000620">QVESITO VIGESIMOPRIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Capo de Bombardieri.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000621">BOMBARDIERO. V<emph type="italics"/>euoglio raccontar una nouella, della quale &longs;oncerto <lb/>ue ne marauigliarcti molto, la qual è que&longs;ta. </s> <s id="s.000622">Rurouandomi una uolta à fare una <lb/>ba<gap/>la, & dapoi moluuri, accadete che per uno certo di&longs;concio, il pezzo nel di-<pb xlink:href="042/01/048.jpg"/>&longs;cargar&longs;e &longs;e elleu<gap/> talmente che andete con la bocca in terra, & in tanto che io tende­<lb/>ua à ragunar facchini con &longs;tanghe per ritornar tal pezzo al &longs;uo luoco un cagnolino <lb/><gap/>ol&longs;e andar (come accade) à na&longs;are la bocca di tal pezzo, & &longs;ubito che il detto cagno­<lb/>lino fu gionto alla bocca di tal pezzo, immediate lo detto pezzo lo tiro dentro della <lb/>canna, la qual co&longs;a uista dalli circo&longs;tanti, alcuni cor&longs;e per aiutare il detto cagnolino, & <lb/>lo trouorno e&longs;&longs;er stato tirato qua&longs;t in capo della canna, cioe qua&longs;t in capo del uacuo del <lb/>la canna di tal pezzo, pur lo cauorno, come morto, non &longs;o quello che dapoi &longs;egui&longs;&longs;e <lb/>de lui, ma credo che mori&longs;&longs;e, hor cheue pare di que&longs;to.<emph.end type="italics"/> N. D<emph type="italics"/>i que&longs;ta co&longs;a non <lb/>me ne mar auiglio, perche un pezzo per il molto tirar, diuenta caldo, & per tal cal­<lb/>dezza (come fu detto nel quinto que&longs;ito) quel tal pe<emph.end type="italics"/>zz<emph type="italics"/>o &longs;i fa attrattiuo, cioe alla &longs;imi­<lb/>litudine di una uento&longs;a, quando ui è ar&longs;a di dentro la stoppa.<emph.end type="italics"/> E <emph type="italics"/>pero non è marauiglia, <lb/>che &longs;orbe&longs;&longs;e &longs;u&longs;o quel tal cagnolino, anci credo, che quando un tal pezzo è molto caldo <lb/>&longs;euno ui anda&longs;&longs;e ad appoggiar la pancia nuda alla bocca di quello, colui in tal luoco ui <lb/>re&longs;taria talmente appre&longs;o, che con difficulta ui &longs;e di&longs;taccaria. </s> <s id="s.000623">Et molto piu attrattiuo <lb/>tal pezzo diuentaria in tal ca&longs;o, che ui attura&longs;&longs;e, ouer a&longs;troppa&longs;&longs;e quel bu&longs;etto doue &longs;e <lb/>gli da il fuoco.<emph.end type="italics"/> B. Q<emph type="italics"/>ue&longs;ta uo&longs;tra ragione mi con&longs;ona molto.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000624">QVESITO VIGESIMOSECVNDO FATTO <lb/><emph type="italics"/>da uno Gettador di Artegliaria.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000625">GETTADORE. D<emph type="italics"/>onde procede che di tutte le artegliarie che creppano, la <lb/>maggior parte creppano, de drio doue &longs;ta la poluere, ouer alla bocca, & rare <lb/>uolte nel meggio, uero è che del creppar nella parte de drio doue &longs;ta la poluere non me <lb/>ne marauiglio, perche in tal luoco la poluere ui mo&longs;tra ogni &longs;ua po&longs;&longs;anza, ma del crep <lb/>pare in bocca ne &longs;tago molto ammir atiuo, perche à me mi pare che piu pre&longs;to doueria <lb/>creppar nel meggio della canna che alla bocca, perche la e&longs;&longs;alatione del &longs;almitrio alla <lb/>bocca uitroua luoco largo da sborare, co&longs;a che non troua co&longs;i di dentro nel meggio del <lb/>la canna.<emph.end type="italics"/> N. C<emph type="italics"/>irca à questa co&longs;a bi&longs;ogna pen&longs;are, che ogni mouente puo riceuere <lb/>due difficulta, ouer nocumenti nel mouere un corpo rotondo graue che stia ripo&longs;ato é <lb/>quieto nel mouerlo per tra&longs;uer&longs;o la prima è à mouerlo nel principio, perche dapoi che <lb/>mo&longs;&longs;o &longs;ia non ui ha tanta dif&longs;iculta à mantenerlo continuamente in moto, l'altra diffi­<lb/>culta che puo riceuere tal mouente è que&longs;ta, che dapoi che ha moue&longs;to quel tal corpo <lb/>rotondo, e graue, e quel redutto in moto continuo, ouer &longs;ucceßiuo per trauer&longs;o ritro­<lb/>uando poialcuno repentino o&longs;tacolo, ouer, te&longs;i&longs;tente à tal moto, tal mouente riceue no <lb/>cumento a&longs;&longs;ai. </s> <s id="s.000626">Et per tanto dico, che à quella e&longs;&longs;alatione di uento cau&longs;ata dal &longs;alnitrio, <lb/>dapoi che e generata nel pezzo ui occorre due gran difficulta, la prima è à mouere co <lb/>&longs;i repentmamente la balla ripo&longs;&longs;ante quieta, e pero in tal accidente &longs;ubitano trouando&longs;i <lb/>il pezzo in tal luoco debole di metallo, ouer di metallo, nel getto mal con&longs;olidato, ouer <lb/>piu &longs;ottile da una banda che dall'altra, facilmente in tal luoco creppa, ma &longs;e per ca&longs;o il <lb/>metallo di tal luoco re&longs;i&longs;ta gagliardamente tanto che tal e&longs;&longs;alatione moue la balla, mo&longs;­<lb/>&longs;a che &longs;ia dal &longs;uo luoco, non ui è piu pericolo in tal parte di creppare (&longs;aluo &longs;e à tal balla <lb/>non ui occorre&longs;&longs;e dentro dal pezzo qualche &longs;trano accidente (come in fine &longs;e dira,)<emph.end type="italics"/><pb pagenum="25" xlink:href="042/01/049.jpg"/><emph type="italics"/>perche &longs;ubito, che la balla &longs;ia in moto con facilita tal e&longs;&longs;alatione ue landaria mantenen <lb/>do, non occorrendoui altro impedimento, ma &longs;ubito, come la balla aggionge alla bocca <lb/>del pezzo iui truoua tutto lo aere e&longs;trin&longs;ico: el quale, quanto che <expan abbr="cõ">com</expan> piu maggiore pre <lb/>stezza uien la balla in&longs;ieme con la detta e&longs;&longs;alatione, che la &longs;pinge ad a&longs;&longs;altarlo <expan abbr="tãto">tanto</expan> piu <lb/>unitamente, et con maggiore uigoro&longs;ita ui &longs;i oppone gagliardamente all'incontro, per <lb/>re&longs;i&longs;tere à tal moto &longs;ubitano, onde in tal luoco ui &longs;e uiene à cau&longs;are un'altra difficulta, <lb/>ouer ri&longs;&longs;a fra la e&longs;&longs;alatione intrin&longs;ica (che &longs;pinge la balla) & laere e&longs;trin&longs;ico, cioe lun <lb/>uoria u&longs;cire, & laltro non uoria che u&longs;cide&longs;&longs;e, pur &longs;inalmente lo intrin&longs;ico per e&longs;&longs;er di <lb/>maggior po&longs;&longs;anza, e uigore u&longs;ci&longs;&longs;e con uittoria rompendo, & &longs;pezzando el &longs;uo nemi <lb/>co, nel quale rompimento &longs;e cau&longs;a quel co&longs;i gran &longs;uono, perche ogni &longs;uono dalli Sapien <lb/>ti&longs;e diffini&longs;&longs;e non e&longs;&longs;er altro, che la percußione fatta de dui corpi inanimati, in&longs;ieme, e <lb/>pero in que&longs;to ca&longs;o non puo procedere da altro, che dalla percußione fatta da quella <lb/>e&longs;&longs;alatione, cau&longs;ata dentro dal pezzo, con lo acre e&longs;trin&longs;ico, trouando&longs;e <expan abbr="adũque">adunque</expan> la boc <lb/>ca del pe<emph.end type="italics"/>zz<emph type="italics"/>o qua&longs;i nel mezzo di tal abbattimento, uiene à patire grandamente in ge­<lb/>nerale, e que&longs;ta è la cau&longs;a, che in tal luoco el pezzo non hauendoui la &longs;ua conueniente <lb/>gro&longs;&longs;ezza, ouer e&longs;&longs;endoui qualche occulto diffetto cau&longs;ato nel gettarlo, <expan abbr="facilm&etilde;te">facilmente</expan> cre <lb/>pa.<emph.end type="italics"/> G. Q<emph type="italics"/>ue&longs;te due uo&longs;tre ragioni molto me quadrano, ma re&longs;ta un'altro dubbio, el <lb/>quale è que&longs;to, che quantunque la maggior parte delle uolte creppano (come di &longs;opra è <lb/>detto) nella parte de drio doue &longs;ta la poluere, ouer nella bocca, pur alcune uolte crep­<lb/>pano anchora nel mezzo, e pero haria à caro, che me aßigna&longs;ti la cau&longs;a di que&longs;to.<emph.end type="italics"/> N. <lb/>L<emph type="italics"/>e due cau&longs;e di &longs;opra per me aßignate, &longs;ono cau&longs;e generale, che &longs;empre per ordinario <lb/>fanno patire generalmente ogni &longs;pecie di pe<emph.end type="italics"/>zz<emph type="italics"/>o nelli preditti dui luochi piu che in al­<lb/>tro luoco, ma oltra le dette cau&longs;e generale, bi&longs;ogna pen&longs;are, & credere, che per acci­<lb/>dente ue ne po&longs;&longs;a occorrere molte altre, le quale non &longs;olamente puono <expan abbr="augum&etilde;tar">augumentar</expan> pa&longs; <lb/>&longs;ion al pe<emph.end type="italics"/>zz<emph type="italics"/>o nelli medemi dui luochi, cioe de drio, & nella bocca, ma anchora nel mez <lb/>zo della canna, e&longs;&longs;empigratia, &longs;e per mala &longs;orte la balla nel &longs;correre per la canna tro­<lb/>ua&longs;&longs;e qualche piccìol pieretta in &longs;orma di cuneo, ouer altro corpetto duro, & che per <lb/>&longs;orte la balla ui &longs;corre&longs;&longs;e per di &longs;opra tal pieretta, ouer corpetto interromperia nece&longs; <lb/>&longs;ariamente el moto, ouer cor&longs;o della balla, per il che la balla &longs;ariasforzata in tal luoco <lb/>à far de due co&longs;e luna, ò à intertener &longs;i (& que&longs;to &longs;eguiria quando la balla anda&longs;&longs;e mol­<lb/>to &longs;errata nel pezzo) ouer tal balla nel pa&longs;&longs;arui &longs;opra faceße un &longs;alteto, & questo po<lb/>tria far, quando la canna del pezzo fu&longs;&longs;e alquanto piu larga della gro&longs;&longs;ezza della bal <lb/>la, &longs;e per ca&longs;o adunque la balla fuße intertenuta da tal pieretta, ouer corpetto in for­<lb/>ma de cuneo, per tal intertenimento (e&longs;&longs;endo gaiardo) &longs;ariasforzato tal pezzo di cre <lb/>pare, & &longs;e tal cuneo fu&longs;&longs;e trouato dalla balla nel principio del &longs;uo moto, tal pezzo cre <lb/>paria pur nella parte doue &longs;ta la poluere, & &longs;e tal cuneo fu&longs;&longs;e trouato nel mezzo della <lb/>canna, & nel mezzo della canna <expan abbr="naturalm&etilde;te">naturalmente</expan> crepparia, & &longs;e fu&longs;&longs;e trouato appreßo <lb/>alla bocca, & nella bocca crepperia. </s> <s id="s.000627">Ma&longs;e per ca&longs;o la balla hauera luoco di poßer pa&longs; <lb/>&longs;ar di &longs;opra à tal corpetto, nel paßarui (come di &longs;opra dißi neceßariamente fara un &longs;al <lb/>tetto, nel qual &longs;altetto percottera nella &longs;ummita della canna, & rebattera poi nel fon­<lb/>do, la qual percußione, & repercußion, non puo eßer tanto debile, che non &longs;ia atta à <lb/>fa creppare el pezzo in tal luoco, et que&longs;ta è una delle cau&longs;e accidentale, che è atta à<emph.end type="italics"/><pb xlink:href="042/01/050.jpg"/><emph type="italics"/>far creppar el pezzo qua&longs;i in ogni luoco. </s> <s id="s.000628">Anchora quando che una balla non è egual <lb/>mente tonda, ouer che haue&longs;&longs;e qualche parte piu elleuata in un luoco, che in un'altro, <lb/>potria alle uolte far accadere un tal inconueniente uer&longs;o la bocca del pezzo. </s> <s id="s.000629">Anchora <lb/>quando, che el pezzo è molto caldo per el lungo tirare, è molto piu atto al crep­<lb/>pare, che e&longs;&longs;endo freddo (e&longs;&longs;endo pero di bronzo) perche el bronzo è di tal na­<lb/>tura, che per il caldo &longs;e fa frangibile. </s> <s id="s.000630">Anchora un pezzo quanto piu tira in alto <lb/>tanto piu pati&longs;&longs;e di quello fa tirandolo in piano. </s> <s id="s.000631">Anchora nel gettare il pezzo, ui &longs;e <lb/>puo cau&longs;ar alcune come&longs;&longs;ure, & cauerno&longs;ita parte occulte al &longs;en&longs;o, & parte pale&longs;e: ma <lb/>per e&longs;&longs;er di dentro dal pezzo non &longs;i po&longs;&longs;ono uedere, le quale fanno piu debile in tal luo <lb/>co el pezzo di quello ui &longs;i conuiene, e per que&longs;to alle uolte &longs;enza altro particolar acci­<lb/>dente, in talluoco creppa, ò &longs;ia de drio, ouer dauanti, ouer in mezzo. </s> <s id="s.000632">Alcuna fiata an­<lb/>chora el foro del pezzo <expan abbr="nõ">non</expan> pa&longs;&longs;a preci&longs;amente per mezzo dil mettallo, ma tende piu <lb/>da una banda, che dall'altra: per il che il mettallo uien à restare da una banda piu &longs;otti <lb/>le, & dall'altra piu gro&longs;&longs;o del &longs;uo douere, e per tanto da quella banda doue che el met <lb/>tallo è piu &longs;ottile, et debile del &longs;uo douere el pezzo alle uolte creppa, et questo è quan­<lb/>to che alle cau&longs;e del creppare, ui&longs;o dire<emph.end type="italics"/>, G. V<emph type="italics"/>oime haueti largamenta di mei dub­<lb/>bij &longs;atisfatto.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000633">QVESITO VIGESIMOTERZO FATTO DA <lb/>M. A<emph type="italics"/>lberghetto di Alberghetti gettadore de artegliaria.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000634"><emph type="italics"/>l'anno. </s> <s id="s.000635">1545. adi Aprile. <!-- KEEP S--></s> <s id="s.000636">In Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000637">ALBER GHETTO. S<emph type="italics"/>aria poßibel di poter &longs;apere, de una artegliaria noua <lb/>uamente inca&longs;&longs;ata, ouer fornita, & non mai tirata &longs;e quella tirara li &longs;uoi tirirct <lb/>ti, ouer co&longs;teri, ouer in &longs;galembro, &longs;enza tirarla altramente.<emph.end type="italics"/> N. Q<emph type="italics"/>uesto uostro que <lb/>&longs;ito in &longs;o&longs;tantia non uuol dir altro, che &longs;apere cono&longs;cere &longs;e el foro di tal pezzo giace <lb/>rettamente nel me<emph.end type="italics"/>zz<emph type="italics"/>o del mettallo, ouer non, & non giacendo in mezzo del detto met <lb/>tallo &longs;apere determinare in qual uer&longs;o pende tal foro: la qual co&longs;a non ho per difficile, <lb/>& con&longs;idero che eglie una co&longs;a, che per molte uie &longs;e potria inuestigare, & &longs;apere: ma <lb/>à uoler dare un modo, che &longs;ia i&longs;pediente e facile, bi&longs;ogneria pen&longs;arui alquanto.<emph.end type="italics"/> A. P<emph type="italics"/><expan abbr="&etilde;">em</expan> <lb/>&longs;atigli un poco, perche ho addimandato questo dubbio à molti, che fanno profeßione <lb/>de ingegno, & non ho ritrouato alcun, che me habbia &longs;aputo dar re&longs;olutione.<emph.end type="italics"/> N. I<emph type="italics"/>o <lb/>ho pen&longs;ato &longs;opra que&longs;ta materia, & ritrouo in effetto tal co&longs;a poter&longs;i inue&longs;tigar per <lb/>piu uie: ma à uolerlo &longs;apere con una co&longs;a &longs;pediente, et di poco arti&longs;icio el &longs;i die tuor due <lb/>a&longs;te, ouer dui ba&longs;toni drittißimi, ouer due cantinelle, ouer li&longs;te ben pianate, & egual­<lb/>mente larghe, longhe quanto che è la canna de tal pe<emph.end type="italics"/>zz<emph type="italics"/>o, & anchora uno brazzo di <lb/>piu, & in quel brazzo di piu metterui, & inchiodar ui dui trauer&longs;i longhi quanto che <lb/>è la mitta della culatta del pezzo uel circa (e nanti piu che meno) & lontani luno da <lb/>l'altro circa un bra<emph.end type="italics"/>zz<emph type="italics"/>o, accio &longs;iano piu atti à con&longs;eruar li dette due a&longs;te, ouer canti­<lb/>nelle, ouer li&longs;te egualmente di&longs;tante, e dapoi ficare luna di quelle a&longs;te, ouer li&longs;te nella <lb/>canna, ouero foro de tal pezzo, & laltra andara de fuora uia. </s> <s id="s.000638">Et uolendo &longs;apere &longs;e <lb/>tal pezzo è piu gro&longs;&longs;o di mettallo in un luoco, che in un'altro, procederemo in que&longs;to<emph.end type="italics"/><pb pagenum="26" xlink:href="042/01/051.jpg"/><emph type="italics"/>modo. </s> <s id="s.000639">La a&longs;ta, che ua per dentro uia prima la di&longs;tendaremo, & giu&longs;taremo rettamen <lb/>te per la parte &longs;uperiore del uacuo de detta canna, & fatto que&longs;to mi&longs;uraremo, ouer <lb/>che faremo mi&longs;urare &longs;ottilmente quanto che &longs;ara di&longs;tante dal mettallo la i&longs;trema par­<lb/>te, cioe il capo di quella asta, ouer li&longs;ta, che procede de fuora uia, fatto que&longs;to el &longs;i de uol <lb/>tar alquanto dalla banda del detto uacuo della canna la detta a&longs;ta, ouer li&longs;ta, che ua per <lb/>dentro, cioe mutarui alquanto luoco, & in que&longs;to &longs;econdo luoco far come primà, cioe <lb/>far guardare, & mi&longs;urare con diligentia quanto che &longs;ara di&longs;tante dal mettallo la detta <lb/>e&longs;trema parte, ouer capo di quella a&longs;ta, ouer li&longs;ta, che procede de fuora uia, & &longs;e in que <lb/>&longs;to &longs;econdo luoco lui &longs;ara preci&longs;amente tanto lontano dal mettallo, quanto che eranel­<lb/>la prima po&longs;itione, &longs;e potra concluder el mettallo e&longs;&longs;er nelli detti dui luochi egualmen <lb/>te gro&longs;&longs;o, ma&longs;e &longs;ara piu lontano, &longs;e potra concludere in que&longs;to &longs;econdo luoco e&longs;&longs;erui <lb/>piu &longs;ottile el mettnllo, che nel primo, & tanto piu &longs;ottile, quanto che la detta lontanan <lb/>za dal detto mettallo in que&longs;ta &longs;econda po&longs;itione &longs;ara maggiore della prima. </s> <s id="s.000640">Et &longs;imel­<lb/>mente, &longs;e per ca&longs;o in que&longs;ta &longs;econda po&longs;itione el detto capo della detta a&longs;ta, ouer li&longs;ta &longs;a <lb/>ra piu propinquo al mettallo della prima, &longs;eguira tutto al contrario, cioe, che in que&longs;to <lb/>&longs;econdo luoco ui &longs;ara piu gro&longs;&longs;o el mettollo, che nel primo, & con tal ordine proceden <lb/>do de in parte in parte, ouer de banda in banda d'intorno à tutto el pezzo con tal eui­<lb/>dentia&longs;e cono&longs;cera &longs;el detto foro &longs;ara preci&longs;amente, ouer rettamente in me<emph.end type="italics"/>zz<emph type="italics"/>o del <lb/>mettallo, ouer non, perche &longs;el mettallo &longs;e trouara egualmente gro&longs;&longs;o, &longs;e potra conclude <lb/>re tal foro e&longs;&longs;er rettamente in mezzo del mettallo, & tirara etiam li &longs;uoi tiri retta­<lb/>mente, &longs;econdo la <expan abbr="appar&etilde;tia">apparentia</expan> di tutto el pezzo: & &longs;e per ca&longs;o &longs;e trouara e&longs;&longs;er piu gro&longs; <lb/>&longs;o e<gap/> mettallo da una banda, che dall'altra, &longs;e potra concludere, tal foro non e&longs;&longs;er retta <lb/>mente in mezzo del mettallo, & con&longs;equentemente non tirara li &longs;uoi tiri retti, &longs;econ­<lb/>do la apparentia de tutto el pezzo: ma li tirara &longs;empre pendenti, ouer obliqui uer&longs;o à <lb/>quella banda doue che &longs;ar a piu gro&longs;&longs;o el mettallo, cioe &longs;i tal gro&longs;&longs;e<emph.end type="italics"/>zz<emph type="italics"/>a &longs;ara dalla ban­<lb/>da de&longs;tra lui tirara co&longs;tero uer&longs;o lv mede&longs;ima parte, ouer banda de&longs;tra, & è conuer&longs;o: <lb/>& &longs;e tal gro&longs;&longs;ezza &longs;ara in &longs;galembro poniamo fra la parte, ouer banda de&longs;tra, & la <lb/>parte &longs;uprema del pezzo luitirara <expan abbr="mede&longs;imam&etilde;te">mede&longs;imamente</expan> li detti &longs;uoitiri in &longs;galembro, cioe <lb/>obliqui, ouer <expan abbr="p&etilde;d&etilde;tii&longs;u&longs;o">pendentii&longs;u&longs;o</expan>: ma uer&longs;o la medema <expan abbr="bãda">banda</expan> doue è tal gro&longs;&longs;ezza, et co&longs;i &longs;i deb <lb/>be <expan abbr="int&etilde;der">intender</expan>, et <expan abbr="cõcludere">concludere</expan> in qual &longs;i uoglia <expan abbr="bãda">banda</expan>, che fu&longs;&longs;e tal maggior gro&longs;&longs;ezza di met <lb/>tallo. </s> <s id="s.000641">Et p eßer meglio inte&longs;o &longs;otto breuita <expan abbr="põgo">pongo</expan> p <expan abbr="eß&etilde;pio">eßempio</expan> figurale, che &longs;ialo &longs;otto &longs;crit <lb/>to pezzo di artegliaria, et che in quello uogliamo inue&longs;tigare <34>llo, che di &longs;opra fu pro <lb/>po&longs;to, cioe &longs;el&longs;uo foro, ouer uacuo della <expan abbr="cãna">canna</expan> giace <expan abbr="rettam&etilde;te">rettamente</expan> in mezzo dil mettallo, <lb/>hor p uoler inue&longs;tigar tal co&longs;a, dico, che el &longs;i die pigliar due a&longs;te dritte, et eguale, ouer <lb/>due li&longs;tette, come &longs;ono le due. </s> <s id="s.000642">a.b. <!-- REMOVE S-->&. </s> <s id="s.000643">c.d. <!-- REMOVE S-->& con dui trauer&longs;i daun capo, ouer &longs;opra un <lb/>brazzo de tabula inchiodaruele, che &longs;tiano <expan abbr="equidi&longs;tãte">equidi&longs;tante</expan>, et <expan abbr="lõtane">lontane</expan> luna dallaltra <expan abbr="alquãto">alquanto</expan> <lb/>piu di <34>llo, che é la mitta della gro&longs;&longs;e<emph.end type="italics"/>zz<emph type="italics"/>a di tutto el pezzo nella parte de drio, et <expan abbr="lõghe">longhe</expan> <lb/><expan abbr="tãto">tanto</expan> piu del uacuo della <expan abbr="cãna">canna</expan> di tal pezzo, <expan abbr="quãto">quanto</expan> che bi&longs;ogna per mettere in li dui tra <lb/>uer&longs;i, ouer tabula, et dapoi cazzar luna de dette a&longs;te, ouer li&longs;te (poniamo la. </s> <s id="s.000644">d.c.) p il <lb/>&longs;oro, ouer uacuo della canna, talmente che stia uniuer&longs;almente per longo contingente <lb/>con la parte &longs;uperiore del foro, ouer uacuo de detta canna, come in que&longs;ta prima figu­<lb/>ra appare, e dapoi mi&longs;urare, ouer far mi&longs;urar &longs;ottilmente la <expan abbr="di&longs;tãtia">di&longs;tantia</expan>, che è dal <expan abbr="põto">ponto</expan>. </s> <s id="s.000645">a.<emph.end type="italics"/><pb xlink:href="042/01/052.jpg"/><figure id="id.042.01.052.1.jpg" xlink:href="042/01/052/1.jpg"/><lb/><emph type="italics"/>(capo de la&longs;ta, ouer li&longs;ta) al mettallo de tal pezzo in tal luoco, & poniamo che tal di­<lb/>&longs;tantia &longs;ia preci&longs;e quanto, che è la lineetta. </s> <s id="s.000646">e. <!-- REMOVE S-->& fatto que&longs;to, el &longs;i de tramutar tai a&longs;te, <lb/>ouer li&longs;te in uno altro luoco, ouer banda di tal pezzo, hor tra&longs;mutamola (per far la dif <lb/>ferentia piu &longs;en&longs;ibile) nella parte oppo&longs;ita, come in que&longs;ta altra figura appare, et co&longs;i <lb/>in tal luoco mi&longs;uraremo pur (ouer faremo mi&longs;ur are) in tal luoco la distantia, che &longs;a­<lb/>ra dal mede&longs;imo ponto. </s> <s id="s.000647">a. (capo de lasta) al pezzo ouer mettallo, la qual di&longs;tantia &longs;up <lb/>ponamo, che la &longs;ta quanto e la linea f. <!-- REMOVE S-->hor dico, che &longs;e per ca&longs;o la linea. </s> <s id="s.000648">f. <!-- REMOVE S-->fu&longs;&longs;e &longs;tata e­<lb/>quale alla linea. </s> <s id="s.000649">e. <!-- REMOVE S-->el mettallo di tal pezzo &longs;aria stato equalmente gro&longs;&longs;o &longs;i de &longs;opra, co <lb/>me di &longs;otto di tal pezzo: ma perche in questo ca&longs;o &longs;en&longs;ibelmente trouamo la linea. </s> <s id="s.000650">f.<emph.end type="italics"/><lb/><figure id="id.042.01.052.2.jpg" xlink:href="042/01/052/2.jpg"/><lb/><emph type="italics"/>e&longs;&longs;er molto maggiore della linea. </s> <s id="s.000651">e. <!-- REMOVE S-->e per tanto concluderemo e&longs;&longs;er molto piu gro&longs;&longs;o el <lb/>mettallo di&longs;opra, che di &longs;otto in tal pe<emph.end type="italics"/>zz<emph type="italics"/>o, & tanto piu gro&longs;&longs;o, quanto che la linea. </s> <s id="s.000652">f. <lb/><!-- REMOVE S-->&longs;ara piu longa della linea. </s> <s id="s.000653">e. <!-- REMOVE S-->& contal ordine, e modo &longs;e die procedere dalla banda de­<lb/>&longs;tra, & dalla &longs;ini&longs;tra etiam in tutte le altre parte, ouer bande a torno a torno di tal pez <lb/>zo notando &longs;empre le dette di&longs;tantie per linee, & con tai linee &longs;e cono&longs;cera minuta­<lb/>mente la gro&longs;&longs;ezza, & &longs;ottigliezza del mettallo à torno à torno del foro di tal pe<emph.end type="italics"/>z­<lb/><emph type="italics"/>zo, etiam per qual uer&longs;o, ouer banda penderanno li &longs;uoi tiri per le ragioni, per auanti <lb/>dette, che è il propo&longs;ito.<emph.end type="italics"/> A. Q<emph type="italics"/>ue&longs;to uostro modo è molto <expan abbr="&longs;pedi&etilde;te">&longs;pediente</expan>, et me piace a&longs;&longs;ai.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000654">QVESITO VIGESIMO QVARTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo<emph.end type="italics"/> M. A<emph type="italics"/>lberghetto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000655">ALBER GHETTO V<emph type="italics"/>n'altro dubbio ue uoglio <expan abbr="addimãdare">addimandare</expan>. </s> <s id="s.000656">Accadete una <lb/>uolta, che prouando&longs;i alcuni pezzi à lio, uno de ditti pezzi dapoi alcuni tiri <lb/>nel di&longs;cargar&longs;e, andete con la te&longs;ta dauanti in terra, cioe con la bocca, et &longs;ubito che tal <lb/>pezzo &longs;u <expan abbr="giõto">gionto</expan> <expan abbr="cõ">com</expan> la detta bocca in terra (doue era molta &longs;abbia, ouer &longs;abbione) tiro<emph.end type="italics"/><pb pagenum="27" xlink:href="042/01/053.jpg"/><emph type="italics"/>gran quantita della detta &longs;abbia dentro da &longs;i, cioe dentro dal &longs;oro della <expan abbr="cãna">canna</expan>, hor ue ad <lb/>mando la cau&longs;a di tal effetto.<emph.end type="italics"/> N. V<emph type="italics"/>n ca&longs;o &longs;imil à que&longs;to, etiam alquanto piu fanta&longs;ti­<lb/>co, mi fu ricercato da uno Bombardiero (come appare in que&longs;to al. <!-- REMOVE S-->21. que&longs;ito) il quale, <lb/>&longs;i come nel uo&longs;tro, il pezzo tiro gran quantita di &longs;abbia dentro dal uacuo della canna, <lb/>nel &longs;uo, tal pezzo ue tiro dentro uno cagnolino, co&longs;a a&longs;&longs;ai ridicolo&longs;a, e pero que&longs;to uo­<lb/>&longs;tro dubbio lo ri&longs;olueremo, &longs;i come ri&longs;olueßimo quello, cioe che per tir ar il pezzo, tal <lb/>pezzo nece&longs;&longs;ariamente &longs;e &longs;calda, & &longs;ubito che il &longs;ia alquanto caldo, &longs;ubito &longs;i fa alquan <lb/>to attrattiuo alla &longs;imilitudine d'una uento&longs;a, e tanto piu, quanto piu &longs;i troua caláo, e pe <lb/>ro non è marauiglia &longs;e tal pezzo tra&longs;&longs;e tal &longs;abbia dentro da &longs;e.<emph.end type="italics"/> A. Q<emph type="italics"/>ue&longs;ta uo&longs;tra <lb/>ragion molto mi con&longs;ona.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000657">QVESITO VIGESIMOQVINTO FATTO DA <lb/><emph type="italics"/>uno Schioppettero, & etiam Bombardiero.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000658">SCHIOPPETIERO. H<emph type="italics"/>auendo io un &longs;chioppo con la &longs;ua mira tanto ben ac­<lb/>concia, che tirando à un &longs;egno po&longs;to in piano, in una certa mia conueniente di&longs;tan­<lb/>tia qua&longs;i la maggior parte delle uolte, dia preci&longs;amente in brocca, cioe nella co&longs;a tolta <lb/>de mira per picciola che la &longs;ia. </s> <s id="s.000659">Ve adimando &longs;e tal mira co&longs;i ben acconcia me &longs;eruira à <lb/>tirare à un &longs;egno, o altra picciola co&longs;a, che &longs;ia po&longs;ta in àlto, in quella mede&longs;ima di&longs;tan­<lb/>tia.<emph.end type="italics"/> N. E<emph type="italics"/>glie co&longs;a chiara, che tal mira non ue &longs;eruira co&longs;i preci&longs;amente tirando al­<lb/>l'alta, & in quella mede&longs;ima di&longs;tantia.<emph.end type="italics"/> S. M<emph type="italics"/>a percheragione.<emph.end type="italics"/> N. L<emph type="italics"/>a ragione è que <lb/>sta, &longs;e tirando in piano in quella uo&longs;tra commune distantia uoi date la maggior parte <lb/>preci&longs;amente in brocca, nece&longs;&longs;ariamente in quella tal di&longs;tantia, & in tal luoco, ui &longs;e con <lb/>gionge, ouer concorre la uo&longs;tra linea ui&longs;uale, o per contingentia, ouer per inter&longs;eccatio <lb/>ne, con il tran&longs;ito, ouer uiaggio qual debbe far la balla. </s> <s id="s.000660">Et perche nelli tiri elleuati, la <lb/>balla ua molto piu per linea retta, ouer linea men curua di quello ua nelli tiri fatti in <lb/>piano, cioe con il pezzo, ouer &longs;chioppo aliuellato, come fu di&longs;putato &longs;opra al &longs;econdo <lb/>que&longs;ito, e perche quanto che piu rettamente &longs;e i&longs;tende il tran&longs;ito, ouer uiaggio, qual deb <lb/>ba far la balla (tirando all'alta) di quello faceua tirando in piano, tanto piupre&longs;to uien <lb/>à concorrere, & à inter&longs;eccar&longs;e, il detto tran&longs;ito, ouer uiaggio, con la detta linea ui&longs;ua <lb/>le, di quello faceua tirando in piano. </s> <s id="s.000661">Facendo&longs;i adunque tal inter&longs;eccatione piu propin­<lb/>qua (per tirar co&longs;iin alto) la co&longs;a à chi &longs;e tira uien à re&longs;tare oltra à tal inter&longs;eccatione <lb/>(per e&longs;&longs;er quella nella mede&longs;ima prima distantia) & e&longs;&longs;endo fuora di tal inter&longs;eccatio­<lb/>ne è impoßibile à dar preci&longs;amente in brocca per ragion delle mire.<emph.end type="italics"/> S. I<emph type="italics"/>o non inten­<lb/>do troppo bene que&longs;te uo&longs;tre ragioni, ne manco uoglio che ue affaticati à darmele ad in <lb/>tendere, perche credo, che uoi ui hauere&longs;ti difficulta ma conchiudetemi pur &longs;e tir ando <lb/>à tal &longs;egno po&longs;to in alto, & nella mede&longs;ima prima di&longs;tantia io daro piu alto, ouer piu <lb/>ba&longs;&longs;o di tal &longs;egno.<emph.end type="italics"/> N. C<emph type="italics"/>onchiudo che uoi dariti piu alto, perche ogni uolta che la li­<lb/>neaui&longs;uale &longs;e inter&longs;ecca con il tran&longs;ito, ouer uiaggio qual debbe far la balla, & che la <lb/>co&longs;a, ouer &longs;egno à che &longs;e tira &longs;ia oltra à tal inter&longs;eccatione, &longs;empre la balla percuotera <lb/>alquanto di &longs;opra del &longs;egno, & tanto piu alto quanto che il detto &longs;egno, &longs;ara piulon­<lb/>tano dalla detta inter&longs;eccatione.<emph.end type="italics"/> S. C<emph type="italics"/>ertamente uoihaueti detto la uerita, et &longs;appiati <pb xlink:href="042/01/054.jpg"/>che io ho morto alli miei giorni. </s> <s id="s.000662">2000. uccelli (dico di piccioli) & la mia longa i&longs;pe­<lb/>rientia mi hafatto chiaro di quello che uoi me haueti detto, e pero ogni uolta che mioc­<lb/>corre à tirare ad alcuno uccello che &longs;ia &longs;opra à qualche alboro nella mia con&longs;ueta <expan abbr="di-&longs;tãtia">di­<lb/>&longs;tantia</expan>, io toglio &longs;empre la mira alli piedi di tal uccello, ma e&longs;&longs;endo tal uccello in piano, io <lb/>toglio la mira <expan abbr="preci&longs;am&etilde;te">preci&longs;amente</expan> nel corpo di tal uccello, ilche <expan abbr="fac&etilde;do">facendo</expan> rare uolte tiro in fallo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000663">QVESITO VIGESIMOSESTO FATTO <lb/><emph type="italics"/>dal mede&longs;imo Schioppettiero.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000664">SCHIOPPETTIERO. A<emph type="italics"/>nchora ui uoglio <expan abbr="adimãdarui">adimandarui</expan> un'oltro pa&longs;&longs;o, qual <lb/>è que&longs;to. </s> <s id="s.000665">Se con il detto mio &longs;chioppo uoglio tirare à un &longs;egno po&longs;to al ba&longs;&longs;o, ma <lb/>pur nella mede&longs;ima di&longs;tantia (detta di&longs;opra) ue adimando &longs;e tal mia mir a mi &longs;eruira, &longs;i <lb/>come fa in piano, cioe &longs;e io daro in brocca, ouer di &longs;opra, ouer di &longs;otto dal detto &longs;egno.<emph.end type="italics"/><lb/>N. S<emph type="italics"/>enza dubbio che tal mira nonue &longs;eruiria in quella mede&longs;ima di&longs;tantia, per le me­<lb/>de&longs;ime ragioni dette di &longs;opra, ma uoi dareti pur anchora piu alto del &longs;egno, cioe di &longs;o­<lb/>pra dal detto &longs;egno.<emph.end type="italics"/> S. V<emph type="italics"/>oi dite pur anchor la uerita, perche ogni uolta che io tiro à <lb/>alcun uccello che &longs;ia in qualche ba&longs;&longs;ura, ouer di&longs;montata, la longa &longs;perientia miha fat­<lb/>to cauto che &longs;empre piglio la mira pur nelli piedi di detto uccello, come faccio anchora <lb/>à quelli che &longs;ono all'alta, cioe &longs;opra à qualche arboro, ouer torre, & co&longs;i facendo rare <lb/>uolte tiro in fallo.<emph.end type="italics"/> N. I<emph type="italics"/>o ho molto à caro, che la uostra longa i&longs;perientia ui habbia <lb/>dato buona te&longs;timonianza, di quello che con ragioni naturale, ui ho conchiu&longs;o.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000666">QVESITO VIGESIMOSETTIMO <lb/><emph type="italics"/>fatto dal mede&longs;imo <lb/>Schioppettiero.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000667">SCHIOPPETIERO. V<emph type="italics"/>n'altro pa&longs;&longs;o ui ho anchora di adimandarui qual è <lb/>questo, tir ando&longs;t con un &longs;chioppo à un ber&longs;aglio, ouer ad altro &longs;egno, de mira, & <lb/>che per &longs;orte la botta dia di &longs;opra dal &longs;egno, tra&longs;portando poi il detto &longs;egno alquanto <lb/>piu lontano, ouer ritir ando&longs;i il &longs;chioppettero alquanto piu in drio, & ritir ando poi an <lb/>chora de mira al detto &longs;egno, &longs;e adimanda&longs;e con tal tiro &longs;i dara piu alto, ouer piu ba&longs;&longs;o <lb/>dell'altro tiro.<emph.end type="italics"/> N. I<emph type="italics"/>n un &longs;imil ca&longs;o alla &longs;econda uolta &longs;i dara molto piu di &longs;opra dal &longs;e <lb/>gno di quello &longs;i fece alla prima.<emph.end type="italics"/> S. V<emph type="italics"/>oi haucti detto la uerita, perche me accaduto à <lb/>me uolendo inuestigare quanto tiraua de mira uno &longs;chioppo nuouo non piu tirato qual <lb/>in una certa commune di&longs;tantia mi da&longs;eua di&longs;opra dal&longs;egno, et facendo tra&longs;portar piu <lb/>di lontano il detto &longs;egno, cioe circa. </s> <s id="s.000668">10. pa&longs;&longs;a con &longs;peranza de dar in brocca, & ritiran <lb/>do al mede&longs;imo &longs;egno, io percoßi molto piu di &longs;opra dal &longs;egno alla &longs;econda uolta che al­<lb/>la prima, la qual co&longs;a, mi parue tanto fuora diragione quanto dir &longs;e po&longs;&longs;a, perche à mi <lb/>me parea, è pare anchora che allontanando il &longs;egno &longs;e doueria battere piu ba&longs;&longs;o, di quel <lb/>lo &longs;i faceua &longs;tandoui piu appre&longs;&longs;o, e per tanto haueria molto accaro à intendere la cau­<lb/>&longs;a di que&longs;to inconueniente.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to non è inconueniente, anci è co&longs;a conueniente à <lb/>far quello che diragion de fare, & inconueniente grandißimo &longs;aria&longs;e &longs;eguita&longs;&longs;e &longs;econ-<emph.end type="italics"/><pb pagenum="28" xlink:href="042/01/055.jpg"/><emph type="italics"/>do il detto uo&longs;tro parere, perche ogni uolta che un &longs;chioppetiero, ouer bombardicro <lb/>tiri de mira à un &longs;egno, & che per uigor, ouer difetto delle due mire lui dia di &longs;opra dal <lb/>&longs;egno. </s> <s id="s.000669">Eglie manife&longs;io che la linea ui&longs;uale inter&longs;ecca, il tran&longs;ito, ouer uiaggio qual deb­<lb/>be far la balla, & che tal inter&longs;eccatione che fa la detta linea ui&longs;uale con il detto uiaggio <lb/>qual debbe far la balla, &longs;e fa de qua dal &longs;egno (per le ragioni adutte nel. </s> <s id="s.000670">7. que&longs;ito) & <lb/>perche per un molto longo &longs;pacio, quanto piu il &longs;egno doue &longs;e tira &longs;ia piu oltra la detta <lb/>inter&longs;eccatione, tanto piu la perco&longs;&longs;a dara di &longs;opra dal&longs;egno, tra&longs;portando adunque il <lb/>detto &longs;egno, per alquanto piu lontano, &longs;imilmente per alquanto piu lontano &longs;ara tra&longs;­<lb/>ferido dalla dalla mede&longs;ima inter&longs;eccatione, et per tanto la botta dara piu alta, ouer piu <lb/>di &longs;opra dal &longs;egno dell'altra, & tanto piu quanto che piu lontano per fin à un certo ter <lb/>mine &longs;ara tras&longs;erito, ouer tra&longs;portato il detto &longs;egno il mede&longs;imo &longs;eguiria &longs;eil &longs;chiop­<lb/>petiero, ouer bombardiero &longs;e ritira&longs;&longs;e per alquan<gap/>o in drio, & tutto que&longs;to che ho det­<lb/>to &longs;e debbe intendere quando che la botta è alta per difetto delle due mire, & non per di <lb/>fetto de colui che tira, perche &longs;e per difetto de colui che tira, cioe che nel di&longs;cargare il <lb/>&longs;chioppo lui face&longs;&longs;e alcun mouimento, & che per tal mouimento lui de&longs;&longs;e di&longs;opra, ouer <lb/>di&longs;otto, ouer co&longs;ter dal &longs;egno, tal inconueniente non &longs;i comprende nel no&longs;tro ragiona­<lb/>mento, ma <expan abbr="&longs;olam&etilde;te">&longs;olamente</expan> quando che tal effetto occorre per difetto delle due mire del&longs;chiop <lb/>po. </s> <s id="s.000671">Anchor bi&longs;ogna auertire, che il detto &longs;egno &longs;e potria tra&longs;portar tanto, & tanto lon <lb/>tano dalla prima po&longs;itione, che non &longs;olamente &longs;e potria dar piu propinquo al&longs;egno del­<lb/>la prima botta, ma anchora &longs;e potria dar nel proprio &longs;egno, per le ragioni adutte nel fi <lb/>ne del. <!-- REMOVE S-->7. que&longs;ito, cioe &longs;e per &longs;orte &longs;e tra&longs;porta&longs;&longs;e tanto, & tanto lontano il detto &longs;egno, <lb/>& che per &longs;orte &longs;e mette&longs;&longs;e nel luoco doue che la nostra linea ui&longs;uale fa la &longs;econda in­<lb/>ter&longs;eccatione, <expan abbr="cõ">com</expan> il <expan abbr="trã&longs;ito">tran&longs;ito</expan> della balla &longs;enza dubbio &longs;e daria in brocca (come fu detto &longs;o <lb/>pra al detto. </s> <s id="s.000672">7. que&longs;ito) & &longs;e p ca&longs;o <expan abbr="nõ">non</expan> fu&longs;&longs;e co&longs;i preci&longs;e in tal &longs;econda inter&longs;eccatione, <lb/>ma propinquo, tal botta non dara co&longs;i preci&longs;amente in brocca, ma ben ui dara propin­<lb/>quo, cioe &longs;e tal &longs;egnó &longs;ara alquanto di qua da tal inter&longs;eccatione, dar a alquanto di&longs;opra <lb/>dal &longs;egno, & &longs;e &longs;ara alquanto de la, dara alquanto di &longs;otto dal detto &longs;egno, & tutto que <lb/>sto facilmente &longs;e apprendera dalle ragioni adutte per figura in fine del detto. </s> <s id="s.000673">7. que&longs;i­<lb/>to. </s> <s id="s.000674">Vero è, che il detto &longs;egno &longs;e potria tra&longs;portar tanto di la della detta &longs;econda inter­<lb/>&longs;eccatione che la balla non potria aggiongere à quello, come per ragion naturale fa­<lb/>cilmente &longs;i puo comprendere.<emph.end type="italics"/> S. H<emph type="italics"/>o inte&longs;o benißimo la uo&longs;tra ragione, & la bo <lb/>molto accara.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000675">QVESITO VIGESIMO OTTAVO <lb/><emph type="italics"/>fatto dal mede&longs;imo <lb/>Schioppettiero.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000676">SCHIOPPETIERO. D<emph type="italics"/>al &longs;opradetto que&longs;ito me ne uenuto un'altro in men <lb/>te, qual è que&longs;to, &longs;e <expan abbr="tirãdo">tirando</expan> <expan abbr="cõ">com</expan> il detto mio &longs;chioppo pur à un &longs;egno de mira, et che p <lb/>di&longs;etto delle due mire io de&longs;&longs;e di &longs;otto dal&longs;egno, <expan abbr="tra&longs;portãdo">tra&longs;portando</expan> anchora il detto &longs;egno al­<lb/>quanto piu lontano, ouer <expan abbr="ritirãdomi">ritirandomi</expan> alquanto in drio, & ritir ando al mede&longs;imo &longs;egno <lb/>de mira, ue adimando &longs;e questa &longs;econda botta &longs;ara piu alta, ouer piu ba&longs;&longs;a della prima.<emph.end type="italics"/><pb xlink:href="042/01/056.jpg"/>N. I<emph type="italics"/>n que&longs;to ca&longs;o puo far uarie mutationi, perche la mira dauanti puo e&longs;&longs;ere <gap/>gual­<lb/>mente alta alla mira de drio, & puo e&longs;&longs;ere anchora piu alta, & anchora piu ba&longs;&longs;a di <lb/>quella, &longs;e per ca&longs;o adunque la mira <expan abbr="dauãti">dauanti</expan> &longs;ara eguale, ouer maggiore di quella de drio <lb/>(per le ragioni adutte nel principio del. <!-- REMOVE S-->7. que&longs;ito) quanto piu &longs;e tra&longs;portara tal &longs;egno <lb/>di lontano, tanto piu ba&longs;&longs;a &longs;ara la botta. </s> <s id="s.000677">Ma &longs;e la mira dauanti &longs;ara piu ba&longs;&longs;a di quella <lb/>de drio, & che per &longs;orte la &longs;ia talmente piu ba&longs;&longs;a di quella, che la no&longs;tra linea ui&longs;uale <lb/>uada realmente à &longs;egare il tran&longs;ito, ouer uiaggio qual debbe far la balla, come &longs;e dimo­<lb/>&longs;tra in fine del. <!-- REMOVE S-->7. que&longs;ito, in tal ca&longs;o, la &longs;econda botta nece&longs;&longs;ariamente &longs;ara di &longs;opra della <lb/>prima, uero è che la puo e&longs;&longs;er anchor lei pur di &longs;otto dal&longs;egno, cioe fra il &longs;egno, & la <lb/>prima botta, & puol e&longs;&longs;er anchora preci&longs;amente nel proprio &longs;egno, cioe in brocca, & <lb/>anchor puol e&longs;&longs;er di&longs;opra dal &longs;egno, perche ogni uolta che la detta mira dauanti &longs;ia tal <lb/>meute piu ba&longs;&longs;a di quella de drio, che la no&longs;tra linea ui&longs;uale uada realmente à &longs;egare il <lb/>detto tran&longs;ito, ouer uiaggio qual debbe far la balla, come di &longs;opra è detto, & che in un <lb/>&longs;imil ca&longs;o alcuno &longs;chioppettero, ouer bombardiero tiri de mira à un &longs;egno, & che per <lb/>uigore delle dette due mire (et <expan abbr="nõ">non</expan> p &longs;uo difetto) lui dia di&longs;otto del &longs;egno, eglie manife­<lb/>&longs;to che la inter&longs;eccatione, che fa la linea ui&longs;uale, conil tran&longs;ito, ouer uiaggio che debbe <lb/>far la bella, per le ragioni adutte in fine del &longs;ettimo que&longs;ito, &longs;ara de la dal &longs;egno, cioe che <lb/>il &longs;egno &longs;ara fra la detta inter&longs;eccatione, & colui che tira. </s> <s id="s.000678">Et per tanto, &longs;e il luoco doue <lb/>&longs;ara tra&longs;portato il detto &longs;egno, &longs;ia anchora di qua da tal inter&longs;eccatione, nece&longs;&longs;aria­<lb/>mente la detta &longs;econda botta &longs;ara di &longs;otto dal &longs;egno, uero è che ui &longs;ara piu propinqua <lb/>della prima, cioe &longs;ara fra il &longs;egno, & la prima botta, ma &longs;e la tra&longs;portatione del &longs;egno <lb/>&longs;ara per &longs;orte nel luoco della propria inter&longs;eccatione, al detto &longs;econdo tiro &longs;i dara pre­<lb/>ci&longs;amente in brocca, cioe nel detto &longs;egno tolto de mira, ma &longs;e per &longs;orte il detto &longs;egno &longs;a­<lb/>ra tra&longs;portato oltra la detta inter&longs;eccatione nece&longs;&longs;ariamente la detta &longs;econda botta da <lb/>ra di&longs;opra dal &longs;egno, & tanto piu dara di &longs;opra quanto che piu oltra la detta inter&longs;ec­<lb/>catione &longs;ara tra&longs;portato detto &longs;egno, per fin à uno certo termine (come in fine del pre­<lb/>cedente que&longs;ito anchor fu detto) ma &longs;e la detta mira dauanti &longs;ara pur alquanto piu ba&longs;­<lb/>&longs;a di quella de drio, ma che tal &longs;ua ba&longs;&longs;ezza &longs;ia tanto poca, che non&longs;ia atta di condure la <lb/>no&longs;tra linca ui&longs;uale tanto ba&longs;&longs;a che &longs;i po&longs;&longs;a congiongere con il uiaggio, ouer tran&longs;ito, <lb/>qual debbe far la balla, anchora in que&longs;to ca&longs;o in ogni tra&longs;portatione del detto &longs;egno, la <lb/>botta dara pur di &longs;otto dal &longs;egno, uero è, che tal &longs;econda botta potria dar di &longs;opra, & <lb/>anchor di &longs;otto della prima, & anchora in quella mede&longs;ima, perche &longs;e la prima po&longs;ition <lb/>del &longs;egno &longs;ara per &longs;orte nel luoco doue che la linea ui&longs;uale pa&longs;&longs;a piu propinquo al tran <lb/>&longs;ito, ouer uiaggio qual debbe far la balla (come &longs;e dimo&longs;tra nel. </s> <s id="s.000679">8. que&longs;ito) tra&longs;portan­<lb/>do poi il detto &longs;egno oltra al detto luoco &longs;enza dubbio la &longs;econda botta &longs;ara piu ba&longs;&longs;a <lb/>della prima, il mede&longs;imo &longs;eguiria quando, che la po&longs;itione del &longs;egno fu&longs;&longs;e oltra al detto <lb/>luoco. </s> <s id="s.000680">Ma quando che la detta prima po&longs;itione de &longs;egno fu&longs;&longs;e de qua da tal luoco (piu <lb/>propinquo tra&longs;portando poi il detto &longs;egno piu appre&longs;&longs;o à tal luoco, la detta &longs;econda <lb/>botta &longs;ara di &longs;opra della prima, ma pur &longs;ara di &longs;otto dal &longs;egno, cioe &longs;ara fra la prima <lb/>botta, & il &longs;egno. </s> <s id="s.000681">Ma quando tal &longs;egno fu&longs;&longs;e tra&longs;portado di la di tal luoco propinquo <lb/>potria e&longs;&longs;er tanto poco di la che pur la detta &longs;econda botta &longs;ara fra la prima, & il &longs;e­<lb/>gno, & potria e&longs;&longs;er anchor tanto di la che la detta &longs;econda botta dara di &longs;otto della pri-<emph.end type="italics"/><pb pagenum="29" xlink:href="042/01/057.jpg"/><emph type="italics"/>ma, & potrìa anchor e&longs;&longs;er co&longs;i proportionalmente di la, che la detta &longs;econda botta da <lb/>ria preci&longs;amente nel luocho della prima, & tutto que&longs;io, che ben con&longs;iderara la figu­<lb/>ratione del ottauo quæ&longs;ito, &longs;ar a manife&longs;to. </s> <s id="s.000682">Ma quando che la mira dauanti haue&longs;&longs;e per <lb/>&longs;orte la &longs;ua debita & conueniente ba&longs;&longs;ezza re&longs;petto à quella de drio, laqual co&longs;a acca <lb/>de rare uolte, cioe che la linea ui&longs;uale anda&longs;&longs;e preci&longs;amente à toccare, ma non &longs;egare, <lb/>el tran&longs;ito, ouer uiaggio: qual debbe far la balla. </s> <s id="s.000683">Et che in un &longs;imel ca&longs;o alcun &longs;cioppet­<lb/>tero, ouer bombardiero tira&longs;&longs;e de mira ad alcun &longs;egno, & che per uigore delle dette <lb/>due mire & non per &longs;uo diffetto, lui de&longs;&longs;e di &longs;otto dal &longs;egno, per le co&longs;e dette & dimo­<lb/>strate nel. </s> <s id="s.000684">9. que&longs;ito, puo occorrer che tal &longs;egno &longs;ia di qua etiam di la dal toccamento <lb/>delle dette due linee, perche co&longs;i e&longs;&longs;endo di qua, come di la da tal toccamento &longs;empre da <lb/>ra di &longs;otto dal &longs;egno, come &longs;opra alla figura del detto. </s> <s id="s.000685">9. Que&longs;ito facilmente &longs;e appren­<lb/>de, uero è, che quando tal prima botta fu&longs;&longs;e molto ba&longs;&longs;a, &longs;aria da giudicare che tal &longs;e­<lb/>gno fu&longs;&longs;e di la dal detto toccamento, perche e&longs;&longs;endo de qua tal botta, non puo e&longs;&longs;er mol <lb/>to ba&longs;&longs;a, per le ragioni adutte nel detto nono Que&longs;ito, &longs;e tal &longs;egno adunque &longs;ara de la <lb/>dal detto toccamento, & tra&longs;portando poi tal &longs;egno anchor piu in la, cioe piu lontano <lb/>dal detto toccamento, &longs;enza dubbio la &longs;econda botta &longs;ara molto piu ba&longs;&longs;a della prima. <lb/></s> <s id="s.000686">Ma quando che tal &longs;egno fu&longs;&longs;e di qua dal detto toccamento, tra&longs;portandolo poi piu in <lb/>la, puo occorrere che tal &longs;egno in tal &longs;econda po&longs;itione, &longs;ia anchor di qua dal detto toc <lb/>camento, & puo accadere, che &longs;ia nel proprio toccamento, & puo e&longs;&longs;er anchor che &longs;ia <lb/>di la da tal toc camento. </s> <s id="s.000687">Sel &longs;egno adunque in tal &longs;econda po&longs;itione &longs;ara de qua dal toc <lb/>camento, la &longs;ecouda botta &longs;ara de &longs;opra della prima, uero è, che &longs;ara pur de &longs;otto dal <lb/>&longs;egno, cioe &longs;ara fra el &longs;egno, & la prima botta. </s> <s id="s.000688">Ma &longs;el detto &longs;egno in tal &longs;econda po&longs;i­<lb/>tione &longs;ara p &longs;orte nel <expan abbr="põto">ponto</expan> del detto toccamento, la detta <expan abbr="&longs;ecõda">&longs;econda</expan> botta dara preci&longs;amen <lb/>te in brocca. </s> <s id="s.000689">Ma &longs;el detto &longs;egno in tal &longs;econda po&longs;itione &longs;ara de la dal detto toccamen­<lb/>to, puo e&longs;&longs;er tanto de la, che la detta &longs;econda botta &longs;ara piu ba&longs;&longs;a della prima, & puo e&longs; <lb/>&longs;er anchora co&longs;i poco di la da tal toccamento, che la detta &longs;econda botta &longs;ara di &longs;opra <lb/>della prima, ma pur di &longs;otto dal &longs;egno, cioe fra il &longs;egno e la prima botta, & puo e&longs;&longs;ere <lb/>anchora co&longs;i proportionalmente di la, che la detta <expan abbr="&longs;ecõda">&longs;econda</expan> botta dara preci&longs;amente nel <lb/>luoco della prima.<emph.end type="italics"/> S. Q<emph type="italics"/>ueste uo&longs;tre ragioni certamente me ingra&longs;&longs;ano, & que&longs;to <lb/>procede, perche le comenzo à intendere, e per que&longs;to mio intendere, <expan abbr="quãdo">quando</expan> che mi cre <lb/>deua di por fine à mei Que&longs;iti, le uo&longs;tre argumentationi me inducono nuoue chimere <lb/>uella mente mia, ouer nuoui dubbij de addimandarui, ma dubito de non farui fa&longs;tidio.<emph.end type="italics"/><lb/>N. S<emph type="italics"/>eguitati pur, che non mi fatti fa&longs;tidio alcuno.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000690">QVESITO VIGESIMONONO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Schioppettero.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000691">SCHIOPPETTERO. P<emph type="italics"/>er quanto po&longs;&longs;o con&longs;iderare per le uo&longs;tre argumen <lb/>tationi do &longs;opra adutte, la openione uo&longs;tra è, che &longs;e il &longs;egno doue &longs;e tira de mira <expan abbr="nõ">non</expan> <lb/>&longs;e imbatte per &longs;orte à e&longs;&longs;er nel ponto doue concorre la lineaui&longs;uale con el tran&longs;ito, o­<lb/>uer uiaggio qual debbe far la balla, non &longs;i po&longs;&longs;a dare preci&longs;amente in brocca. </s> <s id="s.000692">La qual <lb/>co&longs;a, da una <expan abbr="bãda">banda</expan> p <expan abbr="ragiõ">ragiom</expan> naturale <expan abbr="cõ&longs;idero">con&longs;idero</expan>, che eglie neceßario co&longs;i eßer, ma da laltra<emph.end type="italics"/><pb xlink:href="042/01/058.jpg"/><emph type="italics"/>banda, la mia longa i&longs;perientia pare, che non corre&longs;ponda preci&longs;amente à questo: ma <lb/>innanti che io ue dica in que conto la non me corre&longs;ponda, uoglio che me chiariti que­<lb/>&longs;to altro dubbio, cioe. </s> <s id="s.000693">Donde procede, che ogni &longs;chioppettero, & anchor bombar die­<lb/>ro generalmente quanto piu &longs;ta propinquo à un &longs;egno tolto de mira, tanto piu è atto <lb/>à darui dentro, ouer à far piu bella botta, & in ogni qualita de mire.<emph.end type="italics"/> N. P<emph type="italics"/>er ri&longs;ol­<lb/>uere regolatamente que&longs;to uostro dubbio, in tutte le &longs;orte, ouer qualita de differentie <lb/>che occorrer po&longs;&longs;a nelle due mire. </s> <s id="s.000694">Incominciaremo prima, <expan abbr="quãdo">quando</expan> che per &longs;orte la mi <lb/>ra dauanti fu&longs;&longs;e preci&longs;amente di quella mede&longs;ima altezza, che è quella de drio. </s> <s id="s.000695">Dico <lb/>adunque, che quando la mira dauanti &longs;ara egualmente alta à quella de drio in tal ca&longs;o, <lb/>quanto piu colui, che tirara stara propinquo al &longs;egno, tanto piu &longs;ara atto à darui den­<lb/>tro, ouer à far piu bella botta, & que&longs;to &longs;eguita per due cau&longs;e. </s> <s id="s.000696">La prima è, perche &longs;em <lb/>pre (come fu detto &longs;opra el &longs;ettimo Que&longs;ito) tal &longs;chioppo, ouer pezzo dara di &longs;otto <lb/>dal &longs;egno, che &longs;e tol de mira, & tanto piu ba&longs;&longs;a &longs;ara tal botta, quanto che piu lontano <lb/>&longs;ara dal detto &longs;egno, & è conuer&longs;o, quanto che piu propinquo &longs;ara al &longs;egno, tanto men <lb/>ba&longs;&longs;a &longs;ara tal botta, & la menor ba&longs;&longs;e<emph.end type="italics"/>zz<emph type="italics"/>a, che ui po&longs;&longs;a occorrere in &longs;imel ca&longs;o, &longs;aria <lb/>quella, quando, che &longs;e &longs;te&longs;&longs;e tanto propinquißimo al&longs;egno, che la i&longs;tremita della mira <lb/>de nanti, tocca&longs;&longs;e qua&longs;i el detto &longs;egno, che &longs;i tol de mira, la qual ba&longs;&longs;ezza puo e&longs;&longs;er cir <lb/>ta à tanto, quanto che è la di&longs;tantia, che è dalla i&longs;tremita de l'una, e l'altra mira al ua­<lb/>cuo della canna, la quale puo e&longs;&longs;er poco piu della gro&longs;&longs;ezza del mettallo del pe<emph.end type="italics"/>zz<emph type="italics"/>o ne <lb/>la parte de drio, che in un &longs;chioppo puo e&longs;&longs;er circa à tanto, quanto è la gro&longs;&longs;ezza di <lb/>un dedo, & in un pe<emph.end type="italics"/>zz<emph type="italics"/>o gro&longs;&longs;o tanto piu, quanto piu &longs;ara gro&longs;&longs;o di mettallo nella par <lb/>te de drio. </s> <s id="s.000697">Et <expan abbr="quãtunque">quantunque</expan> la balla &longs;ubito, che è u&longs;cita della bocca del &longs;chicppo, ouer pez <lb/>zo, uada continuamente declinando al ba&longs;&longs;o (come &longs;i dimo&longs;tra nel terzo Que&longs;ito) ta­<lb/>men per un poco di tempo, ouer &longs;patio, quando che tal balla &longs;i pote&longs;&longs;e uedere tal &longs;uo de­<lb/>clinare non &longs;aria &longs;en&longs;ibile, cioe chel no&longs;tro occhio non lo potria di&longs;cernere, e pero in <lb/>un corto &longs;patio, per conto delle dette mire, tal &longs;chioppo puo dar poco piu ba&longs;&longs;o del &longs;e­<lb/>gno tolto de mira di quella gro&longs;&longs;ezza d'un dedo, detta di &longs;opra, dico per uigor delle mi <lb/>re, e non per difetto di colui che tira, perche li difetti, & accidenti, che puo occorrere <lb/>per difetto di colui che tira, non &longs;e comprendono nelli no&longs;trir agionamenti, & que&longs;ta <lb/>é la prima cau&longs;a, che un &longs;chioppettero, & anchor bombardiero, quando che la mira da <lb/>uanti è di quella mede&longs;ima alte<emph.end type="italics"/>zz<emph type="italics"/>a, che è quella de drio, quanto piu stara propinquo <lb/>al &longs;egno tolto de mira, tanto piu &longs;ara atto à darui dentro, ouer à far piu bella botta di <lb/>quello fara à &longs;tarui piu lontano, et per que&longs;ta mede&longs;ima cau&longs;a occorreria el mede&longs;imo, <lb/>quando che la mira de nanti fu&longs;&longs;e alquanto piu alta di quella de drio, perche in &longs;imel ca <lb/>&longs;o, come fu detto nel detto &longs;ettimo Que&longs;ito, &longs;empre tal pezzo dara di &longs;otto dal &longs;egno <lb/>tolto de mira, & tanto piu di &longs;otto, qoanto che piu &longs;ara lontano dal detto &longs;egno, & la <lb/>menor ba&longs;&longs;ezza che ui poßi occorrere in tal ca&longs;o puo e&longs;&longs;er circa à tanto, quanto che <lb/>&longs;ara dalla i&longs;tremita della mira dauanti, al uacuo della canna de tal &longs;chioppo, ouer arte­<lb/>gliaria, ouer poco piu, la qual co&longs;a, quando chel &longs;egno fu&longs;&longs;e, come di &longs;opra dißi, propin <lb/>quißimo alla bocca del &longs;chioppo potria e&longs;&longs;er poco piu dell'altra, cioe poco piu della <lb/>gro&longs;&longs;ezza dun dedo, uero é che in di&longs;tantie equale daria alquanto piu ba&longs;&longs;o dell altra, <lb/>detta di &longs;opra, ma poco piu ba&longs;&longs;o, maßime in una piccola di&longs;tantia, &longs;i che, come di &longs;o-<emph.end type="italics"/><pb pagenum="30" xlink:href="042/01/059.jpg"/><emph type="italics"/>pra è detto, que&longs;ta è la prima cau&longs;a, che un &longs;chioppettero, & anchor bombardiero, <lb/>quando che la mira dauanti fu&longs;&longs;e ben alquanto piu alta di quella de drio, quanto piu <lb/>&longs;tara propinquo al &longs;egno tolto de mira, tanto piu &longs;ara atto à darui dentro, ouer à fare <lb/>piu bella botta di quello &longs;aria à &longs;tarui piu lontano. </s> <s id="s.000698">Ma oltra à que&longs;ta prima cau&longs;a io re <lb/>puto, che la ragion naturale ne in&longs;egni una altra al detto bombardiero, ouer &longs;chioppet <lb/>tero, la qual è que&longs;ta, che ogni uolta, che lui è molto propinquo al &longs;egno doue uol tira <lb/>re, che lui non pigli la mira nel proprio &longs;egno, ma alquanto di &longs;opra dal &longs;egno, perche <lb/>el die comprendere per di&longs;cretione naturale, che le istremita delle due mire &longs;ono <expan abbr="alquã">alquam</expan> <lb/>to piu ad alto della bocca del pezzo, doue u&longs;ci&longs;&longs;e la balla, la qual co&longs;a facendo, uiene à <lb/>medicare quel poco errore, detto di &longs;opra, che doueria far in ba&longs;&longs;ezza quel tal tiro, <lb/>il che lo fa piu atto à dar preci&longs;amente in brocca. </s> <s id="s.000699">Et per tanto dico, &longs;e quando la mi­<lb/>ra dauanti è equalmente alta, & anchor alquanto piu alta di quella de drio, el bombar <lb/>diero, ouer &longs;chioppettero è tanto piu atto à dar nel &longs;egno doue tira, ouer à far piu bel­<lb/>la botta, quanto piu ui sta propinquo, per le due ragioni di &longs;opra adutte, molto mag­<lb/>giormente, per le mede&longs;ime ragione, &longs;eguiria el mede&longs;imo, quando che la mira dauanti <lb/>&longs;ara alquanto piu ba&longs;&longs;a di quella de drio, & &longs;ia tal &longs;ua ba&longs;&longs;ezza troppo, ouer poco à <lb/>&longs;ufficienza: perche in qual &longs;i uoglia modo, che la &longs;ia piu ba&longs;&longs;a, la uien à unir piu la linea <lb/>ui&longs;uale con el uiaggio qual debba far la balla, et continuamente piu per fina al luoco do <lb/>ue che tal linea uisuale &longs;ega, ouer tocca, ouer che paßa piu propinqua al detto tran&longs;i­<lb/>to, ouer uiaggio, qual debbe far la balla di quello &longs;i fa nelle due po&longs;itione dette di &longs;opra, <lb/>perche in quella la detta linea uisuale continuamente &longs;i ua discostando dal detto tran&longs;i­<lb/>to, ouer uiaggio, che debbe far la balla, & in que&longs;te continuamente la ui &longs;i ua piu acco­<lb/>&longs;tando, per fin al luoco detto di&longs;opra, & quantunque anchora in que&longs;ta &longs;econda po&longs;i­<lb/>tione de mire quanto piu el &longs;egno, che &longs;e tuol de mira, sara de qua dal luoco doue con­<lb/>correra la linea ui&longs;uale con el detto tran&longs;ito, ouer uiaggio, ouer dal luoco, doue che piu <lb/>tran&longs;iranno uicine, ouer propinque, dette linee, tanto piu ba&longs;&longs;a sara la botta, come &longs;e <lb/>dimo&longs;tra nel &longs;ettimo, ottauo, & nono Que&longs;ito, tamen la ba&longs;&longs;ezza puo e&longs;&longs;er poca, co­<lb/>me fu detto &longs;opra li predetti Que&longs;iti, pche la maggiore che ui po&longs;&longs;a occorrere saria <lb/>quella, che nelle altre due prime era la maggiore, cioe quando chel segno, che &longs;e tol de <lb/>mira fu&longs;&longs;e propinquißimo alla mira dauanti, cioe alla bocca del &longs;chioppo, ouer pez­<lb/>zo, la qual di sopra determinaßimo in un &longs;chioppo poter e&longs;&longs;er poco piu della gro&longs;&longs;ez <lb/>za dun dedo, se la maggior ba&longs;&longs;ezza adunque é poco piu dun dedo in un &longs;chioppo &longs;tan <lb/>do al segno propinquißimo alla bocca di quello. </s> <s id="s.000700">E&longs;&longs;endo adunque tal &longs;egno alquanto <lb/>lontano da detta bocca, nece&longs;&longs;ariamente men ba&longs;&longs;a &longs;ara la &longs;ua botta, cioe men di quella <lb/>gro&longs;&longs;e<emph.end type="italics"/>zz<emph type="italics"/>a dun dedo, & tanto men ba&longs;&longs;a, quanto che &longs;ara piu lontano dalla bocca del <lb/>&longs;chioppo, pur che non &longs;ia oltra alla detta intersecatione, ouer toccamento che fa la det <lb/>ta linea uisuale con el tran&longs;ito della balla, ouer alla maggior propinquita di quelle, <expan abbr="eß&etilde;">eßem</expan> <lb/>do adunque tal segno lontano al men diece pa&longs;&longs;a della detta bocca del &longs;chioppo, qua&longs;i <lb/>che la ba&longs;&longs;ezza de tal botta non &longs;aria &longs;en&longs;ibile, oltra che, come di &longs;opra dißi, <expan abbr="quãdo">quando</expan> che <lb/>colui, che tira è molto propinquo al &longs;egno doue tira, credo per una certa de&longs;cretione <lb/>naturale, che lui non pigli la mira preci&longs;amente nella brocca, ma una minima co&longs;a piu <lb/>alto, perche lui die comprendere per ragion naturale, come di &longs;opradißi, che la i&longs;tre-<emph.end type="italics"/><pb xlink:href="042/01/060.jpg"/><emph type="italics"/>mita delle due mire &longs;ono alquanto piu alte della brocca del &longs;chioppo doue u&longs;ci&longs;&longs;e la bal­<lb/>la. </s> <s id="s.000701">la qual co&longs;a facendo (come credo che faccia) ueneria ad annular quel poco errore, <lb/>che doueria far in ba&longs;&longs;ezza la detta balla, & per que&longs;te due cau&longs;e tal &longs;chioppettero, <lb/>ouer bombardero con tal &longs;orte di mire generalmente &longs;ara molto piu atto à dar nel &longs;e­<lb/>gno, ouer à far piu bella botta in un luoco propinquo di quello &longs;aria con le due prime <lb/>qualita de mire dette nel principio di que&longs;to Que&longs;ito, perche in que&longs;ta qualita la linea <lb/>ui&longs;uale per molto &longs;patio ua qua&longs;i congionta, ouer poco di&longs;tante dal tran&longs;ito della balla, <lb/>e pero in tutto quel &longs;pacio che è fra la bocca del &longs;chioppo, & el luoco doue concorano <lb/>le dette due linee, ouer doue che &longs;ono piu propinque, non &longs;e è &longs;uggetto qua&longs;i ad alcuno <lb/>errore per le ragion dette di &longs;opra, dico ad alcuno errore p conto delle mire.<emph.end type="italics"/> S. C<emph type="italics"/>er <lb/>tamente con que&longs;to uo&longs;tro ragionamento uoi me haueti &longs;atisfatto in tutto, e per tutto, <lb/>perche da una banda io teneua, per le ragioni da uoi adutte nel precedente Que&longs;ito, <lb/>che fu&longs;&longs;e impoßibile à dar in un &longs;egno tolto de mira, quando che tal &longs;egno non fu&longs;&longs;e pre <lb/>ci&longs;amente nel ponto della inter&longs;ecatione, ouer del toccamento delle due linee concor­<lb/>rente, cioe della linea ui&longs;uale, & del tran&longs;ito della balla, & dell'altra banda, me parcua <lb/>che la mia longa i&longs;perientia non corre&longs;ponde&longs;&longs;e à questo, perche con el mio &longs;chioppo <lb/>ho tirato, & morto infiniti uccelli, alcuni à &longs;tarui competentamente da lontano, alcu­<lb/>ni altri à &longs;tarui co&longs;i <expan abbr="mediocrem&etilde;te">mediocremente</expan> di lontano, et alcuni altri &longs;tarui molto propinquo, <lb/>la qual co&longs;a non potria accadere, e&longs;&longs;endo, come prima tenea (perche &longs;e le mire del detto <lb/>mio &longs;chioppo &longs;ono tale, che mi facciano concorrere la mia linea ui&longs;uale con el tran&longs;ito <lb/>della balla, el ponto di tal <expan abbr="cõcor&longs;o">concor&longs;o</expan> eglie da credere, che &longs;empre &longs;i faccia qua&longs;i in una me <lb/>de&longs;ima di&longs;tantia (maßime tir ando per un mede&longs;imo uer&longs;o, e cargandolo &longs;empre à uno <lb/>mede&longs;imo modo) e per tanto e&longs;&longs;endo &longs;tata la co&longs;a à che &longs;e tira piu, ouer men distante di <lb/>quella tal determinata di&longs;tantia, &longs;aria &longs;tato impoßibile à imbroccar la detta co&longs;a tol­<lb/>ta de mira, e gia (come di &longs;opra ho detto) per i&longs;perientia ritrouaua al contrario, cioe <lb/>che in di&longs;tantie commune, & mediocre, & propinque, & in un mede&longs;imo uer&longs;o me oc­<lb/>cor&longs;o molte uolte à dar imbrocca con el mio &longs;chioppo, la qual co&longs;a mi faceua &longs;tar mol <lb/>to ambiguo, ma uoi me haueti ottimamente da ogni dubbio fatto chiaro, & maßime <lb/>che ogni uolta che mi occorre à tirare à qualche uccello, che me &longs;ia molto propinquo, <lb/>io co&longs;tumo come di &longs;opra dicesti, cioe à pìgliar la mira talmente piu alto, che la bocca <lb/>del mio &longs;chioppo uenga à <expan abbr="cõuerzerme">conuerzerme</expan> lo uccello, il che <expan abbr="fac&etilde;do">facendo</expan> rare uolte tiro in fallo.<emph.end type="italics"/><lb/>N. M<emph type="italics"/>i piace a&longs;&longs;ai, che la uo&longs;tra longa &longs;perientia ui renda bona te&longs;timonianza di quel <lb/>lo, che per ragion naturale, e geometrica la mia mente &longs;ente.<emph.end type="italics"/> S. Q<emph type="italics"/>uantunque del mio <lb/>dubbio me habbiati fatto chiaro, nondimeno pen&longs;ando &longs;oprala uo&longs;tra argumentatio­<lb/>ne, me ne occor&longs;o nouamente un'altro in mente, ma dubito <expan abbr="dinõ">dinon</expan> farui fa&longs;tidio.<emph.end type="italics"/> N. S<emph type="italics"/>e <lb/>guitati pur che non mi fatte fastidio alcuno, anci me fatti appiacere.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000702">QVESITO TRIGESIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Schioppetero.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000703">SCHIOPPETTERO N<emph type="italics"/>ella argumentatione per uoi fatta &longs;opra al <expan abbr="preced&etilde;">precedem</expan> <lb/>te Que&longs;ito, <expan abbr="cõ">com</expan> bonißime ragionihauete dimo&longs;trato <expan abbr="qualm&etilde;te">qualmente</expan> un &longs;chioppettero in<emph.end type="italics"/><pb pagenum="31" xlink:href="042/01/061.jpg"/><emph type="italics"/>un &longs;egno propinquo è <expan abbr="s&etilde;pre">sempre</expan> &longs;uggetto à dar <expan abbr="alquãto">alquanto</expan> di &longs;otto dal &longs;egno, cioe piu ba&longs;&longs;o del <lb/>&longs;egno, & che tal ba&longs;&longs;ezza non puo eccedere la gro&longs;&longs;ezza d'un dedo, o poco piu, & lo <lb/>ho ui&longs;to molti, che con uno mede&longs;imo &longs;chioppo, in una non molto longa di&longs;tantia tir an­<lb/>do de continuo à un &longs;egno hauer dato talhora molto di &longs;opra dal &longs;egno, & talhora mol <lb/>to di &longs;otto, & talhora molto co&longs;tero, & talhora nel proprio &longs;egno, e per tanto ue adi­<lb/>mando la cau&longs;a di que&longs;to inconueniente, il quale me pare e&longs;&longs;er molto di&longs;cordante à tutte <lb/>le uostre ragioni adutte in tutte le uo&longs;tre argumentationi.<emph.end type="italics"/> N. B<emph type="italics"/>i&longs;ogna &longs;apere, che tut <lb/>ti gli errori occorrenti nel tirar de &longs;chioppo, alcuni ponno e&longs;&longs;er cau&longs;ati &longs;olamente dal­<lb/>le mire, & alcuni altri &longs;olamente per difetto da colui che tira, & alcuni altri per difet­<lb/>to dell'uno, & dell'altro, cioe & dalle mire, & da colui che tira. </s> <s id="s.000704">Gli errori adunque, del <lb/>li quali nelle precedente no&longs;tre argumentationi hauemo parlato, &longs;ono quelli che &longs;ola­<lb/>mente dalle mire ponno e&longs;&longs;er cau&longs;ati, non interponendoui alcuno minimo difetto de co­<lb/>lui, che tira (come piu uolte alli &longs;uoi lochi è &longs;tato detto) perche gli errori che proce­<lb/>deno &longs;implicemente dalle due mire hanno in &longs;e regola è mi&longs;ura, come alli &longs;uoi lochi è &longs;ta <lb/>to detto, ma quelli che &longs;implicemente procedeno per difetto di colui che tira, non hanno <lb/>in &longs;e alcun ordine, ouer regolarita, perche la maggior parte de tai errori, procedeno <lb/>per cau&longs;a de qualche <expan abbr="mouim&etilde;to">mouimento</expan>, che ha fatto con il &longs;chioppo colui che tira dapoi che ha <lb/>pre&longs;a la mira, ouer nel di&longs;cargar del &longs;chioppo, perche ogniminimo moto fatto in quel <lb/>lo i&longs;tante, che &longs;e di&longs;carga il detto &longs;chioppo puo cau&longs;ar grande errore al luoco, ouer al &longs;e <lb/>gno doue &longs;e tira de mira, & tanto piu quanto piu tal &longs;egno &longs;ara lontano, & perche tal <lb/>mouimento del &longs;chioppo (qual puo occorrere, per il menar del fiato, ouer per il batter <lb/>del pol&longs;o, ouer per tremar della mano) non ha in &longs;i regolarita alcuna e per tanto quan­<lb/>do che il &longs;egno fu&longs;&longs;e ben preci&longs;amente nel ponto doue concorre la linea ui&longs;uale con il <lb/>uiaggio qual doueria far la balla (nel qual luoco alla ragion delle mire lui doueria dar <lb/>preci&longs;amente in brocca) nondimeno quel tale, mouendo il &longs;chioppo lui é &longs;oggetto à er­<lb/>rare in tutti i uer&longs;i, cioe che eglie &longs;oggetto &longs;i à dar di&longs;opra, come di &longs;otto dal&longs;egno, & <lb/>co&longs;i anchora à dar co&longs;tero &longs;i dalla banda de&longs;tra, come dalla &longs;ini&longs;tra, uero è, che eglie <lb/>etiam &longs;oggetto à dar per &longs;orte in brocca, & tutti questi mede&longs;imi accidenti gli puo ac­<lb/>ca&longs;are quando che il &longs;egno fu&longs;&longs;e di qua, ouer di la di tal concor&longs;o, uero è, che quando il <lb/>detto &longs;egno fu&longs;&longs;e di la da tal concor&longs;o, glierrori &longs;i cau&longs;ano maggiori (per la gran di­<lb/>&longs;tantia) di quello fariano e&longs;&longs;endo di qua, per e&longs;&longs;er piu propinquo, perche in uero quan­<lb/>to piu il &longs;egno è propinquo à colui, che tira, tanto piu ogni &longs;pecie di errore &longs;e &longs;minui&longs;&longs;e <lb/>in lui, e pero tanto piu &longs;e è &longs;oggetto à darui dentro, ouer à far piu bella botta, come &longs;u<lb/>detto nel precedente que&longs;ito; & à tutti que&longs;ti mede&longs;imi accidenti, anchora è &longs;oggetto <lb/>quando che nelle mire fu&longs;&longs;e qualche difetto, cioe che per il mouimento del detto &longs;chiop <lb/>po lui è &longs;oggetto à dare &longs;i di &longs;opra, come di &longs;otto del &longs;egno, & etiam co&longs;tero. </s> <s id="s.000705">Anchora <lb/>eglie &longs;oggetto à dar preci&longs;amente in brocca, perche quel moto del &longs;chioppo potria per <lb/>&longs;orte e&longs;&longs;er tale che medicaria il difetto delle mire, & darla in brocca, uero è, che non &longs;a <lb/>riu per &longs;uo &longs;apere, ma&longs;olamente per &longs;orte.<emph.end type="italics"/> S. N<emph type="italics"/>on piu, che ue ho inte&longs;o benißimo, et <lb/>que&longs;ta uo&longs;tra argumentatione, me ha certamente da ogni mio &longs;cropolo&longs;o dubbio ret­<lb/>camente chiarito.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000706">I<emph type="italics"/>l fine del Primo Libro.<emph.end type="italics"/><!-- KEEP S--></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/062.jpg"/> <p type="head"> <s id="s.000707">LIBRO SECVNDO DE LI <lb/>QVESITI ET INVENTION DIVERSE.</s> </p> <p type="head"> <s id="s.000708">DE NICOLO TARTAGLIA, <lb/>S<emph type="italics"/>opra la differentia, che occorre nelli tiri, & effetti <lb/>fatti con balla de Piombo, ouer di Ferro, ouer <lb/>di Pietra, & altre uarie particola­<lb/>rita, circa la proportione, <lb/>pe&longs;o, & mi&longs;ura delle <lb/>dette balle.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000709">QVESITO PRIMO FATTO DAL SIGNOR <lb/>G<emph type="italics"/>abriel Tadino Cauallier de Rodi, & Prior <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000710">PRIORE. D<emph type="italics"/>apoi che non &longs;appiamo piu che dire, per al pre&longs;en­<lb/>te &longs;opra le qualita di tiri, & altri accidenti delle Artegliarie, per <lb/>non &longs;tar otio&longs;i dapoi la lettione di Euclide, uoglio che parlamo al­<lb/>quanto delle qualita, & accidenti delle diuer&longs;ita delle balle.<emph.end type="italics"/> E <emph type="italics"/>per <lb/>tanto, ditemi un poco, qual credeti che andara piu lontano, & quan <lb/>to una balla di piombo, ouer di ferro, tirate con una i&longs;te&longs;&longs;a arte­<lb/>gliaria, & à una iste&longs;&longs;a elleuatione, & con egual quantita di polue­<lb/>re.<emph.end type="italics"/> N. B<emph type="italics"/>i&longs;ogna che quella me dica, con quanta quantita di polue­<lb/>re.<emph.end type="italics"/> P. P<emph type="italics"/>oniamo con li dui terzi di quello pe&longs;ara la balla di piombo.<emph.end type="italics"/> N. S<emph type="italics"/>enza dub <lb/>bio la balla di ferro andara piu lontano.<emph.end type="italics"/> P. Q<emph type="italics"/>uanto piu.<emph.end type="italics"/> N. N<emph type="italics"/>elli tiri baßi, cioe <lb/>con il pezzo aliuellato andara qua&longs;i un terzo de piu, ma alla elleuatione d'un ponto, an <lb/>dara alquanto meno d'un terzo piu, & quanto piu la &longs;e andara elleuando tanto piu an­<lb/>dara &longs;cemando di tal proportione, talmente che tirandola alla elleuatione del quinto, <lb/>ouer &longs;e&longs;to ponto, tal balla de ferro andara piu lontano di quella di piombo &longs;olamente <lb/>poco piu d'un quinto, & accio che<emph.end type="italics"/> V.S. <emph type="italics"/>meglio me intenda, poniamo che la balla di <expan abbr="piõ">piom</expan> <lb/>bo, &longs;tando il pezzo aliuellato, uada di lontano pa&longs;&longs;a. </s> <s id="s.000711">300. dico che la balla di ferro (ti­<lb/>rata con quella mede&longs;ima quantita di poluere con che fu tir ata quella de piombo (cioe <lb/>con li dui terzi di quello pe&longs;a la detta balla di piombo) andara di lontano qua&longs;i pa&longs;&longs;a. <lb/></s> <s id="s.000712">400. cioe qua&longs;i in &longs;e&longs;quitertia proportione, ma &longs;e tal balla de piombo alla elleuatione <lb/>del quinto, ouer &longs;esto ponto anda&longs;&longs;e di lontano poniamo pa&longs;&longs;a. </s> <s id="s.000713">3000. dico che la balla <lb/>di ferro à tal elleuatione, con la mede&longs;ima poluere, andara di lontano poco piu di pa&longs;&longs;a. <lb/></s> <s id="s.000714">3600. cioe poco piu che in &longs;equi quinta proportione.<emph.end type="italics"/> P. P<emph type="italics"/>erche ragione &longs;eguita tal <lb/>co&longs;a, cioe che co&longs;i nelli tiri elleuati, non eccede &longs;econdo la mede &longs;ima proportione che fa <lb/>nelli baßi.<emph.end type="italics"/> N. P<emph type="italics"/>erche lo aere fa maggior re&longs;istentia <expan abbr="proportionalm&etilde;te">proportionalmente</expan> al corpo men <lb/>graue, &longs;econdo la&longs;pecie, di quello fa al piu graue, & tanto piu <expan abbr="quãto">quanto</expan> piu la ritroua quel <lb/>lo men ueloce, ouer piu lento, e la&longs;&longs;o. </s> <s id="s.000715">Et perche nelli tiri baßi, non pertran&longs;i&longs;&longs;e per aere <lb/>&longs;aluo che nella &longs;ua piu uigoro&longs;a uelocita, perche pre&longs;to ritroua la terra che ue impe-<emph.end type="italics"/><pb pagenum="32" xlink:href="042/01/063.jpg"/><emph type="italics"/>di&longs;&longs;e il moto, e pero non ui &longs;e moltiplica tanto la offen&longs;ione dell'aere, quanto che fanelli <lb/>tiri elleuati, perche in quelli pertran&longs;i&longs;&longs;e a&longs;&longs;ai piu tempo per l'aere, & maßime nella <lb/>&longs;ua laßitudine, nella qual laßitudine (come di &longs;opra dißi) lo aere ui ha proportional­<lb/>mente maggior potesta, & dominatione di quello ha nelli tiri baßi, & per tanto la det <lb/>ta balla di ferro non eccede tanto la balla di piombo nelli tiri elleuati (proportional­<lb/>mente) quanto fa nelli tiri baßi.<emph.end type="italics"/> P. V<emph type="italics"/>e ho inte&longs;o benißimo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000716">QVESITO SECONDO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000717">PRIORE. Q<emph type="italics"/>ual credeti poi che andara piu lontano, o la detta balla di piom­<lb/>bo, ouer di ferro, tirate pur con una i&longs;te&longs;&longs;a artegliaria, & à una i&longs;te&longs;&longs;a elleuatio <lb/>ne, ma cia&longs;caduna con la &longs;ua poluere ordinaria, cioe con li dui terzi di quello pe&longs;a cia­<lb/>&longs;caduna balla per &longs;e.<emph.end type="italics"/> N. N<emph type="italics"/>elli tiri baßi, cioe aliuellati, ouer poco elleuati non ui &longs;ara <lb/>gran differentia, ma nelli tiri molto elleuati, come &longs;aria à dire alla elleuatione del terzo, <lb/>quarto, quinto, & &longs;esto ponto, la balla de piombo andara a&longs;&longs;ai piu lontano di quella di <lb/>ferro, & tutto questo procedera per le ragioni adutte nel precedente que&longs;ito.<emph.end type="italics"/> P. I<emph type="italics"/>o <lb/>haueua in animo di uolerui adimandare, quando che cadauna di dette balle fu&longs;&longs;e tirata <lb/>con li dui terzi poluere di quello pe&longs;a la balla di ferro, qual &longs;aria andata piu lontano, <lb/>ma per le ragion di &longs;opra adutte comprendo che la balla di ferro andaria piu lontano.<emph.end type="italics"/><lb/>N. C<emph type="italics"/>o&longs;i è.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000718">QVESITO TERZO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Priore <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000719">PRIORE. Q<emph type="italics"/>ual credeti poi che andara piu lontano, & quanto una balla di fer­<lb/>ro, ouer una di pietra pur tirate con una i&longs;te&longs;&longs;a artegliaria, & à una i&longs;te&longs;&longs;a elleua­<lb/>tione, & con egual quantita di poluere, cioe con li dui terzi poluere di quello pe&longs;a la <lb/>balla di ferro.<emph.end type="italics"/> N. S<emph type="italics"/>enza alcun dubbio la ragion ne dimostra che nelli tiri baßi, et nel <lb/>la maggior parte delli elleuati, la balla di pietra andara piu lontano di quella di ferro.<emph.end type="italics"/><lb/>P. E<emph type="italics"/>t quanto andara piu lontano.<emph.end type="italics"/> N. N<emph type="italics"/>elli tiri baßi (poniamo dal &longs;ito della equali­<lb/>ta, per fina alla elleuation de un &longs;ol ponto) la balla de pietra andara piu lontano, circa à <lb/>un quarlo piu di quello &longs;ara andata, ouer che andaria la balla di ferro, & inanti piu che <lb/>manco, ma poi nelli tiri piu elleuati, non cre&longs;&longs;aria tanto, & tanto meno quanto piu &longs;a­<lb/>ranno elleuati, & talmente andara &longs;cemando che alla elleuatione del quarto ponto ui &longs;a <lb/>ra pochißima differentia, cioe che à tal elleuatione andara qua&longs;i tanto lontano la balla <lb/>di ferro quanto quella di pietra, ma alla elleuatione del quinto, & &longs;e&longs;to ponto la balla <lb/>di ferro andara poi alquanto piu lontano di quella di pietra, & tutto que&longs;to procede <lb/>per le ragioni adutte &longs;opra il primo que&longs;ito.<emph.end type="italics"/> P. C<emph type="italics"/>ertamente le &longs;ono co&longs;e belle da <lb/>con&longs;iderare.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/064.jpg"/> <p type="head"> <s id="s.000720">QVESITO QVARTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000721">PRIORE. Q<emph type="italics"/>ual credeti poi che andara anchora piu <expan abbr="lõtano">lontano</expan>, o la detta balla di <lb/>ferro, o quella di pietra, pur tirate <expan abbr="cõ">com</expan> una i&longs;te&longs;&longs;a artegliaria, et à una i&longs;te&longs;&longs;a elle <lb/>uatione, ma con la &longs;ua poluere ordinaria, cioe tirando la balla di ferro con li dui terzi, <lb/>poluere di quello pe&longs;a la balla, & quella di pietra con un terzo di quello pe&longs;a la mede&longs;i <lb/>ma balla di pietra.<emph.end type="italics"/> N. L<emph type="italics"/>a determination di que&longs;to non è molto facile per il uariar <lb/>della proportione del pe&longs;o di cadauna balla alla &longs;ua poluere, nondimeno conchiudo che <lb/>la balla di ferro andara piu lontano di quella di pietra in ogni elleuatione, uero è, che <lb/>quanto piu il tiro &longs;ara elleuato, tanto piu andara piu lontano la detta balla di ferro pro <lb/>portionalmente di quella di pietra, & econuer&longs;o, cioe che quanto piu il tiro &longs;e acco&longs;te­<lb/>ra al &longs;ito della equalita, ui occorrera menor differentia<emph.end type="italics"/>. </s> <s id="s.000722">P. C<emph type="italics"/>omprendo adunque che <lb/>quelli primi che determinorno che alla balla di pietra ui &longs;i doue&longs;&longs;e dar &longs;olamente il ter­<lb/>zo poluere, di quello pe&longs;a la balla, il ferno, perche for&longs;i con con la &longs;perientia trouaro <lb/>quello che uoi diceti, cioe che &longs;e agguagliaua à quella di ferro.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000723">QVESITO QVINTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000724">PRIORE. Q<emph type="italics"/>ual teneti che fara maggior effetto, ouer pa&longs;&longs;ata (in una egual di <lb/>&longs;tantia) una balla di piombo, ouer di ferro tirate con una i&longs;te&longs;&longs;a artegliaria, & à <lb/>una i&longs;te&longs;&longs;a elleuatione, & prima con egual quantita di poluere, cioe con li dui terzi di <lb/>quello pe&longs;a la balla de piombo) & dapoi con la &longs;ua poluere ordinarìa.<emph.end type="italics"/> N. D<emph type="italics"/>i &longs;opra <lb/>nel primo que&longs;ito fu conchiu&longs;o che la balla di ferro in ogni elleuatione andara piu lon­<lb/>tano di quella di piombo (e&longs;&longs;endo pero ambedue tirate con quella detta egual quantita <lb/>di poluere) e pero &longs;e la co&longs;a doue &longs;e tira fu&longs;&longs;e tanto lontano che la balla di piombo non <lb/>ui pote&longs;&longs;e arriuare, & che quella di ferro ui arriua&longs;&longs;e, cadauno &longs;apra far que&longs;to giudi­<lb/>cio &longs;enza che io il dica, ma &longs;e la detta co&longs;a doue &longs;e tira&longs;ara in una di&longs;tantia conueniente <lb/>all uno, e l'altro tiro, & che la detta co&longs;a non &longs;ia di tal durezza che &longs;ia atta à &longs;mac care <lb/>la balla de piombo, &longs;enza dubbio la balla de piombo fara molto maggior effetto, ouer <lb/>pa&longs;&longs;ata di quello fara la balla di ferro, per cau&longs;a della &longs;ua maggior grauita, perche mol <lb/>to piu opera la grauita che la uelocita (come &longs;opra al. <!-- REMOVE S-->16. que&longs;ito del primo anchor fu <lb/>detto) uero è, che quando la detta co&longs;a doue &longs;e tira fu&longs;&longs;e di tal durezza che fu&longs;&longs;e atta à <lb/>&longs;maccar la detta balla di piombo, ui&longs;aria da dubitare, che la balla di ferro doue&longs;&longs;e pene <lb/>trare alquanto piu di quella di piombo, uero è, che &longs;e ben la balla di piombo non pene­<lb/>tra&longs;&longs;e tanto quanto quella di ferro, il non re&longs;tara ch'ella non conquaßimolto piu la det <lb/>ta co&longs;a perco&longs;&longs;a di quello fara la detta balla di ferro, per cau&longs;a della &longs;ua maggior gra­<lb/>uita, & tutto que&longs;to che &longs;e detto di tai balle tirate, con la detta egual quantita di polue­<lb/>re meglio &longs;e uerificara tir andole con la &longs;ua poluere ordinaria, cioe con li dui terzi di <lb/>quello chi pe&longs;a cadauna balla per &longs;e, cioe che nelle co&longs;e che non &longs;iano atte per &longs;ua durez <lb/>za à &longs;maccare la balla de piombo molto piu &longs;ara di maggior effetto, ouer pa&longs;&longs;ata la<emph.end type="italics"/><pb pagenum="33" xlink:href="042/01/065.jpg"/><emph type="italics"/>detta balla di piombo di quella di ferro, di quello era tirandole cadauna con la &longs;opra <lb/>detta equal quantita di poluere, & &longs;imelmente in quelle co&longs;e, che per la &longs;ua durezza <lb/>&longs;iano atte à &longs;maccar la balla de piombo, quantunque for&longs;i la balla di ferro potria eßer <lb/>che penetra&longs;&longs;e alquanto piu, nondimeno molto maggior botta, & <expan abbr="conqua&longs;&longs;am&etilde;to">conqua&longs;&longs;amento</expan> fara <lb/>la balla di piombo di quella di ferro.<emph.end type="italics"/> P. E<emph type="italics"/>glie co&longs;a, che a&longs;&longs;ai mi con&longs;ona.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000725">QVESITO SESTO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Priore di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000726">PRIORE. Q<emph type="italics"/>ual credeti poi che fara maggior effetto, ouer pa&longs;&longs;ata (in equal <lb/>di&longs;tantia) una balla di ferro, ouer di pietra, tir ate con una i&longs;te&longs;&longs;a artegliaria, & <lb/>a una i&longs;te&longs;&longs;a elleuatione, & prima con equal quantita di poluere, cioe con li dui terzi <lb/>di quello pe&longs;a la balla di ferro, & dapoi con la &longs;ua poluere ordinaria.<emph.end type="italics"/> N. I<emph type="italics"/>n que&longs;ta <lb/>non ui è alcun dubbio, che la balla di ferro fara molto maggior effetto, ouer pa&longs;&longs;ata, et <lb/>in ogni qualita di materia, di quello fara la balla di pietra, domente che la co&longs;a doue &longs;e <lb/>tira non fu&longs;&longs;e tanto lontana, che la balla di ferro non ui pote&longs;&longs;e arriuare, & che quel­<lb/>la di pietra ui arriua&longs;&longs;e (come fu detto anchora&longs;opra la balla di piombo, & di ferro <lb/>nel precedente Que&longs;ito) & &longs;e adunque la balla di ferro fara maggior effetto, ouer pa&longs; <lb/>&longs;ata, della balla di pietra tirandole ambe due con quella equal quantita di poluere, mol <lb/>to maggior effetto, ouer pa&longs;&longs;ata fara la poi tirandole ambe due con la &longs;ua poluere ordi <lb/>naria, cioe la balla di ferro con li dui terzi di quello pe&longs;a la detta balla, & quella di pie <lb/>tra con un &longs;olterzo di quello pe&longs;a detta balla di pietra.<emph.end type="italics"/> P. I<emph type="italics"/>o ho &longs;empre tenuto, che <lb/>co&longs;i fu&longs;&longs;e, come uoi hauete detto, & determinato.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000727">QVESITO SETTIMO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000728">PRIORE. E<emph type="italics"/>&longs;&longs;endo io à Rhodi al tempo, che il Turco ui era à torno, & e&longs;&longs;en <lb/>do io andato in una certa parte della terra con molti gua&longs;tadori per far fare al <lb/>cuni ripari, accadete, che ne fu tirato da Turchi con una artegliaria, & la balla con el <lb/>&longs;uo ciffolare &longs;e fece &longs;entire tanto di lontano, che ogn uno hebbe a&longs;&longs;ai commodita di po<lb/>ter dar luoco alla detta balla, & &longs;chiuar&longs;i da quella, & co&longs;i ogn'un fece. </s> <s id="s.000729">Et dapoi che <lb/>la detta balla hebbe fatto il &longs;uo effetto fru&longs;tatorio, ogniuno retornorno à lauorare &longs;icu <lb/>ramente confidando&longs;i, che &longs;e ben ue retirauano piu di &longs;aluar&longs;i &longs;empre al aui&longs;o della bal <lb/>a, cioe al&longs;uo ciffolare, hor accadete, che ue retirorno un'altra uolta, & la detta balla <lb/>uenne tanto quietamente, che alcun non la &longs;entete, &longs;aluo nel aggiongere, ouer nel far el <lb/>&longs;uo effetto, talmente che quella ucci&longs;e quattro gua&longs;tadori, hor ue adimando la cau&longs;a di <lb/>tal &longs;uo uenir co&longs;i tacito, & quieto, & maßime, che ue retirorno molte altre nolte, & <lb/>faceua el mede&longs;imo.<emph.end type="italics"/> N. L<emph type="italics"/>a cau&longs;a di tal effetto procede, per le ragioni adutte nel. </s> <s id="s.000730">4. <lb/>Que&longs;ito del primo libro, cioe, perche la prima uolta, che ui fu tirato, tal balla ritrouo <lb/>lo aere quieto, per la qual quietitudine, fa maggior re&longs;i&longs;tentia al moto della balla di <lb/>quello faria e&longs;&longs;endo commo&longs;&longs;o, per la qual re&longs;i&longs;tentia &longs;e cau&longs;a quel&longs;uo &longs;i <expan abbr="grã">gram</expan> ciffolare,<emph.end type="italics"/><pb xlink:href="042/01/066.jpg"/><emph type="italics"/>cioe, che tal ciffolare, na&longs;&longs;e dalla gran difficulta, che ritroua la detta balla in penetrar <lb/>tal aere ripo&longs;ante, e quieto: ma perche alla <expan abbr="&longs;ecõda">&longs;econda</expan> uolta tal balla, non &longs;olamente la ritro <lb/>uo tal aere tutto commo&longs;&longs;o, rotto, & conqua&longs;&longs;ato, dalla prima balla tirata, ma ancho­<lb/>ra molto tendente, ouer &longs;corrente uer&longs;o al luoco doue &longs;e tira, cioe &longs;econdando el moto <lb/>della detta halla, per le qual co&longs;e la detta balla, per non ritrouar quell'ostacolo alla &longs;e <lb/>conda uolta, che fece alla prima, la non ciffolaua co&longs;i forte, come fece alla prima uolta, <lb/>& per le mede&longs;ime ragioni molto meno doueua ciffolare nelli altri tiri, e&longs;&longs;endo pero ti <lb/>rati con&longs;equentemente.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;ta uo&longs;tra ragione mi con&longs;ona a&longs;&longs;ai.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000731">QVESITO OTTAVO FATTO DAL <lb/>M<emph type="italics"/>agnifico<emph.end type="italics"/> M. B<emph type="italics"/>ernardo Segreo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000732">MAGN. M. BERNARDO Q<emph type="italics"/>ual credeti che andara piu <expan abbr="lõtano">lontano</expan>, una balla <lb/>graue, ò una leggiera, <expan abbr="tirãdo">tirando</expan> l'una e laltra <expan abbr="cõ">com</expan> una i&longs;te&longs;&longs;a artegliaria, et à una i&longs;te&longs; <lb/>&longs;a elleuatione, & con equal quantita di poluere.<emph.end type="italics"/> N. <!-- KEEP S--></s> <s id="s.000733">A <emph type="italics"/>que&longs;to non ui &longs;i puo dare de­<lb/>terminata re&longs;po&longs;ta, che non di&longs;tingue la differentia della lor grauita, & la quantita de <lb/>la poluere, perche, & la grauita della co&longs;a, & la leuita &longs;e é uista fru&longs;tare la uirtu del <lb/>mouente, perche la co&longs;a tirata puo e&longs;&longs;er di tal leuita, che à pena, ouer poco lontano dal <lb/>la bocca del pezzo &longs;ara &longs;penta, ouer tirata, & &longs;imelmente potria eßer di tanta gran <lb/>grauita (ri&longs;petto alla poca quantita della poluere) che &longs;eguitaria el mede&longs;imo inconue <lb/>niente, e pero eglie neceßario à di&longs;tinguere la differentia della lor grauita, etiam di <lb/>che materia &longs;ia cadauna balla, etiam la quantita della poluere, perche &longs;e l'una fu&longs;&longs;e de <lb/>piombo, & l'altra di ferro, ouer di pietra, & tirandole con i dui terzi di poluerè di <lb/>quello pe&longs;a la balla de piombo, eglie co&longs;a chiara (per le ragioni adutte di &longs;opra nel pri­<lb/>mo, & terzo Que&longs;ito) che la balla di ferro, ouer di pietra andara piu lontano di quel <lb/>la di piombo, ma &longs;e l'una de dette balle fu&longs;&longs;e di piombo, ouer di ferro, et l'altra di legno <lb/>leggiero, ouer di quel &longs;uore, che &longs;i mette nelli &longs;ubri, ouer zocoli delle donne, eglie da <lb/>credere che la balla graue, cioe quella di piombo, ouer di ferro (tirata con la &longs;ua pol­<lb/>uere or dinaria) andara molto piulontano, della balla leue (cioe di quella balla di le­<lb/>gno leggiero, ouer di&longs;uore) tirate anchor quelle con la mede&longs;ima quantita di polue­<lb/>re. </s> <s id="s.000734">Ma uoltando carta, che uole&longs;&longs;e tirare una balla de piombo da lire cento con un ca­<lb/>non da cento, & &longs;imelmente una balla di legno di quella mede&longs;ima grandezza, ouer <lb/>gro&longs;&longs;ezza, che é quella di piombo, ma tirare l'una, e l'altra &longs;olamente con una lira, <lb/>ouer due di poluere, eglie da credere in que&longs;to ca&longs;o, che la balla di legno andara piu <expan abbr="lõ">lom</expan> <lb/>tano di quella di piombo, la qual co&longs;a ne auerti&longs;&longs;e qualmente eglie nece&longs;&longs;ario, che tra <lb/>la grauita della co&longs;a tirata, & la uirtu della co&longs;a mouente (ouer che &longs;penge) ui ca&longs;ca <lb/>una &longs;ua limitata proportione.<emph.end type="italics"/> M. B. Q<emph type="italics"/>ue&longs;to uo&longs;tro di&longs;cor&longs;o non me di&longs;piace, & <lb/>&longs;appiati, che una uolta mi uol&longs;i chiarire di que&longs;to dubbio, & feci far una balla, pur di <lb/>mettallo, ma bu&longs;a, cioe uacua di dentro, & la feci tirare, & quella ando a&longs;&longs;ai meno del <lb/>la balla or dinaria di ferro.<emph.end type="italics"/></s> </p> <pb pagenum="34" xlink:href="042/01/067.jpg"/> <p type="head"> <s id="s.000735">QVESITO NONO FATTO DAL MAGNIFICO <lb/>S<emph type="italics"/>ignor Giulio Sauorgnano.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000736">SIGNOR GIVLIO E<emph type="italics"/>glie una balla, che per diametro è onze quatro di mi <lb/>&longs;ura, & pe&longs;a lire otto, hor ue adimando quanto pe&longs;aria unaltra, che fu&longs;&longs;e per dia <lb/>metro onze.<emph.end type="italics"/> 6. N. L<emph type="italics"/>a pe&longs;aria lire.<emph.end type="italics"/> 27. S. G. C<emph type="italics"/>ome è poßibile, che una balla, che <lb/>&longs;ia per diametro onze. </s> <s id="s.000737">6. de mi&longs;ura (che &longs;aria mezzo pie) non pe&longs;i piu de lire. </s> <s id="s.000738">27. an <lb/>zi tengo, che debbia pe&longs;are piu de lire.<emph.end type="italics"/> 60. N. E<emph type="italics"/>glie il uero, che &longs;e tal balla fu&longs;&longs;e di <lb/>ferro, et che per diametro la fu&longs;&longs;e onze. </s> <s id="s.000739">6. de mi&longs;ura ordinaria (che &longs;aria me<emph.end type="italics"/>zz<emph type="italics"/>o pie) <lb/>&longs;enza dubbio tengo, che pe&longs;aria circa à dette lire.<emph.end type="italics"/> 60. S. G. P<emph type="italics"/>erche diceti adunque <lb/>che la pe&longs;ara &longs;olamente lire.<emph.end type="italics"/> 27. N. I<emph type="italics"/>o dico, che la pe&longs;ara lire. </s> <s id="s.000740">27. stante, che quella <lb/>che è di diametro onze quattro pe&longs;i &longs;olamente lire otto: ma&longs;e tal balla fu&longs;&longs;e de &longs;erro, <lb/>& che de diametro la fu&longs;&longs;e (come è detto) onze quattro de mi&longs;ura ordmaria (cioe un <lb/>terzo dun pie) la pe&longs;aria piu de lire. </s> <s id="s.000741">18. uel circa, e pero io ho ri&longs;posto &longs;econdo la pro <lb/>po&longs;ta.<emph.end type="italics"/> S. G. E<emph type="italics"/>t come haueti trouato quelle lire.<emph.end type="italics"/> 27. N. I<emph type="italics"/>o le ho ritrouate in que­<lb/>&longs;to modo, io ho cubato quelle onze. </s> <s id="s.000742">4. (diametro della prima balla) el cubo delle quale <lb/>è. </s> <s id="s.000743">64. & <expan abbr="&longs;imelm&etilde;te">&longs;imelmente</expan> ho cubato quelle. </s> <s id="s.000744">6. onze (diametro della <expan abbr="&longs;ecõda">&longs;econda</expan> balla) el cubo del <lb/>le quale è. </s> <s id="s.000745">216. et dapoi per la regola del tre, dico: &longs;e. </s> <s id="s.000746">64. pe&longs;a lire. </s> <s id="s.000747">8. che pe&longs;ara. </s> <s id="s.000748">216. <lb/>multiplico, & parto &longs;econdo l'ordine di tal regula, & mene uenuto le dette lire. </s> <s id="s.000749">27. e <lb/>pero ho conclu&longs;o, che la detta &longs;econda balla pe&longs;aria lire. </s> <s id="s.000750">27. &longs;tante che la prima pe&longs;a&longs;­<lb/>&longs;e &longs;olamente lire.<emph.end type="italics"/> 8. S. G. V<emph type="italics"/>eho inte&longs;o benißimo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000751">QVESITO DECIMO FATTO DA M. ZANAN­<lb/><emph type="italics"/>tonio di Ru&longs;coni Pittor, & Architettor.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000752">ZANANTONIO E<emph type="italics"/>glie una balla, che per diametro è. </s> <s id="s.000753">5. deda ui <lb/>adimando <lb/>come faro io aritrouare quanto che &longs;ia el diametro duna altra balla che &longs;ia dop­<lb/>pia à questa.<emph.end type="italics"/> N. V<emph type="italics"/>oi doueti cubar quelli cinque deda de diametro, el qual cubo &longs;ara <lb/>125. & questo. </s> <s id="s.000754">125. uoi lo adoppiareti, fara. </s> <s id="s.000755">250. & la radice cuba di que&longs;to. </s> <s id="s.000756">250. &longs;a­<lb/>ra el diametro di quella <expan abbr="&longs;ecõda">&longs;econda</expan> balla (doppia alla prima) la qual radice cuba de 250. <lb/>cauandola per el modo, che ui ho mo&longs;trato uoi trouareti, che la &longs;ara alquanto piu de <lb/>&longs;ei deda, cioe ui auanzara. </s> <s id="s.000757">34. rotti.<emph.end type="italics"/> Z. C<emph type="italics"/>ome mi debbio gouernare con quello. </s> <s id="s.000758">34. <lb/>che mi auanza per formar il conueniente rotto da accompagnar con quelli &longs;ei deda.<emph.end type="italics"/><lb/>N. L<emph type="italics"/>a bona regola di formar el rotto di quel re&longs;iduo, che auanza nella e&longs;tratione <lb/>della radice cuba (nelli numeri non cnbi) per fin à que&longs;ta hora maiho ritrouato in al­<lb/>cun Autore, che di tal materia habbia trattato, che l'habbia rettamente inte&longs;a, & que <lb/>&longs;to procede (&longs;e non me inganno) perche el retto modo da cauar la detta radice cuba, <lb/>dalla maggior parte è ignorato, <expan abbr="nõ">non</expan> dico ignorato, che quelli tali <expan abbr="nõ">non</expan> la &longs;appiano caua <lb/>re, ouer che le regole da lor po&longs;te, non &longs;eruino per cauarla, ma uoglio dire, che tai <lb/>&longs;ue regole non procedeno per la uera, & retta uia naturale, perche &longs;e que&longs;ti tali proce <lb/>de&longs;&longs;eno per la &longs;ua rettauia nel cauar la detta radice cuba, & che intendeßino po<gap/>la <lb/>cau&longs;a di tal &longs;uo operare, facile ui &longs;aria ad aßignare con ragione la uera regola da<emph.end type="italics"/><pb xlink:href="042/01/068.jpg"/><emph type="italics"/>&longs;ormar el &longs;uo rotto, nelli re&longs;idui restanti nel &longs;uo operare.<emph.end type="italics"/> Z. L<emph type="italics"/>a retta uia da cauare <lb/>la detta radice cuba, non eglie quella, che uoime baueti mo&longs;trata.<emph.end type="italics"/> N. Q<emph type="italics"/>uella pro­<lb/>pria.<emph.end type="italics"/> Z. D<emph type="italics"/>apoi che uoi me haueti mo&longs;trata tal regola, uoi me mo&longs;trareti pur ancho <lb/>ra el modo da formar rettamente el detto rotto.<emph.end type="italics"/> N. P<emph type="italics"/>er al pre&longs;ente uoi hareti pa­<lb/>tientia, ma ben ui prometto, che in breue con alcune altre co&longs;e in&longs;ieme ue le faro uede­<lb/>re à uoi, et alli altri.<emph.end type="italics"/> Z. N<emph type="italics"/>on potendo far altro haro patientia per fin a quel <expan abbr="t&etilde;po">tempo</expan>.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000759">QVESITO VNDECIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> M. Z<emph type="italics"/>anantonio di Ru&longs;coni.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000760">ZANANTONIO. C<emph type="italics"/>on che regola, ouer uia determina adunque Vetruuio <lb/>la proportione delle pietre, che &longs;e hanno da mettere al forame della Balista.<emph.end type="italics"/> N. <lb/>A<emph type="italics"/>de&longs;&longs;o me aricordo, che la ragione, che uoi me adimanda&longs;ti nel precedente Que&longs;ito é <lb/>proprio quella mede&longs;ima, che pone il detto Vittruuio al. <!-- REMOVE S-->17. capitulo del &longs;uo decimo li­<lb/>bro, nel qual luoco lui conclude, che &longs;el&longs;a&longs;&longs;o qual debbe tirare la bali&longs;ta &longs;ara dui pe&longs;i, <lb/>cioè de due libre) che el forame del &longs;uo capitello &longs;ara de. </s> <s id="s.000761">5. digiti, ouer dedi, e che &longs;e tal <lb/>&longs;a&longs;&longs;o &longs;ara de. </s> <s id="s.000762">4. libre, dice chel detto forame &longs;ia fatto de. </s> <s id="s.000763">6. digiti, ouer dedi, la qual de <lb/>terminatione é &longs;imile alla no&longs;tra fatta nel precedente Que&longs;ito re&longs;petto al numero &longs;a­<lb/>no, cioe al &longs;e&longs;to, ma non al rotto, perche quello. </s> <s id="s.000764">34. che in tal luoco ne auanzo ne <expan abbr="ri&longs;põ">ri&longs;pom</expan> <lb/>de a&longs;&longs;ai piu dun quarto de digito, cioe, che tal forame doueria e&longs;&longs;er alquanto piu de di­<lb/>giti. </s> <s id="s.000765">6. c un quarto.<emph.end type="italics"/> Z. P<emph type="italics"/>otria e&longs;&longs;er, che il fu&longs;&longs;e &longs;tato mal tradutto.<emph.end type="italics"/> N. E<emph type="italics"/>l mede&longs;i­<lb/>mo &longs;i trouanel Latino.<emph.end type="italics"/> Z. V<emph type="italics"/>edeti mo, &longs;e nelle altre &longs;ue determinationi, che &longs;eguitano <lb/>in tal luoco, &longs;ono giu&longs;tamente <expan abbr="cõclu&longs;e">conclu&longs;e</expan>.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio ui è qualche errore, ma piu <lb/>in una, che nell'altra, & credo tutto que&longs;to proceda per ignorare quella regola da noi <lb/>ritrouata (detta nel precedente Que&longs;ito) di &longs;apere formare el &longs;uo conueniente rotto <lb/>di quel re&longs;iduo, che auanza nelle e&longs;trationi delle radice cube, nelli numeri non cubi, & <lb/>che el &longs;ia eluero, lui conclude, che &longs;el&longs;a&longs;&longs;o, che &longs;e ha da tirare &longs;ara de. </s> <s id="s.000766">7. libre, che el fo <lb/>rame del capitello de detta bali&longs;ta &longs;i debbia far de digiti. </s> <s id="s.000767">7. & per el rotto, che debbe <lb/>e&longs;&longs;er de piu de detti digiti. </s> <s id="s.000768">7. lui mette noue ponti in forma qua&longs;i circulare.<emph.end type="italics"/> Z. C<emph type="italics"/>he <lb/>&longs;a, che quelli. </s> <s id="s.000769">9. ponti non &longs;ignificano el conueniente rotto, ouer parte de digiti, che uol <lb/>e&longs;&longs;er el detto forame de piu delli detti. </s> <s id="s.000770">7. digiti, quantunque che noi non intendamo el <lb/>&longs;igni&longs;icato de detti noue ponti, per e&longs;&longs;er co&longs;a antiqua.<emph.end type="italics"/> N. Q<emph type="italics"/>uando co&longs;i fu&longs;&longs;e nece&longs;­<lb/>&longs;ariamente &longs;eguitaria, che in qualunque luoco doue &longs;ono po&longs;ti quelli tali noue ponti, ui <lb/>repre&longs;enta&longs;&longs;ono uno mede&longs;imo rotto, la qual co&longs;a non è uera, perche nelli detti luochi <lb/>ui occorre rottimolto diuer&longs;i in quantita, e&longs;&longs;empi gratia, al detto &longs;a&longs;&longs;o de &longs;eilibre, el <lb/>detto forame uora e&longs;&longs;er de. </s> <s id="s.000771">7. digiti, & circa a uno ottauo de digito, cioe uol e&longs;&longs;er al­<lb/>quanto &longs;car&longs;o de. </s> <s id="s.000772">7. digiti, & uno ottauo de digito. </s> <s id="s.000773">Et per tanto quellinoue ponti, in <lb/>tal luoco ueneriano a &longs;ignificare alquanto manco de uno ottauo de digito. </s> <s id="s.000774">Et nel &longs;a&longs;&longs;o <lb/>de diece libre lui conclude, che el detto forame uora e&longs;&longs;er de. </s> <s id="s.000775">8. digiti, & piu el &longs;ignifi­<lb/>cato de detti noue ponti, & noi procedendo per l'ordine dato nel precedente Que&longs;ito, <lb/>ritrouamo che el detto &longs;a&longs;&longs;o de diece libre, uora di forame alquanto piu de digiti otto e <lb/>mezzo, per il che &longs;eguitaria, che li detti noue ponti nel detto luoco &longs;ignifica&longs;&longs;ono al-<emph.end type="italics"/><pb pagenum="35" xlink:href="042/01/069.jpg"/><emph type="italics"/>quanto piu d'un mezz digito, & gia di &longs;opra trouaßimo, che &longs;ignificauano manco d'un <lb/>ottauo de digito, la qual co&longs;a ne manife&longs;ta qualmente li detti nuoue ponti non hanno al­<lb/>cuna regolata &longs;ignificatione, & &longs;imilmente ne aduerti&longs;&longs;e qualmente Vitruuio non haue <lb/>uaregola di &longs;apere formare rettamente il rotto di quel re&longs;iduo che &longs;oprauanza nelle <lb/>e&longs;trattioni delle radice, cube, nelli numeri non cubici (che di &longs;opra nel precedente que­<lb/>&longs;ito diceßimo hauer ritrouata) la qual diceßimo anchora e&longs;&longs;er &longs;tata ignorata da quanti <lb/>Autori habbiamo letto, che di tal materia habbiam trattato.<emph.end type="italics"/> Z. N<emph type="italics"/>on po&longs;&longs;o credere, <lb/>che Vitruuio ignora&longs;&longs;e tal co&longs;a, ma la cau&longs;a debbe e&longs;&longs;er proce&longs;&longs;a dalli traduttori.<emph.end type="italics"/> N. <lb/>I<emph type="italics"/>l mede&longs;imo è nelli antichißimi in lingua Latina, ma piu che nel &longs;a&longs;&longs;o de. </s> <s id="s.000776">20. libre, lui <lb/>determina che il detto forame uorra e&longs;&longs;er de digiti diece, & piu il &longs;ignificato di detti <lb/>nuoue ponti, & noi ritrouamo, che tal forame uorra e&longs;&longs;er de digiti diece, & piu de tre <lb/>quarti d'un' altro digito, onde in que&longs;to luoco li detti nuoue ponti ueneriano à &longs;ignifi­<lb/>care piu de tre quarti d'un digito, & co&longs;i ua procedendo, & errando qua&longs;i in tutte le <lb/>altre &longs;ue determinationi che &longs;eguitano.<emph.end type="italics"/> Z. M<emph type="italics"/>e &longs;tupi&longs;co che tal huomo habbia erra­<lb/>to in &longs;imil ca&longs;o.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000777">QVESITO DVODECIMO FATTO DAL <lb/>S<emph type="italics"/>ignor lacomo di Achaia, Con una &longs;ua lettera <lb/>mandata da Lezze.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000778">SIGNOR IACOMO. I<emph type="italics"/>o ui prego di gratia, che per il lattor della pre&longs;ente, <lb/>me uogliati mandar in di&longs;&longs;egno quanto &longs;ia, ouer debbia e&longs;&longs;ere il diametro di una <lb/>palla di uno rotulo à pe&longs;o, & co&longs;i quello di una, di dui rotuli, & &longs;imilmente datre, da <lb/>quattro, da cinque, da &longs;ei, & co&longs;i procedendo per fina à quella maggior quantita de <lb/>rotuli, che à uoi parera.<emph.end type="italics"/> N. <!-- KEEP S--></s> <s id="s.000779">A <emph type="italics"/>douer &longs;atisfare alla dimanda di uostra Signoria, eglie <lb/>nece&longs;&longs;ario che quella me dia notitia del diametro, & del pe&longs;o di una balla con &longs;omma di <lb/>ligentia mi&longs;urata, & pe&longs;ata, cioe ueder di trouare una balla, & quanto piu è gro&longs;&longs;a tan <lb/>to è meglio, & quella pe&longs;arla &longs;ottilmente, come &longs;e fu&longs;&longs;e di argento, & dapoi trouar dili<lb/>gentemente quanto è per diametro, cioe quanto è per linea, & dapoi mandarme in di&longs;­<lb/>&longs;egno la longhezza di tal diametro, etiam la quantita del pe&longs;o di tal balla, & darmi an <lb/>chor notitia, ouer in&longs;ormatione che pe&longs;o &longs;ia un rotulo, & come &longs;e diuide, cioe quante li <lb/>re, ouer onze &longs;ia, perche tal &longs;orte de pe&longs;o non &longs;e co&longs;tuma in que&longs;te bande, & facendo <lb/>questo &longs;atisfaro alla petitione, ouer que&longs;ito de uo&longs;tra Signoria.<emph.end type="italics"/> S.I. M. N<emph type="italics"/>icolo cari&longs;­<lb/>&longs;imo ho riceuuta la uo&longs;tra, & inte&longs;o il tutto, e per tanto ui aui&longs;o qualmente la &longs;otto&longs;crit <lb/>ta linea è il diametro di una balla di ferro, qual pe&longs;a preci&longs;amente. </s> <s id="s.000780">9. rotuli, & &longs;appiati <lb/>che un rotulo è un certo pe&longs;o che &longs;i u&longs;a qua in Lezze, il qual rotulo è onze. </s> <s id="s.000781">33. e un ter <lb/>zo di on za, cioe onze. </s> <s id="s.000782">100. &longs;ono tre rotuli.<emph.end type="italics"/> N. S<emph type="italics"/>ignor Iacomo honor andißimo ho ri<lb/>ceuuta la uostra in&longs;ieme con il diametro di una balla de rotuli. </s> <s id="s.000783">9. con il qual diametro <lb/>ue ho ritrouato il diametro delle &longs;otto&longs;critte, & piu ue ne haria ritrouato, ma mi ho <lb/>pen&longs;ato, che que&longs;ti debbano e&longs;&longs;er à &longs;ufficientia, per quello de&longs;idera uo&longs;tra Signoria, & <lb/>per piu commune &longs;atisfattione ho uoluto tirar tal pe&longs;o de rotuli al pe&longs;o de queste ban­<lb/>de, cioe à onze. </s> <s id="s.000784">33. e un terzo per rotulo, & perche alcuni diametri ueniuano tanto lon <pb xlink:href="042/01/070.jpg"/>ghi che non poteuduo capire nel foglio, ui ho notato &longs;olamente la mitade di tal diame­<lb/>tro, come quella potra uedere, & &longs;e il diametro, che quella me ha mandato è giu&longs;to, an­<lb/>chora questida me geometricamente ritrouati, &longs;ar anno giu&longs;ti, & &longs;e quella hauera <expan abbr="cõ-me&longs;&longs;o">con­<lb/>me&longs;&longs;o</expan> alcuno errore, nel detto diametro à me mandato, anchor li miei non &longs;aranno &longs;en-<emph.end type="italics"/><lb/><figure id="id.042.01.070.1.jpg" xlink:href="042/01/070/1.jpg"/><pb pagenum="36" xlink:href="042/01/071.jpg"/><emph type="italics"/>zamenda, &longs;imilmente &longs;e il uo&longs;tro rotulo è giu&longs;tamente onze. </s> <s id="s.000785">33. e un terzo, & le lire <lb/>da me determinate &longs;opra detti diametri &longs;tar anno bene à ragion de onze. </s> <s id="s.000786">12. per lira, <lb/>& &longs;i taluo&longs;tre onze &longs;aranno eguale alle no&longs;tre onze qua da Venetia, anchora le dette <lb/>balle &longs;e uerificaranno al no&longs;tro pe&longs;o da Venetia, altr amente non.<emph.end type="italics"/></s> </p> <figure id="id.042.01.071.1.jpg" xlink:href="042/01/071/1.jpg"/> <pb xlink:href="042/01/072.jpg"/> <p type="main"> <s id="s.000787">VERO <emph type="italics"/>è, che tutte le balle gettate in una mede&longs;ima forma non <lb/>&longs;aranno pre­<lb/>ci&longs;amente d'un mede&longs;imo pe&longs;o, perche in una il metallo ui &longs;e congella alle uol­<lb/>te piu fi&longs;&longs;o, ouer piu poro&longs;o che nell'altra per molte cau&longs;e le quale non uoglio al pre­<lb/>&longs;ente &longs;tar à narrarle, ma &longs;olamente me appar&longs;o de aduertirui, accio che &longs;e la nostra de­<lb/>terminatione, non ui ri&longs;ponde&longs;&longs;e co&longs;i preci&longs;amente, come habbiamo determinato, che <lb/>quella non &longs;e ne debbia &longs;candalizzare, perche tutte le co&longs;e operate in materia, mai pon <lb/>no e&longs;&longs;er fatte co&longs;iuere è preci&longs;e, che &longs;empre le <expan abbr="nõ">non</expan> poßano e&longs;&longs;ere piu uere, et piu preci&longs;e.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000788">ANCHORA V<emph type="italics"/>ostra Signoria aduerti&longs;ca, che &longs;e il detto diametro <lb/>à me man­<lb/>dato fu di una balla di ferro (come me haueti &longs;critto) tutti li no&longs;tri &longs;e debbono <lb/>intendere &longs;olamente &longs;opra balle di ferro, & non di piombo, ma uolendoli etiam adat­<lb/>tare alle balle di piombo, bi&longs;ogna augumentarui il &longs;uo pe&longs;o per la &longs;ua mita, cioe &longs;elo <lb/>detto diametro è di balla di ferro, & che quella pe&longs;i, come detto rotuli.<emph.end type="italics"/> 9 (<emph type="italics"/>ouer lire.<emph.end type="italics"/><lb/>25.) <emph type="italics"/>dico che un'altra di piombo gettata in quella mede&longs;ima forma pe&longs;ara, circa à un <lb/>tanto è me<emph.end type="italics"/>zz<emph type="italics"/>o, cioe rotuli. </s> <s id="s.000789">13. e mezzo, ouer lire. </s> <s id="s.000790">37. e mezza, perche il piom­<lb/>bo, al ferro in grauita &longs;ta qua&longs;i in &longs;e&longs;quialtera proportione, & co&longs;i &longs;i debbe intendere <lb/>in tutti glialtri. </s> <s id="s.000791">Et che ne uole&longs;&longs;e farne far de pietra commune &longs;opra la mi&longs;ura di alcu­<lb/>no di detti diametri, tal balla pe&longs;ara circa la quarta parte di quello pe&longs;aria quella de <lb/>piombo, cioe che la proportione della pietra marmorina al piombo in pondero&longs;ita é <lb/>qua&longs;i &longs;ubquadrupla, & con il ferro è qua&longs;i come da. </s> <s id="s.000792">15. à. </s> <s id="s.000793">38. per la qual notitia &longs;e po­<lb/>tra trouar la grauita di qual &longs;iuoglia balla, &longs;opra qual &longs;i uoglia diametro aßignato, & <lb/>accio che meglio quella lo po&longs;&longs;a tener in memoria qua di &longs;otto ui ho notata la detta lor <lb/>proportione di&longs;tintamente.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000794">I<emph type="italics"/>l piombo al ferro è qua&longs;i come. </s> <s id="s.000795">30. à. </s> <s id="s.000796">19. cioe qua&longs;i &longs;e&longs;quialtera.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000797">I<emph type="italics"/>l piombo al pietra marmorina è qua&longs;i come. </s> <s id="s.000798">4. à.<emph.end type="italics"/> 1. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000799">I<emph type="italics"/>l ferro alla pietra è qua&longs;i come. </s> <s id="s.000800">38. à.<emph.end type="italics"/> 15. </s> </p> <p type="head"> <s id="s.000801">I<emph type="italics"/>l fine del Secondo Libro.<emph.end type="italics"/><!-- KEEP S--></s> </p> </subchap1><subchap1> <pb pagenum="37" xlink:href="042/01/073.jpg"/> <p type="head"> <s id="s.000802">LIBRO TERZO DELLI <lb/>QVESITI ET INVENTIONI DIVERSE, <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000803">S<emph type="italics"/>opra del Salnitrio, & delle uarie compo&longs;itioni della poluere delle arte­<lb/>gliarie, & della proprietà, ouer particular officio, che ha <lb/>cadauno di &longs;uoi tre materiali in tal compo&longs;itione, <lb/>& altre particolarita.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000804">QVESITO PRIMO FATTO DAL SIGNOR <lb/>G<emph type="italics"/>abriel Tadino Priore di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000805">PRIORE. N<emph type="italics"/>on é da mar auigliar&longs;i, che gli autiqui non haue&longs;&longs;ero <lb/>notitia del &longs;alnitrio, qual à noi moderni è fatto tanto famigliare.<emph.end type="italics"/><lb/>N. A<emph type="italics"/>nzi la notitia di tal &longs;implice è antiquißima, perche el &longs;i uede <lb/>tutti li antiqui Phy&longs;ici, ouer naturali farne mentione, uero è che al <lb/>cuni (& maßime Auicenna) l'hanno chiamata, Baurach, perche co <lb/>&longs;i in lingua Arabica è nominato, & alcuni altri gli dicono, Afro­<lb/>nitrum, perche da Greci co&longs;i è detto, & altri poi (& maßime Sera <lb/>pione, Dia&longs;coride, & Plinio) lo chiamano Nitro, ouer &longs;puma ni­<lb/>tri, perche in lingua Latina co&longs;i è nominato, & nelle Pandete &longs;e affermale &longs;pecie del <lb/>nitro, ouer &longs;alnitri, e&longs;&longs;er due, cioe minerale, & artificiale, & del minerale, dicono e&longs;­<lb/>&longs;eruen di. </s> <s id="s.000806">4. &longs;orte, cioe Armeno, Affricano, Romano, & Egyptio. </s> <s id="s.000807">Et Serapione dice, <lb/>che le minere del &longs;alnitrio, &longs;ono come le minere de &longs;ali, perche di quello &longs;e ne troua, che <lb/>&longs;ono acque &longs;corrente, le quale acque &longs;e congellano, et &longs;i conden&longs;ano qua&longs;i, come pietra, <lb/>& que&longs;to mede&longs;imo afferma Plinio, & &longs;e ne troua anchora, che nella &longs;ua minera è co­<lb/>me pietra, & chiama&longs;i &longs;al petro&longs;o, anchor dice, che di que&longs;to &longs;alnitrio &longs;e ne troua de <lb/>bianco, de ro&longs;&longs;o, & de molti colori, & per tanto a&longs;&longs;erma le &longs;pecie di quello e&longs;&longs;er molte, <lb/>non &longs;olamente per la diuer&longs;ita del colore, ma perche ui &longs;e ne troua prima una &longs;pecie, <lb/>che è molto &longs;pongo&longs;o, cioe pieno de forami, & un'altra poi che uiene in lamine frangi <lb/>bìle, & de molte altre qualita, che longo &longs;aria à starle à narrare à una per una: delle <lb/>quale una è piu mordente, & potente dell'altra, del Artificiale poi non accade à par­<lb/>larne, per e&longs;&longs;er à que&longs;ti tempi piu cognito, che la herba Betonica.<emph.end type="italics"/> P. C<emph type="italics"/>erto credeua <lb/>che la notitia &longs;ua fu&longs;&longs;e moderna.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000808">QVESITO SECONDO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000809">PRIORE. D<emph type="italics"/>itime un poco, &longs;e gli antiqui bebbero cognitione del &longs;alnitrio &longs;i <lb/>del naturale, come del artificiale (come di &longs;opra haueti approuato) per autori­<lb/>ta de antiqui Phy&longs;ici, hebbero poi notitia che quello arde&longs;&longs;e abbru&longs;a&longs;&longs;e co&longs;i uigoro&longs;a­<lb/>mente come fa.<emph.end type="italics"/> N. C<emph type="italics"/>ertamente li&longs;opradetti antiqui naturali non fanuo mentione,<emph.end type="italics"/><pb xlink:href="042/01/074.jpg"/><emph type="italics"/>&longs;aluo di quelle proprietà, che in lui&longs;e ritruoua, alla medicina nece&longs;&longs;arie, & non d'al­<lb/>tro: ma molti altri antiqui autori, ne fanno certißimi, che lor &longs;eppero, che abbru&longs;aua, <lb/>perche loro &longs;e ne &longs;eruiuano nelle compo&longs;itioni de alcuni fuochi, per abbru&longs;are le te&longs;tu <lb/>dine, ouer ariete, & le ellepoli, & altre torre portatile, che nelle i&longs;pugnationi delle cit <lb/>ta à quel tempo &longs;i u&longs;aua: Et &longs;imilmente per abbru&longs;are le armate nauale, uero e che in <lb/>tai compo&longs;itioni alcuni el chiamano &longs;al ardente, altri el chiamano &longs;al petro&longs;o, altri el <lb/>chiamano &longs;al praticha, & altri el chiamano proprio, &longs;alnitrio.<emph.end type="italics"/> P. C<emph type="italics"/>irca di que&longs;io ui <lb/>ho da adimandarui un'altro dubbio: ma perche el mi dole alquanto la te&longs;ta, lo uoglio re <lb/>mettere à doman de &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000810">QVESITO TERZO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000811">PRIORE. S<emph type="italics"/>e gli antiqui hebbero cognitione, chel &longs;alnitrio bru&longs;aua, & arde­<lb/>ua con quella uigoro&longs;ita che fa, perche non &longs;eppero far la poluere delle arte­<lb/>gliarie di tanta importanza nell'arte militare, come noi moderni.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;ta con­<lb/>&longs;e que ntia non è bona, à dire, che &longs;e li antiqui hebbero notitia del &longs;alnitrio, & che &longs;a­<lb/>pe&longs;&longs;ono, che ardeua, ouer bru&longs;aua, che de neceßita doue&longs;&longs;ono &longs;aper componere la pol <lb/>uere delle artegliarie, perche la detta poluere non &longs;i fa de &longs;alnitrio puro, anzi &longs;e com <lb/>pone de tre materiali (come credo, che quella &longs;appia) cioe di &longs;alnitrio, &longs;olfere, & car <lb/>bone. </s> <s id="s.000812">Et pero eglie co&longs;a credibile, chel &longs;ia poßibile hauer <expan abbr="cognītione">cognintione</expan> del &longs;alnitrio, <lb/>& della natura di quello, & ignorare la compo&longs;itione della detta poluere.<emph.end type="italics"/> P. V<emph type="italics"/>oi <lb/>haueti ragione.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000813">QVESITO QVARTO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000814">PRIORE. C<emph type="italics"/>on che ragione, ouer perche cau&longs;a la detta poluere delle arteglia <lb/>rie, &longs;e compone co&longs;i de que&longs;ti tre materiali, cioe de &longs;alnitrio, &longs;olfere, et carbone, <lb/>& non de altri &longs;implici, & que uirtu, ouer officio particolare ha cadauno di detti tre <lb/>materiali, ouer &longs;implici per &longs;e in tal compo&longs;itione, & que effetto faria ogni dui di lo <lb/>ro &longs;enza el terzo.<emph.end type="italics"/> N. T<emph type="italics"/>al poluere &longs;e compone co&longs;i de detti tre materiali, perche ca <lb/>dauno loro medica, & &longs;uppli&longs;&longs;e ad alcun difetto de alcun delli altri dui, perche el &longs;ol­<lb/>fere è piu atto di accendere il fuoco con fiamma (e&longs;&longs;endo alquanto tocco da quello) de <lb/>alcun delli altri dui, el qual fuoco con fiamma é molto piu atto à introdur in fuoco el <lb/>&longs;alnitrio di qualunque altro fuoco, & perche el detto &longs;alnitrio bru&longs;ando &longs;e ri&longs;olue in <lb/>e&longs;&longs;alatione uento&longs;a, la quale è tanto potente, che &longs;ubito amorzarebbe la fiamma gia <lb/>introdutta nel &longs;olfere, & con&longs;equentemente quella introduta (per quella del &longs;olfere) <lb/>nel medemo &longs;alnitrio, & perche la natura del &longs;olfere, & &longs;imelmente quella del &longs;alni­<lb/>trio è tale, che morta la fiamma, non ui re&longs;ta alcuna minima in&longs;egna di fuoco, & per <lb/>tanto componendo in&longs;ieme &longs;olamente &longs;alnitrio, & &longs;olfere ottimamente pi&longs;ti, & acco­<lb/>&longs;tandoui el fuoco, immediate tal fuoco ui &longs;e accendera, & immediate ui &longs;e de&longs;tuara,<emph.end type="italics"/><pb pagenum="38" xlink:href="042/01/075.jpg"/><emph type="italics"/>per le ragioni di &longs;opra dette, cioe, che tal fuoco non continuera per fina che &longs;ia con&longs;u­<lb/>mata, ouer abbru&longs;ata tutta la materia, ma &longs;olamente ne abbru&longs;ara un poco, & lo re­<lb/>&longs;tante re&longs;tara non offe&longs;a dal detto fuoco, onde per medicare que&longs;to difetto, ui&longs;e mc&longs;co <lb/>la con ambidui el carbone ottimamente poluerizato, perche el carbone è di tal natu­<lb/>ra, che tocco dalla fiamma del fuoco &longs;ubito &longs;i accende, & &longs;i conuerte in fuoco &longs;enza <lb/>fiamma, el qual fuoco &longs;enza fiamma, quanto piu è ue&longs;&longs;ado dalcun uento, tanto piu&longs;i ac <lb/>cende, & con&longs;erua per fina à tanto, che ogni &longs;ua &longs;o&longs;tantia &longs;ia conuer&longs;a in cenere, e per <lb/>tanto, toccando tal compo&longs;itione con el fuoco immediate el &longs;olfere &longs;i apprende <expan abbr="cõ">com</expan> <expan abbr="fiã-ma">fian­<lb/>ma</expan> (come detto) la qual fiamma non &longs;ola nente mtrodu&longs;&longs;e immediate fuoco e fiamma <lb/>nel &longs;alnitrio, ma etiam in quello i&longs;tante introdu&longs;&longs;e fuoco &longs;enza fiamma nel carbone, el <lb/>qual fuoco, per alcun uento non &longs;e e&longs;tingue, anzi &longs;e augmenta, & pero quel uento cau­<lb/>&longs;ato dal &longs;alnitrio, non è atto à poter ammorzar quel fuoco &longs;enza fiamma, che é nel car <lb/>bone anzi, come ho detto lo augmenta, & perche il &longs;olfer e&longs;&longs;endo contiguo con el fuo <lb/>co, ò &longs;ia con fiamma, ouer &longs;enza fiamma, non puo &longs;tar &longs;enza fiamma la qual fiamma, <lb/>come detto infiamma el &longs;alnitrio, e pero que&longs;titre materiali pi&longs;ti, & mi&longs;ti ottimamen <lb/>te in&longs;ieme, & in tal mi&longs;tur a introdutoui el fuoco tal fuoco uien à e&longs;&longs;ere ine&longs;tinguibile, <lb/>per fin che non &longs;ia con&longs;umata ogni &longs;ostantia (&longs;aluo &longs;e in alcuno de detti materiali non <lb/>fu&longs;&longs;e qualche accidental di&longs;etto, ò de humidita, ouer che fu&longs;&longs;eno tolti molto differenti <lb/>di la &longs;ua conueniente proportione) & pero &longs;e conclude, che lo officio del &longs;olfere in tal <lb/>compo&longs;itione è &longs;olamente per apprendere il fuoco con fiamma, & introdurlo nelli al­<lb/>tri dui materiali, & quello del carbone è &longs;olamente de mantenere el detto fuoco &longs;enza <lb/>fiamma, gia introdutoui dal &longs;olfere, & maßime contra quel gran uento, che cau&longs;a el <lb/>&longs;alnitrio, ma lo officio poidel detto &longs;alnitrio è &longs;olamente per cau&longs;ar quella co&longs;i gran­<lb/>dißima e&longs;&longs;alatione di uento, perche in quel tal uento con&longs;i&longs;te tutta la uirtu, et proprie <lb/>ta di la poluere, perche quello è &longs;olamente quello, che fpmge co&longs;t uigoro&longs;amente ogni <lb/>balla, & per tanto &longs;e conclude, che &longs;olamente dal &longs;alnitrio depende tutta la uirtu, e <lb/>po&longs;&longs;anza della poluere, & li altri dui &longs;implici, ouer materiali, cioe el &longs;olfere, & el car <lb/>bone ui&longs;e pongono &longs;olamente per ri&longs;oluere in fuoco, e uento el detto &longs;alnitrio, e non <lb/>per altro, perche chi compone&longs;&longs;e poluere &longs;olamente de &longs;olfere, e carbone, & che di <lb/>quella &longs;e ne carga&longs;&longs;e una artegliaria à gran misura, dico che in tal &longs;orte di poluere in­<lb/>troducendoui el fuoco, la non &longs;aria atta à &longs;pingere fora di detta artegliaria un minime <lb/>legnetto, ouer una paglia, & que&longs;to procede, perehe tutta quella utrtu e&longs;pul&longs;iua de­<lb/>pende &longs;olamente dal puro &longs;alnitrio, & non da altro, e per tanto el&longs;e potria piu pre&longs;to <lb/>concludendo dire e&longs;&longs;er piu poßibile à fare poluere de artegliaria, &longs;enza carbone, & <lb/>&longs;olfere, che &longs;enza &longs;alnitrio, perche eglie da credere e&longs;&longs;er piu poßibile à trouar altri <lb/>materiali, che face&longs;&longs;eno lo officio del &longs;olfere in apprendere el fuoco con fiamma, & <lb/>&longs;imelmente del carbone in mantenerui el detto fuoco &longs;enza fiamma, che à ritrouarne <lb/>uno altro, che fu&longs;&longs;e atto à cau&longs;ar tanto grande, & impetuo&longs;o uento, come fa el detto &longs;al <lb/>nitrio.<emph.end type="italics"/> P. E<emph type="italics"/>glie da credere che &longs;ia piu pre&longs;to poßibile à componere poluere buona <lb/>&longs;enza carbone e&longs;olfere, che &longs;enza &longs;alnitrio, perche tutta la uirtu e po&longs;&longs;anza della pol <lb/>uere (come di &longs;opra haueti detto) depende dal puro &longs;alnitrio, & non da altro, ma per <lb/>ßer hora tarda, uoglio facciamo fine.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/076.jpg"/> <p type="head"> <s id="s.000815">QVESITO QVINTO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Priore di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000816">PRIORE. H<emph type="italics"/>ier&longs;erauoi aßigna&longs;tila cau&longs;a, perche la poluere &longs;e compone co&longs;i <lb/>co&longs;i di quelli tre materiali, & che officio ha cadauno de dittimateriali, in tal <expan abbr="cõ">com</expan> <lb/>po&longs;itione, hor ue adimando, che fu inuentor di tal poluere, & con che ragione fu de­<lb/>terminata da quello, la proportione della quantita di cadauno materiale conueniente à <lb/>tal compo&longs;itione.<emph.end type="italics"/> N. C<emph type="italics"/>he fu&longs;&longs;e inuentor di que&longs;ta poluere, & della artegliaria, fra <lb/>el uulgo è &longs;parto, per autorita del Cornazano, qual dice, che futrouata à ca&longs;o da un <lb/>Tode&longs;co Alchimista, ma io &longs;on di openione, che di tal compo&longs;itione Archimede Sira­<lb/>cu&longs;ano<emph.end type="italics"/> (P<emph type="italics"/>hilo&longs;opho, & Mathematico peritißimo) ne fu&longs;&longs;e inuentore (& di que&longs;ta me <lb/>dema opinione è il commentator di Vitruuio &longs;opra el primo libro à carte.<emph.end type="italics"/> 8.) <emph type="italics"/>perche <lb/>di lui &longs;i troua in molti luochi in &longs;critto (come narra Valturio nel decimo libro de remi­<lb/>litare) qualmente lui trouo una certa &longs;pecie di machina di ferro, con la quale lui tra&longs;e <lb/>ua uer&longs;o lo e&longs;&longs;ercito terre&longs;to &longs;aßi di grandißimo pe&longs;o, e grandezza, & con uno incre­<lb/>dibel &longs;uono, la qual co&longs;a ne da ad intendere, che fu&longs;&longs;e una machina &longs;imile à una arteglia <lb/>ria, ma che tir a&longs;&longs;e balle di pietra großißime, come che anchor a non è molto tempo, che <lb/>fra moderni&longs;i co&longs;tumaua, & maßime per quel incredibel &longs;uono, che nel tirarla ui oc­<lb/>corre, el qual &longs;uono, in altra&longs;orte di machina da tirar, à me non pare, che ui&longs;e po&longs;&longs;a <lb/>cau&longs;are, &longs;aluo che in una &longs;imile alla artegliaria, uero é, che à quel tempo io tengo, che <lb/>fu&longs;&longs;eno molto difforme, & piu di&longs;conze di quelle, che alli pre&longs;enti tempi &longs;i co&longs;tuma, <lb/>perche &longs;empre le prime inuentioni teneno del rustico, ma con el tempo &longs;e uanno meglio <lb/>rando, per e&longs;&longs;er co&longs;a facile aggiongere alle co&longs;e trouate, & il mede&longs;imo dico della pol <lb/>uere, cioe, che al principio, che la fu trouata (ò da Archimede, ouer da chi &longs;i uoglia) <lb/>eglie da credere, che in quel tempo la non&longs;e compone&longs;&longs;e con tal ordine e proportione, <lb/>come che al pre&longs;ente &longs;i co&longs;tuma, anzi giudico, che da quel tempo in qua &longs;e &longs;ia uariato <lb/>l'ordine da componerla qua&longs;i infiniti modi, & che el &longs;ia el uero, io ho ritrouato &longs;opra <lb/>alcuni libri non molto antiqui certi modi, & ordinida componerla, molto differenti <lb/>dalli piu moderni.<emph.end type="italics"/> P. D<emph type="italics"/>itime un poco, che proportion o&longs;&longs;eruamo, & o&longs;&longs;eruauano.<emph.end type="italics"/><lb/>N. I<emph type="italics"/>o ho ritrouato in alcuni piu antiqui libri, che à uoler far poluere di bombarda uo <lb/>leuano, che &longs;e piglia&longs;&longs;e de cadauno di &longs;opra detti tre materiali parte equale, cioe tanto <lb/>de l'uno, quanto de l'altro. </s> <s id="s.000817">Et alcuni altri dapoi uoleuano che &longs;e piglia&longs;&longs;e parte. </s> <s id="s.000818">3. di <lb/>&longs;alnitrio, & parte. </s> <s id="s.000819">2. di &longs;olfere, & parte. </s> <s id="s.000820">2. di carbone. </s> <s id="s.000821">Alcuni altri poi uoleuano, che <lb/>per far la detta poluere di bombarda &longs;e toglie&longs;&longs;e lire. </s> <s id="s.000822">10. di &longs;alnitrio, & lire. </s> <s id="s.000823">3. di &longs;olfe <lb/>re, & lire. </s> <s id="s.000824">3. di carbone. </s> <s id="s.000825">Et alcuni altri uoleuano, che &longs;e piglia&longs;&longs;e lire. </s> <s id="s.000826">12. di &longs;alnitrio, <lb/>& lire. </s> <s id="s.000827">3. di &longs;olfere, & lire. </s> <s id="s.000828">2. di carbone. </s> <s id="s.000829">Altriuoleuano che &longs;i toglie&longs;&longs;e parte. </s> <s id="s.000830">9. di &longs;al <lb/>nitrio, & parte. </s> <s id="s.000831">2. di &longs;olfere, e parte. </s> <s id="s.000832">3. di carbone, et alcuni altri piu moderni per far <lb/>la per &longs;chioppiuoleuano, che &longs;e piglia&longs;&longs;e parti. </s> <s id="s.000833">4. de &longs;alnitrio, & parte una di &longs;olfere, <lb/>& parte. </s> <s id="s.000834">1. di carbone: alcuni altri han detto, che per far poluere gro&longs;&longs;a&longs;i doue&longs;&longs;e pi­<lb/>gliare parti. </s> <s id="s.000835">20. di &longs;alnitrio, et parti. </s> <s id="s.000836">3. di &longs;olfere, et parti. </s> <s id="s.000837">10. di carbon, & <21> farla al <lb/>quanto piu fina per &longs;chioppi <expan abbr="hãno">hanno</expan> detto, che &longs;i doue&longs;&longs;e tore parti. </s> <s id="s.000838">100. di &longs;alnitrio, & <lb/>parti. </s> <s id="s.000839">10. di &longs;olfe re, et parti. </s> <s id="s.000840">36. di carbone, altri dicono che <21> far poluere gro&longs;&longs;a, che<emph.end type="italics"/><pb pagenum="39" xlink:href="042/01/077.jpg"/><emph type="italics"/>&longs;i debbiatuor parti. </s> <s id="s.000841">100. di &longs;alnitrio, et parti. </s> <s id="s.000842">20. di &longs;olfere, et parti. </s> <s id="s.000843">37. dicarbone. </s> <s id="s.000844">Et <lb/><21> farla fina parti. </s> <s id="s.000845">9. &longs;alnitrio, parti. </s> <s id="s.000846">3. &longs;olfere, et parti. </s> <s id="s.000847">6. de fior de mirochea (cioe <expan abbr="hã-no">han­<lb/>no</expan> tentato di farla &longs;enza carbone, anchor che tal herba à me &longs;ia incognita, perche tal <lb/>nome di herba mai ho potuto ritrouare, ne in le Pandete, ne in Auicenna, ne in alcun <lb/>herbolario) alcuni altri piu moderni poi hanno detto, che per fare la poluer gro&longs;&longs;a &longs;e <lb/>debbia pigliare &longs;alnitrio parti. </s> <s id="s.000848">2. &longs;olfere parti. </s> <s id="s.000849">1. carbon de &longs;alice parti. </s> <s id="s.000850">1. Et per far <lb/>quella de archibu&longs;i dicono che &longs;i debbia pigliare &longs;alnitrio parti. </s> <s id="s.000851">3. carboni de rami di &longs;a <lb/>lice giouani, parte. </s> <s id="s.000852">1. &longs;olfere parti. </s> <s id="s.000853">1. Et à far la poluer fina de &longs;chioppo dicono, che &longs;e <lb/>debbia pigliare &longs;alnitrio raffinato piu uolte parti. </s> <s id="s.000854">5. &longs;olfere parti. </s> <s id="s.000855">1. carbone de uerghet <lb/>te di Auellane, ouer nocelle giouine de un'anno parti. </s> <s id="s.000856">1. alcuni altri dicono, che per far <lb/>poluer gro&longs;&longs;a, che &longs;i debbia tuor parti. </s> <s id="s.000857">3. de &longs;alnitrio raffinato, & parti. </s> <s id="s.000858">1. di &longs;olfere, et <lb/>parti. </s> <s id="s.000859">2. di carbon de &longs;alice, & per fare la poluere mezzana dicono, che &longs;i debbia pi­<lb/>gliare parti. </s> <s id="s.000860">10. di &longs;alnitrio raffinato, & parti. </s> <s id="s.000861">2. di &longs;olfere, & parti. </s> <s id="s.000862">3. di carbon de &longs;a <lb/>lice, & per farla fina de archibu&longs;i dicono, che &longs;e debbia pigliar parti. </s> <s id="s.000863">10. di &longs;alnitrio <lb/>raffinato &longs;olfer parti. </s> <s id="s.000864">1. carbon de uerzelle de nizola monde pur parte. </s> <s id="s.000865">1. Et per farla <lb/>migliore, eioe per &longs;chioppo, uogliono che &longs;e toglia parti. </s> <s id="s.000866">27. de &longs;alnitrio raffinato &longs;ol­<lb/>fere parti. </s> <s id="s.000867">3. carbone pur de uerzelle de nizola monde parti. </s> <s id="s.000868">4. alcuni altri dicono, che <lb/>per farla piu gagliarda che &longs;i debbia tuore &longs;alnitro raffinato lire. </s> <s id="s.000869">7. &longs;olfere lire. </s> <s id="s.000870">1. car­<lb/>bon de uerzella de nizola monde lire. </s> <s id="s.000871">1. altri per farla molto migliore uoleno che &longs;i to <lb/>glia &longs;alnitrio raffinato parti. </s> <s id="s.000872">8. &longs;olfere parte. </s> <s id="s.000873">1. carbon de uerzelle de uizola gioueni, <lb/>& monde parte. </s> <s id="s.000874">1. alcuni per farla piu forte hanno uoluto aggiongere dell'argento ui <lb/>uo, alcuni acqua de uitta, alcuni &longs;al armoniaco, alcuni canfora, alcuni farla con carboni <lb/>de tor&longs;i de uerzi, alcuni con carbone de gionchi, ouer di tela di lino bru&longs;iata, alcuni han <lb/>no tentato à farla in uari colori &longs;enza carboni, cioe bianca, ro&longs;&longs;a, biaua, ponendoui alcu <lb/>ni fiori di herbe &longs;ecche in poluere che faceuano lo officio del carbone, & chi ue da&longs;e­<lb/>uano quel tal colore, le qual co&longs;e, à uolerle de&longs;criuere à una per una ci haueria da dire <lb/>per fin à diman da mattina, & accio che quella po&longs;&longs;a uedere la differentia, che &longs;ia fra <lb/>que&longs;ti modi li uoglio de&longs;criuere qua &longs;otto a uno per uno di&longs;tintamente, &longs;econdo che di <lb/>&longs;opra gliho recitati, & de molti altri non recitati per piu breuita. <lb/> Poluere di bombarda al modo piu an­<lb/> tico. <lb/></s> <s id="s.000875">1 Salnitrio parte.1. <lb/> Solfere parte.1. <lb/> Carbone parte.1. <lb/> Poluer di bombarda al modo non tanto <lb/> antico. <lb/></s> <s id="s.000876">2 Salnitrio parti.3. <lb/> Solfere parti.2. <lb/> Carbone parti.2. <lb/> Poluer di bombarda al modo non tan­<lb/> to antico. <lb/></s> <s id="s.000877">3 Salnitrio parti.10. <lb/> Solfere parti.3. <lb/> Carbone parti.3. <lb/> Poluer di bombarda al modo non tan­<lb/> to antico. <lb/></s> <s id="s.000878">4 Salnitrio parti.12. <lb/> Solfere parti.3. <lb/> Carbone parti.2. <pb xlink:href="042/01/078.jpg"/> Poluer di bombarda al modo non trop <lb/> po antico. <lb/></s> <s id="s.000879">5 Salnitrio pari.9.. <lb/> Solfere partti.2 <lb/> Carbone parti.3. <lb/> Poluer a&longs;&longs;ai moderna de &longs;chioppo. <lb/> Salnitrio parti.4. <lb/>6 Solfere parte.1. <lb/> Carbone parte.1. <lb/> Poluer di bombarda al modo piu mo­<lb/> derno. <lb/> Salnitrio parti.20. <lb/>7 Solfere parti.3. <lb/> Carbone parti.10. <lb/> Poluer di bombarda al modo piu mo­<lb/> derno. <lb/></s> <s id="s.000880">8 Salnitrio parti.100. <lb/> Solfere parti.10. <lb/> Carbone parti.36. <lb/> Poluer gro&longs;&longs;a al modo moderna. <lb/> Salnitrio parti.100. <lb/>9 Solfere parti.20. <lb/> Carbone parti.37. <lb/> Poluer fina non molto antica. <lb/> Salnitrio parti.9. <lb/>10 Solfere parti.3. <lb/> Pior de mirochea parti.6. <lb/> Poluer gro&longs;&longs; a piu moderna. <lb/> Salnitrio parti.2. <lb/> Solfere parte.1. <lb/>11 Carbone de&longs;alice parte.1. <lb/> Poluer di archibu&longs;o piu moderna. <lb/> Salnitrio parti.3. <lb/>12 Solfere parti.1. <lb/> Carbone de rami de &longs;alice giouani <lb/> parte.1. <lb/> Poluer fina piu moderna. <lb/></s> <s id="s.000881">13 Salnitrio raffinato piu uolte parti.5. <lb/> Solfere parte.1. <lb/> Carbone de uerga de auolane gioue­<lb/> ni parte.1. <lb/> Poluer gro&longs;&longs;a piu moderna. <lb/> Salnitrio raffinato parti.3. <lb/>14 Solfere parte.1. <lb/> Carbone di &longs;alice parti.2, <lb/> Poluer mezzana piu moderna. <lb/> Salnitrio raffinato parti.10. <lb/>15 Solfere parti.2. <lb/> Carbone de &longs;alice parti.3. <lb/> Poluer di archibu&longs;o moderno. <lb/> Salnitrio raffinato piu uolte parti.10. <lb/>16 Solfere parte.1. <lb/> Carbone de uerzelle di nizola mon­<lb/> de parte.1. <lb/> Poluer de &longs;chioppo piu moderna. <lb/> Salnitrio raffinato parti.27. <lb/>17 Solfere parti.3. <lb/> Carbone de uerzelle de nizola mon­<lb/> de parti.4. <lb/> Poluer de &longs;chioppo piu gagliarda, & <lb/> piu moderna. <lb/> Salnitrio raffinato parti.7. <lb/>18 Solfere parte.1. <lb/> Carbone de uerzelle de nizola mon­<lb/> de è giouene parte.1. <lb/> Poluer de &longs;chioppo piu fina è ga­<lb/> gliarda. <lb/> Salnitrio raffinato piu uolte <lb/> parti6. <lb/>19 Solfere parte.1. <lb/> Carbone de uerzelle de nizo la gioue­<lb/> ne è monde parte.<emph.end type="italics"/>1. <pb pagenum="40" xlink:href="042/01/079.jpg"/> P<emph type="italics"/>oluer gro&longs;&longs;a moderna <lb/> Salnitrio parti.4. <lb/>20 Solfere parte.1. <lb/> Carbone de &longs;alice parte.1. <lb/> Poluer gro&longs;&longs;a moderna. <lb/> Salnitrio parti.20. <lb/>21 Solfere parti.4. <lb/> Carbone de &longs;alice parti.5. <lb/> Poluer de &longs;chioppo moderna. <lb/> Salnitrio raffinato à &longs;ecco parti.48. <lb/>22 Solfero cetrino parti.7. <lb/> Carbone de nizolaro, ouer de legni <lb/> del caneuo &longs;ecchi parti.8. <lb/> Poluer da &longs;chioppo moderna. <lb/> Salnitrio raffinato parti.18. <lb/>23 Solfere parti.2. <lb/> Carbon de legno de nizolaro parti.<emph.end type="italics"/>3. </s> </p> <p type="main"> <s id="s.000882">P<emph type="italics"/>er fare qual &longs;i uoglia delle &longs;opra&longs;critte &longs;orte di poluere, bi&longs;ogna notare, che à uoler <lb/>che la &longs;ia buona, &longs;econdo la qualita &longs;ua, eglie nece&longs;&longs;ario, che il &longs;alnitrio &longs;ia puro, e netto, <lb/>& potente (la qual co&longs;a &longs;i cono&longs;ce da pratici à bru&longs;arne un poco) &longs;imilmente che il &longs;ol­<lb/>fere &longs;ia netto di terra, & da altre &longs;porcitie, che in e&longs;&longs;o &longs;i troua, & che il carbone an­<lb/>chora non &longs;ia &longs;uboido per stare in luoco humido, ouer che il non &longs;ia mi&longs;to con poluere, <lb/>ouer terra, ultimamente bijogna aduertire, che tal poluere &longs;ia ottimamente pe&longs;ta, & <lb/>li detti tre materiali in&longs;ieme ben incorpor ati ilche facendo tal poluere non mancara di <lb/>&longs;uoi effetti &longs;econdo la &longs;pecie di quella, domente, che anchora &longs;ia da ogni humidita bene <lb/>eßicata, e pero la non uol e&longs;&longs;er tenuta in luoco humido ma in luoco &longs;utto. </s> <s id="s.000883">Anchora per <lb/>un'altra ragione uol &longs;tar in luoco &longs;utto, che la humidita ri&longs;olue il &longs;alnitrio in acqua, & <lb/>ri&longs;olto che &longs;ia di&longs;cende pian piano uer&longs;o il fondo del ua&longs;o doue reposta tal poluere, per <lb/>ilche nella poluere del fondo uien à e&longs;&longs;er piu &longs;alnitrio, che in quella che &longs;tanella parte <lb/>di &longs;opra del detto ua&longs;o.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000884">HOR V<emph type="italics"/>o&longs;tra Reuerentia puo uedere in quanti uarij modi è <lb/>&longs;tato determinato <lb/>l'ordine, ouer la proportione della quantita di &longs;opradetti tre materiali nella <lb/>compo&longs;itione della detta poluere.<emph.end type="italics"/> P. C<emph type="italics"/>ertamente eglie da marauigliare de tante ua­<lb/>rie mutationi de ordini, & non po&longs;&longs;o pen&longs;are con che ragione quelli tali &longs;e &longs;iano moßi à <lb/>determinar tai ordmi.<emph.end type="italics"/> N. L<emph type="italics"/>a prima inuentione (quantunque alcuni dicono che la fu <lb/>trouata à ca&longs;o) io tengo che la fu&longs;&longs;e ritrouata con ragion naturale, &longs;peculatiuamente, <lb/>cioe che tai tre materiali ben pi&longs;ti, & me&longs;colati in&longs;ieme doue&longs;&longs;eno e&longs;&longs;er atti à formar <lb/>un fuoco co&longs;i gagliardo, & ine&longs;tinguibile, per fin che ogni materia non fu&longs;&longs;e con&longs;u­<lb/>mata, perche ui &longs;ono le ragionuiue co&longs;i douer e&longs;&longs;er, ma à determinare la proportione <lb/>della quantita de detti materiali, credo che con la i&longs;perientia &longs;e &longs;iano con&longs;igliati, per­<lb/>che nel primo ordine &longs;e fondorno &longs;u la proportion della equalita, perche il &longs;iuede, <lb/>che pigliauano tanto de l un materiale quanto che dell'altro, & quantunque tal pol­<lb/>uere in gran quantita face&longs;&longs;e for&longs;i qualche buon effetto, nondimeno con&longs;iderando che <lb/>tal effetto procedeua dal &longs;alnitrio, &longs;ecero un'altro ordine, cioe <expan abbr="pigliãdo">pigliando</expan> maggior parte <lb/>de &longs;almtrio di quello faceano de cadauno delli altri, et ritrouorno tal poluer piu <expan abbr="pot&etilde;te">potente</expan> <pb xlink:href="042/01/080.jpg"/>della prima, et co&longs;i con tai aui&longs;i ragioneuoli, alcuni &longs;ono andati uariando tal ordine per <lb/>fin à que&longs;titempi, uero è, che ui &longs;o no alcuni ordini delli &longs;opra notati, che con poca ra­<lb/>gion, & manco giudicio &longs;ono &longs;tati ordinati, anzi credo che &longs;tano &longs;tati alcuni, che per <expan abbr="nõ">non</expan> <lb/>uoler far, come faceuano gli altri) per mo&longs;trar di&longs;aper piu di loro) &longs;enza altra ragio­<lb/>ne hanno uoluto formar nuoui ordini, cioe cre&longs;cendo il carbone, & &longs;minuendo il &longs;olfe­<lb/>re, altri in cre&longs;cere il &longs;olfere, & &longs;minuire il carbone, altri uariando tutti tre li detti ma <lb/>teriali in certe &longs;tranie proportioni, accio che para con maggior &longs;apientia, & &longs;ottilita <lb/>ritrouato.<emph.end type="italics"/> P. E<emph type="italics"/>glie que&longs;to, &longs;i come &longs;ono anchora quelli compo&longs;itori, che non &longs;anno <lb/>dire, ne fare, &longs;e non quello, che hanno detto, ouer fatto gli altri, ma perche &longs;i uergogna <lb/>no alle uolte apparere che habbiano imparato, ouer tolto da quelli tali &longs;e sforzan di ua <lb/>riar alquanto il modo, ouer il parlare.<emph.end type="italics"/> N. C<emph type="italics"/>o&longs;i è preci&longs;o.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;to ragionamen­<lb/>to è &longs;tato molto longo, e pero uoglio che facciamo fine.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000885">QVESITO SESTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo<emph.end type="italics"/> S. P<emph type="italics"/>rior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000886">PRIORE. H<emph type="italics"/>ier&longs;erauoi dimo&longs;tra&longs;ti in quanti modi (da non molto <expan abbr="t&etilde;po">tempo</expan> in qua) <lb/>è &longs;tato uariato l'ordine, ouer la proportione della quantita di tre materiali nel <lb/>componere la poluere, hor ue adimando, qual di &longs;opra notati ordini (&longs;i di piu antichi, <lb/>come di piu moderni) giudicati e&longs;&longs;er migliore, cioe che ne dia piu perfetta, & piu ga­<lb/>gliarda, ouer potente poluere.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio quella poluere &longs;e de giudicar e&longs;&longs;er <lb/>piu gagliarda, & potente che contien maggior parte de &longs;alnitrio, dico maggior parte <lb/>ri&longs;petto al tutto. </s> <s id="s.000887">E&longs;&longs;empi gratia, il primo ordine di &longs;opra annotati, cioe quello doue &longs;i <lb/>tuol de cadauno materiale parte una, tal compo&longs;itione uenira à tener un terzo &longs;alnitrio <lb/>& li dui terzifra&longs;olfere è carbone, & lo &longs;econdo con&longs;equente à quello, cioe quello do­<lb/>ue &longs;e tuol &longs;alnitrio parte. </s> <s id="s.000888">3. &longs;olfere parte. </s> <s id="s.000889">2. e carbone parte. </s> <s id="s.000890">2. ueniria à tener li tre <lb/>&longs;ettimi &longs;alnitrio, & li quattro &longs;ettimi fra&longs;olfere, e carbone, & perche li tre &longs;ettimi è <lb/>maggior parte de un terzo, e pero diremo che la poluere del detto &longs;econdo ordine &longs;ara <lb/>piu gagliarda, e potente di quella del primo ordine, &longs;imilmente la poluere del terzo or <lb/>dine &longs;ara piu potente di quella del &longs;econdo, perche quella del detto terzo ordine tien li <lb/>cinque ottaui &longs;alnitrio, li quai cinque ottaui &longs;ono molto maggior parte de tre &longs;ettimi, <lb/>& il quarto uien à tener li dodeci. </s> <s id="s.000891">17. eßimi &longs;alnitrio, & perche dodeci. </s> <s id="s.000892">17. eßimi è <lb/>maggior de cinque ottaui, e pero diremo, che la poluere del detto quarto ordine è piu <lb/>gagliarda di quella del terzo, & il quinto ordine uien à tener li nuoue. </s> <s id="s.000893">14. eßimi &longs;al­<lb/>nitrio, & perche li nuoue. </s> <s id="s.000894">14. eßimi è menor parte de dodeci. </s> <s id="s.000895">17. eßimi diremo che la <lb/>poluer del detto quinto ordine e&longs;&longs;er peggiore, ouer men potente di quella del quarto, <lb/>& il &longs;e&longs;to ordine uien à tener li dui terzi &longs;alnitrio, & perche li dui terzi è maggior <lb/>delli nuoue. </s> <s id="s.000896">14. eßimi, diremo che la poluere del &longs;e&longs;to ordine e&longs;&longs;er migliore, ouer piu <lb/>potente di quella del quinto, & con tal modo procedendo in tutti glialtri con&longs;equenti <lb/>ordini (à che non ignorara lo operar, & cognition di rotti) con facilita cono&longs;cera <lb/>qual ordine &longs;ia migliore, ouer peggiore, cioe qual poluere &longs;ara piu gagliarda è poten­<lb/>te, & econuer&longs;o, intendendo pero in una i&longs;te&longs;&longs;a &longs;orte di &longs;alnitrio, & co&longs;i&longs;e potra far<emph.end type="italics"/><pb pagenum="41" xlink:href="042/01/081.jpg"/><emph type="italics"/>comparatione di quelle gro&longs;&longs;e, ouer de artegliarie alle altre &longs;ue &longs;imile, et co&longs;t delle fine, <lb/>ouer de&longs;chioppo, alle altre &longs;ue &longs;imile, perche &longs;aria co&longs;a longa à uoler dare e&longs;&longs;empio à <lb/>tutti li &longs;apra detti ordini à uuo per uno.<emph.end type="italics"/> P. C<emph type="italics"/>oncludetemi al manco de tutti li &longs;opra <lb/>notati or dini qual &longs;ara la piu gagliarda é <expan abbr="pot&etilde;te">potente</expan> de tutte le altre.<emph.end type="italics"/> N. Q<emph type="italics"/>uella del. <!-- REMOVE S-->16. <lb/>ordine &longs;ara la piu potente, & gagliarda de tutte le &longs;opra notate (cioe quella doue &longs;e tol <lb/>&longs;alnitrio raffmato piu uolte parte. </s> <s id="s.000897">10. &longs;olfere parte. </s> <s id="s.000898">1. carbon de uerzelle de nizola <lb/>giouene e monde parte. </s> <s id="s.000899">1. & que&longs;ta &longs;ara la piu potente per due cau&longs;e. </s> <s id="s.000900">La prima è, per <lb/>che tal poluere uien à tener li cinque &longs;e&longs;ti &longs;alnitrio, el qual cinque &longs;e&longs;ti è maggiore di <lb/>qual &longs;i uoglia parte occorrente in qual &longs;i uoglia delli altri &longs;opra notati ordini. </s> <s id="s.000901">La &longs;e­<lb/>conda cau&longs;a è, che tal &longs;alnitrio ua raffinato piuuolte, che lo fa piu perfetto etiam ui <lb/>concorre piu perfetto carbone, perche in effetto quanto piu el carbone è di materia le­<lb/>ue, e dolce, eglie piu atto à riceuere, & mantenere piu facilmente il fuoco, e pero tan­<lb/>to piu è perfetto, per e&longs;&longs;er piu atto, & di&longs;po&longs;to à far con celerita lo officio &longs;uo.<emph.end type="italics"/> P. <lb/>Q<emph type="italics"/>ue&longs;ta uostra openione mi con&longs;ona molto, ma mi resta un dubbio di adimandarui, ma <lb/>per e&longs;&longs;er tardi lo uoglio la&longs;&longs;ar à diman di &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000902">QVESITO SETTIMO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000903">PRIORE. H<emph type="italics"/>ier&longs;era uoi conclude&longs;ti, che quella del decimo&longs;e&longs;to ordine, e&longs;&longs;er la <lb/>piu fina, & piu potènte, ouer gagliarda poluere de cadauno altro di &longs;opra nota <lb/>ti ordini, perche contien ma ggior parte de &longs;alnitrio, de cadauno delli predetti ordeni <lb/>la qual parte è li cinque &longs;esti del tutto, hor ue adimando &longs;e la non &longs;aria a&longs;&longs;ai piu ga­<lb/>gliarda, e potente, che la face&longs;&longs;e con maggior parte de detti cinque &longs;e&longs;ti del mede&longs;imo <lb/>&longs;alnitrio, & menor parte de un &longs;e&longs;to fra &longs;olfere, e carbon, cioe carbon della mede&longs;ima <lb/>&longs;orte.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio, che la &longs;aria piu gagliarda, e potente, domente, che tal mini <lb/>ma parte de &longs;olfere, & carbone fu&longs;&longs;e atta, & &longs;officiente à far quel&longs;uo officio, che ui&longs;e <lb/>a&longs;petta, cioe ad apprendere con prestezza el fuoco, etiam à introdurlo, & mantener­<lb/>lo nel &longs;alnitrio per fina che &longs;ia totalmente ri&longs;&longs;olto in fuoco, perche &longs;el fu&longs;&longs;e tanto poca <lb/>la quantita, ouer parte del detto &longs;olfere, & carbone, che la non fu&longs;&longs;e atta, e &longs;officiente <lb/>à far tal officio, tal compo&longs;itione re&longs;taria inutile, & qua&longs;i de niun ualore, e pero bi&longs;o­<lb/>gna &longs;opra questo molto ben aduertire, perche &longs;el fu&longs;&longs;e poßibile à far tal poluere de pu <lb/>ro, e perfetto &longs;alnitrio, &longs;enza dubbio quella &longs;aria piu potentißima, ouer gagliardißima <lb/>di qualunque altra compo&longs;ta de mede&longs;imo &longs;alnitrio con &longs;olfere, & carbone: ma petche <lb/>el detto &longs;alnitrio per &longs;e &longs;olo non é atto ne &longs;officiente ad apprendere con tal cellerita el <lb/>&longs;uoco con uiua fiamma, come fa el &longs;olfere, ne etiam à con&longs;eruarlo per fina à tanto, che <lb/>fu&longs;&longs;e totalmente ar&longs;o, & di&longs;trutto (come fa el carbone) e pero eglie nece&longs;&longs;ario à dargli <lb/>la compagnia delli altri dui, cioe &longs;olfere, & carbone, & tanta quantita, che &longs;ia atta, e <lb/>&longs;officiente à fare quel tal &longs;uo officio, che ui&longs;e a&longs;petta (detto di &longs;opra.)<emph.end type="italics"/> P. E<emph type="italics"/>ue ho in­<lb/>te&longs;o benißimo, & uoglio, che que&longs;to ba&longs;ti per que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/082.jpg"/> <p type="head"> <s id="s.000904">QVESITO OTTAVO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Priore di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000905">PRIORE. H<emph type="italics"/>ier&longs;era uoi determina&longs;ti, che quella poluere, che <expan abbr="cõtien">contien</expan> maggior <lb/>parte de &longs;alnitrio, et menor parte fra&longs;olfere e carbone (domente che tal&longs;olfere, <lb/>& carbone &longs;ia &longs;officiente à far cl&longs;uo officio) e migliore, e piu potente di qualunque al <lb/>tra compo&longs;ta della mede&longs;ima &longs;orte di &longs;alnitrio, &longs;olfere, e carbone, ma con menor parte <lb/>del detto &longs;alnitrio, & maggiore fra &longs;olfere e carbone (et que&longs;to credo anchor a io) ma <lb/><expan abbr="cõfidero">confidero</expan>, che tal regola <expan abbr="nõ">non</expan> è generale à ogni &longs;pecie di artegliaria, perche el &longs;e &longs;a commu <lb/>namente che li &longs;chioppi, la uogliono piu fina delli archibu&longs;t, & li archibu&longs;t la uogliono <lb/>piu fina delli mo&longs;chetti, et falconetti, & li falconetti la uogliono megliore delle altre <lb/>&longs;or te de artegliarie gro&longs;&longs;e, & per tanto ue adimando &longs;el non ui pare, che el &longs;ianece&longs;&longs;a <lb/>rio à limitare questa &longs;ua compo&longs;itione. </s> <s id="s.000906">& finezza &longs;econdo la &longs;orte di pezzi.<emph.end type="italics"/> N. <!-- KEEP S--></s> <s id="s.000907">A <lb/><emph type="italics"/>me non pare, che tal co&longs;a &longs;ia nece&longs;&longs;aria, anchor che la&longs;e co&longs;tumi, anzi ho una openio­<lb/>ne, che que&longs;to &longs;ia un errore a&longs;&longs;ai maggiore di quello fu detto delle collobrine, & &longs;uoi <lb/>canoni al. <!-- KEEP S--></s> <s id="s.000908">11. Que&longs;ito del. <!-- REMOVE S-->1. libro.<emph.end type="italics"/> P. M<emph type="italics"/>o come uore&longs;ti uoi, che &longs;i face&longs;&longs;e.<emph.end type="italics"/> N. A<emph type="italics"/>lpre <lb/>&longs;ente <expan abbr="nõ">non</expan> uoglio co&longs;i <expan abbr="ab&longs;olutam&etilde;te">ab&longs;olutamente</expan> dar determinata ri&longs;po&longs;ta à <27>sta materia, <21>che la uo <lb/>glio un poco con&longs;ider arla meglio, et &longs;pero di farui cono&longs;cere un errore in <27>&longs;ta co&longs;a, el <lb/>quale &longs;e ne tira drio molri altri de piu di&longs;comodita, interre&longs;&longs;o, et &longs;pe&longs;a di quello <expan abbr="fãnole">fannole</expan> <lb/>dette colobrine ri&longs;petto alli &longs;uoi canoni (come &longs;i fece cono&longs;cere &longs;opra lo detto. </s> <s id="s.000909">11. Que <lb/>&longs;ito del. <!-- REMOVE S-->1. libro.<emph.end type="italics"/> P. C<emph type="italics"/>on&longs;ideratila un poco bene, perche le &longs;ono co&longs;e che importano a&longs; <lb/>&longs;ai à longo andare, & tal hora a&longs;&longs;ai piu di quello che l'huom &longs;i pen&longs;a.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000910">QVESITO NONO FATTO DA VN HIERONIMO <lb/><emph type="italics"/>qual di&longs;&longs;e e&longs;&longs;er &longs;otto capo de bombar dieri nella i&longs;ola de Cipri.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000911">HIERONIMO. P<emph type="italics"/>erche cau&longs;a credeti, che &longs;e dia la grana alla poluere fina, <lb/>(cioe à quella de &longs;chioppo, & de archibu&longs;o) & non alla gro&longs;&longs;a (cioe à quella del <lb/>le artegliarie.<emph.end type="italics"/> N. I<emph type="italics"/>o &longs;o bene, che la cau&longs;a di que&longs;ta tal particolarita non è da uoiigno <lb/>rata, & che non me adimiandati tal co&longs;a, perche non la &longs;appiati: ma &longs;olamente per far <lb/>i&longs;perientia di me.<emph.end type="italics"/> H. A<emph type="italics"/>nziue la adimando per saperla, & non per far i&longs;perientia di <lb/>uoi: perche non solamente con&longs;e&longs;&longs;o non &longs;aper tal cau&longs;a, cioe perche ragione ui &longs;e dia. <lb/></s> <s id="s.000912">tal grana, ma ui giuro da real Chri&longs;tiano, che ho ricer cato que&longs;ta tal cosa da molti che <lb/>fanno poluere, dico proui&longs;ionati dalla &longs;ignoria per far poluere d'ogni &longs;orte, & niuno <lb/>me ne ha &longs;aputo aßignar ragion alcuna, &longs;aluo quello che lauora qua in lar&longs;enale di Ve­<lb/>netia, el quale me ha ri&longs;po&longs;to, che per darui la detta grana tal poluere &longs;i fa, ouer diuen­<lb/>ta piu gagliarda, e potente, la qual &longs;ua ragione mi con&longs;ona alquanto ma non tanto che <lb/>ba&longs;ti, e pero &longs;on uenuto da uoi per chiarirme meglio, e per uedere &longs;e la uo&longs;tra openio­<lb/>ne é &longs;imile alla &longs;ua.<emph.end type="italics"/> N. Q<emph type="italics"/>ua&longs;i che non po&longs;&longs;o credere que&longs;to, che uoime dite, perche el <lb/>mi pare qua&longs;i impoßibile, che uno arti&longs;ta faccia alcuna co&longs;a, &longs;enza &longs;apere à che fine el <lb/>la faccia, & maßime di quelle co&longs;e, che lui fa de continuo, perche el bi&longs;ogna che larte <lb/>imiti la natura in que&longs;to, che tutte le co&longs;e che lei &longs;a, la lifaccia à qualche fine. </s> <s id="s.000913">Et pero<emph.end type="italics"/><pb pagenum="42" xlink:href="042/01/083.jpg"/><emph type="italics"/>non po&longs;&longs;o credere, che co&longs;tui del Ar&longs;enale (qual me haueti detto, che è proui&longs;ionate <lb/>dalla &longs;ignoria per far poluere &longs;i fina come gro&longs;&longs;a) non &longs;appia à que fine &longs;e dia co&longs;i la <lb/>grana alla poluere de &longs;chioppo, e de archibu&longs;o, & non à quella dalle artegliarie, et ma&longs;<lb/>&longs;ime facendone continuam ente ogni giorno.<emph.end type="italics"/> H. I<emph type="italics"/>o ui &longs;o dir certo, che non ui &longs;a aßi­<lb/>gnare altra meglior ragione di quella, che ui ho detta.<emph.end type="italics"/> N. I<emph type="italics"/>nanti che di questa cosa <lb/>ue dica la mia opinione, uoglio che ritornati da lui, & pregarlo di gratia, che ue di­<lb/>ca realmente, perche ragione ui da tal grana.<emph.end type="italics"/> H. N<emph type="italics"/>on accade che ui uada altramen­<lb/>te, perche io &longs;on certo, che mi replicara el mede&longs;imo, cioe, che tal grana la fa diuentar <lb/>piu gagliarda, e potente.<emph.end type="italics"/> N. S<emph type="italics"/>e pur el ue replica que&longs;to, re&longs;pondetegli in que&longs;to mo <lb/>do, &longs;e tal grana fala poluere piu gagliarda, e potente, mo non &longs;aria benfatto à ingra­<lb/>nire anchora quella gro&longs;&longs;a (cioe quella delle artegliarie) per farla diuentare piu ga­<lb/>gliarda e potente.<emph.end type="italics"/> H. L<emph type="italics"/>a&longs;&longs;atifar à me, che ui uoglio ritornare (& for&longs;i hoggi) & <lb/>diman ue refferiro quello me hauera ri&longs;po&longs;to.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000914">QVESITO DECIMO FATTO DAL MEDESIMO <lb/>H<emph type="italics"/>ieronimo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000915">HIERONIMO. D<emph type="italics"/>apoi che fui partito da uoi hieri, io andai &longs;ubito in lar­<lb/>&longs;enale, & andai à ritrouar l'amico, & lo pregai de nouo, che &longs;e lui haueua al­<lb/>tra ragione di quella, che lui me haueua detta, che non me la uole&longs;&longs;e cellare, che di cio <lb/>&longs;empre gline re&longs;teria obligatißimo, lui me giuro, che non &longs;apeua altra ragione di quel <lb/>la, che gia me haueua detta, cioe, che la &longs;e ingraniua per augumentarla in uirtu, & po&longs; <lb/>&longs;anza, cioe per farla piu gagliarda, & potente, & io gli dißi quello, che me ordina&longs;ti, <lb/>cioe &longs;el non &longs;aria buono à ingr anire anchora la poluere delle artegliarie, cioe la gro&longs; <lb/>&longs;a, per farla anchor lei piu gagliarda, e potente di quello che la é, lui me ri&longs;po&longs;e, che &longs;i <lb/>andaria à pericolo di far creppar li pezzi, et co&longs;i meri&longs;ol&longs;e.<emph.end type="italics"/> N. V<emph type="italics"/>oi gli doueui pur <lb/>ri&longs;pondere, che &longs;e potriano poi cargare tai pezzi con manco poluere del &longs;olito, & tan <lb/>to &longs;aria auanzato, ouer amente ponerui dentro alquanto manco &longs;alnitrio del &longs;olito.<emph.end type="italics"/><lb/>H. I<emph type="italics"/>o non ho hauuto tanto aui&longs;o di &longs;aperui far tal ri&longs;po&longs;ta, ma che credeti, tutti que­<lb/>&longs;ti che fanno poluere, uanno facendo &longs;econdo, che hanno ui&longs;to far alli altri, ouer &longs;econ <lb/>do, che gli è &longs;tato in&longs;egnato, & non &longs;i curano di cercare, ne manco di &longs;apere la cau&longs;a <lb/>delle co&longs;e, che loro fanno, cioe à che fin le faceiano. </s> <s id="s.000916">Et uoi dir di me, che anchora mi ho <lb/>fatto della poluere gro&longs;&longs;a, e fina, & quando ne faceua de fina, io la ingraniua anchora <lb/>mi, anchor che non &longs;ape&longs;&longs;e, ne anchor &longs;o à que fine la &longs;e ingrani&longs;cha, & que&longs;to faceua, <lb/>perche haueua uisto che tuttili altri co&longs;i faceuano.<emph.end type="italics"/> N. C<emph type="italics"/>redo, che &longs;ia, come uoi di­<lb/>ceti.<emph.end type="italics"/> H. D<emph type="italics"/>i gratia ditime la uo&longs;tra opinione circa à que&longs;ta co&longs;a.<emph.end type="italics"/> N. H<emph type="italics"/>auendoui <lb/>qua&longs;i prome&longs;&longs;o de diruela, eglie il douer ch'io ui attenda, & per tanto dico, che da­<lb/>poi, che hieri ui parti&longs;ti da me, ho con&longs;iderato &longs;opra di tal co&longs;a, & in effetto ho ritro­<lb/>uato, che &longs;olamente la neceßita, ouer commoditaha indutto gli huomini à inue&longs;tigar <lb/>il modo de ingranire la detta poluere de &longs;chioppo, & de archibu&longs;o, & non quella de <lb/>artegliaria, perche la detta poluere granita e molto piu &longs;corrente, de la non gra­<lb/>nita alla &longs;imilitudine, che &longs;aria uno pugno di &longs;rcmento, de un pugno de farina,<emph.end type="italics"/><pb xlink:href="042/01/084.jpg"/><emph type="italics"/>cioe ponendo &longs;opra una tabula piana un pugno di fromento, & &longs;eparatamente un pu­<lb/>gno di farina, & inclinando poi al quanto da una banda la detta tabula, &longs;enza dubbio <lb/>piu facilmente &longs;correra el detto fromento zo&longs;o della detta tabula, di quello fara la det <lb/>ta farina, ma tal farina restara amaccata, & piu immobile, & &longs;e pur anchora lei ui <lb/>&longs;corre&longs;&longs;e per la molta dependetia di tal tabula, la ui &longs;correra qua&longs;i tutta in un colpo, <lb/>& il frumento ui &longs;corrir a à parte a parte, cioe piu di&longs;gregatamente.<emph.end type="italics"/> H. <!-- KEEP S--></s> <s id="s.000917">E <emph type="italics"/>ue ho in­<lb/>te&longs;o benißimo, ma che mi gioua quella &longs;ua &longs;correntia.<emph.end type="italics"/> N. M<emph type="italics"/>o <expan abbr="nõ">non</expan> &longs;apeti, che uolendo <lb/>portar un &longs;chioppo, ouer un'archibu&longs;o per &longs;eruir&longs;ene alli bi&longs;ogni, eglie nece&longs;&longs;ario an­<lb/>chora portar&longs;e drio della poluere, per poterlo cargar ad ogni &longs;uo piacere, & che tal <lb/>poluere &longs;e porta nelle fia&longs;che, & per cargarli con mi&longs;ura in quelle tai fia&longs;che ui&longs;e fa <lb/>u&longs;cire, come &longs;apeti, un certo canoncino atto a riceuere tanta poluere, quanta ui &longs;i con­<lb/>uiene a cargare quel tal &longs;chioppo, ouer archibu&longs;o con un certo ingegno da rechiuderlo <lb/>poi di dentro uia, quando che e pieno, accioche tal poluere non po&longs;&longs;a u&longs;cire fora del ca <lb/>noncino, & ritornar nella fia&longs;cha.<emph.end type="italics"/> H. I<emph type="italics"/>o &longs;o tutte que&longs;te particolarita, &longs;i che non <lb/>accade che uoi me le dicate.<emph.end type="italics"/> N. A<emph type="italics"/>nchor che &longs;o, che uoi le &longs;apeti meglio di me, ue le <lb/>ho uolute dire, accioche meglio me intendiati per l'auenire. </s> <s id="s.000918">Et per tanto concludo, <lb/>che &longs;e la poluere, che &longs;i mette nelle dette fia&longs;che, non fu&longs;&longs;e granita, con difficulta &longs;e po<lb/>tria fare impire quel tal canoncino, perche nel riuoltar la fia&longs;cha per far impire <lb/>quel tal canoncino la poluere che fu&longs;&longs;e nella detta fia&longs;cha, ca&longs;caria qua&longs;i tutta in un <lb/>tratto &longs;opra alla intrata di tal canoncino, chiudendo, ouer re&longs;&longs;er ando in quello qua&longs;i <lb/>tutto quello aere, che in quello &longs;i troua&longs;&longs;e, per e&longs;&longs;er uodo, el qual aereueneria a impedi <lb/>re lo ingre&longs;&longs;o alla poluere, talmente, che tal canoncino la maggior parte delle uolte &longs;i <lb/>trouaria qua&longs;i uacuo, ouer molto &longs;cemo, la qual co&longs;a non ui occorrera co&longs;i, &longs;e la detta <lb/>poluere &longs;ara granita, perche tal poluere granita &longs;correra nel detto canoncino piu di­<lb/>&longs;gregatamente (come fu detto del <expan abbr="from&etilde;to">fromento</expan>, et della farina) la qual di&longs;gregatione dara <lb/>adito a quello aere, che &longs;i ritrouara nel detto <expan abbr="canõcino">canoncino</expan> da poter u&longs;cire, et de intrare ne <lb/>la fia&longs;ca a impire quel loco che occupaua quella poluere, che intrara nel detto <expan abbr="canõci-no">canonci­<lb/>no</expan>, e pero el detto <expan abbr="canõcino">canoncino</expan> la maggior parte delle uolte &longs;e trouara pieno, come &longs;i <expan abbr="cõuie">conuie</expan> <lb/>ne, et co&longs;i <21> que&longs;ta cau&longs;a li huomini &longs;ono &longs;tati a&longs;tretti a inui&longs;tigar el modo de ingranire <lb/>la detta poluere de &longs;chioppo, & de archibu&longs;o, & <expan abbr="nõ">non</expan> quella di artegliaria, perche nelle <lb/>artegliarie ui &longs;e mette la poluere <expan abbr="cõ">com</expan> una cazza, come &longs;apeti, et <expan abbr="cõ">com</expan> quella la ui &longs;e porta <21><lb/>fin nel fondo della &longs;ua canna, et pero <expan abbr="nõ">non</expan> importa che tal poluere &longs;ia <expan abbr="&longs;corr&etilde;te">&longs;corrente</expan>, ò <expan abbr="nõ">non</expan> &longs;cor <lb/>rente, anzi &longs;aria co&longs;a &longs;uperflua a ingranire quella delle artigliarie, ma piu, che per ine <lb/>&longs;car quel bu&longs;ettino doue &longs;e da el fuocho alli &longs;chioppi, & alli archibu&longs;i &longs;e costuma por­<lb/>tar. </s> <s id="s.000919">come &longs;apeti, un fia &longs;chettino piccolino pieno di poluer finißima, la qual poluere, &longs;e <lb/>per &longs;orte non fu&longs;&longs;e menutamente granita, la non uoria, ne potria u&longs;cire di quel tal bu&longs;o <lb/>co&longs;i piccolino, <21> le ragioni di &longs;opra dette, e pero fu nece&longs;&longs;ario a farla <expan abbr="minutam&etilde;te">minutamente</expan> grani <lb/>ta, la qual co&longs;a <expan abbr="nõ">non</expan> accade nelle artegliarie, perche, <21> quanto ho inte&longs;o, uoi ue la metteti <lb/><expan abbr="cõ">com</expan> la mano.<emph.end type="italics"/> H. E<emph type="italics"/>glie co&longs;i, & certamente que&longs;te uostre ragioni &longs;ono lo euangelio, ne <lb/>mai haria pen&longs;ato, che per &longs;imel cau&longs;a ui &longs;e li de&longs;&longs;e tal grana, & que&longs;ta co&longs;a la ho acca <lb/>ro piu di dieci &longs;cudi, & pero di que&longs;to ue ne ringratio grandamente.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000920">I<emph type="italics"/>l fine del terzo libro.<emph.end type="italics"/></s> </p> </subchap1><subchap1> <pb pagenum="43" xlink:href="042/01/085.jpg"/> <p type="head"> <s id="s.000921">LIBRO QVARTO DELLI <lb/>QVESITI ET INVENTIONI DIVERSE, <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000922">S<emph type="italics"/>opra l'ordinar delle &longs;chiere, ouer e&longs;&longs;erciti in battaglia &longs;otto <lb/>uarie & diuer&longs;e forme, & del modo de far caminar <lb/>quelli, con altre uarie particolarita.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000923">QVESITO PRIMO FATTO DAL <lb/>C<emph type="italics"/>onte Hieronimo da Piagnano.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000924">CONTE HIERONIMO. V<emph type="italics"/>olendo io redure una quantita <lb/>de Fanti, ouer un e&longs;&longs;ercito in una battaglia quadra di gente, ue do­<lb/>mando in che modo, ouer con che regola potria &longs;apere quanti Fan­<lb/>ti &longs;e doueria mettere per fila.<emph.end type="italics"/> N. P<emph type="italics"/>igliando la radice quadrata <lb/>di quel tal numero de Fanti, e tanto quanto &longs;ara quella tal radice, <lb/>tanti Fanti &longs;e ne douera mettere per fila.<emph.end type="italics"/> C.H. D<emph type="italics"/>atime uno e&longs;­<lb/>&longs;empio in uno piccolo numero, perche ue intendero meglio.<emph.end type="italics"/> N. <lb/>P<emph type="italics"/>oniamo che &longs;ia. </s> <s id="s.000925">100. Fanti, dico che uolendoli mettere in una ordinanza, ouer batta­<lb/>glia quadra di <expan abbr="g&etilde;te">gente</expan>, il &longs;e debbe cauare la radice quadra de. </s> <s id="s.000926">100. quala come, &longs;apeti è. <lb/></s> <s id="s.000927">10. hor dico che mettendo. </s> <s id="s.000928">10. de questi Fanti per fila faranno file. </s> <s id="s.000929">10. à. </s> <s id="s.000930">10. Fanti per <lb/>fila, le quale. </s> <s id="s.000931">10. file a&longs;&longs;ettandole ordinatamente l'una drieto all'altra, talmente che tut <lb/>ti li interualli che &longs;ara fra Fante, è Fante, &longs;i dalle bande, come dauanti, & de drio &longs;ia­<lb/>no equali, tai. </s> <s id="s.000932">100. Fanti formaranno una figura quadrata, &longs;i di <expan abbr="g&etilde;te">gente</expan>, come diterre­<lb/>no, come di &longs;otto appare in figura.<emph.end type="italics"/></s> </p> <figure id="id.042.01.085.1.jpg" xlink:href="042/01/085/1.jpg"/> <p type="main"> <s id="s.000933">MA <emph type="italics"/>perche in effetto li Fanti po&longs;ti in ordinanza non stanno, ne caminano, come <lb/>di &longs;opra è sta &longs;upposto, cioe in eguale di&longs;tantie, perche ogni Fante (come a&longs;­<lb/>&longs;erma Vegetio) uol per larghezza piedi tre, cioe da&longs;palla, à &longs;palla, & per longhez­<lb/>za picdi. </s> <s id="s.000934">7. cioe piedi. </s> <s id="s.000935">3. dauanti di &longs;e, & piedi. </s> <s id="s.000936">3. de drio, & un piede uol che occupi la <lb/>&longs;ua per&longs;ona, per la qual co&longs;a la &longs;opra&longs;critta or dinanza, &longs;tando li Fanti &longs;econdo le det-<pb xlink:href="042/01/086.jpg"/>te di&longs;tantie ordinarie, non &longs;ara quadrata di terreno anci occupara in longhezza piedi. <lb/></s> <s id="s.000937">70. & in larghezza &longs;olamente piedi. </s> <s id="s.000938">30. onde che all'oc chio parera piu che bislonga, <lb/>come di &longs;otto appare in figura.<emph.end type="italics"/></s> </p> <figure id="id.042.01.086.1.jpg" xlink:href="042/01/086/1.jpg"/> <p type="main"> <s id="s.000939">CONTE HIERONIMO. V<emph type="italics"/>e ho inte&longs;o benißimo in quanto à questo, ma <lb/>quando, che tal numero de fanti non fu&longs;&longs;e co&longs;i quadrato, come &longs;aria &longs;e fu&longs;&longs;eno. <lb/></s> <s id="s.000940">200. fanti, la radice di quali, &longs;e non me inganno, &longs;aria. </s> <s id="s.000941">14. ma auanzaria. </s> <s id="s.000942">4. fanti, hor <lb/>come doueria fare in tal ca&longs;o.<emph.end type="italics"/> N. I<emph type="italics"/>n que&longs;to ca&longs;o uoi ne douere&longs;ti pur mettere. </s> <s id="s.000943">14. per <lb/>fila, & ueneria pur la detta battaglia quadra di gente, &longs;i come la precedente, cioe &longs;ara <lb/>de. </s> <s id="s.000944">14. file à fanti. </s> <s id="s.000945">14. per fila, uero è, che ui auanzara, quelli fanti. </s> <s id="s.000946">4. fuora di tal ordi <lb/>nanza, li quali il Sargente li a&longs;&longs;etta doue à lui pare, fuora di tal ordinanza, ouer che li <lb/>pone for&longs;i nella coda de tal ordinanza.<emph.end type="italics"/> C.H. A<emph type="italics"/>nchor que&longs;ta parte ho inte&longs;a benißi­<lb/>mo, ma &longs;e il fu&longs;&longs;e un grande e&longs;&longs;ercito, che mi occorre&longs;&longs;e di mettere pur in forma quadra <lb/>di gente, come doueria procedere.<emph.end type="italics"/> N. P<emph type="italics"/>er il mede&longs;imo modo, e&longs;&longs;empi gratia, ponia­<lb/>mo che tal e&longs;&longs;ercito &longs;ia de fanti. </s> <s id="s.000947">35000. dice che di questi. </s> <s id="s.000948">35000. fanti uoi ne douetica <lb/>uar la radice quadrata per l'ordine che ue ho in&longs;ignato, & trouareti quella e&longs;&longs;er. </s> <s id="s.000949">187. <lb/>& auanzara fanti. </s> <s id="s.000950">31. e per tanto &longs;e douera mettere fanti. </s> <s id="s.000951">187. per fila, & tal e&longs;&longs;ercito <lb/>uerra in forma quadra di gente, cioe uenira de. </s> <s id="s.000952">187. file à fanti. </s> <s id="s.000953">187. per fila, uero è, <lb/>che ui auanzara quelli fanti. </s> <s id="s.000954">31. detti di &longs;opra, li quali il Sargente li accommoda doue li <lb/>pare, ma io tengo che tai re&longs;idui &longs;empre li pongano nella coda di tal e&longs;&longs;ercito.<emph.end type="italics"/> C. H. <lb/>C<emph type="italics"/>o&longs;i credo anchora io.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000955">QVESITO SECONDO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> C. H<emph type="italics"/>ieronimo da Piagnano.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000956">CONTE HIERONIMO. M<emph type="italics"/>o occorrendomi à douer condure una quan­<lb/>tita de fanti, ouer uno e&longs;&longs;ercito in uiaggio, ouer per camino, ue adimando, come <lb/>&longs;e potria &longs;apere à quanti fanti per fila li &longs;e doueria far caminare, accio che occor­<lb/>rendo il bi&longs;ogno, &longs;e pote&longs;&longs;ono mettere in un &longs;ubijo in battaglia quadra di gente, & che<emph.end type="italics"/><pb pagenum="44" xlink:href="042/01/087.jpg"/><emph type="italics"/>la bandera &longs;e ueni&longs;&longs;e à ritrouare nel meggio de tal ordinanza, ouer battaglia.<emph.end type="italics"/> N. <lb/>P<emph type="italics"/>er &longs;aper far questa co&longs;a con pre&longs;tezza, &longs;ubito pigliati la radice quadra di quella tal <lb/><expan abbr="quãtita">quantita</expan> de fanti, et &longs;e tal radice &longs;ara diui&longs;ibile per tre, <expan abbr="tãto">tanto</expan> <expan abbr="quãto">quanto</expan> &longs;ara la detta terza par <lb/>te di tal radice, à tanti per fila &longs;e douera far caminar li detti fanti per camino.<emph.end type="italics"/> C.H. <lb/>D<emph type="italics"/>e gratia datime un e&longs;&longs;empio, & in piccol numero, perche meglio ue intendero, in uno <lb/>numero piccolo, che in uno grande.<emph.end type="italics"/> N. P<emph type="italics"/>oniamo per e&longs;&longs;empio, che li fanti, che &longs;e ha <lb/>da condur, &longs;iano fanti. </s> <s id="s.000957">81. dico che il &longs;i debbe tuor la radice de. </s> <s id="s.000958">81. la qual è. </s> <s id="s.000959">9. & per­<lb/>che que&longs;ta tal radice è diui&longs;ibile per tre, & la &longs;ua terza parte è tre, e per tanto dico che <lb/>li detti fanti. </s> <s id="s.000960">81. &longs;i debbono far caminar per uiaggio à tre fanti per fila, & far anno in <lb/>tutto file. </s> <s id="s.000961">27. come qui &longs;otto appare.<emph.end type="italics"/></s> </p> <figure id="id.042.01.087.1.jpg" xlink:href="042/01/087/1.jpg"/> <p type="main"> <s id="s.000962">E<emph type="italics"/>t quando l'occorre&longs;&longs;e el bi&longs;ogno di uolerli redure in battaglia quadra tutte que&longs;te. </s> <s id="s.000963">27. <lb/>file &longs;i debbono &longs;membrare in tre parti eguale, come dimo&longs;tra. </s> <s id="s.000964">a.b. <!-- REMOVE S-->& c.d. <!-- REMOVE S-->che in ogni <lb/>parte uenira à re&longs;tare. </s> <s id="s.000965">9. file à tre fanti per fila, & dapoi il &longs;i debbe far fermar la pri­<lb/>ma parte uer&longs;o la fronte, & che le altre due procedano auanti dalla banda de&longs;tra, ouer <lb/>&longs;ini&longs;tra della prima (gia fermata) per fina à tanto che la te&longs;ta, ouer fronte della &longs;econ­<lb/>da parte &longs;e uni&longs;ca con la te&longs;ta, ouer fronte della prima, & iui fermar&longs;e, & fermata la <lb/>prima, & &longs;econda parte &longs;i debbe far il mede&longs;imo con la terza parte, cioe farla camina­<lb/>re, e procedere à canto della &longs;econda parte (gia fermata) per fina à tanto che la &longs;ua te­<lb/>&longs;ta, ouer fronte &longs;e uni&longs;ca con la testa, ouer fronte della prima, & &longs;econda (come nella <lb/>&longs;otto&longs;critta figura.<emph.end type="italics"/></s> </p> <figure id="id.042.01.087.2.jpg" xlink:href="042/01/087/2.jpg"/> <p type="main"> <s id="s.000966">L<emph type="italics"/>e qual tre parti co&longs;i redutte, & a&longs;&longs;ettate, haueranno redutta tal battaglia in forma <lb/>quadra di gente, come di &longs;otto appare in figura, & per far che la bandiera ca&longs;chinel <lb/>meggio di tal battaglia &longs;empre la &longs;e debbe a&longs;&longs;ettar nel meggio della &longs;econda parte, co­<lb/>me di&longs;opra appare in ponto.<emph.end type="italics"/> B. E<emph type="italics"/>t bi&longs;ogna auertire che anchor che tal figura &longs;ia qua­<lb/>dra di terreno, come &longs;en&longs;ibilmente &longs;i uede, nondimeno in atto proprio tal figura &longs;e <lb/>trouora occupare per longhezza predi. </s> <s id="s.000967">63. & per larghezza piedi uenti&longs;ette, <pb xlink:href="042/01/088.jpg"/>(per le ragion adutte nel pre&longs;ente que&longs;ito) le qual di&longs;tantie <lb/>non hauemo o&longs;&longs;eruate, ne anchora &longs;e o&longs;&longs;eruara nella mag­<lb/>gior parte delle figure che hanno da uenire, per che occupa­<lb/>riano troppo gran &longs;pacio.<emph.end type="italics"/> C.H. Q<emph type="italics"/>ue&longs;to non me impor­<lb/>ta, ma ditemi pur, come &longs;e potra &longs;aper, ouer cono&longs;cer li luo­<lb/>chi doue &longs;e debbia &longs;membrare le dette. </s> <s id="s.000968">27. file in tre parte <lb/>eguale, &longs;enza &longs;tare à numerare le dette file à. </s> <s id="s.000969">9. per che quan <lb/>do che il fu&longs;&longs;e una gran quantita de fanti &longs;aria co&longs;a molto lon <lb/>ga.<emph.end type="italics"/> N. I<emph type="italics"/>o ho inte&longs;o che ogni quantita de fanti ui &longs;e li da una<emph.end type="italics"/><lb/><figure id="id.042.01.088.1.jpg" xlink:href="042/01/088/1.jpg"/><lb/><emph type="italics"/>fila de archibu&longs;eri nella fronte, & un'altra nelle &longs;palle che in que&longs;ti &longs;opra&longs;critti fanti. <lb/></s> <s id="s.000970">81. ui uorria. </s> <s id="s.000971">18. archibu&longs;eri, cioe 9. nella fronte, &. </s> <s id="s.000972">9. nella coda, & per tanto nelli luo <lb/>chi doue &longs;e doueria far la diui&longs;ione ui metteria due file de archibu&longs;eri, come di&longs;otto ap <lb/>pare in figura, intendendo li archibu&longs;eri per que&longs;ta lettera o.<emph.end type="italics"/><!-- KEEP S--></s> </p> <figure id="id.042.01.088.2.jpg" xlink:href="042/01/088/2.jpg"/> <p type="main"> <s id="s.000973">L<emph type="italics"/>i quali archibu&longs;eri ui auertir anno &longs;empre delli luochi doue &longs;e douer anno &longs;membr are <lb/>le dette file. </s> <s id="s.000974">27. & co&longs;i in ogni altro maggior numero.<emph.end type="italics"/> C.H. E<emph type="italics"/>ue ho inte&longs;o be&longs;iißi­<lb/>mo, fin qua, ma uorria che me dicesti, come &longs;e doueria procedere quando che la radice <lb/>de detti fanti non &longs;i pote&longs;&longs;e diuidere in tre partieguale.<emph.end type="italics"/> N. Q<emph type="italics"/>uando che tal radice <lb/>non è diui&longs;ibile in tre parti eguali, io non &longs;o come &longs;e procedano li periti Sargenti, ma <lb/>ben ue diro in che modo in tal ca&longs;o, &longs;e potria procedere, il qual modo, &longs;e il &longs;ara per ca­<lb/>&longs;o &longs;imil à quello che lor co&longs;tumano, io lo hauero accaro, & &longs;e per ca&longs;o il &longs;ara meglio di <lb/>quello che lor co&longs;tumano, io lo hauero molto piu accaro, & &longs;e per ca&longs;o il &longs;ara peggio­<lb/>re, imputareti la mia poca pratica, ouer i&longs;perientia di tal e&longs;&longs;ercitio. </s> <s id="s.000975">Dico adunque che <lb/>quando la radice di detti fanti non &longs;ia diui&longs;ibile in tre parti eguali, nece&longs;&longs;ariamente in <lb/>tal diui&longs;ione auanzara uno, ouer dui, hor pigliamo prima per e&longs;&longs;empio quella che auan <lb/>za &longs;olamente uno, come &longs;aria &longs;e fu&longs;&longs;eno fanti. </s> <s id="s.000976">100. la radice di quali è. </s> <s id="s.000977">10. il qual. </s> <s id="s.000978">10. <lb/>partendolo per. </s> <s id="s.000979">3. ne uien. </s> <s id="s.000980">3. & auanza uno, hor dico che io faria caminar diece file, à <lb/>tre, à tre (cioe tante file quanto è il numero della radice) & altre diece file, à quattro, <lb/>à quattro, & altre diece pur à tre, à tre, come qui &longs;otto appare con li &longs;uoi. </s> <s id="s.000981">20. archi­<lb/>bu&longs;i oltra li detti. </s> <s id="s.000982">100. fanti.<emph.end type="italics"/></s> </p> <figure id="id.042.01.088.3.jpg" xlink:href="042/01/088/3.jpg"/> <p type="main"> <s id="s.000983">E<emph type="italics"/>t queste tre parti, quando l'occorre&longs;&longs;e di uolerli redur in battaglia quadra di gente, <lb/>&longs;e procedaria, &longs;i come di &longs;opra, cioe far affermar la prima parte uer&longs;o la fronte, &<emph.end type="italics"/><pb pagenum="45" xlink:href="042/01/089.jpg"/><emph type="italics"/>fermata che &longs;ia far procedere auanti la &longs;econda anchor la terza per fina à tanto che la <lb/>te&longs;ta, ouer fronte della &longs;econda parte &longs;e &longs;ia unita con la te&longs;ta, ouer fronte della prima, <lb/>& co&longs;i fermata la detta &longs;econda parte, far procedere auanti, per el mede&longs;imo modo an <lb/>chor la terza parte, la qual co&longs;a <expan abbr="fac&etilde;do">facendo</expan> &longs;e uedera e&longs;&longs;er redutta tal battaglia in forma <lb/>quadra di gente, come di &longs;otto appare con li &longs;uoi archibu&longs;eri alla fronte, et alle &longs;palle.<emph.end type="italics"/></s> </p> <figure id="id.042.01.089.1.jpg" xlink:href="042/01/089/1.jpg"/> <p type="main"> <s id="s.000984">M<emph type="italics"/>a quando che nel partire la detta radice auanza&longs;&longs;e. </s> <s id="s.000985">2. come &longs;aria, quando che li fan <lb/>ti fu&longs;&longs;eno. </s> <s id="s.000986">121. la radice di quali è. </s> <s id="s.000987">11. el qual. </s> <s id="s.000988">11. partendolo per tre, ne uien tre, & <lb/>auanza. </s> <s id="s.000989">2. (come habbiamo detto) dico che in que&longs;to ca&longs;o, & in altri &longs;imili io faria ca <lb/>minare. </s> <s id="s.000990">11. file (cioe tante quanto è la radice) à. </s> <s id="s.000991">4. fanti per fila, & altre. </s> <s id="s.000992">11. file à. </s> <s id="s.000993">3. <lb/>fanti per fila, & altri. </s> <s id="s.000994">11. file pur à. </s> <s id="s.000995">4. fanti per fila, come di &longs;otto appar in figura <expan abbr="cõ">com</expan> <lb/>li &longs;uoi. </s> <s id="s.000996">22. archibu&longs;eri oltra li detti fanti. </s> <s id="s.000997">121. li quali fanti ogni uolta che &longs;e uole&longs;&longs;eno<emph.end type="italics"/><lb/><figure id="id.042.01.089.2.jpg" xlink:href="042/01/089/2.jpg"/><lb/><emph type="italics"/>redure in battaglia quadra di gente &longs;e procederia, come di &longs;opra fu fatto.<emph.end type="italics"/> C.H. Q<emph type="italics"/>ue <lb/>&longs;to uo&longs;iro di&longs;cor&longs;o non me di&longs;piace, anchor che tai tre parti per e&longs;&longs;ere di&longs;eguale, par <lb/>che di&longs;dicano a&longs;&longs;ai, ma diteme un poco que&longs;ta regola &longs;eruila co&longs;i in ogni gran numero <lb/>de fanti.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio, che la &longs;eruira in ogni numero, &longs;i quadrato, come <expan abbr="nõ">non</expan> qua­<lb/>drato.<emph.end type="italics"/> C.H. D<emph type="italics"/>atime un'e&longs;&longs;empio in parole &longs;olamente.<emph.end type="italics"/> N. P<emph type="italics"/>oniamo per e&longs;&longs;empio, <lb/>che &longs;iano fanti. </s> <s id="s.000998">3969. delli quali uolendo uoi&longs;apere à quanti fanti per fila uoi li debbia­<lb/>ti far caminar per camino, accioche &longs;iano commodi à poterli in un &longs;ubito mettere in <lb/>battaglia quadra di gente, dico che de que&longs;ti tai fanti uoi debbiati pigliar la radice qua <lb/>drata (per el, modo che ui ho in&longs;ignato) quala trouareti e&longs;&longs;er. </s> <s id="s.000999">63. &. </s> <s id="s.001000">63. fanti &longs;ara per <lb/>fila tutta la battaglia in quadro di gente, & perche questa radice (cioè. </s> <s id="s.001001">63.) è diui&longs;ibi­<lb/>le in tre parti equale, ne pigliareti el terzo (per regola ferma) qual &longs;ara. </s> <s id="s.001002">21. & co&longs;i à <lb/>21. fante per fila uoi li douete far caminare in camino.<emph.end type="italics"/> C.H. M<emph type="italics"/>o quante file potro <lb/>io &longs;apere che &longs;iano in tutto co&longs;i à. </s> <s id="s.001003">21. fante per fila.<emph.end type="italics"/> N. S<emph type="italics"/>empre &longs;ar anno el treppio<emph.end type="italics"/><pb xlink:href="042/01/090.jpg"/><emph type="italics"/>della uo&longs;ira radice, cioe el treppio de &longs;e&longs;&longs;antatre, che &longs;aria. </s> <s id="s.001004">189. et. </s> <s id="s.001005">189. file à fanti. </s> <s id="s.001006">21. <lb/>per fila ue ne peruenira.<emph.end type="italics"/> C.H. D<emph type="italics"/>oue &longs;apro io doue &longs;e debbia mettere quelle due, & <lb/>due file de archibu&longs;eri, per cogno&longs;cere el luoco doue &longs;e debbia &longs;membrare in tre par­<lb/>te per metter li in battaglia quadra di gente.<emph.end type="italics"/> N. L<emph type="italics"/>a uo&longs;tra radice (cioe &longs;e&longs;&longs;antatre) <lb/>ui da el tutto, cioe, che tal diui&longs;ione &longs;e fa alle. </s> <s id="s.001007">63. &. </s> <s id="s.001008">63. file talmente, che la prima par­<lb/>te &longs;ara de &longs;e&longs;&longs;antatre file, & co&longs;i etiam la &longs;econda, & la terza.<emph.end type="italics"/> C.H. V<emph type="italics"/>e ho inte&longs;o be <lb/>nißimo in quanto a questa parte, e pero &longs;eguitate.<emph.end type="italics"/> N. M<emph type="italics"/>a&longs;e nel partire la uo&longs;tra ra­<lb/>dice per tre ui auanza&longs;&longs;e uno (come accaderia &longs;e li propo&longs;ti fanti fu&longs;&longs;eno. </s> <s id="s.001009">5776. che la <lb/>radice di quelli &longs;aria &longs;ettanta&longs;ei, la qual radice diuidendola per tre, ne ueneria. </s> <s id="s.001010">25. & <lb/>auanzeria uno: hor dico, che tutte le file, che reu&longs;ciran de que&longs;ti tai fanti &longs;ar anno pur <lb/>el treppio della radice, cioe el treppio de &longs;ettanta&longs;ei, che &longs;aria. </s> <s id="s.001011">228. & perche tutta <lb/>que&longs;ta fila de file ua diui&longs;a &longs;empre in tre parti (come di&longs;opra fu detto, etiam fatto) a <lb/>&longs;ettanta &longs;ei file per parte (cioe tanto quanto e la no&longs;traradice) hor dico, che la prima, <lb/>& la ultima de que&longs;te tre parte, &longs;i debbano far caminar a uinticinque fanti per fila, <lb/>cioe quanto che é il terzo della no&longs;tra radice, & perche el ne auanzo uno (come di &longs;o­<lb/>pra appare) dico che quel tal. </s> <s id="s.001012">1. &longs;i debbe mettere &longs;empre nella &longs;econda parte, cioe in <lb/>quella di mezzo, cioe facendo caminar quelli della detta &longs;econda parte à. </s> <s id="s.001013">26. fanti per <lb/>fila, talmente, che la prima, & la ultima parte della gran fila delle file, &longs;aranno à. </s> <s id="s.001014">25. <lb/>fanti per fila, & la &longs;eeonda parte &longs;ara de fanti. </s> <s id="s.001015">26. per fila, & il mede&longs;imo &longs;i debbe fa <lb/>re in ogni altra radice, che partita per. </s> <s id="s.001016">3. ue auanzi &longs;olamente. </s> <s id="s.001017">1. ma quando l'auan­<lb/>za&longs;&longs;e. </s> <s id="s.001018">2. &longs;eguita tutto al contrario, cioe, che la prima, & la ultima parte uuol e&longs;&longs;er de <lb/>uno fante de piu, di quello &longs;ara el terzo della nostra radice, come, e&longs;&longs;empi gratia &longs;e li <lb/>detti fanti fu&longs;&longs;eno. </s> <s id="s.001019">2809. la &longs;ua radice &longs;ara. </s> <s id="s.001020">53. la qual partita per tre, ne uien. </s> <s id="s.001021">17. & <lb/>auanza. </s> <s id="s.001022">2. e per <expan abbr="tãto">tanto</expan> dico, che tai fanti &longs;e ne formara file.<emph.end type="italics"/> 159. (<emph type="italics"/>cioe el treppio de.<emph.end type="italics"/> 53.) <lb/><emph type="italics"/>le quale file. </s> <s id="s.001023">159. diuidendole pur i tre parti, ne uenira. </s> <s id="s.001024">53. per parte, cioe el numero del <lb/>la radice, & la prima, & terza parte uol e&longs;&longs;er de uno fante de piu del terzo della no­<lb/>&longs;tra radice, cioe uoleno e&longs;&longs;er de fanti. </s> <s id="s.001025">18. per fila, & la &longs;econda parte, cioe la parte de <lb/>mezzo, uol e&longs;&longs;er puramente el terzo della nostra radice, cioe de fanti. </s> <s id="s.001026">17. per fila tal­<lb/>mente, che de tutte le. </s> <s id="s.001027">159. file, le prime. </s> <s id="s.001028">53. file, & co&longs;i le ultime. </s> <s id="s.001029">53. file uoranno e&longs;&longs;er <lb/>de fanti. </s> <s id="s.001030">18. per fila, & le. </s> <s id="s.001031">53. file di mezzo uoranno e&longs;&longs;er &longs;olamente de fanti. </s> <s id="s.001032">17. per <lb/>fila. </s> <s id="s.001033">Et in quella che nel partire la radice per. </s> <s id="s.001034">3. auanza &longs;olamente uno ua al contrario <lb/>di que&longs;ta, cioe, che la prima, & terza parte della detta gran fila delle file, uoleno &longs;em­<lb/>pre tanti fanti per fila, quanto &longs;ara la terza parte integra della nostra radice, & la <lb/>parte di mezzo, cioe la &longs;econda uora uno fante de piu del ditto terzo della nostra radi <lb/>ce. </s> <s id="s.001035">Et perche mai puo auanzar piu che uno, ouer dui, à partire la detta no&longs;tra radice <lb/>per. </s> <s id="s.001036">3. le dette nostre regole ue &longs;atisfar anno in ogni quantita de fanti &longs;i quadrata, ouer <lb/>non quadrata, perche, come di &longs;opra fu detto, nelle quantita, ouer numerinon quadra­<lb/>ti, &longs;empre &longs;e piglia la radice propinqua di quel tal numero, & di quella &longs;e ne &longs;erue, co <lb/>me di &longs;opra è &longs;tato detto, & de quello re&longs;iduo, ouer &longs;uperfluo de fanti, che &longs;operchia&longs;­<lb/>&longs;eno el quadrato di tal radice el &longs;argente li a&longs;&longs;etta &longs;econdo el &longs;uo parere, e&longs;&longs;empi gra­<lb/>tia, &longs;e li detti fanti fu&longs;&longs;eno quattromilla, el qual numero non è quadrato, nondimeno di <lb/>co, che di quello &longs;e debbia cauar la &longs;ua radice propinqua, la quale &longs;ara<emph.end type="italics"/> 63. (<emph type="italics"/>uero è, che<emph.end type="italics"/><pb pagenum="46" xlink:href="042/01/091.jpg"/><emph type="italics"/>auanzara fanti.<emph.end type="italics"/> 31.) <emph type="italics"/>& di tal radice &longs;eruir&longs;ene &longs;econdo il &longs;uo uolere, e&longs;&longs;empi gratia, uo <lb/>lendoli de &longs;ubito mettere in btttaglia quadra di gente, &longs;e ne doueria mettere &longs;e&longs;&longs;anta­<lb/>tre fanti per fila, & tal battaglia uenira quadra di gente, come nel primcipio fa det­<lb/>to, uero è, che ui auanzaria fora di tal ordinanza quelli fanti. </s> <s id="s.001037">31. li quali il &longs;argente li <lb/>a&longs;&longs;ettara &longs;econdo el &longs;uo uolere, &longs;imilmente uolendo mettere li detti fanti quattro mille <lb/>in camino &longs;e die pur tore la detta &longs;ua radice propinqua, la quale, come detto è &longs;e&longs;&longs;anta <lb/>tre, la qual partendola per tre, ne uien. </s> <s id="s.001038">21. & non auanza co&longs;a alcuna, e per tanto gli <lb/>detti fanti &longs;i debbouo far caminare à fanti. </s> <s id="s.001039">21. per fila, & partire le dette file in tre <lb/>parte à. </s> <s id="s.001040">63. file per parte, uero é, che la ultima parte uerra à e&longs;&longs;er de. </s> <s id="s.001041">64. file, & an­<lb/>chor. </s> <s id="s.001042">10. fanti de piu (per quelli fanti. </s> <s id="s.001043">31. che auanzorno in principio, li quali (come è <lb/>detto) re&longs;tar anno fora della ordinanza, &longs;econdo il parere del &longs;argente, & per lo me­<lb/>de&longs;imo modo &longs;e procedaria, quando che la radice di tal numero non quadrato non re­<lb/>ceue&longs;&longs;e la perfetta diui&longs;ion per tre, cioe, &longs;el auanza&longs;&longs;e uno, procedere, come di &longs;opra <lb/>dißi, cioe dar uno fante de piu per fila alla parte di mezzo, & alle altre due parti, <lb/>cioe alla prima, & alla terza porui &longs;olamente tanti fanti per fila, quanto &longs;ara la ter­<lb/>za parte della nostra radice, & quando auanza&longs;&longs;e. </s> <s id="s.001044">2. procedere al contrario, cioe <lb/>dar uno fante per fila de piu alla prima, & alla terza parte, & alla &longs;econda porui &longs;ola <lb/>mente tanti fanti per fila, quanto &longs;ara el terzo della no&longs;tra radice, & quelli fanti che <lb/>fu&longs;&longs;eno auanzati nel cauar della radice in principio, a&longs;&longs;ettarli, come di &longs;opra è &longs;tato <lb/>detto.<emph.end type="italics"/> C.H. N<emph type="italics"/>on procedati piu oltra, che ue ho inte&longs;o benißimo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001045">QVESITO TERZO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> C.H<emph type="italics"/>ieronimo da Piagnano.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001046">CONTE HIERONIMO. I<emph type="italics"/>o adimandai una uolta à uno famo&longs;o Sargen­<lb/>te, come ordinaria una battaglia de. </s> <s id="s.001047">1000. fanti, lui me ri&longs;po&longs;e, che lui faria el fi <lb/>le de fanti. </s> <s id="s.001048">49. per te&longs;ta, hor ue adimando, uolendo io ordinare una battaglia &longs;imile à <lb/>que&longs;ta de una altra maggiore, ouer menore quantita de fanti, come me doueria gouer­<lb/>nare.<emph.end type="italics"/> N. Q<emph type="italics"/>uadrati quello numero de. </s> <s id="s.001049">49. cioe multiplicatilo in &longs;e mede&longs;imo, che fara <lb/>2401. & que&longs;to. </s> <s id="s.001050">2401. moltiplicareti fia quella quantita de fanti, che uoreti mettere <lb/>in battaglia, & quel produtto, partiritele per el uo&longs;tro. </s> <s id="s.001051">1000. & la radice di que&longs;to <lb/>aduenimento &longs;ara nel numero di fanti, che douereti metter in cadauna fila per te&longs;ta, <lb/>e&longs;&longs;empigratia, &longs;e quelli fanti, che de&longs;iderareti di mettere in una battaglia &longs;imile fu&longs;­<lb/>&longs;eno. </s> <s id="s.001052">2500. multiplicati que&longs;ti fanti. </s> <s id="s.001053">3500. per. </s> <s id="s.001054">2401. cioe per el quadrato de. </s> <s id="s.001055">49. fa­<lb/>ra. </s> <s id="s.001056">8403500. & que&longs;to tal produtto, partireti per el uo&longs;tro. </s> <s id="s.001057">1000. ne uenira. </s> <s id="s.001058">8403. <lb/>(la&longs;&longs;ando el rotto, perche uno huomo non &longs;i puo &longs;pezzare, che non peri&longs;ca el tutto,) <lb/>& di que&longs;to. </s> <s id="s.001059">8403. ne cauareti la radice, la qual &longs;ara. </s> <s id="s.001060">91. & auanzara. </s> <s id="s.001061">112. & fanti <lb/>91. douereti mettere in cadauna fila per te&longs;ta, & per fianco ne uerra à e&longs;&longs;er fanti. </s> <s id="s.001062">38. <lb/>uero è che anchor ne auanzara fora fanti. </s> <s id="s.001063">42. quali non compir anno la ultima fila de <lb/>drio. </s> <s id="s.001064">Et con &longs;imel ordine uoi procedareti in ogni altra maggior, ouer menor quantita.<emph.end type="italics"/><lb/>C.H. V<emph type="italics"/>eho inte&longs;o benißimo, & questa uo&longs;tra regola la ho piu accara, che co&longs;a, che <lb/>me habbiati in&longs;egnato, perche me gli &longs;on affaticato molti giorni, per trouarui rego­<lb/>la, & mai ue la ho potuta ritrouare.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/092.jpg"/> <p type="head"> <s id="s.001065">QVESITO QVARTO FATTO DAL SARGENTE <lb/><emph type="italics"/>maggiore del Duca di Vrbino.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001066">SARGENTE. C<emph type="italics"/>ome ordinare&longs;ti una battaglia quadra di terreno, & non di <lb/>gente.<emph.end type="italics"/> N. V<emph type="italics"/>olendo limitar à cadauno fante piedi. </s> <s id="s.001067">7. per <expan abbr="lõghezza">longhezza</expan>, & piedi. </s> <s id="s.001068">3. <lb/>per larghezza (come uol Vegetio) cioe piedi. </s> <s id="s.001069">3. dauanti, & piedi. </s> <s id="s.001070">3. de drio. </s> <s id="s.001071">et piedi. </s> <s id="s.001072">1. <lb/>uol che occupi la &longs;ua per&longs;ona, che in &longs;umma &longs;arian piedi. </s> <s id="s.001073">7. in lungo, et da &longs;palla à &longs;pal <lb/>la uol che occupi piedi. </s> <s id="s.001074">3. come di &longs;opra è detto, io procedaria in que&longs;to modo multipli <lb/>carei quella quantita de fanti, che de&longs;idera&longs;&longs;e di metter in battaglia, per el quadrato <lb/>de &longs;ette. </s> <s id="s.001075">cioe per. </s> <s id="s.001076">49. & quel produtto parteria per. </s> <s id="s.001077">21. & quanto fu&longs;&longs;e la radice di <lb/>tal aduenimento, tantifanti mettaria in cadauna fila per te&longs;ta, e&longs;&longs;empi gratia, &longs;el fu&longs;&longs;e <lb/>fanti. </s> <s id="s.001078">3600. li quali de&longs;ideraßi di mettere in battaglia quadra di terreno, & non di <lb/>gente, io moltiplicaria li detti fanti. </s> <s id="s.001079">3600. per el quadrato de. </s> <s id="s.001080">7. cioe per. </s> <s id="s.001081">49. fariano <lb/>176400. & que&longs;to produtto lo parteria per. </s> <s id="s.001082">21. del qual partimento ne ueneria <lb/>8400. & di que&longs;to <expan abbr="aduenim&etilde;to">aduenimento</expan> ne cauaria la radice, laqnal &longs;aria.<emph.end type="italics"/> 91. (<emph type="italics"/>uero è che auan <lb/>zaria.<emph.end type="italics"/> 119.) <emph type="italics"/>& de fanti. </s> <s id="s.001083">91. faria le file per te&longs;ta, uero è che la maggior parte delle uol <lb/>te nella coda ui re&longs;tara una fila non compita, cioe imperfetta, perche li numeri rare <lb/>uolte ne &longs;eruano preci&longs;amente &longs;econdo el no&longs;tro intento, &longs;i, come anchora occorre nel <lb/>fare le battaglie quadre di gente, cioe, che la maggior parte delle uolte ne <expan abbr="auãza">auanza</expan> qual <lb/>che fante de piu, tamen una fila de piu, ouer de manco, non fa error troppo apparente.<emph.end type="italics"/><lb/>S. D<emph type="italics"/>oue cauati quel. </s> <s id="s.001084">21. con el quale uoi parteti quella uo&longs;tra multiplicatione.<emph.end type="italics"/> N. <lb/>I<emph type="italics"/>o imagino una battaglia de tre file a fanti. </s> <s id="s.001085">7. per fila, la qual batt aglia &longs;aria quadra di <lb/>terreno, perche le tre file in longo <expan abbr="uorãno">uoranno</expan> piedi. </s> <s id="s.001086">21. di terreno (a piedi. </s> <s id="s.001087">7. per fila fra <lb/>dauanti, & de drio con quel piede, che occupa ogni fila, & &longs;imelmente li fanti. </s> <s id="s.001088">7. in lar <lb/>ghezza uoranno mede&longs;imamente piedi. </s> <s id="s.001089">21. di terreno a piedi. </s> <s id="s.001090">3. per fante, onde&longs;e tal <lb/>battaglia occupa piedi. </s> <s id="s.001091">21. di terreno in ogni uer&longs;o la &longs;ara quadra di terreno, & tutta <lb/>tal battaglia contenera fanti. </s> <s id="s.001092">21. & que&longs;ti fanti. </s> <s id="s.001093">21. me ne &longs;eruo per partitore nella &longs;o <lb/>pra&longs;critta mia operatione.<emph.end type="italics"/> S. S<emph type="italics"/>ta benißimo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001094">QVESITO QVINTO FATTO DAL S. GABRIEL <lb/>T<emph type="italics"/>admo da Martinengo, Cauallier de Rhodi, <lb/>e Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001095">PRIORE. D<emph type="italics"/>apoi che &longs;opra la compo&longs;itione della poluere non ui habbiamo <lb/>altro che dire, per non star ocio&longs;i dapoi la no&longs;tra lettione di Euclide, uoglio che <lb/>ragionamo un poco del modo de ordinare li e&longs;&longs;erciti in battaglia, & maßime in alcu­<lb/>ne ingenio&longs;e forme, u&longs;itate da no&longs;tri antiqui, el qual modo, alli pre&longs;enti tempi, par &longs;ia <lb/>totalmente per&longs;o, & anullato, per non trouar&longs;e alcuno autore antiquo, ne moderno, <lb/>che ne dia el modo, ouer regola di &longs;aperli ordinare, & que&longs;te tai figure, ouer forme &longs;o <lb/>no el cuneo, la forfice, la &longs;erra, el <expan abbr="rhũbo">rhumbo</expan>, el cerchio, et la forma lunare, uero è che el ual <lb/>lo ha posto alcune str anie &longs;orme di battaglie, ma rare di quelle è che &longs;ia atta a poter ca <lb/>minare, che <expan abbr="nõ">non</expan> ui &longs;egua immediate di&longs;ordine, <21> che ogni ordinata battaglia &longs;e la debbe<emph.end type="italics"/><pb pagenum="47" xlink:href="042/01/093.jpg"/><emph type="italics"/>e&longs;&longs;er atta à poter caminare in quel tal ordine eglie nece&longs;&longs;ario che ogni fante habbia uno <lb/>altro fante in debita di&longs;tantia, che ui camini auanti di &longs;e, eccetto quelli della prima fron <lb/>te, & co&longs;i un'altro per banda, eccetto quelli che &longs;ono nei fianchi, et co&longs;i un'altro de drio <lb/>eccetto la ultima fila, perche ogni fante nel caminare &longs;e regge dal &longs;uo compagno che gli <lb/>camina auanti di &longs;e, eccetto quelli della prima fila, e pero &longs;e una ordinanza uorra cami <lb/>nare, & che tutti li fanti non habbiano un'altro fante, che gli camini auanti di &longs;e nella <lb/>&longs;ua debita di&longs;tantia, accettuando quelli della prima fronte, &longs;ubito tal ordinanza uerra <lb/>in confu&longs;ione.<emph.end type="italics"/> N. C<emph type="italics"/>redo che &longs;ia co&longs;i, perche ogni fante piglia la meta nel &longs;uo cami­<lb/>nare pian, e forte, dal compagno che gli camina auanti, eccetto quelli che &longs;ono nella pri <lb/>ma fila della fronte, li quali non &longs;i reggono da niuno nel caminare, ancitutte le altre fi­<lb/>le &longs;e reggono da quella &longs;ola.<emph.end type="italics"/> P. C<emph type="italics"/>o&longs;i è, hor dapoi che uedo che haueti inte&longs;o la mia o­<lb/>pinione, ue adimando, come &longs;e douera procedere, uolendo ordinare una quantita de fan <lb/>ti, ouer uno e&longs;&longs;ercito in forma cunea, ouer triangolare talmente che fu&longs;&longs;eno atti à po­<lb/>ter caminare uer&longs;o la ponta de tal cuneo, cioe che tal ordinanza po&longs;&longs;a caminare con la <lb/>ponta di tal cuneo uer&longs;o li nemici.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;ta forma di ordinanza, ouer di battaglia <lb/>na&longs;ce, ouer &longs;e forma dalla progreßione a&longs;cendente per numero binario, cominciando <lb/>dalla unita, cioe ponendo prima un fante, & dapoi. </s> <s id="s.001096">3. & dapoi. </s> <s id="s.001097">5. & dapoi. </s> <s id="s.001098">7. & dapoi. <lb/></s> <s id="s.001099">9. & dapoi. </s> <s id="s.001100">11. & co&longs;i andar procedendo, & accre&longs;cendo &longs;empre dui fanti de piu, per <lb/>fina à tanto che non ui &longs;ia piu fanti, uero è, che potria e&longs;&longs;er tal numero de fanti, che in <lb/>ultimo non potranno, ouer non &longs;aranno &longs;officienti à compir la ultima fila, ilche e&longs;&longs;en­<lb/>do &longs;e potriano la&longs;&longs;ar co&longs;i fuora della ordinanza da &longs;eruir&longs;ene &longs;econdo parera al buon <lb/>Sargente, perche tal co&longs;a occorre la maggior parte delle uolte, & in ogni &longs;pecie de or­<lb/>dinanza, cioe che &longs;empre ui re&longs;ta qualche fante fuora di tal ordinanza.<emph.end type="italics"/> P. C<emph type="italics"/>redo <lb/>que&longs;to che uoi diceti, ma datime uno e&longs;&longs;empio in figura &longs;opra tal materia, & in piccol <lb/>numero, perche nelli numeri piccoli meglio &longs;e intende la co&longs;a.<emph.end type="italics"/> N. P<emph type="italics"/>oniamo che li fan <lb/>ti che de&longs;ideriamo di mettere in battaglia cunea &longs;iano. </s> <s id="s.001101">100. dico che prima &longs;e ne pon­<lb/>ga uno, dapoi. </s> <s id="s.001102">3. dapoi. </s> <s id="s.001103">5. dapoi. </s> <s id="s.001104">7. dapoi. </s> <s id="s.001105">9. dapoi. </s> <s id="s.001106">11. & co&longs;i andar procedendo &longs;empre <lb/>mettendoui. </s> <s id="s.001107">2. fanti de piu per fina à tanto che ue &longs;ia fanti, come di &longs;otto appare in fi­<lb/>gura, onde la ultima fila, in que&longs;to ca&longs;o uenira à e&longs;&longs;er de fanti. </s> <s id="s.001108">19. & non ui auanzara <lb/>alcun fante, & que&longs;to è, perche il numero delli fanti (cioe il. </s> <s id="s.001109">100.) è numero quadrato,<emph.end type="italics"/><lb/><figure id="id.042.01.093.1.jpg" xlink:href="042/01/093/1.jpg"/><pb xlink:href="042/01/094.jpg"/><emph type="italics"/>& co&longs;i in ogni altro numero, che &longs;ia quadrato &longs;e formara il detto cuneo &longs;enza alcuno <lb/>&longs;oprauanzamento de fanti, ma &longs;e il detto numero de fanti non &longs;ara numero quadrato <lb/>&longs;empre ui auanzara tanti fanti, quanto che il detto numero de fanti auanzara il mag­<lb/>gior numero quadrato contenuto da quello, e&longs;&longs;empi gratia &longs;e gli propo&longs;ti fanti da far <lb/>il cuneo fu&longs;&longs;eno. </s> <s id="s.001110">120. dico che ui auanzara. </s> <s id="s.001111">20. fanti fuora della ordinanza del cuneo, <lb/>cioe tanti quanto che. </s> <s id="s.001112">120. eccede el. </s> <s id="s.001113">100. (maggior numero quadrato contento da <lb/>quello) che &longs;aria pur. </s> <s id="s.001114">20. ma fe gli detti fanti fu&longs;&longs;eno. </s> <s id="s.001115">123. ui auanzaria &longs;olamente fan <lb/>ti. </s> <s id="s.001116">2. perche il maggior numero quadrato contenuto da. </s> <s id="s.001117">123. &longs;aria. </s> <s id="s.001118">121. e pero. </s> <s id="s.001119">123. <expan abbr="auã">auam</expan> <lb/>za il detto. </s> <s id="s.001120">121. nel detto. </s> <s id="s.001121">2. & questo mede&longs;imo &longs;i debbe intendere in ogni gran nu­<lb/>mero.<emph.end type="italics"/> P. E<emph type="italics"/>ue ho inte&longs;o benißimo, & me ba&longs;ta a&longs;&longs;ai per que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001122">QVESITO SESTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001123">PRIORE. C<emph type="italics"/>ome &longs;e potria formar quella figura chiamata la forfice, la quale <lb/>u&longs;auano gliantichi per opponere alla forma cunea.<emph.end type="italics"/> N. L<emph type="italics"/>a forfice &longs;e costitui&longs; <lb/>&longs;e con due forme cunee congionte per tuor la detta figura cunea in meggio.<emph.end type="italics"/> P. D<emph type="italics"/>ati­<lb/>me uno e&longs;&longs;empio figurale, & in piccol numero.<emph.end type="italics"/> N. L<emph type="italics"/>o e&longs;&longs;empio di questa lo uoglio <lb/>adure nel mede&longs;i no numero de fanti. </s> <s id="s.001124">100. con che fu fatto il cuneo, accio che quella <lb/>po&longs;&longs;a far giudicio, &longs;e il fu&longs;&longs;e dui e&longs;&longs;erciti eguali de quantita de fanti, & che l'uno for­<lb/>ma&longs;&longs;e il cuneo, & l'altro la forfice, qual de loro haueria auantaggio, dico adunque che <lb/>e&longs;&longs;endo fanti. </s> <s id="s.001125">100. & uolendo de quelli formare la forfice, li &longs;e debbono diuidere in due <lb/>parti eguali, che ne ueneria. </s> <s id="s.001126">50. per parte, & de cadauna de que&longs;te parti &longs;e ne debbe<emph.end type="italics"/><lb/><figure id="id.042.01.094.1.jpg" xlink:href="042/01/094/1.jpg"/><pb pagenum="48" xlink:href="042/01/095.jpg"/><emph type="italics"/>&longs;ormar uno cuneo, &longs;econdo il modo di &longs;opra detto, & congionger li in&longs;ieme, come di <lb/>&longs;opra appare in figura con le &longs;ue ponte uer&longs;o delli nemici, cioe ner &longs;o del cuneo per tor <lb/>lo in meggio, & bi&longs;ogna notare qualmente nella formatione di que&longs;ti dui cunei, ui auan <lb/>zara un fante per cadauno de loro fuora della <expan abbr="ordinãza">ordinanza</expan>, <21> che il numero. </s> <s id="s.001127">50. <expan abbr="nõ">non</expan> è nume <lb/>ro quadrato, & auanza il maggior numero quadrato contenuto da quello (qual è.<emph.end type="italics"/> 49.)<emph type="italics"/><lb/><21> un fante &longs;olo, cioe fra tutti dui ui <expan abbr="auãzaria">auanzaria</expan> dui fanti, come di &longs;opra appare in figura.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001128">PRIORE. C<emph type="italics"/>ertamente non è huomo che non reputa&longs;&longs;e che li fanti che &longs;ono <lb/>in quelli dui cunei che formano la detta forfice, non fu&longs;&longs;eno piu d'un tanto, e meg <lb/>gio de quelli, che &longs;ono nel primo cuneo, & &longs;e io non gli haue&longs;&longs;e numerati, io non lo cre­<lb/>derei che fu&longs;&longs;eno eguali, e per tanto, io giudicarei, in dui e&longs;&longs;erciti co&longs;i ordinati, e&longs;&longs;er <lb/>maggior auantaggio nella forfice, che nel cuneo, perche la forfice piglia in meggio il <lb/>detto cuneo, & quello ha da tendere nel combattere dall'una é l'altra banda, & li dui <lb/>cunei della forfice non hanno da tendere nel combattere, &longs;aluo che da una banda &longs;ola <lb/>cadauno de loro.<emph.end type="italics"/> N. C<emph type="italics"/>o&longs;i è da giudicare.<emph.end type="italics"/> P. N<emph type="italics"/>on uoglio che intramo in altra ma­<lb/>teria per questa &longs;era, ma diman de &longs;era uoglio che di&longs;putamo la proprieta di que&longs;ta fi­<lb/>gura cunea, quando che il nemico non &longs;ape&longs;&longs;e formar la detta forfice.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001129">QVESITO SETTIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barleata.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001130">PRIORE. B<emph type="italics"/>en quando &longs;e ordina&longs;&longs;e uno e&longs;&longs;ercito in forma cunea, & che li ne­<lb/>mici non haue&longs;&longs;ono l'arte di &longs;aper far la forfice, che auantaggio &longs;e potria giudi­<lb/>care per quella &longs;orte figura, maßime hauendo tanta gente l'una parte quanto l'altra.<emph.end type="italics"/><lb/>N. Q<emph type="italics"/>uando che la contraria parte uole&longs;&longs;e opponer&longs;e à tal figura cunea, con una for­<lb/>ma quadra di terreno, come al pre&longs;ente &longs;i co&longs;tuma, à tutte le ragion del mondo restara<emph.end type="italics"/><lb/><figure id="id.042.01.095.1.jpg" xlink:href="042/01/095/1.jpg"/><pb xlink:href="042/01/096.jpg"/><emph type="italics"/>rotto è &longs;bezzato.<emph.end type="italics"/> P. P<emph type="italics"/>erche ragione.<emph.end type="italics"/> N. L<emph type="italics"/>a ragion ue la diro, &longs;ia e&longs;&longs;empi gra­<lb/>tia fanti. </s> <s id="s.001131">100. in forma cunea, & altri fanti. </s> <s id="s.001132">100. in forma quadra di terreno all'op­<lb/>po&longs;ition del detto cuneo, come di &longs;otto appare in figura, & perche l'ordine del ferir <lb/>del cuneo, e que&longs;to che tutti quelli che tirano de alcuna &longs;orte i&longs;trumento, come &longs;ono ar­<lb/>tegliarie, archibu&longs;i, dardi, archi, ouer bale&longs;tre, tutti debbono tendere à tirare, & à &longs;e­<lb/>rire &longs;olamente in quel luoco doue ua à inferire la ponta del cuneo, cioe in ponto. </s> <s id="s.001133">a. <!-- REMOVE S-->on­<lb/>de li fanti che in quel luoco &longs;e ritrouar anno, ui &longs;ara nece&longs;&longs;ario, o a morire, ouer à dar <lb/>luoco alla ponta del detto cuneo, per la grande moltitudine delle archibu&longs;ate, & friz­<lb/>zate tutte in quel &longs;olo luoco tirate, intrando adunque dentro la ponta del detto cu­<lb/>neo in tal luoco, continuamente andara preforando, & penetrando tutta quella or <lb/>dinanza da banda, à banda, perche tutti archibu&longs;eri, & arceri che re&longs;tano di fuora, <lb/>non debbono ce&longs;&longs;ar de tirare in quel i&longs;te&longs;&longs;o luoco, & non altroue, la qual co&longs;a facendo <lb/>eglie impoßibile che non ui &longs;ia dato luoco al detto cuneo da penetrare, et penetrato che <lb/>&longs;ia tal e&longs;&longs;ercito è rotto &longs;enza alcun remedio.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;ta co&longs;a è chiara, che &longs;e il detto <lb/>cuneo penetra tutta la detta ordinanza quella &longs;enza dubbio re&longs;ta rotta, e fraca&longs;&longs;ata, et <lb/>è qua&longs;i impoßibile che non gli uenga ad ef&longs;etto, perche tutta la po&longs;&longs;anza & uirtu de <lb/>quel tal cuneo uien à operare in quel luoco &longs;olo, e pero eglie qua&longs;i impoßibile che in <lb/>quel tal luoco ui po&longs;&longs;ano durare anchor, che fu&longs;&longs;eno molto piu in tal <expan abbr="ordinãza">ordinanza</expan>, de quel­<lb/>li che fu&longs;&longs;eno nel detto cuneo, perche tal luoco non puo e&longs;&longs;er &longs;occor&longs;o da alcuno de quel <lb/>li di tal ordinanza, perche &longs;e quelli che &longs;ono uer&longs;o. </s> <s id="s.001134">b. <!-- REMOVE S-->ouer uer&longs;o. </s> <s id="s.001135">c. <!-- REMOVE S-->uole&longs;&longs;eno uenire à <lb/>dar &longs;occor&longs;o à quel tal luoco, &longs;aria forza à de&longs;ordinar&longs;e, & de&longs;ordinati che fu&longs;&longs;ono, <lb/>incorrariano nel mede&longs;imo &longs;candolo, cioe re&longs;tariano rottitotalmente, & re&longs;tando nel <lb/>&longs;uo luoco la &longs;ua uirtu, ouer po&longs;&longs;anza, re&longs;ta qua&longs;i morta, perche niun de loro la puo mo <lb/>&longs;trare per ualente che &longs;ia, & hor comprendo di quanta importantia &longs;ia que&longs;ta forma <lb/>cunea, à chinon ui &longs;apeßi, trouar la&longs;ua medicina, ouer rimedio.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio che <lb/>onv buona forma alle uolte è di tal autorita quanto che è la &longs;ua materia, & anchor piu.<emph.end type="italics"/><lb/>P. C<emph type="italics"/>ertamente que&longs;ta uo&longs;tra opinione mi è piace&longs;ta a&longs;&longs;ai, et mi ba&longs;ta per que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001136">QVESITO OTTAVO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001137">PRIORE. C<emph type="italics"/>ome &longs;e potria formare, de una quantita de fanti, ouer di uno e&longs;&longs;er <lb/>cito, quella forma, ouer figura di battaglia dalli antichi chiamata la Serra.<emph.end type="italics"/> N. <lb/>Q<emph type="italics"/>ue&longs;ta forma di battaglia, &longs;econdo la qualita del &longs;uo nome, à mi me pare che debbia <lb/>e&longs;&longs;ere dentata, &longs;i come è la &longs;ega con che &longs;e co&longs;tuma &longs;egar li traui, e per tanto uolendo re <lb/>dure una quantita de fanti, ouer uno e&longs;&longs;ercito in tal forma. </s> <s id="s.001138">bi&longs;ogna con&longs;iderare due co <lb/>&longs;e, l'una de quanti denti&longs;e uol far que&longs;ta Serra, ouer &longs;ega, & &longs;e oltra tai denti ui &longs;i uol <lb/>altra ordinanza da &longs;ostentar quelli denti, ouer non.<emph.end type="italics"/> P. D<emph type="italics"/>atime uno e&longs;&longs;empio in figu <lb/>ra&longs;opra quello che uoleti in ferire, ma in poco numero de fanti, perche meglio appren <lb/>dero la co&longs;a.<emph.end type="italics"/> N. P<emph type="italics"/>oniamo che li fanti delli quali &longs;e uol formare li puri denti della det­<lb/>ta Serra &longs;iano. </s> <s id="s.001139">100. hor que&longs;ti. </s> <s id="s.001140">100. fanti &longs;i debbono diuidere nel numero delli denti che <lb/>&longs;i uol dar à que&longs;ta Serra, & de cadauna de quelle parti formarne un cuneo, per la re-<emph.end type="italics"/><pb pagenum="49" xlink:href="042/01/097.jpg"/><emph type="italics"/>gola data nel. </s> <s id="s.001141">5. Que&longs;ito, & quelli tai cunei, congiongerli in diretto, &longs;econdo che fu fat <lb/>to di quelli dui nel formar la forfice, e&longs;&longs;empi gratia, poniamo, che delli detti fanti cen <lb/>to &longs;e uoglia far quattro denti di una &longs;erra, dico, che li detti fanti <expan abbr="c&etilde;to">cento</expan> li &longs;e debbono par <lb/>tire in quattro parti, del qual partimento ne uenira fanti. </s> <s id="s.001142">25. per parte, hor di cadau <lb/>na di queste parti &longs;e ne debbe formar un cuneo &longs;econdo lordine dato nel detto. </s> <s id="s.001143">5. Que <lb/>&longs;ito, & que&longs;ti quattro cunei congiongerli in diretto, come di&longs;otto appar in figura, & <lb/>que&longs;to è in quanto al far delli puri denti, ma &longs;e per ca&longs;o &longs;e uole&longs;&longs;e mettere una altra or <lb/>dinanza drio alli detti quattro denti, bi&longs;ognaria prima determinare de quanti fanti <lb/>tal ordinanza&longs;e uora fare, & quella cauarla de per &longs;e, & del resto formar li denti, &<emph.end type="italics"/><lb/><figure id="id.042.01.097.1.jpg" xlink:href="042/01/097/1.jpg"/><lb/><emph type="italics"/>de drio de detti denti ponerui quella quantita de fanti, che prima fu cauata, & ordi­<lb/>narli à tanti fanti per fila, quanti fanti &longs;e trouara direttamente in longo e&longs;&longs;ere in tutte <lb/>le ba&longs;e delli denti formati, e&longs;&longs;empi gratia, poniamo che &longs;iano fanti. </s> <s id="s.001144">244. et che de fan <lb/>ti. </s> <s id="s.001145">100. de quelli &longs;e uoglia fare quattro denti di una &longs;erra, & delli altri. </s> <s id="s.001146">144. &longs;e uoglia <lb/>fare una ordinanza &longs;u&longs;tentante li detti quattro denti, dico, che redutti li fanti cento in <lb/>quattro denti, come di &longs;opra fu detto, con&longs;equentemente drieto à quelli ui &longs;e debbe a&longs;&longs;et <lb/>tar quelli cento quar antaquattro fanti à fanti trenta&longs;ei per fila, perche in tutte quat­<lb/>tro le ba&longs;e de detti quattro denti ui &longs;ono fanti trenta&longs;ei, come nella &longs;otto &longs;critta figura <lb/>appare, & co&longs;i con tal modo, & ordine &longs;e potra ordinare, &longs;e fu&longs;&longs;eno bene cento milia <lb/>fanti de&longs;tinguendo, come di &longs;opra &longs;e fatto in quel poco numero.<emph.end type="italics"/> P. V<emph type="italics"/>eho inte&longs;o be­<lb/>nißimo, & ba&longs;ta per que&longs;ta&longs;era.<emph.end type="italics"/></s> </p> <figure id="id.042.01.097.2.jpg" xlink:href="042/01/097/2.jpg"/> <p type="head"> <s id="s.001147">QVESITO NONO FATTO DAL MEDESIMO <lb/>S<emph type="italics"/>ignor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001148">PRIORE. C<emph type="italics"/>ome &longs;e potria redure una quantita de fanti, ouer uno e&longs;&longs;ercito in <lb/>figura Rhombica di gente, che fu&longs;&longs;eno atti à poter caminar con uno angolo uer-<emph.end type="italics"/><pb xlink:href="042/01/098.jpg"/><emph type="italics"/>&longs;o li nemici.<emph.end type="italics"/> N. C<emph type="italics"/>on la regola che &longs;i fa el cuneo, con quella mede&longs;ima qua&longs;i &longs;i fa el <expan abbr="rhõ">rhom</expan> <lb/>bo, perche diuidendo tutti quei fanti, ouer quello e&longs;&longs;ercito con, che &longs;i uuol formar el <lb/>detto rhombo in due parti equali, & di quella mita formar el cuneo, & formato che le <lb/>&longs;opra el me de&longs;imo ultimo lato, ui&longs;e debbe andar a&longs;&longs;ettando l'altra mita de fanti, ouer <lb/>del a&longs;&longs;ercito con file, che continuamente anda&longs;&longs;eno declinando per dui fanti <expan abbr="mãco">manco</expan>, cioe <lb/>al contrario di quello &longs;e fa comenzandolo dalla unita, cioe comenzando à far la ponta <lb/>del cuneo, nel qual &longs;i ua continuamente accre&longs;cendo le file per dui fanti piu, ma bi&longs;o­<lb/>gna aduertire, che &longs;e nella fabricatione del primo cuneo, ui ananza&longs;&longs;e qualche fanti, <lb/>che non fu&longs;&longs;eno à &longs;officienza de farui un'altra fila, quella mede&longs;ima fila &longs;e debbe pur <lb/>compire con li fanti dell'altra mita de fanti, perche uno di que&longs;ti dui cunei congionti, <lb/>uiene a e&longs;&longs;er de una fila piu de l'altro.<emph.end type="italics"/> P. D<emph type="italics"/>atime un'e&longs;&longs;empio in figura ma in picciol <lb/>numero.<emph.end type="italics"/><lb/><figure id="id.042.01.098.1.jpg" xlink:href="042/01/098/1.jpg"/><pb pagenum="50" xlink:href="042/01/099.jpg"/>N. P<emph type="italics"/>oniamo, e&longs;&longs;empi gratia, che li fanti, con li quali &longs;e de&longs;idera di uoler &longs;ormar el <lb/>rhombo &longs;iano. </s> <s id="s.001149">320. dico, che &longs;i debbono partire in due parti equali, che de tal partinen <lb/>to ne uenira fanti. </s> <s id="s.001150">160. per parte, & de l'una di que&longs;te parti&longs;e ne debbe far uno cuneo <lb/>&longs;econdo l'ordine datto nel quinto Que&longs;ito, el qual fatto &longs;i trouara auanzar fanti. </s> <s id="s.001151">16. <lb/>(per le ragioni adutte nel detto quinto Que&longs;ito) cioe ui mancara fanti noue à compi­<lb/>re la detta ultima fila de tal primo rhombo, hor dico, che tal fila &longs;i debbe compire con <lb/>li fanti dell'altra mita, cioe pigliarne quelli fanti. </s> <s id="s.001152">19. che ui manca, che nel detto primo <lb/>rhombo uenira à e&longs;&longs;er fanti. </s> <s id="s.001153">169. & nell'altra parte uenira à re&longs;tare &longs;olamente fanti <lb/>151. coni quali formandone l'altro rhombo, &longs;opra la ultima fila del primo, la qual ulti <lb/>ma fila &longs;ara de fanti uinticinque, onde bi&longs;ognara &longs;opra di quella a&longs;&longs;ettaruene un'altra <lb/>fila de dui fanti manco, cioe de fanti uimitre, & di &longs;opra à quella de detti fanti uintitre <lb/>a&longs;&longs;ettaruene un'altra de fanti uintiuno, & &longs;opra à quella de fanti uintiuno, un'altra <lb/>de fanti de&longs;noue, & &longs;opra à quella de fanti de&longs;noue un'altra de fanti dieci&longs;ette, & co&longs;i <lb/>andar procedando &longs;empre con dui fanti manco, per fina à tanto che &longs;e peruenira alla fi <lb/>la dun fante &longs;olo (come di &longs;opra appar in figura) uero è, che &longs;i trouara in ultimo auan­<lb/>zar fanti&longs;ette, li quali il &longs;acente Sargente li a&longs;&longs;ettara &longs;econdo il &longs;uo parere, & co&longs;i con <lb/>tal modo, & ordine &longs;e potra redure in una &longs;imel ordinanza ogni grande e&longs;&longs;ercito, & <lb/>potranno uoltar&longs;e, & caminar facendo de&longs;palle fronte, & &longs;imelmente de qual &longs;i uo­<lb/>glia fianco.<emph.end type="italics"/> P. I<emph type="italics"/>o ue ho inte&longs;o ottimamente, & chel &longs;ia el uero, uoi uoleti primamen <lb/>te, che &longs;e aduerti&longs;ca, come chel primo cuneo ui à e&longs;&longs;er de una fila di fanti de piu del &longs;e­<lb/>condo, e pero e&longs;&longs;endo diui&longs;o lo e&longs;&longs;ercito in due parti equali, & ponendo poi quelli fan­<lb/>ti de&longs;noue, che auanzano nella formation del primo cuneo, in&longs;ieme <expan abbr="cõ">com</expan> quelli fanti. </s> <s id="s.001154">160. <lb/>dell'altra mita fariano poi fanti cento &longs;ettantanoue, delli quali uolendone poi formar <lb/>l'altro cuneo &longs;opra la ultima fila del detto primo cuneo, laquale &longs;aria &longs;olamente de fan <lb/>ti uintitre, & cominciando poi el &longs;econdo cuneo de fanti uintiuno (cioe per dui fanti <lb/>manco) & co&longs;i andar procedendo (per duo fanti meno) per fin al compimento di que <lb/>&longs;to &longs;econdo cuneo, ne uenira auanzar fanti cinquantacinque, & uoi per far auanzar <lb/>men fanti uoleti, che quella ultima fila (imperfetta del primo cuneo, quala è &longs;olamente <lb/>di fanti de&longs;noue, che la &longs;e compi&longs;ca delli fanti dell'altra mita (cioe pigliando quelli fan­<lb/>ti noue che ui manca) il che facendo, & procedendo poi come di &longs;opra fudetto, inul­<lb/>tima ui uenira auanzar &longs;olamente fanti &longs;ette, come di &longs;opra fu detto, et dapoi&longs;otto <expan abbr="giõ">giom</expan> <lb/>geti qualmente que&longs;ta figura rhombica ha quella pote&longs;ia, che &longs;e ritroua nelle ordinan <lb/>ze quadre di gente, ouer diterreno, cioe, che ella è atta à uoltar&longs;e, & far de &longs;palle <expan abbr="frõ">from</expan> <lb/>te, & caminar etiam per queluer&longs;o, & &longs;imelmente è atta à far da qual &longs;i uoglia fianco <lb/>te&longs;ta, uero è, che ui occorre in taiuer&longs;i à douer&longs;i re&longs;tringer per un uer&longs;o, & allargar­<lb/>&longs;e per un'altro, come medemamente, occorre anchora nelle dette ordinanze qua­<lb/>dre di gente, ouer di terreno.<emph.end type="italics"/> N. N<emph type="italics"/>on altro che que&longs;to uolemo inferire.<emph.end type="italics"/> P. A<emph type="italics"/>dun <lb/>que ue ho inte&longs;o, e pero al pre&longs;ente non uoglio che procedamo piu oltra <21> que&longs;ta &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001155">QVESITO DECIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <pb xlink:href="042/01/100.jpg"/> <p type="main"> <s id="s.001156">PRIORE. <emph type="italics"/>Come &longs;e potria ordinare una quantita de fanti, ouer uno e&longs;&longs;ercito <lb/>in una battaglia cornuta, che fu&longs;&longs;e atta à poter caminare in tal ordine contra à <lb/>li <expan abbr="nemicī">nemicim</expan>, & chi fu&longs;&longs;e anchora atta occorrendo il bi&longs;ogno à poter allongar i corni, cioe <lb/>buttarli in fuora etiam à tirarli in dentro (come &longs;uol far la lumaca, ouer bouolo) &longs;en <lb/>za alcum pericolo de alcun de&longs;ordine.<emph.end type="italics"/> N. V<emph type="italics"/>olendo e&longs;&longs;eguir tal co&longs;a, io diuideria tut <lb/>ti quelli fanti, ouer tutto quel e&longs;&longs;ercito in tre partiequali, & una di quelle parti redu­<lb/>ria in battaglia quadr a diterreno, & cadauna delle altre due le reduria in battaglia <lb/>quadra di gente, & <expan abbr="nõ">non</expan> di terreno, et una di que&longs;te due battaglie, la mettaria alla <expan abbr="bãda">banda</expan> <lb/>de&longs;tr a della prima battaglia (gia fatta in forma quadra di gente) & l'altraue la pone <lb/>ria alla banda &longs;ini&longs;tra, non continuate con quella, ma alquanto di&longs;tante: accio poßino <lb/>caminar piu pre&longs;to, ouer piutardi di quella di mezzo (occorrendo el bi&longs;ogno) &longs;enzæ <lb/>interrompere l'andare, ouer el &longs;tare della detta battaglia di mezzo.<emph.end type="italics"/> P. <!-- KEEP S--></s> <s id="s.001157">E <emph type="italics"/>ue ho qua&longs;t <lb/>inte&longs;o, nondimeno datime uno e&longs;&longs;empio in figura, ma &longs;opra tutto in poca quantita de <lb/>fanti, perche molto meglio &longs;e apprende la co&longs;a nelli numeri piccoli, che nelli numeri <lb/>grandi.<emph.end type="italics"/> N. P<emph type="italics"/>oniamo, che tutti li no&longs;tri fanti fu&longs;&longs;eno trecento, li quali uolendo li re­<lb/>dure in quella forma di battaglia, che me adimanda uo&longs;tra<emph.end type="italics"/> R <emph type="italics"/>euerentia, dico, che li diui <lb/>deria in tre parti equali, che in cadauna &longs;aria fanti cento, & l'una di que&longs;te partiredu <lb/>ria in battaglia quadra di terreno (per el modo dato nel quarto Que&longs;ito) & cadauna <lb/>delle altre due reduria in battaglia quadra di gente (per el modo dato nel primo Que­<lb/>&longs;ito) & fra queste due battaglie, gli a&longs;&longs;ettaria la prima battaglia detta di &longs;opra, cioe <lb/>quella quadra diterreno, talmente, che fu&longs;&longs;e alquanto di&longs;tinta, ouer di&longs;gionta da quel­<lb/>le, come di &longs;otto appar in figura, accio che occorrendo à uoler far procedere auanti<emph.end type="italics"/><lb/><figure id="id.042.01.100.1.jpg" xlink:href="042/01/100/1.jpg"/><lb/><emph type="italics"/>uno, ouer ambidue li corni, chel &longs;i po&longs;&longs;a fare &longs;enza di&longs;tur bar la ordinauza dimezzo, <lb/>ouer amente occorrendo à uoler retir are uno, ouer ambidui di ditti corni in drio, che <lb/>mede&longs;imamente el &longs;i po&longs;&longs;a fare &longs;enza impedimento della detta ordinanza di mezzo.<emph.end type="italics"/><lb/>P. C<emph type="italics"/>redeti che tai &longs;orte de corni fu&longs;&longs;eno quelli, che u&longs;auano li antiqui in alcune &longs;ue <lb/>battaglie.<emph.end type="italics"/> N. N<emph type="italics"/>on ui&longs;aprei dire di certo &longs;e fu&longs;&longs;eno &longs;un que&longs;ta forma, ma qu&longs;tea &longs;or­<lb/>te me la ho imaginata da me, perche la me par hauer in &longs;e tutto quello che mi ba ri­<lb/>cercato<emph.end type="italics"/> V.R. P. B<emph type="italics"/>a&longs;ta che la non me di&longs;piace, anchor che la non fu&longs;&longs;e &longs;imile à questo <lb/>che u&longs;auano li antichi.<emph.end type="italics"/></s> </p> <pb pagenum="51" xlink:href="042/01/101.jpg"/> <p type="head"> <s id="s.001158">QVESITO VNDECIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001159">PRIORE. E<emph type="italics"/>&longs;&longs;endo uno e&longs;&longs;ercito ordinato in qual &longs;i uoglia forma, & che per <lb/>&longs;orte li nemici inuistide&longs;&longs;ono dentro con le &longs;ue artegliarie, talmente che amaz­<lb/>za&longs;&longs;eno molti de quelli fanti di tal e&longs;&longs;ercito, &longs;e adimanda qual &longs;aria meglio che tal e&longs;&longs;er <lb/>cito camina&longs;&longs;e &longs;econdo che lui &longs;e ritroua&longs;&longs;e, cioe la&longs;&longs;ando quelli lochi co&longs;i uacui di quel <lb/>le per&longs;one morte dalle artegliarie, ouer à restringer&longs;i in&longs;ieme per impire quelli tali <lb/>lochiuacui.<emph.end type="italics"/> N. A<emph type="italics"/>ll'uno modo mi par male, & all'altro peggio, perche la&longs;&longs;ando quel <lb/>li lochi co&longs;i uacui, & maßime nella fronte, &longs;i da facilita <expan abbr="grãdißima">grandißima</expan> alli nemici di entrar <lb/>nella detta ordinanza, & diromperla, & facendo poirestringere la detta ordinanza <lb/>per empir li detti lochi, nece&longs;&longs;ariamente tal or dinanza &longs;e di&longs;ordina totalmente, & &longs;e <lb/>redu&longs;&longs;e qua&longs;i in confu&longs;ione, perche eglie da credere, che le dette artegliarie, non con&longs;u <lb/>mano alcuna fila de fanti integralmente da un capo all altro per longo, ma &longs;olamente <lb/>una parte di que&longs;ta, & una parte di quell'altra, & alcune re&longs;tano ille&longs;e, ouer non offe­<lb/>&longs;e, ma intiere, & &longs;ane, onde uolendole far re&longs;tringere per empir li detti lochiuacui, <lb/>eglie nece&longs;&longs;ario à di&longs;conciar le file acconcie, per integrar le di&longs;concie, tal che tal ordi­<lb/>nanza uerra à restar con piu numero de file de fanti (al longo)nella coda, che nella fron <lb/>te, la qual co&longs;a, &longs;e tal ordinanza uorra caminare, eglie nece&longs;&longs;ario che immediate uenghi <lb/>in confu&longs;ione, per cau&longs;a di quelle file imperfette per longo.<emph.end type="italics"/> P. E<emph type="italics"/>glie co&longs;a con&longs;onan­<lb/>te, ma come uorresti che &longs;e face&longs;&longs;e altramente.<emph.end type="italics"/> N. I<emph type="italics"/>o laudarei che &longs;e amae&longs;tra&longs;&longs;e li <lb/>fanti in &longs;imil ca&longs;o, à non re&longs;tar mai&longs;enza compagno auanti di&longs;e, eccetto che nella fron <lb/>te, cioe auertir cadauno de loro, che &longs;e per ca&longs;o gli ueni&longs;&longs;e à manco quello fante che gli <lb/>camina auanti di &longs;e, ouer piu, che &longs;ubito, & con gran pre&longs;tezza debbia caminare tan­<lb/>to auanti che ritroui un'altro compagno nella con&longs;ueta distantia auanti di &longs;e, & &longs;e <21><lb/>ca&longs;o non ui ne ritroua&longs;&longs;e alcuno auertirli, come debbiano procedere per fin alla te&longs;ta, <lb/>ouer fronte, et in tal luoco fermar&longs;e, ouer caminare &longs;econdo che fara tal fila della te&longs;ta, <lb/>ouer della fronte.<emph.end type="italics"/> P. M<emph type="italics"/>oglialtri che &longs;aranno nella mede&longs;ima fila de drio da quel tal <lb/>compagno, per longo, che uorreti che facciano.<emph.end type="italics"/> N. E<emph type="italics"/>ßendo que&longs;taregola ferma che <lb/>ogni fante piglia la mi&longs;ura del &longs;uo caminar pian, e forte dal &longs;uo compagno che gli ca­<lb/>mina dauanti, & non da quelli che gli &longs;ono dalle bande, e per tanto tutti quelli fanti che <lb/>&longs;e ritrouaranno in quella mede&longs;ima fila de drio da quel tal fante à che &longs;ara mancato il <lb/>&longs;uo compagno, ouer piu compagni dauanti, &longs;aranno sforzati à correre, ouer camina­<lb/>re à longhi paßi&longs;econdo che caminara quel tal compagno, la qual co&longs;a eßendo oßerua <lb/>ta da tutti, tal or dinanza, ouer battaglia &longs;e trouara &longs;empre nella fronte integra, e&longs;ana, <lb/>& quelli &longs;paci uacui, delli ucci&longs;i fanti, &longs;e tra&longs;portar anno nella coda, nel qual luoco non <lb/>&longs;aranno qua&longs;i de alcuno pericolo.<emph.end type="italics"/> P. D<emph type="italics"/>e gratia datime uno eßempio, & in poco nu­<lb/>mero de fanti, per non mi confonder lo intelletto.<emph.end type="italics"/> N. P<emph type="italics"/>oniamo per eßempio che in <lb/>una nostra battaglia de fanti. </s> <s id="s.001160">144. in forma quadra di <expan abbr="g&etilde;te">gente</expan>, linemici ui habbiano mor <lb/>to fanti.12.come per li &longs;uoilochiuacuati nella &longs;otto&longs;critta figura appare, dico che ha­<lb/>uendo auertito cadaun fante à far quanto che di &longs;opra habbiamo narrato, cioe che ogni <lb/>uolta che ui mancaße il &longs;uo compagno che glicamina dauanti (ouer piu) &longs;ubito debbia <pb xlink:href="042/01/102.jpg"/>à longare i paßi, & con quella pre&longs;tezza che à lui &longs;ia poßibile, non de ce&longs;&longs;are de cami­<lb/>nare tanto auanti, che ritroua un'altro compagno nella con&longs;ueta di&longs;tantia, che gli ca­<lb/>mini auanti di&longs;e, et &longs;e per ca&longs;o in quella tal fila per longo non ue ne troua&longs;&longs;e alcuno, deb <lb/>ba procedere tanto, che peruenga alla ultima fila uer&longs;o la fronte, cioe nella fila della<emph.end type="italics"/><lb/><figure id="id.042.01.102.1.jpg" xlink:href="042/01/102/1.jpg"/><lb/><emph type="italics"/>fronte, & li affermar&longs;e, ouer caminar &longs;econdo l'ordine di detta fila, & &longs;imilmente <lb/>&longs;i debbe auertire cadauno, che nel &longs;uo caminare piano, e forte, &longs;i debbia regge­<lb/>re &longs;empre dal &longs;uo compagno che gli camina dauanti, & non da alcuno de quelli <lb/>che gli è dalle bande, la qual co&longs;a e&longs;&longs;endo o&longs;&longs;eruata, nella &longs;opra&longs;critta figurata or­<lb/>dinanza quella &longs;e tr as ferira in que&longs;t'altra forma, che qui di&longs;otto appar, cioe che quel-<emph.end type="italics"/><lb/><figure id="id.042.01.102.2.jpg" xlink:href="042/01/102/2.jpg"/><lb/><emph type="italics"/>li dodecilochi uacui &longs;aranno traslatati nella coda, come &longs;en&longs;ibilmente &longs;ipuo uedere, nel <lb/>qual luoco non &longs;aranno qua&longs;i de alcun pericolo, ouer di&longs;ordine.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;ta uo&longs;tra <lb/>opinione è bonißima, & non credo che la &longs;i po&longs;&longs;a megliorare in &longs;imil ca&longs;o.<emph.end type="italics"/></s> </p> <pb pagenum="52" xlink:href="042/01/103.jpg"/> <p type="head"> <s id="s.001161">QVESITO DVODECIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001162">PRIORE. D<emph type="italics"/>itemi un poco, &longs;aria poßibile di potere tra&longs;mutar con pre&longs;trez­<lb/>za uno e&longs;&longs;ercito in forma quadra di gente, in una forma cunea, &longs;enza di&longs;ordi­<lb/>nar la prima ordinanza, & &longs;enza pericolo di confu&longs;ione.<emph.end type="italics"/> N. T<emph type="italics"/>roppo &longs;aria poßibi­<lb/>le.<emph.end type="italics"/> P. <!-- KEEP S--></s> <s id="s.001163">E <emph type="italics"/>come.<emph.end type="italics"/> N. S<emph type="italics"/>econdo che con il &longs;uono, ouer con uoce uoi ue fati intendere <expan abbr="quã">quam</expan> <lb/>do che uoleti che quelli &longs;i uoltano con la faccia uer&longs;o la banda de&longs;tra, ouer &longs;ini&longs;tra, ouer <lb/>à &longs;palle, con un diuer&longs;o &longs;uono, ouer con la uoce uoglio che &longs;iano auertiti, & amae&longs;trati <lb/>à &longs;aper&longs;i uoltare in quel uer&longs;o, che è fra la fronte, & il fianco de&longs;tro, ouer il &longs;ini&longs;tro, <lb/>& &longs;imilmente in quello che è fra il fianco de&longs;tro, ouer il &longs;ini&longs;tro, & le &longs;palle, & dapoi <lb/>che &longs;aranno ben informati di que&longs;ta particolarita, uoglio che anchora &longs;iano ben auer­<lb/>titi di quello fu detto nel precedente que&longs;ito, cioe de auertire, & amaestr are cadauno <lb/>fante, che ogni uolta che fu&longs;&longs;e fatto uoltare in alcun di &longs;opradetti uer&longs;i, et che non &longs;i tro <lb/>ua&longs;&longs;e hauer compagno nella con&longs;ueta <expan abbr="di&longs;tãtia">di&longs;tantia</expan> auanti di &longs;e, che quel debbia con gran pre <lb/>&longs;tezza procedere, ouer caminare tanto rettamente auanti, che ritroui un compagno <lb/>nella con&longs;ueta di&longs;tantia auanti di &longs;e, delle qual co&longs;e e&longs;&longs;endo tutti ben informati, & amae <lb/>&longs;trati, in uno batter d'occhio &longs;e potra e&longs;&longs;equire quello ricerca Vo&longs;tra Signoria, cioe uo <lb/>lendo tra&longs;mutare uno e&longs;&longs;ercito che &longs;ia in forma quadra di gente, in una forma cunea, et <lb/>uolendo che l'angolo de&longs;tro della fronte re&longs;ti la ponta della detta forma cunea, dico che <lb/>facendo uoltar con il &longs;uono, ouer con uoce, tutti li fanti di tal e&longs;&longs;ercito con la faccia in <lb/>quel uer&longs;o, che è fra la fronte, & il fianco de&longs;tro, & &longs;ubito uoltati che &longs;iano, o&longs;&longs;eruan­<lb/>do cadauno l'ordine detto di &longs;opra, cioe che tutti quelli che non &longs;i trouaranno hauer <lb/>compagno nella con&longs;ueta di&longs;tantia auanti di &longs;e, procedino rettamente auanti tanto che <lb/>ne ritrouano uno, la qual co&longs;a e&longs;&longs;equida, &longs;e trouara e&longs;&longs;er trasformata la detta forma <lb/>guadrata di gente in una forma cunea, & la ponta di tal figura cunea uerra à e&longs;&longs;er lo <lb/>detto angolo de&longs;tro della fronte della prima figura.<emph.end type="italics"/> PRIORE. Q<emph type="italics"/>ue&longs;ta uo&longs;tra <lb/>regola me par molto bellißima, e pre&longs;ta, ma non la ho ben capita, e pero ui prego <lb/>che me dati uno e&longs;&longs;empio in figura, ma &longs;opra tutto in poco numero, perche la<emph.end type="italics"/><lb/><figure id="id.042.01.103.1.jpg" xlink:href="042/01/103/1.jpg"/><pb xlink:href="042/01/104.jpg"/><emph type="italics"/>me par molto difficile da intendere.<emph.end type="italics"/> N. L<emph type="italics"/>a non è co&longs;i difficile, come la pare, & che il <lb/>&longs;ia il uero, &longs;ia eßempi gratia fanti.25.in forma quadra digente, come di&longs;opra appare <lb/>in figura, & per eßer meglio inte&longs;o me appar&longs;o di formar tal figura co n.25.lettere <lb/>del no&longs;tro alphabeto, hor uolendo tra&longs;mutare cal figura quadrata di gente, in una fi­<lb/>gura cunea, primamente gli faccio uoltar tutti con la faccia in quel uer&longs;o che è fra la <lb/>fronte, & quel fianco doue mi pare di uoler co&longs;tituire la ponta del cuneo, eßempi gra­<lb/>tia uolendo che la ponta di tal figura cunea &longs;ia l'angolo.e.faro che tutti &longs;i uoltano con<emph.end type="italics"/><lb/><figure id="id.042.01.104.1.jpg" xlink:href="042/01/104/1.jpg"/><lb/><emph type="italics"/>la faccia per quel uer&longs;o che è fra la fronte, & il fianco de&longs;tro, cioe uer&longs;o l'angolo.e.la <lb/>qual co&longs;a eßequida tal figura uerra à &longs;tare, come qui&longs;otto appare, nella qual figura il &longs;i <lb/>uede che ui &longs;ono molti fanti che non hanno compagno nella con&longs;ueta di&longs;tantia auanti di <lb/>&longs;e, uero che hanno ben compagno rettamente auanti di &longs;e, ma molto piu lontano del &longs;o­<lb/>lito, cioe il doppio del &longs;olito, come appare al.f.il qual harettamente auanti di &longs;e il.b. <lb/></s> <s id="s.001164">ma la di&longs;tantia che è dal detto.f.al detto.b.è il doppio della di&longs;tantia con&longs;ueta, onde &longs;el <lb/>.f.uorra oßeruare li precetti di &longs;opra adutti, &longs;ubito che hauera uoltato la faccia uer&longs;o <lb/>tal uer&longs;o immediate &longs;e andara ad approßimar&longs;e al detto.b.nella con&longs;ueta di&longs;tantia, il­<lb/>che facendo &longs;e cacciara fra.a.et.g.uero è, che il detto.g.non re&longs;tara nel &longs;uo luoco pre <lb/>&longs;ente, ma &longs;e trasferira appreßo al.c.in distantia con&longs;ueta, & nel luoco doue prima era <lb/>il.g.ui conueneria uenir.l.tal chel.f.&longs;e trouara fra.a.&.l.& co&longs;i &longs;e tutti glialtri pro <lb/>cederanno auanti &longs;econdo il detto ordine, cioe per fina che trouano compagno in <expan abbr="di&longs;tã">di&longs;tam</expan> <lb/>tia con&longs;ueta auanti di &longs;e la.h.&longs;e andara ad approßimar&longs;e al.d.& lo.m.&longs;eguitara la det <lb/>ta.h.& il.q.&longs;eguitara drio al detto.m.tutti per fina alla con&longs;ueta di&longs;tantia, & co&longs;ilo.i. <lb/></s> <s id="s.001165">&longs;eapproßimara al.e.& lo.n.&longs;eguitara lo.i.& lo.r.&longs;eguitara lo.n.& lo.x.&longs;eguitara il <lb/>detto.r.tutti per fin alla con&longs;ueta di&longs;tantia &longs;imilmente lo.o.&longs;e approßimara al.<emph.end type="italics"/>k.<emph type="italics"/>& lo. <lb/></s> <s id="s.001166">&longs;.&longs;eguitara lo.o.&.y.&longs;eguitara.&longs;.pur per fin à di&longs;tantia con&longs;ueta, & co&longs;i.t.&longs;e approßi­<lb/>mara al.p.&.z.&longs;eguitara.t.pur per fin alla con&longs;ueta di&longs;tantia, & &longs;imilmente, & &longs;e ap­<lb/>proßimata al.u.pur nella detta con&longs;ueta di&longs;tantia, la qual co&longs;a oßeruata tal ordinan­<lb/>za quadra di gente &longs;e &longs;ara tra&longs;mutata in una ordinanza cunea, come di &longs;otto appare in <lb/>figura, & la ponta di tal figurauerra à eßer l'angolo.e.& con tal ordine &longs;e procede­<lb/>ria&longs;e tal eßercito fuße ben de.100000.fanti, pur che li detti fanti &longs;iano ben auertiti, <lb/>& amae&longs;trati di quanto di&longs;opra è&longs;tato detto, &longs;i del &longs;aper&longs;i uoltar, come del caminare.<emph.end type="italics"/><lb/>P. Q<emph type="italics"/>ue&longs;ta è una bella inuentione, & dimolta importantia, perche reducendo co&longs;i al-<emph.end type="italics"/><pb pagenum="53" xlink:href="042/01/105.jpg"/><emph type="italics"/>Pimproui&longs;o uno eßereito in forma cunea, eglie qua&longs;i impoßibile che linemici poßano, <lb/>oue&longs;appiano formar la forfice da opponerui, talmente che&longs;e ueniria ad hauer gran-<emph.end type="italics"/><lb/><figure id="id.042.01.105.1.jpg" xlink:href="042/01/105/1.jpg"/><lb/><emph type="italics"/>de auantaggio, come &longs;e uerifico di&longs;opra nel &longs;ettimo Que&longs;ito, perche à mi me pare che <lb/>una battaglia cunea &longs;ia &longs;empre atta e &longs;officiente à rompere ogni altra battaglia in <lb/>forma quadra di terreno, come che al pre&longs;ente &longs;i costuma, anchor che quella fu&longs;&longs;e di <expan abbr="g&etilde;">gem</expan> <lb/>te, ouer de fanti un tanto e mezzo de piu, domente, che quelli della forma cunea &longs;iano <lb/>ben istrutti del modo del ferire (detto nel &longs;ettimo Que&longs;ito.)<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001167">QVESITO DECIMOTERZO FATTO DAL MEDESIMO <lb/><emph type="italics"/>Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001168">PRIORE. I<emph type="italics"/>o ho pen&longs;ato a&longs;&longs;ai que&longs;ta notte &longs;opra à quella tra&longs;mutatione de <lb/>hier&longs;era, & à tutte quelle altre uarieta di forme, di che hauemo fin à que&longs;ta ho­<lb/>ra parlato, & certamente el non &longs;i puo negare, che le non &longs;iano co&longs;e molto ingenio&longs;e, <lb/>& atte à dare alle uolte honor atamente una uittoria, anchor che li nimici fu&longs;&longs;eno un <expan abbr="tã">tam</expan> <lb/>to e mezzo piu di no&longs;tri, come dißi anchor hier&longs;era, nondimeno non &longs;ono di tanta au­<lb/>torita, quanto che à questitempi bi&longs;ognaria, perche contra à una <expan abbr="pot&etilde;tia">potentia</expan>, come è quel <lb/>la del Turco, comprendo, che alcuna de loro non &longs;aria &longs;officiente a darli noia, la cau&longs;a <lb/>è che quello è &longs;empre atto a fare, & fa continuamente (come &longs;apeti) uno e&longs;&longs;ercito di <lb/>tre, & quattro tanta moltitudine de fanti de noi Christiani, delli caualli poi non ne par <lb/>lo, che &longs;empre ne ha una infinita, da non comparare alli no&longs;tri.<emph.end type="italics"/> E <emph type="italics"/>pero uolendo e&longs;&longs;ere <lb/>&longs;icuri di poter&longs;i opporre &longs;itur amente a quello in campagna, el bi&longs;ognaria inue&longs;tigare <lb/>qualche altro artificio&longs;o modo di ordinare uno e&longs;&longs;ercito de fantaria, che fu&longs;&longs;e at­<lb/>to, & &longs;icuro di poter re&longs;istcre in una nuda campagna a uno altro e&longs;&longs;ercito almen ditre <lb/>tanta moltitudine ac, anti, & che anchora el fu&longs;&longs;e &longs;icuro di non poter e&longs;&longs;er turbato,<emph.end type="italics"/><pb xlink:href="042/01/106.jpg"/><emph type="italics"/>ne offe&longs;o da alcuna moltitudine de caualli, & circa cio ui ho &longs;tudiato molti giorni, & <lb/>me&longs;t, ma finalmente per certe ragioni ho compre&longs;o non e&longs;&longs;er poßibile, perche una co&longs;a <lb/>&longs;ola mi gua&longs;ta ogni di&longs;egno.<emph.end type="italics"/> N. E<emph type="italics"/>glie il uero, che tal co&longs;a non é molto facile, nondime <lb/>no el non è da concludere co&longs;i ab&longs;olutamente, che la &longs;ia impoßibile, perche &longs;econdo, che <lb/>lo ingegno de l'huomo ha ritrouato (con ragion & arte) che uno &longs;olhuomo leui, ouer <lb/>conduca tal pe&longs;o, che quattro, e piu huomini natur almente per &longs;e non &longs;ariano atti ad <lb/>alleuarlo, ouer condurlo, co&longs;i anchora eglie da pen&longs;are, che con ragion, & arte &longs;ia po&longs; <lb/>&longs;ibile di ritrouare tal modo, eforma di ordinare uno e&longs;&longs;ercito che &longs;ia atto, & &longs;icuro à <lb/>&longs;uperare, & rompere ogni altro e&longs;&longs;ercito, quantunque el fu&longs;&longs;e di tre, & anchor de <lb/>quattro tanta moltitudine di gen&longs;è di piu, & in qual&longs;i uoglia forma.<emph.end type="italics"/> P. E<emph type="italics"/>l potria e&longs; <lb/>&longs;er que&longs;to, che uoi diceti, quando che el non ui&longs;e interpone&longs;&longs;e artegliarie, archibu&longs;i, et <lb/>archi, perche in uero doue è maggior e&longs;&longs;ercito à que&longs;ti tempi, eglie da giudicare, che <lb/>iui&longs;ia anchor maggior numero de tai bellici i&longs;trumenti, per la autorita de guali, & <expan abbr="nõ">non</expan> <lb/>per altro el detto Turco riportò honor at a uittoria contra el Sophi, al qual Sophi non <lb/>li giouò hauer uno e&longs;&longs;ercito tutto de huomini genero&longs;i, & honoratamente armati, & <lb/>con mir abel ordine ordinati, perche, come cominciorno ad e&longs;&longs;er &longs;alutati dalle arte­<lb/>gliarie, archibu&longs;i, & archi Turche&longs;chi ogni&longs;uo ordine diuento uano. </s> <s id="s.001169">Et me arricor­<lb/>do quando, chel Turco uenne all'impre&longs;a de Rhodi, che io uol&longs;i andare con una bona <lb/>banda de ottimi fanti, ad a&longs;&longs;altare una grande moltitudine de Turchi, che erano uenu­<lb/>ti in un certo luoco non molto lontano dalla terra:ma&longs;coperti, che nui fu&longs;&longs;emo à quel&longs;i <lb/>&longs;u <expan abbr="tãta">tanta</expan> la moltitudine delle frizze, che ne incominciorno à piouere &longs;oprala testa, che <lb/>fu&longs;&longs;emo sforzati immediate à ritornar nella terra, uero è, ohe erano piu di tre tanti de <lb/>noi, & nondimeno &longs;e la tanta moltitudine delle &longs;ue frizze non fu&longs;&longs;e &longs;tata, & che &longs;e fu&longs; <lb/>&longs;emo potesti approßimar à quelli con le no&longs;tre picche, & &longs;pade, &longs;enza dubbio li ha­<lb/>uereßimo &longs;baratati, & maßime, che non haueuano artegliaria con loro, per e&longs;&longs;er gen <lb/>teche anda&longs;euano robando, & depredando per l'i&longs;ola: &longs;i che uoglio inferire, che &longs;e tai <lb/>machine non fu&longs;&longs;e, credo chel &longs;e potria ritrouare de or dinare uno e&longs;&longs;ercito con tal ar­<lb/>tificio&longs;o modo, che fu&longs;&longs;e atto a rompere un'altro e&longs;&longs;ercito molto maggior di lui, come <lb/>fudetto &longs;opra al cuneo, ma quando, che la parte contraria habbia gran coppia de arte <lb/>gliarie, archibu&longs;i, & archí, non credo che la natura, ne l'arte ui pote&longs;&longs;e fare equiualen <lb/>te riparo, &longs;aluo, che con altre tante, ouer con maggior quantita di quelle, perche à tai <lb/>machine, & maßime alle artegliarie, non ui &longs;i puo trouar ingegno, che ui duri, ne me­<lb/>dicina, che ui uaglia, & &longs;e que&longs;te tai machine fu&longs;&longs;eno &longs;tate al tempo antiquo, li elephan <lb/>ti haueriano per&longs;ala &longs;crimia, & li carri falcati ui &longs;ariano &longs;tati di poco giouemento, <lb/>ouer profitto.<emph.end type="italics"/> N. E<emph type="italics"/>glie da tener per fermo, che la natura mai crea&longs;&longs;e, ne crea alcun <lb/>&longs;i crudo ueleno, che anchor immediate non crea&longs;&longs;e, ouar crei la &longs;ua propria medecina, <lb/>quantunque co&longs;i immediate la non &longs;ia cono&longs;ciuta dalli huomini, &longs;imelmente dico, che <lb/>l'arte mai ritrouo; ne puo ritrouare co&longs;a co&longs;i noceuole all'huomo, che quella non &longs;ia an <lb/>chor atta à ritrouarui immediate il&longs;uo conueniente rimedio, anchor che la ignorantia <lb/>delli huomini non lo &longs;appia alle uolte co&longs;i all'improui&longs;o immaginare, ouer ritrouare.<emph.end type="italics"/><lb/>P. I<emph type="italics"/>o non credero mai, che l'arte &longs;ia atta à poter ouiare, che le artegliarie non &longs;iano <lb/>&longs;empre atte à dannificare ogni e&longs;&longs;ercito ordinato in campagna&longs;econdo el &longs;olito, & &longs;ia<emph.end type="italics"/><pb pagenum="54" xlink:href="042/01/107.jpg"/><emph type="italics"/>pur tal e&longs;&longs;ercito ordinato in forma quadrata, cunea; ouer come &longs;i uoglia, &longs;aluo che non <lb/>circonda&longs;&longs;e tal e&longs;&longs;ercito de großißime mura, ouer ba&longs;tioni, come &longs;i co&longs;tuma alli pre&longs;en <lb/>ti tempi nelli alloggiamenti, ma uolendo poi uenir alla frontera, eglie forza u&longs;cir de <lb/>quelli, &longs;i che nel atto del combattere, io non credo, ne reputo, che ue &longs;ia alcun meglior ri <lb/>medio a uoler uinzere, & &longs;uperchiar el nemico, che hauere gente, artegliarie, archibu<lb/>&longs;i, & archi piu di lui, & per&longs;one pratiche, & e&longs;&longs;ercitate nella guerra.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to, <lb/>che conclude uo&longs;tra Signoria, &longs;e intende natur almente co&longs;i douer &longs;eguire, cioe non ui <lb/>&longs;e interponendo alcuna artificialita, perche eglie co&longs;a naturale, che el numero maggio <lb/>re in ogni attione &longs;uperi el menore, cioe che lo e&longs;&longs;ercito maggiore &longs;uperi el menore, et <lb/>che el maggior numero de artegliarie, archibu&longs;i, & archi, &longs;iano de molta maggior fac <lb/>cione, che non &longs;ara el menore: ma nelle co&longs;e fatte, & ordinate con arte non &longs;eguita &longs;eni <lb/>pre que&longs;to, perche l'arte tende &longs;empre a l'uno de que&longs;ti dui fini, oueramente ad emitar <lb/>la natura ad ogni &longs;uo potere, oueramente a &longs;upplire alli diffetti di e&longs;&longs;anatura, cioe a fa <lb/>re quelle co&longs;e, che la natura non puo fare, ouer che natur almente non &longs;i po&longs;&longs;ono e&longs;&longs;e­<lb/>quire (co&longs;a certamente magnanima, & genero&longs;a)e pero non è da concludere, ne da di <lb/>re, che con arte non &longs;ia poßibile a &longs;uperare quelle co&longs;e, che per natura &longs;iamo uenti.<emph.end type="italics"/><lb/>P. D<emph type="italics"/>apoi che haueti que&longs;ta tal openione, che uia ui pare, che &longs;i potria tenere, ouer <expan abbr="cõ">com</expan> <lb/>che mezzo credeti, che tal co&longs;a pote&longs;&longs;e fare.<emph.end type="italics"/> N. C<emph type="italics"/>irca cio bi&longs;ognaria pen&longs;arui <expan abbr="alquã">alquam</expan> <lb/>to.<emph.end type="italics"/> P. P<emph type="italics"/>en&longs;atigli un poco (dico con &longs;umma diligentia) perche eglie una co&longs;a molto <lb/>importantißima, & nece&longs;&longs;aria a questi tempi, & in cio cono&longs;cero quanto ualeti, per­<lb/>che nelle infirmita, che &longs;ono giudicate incurabile, &longs;i cono&longs;ce la &longs;ufficienza del medico.<emph.end type="italics"/><lb/>N. I<emph type="italics"/>o certamente ui pen&longs;aro, ma molto piu con diligentia, quando pre&longs;entiro appro&longs; <lb/>&longs;imar&longs;i el bi&longs;ogno.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001170">I<emph type="italics"/>l fine del quarto libro.<emph.end type="italics"/></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/108.jpg"/> <p type="head"> <s id="s.001171">LIBRO QVINTO DELLI <lb/>QVESITI, ET INVENTIONI DIVERSE, <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001172"><emph type="italics"/>Sopra el mettere, ouer tuore rettamente in di&longs;egno con el bo&longs;&longs;olo, li &longs;iti, <lb/>pae&longs;i, & &longs;imelmente le piante delle citta, con el modo de &longs;a­<lb/>pere fabricare el detto bo&longs;&longs;olo, & in diuer&longs;i <lb/>modi, la cui &longs;cientia da Ptolomeo è <lb/>detta Chorografia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001173">QVESITO PRIMO FATTO DAL MIO HONO­<lb/><emph type="italics"/>rando Compare.<emph.end type="italics"/> M. R<emph type="italics"/>ichardo Ventuorth, gentil'huomo <lb/>della Mae&longs;tà del Re d'inghilterra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001174">RICHARDO. C<emph type="italics"/>ompare carißimo haria molto accaro, che me <lb/>dichiara&longs;ti, come &longs;e poteria mettere in di&longs;egno rettamente un &longs;ito­<lb/>ouer un particolar pae&longs;e, & &longs;imelmente la pianta di una citta, la <lb/>cui pratica da Ptolomeo, come &longs;apeti nella &longs;ua Geographia, è det­<lb/>ta Chorographia.<emph.end type="italics"/> N. T<emph type="italics"/>al co&longs;a &longs;i puo &longs;are con un bo&longs;&longs;olo artifi­<lb/>cialmente fatto con la &longs;ua calamita, che &longs;ia giu&longs;to.<emph.end type="italics"/> R. V<emph type="italics"/>i prego <lb/>me dicati in che forma uol e&longs;&longs;er fatto que&longs;to bo&longs;&longs;olo.<emph.end type="italics"/> N. L<emph type="italics"/>a for <lb/>ma di tal bo&longs;&longs;olo &longs;i puo far in dui modi.<emph.end type="italics"/> L'<emph type="italics"/>uno, qual è il piu communo, &longs;i é à farlo con <lb/>una dioptra, ouer tra&longs;guar do mobile, cioe, che &longs;i puol girare à torno per poter tra&longs;­<lb/>guardare in ogni uer&longs;o &longs;econdo che occorre il bi&longs;ogno.<emph.end type="italics"/> L'<emph type="italics"/>altro &longs;i fa da poter&longs;ene&longs;er­<lb/>uire&longs;enza quella tal dioptra, ouer tra&longs;guardo mobile, il che è molto accommodo, e di <lb/>menor artificio, ma ben ui oceorre un bo&longs;&longs;olo con una lancetta molto longa.<emph.end type="italics"/> R. M<emph type="italics"/>o <lb/>stratime pur per al pre&longs;ente &longs;olamente quella forma, che é piu in u&longs;o, cioe quella che <lb/>piu &longs;i co&longs;tuma. </s> <s id="s.001175">perche quando &longs;aro in Inghilterra me ne &longs;appia far far uno.<emph.end type="italics"/> N. L<emph type="italics"/>a <lb/>piu frequentata &longs;i fa in que&longs;to modo. </s> <s id="s.001176">Prima&longs;e fa far un tondo di lama di rame, ouer di <lb/>ottone gro&longs;&longs;a una co&longs;ta di cortello uel circa el diametro, del qual tondo non uoria e&longs;&longs;er <lb/>men de una&longs;panna, perche quanto piu tal i&longs;trumento è maggiore, tanto piu eglie men <lb/>fallace, uero è, che eglie poi piu di&longs;commodo da portar&longs;e drio, & per questa cau&longs;amol <lb/>ti lo co&longs;tumano piu piccolo a&longs;&longs;ai per e&longs;&longs;er piu commodo, & que&longs;to tal tondo di lama <lb/>&longs;e fa &longs;pianar bemßimo alla mola, & dapoi, che é ben &longs;pianato &longs;opra el centro del mede <lb/>&longs;imo tondo ui &longs;i de&longs;criue prima un cerchio piu &longs;car&longs;o una co&longs;ta di corteilo del tondo di <lb/>detta lama et anchora un'altro piu piccolo di que&longs;to <36> due bone co&longs;te di cortello, et tut <lb/>ta la <expan abbr="circõfer&etilde;tia">circonferentia</expan> del primo cerchio, prima&longs;e diuide <expan abbr="cõ&longs;umma">con&longs;umma</expan> <expan abbr="dilig&etilde;tia">diligentia</expan> in quatro par <lb/>ti equali, et à una di que&longs;te diui&longs;ione ui &longs;e&longs;criue <expan abbr="Leuãte">Leuante</expan>, et all'altra à que&longs;ta oppo&longs;icaui <lb/>&longs;e &longs;criue <expan abbr="Pon&etilde;te">Ponente</expan>, & à quella diui&longs;ione, che é fra queste due uer&longs;o <expan abbr="Tramõtana">Tramontana</expan>, ui&longs;e&longs;cri <lb/>ue Tramontana, & à quella che è uer&longs;o O&longs;tro, ui &longs;e&longs;criue Ostro, & co&longs;i la <expan abbr="circõferen-tia">circonferen­<lb/>tia</expan> del detto primo cerchio uenira a e&longs;&longs;er diui&longs;a in le dette quattro parti equali, delle <lb/>quali una uenira à e&longs;&longs;er fra <expan abbr="Leuãte">Leuante</expan>, et <expan abbr="Tramõtana">Tramontana</expan>, et una fra <expan abbr="Tramõtana">Tramontana</expan>, & <expan abbr="Pon&etilde;te">Ponente</expan>,<emph.end type="italics"/><pb pagenum="55" xlink:href="042/01/109.jpg"/><emph type="italics"/>& una fra Ponente, & O&longs;tro, & una fra O&longs;tro, & Leuante. <!-- KEEP S--></s> <s id="s.001177">Anchora cadauna di que <lb/>&longs;te quattro parti &longs;e diuide pur in due parti eguali, & quella diui&longs;ione che fra Leuan­<lb/>te, & Tramontana, ui &longs;e&longs;criue Grego, & à quella che è fra Tramontana, e Ponente, <lb/>ui &longs;e &longs;criue Mai&longs;tro, & à quella che é fra Ponente, & Ostro, ui &longs;e &longs;criue Gar­<lb/>bino. </s> <s id="s.001178">Et à quella, che è fra O&longs;tro, e Leuante, ui &longs;e &longs;criue Sirocco, & co&longs;i la cir­<lb/>conferentia di tal primo cerchio uenira à e&longs;&longs;er diui&longs;a in otto parti eguali, & cadaun­<lb/>di quelle diui&longs;ioni &longs;e chiama uento, e pero tal circonferentia &longs;era diui&longs;a in otto uenti, <lb/>& cadauno de quelli &longs;i chiama, come di &longs;opra è &longs;tato detto, nondimeno per abbreuia­<lb/>&longs;crittura in luoco di Leuante, ui &longs;e &longs;criue un.<emph.end type="italics"/> L.<emph type="italics"/>et in luoco di Ponente, ui &longs;e &longs;criue un.<emph.end type="italics"/> P. <lb/><emph type="italics"/>& in luoco di Tramontana, ui &longs;e &longs;criue un.<emph.end type="italics"/> T.<emph type="italics"/>& in luoco di O&longs;tro, ui &longs;e &longs;criue un.<emph.end type="italics"/> O. <lb/><emph type="italics"/>& in luoco di Grego, ui&longs;e &longs;criue un.<emph.end type="italics"/> G.<emph type="italics"/>& in luoco di Garbino, ui&longs;e &longs;criue un'altro.<emph.end type="italics"/> G. <lb/><emph type="italics"/>& in luoco di Mai&longs;tro, ui &longs;e &longs;criue un.<emph.end type="italics"/> M.<emph type="italics"/>& in luoco de Sirocco, ui &longs;e &longs;criue un.<emph.end type="italics"/> S.<emph type="italics"/>co­<lb/>me di &longs;otto nella figura appare. </s> <s id="s.001179">Anchora &longs;e diuide cadauna di quelle ottaue parti di det <lb/>ta circon&longs;erentia, primamente in tre partieguali, & cadauna di quelle terze parti &longs;e <lb/>diuide anchora in altre tre partieguali, & cadauna di queste ultime parti (e&longs;&longs;endo lo <lb/>detto tondo di lamma, di competente grandezza) &longs;i debbono ultimamente diuidere in <lb/>tinque parti eguali, il che facendo &longs;e trouara tutta la circonferentia del detto primo ce<gap/><lb/>chio e&longs;&longs;er diui&longs;a in.360.parti eguali (&longs;econdo l'ordine, & diui&longs;ione delli antichi cho­<lb/><gap/>ographi) & cadauna di que&longs;te tal parti&longs;e chiama grado, & accio che tai diui&longs;ioni, &longs;ia <lb/>no apparente &longs;e &longs;egnano cadauna con una linceta long a una meggia co&longs;ta di cortello, et <lb/>que&longs;te tai lineete (accio che tutte tendano al centro di tal cerchio) &longs;e de&longs;criuono con <lb/>unaregagiu&longs;tando talrega con il centro di tal cerchio, & con il ponto di quella diui&longs;io <lb/>ne che &longs;i uol &longs;ignare nella detta circonferentia, & accio che tai diui&longs;ioni &longs;i po&longs;&longs;ano con <lb/>facilita numer are (occorrendo il bi&longs;ogno) à ogni cinque de tai diui&longs;ioni piccole ui &longs;e &longs;a <lb/>una diui&longs;iont che trauer&longs;i tutto quel &longs;pacio che è fra la circonferentia del detto primo <lb/>cerchio, & la circonferentia del &longs;econdo. </s> <s id="s.001180">Ma &longs;e per ca&longs;o il &longs;opradetto tondo di lamma, <lb/>fu&longs;&longs;e talmente piccolo, che quelle ultime terze partinon fu&longs;&longs;eno atte, per la &longs;ua picco­<lb/>lezza, à e&longs;&longs;er diui&longs;e nelle &longs;opradette cinque parti eguali, &longs;e la&longs;&longs;ariano &longs;tar co&longs;i, per il­<lb/>che la circonferentia del detto primo cerchio ueneria à e&longs;&longs;er diui&longs;a &longs;olamente in.72. <lb/>partieguali, onde facendo tai.72.parti, apparente con il tirarui quella lineeta per fi­<lb/>na alla circon&longs;erentia del menor cerchio &longs;econdo l'ordine detto di&longs;opra, cioe che tutte <lb/>le dette lineete <expan abbr="tendanõ">tendanon</expan> al centro delli detti cerchij, &longs;i come appare nella figura &longs;otto­<lb/>&longs;critta, ma bi&longs;ognanotare che &longs;i ben la circonferentia di tallamma, per la &longs;ua piccoleæ <lb/>za, &longs;ara diui&longs;a&longs;olamente nelle &longs;opradette.72.partieguali, come nella detta &longs;otto&longs;crita <lb/>figura appare, nondimeno tutta la detta circonferentia con lo intelletto &longs;e debbe inten­<lb/>dere e&longs;&longs;er diui&longs;a pur nelle dette.360.partieguali, cioe in.360.gradi, & pero nel com­<lb/>putar le &longs;otto&longs;critte.72.diui&longs;ioni, per cadauna di quelle, ui &longs;e computa cinque gradi, <lb/>perche.5.fia.72.uien à fare li detti.360.gradi, & dapoi che &longs;e haueran fatte tutte <lb/>que&longs;te co&longs;e, ouer diui&longs;ioni, ui &longs;e debbe far a&longs;&longs;aldare una armilla della mede&longs;ima &longs;orte di <lb/>banda di ottone, ouer di rame à torno al centro, cioe uno cerchio della detta banda lar­<lb/>ga almen dul dedi, qual uenghi affare à modo di una &longs;catolina à torno al detto centro <lb/>della detta prima lamma circolare, talmente che &longs;ia concentrica con quella, & nel cen-<pb xlink:href="042/01/110.jpg"/>tro poiui &longs;e de far a&longs;&longs;ettar una ponta alta circa per la mita della detta &longs;catolina, e que­<lb/>&longs;ta ponta è per metterui &longs;u&longs;o la lanzetta acconcia con la calamita, alla &longs;imilitudine di <lb/>quelle, che hanno quelli horologietti, che uengono de Alamagna, ma alquanto piu gran­<lb/>da, & nel fondo di questa &longs;catola ui &longs;e de &longs;egnar una linea qua&longs;i alla &longs;imilitudine della <lb/>lanzetta che uada da. </s> <s id="s.001181"><expan abbr="Tramõtana">Tramontana</expan> uer&longs;o O&longs;tro rettamente, accio che &longs;i po&longs;&longs;a cono&longs;cere <lb/>quando che il bo&longs;&longs;olo &longs;ia ben a&longs;&longs;ettato (perche il <lb/>bo&longs;&longs;olo &longs;e intende e&longs;&longs;er ben a&longs;&longs;ettato, quando che <lb/>la ponta della dettalanzetta guarda rettamente <lb/>uer&longs;o la Tramontana (&longs;i come nella figura appa­<lb/>re) la qual co&longs;a facilmente &longs;i cono&longs;ce per meggio <lb/>della detta linea, cioe come &longs;e fa preci&longs;o con li &longs;o­<lb/>pradetti horologietti quando &longs;e uol &longs;aper quan­<lb/>te hore &longs;ono, & fatto que&longs;to ui&longs;e de poner la det <lb/>ta lanzetta acconcia (come è detto) con la cala­<lb/>mita, & dapoi &longs;i fa un coperchio alla detta &longs;ca­<lb/>tolina de uitrio chiaro, come &longs;e co&longs;tuma alli bo&longs;-<emph.end type="italics"/><lb/><figure id="id.042.01.110.1.jpg" xlink:href="042/01/110/1.jpg"/><lb/><emph type="italics"/>&longs;oli da nauicare, accio &longs;i po&longs;&longs;a uedere il &longs;tar, & l'andar della detta lanzetta, & dopo <lb/>que&longs;to ui&longs;e de metter una dioptra, ouer tra&longs;guardo, la qual dioptra, ouer tra&longs;guardo <lb/>&longs;olea co&longs;tumar&longs;i alla &longs;imilitudine della prima figura.a.b.con quelli dui bracci.c.d.&.e. <lb/></s> <s id="s.001182">&longs;.il qual modo <21> mettere in di&longs;&longs;egno un pae&longs;e era <expan abbr="&longs;offici&etilde;te">&longs;officiente</expan> a&longs;&longs;ai, ma <21> mettere in di&longs;&longs;e <lb/>gno la <expan abbr="piãta">pianta</expan> de una citta era <expan abbr="alquãto">alquanto</expan> <expan abbr="di&longs;cõmodo">di&longs;commodo</expan>, onde <21> farlo piu <expan abbr="accõmodo">accommodo</expan>, & genera <lb/>le ui &longs;e co&longs;tuma à ponerui un'altro tra&longs;uer&longs;o in croce, <21> <expan abbr="fettam&etilde;te">fettamente</expan> &longs;quadra <expan abbr="eß&etilde;pi">eßempi</expan> gratia <lb/>à quella armilla uacua.a.b.ui &longs;e a&longs;&longs;alda prima nelli dui bracci.c.d.et.e.f.della principal <lb/>dioptra, ouer tra&longs;guardo, con quelle due lamette in alto elleuate nelle istremita di quel­<lb/>la, con uno bu&longs;ettino in cadauna da tra&longs;guardare, per quelli le co&longs;e che accadera, à ben <lb/>che anchor due pontine acute &longs;eruiriano, &longs;i come quelli dui bu&longs;ettini, & for&longs;i meglio, <lb/>& dapoi ui &longs;e &longs;alda anchora quelli altri dui brazzetti.g.h.&.i.<emph.end type="italics"/>k.<emph type="italics"/>per fettamente in cro <lb/>ce, cio perfettamente à &longs;quara &longs;opra la principal dioptra, & nel capo dell'un de questi <lb/>&longs;econdi bracciui &longs;i a&longs;&longs;etta, ouer &longs;alda quell'altro brazzetto.l.m.pur à &longs;quadra, come <lb/>nella &longs;econda figur a appare, & la forma di quala &longs;i uoglia delle due &longs;otto&longs;critte &longs;orte <lb/>de dioptreuol e&longs;&longs;ere totalmente fabricata che la detta armilla.a.b.&longs;ia de tal grandez-<emph.end type="italics"/><lb/><figure id="id.042.01.110.2.jpg" xlink:href="042/01/110/2.jpg"/><pb pagenum="56" xlink:href="042/01/111.jpg"/><emph type="italics"/>za che ui po&longs;&longs;a entrare &longs;azzatamente quell'altra armilla, ouer &longs;catolina del &longs;opra­<lb/>&longs;critto no&longs;tro <expan abbr="istrom&etilde;to">istromento</expan>, et che quelli dui, ouer quattro bracci, cioe.c.d.e.f.g.b.&.i.<emph.end type="italics"/>k. <lb/><emph type="italics"/>&longs;iano talmente fabricati che dall'una, & l'altra banda dimo&longs;trino giustamente li gradi <lb/>&longs;epra la prima lamma circolare gia &longs;ignati, & li dui principali, cioe.c.d.&.e.f.uoleno <lb/>e&longs;&longs;er di tanta longhezza che dall'una, & l'altra banda ufci&longs;cano alquanto fuora del <lb/>cerchio della no&longs;tra prima lamma circolare, & nella istremita dell'uno, & l'altro de <lb/>que&longs;ti dui bracci ui &longs;e &longs;alda le &longs;opradette due lamette, ouer figure quadrangole in alte <lb/>elleuate di tal altezza che &longs;opra auanzano la altezza della &longs;catolina del no&longs;tro bo&longs;&longs;o­<lb/>lo, & talmente larghe, che facendoli uno bu&longs;ettino in meggio di cadauna di quelle, cioe <lb/>in quella parte che &longs;operchia di &longs;opra del detto bo&longs;&longs;olo, uno rettamente oppo&longs;ito all al <lb/>tro, talmente che tra&longs;guardando per li detti dui bu&longs;ettini la no&longs;tra linea ui&longs;uale tran&longs;i­<lb/>&longs;ca preci&longs;amente &longs;opra al centro del cerchio del detto no&longs;tro i&longs;tromento, & dapoi tal <lb/>dioptra &longs;i debbe con diligentia inca&longs;&longs;are &longs;opra al detto no&longs;tro bo&longs;&longs;olo, cioe &longs;opra à quel <lb/>la armilla, ouer &longs;catolina, che interchiude il detto bo&longs;&longs;olo, ilche facendo il detto no&longs;tro <lb/>i&longs;tromento &longs;tara preci&longs;amente, come di &longs;otto appare in figura, & la dioptra, ouer tra&longs; <lb/>guardo, &longs;ara girabile, cioe che la &longs;e potragir are per ogniuer&longs;o à torno à torno, et per <lb/>quelli dui bu&longs;ettini, che &longs;ar anno in quelle due lamette quadrangole in alto elleuate, &longs;e po<lb/>tratra&longs;guardar con un'occhio li &longs;egni, & termini, che &longs;i uorra uedere, come per l'aue­<lb/>nire per e&longs;&longs;empio &longs;e mo&longs;trara, uero è, che in luoco de quelli dui bu&longs;ettini à me mi pia-<emph.end type="italics"/><lb/><figure id="id.042.01.111.1.jpg" xlink:href="042/01/111/1.jpg"/><lb/><emph type="italics"/>ce, & me pare anchora piu &longs;pediente due pontine acute, come di&longs;opra dißi.<emph.end type="italics"/> R. Q<emph type="italics"/>ue­<lb/>&longs;ta forma de i&longs;tromento molto mi piace, dimane parlaremo poi del modo di operarlo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001183">QVESITO SECONDO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> M.R<emph type="italics"/>ichardo Ventuorth.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001184">RICHARDO. H<emph type="italics"/>or uorria Compare che &longs;otto breuita me dichiar asti il <lb/>modo <lb/>di operare l'i&longs;tromento, che hieri me in&longs;igna&longs;ti à fare.<emph.end type="italics"/> N. P<emph type="italics"/>er uoler operar <lb/>tal i&longs;tromento à uoler mettere in di&longs;&longs;egno qualche &longs;ito, ouer pae&longs;e, bi&longs;ogna hauere un <lb/>ba&longs;tone longo, circa piedi tre, & che tal ba&longs;ione in un di capi habbia un ferro ap­<lb/>pontito, per poter lo piantare in terra, & dall'altro capo un tondo di legno alla gran­<lb/>dezza dello i&longs;tromento con un poco di orlo, che &longs;ia atto à tener tale i&longs;tromento <pb xlink:href="042/01/112.jpg"/>inca&longs;&longs;ato, & fermo in cima de quel tal bastone, come di&longs;otto appare in figura, & che <lb/>cal orlo &longs;ia tanto ba&longs;&longs;o che il non impedi&longs;ca il poter girar la dioptra in ogni uer&longs;o.<emph.end type="italics"/> R. <lb/>N<emph type="italics"/>on &longs;e potria far &longs;aldar un canon di banda bu&longs;o &longs;otto à tal i&longs;tromento per &longs;icar dentro <lb/>tal ba&longs;tone, ouer una ponta da poterlo piantar in cima di tal ba&longs;tone, facendo prima un <lb/>bu&longs;o nella cima di tal bastone.<emph.end type="italics"/> N. L'<emph type="italics"/>uno è l'altro de que&longs;ti, daria impedimento per <lb/>mettere tal di&longs;&longs;egno in carta, come alli &longs;uoiluochi &longs;i potra giudicare.<emph.end type="italics"/> R. S<emph type="italics"/>eguitati.<emph.end type="italics"/><lb/>N. I<emph type="italics"/>nte&longs;o adunque tutte que&longs;te co&longs;e bi&longs;ogna notare, che per mettere in di&longs;&longs;egno un &longs;i­<lb/>to, ouer un pae&longs;e, &longs;i puo procedere in dui modi, l'uno è <lb/>à &longs;tare in meggio, cioe dentro dal detto &longs;ito, ouer pae­<lb/>&longs;e con il detto i&longs;tromento piantato, fermo è &longs;tabile, & <lb/>l'altro é à andare à torno, à torno per la circonferen­<lb/>tia di tal &longs;ito, ouer pae&longs;e.<emph.end type="italics"/> R. Q<emph type="italics"/>ual è meglio de que&longs;ti <lb/>dui modi.<emph.end type="italics"/> N. C<emph type="italics"/>ertamente piu giusto, ouer men fal­<lb/>lace riu&longs;cira tal di&longs;&longs;egno à &longs;tare fermo è fi&longs;&longs;o nel meg­<lb/>gio, cioe dentro di tal &longs;ito, ouer luoco, perche in ogni <lb/>tra&longs;mutatione che &longs;i fa del detto bu&longs;&longs;olo nel tra&longs;por­<lb/>tario da un luoco in un'altro &longs;empre &longs;e incorre in qual­<lb/>che poco di errore, & perche à tuor in di&longs;&longs;egno un luo <lb/>co, ouer &longs;ito andando per la circonferentia di quello &longs;e <lb/>famolte tra&longs;mutationi, del detto bo&longs;&longs;olo, come per lo<emph.end type="italics"/><lb/><figure id="id.042.01.112.1.jpg" xlink:href="042/01/112/1.jpg"/><lb/><emph type="italics"/>auenire &longs;e potrauedere, e pero delli molti pochi errori &longs;e ne uiene à cau&longs;are poila mag <lb/>gior parte delle uolte, in fine uno maggiore.<emph.end type="italics"/> R. M<emph type="italics"/>o&longs;tratime adunque quello che de <lb/>&longs;tar dentro in meggio, perche l'altro e&longs;&longs;endo co&longs;i fallace non me ne curo.<emph.end type="italics"/> N. A<emph type="italics"/>nci é <lb/>nece&longs;&longs;ario, che uoi intendiati l'uno è l'altro modo perche non &longs;empre &longs;i puo tuor in di&longs;­<lb/>&longs;egno un &longs;ito, ouer pae&longs;e à star dentro nel detto &longs;ito, perche &longs;pe&longs;&longs;e uolte ui &longs;e troua del <lb/>li arbori, monticelli, ca&longs;amenti, & altre co&longs;e, che impedi&longs;cono il poter uedere tutti li <lb/>termini di tal &longs;ito, alcuna fiata per la grandezza &longs;ua non &longs;i potra e&longs;&longs;equire tal effetto à <lb/>star co&longs;i fermo nel meggio anchor che non ui fu&longs;&longs;e arbori, ne altri impedimenti, come <lb/>che uole&longs;&longs;e mettere in di&longs;&longs;egno uno grandißimo pae&longs;e, che per la &longs;ua grandezza in al­<lb/>cun luoco dentro di quello non &longs;i pote&longs;&longs;e uedere tutti li &longs;uoitermini, e pero quantunque <lb/>il modo di quelluor in di&longs;&longs;egno à &longs;tar dentro di tal &longs;ito, ouer luoco &longs;ia piu giu&longs;to, ouer <lb/>men fallace dell'altro, nondimeno l'altro è poi piu generale, perche con quello &longs;e puo <lb/>operare, &longs;i nelli pae&longs;i grandi, come nelli piccoli, o con arbori, monti, & ca&longs;amenti, co­<lb/>me e&longs;&longs;endo piani, & con questo tale &longs;i puol tuor in di&longs;&longs;egno, non &longs;olamente le piante del <lb/>le citta, ma anchora tutto il territorio di quelle, et &longs;imilmente I&longs;ole, prouincie, & altre <lb/>co&longs;e &longs;imile.<emph.end type="italics"/> R. A<emph type="italics"/>dunque me li dichiarereti ambi dui. </s> <s id="s.001185">tamen cominciatemi prima à di <lb/>chiarire quel primo modo, cioe à &longs;tar dentro nel meggio di tal &longs;ito, ouer pae&longs;e, & da­<lb/>poi me dichiarereti l'altro.<emph.end type="italics"/> N. A<emph type="italics"/>ccio che meglio me intendiati, &longs;upponeremo che il <lb/>&longs;ia uno pae&longs;etto de cinque fazze, ouer lati, alla &longs;imilitudine della &longs;otto&longs;critta figura. <lb/></s> <s id="s.001186">a.b.c.d.e.& che &longs;ia di tal qualita, che &longs;tando dentro in meggio, ouer circa al meggio di <lb/>quella, & che facendo poi piantar una bacchetta in cadauno di quelli cinque angoli, <lb/>ouer cantoni che tai bacchette &longs;i po&longs;&longs;ano uedere à una per una, hor dico, che à uoler<emph.end type="italics"/><pb pagenum="57" xlink:href="042/01/113.jpg"/><emph type="italics"/>metter rottamente in di&longs;egno&longs;opra à uno foglio di carta un'altra figura &longs;imile alla <lb/>propo&longs;ia.a.b.c.d.e.el &longs;i debbe far piantare una bacchettina per cia&longs;caduno delli detti <lb/>cinque angoli, ouer <expan abbr="cãtoni">cantoni</expan>.a.b.c.d.e.& dapoiel &longs;i debbe intrare nel detto &longs;ito, ouer lo <lb/>co, & andare nel mezzo di quello, ouer cir ca al mezzo (perche piue manco del mez­<lb/>zo non importa, & iui piantarui quel ba&longs;tone con el detto no&longs;tro bo&longs;&longs;olo in cima, et da <lb/>poi che &longs;ara piantato bi&longs;ognara torzerlo, & fermarlo talmente, che el detto bo&longs;&longs;olo <lb/>&longs;tia ben a&longs;&longs;ettato, cioe, che la lenguella della calamita stia giu&longs;ta &longs;econdo el &longs;uo ordine, <lb/>come fu detto di &longs;opra, cioe, che la ponta di detta lenguella, ouer lanzetta guardi retta <lb/>mente uer&longs;o la Tramontana del detto i&longs;trumento, il che &longs;i cono&longs;ce facilmente per mez <lb/>zo di quella linea, che ua da Tramontana al O&longs;tro, di &longs;otto della detta lenguella, ouer <lb/>lanzetta, cioe, come &longs;e co&longs;tuma in a&longs;&longs;ettar quelli horologietti, che uien de Alemagna, <lb/>quando &longs;e uol &longs;aper quante hore &longs;ono, con el &longs;ole, & dapoi che tal i&longs;trumento &longs;ara tal <lb/>mente a&longs;&longs;ettato, el &longs;i de girar la dioptra, ouer tra&longs;guardo del detto i&longs;trumento, <expan abbr="talm&etilde;">talmen</expan> <lb/>te che cignando con uno occhio per quelli dui bu&longs;ettini della detta dioptra (&longs;e tal dio­<lb/>ptra hauera detti bu&longs;ettini) chel &longs;i ueda una di quelle.5.bacchette piantate, ouer amente <lb/>&longs;e la detta dioptra non hauer a li detti dui bu&longs;ettini, ma che haue&longs;&longs;e quelle due pontine <lb/>acute, come di &longs;opra fu detto, le qual due pontine à me mi pareno molto pin accommo <lb/>de che li hu&longs;i, el &longs;i de guardare una di dette bacchette, & uoltar tanto la detta dioptra, <lb/>che la line a ui&longs;uale &longs;e incontri con le dette due pontine de detta dioptra, & con quella <lb/>bacchetta che &longs;i guardara, & fatto questo el &longs;i de annotare &longs;opra una policetta, per <lb/>qual grado (de quelli.360.&longs;e &longs;aranno.360.oueramenta de quelle.72.parti &longs;el detto i­<lb/>&longs;trumento &longs;ara diui&longs;o in.72.parti à gradi.5.per parte, pa&longs;&longs;ara la detta linea ui&longs;uale (il <lb/>qual grado la dioptra lo fara manife&longs;to) & per e&longs;&longs;er impoßibile à dar in un piccol &longs;pa<lb/>tio perfetto e&longs;&longs;empio in figura à que&longs;ta materia, &longs;e sforzaremo al men con parole di <lb/>&longs;upplire à quello, che non &longs;i puo dar in figura, hor poniamo che à tra&longs;guardare quella <lb/>bacchetta po&longs;ta in <expan abbr="põto">ponto</expan>.a.la no&longs;tra linea ui&longs;uale paßi alli.3.gradi de Sirocco uer&longs;o<emph.end type="italics"/> O­<lb/><emph type="italics"/>&longs;tro, fatto que&longs;to, el &longs;i de mi&longs;urare, ouer far mi&longs;urare <expan abbr="quãto">quanto</expan> è dal pede del no&longs;tro i&longs;tru<emph.end type="italics"/><lb/><figure id="id.042.01.113.1.jpg" xlink:href="042/01/113/1.jpg"/><pb xlink:href="042/01/114.jpg"/><emph type="italics"/>mento alla detta bacchetta po&longs;ta in ponto.a.hor poniamo che ui &longs;ia pa&longs;&longs;a.54.hor dico, <lb/>che di tutto que&longs;to &longs;e ne debbe far memoria&longs;opra una policetta in que&longs;ta forma, cioe à <lb/>gradi tre de Sirocco uer&longs;o Ostro pa&longs;&longs;a.54.fatto que&longs;to, el &longs;i de uoltar la detta dioptra <lb/>(stando pero lo i&longs;trumento &longs;empre fermo e fi&longs;&longs;o &longs;econdo el &longs;uo ordine) talmente, che <lb/>per el mede&longs;imo modo el &longs;i ueda l'altra bacchetta che &longs;eguita, poniamo quella po&longs;ta in <lb/>ponto.b.& ui&longs;to, et notato el grado, etiam la di&longs;tantia, che &longs;ara dal pie del no&longs;tro i&longs;tru <lb/>mento per fin al ponto.b.&longs;opra la nostra polizetta alla &longs;imilitudine dell'altra, & con <lb/>tal modo, e uia &longs;i de procedere à cadauna delle altre tre bacchette poste nelli altri tre <lb/>angoli, ouer cantoni.c.d, &.e.& per abbreuiar &longs;crittura, poniamo che le dette cinque <lb/>di&longs;tantie annotate &longs;opra alla detta polizetta uadano, & &longs;iano tanto quanto qua di &longs;ot <lb/>to appare, perche co&longs;i debbono e&longs;&longs;er notate.<emph.end type="italics"/><lb/>A <emph type="italics"/>gradi. </s> <s id="s.001187">3. de Siroccouer&longs;o O&longs;tro pa&longs;&longs;a.<emph.end type="italics"/> 54. <lb/>A <emph type="italics"/>gradi. </s> <s id="s.001188">29. de Greco uer&longs;o Leuante pa&longs;&longs;a.<emph.end type="italics"/> 63. <lb/>A <emph type="italics"/>gradi. </s> <s id="s.001189">28. de Tramontana uer&longs;o Greco pa&longs;&longs;a.<emph.end type="italics"/> 81. <lb/>A <emph type="italics"/>gradi. </s> <s id="s.001190">9. de Mai&longs;tro uer&longs;o Ponente pa&longs;&longs;a.<emph.end type="italics"/> 72. <lb/>A <emph type="italics"/>gradi. </s> <s id="s.001191">5. de Garbino uer&longs;o O&longs;tro pa&longs;&longs;a.<emph.end type="italics"/> 62. </s> </p> <p type="main"> <s id="s.001192">H<emph type="italics"/>or fatto que&longs;to, &longs;e de cauare lo istrumento, & andar&longs;ene à ca&longs;a con la &longs;opradetta &longs;ua <lb/>poliza, & quando lí pare di uoler mettere in di&longs;&longs;egno quella tal figura de pae&longs;e &longs;opra <lb/>una carta, ouer tela primamente el &longs;i debbe di&longs;tendere quella tal carta, ouer tela &longs;opra <lb/>una tabula pianißima, & &longs;opra à quella imbroccaruela, ouer taccaruela con cera tal­<lb/>mente, che la non &longs;i po&longs;&longs;a muouere, & dapoi tirare una linea retta, in mezzo di quella <lb/>tal carta, ouer tela alla &longs;imilitudine della &longs;otto&longs;critta linea.a.b.& al mezzo di quella <lb/>a&longs;&longs;ettarui el detto nostro istrumento, talmente, che la detta linea uenghi à pa&longs;&longs;ar per <lb/>el centro del detto i&longs;trumento, & che anchor el detto i&longs;trumento ui &longs;tia &longs;opra ben agiu <lb/>stato, cioe, che la &longs;ua lanzetta &longs;tia &longs;econdo el &longs;uo debito ordine (piu uolte detto) & da <lb/>poi da l'una e l'altra parte del detto i&longs;trumento el &longs;e die di&longs;tinguere quella parte della <lb/>detta linea.a.b.che uien à e&longs;&longs;er &longs;otto al i&longs;trumento (cioe coperta da quello) da quella, <lb/>che é di&longs;coperta con dui piccoli ponti, quali&longs;iano li dui ponti.c.&.d.et questo &longs;i fa per <lb/>poter ritrouar con facilita el luoco, doue &longs;e ripoßi el centro del detto i&longs;trumento, per­<lb/>che la detta parte.c.d.uien à e&longs;&longs;er equal al diametro del detto i&longs;trumento, & pero nel <lb/>mezzo di quella, cioe in ponto.e.&longs;e ripo&longs;ara el centro del detto i&longs;trumento. </s> <s id="s.001193">Dapoi che <lb/>&longs;e hauera fatte que&longs;te co&longs;e, el &longs;i de &longs;ignar.5.ponti &longs;opra alla detta carta à torno del i-<emph.end type="italics"/><lb/><figure id="id.042.01.114.1.jpg" xlink:href="042/01/114/1.jpg"/><lb/><emph type="italics"/>&longs;trumento &longs;econdo l'ordine della no&longs;tra polizetta, cioe uno à dirimpetto alli.3.gradi <lb/>de Sirocco uer&longs;o O&longs;tro, & co&longs;i un'altro à derimpetto delli.29.gradi de Greco uer&longs;o <lb/>Leuante, co&longs;i un'altro à dirimpetto delli.28.gradi de Tramontana uer&longs;o Greco, & <lb/>un'altro alli.9.gradi de Mai&longs;tro uer&longs;o Ponente, & un'altro alli.5.gradi di Garbino <lb/>uer&longs;o O&longs;tro el giu&longs;to loco da &longs;egnar li &longs;opradetti.5.ponti &longs;i troua per mezzo della dio <lb/>ptra, cioe uoltando prima la detta dioptra talmente, che la &longs;e ripoßi giustamente alli <lb/>detti.3.gradi de Sirocco uer&longs;o O&longs;tro, & &longs;econdo l'ordine di quel poco brazzo della <lb/>detta dioptra, che pa&longs;&longs;a fuora del i&longs;trumento, &longs;ignar el detto ponto &longs;u la carta perpen<emph.end type="italics"/><pb pagenum="58" xlink:href="042/01/115.jpg"/><emph type="italics"/>dicolarmente &longs;otto al loco doue procede la no&longs;tra linea ui&longs;uale per quelli dui bu&longs;etti­<lb/>ni, ouer per quelle due ponte, & &longs;ignato quel tal ponto, uoltar la detta dioptra, & <lb/>giu&longs;tarla alli.29.gradi di Greco uer&longs;o Leuante, come parla la polizetta, & &longs;iguar el <lb/>&longs;econdo ponto, & co&longs;i andar procedendo alli.28.gradi di Tramontana uer&longs;o Greco, <lb/>& alli.9.gradi di Mai&longs;tro uer&longs;o Ponente, & ultimamente alli.5.gradi di Garbino uer <lb/>&longs;o O&longs;tro, come con lo intelletto facilmente &longs;i puo comprender &longs;opra la figura &longs;equen­<lb/>te, & dapoi che &longs;e hauera &longs;ignati li detti ponti, &longs;e potra leuar lo detto i&longs;trumento, & <lb/>&longs;ignar el luoco doue &longs;e ripo&longs;&longs;auael centro di quello (come di &longs;opra dißi e&longs;&longs;er nella mit­<lb/>ta della &longs;opradetta partial linea.c.d.in ponto.e.) & dal detto centro, con una rega, <lb/>ouer una regola tirar.5.linee de indiffinita quantita, che paßino per li detti.5.ponti, <lb/>cioe la prima dal detto centro al primo ponto, cioe a quello &longs;ignato alli.3.gradi de Si­<lb/>rocco uer&longs;o O&longs;tro, & quella tirarla de longo &longs;enzafarui termine, & co&longs;i procedere <lb/>alli altri quattro ponti, & dapoi che &longs;e haueran tirate le dette.5.linee, di cadauna di <lb/>quelle bi&longs;ognara cauarne com un compa&longs;&longs;o una parte de <expan abbr="tãte">tante</expan> mi&longs;urette, ouer apriture <lb/>di compa&longs;&longs;o, quanto &longs;aranno li paßi della &longs;ua relatiua nella no&longs;tra polizetta, <expan abbr="comenzã">comenzam</expan> <lb/>do pero &longs;empre à mi&longs;urare à quel loco, doue &longs;e ripo&longs;&longs;aua el centro del nostro istrumen <lb/>to, cioe à quel ponto.e. (di &longs;opra detto) e&longs;&longs;empi gratia, da quella linea, che pa&longs;&longs;ara per <lb/>li.3.gradi di Sirocco uer&longs;o O&longs;tro, &longs;e ne douer a mi&longs;urar fora.54.apriture di compaßo, <lb/>per e&longs;&longs;er la &longs;ua relatiua nella polizetta pa&longs;&longs;a.54.et in capo delle dette.54.apriture di <lb/>compa&longs;&longs;o, ui &longs;e douera far un ponto fermo <expan abbr="terminãte">terminante</expan> detta linea, & co&longs;i &longs;enza mouere <lb/>il <expan abbr="cõpa&longs;&longs;o">compa&longs;&longs;o</expan>, cioe <expan abbr="cõ">com</expan> la mede&longs;ima apritura, &longs;i debbe mi&longs;urare fuora à cadauna delle altre <lb/>quattro linee, <expan abbr="tãte">tante</expan> apriture, quanto &longs;ara el numero di pa&longs;&longs;a della &longs;ua relatiua nella no <lb/>&longs;tra polizetta, cioe à quella che pa&longs;&longs;a per li.29.gradi di Greco uer&longs;o <expan abbr="Leuãte">Leuante</expan>, <21> e&longs;&longs;ere <lb/>la &longs;ua relatiua pa&longs;&longs;a.63.&longs;e ne mi&longs;urara fuora.63.apriture di <expan abbr="cõpa&longs;&longs;o">compa&longs;&longs;o</expan>, et in fine di <34>lla <lb/>farui un ponto fermo, & co&longs;i <21> non abondar in parole, de l'altra con&longs;equente &longs;e ne do <lb/>uer a mi&longs;urar fuora.81 & far ponto, & de l'altra.72.& della ultima.62.emezzo, <lb/>& in fine di cadauna di quelle farui un ponto fermo (come di &longs;opra fu detto) & fatto <lb/>que&longs;to, el &longs;i de congiongere li detti.5.ponti fermi con.5.linee rette, le quale.5.linee ti­<lb/>rate, che &longs;iano, repre&longs;entaranno li.5.lati del no&longs;tro &longs;ito, ouer pae&longs;e proportionalmen­<lb/>te, come di &longs;otto appare in figura, cioe, che tal piccol di&longs;egno, ouer figura &longs;ara &longs;imile à <lb/>quella figura del no&longs;tro pae&longs;e, ouer &longs;ito, & langolo.a.della &longs;otto&longs;critta figura &longs;ara re <lb/>latiuo, & equale a langolo.a.della figura del no&longs;tro pae&longs;e, & langolo.b.a langolo.b. <lb/></s> <s id="s.001194">& co&longs;i tutti li altri al &longs;uo relatiuo. </s> <s id="s.001195">Et bi&longs;ogna notar, che quantunque io habbia ti­<lb/>rate quelle.5.linee, che uien dal centro à cia&longs;cun angolo del no&longs;tro di&longs;&longs;egno, tutte ap­<lb/>parente (come nella figura appare) nondimeno uoleno e&longs;&longs;er tirate occulte, cioe &longs;enza <lb/>inchio&longs;tro, perche gua&longs;tano la figura, ma co&longs;i le ho tirate, accio che uoi intendiate me­<lb/>glio la co&longs;a. </s> <s id="s.001196">Anchor bi&longs;ogna notar, che per mi&longs;urar fora delle &longs;opra &longs;critte.5.linee <lb/>quelle apriture di <expan abbr="cõpaßo">compaßo</expan> che bi&longs;ogna, <expan abbr="cõ">com</expan> piu breuita, &longs;e puo &longs;ignar dacanto una lineet <lb/>ta de.100.apriture di <expan abbr="cõpaßo">compaßo</expan>, ouer de piu, <expan abbr="&longs;ecõdo">&longs;econdo</expan> che tal pae&longs;e &longs;ara <expan abbr="grãde">grande</expan>, ouer picco <lb/>lo, et <34>lla tal lineetta diuiderla <expan abbr="ĩ">im</expan> parte a.10.apritura <21> parte, et que&longs;ta tal linea &longs;e chia <lb/>ma &longs;chala della no&longs;tra mi&longs;ura, et quando poi occorreße de mi&longs;urare &longs;ora da una data <lb/>linea una qualche <expan abbr="grã">gram</expan> <expan abbr="distãtia">distantia</expan>, ouer <expan abbr="lõghezza">longhezza</expan>, poniamo una <expan abbr="lõghezza">longhezza</expan> de.795.pa&longs;&longs;a,<emph.end type="italics"/><pb xlink:href="042/01/116.jpg"/><figure id="id.042.01.116.1.jpg" xlink:href="042/01/116/1.jpg"/><lb/><emph type="italics"/>&longs;e tal no&longs;tra&longs;cala &longs;ara &longs;uppo&longs;ta poniamo de cento apriture di compa&longs;&longs;o, le quale repre <lb/>&longs;enta&longs;&longs;e.100.pa&longs;&longs;a, prima con un compa&longs;&longs;o largo alla equalita di tal &longs;cala, &longs;e mi&longs;urara <lb/>fora &longs;ette apriture di quel tal compa&longs;&longs;o, le quale denotaranno.700.pa&longs;&longs;a, dapoi &longs;e re <lb/>&longs;tringera el detto compa&longs;&longs;o alla equalita de una decima parte de tal &longs;cala, la quale re­<lb/>pre&longs;entara dieci pa&longs;&longs;a, & <expan abbr="cõ">com</expan> tal apritura &longs;e mi&longs;urara fora anchora.9.e meggio di tal <lb/>apriture, & co&longs;i &longs;e hauera mi&longs;urato fuora li &longs;opradetti pa&longs;&longs;a &longs;ettecento nouantacin­<lb/>que, & questo &longs;i fa, perche &longs;aria co&longs;a molto longa à uoler &longs;tare à mi&longs;ur are una tanta <lb/>gran quantita di pa&longs;&longs;a, con una apritura di compa&longs;&longs;o che repre&longs;enta&longs;&longs;e un &longs;ol pa&longs;&longs;o, & <lb/>maßime, che tal hora el di&longs;&longs;egno &longs;i uora far tanto piccolo, che un pa&longs;&longs;o non&longs;aria quan­<lb/>tita &longs;en&longs;ibile, & per que&longs;to &longs;empre &longs;i co&longs;tuma far la detta linea (chiamata &longs;cala) & <lb/>quella &longs;e &longs;uppone de quanti pa&longs;&longs;a pare all'operante, nondimeno la maggior parte la <lb/>&longs;uppone de cento pa&longs;&longs;a nelle di&longs;cretion piccole, ma nelle grande in Geographia &longs;e &longs;up­<lb/>pongano de milliari, & non de pa&longs;&longs;a, cioe de cento, ouer piu milliari. </s> <s id="s.001197">Anchora bi&longs;ogna <lb/>notar, che quella prima linea, che di &longs;opra fu detto, che &longs;i debbe tirare in mezzo della <lb/>carta, doue &longs;e uol de&longs;criuere el nostro di&longs;&longs;egno (cioe quella linea.a.b.) la &longs;e puo fuppo­<lb/>nere, che uada rettamente da Leuante à Ponente, ouer da O&longs;tro à Tramontana, il che <lb/>&longs;upponendola, bi&longs;ogna poi giu&longs;tar la mede&longs;ima del no&longs;iro istrumento &longs;opra à quella, <lb/>& dapoitorcere talmente la tabula, che la lancetta della calamita &longs;e uada à giu&longs;tar (in <lb/>tal po&longs;itione) &longs;econdo el &longs;uo ordine, & dapoi procedere, come di &longs;opra fu detto.<emph.end type="italics"/> R. <lb/>E<emph type="italics"/>ue ho inte&longs;o benißimo, & ba&longs;ta per hoggi.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001198">QVESITO TERZO FATTO DAL MEDESIMO <lb/>M. R<emph type="italics"/>ichardo Ventuorth.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001199">RICHARDO. H<emph type="italics"/>or uoria, che uoi mi dichiara&longs;ti un poco quando che li lati <lb/>del detto pae&longs;e non fu&longs;&longs;eno perfettamente retti, come &longs;e doueria procedere.<emph.end type="italics"/><lb/>N. Q<emph type="italics"/>uando che quello pae&longs;e, che &longs;e de&longs;idera&longs;&longs;e da mettere in di&longs;&longs;egno fu&longs;&longs;e contenu <lb/>to parte da linee curue, & parte da rette, ouer amente tutto da linee curue, eglie ne­<lb/>ce&longs;&longs;ario à formar in tal figura curuilinea una figura rettilinea de molti lati per acco­<lb/>&longs;tar&longs;e piu che &longs;ia poßibile à quelle linee curue, & mettere in di&longs;&longs;egno quella figura<emph.end type="italics"/><pb pagenum="59" xlink:href="042/01/117.jpg"/><emph type="italics"/>rettilinea in &longs;critta in quella curuilinea, & darui poi alli &longs;uoi debiti luochi alquanto di <lb/>curuita per pratica, cioe à de&longs;crittione, & per e&longs;&longs;or meglio inte&longs;o, &longs;upponeremo che il <lb/>&longs;ia uno pae&longs;e contenuto la maggior parte da linee curue, come di &longs;otto appare in figu­<lb/>ra. </s> <s id="s.001200">Dico à uoler metter in di&longs;&longs;egno questa tal figura, etaltre &longs;imile piantato, che &longs;e hab <lb/>bia il detto nostro i&longs;tromento in meggio del detto &longs;ito, uel circa, come di &longs;otto appare, <lb/>& quello agiu&longs;tato, ouer a&longs;&longs;ettato &longs;econdo il &longs;uo ordine el &longs;i de far piantar molte bac­<lb/>chette per la circonferentia di quelle curaita, & doue è maggior curuita piantarui mol <lb/>to piu &longs;pe&longs;&longs;e le dette bacchette per poter &longs;i con linee rette piu approßimar&longs;e à quella <lb/>curuita, come di &longs;otto appare, & &longs;upponer che quelle differentie che è da bacchetta à <lb/>bacchetta &longs;iano lati de una figura rettelinea in &longs;critta in quella figura curuilinea, e per <lb/>tanto el &longs;i debbe andar tra&longs;guardando con la no&longs;tra dioptra cadauna di dette bacchet­<lb/>te, & notare nella pollicetta per qual grado pa&longs;&longs;ara cadauna linea ui&longs;uale con la &longs;ua <lb/>quantìta di pa&longs;&longs;a, che &longs;ara dal piede dell'i&longs;tromento à cadauna bacchetta, & fatto que­<lb/>sto, il&longs;e debbe far un qualche &longs;egno, ouer nota per memoria de quelle &longs;ue curuita, cioe <lb/>&longs;e tai curuita danno in fuora, ouer &longs;e &longs;e incarnano in dentro della figura, & dapoi ca­<lb/>uar l i&longs;tromento, & andar&longs;ene à ca&longs;a, & uolendo poi mettere tal di&longs;&longs;egno in carta, <lb/>ouer in tela, di&longs;te&longs;a quella &longs;opra una tauola &longs;econdo il &longs;olito, il &longs;i de prima mettere in <lb/>di&longs;&longs;egno quella figura rettelinea in &longs;critta (ma non tirar li &longs;uoi lati per linea retta, ma <lb/>andar congiongendo le istremita di quelle linee (terminate con il &longs;olito ponto fermo) <lb/>con una linea alquanto curuata in fuora, ouer in dentro &longs;econdo che dinotara quel &longs;e­<lb/>gno che gia fu annotato per memoria, ilche facendo &longs;e fara una figura &longs;imile à quella di <lb/>quel tal pae&longs;e. </s> <s id="s.001201">ouer &longs;ito, granda, ouer piccola &longs;econdo che &longs;iuorra, cioe uolendola far <lb/>granda &longs;e fara anchora la no&longs;tra &longs;cala (detta nel precedente que&longs;ito) de.100.pa&longs;&longs;a al­<lb/>quanto longa, & uolendola piccola, &longs;e fara la detta &longs;cala alquanto curta, & bi&longs;ognano <lb/>tare, che quantunque io habbia tirate quelle.25.linee nel no&longs;tro di&longs;&longs;egno tutte appa­<lb/>rente, et l'haggio fatto, accio che piu euidentemente &longs;i ueda il modo de procedere per­<lb/>che le dette.25.linee &longs;ono relatiue à quelli.25.interualli, che &longs;ono dal piede del no&longs;tro<emph.end type="italics"/><lb/><figure id="id.042.01.117.1.jpg" xlink:href="042/01/117/1.jpg"/><pb xlink:href="042/01/118.jpg"/><emph type="italics"/>&longs;tromento à cadauna bacchetta piantata nel <expan abbr="cõtorno">contorno</expan> del nostro &longs;ito, ouer pae e, le qual <lb/>bacchette, &longs;e non me inganno, &longs;ono <gap/>r.25.tamen in fatto proprio non uoleno e&longs;&longs;er ti <lb/>rate apparente (come di&longs;opra nell'altro di&longs;&longs;egno fu anchor detto) perche gua&longs;tano la <lb/>figura de&longs;ignata, ma &longs;olamente quelle del contorno uoleno e&longs;&longs;er tirate apparente, per­<lb/>che quelle &longs;ono che ne rappre&longs;entano la figura, & que&longs;te tale, che uoleno e&longs;&longs;er tirate, <lb/>non le ho uole&longs;te tirare, ma &longs;olamente ui ho annotato li ponti fermi, accio meglio &longs;i ap <lb/>prenda il modo operatiuo, li quali ponti fermi, che li congiongera con una linea retta.<emph.end type="italics"/><lb/><figure id="id.042.01.118.1.jpg" xlink:href="042/01/118/1.jpg"/><lb/><emph type="italics"/>ouer curua, conue&longs;&longs;a, ouer concaua, &longs;econdo il bi&longs;ogno, &longs;e uedera rappre&longs;entar&longs;e una <lb/>figuretta &longs;imile à quella del no&longs;tro &longs;ito, ouer pae&longs;e.<emph.end type="italics"/> R. A<emph type="italics"/>nchora questa parte l'ho <lb/>inte&longs;a benißimo, & uoglio che ba&longs;ti per hoggi.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001202">QVESITO QVARTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> M. R<emph type="italics"/>ichardo Ventuorth.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001203">RICHARDO. H<emph type="italics"/>or uorria Compare che me dichiara&longs;ti quel &longs;econdo modo <lb/>de tuor in di&longs;&longs;egno, che in principio dice&longs;ti, cio procedendo, ouer andando per <lb/>la circonferentia, ouer contorno di tal &longs;ito, ouer pae&longs;e.<emph.end type="italics"/> N. H<emph type="italics"/>auendo uoi ben inte&longs;o il <lb/>primo modo, uoi ueniti hauer anchor a inte&longs;o piu della mita di que&longs;to &longs;econdo, perche <lb/>&longs;imilmente uolendo proceder per la circonferentia di tal &longs;ito, ouer pae&longs;e, e&longs;&longs;endo quel <lb/>lo contenuto de lati, ouer linee rette nelli angoli de quello, ui bi&longs;ogna pur mettere una <lb/>bacchetta, ouer qualche altro &longs;ignale da potere tra&longs;guardare, & dapoi piantare il det <lb/>to no&longs;tro i&longs;tromento in uno di &longs;uoi angoli, & quello a&longs;&longs;ettarlo &longs;econdo l'ordine piu uol <lb/>te detto, & dapoitra&longs;guardare quella bacchetta, o altro &longs;ignale, che &longs;ia nell'altro ango <lb/>lo auanti di &longs;e, & girare talmente la dioptra che la linea ui&longs;uale paßi per quelli dui bu­<lb/>&longs;ettini (hauendo dettibu&longs;ettini) ouer amente che la &longs;e incontri con quelle due ponte (ha <lb/>uendo dette ponte, quale à me mi pareno piu &longs;pediente) & dapoi notar &longs;opra una pol­<lb/>licetta il uento, & numero di gradi per donde pa&longs;&longs;ara la detta linea ui&longs;uale (ilche la <lb/>dioptra fara manife&longs;to) & dapoi far mi&longs;urare quanto è dal piede dell'i&longs;tromento à <lb/>quella bacchetta, o altro &longs;ignale, che &longs;ara &longs;u l'altro angolo: & tal quantita de pa&longs;&longs;a, à <lb/>notarli &longs;u la pollicetta con&longs;equentemente drio à quello uento, & numero de gradi per<emph.end type="italics"/><pb pagenum="60" xlink:href="042/01/119.jpg"/><emph type="italics"/>auanti annotati (&longs;i come nella precedente operatione fu anchor fatto) & dapoi cauar <lb/>il detto i&longs;tromento di quell angolo, & andarlo à piantare in &longs;u quell'altro (doue è quel <lb/>la bacchetta, ouer &longs;ignale, gia tra&longs;guardato) et con il mede&longs;imo modo tra&longs;guardar quel <lb/>la bacchetta, o altro &longs;ignale che &longs;ara &longs;u l'altro terzo angolo, & annotar &longs;imilmente <lb/>nella pollicetta per qual uento, & numero de gradi pa&longs;&longs;ara la linea ui&longs;uale, & con&longs;e­<lb/>quentemente à notarui drio il numero di pa&longs;&longs;a, che &longs;ara dal piede del no&longs;tro i&longs;tromen­<lb/>to per fina al detto &longs;egno, & co&longs;i con tal ordine &longs;i debbe andar procedendo per fin che <lb/>&longs;i hauera totalmente circondato quel tal pae&longs;e grande, ouer piccolo che &longs;ia, ilche &longs;e ha­<lb/>uera totalmente circondato, quando &longs;e &longs;ara peruenuto à tra&longs;guardare quel &longs;egno po&longs;to <lb/>in &longs;u quel angolo, ouer cantone, doue che nel principio fu piantato la prima uolta lo <lb/>i&longs;tromento, & fatto que&longs;to il &longs;i puo cauar lo &longs;uo i&longs;tromento, & andar&longs;ene à ca&longs;a, & <lb/>quando &longs;e uorra mettere tal pae&longs;e in di&longs;&longs;egno, in carta, ouer in tela, il &longs;i debbe proce­<lb/>der qua&longs;i, come nell'altra de&longs;crittione, cioe distendere tal carta, ouer tela, &longs;oprauna <lb/>tauola piana, & da quella banda, che parera piu conuenire al primo lato del no&longs;tro pae <lb/>&longs;e, & non nel meggio de tal carta, come nell'altra fu fatto, &longs;e douera a&longs;&longs;ettare il detto <lb/>nostro i&longs;tromento talmente che la lancetta del bo&longs;&longs;olo &longs;tia &longs;econdo l'ordine &longs;uo, & da­<lb/>poi a&longs;&longs;ettare anchora la dioptra à quel uento, & numero de gradi annotati nella prima <lb/>partita della nostra pollicetta, & a&longs;&longs;ettata che ui &longs;ia, il &longs;i debbe &longs;ignar dui pontini &longs;u la <lb/>càrta piccolißimi (con un'ago, ouer altra co&longs;a pontita) cioe l'uno da l'un capo della dio­<lb/>ptra, & l'altro dall'altro per pendicolarmente &longs;otto al luoco doue &longs;uol procedere ret­<lb/>tamente la nostra linea ui&longs;uale, & que&longs;to facilmente &longs;e puo cono&longs;cere per meggio de <lb/>quella poca parte della dioptra che u&longs;ci&longs;&longs;e fuora dell'i&longs;tromento (come nell'altro que­<lb/>&longs;ito anchor fu detto) & dapoi che &longs;e hauera &longs;ignati li detti dui ponti, il &longs;i debbe leuar <lb/>uia l'i&longs;tromento, & con una rega il &longs;i debbe tirare, ouer &longs;ignare una linea retta de indif <lb/>finita quantita, la qual paßi preci&longs;amente per li detti dui pontini, & di que&longs;ta tal linea <lb/>il &longs;i ne debbe mi&longs;urar fuora con il compa&longs;&longs;o (con l'ordine della no&longs;tra &longs;cala) tanti pa&longs;­<lb/>&longs;a quanti dira la no&longs;tra pollicetta, & principiare à mi&longs;urare doue ne parera piu con­<lb/>ueniente nella detta linea, & nel principio, & fine di tal parte mi&longs;urata ui &longs;e debbe far <lb/>un ponto fermo, fatto que&longs;to il &longs;i debbe giu&longs;tar la dioptra, à quel uento, & numero de <lb/>gradi, che &longs;i contiene nella &longs;econda partita della no&longs;tra pollicetta (cioe nella &longs;econda sta<lb/>tione) & dapoi giu&longs;t arlo al capo de drio di detta dioptra à quel ponto fermo, che fu &longs;i­<lb/>gnato in fine della no&longs;tra prima linea, & agiustato, che ui&longs;ia, il &longs;i debbe torcere tanto <lb/>in qua, & in la il detto i&longs;tromento in&longs;ieme con la dioptra, che la lancetta del bo&longs;&longs;olo ua <lb/>da al &longs;uo &longs;egno &longs;enza che la dioptra &longs;i muoua dell' or dine, che fu prima a&longs;&longs;ettata, ma &longs;o­<lb/>lamente girare à torno à quel ponto fermo, come &longs;uo centro, talmente che que&longs;te tre <lb/>co&longs;e &longs;i accordano, cioe che la lancetta &longs;tia giu&longs;ta al &longs;uo &longs;egno, & che la dioptra &longs;tia al <lb/>&longs;uo uento, & numero de gradi, & che anchora la detta dioptra con il capo da drio <lb/>uenghi à terminare preci&longs;amente à quel ponto fermo della prima linea &longs;ignata, & <lb/>quando che que&longs;te tre co&longs;e &longs;iano ben accordate, il &longs;i debbe &longs;ignare uno pontino dal­<lb/>l'altro capo della dioptra con uno ago, ouer altra co&longs;a appontita, cioe &longs;otto al luoco do <lb/>ue pa&longs;&longs;a, ouer &longs;uol pa&longs;&longs;are la no&longs;tra linea ui&longs;uale, et &longs;ignato tal pontino, il &longs;i debbe leuar <lb/>uia lo i&longs;tromento, & con una rega il &longs;i debbe tirare una linea retta, che paßi per <pb xlink:href="042/01/120.jpg"/>quel ponto fermo, & anchora per quello pontino, & di que&longs;ta &longs;econda linea il &longs;e ne <lb/>debbe con un compa&longs;&longs;o (&longs;econdo l'ordine della no&longs;tra &longs;cala) mi&longs;urar fuora tanti pa&longs;&longs;a, <lb/>quanti dira la &longs;econda partita della no&longs;tra pollicetta, & principiare à mi&longs;urare à quel <lb/>ponto fermo, terminante la prima linea, & in capo de tal commen&longs;uratione, farui pur <lb/>un ponto fermo &longs;econdo il &longs;olito, & de nuouo il &longs;i debbe agiu&longs;tar la dioptra à quel uen­<lb/>to, & numero de gradi, come &longs;e contien nella terza partita della no&longs;tra pollicetta, & <lb/>agiu&longs;tarla à tal ponto fermo, & accordar quelle tre co&longs;e (dette di &longs;opra) & &longs;ignare <lb/>quel pontino, dall'altro capo della dioptra, & leuar l'i&longs;tromento, & mi&longs;urar fuora <lb/>(con il compa&longs;&longs;o) da tal linea, tanti pa&longs;&longs;a (con l'ordine della no&longs;tra &longs;cala) quanti dira la <lb/>detta terzapartita della no&longs;tra pollicetta, & co&longs;i andar procedendo per fin che &longs;e hab <lb/>bia circondato, ouer &longs;errato tutto tal di&longs;&longs;egno, & &longs;e per ca&longs;o &longs;e hauera comme&longs;&longs;o qual <lb/>che errore, &longs;e ne accorgera nell'ultimo lato, ouer linea, che compira di &longs;errare tal di&longs;­<lb/>&longs;egno, perche quella&longs;ara nece&longs;&longs;ario à tirarla &longs;enza mi&longs;urarla altramente con il com­<lb/>pa&longs;&longs;o, perche quella &longs;e tirara dal ponto fermo, terminante il penultimo lato, ouer linea <lb/>di tal di&longs;&longs;egno, al ponto fermo, doue principiara lo primo lato, ouer linea, che prima fu <lb/>tirata, cioe doue fupo&longs;to lo i&longs;tromento nel principio, cioe la prima uolta, & &longs;e per ca­<lb/>&longs;o, dapoi che la &longs;e hauera tirata la &longs;e ritrouara, con il compa&longs;&longs;o à e&longs;&longs;er de tanti paßa, <lb/>(&longs;econdo l'ordine della no&longs;tra &longs;cala) quanto che &longs;ara not ato nella ultima partita della <lb/>no&longs;tra pollicetta (ilcherare uolte accade) dinotara non eßer&longs;i commeßo alcuno mini­<lb/>mo errore in tutto quanto il no&longs;tro operare, ma &longs;e per ca&longs;o il detto ultimo lato, ouer <lb/>linea, del no&longs;tro dißegno &longs;e trouara de piu, ouer men apriture di compaßo di quello &longs;a­<lb/>ra il numero di paßa, annotati nella pollicetta, di tal &longs;uo relatiuo lato del no&longs;tro &longs;ito, <lb/>ouer pae&longs;e, dinotara eßer&longs;i fatto errore nell'operare, & tanto maggior quanto mag­<lb/>gior differentia &longs;i trouara fra quelli, & &longs;e il ui pare ue ne daro uno eßempio in figura.<emph.end type="italics"/><lb/>R. N<emph type="italics"/>on accade che uoi me dati altro eßempio, perche ue ho inte&longs;o benißimo, & ba­<lb/>sta per hoggi.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001204">QVESITO QVINTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo.<emph.end type="italics"/> M. R<emph type="italics"/>ichardo <lb/>Ventuorth.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001205">RICHARDO. A<emph type="italics"/>nchor che qua&longs;i comprenda, come &longs;e doueria procedere qun <lb/>do che tal &longs;ito fu&longs;&longs;e contenuto da linee, ouer lati curui, ouer montuo&longs;i, nondime <lb/>no hauero accaro à intendere la uo&longs;tra opinione per uedere &longs;e la mia &longs;e conforma con <lb/>la uo&longs;tra.<emph.end type="italics"/> N. B<emph type="italics"/>i&longs;ogna procedere pur, come fu detto nel terzo que&longs;ito, cioe nella cur­<lb/>uita de tai lati piantarui de molte bacchette, et tanto piu &longs;pe&longs;&longs;e quanto che piu &longs;ono cur <lb/>ui, & dapoi procedere, come &longs;e fece nel precedente que&longs;ito, cioe procedere propria­<lb/>mente, come &longs;e tal figura fu&longs;&longs;e contenuta de tante linee, ouer lati retti, quante &longs;aranno <lb/>quelle differentie, che &longs;ara da bacchetta, à bacchetta, ma nel di&longs;&longs;egnarli poi, bi&longs;ogna <lb/>darui un poco del curuo in fuora, ouer in dentro, &longs;econdo che con qualche &longs;egno ue ne <lb/>haucti fatto memoria nella pollicetta.<emph.end type="italics"/> R. C<emph type="italics"/>o&longs;i preci&longs;amente haueua in opinione, che <lb/>&longs;i doue&longs;&longs;e fare, e pero non uoglio, che per hoggi entramo in altro.<emph.end type="italics"/></s> </p> <pb pagenum="61" xlink:href="042/01/121.jpg"/> <p type="head"> <s id="s.001206">QVESITO SESTO FATTO DAL MEDESIMO <lb/>M. R<emph type="italics"/>ichardo Ventuorth.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001207">RICHARDO. P<emph type="italics"/>er le ragioni dette nelli precedenti dui Que&longs;iti à me mi pa­<lb/>re, che &longs;enza alcun uo&longs;tro aui&longs;o io &longs;aperia anchor tor in di&longs;egno la pianta de <lb/>una citta.<emph.end type="italics"/> N. S<emph type="italics"/>i bene, ma in questo bi&longs;ogna con&longs;iderar, che li lati di una citta &longs;ono <lb/>muraglie, & perche nel proprio loco, doue che è la detta muraglia non ui &longs;i puo anda <lb/>re, ne piantarui el no&longs;tro i&longs;tromento, ne etiam le bacchette, ouer &longs;ignali, perche la det <lb/>ta muragliane impedi&longs;&longs;e, e per tanto bi&longs;ogna procedere per l'uno de dui modi, el pri­<lb/>mo di quali è <expan abbr="&qacute;ue&longs;to">que&longs;to</expan>: che el &longs;i puo procedere per el mede&longs;imo modo, ma andando egual <lb/>mente di&longs;tante à cadauna muraglia, cioe piantare el no&longs;tro i&longs;tromento alquanto lonta <lb/>no dalla detta muraglia, come &longs;aria à dire tre piedi, & co&longs;i &longs;e de far piantare la bac­<lb/>chetta, che &longs;i uuol tra&longs;guardare, mede&longs;imamente lontana dalla detta muraglia li detti <lb/>tre piedi, onde tra&longs;guardando la detta bacchetta &longs;econdo l'ordinario, & annotar nel <lb/>la policetta, per qual uento, & numero de gradi pa&longs;&longs;ara la no&longs;tra linea ui&longs;uale, & da <lb/>poi far mi&longs;ur are la longhezza di quella tal muraglia, ouer cortina, & tal numero de <lb/>pa&longs;&longs;a annotarlo nella policetta con&longs;equentemente drio à quel uento, et numero de gra <lb/>di, che prima fu annotati, & co&longs;i con tal ordine andar procedendo in cadauna corti­<lb/>na, & &longs;e per &longs;orte in alcuna di dette muraglie, ouer cortine ui fu&longs;&longs;e qualche porta, ba <lb/>luardo, ouer torrione, bi&longs;ogna farne un poco di memoria nella policetta, cioe à quan­<lb/>ti pa&longs;&longs;a &longs;ara della detta cortina, etiam di quanti pa&longs;&longs;a &longs;ara la &longs;ua larghezza, per po­<lb/>terli, & &longs;aper li poi mettere, ouer de&longs;ignare nel no&longs;tro di&longs;egno alli &longs;uoi debiti luochi, <lb/>& con le &longs;ue debite mi&longs;ure, & que&longs;to mede&longs;imo modo &longs;e douera anchora o&longs;&longs;eruare, <lb/>quando l'occorre&longs;&longs;e à uoler mettere in di&longs;egno un pae&longs;e, doue fu&longs;&longs;e nece&longs;&longs;ario à pro­<lb/>ceder per la circonferentia, ouer contorno di quello, & che nella detta &longs;ua circonfe­<lb/>rentìa, ouer contorno ui fu&longs;&longs;e qualche fo&longs;&longs;o, cie&longs;e, ouer qualche altra co&longs;a, che ne im­<lb/>pedideße il poter andare à piantar el no&longs;tro i&longs;tromento, & le bacchette da tra&longs;guar­<lb/>dare, in la uera circonferentia di tal &longs;ito, ouer pae&longs;e, cioe, chel &longs;i doueria procedere <expan abbr="e-quīdi&longs;tantemente">e­<lb/>quindi&longs;tantemente</expan> à quel tal lato, cioe &longs;el tal nostro i&longs;tromento, &longs;aremo sforzati à pian <lb/>tarlo lontano dal uero lato de tal &longs;ito, poniamo pa&longs;&longs;a.4.ouer piu, altertanti anchora <lb/>&longs;e douera piantar lontano la bacchetta dall'altro capo di tal lato.<emph.end type="italics"/> R. E<emph type="italics"/>ue ho inte&longs;o <lb/>benißimo circa à que&longs;to primo modo, hor diteme pur l'altro modo.<emph.end type="italics"/> N. L'<emph type="italics"/>altro mo <lb/>do certamente è molto piu e&longs;pediente, & presto, perche in quello non ui occorre à far <lb/>piantar bacchette, ne metter altri&longs;ignali, perche quel brazzetto, ouer trauer&longs;o.l.m. <lb/></s> <s id="s.001208">che fu po&longs;to a &longs;quadra nella i&longs;tremita di quello brazzo.g.h. </s> <s id="s.001209">ne caua de tal fa&longs;tidio, <lb/>perche uolendo &longs;apere per qual uento, & grado proceda, ouer &longs;tia una cortina, ouer <lb/>muraglia di tal citta, ba&longs;ta &longs;olamente a tuor el detto no&longs;tro i&longs;tromento in mani, & an­<lb/>dare adappozzare quel tal brazzo, ouer trauer&longs;o.l.m.in un luoco piano di tal corti­<lb/>na, ouer muraglia, & dapoi girarui fotto lo detto i&longs;tromento, ouer bo&longs;&longs;olo, per fina a <lb/>tanto, che la lenguella, ouer lancetta &longs;tia &longs;econdo el &longs;uo ordine, & fatto questo bi&longs;ogna <lb/>notare nella no&longs;tra policetta, per qual uento, e numero de gradi pa&longs;&longs;ara, ouer che di­<lb/>&longs;couerzera la no&longs;tra principal dioptra, perche, per quel mede&longs;imo procedera ancho-<emph.end type="italics"/><pb xlink:href="042/01/122.jpg"/><emph type="italics"/>ra quella tal cortina, ouer muraglia (per e&longs;&longs;er la detta principal dioptra in tal po&longs;i­<lb/>tione equidistante à tal cortina, ouer muraglia, & dapoi far mi&longs;urare tal cortina, o­<lb/>uer muraglia, & tal &longs;ua quantita de pa&longs;&longs;a annotarli con&longs;equentemente drio à quel <expan abbr="u&etilde;">uem</expan> <lb/>to, & numero de gradi, gia annotati, & co&longs;i andar facendo à cadauna dell'altre corti <lb/>ne (facendo memoria delli luochi delle &longs;ue porte, & baluardi (come di &longs;opra fu det­<lb/>to) & fatto que&longs;to andar&longs;ene à ca&longs;a, & quando &longs;e uora poi mettere in di&longs;egno la pian <lb/>ta di tal citta, &longs;e potra procedere preci&longs;amente, come fu fatto di quel pae&longs;e nel.4.Que <lb/>&longs;ito, uero è, che &longs;e potria tirar anchora le linee, &longs;econdo l'ordine di quel brazzo.l.m. <lb/></s> <s id="s.001210">cioe a&longs;&longs;ettato, che &longs;e habbia tal no&longs;tro i&longs;tromento &longs;u la carta da quella banda, doue pa­<lb/>re piu conuegnir&longs;e alla prima cortina di tal citta, & agiu&longs;tato la dioptra à quel uento,<emph.end type="italics"/><lb/><figure id="id.042.01.122.1.jpg" xlink:href="042/01/122/1.jpg"/><lb/><emph type="italics"/>& numero de gradi, come parlara la prima partita della no&longs;tra policetta, & fatto <lb/>que&longs;to, tir are una linea retta de indiffinita quantita, &longs;econdo l'ordine del detto braz­<lb/>zetto.l.m.& datal linea cauarne, ouer mi&longs;urarne fora con el compa&longs;&longs;o, tanti paßa (&longs;e <lb/>condo l'ordine della no&longs;tra &longs;cala) come parlara la detta prima partita della no&longs;tra po <lb/>licetta, & nel principio, & fine di tal linea farui un ponto fermo, come piu uolte è &longs;ta <lb/>to detto, & dapoi reconzar la dioptra al uento, & grado, come parlara la &longs;econda <lb/>partita della nostra policetta, & con tal po&longs;itione a&longs;&longs;ettarla quel brazzetto.l.m. </s> <s id="s.001211">à <lb/>quel ponto fermo gia fatto nel fin della detta prima linea, con tal modo, & forma che <lb/>&longs;e accorda quelle tre co&longs;e dette nel precedente Que&longs;ito, cioe, che la lancetta della cala­<lb/>mita, &longs;tia &longs;econdo el &longs;uo ordine, & che la dioptra &longs;tia à quel uento, & nomero de gr­<lb/>di, come parla la detta&longs;econda partita della policetta terzo, & ultimo, che el detto <lb/>brazzetto.l.m.termini preci&longs;amente à quel ponto fermo, terminante la prima linea, <lb/>& accordate que&longs;te tre co&longs;e, tirate un'altra linea de indeffinita quantita, &longs;econdo l'or <lb/>dine del detto brazzetto.l.m.la qual paßi per el detto ponto fermo, terminante la pri <lb/>ma linea, & di que&longs;ta &longs;econda linea, con el compa&longs;&longs;o &longs;e ne debbe pur mi&longs;urar fuora tan <lb/>ti pa&longs;&longs;a (&longs;econdo l'ordine della no&longs;tra&longs;eala) quanti &longs;ara notati nella detta &longs;econda par <lb/>tita della no&longs;tra policetta, comenzando pero à mi&longs;urare al detto ponto fermo, termi­<lb/>ne della prima linea, & principio della &longs;econda, & in fine farui pur un ponto fermo, <lb/>& co&longs;i con tal modo, & ordine &longs;e douera andar procedendo, per fin che &longs;e hauera <expan abbr="cõ-pito">con­<lb/>pito</expan> da de&longs;ignare la <expan abbr="piãta">pianta</expan> di cadauna cortina di tal citta, et chi uoleße &longs;apere che <expan abbr="u&etilde;to">uento</expan><emph.end type="italics"/><pb pagenum="62" xlink:href="042/01/123.jpg"/><emph type="italics"/>percoteße <expan abbr="perp&ebreve;dicolarm&etilde;te">perp&ebreve;dicolarmente</expan> &longs;opra à cadauna cortina, &longs;empre el brazzo.g.h. </s> <s id="s.001212">lo fara <lb/>manife&longs;to.<emph.end type="italics"/> R. V<emph type="italics"/>oi me haueti certamenti molto &longs;atisfatto, uero è, che el me è occor­<lb/>&longs;o un'altra particolarita de <expan abbr="adimãdarui">adimandarui</expan>, ma per e&longs;&longs;er tardi, la uoglio la&longs;&longs;ar à dimane.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001213">QVESITO SETTIMO FATTO DAL MEDESIMO <lb/>M. R<emph type="italics"/>ichardo Ventuorth.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001214">RICHARDO. A<emph type="italics"/>nchor che me habbiati<emph.end type="italics"/> (C<emph type="italics"/>ompar carißimo) molto &longs;atisfat <lb/>to in tutto quello, che nel principio ue richie&longs;e, nondimeno pen&longs;ando poi, che in <lb/>ogni luoco, ouer citta, <expan abbr="nõ">non</expan> potero for&longs;i trouare mae&longs;tro, che mi pote&longs;&longs;e, ouer &longs;ape&longs;&longs;e &longs;er <lb/>uire in farmi tal <expan abbr="i&longs;trom&etilde;to">i&longs;tromento</expan>, ouer bo&longs;&longs;olo, per e&longs;&longs;er quello, &longs;econdo el mio parere, di <expan abbr="nõ">non</expan> <lb/>poco artificio, & per tanto uiprego, che &longs;el fu&longs;&longs;e poßibile de immaginare una qualche <lb/>altra forma, che fu&longs;&longs;e de tal facilita, che fu&longs;&longs;e &longs;icuro di poter in ognicitta ritrouare <lb/>mae&longs;tri, che me pote&longs;&longs;ono, ouer &longs;ape&longs;&longs;ono fare.<emph.end type="italics"/> N. I<emph type="italics"/>o ue ne uoglio in&longs;ignare à for­<lb/>marne uno di legno, el quale non &longs;olamente in ogni cittauoi trouareti molte per&longs;one, <lb/>che uel &longs;apranno, & potrauno fare, ma anchora per uoi mede&longs;imo aun bi&longs;ogno lo &longs;a­<lb/>pereti, & potreti fare.<emph.end type="italics"/> R. V<emph type="italics"/>oi non mi potre&longs;ti fare co&longs;a piu grata, ma dubito a&longs;&longs;ai <lb/>che tal co&longs;a non &longs;ia el uero, & la cau&longs;a, che mi fa dubbitare è questa, che &longs;olamente in <lb/>le citta maritime, &longs;e ritroua per&longs;one, che &longs;appiano far li bo&longs;&longs;oli, & temperare quella <lb/>&longs;ua lancetta, la qual è il timone, che gouerna la naue di questa no&longs;tra pratica.<emph.end type="italics"/> N. E­<lb/><emph type="italics"/>glie ben il uero, che in ogni citta non &longs;i troua co&longs;i per&longs;one, che &longs;iano atte a far tal co&longs;a, <lb/>ma non me potretinegare, che in ogni citta non ui &longs;i troua di quelli horologietti, che <lb/>uengono dalla Lemagna, con li quali al&longs;ole &longs;e pol &longs;apere quante hore &longs;ono, & &longs;i uendo <lb/>no tre, ouer quattro &longs;oldi luno.<emph.end type="italics"/> R. C<emph type="italics"/>he de quelli, che hanno una Tramontanella pic <lb/>cola, cioe poco piu della ungia del dedo gro&longs;&longs;o.<emph.end type="italics"/> N. P<emph type="italics"/>roprio de quelli.<emph.end type="italics"/> R. S<emph type="italics"/><expan abbr="&etilde;za">enza</expan> dub <lb/>bio, che de tali horologietti&longs;e ne ritroua per egni citta.<emph.end type="italics"/> N. E<emph type="italics"/>t con uno de quelli ue <lb/>uoglio in&longs;ignare a far ui uno i&longs;trumento, & con gran facilita, con el quale ue ne potre­<lb/>ti &longs;eruir in tutte que&longs;te prasiche, di che hauemo fin hora parlato.<emph.end type="italics"/> R. E<emph type="italics"/>come.<emph.end type="italics"/> N. <lb/>I<emph type="italics"/>o uoglio, che uoi di&longs;egnati con un compa&longs;&longs;o &longs;opra a un foglio di carta <expan abbr="alquãto">alquanto</expan> großa <lb/>e ferma, e <expan abbr="b&etilde;">bem</expan> lißa, una figura &longs;imile a quella, che <expan abbr="ĩ">im</expan> principio ui mo&longs;trai di far &longs;opra quel <lb/>la <expan abbr="lãma">lamma</expan> di ottone, cioe quelli mede&longs;imi circuli, <expan abbr="cõ">com</expan> le me de&longs;ime diui&longs;ioni de uenti, & de <lb/>gradi, come che anchora di &longs;otto appar in figura, ma farlo, che <21> diametro &longs;ia al men <lb/>una <expan abbr="&longs;pãna">&longs;panna</expan>, accio che la &longs;ua circonferentia po&longs;&longs;a e&longs;&longs;er diui&longs;a in.360.gradi, et dapoi che <lb/>baueriti fatto que&longs;to tal di&longs;egno in carta, uoglio che tal di&longs;egno l'incollati &longs;opra ad un <lb/>quadretto di tabula di legno <expan abbr="b&etilde;">bem</expan> piana, et di legno <expan abbr="b&etilde;">bem</expan> &longs;ecco, gro&longs;&longs;a circa a un dedo, & &longs;e <lb/>poßibil fu&longs;&longs;e farla far de legno d'ancipre&longs;&longs;o (perche tal legno <expan abbr="nõ">non</expan> fa mutatione &longs;en&longs;ibile <lb/>ne &longs;e &longs;torge <21> <expan abbr="t&etilde;po">tempo</expan>) & far che el detto quadretto di tabula habbia nel mezzo de un di <lb/>&longs;uoi lati un'altro quadrettino congionto di <expan abbr="tãta">tanta</expan> <expan abbr="grãdezza">grandezza</expan>, che &longs;ia capace di poterui &longs;o <lb/>pra di quello inca&longs;&longs;arui, & incollarui uno delli &longs;opradetti horologietti, che uengono <lb/>da Allemagna, ma bi&longs;ogna aduertire ne l'incollar el detto di&longs;egno, & el detto horolo­<lb/>gietto di far, che la <expan abbr="Tramõtana">Tramontana</expan> del detto di&longs;egno, et <expan abbr="&longs;imilm&etilde;te">&longs;imilmente</expan> quella del detto horolo <lb/>gietto guardino rettamente per uno mede&longs;imo uer&longs;o, come di &longs;otto appar in figura.<emph.end type="italics"/><pb xlink:href="042/01/124.jpg"/>E <emph type="italics"/>dapoì que&longs;to, bi&longs;ogna farui una dio­<lb/>ptra pur li legno d'ancipre&longs;&longs;o (&longs;e poßi­<lb/>bil è) ouer di qualche altro, che &longs;ia ben <lb/>&longs;ecco, talmente, che per tempo non fac­<lb/>cia mutatione, che in cio l'ancipre&longs;&longs;o lau <lb/>piu de tutti. </s> <s id="s.001215">Et per far que&longs;ta dioptra, <lb/>che &longs;ia giu&longs;tißima, bi&longs;ogna far fare una <lb/>reghetta, ouer li&longs;tetta del detto legno, <lb/><expan abbr="lõga">longa</expan> circa un brazzo, e mezzo, & lar <lb/>ga circa a un dedo, & gro&longs;&longs;a circa a <lb/>una co&longs;ta di cortello, & que&longs;ta tal ri-<emph.end type="italics"/><lb/><figure id="id.042.01.124.1.jpg" xlink:href="042/01/124/1.jpg"/><lb/><emph type="italics"/>ghetta uol e&longs;&longs;er rettißima, & giu&longs;tißima, & per cono&longs;cere &longs;e tal regha &longs;ara giu&longs;ta, <lb/>&longs;e potra cono&longs;cere per quel modo po&longs;to nel terzo libro della no&longs;tra noua&longs;cientia, & <lb/>dapoi fatta que&longs;ta tal regha, di quella bi&longs;ogna &longs;egarne fuora otto pezzetti, cioe quat­<lb/>tro maggiori, & quattro menori, li quattro maggiori uoleno e&longs;&longs;er di tal longhezza, <lb/>che &longs;opragionti, & incolati, come di &longs;otto appar in ponto.e.&.f. </s> <s id="s.001216">&longs;iano alquanto piu <lb/>del diametro del detto istromento. </s> <s id="s.001217">Et bi&longs;ogna notar, che tal &longs;opragiontion uol e&longs;&longs;er <lb/>fatta per gro&longs;&longs;ezza, & uol e&longs;&longs;er tanta, quanto che è la &longs;ua larghezza, & con tal mo-<emph.end type="italics"/><lb/><figure id="id.042.01.124.2.jpg" xlink:href="042/01/124/2.jpg"/><lb/><emph type="italics"/>do, & ordine, che que&longs;ti dui par de pezzi (co&longs;i congionti, & incolati) ponendoli luno <lb/>&longs;opra l'altro in perfetta croce, cioe perfetta linea a &longs;quadra (come di &longs;opra appar in <lb/>figura) <expan abbr="u&etilde;gono">uengono</expan> a fare, ouer a formare nella &longs;ua <expan abbr="cõgiontione">congiontione</expan> uno quadretto (come nella <lb/>detta &longs;otto&longs;critta figura appare) el qual quadretto uenghia cau&longs;ar un angolo in pon­<lb/>to.g.& un altro a quel oppo&longs;ito in ponto.h. </s> <s id="s.001218">Et co&longs;i que&longs;ti dui par de pezzi uogliono <lb/>e&longs;&longs;er perfettamente incolati in tal po&longs;itione, cioe, come nella detta&longs;otto&longs;critta figura <lb/>appare. </s> <s id="s.001219">Gli altri.4.pezzetti menori, li quali po <lb/>niamo che &longs;iano li &longs;opra notati <21>.a.b.c.d.uoglio <lb/>no e&longs;&longs;er piu corti delli altri.4.maggiori, tanto <lb/>quanto è la larghezza de cadauno de loro, <21> che <lb/>de quelli uoglio che &longs;e ne &longs;erui <21> redure la &longs;opra <lb/>&longs;critta croce tutta piana, e &longs;olida, <21> che eglie ma­<lb/>nifesto, che li dui brazzi.i.h.g.<emph.end type="italics"/> k <emph type="italics"/><21> e&longs;&longs;er &longs;opra <lb/>posti alli altri dui, <expan abbr="nõ">non</expan> toccano el piano doue &longs;eri<emph.end type="italics"/><lb/><figure id="id.042.01.124.3.jpg" xlink:href="042/01/124/3.jpg"/><lb/><emph type="italics"/>po&longs;&longs;a li detti altri dui brazzi a <34>lli &longs;ottopo&longs;ti, anci <expan abbr="&longs;tãno">&longs;tanno</expan> in aere, cioe <expan abbr="lõtani">lontani</expan> dal detto <lb/>piano <expan abbr="tãto">tanto</expan> <expan abbr="quãto">quanto</expan> è la gro&longs;&longs;ezza de cadauno de loro, e pero <21> impir quel uacuo uoglio,<emph.end type="italics"/><pb pagenum="63" xlink:href="042/01/125.jpg"/><emph type="italics"/>che otto à cadauno de detti dui bracci.i.h.g.<emph.end type="italics"/>k.<emph type="italics"/>ui &longs;ia incollato uno de quelli.4.pezzi <lb/>menori.a.b.c.d.detti di &longs;opra, li quali ueniranno à empire perfettamente quelli duiua­<lb/>cui, perche &longs;e conueneranno preci&longs;amente in quelli, & co&longs;i &longs;era redutta tal croce piana <lb/>dalla parte di &longs;otto uer&longs;o il piano, ma non di &longs;opra, perche quelli dui primi bracci po&longs;ti <lb/>in piano non a&longs;cendono alla altezza delli dui &longs;opra po&longs;ti, cioe de.i.h.<emph.end type="italics"/> g.k.<emph type="italics"/>anci ui manca <lb/>tanto quanto è la gro&longs;&longs;ezza de cadauno de loro, e pero per empir quel uacuo, uoglio <lb/>che ui &longs;ia incollato &longs;opra à cadauno de loro uno de quelli altri dui pezzi menori giare­<lb/>&longs;tati, li quali uenir anno à empire perfettamente quel uacuo, perche &longs;e conueniranno <lb/>preci&longs;amente in quelli, & fatto que&longs;to, tal croce &longs;ara redutta tutta &longs;olida, & piana da <lb/>ambe le bande, e &longs;ara fortificata, perche &longs;ara fatta tutta doppia, et tutto que&longs;to meglio <lb/>&longs;e uedera nel fabricarla, che per figura. </s> <s id="s.001220">Et dapoi que&longs;to nel capo de dui di detti bracci <lb/>oppo&longs;iti, bi&longs;ogna incollarui un'altro pezzetto dellamede&longs;ima li&longs;tetta pur doppia, co­<lb/>me di &longs;otto appare in ponto.a.& in ponto.b.& in l'uno, el'altro de que&longs;ti dui lochi ui <lb/>douera piantar una ponta acuta, come &longs;aria una ponta de ago, che &longs;eruino per tra&longs;­<lb/>guardar, in luoco delli dui bu&longs;i. </s> <s id="s.001221">Et &longs;e piu ag-gradara li bu&longs;i che tai due ponte, in tai me­<lb/>de&longs;imi lochi ui &longs;e potra inca&longs;&longs;ar, & incollar <lb/>dui quadratini in alto elleuati con li detti dui <lb/>bu&longs;i, ma piu mi piace le due ponte, che li bu <lb/>&longs;i. </s> <s id="s.001222">Et per poter&longs;i &longs;eruire di que&longs;to tal istro­<lb/>mento per tuor in di&longs;&longs;egno le piante delle cit <lb/>ta, nella i&longs;tremita del braccio.c.d.ui &longs;e potra <lb/>inca&longs;&longs;ar, & incollar il brazzetto.e.f.à &longs;qua<emph.end type="italics"/><lb/><figure id="id.042.01.125.1.jpg" xlink:href="042/01/125/1.jpg"/><lb/><emph type="italics"/>dra, come nella &longs;opra&longs;critta figura appare. </s> <s id="s.001223">Et dapoi que&longs;to nel centro di tal dioptra bi <lb/>&longs;ogna farui un bu&longs;ettino, & con un pironcino di ferro, ouer di ottone piantare tal dio­<lb/>ptra nel centro di tal i&longs;tromento, la qual co&longs;a facendo tal i&longs;tromento &longs;tara preci&longs;e, come <lb/>me di &longs;otto appare in figura, & di que&longs;to ue ne potreti&longs;eruire, &longs;i come di quello di ot­<lb/>tone.<emph.end type="italics"/> R. Q<emph type="italics"/>uesto mi pare una co&longs;a molto facile, & di poco artificio, & qua&longs;i di niu­<lb/>na &longs;pe&longs;a, perche tutta la &longs;pe&longs;a che ui entrara non credo che a&longs;cendera à un marcello, ma <lb/>dubito che il <expan abbr="nõ">non</expan> &longs;ara di quella mede&longs;ima giu&longs;tezza che &longs;ara quello di ottone.<emph.end type="italics"/> N. A<emph type="italics"/>n <lb/>ci per molte ragioni, eglie nece&longs;&longs;ario, che que&longs;to &longs;ia molto piu giu&longs;to di quello di ot-<emph.end type="italics"/><lb/><figure id="id.042.01.125.2.jpg" xlink:href="042/01/125/2.jpg"/><pb xlink:href="042/01/126.jpg"/><emph type="italics"/>tone, perche in quello di ottone, oltra che ui occorre maggior difficolta in far quelli dui <lb/>bracci della &longs;ua dioptra, che &longs;iano rettißimi (per e&longs;&longs;er di metallo) di quello, che occorre <lb/>nelli dui bracci della &longs;opra&longs;critta dioptra.a.b. (per e&longs;&longs;er piu facile da lauorar con la <lb/>piona il legno del metallo) ma poniamo anchora che gli detti bracci di ottone (per la <lb/>buona diligentia del mae&longs;tro fu&longs;&longs;eno fatti di tanta giu&longs;tezza, quanto quelli di legno) <lb/>dico che eglie difficile a&longs;&longs;ai ad a&longs;&longs;ettarli poi in quella &longs;ua armilla, che &longs;i incontr ano ret­<lb/>tamente, & non in contrando &longs;i tal i&longs;tromento &longs;aria fal&longs;o, & oltra di questo, eglie an­<lb/>chora molto difficolto&longs;o, che tal armilla uada, ouer intraga talmente giu&longs;ta, ouer &longs;az­<lb/>zadamente, in quella altra armilla &longs;aldata à torno del bo&longs;&longs;olo, che non &longs;cantini piu in <lb/>un luoco, che in un'altro, ilche facendo tal dioptra non ri&longs;pondera il uero grado, ilche <lb/>facendo tal <expan abbr="i&longs;trom&etilde;to">i&longs;tromento</expan> &longs;aria fal&longs;o. </s> <s id="s.001224">Et oltra di que&longs;to, non è molto facile ad a&longs;&longs;aldare quel <lb/>la prima armilla à torno al centro di tal i&longs;tromento di ottone, che &longs;ia perfettamente <expan abbr="cõ">com</expan> <lb/>centrica con il detto i&longs;tromento, & non e&longs;&longs;endo concentrica tal i&longs;tromento &longs;aria fal&longs;o, <lb/>e per tanto dico, che à far tal dioptra di legno per il modo dato di &longs;opranon ui occorre <lb/>alcune delle &longs;opr adette difficolta, ma &longs;olamente bi&longs;ogna e&longs;&longs;er diligente in far, che quel­<lb/>la prima righetta, ouer li&longs;tetta &longs;ia giu&longs;tißima (ilche facilmente per lo &longs;opradetto mo­<lb/>do da noi po&longs;to nel Terzo libro detto Nuona Scientia) &longs;i puo cono&longs;cere, & uedere.<emph.end type="italics"/> R. <lb/>C<emph type="italics"/>on&longs;idero che eglie il uero quello, che uoi diceti, ma eglie &longs;e non una co&longs;a, che quel qua­<lb/>dretto doue uoleti che ui &longs;e incaßt il detto horologietto, par che molto di&longs;dica co&longs;i con­<lb/>gionto in quel lato, de fuor a uia.<emph.end type="italics"/> N. C<emph type="italics"/>ir ca à que&longs;to, ui &longs;e gli potria rimediare in piu mo <lb/>di, l'uno di quali è questo, il &longs;e potria da tal horologietto &longs;egarui, ouer tagliarui fuora <lb/>quel poco bo&longs;&longs;oletto, cioe quella tramontanella, & tal tramontanella inca&longs;&longs;ar la in uno <lb/>de quelli &longs;paci uacui de quelli angoli del quadrato, che conterminorno con il mede&longs;imo <lb/>lato doue che è congionto tal quadretto, cioe in quel &longs;pacio doue é &longs;ignato.o.ouer nel­<lb/>l'altro, mabi&longs;ogna auertire nell'inca&longs;&longs;ar tal bo&longs;&longs;oletto, ouer tramontanella, in tal luo­<lb/>co de far che la Tramontana de tal bo&longs;&longs;oletto, guardi per quel mede&longs;imo uer&longs;o, che <lb/>guardara quella del no&longs;tro di&longs;&longs;egno, cioe che la linea che ua da O&longs;tro à Tramontana <lb/>nel bo&longs;&longs;oletto &longs;tia equidi&longs;tante à quella, che mede&longs;imamente ua da O&longs;tro à Tramonta­<lb/>na del no&longs;tro di&longs;&longs;egno, il qual bo&longs;&longs;oletto e&longs;&longs;endo co&longs;i a&longs;&longs;ettato, tanto ui &longs;eruira, come &longs;e <lb/>quel fu&longs;&longs;e, come era prima, cioe congionto con quel lato de fuor a uia.<emph.end type="italics"/> R. <!-- KEEP S--></s> <s id="s.001225">A <emph type="italics"/>que&longs;to <lb/>modo sta molto meglio, & molto piu mi piace dell'altro. </s> <s id="s.001226">Nondimeno ho à caro di ba­<lb/>uer inte&longs;o l'uno, e l'altro, & per al pre&longs;ente non ui uoglio dare altro fa&longs;tidio. </s> <s id="s.001227">Ma un'al <lb/>tra uolta con piu uo&longs;tro, & mia commodita, uorro poi che anchora mi dichiarati di <lb/>quell'altra forma de i&longs;tromento, ouer bo&longs;&longs;olo, che &longs;erue &longs;enza dioptra.<emph.end type="italics"/> N. O<emph type="italics"/>gni uol <lb/>ta che ui &longs;ia accommodo &longs;on &longs;empre apparato à farui appiacere. </s> <s id="s.001228">Ma una co&longs;a ui ho da <lb/>ricordare, ogni uolta che uoleti operare tal i&longs;tromento auertir, che non ui &longs;ta propin­<lb/>quo ferro di&longs;orte alcuna, perche il bo&longs;&longs;olo, ouer calamita, non ui ri&longs;ponderia il uero, e <lb/>pero in tal negocio non &longs;i debbe portar &longs;pada, ne pugnal cinto, perche il pomo &longs;pe&longs;&longs;e <lb/>uolte ui faria errare, & non di poco.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001229">I<emph type="italics"/>l fine del Quinto Libro.<emph.end type="italics"/><!-- KEEP S--></s> </p> </subchap1><subchap1> <pb pagenum="64" xlink:href="042/01/127.jpg"/> <p type="head"> <s id="s.001230">LIBRO SESTO DELLI <lb/>QVESITI, ET IN VENTIONI DIVERSE, <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001231">S<emph type="italics"/>opra il modo di fortificar le Citta <lb/>ri&longs;petto alla forma.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001232">QVESITO PRIMO FATTO DAL S. GABRIEL <lb/>T<emph type="italics"/>adino, Cauallier de Rodi, & Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001233">PRIORE. N<emph type="italics"/>on credeti uoi che lo ingegno dell'huomo al pre&longs;ente <lb/>&longs;ia peruenuto à quel &longs;ublime grado doue &longs;ia poßibile à peruenire, <lb/>per fortificare una citta.<emph.end type="italics"/> N. D<emph type="italics"/>i que&longs;to non ui &longs;aprei ri&longs;pondere, <lb/>perche non &longs;olamente ho praticato poco per Italia, & manco fuor <lb/>de Italia, ma da dodeci anni in qua mai &longs;on &longs;tato fuora di Venetia, <lb/>&longs;aluo una uolta che andai à Verona per un mio negocio qua&longs;i à &longs;taf­<lb/>fetta.<emph.end type="italics"/> P. M<emph type="italics"/>o non uede&longs;ti Padoua, & Verona, non haueti ancho­<lb/>ra ui&longs;to Bre&longs;&longs;a uo&longs;tra Patria.<emph.end type="italics"/> N. P<emph type="italics"/>adoua ho ui&longs;to per tran&longs;ito &longs;im <lb/>plicemente in trauer&longs;arla per andare alle barche dal Fraßine, ma non con&longs;iderata. </s> <s id="s.001234">Si­<lb/>milmente ho ui&longs;to Verona, & &longs;tantiato per diece anni in quella, ma mai la circondai, <lb/>ne manco con&longs;iderai, la figura del contorno di quella. </s> <s id="s.001235">La can&longs;a fu che à quel tempo non <lb/>mi dilettaua de tai particolarita, ne mai hebbi in animo di dilettarmene in conto alcu­<lb/>no, ma que&longs;ti &longs;o&longs;petti, & mouimenti Turche&longs;chi me hanno dato nuouamente occa&longs;ione <lb/>di ponerui alquanto cura, come co&longs;a utile, & nece&longs;&longs;aria, & quello che ho detto di Ve­<lb/>rona, il mede&longs;imo dico di Bre&longs;&longs;a<emph.end type="italics"/> (P<emph type="italics"/>atria mia) & &longs;imilmente di Crema, Bergamo, & <lb/>Millano. </s> <s id="s.001236">Le quai citta tutte le ho uedute quando era giouene, & gargione. </s> <s id="s.001237">Ma non <lb/>con&longs;iderata la forma delle mura di alcuna di quelle, eglie ben uero, che quando stantia­<lb/>ua à Verona, io fui alcune uolte à San Georgio, & uidi à quella porta e&longs;&longs;erui princi­<lb/>piati alcuni fondamenti dimura di una i&longs;mi&longs;urata gro&longs;&longs;ezza, & &longs;imilmente me aricor <lb/>do hauer ui&longs;to à cadauna delle altre porte certi ba&longs;tioni, torrioni, ouer baluardi, alcuni <lb/>&longs;olamente principiati, alcuni meggi fatti, & alcuni compiti, di una gro&longs;&longs;ezza ine&longs;tima <lb/>bile, ma come ho detto, mai poßicura alla forma del contorno di quella, il mede&longs;imo di­<lb/>co hauer ui&longs;to Bre&longs;&longs;a<emph.end type="italics"/> (P<emph type="italics"/>atria mia) & stantiato per tutta la mia pueritia, in quella, & <lb/>me aricordo delli &longs;uoi großißimi terrai, muri, et torrioni, ma non della forma.<emph.end type="italics"/> P. M<emph type="italics"/>o <lb/>hauendo ui&longs;to quelli &longs;ondamenti de mura, & torrioni co&longs;i großißimi di Verona, et quel <lb/>li großißimi terrai, mura, & torrioni, che circonda Bre&longs;&longs;a, non poteti far giudicio del <lb/>la&longs;ua fortezza.<emph.end type="italics"/> N. L<emph type="italics"/>o ingegno dell'huomo, nel fortificar una citta (&longs;econdo il mio <lb/>parere) &longs;e cono&longs;ce per la forma, & non per la materia, perche à fortificare una citta <lb/>&longs;implicemente per uigore, & forza de materia. </s> <s id="s.001238">La non mi pare co&longs;a molto ingenio­<lb/>&longs;a, ne di molte laude degna.<emph.end type="italics"/> P. I<emph type="italics"/>o non ue intendo troppo bene.<emph.end type="italics"/> NIC. I<emph type="italics"/>o dico, <lb/>che à fortificare una Citta ui concorre la materia, & la forma, & che lo inge­<lb/>gno dillo huomo &longs;e approua per la forma delle &longs;ue mura, & non per la materia, <pb xlink:href="042/01/128.jpg"/>cioe per la gro&longs;&longs;ezza de quelle. </s> <s id="s.001239">Et per tanto quantunque habbia ui&longs;to la gro&longs;&longs;ezza del <lb/>le mura, et torrioni de tai citta, non hauendo con&longs;iderata la &longs;ua forma non po&longs;&longs;o far giu <lb/>dicio di quello, che me ha adimandato<emph.end type="italics"/> V.S.<emph type="italics"/>perche quella (&longs;e ben me aricordo) me ha adi <lb/>mandato, &longs;e à me mi pare che lo ingegno dell'huomo &longs;ia peruenuto à quel &longs;ublime gra­<lb/>do doue &longs;ia poßibile de peruenire, nel fortificare una citta. </s> <s id="s.001240">Onde &longs;e lo ingegno dell huo <lb/>mo, in &longs;imil ca&longs;o (come di &longs;opra è detto) &longs;e approua per la forma, & non hauendo io <lb/>con&longs;iderato alcuna forma non po&longs;&longs;o far alcun giudicio.<emph.end type="italics"/> P. D<emph type="italics"/>oman de &longs;era ui uoglio <lb/>mo&longs;trar il di&longs;&longs;egno d'una citta de Italia, la qual è giudicata ine&longs;pugnabile, uorro poi <lb/>che &longs;opra la forma di quella me dicati la uo&longs;tra opinione, cioe &longs;e la &longs;ara ingenio&longs;a­<lb/>mente fabricata.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001241">QVESITO SECONDO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001242">PRIORE. V<emph type="italics"/>edeti qua, que&longs;to è il di&longs;&longs;egno della pianta de <lb/>Turino, qual da gli <lb/>huomini de ingegno è giudicato e&longs;&longs;er ine&longs;pugnabile. </s> <s id="s.001243">Hor che diceti di que&longs;ta figu <lb/>ra.<emph.end type="italics"/> N. I<emph type="italics"/>n questa tal figura, non ui dicerno alcuna gran &longs;ottilita d'ingegno.<emph.end type="italics"/> P. <!-- KEEP S--></s> <s id="s.001244">O <emph type="italics"/>uoi <lb/>&longs;eti, non &longs;olamente contra alla opinione d'ogn'uno, ma anchora contra à tutto quello, <lb/>che per &longs;perientia &longs;e è ueduto, toccato, e palpato.<emph.end type="italics"/> N. N<emph type="italics"/>on dico, ne manco uoglio di­<lb/>re, che Turino non &longs;ia forte, & for&longs;i forti&longs;­<lb/>&longs;imo, perche una citta puo e&longs;&longs;ere alle uolte <lb/>forte per la natura del luoco doue che la &longs;e <lb/>ritroua, & alle uolte &longs;olamente per artificio <lb/>dell'huomo, & alle uolte per l'uno, e per l'al <lb/>tro. </s> <s id="s.001245">Quelle che &longs;ono forte &longs;olamente per la <lb/>natura del luoco (cioe quando che quella fu&longs;­<lb/>&longs;e cinta, ouer cir <expan abbr="cõdata">condata</expan> da acque, fiumi, ouer <lb/>paludi) io non ne parlo, perche il laude di tal <lb/>&longs;ua fortezza &longs;i debbe attribuire piu pre&longs;to <lb/>alla natura, che all'ingegno dell'huomo. </s> <s id="s.001246">Ma <lb/>quelle che &longs;ono forte &longs;olamente per artificio <lb/>dell'huomo, tal &longs;ua fortezza puo accadere<emph.end type="italics"/><lb/><figure id="id.042.01.128.1.jpg" xlink:href="042/01/128/1.jpg"/><lb/><emph type="italics"/>in dui modi, cioe tal hora puo e&longs;&longs;er forte, piu per uigor della pura materia, che della for <lb/>ma, cioe piu per uigor delle &longs;ue gro&longs;&longs;e mura, ba&longs;tioni, larghe & profonde fo&longs;&longs;e, che dal <lb/>la forma di quella, il qual modo, anchor che faccia qua&longs;i lo effetto di&longs;iderato, à me non <lb/>pare che &longs;ia de molto ingegno.<emph.end type="italics"/> L'<emph type="italics"/>altro modo è, che talhora una citta puo e&longs;&longs;er forte piu <lb/>per uigore della forma, che della materia, cioe che la forma delle mura del circuito de <lb/>tal citta, potria e&longs;&longs;er alle uolte di tal &longs;orte, che quella non &longs;aria di menor impedimento, <lb/>ouer ostacolo alli nemici, di quello che &longs;aria le &longs;ue gro&longs;&longs;e mura, bastioni, larghe et pro­<lb/>fonde fo&longs;&longs;e, la qual co&longs;a e&longs;&longs;endo, giudicareital oprae&longs;&longs;er compo&longs;ta, ouer ordinata da <lb/>non mediocre ingegno.<emph.end type="italics"/> P. M<emph type="italics"/>auoglio che &longs;appiati qualmente la detta citta è fortißi­<lb/>ma, & non&longs;olamente per la pura materia, ma anchora per la buona forma, & accio<emph.end type="italics"/><pb pagenum="65" xlink:href="042/01/129.jpg"/><emph type="italics"/>meglio intendiati il tutto, questa tal citta è di forma quadrangola, come in el &longs;otto&longs;crit <lb/>to di&longs;egno appare, & la fazzata, che ua da Leuante à Ponente, uer&longs;o Septentrione é <lb/>circa pa&longs;&longs;a.360.el mede&longs;imo è l'altra fazzata à que&longs;ta oppo&longs;ita. </s> <s id="s.001247">Le altre due faz­<lb/>zate, ouer te&longs;te &longs;ono alquanto piu corte, cioe <lb/>meno de detti pa&longs;&longs;a.360.& in cadauno delli <lb/>quattro angoli di que&longs;ta citta ui è un Baluar­<lb/>do, ouer ba&longs;tione de i&longs;mi&longs;urata gro&longs;&longs;ezza. <lb/></s> <s id="s.001248">La fazzata de fora uia, cioe la co&longs;ta.a.b.o­<lb/>uer.b.c.de cadauno de quelli, me &longs;ta referto <lb/>e&longs;&longs;er pa&longs;&longs;a.40.Le quattro fazze di que&longs;ta <lb/>citta con li detti baluardi, ouer ba&longs;tioni &longs;ono <lb/>&longs;tati fatti modernamente, cioe di muraglia no <lb/>ua großißima, & hanno &longs;errato dentro da &longs;e <lb/>tutta la muraglia uecchia, con <expan abbr="alquãto">alquanto</expan> de in­<lb/>teruallo fra la muraglia noua, & la muraglia <lb/>uecchia, & cadauno di quattro baluardi ha <lb/>due canonere di dentro della noua muraglia,<emph.end type="italics"/><lb/><figure id="id.042.01.129.1.jpg" xlink:href="042/01/129/1.jpg"/><lb/><emph type="italics"/>che guardano quel &longs;pacio, ouer interuallo, che è fra la muraglia noua, e la uecchia <lb/>(detto di &longs;opra.) Anchora fra baluardo, e baluardo, cioe nel mezzo di cadauna faz­<lb/>zata ui é una forma piatta, ouer caualliero, le quale guardano li baluardi, & cadauna <lb/>di queste forme piatte ha due canonere di dentro della noua muraglia oppo&longs;ite à quel­<lb/>le di baluardi, che guardano quel detto &longs;patio, che è fra la muraglia noua, & la mura­<lb/>gliauecchia. </s> <s id="s.001249">Le fo&longs;&longs;e poi che cercondano questa citta nel fondo &longs;ono larghe pa&longs;&longs;a.14. <lb/>& nella &longs;ommita, ouer bocca pa&longs;&longs;a.16.& alte pa&longs;&longs;a.4.hor ue adimando, &longs;el non ui pa <lb/>re, che que&longs;ta tal citta &longs;ia fortißima, &longs;i &longs;econdo la forma, come &longs;econdo la materia.<emph.end type="italics"/><lb/>N. I<emph type="italics"/>o confirmo, che la é forte re&longs;petto alla materia, cioe in quanto alle &longs;ue gro&longs;&longs;e mu <lb/>ra, baluardi, cauallieri, profonde, & larghe fo&longs;&longs;e. </s> <s id="s.001250">Ma in quanto alla forma delle dette <lb/>&longs;ue mura, non ui di&longs;cerno alcuna artificio&longs;a particolarita.<emph.end type="italics"/> P. E<emph type="italics"/>t à me mi pare, che <lb/>la forma di tal &longs;uo contorno, ouer mura non potria e&longs;&longs;er megliore, & credo chel &longs;ia <lb/>qua&longs;i impoßibile à poterla megliorare in conto alcuno.<emph.end type="italics"/> N. I<emph type="italics"/>n que&longs;to uo&longs;tra Reue­<lb/>rentia &longs;e inganna grandemente.<emph.end type="italics"/> P. H<emph type="italics"/>aro de caro, che mel fatti cono&longs;cere, ma per <lb/>e&longs;&longs;er hora tarda, ucglio che la remettiamo à diman de &longs;era.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001251">QVESITO TERZO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001252">PRIORE. V<emph type="italics"/>oi <expan abbr="cõchiude&longs;ti">conchiude&longs;ti</expan> hier&longs;era, che la detta citta de <lb/>Turino, <expan abbr="nõ">non</expan> ha in &longs;e <lb/>gran fortezza, per uigor della forma delle &longs;ue mura, ma &longs;olamente per uigore <lb/>della gro&longs;&longs;ezza de quelle, et delle &longs;ue profonde, & larghe fo&longs;&longs;e hor uoria, che me dice <lb/>&longs;ti, le <expan abbr="cõditioni">conditioni</expan>, qualita, ouer particularita, che à uoi par, che &longs;e doueria fare, ouer che <lb/>doueria hauere la &longs;orma delle mura de una citta à douer e&longs;&longs;er forte per uigor di tal for <lb/>ma, accio ch'io &longs;appia in che riprendeti, ouer in che co&longs;a pecca, ouer manca la forma<emph.end type="italics"/><pb xlink:href="042/01/130.jpg"/><emph type="italics"/>de Turino.<emph.end type="italics"/> N. L<emph type="italics"/>e <expan abbr="cõditioni">conditioni</expan>, qualita, & particolarita, che douria hauere, ouer che&longs;t <lb/>potria adattare, alla forma, & mura de una citta, &longs;i per re&longs;i&longs;tere à que&longs;ti tempi alli ui­<lb/>goro&longs;i colpi delle artegliarie, come anchora per potere confacilita, rebattere, & of <lb/>fendere in uarij modi li nimici in ogni lor impetuo&longs;o a&longs;&longs;alimento, eglie da credere, che <lb/>&longs;iano molti. </s> <s id="s.001253">Ma quelle, che co&longs;i per al pre&longs;ente me ho imaginate, &longs;ono &longs;olamente &longs;ei, <lb/>& perche que&longs;te &longs;ei &longs;e po&longs;&longs;ono alterare, & uariare in uarij, & diuer&longs;i modi, &longs;econdo <lb/>uarij, & diuer&longs;i ri&longs;petti, à me &longs;arianece&longs;&longs;ario (à uolere à &longs;officienza ben dechiarire, <lb/>& con ragione dimo&longs;trare di cadauna di quelle particolarmente &longs;ua ualuta) à de&longs;igna <lb/>re, uarie, & diuer&longs;e piante, ouer à fabricare materialmente uarij, & diuer&longs;i modelli, <lb/>la qual co&longs;a non &longs;i puo fare co&longs;i all'improui&longs;o, anci ui uol tempo, & non poco, & maßi­<lb/>me à me, che nel operar manuale non &longs;on molto i&longs;perto.<emph.end type="italics"/> P. A<emph type="italics"/>nchor, che co&longs;i al im­<lb/>proui&longs;o non poßiati de&longs;ignare le dette piante, ne fabricar materialmente li detti mo­<lb/>delli, non poteti almen &longs;otto breuita narrare la conditione, & proprieta di que&longs;te uo­<lb/>stre &longs;ei imaginate particolarita, & dapoi de&longs;ignare con uo&longs;tra commodita le dette <expan abbr="piã">piam</expan> <lb/>te, ouer modelli.<emph.end type="italics"/> N. L<emph type="italics"/>e po&longs;&longs;o dir &longs;i.<emph.end type="italics"/> P. M<emph type="italics"/>o ditteli adunque con&longs;equentemente <lb/>l'una dietro l'altra, perche in effetto à me mi pare, che &longs;ia qua&longs;i impoßibile di poter <lb/>ta&longs;&longs;are la forma de Turino de un&longs;olo non che de &longs;ei diffetti.<emph.end type="italics"/> N. L<emph type="italics"/>a prima co&longs;a, che <lb/>à me mi pare, che doueria hauere la forma delle mura de una citta, ouer che ui &longs;e do­<lb/>ueria fare, uolendo à questi tempi fortificar quella è que&longs;ta, che mai in conto alcuno &longs;e <lb/>doucria far pala de alcuna &longs;ua cortina, ouer muraglia, talmente, che li nemici ui pote&longs;­<lb/>&longs;ono percotere, ouer tirare <21> pendicolarmente con le artegliarle, perche, ogni mura­<lb/>glia cede molto piu facilmente alle <21>cußioni delle balle, che feri&longs;cono <21> pendicolermen <lb/>te &longs;opra à quella, di quello fa à quelle, che gli feri&longs;cono obliquamente, cioe in &longs;guinzo, <lb/>& quanto piu ueneranno, ouer feriranno obliquamente, cioe in &longs;guinzo, tanto menor <lb/>nocumento faranno in detta cortina, ouer muraglia. </s> <s id="s.001254">La cau&longs;a è, che ogni <expan abbr="cõmuna">communa</expan> per <lb/>co&longs;&longs;a fatta perpendicolarmente &longs;opra à una muraglia è molto piu ri&longs;entita in tutte le <lb/>parte di tal muraglia, di quello &longs;ara ogni altra molto maggiore, che percottera obli­<lb/>quamente, ouer in &longs;guinzo &longs;opra alla mede&longs;ima.<emph.end type="italics"/> P. C<emph type="italics"/>redo questo, che uoi diceti, per <lb/>che delle per cußioni fatte co&longs;i obliquamente, ouer in &longs;guinzo, la muraglia non riceue <lb/>tutta la botta, ma &longs;olamente parte di quella, la qual parte tanto &longs;ara menore, quanto <lb/>che piu obliquamente, ouer in &longs;guinzo tal balla ferira &longs;opra à quella.<emph.end type="italics"/> N. A<emph type="italics"/>dunque <lb/>la forma de Turino incorre in que&longs;to errore, perche cadauna delle &longs;ue quattro mura­<lb/>glie, ouer cortine, che la circonda, &longs;ono a&longs;&longs;ettate di tal &longs;orte (come &longs;i uede nel &longs;uo di&longs;e­<lb/>gno) che li nemici ui potranno ageuolmente tir are perpendicolarmente in cadauna di <lb/>quelle.<emph.end type="italics"/> P. Q<emph type="italics"/>uando, che tal uostra opinione &longs;i pote&longs;&longs;e mandar ad e&longs;&longs;ecutione in ogni <lb/>cortina, el non &longs;e potria negare, che la non fu&longs;&longs;e una co&longs;a molto ingenio&longs;a, & utile. <lb/></s> <s id="s.001255">Ma non &longs;olamente dubito, che uoi non ue ingannati. </s> <s id="s.001256">Ma tengo, che tal co&longs;a &longs;ta impoßi <lb/>bile, perche de quante citta ho pratticate, & ui&longs;te mai, ne bo ui&longs;to alcuna (che batter &longs;i <lb/>po&longs;&longs;a) che in ogni &longs;ua cortina, non ui&longs;e po&longs;&longs;a tirare per pendicolarmente con le arte­<lb/>gliarie.<emph.end type="italics"/> N. D<emph type="italics"/>apoi, che noi haueremo compito da narrare tutte que&longs;te nostre &longs;ei ima <lb/>ginate qualita, ouer conditioni, non &longs;olamente faro cono&longs;cere, & uedere à uo&longs;tra Si­<lb/>gnoria in figura (ouer con modelli) qualmente eglie poßibile di mandar ad effetto tal<emph.end type="italics"/><pb pagenum="66" xlink:href="042/01/131.jpg"/><emph type="italics"/>no&longs;tra imaginata qualita, ouer particolarita in ogni cortina. </s> <s id="s.001257">Ma che anchora eglie <lb/>poßibile à farlo in tre diuer&longs;i modi, & for&longs;i piu.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;to bauero molto a caro, <lb/>di uedere.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001258">QVESITO QVARTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo &longs;ignor Priore <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001259">PRIORE. H<emph type="italics"/>or &longs;eguitati anchora la &longs;econda qualita, ouer particolarita.<emph.end type="italics"/><lb/>N. <lb/>L<emph type="italics"/>a &longs;econda qualita, ouer conditione e que&longs;ta, che bi&longs;ogna ben antiuedere di a&longs;&longs;et <lb/>tar tutte le &longs;ue cortine, & baluardi, con tal modo e forma, che li nimici non po&longs;&longs;ano <lb/>trouar luoco alcuno di poter piantare le &longs;ue artegliarie, che &longs;empre non &longs;ia menor di <lb/>&longs;tantia di alcuno di baluardi di tal citta al detto luoco, di quella, che &longs;ara dal detto loco <lb/>à quella cortlna, che de&longs;iderar anno da battere. </s> <s id="s.001260">Il che facendo, li detti nimici non po­<lb/>tranno piantare le dette &longs;ue artegliarie per battere detta citta, &longs;e non con&longs;uo gran di­<lb/>&longs;auantaggio. </s> <s id="s.001261">Et di que&longs;ta qualita, ouer <expan abbr="cõditione">conditione</expan>, manca anchora la forma di Turino, <lb/>perche el &longs;i uede, che in qualunque luoco &longs;i uora a&longs;&longs;ettar li nemici con le artegliarie <lb/>per battere tal citta &longs;empre &longs;ara maggior di&longs;tantia di qual &longs;tuoglia baluardo al detto <lb/>luoco, che non &longs;ara dal mede&longs;imo luoco à quella cortina, che de&longs;iderar anno da battere.<emph.end type="italics"/><lb/>P. Q<emph type="italics"/>ue&longs;to mi par qua&longs;i impoßibile.<emph.end type="italics"/> N. I<emph type="italics"/>o non diria una co&longs;a a uo&longs;tra Signoria, che <lb/>fu&longs;&longs;e impoßibile di fare. </s> <s id="s.001262">Anci in fine à quella faro non &longs;olamente figur almente uedere <lb/>qualmente tal co&longs;a &longs;ia poßibile, ma che eglie poßibile à farlo in uarij, & diuer&longs;t modi.<emph.end type="italics"/><lb/>P. D<emph type="italics"/>i que&longs;to ne hauero appiacer grandißimo. </s> <s id="s.001263">Et ui uoglio dire, che con que&longs;ta uo&longs;tra <lb/>&longs;econda conditione mi haueti auerto lo intelletto talmente, che &longs;pero fra pochi giorni <lb/>di farue uedere una pianta de&longs;ignata de mia mano, che hauera in &longs;e que&longs;te uo&longs;tre due <lb/>dette conditioni.<emph.end type="italics"/> N. I<emph type="italics"/>o &longs;on certißimo, che &longs;e uo&longs;tra Signoria ui pen&longs;ara alquan­<lb/>to &longs;opra, facilmente le ritrouara, & de&longs;ignera: perche ogni commun ingegno, che <lb/>di tai particolarita &longs;ia auertito, facilmente ritruouara il tutto, tanto piu uo&longs;tra <lb/>Signoria, che è colma de ingegno.<emph.end type="italics"/> P. H<emph type="italics"/>or &longs;u per que&longs;ta &longs;era, non uoglio, che <lb/>procedamo in altro.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001264">QVESITO QVINTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001265">PRIORE. H<emph type="italics"/>or uegnamo alla terza conditione, ouer particolarita.<emph.end type="italics"/> N. <lb/>L<emph type="italics"/>a <lb/>terza conditione è que&longs;ta, che el bi&longs;ogna, che la forma di tal citta &longs;ia talmente di <lb/>&longs;po&longs;ita, che &longs;e li nemici delibera&longs;&longs;eno di darui una battaglia ordinata, chel non &longs;i troui <lb/>alcuna parte di quella tal citta, che po&longs;&longs;a e&longs;&longs;er a&longs;&longs;altata da nemici, che quelli non poßa <lb/>no &longs;empre e&longs;&longs;er offe&longs;i da quelli dalla terra almen da quattro diuer&longs;e bande con le arte <lb/>gliarie (& da piu bande &longs;e eglie poßibile) della qual co&longs;a manca la ditta citta <lb/>de Turino, perche ogni uolta, che li nemici a&longs;&longs;alta&longs;&longs;ero tal citta in una (qual &longs;i uoglia)<emph.end type="italics"/><pb xlink:href="042/01/132.jpg"/><emph type="italics"/>delle &longs;ue quattro fazzate, ouer cortine, quelli non potranno e&longs;&longs;er offe&longs;i, da quelli dalla <lb/>terra, con lartegliaria, &longs;aluo che da due bande, cioe dalli dui baluar di, che guardano <lb/>quella tal cortina, ouer mur aglia, perche la forma piatta, ouer caualliero, <expan abbr="nõ">non</expan> debbe po<lb/>ter tirar tanto ba&longs;&longs;o, che po&longs;&longs;a offendere li nemici, che &longs;iano &longs;otto alle mura.<emph.end type="italics"/> P. D<emph type="italics"/>i <lb/>questa particolarita manca anchora ogni altra fortificata citta de Italia, & anchora <lb/>fuor de Italia, perche de quante ne ho uiste maine ho ui&longs;ta alcuna, che le &longs;ue cortine <lb/>&longs;tano guardate, &longs;aluo che da due bande, cioe da dui baluar di. </s> <s id="s.001266">Et quando, che que&longs;ta uo <lb/>&longs;tra particolarita &longs;i pote&longs;&longs;e condur ad effetto in ogni cortina, certo la &longs;aria una co&longs;a <lb/>di molto profitto, ma ui dubito grandemente.<emph.end type="italics"/> N. I<emph type="italics"/>n fine di que&longs;ti no&longs;tri ragiona­<lb/>menti (&longs;i come ho prome&longs;&longs;o) faro ueder à quella il tutto in figura, & quando, che uo­<lb/>&longs;tra &longs;ignoria hauera ui&longs;to el di&longs;egno di tal pianta, &longs;on certo, che quella non ui hauera <lb/>dubbio alcuno, & tanto piu, che gli farò uedere, tal co&longs;a poter&longs;i far in piu modi.<emph.end type="italics"/> P. <lb/>Q<emph type="italics"/>ue&longs;to hauero molto accaro.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001267">QVESITO SESTO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001268">PRIORE. H<emph type="italics"/>or &longs;eguitati anchora la quarta qualita, perche eglie à <lb/>buon'ho­<lb/>ra.<emph.end type="italics"/> N. L<emph type="italics"/>a quarta conditione, che &longs;i conuien nel fortificar una citta, re&longs;petto <lb/>alla forma delle mura è que&longs;ta. </s> <s id="s.001269">Che nelfar fabricar, et in alzar le &longs;ue mura, ouer corti <lb/>ne. </s> <s id="s.001270">Bi&longs;ogna fra le altre co&longs;e e&longs;&longs;er cauto de farle in alzar con tal modo eforma, che &longs;e <lb/>per ca&longs;o quelle fu&longs;&longs;eno ruinate da nemici con le artegliarie, che tai mura co&longs;i ruinate, <lb/>rendano qua&longs;i maggior difficultà, & pericolo alli dettinemici, uolendo quelli intrare <lb/>nella detta citta, di quello che faceuano, quando, che quelle erano intiere, & &longs;ane. </s> <s id="s.001271">De <lb/>la qual co&longs;a &longs;on certo, che manca la forma di Turino.<emph.end type="italics"/> P. Q<emph type="italics"/>ue&longs;ta non me pare co&longs;a <lb/>da credere, perche &longs;e tal co&longs;a fu&longs;&longs;e poßibile, &longs;eguiria, che tal citta fu&longs;&longs;e qua&longs;i piu for­<lb/>te &longs;enza le mura, che con le mura.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to è uero, che la &longs;aria qua&longs;i piu forte, <lb/>perche &longs;e le mura cadute, & ruinate cau&longs;ar anno qua&longs;i maggior difficulta, & pericolo <lb/>alli nimici à uoler intrar dentro della detta citta, di quello fariano e&longs;&longs;endo intiere, & <lb/>&longs;ane. </s> <s id="s.001272">Seguira de neceßita, che la detta citta&longs;ia piu forte con le mura ruinate, che con <lb/>quelle intiere e&longs;ane.<emph.end type="italics"/> P. I<emph type="italics"/>o non po&longs;&longs;o qua&longs;i credere questa co&longs;a.<emph.end type="italics"/> N. Q<emph type="italics"/>uando che uo <lb/>&longs;tra Reuerentia hauera ui&longs;to el modello de tal forma de mura, &longs;on certo, che quella af­<lb/>fermera tutto quello, che hauemo detto. </s> <s id="s.001273">Ma piu, che gli faro uedere, & con ragion <lb/>toccare, poter&longs;i tal particolarita condur ad effetto in tre diuer&longs;i modi.<emph.end type="italics"/> P. Q<emph type="italics"/>uando <lb/>che que&longs;to fu&longs;&longs;e la uerita, le artegliarie haueriano per&longs;o la mita della &longs;ua reputatione, <lb/>nelle i&longs;pugnation delle citta. </s> <s id="s.001274">Et ui uo dire, che co&longs;i ragionando, & tutta uia pen&longs;ando <lb/>&longs;opra à que&longs;ta uo&longs;tra particolarita, e me ho qua&longs;i imaginato, come &longs;e potria far que­<lb/>&longs;ta tal co&longs;a, ma la uoglio un poco meglio con&longs;iderare, & farne un modelletto, perche <lb/>nel far di modelli meglio &longs;e delucida la co&longs;a, dapoi uoro uedere &longs;e la mia opinione &longs;ara <lb/>&longs;imile alla uostra.<emph.end type="italics"/> N. I<emph type="italics"/>o &longs;on certißimo, che &longs;e uo&longs;tra Signoria ui pen&longs;ara alquanto <lb/>&longs;opra, quella ritrouara il tutto, auanti che ueda altramente gli miei modelli, perche<emph.end type="italics"/><pb pagenum="67" xlink:href="042/01/133.jpg"/><emph type="italics"/>ogni commun ingegno (come di &longs;opra dißi) che di tai particolarita &longs;ia auertito facil­<lb/>mente da &longs;e le ritrouara, non che Vo&longs;tra Reuerentia.<emph.end type="italics"/> P. C<emph type="italics"/>on&longs;idero ueramente, che <lb/>il molto praticare, ragionare, & di&longs;putare de una materia, fa ritrouar molte co&longs;e, cir <lb/>ca à quella, perche nel praticare, ragionare, et di&longs;putare, l huomo uien &longs;empre auerti­<lb/>to de qualche nuoua particolarita, et dapoi ch eglie auertito, et &longs;opra à quella <expan abbr="p&etilde;&longs;ando">pen&longs;ando</expan> <lb/>facilmente la ritroua.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001275">QVESITO SETTIMO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001276">PRIORE. S<emph type="italics"/>eguitati anchora la quinta particolarita, ouer conditione, per <lb/>fin <lb/>che uenga hora da cena.<emph.end type="italics"/> N. L<emph type="italics"/>a quinta qualita, ouer conditione, che debbe ha­<lb/>uer una citta è que&longs;ta, che &longs;empre &longs;i debbe adattare qualche particolare, & &longs;icuro in­<lb/>gegno alla guardia de cadauna cortina, ouer muraglia, che occorrendo che li nemici ue <lb/>ni&longs;&longs;ono per &longs;calarla con &longs;cale, che con facilita ui &longs;i pote&longs;&longs;e rompere totalmente ogni &longs;uo <lb/>di&longs;&longs;egno, & con &longs;uo grandißimo danno, et uergogna, della qual co&longs;a &longs;on certo, che man <lb/>ca le cortine, ouer mura de Turino.<emph.end type="italics"/> P. A<emph type="italics"/>nci di questa tal particolarita, non &longs;olamen­<lb/>te, non manca la citta de Turino, ma nanche alcun'altra citta de Italia, perche &longs;empre <lb/>ui &longs;e mette dui, & tal hora quattro pezzi di artegliaria per banda in cadauno baluar <lb/>do, li quali guardano, & defendano tal cortina da chi la uole&longs;&longs;e &longs;calare.<emph.end type="italics"/> N. I<emph type="italics"/>l non bi­<lb/>&longs;ogna <expan abbr="totalm&etilde;te">totalmente</expan> aßicurar&longs;e &longs;opra dui, ne quattro pezzi di artegliaria, che fu&longs;&longs;eno per <lb/>banda in cadauno baluardo, ne tenere, che quelli &longs;iano &longs;officienti à difendere tal corti­<lb/>na, da uno impetuo&longs;o, & grandißimo a&longs;&longs;alimento, perche anchor che le artegliarie &longs;ia <lb/>no de gran terrore, & de mirabile effetto (doue che percuoteno) nondimeno tai &longs;uoi <lb/>effettila maggior parte delle uolte, ouer che uanno totalmente falliti, ouer che manca­<lb/>no a&longs;&longs;ai di quello, che le per&longs;one &longs;e i&longs;timano, ouer pen&longs;ano, perche le lor balle pa&longs;&longs;ano <lb/>&longs;empre per &longs;tretto luoco, e pero offendono li nemici &longs;olamente in particolare (cioe à <lb/>chi la tocca per &longs;orte) & non in generale. </s> <s id="s.001277">Et per tanto dico, che bi&longs;ogna prepar arui <lb/>co&longs;e che offendono li detti nemici in generale cioe di tal qualita che &longs;ubito che li nemici <lb/>comincia&longs;&longs;eno ad aggiongere nella &longs;ommita di tal cortina, che non &longs;olamente fu&longs;&longs;eno <lb/>atte di ributtare in drio generalmente tutti quelli, che fu&longs;&longs;eno peruenuti nella &longs;ommi­<lb/>ta di tal cortina, in&longs;teme con quelli, che &longs;u per tai &longs;cale &longs;t troua&longs;&longs;eno. </s> <s id="s.001278">Ma che anchora <lb/>offende&longs;&longs;ono generalmente tutti quelli altri, che &longs;opra à tai &longs;cale &longs;te&longs;&longs;ono per a&longs;&longs;alire.<emph.end type="italics"/><lb/>P. Q<emph type="italics"/>uando che il non fu&longs;&longs;e le artegliarie. </s> <s id="s.001279">Credo ben che facilmente &longs;e potria trouar <lb/>qualche particolar ingegno chi face&longs;&longs;e in gran parte quello, che haueti detto. </s> <s id="s.001280">Ma uo­<lb/>glio che &longs;appiati, che quando li nemici deliberano di dare l'a&longs;&longs;alto, ouer battaglia à una <lb/>citta, &longs;empre cercano da daruela da tal banda, ouer in tal luoco, che con le &longs;ue arteglia <lb/>rie lor poßino leuare facilmente quelli della terra dalle diffe&longs;e & doue che le arteglia­<lb/>rie po&longs;&longs;ono giuocare, non credo che &longs;ia poßibile di accommodarui alcuna &longs;orte de inge <lb/>gno, che da quelle non &longs;ia immediate rotto, & dißipato, come dißi anchora &longs;opra il far <lb/>delle ordinanze.<emph.end type="italics"/> N. O<emph type="italics"/>gni dritto ha il &longs;uo rouer&longs;o, ba&longs;ta che in fine nel far di no&longs;tri <lb/>modelli, &longs;econdo la prome&longs;&longs;a, faro uedere à<emph.end type="italics"/> V.R. <emph type="italics"/>& con ragion toccare, che non &longs;ola-<pb xlink:href="042/01/134.jpg"/>mente eglie poßibile di far una tal particolarita ad ogni cortina. </s> <s id="s.001281">Mache eglie poßibile <lb/>à far la in tre diuer&longs;i modi, & che eglie una co&longs;a facile, & dur abile, & di pochißimo ar <lb/>teficio, & manco &longs;pe&longs;a. </s> <s id="s.001282">Et dico di tal proprieta, che. </s> <s id="s.001283">25. ouer. </s> <s id="s.001284">30. huomini al piu &longs;aran­<lb/>no &longs;officientißimi à difendere. </s> <s id="s.001285">150. pa&longs;&longs;a di cortina, ouer muraglia da ogni grandißma <lb/>moltitudine de nemici, che con &longs;cale la uenißono per &longs;calare, ouer che la haueßono gia <lb/>&longs;calata (come di&longs;opra è detto) & tal particolarita &longs;ara &longs;icura dalle artegliarie nemi­<lb/>che.<emph.end type="italics"/> P. Q<emph type="italics"/>uando che que&longs;to fuße la uerita, ne &longs;eguiria due cofe digrandißimo momen <lb/>to, & utilita l'una è, che con pochißima gente, et con&longs;e quentemente con pochißima &longs;pe <lb/>&longs;a &longs;i faria guardar una tal citta.<emph.end type="italics"/> (A<emph type="italics"/>nchor che fuße molto granda<emph.end type="italics"/>) <emph type="italics"/>l'altra è, che una cit <lb/>ta da poca gente guardata, con difficolta, puo eßer aßediata, ilche importa aßai.<emph.end type="italics"/> N. <lb/>E<emph type="italics"/>glie ben uero, che una citta da poca gente guardata, ui uol molto piu tempo à douerla <lb/>aßediare, di quello uorria, quando che quella fuße di gente molto piena, nondimeno à <lb/>questi tempi questo non &longs;atisfa tanto che ba&longs;ti, perche<emph.end type="italics"/> V.R. <emph type="italics"/>&longs;a la po&longs;&longs;anza del Turco, <lb/>per la difen&longs;ion del quale, hauemo inue&longs;tigato, tutto quello, che per fina à que&longs;ta hora <lb/>hauemo detto, & di&longs;putato. </s> <s id="s.001286">Et per tanto dico, quando che di quel &longs;e dubita&longs;&longs;e, ouer de <lb/>altra, po&longs;&longs;anza &longs;imile, che fu&longs;&longs;e atta à mantenere longamente l'a&longs;&longs;edio à tal citta, accio <lb/>che à longo andare tal citta non incorre&longs;&longs;e in tal errore. </s> <s id="s.001287">Il &longs;arianece&longs;&longs;ario à fargli al­<lb/>tra proui&longs;ione, come nella &longs;eguente &longs;e&longs;ta particolarita, ouer conditione &longs;i narrara, la <lb/>quale per e&longs;&longs;er hora tarda la la&longs;&longs;aremo à diman de &longs;era.<emph.end type="italics"/> P. H<emph type="italics"/>or&longs;u doman ui a&longs;petto, <lb/>& ueniti à bon'hora.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001288">QVESITO OTTAVO FATTO DAL <lb/><emph type="italics"/>mede&longs;imo Signor Prior <lb/>di Barletta.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001289">PRIORE. H<emph type="italics"/>or&longs;u &longs;eguitati la &longs;e&longs;ta qualita, ouer particolarita.<emph.end type="italics"/> N. <lb/>L<emph type="italics"/>a &longs;e&longs;ta <lb/>qualita, ouer conditione è que&longs;ta. </s> <s id="s.001290">Quando che la citta, che &longs;e ha da fortificare, &longs;e <lb/>dubita&longs;&longs;e del Turco (come dißi hier&longs;era) ouer de qualche altra potentia &longs;imile, cioe che <lb/>fu&longs;&longs;e atta, & &longs;officiente à mantenerui molti anni l'a&longs;&longs;edio. </s> <s id="s.001291">Bi&longs;ognaria al tutto auertire <lb/>di dar una tal forma, alle mura, & circuito di quella, talmente che quelli di detta citta <lb/>pote&longs;&longs;ono &longs;icur amente andare, ouer mandare à lauorare, &longs;eminare, & raccogliere, al <lb/>men tanto terreno, che fu&longs;&longs;e atto, & &longs;officiente à dargli qua&longs;i il uiuere, cioe che li ne­<lb/>mici (per großi che fu&longs;&longs;eno) non ui pote&longs;&longs;ono uenire, ne &longs;correre in conto alcuno à <lb/>danneggiare li raccolti, ne gli lauoranti, ouer raccoglienti quelli.<emph.end type="italics"/> P. S<emph type="italics"/>enza dubbio <lb/>che que&longs;to &longs;aria una co&longs;a ottima, & &longs;anta, & credo anchora che il &longs;e potria fare, maue <lb/>entraria una troppo gran &longs;pe&longs;azza.<emph.end type="italics"/> N. A<emph type="italics"/>nci io ho opinione che à fortificare, & a&longs;­<lb/>&longs;icurare il pae&longs;e di una citta per un commun &longs;pacio à torno, ui entraria molto manco <lb/>&longs;pe&longs;a di quello che entraria à fortificare la &longs;implice citta.<emph.end type="italics"/> P. M<emph type="italics"/>o ditemi un poco, non <lb/>uoleti che prima &longs;e fortifichi la &longs;implice citta, auanti che &longs;e fortifichi il pae&longs;e.<emph.end type="italics"/> N. F<emph type="italics"/>or <lb/>tificando il pae&longs;e non accade à fortificare altramente la citta, perche la detta citta &longs;ara <lb/>fatta forte per la fortezza del pae&longs;e, perche &longs;e tal pae&longs;e &longs;ara fatto forte (poniamo)<emph.end type="italics"/><pb pagenum="68" xlink:href="042/01/135.jpg"/><emph type="italics"/>per. </s> <s id="s.001292">200. ouer piu pa&longs;&longs;a da lontano à torno à torno di talcitta, & che &longs;ia fortificato <lb/>di tal &longs;orte, che dentro di tai termini alcun e&longs;&longs;ercito (per gro&longs;&longs;o che &longs;ia) non &longs;olamen­<lb/>te non &longs;ia atto, ne &longs;officiente à poter penetrare, ma nanche per altri. </s> <s id="s.001293">100. pa&longs;&longs;a oltra <lb/>à tai termini po&longs;&longs;a &longs;icuramente piantar la &longs;ua artegliaria, per battere detta citta. </s> <s id="s.001294">Sen­<lb/>za dubbio tal citta uenira ad e&longs;&longs;er &longs;icura da non poter e&longs;&longs;er danneggiata da nemici con <lb/>le artegliarie. </s> <s id="s.001295">Et per tanto e&longs;&longs;endo &longs;icura detta citta da non poter e&longs;&longs;er battuta con <lb/>le artegliarie danemici, non ui occorrer a à farui altra &longs;pe&longs;a in fortificarla. </s> <s id="s.001296">Ma ui ba­<lb/>&longs;tara una &longs;implice muraglia per una battaglia da mano per buonri&longs;petto.<emph.end type="italics"/> P. I<emph type="italics"/>n ef­<lb/>fetto ogni uolta che &longs;i poteße aßicurare una citta, da non poter eßer battuta da nemi­<lb/>ci con le artegliarie, la non puo eßer &longs;e non fortißima, quantunque haueße le mura niol <lb/>to debole, perche le artegliarie (à questitempi) &longs;ono il uerbo principale per debel­<lb/>lare una citta. </s> <s id="s.001297">Et quando che il fuße poßibile à condure ad effetto que&longs;to che uoi haue­<lb/>ti detto, anchor che ui entraße il doppio &longs;pe&longs;a, di quello che entraria à fortificar la &longs;im <lb/>plice citta, la &longs;aria una co&longs;a molto laudabile, & degna, & le artegliarie nelle i&longs;pugna­<lb/>tioni de tai citta haueriano per&longs;o tutto il credito. </s> <s id="s.001298">Ma per non ue dir bugia, non credo <lb/>che il &longs;ia poßibile di far una tal co&longs;a (come di &longs;opra dißi) &longs;aluo, che con una grandißi­<lb/>ma, & intolerabil &longs;pe&longs;a.<emph.end type="italics"/> N. Q<emph type="italics"/>uando che uo&longs;tra Reuerentia hauera uisto in diße­<lb/>gno la forma delle piante, oueramente li modelli di tai &longs;orte de fortificationi, & &longs;opra <lb/>de quelli calculata la &longs;pe&longs;a che ui entrara, &longs;pero che quella ritrouara entrarui manco <lb/>&longs;pe&longs;a di quello, che di &longs;opra dißi.<emph.end type="italics"/> P. M<emph type="italics"/>o quando uoleti dar principio à far que&longs;te uo­<lb/>stre piante, ouer modelli.<emph.end type="italics"/> N. P<emph type="italics"/>artito che &longs;ia da uo&longs;tra Signoria non tendaro ad altro.<emph.end type="italics"/><lb/>P. D<emph type="italics"/>itemiun poco, in que&longs;ti uo&longs;tri modelli non gli fareti li &longs;uoi baluar di, & cauallie­<lb/>ri, ouer forme piatte, & &longs;imilmente le &longs;ue foße.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio. </s> <s id="s.001299">Anci uolendo io <lb/>dimo&longs;trare con ragioni &longs;en&longs;ibili, la proprieta, & ualuta di cadauna di dette forme, <lb/>&longs;ono a&longs;tretto à farui großo modo tutte que&longs;te co&longs;e.<emph.end type="italics"/> P. D<emph type="italics"/>itemi anchora haueti pra­<lb/>tica, ouer notitia della forma, & mi&longs;ura di baluardi, cauallieri, ouer forme piatte, che <lb/>al pre&longs;ente &longs;i co&longs;tuma nelle moderne fortificationi, cioe di quanta longhezza, larghez <lb/>za, & altezza &longs;i formino, & &longs;imilmente di quanta großezza, & altezza &longs;i fac­<lb/>ciano li loro mura, & parapetti, & &longs;imilmente, di quanta longhezza, altezza, & <lb/>großezza, &longs;i faccia cadauna cortina, & par apetti di quelle, & &longs;imilmente di quan­<lb/>ta larghezza, & altezza, &longs;i co&longs;tumano, far le foße.<emph.end type="italics"/> N. V<emph type="italics"/>eramente che di questo <lb/>non ue ne &longs;aperia dire alcuna minima particolarita, ne per alduta, ne manco per ue­<lb/>duta, perche (come nel principio dißi à uo&longs;tra Signoria) giamai ho praticato in luo­<lb/>co doue &longs;e fortifica&longs;&longs;e, ne manco ho conuer&longs;ato con alcuno che di tal co&longs;a habbia no­<lb/>titia.<emph.end type="italics"/> P. M<emph type="italics"/>o di que&longs;ta materia ue ne &longs;apro rendere buon conto, la qual co&longs;a, ui po­<lb/>tra giouare, per far li &longs;opradetti uo&longs;tri modelli ben proportionati, &longs;econdo il co&longs;tu­<lb/>me moderno.<emph.end type="italics"/> N. I<emph type="italics"/>o hauero molto accaro di hauerne notitia. </s> <s id="s.001300">Anchor che di tal <lb/>co&longs;a non credo di &longs;eruirmene molto, nondimeno hauero &longs;ommo appiacere ad inten­<lb/>dere il tutto, per piuri&longs;petti.<emph.end type="italics"/> P. V<emph type="italics"/>oglio incominciare dalle cortine. </s> <s id="s.001301">Hor &longs;appiati, <lb/>che alli pre&longs;enti tempi, &longs;i co&longs;tuma di far le cortine nel fondo communamente di gro&longs;­<lb/>&longs;ezza piedi &longs;ette, & co&longs;i le fanno andar procedendo per fina alla altezza de piedi <lb/>diece, & da li in &longs;u&longs;o &longs;e fanno &longs;olamente de piedi dui, ma ui fanno poi li contrafortide <pb xlink:href="042/01/136.jpg"/>piedi. </s> <s id="s.001302">8. che con li piedi dui di detta cortina uengono poi à fare piedi. </s> <s id="s.001303">10. di parapetto, <lb/>la altezzadi detta cortine, &longs;i co&longs;tuma far de piedi. </s> <s id="s.001304">34 cominciando dal pian del fo&longs;&longs;o. <lb/></s> <s id="s.001305">La <expan abbr="lõghezza">longhezza</expan> di dette cortine &longs;i fa tal hora de pa&longs;&longs;a. </s> <s id="s.001306">250. tal hora de pa&longs;&longs;a. </s> <s id="s.001307">300. et tal <lb/>hora de piu <expan abbr="&longs;ecõdo">&longs;econdo</expan> il bi&longs;ogno, come haueti inte&longs;o, &longs;opra la <expan abbr="piãta">pianta</expan> di Turino, che due del <lb/>le &longs;ue cortine &longs;on de pa&longs;&longs;a. </s> <s id="s.001308">360. l'una, & l'altre poco meno. </s> <s id="s.001309">Libaluardi poi nel fondo &longs;i <lb/>fanno di gro&longs;&longs;ezza de piedi. </s> <s id="s.001310">8. ma per fin alla altezza de piedi. </s> <s id="s.001311">10. &longs;e uanno re&longs;tringen <lb/>do talmente che &longs;e reduce in piedi. </s> <s id="s.001312">6. (per il retirar della &longs;carpa, la qual &longs;e ua retiran­<lb/>do in ogni. </s> <s id="s.001313">5. piedi, un piede. </s> <s id="s.001314">Et da quel in &longs;u&longs;o &longs;e fa de piedi. </s> <s id="s.001315">2. Ma ui fanno poi li con­<lb/>traforti, di gro&longs;&longs;ezza de piedi. </s> <s id="s.001316">2. & longhinel fondo piedi. </s> <s id="s.001317">27. ma in cima &longs;olamente <lb/>piedi. </s> <s id="s.001318">22. che con li piedi. </s> <s id="s.001319">2. della muraglia fanno piedi. </s> <s id="s.001320">24. di gro&longs;&longs;ezza, & di que­<lb/>sta gro&longs;&longs;ezza&longs;e ne fa il parapetto de piedi. </s> <s id="s.001321">18. & il corritore de piedi.<emph.end type="italics"/> 6. L'<emph type="italics"/>altezza di <lb/>baluardi &longs;e fa de piedi. </s> <s id="s.001322">37. che uien ad auanzare piedi. </s> <s id="s.001323">3. di &longs;opra alle cortine. </s> <s id="s.001324">Le pri­<lb/>me piazze da ba&longs;&longs;o delli detti baluardi &longs;ono alte dal pian del fo&longs;&longs;o piedi. </s> <s id="s.001325">17. & co&longs;i le <lb/>lor canonere, & lor parapettide piedi. </s> <s id="s.001326">24. di gro&longs;&longs;ezza. </s> <s id="s.001327">Il merlon &longs;e fa di altezza <lb/>piedi. </s> <s id="s.001328">8. dal pian delle canonere. </s> <s id="s.001329">Et le dette canonere, &longs;e fanno de piedi. </s> <s id="s.001330">10. in bocca, & <lb/>in meggio de piedi. </s> <s id="s.001331">5. La retirata della piazza da ba&longs;&longs;o &longs;i fa di pa&longs;&longs;a. </s> <s id="s.001332">10. & la larghez <lb/>za&longs;e fa de pa&longs;&longs;a. </s> <s id="s.001333">11. Del piano della piazza di &longs;otto, à quello della piazza di&longs;opra, &longs;e <lb/>fapiedi. </s> <s id="s.001334">13. di altezza. </s> <s id="s.001335">La piazza granda in &longs;u la entrata &longs;e fa di larghezza pa&longs;&longs;a. </s> <s id="s.001336">16. <lb/>& nel meggio pa&longs;&longs;a. </s> <s id="s.001337">28. & di larghezza pa&longs;&longs;a. </s> <s id="s.001338">25. & piede uno, cioe piedi. </s> <s id="s.001339">126. & <lb/>co&longs;icon tal ordine, e mi&longs;ura &longs;e fanno qua&longs;i tutti li baluardi. </s> <s id="s.001340">Li cauallieri, ouer forme <lb/>piatte, &longs;e fanno nel meggio delle cortine, & tai cauallieri&longs;e fanno alcuni di longhez­<lb/>za pa&longs;&longs;a. </s> <s id="s.001341">32. (cioe &longs;econdo l'andar della cortina) & di larghezza paßa. </s> <s id="s.001342">18. Alcuni al­<lb/>tri &longs;i fanno di longhezza paßa. </s> <s id="s.001343">26. & di larghezza paßa. </s> <s id="s.001344">14. Et la altezza de detti <lb/>cauallieri &longs;e fanno communamente de piedi. </s> <s id="s.001345">44. che ueneria ad a&longs;cendere piedi. </s> <s id="s.001346">10. di <lb/>&longs;opra la cortina. </s> <s id="s.001347">Li parapetti de detti cauallieri &longs;e fanno di gro&longs;&longs;ezza de piedi. </s> <s id="s.001348">24. Et <lb/>co&longs;i con tal ordine, e mi&longs;ura &longs;e fanno qua&longs;i tutti li cauallieri, ouer forme piatte. </s> <s id="s.001349">Il foßo <lb/>poi nel fondo &longs;i fa di larghezza paßa. </s> <s id="s.001350">14. & in bocca paßa. </s> <s id="s.001351">16. & di altezza paßa. </s> <s id="s.001352">4. <lb/>& co&longs;i con tal ordine, & mi&longs;ura &longs;i fa communamente tutte le foße. </s> <s id="s.001353">La contramina poi <lb/>&longs;e fa di larghezza piedi. </s> <s id="s.001354">3. e meggio, & di altezza piedi. </s> <s id="s.001355">7. & ha li &longs;uoi &longs;oratori, & ui <lb/>&longs;i fanno anchora due porte per u&longs;cir li fanti, & que&longs;ta contramina la fanno &longs;otto ter­<lb/>ra, per non indebelir il muro. </s> <s id="s.001356">Et co&longs;i con tal ordine, e mi&longs;ura &longs;e procede generalmente <lb/>qua&longs;i in tutte le moderne fortificationi.<emph.end type="italics"/> N. Q<emph type="italics"/>uinti pezzi di artegliaria &longs;i co&longs;tuma à <lb/>mettere per ogni baluardo.<emph.end type="italics"/> P. N<emph type="italics"/>ella prima piazza da baßo ui &longs;e ne mette dui pez­<lb/>zi per banda, & que&longs;ti tali ui &longs;e pongono &longs;olamente per guardia delle cortine, & del <lb/>foßo. </s> <s id="s.001357">Et &longs;imilmente nella piazza di &longs;opra ui &longs;e aßetta per quanto ho inte&longs;o nuouamen­<lb/>te dui, & tal hora tre altri pezzi per banda in cadaun baluardo, & que&longs;ti tali guar­<lb/>dano pur anchorale cortine, e parte del foßo, & credo, che guardano anchora l'altro <lb/>baluardo, & maßime uno de detti pezzi.<emph.end type="italics"/> N. E<emph type="italics"/>t &longs;opra li cauallieri quanti pezzi ui &longs;i <lb/>co&longs;tuma tenere.<emph.end type="italics"/> P. C<emph type="italics"/>inque communamente, cioe dui per banda, li quali guardano li <lb/>baluardi, & uno che per faccia guarda la campagna.<emph.end type="italics"/> N. D<emph type="italics"/>i che qualita &longs;ono que&longs;ti <lb/>tai pezzi, &longs;i di baluardi, come di cauallieri.<emph.end type="italics"/> P. A<emph type="italics"/>lcuni &longs;ono da. </s> <s id="s.001358">20. alcuni da. </s> <s id="s.001359">30. al­<lb/>cunida. </s> <s id="s.001360">50. & alcuni da. </s> <s id="s.001361">100. lire di balla.<emph.end type="italics"/> N. <!-- KEEP S--></s> <s id="s.001362">A <emph type="italics"/>me non pare, che nelli cauallieri, ne<emph.end type="italics"/><pb pagenum="69" xlink:href="042/01/137.jpg"/><emph type="italics"/>&longs;imilmente nelli baluardi ui &longs;i conuengono co&longs;i großi pezzi, perche li pezzi großi&longs;o­<lb/>no (&longs;econdo il mio parere) &longs;olamente per rouinar le mura delle citta, & non per tirar <lb/>nelli e&longs;&longs;erciti, & li pezzi piccoli, & meggiani, &longs;ono per tirare nelle ordinanze, ouer <lb/>nelli eßerciti, & non per rouinar le mura delle citta, perche un pezzo piccolo, ouer un <lb/>meggiano, à me mi pare e&longs;&longs;er di tanta faccione, per tirare in una banda de fantaria che <lb/>ueni&longs;&longs;e &longs;otto à tal citta, quanto che &longs;aria un canon da. </s> <s id="s.001363">50. ouer da. </s> <s id="s.001364">100. & for&longs;i piu.<emph.end type="italics"/><lb/>P. Q<emph type="italics"/>ue&longs;ta uo&longs;tra opinione non me di&longs;piace, perche un &longs;acro, & altri pezzi &longs;imili, <lb/>nel tempo che uorra uno di detti pezzi großi à tirarlo due uolte, &longs;e potranno tirare <lb/>tre uolte, & for&longs;ipiu, & tanto effetto fara for&longs;i l'uno, quanto l'altro per cadauna uol <lb/>ta.<emph.end type="italics"/> N. C<emph type="italics"/>o&longs;i è da credere, oltra che &longs;ariano di molto menor &longs;pe&longs;a, et occupariano man <lb/>co luoco.<emph.end type="italics"/> P. C<emph type="italics"/>ertamente pen&longs;ando &longs;opra di uoi &longs;tago &longs;tupefatto, che non hauendo uoi <lb/>mai tirato, ne dilettato da tirare di artegliaria, archibu&longs;o, ne &longs;chioppo, ne e&longs;&longs;erui gia­<lb/>mai e&longs;&longs;ercitato, nell'arte militare, ne praticato doue &longs;e fortifichi alcuna citta, ouer for­<lb/>tezza. </s> <s id="s.001365">Et che ui ba&longs;ti l'animo non &longs;olamente di parlare, ma ditrattar di queste co&longs;e.<emph.end type="italics"/><lb/>N. I<emph type="italics"/>l non è da mar auigliar&longs;i di que&longs;to, perche l'occhio mentale uede piu intrin&longs;eca­<lb/>mente nelle co&longs;e generale, di quello, che fa l'occhio corporale, nelle particolare.<emph.end type="italics"/> P. D<emph type="italics"/>i <lb/>temi un poco, ue aricordati hauermi cono&longs;ciuto, quando che io &longs;tantiaua à Bre&longs;&longs;a.<emph.end type="italics"/><lb/>N. M<emph type="italics"/>e ne ariccordo &longs;i, <expan abbr="quãtunque">quantunque</expan> à quel tempo io fu&longs;&longs;e molto piccolo, & per tal &longs;i­<lb/>gnale uo&longs;tra Signoria stantiaua in quella contrata, che è fra li Carmini, & Santo Chri <lb/>&longs;tofolo, ouer Santa Chiara nuoua.<emph.end type="italics"/> P. V<emph type="italics"/>oi diceti la uerita: Ditemi anchora, come &longs;e <lb/>chiamaua uo&longs;tro padre.<emph.end type="italics"/> N. M<emph type="italics"/>io padre hebbe nome Michele. </s> <s id="s.001366">Et perche la natura <lb/>non gli fu manco auara in dare à &longs;ua per&longs;ona grandezza conneniente, di quello, che fu <lb/>la fortuna in farlo partecipe di &longs;uoi beni, fu chiamato Micheletto.<emph.end type="italics"/> P. C<emph type="italics"/>ertamente &longs;e <lb/>la natura fu alquanto auara, in dare alla per&longs;ona di uo&longs;tro padre grandezza conuenien <lb/>te, nanche con uoi è &longs;tata molto liberale.<emph.end type="italics"/> N. I<emph type="italics"/>o me ne allegro, perche l'e&longs;&longs;er di per&longs;o <lb/>na co&longs;i piccolo, mi fa te&longs;timoniaza che ueramente fui &longs;uo figlio, perche anchor che il <lb/>non mi la&longs;cia&longs;&longs;e al mondo, à me con un'altro mio fratello, & due &longs;orelle, qua&longs;i &longs;aluo, che <lb/>l'e&longs;&longs;er per buona memoria de lui, mi ba&longs;ta hauer &longs;entito à dire da molti che il cono&longs;ceua <lb/>& praticaua, che egliera huomo da bene, della qual co&longs;a molto piu me ne contento, & <lb/>allegro di quello haueria fatto &longs;e mi haue&longs;&longs;e la&longs;ciato di molta facolta con un tri&longs;to no­<lb/>me.<emph.end type="italics"/> P. C<emph type="italics"/>he e&longs;&longs;ercitio faceua uo&longs;tro padre.<emph.end type="italics"/> N. M<emph type="italics"/>io padre teneua un cauallo, & con <lb/>quello correua alla po&longs;ta ad i&longs;tantia di Cauallari da Bre&longs;&longs;a, cioe portando lettere della <lb/>Illu&longs;trißima Signoria, da Bre&longs;&longs;a, à Bergamo, à Crema, à Verona, & altri luochi &longs;imili.<emph.end type="italics"/><lb/>P. D<emph type="italics"/>i che ca&longs;ata&longs;e chiamaua.<emph.end type="italics"/> N. P<emph type="italics"/>er Dio che io non &longs;o, ne me aricordo de altra &longs;ua <lb/>ca&longs;ata ne cognome, &longs;aluo che &longs;empre il &longs;entei da piccolino chiamar &longs;implicemente Mi <lb/>cheletto Cauallaro, potria e&longs;&longs;er che haue&longs;&longs;e hauuto qualche altra ca&longs;ata, ouer cogno­<lb/>me, ma non che io &longs;appia, la cau&longs;a è, che il detto mio padre mi mor&longs;e e&longs;&longs;endo io di eta de <lb/>anni &longs;ei, uel circa, & co&longs;i restai io, & un'altro mio fratello (poco maggior di me) & <lb/>una mia &longs;orella (menora di me) in&longs;ieme con nostra madre uedoua, & liquida di beni <lb/>della fortuna, con la quale, non poco dapoi fu&longs;&longs;emo dalla fortuna conqua&longs;&longs;ati, che à uo <lb/>lerlo raccontar jaria co&longs;a longa, la qual co&longs;a mi dete da pen&longs;are in altro, che de inque­<lb/>rire di che ca&longs;ata &longs;e chiama&longs;&longs;e mio padre.<emph.end type="italics"/> P. N<emph type="italics"/>on &longs;apendo di che ca&longs;ata &longs;i chiama&longs;&longs;e<emph.end type="italics"/><pb xlink:href="042/01/138.jpg"/><emph type="italics"/>uo&longs;to o padre, perche ue chiamati co&longs;t Nicolo Tartaglia.<emph.end type="italics"/> N. I<emph type="italics"/>o ue diro, quando che <lb/>li Frarce&longs;i &longs;accheggiorno Bre&longs;&longs;a (nel qual &longs;acco fu pre&longs;o la bona memoria del Magni <lb/>fico me&longs;&longs;er Andrea Gritti (à quel tempo Proueditore) & fu menato in Franza, oltra <lb/>che ne fu &longs;uali&longs;ata la ca&longs;a (anchor che poco uifu&longs;&longs;e) ma piu, che e&longs;&longs;endo io fuggito nel <lb/>domo di Bre&longs;&longs;a in&longs;ieme con mia madre, & mia&longs;orella, & molti altri huomini, & don­<lb/>ne della no&longs;tra contrata, credendone in tal luoco e&longs;&longs;er &longs;alui almen della per&longs;ona, ma tal <lb/>pen&longs;ier ne ando falito, perche in tal chie&longs;a, alla pre&longs;entia di mia madre mi fur date cin <lb/>que ferite mortale, cioe tre &longs;u la testa (che in cadauna la panna del ceruello &longs;i uedeua) <lb/>& due &longs;u la fazza, che &longs;e la barba non me le occulta&longs;&longs;e, io pareria un mostro, frale <lb/>quale una ue ne haueua à trauer&longs;o la bocca, & denti, la qual della ma&longs;&longs;ela, & palato <lb/>&longs;uperiore me ne fece due parti, & el mede&longs;imo della inferiore: per la qual ferita, non <lb/>&longs;olamente io non poteua parlare (&longs;aluo, che in gorga, come fanno le gazzole) ma nan <lb/>che poteua manzare, perche io non poteua mouere la bocca, nelle ma&longs;&longs;ele in conto al­<lb/>cuno, per e&longs;&longs;er quelle (come detto) in&longs;teme con li denti tutte fracca&longs;&longs;ate, talmente, che <lb/>bi&longs;ognaua cibarme &longs;olamente con cibi liquidi, & con grande indu&longs;tria. </s> <s id="s.001367">Ma piu forte <lb/>che à mia madre, per non hauer co&longs;i il modo da comprar li unguenti (non che da tuor <lb/>medico) fu a&longs;tretta à medicarme &longs;empre di &longs;ua propria mano, & non con unguenti, <lb/>ma &longs;olamente con el tenermi nettate le ferite &longs;pe&longs;&longs;o, & tol&longs;e tal e&longs;&longs;empio dalli cani, <lb/>che quando quelli &longs;i trouano feriti, &longs;i &longs;anano &longs;olamente con el tener&longs;i netta la ferita con <lb/>la lingua. </s> <s id="s.001368">Con la qual cautella, in termine di pochi me&longs;i me ridu&longs;&longs;e à bon porto, hor <lb/>per tornare al no&longs;tro propo&longs;ito, e&longs;&longs;endo io qua&longs;i guarrito di tale, et tai ferite, &longs;tetti un <lb/>tempo, che io non poteua ben proferire parole, ma &longs;empre balbutaua nel parlare, per <lb/>cau&longs;a di quella ferita à trauer&longs;o della bocca, & denti (non anchor ben <expan abbr="cõ&longs;olidata">con&longs;olidata</expan>) per <lb/>il che li putti della mia eta con chi conuer&longs;aua, me impo&longs;ero per &longs;opra nome Tarta­<lb/>glia. </s> <s id="s.001369">Et perche tal cognome me duro molto tempo, per bona memoria di tal mia di­<lb/>&longs;gratia, me appar&longs;o de uolermi chiamare p Nicolo Tartaglia.<emph.end type="italics"/> P. D<emph type="italics"/>iche eta erate uoi <lb/>à quel tempo.<emph.end type="italics"/> N. D<emph type="italics"/>e anni. </s> <s id="s.001370">12. uel circa.<emph.end type="italics"/> P. C<emph type="italics"/>ertamente la fu co&longs;a molto crudele à <lb/>ferire un putto di quella eta, aui&longs;andoui, che mi mar auigliaua di tal uo&longs;tro str anio co <lb/>gnome, pche à me mi pareua di <expan abbr="nõ">non</expan> hauer mai alduto ne &longs;entito à nominar una tal ca&longs;a­<lb/>ta in Bre&longs;&longs;a.<emph.end type="italics"/> N. L<emph type="italics"/>a co&longs;a sta preci&longs;amente, come ho narrato à uo&longs;tra Reuerentia.<emph.end type="italics"/><lb/>P. C<emph type="italics"/>he fu uo&longs;tro precettore.<emph.end type="italics"/> N. A<emph type="italics"/>uanti, che mio padre mori&longs;&longs;e, fui mandato al­<lb/>quanti me&longs;i à &longs;cola di leggere, ma perche à quel tempo io era molto piccolo, cioe di <lb/>eta de anni cinque in &longs;ei, <expan abbr="nõ">non</expan> me aricordo el nome di tal mae&longs;tro, uero è, che e&longs;&longs;endo poi <lb/>di eta di anni. </s> <s id="s.001371">14. uel circa. </s> <s id="s.001372">Andei uolontar iamente circa giorni. </s> <s id="s.001373">15. à &longs;cola de &longs;criuere <lb/>da uno chiamato mae&longs;tro France&longs;co, nel qual tempo imparaia fare la.<emph.end type="italics"/> A.<emph type="italics"/>b.c.per fin al<emph.end type="italics"/><lb/>k. <emph type="italics"/>de lettra mer cante&longs;ca.<emph.end type="italics"/> P. P<emph type="italics"/>erche co&longs;i per fina al.<emph.end type="italics"/> k. <emph type="italics"/>& non piu oltra.<emph.end type="italics"/> N. P<emph type="italics"/>er­<lb/>che li termini del pagamento (con el detto mae&longs;tro) erano di darui cl terzo <expan abbr="auãti">auanti</expan> trat <lb/>to, & un'altro terzo quando che &longs;apeua fare la detta.<emph.end type="italics"/> A.<emph type="italics"/>b.c.per fina al.<emph.end type="italics"/> k. <emph type="italics"/>& el re&longs;to <lb/>quando, che &longs;apeua fare tutta la detta.<emph.end type="italics"/> A.<emph type="italics"/>b.c. </s> <s id="s.001374">& perche al detto termine non mi troua <lb/>ua co&longs;i li danari de far el debito mio (& de&longs;idero&longs;o de imparare) cercai di hauere alcu <lb/>ni di&longs;uoi Alphabeti compiti, & e&longs;&longs;empi de lettera &longs;critti di &longs;ua mano, & piu non ui <lb/>tornai, perche &longs;opra de quelli imparai da mia po&longs;ta, & co&longs;i da quel giorno in qua, mai<emph.end type="italics"/><pb pagenum="70" xlink:href="042/01/139.jpg"/><emph type="italics"/>piu fui, ne andai da aleun'altro precettore, ma &longs;olamente in compagnia di una figlia di <lb/>pouerta, chiamata Indu&longs;tria. </s> <s id="s.001375">Soprale opere de gli huomini defonti continuamente mi <lb/>&longs;on trauagliato. </s> <s id="s.001376">Quantunque della età d'anni uinti in qua &longs;empre &longs;la &longs;tato da non poca <lb/>cura famigliare straniamente impedito. </s> <s id="s.001377">Et finalmente poi la crudel morte mi ha fatto <lb/>re&longs;tare nouamente poco men che &longs;olo.<emph.end type="italics"/> P. N<emph type="italics"/>on haueti fatto poco, hauendo hauuto cu <lb/>ra famigliare a frequentar el &longs;tudio.<emph.end type="italics"/> SERVO. S<emph type="italics"/>ignor, eglie &longs;onato cinque hore.<emph.end type="italics"/><lb/>P. Q<emph type="italics"/>ue&longs;to nostro ragionamento é &longs;tato molto piu longo del &longs;olito, e pero uoglio fac­<lb/>ciamo fine, ui prego, che piu pre&longs;to, che poteti, me fatti quelli modelli, perche molto de <lb/>&longs;idero di uedergli.<emph.end type="italics"/> N. N<emph type="italics"/>on mancaro de &longs;olicitudine.<emph.end type="italics"/> P. D<emph type="italics"/>itemi un poco, uolendo <lb/>far que&longs;ti modelli, non de&longs;ignareti prima le &longs;ue piante.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio della mag­<lb/>gior parte de&longs;ignaro prima le &longs;ue piante, & dapoi &longs;opra a quelle andaro eleuando le <lb/>&longs;ue cortine, & baluardi, &longs;econdo, che occorrera.<emph.end type="italics"/> P. H<emph type="italics"/>auero molto accaro, che co­<lb/>me hauereti de&longs;ignate le dette piante, &longs;ubito me le fatte uedere, & de&longs;ignatele tutte <lb/>pur &longs;opra la pianta de Turino, perche a mi me pare, che tal forma de Turino (come <lb/>nel principio ue dißi) non &longs;i po&longs;&longs;a megliorare.<emph.end type="italics"/> N. F<emph type="italics"/>aro molto uolentiera, & di que­<lb/>&longs;to in breue me ne i&longs;pedirò, perche le piante &longs;e <expan abbr="de&longs;ignarã">de&longs;ignaram</expan> pre&longs;to.<emph.end type="italics"/> P. E<emph type="italics"/>t que&longs;to è quel <lb/>lo, che uoglio dire, che le i&longs;pedireti piu pre&longs;to. </s> <s id="s.001378">Et &longs;pe&longs;&longs;e uolte tanto &longs;e intende la co&longs;a <lb/>&longs;opra della pianta, quanto che &longs;opra un modello de releuo.<emph.end type="italics"/> N. C<emph type="italics"/>o&longs;iè, & &longs;e pur ui &longs;a <lb/>ra qualche particolarita, che nella pura pianta non &longs;i po&longs;&longs;a dimo&longs;trare, cercaremo de <lb/>delucidarla con parole, & &longs;e per ca&longs;o con quelle non potro &longs;odisfare uostra Signoria, <lb/>la faremo poi de releuo.<emph.end type="italics"/> P. A<emph type="italics"/>lla buon'hora &longs;ia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001379">I<emph type="italics"/>l fine del &longs;esto Libro.<emph.end type="italics"/><!-- KEEP S--></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/140.jpg"/> <p type="head"> <s id="s.001380">LA GIONTA DEL SESTO <lb/>LIBRO DI QVESITI, ET INVENTIONI DIVERSE <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001381">N<emph type="italics"/>ella quale &longs;i dimo&longs;tra un primo modo diredure una citta ine&longs;pugnabi­<lb/>le, & che non potra e&longs;&longs;er battuta, ne danneggiata da nemici <lb/>con le artegliarie, con altre particolar <lb/>&longs;ottilita.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001382">QVESITO PRIMO FATTO DAL MAGNIFICO, <lb/><emph type="italics"/>& Clarißimo Signor Marc' Antonio Moro&longs;ini Dottor, <lb/>& Philo&longs;opho Eccellentißimo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001383">SIGNOR MARC'ANTONIO. S<emph type="italics"/>on molto de&longs;idero&longs;o <lb/>&longs;ier Nicolo di uedere in di&longs;egno, ouer in figura quelle piante de <lb/>fortificationi, che gia promette&longs;ti di mostrare al Prior di Barlet <lb/>ta, cioe con quelle &longs;ei qualita, ouer conditioni, che nel uo&longs;tro &longs;e&longs;to <lb/>libro preponete: perche tutte me paiono co&longs;e ingenio&longs;e, <expan abbr="nõ">non</expan> piu au <lb/>dite, ne uedute, ne con&longs;iderate d'alcuno altro, & &longs;e poßibel é di po<lb/>terle mandar à e&longs;&longs;ecutione (come credo) &longs;ara co&longs;a utilißima, & <lb/>maßime quella uostra terza qualita, ouer conditione, nella quale diceti, che uoleti, che <lb/>la forma delle mura di una citta &longs;ia talmedte di&longs;po&longs;ita, che &longs;e per &longs;orte li nemici delibe­<lb/>ra&longs;&longs;eno di darui la battaglia generale, chel non &longs;i troui alcuna parte di quella, che po&longs; <lb/>&longs;a e&longs;&longs;er a&longs;&longs;altata da nemici, che quelli non poßino e&longs;&longs;er &longs;empre offe&longs;i da quelli dalla <lb/>terra, al men da quattro bande con le artegliarie: il che potendo&longs;i fare, me pareria co­<lb/>&longs;a grande, e pero que&longs;ta tal qualita, ouer conditione haueria piu accaro di uedere de <lb/>qual &longs;i uoglia delle altre cinque.<emph.end type="italics"/> N. V<emph type="italics"/>o&longs;tra Eccellentia, Signor Magnifico, &longs;a, che <lb/>mi puo comandare, & per tanto non &longs;olamente le predette &longs;ei qualita mo&longs;traro in di­<lb/>&longs;egno à Vo&longs;tra Magnificentia, ma molte altre inue&longs;tigate dapoi: perche (come dice il <lb/>prouerbio) di co&longs;a &longs;empre na&longs;ce co&longs;a, cioe trouata che &longs;ia una co&longs;a, &longs;empre ui &longs;i troua <lb/>di megliorarla, & di farla molto meglio. </s> <s id="s.001384">Ma bi&longs;ogna notare, che tutte tai qualita, <lb/>ouer conditioni non &longs;i conuengono in una mede&longs;ima forma de fortificatione, anci par­<lb/>te &longs;e conuengono in una, & parte in un'altra: & perche le forme de fortificare da me <lb/>immaginate, & ritrouate &longs;ono molte, &longs;econdo uarij re&longs;petti delle quale alcune &longs;i difen <lb/>dono con baluardi, & cauallieri, &longs;econdo, che communamente &longs;i co&longs;tuma nelle moder­<lb/>ne fortificationi, ma &longs;otto altra forma. </s> <s id="s.001385">Altre poi &longs;i difendono per altri uarij, & inge­<lb/>nio&longs;i modi, l'uno molto piu &longs;icuro, & di molto manco &longs;pe&longs;a dell'altro: Ma perche à uo­<lb/>ler mo&longs;tr are in di&longs;egno tutte le dette forme in un tratto generariano confu&longs;ione à Vo­<lb/>&longs;tra Eccellentia, e pero li andaro mostrando à una per una, & uoglio cominciare dalla <lb/>piu tri&longs;ta, come co&longs;tumano li botegheri nel mo&longs;trar le &longs;ue merce, che tengono da uen­<lb/>dere. </s> <s id="s.001386">Et que&longs;to tal modo, ouer forma&longs;ara di maggior &longs;pe&longs;a de tutti li altri: perche &longs;ara <lb/>di&longs;e&longs;o con baluardi, & cauallieri, &longs;i come, che alli pre&longs;enti tempi &longs;i co&longs;tuma, ma &longs;otto<emph.end type="italics"/><pb pagenum="71" xlink:href="042/01/141.jpg"/><emph type="italics"/>altra forma & con altre particolarita de piu. </s> <s id="s.001387">Et que&longs;to tal modo, ouer forma non&longs;o <lb/>lamente hauera in &longs;e quella no&longs;tra terza qualita, ouer conditione, che Vo&longs;tra Magni­<lb/>ficentia tanto de&longs;idera di uedere: ma hauera anchora in &longs;e la &longs;econda, & terza, & <lb/>piu, che la non potra eßer danneggiata da nemici con le artegliarie, come, che &longs;opra <lb/>il di&longs;egno de due &longs;ole cortine intiere, & parte de due altre in&longs;ieme congionte con le &longs;ue <lb/>fo&longs;&longs;e, baluardi, & cauallieri alli &longs;uoi con&longs;ueti luochi, à quella faro uedere, & toccare.<emph.end type="italics"/><lb/>S.M. Q<emph type="italics"/>ue&longs;to hauero ben accaro di uedere.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to &longs;otto &longs;critto, Signor Clari&longs; <lb/>&longs;imo, è il di&longs;egno di quelle cortine di &longs;opra narrate à Vo&longs;tra Magnificentia, &longs;econdo la <lb/>forma delle quale, uoglio, che &longs;iano fatte tutte le cortine, fo&longs;&longs;e, baluardi, & cauallieri, <lb/>che circondano tal citta, cioe far, che ogni due cortine uadino à ingolfar&longs;i con dui capi <lb/>uer&longs;o il corpo della citta, formando un angolo ottu&longs;o, &longs;i come fanno le &longs;otto &longs;critte due <lb/>a.b.&.c.b. <!-- REMOVE S-->in ponto. </s> <s id="s.001388">b. <!-- REMOVE S-->& che li altri dui capi &longs;e i&longs;tendino in fuora, cau&longs;ando con le al <lb/>tre due circon&longs;tante cortine dui alti angoli ottu&longs;i, uer&longs;o la campagna, come fanno le <lb/>mede&longs;ime &longs;otto&longs;critte.a.b.&.b.c.con le due parti.a.d.&.c.e. </s> <s id="s.001389">in li dui ponti.a.&.c. </s> <s id="s.001390">et <lb/>in cia&longs;cun de detti angoli ui &longs;e gli debbe con&longs;tituir un baluardo, &longs;econdo, che nelle det­<lb/>te moderne fortificationi &longs;i co&longs;tuma <expan abbr="cõ">com</expan> le &longs;ue canonere nella piazza da ba&longs;&longs;o, che guar <lb/>dino non &longs;olamente le due circostante cortine, & fo&longs;&longs;e, ma anchora li dui circo&longs;tanti <lb/>baluardi: male canonere della piazza di &longs;opra parte debbono guardare pur le due <lb/>circo&longs;tante cortine, fo&longs;&longs;e, & baluardi, et parte guardino minutamente quel &longs;patio in­<lb/>golfato dentro dalle lettere.o.y.<emph.end type="italics"/> 4.z.<emph type="italics"/>m.l.<emph.end type="italics"/>k.<emph type="italics"/>h.i.n.o.& anchora la campagna di fuora <lb/>dalle lettere.o.y.<emph.end type="italics"/>z.<emph type="italics"/>m.& maßime li dui baluardi.a.&.c.non &longs;olamente debbono guar <lb/>dar la campagna, ma l'uno debbe guardar l'argine, che è oppo&longs;ito all'altro, cioe il ba­<lb/>luardo.a.debbe guardar quel &longs;pacio, che è di fora dil ponto.o. </s> <s id="s.001391">& il baluardo. </s> <s id="s.001392">c. <!-- REMOVE S-->debbe <lb/>guardare quel &longs;pacio, che è di fora del ponto. </s> <s id="s.001393">m. <!-- REMOVE S-->& il baluardo. </s> <s id="s.001394">b. <!-- REMOVE S-->non &longs;olamente deb­<lb/>te guardar per tutto il detto &longs;patio, dentro delle dette lettere.o.y. </s> <s id="s.001395">4. z.m.l.<emph.end type="italics"/>k.<emph type="italics"/>h.i.n.o. <lb/><!-- REMOVE S-->& anchora di fora da dette lettere: ma particolarmente debbe guardare à longo, do­<lb/>ue &longs;ono.<emph.end type="italics"/>k.<emph type="italics"/>l.m. </s> <s id="s.001396">&. </s> <s id="s.001397">i.n.o. <!-- KEEP S--></s> <s id="s.001398">Et fatto que&longs;to, uolendo &longs;eguir il moderno u&longs;o di fortificare, <lb/>&longs;i debbe far nel meggio della &longs;ummita de cia&longs;cuna cortina un caualleretto, &longs;i come &longs;o­<lb/>no li dui.f.g.nou molto larghi, ne longhi, ma &longs;olamente di tal capacita, che ui po&longs;&longs;a &longs;tar <lb/>&longs;u&longs;o dui, ouer tre &longs;acri, per cadauno, & l'officio de questi dui caualleretti &longs;ia princi­<lb/>palmente di guardar li dui circo&longs;tanti baluardi: & oltra di que&longs;to uoglio, che guardi­<lb/>no quel &longs;patio ingolfato, & anchora la campagna istrin&longs;eca, uero è, che il caualliero <lb/>f. <!-- REMOVE S-->for&longs;i con difficulta potra guardare quella riuera de fora della fo&longs;&longs;a, che procede &longs;e­<lb/>condo le lettere.<emph.end type="italics"/>k.<emph type="italics"/>l.m.per e&longs;&longs;er troppo &longs;otto di lui: ma tal riuera.<emph.end type="italics"/>k.<emph type="italics"/>l.m.&longs;ara commo­<lb/>damente guardata dall'altro caualleretto. </s> <s id="s.001399">g. <!-- REMOVE S-->& dal baluardo. </s> <s id="s.001400">b. <!-- REMOVE S-->& il detto caualliero <lb/>f.in&longs;ieme con el detto baluardo. </s> <s id="s.001401">b. <!-- REMOVE S--><expan abbr="guardarãno">guardaranno</expan> commodamente la riuera, ouer argine, <lb/>che procede &longs;econdo le lettere.i.n.o. </s> <s id="s.001402">Oltra di que&longs;to uoglio, che da l'una, et l'altra ban <lb/>da del baluardo. </s> <s id="s.001403">b. <!-- REMOVE S-->&longs;ia fatto un caualleretto piccolo quadrangolo (&longs;i come &longs;ono li dui.f. <lb/></s> <s id="s.001404">&.g.) oueramente tondo nella &longs;ummita, &longs;i come &longs;ono li dui &longs;ignati per. </s> <s id="s.001405">2. & 3. di tal ca <lb/>pacita, che ui &longs;e po&longs;&longs;a accommodar &longs;opra, pur dui, ouer tre &longs;acri da. </s> <s id="s.001406">12. lire di balla p<lb/>cia&longs;cadun de loro, & uoglio, che cia&longs;caduno de loro &longs;ia talmente a&longs;&longs;ettato, che po&longs;&longs;a <lb/>guardare l'uno, & l'altro di dui baluardi. </s> <s id="s.001407">a. <!-- REMOVE S-->&. </s> <s id="s.001408">c. <!-- REMOVE S-->la qual co&longs;a &longs;i potra fare facilmente <pb xlink:href="042/01/142.jpg"/>perche &longs;en&longs;ibilmente &longs;i uede, che il cauallero. </s> <s id="s.001409">2. puo guardare, et difendere la banda. u.<lb/>x, del baluardo. </s> <s id="s.001410">c. <!-- REMOVE S-->& &longs;imilmente la banda.s.t.del baluardo. </s> <s id="s.001411">a. <!-- REMOVE S-->& quelle mede&longs;ime puol <lb/>guardar anchora lo cauallero. </s> <s id="s.001412">3. Et oltra di que&longs;to uoglio che guardino per longo uia <lb/>tutto quel &longs;pacio ingolfato per fin nella campagna i&longs;trin&longs;eca, & maßime uoglio, che <lb/>guardino quelle riuere, ouer &longs;pacij arginati, che procedono &longs;econdo le lettere.i.n.o.&<emph.end type="italics"/><lb/>k.<emph type="italics"/>l.m.ilche commodamente far anno, uero è, che di&longs;commodamente potr anno guar da­<lb/>re il &longs;pacio, che procede &longs;econdo le lettere.<emph.end type="italics"/>k.<emph type="italics"/>h.i.per e&longs;&longs;er for&longs;i troppo &longs;otto de loro, ma <lb/>tal parte potra e&longs;&longs;er facilmente guardata, & dife&longs;a dalli dui baluardi. </s> <s id="s.001413">a. <!-- REMOVE S-->&. </s> <s id="s.001414">c. <!-- REMOVE S-->& dalli <lb/>dui caualleri. </s> <s id="s.001415">f. <!-- REMOVE S-->&. </s> <s id="s.001416">g. <!-- REMOVE S-->& da molte altre bande, come nel no&longs;tro proce&longs;&longs;o &longs;e intendera. <lb/></s> <s id="s.001417">Perche uoglio anchora, che nella &longs;ommita di cia&longs;c aduna cortina (per longo uia) &longs;ia fat­<lb/>to contr auetti piantati, & buone tauole molte parianette alte alquanto piu dell'altez­<lb/>za de un'huomo, le quai parianette trauer&longs;ino tutta la &longs;ommita della detta cortina, ma <lb/>che tal trauer&longs;amento non uadi ad angolo retto &longs;opra alla detta cortina, anci uoglio, <lb/>che procedano con la parte di fuora alquanto uer&longs;o la citta, & conla parte di dentro <lb/>obliquar&longs;i in fuora uer&longs;o la campagna, come &longs;i uede de&longs;ignato nella pre&longs;ente figura, ue <lb/>ro è, che le dette parianette uogliono e&longs;&longs;er alquanto piu oblique di quello che mo&longs;tra la <lb/>figura per le ragioni, che di &longs;otto &longs;e dira, fatto que&longs;to, uoglio che dalla banda che guar <lb/>da uer&longs;o la campagna di cia&longs;caduna di dette parianette ue &longs;ia fatto un'arginetto di ter­<lb/>ra (come &longs;i uede nelle due parianette. </s> <s id="s.001418">p.&.r.) di tanta gro&longs;&longs;ezza, che non po&longs;&longs;a e&longs;&longs;er <lb/>danneggiato da nemici con le &longs;ue artegliarie, & &longs;otto à cia&longs;caduno de detti argenetti, <lb/>uoglio che ui &longs;ia a&longs;&longs;ettato, ouer po&longs;to un falconetto da. </s> <s id="s.001419">6. ouer da. </s> <s id="s.001420">3. lire di balla, & per <lb/>que&longs;to uoglio che le dette parianette, & argenetti &longs;iano alti alquanto piu de un'huomo, <lb/>accio che facciano &longs;cudo à cia&longs;cun de detti falconetti, che non po&longs;&longs;ano e&longs;&longs;er danneggiati <lb/>da nemici con le &longs;ue artegliarie, & uoglio anchora che tai argenetti &longs;tiano alquanto <lb/>obliqui con la parte dauanti uer&longs;o la citta, accio che li nemici non poßino uedere ne ti­<lb/>rare per la parte dauanti &longs;otto alli detti argenetti, cioe nel luoco doue &longs;ta li detti falco­<lb/>netti, perche il proprio officio de tutti que&longs;ti falconetti, uoglio che &longs;ia di guardare mi­<lb/>nutamente tutto quel &longs;pacio ingolfato fra le gia dette lettere.o.y.z.m.l.<emph.end type="italics"/>k.<emph type="italics"/>h.i.n. </s> <s id="s.001421">& al­<lb/>quanto piu in fuora del angolo.o.&.m.cioe cercar de far che gli falconetti della cor­<lb/>tina.a.b.tutti poßino tirare, & guardare &longs;tanti &longs;otto al &longs;uo arginetto, per otto, ouer <lb/>dieci pa&longs;&longs;a piu in fuora del ponto.o.& quelli della cortina.c.b. </s> <s id="s.001422">guardino il mede&longs;imo <lb/>piu in fuora del ponto.m.accio che niun &longs;ia &longs;icuro &longs;otto alli argini di terra, che &longs;ar an­<lb/>no di fuora del fo&longs;&longs;o à de rimpetto delli dui baluardi.a.&.c.perche nel far delli foßi, <lb/>ouer fo&longs;&longs;e, uoglio che la mitta della terra, che &longs;ene caua &longs;ia gettata di dentro della citta <lb/>per far li argeni de drio alle cortine con li &longs;uoi contraforti, come &longs;i co&longs;tuma nelle mo­<lb/>derne fortificationi. </s> <s id="s.001423">Et uoglio che per piedi. </s> <s id="s.001424">12. (uel circa) lontano da lhoro della fo&longs;­<lb/>&longs;a di fuora uia &longs;ia fatto un muro commune &longs;econdo l'andar della detta fo&longs;&longs;a, alto circa <lb/>dui piedi manco della cortina di dentro, & à quel tal muro di fuora uia farui li &longs;uoi con <lb/>traforti, & fra quelli contr aforti gettarui quella mitta della terra, che &longs;e caua della gia <lb/>detta fo&longs;&longs;a, facendo con tal terra ungro&longs;&longs;o argine di fuora uia di tal muro il qual argi­<lb/>ne uada procedendo &longs;econdo le lettere.m.l.<emph.end type="italics"/>k.<emph type="italics"/>h.i.n.o. </s> <s id="s.001425">& di&longs;cendendo à &longs;carpa uer&longs;o lo <lb/>ingolfato &longs;pacio, che è di&longs;uora uia, il qual argine oltra che uenira à far &longs;cudo qua&longs;i à tut<emph.end type="italics"/><pb xlink:href="042/01/143.jpg"/><figure id="id.042.01.143.1.jpg" xlink:href="042/01/143/1.jpg"/><pb pagenum="72" xlink:href="042/01/144.jpg"/><emph type="italics"/>ta la cortina, et à tutti li baluardi <21>che de <27>lli <expan abbr="nõ">non</expan> potra e&longs;&longs;er uisto ne battuto da nemici <lb/><expan abbr="cõ">com</expan> le &longs;ue artegliarie, eccetto che <27>lla &longs;oprema parte de dui piedi, che&longs;e la&longs;cera &longs;coperiæ <lb/><21> poter tirar di fuora <expan abbr="cõ">com</expan> le artegliarie della citta. </s> <s id="s.001426">Et <27>l &longs;pacio largo. </s> <s id="s.001427">12. piedi, uel cir <lb/>ca (la&longs;ciato fra la fo&longs;&longs;a, et lo detto argine di fuora) formara una uia coperta, ouer &longs;e­<lb/>creta, <21> laquale potra andare <expan abbr="&longs;ecretam&etilde;te">&longs;ecretamente</expan> caualli, et fanti, et altri &longs;icuramente à torno <lb/>atorno di fuora uia di tal citta, cioe atorno della fo&longs;&longs;a di fuora uia, et &longs;e douera la&longs;ciar al <lb/>cune aperture <expan abbr="penetrãte">penetrante</expan> il muro, qua&longs;i tutto l'argine, che&longs;e dicono porte fal&longs;e fatte di <lb/>muro &longs;empio, cioe duna piera, coperte difuora uia <expan abbr="leggierm&etilde;te">leggiermente</expan> di terra, accio che <21> tut <lb/>to ui paia argine, le quai porte fal&longs;e &longs;i poßino <expan abbr="facilm&etilde;te">facilmente</expan> rouinare <21> poter u&longs;cir <expan abbr="tacitam&etilde;">tacitamen</expan> <lb/>te la notte, & andare à far qualche &longs;trettagema, ouer iproui&longs;oa&longs;&longs;alto alli nemici, le quai <lb/>porte fal&longs;e &longs;e potriano fare fra il <expan abbr="põto">ponto</expan>.m.et.l.et fra il <expan abbr="põto">ponto</expan>.n.et.o.ouer in altri &longs;imili lo <lb/>chi, uero è, che tal uia &longs;ecreta, o uogliam dir coperta non &longs;i di&longs;cernera nella no&longs;tra figu <lb/>ra, perche la non ui è stata po&longs;ta, perche <expan abbr="uol&etilde;dola">uolendola</expan> far à mi&longs;ura &longs;aria da &longs;e co&longs;a in&longs;en&longs;ibi <lb/>le, et re&longs;taria in tutto coperta dal no&longs;tro argine, e pero bi&longs;ogna che <expan abbr="cõ">com</expan> la pura imaginæ <lb/>tiua &longs;ia ui&longs;ta, et inte&longs;a. </s> <s id="s.001428">Et que&longs;ta tal uia uenira à e&longs;&longs;er ottimamente guardata, et dife&longs;a, <lb/>non &longs;olamente dalli baluardi, et dalli dui caualleretti. </s> <s id="s.001429">2. et. </s> <s id="s.001430">3. et dalli falconetti che <expan abbr="&longs;tarã">&longs;taram</expan> <lb/>no &longs;otto à quelli argenetti della &longs;ua oppo&longs;ita cortina, ma anchora piu minutamente &longs;aræ <lb/>guardata, et dife&longs;a da quelli archibu&longs;eri, che <expan abbr="&longs;arãno">&longs;aranno</expan> &longs;otto alli mede&longs;imi arginetti, <21>che <lb/>tal uia uoglio che la &longs;ia totalmente di&longs;coperta uer&longs;o la citta, la qual uia hauera anchora <lb/>que&longs;t'altra proprieta, che&longs;e nella fo&longs;&longs;a non ui fu&longs;&longs;e acqua, et che li nemici per &longs;orte con <lb/>trincere penetr a&longs;&longs;ono nella detta fo&longs;&longs;a, per minare, ouer &longs;calare le mura, ouer corti­<lb/>ne di tal citta quelli della terra <expan abbr="potrãno">potranno</expan> uenire <expan abbr="&longs;icuram&etilde;te">&longs;icuramente</expan> per tal uia à offendere li det <lb/>ti nemici nella &longs;chena con archibu&longs;i, balestre, archi, et altre co&longs;e &longs;imili. </s> <s id="s.001431">Dico oltra à quel <lb/>lo, che <expan abbr="farãno">faranno</expan> poi li baluardi, caualleri, falconetti, et archibu&longs;i, che <expan abbr="&longs;arãno">&longs;aranno</expan> &longs;u la cortina <lb/>di <expan abbr="d&etilde;tro">dentro</expan> della citta. </s> <s id="s.001432">Et co&longs;i &longs;ara <expan abbr="cõpita">compita</expan> <27>&longs;ta no&longs;tra prima forma de fortificare, la qual <lb/>forma &longs;e trouara bauere in &longs;e non &longs;olamente tutte quelle. </s> <s id="s.001433">3. qualita, ouer <expan abbr="cõditioni">conditioni</expan> det <lb/>te, nel. </s> <s id="s.001434">3. 4. et. </s> <s id="s.001435">5. que&longs;ito del no&longs;tro. </s> <s id="s.001436">6. libro (come che.<emph.end type="italics"/> V.M. <emph type="italics"/><expan abbr="cõ">com</expan> il &longs;uo &longs;ano intelletto puo <lb/><expan abbr="facilm&etilde;te">facilmente</expan> <expan abbr="cõpr&etilde;dere">comprendere</expan>) ma ui ba anchora que&longs;to de piu, che tal citta (come fu detto di&longs;o­<lb/>pra) <expan abbr="nõ">non</expan> puo e&longs;&longs;er <expan abbr="dãneggiata">danneggiata</expan> da nemici <expan abbr="cõ">com</expan> le artegliarie, la qual co&longs;a di <expan abbr="quãta">quanta</expan> autorita, <lb/>et importantia la &longs;ta, à<emph.end type="italics"/> V.M. <emph type="italics"/>ne la&longs;&longs;o il giudicio. </s> <s id="s.001437">Poi di quella uia coperta, o <expan abbr="uogliã">uogliam</expan> dir <lb/>&longs;ecreta, <expan abbr="nõ">non</expan> uoglio &longs;tar à narrare di <expan abbr="quãta">quanta</expan> <expan abbr="cõmodita">commodita</expan>, et utilita, la &longs;ia à quelli della terra, <lb/>et de <expan abbr="dãno">danno</expan> et terrore alli nemici <21> cau&longs;a delli improui&longs;i <expan abbr="a&longs;&longs;alim&etilde;ii">a&longs;&longs;alimenii</expan>, che di notte gli <expan abbr="uerrã">uerram</expan> <lb/>no fatti da diuer&longs;e <expan abbr="bãde">bande</expan> <21> uia di quelle porte fal&longs;e. </s> <s id="s.001438">Et accio che<emph.end type="italics"/> V.M. <emph type="italics"/>po&longs;&longs;a gro&longs;&longs;o mo­<lb/>do <expan abbr="int&etilde;dere">intendere</expan>, le mi&longs;ure, et <expan abbr="di&longs;tãtie">di&longs;tantie</expan> di tal no&longs;tra forma ui ho de&longs;critta la &longs;cala, da noi u&longs;ata <lb/>nella de&longs;ignation di quella, la qual &longs;cala è la linea.<emph.end type="italics"/> <22>. <emph type="italics"/><expan abbr="lõga">longa</expan> pa&longs;&longs;a. </s> <s id="s.001439">120. uero che nelle ma <lb/>terie piccole <expan abbr="nõ">non</expan> ui &longs;e è o&longs;&longs;eruato le &longs;ue debite mi&longs;ure.<emph.end type="italics"/> S.M. N<emph type="italics"/><expan abbr="õ">om</expan> me importa à uederla <lb/><expan abbr="tãto">tanto</expan> p &longs;ottile, mi ba&longs;ta a&longs;&longs;ai, che gli uedo quella uostra. </s> <s id="s.001440">3. qualita, ouer <expan abbr="cõditione">conditione</expan> da me <lb/>de&longs;ider ata di uedere, et molto maggiore di quello preponeti nel. </s> <s id="s.001441">5. que&longs;ito. </s> <s id="s.001442">Perche ue­<lb/>do chiaramente, che &longs;e li nemici deliberaßeno di dar una battagia generale à tal citta <lb/>&longs;ubito, che quelli &longs;ar anno entrati in quello ingolfato piano, cioe di dentro da quelle <lb/>lettere m.z. <!-- REMOVE S-->4. y.o.nõ &longs;olamente &longs;ar anno offe&longs;i da quelli della terra da quattro ban­<lb/>de con le artegliarie, ma da piu de. </s> <s id="s.001443">20. bande, perche cono&longs;co, che non &longs;olamente &longs;a­<lb/>ranno offe&longs;i dalli. </s> <s id="s.001444">3. baluardi, & dalli. </s> <s id="s.001445">4. caualleretti. </s> <s id="s.001446">Ma anchora da tutti quelli <pb xlink:href="042/01/145.jpg"/>falconetti, che &longs;ar anno &longs;ot­<lb/>to à quelli argenetti per lon <lb/>go all'una, e l'altra cortina, <lb/>e perche comprendo e&longs;&longs;ere <lb/>impoßibile da potere e&longs;&longs;ere <lb/>ouiate tai dife&longs;e da nemici, <lb/>non credo che &longs;ariano co&longs;i <lb/>pazzi, per großi che fu&longs;&longs;e­<lb/>no che &longs;e metteßono à tal im <lb/>pre&longs;a, cioe à uoler dar batta <lb/>glia à una citta, talmente for <lb/>tificata, eglie <expan abbr="b&etilde;">bem</expan> uero, che tal <lb/>forma è alquanto mo&longs;truo&longs;a <lb/>dauedere, nel re&longs;to poi la <expan abbr="cõ">com</expan> <lb/>mendamo a&longs;&longs;ai.<emph.end type="italics"/> N. S<emph type="italics"/>ignor <lb/>Clarißimo, &longs;e la natura ha­<lb/>ue&longs;&longs;e principiato, & &longs;empre <lb/>continuato à far tutti glihuo <lb/>mini &longs;enza na&longs;o, et &longs;enzao­<lb/>recchie, et che dapoi per &longs;or <lb/>te ne face&longs;&longs;e uno con il na&longs;o, <lb/>et orecchie, certamente à tut <lb/>ti glialtri huomini pareria <lb/>co&longs;a mo&longs;truo&longs;a da uedere, il <lb/>mede&longs;imo dico di questa no­<lb/>&longs;tra forma de fortificatione, <lb/>la quale per e&longs;&longs;er molto di­<lb/>uer&longs;a dall'u&longs;o <expan abbr="cõmune">commune</expan>, à quel <lb/>la pare, & à molti altri pa­<lb/>rera mostruo&longs;a co&longs;a da ue­<lb/>dere, pur &longs;ia, come &longs;i uoglia, <lb/>doue, che è nece&longs;&longs;ario la for <lb/>tezza, non &longs;i debbe far con­<lb/>to di bellezza.<emph.end type="italics"/> S. M. E­<lb/><emph type="italics"/>glie il uero.<emph.end type="italics"/></s> </p> <figure id="id.042.01.145.1.jpg" xlink:href="042/01/145/1.jpg"/> <pb pagenum="73" xlink:href="042/01/146.jpg"/> <p type="head"> <s id="s.001447">QVESITO SECONDO FATO CONSEQ VENTE­<lb/><emph type="italics"/>mente dal mede&longs;imo Magnifico, & Eccellentißimo <lb/>Dottor, Signor Marc' Antonio <lb/>Moro&longs;ini.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001448">SIGNOR MARC'ANTONIO. M<emph type="italics"/>a ditime un pnco, uolendo uoi, che <lb/>tutte le cortine, che hanno da circondare tal citta procedano &longs;econdo l'ordine de <lb/>le predette, doue uorete poi, che &longs;iano fatte le porte nece&longs;&longs;arie à tal citta.<emph.end type="italics"/> N. S<emph type="italics"/>ignor <lb/>Magnifico tutte le porte nece&longs;&longs;arie à tal citta, uoglio, che &longs;iano fatti in quelli angoli <lb/>ingolfati uer&longs;o la citta, cioe, doue, che nella figura pa&longs;&longs;ata fu fatto il baluardo. </s> <s id="s.001449">b. <!-- REMOVE S-->per­<lb/>cha tai angoli, ouer luochi &longs;ono le piu &longs;icure parti di tutto il contorno di tal citta. </s> <s id="s.001450">Ma <lb/>bi&longs;ogna farle far con tal modo, e forma, che dalla banda de&longs;tra, & &longs;ini&longs;tra di quella ui <lb/>&longs;e gli po&longs;&longs;a accommodar dui, ouer tre &longs;acri, che guardino non &longs;olamente l'una, e l'altra <lb/>cortina, & &longs;imelmente li dui circostanti baluardi, in&longs;iene <expan abbr="cõ">com</expan> el fo&longs;&longs;o, ma anchora quel­<lb/>la uia coperta dal argine, cioe, che fu la&longs;&longs;ata fra l'argine, & il fo&longs;&longs;o, ouer fo&longs;&longs;a, la qual <lb/>co&longs;a &longs;ara facilißima da fare, et <expan abbr="&longs;imelm&etilde;te">&longs;imelmente</expan>, far &longs;opra alla detta porta, cioe nella &longs;ummita <lb/>de la cortina, fra li dui caualleretti, un luoco di poterui a&longs;&longs;ettar tre, ouer quattro &longs;a­<lb/>cri, che poßino tirare, & guardare à <expan abbr="lõgo">longo</expan> per tutto quel &longs;pacio ingolfato, & maßime <lb/>per longo alli argini, cioe doue procedono le lettere.m.l.<emph.end type="italics"/>k.<emph type="italics"/>i.n.o. </s> <s id="s.001451">& anchora per quel <lb/>la uia coperta, & nella campagna i&longs;teriore, uero è, che lo ingre&longs;&longs;o di andare alla det­<lb/>ta porta non uoglio, che &longs;i faccia nel argine.<emph.end type="italics"/>k.<emph type="italics"/>h.i. </s> <s id="s.001452">Anci uoglio, che tal ingre&longs;&longs;o &longs;ia fat <lb/>to in quel interuallo de argine, che è fra le due lettere.l.&.m.ouer, che è fra. </s> <s id="s.001453">n. <!-- REMOVE S-->&. </s> <s id="s.001454">o. <lb/><!-- REMOVE S-->& tal ingre&longs;&longs;o, ouer intrata &longs;i debbe far con una porta &longs;oda. </s> <s id="s.001455">ouer con un ponte leuato <lb/>re, che habbia un poco di fo&longs;&longs;etta&longs;otto, & co&longs;i tal ingre&longs;&longs;o &longs;ara &longs;icurißimo, perche tut <lb/>ti quelli, che uor anno intrar dentro di tal citta, ò &longs;iano carri, caualli, ouer pedoni, &longs;ara <lb/>nece&longs;&longs;ario, che per un pezzo camineno per quella uia coperta à quelli di fuora, ma tut <lb/><gap/> di&longs;coperta à quelli, che &longs;ar anno &longs;opra le cortine della citta &longs;otto à quelli argenetti <lb/>piu uolte detti, nelli quali luochi, oltra li falconetti, ui puo &longs;tare &longs;icur amente molti ar­<lb/>chibu&longs;eri, come fu detto nel principio, e pero &longs;e li nemici con qualche inganno pigliaße <lb/>no tal ingre&longs;&longs;o, porta, ouer ponte, nanti che pote&longs;&longs;ono peruenir alla principal porta, <lb/>da piu bande &longs;aranno rebattuti, & mal trattati, & la detta porta principale hauera <lb/>commodita, & tempo abondante da e&longs;&longs;er &longs;errata, & quella &longs;errata, che &longs;ia, li nemici <lb/>&longs;ar anno sforzati (&longs;e non uor anno morire) à tor&longs;e fuora di tal uia, & ritornar&longs;ene alli <lb/>&longs;uoi alloggiamenti con&longs;uo grandißimo danno, & uergogna per e&longs;&longs;er tal uia in ogni lo <lb/>co di&longs;coperta à quelli, che &longs;ar anno &longs;opra la &longs;ummita della cortina, & anchora alli ba­<lb/>luardi, et cauallereti, come di &longs;opra fu detto, uero é, che tal uia dal primo ingre&longs;&longs;o per <lb/>fin alla porta principale della citta uuol e&longs;&longs;er tanto larga, che incontr ando&longs;i dui carri <lb/>carghi l'uno po&longs;&longs;a dar luoco all'altro di pa&longs;&longs;are.<emph.end type="italics"/> S.M. C<emph type="italics"/>ertamente, che que&longs;ta uo­<lb/>&longs;tra prima forma è molto artificio&longs;amente compo&longs;ta, tal che à me pare e&longs;&longs;er ine&longs;pu­<lb/>gnabile. </s> <s id="s.001456">Et uoi dite, che la è la piu tri&longs;ta de tutte le altre, & io non po&longs;&longs;o imaginare, co <lb/>me &longs;ia poßibile de megliorarla, ma per e&longs;&longs;er bora tarda, uoglio, che poniamo fine à tal <lb/>ragionamento.<emph.end type="italics"/> N. A<emph type="italics"/>l piacer di quella.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/147.jpg"/> <p type="head"> <s id="s.001457">QVESITO TERZO FATTO DAL MEDESIMO <lb/>M<emph type="italics"/>agnifico, & Eccellentißimo Dottor, Signor <lb/>Marc' Antonio Moro&longs;ini.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001458">SIGNOR MARC'ANTONIO. N<emph type="italics"/>on &longs;aria buona co&longs;a à far far ancho­<lb/>ra quel tal argine, & quella uia coperta alle citta, che &longs;ono gia fortificate, accio, <lb/>che li nemici non le poteßino battere con le artegliarie, accettuando in quella poca par <lb/>te apparente di &longs;opra di tai argini.<emph.end type="italics"/> N. N<emph type="italics"/>on &longs;ignor Magnifico, perche le forme, che <lb/>&longs;i costuma à dare à tai fortificationi nol comportano, anci &longs;aria tai argini molto noci­<lb/>ui à quelli della citta: perche &longs;otto de quelli (cioe dalla banda de fora) ui potria &longs;icura­<lb/>mente &longs;tar li nemici, & quelli con trincere potriano penetrar in diuer&longs;i luochi li detti <lb/>argini, & anchora intrar nella fo&longs;&longs;a, con el farui larghe, & profonde aperture, e per <lb/>quelle battere in diuer&longs;i luochi &longs;icuramente le mura, ouer cortine di tal citta, la qual <lb/>co&longs;a non puo occorrere nella no&longs;tra forma, perche &longs;e quella ben &longs;e arricorda, la parte <lb/>de fora dello detto argine, ouer argini (cioe, doue &longs;ono le lettere.m.l.<emph.end type="italics"/>k.<emph type="italics"/>h.i.n.o.è otti­<lb/>mamente guardata, & dife&longs;a da uarie, & diuer&longs;e bande.<emph.end type="italics"/> S.M. M<emph type="italics"/>e ne arricordo, et <lb/>comprendo, che uoi diceti il uero. </s> <s id="s.001459">Questo debbe e&longs;&longs;ere quel modo de fortificare, <lb/>che preponeti nello ottauo Que&longs;ito del uo&longs;tro &longs;esto Libro: Perche uedo, che quelli <lb/>della terra potr anno andare &longs;icuramente à lauorare, &longs;eminare, e riccogliere per <lb/>tutti quelli &longs;pacij di terreno, che &longs;e <expan abbr="ingoifarãno">ingoifaranno</expan> à torno al circuito di tal citta, &longs;imili à <lb/>quello, che è dentro delle lettere.m.z. </s> <s id="s.001460">4. y.o. <!-- REMOVE S-->ma anchora molto piu in fora delle det­<lb/>te lettere: & oltra di que&longs;to tal citta non potra e&longs;&longs;er battuta, ne danneggiata da nemi­<lb/>ci con le artegliarie, come &longs;e prepone del detto Que&longs;ito.<emph.end type="italics"/> 8. N. N<emph type="italics"/>on &longs;ignor Magnifico, <lb/>che tal modo non è que&longs;to, anci quello aßicurara tal pae&longs;e, per piu di tre tanto lontano <lb/>dalle mura di tal citta, & con molto e molto <expan abbr="mãco">manco</expan> &longs;pe&longs;a, di quello intrara in que&longs;ta&longs;or <lb/>te de fortificatione, & que&longs;to mo&longs;traro da far per due diuer&longs;e uie, come, che in fine à <lb/>uo&longs;tra Eccellentia gli faro uedere.<emph.end type="italics"/> S.M. C<emph type="italics"/>erto gran co&longs;a me parera, &longs;e uoi me fare <lb/>tiucder una tal opra con &longs;i poca&longs;pe&longs;a.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001461">QVESITO QVARTO FATTO DAL MEDESIMO <lb/>M<emph type="italics"/>agnifico, & Eccellentißimo Dottor, Signor <lb/>Marc' Antonio Moro&longs;ini.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001462">SIGNOR MARC'ANTONIO. M<emph type="italics"/>ire&longs;ta da dirui, perche cau&longs;a uoleti <lb/>co&longs;i, che langolo fatto delle due cor tine in ponto.b.&longs;ia ottu&longs;o, & non retto, ne acu <lb/>to.<emph.end type="italics"/> N. P<emph type="italics"/>erche &longs;e langolo.b.fo&longs;&longs;e retto, ouer acuto (uolendo procedere regolatamen <lb/>te) &longs;aria nece&longs;&longs;ario à far li angoli.a.&.c.di quella mede&longs;ima qualita, & nelli angoli <lb/>retti, ouer ottu&longs;i non ui &longs;e puo far baluardo, che uaglia, & que&longs;to procede, perche lan <lb/>golo del baluardo è nece&longs;&longs;ario à farlo menore del angolo delle dette cortine, perche, <lb/>che lo face&longs;&longs;e equale, ouer maggior di quello, el &longs;aria impoßibile tal baluardo à poter <lb/>e&longs;&longs;er guardato da alcun delli altri dui circo&longs;tanti baluardi. </s> <s id="s.001463">Et &longs;aria anchora impoßi­<lb/>bile à poter far in alcun luoco &longs;opra l'una, & l'altra cortina un cauallero, che lo po-<emph.end type="italics"/><pb pagenum="74" xlink:href="042/01/148.jpg"/><emph type="italics"/>te&longs;&longs;e guardare: onde facendo <expan abbr="lãgolo">langolo</expan> di tal baluardo acuto, ueneria debelißimo, tal che <lb/>con facilita potria e&longs;&longs;er ruinato da nemici con le artegliarie.<emph.end type="italics"/> S.M. P<emph type="italics"/>erche cau&longs;a &longs;e­<lb/>guitaria, che&longs;e langolo del baluardo fu&longs;&longs;e eguale, ouer maggiore del angolo compre&longs;o <lb/>dalle due cortine, e&longs;&longs;er impoßibile à poter e&longs;&longs;er guardato dalli dui circo&longs;tanti baluar­<lb/>di, & manco da alcun cauallero, che fu&longs;&longs;e &longs;opra à l'una, e l'altra cortina.<emph.end type="italics"/> N. S<emph type="italics"/>ignor <lb/>Magnifico, per aßignar la cau&longs;a di que&longs;to, &longs;upponamo, che langolo compre&longs;o da due <lb/>cortine &longs;ia langolo.a.b.c.& che le dette due cortine, ouer che la i&longs;ten&longs;ion di quelle &longs;ia <lb/>&longs;econdo le due linee.a.b.&.b.c.hor uolendo con&longs;tituir rettamente un baluardo &longs;opra <lb/>à tal angolo.a.b.c.diuideremo tal angolo in due partiequali (&longs;econdo l'ordine dato de <lb/>Euclide nella nona del primo) con la linea.d.b.e.f.& in qual ponto ne parera nella li­<lb/>nea i&longs;trin&longs;ica.b.e.f.con&longs;tituiremo un angolo (per la. </s> <s id="s.001464">31. del primo di Eutlide) equale &longs;i <lb/>quel angolo, che ne parera di fare langolo del no&longs;tro baluardo, ma farlo contal condi­<lb/>tione, che tal angolo &longs;ia diui&longs;o pur in due parti equali dalla detta linea.b.e.f. </s> <s id="s.001465">& que&longs;to <lb/>&longs;i fara facendo la mita di tal angolo da una banda, & l'altra mita dall'altra di detta li <lb/>nea, hor &longs;upponemo, che questo tal angolo &longs;ia langolo.g.e.h.hor dico, che &longs;e tal angolo <lb/>g.e.h.&longs;ara equale, ouer maggiore del angolo.a.b.c. </s> <s id="s.001466">e&longs;&longs;er impoßibile à poter fare in al <lb/>cun luoco della cortina.a.b. </s> <s id="s.001467">una canonera, che po&longs;&longs;a uedere, ne tirare, ne difendere lo <lb/>lato.g.e.del detto baluardo. </s> <s id="s.001468">Il mede&longs;imo dico della cortina.c.b.cioe e&longs;&longs;er impoßibile di <lb/>fare in aleun luoco di quella una canonera, ouer bombardera, che po&longs;&longs;a uedere, ne tira <lb/>re, ne difendere l'altro lato.e.h.del detto baluardo, la qual co&longs;a&longs;e dimo&longs;tra in questo <lb/>modo, &longs;e tutto langolo.g.e.h.è equale a tutto langolo.a.b.c. </s> <s id="s.001469">anchora la mitta di l'una<emph.end type="italics"/><lb/><figure id="id.042.01.148.1.jpg" xlink:href="042/01/148/1.jpg"/><lb/><emph type="italics"/>(per communa &longs;cientia) &longs;ara eguale alla mitta de l'altro, e pero langolo.g.e.b. </s> <s id="s.001470">&longs;ara e­<lb/>guale al angolo.a.b.d. </s> <s id="s.001471">onde (per la. </s> <s id="s.001472">29. del primo di Euclide) le due linee.g.e.&.a.b. <lb/></s> <s id="s.001473">&longs;aranno equidi&longs;tante, & per le mede&longs;ime ragioni la linea. </s> <s id="s.001474">e.h.&longs;ara equidistante alla li-<emph.end type="italics"/><pb xlink:href="042/01/149.jpg"/><emph type="italics"/>nea.b.c.per la qual co&longs;a il nostro primo propo&longs;ito uenera à e&longs;&longs;er manife&longs;to: perche, &longs;e <lb/>la linea.e.g. (lato del baluardo) non puo concorrere con la linea.a.b.eglie co&longs;a chiara <lb/>che in alcun luoco di detta linea, ouer cortina.a.b.poter e&longs;&longs;er fatto una canonera, che <lb/>po&longs;&longs;a ueder, ne tirar, ouer difendere il detto lato.g.e.di tal baluardo, et <expan abbr="cõ">com</expan> le mede&longs;ime <lb/>ragioni&longs;e approuara, l'altro lato.e.h.dal detto baluardo e&longs;&longs;er equidi&longs;tante alla linea, <lb/>ouer cortina.b.c.e <21> questo e&longs;&longs;er impoßibile poter&longs;i far una canonera in alcun luoco di <lb/>detta cortina.b.c. </s> <s id="s.001475">che po&longs;&longs;a guardare il lato.e.h.dil detto baluardo. </s> <s id="s.001476">Et molto piu&longs;egui <lb/>ria tal impoßibilita, <expan abbr="quãdo">quando</expan>, che tutto langolo.g.e.h.del detto baluardo fu&longs;&longs;e maggior <lb/>del angolo.a.b.c.perche &longs;eguiria, che anchora la mitta di tal angolo fu&longs;&longs;e anchor mag <lb/>giore della mitta del angolo della cortina, cioe, che <expan abbr="lãgolo">langolo</expan>.g.e.b.fu&longs;&longs;e maggiore del an <lb/>golo.a.b.d. </s> <s id="s.001477">Et perche lo detto angolo.a.b.d.in&longs;ieme con langolo.a.b.e. (per la. </s> <s id="s.001478">13. del <lb/>primo di Euclide) &longs;ar anno eguali à dui angoli retti, per il che li dui angoli.a.b.e.&.g. <lb/></s> <s id="s.001479">e.b.&longs;ar anno maggiori di dui angoli retti, onde (per lo conuer&longs;o modo della quinta pe­<lb/>titione del no&longs;tro Euclide) protratta la linea.e.g. </s> <s id="s.001480">dalla banda dal.g. </s> <s id="s.001481">continuamente &longs;e <lb/>andara allargando, & alluntanando dalla cortina.b.a.e pero molto piu euidente &longs;e ma­<lb/>nife&longs;ta la &longs;opra detta impoßibilita, & <21> le mede&longs;ime ragioni &longs;e dimo&longs;trara dell'altro la <lb/>to e.h.con la cortina.b.c. </s> <s id="s.001482">Ma &longs;e lo detto angolo.g.e.h.del baluardo &longs;ara menore del an <lb/>golo.a.b.c.della cortina, &longs;eguira, che <expan abbr="lãgolo">langolo</expan>.g.e.b.&longs;ia anchor minore del angolo.a.b.d. <lb/></s> <s id="s.001483">& &longs;imelmente (per la detta. </s> <s id="s.001484">13. del primo di Euclide) &longs;eguira, che li dui angoli.g.e.b. <lb/></s> <s id="s.001485">&. </s> <s id="s.001486">e.b.a.&longs;iano menori de dui angoli retti, onde (per la detta quinta petitione) protrat <lb/>ta la linea.e.g.in&longs;ieme con la linea.b,a.eglie nece&longs;&longs;ario, che concorreno in&longs;ieme, e pero <lb/>tutte le canonere fatte à canto al luoco di tal concor&longs;o, quelle guardar anno rettamen­<lb/>te il detto lato.g.e.& que&longs;to mede&longs;imo &longs;eguira nella cortina.b.c.cioe, che quella <expan abbr="cõcor">concor</expan> <lb/>rera con la linea.e.h.e&longs;&longs;endo protratta in diretto uer&longs;o.c.et co&longs;i tutte le canonere, che <lb/>&longs;ar an fatte à canto al luoco di tal concor&longs;o, ò &longs;iano di &longs;opra, ouer di &longs;otto di tal luoco, <lb/>cioe, ò &longs;iano de baluardi, ouer de caualleri guardar anno rettamente il detto lato.e.h. <lb/></s> <s id="s.001487">del baluardo. </s> <s id="s.001488">Et ai&longs;ogna notar, che quanto piu &longs;ara menore langolo del baluardo del <lb/>angolo delle cortine, tanto piu propinquo al detto baluardo &longs;e fara tal concor&longs;o, et tan <lb/>to piu debile &longs;ara tal baluardo, & per il contrario, quanto manco &longs;minuera langolo del <lb/>detto baluardo del angolo delle due cortine, tanto piu lontano dal detto baluardo &longs;e fa­<lb/>ra tal concor&longs;o, & piu gagliardo, ouer forte &longs;ara tal baluardo, e per tanto dico, che uo <lb/>lendo far un baluardo &longs;opra à un angolo retto de due cortine, eglie nece&longs;&longs;ario (uolen­<lb/>do far, che tal baluardo &longs;ia guardato da altri baluardi, ouer caualleri) à far tal ba­<lb/>luardo de angolo acuto, & ogni baluardo de angolo acuto uien à e&longs;&longs;er debole, & <lb/>tanto piu debole &longs;ara, quanto piu acuto angolo contenera: e pero, quando, che <lb/>langolo contenuto dalle due cortine &longs;ara poiacuto, de neceßita molto piu acuto bi&longs;ogna <lb/>ra far langolo del detto baluardo, & con&longs;e quentemente molto piu debole uenira à e&longs;­<lb/>&longs;er tal baluardo.<emph.end type="italics"/> S.M. E<emph type="italics"/>ho ben inte&longs;o da molti pratici forti&longs;icatoride citta e&longs;&longs;er <lb/>difficulto &longs;ißimo à poter fortificar un angolo retto de una citta, & molto piu un ango­<lb/>lo acuto, & quantunque la i&longs;perienza ne faccia chiaridi que&longs;to, nondimeno con que&longs;te <lb/>uostre Euclidiane argumentationi, me haueti fatto perfettamente cono&longs;cere la cau&longs;a <lb/>propinqua de tali effetti.<emph.end type="italics"/> N. S<emph type="italics"/>ignor Magnifico non &longs;olamente l'hanno per difficul<emph.end type="italics"/><pb pagenum="75" xlink:href="042/01/150.jpg"/><emph type="italics"/>toßßimo: ma un certo me&longs;&longs;er Ce&longs;are Napolitano zotto (qual faceua gran pro&longs;eßione <lb/>de fortificar citta) me affermo e&longs;&longs;er impoßibil edi poter fortificare l'angolo retto, & <lb/>manco l'acuto, della qual co&longs;a fra me molto me ne ri&longs;i, ma allui fin&longs;i da credere tal &longs;ua <lb/>conclu&longs;ione.<emph.end type="italics"/> S.M. A<emph type="italics"/>dunque haueti opinione, che li detti angoli &longs;i po&longs;&longs;ano &longs;icuramen <lb/>te fortificare.<emph.end type="italics"/> N. S<emph type="italics"/>enza dubbio Signor Magnifico, che &longs;i po&longs;&longs;ono fortificare.<emph.end type="italics"/> S.M. <lb/>Q<emph type="italics"/>ue&longs;to hauero ben accaro di uedere.<emph.end type="italics"/> N. V<emph type="italics"/>n'altra uolta di cio &longs;atisfaro Vo&longs;tra Ma­<lb/>gnificentia, perche al pre&longs;ente è hora tarda de intrar in tal ragionamento.<emph.end type="italics"/> S.M. <lb/>M<emph type="italics"/>or&longs;u diman ui a&longs;petto.<emph.end type="italics"/> N. I<emph type="italics"/>o ueniro Signor Magnifico.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.001489">QVESITO QVINTO FATTO DAL MEDESIMO <lb/>M<emph type="italics"/>agnifico, & Eccellentißimo Dottor. </s> <s id="s.001490">Signor <lb/>Marc' Antonio Moro&longs;ini.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001491">SIGNOR MARC'ANTONIO. H<emph type="italics"/>or narratime un poco que&longs;to uo&longs;tro <lb/>modo de fortificare un'angolo retto, ouer acuto de unacitta.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;to &longs;i fa­<lb/>ra Signor Magnifico, facendo prima di &longs;opra al detto angolo, o uogliamo dir cantone <lb/>uno cauallero, il qual cauallero trauer&longs;i da una cortina all'altra, ma che tal cauallero &longs;ia <lb/>molto in dentro dal detto angolo, retto, ouer acuto, perche &longs;e tal cauallero fu&longs;&longs;e fatto <lb/>terminare con alcuna parte di quello &longs;opra al detto angolo facil co&longs;a &longs;aria alli nemici à <lb/>rouinare tal angolo con le &longs;ue artegliarie (per e&longs;&longs;er debile) onde &longs;e tal angolo fu&longs;&longs;e fon <lb/>dameuto del detto cauallero, ueneria à rouinare il detto cauallero in&longs;ieme con tal ango <lb/>lo, la qual co&longs;a non poco pericolo cau&longs;aria à quelli della citta, perche tal rouinazzo ca <lb/>deria nella fo&longs;&longs;a, & ueneria à far &longs;cala alli nemici di poter a&longs;cendere, & entrare per <lb/>tal luoco dentro della citta.<emph.end type="italics"/> E <emph type="italics"/>per que&longs;to uoglio, che tal cauallero trauer&longs;i rettamente <lb/>da una cortina all'altra molto in dentro di tal angolo, & perche tal angolo retto, ouer <lb/>acuto (anchor che &longs;opra di quello non ui fu&longs;&longs;e il detto cauallero) potria pur e&longs;&longs;er roui <lb/>nato da nemici ad ogni &longs;uo piacer, etmaßime tutta quella parte, che fu&longs;&longs;e <expan abbr="appar&etilde;te">apparente</expan> di &longs;o <lb/>pra dalla fo&longs;&longs;a, e pero meglio è à fare di uolonta quello, che li nemici (parendogli) ne <lb/>potriano far per forza, & con no&longs;tro maggior pericolo, perche rouinando &longs;implice­<lb/>mente tal angolo per forza tal luoco rouinato in&longs;ieme con il rouinazzo, che caderia <lb/>nel fo&longs;&longs;o (come è detto) ueneriano pur à far &longs;cala alli nemici di a&longs;cendere, & entrare <lb/>nel cauallero, & nella detta citta.<emph.end type="italics"/> E <emph type="italics"/>per tanto uoglio, che tutto tal angolo, ouer canton <lb/><expan abbr="appar&etilde;te">apparente</expan> dalla fo&longs;&longs;a in &longs;u&longs;o &longs;ia <expan abbr="totalm&etilde;te">totalmente</expan> tagliato, ouer &longs;mu&longs;&longs;ato à &longs;carpa per fin à <expan abbr="cãto">canto</expan> <lb/>del <expan abbr="fondam&etilde;to">fondamento</expan> del cauallero, la qual co&longs;a <expan abbr="fac&etilde;do">facendo</expan> tal loco uenira à re&longs;tar a&longs;&longs;ai gagliardo, <lb/>eforte. </s> <s id="s.001492">Oltra di que&longs;to uoglio, che circa al meggio dell'una, & l'altra cortina &longs;ia fatto <lb/>un baluardo, <expan abbr="cõ">com</expan> tal ordine, che li lati, che &longs;ono dalla <expan abbr="bãda">banda</expan> uer&longs;o il detto cauallere dell'<gap/><lb/>no, e l'altro de quelli, &longs;iano <expan abbr="rettam&etilde;te">rettamente</expan> &longs;ignoreggiati, & guardati dal detto cauallero, ol <lb/>tra di que&longs;to uoglio che <expan abbr="acã">acam</expan><gap/>o dell'uno, e l'altro baluardo, dalla <expan abbr="bãda">banda</expan> uer&longs;o l'angolo, ret <lb/>to, ouer acuto &longs;ia fatto un caualleretto (qua<gap/>r <expan abbr="ãgolo">angolo</expan>, ouer <expan abbr="tõdo">tondo</expan>, ouer ouale) di tal capa <lb/>cita, che &longs;opra all'uno, & l'altro de quelli ui &longs;e po&longs;&longs;a <expan abbr="accõmodare">accommodare</expan>. </s> <s id="s.001493">3. ouer. </s> <s id="s.001494">4. falconetti <lb/>da. </s> <s id="s.001495">6. lire di balla, oueramente. </s> <s id="s.001496">2. ouer. </s> <s id="s.001497">3. &longs;acri, & che li detti caualleretti &longs;iano &longs;ituati di <lb/>&longs;orte, che poßino <expan abbr="rettam&etilde;te">rettamente</expan> difendere, et guardar tal angolo.<emph.end type="italics"/> S.M. E<emph type="italics"/>ui ho <expan abbr="ottimam&etilde;-te">ottimamen­<lb/>te</expan> inte&longs;o, nondimeno fatime un poco di e&longs;&longs;empio in figura.<emph.end type="italics"/> N. S<emph type="italics"/>ignor clarißimo, per <pb xlink:href="042/01/151.jpg"/>&longs;atlsfar meglio<emph.end type="italics"/> V. M<emph type="italics"/>ag. <!-- KEEP S--></s> <s id="s.001498">ho portato in di&longs;&longs;egno un modelletto di tal &longs;orte angolo forti­<lb/>ficato, qual è que&longs;to &longs;otto&longs;critto, cioe l'angolo.a.è l'angolo terreo contenuto dalle due <lb/>cortine, retto, ouer acuto. </s> <s id="s.001499">Et.b.è lo cauallero fatto &longs;opra di quello, & lo triangolo.c. <lb/></s> <s id="s.001500">d.e.è il taglio, ouer &longs;mu&longs;&longs;atura à &longs;carpa, dell'angolo, ouer cantone, che era apparente <lb/>di &longs;opra della fo&longs;&longs;a, che gia conteneua le due cortine, et la linea.a.e.è il restante dell'an <lb/>golo contenuto pur dalle dette due cortine, il quale uien à eßere alto, quanto è alta la fo&longs; <lb/>&longs;a, cioe la linea.a.e. </s> <s id="s.001501">debbe eßer eguale alla detta altezza della fo&longs;&longs;a, la qual foßa non <lb/>ue la ho uoluta de&longs;ignare, accio meglio &longs;i ueda il tutto, l'uno, e l'altro baluardo &longs;ono.f. <lb/></s> <s id="s.001502">&. </s> <s id="s.001503">g. <!-- REMOVE S-->Et li dui caualleretti &longs;ono.h.&.i.le qual co&longs;e <expan abbr="difenderãno">difenderanno</expan> honoratamente tal &longs;pe <lb/>cie di angolo, & lo far anno gagliardo, & forte, uero è, che io laudarei, che &longs;opra à <lb/>l'un, e l'altro di dui baluardi (&longs;i nella piazza di &longs;opra, come in quella da baßo) ui &longs;e gli <lb/>metteße piu pre&longs;to pezzi piccoli, che großi, cioe &longs;acri, ouer falconetti da. </s> <s id="s.001504">6. & met-<emph.end type="italics"/><lb/><figure id="id.042.01.151.1.jpg" xlink:href="042/01/151/1.jpg"/><lb/><emph type="italics"/>teruene tanto piu numero.<emph.end type="italics"/> S.M. M<emph type="italics"/>e piace aßai questa uo&longs;tra opinione, pur pen&longs;o, <lb/>che con&longs;iderando ben questa co&longs;a ui &longs;e ritrouera molte co&longs;e da poterui opponere, e pe <lb/>ro uoglio che rimettemo à di&longs;putar meglio que&longs;ta uo&longs;tra opinione à un'altra fiata<emph.end type="italics"/><lb/>N. C<emph type="italics"/>ome pare à uo&longs;tra Magnificentia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001505">QVESITO SESTO FATTO DAL MEDESIMO <lb/>M<emph type="italics"/>agnifico, & Eccellentißimo Dottor, Signor <lb/>Marc' Antonio Moro&longs;ini.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001506">SIGNOR MARC'ANTONIO. N<emph type="italics"/>el Sesto Que&longs;ito del uostro Se&longs;to li­<lb/>bro, uoi diceti, che à uoler fortificar una citta, che &longs;i debbe dar tal forma alle mu­<lb/>ra, ouer cortine di quella, che &longs;e per &longs;orie quelle tai mura, ouer cortine fu&longs;&longs;eno roui-<emph.end type="italics"/><pb pagenum="76" xlink:href="042/01/152.jpg"/><emph type="italics"/>nate da nemici con le artegliarie, che tal citta &longs;ia qua&longs;i piu forte con tai mura rouina­<lb/>te, che &longs;i quelle fu&longs;&longs;eno intiere, & &longs;ane, della qual co&longs;a molti &longs;e &longs;ono &longs;candalizzati di <lb/>uoi.<emph.end type="italics"/> N. S<emph type="italics"/>ignor clarißimo, credo uer amente, che molti &longs;e ne &longs;iano &longs;candalizzati, pen <lb/>&longs;ando loro, che io uoglia for&longs;i dire, che rouinate le dette mura per fin alli fondamenti, <lb/>ma io non uoglio dir co&longs;i, anciuoglio dire, che rouinata quella parte apparente di &longs;o­<lb/>pra al horo della fo&longs;&longs;a (come &longs;i co&longs;tuma communamente nelle batterie) che ne &longs;eguiria <lb/>poi quello, che hauemo detto nel detto Se&longs;to Que&longs;ito del no&longs;tro Se&longs;to libro, cioe che tal <lb/>citta &longs;aria qua&longs;i piu forte con tai parti de mura rouinate di quello &longs;aria e&longs;&longs;endo intiere, <lb/>e &longs;ane.<emph.end type="italics"/> S.M. I<emph type="italics"/>ntendetela mo, come uoleti, che per qual modo &longs;i uoglia la me par co­<lb/>&longs;a granda, & &longs;e poßibil fu&longs;&longs;e di farme intendere con parole la qualita di tal uo&longs;tra for <lb/>ma de mura, me fare&longs;ti co&longs;a gratißima, delle altre co&longs;e poi, che me haueti prome&longs;&longs;o a­<lb/>&longs;pettaro fin che uorreti uoi, accio le po&longs;&longs;ate far con uostra commodita.<emph.end type="italics"/> N. S<emph type="italics"/>ignor <lb/>Magnifico, eglie co&longs;a chiara per ragion naturale, che quando li nemici uogliono bat­<lb/>tere una citta còn le artegliarie non cercano da battere, ne darouinare quella parte de <lb/>te de mura, ouer cortina, che non uedono, ma &longs;olamente quella parte, che è apparente <lb/>di &longs;opra al horo della fo&longs;&longs;a, perche rouinata che &longs;ia tal parte apparente, cadendo tal <lb/>rouinamento nella fo&longs;&longs;a gli uien à far una &longs;cala di poter a&longs;cendere, & da entrare com­<lb/>modamente nella detta citta.<emph.end type="italics"/> E <emph type="italics"/>per tanto nel fabricar le dette mura, ouer cortine, quan <lb/>do che &longs;ono elleuate qua&longs;i alla altezza del horo della fo&longs;&longs;a, uorria, che quella parte, <lb/>che gli manca à compirle in altezza, fu&longs;&longs;eno fabricate piuin dentro uer&longs;o la citta tal­<lb/>mente, che uenghi à re&longs;tar de fuora uia un &longs;pacio nella &longs;ommita del primo muro, il qual <lb/>&longs;pacio uoglio che&longs;ia di <expan abbr="tãta">tanta</expan> capacita, che &longs;ta atto à riceuere, & tenere &longs;opra di &longs;e qua&longs;i <lb/>tuttoil rouinazzo, di quella <expan abbr="&longs;ecõda">&longs;econda</expan> parte di cortina (fatta piu <expan abbr="id&etilde;tro">identro</expan>) &longs;e rouinata fu&longs;&longs;e <lb/>da nemici con le artegliarie (o poco manco) uero è, che bi&longs;ogna auertire nel far li bal­<lb/>uardi di farli con tal modo, e mi&longs;ura, che habbiano almen due, ouer tre canonere per <lb/>banda, cherettamente po&longs;&longs;ano tirare à longo per tutto quel tal &longs;pacio, ma dico con l'u <lb/>no, & l'altro di dui baluardi, po&longs;ti alla guardia di quella tal cortina, la qual co&longs;a facen­<lb/>do tal forma de cortina hauera in &longs;e la detta no&longs;tra qualita, perche &longs;e quella &longs;econda <lb/>parte di cortina (fatta piu in dentro) apparente di &longs;opra lo horo della fo&longs;&longs;a &longs;ara per <lb/>&longs;orte rouinata da nemici, con le artegliarie. </s> <s id="s.001507">Quel rouinazzo di tal cortina re&longs;tara a&longs;­<lb/>&longs;unato &longs;opra di quel &longs;pacio (gia la&longs;ciato per tal effetto) & perche ogni uolta, che tal <lb/>parte apparente di una tal cortina uenga rouinata da nemici con le artegliarie, non la <lb/>rouinar anno mai totalmente, ma rouinar anno &longs;olamente quella parte compo&longs;ta di pie <lb/>tre, & malta, ma quella parte poi che è di terra fra quelli contraforti (che noi chiama­<lb/>mo argine) non re&longs;tara, mai totalmente rouinata, ma de quella ne rouinara &longs;olamente <lb/>unacerta parte, che &longs;e tirara drio la cortina di pietre, e malta, nel cader chi fara, & <lb/>re&longs;tara poi una certa di&longs;ce&longs;a, ouer montata di terra in&longs;ieme con certe reliquie di quel­<lb/>li contr aforti gia fatti de drio à tal cortina fatta de pietre, e malta, la qual di&longs;ce&longs;a, ouer <lb/>montata non &longs;ara molto facile di a&longs;cendere.<emph.end type="italics"/> E <emph type="italics"/>per tanto &longs;e li nemici dapoi che hauer an­<lb/>no rouinata tal muraglia ouer cortina, deliberar anno di uoler entrare in tal citta, pri <lb/>ma gli&longs;ara nece&longs;&longs;ario à portar &longs;cale di poter a&longs;cendere dal fondo della fo&longs;&longs;a per fin à <lb/>quel <gap/> acio doue&longs;e ripo&longs;&longs;ara quel rouinamento, il qual &longs;pacio per e&longs;&longs;er tutto occupa-<pb xlink:href="042/01/153.jpg"/>to, et <expan abbr="pi&etilde;">piem</expan> di pietre, oltra che nell'appogiar le dette &longs;cale molte pietre &longs;i <expan abbr="farãno">faranno</expan> rouinar <lb/>à do&longs;&longs;o, ma li primi, che <expan abbr="a&longs;cenderãno">a&longs;cenderanno</expan> uolendo montare poi &longs;u&longs;o per quel monte de pie­<lb/>tre non poche de tai pietre ne far anno non &longs;olamente rouinar à do&longs;&longs;o de quelli, che &longs;u <lb/>per le dette &longs;cale con&longs;equentemente a&longs;cender anno, ma anchora à quelli, che nella fo&longs;&longs;a <lb/>&longs;tar anno per a&longs;cendere de mano in mano, oltra che le canonere delle piazze da ba&longs;&longs;o <lb/>dell'uno, o l'altro baluardo romperanno molte de quelle &longs;cale, & uccider anno molti de <lb/>quelli, che a&longs;cender anno, & che staranno per a&longs;cendere per le dette &longs;cale. </s> <s id="s.001508">Ma piu che <lb/>le canonere della piazza di &longs;opra pur dell'uno, e l'altro baluardo in&longs;ieme con quelle, <lb/>che gia furno a&longs;&longs;ettate dall'una, e l'altra banda per guardar à longo per tutto quel &longs;pa <lb/>cio doue &longs;e repo&longs;&longs;er anno le dette pietre della cortina rouinata, &longs;enza comparatione fa <lb/>ranno piu effetto, & danno nelli detti nemici, per cau&longs;a de tal rouinamento de cortina, <lb/>che&longs;e tal cortina fu&longs;&longs;e intiera, & &longs;ana, perche tirando in quelli fanti, che &longs;u&longs;o per quel <lb/>le amontonate pietre a&longs;cenderanno, oltra che amazzar anno, & &longs;troppiar anno con le <lb/>pure balle gran parte de quelli, li quali cadendo per quelle amontonate pietre redola­<lb/>ranno, & far anno redolar quelle pietre giu&longs;o per la te&longs;ta de quelli, che a&longs;cender anno, <lb/>& &longs;tar anno per a&longs;cendere &longs;u per dette &longs;cale. </s> <s id="s.001509">Ma le balle tirate &longs;u per quelle tai pietre <lb/>sbroffar anno quelle per tutte le parti di tal fo&longs;&longs;a, & non ui è dubbio, che li dettinemici <lb/>riceuer anno infinite uolte piu danno, & offen&longs;ione dalle pure pietre, che dalle pure bal <lb/>le tirate dall'un, e l'altro baluardo, & canonere.<emph.end type="italics"/> S.M. S<emph type="italics"/>enza dubbio che li detti ne­<lb/>mici &longs;ar anno piu offe&longs;i, & mal trattati dalle dette pietre, che dalle pure balle, & que­<lb/>&longs;ta uo&longs;tra opinion me piace a&longs;&longs;ai, perche comprendo che tai pietre rouinate co&longs;titue­<lb/>ranno, & formar anno un'altra altezza de pietre rouinate &longs;opra della prima fonda­<lb/>mental cortina, oltra quella di&longs;ce&longs;a, ouer montata di quel argine di terra mi&longs;to, & col­<lb/>ligato con le reliquie di contr aforti gia fatti nell'arginar la cortina rouinata, la qual <lb/>altezza à uolerla a&longs;cendere li nemici trouar anno de molte difficolta, e for&longs;i molto piu, <lb/>che&longs;e tal cortina fu&longs;&longs;e intiera, e &longs;ana. </s> <s id="s.001510">Ma ditemi un poco, quel tal &longs;pacio uoleti che &longs;ia <lb/>per fettamente quadrangolo, & rettangolo.<emph.end type="italics"/> N. N<emph type="italics"/>on Signor magnifico, anci uoglio <lb/>che tal &longs;pacio dall'uno, e l'altro capo uada tondezando in uer&longs;o la citta, cioe &longs;can&longs;ando, <lb/>& annullando l'uno, e l'altro de quelli dui angoli che doueriano formar &longs;i uer&longs;o la detta <lb/>citta, tal che il detto &longs;pacio uenira à formar una figura biangola qua&longs;i alla &longs;imilitudine <lb/>di quella figura, che fa la Luna <expan abbr="quãdo">quando</expan> è in quadrato con il Sole, dico dalli capi di tal &longs;pa <lb/>cio, cioe che l'un, e l'altro uengano à formar un'angolo &longs;olo qua&longs;i contiguo con il bal­<lb/>uardo à &longs;e conterminale dall'uno, & dall'altro capo.<emph.end type="italics"/> S.M. E<emph type="italics"/>ue ho inte&longs;o.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001511">QVESITO SETTIMO FATTO DAL MEDESIMO <lb/>M<emph type="italics"/>agnifico, & Eccellentißimo Dottor, Signor <lb/>Marc' Antonio Moro&longs;ino.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001512">SIGNOR MARC'ANTON. S<emph type="italics"/>o che doueti &longs;aper <expan abbr="minutam&etilde;te">minutamente</expan>, come &longs;i fan <lb/>no al pre&longs;ente li baluardi di dentro uia, cioe la piazza da ba&longs;&longs;o, & quella di &longs;opra <lb/>& &longs;o, che doueti hauer trouato qualche bella &longs;ottilita &longs;opra la co&longs;trution de quelli, e <lb/>per non &longs;tare otio&longs;i fina à hora da cena, uorria, che di cio ne ragionaßimo un poco.<emph.end type="italics"/><pb pagenum="77" xlink:href="042/01/154.jpg"/>N. A<emph type="italics"/>nci eglie tutto al contrario Signor Magnifico, che delle &longs;ue particolarita non <lb/>gli ne ho altra&longs;pecial cognitione, che quello, che mi fu narrato in parole dal<emph.end type="italics"/> S. P<emph type="italics"/>rior <lb/>di Barletta, qua&longs;i in fine del ottauo Que&longs;ito del mio &longs;e&longs;to libro, perche gia mai fui in <lb/>luoco, che pote&longs;&longs;e uedere realmente la piazza di &longs;opra, ne manco quella da ba&longs;&longs;o de al­<lb/>cun baluardo, & la cau&longs;a di que&longs;to fu da me narrata al detto Signor Priore nel primo, <lb/>& anchora in fine del ottauo Que&longs;ito del detto no&longs;tro &longs;e&longs;to libro, eglie ben uero, che <lb/>ho compre&longs;o, come &longs;ia fatta l'una, e l'altra piazza, per uigor de un di&longs;egno retratto <lb/>da un baluardo de una citta maritima, el qual è que&longs;to.<emph.end type="italics"/> S.M. S<emph type="italics"/>eti &longs;tato per mare.<emph.end type="italics"/><lb/>N. S<emph type="italics"/>on &longs;tato fina à lio Signor Magnifico, quando, che la Illu&longs;trißima Signoria ua a<lb/>&longs;po&longs;ar el mare, & non piu oltra.<emph.end type="italics"/> S.M. C<emph type="italics"/>ome caua&longs;ti adunque il ritratto di tal ba-<emph.end type="italics"/><lb/><figure id="id.042.01.154.1.jpg" xlink:href="042/01/154/1.jpg"/><lb/><emph type="italics"/>luardo da tal citta maritima.<emph.end type="italics"/> N. T<emph type="italics"/>al ritratto non fu da me cauato, ma mi fu dato da <lb/>un mio di&longs;cipulo Pittore eccellente.<emph.end type="italics"/> S.M. S<emph type="italics"/>apeti come &longs;tia, ouer come &longs;ia fatta la <lb/>piazza da ba&longs;&longs;o di tal baluardo, & altri &longs;imili.<emph.end type="italics"/> N. D<emph type="italics"/>i ueduta non ui &longs;aprei dire, ne <lb/>di questo, ne manco de altri &longs;imili, come di &longs;opra ho detto. </s> <s id="s.001513">ma diro bene, come i&longs;timo, <lb/>che &longs;ia fatta. </s> <s id="s.001514">Pen&longs;o, che tal piazza da ba&longs;&longs;o &longs;ia fatta in uolti &longs;opra, de großi, & ga­<lb/>gliardi pila&longs;troni, & che la intrata di andar, & condur le artegliarie in tal piazza da <lb/>ba&longs;&longs;o &longs;ia doue &longs;iuede il <expan abbr="põto">ponto</expan>.a.et che quelle fene&longs;trelle, che &longs;ono per el piano della piaz <lb/>za di&longs;opra &longs;iano fatte per dar luce alla detta piazza da ba&longs;&longs;o.<emph.end type="italics"/> S.M. V<emph type="italics"/>oi non haueti <lb/>in tutto mal pen&longs;ato, ma molto me marauiglio di uoi, che non ue &longs;iati dilettato de anda <lb/>re à uedere minutamente tai particolarita.<emph.end type="italics"/> N. N<emph type="italics"/>on ho tempo Signor Eccellentiß. <!-- REMOVE S-->di <lb/>andar à cercar di uedere tai co&longs;e, & maßime, che io <expan abbr="nõ">non</expan> mi curo, ne tengo conto di quel <lb/>le co&longs;e, che molti le &longs;anno fare, anchor, che &longs;iano da me ignorate (come che nel &longs;uppli­<lb/>mento della nostra trauagliata inuentione da me fu anchor detto) ma &longs;olamente di quel <lb/>le co&longs;e che niuno le &longs;anno e&longs;&longs;equire molto me diletto, & curo ditrouare. </s> <s id="s.001515">Io non uo di­<lb/>re, che quando fu&longs;&longs;e uno de detti baluardi qua in Venetia, & appre&longs;&longs;o della mia <expan abbr="&longs;tãtia">&longs;tantia</expan>,<emph.end type="italics"/><pb xlink:href="042/01/155.jpg"/><emph type="italics"/>che non lo anda&longs;&longs;e qualche uolta à uedere, ma non con altro mio maggior di&longs;conzo.<emph.end type="italics"/><lb/>S.M. C<emph type="italics"/>redo, che &longs;iati molto occupato nel e&longs;&longs;ercitio uostro. </s> <s id="s.001516">Dimane &longs;on per andare <lb/>alla uilla, doue &longs;taro alquanti giorni, per certe mie occorrentie. </s> <s id="s.001517">In questo mezzo pre­<lb/>parareti quelle altre forme de fortificationi, accio &longs;iano in ordine alla tornata mia. </s> <s id="s.001518">Et <lb/>maßime quella, che preponetinel. </s> <s id="s.001519">7. Que&longs;ito del uo&longs;tro &longs;e&longs;to Libro, cioe di fare quel <lb/>uo&longs;tro particolar ingegno di accommodar à ogni cortina, che &longs;icur amente potra e&longs;&longs;er <lb/>guardata, & dife&longs;a da. </s> <s id="s.001520">25. ouer. </s> <s id="s.001521">30. fanti al piu, contra à ogni grandißimo aßalimen­<lb/>to, che con &longs;cale la uole&longs;&longs;eno &longs;calare. </s> <s id="s.001522">Et preparate anchora quel modo de fortificar el <lb/>pae&longs;e atorno de una citta (come, che preponeti nell'ottauo Que&longs;ito) talmente, che quel <lb/>li della citta po&longs;&longs;eno &longs;icuramente andare à lauorare, &longs;eminare, & raccogliere qua&longs;i <expan abbr="tã">tam</expan> <lb/>to, che &longs;ia atto à dar il uiuere à quelli della citta, perche &longs;on molto de&longs;idero&longs;o de ueder <lb/>tal uo&longs;tra inuentione, perche la me par co&longs;a granda à farlo con co&longs;i poca &longs;pe&longs;a, come di <lb/>ceti.<emph.end type="italics"/> N. F<emph type="italics"/>aro Signor Magnifico.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.001523">F<emph type="italics"/>ine della Gionta del &longs;e&longs;to Libro delli Que&longs;iti, & Inuentioni <lb/>diuer&longs;e de Nicolo Tartaglia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001524">CON <emph type="italics"/>gratia, & priuilegio dall'Illustrißimo Senato Veneto, che niuno ardi&longs;ca, ne <lb/>pre&longs;uma di &longs;tampar, ne far &longs;tampare la pre&longs;ente Gionta, ne &longs;tampate altroue uen­<lb/>dere, ne far uendere in Venetia, ne in alcuno altro luoco, ò terra del Dominio Ve­<lb/>neto, per anni diece, &longs;otto pena de duc. </s> <s id="s.001525">300. & perdere le opere in qual &longs;i uoglia lo <lb/>co, che &longs;ar anno trouate, el terzo della qual pena pecuniaria &longs;ia applicata all'Ar&longs;e­<lb/>nale, & un terzo &longs;ia del Magi&longs;trato, doue &longs;e fara la e&longs;&longs;ecutione, & l'altro terzo &longs;ia <lb/>del denonciante, & le opere &longs;iano del pre&longs;ence Autore, come che nel priuilegio &longs;i <lb/>contiene.<emph.end type="italics"/></s> </p> </subchap1><subchap1> <pb pagenum="78" xlink:href="042/01/156.jpg"/> <p type="head"> <s id="s.001526">LIBRO SETTIMO DELLI <lb/>QVESITI, ET INVENTIONI DIVERSE, <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001527">S<emph type="italics"/>opra gli principij delle Que&longs;tioni Mechanice di <lb/>Ari&longs;totile.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.001528">QVESITO PRIMO FATTO DAL ILLVSTRISS. <lb/>S<emph type="italics"/>ignor Don Diego Hurtado di Mendozza, Amba&longs;ciator <lb/>Ce&longs;areo in Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001529">SIGNOR AMBASCIATORE. T<emph type="italics"/>artaglia, dapoi, che <lb/>noi deßimo uacatione alle lettioni di Euclide, ho ritrouato co&longs;e <lb/>nuoue &longs;opra le Mathematice.<emph.end type="italics"/> N. C<emph type="italics"/>he co&longs;a ha ritrouato uo&longs;tra <lb/>Signoria.<emph.end type="italics"/> S.A. L<emph type="italics"/>e Que&longs;tioni Mechanice di Ari&longs;totile, Grece, <lb/>& Latine.<emph.end type="italics"/> N. E<emph type="italics"/>glie tempo a&longs;&longs;ai che io le uidi, maßime Lati­<lb/>ne.<emph.end type="italics"/> S.A. C<emph type="italics"/>he ue ne pare.<emph.end type="italics"/> N. B<emph type="italics"/>enißimo, & certamente le &longs;o <lb/>no co&longs;e &longs;uttilißime, & di profonda dottrina.<emph.end type="italics"/> S.A. A<emph type="italics"/>nchora io <lb/>le ho &longs;cor&longs;e, & inte&longs;o di quelle la maggior parte, nondimeno me resta molti dubbij &longs;o­<lb/>pra di quelle, li quali uoglio, che me li dichiarati.<emph.end type="italics"/> N. S<emph type="italics"/>ignore, ui &longs;ono dubbij a&longs;&longs;ai, che <lb/>à uolergli à &longs;officienza delucidare, à me &longs;aria nece&longs;&longs;ario prima à dechiarare à uo&longs;tra <lb/>Signoria li principij della &longs;cientia di pe&longs;i.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.001530">A <emph type="italics"/>me mi pare, che Ari&longs;totile dimo­<lb/>&longs;tri il tutto, &longs;enza procedere, ouer intendere altramente la &longs;cientia di pe&longs;i.<emph.end type="italics"/> N. E<emph type="italics"/>glie <lb/>ben uero, che lui approua cadauna de dette que&longs;tioni, parte con ragioni, & argomenti <lb/>naturali, & parte con ragioni, & argomenti Mathematici. <!-- KEEP S--></s> <s id="s.001531">Ma alcuni di quelli &longs;uoi <lb/>argomenti naturali, con altri argomenti naturali ui &longs;i puol opponere. </s> <s id="s.001532">Et alcuni altri <lb/>con argomenti Mathematici (mediante la &longs;cientia di pe&longs;i detta di&longs;opra) &longs;e po&longs;&longs;ono re <lb/>probar per fal&longs;i. </s> <s id="s.001533">Et oltra di questo lui pretermette, ouer tace una questione &longs;opra del­<lb/>le libre, ouer bilanze di non poca importanza, ouer &longs;peculatione, & que&longs;to è proce&longs;­<lb/>&longs;o (per quanto po&longs;&longs;o con&longs;iderare) perche di tal que&longs;tione, non &longs;i puo aßignar la cau&longs;a <lb/>per ragion naturale, ma &longs;olamente con la detta &longs;cientia di pe&longs;i.<emph.end type="italics"/> S.A. N<emph type="italics"/>on credo, che <lb/>que&longs;to &longs;ia la uerita, cioe, che alcuna &longs;ua argumentatione pati&longs;ca oppo&longs;itione, perche <lb/>Ari&longs;totile non fu uu'ocha, ne manco credo, che lui habbia preterme&longs;&longs;o, ouer taciuto <lb/>que&longs;tione alcuna &longs;opra delle libre, che &longs;ia de importantia.<emph.end type="italics"/> N. A<emph type="italics"/>nci eglie troppoel ue <lb/>ro, <21>che <expan abbr="uol&etilde;do">uolendo</expan> <expan abbr="cõ&longs;iderare">con&longs;iderare</expan>, giudicare, et dimo&longs;trare la cau&longs;a della &longs;ua prima <27>stione, &longs;i <lb/>come naturale, cioe <expan abbr="cõ">com</expan> <27>lli ultimi <expan abbr="argom&etilde;ti">argomenti</expan> naturali, che lui aduce &longs;opra le libre ouer bi <lb/><expan abbr="lãce">lance</expan> materiale. </s> <s id="s.001534"><expan abbr="Mede&longs;imam&etilde;te">Mede&longs;imamente</expan> <expan abbr="cõ">com</expan> altri <expan abbr="argom&etilde;ti">argomenti</expan> naturali (come di &longs;opra dißi) &longs;i puo ap <lb/>prouare, che &longs;eguita tutto al <expan abbr="cõtrario">contrario</expan> di <27>llo, che in tal <27>&longs;tione <expan abbr="cõclude">conclude</expan>, ouer &longs;uppone. <lb/></s> <s id="s.001535">Et <expan abbr="uol&etilde;do">uolendo</expan> poi <expan abbr="cõ&longs;iderare">con&longs;iderare</expan>, & giudicare tal Que&longs;tione, &longs;i come Mathematico, & <expan abbr="cõ">com</expan> ar <lb/><expan abbr="gom&etilde;ti">gomenti</expan> Mathematici &longs;i puo mede&longs;imamente li detti &longs;ui argomenti reprobar per fal&longs;i, <lb/>mediante la &longs;cientia di pe&longs;i detta di &longs;opra.<emph.end type="italics"/> S.A. C<emph type="italics"/>ome &longs;e con&longs;iderano, & giudicano <lb/>le co&longs;e, &longs;i come natura le, & come &longs;e con&longs;iderano, & giudicano, &longs;i come Mathematico.<emph.end type="italics"/><pb xlink:href="042/01/157.jpg"/>N. E<emph type="italics"/>l naturale <expan abbr="cõ&longs;idera">con&longs;idera</expan>, giudica, et determina le co&longs;e, <expan abbr="&longs;ecõdo">&longs;econdo</expan> el &longs;en&longs;o, & <expan abbr="appar&etilde;tia">apparentia</expan> di <lb/>quelle in materia. </s> <s id="s.001536">Ma el Mathematico le con&longs;idera, giudica, & determina, non &longs;econ <lb/>do el &longs;en&longs;o, ma &longs;econdo la ragione (a&longs;trate da ogni materia &longs;en&longs;ibile) come che<emph.end type="italics"/> V. S<emph type="italics"/>ig. <lb/><!-- REMOVE S-->&longs;a, che co&longs;tuma Euclide.<emph.end type="italics"/> S.A. C<emph type="italics"/>irca di que&longs;to non &longs;o che ri&longs;pondere, perche io non <lb/>me arricordo co&longs;i all'improui&longs;o il &longs;oggetto di tal &longs;ua prima que&longs;tione, e pero ditime. <lb/></s> <s id="s.001537">come, che quella parla, & dice.<emph.end type="italics"/> N. L<emph type="italics"/>a dice, & parla preci&longs;amente in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001538">P<emph type="italics"/>erche cau&longs;a le maggior libre, ouer bilanze, &longs;ono piu diligente delle menore.<emph.end type="italics"/><lb/>S.A. B<emph type="italics"/>en? </s> <s id="s.001539">che uoleti dire &longs;opra di tal que&longs;tione.<emph.end type="italics"/> N. V<emph type="italics"/>oglio dir que&longs;to, che &longs;umen­<lb/>dola, ouer con&longs;iderandola, &longs;i come Mathematico (cioe astrata da ogni materia) &longs;enza <lb/>alcun dubbio tal que&longs;tione è uniuer&longs;almente uera, &longs;i per le ragioni da lui adutte per <lb/>auanti, come, che per molte altre, che nella &longs;cientia di pe&longs;i addur &longs;e potria. </s> <s id="s.001540">Perche quel <lb/>la linea, che con la &longs;ua mobile i&longs;tremita piu &longs;e allontana dal centro d'un cerchio, moue­<lb/>sta dauna mede&longs;ima uirtu, ouer potentia (in tal &longs;ua i&longs;tremita) piu facilmente, & con <lb/>maggior celerita, ouer pre&longs;te<emph.end type="italics"/>zz<emph type="italics"/>a &longs;aramo&longs;&longs;a, &longs;penta, ouer portata, di quella, che <expan abbr="cõ">com</expan> la <lb/>detta &longs;ua i&longs;tremita men &longs;e alluntanara dal detto centro, & per tal ragione le libre, o­<lb/>uer bilanze maggiori, &longs;e uerificano e&longs;&longs;er piu diligente delle menore. </s> <s id="s.001541">Ma uolendo poi <lb/>con&longs;iderare, & approuare tal que&longs;tione in materia, & con argomenti naturali, co­<lb/>me, che in ultimo lui con&longs;idera, & approua, cioe per el &longs;en&longs;o del uedere in e&longs;&longs;e libre, <lb/>ouer bilanze materiale. </s> <s id="s.001542">Dico, che con tai &longs;orte de argomenti non &longs;e uerifica general­<lb/>mente tal que&longs;tione, anzi &longs;e trouara &longs;eguir tutto al contrario, cioe le libre, ouer bilan <lb/>ze menori e&longs;&longs;er piu diligente delle maggiori, & che questo &longs;ia el uero nelle libre, ouer <lb/>bilanze materiale, la &longs;perientia lo fa manife&longs;to: perche &longs;e de uno ducato &longs;car&longs;o uoremo <lb/>&longs;apere de quani grani lui &longs;ia &longs;car&longs;o, con una libra, ouer bilanza granda, cioe con una <lb/>de quelle, che adoprano li &longs;peciali per pe&longs;ar &longs;pecie, zuccaro, zenzero, e canella, & al <lb/>tre co&longs;e &longs;imile, malamente &longs;e ne potremo chiarire, ma con una di quelle librette, ouer <lb/>bilancette piccole, che oprano li bancheri, or efici, & gioieleri, &longs;enza dubbio &longs;e ne po­<lb/>tremo totalmente certificare. </s> <s id="s.001543">Per il che &longs;eguitaria tutto al contrario, di quello, che in <lb/>tal que&longs;tione &longs;e conchiude, & dimo&longs;tra, cioe, che tai bilancette piu piccole &longs;iano piu di <lb/>ligente, delle piu grande, perche piu diligentemente, ouer &longs;ottilmente dimo&longs;trano la <lb/>differentia di pe&longs;i. </s> <s id="s.001544">Et la cau&longs;a di que&longs;to inconueniente non procede da altro, che dalla <lb/>materia, perche le co&longs;e costrutte, ouer fabricate in quella, mai ponno e&longs;&longs;er co&longs;i preci­<lb/>&longs;amente fatte, come, che con la mente uengono imaginate fuora di e&longs;&longs;a materia, per il <lb/>che tal hor &longs;e uien à cau&longs;ar in quelle alcuni effetti molto contr arij alla ragione. </s> <s id="s.001545">Et per <lb/>questo, & altri &longs;imili re&longs;petti, el Mathematico non accetta, ne con&longs;ente alle dimo&longs;tra­<lb/>tioni, ouer probationi fatte per uigor, & autoritadi &longs;en&longs;i in materia, ma <expan abbr="&longs;olam&etilde;te">&longs;olamente</expan> à <lb/>quelle fatte <21> demostrationi, et <expan abbr="argom&etilde;ti">argomenti</expan> a&longs;trati da ogni materia &longs;en&longs;ibile. </s> <s id="s.001546">Et <21> questa <lb/>cau&longs;a, le di&longs;cipline Mathematice. <!-- KEEP S--></s> <s id="s.001547">non &longs;olamente &longs;ono giudicate dalli &longs;apienti e&longs;&longs;er piu <lb/>certe delle naturale, ma quelle e&longs;&longs;er anchora nel primo grado di certezza. </s> <s id="s.001548">Et pero <lb/>quelle que&longs;tioni, che con argomenti Mathematici &longs;e po&longs;&longs;ono dimo&longs;trare, non è co&longs;a <lb/>conueniente ad approbarle con argomenti naturali. </s> <s id="s.001549">Et &longs;imelmente quelle, che &longs;o­<lb/>no gia dimo&longs;trate con argomenti Mathematici (che &longs;ono piu certi) non é da ten­<lb/>tare, ne da per&longs;uader &longs;i de certificarle meglio con argomenti naturali, li quali &longs;ono<emph.end type="italics"/><pb pagenum="79" xlink:href="042/01/158.jpg"/><emph type="italics"/>men certi.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.001550">A <emph type="italics"/>me mi pare che lui uoglia, in tal prima que&longs;tione, che quella resti <lb/>ot timamente chiarita (come è il uero) per le ragioni, & argomenti per auanti adutti, <lb/>& dimo&longs;trati, le quale ragioni, ouer argomenti &longs;cno tutti Mathematici, & non natu­<lb/>rali, perche parte de quelli &longs;e uerificano per la. </s> <s id="s.001551">23. del Se&longs;to di Euclide, & parte per <lb/>la quarta del mede&longs;imo.<emph.end type="italics"/> N. V<emph type="italics"/>o&longs;tra Signoria in&longs;ieme con lui dice la uerita, che tal que <lb/>&longs;tione è manife&longs;ta per le &longs;ue ragioni adutte per auanti, & questo mede&longs;imo anchoraio <lb/>di &longs;opra lo affermai, perche tai antecedenti&longs;ono &longs;tati da lui dimo&longs;trati con argomenti <lb/>Mathematici, ma in fine de tai buone argomentationi, ui &longs;ottogionge due altre con­<lb/>clu&longs;ioni, la prima delle quale dice preci&longs;amente in que&longs;ta forma. </s> <s id="s.001552">Et certamente &longs;ono <lb/>alcuni pe&longs;i, li quali po&longs;ti nelle piccol libre, non &longs;ono manifesti al &longs;en&longs;o, & nelle grande <lb/>&longs;ono manifesti. </s> <s id="s.001553">La qual conclu&longs;ione, uolendola con&longs;iderare, giudicare, & approuare, <lb/>&longs;i come naturale, cioe per uigore, & autorita del &longs;en&longs;o del uedere, nelle libre materia­<lb/>le, &longs;enza dubbio tal &longs;ua conclu&longs;ione pati&longs;&longs;e oppo&longs;itioni a&longs;&longs;ai, perche nelle dette libre, <lb/>ouer bilanze materiale, la maggior parte delle uolte &longs;e trouara &longs;eguir tutto al contra­<lb/>rio, cioe che &longs;ono alcuni pe&longs;i, li quali po&longs;ti, nelle libre, ouer bilanze grande, non &longs;e fa­<lb/>ranno con alcuna inclinatione manife&longs;ti al &longs;en&longs;o del uedere. </s> <s id="s.001554">Et nelle bilanzette piccole <lb/>&longs;e manifestar anno, cioe che far anno inclinatione ui&longs;ibile, & tutto questo, la &longs;perien­<lb/>tia lo manife&longs;ta. </s> <s id="s.001555">Perche &longs;e &longs;opra una di quelle &longs;opradette bilanze grande de Speciali, ui <lb/>&longs;ara posto un grano di formento. </s> <s id="s.001556">Eglie co&longs;a chiara, che nella maggior parte di quelle, <lb/>non fara alcuna ui&longs;ibil inclinatione. </s> <s id="s.001557">Et nella maggior parte di quelle piccolette che u&longs;a <lb/>no li Banchieri, far anno inclinatione molto cuidente. </s> <s id="s.001558">Ma uolendo poi con&longs;iderare, <lb/>giudicare, & dimo&longs;trare tal &longs;ua que&longs;tione, ouer conclu&longs;ione, &longs;i come Mathematico, <lb/>cioe fuora de ogni materia, &longs;enza dubbio tal &longs;ua conclu&longs;ione &longs;aria fal&longs;a, perche ogni <lb/>piccol pe&longs;o po&longs;to in qual &longs;e uoglia libra fara inclinar quella continuamente per fina <lb/>all'ultimo, ouer piu ba&longs;&longs;o luoco, che inclinar &longs;e po&longs;&longs;a, & tutto que&longs;to nelli principij del­<lb/>la &longs;cientia di pe&longs;i à Vo&longs;tra Signoria, lo faro manife&longs;to. </s> <s id="s.001559">Dapoi lui &longs;ottogionge anchora <lb/>que&longs;t'altra conclu&longs;ione, & dice in que&longs;ta forma. </s> <s id="s.001560">Et certamente &longs;ono alcuni pe&longs;i, le <lb/>quali &longs;ono manife&longs;ti nell'una, & l'altra &longs;orte de libre (cioe nelle maggiori, & nelle me <lb/>nori) ma molto piu nelle maggiori, perche molto piu granda inclinatione, uien fatta dal <lb/>mede&longs;imo pe&longs;o nelle maggiori. </s> <s id="s.001561">La qual conclu&longs;ione, uolendolo con&longs;iderare, giudicare, <lb/>& approuare, &longs;i come naturale (come fu detto dell'altra) cioe per uigore, & autorita <lb/>del &longs;en&longs;o del uedere, nelle dette libre materiale, certamente que&longs;ta non patira men op­<lb/>po&longs;itioni dell'altra, per le mede&longs;ime ragioni in quella adutte. </s> <s id="s.001562">Et &longs;imilmente, <expan abbr="uol&etilde;do">uolendo</expan> poi <lb/>con&longs;iderare, giudicare, & dimo&longs;trare tal conclu&longs;ione, come Mathematico, cioe fuora <lb/>de ogni materia mede&longs;imamente tal&longs;ua conclu&longs;ione &longs;aria fal&longs;a, perche ogni &longs;orte di pe <lb/>&longs;o po&longs;to in qual &longs;i uoglia &longs;orte de libra, fara inclinar quella de continuo per fina à tan <lb/>to che quella &longs;ia gionta all'ultimo, ouer piu ba&longs;&longs;o luoco, che quella inclinar &longs;i po&longs;&longs;a, & <lb/>tutto que&longs;to, nelli detti principij della &longs;cientia di pe&longs;i dimostr atiuamente à quella &longs;i fara <lb/>manife&longs;to.<emph.end type="italics"/> S.A. A<emph type="italics"/>nchor che tutte queste uo&longs;tre oppo&longs;itioni, & argomenti naturali, <lb/>habbiano del ueri&longs;imile non po&longs;&longs;o credere, che il non ue &longs;ia altre ragioni, & argo­<lb/>menti, &longs;i naturali, come Mathematici da poter difendere, & &longs;aluare, tal &longs;ua questione <lb/>in&longs;ieme con quell altre due conclu&longs;ioni. </s> <s id="s.001563">Anci è ho ferma opinione che chi &longs;tudia&longs;&longs;e con <pb xlink:href="042/01/159.jpg"/><expan abbr="dilig&etilde;tia">diligentia</expan> &longs;opra à tal materia, ritrouaria tutte <expan abbr="&qtilde;lle">qualle</expan> particolarita materiale, che &longs;ono cais <lb/>&longs;a, che tal que&longs;tione, & <expan abbr="cõclu&longs;ioni">conclu&longs;ioni</expan> <expan abbr="nõ">non</expan> &longs;e uerificano in materia, come che l'autor <expan abbr="cõchiu">conchiu</expan> <lb/>de, et dice. </s> <s id="s.001564">Et dapoi che quelle fu&longs;&longs;eno ritrouate, et cono&longs;ciute, <expan abbr="t&etilde;go">tengo</expan> che &longs;aria co&longs;a facile <lb/>à rimediarli, & fare che &longs;e uerifica&longs;&longs;eno in materia preci&longs;amente, come che l'autor <lb/>propone.<emph.end type="italics"/> N. V<emph type="italics"/>o&longs;tra Signoria non è di uana opinione, perche in effetto tutte quelle <lb/>co&longs;e che nella mente &longs;ono cono&longs;ciute uere, & maßime per dimo&longs;trationi a&longs;tratte da o­<lb/>gni materia, ragioneuolmente &longs;i debbono anchora uerificare al &longs;en&longs;o del uedere in ma­<lb/>teria (altramente le Mathematice &longs;ariano in tutto uane, & dinullo giouamento, ouer <lb/>profitto all'huomo, & &longs;e per ca&longs;o quelle non &longs;e uerificano, comc che nelle &longs;opradette li <lb/>bre, ouer bilance maggior, & menor, e &longs;tato detto, & di&longs;putato. </s> <s id="s.001565">Eglie da credere, anci <lb/>da tener per fermo, che il tutto proceda dalla di&longs;proportionalita, & inequalita delle <lb/>parti, & membri materiali, dalli quali uengono compo&longs;te, cioe che le dette parti, & <lb/>memibri dell'una piu &longs;e di&longs;co&longs;tano, ouer allontanano da quelle con&longs;iderate fuora de ogni <lb/>materia, di quello che fanno quelli dell'altra.<emph.end type="italics"/> E <emph type="italics"/>per tanto uolendo difendere, & &longs;alua­<lb/>re tal que&longs;tione Aristotelica, cioe far che quella &longs;empre &longs;e uerifichi in materia, & in <lb/>ogni qualita de libre, ouer bilance &longs;i grande, come piccole. </s> <s id="s.001566">Bi&longs;ogna agguagliar le dette <lb/>parti, ouer membri dicadauna di quelle, talmente che quelli &longs;iano egualmente di&longs;tanti <lb/>da quelle con&longs;iderate fuora de ogni materia &longs;en&longs;ibile. </s> <s id="s.001567">Ilche <expan abbr="fac&etilde;do">facendo</expan> non &longs;olamente &longs;e ue <lb/>rificara tal &longs;ua que&longs;tione al &longs;en&longs;o in materia, cioe nelle dette libre, ouer bilance materia <lb/>le, ma anchora &longs;e uerificaranno quelle altre due conclu&longs;ioni, che &longs;ottogion&longs;e in fine.<emph.end type="italics"/><lb/>S.A. I<emph type="italics"/>o ho accaro che la mia opinione &longs;e &longs;ia uerificata.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001568">QVESITO SECONDO FATTO CONSEQ VEN­<lb/><emph type="italics"/>temente dal mede&longs;imo Illustrißimo Signor Don <lb/>Diego Amba&longs;ciator <lb/>Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001569">SIGNOR AMBASCIATORE. M<emph type="italics"/>a per non hauer troppo ben inte&longs;o le <lb/>ragioni da uoi allegate, uorria che un'altra uolta, & piu chiar amente me le repli <lb/>casti.<emph.end type="italics"/> N. D<emph type="italics"/>ico Signore, che la cau&longs;a che le &longs;opradette libre, ouer bilance maggiore, <lb/>& menore, non ri&longs;pondeno &longs;econdo che l'autor conchiude, & dimo&longs;tra, non procede <lb/>d'altro, che dalla inequalita delle parti, ouer membrimateriali, dalli quali uengono com <lb/>po&longs;te, le quai parti, ouer membri, &longs;ono li dui bracci, & anchora il &longs;parto (cioe quel <lb/>axis ouer centro, &longs;opra del qual girano li detti bracci in cadauna de loro, perche li <lb/>detti bracci, & &longs;parto nelle libre, ouer bilance maggiore &longs;ono molto piu großi, & cor <lb/>pulenti di quelle delle menore. </s> <s id="s.001570">Et perche li bracci di quelle libre, ouer bilance che uen­<lb/>gono con&longs;iderate, come Mathematico, cioe fuora de ogni materia, &longs;ono con&longs;iderati, et <lb/>&longs;uppo&longs;ti, come &longs;implice linee, cioe &longs;enza larghezza, ne gro&longs;&longs;ezza, & il &longs;parto, ouer <lb/>axis di quelle uien con&longs;iderato, & &longs;uppo&longs;to un &longs;implice ponto indiui&longs;ibile, le qual &longs;orte <lb/>de libre, ouer <expan abbr="bilãce">bilance</expan>. </s> <s id="s.001571"><expan abbr="Quãdo">Quando</expan> che poßibil fo&longs;&longs;e à darne una co&longs;i realmente &longs;pogliata, & <lb/>nuda de ogni materia &longs;en&longs;ibile, come che con la <expan abbr="m&etilde;te">mente</expan> uengono con&longs;iderate, &longs;enza alcun<emph.end type="italics"/><pb pagenum="80" xlink:href="042/01/160.jpg"/><emph type="italics"/>dubbio quella &longs;aria agilißima, & diligentißima &longs;opra à tutte lelibre, ouer bilance ma <lb/>teriale, di quella mede&longs;ima grandezza, perche quella &longs;aria totalmente libera da ogni <lb/>material impedimento. </s> <s id="s.001572">Et per tanto conchiudendo dico, che quanto piu le parti, ouer <lb/>membri di una libra, ouer bilanza materiale, &longs;e acco&longs;tano, ouer appropinquano alle <lb/>parti, ouer membri della non materiale (qual è la originale, ouer ideale di tutte le mate <lb/>riale) tanto &longs;ara piu agile, & diligente di quelle che men ui &longs;e accostaranno, ouer ap­<lb/>propinquaranno (di quella mede&longs;ima grandezza') Et perche le parti, ouer membri di <lb/>quelle bilancette, che adoprano li Bancheri, & Gioieleri (di&longs;opra allegate) molto piu <lb/>&longs;e acco&longs;tano, ouer appropinquano alle parti, ouer membri della detta &longs;ua ideale, di <lb/>quello che fanno le parti, ouer membri di quelle libre, ouer bilance maggiori, che ado­<lb/>prano li Speciali (di&longs;opra allegate) perche li brazzetti delle dette bilancette piccole <lb/>&longs;ono &longs;ottilißimi, & quelli delle grande &longs;ono piu großi. </s> <s id="s.001573">Onde li &longs;ottili piu &longs;e acco&longs;tano <lb/>alla &longs;implice linea (quale manca de larghezza, & gro&longs;&longs;ezza) di quello fanno li piu <lb/>großi, & corpulenti, & &longs;imilmente il &longs;parto, ouer axis delle dette librette, ouer bilan­<lb/>cette piccole, è piccolino, & &longs;ottile, & quello delle grande, è piu grande, & gro&longs;&longs;o. <lb/></s> <s id="s.001574">Onde il detto &longs;parto delle dette bilancette piccole piu &longs;e accosta, ouer appropinqua al <lb/>&longs;parto della &longs;ua ideale (qual è un ponto indiui&longs;ibile) di quello fa il &longs;parto delle dette bi­<lb/>lance grande per e&longs;&longs;er piu grande, & gro&longs;&longs;o. </s> <s id="s.001575">Et que&longs;ta è la principal cau&longs;a che le &longs;opra <lb/>dette librette, ouer bilancette menori, &longs;e dimo&longs;trano al &longs;en&longs;o piu diligente delle mag­<lb/>giori, cofa totalmente contraria alla &longs;opra allegata Ari&longs;totelica que&longs;tione.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001576">QVESITO TERZO FATTO CONSE­<lb/><emph type="italics"/>quentemente dal mede&longs;imo Illu&longs;trißimo <lb/>Signor Don Diego Amba&longs;cia­<lb/>tor Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001577">SIGNOR AMBASCIAT ORE. B<emph type="italics"/>en in che modo &longs;i puo difendere, & <lb/>&longs;aluare tal&longs;ua que&longs;tione, cioe far che quella &longs;e uerifichi al &longs;en&longs;o in materia &longs;econ­<lb/>do che lui propone, ouer conchiude.<emph.end type="italics"/> N. B<emph type="italics"/>i&longs;ogna fondar&longs;e &longs;opra le libre, ouer bilan­<lb/>ce ideale, cioe &longs;opra quelle che uengono con&longs;iderate con la mente a&longs;tratte da ogni mate­<lb/>ria, & uedere in che co&longs;ale maggiore &longs;iano differente dalle menore, la qual co&longs;a e&longs;&longs;en <lb/>do o&longs;&longs;eruata nelle libre, ouer bilance materiale &longs;ara dife&longs;a, & &longs;aluata tal que&longs;tione Ari <lb/>&longs;totelica, cioe che quella &longs;empre &longs;e uerificara al &longs;en&longs;o nelle dette libre materiale.<emph.end type="italics"/> S. A. <lb/>N<emph type="italics"/>on ue intendo parlatime piu chiaro.<emph.end type="italics"/> N. D<emph type="italics"/>ico Signore, che à uoler difendere, & <lb/>&longs;aluare tal que&longs;tione, bi&longs;ogna fondar&longs;e, ouer regger&longs;i per le libre, ouer bilance idea­<lb/>le, cioe per quelle, che con la mente uengono con&longs;iderate fuora de ogni materia, & <lb/>uedere in che co&longs;a le maggiori &longs;iano differente dalle menori, &longs;opra la qual co&longs;a con­<lb/>&longs;iderando, & guardando, &longs;e trouara, che le dette libre, ouer bilance maggiori, nen <lb/>&longs;ono differente dalle menori, eccetto che nella longhezza di &longs;uoi bracci, & in tut­<lb/>te le altre co&longs;e &longs;e agguagliano, perche anchor che li bracci delle libre maggiori &longs;ia­<lb/>no piu longhi de quelli delle menori, tamen non &longs;ono ne piu großi, ne piu &longs;otti­<lb/>li de quelli, perche, &longs;i nelle maggiori, come nelle menori, &longs;ono con&longs;iderati, <pb xlink:href="042/01/161.jpg"/>come &longs;tmplice linee, le quale mancano dilarghezza, & gro&longs;&longs;ezza, e pero in larghez­<lb/>za, & gro&longs;&longs;ezza non ui è alcuna differentia. </s> <s id="s.001578">Et &longs;imilmente li &longs;parti, ouer axi delle li­<lb/>bre, ouer bilance maggiori &longs;ono eguali alli &longs;parti, ouer axi delle menori, perche &longs;i nelle <lb/>maggiori, come nelle menori &longs;ono con&longs;iderati, come &longs;implici ponti, li quali ponti per e&longs;­<lb/>&longs;er tutti indiui&longs;ibili, &longs;ono eguali, le qual co&longs;e e&longs;&longs;endo diligentemente o&longs;&longs;eruate nelle li­<lb/>bre, ouer bilance materiale, cioe che le maggiore non &longs;iano differente dalle menore, ec­<lb/>cetto che nella longhezza di &longs;uoi bracci, ma che in larghezza, et gro&longs;&longs;ezza &longs;iano egua <lb/>li, & co&longs;i li lor &longs;parti materiali &longs;enza dubbio in quelle, non &longs;olamente &longs;e uerificara al <lb/>&longs;en&longs;o quello, che Aristotile nella detta &longs;ua que&longs;tione conchiude. </s> <s id="s.001579">Ma anchora &longs;e uerifica <lb/>ranno, quelle altre due conclu&longs;ioni che ui &longs;ottogion&longs;e in fine.<emph.end type="italics"/> (A<emph type="italics"/>nchor che in a&longs;tratto, <lb/>cioe fuora de ognimateria, ambedue fal&longs;e &longs;iano, come che per li principij della &longs;cientia <lb/>di pe&longs;i à<emph.end type="italics"/> V.S. <emph type="italics"/>faro manife&longs;to.<emph.end type="italics"/>) E<emph type="italics"/>t &longs;iano le dette libre, ouer bilance di che qualita, mate­<lb/>ria, & condition fi uoglia, pur che o&longs;&longs;eruino la detta egualita nella gro&longs;&longs;ezza di detti <lb/>bracci, & &longs;partiloro.<emph.end type="italics"/> S.A. C<emph type="italics"/>ertamente che que&longs;to uo&longs;tro di&longs;cor&longs;o me piace a&longs;&longs;ai.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001580">QVESITO QVARTO FATTO CONSE­<lb/><emph type="italics"/>quentemente dal mede&longs;imo Illu&longs;trißimo Signor <lb/>Don Diego Amba&longs;ciator Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001581">SIGNOR AMBASCIATORE. M<emph type="italics"/>a &longs;e ben me aricordo uoi dicesti an­<lb/>chora nel principio del no&longs;tro ragionamento, che Ari&longs;totile pretermette, ouer ta <lb/>ce una que&longs;tione &longs;opra delle dette libre di non poca importantia, ouer &longs;peculatione, hor <lb/>ditemi, che que&longs;tione è que&longs;ta.<emph.end type="italics"/> N. S<emph type="italics"/>e<emph.end type="italics"/> V.S. <emph type="italics"/>ben &longs;e aricorda della &longs;ua &longs;econda que&longs;tione, <lb/>in quella lui mterrogatiuamente adimanda, & con&longs;equentemente dimo&longs;tra, perche cau <lb/>&longs;a quando che <gap/> &longs;parto &longs;era di&longs;opra della libra, & che l'uno di bracci di qu<gap/>lla da qual­<lb/>che pe&longs;o &longs;ia portato, ouer &longs;pinto à ba&longs;&longs;o, remo&longs;&longs;o che&longs;ia, ouer leuato uia quel tal pe&longs;o, <lb/>la detta libra di nuouo rea&longs;cende, & ritorna al &longs;uo primo luoco. </s> <s id="s.001582">Et &longs;e il detto &longs;parto é <lb/>di &longs;otto della detta libra, & che mede&longs;imamente l'uno di &longs;uoi bracci &longs;ia da qualche pe&longs;o <lb/>pur portato, ouer &longs;pinto à ba&longs;&longs;o remo&longs;&longs;o, ouer leuato che &longs;ia uia quel tal pe&longs;o la detta li <lb/>bra non rea&longs;cende, ne ritorna al &longs;uo primo luoco (come che fa nell'altra po&longs;itione) ma <lb/>rimane di&longs;otto, cioe à ba&longs;&longs;o. </s> <s id="s.001583">Hor dico, che lui pretermette, ouer tace un'altra que&longs;tio­<lb/>ne, che in que&longs;to luoco &longs;e conueneria, di molta maggior &longs;pcculatione di cadauna delle &longs;o­<lb/>pradette, la qual que&longs;tione è que&longs;ta. </s> <s id="s.001584">Perche cau&longs;a quando che il &longs;parto è preci&longs;amente <lb/>in e&longs;&longs;a libra, et che l'un di bracci di quella &longs;ta da qualche pe&longs;o portato, ouer urtato à ba&longs; <lb/>&longs;o, remo&longs;&longs;o, ouer ieuato che &longs;ia uia quel tal pe&longs;o, la detta libra di nuouo rea&longs;cende al &longs;uo <lb/>primo luoco, &longs;i come che fa anchora quella, che ha il &longs;parto di &longs;opra da lei.<emph.end type="italics"/> S. A. <lb/>Q<emph type="italics"/>ue&longs;ta mi pare una bella que&longs;tione, & molto piu remota dal no&longs;tro intelletto natu­<lb/>rale che le due &longs;opradette, & molto hauero accaro ad intendere la cau&longs;a di tal effetto, <lb/>ma prima noglio che me chiariti un dubbio, che nella mente me intona &longs;opra delle &longs;opra <lb/>allegate que&longs;iioni, il quale è que&longs;to.<emph.end type="italics"/></s> </p> <pb pagenum="81" xlink:href="042/01/162.jpg"/> <p type="head"> <s id="s.001585">QVESITO QVINTO FATO CONSE QVENTE­<lb/><emph type="italics"/>temente dal mede&longs;imo Illustrißimo Signor Don Diego, <lb/>Amba&longs;ciator Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001586">SIGNOR AMBASCIATORE. D<emph type="italics"/>oue &longs;e troua una libra, ouer bilanza <lb/>materiale, che il &longs;uo &longs;parto &longs;ia di &longs;opra, ouer di &longs;otto di quella, anci à me mi pare, <lb/>che il detto &longs;parto in tutte &longs;ia preci&longs;amente in e&longs;&longs;e libre, come, che nella uo&longs;tra terza <lb/>question &longs;e &longs;uppone, & non di &longs;opra, ne manco di &longs;otto.<emph.end type="italics"/> N. A<emph type="italics"/>nchor, che di tal &longs;orte <lb/>bilance non &longs;i faccia, ouer &longs;i troui el non re&longs;ta pero, chel non &longs;e ne pote&longs;&longs;e fare.<emph.end type="italics"/> S.A. <lb/><!-- KEEP S--></s> <s id="s.001587">A <emph type="italics"/>me mi pare una materia, à mouer que&longs;tione &longs;opra à <expan abbr="cō&longs;e">con&longs;e</expan>, che non &longs;i costumano, ne &longs;i <lb/>trouino in eßere.<emph.end type="italics"/> N. I<emph type="italics"/>l tutto &longs;ifa Signore, perche tutti li artificio&longs;i i&longs;tromenti, che <lb/>per augumentare le forze del huomo &longs;e oprano, in qual &longs;i uoglia arte Mechanica &longs;e re <lb/>feri&longs;cono à una delle &longs;opradettetre &longs;pecie de libre, ouer bilance, et co&longs;i in ogni dubbio, <lb/>ouer que&longs;tione, che &longs;opra ad alcuno de tai i&longs;tromenti na&longs;cer pote&longs;&longs;e, uolendone cono&longs;ce <lb/>re, ouer aßignare la intrin&longs;ica cau&longs;a. </s> <s id="s.001588">Eglie nece&longs;&longs;ario prima uenir a quella &longs;orte libra, <lb/>ouer bilanza, alla qual piu &longs;e referi&longs;&longs;e quel tal i&longs;tromento, & dalla detta libra, ouer bi <lb/>lanza &longs;e uien al cerchio, per la mirabil uirtu, & potentia del qnale &longs;e ri&longs;olue il tutto, <lb/>come, che nella &longs;cientia di pe&longs;i &longs;i fara manife&longs;to.<emph.end type="italics"/> S. A. E<emph type="italics"/>&longs;&longs;endo adunque co&longs;e di tan­<lb/>ta importantia, uoglio, che me replicati, & dimo&longs;trati figuralmente cadauna de det <lb/>te tre Que&longs;tioni, ouer parti a una per una: perche le uoglio ben intendere, & comin­<lb/>ciati alla prima.<emph.end type="italics"/> N. P<emph type="italics"/>er dimo&longs;trar in figura la prima parte di tal Que&longs;tione. </s> <s id="s.001589">Sia la <lb/>libra. </s> <s id="s.001590">a. <!-- REMOVE S-->b. <!-- REMOVE S-->el &longs;parto della quale &longs;ia el ponto. </s> <s id="s.001591">c. (qual &longs;parto &longs;ia alquanto di &longs;opra del­<lb/>la detta libra.a. </s> <s id="s.001592">b. <!-- REMOVE S-->come nella figura appare) & &longs;ia che per la impo&longs;itione del pe&longs;o. </s> <s id="s.001593">e. <lb/><!-- REMOVE S-->el &longs;uo brazzo. </s> <s id="s.001594">a. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.001595">&longs;ia da quel tirato a ba&longs;&longs;o, come che di &longs;otto appare in detta figu <lb/>ra: hor dico, che chileua&longs;&longs;euia el detto pe&longs;o.e.tal brazzo. </s> <s id="s.001596">a. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.001597">rea&longs;cendaria, &<emph.end type="italics"/><lb/><figure id="id.042.01.162.1.jpg" xlink:href="042/01/162/1.jpg"/><lb/><emph type="italics"/>retornaria al &longs;uo primo, & condecente luoco, el qual luoco &longs;aria nel ponto, ouer <lb/>&longs;ito.<emph.end type="italics"/> k. <emph type="italics"/>& co&longs;i l'altro brazzo. </s> <s id="s.001598">d. <!-- KEEP S--></s> <s id="s.001599">b. <!-- REMOVE S-->de&longs;cendaria per fina al ponto, ouer &longs;ito. </s> <s id="s.001600">l. <!-- KEEP S--></s> <s id="s.001601">& <lb/>tutto que&longs;to procede: perche nel tra&longs;portar el detto brazzo. </s> <s id="s.001602">a. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.001603">a ba&longs;&longs;o, piu del­<lb/>la mitta di tutto el fu&longs;to della detta libra. </s> <s id="s.001604">a. <!-- REMOVE S-->b. <!-- REMOVE S-->&longs;e uien a trasferrir&longs;i in alto, cioe <lb/>oltra la perpendicolar.n.m. </s> <s id="s.001605">pa&longs;&longs;ante per il &longs;parto.c.la qual perpendicolar &longs;e chiama<emph.end type="italics"/><pb xlink:href="042/01/163.jpg"/><emph type="italics"/>la lined della direttione, cioe, che la parte.b.d. </s> <s id="s.001606">g. <!-- REMOVE S-->in alto elleuata uien à e&longs;&longs;er tan­<lb/>to piu della mita de tutto el fu&longs;to.a.b.quanto che è dal.d.al.g.& la re&longs;tante parte.a.g. <lb/></s> <s id="s.001607">ridutta al ba&longs;&longs;o uien à e&longs;&longs;er tanto manco della mita di tutto el detto fu&longs;to.a.b. </s> <s id="s.001608">quanto <lb/>che è dal detto ponto.g.al ponto.d. </s> <s id="s.001609">perche adunque tal parte.b.d.g.in alto elleuata è <lb/>molto maggiore del restante brazzo.a.g.al ba&longs;&longs;o trasferto, leuando&longs;e uia el detto pe­<lb/>&longs;o.e.la detta parte.a.g. (piu debole) uien à eßer urtata, & &longs;pinta dall'altra maggior <lb/>parte.b.d.g.in alto elleuata (per e&longs;&longs;er di lei piu potente) per fin à tanto, che la detta li <lb/>nea della direttione ca&longs;chi perpendicolarmente &longs;opra el detto fu&longs;to, ouer libra.a.b. </s> <s id="s.001610">& <lb/>che &longs;eghi quello in due parti equali in ponto.d.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;taragion è qua&longs;i &longs;imile à <lb/>quella che aduce Ari&longs;totile, ma è alquanto piu chiara, & miglior figura.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001611">QVESITO SESTO FATTO CONSE­<lb/><emph type="italics"/>quentemente dal mede&longs;imo Illu&longs;trißimo Signor <lb/>Don Diego Amba&longs;ciator Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001612">SIGNOR AMBASCIATORE. H<emph type="italics"/>or &longs;eguitati la &longs;econda parte.<emph.end type="italics"/> N. <lb/>P<emph type="italics"/>er dimo&longs;trare la &longs;econda à uo&longs;tra Signoria. </s> <s id="s.001613">Pongo &longs;ia la libra.a. </s> <s id="s.001614">b. <!-- REMOVE S-->la qual hab­<lb/>bia il &longs;parto (cioe quel ponto, ouer polo, &longs;opra del qual lei gira) alquanto di &longs;otto, cioe <lb/>di&longs;otto dal fu&longs;to.a.b.come di&longs;otto appar in ponto.c. </s> <s id="s.001615">& &longs;ia anchor, che per la impo&longs;i­<lb/>tion del pe&longs;o.e.el &longs;uo brazzo.a.d.&longs;ia da quel tirato à ba&longs;&longs;o, come che di &longs;otto nella figu <lb/>ra appar, hor dico, che chi leua&longs;&longs;e uia el detto pe&longs;o.e.tal brazzo nonrea&longs;cenderia ne ri <lb/>tornaria al &longs;uo primo luoco, cioe in ponto.<emph.end type="italics"/> k. <emph type="italics"/>(come, che fa in quella, che ha il &longs;parto di <lb/>&longs;opra) ma rc&longs;taria co&longs;i inclinato à ba&longs;&longs;o, & la cau&longs;a di que&longs;to procede, perche nel tra <lb/>&longs;portar&longs;e el detto brazzo.a.d.al ba&longs;&longs;o piu della mitta di tutto el fu&longs;to, ouer libra.a.b.<emph.end type="italics"/><lb/><figure id="id.042.01.163.1.jpg" xlink:href="042/01/163/1.jpg"/><lb/><emph type="italics"/>&longs;i uien à trasferire drio à quello, oltra la linea della direttione, cioe oltra la perpendi­<lb/>colar.n.m.qual pa&longs;&longs;a per il &longs;parto.c.tal che tutta la parte.a.g. </s> <s id="s.001616">al ba&longs;&longs;o ridutta, uien à <lb/>e&longs;&longs;er tanto piu della mitta di tutta la libra.a.b.quanto, che è dal.d.al.g. </s> <s id="s.001617">& la parte.g. <lb/></s> <s id="s.001618">b. <!-- REMOVE S-->in alto elleuata uien à re&longs;tare tanto meno della detta mitta, quanto, che è dal detto.d. <lb/></s> <s id="s.001619">al detto.g.per e&longs;&longs;er adunque la elleuata parte.g.b.di menor quantita della inelinata.a. <lb/></s> <s id="s.001620">g.uien à e&longs;&longs;er piu debole, ouer men potente di lei, e pero, non é atta, ne <expan abbr="&longs;offici&etilde;te">&longs;officiente</expan> à po-<emph.end type="italics"/><pb pagenum="82" xlink:href="042/01/164.jpg"/><emph type="italics"/>terla urtare, & sforzare à farla a&longs;cendere al &longs;uo primo luoco in.<emph.end type="italics"/> k. <emph type="italics"/>come fece nella pa&longs; <lb/>&longs;ata, anci quella restara co&longs;i inclinata al ba&longs;&longs;o, & la retenera lei co&longs;i in aere clleuata, <lb/>che è il propo&longs;ito.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ueste due parti qua&longs;i, che il no&longs;tro intelletto le apprende <lb/>per ragion naturale, &longs;enza altra dimo&longs;tratione.<emph.end type="italics"/> N. C<emph type="italics"/>o&longs;t è Signore.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.001621">QVESITO SETTIMO FATTO CONSEQ VENTEMEN­<lb/><emph type="italics"/>te dal mede&longs;imo Illustrißimo Signor Don Diego, <lb/>Amba&longs;ciator Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001622">SIGNOR AMBASCIATORE. H<emph type="italics"/>or &longs;eguitati mo la terza parte, quale <lb/>diceti, che manca in que&longs;to luoco, cioe doue na&longs;ce la cau&longs;a, che quando el &longs;parto de <lb/>una libra &longs;ara preci&longs;amente nel mezzo di e&longs;&longs;a, cioe ne di &longs;otto, ne di &longs;opra, ma nel me<emph.end type="italics"/>z <lb/><emph type="italics"/>zo di quella, come, che &longs;ono tutte le libre, ouer bilance, che communamente &longs;e oprano, <lb/>& che l'uno di bra<emph.end type="italics"/>zz<emph type="italics"/>i di quella &longs;ia da qualche pe&longs;o (ouer dalla no&longs;tra mano) urtato à <lb/>ba&longs;&longs;o, leuado, che &longs;ia uia quel tal pe&longs;o (ouer mano) immediate tal bra<emph.end type="italics"/>zz<emph type="italics"/>o ria&longs;cende, et <lb/>ritorna al &longs;uo primo luoco &longs;i come che anchor fa <expan abbr="&qtilde;lla">qualla</expan> libra, qual <expan abbr="ti&etilde;">tiem</expan> il &longs;parto di &longs;opra <lb/>da e&longs;&longs;a libra. </s> <s id="s.001623">Perche in effetto la cau&longs;a di que&longs;to ultimo effetto mi par molto piu remo <lb/>ta dal no&longs;tro intelletto de cadauna delle altre due.<emph.end type="italics"/> N. E<emph type="italics"/>ho detto à uo&longs;tra Signoria, <lb/>che à uoler dimostrare la cau&longs;a di tal effetto à me è neceßario à diffinire, & dechiari­<lb/>re prima à uo&longs;tra Signoria alcuni termini, & principij della &longs;cientia di pe&longs;i.<emph.end type="italics"/> S.A. S<emph type="italics"/>o <lb/>no co&longs;a longa questi principij, che ui bi&longs;ogna dechiarare.<emph.end type="italics"/> N. P<emph type="italics"/>er <expan abbr="quãto">quanto</expan> a&longs;petta à uo <lb/>ler demo&longs;tr are &longs;implicemente que&longs;ta particolarita &longs;ara co&longs;a breuißima, uero è, che <lb/>quando, che uo&longs;tra &longs;ignoria uole&longs;&longs;e intendere ordinariamente tutti li principij di tal <lb/>&longs;cientia, ui &longs;aria da dire a&longs;&longs;ai.<emph.end type="italics"/> S.A. B<emph type="italics"/>en&longs;a, che uoglio intendere il tutto <expan abbr="ordinariam&etilde;">ordinariamen</expan> <lb/>te, come &longs;i de.<emph.end type="italics"/> N. L'<emph type="italics"/>hora è tarda Signore per far que&longs;to effetto.<emph.end type="italics"/> S.A. B<emph type="italics"/>en andati, <lb/>& ritornati dimane da mattina.<emph.end type="italics"/> N. R<emph type="italics"/>itornaro Signore.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.001624">I<emph type="italics"/>l fine del &longs;ettimo Libro.<emph.end type="italics"/><!-- KEEP S--></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/165.jpg"/> <p type="head"> <s id="s.001625">LIBRO OTTAVO DELLI <lb/>QVESITI, ET INVENTIONI DIVERSE, <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001626">S<emph type="italics"/>oprala Scientia di Pe&longs;i.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001627">QVESITO PRIMO FATTO DAL ILLVSTRISS.<!-- REMOVE S-->S<emph type="italics"/>ignor Don Diego Hurtado di Mendozza, Amba&longs;ciator <lb/>Ce&longs;areo in Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001628">SIGNOR AMBASCIATORE. H<emph type="italics"/>or uoria Tartaglia, <lb/>che me incomenciasti à dechiarire ordinariamente quella &longs;cien­<lb/>tia de pe&longs;i, di che me parla&longs;ti hiæri. </s> <s id="s.001629">Ma, perche cono&longs;co tal &longs;cien <lb/>tia non e&longs;&longs;er &longs;emplicemente per &longs;e (per non e&longs;&longs;er le arte liberale, <lb/>&longs;aluo che &longs;ette) ma &longs;ubalternata, uoria che prima me dice&longs;ti, da <lb/>che &longs;cientia, ouer di&longs;ciplina quella deriui, & na&longs;ci.<emph.end type="italics"/> N. S<emph type="italics"/>ignor <lb/>Clarißimo parte di que&longs;ta&longs;cientia na&longs;ce, ouer deriua dalla Geo­<lb/>metria, & parte dalla Natur al Philo&longs;ophia: perche, parte delle &longs;ue conclu&longs;ioni &longs;e dimo <lb/>&longs;trano Geometricamente, & parte &longs;e approuano Phy&longs;icalmente, cioe naturalmente.<emph.end type="italics"/><lb/>S.A. <!-- KEEP S--></s> <s id="s.001630">E <emph type="italics"/>ue ho inte&longs;o circa questa particolarita.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001631">QVESITO SECONDO FATTO CONSEQ VEN­<lb/><emph type="italics"/>temente dal mede&longs;imo Illustrißimo Signor Don <lb/>Diego Amba&longs;ciator <lb/>Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001632">SIGNOR AMBASCIATORE. M<emph type="italics"/>a ditime anchora, che co&longs;trutto &longs;i puo <lb/>cauar di tal &longs;cientia.<emph.end type="italics"/> N. L<emph type="italics"/>i co&longs;trutti, che di tal &longs;cientia &longs;i potriano cauare, &longs;a­<lb/>ria qua&longs;i impoßibile à poterli à uo&longs;tra Signoria i&longs;primere, ouer connumerare, nondi­<lb/>meno io ue referiro quelli, che per al pre&longs;ente à me &longs;ono manife&longs;ti. </s> <s id="s.001633">Et per tanto dico, <lb/>che primamente per uigore di tal &longs;cientia, eglie poßibile à cono&longs;cere, & mi&longs;urare con <lb/>ragione la uirtu, & potentia di tutti que&longs;ti i&longs;tromenti Mechanici, che da no&longs;tri anti­<lb/>qui &longs;ono &longs;tati ritrouati, per augumentare la forza de l'huomo, nel elleuare, condurre, <lb/>ouer &longs;pingere auanti ogni graue pe&longs;o cioe in qual &longs;i uoglia grandezza, che quelli &longs;iano <lb/>con&longs;tituidi, ouer fabricati, &longs;econdariamente per uirtu di tal &longs;cientia, non &longs;olamente <lb/>eglie poßibile di poter con ragion cono&longs;cere, & mi&longs;urare &longs;implicemente la forza de <lb/>l'huomo, ma anchora eglie poßibile di trouar el modo di augumentar quella in infini­<lb/>to, & in uarij modi, & co&longs;i in qual &longs;i uoglia modo eglie poßibile à cono&longs;cere l'ordine, <lb/>& proportione di tal augumentatione, come, che in fine con uarij i&longs;tromenti Mecha­<lb/>nici à Vo&longs;tra Signoria faro cono&longs;cere, & uedere.<emph.end type="italics"/> S. A. Q<emph type="italics"/>uesto hauero molto <lb/>accaro.<emph.end type="italics"/></s> </p> <pb pagenum="83" xlink:href="042/01/166.jpg"/> <p type="head"> <s id="s.001634">QVESITO TERZO FATTO CONSE­<lb/><emph type="italics"/>quentemente dal mede&longs;imo Illu&longs;trißimo Signor <lb/>Don Diego Amba&longs;cia <lb/>tor Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001635">SIGNOR AMBASCIAT ORE. H<emph type="italics"/>or &longs;eguitati, come ui pare circa à tal <lb/>&longs;cientia.<emph.end type="italics"/> N. P<emph type="italics"/>er procedere regolatamente, hoggi diffiniremo &longs;olamente alcuni <lb/>termini, & modi di parlare occorrenti in que&longs;ta &longs;cientia, accio che il frutto della intel <lb/>ligentia di quella,<emph.end type="italics"/> V.S.<emph type="italics"/>piu facilmente apprenda. </s> <s id="s.001636">Dimane poi dichiariremo li principij <lb/>di tal &longs;cientia, cioe quelle co&longs;e che in tal &longs;cientia non &longs;i po&longs;&longs;ono dimo&longs;trare, perche (co <lb/>me che<emph.end type="italics"/> V.S. <emph type="italics"/>&longs;a) ogni &longs;cientia ha li &longs;uoi primi princpij indemo&longs;trabili, li quali e&longs;&longs;endo <lb/>do conceßi, ouer &longs;uppo&longs;ti per lor meggio &longs;i di&longs;puta, & &longs;o&longs;tenta tutta la &longs;cientia, dapoi <lb/>que&longs;to andaremo preponendo uarie propo&longs;itioni, ouer conclu&longs;ioni &longs;opra di tal &longs;cien­<lb/>tia, & parte de quelle dimostraremo à<emph.end type="italics"/> V.S. <emph type="italics"/>con argomenti Geometrici, & parte ap­<lb/>prouaremo con ragioni naturali, come di &longs;opra dißi. </s> <s id="s.001637">Et dapoi questo,<emph.end type="italics"/> V.S. <emph type="italics"/>preponera <lb/>tutti quei dubbij, ouer que&longs;tioni che à quella gli parera, nelle co&longs;e Mecanice, & maßi­<lb/>me &longs;opra li mir abili effetti delli &longs;opradetti i&longs;tromenti materiali che augumentano la <lb/>forza dell'huomo, che per le co&longs;e dette, & approbate, nella detta &longs;cientia de pe&longs;i, tutte <lb/>&longs;e re&longs;olueranno.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;to uo&longs;tro procedere co&longs;i regolatamente molto mi piace.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001638">QVESITO QVARTO FATTO CONSE­<lb/><emph type="italics"/>quentemente dal mede&longs;imo Illu&longs;trißimo Signor Don <lb/>Diego Amba&longs;ciator Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001639">SIGNOR AMBASCIATORE. H<emph type="italics"/>or &longs;eguitate adunque le dette diffini­<lb/>tioni con&longs;equentemente.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001640">QVESITO. IIII. DIFFINITIONE PRIMA.</s> </p> <p type="main"> <s id="s.001641">Li <emph type="italics"/>corpi&longs;e dicono di grandezza eguali, quando che quelli occupano, ouer empi­<lb/>no luochi eguali.<emph.end type="italics"/> S.A. D<emph type="italics"/>atemi qualche material e&longs;&longs;empio.<emph.end type="italics"/> N. E<emph type="italics"/>&longs;&longs;empi gra <lb/>tia, doi corpi &longs;pherici gettati, ouer prontati in una mede&longs;ima forma, ouer in forme e­<lb/>guale, &longs;e diriano eguali di grandezza, anchor che fu&longs;&longs;eno di materia diuer&longs;a, cioe che <lb/>l'uno fu&longs;&longs;e di piombo, & l'altro di ferro, ouer di pietra, & co&longs;i &longs;i debbe intendere in <lb/>qual &longs;i uoglia altra diuer&longs;ita di forma.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.001642">E <emph type="italics"/>ue ho inte&longs;o, &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001643">QVESITO. V. DIFFINITIONE II.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001644">Si<emph type="italics"/>milmente li corpi &longs;e dicono di grandezza diuer&longs;i, ouer ineguali, quando che <lb/>quelli occupano, ouer empino luochi diuer&longs;i, ouer ineguali. </s> <s id="s.001645">Et maggiore &longs;e in­<lb/>tende quello, che occupa maggior luoco.<emph.end type="italics"/> S. AMBASCIA. </s> <s id="s.001646">E <emph type="italics"/>ue ho inte&longs;o, <lb/>&longs;eguitati.<emph.end type="italics"/> NIC. <!-- KEEP S--></s> </p> <pb xlink:href="042/01/167.jpg"/> <p type="head"> <s id="s.001647">QVESITO. VI. DIFFINITIONE TERZA.</s> </p> <p type="main"> <s id="s.001648">La <emph type="italics"/>uertu d'un corpo graue &longs;e intende, & piglia per quella potentia, che lui ha da <lb/>tendere, ouer di andare al ba&longs;&longs;o, & anchora da re&longs;i&longs;tere al moto contrario, cioe <lb/>à che il uole&longs;&longs;e tirar in &longs;u&longs;o.<emph.end type="italics"/> S.A. Q<emph type="italics"/>uando che non ui dico altro &longs;eguitati, perche col <lb/>mio tacere, e ue dinoto hauerui inte&longs;o, & che debbiati &longs;eguitare.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001649">QVESITO. VII. DIFFINITIONE QVARTA.</s> </p> <p type="main"> <s id="s.001650">Li <emph type="italics"/>corpi &longs;e dicono de uertu, ouer potentia, equali, quando che quelli in tempi egua <lb/>li di moto pertran&longs;i&longs;cono &longs;pacij eguali.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001651">QVESITO. VIII. DIFFINITIONE QVINTA.</s> </p> <p type="main"> <s id="s.001652">Li <emph type="italics"/>corpi &longs;e dicono de uertu, ouer potentia diuer&longs;a, quando che quelli in tempi di­<lb/>uer&longs;i, pertran&longs;i&longs;cono di moto, &longs;pacij eguali, ouer che in tempi eguali pertran&longs;i­<lb/>&longs;cono interualli ineguali.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001653">QVESITO. IX. DIFFINITIONE SESTA.</s> </p> <p type="main"> <s id="s.001654">La <emph type="italics"/>uertu, ouer potentia de corpi diuer&longs;i, quella &longs;e intende e&longs;&longs;er maggiore, la qua <lb/>le nel pertran&longs;ire uno mede&longs;imo &longs;pacio &longs;umme manco tempo. </s> <s id="s.001655">Et menor quella <lb/>che &longs;umme piu tempo, ouer amente quella che in tempi eguali pertran&longs;i&longs;&longs;e mag­<lb/>gior &longs;pacio.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001656">QVESITO. X. DIFFINITIONE SETTIMA.</s> </p> <p type="main"> <s id="s.001657">Qv<emph type="italics"/>elli corpi &longs;e dicono e&longs;&longs;ere di uno mede&longs;imo genere, quando che &longs;ono di egual <lb/>grandezza, & che &longs;ono anchora di egual uertu, ouer potentia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001658">QVESITO. XI. DIFFINITIONE OTTAVA.</s> </p> <p type="main"> <s id="s.001659">Qv<emph type="italics"/>ellicorpi &longs;e dicono e&longs;&longs;ere de diuer&longs;i generi, quando che &longs;ono di egual gran­<lb/>dezza, & che non &longs;ono di egual uertu, ouer potentia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001660">QVESITO. XII. DIFFINITIONE NONA.</s> </p> <p type="main"> <s id="s.001661">Qv<emph type="italics"/>elli corpi &longs;e dicono e&longs;&longs;ere &longs;implicemente eguali in grauita, li quali &longs;ono real­<lb/>mente di egual pe&longs;o, anchor che fu&longs;&longs;eno dimateria diuer&longs;a.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001662">QVESITO. XIII. DIFFINITIO­<lb/>NE DECIMA.</s> </p> <pb pagenum="84" xlink:href="042/01/168.jpg"/> <p type="main"> <s id="s.001663">Vn <emph type="italics"/>corpo &longs;e dice e&longs;&longs;ere &longs;iinplicemente piu graue d'un'altro, quando che quello <lb/>è realmente piu pondero&longs;o di quello, anchor che fu&longs;&longs;e di materia diuer&longs;a.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001664">QVESITO. XIIII. DIFFINITIONE XI.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001665">Vn <emph type="italics"/>corpo &longs;e dice e&longs;&longs;ere piu graue d'un'altro &longs;econdo la &longs;pecie, quando che la &longs;o­<lb/>&longs;tantia material di quello è piu pondero&longs;a della &longs;o&longs;tantia material dell'altro, co­<lb/>me che è il piombo del ferro, & altri &longs;imili.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001666">QVESITO. XV. DIFFINITIONE XII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001667">Vn <emph type="italics"/>corpo &longs;e dice e&longs;&longs;ere piu, ouer men graue d'un'altro nel de&longs;cendere, quando <lb/>che la rettitudine, obliquita, ouer dependentia del luoco, ouer &longs;pacio doue de­<lb/>&longs;cende lo fa de&longs;cendere piu, ouer men graue dell'altro, & &longs;imilmente piu, ouer menue­<lb/>loce dell'altro, anchor che &longs;iano ambidui &longs;implicemente eguali in grauita.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001668">QVESITO. XVI. DIFFINITIONE XIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001669">Vn <emph type="italics"/>corpo &longs;i dice e&longs;&longs;ere piu graue, ouer men graue d'un'altro, &longs;econdo il luoco, <lb/>ouer &longs;ito, quando che la qualita del luoco doue che lui &longs;eripo&longs;a, & giace, lo fa <lb/>e&longs;&longs;ere piu graue dell'altro anchor che fu&longs;&longs;eno &longs;implicemente egualmente gr aui.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001670">QVESITO. XVII. DIFFINITIONE XIIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001671">La <emph type="italics"/>grauita d'un corpo &longs;e dice e&longs;&longs;erenota, quando che il numero delle libre, che <lb/>lui pe&longs;ane &longs;ia noto, ouer altra denomination de pe&longs;o.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001672">QVESITO. XVIII. DIFFINITIONE XV.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001673">Li <emph type="italics"/>bracci de una libra, ouer bilancia &longs;e dicono e&longs;&longs;ere nel &longs;ito, ouer luoco della e­<lb/>qualita, quando che quelli &longs;tanno equidi&longs;tanti al piano dell'Orizonte.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.001674">QVESITO. XIX. DIFFINITIONE XVI.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001675">La <emph type="italics"/>linea della diretttione é una linearetta imaginata uenire perpendicolarmen­<lb/>te da alto al ba&longs;&longs;o, & pa&longs;&longs;are per il &longs;parto, polo, ouer aßis de ogni &longs;orte libra, <lb/>ouer bilancia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001676">QVESITO. XX. DIFFINITIONE XVII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001677">Pi<emph type="italics"/>u obliquo &longs;e dice e&longs;&longs;ere quel de&longs;cen&longs;o, d'un corpo graue, il quale in una mede&longs;i­<lb/>ma quantita, capi&longs;&longs;e manco della linea della direttione, oueramente del de&longs;cen&longs;o <pb xlink:href="042/01/169.jpg"/>vetto uer&longs;o il centro del mondo.<emph.end type="italics"/> S. A. I<emph type="italics"/>n que&longs;ta non ue intendo troppo bene. </s> <s id="s.001678">e pero <lb/>datemi uno e&longs;&longs;empio.<emph.end type="italics"/> N. P<emph type="italics"/>er e&longs;&longs;emplificare que&longs;ta diffinitione &longs;ia il corpo.a. <!-- REMOVE S-->& il <lb/>retto de&longs;cen&longs;o di quello uer&longs;o il centro del mondo &longs;ia la linea.a.b. </s> <s id="s.001679">& &longs;ia anchora li de­<lb/>&longs;cen&longs;i.a.c. </s> <s id="s.001680">&. </s> <s id="s.001681">a.d. <!-- REMOVE S-->& de que&longs;ti dui ne &longs;ia &longs;ignati le due quantita, ouer parti.a.e. </s> <s id="s.001682">&. </s> <s id="s.001683">a.f. <lb/><!-- REMOVE S-->eguale, & dalli dui ponti.e. </s> <s id="s.001684">&. </s> <s id="s.001685">f. <!-- REMOVE S-->&longs;iano tirate le <lb/>due linee.e.g. </s> <s id="s.001686">&. </s> <s id="s.001687">f.h. <!-- REMOVE S-->equidi&longs;tanti al piano del­<lb/>l'Orizonte, e perche la parte.a.b.è menore della <lb/>parte.a.g. </s> <s id="s.001688">il de&longs;cen&longs;o.a.f.d.&longs;e dira e&longs;&longs;er piu obli <lb/>quo del de&longs;cen&longs;o.a.e.c.perche lui capi&longs;&longs;e manco <lb/>del de&longs;cen&longs;o retto, cioe della linea.a.b.in una me <lb/>de&longs;ima quantita. </s> <s id="s.001689">Et que&longs;to mede&longs;imo &longs;i debbe in­<lb/>tendere in tutti li de&longs;cen&longs;i che pote&longs;&longs;e fare il det­<lb/>to corpo.a. (ouer altro &longs;imile) &longs;tante appe&longs;o al <lb/>al braccio di alcuna libra, cioe che quel de&longs;cen&longs;o <lb/>&longs;e dira e&longs;&longs;er piu obliquo, che per lo mede&longs;imo mo <lb/>do capira manco della linea della direttione, in <lb/>una mede&longs;ima quantita de de&longs;cen&longs;o.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.001690">E <emph type="italics"/>ue<emph.end type="italics"/><lb/><figure id="id.042.01.169.1.jpg" xlink:href="042/01/169/1.jpg"/><lb/><emph type="italics"/>ho inte&longs;o à&longs;officientia, e pero &longs;eguitati &longs;e haueti altra co&longs;a da diffinire.<emph.end type="italics"/> N. S<emph type="italics"/>ignore <lb/>que&longs;ta é la ultima co&longs;a che habbiamo da diffinire &longs;opra à que&longs;ta materia. </s> <s id="s.001691">Dimane poi <lb/>dichiariremo li principij di que&longs;ta &longs;cientia, <expan abbr="&longs;ecõdo">&longs;econdo</expan> la prome&longs;&longs;a.<emph.end type="italics"/> S.A. A<emph type="italics"/>lla bon'hord.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001692">QVESITO. XXI. FATTO CONSE­<lb/><emph type="italics"/>quentemente dal mede&longs;imo Illu&longs;trißimo Signor <lb/>Don Diego Amba&longs;ciator Ce&longs;areo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001693">SIGNOR AMBASCIATORE. H<emph type="italics"/>or &longs;eguitati Tartaglia questi uo&longs;tri <lb/>principij.<emph.end type="italics"/> N. L<emph type="italics"/>iprincipij de qual &longs;i uoglia &longs;cientia alcuni uogliano che &longs;iano det <lb/>ti dignita, perche quelli approuano altri, & loro non ponno e&longs;&longs;ere approuati da altri, <lb/>alcuni le chiamano &longs;uppo&longs;itioni, perche &longs;e &longs;uppongono per ueri in detta &longs;cientia, altri <lb/>piacque chiamarli petitioni, perche uolendo di&longs;putare tal &longs;cientia, & quella &longs;o&longs;tentare <lb/>con dimo&longs;trationi, bi&longs;ogna prima adimandar e all'auer&longs;ario la conceßione de quelli, <lb/>perche &longs;e lui non li uole&longs;&longs;e concedere (ma negare) &longs;aria negata tutta la &longs;cientia, ne ui <lb/>occorreria à di&longs;putarla altr amente. </s> <s id="s.001694">Et perche que&longs;ta ultima opinione mi piace alqnan­<lb/>to piu delle altre due, petitioni le chiamaremo, & co&longs;i anchora in forma de petitioni <lb/>li proferiremo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001695">QVESITO. XXII. PETITIONE PRIM A.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001696"><emph type="italics"/>&<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001697">Ad<emph type="italics"/>imandamo che ne &longs;ia conce&longs;&longs;o, che il mouimento natur ale de ogni corpo pon­<lb/>dero&longs;o, e graue &longs;ia rettamente uer&longs;o il centro del mondo.<emph.end type="italics"/> S. AMB. Q<emph type="italics"/>ue&longs;to <lb/>non è da negare.<emph.end type="italics"/></s> </p> <pb pagenum="85" xlink:href="042/01/170.jpg"/> <p type="head"> <s id="s.001698">QVESITO XXIII. PETITIONE II.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001699">Si<emph type="italics"/>melmente adimandamo, che na&longs;ia conce&longs;&longs;o quel corpo, ch'è di maggior potentia <lb/>debbia anchora di&longs;cendere piu uelocemente, et nelli moti contrarij, cioe nelli <expan abbr="a&longs;c&etilde;-&longs;i">a&longs;cen­<lb/>&longs;i</expan>, a&longs;cendere piu pigramente, dico nella libra.<emph.end type="italics"/> S.A. D<emph type="italics"/>atime uno e&longs;&longs;empio materiale <lb/>&longs;opra di que&longs;ta petitione, &longs;e uoleti, che ue intenda.<emph.end type="italics"/> N. S<emph type="italics"/>ia, e&longs;&longs;empi gratia, le due li­<lb/>bre.a.b.c. </s> <s id="s.001700">&. </s> <s id="s.001701">d.e.f.equali, cioe, che li dui brazzi. </s> <s id="s.001702">a.b. <!-- REMOVE S-->&. </s> <s id="s.001703">b.c.&longs;iano equali alli dui braz <lb/>zi.d.e. </s> <s id="s.001704">&. </s> <s id="s.001705">e.&longs;. <!-- REMOVE S-->& li lor &longs;parti, ouer centri&longs;iano.b. </s> <s id="s.001706">&. </s> <s id="s.001707">e. <!-- REMOVE S-->& nella i&longs;tremita del brazzo. <lb/></s> <s id="s.001708">b.a.ui &longs;ia appe&longs;o il corpo.a.poniamo de libre due in grauita, & nella i&longs;tremita de l'al­<lb/>tro brazzo, cioe in ponto.c.non ui &longs;ia alcuna altra grauita, & co&longs;i nella i&longs;tremita del <lb/>brazzo.e.d.ai &longs;ia appe&longs;o el corpo.d.poniamo di una libra &longs;ola in grauita, & nellà i­<lb/>&longs;tremita dell'altro brazzo, cioe in ponto.f.non ui &longs;ia alcuna grauita, & &longs;iano li detti <lb/>dui corpi, co&longs;i congionti elleuati con la mano in alto egualmente, come che di &longs;otto ap­<lb/>par in figura: hor adimando, che me &longs;ia conce&longs;&longs;o, la&longs;ciando andare cadauno de detti dui <lb/>corpi co&longs;i in alto elleuati, che il corpo.a. (per e&longs;&longs;er piu graue) di&longs;cenda piu ueloce-<emph.end type="italics"/><lb/><figure id="id.042.01.170.1.jpg" xlink:href="042/01/170/1.jpg"/><lb/><emph type="italics"/>mente al ba&longs;&longs;o del corpo.d.cioe, che il detto corpo.a. <!-- REMOVE S-->&longs;umara manco tempo à pertran <lb/>&longs;ire il curuo &longs;pacio.a.g.di quello fara il detto corpo. <!-- REMOVE S-->d o pertran&longs;ire il curuo &longs;patio.d. <lb/></s> <s id="s.001709">h.li quali &longs;pacij uengono à e&longs;&longs;er eguali, perche li brazzi de dette libre &longs;ono eguali dal <lb/>pre&longs;uppo&longs;ito, e pero li detti dui &longs;pacij, ouer de&longs;cen&longs;i curui, uengono à e&longs;&longs;er <expan abbr="circõferen">circonferen</expan> <lb/>tie di cerchij eguali. </s> <s id="s.001710">Et é conuer&longs;o, quando, che li detti <expan abbr="corpi&longs;arãno">corpi&longs;aranno</expan> di&longs;ce&longs;inel &longs;uo in­<lb/>mo, ouer piu ba&longs;&longs;o luoco, cioe l'uno in ponto.g. </s> <s id="s.001711">& l'altro in ponto.h.adimando, che me <lb/>&longs;ia conce&longs;&longs;o, che quella uirtu, ouer potentia, la qual o&longs;&longs;endo appe&longs;a nell'altro brazzo <lb/>della libra in ponto.c.&longs;ara atta ad elleuare el detto corpo.a.per fin al luoco, doue, che <lb/>al pre&longs;ente &longs;e ritroua nella figura &longs;uperiore, quella mede&longs;ima &longs;ia atta ad alleuar piu ue <lb/>locemente il corpo.d.e&longs;&longs;endo appe&longs;a nell'altro brazzo della &longs;ua libra, cioe in <expan abbr="põto">ponto</expan>.f.<emph.end type="italics"/><lb/>S.A. Q<emph type="italics"/>uesto ui concedo, perche la &longs;perientia ne rende buona <expan abbr="te&longs;timoniãza">te&longs;timonianza</expan>.<emph.end type="italics"/> N. M<emph type="italics"/>a <lb/>uo&longs;tra Signoria&longs;appia, che quello, che hauemo detto, & adimandato delli detti dui cor <lb/>pi, delli quali l'uno é &longs;implicemente piu potente dell'altro, il mede&longs;imo adimandamo de <lb/>dui corpi &longs;implicemente eguali in potentia ma inequali per uigor della lor po&longs;itione, <lb/>ouer &longs;ito nel brazzo de una mede&longs;ima libra, e&longs;&longs;empigratia, &longs;e nel brazzo.a.b. </s> <s id="s.001712">della<emph.end type="italics"/><pb xlink:href="042/01/171.jpg"/><emph type="italics"/>libra.a.b.c. </s> <s id="s.001713">ue &longs;ia appe&longs;o li dui corpi.a. </s> <s id="s.001714">&. </s> <s id="s.001715">d.ēguali &longs;implicemente in potentia, cioe, <lb/>luno in ponto.a. </s> <s id="s.001716">& l'altro in ponto.d.come di &longs;otto appar in figura, anchor, che &longs;iano <lb/>&longs;implicemente egualmente potenti, nondimeno il corpo.a. <!-- REMOVE S-->in tal po&longs;itione per la. </s> <s id="s.001717">13. <lb/>diffinitione &longs;e dira e&longs;&longs;er piu grauedel corpo.d. <!-- REMOVE S-->come per lauenire &longs;e fara manife&longs;to, <lb/>perche in que&longs;to luoco non &longs;i puo aßignar la ragioue per le co&longs;e dette, ma per laueni­<lb/>re &longs;e prouara el corpo.a. <!-- REMOVE S-->in &longs;imel &longs;ito e&longs;&longs;er piu graue del corpo.d.e pero. </s> <s id="s.001718">e&longs;&longs;endo quelli <lb/>elleuati luno in <expan abbr="põto">ponto</expan>.e. </s> <s id="s.001719">& laltro in <expan abbr="põto">ponto</expan>.g. </s> <s id="s.001720">& dapoi <expan abbr="eß&etilde;do">eßendo</expan> ambi dui abandonati, dico, <lb/>che il corpo.a.di&longs;c&etilde;dera piu ueloce del corpo.d. <!-- REMOVE S-->& é <expan abbr="cõuer&longs;o">conuer&longs;o</expan>, e&longs;&longs;endo luno, e l'altro di <lb/>&longs;ce&longs;i nelli loro infimi luochi, cioe luno in ponto.f. </s> <s id="s.001721">& laltro in ponto. </s> <s id="s.001722">h. <!-- REMOVE S-->quella potentia <lb/>che &longs;ara atta in ponto.c.ad elleuare il corpo.a.dal ponto.f.per fina al ponto.e. </s> <s id="s.001723">quella <lb/>mede&longs;ima &longs;ara atta ad elleuare nel mede&longs;imo luoco, molto piu uelocemente il corpo.d.<emph.end type="italics"/><lb/><figure id="id.042.01.171.1.jpg" xlink:href="042/01/171/1.jpg"/><lb/><emph type="italics"/>dal ponto.h.per fi al ponto.g.<emph.end type="italics"/> S. A. A<emph type="italics"/>nchora que&longs;ta è co&longs;a chiara, ma uoria inten­<lb/>dere due co&longs;e da uoi. </s> <s id="s.001724">la prima é, che uoria intendere, perche non fingeti la &longs;opra&longs;critta <lb/>figura de libra, con quelle &longs;ue due tazzette appe&longs;e luna da un capo, & laltra da laltro <lb/>(come nelle material libre &longs;i co&longs;tuma) per imponeruili pe&longs;i, ouer campioni in luna, & <lb/>nell'altra le co&longs;e, che &longs;e hanno da ponderare; la &longs;econda è, che uoria &longs;apere &longs;e que&longs;to e&longs; <lb/>&longs;empio de libra &longs;i debbe intendere di quelle, che hanno il lor &longs;parto di &longs;opra, ouer di <lb/>quelle, che l'hanno di &longs;otto, ouer di quelle, che non l'hanno, ne di &longs;opra, ne di &longs;otto, ma <lb/>in e&longs;&longs;e libre proprie.<emph.end type="italics"/> N. C<emph type="italics"/>irca alla prima, ri&longs;pondo, che la pura libra &longs;e intende per <lb/>quella pura <expan abbr="lõghezza">longhezza</expan>, che fcrma quelli dui brazziluno di qua, laltro di la dal &longs;parto, <lb/>ò &longs;iano li detti bra<emph.end type="italics"/>zz<emph type="italics"/>iequali tra loro, ouer inequali, & quelle due tazzette, che dice<emph.end type="italics"/><lb/>V.S. <emph type="italics"/>non &longs;ono parte della libra, ma ui &longs;e aggiongono per commodita del ponder ante, <lb/>per imponerui li campioni, & pe&longs;i, che ha da ponderare, &longs;i come ch'è anchora la &longs;ella <lb/>dun cauallo, la quale non è parte del cauallo, ma una co&longs;a aggionta per <expan abbr="cõmodita">commodita</expan> di co <lb/>lui, che l'ha da caualcare, e perche meglio &longs;i uede, & comprende uno cauallo nudato <lb/>della &longs;ua &longs;ella, che <expan abbr="cõ">com</expan> la&longs;ella, et <expan abbr="&longs;imelm&etilde;te">&longs;imelmente</expan> una libra nudata di quelle &longs;ue due tazzette, <lb/>che con le tazzette &longs;enza tazzette la eßemplificamo. </s> <s id="s.001725">Circa alla &longs;econda particolari <lb/>ta, dico, che la pre&longs;ente libra, & &longs;imelmente tutte quelle, che per lauenir &longs;i proponera <lb/>(non &longs;pecificando altro) &longs;i debbono intendere di quelle, che hanno il &longs;parto in lor me­<lb/>defime, come nelle materiale &longs;i costuma.<emph.end type="italics"/> S.A. E<emph type="italics"/>ue ho inte&longs;o, &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <pb pagenum="86" xlink:href="042/01/172.jpg"/> <p type="head"> <s id="s.001726">QVESITO. XXIIII. PETITIONE III.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001727">An<emph type="italics"/>chora adimandamo, che ne &longs;ia conce&longs;&longs;o un corpo graue e&longs;&longs;er in el di&longs;cendere <lb/>tanto piu graue, quanto che il moto di quello è piu retto al centro del mondo.<emph.end type="italics"/><lb/>S.A. D<emph type="italics"/>atime anchora uno qualche material e&longs;&longs;empio &longs;opra à que&longs;t'altra petitione <lb/>&longs;e uoleti, che ui intenda.<emph.end type="italics"/> N. S<emph type="italics"/>ia, eßempi gratia, il corpo graue.a. </s> <s id="s.001728">& poniamo, che le <lb/>quattro linee.a.b.a.c.a.d.a.e.&longs;iano <expan abbr="quattrō">quattrom</expan> luochi, ouer &longs;pacij da poter de&longs;cendere el <lb/>detto corpo.a. <!-- REMOVE S-->& poniamo anchora, che la linea. </s> <s id="s.001729">a.b. <!-- REMOVE S-->&longs;tail rettißimo, & perpendico­<lb/>lar de&longs;cen&longs;o uer&longs;o il <expan abbr="c&etilde;tro">centro</expan> del mondo, onde la linea.a. </s> <s id="s.001730">d.ueneria ad eßer piu retta uer <lb/>&longs;o il detto centro del mondo della linea.a.e. </s> <s id="s.001731">& per tanto in que&longs;to ca&longs;o adimandamo, <lb/>chene &longs;ia conce&longs;&longs;o ildetto corpo.a. <!-- REMOVE S-->e&longs;&longs;er piu graue nel di&longs;cendere per la linea a.d. </s> <s id="s.001732">che <lb/>per la linea.a.e.per e&longs;&longs;er (come detto) piu retta di quella al centro del mondo, & &longs;i­<lb/>melmente per la linea.a.c.de&longs;cendere piu graue, che per la linea.a.d.per e&longs;&longs;er tal linea <lb/>a.c.piu retta al centro del mondo della detta tinea.a.d. </s> <s id="s.001733">& co&longs;t quanto piu el detto cor <lb/>po.a.&longs;e andara acco&longs;tando alla detta linea. </s> <s id="s.001734">a. <!-- REMOVE S-->b. <!-- REMOVE S-->nel &longs;uo de&longs;cendere &longs;e &longs;uppone tanto <lb/>piu graue de&longs;cendere, perche quel tran&longs;ito, ouer de&longs;cen&longs;o, che forma piu acuto angolo <lb/>con la linea.b.a.in ponto.a.&longs;e intende eßer piu retto al centro del mondo, di quello, che <lb/>lo forma men acuto. </s> <s id="s.001735">Onde per la linea.a.b.uien à di&longs;cendere piu graue, che per qual &longs;i <lb/>uoglia altro uer&longs;o.<emph.end type="italics"/></s> </p> <figure id="id.042.01.172.1.jpg" xlink:href="042/01/172/1.jpg"/> <p type="main"> <s id="s.001736">E<emph type="italics"/>t que&longs;to, che hauemo detto, & adimandato dal &longs;opradetto corpo. <!-- REMOVE S-->a. <!-- REMOVE S-->&longs;eparato <lb/>da ogni libra, il mede&longs;imo adim andamo de quelli, che de&longs;cendono appe&longs;i al brazzo di <lb/>qualche libra. </s> <s id="s.001737">E&longs;&longs;empi gratia, &longs;ia anc hora el detto corpo.a. <!-- REMOVE S-->appe&longs;o al brazzo della <lb/>libra.a.b.c. </s> <s id="s.001738">girante&longs;opra al &longs;parto, ouer centro.b. </s> <s id="s.001739">oueramente al brazzo della libræ <lb/>a.d.e.girante &longs;opra al &longs;parto, ouer centro. </s> <s id="s.001740">d. <!-- KEEP S--></s> <s id="s.001741">& &longs;ia el perpendicolar de&longs;cen&longs;o uer&longs;o il <lb/>centro del <expan abbr="mõdo">mondo</expan> la linea retta.a.f. </s> <s id="s.001742">& el de&longs;cen&longs;o, che faria el detto corpo.a. <!-- REMOVE S--><expan abbr="cõ">com</expan> el braz <lb/>zo.a.b.della libra.a.b.c.&longs;opra elcentro.b.la linea curua.a.g. </s> <s id="s.001743">Et el de&longs;cen&longs;o, che faria <lb/>el mede&longs;imo corpo.a.con el brazzo.a.d.della li<gap/>ra.a.d.e. </s> <s id="s.001744">&longs;opra el centro.d. </s> <s id="s.001745">la linea <lb/>curua.a.h. </s> <s id="s.001746">Hor dico, & adimando, che ne &longs;ia conce&longs;&longs;o il detto corpo.a.e&longs;&longs;er piu graue <lb/>nel de&longs;cendere per il de&longs;cen&longs;o.a<gap/>h. </s> <s id="s.001747">che p el de&longs;cen&longs;o.a g. <!-- KEEP S--></s> <s id="s.001748">per e&longs;&longs;ere el detto de&longs;cen&longs;o <lb/>a. <!-- REMOVE S-->h. <!-- REMOVE S-->piu retto al centro del mondo del de&longs;cen&longs;o. </s> <s id="s.001749">a. <!-- REMOVE S-->g. <!-- REMOVE S-->perche el detto de&longs;en&longs;o. </s> <s id="s.001750">a. <!-- REMOVE S-->h.<emph.end type="italics"/><pb xlink:href="042/01/173.jpg"/><emph type="italics"/>forma piu acuto angolo con la linea.a.f. (qual è l'angolo.h.a.f. </s> <s id="s.001751">della contingentia) di <lb/>quello fa lo decen&longs;o.a.g.<emph.end type="italics"/></s> </p> <figure id="id.042.01.173.1.jpg" xlink:href="042/01/173/1.jpg"/> <p type="main"> <s id="s.001752">S.A. <!-- KEEP S--></s> <s id="s.001753">E <emph type="italics"/>ue ho inte&longs;o benißimo, & tal petitione non è da negare, e pero &longs;eguitati nel­<lb/>l'altra.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001754">QVESITO. XXV. PETITIONE IIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001755">An<emph type="italics"/>chora adimandamo, che ne &longs;ia conce&longs;&longs;o quelli corpi e&longs;&longs;er egualmente graui, <lb/>&longs;econdo el &longs;ito, ouer po&longs;itione, quando che li lor de&longs;cen&longs;i in tai &longs;iti &longs;ono <expan abbr="egualm&etilde;">egualmen</expan> <lb/>te obliqui, & piu graue e&longs;&longs;er quello, che nel &longs;uo &longs;ito, ouer luoco doue &longs;e ripo&longs;a, ouer gia <lb/>ce ha il de&longs;cen&longs;o manco obliquo.<emph.end type="italics"/> S.A. A<emph type="italics"/>nchora questa <expan abbr="ui&etilde;">uiem</expan> a e&longs;&longs;er manife&longs;ta per quello <lb/>fu detto nella precedente, & anchora &longs;opra la &longs;econda petitione, e pero &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001756">QVESITO. XXVI. PETITIONE V.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001757">Si<emph type="italics"/>melmente adimandamo, che ne&longs;ta conce&longs;&longs;o quel corpo e&longs;&longs;er men graue dun altro <lb/>&longs;econdo el &longs;ito, ouer luoco, <expan abbr="quãdo">quando</expan> che per el <expan abbr="de&longs;c&etilde;&longs;o">de&longs;cen&longs;o</expan> di quello altro, nell'altro braz <lb/>zo della libra in lui &longs;eguita il moto contrario, cioe, che da lui uien elleuato in&longs;u&longs;o uer&longs;o <lb/>il ciclo, & é conuer&longs;o.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;ta è co&longs;a troppo chiara da concedere.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001758">QVESITO. XXVII. PETITIONE VI.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001759">An<emph type="italics"/>chora adimandamo, che ne &longs;ia conce&longs;&longs;o, niun corpo e&longs;&longs;er graue in &longs;e mede&longs;i­<lb/>mo.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;ta uostra petitione non intendo.<emph.end type="italics"/> N. C<emph type="italics"/>ioe, che l'acqua nella <lb/>acqua, il uino nel uino, l'olio nel olio, & l'aere nel aere non e&longs;&longs;ere di alcuna grauita.<emph.end type="italics"/><lb/>S.A. <!-- KEEP S--></s> <s id="s.001760">E <emph type="italics"/>ue ho inte&longs;o, & è co&longs;a conceßibile, perche la &longs;perientia nel manifesta, &longs;i che, &longs;e <lb/>guitati.<emph.end type="italics"/> N. N<emph type="italics"/>on ci è altra co&longs;a da adimandare à.<emph.end type="italics"/> V. S. <emph type="italics"/>diman, piacendo à Iddio, in­<lb/>traremo nelle propo&longs;itioni.<emph.end type="italics"/> S. A. S<emph type="italics"/>aranno propo&longs;itiom a&longs;&longs;ai.<emph.end type="italics"/> N. N<emph type="italics"/>on troppo <lb/>&longs;ignore.<emph.end type="italics"/> S. A. C<emph type="italics"/>redeti, che le&longs;pediremo dimane.<emph.end type="italics"/> N. N<emph type="italics"/><expan abbr="õ">om</expan> credo Signore, che le &longs;pe <lb/>diremo <expan abbr="nãche">nanche</expan> fra diman, e l'altro.<emph.end type="italics"/> S.A. B<emph type="italics"/><expan abbr="&etilde;">em</expan> andate, ritornate da mattina à bon'hora.<emph.end type="italics"/></s> </p> <pb pagenum="87" xlink:href="042/01/174.jpg"/> <p type="head"> <s id="s.001761">QVESITO. XXVIII. PROPOSITIONE <lb/>PRIMA.</s> </p> <p type="main"> <s id="s.001762">SIGNOR AMBASCIATORE. H<emph type="italics"/>or &longs;eguitati Tartaglia que&longs;te uo&longs;tre <lb/>propo&longs;itioni, ouer conclu&longs;ioni con&longs;equentemente l'una drieto all'altra, & &longs;otto <lb/>breuita.<emph.end type="italics"/> NICOLO. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001763">La <emph type="italics"/>proportione della grandezza di corpi de un mede&longs;imo genere, & quella del­<lb/>la lor potentia è una mede&longs;ima.<emph.end type="italics"/> S.A. D<emph type="italics"/>atemi uno e&longs;&longs;empto.<emph.end type="italics"/> N. S<emph type="italics"/>iano li dui <lb/>corpì.a.b. </s> <s id="s.001764">&. </s> <s id="s.001765">c. <!-- REMOVE S-->de uno mede&longs;imo genere, & &longs;ia.a.b. </s> <s id="s.001766">maggiore, & &longs;ia la potentia del <lb/>corpo.a.b.la.d.e.& quella de corpo.c.la.f. </s> <s id="s.001767">Hor dico che quella proportione, che è dal <lb/>corpo.a.b.al.corpo.c. <!-- REMOVE S-->quella mede&longs;ima è della potentia.d.e.alla potentia.f. </s> <s id="s.001768">Et &longs;e poßi­<lb/>bile è e&longs;&longs;er altramente (per l'auer&longs;ario) &longs;ia che la proportione del corpo.a.b.al corpo. <lb/><!-- REMOVE S-->c. <!-- REMOVE S-->&longs;ia menore di quella della potentia.d.e.alla potentia.f. </s> <s id="s.001769">Hor &longs;ta del corpo.a.b. (mag­<lb/>giore) compre&longs;o una parte eguale al corpo.c.menore, quale &longs;ia la parte.a. </s> <s id="s.001770">& perche <lb/>la uertu, ouer potentia del compo&longs;ito è compo&longs;ta dalla uertu di componenti. </s> <s id="s.001771">Sia adun­<lb/>que la uertu, ouer potentia della parte.a.la.d. </s> <s id="s.001772">& la uertu, ouer potentia del re &longs;iduo. </s> <s id="s.001773">b <lb/>de neceßita &longs;ara la re&longs;tante potentia.e.et perche <lb/>la parte.a.è tolta egual al.c.la potentia.d. (per <lb/>il conuer&longs;o della. </s> <s id="s.001774">7. diffinitione) &longs;ara eguale alla <lb/>potentia.f.& la proportione de tutto il corpo. <lb/><!-- REMOVE S-->a.b.alla &longs;ua parte.a. (per la &longs;econda parte della. <lb/></s> <s id="s.001775">7. del quinto di Euclide) &longs;ara, &longs;i come quella del <lb/>mede&longs;imo corpo. <!-- REMOVE S-->a. <!-- REMOVE S-->b.al corpo.c. (per e&longs;&longs;er.a. <lb/></s> <s id="s.001776">egual al.c.) & &longs;imilmente la proportione della <lb/>potentia.d.e.alla potentia.f.&longs;ara, &longs;i come quella <lb/>della detta potentia.d. </s> <s id="s.001777">e. <!-- REMOVE S-->alla &longs;ua parte.d. (per<emph.end type="italics"/><lb/><figure id="id.042.01.174.1.jpg" xlink:href="042/01/174/1.jpg"/><lb/><emph type="italics"/>e&longs;&longs;er la.d.egual alla.f.) Adunque la proportione de tutto il corpo.a.b.alla &longs;ua parte. <lb/></s> <s id="s.001778">a.&longs;ara menore di quella di tutta la potentia.d.e.alla &longs;ua parte.d. </s> <s id="s.001779">Adunque euer&longs;amente <lb/>(per la. </s> <s id="s.001780">30. del quinto di Euclide) la proportione del mede&longs;imo corpo.a.b. <!-- REMOVE S-->al re&longs;iduo <lb/>corpo.b. <!-- REMOVE S-->&longs;ara maggiore di quella di tutta la potentia.d.e. </s> <s id="s.001781">alla re&longs;tante potentia. </s> <s id="s.001782">e. <!-- REMOVE S-->la <lb/>qual co&longs;a &longs;aria inconueniente, & contra la opinion dell'auer&longs;ario, il qual uol che la <lb/>proportione del maggior corpo al menore &longs;ia menore, di quella della &longs;ua potentia alla <lb/>potentia del detto menore. </s> <s id="s.001783">Adunque de&longs;trutto l'oppo&longs;ito rimane il propo&longs;ito.<emph.end type="italics"/> S. A. <lb/>S<emph type="italics"/>ta bene, &longs;eguitati.<emph.end type="italics"/> NIC. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001784">QVESITO. XXIX. PROPOSITIONE <lb/>SECONDA.</s> </p> <p type="main"> <s id="s.001785">La <emph type="italics"/>proportione della potentia di corpi graui de uno mede&longs;imo genere, & quella <lb/>della lor uelocita (nelli de&longs;cen&longs;i) &longs;e conchiude e&longs;&longs;er una mede&longs;ima, anchor quel-<pb xlink:href="042/01/175.jpg"/>la delli lor moti contr arij (cioe delli lor a&longs;cen&longs;i) &longs;e conchiude e&longs;&longs;er la mede&longs;ima, ma tra&longs; <lb/>mutatiuamente.<emph.end type="italics"/> S.A. E<emph type="italics"/>&longs;&longs;emplificatemi tal propo&longs;itione.<emph.end type="italics"/> NIC. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001786">Si<emph type="italics"/>a anchora li dui corpi.a.b.&.c.de uno mede&longs;imo genere, & di grandezza diuer <lb/>&longs;a, & &longs;ia lo.a.b.maggiore, & &longs;ia la potentia del.a.b.la.d.e.& del.c.la.f. </s> <s id="s.001787">& per­<lb/>che il corpo di potentia, ouer grauita maggiore (per la &longs;econda petitione) de&longs;cende piu <lb/>uelocemente, &longs;ia adunque la uelocita nel de&longs;cender del corpo.a.b.la.g.h. <!-- REMOVE S-->& quella del <lb/>corpo.c.la.<emph.end type="italics"/> k. <emph type="italics"/>hor dico, che la proportione della potentia. </s> <s id="s.001788">d. <!-- REMOVE S-->e. <!-- REMOVE S-->alla potentia. </s> <s id="s.001789">f. <!-- REMOVE S-->& quella <lb/>della uelocita.g.h.alla uelocita.<emph.end type="italics"/>k.<emph type="italics"/>e&longs;&longs;er una mede&longs;ima, & quella delli lor moti contrarij <lb/>e&longs;&longs;er quella mede&longs;ima, ma tra&longs;mutatiuamente, cioe che la proportione della uelocita <lb/>del corpo.a.b.alla uelocita del corpo.c.nel moto contrario (cioe nell'a&longs;cendere) e&longs;&longs;er, <lb/>&longs;i come quella della potentia.f.alla potentia.d.e.ouer, come del corpo.c.al corpo.a.b. <lb/><!-- REMOVE S-->la qual co&longs;a &longs;e dimo&longs;tra per il mede&longs;imo modo, che fu dimo&longs;trata la precedente, cioe <lb/>&longs;e la proportione della potentia.d.e.alla po<lb/>tentia.f.non è (per l'auer&longs;ario) &longs;i come quel <lb/>la della uelocita.g.h.alla uelocita.<emph.end type="italics"/>k. <emph type="italics"/>nece&longs;&longs;a <lb/>riamente la &longs;ara maggiore, ouer menore, <lb/>hor poniamo che la &longs;ia menore, della poten­<lb/>tia.d.e.ne aßignaremo la parte.d.eguale al­<lb/>la.f.& co&longs;i della uelocita.g.h.ne aßignare­<lb/>mo la parte.g.eguale alla.<emph.end type="italics"/>k. <emph type="italics"/>& arguiremo, <lb/>come nella <expan abbr="preced&etilde;te">precedente</expan>, <expan abbr="dic&etilde;do">dicendo</expan> che la pportio <lb/>ne di tutta la potentia.d.e.alla &longs;ua parte.d. <lb/></s> <s id="s.001790">&longs;ara (per la &longs;econda parte della. </s> <s id="s.001791">7. del quin-<emph.end type="italics"/><lb/><figure id="id.042.01.175.1.jpg" xlink:href="042/01/175/1.jpg"/><lb/><emph type="italics"/>io di Euclide) &longs;i come quella della mede&longs;ima potentia.d.e.alla potentia.f. (per e&longs;&longs;er la <lb/>d.&.f.eguale) & &longs;imilmente la proportione de tutta la uelocita.g.h.alla &longs;ua parte.g. <lb/></s> <s id="s.001792">e&longs;&longs;er, &longs;i come quella della mede&longs;ima.g.h.alla.<emph.end type="italics"/>k. </s> <s id="s.001793">A<emph type="italics"/>dunque la proportione di tutta la po­<lb/>tentia.d.e.alla &longs;ua parte.d.&longs;ara menore di quella di tutta la uelocita.g.h.alla &longs;ua par­<lb/>te.g. </s> <s id="s.001794">Onde (per la. </s> <s id="s.001795">30. del quinto di Euclide) la proportione di tutta la mede&longs;ima po­<lb/>tentia.d.e.al &longs;uo re&longs;iduo.e.hauera maggior proportione, che tutta la uelocita.g.h.al <lb/>&longs;uo re&longs;iduo.h.la qual co&longs;a &longs;aria contra la opinione dell'auer&longs;ario qual <expan abbr="&longs;upponē">&longs;upponem</expan>, che la <lb/>proportione della maggior potentia alla menore e&longs;&longs;er menore di quella della maggior <lb/>uelocita alla menore. </s> <s id="s.001796">Et con li mede&longs;imi argomenti&longs;e procederia quando che quel &longs;up­<lb/>pone&longs;&longs;e che la proportione della maggior potentia alla menore fu&longs;&longs;e maggiore di quel <lb/>la della maggior uelocita alla menore, di&longs;trutto adunque l'oppo&longs;ito rimane il propo&longs;i­<lb/>to, hor per la &longs;econda parte della no&longs;tra conclu&longs;ione, dico, che la proportione della ue­<lb/>locita delli de&longs;cen&longs;i, & delli contrari moti, cioe delli a&longs;cen&longs;i de detti corpi è una mede&longs;i­<lb/>ma, ma tra&longs;mutatiuamente, cioe che la proportione della uelocita del corpo.a.b. <!-- REMOVE S-->e&longs;&longs;en <lb/>do da qualche altra uertu impo&longs;ta nell'altro braccio della libra in alto elleuato (ponia­<lb/>mo per fin alla linea della direttione) alla uelocita del corpo.c.dalla mede&longs;ima uertu, <lb/>pur in alto elleuato per fin all mede&longs;ima linea della direttione &longs;ara, &longs;i come quella del­<lb/>la uelocita.<emph.end type="italics"/>k.<emph type="italics"/>alla uelocita.g.h.ouer della potentia.f.alla petentia.d.e.ouer del cor-<emph.end type="italics"/><pb pagenum="88" xlink:href="042/01/176.jpg"/><emph type="italics"/>po.c.al corpo.a.b.perche quanta uertu, ouer potentia ha uncorpo graue per de&longs;cen­<lb/>dere al ba&longs;&longs;o, tantane ha anchora per re&longs;i&longs;tere al moto contrario, cioe à che il uole&longs;&longs;e <lb/>tirare, ouer à leuare in alto adunque la potentia del corpo.a.b. <!-- REMOVE S-->per re&longs;i&longs;tere à che il uo <lb/>le&longs;&longs;e elleuare in alto, &longs;aratanto quanto la &longs;opradetta.d.e.& quella del corpo.c.&longs;ara <lb/>tanto quanto la &longs;opradetta.f. </s> <s id="s.001797">Adunque quella uertu che nell'altro braccio della libra <lb/>&longs;ara atta ad elleuare co&longs;i à pena il detto corpo.a.b.per fin alla linea della direttione, <lb/>quella mede&longs;ima &longs;ara atta ad elleuare il detto corpo.c.tanto piu uelocemente (per fin <lb/>alla detta linea della direttione) quanto che la &longs;ua re&longs;i&longs;tentia &longs;ara proportionalmente <lb/>menore di quella del corpo.a.b.& perche la detta re&longs;i&longs;tentia del detto corpo.c. </s> <s id="s.001798">e tan­<lb/>to menore della re&longs;i&longs;tentia del corpo.a.b.quanto che la &longs;ua potentia.f.della potentia. <lb/></s> <s id="s.001799">d.e. <!-- KEEP S--></s> <s id="s.001800">Adunque la uelocita del corpo.c. (nel moto contrario) alla uelocita del corpo.a. <lb/><!-- REMOVE S-->b.&longs;ara, &longs;i come la potentia.e.d.alla potentia.f.ouer come che il corpo.a.b.al corpo. <lb/><!-- REMOVE S-->c. <!-- REMOVE S-->che il propo&longs;ito.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001801">CORRELARIO.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001802">Da <emph type="italics"/>qui &longs;e manife&longs;ta qualmente la proportione della grandezza di corpi di uno <lb/>mede&longs;imo genere, & quella della lor potentia, & quella della lor uelocita nelli <lb/>lor de&longs;cen&longs;i e&longs;&longs;er una mede&longs;ima. </s> <s id="s.001803">Et &longs;imilmente quella della lor uelocita nelli moti <lb/>contrarij, ma tra&longs;mutatiuamente.<emph.end type="italics"/> S. AMBASCIATORE. </s> <s id="s.001804">E <emph type="italics"/>ue ho inte&longs;o, <lb/>&longs;eguitati pur.<emph.end type="italics"/> NICOLO. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001805">QVESITO XXX. PROPOSITIONE III.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001806">Se <emph type="italics"/>&longs;aranno dui corpi &longs;implicemente eguali di grauita, ma ineguali per uigor del <lb/>&longs;ito, ouer po&longs;itione, la preportione della lor potentia, & quella della lor ueloci­<lb/>ta nece&longs;&longs;ariamente &longs;ara una mede&longs;ima. </s> <s id="s.001807">Ma nelli lor moti contrarij, cioe nelli a&longs;ceo­<lb/>&longs;i, la proportione della lor potentia, & quella della lor uelocita &longs;e afferma e&longs;&longs;er la <lb/>mede&longs;ima, ma tra&longs;mutatiuamente.<emph.end type="italics"/> S. AMB ASCIA. F<emph type="italics"/>atemi la dimo&longs;tratione di <lb/>que&longs;to.<emph.end type="italics"/> NICOLO. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001808">SIANO L<emph type="italics"/>i dui corpi.a.&.b. </s> <s id="s.001809">&longs;implicemente eguali di grauita, & &longs;ia la libra. <lb/></s> <s id="s.001810">c. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.001811">il cui centro, ouer &longs;parto il ponto. </s> <s id="s.001812">e. <!-- REMOVE S-->& &longs;ia nella &longs;trema parte del braz­<lb/>zo.e.c.cioe in ponto.c.appe&longs;o, & &longs;o&longs;tentato il corpo.a.& in uno altro luoco piu pro­<lb/>pinquo al &longs;parto nel mede&longs;imo brazzo, hor &longs;ia in ponto.f.ui &longs;ia &longs;o&longs;tentato il corpo.b. <lb/><!-- REMOVE S-->Et à ben che que&longs;ti dui corpi &longs;tano &longs;implicemente eguali di grauita, nondimeno (per <lb/>la quarta petitione) il corpo.a. <!-- REMOVE S-->&longs;ara (per uigor del luogo) piu graue del corpo. <!-- REMOVE S-->b. <lb/><!-- REMOVE S-->perche il de&longs;cen&longs;o di quello qual &longs;ia lo.c.h. </s> <s id="s.001813">e manco obliquo del de&longs;cen&longs;o del corpo.b. <lb/><!-- REMOVE S-->qual &longs;ia lo.f.g. (per la terza, & quarta petitione) e&longs;&longs;endo adunque il corpo.a. <!-- REMOVE S-->piu <lb/>graue, &longs;econdo il &longs;ito del corpo.b.&longs;ara etiom piu potente, & e&longs;&longs;endo piu potente (per <lb/>la &longs;econda petitione) nelli de&longs;cen&longs;i de&longs;cendera piu uelocemente del corpo.b. <!-- REMOVE S-->& nelli <lb/>moti contr arij, cioe nelli a&longs;cen&longs;ipiu tardamente. </s> <s id="s.001814">Dico adunque che la proportione <lb/>della lor uelocita nelli de&longs;cen&longs;i e&longs;&longs;er &longs;imile à quella della loro potentia, & quella delli lo-<pb xlink:href="042/01/177.jpg"/>ro a&longs;cen&longs;i e&longs;&longs;er pur la mede&longs;ima, ma tra&longs;mutatiuamente, et per dimo&longs;trar la prima par <lb/>te, &longs;ia la potentia del corpo.a.la.l. <!-- REMOVE S-->& quella del corpo.b.la.m. </s> <s id="s.001815">& la uelocita del corpo <lb/>a. (nelli de&longs;cen&longs;i) la.n. </s> <s id="s.001816">& quella del corpo.b.la.o. </s> <s id="s.001817">Dico che la proportione della ueloci­<lb/>ta.n.alla uelocita.o.e&longs;&longs;er, &longs;i come quella della potentia.l.alla potentia.m.la qual co&longs;a &longs;e <lb/>dimostra, &longs;i come la precedente, cioe &longs;e poßibil fu&longs;&longs;e, che la proportione della poten­<lb/>tia.l.alla potentia.m. (per l'auer&longs;ario) pote&longs;&longs;e e&longs;&longs;er menore di quella della uelocita.n. <lb/></s> <s id="s.001818">alla uelocita.o.&longs;umendo della potentia.l.la parte.p.eguale alla.m. </s> <s id="s.001819">& della uelocita.n.la <lb/>parte.q.eguale alla.o.& arguendo, come nella precedente, cioe che la proportione di <lb/>tutta la potentia.l. </s> <s id="s.001820">alla &longs;ua parte.p. (per la. </s> <s id="s.001821">7. del quinto di Euclide) &longs;ara menore di <lb/>quella di tutta la uelocita.n. <lb/></s> <s id="s.001822">alla &longs;ua parte.q. </s> <s id="s.001823">Onde (per <lb/>la. </s> <s id="s.001824">30. del quinto di Euclide) <lb/>la proportione della mede&longs;i <lb/>ma potentia. </s> <s id="s.001825">l. <!-- KEEP S--></s> <s id="s.001826">all'altra &longs;ua <lb/>parte, ouer re&longs;iduo.r.haue­<lb/>ra maggior proportione di <lb/>quello, che hauera tutta la <lb/>uelocita.n.all'altra &longs;ua par <lb/>te, ouer re&longs;iduo.s.la qual co <lb/>&longs;a &longs;aria <expan abbr="inconuem&etilde;te">inconuemente</expan>, et con <lb/>tra la opinione dell'auer&longs;a­<lb/>rio, qual &longs;uppone che la pro <lb/>porclone della maggior po­<lb/>tentia alla menore, e&longs;&longs;er me <lb/>nore di quella dellamaggior <lb/>uelocita, alla menore, & il <lb/>mede&longs;imo inconueniente &longs;e-<emph.end type="italics"/><lb/><figure id="id.042.01.177.1.jpg" xlink:href="042/01/177/1.jpg"/><lb/><emph type="italics"/>guiria quando che l'auer&longs;ario, &longs;uppone&longs;&longs;e che la proportione della potentia.l.al­<lb/>la potentia.m. </s> <s id="s.001827">fu&longs;&longs;e maggiore di quella della uelocita.n.alla uelocita.o. </s> <s id="s.001828">distrutto adun <lb/>que l'oppo&longs;ito rimane il propo&longs;ito. </s> <s id="s.001829">La &longs;econda parte &longs;e ri&longs;olue, ouer argui&longs;&longs;e, &longs;i come <lb/>nella precedente, cioe che quella potentia, che nell'altro brazzo della libra (poniamo <lb/>in ponto.d.) &longs;ara atta ad ellcuare il corpo.a.per fin alla linea della direttione, cioe in <lb/>ponto.<emph.end type="italics"/>k.<emph type="italics"/>quella mede&longs;ima &longs;ara atta ad elleuare tanto piu uelocemente il corpo.b.per fi <lb/>na al ponto. </s> <s id="s.001830">1. quanto che la potentia del detto corpo.b. (qual'è la.m.) è menore della <lb/>potentia del corpo.b. (qual'è la.l.) perche quanto che la potentia d'un corpo è menore <lb/>tanto men re&longs;i&longs;te al moto contrario, & econuer&longs;o, adunque la uelocita del corpo.b. <!-- REMOVE S-->à <lb/>quella del corpo.a. (nelli a&longs;cen&longs;i) &longs;ara, &longs;i come quella della potentia.l.alla potentia. </s> <s id="s.001831">m. <lb/><!-- REMOVE S-->che è il &longs;econdo propo&longs;ito.<emph.end type="italics"/> S. AMB. Q<emph type="italics"/>ue&longs;ta è stata a&longs;&longs;ai bella propo&longs;itione, ma <lb/>&longs;eguitati pur.<emph.end type="italics"/> NIC. <!-- KEEP S--></s> </p> <pb pagenum="89" xlink:href="042/01/178.jpg"/> <p type="head"> <s id="s.001832">QVESITO XXXI. PROPOSITIONE IIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001833">La <emph type="italics"/>proportione della potentia di corpi&longs;implicemente equali in grauita, ma ine­<lb/>quali per uigor del&longs;ito, ouer po&longs;itione, & quella delle lor di&longs;tantie dal &longs;parto, <lb/>euer centro della libra, &longs;e approuano e&longs;&longs;er equali.<emph.end type="italics"/> S.A. D<emph type="italics"/>atime uno e&longs;&longs;empio.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001834">Si<emph type="italics"/>ano li dui corpi.a.&.b.della figura precedente &longs;implicemente equali in grauita <lb/>& &longs;ia la libra.c.e.d.el centro, ouer &longs;parto della quale &longs;ia el ponto.e.& &longs;ia appe&longs;o <lb/>el corpo.a. <!-- REMOVE S-->in ponto.c.& lo corpo.b.nel ponto.f.come nella figura precedente appa­<lb/>re. </s> <s id="s.001835">Dico, che la proportione della potentia del corpo.a. (quale &longs;ia la.l.) alla potentia <lb/>del corpo.b. (quale &longs;ia la.m.) e&longs;&longs;er &longs;imile à quella, ch'è dalla di&longs;tantia, ouer brazzo.e. <lb/></s> <s id="s.001836">c.alla distantia, ouer brazzo.e.f.& tutto que&longs;to &longs;i approua&longs;econdo lordine della pre <lb/>cedente, cioe, &longs;e la proportione della di&longs;tantia, ouer brazzo. </s> <s id="s.001837">c. <!-- REMOVE S-->e. <!-- REMOVE S-->alla distantia, ouer <lb/>brazzo.f.e.non è (per lauer&longs;ario, &longs;i come quella, ch'é dalla potentia.l.alla poteutia.m. <lb/></s> <s id="s.001838">adunque nece&longs;&longs;ariamente &longs;ara maggiore, ouer minore, hor &longs;ia prima (&longs;e poßibil è) me <lb/>nore &longs;ia del brazzo, ouer di&longs;tantia.c.e.maggiore cauato el brazzo, ouer distantia.e. <lb/></s> <s id="s.001839">f.menore dalla banda uer&longs;o.c.quale &longs;ia la.c.x.& dalla potentia.l.ne &longs;ia cauata la par­<lb/>te.p.equal alla.m. </s> <s id="s.001840">Adunque per la. </s> <s id="s.001841">7. del quinto di Euclide) la proportione di tutta la <lb/>distantia, ouer brazzo.e.c.alla &longs;ua parte.c.x.hauera menor proportione, di quello, <lb/>che hauera tutta la potentia.l.alla &longs;ua parte. </s> <s id="s.001842">p. <!-- KEEP S--></s> <s id="s.001843">Onde per la. </s> <s id="s.001844">30. del quinto di Euclide) <lb/>la proportione del brazzo, ouer distantia.c.e.alla restante di&longs;tantia, ouer bra<emph.end type="italics"/>zz<emph type="italics"/>o. </s> <s id="s.001845">e. <lb/><!-- REMOVE S-->x.hauera maggior proportione di quello hauera la potentia.l.alla re&longs;tante <expan abbr="pot&etilde;tia">potentia</expan>.r. <lb/></s> <s id="s.001846">la qual potentia.r.uerria ad e&longs;&longs;er la potenza del mede&longs;imo corpo.b. <!-- REMOVE S-->&longs;tante nel ponto <lb/>x.la qual co&longs;a &longs;aria inconueniente, perche, &longs;e la proportione della maggiore di&longs;tantia <lb/>dal &longs;parto alla menore (per lauer&longs;ario) hauera maggior proportione, che la maggior <lb/>potentia alla menore, que&longs;to doueria &longs;eguire in ogni po&longs;itione, & tamen&longs;e uede occor­<lb/>rere al contrario, cioe, che la proportione della di&longs;tantia.c.e.alla di&longs;tantia.e. </s> <s id="s.001847">x. <!-- REMOVE S-->&longs;aria <lb/>maggiore di quella della potentia.l.alla potentia del corpo.b.nel &longs;ito, ouer luoco, do­<lb/>ue.x.di&longs;trutto adunque lo oppo&longs;ito rimane il propo&longs;ito.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001848">CORRELARIO.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001849">Da<emph type="italics"/>lle co&longs;e dette, & dimostrate, &longs;e manife&longs;ta non &longs;olamente la proportione delle <lb/>di&longs;tantie dal &longs;parto nel bra<emph.end type="italics"/>zz<emph type="italics"/>o della libra, & quella delle <expan abbr="pot&etilde;tie">potentie</expan> di cor pi &longs;im <lb/>plicementi equali in grauita, in tai&longs;iti, ouer luochi, & &longs;imelmente la uelocita de quelli <lb/>nelli dc&longs;cen&longs;i e&longs;&longs;er una mede&longs;ima, ma anchora li lor de&longs;cen&longs;i, & anchora li loro <expan abbr="aßc&etilde;&longs;i">aßcen&longs;i</expan> <lb/>oßeruano la mede&longs;ima, perche qual proportione è dal bra<emph.end type="italics"/>zz<emph type="italics"/>o.e.c.al brazzo.e.f.tala <lb/>è dal curuo de&longs;cen&longs;o.c.h.al curuo de&longs;cen&longs;o.f.g.& <expan abbr="&longs;imelm&etilde;te">&longs;imelmente</expan> del curuo a&longs;&longs;en&longs;o. </s> <s id="s.001850">c.<emph.end type="italics"/>k.<emph type="italics"/>al <lb/>curuo a&longs;&longs;cen&longs;o.f.i.pche li dette de&longs;cen&longs;i, & a&longs;&longs;cen&longs;i uengono à e&longs;&longs;er cadauno de loro la <lb/>quarta parte della circonferentia de dui ceochij. </s> <s id="s.001851">delli quali el &longs;emidiametro del mag­<lb/>giore uerria à e&longs;&longs;er el brazzo, ouer di&longs;tantia.e.c.et del menore el brazzo, ouer <expan abbr="di&longs;tã">di&longs;tam</expan> <lb/>tia.e.f.<emph.end type="italics"/> S.A. A<emph type="italics"/>nchor que&longs;ta é &longs;tata una bella propo&longs;itione &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <pb xlink:href="042/01/179.jpg"/> <p type="head"> <s id="s.001852">QVESITO XXXII. PROPOSITIONE V.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001853">Qv<emph type="italics"/>ando, che la po&longs;itione de una libra de brazzi equali &longs;ta nel &longs;ito della equali­<lb/>ta, & nella i&longs;tremita de l'uno, e l'altro brazzo ui &longs;iano appe&longs;i corpi &longs;implice­<lb/>mente equali in grauita, tal libra non &longs;e &longs;eparara dal detto &longs;ito della equalita, & &longs;e per <lb/>ca&longs;o la &longs;ia da qualche altro pe&longs;o in luno de detti bra<emph.end type="italics"/>zz<emph type="italics"/>i impo&longs;to &longs;eparata dal detto &longs;i­<lb/>to della equalita, oueramente con la mano, remo&longs;&longs;o quel tal pe&longs;o, ouer mano, tal libra <lb/>de neceßita ritornara al detto &longs;ito della equalita.<emph.end type="italics"/> S. A. Q<emph type="italics"/>ue&longs;ta è quella Que&longs;tione, <lb/>della quale uoi dite, che manca Ari&longs;totile nelle &longs;ue Que&longs;tioni Mechanice.<emph.end type="italics"/> N. C<emph type="italics"/>o&longs;i è <lb/>Signore.<emph.end type="italics"/> S.A. M<emph type="italics"/>olto haro à caro à intendere la cau&longs;a di tal effetto, e pero &longs;eguita­<lb/>te.<emph.end type="italics"/> N. S<emph type="italics"/>ia e&longs;&longs;empi gratia la libra.a.c.b.el centro della quale &longs;ia il ponto. </s> <s id="s.001854">c. <!-- REMOVE S-->& &longs;ia el <lb/>bra<emph.end type="italics"/>zz<emph type="italics"/>o.a.c.equale al bra<emph.end type="italics"/>zz<emph type="italics"/>o.b.e.& stia nel &longs;ito della equalita, come &longs;e prepone. </s> <s id="s.001855">Et <lb/>che nella i&longs;tremita de luno, e laltro bra<emph.end type="italics"/>zz<emph type="italics"/>o ui&longs;ia appe&longs;o uno corpo (poniamo el cor­<lb/>po.a.&.a.) li quali corpi&longs;iano &longs;implicemente equali in grauita. </s> <s id="s.001856">Dico che la detta li­<lb/>bra (per la impo&longs;itione de detti corpi) non &longs;e &longs;eparara dal detto &longs;ico della equalita, & <lb/>&longs;e pur quella fu&longs;&longs;e &longs;eparata dal detto &longs;ito, ò per la impo&longs;itione di qualche altro pe&longs;o, <lb/>ouer con la mano, remo&longs;&longs;o che &longs;ia quel tal imposto pe&longs;o, ouer mano, tal libra de neceßi <lb/>ta ritornara al detto &longs;ito della equalita. </s> <s id="s.001857">La prima parte è manife&longs;ta, perche li detti dui <lb/>corpi &longs;ono &longs;implicemente di equal grauita (dal pre <lb/>&longs;uppo&longs;ito) et <expan abbr="&longs;imelm&etilde;te">&longs;imelmente</expan> &longs;ono equalmente graui per <lb/>uigor del &longs;ito, per la quarta petitione (per e&longs;&longs;er li <lb/>loro de&longs;cen&longs;i equalmente obliqui) e pero e&longs;&longs;endo <lb/>quelli &longs;i per uigor del &longs;ito, come che <expan abbr="&longs;implicem&etilde;te">&longs;implicemente</expan> <lb/>duna equal grauita, e potentia, e pero niun de loro <lb/>fara atto à poter elleuar l'altro, cioe à farlo a&longs;cen <lb/>dere di moto contrario, e pero restaranno nel me­<lb/>de&longs;imo &longs;ito della equalita.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;to ue credo <lb/>& ue lo haueria largamente conce&longs;&longs;o &longs;enza altra<emph.end type="italics"/><lb/><figure id="id.042.01.179.1.jpg" xlink:href="042/01/179/1.jpg"/><lb/><emph type="italics"/>demon&longs;tratione, per e&longs;&longs;er co&longs;a naturale. </s> <s id="s.001858">Ma &longs;eguitati la &longs;econda parte, la qual me pare <lb/>molto piu a&longs;trata, ouer lontana dal no&longs;iro intelletto naturale dell'altra.<emph.end type="italics"/> N. P<emph type="italics"/>er la &longs;e <lb/>condu parte &longs;ia pur anchora la libra.a.c.b.de braz <lb/>zi equali et nella i&longs;tremita de quelli &longs;iano pur ap­<lb/>pe&longs;i li dui corpi.a.et.b.&longs;implicemente equali in gra<lb/>uita, la qual librap le ragioni di &longs;opra adutte &longs;tara <lb/>nel &longs;ito della equalita, come di &longs;otto appar <expan abbr="ĩ">im</expan> figura.<emph.end type="italics"/></s> </p> <figure id="id.042.01.179.2.jpg" xlink:href="042/01/179/2.jpg"/> <p type="main"> <s id="s.001859">HOR <emph type="italics"/>e&longs;&longs;endo &longs;pinto el brazzo.a.c.al ba&longs;&longs;o con la mano, ouer per la impo&longs;itio <lb/>ne di qualche altro pe&longs;o &longs;opra el corpo.a.remo&longs;&longs;o uia la mano, ouer quel tal <lb/>pe&longs;o, el brazzo di tal libra rea&longs;cendera, & ritornera al &longs;uo primo luoco della <gap/>quali­<lb/>ta, & per aßignar la cau&longs;a propinqua di tal effetto, fla de&longs;critto &longs;opra el centro.c. </s> <s id="s.001860">el <lb/>cerchio.a.c.b.f. </s> <s id="s.001861">per el uiazzo, che fariano li detti dui corpi alzando, ouer arba&longs;&longs;ando <lb/>li brazzi della detta libra, & &longs;ia tirata la linea della direttione, quale &longs;ia la.e.f. </s> <s id="s.001862">& &longs;ia <lb/>diui&longs;o l'arco.a.f.in quanti parti equali &longs;i uoglia (hor &longs;ia in quattro) nelli trei ponti,<emph.end type="italics"/><pb pagenum="90" xlink:href="042/01/180.jpg"/><emph type="italics"/>q.&longs;.u.& in altre tante &longs;la anchor diui&longs;o l'arco.e.b. </s> <s id="s.001863">nelli trei ponti.i.l.n. </s> <s id="s.001864">& dalli detti <lb/>trei ponti.n.l.i.&longs;iano tirate le tre linee.n.o.l.m.&.i.<emph.end type="italics"/>k.<emph type="italics"/>equidi&longs;tante al&longs;ito della equa­<lb/>lita, cioe al diametro, ouer linea.a.b.le quale &longs;egaranno la linea.e.f. </s> <s id="s.001865">della direttione ne <lb/>li tre ponti.z y.x. <!-- KEEP S--></s> <s id="s.001866">Simelmente dalli tre ponti.q.&longs;.u.&longs;iano tirate le tre linee.q.p.&longs;.r.&. <lb/></s> <s id="s.001867">u.t.pur equidi&longs;tante alla mede&longs;ima linea.a.b.le quale &longs;egaranno la mede&longs;ima linea del <lb/>la direttione.e.f.nelli trei ponti.&.<emph.end type="italics"/><36>.<38>. </s> <s id="s.001868">E<emph type="italics"/>t dapoi &longs;ia arba&longs;&longs;ato con la mano il corpo.a. <lb/>(ouer con la impo&longs;itione di qualche altro pe&longs;o) per fin al ponto.u. </s> <s id="s.001869">& laltro corpo.b. <lb/>(à quel oppo&longs;ito) in tal po&longs;itione &longs;e trouar a e&longs;&longs;er a&longs;&longs;e&longs;o de moto contrario per fin al <lb/>ponto.i. </s> <s id="s.001870">Onde per queste co&longs;e co&longs;i di&longs;po&longs;ite ueniremo ad hauer diui&longs;o tutto el de&longs;cen&longs;o <lb/>a.u.fatto dal detto corpo.a.nel di&longs;cendere in ponto.u.in tre de&longs;cen&longs;i, ouer parti equa <lb/>li, le quale&longs;ono.a.q.q.&longs;.&.&longs;.u.& &longs;imelmente tutto el de&longs;cen&longs;o.i.b. </s> <s id="s.001871">qual faria il detto <lb/>corpo.b.nel di&longs;cendere, ouer ritornare al&longs;uo primo luoco (cioe in ponto.b.) uerra ad <lb/>eßer diui&longs;o in trei de&longs;cen&longs;i, ouer in tre parti equalile quali &longs;ono.i.l.l. </s> <s id="s.001872">n. <!-- REMOVE S-->&.n.b. </s> <s id="s.001873">& ca­<lb/>dauno de que&longs;ti tre, & tre partiai de&longs;cen&longs;i capi&longs;&longs;e una parte della linea della direttio­<lb/>ne, cioe il de&longs;cen&longs;o dal.a.al.q.piglia, ouer capi&longs;&longs;e della linea della direttione la parte.e. <lb/></s> <s id="s.001874">&.& lo de&longs;cen&longs;o.q.&longs;.capi&longs;&longs;e la parte.&.<emph.end type="italics"/><36>. <emph type="italics"/>& lo de&longs;cen&longs;o.&longs;.u.capi&longs;&longs;e la parte.<emph.end type="italics"/> <36>. </s> <s id="s.001875"><38>. <lb/><emph type="italics"/>& laltro de&longs;cen&longs;o, che re&longs;ta à de&longs;cendere al detto corpo.a.cioe el de&longs;cen&longs;o. </s> <s id="s.001876">u.f.capiße <lb/>la linea, ouer parte.<emph.end type="italics"/><38>.<emph type="italics"/>f. </s> <s id="s.001877">Et &longs;imelmente el de&longs;cen&longs;o del corpo.b. <!-- REMOVE S-->dal ponto.i. </s> <s id="s.001878">al ponto.l. <lb/></s> <s id="s.001879">capi&longs;&longs;e della mede&longs;ima linea della direttione la parte.x.y.& nel de&longs;cen&longs;o dal ponto.l. <lb/></s> <s id="s.001880">al ponto.n.capi&longs;&longs;e la parte.y.z.& dal ponto.n.al ponto.b.capi&longs;&longs;e la parte.z.c.et tue <lb/>te que&longs;te parti&longs;ono fra loro inequale, cioe la parte.c.z. </s> <s id="s.001881">è maggiore della.z.y.& la. </s> <s id="s.001882">z. <lb/><!-- REMOVE S-->y.della.y.x.& la.y.x.della.x.e.& &longs;imelmente la parte. </s> <s id="s.001883">c. <!-- REMOVE S-->&. </s> <s id="s.001884">è maggiore della par­<lb/>te.&.<emph.end type="italics"/><36>.<emph type="italics"/>& la parte.&.<emph.end type="italics"/><36>.<emph type="italics"/>della parte.<emph.end type="italics"/><36>.<38>.<emph type="italics"/>& la.<emph.end type="italics"/><36>.<38>.<emph type="italics"/>della.<emph.end type="italics"/><38>.<emph type="italics"/>f.& tutto que&longs;to facil­<lb/>mente Geometrice &longs;i puo prouare, & &longs;imelmente &longs;e puo prouare, la parte.<emph.end type="italics"/> <38>.<emph type="italics"/>f. </s> <s id="s.001885">e&longs;&longs;ere <lb/>equale alla porte.e.x.& la parte.<emph.end type="italics"/><38>.<36>.<emph type="italics"/>alla parte.x.y.& la parte.<emph.end type="italics"/><36>.<emph type="italics"/>&.alla parte.y.z. <lb/></s> <s id="s.001886">& la parte.&.c.alla parte.z.c. </s> <s id="s.001887">Hor per tornare al no&longs;tro propo&longs;ito. </s> <s id="s.001888">Dico, che il cor <lb/>po.b.&longs;tante quel nel ponto.i.uien à e&longs;&longs;er piu graue, &longs;econdo il &longs;ito del corpo. <!-- REMOVE S-->a. <!-- REMOVE S-->stante <lb/>quello in ponto.u. (come di&longs;otto appar in figura) perche il de&longs;cen&longs;o del detto corpo <lb/>b.dal ponto.i.nel ponto.l. </s> <s id="s.001889">è piu retto del de&longs;cen&longs;o del corpo.a. <!-- REMOVE S-->dal ponto. </s> <s id="s.001890">u. <!-- REMOVE S-->nel ponto <lb/>f. (per la &longs;econda parte della quarta petitione) perche capi&longs;&longs;e piu della linea della di­<lb/>rettione, cioe, che nel de&longs;cendere il detto corpo.b. <!-- REMOVE S-->dal ponto. </s> <s id="s.001891">i. <!-- REMOVE S-->nel ponto.l. </s> <s id="s.001892">lui capi&longs;&longs;e, <lb/>ouer piglia della linea della direttione, la parte.x.y.& il corpo.a. <!-- REMOVE S-->nel di&longs;cendere dal <lb/>ponto.u.nel ponto.f.lui caperia della detta linea della direttione, la parte.<emph.end type="italics"/><38>.<emph type="italics"/>f.& per­<lb/>che la parte.x.y. </s> <s id="s.001893">é maggiore della linea, ouer parte.<emph.end type="italics"/><38>.<emph type="italics"/>f. (per la. </s> <s id="s.001894">17. diffinitione) piu <lb/>obliquo &longs;ara il de&longs;cen&longs;o dal ponto.u.al ponto.f.di quello dal ponto.i.al ponto.l. </s> <s id="s.001895">Onde <lb/>(per la &longs;econda parte della quarta petitione) il corpo.b.in tal po&longs;itione &longs;ara piu gra­<lb/>ue &longs;econdo il &longs;ito del corpo.a.eßendo adunque piu graue, leuando uia lo impo&longs;to pe&longs;o, <lb/>ouer la mano dal corpo.a. (per il conuer&longs;o della quinta petitione) lui fara rea&longs;cende­<lb/>re di moto contrario il detto corpo. <!-- REMOVE S-->a.dal ponto.u.al ponto.&longs;. </s> <s id="s.001896">& lui de&longs;cendera dal <lb/>ponto.i.nel ponto.l.nel qual ponto.l. </s> <s id="s.001897">lui uenira à trouar&longs;e anchora piu graue del det <lb/>to corpo.a.&longs;econdo el &longs;ito, perche il detto corpo.a. <!-- REMOVE S-->&longs;tante nel ponto. </s> <s id="s.001898">&longs;. <!-- REMOVE S-->hauera il de­<lb/>&longs;cen&longs;o.&longs;.u.piu obliquo del de&longs;cen&longs;o.l. </s> <s id="s.001899">n. <!-- REMOVE S-->del corpo. <!-- REMOVE S-->b. <!-- REMOVE S-->perche capi&longs;&longs;e men parte della<emph.end type="italics"/><pb xlink:href="042/01/181.jpg"/><emph type="italics"/>detta linea della direttione, cioe, che la parte.<emph.end type="italics"/><36>.<38>. <emph type="italics"/>è menore della parte.y.z. </s> <s id="s.001900">Onde per <lb/>le ragioni di &longs;opra adutte, el detto corpo.b.fara elleuare il detto corpo.a. <!-- REMOVE S-->& a&longs;cende­<lb/>re nel ponto.q.& lui de&longs;cendera nel ponto.n.nel qual ponto.n.el mede&longs;imo corpo. <!-- REMOVE S-->b. <lb/><!-- REMOVE S-->&longs;i trouara pur piu graue anchora, &longs;econdo il &longs;ito del corpo.a.perche il de&longs;cen&longs;o dal.q. <lb/></s> <s id="s.001901">in.s.è piu obliquo del defcen&longs;o dal ponto.n.nel ponto.b. </s> <s id="s.001902">per e&longs;&longs;er la parte.z.c.maggio <lb/>re della parte.&.<emph.end type="italics"/><36>. </s> <s id="s.001903">E <emph type="italics"/>pero (per le ragioni di &longs;opra adutte) el detto corpo.b.fara re­<lb/>a&longs;cendere il detto corpo.a.al ponto.a. (&longs;uo primo, & condecente luoco) & lui mede&longs;i <lb/>mamente de&longs;cendara nel ponto.b.pur &longs;uo primo, <lb/>& condecente luoco, cioe nel &longs;ito della equalita, <lb/>nel qual &longs;ito li detti dui corpi&longs;e trouar anno (per <lb/>le ragioni aduttenella prima parte di que&longs;ta) e­<lb/>gualmente graui &longs;econdo el &longs;ito, & perche &longs;ono <lb/>anchora &longs;implicemente egualmente graui, &longs;e con <lb/>&longs;eruarano nel detto luoco, come di &longs;opra fu det­<lb/>to, & approuato, che è il no&longs;tro propo&longs;ito.<emph.end type="italics"/><lb/>S. A. Q<emph type="italics"/>ue&longs;ta è &longs;tata una bella demostratione, <lb/>ma&longs;e ben me arricordo, uoi dice&longs;ti anchor &longs;opra <lb/>la detta prima que&longs;tion Mechanica de Ari&longs;toti­<lb/>le, che quelle &longs;ue due conclu&longs;ioni, che lui ui aduce <lb/>in fine eßer fal&longs;e.<emph.end type="italics"/> N. E<emph type="italics"/>glie il uero.<emph.end type="italics"/> S.A. P<emph type="italics"/>er<emph.end type="italics"/><lb/><figure id="id.042.01.181.1.jpg" xlink:href="042/01/181/1.jpg"/><lb/><emph type="italics"/>che ragione.<emph.end type="italics"/> N. L<emph type="italics"/>a ragione di tal particolarita, ouer oppo&longs;itioni &longs;e uerifica­<lb/>ranno nella &longs;equente propo&longs;itione, mediante alcuni correlarij, che dalle co&longs;e dette, & <lb/>dimostrate nella precedente &longs;i manife&longs;tano, delli quali il primo è que&longs;to.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001904">CORRELARIO.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001905">Da<emph type="italics"/>lle co&longs;e dette, et dimostrate di &longs;opra, &longs;e manife&longs;ta qualmente un corpo graue in <lb/>qual &longs;i uoglia parte, che lui&longs;e parta, ouer remoui dal &longs;ito della equalita lui &longs;i fa <lb/>piu leue, ouer leggiero &longs;econdo el &longs;ito, ouer luoco, & tanto piu, <expan abbr="quãto">quanto</expan> piu&longs;ara remoßo <lb/>da tal &longs;ito, e&longs;&longs;empi gratia. </s> <s id="s.001906">El corpo.a.&longs;i trouara e&longs;&longs;er piu leue nel ponto.u.chi nel <expan abbr="põ">pom</expan> <lb/>to.s.et nel <expan abbr="põto">ponto</expan>.s.piu che nel <expan abbr="põto">ponto</expan>.q.& nel ponto.q.che nel ponto.a.&longs;ito della equali­<lb/>ta, <21> cau&longs;a della uarieta di de&longs;cen&longs;i, cioe, che luno è piu obliquo dell'altro, cioe el de&longs;cen <lb/>&longs;o.u f.ui&etilde; à eßer piu obliquo del <expan abbr="de&longs;c&etilde;&longs;o">de&longs;cen&longs;o</expan>.&longs;.u.perche la parte.f.<emph.end type="italics"/><38>.<emph type="italics"/>della direttione, è me <lb/>nore della.<emph.end type="italics"/><38>.<36>.<emph type="italics"/>et co&longs;i el <expan abbr="de&longs;c&etilde;&longs;o">de&longs;cen&longs;o</expan>.&longs;.u.ui&etilde; à eßer piu obliquo del <expan abbr="de&longs;c&etilde;&longs;o">de&longs;cen&longs;o</expan>.q.s. </s> <s id="s.001907"><21>che la par <lb/>te.<emph.end type="italics"/><38>.<36>.<emph type="italics"/>è menore della parte.<emph.end type="italics"/><36>.<emph type="italics"/>&.& lo <expan abbr="de&longs;c&etilde;&longs;o">de&longs;cen&longs;o</expan>.q.&longs;.ui&etilde; à e&longs;&longs;er piu obliquo del de&longs;cen­<lb/>&longs;o.a.q.perche la parte.<emph.end type="italics"/><36>.<emph type="italics"/>&.è menore della parte.&.c.& per le mede&longs;ime ragioni &longs;i <lb/>manife&longs;ta del corpo.b.cioe, che quello &longs;ara piu leue nel <expan abbr="põto">ponto</expan>.i.che nel <expan abbr="põto">ponto</expan>.l.& nel po<lb/>to.l.che nel ponto.n.& nel ponto.n.che nel ponto.b.&longs;ito della equalita.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001908">CORRELARIO SECONDO.</s> </p> <p type="main"> <s id="s.001909">An<emph type="italics"/>chora per le co&longs;e dette, & dimostrate &longs;e manife&longs;ta, che remuouendo&longs;i li detti <lb/>dui corpi dal detto &longs;ito della equalita, cioe luno <expan abbr="ĩ">im</expan> giu&longs;o, et laltro in&longs;u&longs;o, anchor<emph.end type="italics"/><pb pagenum="91" xlink:href="042/01/182.jpg"/><emph type="italics"/>che l'uno, e l'altro &longs;ia fatto piu leue &longs;econdo il &longs;ito, tamen in ogni po&longs;itìone men leue &longs;i <lb/>trouara quello che &longs;ara in alto elleuato di quello, che &longs;i trouara al ba&longs;&longs;o oppre&longs;&longs;o, & <lb/>que&longs;to é manife&longs;to per la argomentatione di &longs;opra adutta, cioe che il corpo.b.nel &longs;ito, <lb/>ouer ponto.i.e&longs;&longs;er piu graue del corpo.a.nel &longs;ito, ouer ponto.u.& co&longs;i nelli altri &longs;iti <lb/>&longs;uperiori &longs;i trouara piu graue del corpo.a.nelli &longs;iti inferiori, &longs;imili.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.001910">E <emph type="italics"/>ue ho <lb/>inte&longs;o, &longs;eguitati.<emph.end type="italics"/> NICOLO. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001911">QVESITO. XXXIII. PROPOSITIONE VI.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001912">Qv<emph type="italics"/>ando che la po&longs;itione d'una libra de bracci eguali &longs;ia nel &longs;ito della egualita, & <lb/>che nella i&longs;tremita dell'uno è l'altro brazzo ui &longs;iano appe&longs;i corpi &longs;implicemen <lb/><gap/>e ineguali di grauita, dalla parte doue &longs;ara il piugraue &longs;ara sforzata à declinare per <lb/>fin alla linea della direttione.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.001913">A <emph type="italics"/>me non pare che que&longs;ta uo&longs;tra propo&longs;itione po&longs; <lb/>&longs;a e&longs;&longs;er uniuer&longs;almente uera, & que&longs;to uoglio che uoi mede&longs;imo il confe&longs;&longs;ati perche uoi <lb/>&longs;apeti che nel Correlario precedente haueti conchiu&longs;o, che remouendo&longs;i li detti dui cor <lb/>pi.a.&.b. (dalla figura della precedente propo&longs;itione) dal &longs;ito della egualita, cioe l'u­<lb/>no in giu&longs;o, & l'altro in&longs;u&longs;o, anchor che l'uno è l'altro &longs;ia fatto piu leue, ouer leggero, <lb/>&longs;econdo il &longs;ito, tamen in ogni po&longs;itione men leue &longs;i trouara quello, che &longs;ara in alto elle­<lb/>uato di quello, che &longs;i trouara quello, che &longs;ara à ba&longs;&longs;o inclinato.<emph.end type="italics"/> N. E<emph type="italics"/>glie il uero Si­<lb/>gnore.<emph.end type="italics"/> S.A. S<emph type="italics"/>e que&longs;to è uero, eglie da credere, anci da tener per fermo, che chi impo <lb/>ne&longs;&longs;e &longs;opra al corpo.a.à ba&longs;&longs;o inclinato, un'altro corpetto qual in grauita fu&longs;&longs;e eguale <lb/>à quella differentia, che il corpo elleuato è piu graue, &longs;econdo il &longs;ito del corpo à ba&longs;&longs;o <lb/>inclinato, che cadauno de loro re&longs;taria nel proprio luoco doue &longs;i troua&longs;&longs;e, & accio me­<lb/>glio me intendiati, uoi &longs;apeti che il corpo.b.della figura della precedente propo&longs;itione, <lb/>&longs;tante elleuato per fin al ponto.i. (come in quello appare) & il corpo.a.à ba&longs;&longs;o inclina <lb/>to per fin al ponto.u.uoi approua&longs;ti il detto corpo.b.in tal &longs;ito e&longs;&longs;er piu graue del cor <lb/>po.a.<emph.end type="italics"/> N. S<emph type="italics"/>ignore eglie il uero.<emph.end type="italics"/> S.A. A<emph type="italics"/>dunque conchiudo che chi impone&longs;&longs;e in tal <lb/>&longs;ito un'altro corpetto &longs;opra alcorpo.a.qual fu&longs;&longs;e preci&longs;amente di tanta grauita, quan <lb/>to, che è la <expan abbr="differ&etilde;tia">differentia</expan>, che è fra li detti dui corpi.a.&.b.in tal po&longs;itione li detti dui cor <lb/>pire&longs;tariano fermi, & &longs;tabili in tal po&longs;itione, perche in tal&longs;ito &longs;e trouariano egualmen <lb/>te potenti, cioe il corpo.b.non &longs;aria &longs;officiente à far rea&longs;cendere il detto corpo.a.al &longs;i­<lb/>to della egualita, per e&longs;&longs;er il detto corpo.a. (per uigor di quel corpetto aggionto) tan­<lb/>to graue è potente quanto lui, cioe che per quel tanto che il detto corpo.b. <!-- REMOVE S-->è piu poten­<lb/>te, ouer graue per uigor del &longs;ito del corpo.a.per quel tanto &longs;ara piu graue il detto cor <lb/>po.a.del detto corpo.b.per uigore della grauita di quel &longs;implice corpetto aggiontoui <lb/>&longs;opra, per ilche il detto corpo.b.non &longs;ara atto à far rea&longs;cendere il detto corpo.a.al &longs;i­<lb/>to della egualita, & manco il corpo.a.&longs;ara atto à potere piu elleuare il detto corpo.b. <lb/><!-- REMOVE S-->del &longs;ito.i.e pero l'uno è l'altro de neceßita non &longs;e potra partire di tal &longs;uo luoco, cioe il <lb/>corpo.a.con la gionta di quell'altro corpo, non potra rea&longs;cendere al &longs;ito della eguali­<lb/>ta, ne manco potra de&longs;cendere alla linea della direttione, cioe al ponto.f.come &longs;e con­<lb/>chiude nella uostra propo&longs;itione, & pur il detto corpo.a.in&longs;ieme con quell'altro cor­<lb/>petto aggionto, &longs;aria &longs;implicemente piu graue del corpo.b.e per tanto non poteti ne-<pb xlink:href="042/01/183.jpg"/>gare che tal uo&longs;tra propo&longs;itione non &longs;ia fal&longs;a in quanto al generale, eglie ben uero, che <lb/>&longs;e la grauita di quel corpetto che fu&longs;&longs;e aggionto &longs;opra al detto corpo.a.fu&longs;&longs;e maggiore <lb/>della grauita, nella quale il corpo.b.è piu graue per uigor del &longs;ito del corpo.a. <!-- REMOVE S-->&longs;eguiria <lb/>quello che nella detta uo&longs;tra propo&longs;itione &longs;e conchiude, & &longs;e per ca&longs;o tal grauita di cor <lb/>petto fu&longs;&longs;e menore di detta differentia, tal corpo.b.faria a&longs;cendere il detto corpo.a.in <lb/>un'altro &longs;ito piu alto del ponto.u. </s> <s id="s.001914">&longs;econdo che piu, ouer men &longs;car&longs;eza&longs;&longs;e la grauita di <lb/>tal corpetto della detta differentia che è fra loro per uigor del &longs;ito.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;ta oppo <lb/>&longs;itione di<emph.end type="italics"/> V.S. <emph type="italics"/>certamente è molto &longs;peculatiua, & bella, nondimeno auerti&longs;co quella, <lb/>che &longs;e ben il corpo.b.in tal &longs;ito.i.&longs;ia piu graue del corpo.a.nel &longs;ito.u.la differentia di <lb/>que&longs;te due grauita ineguale è tanto piccola, ouer minima, ch'eglie impoßibile à potere <lb/>ritrouare una co&longs;i piccola, ouer minima differentia fra due quantita ineguale.<emph.end type="italics"/> S. A. <lb/>Q<emph type="italics"/>uesto che haueti detto mi pare una co&longs;a molto ab&longs;orda da dire, & manco da crede­<lb/>re, perche e&longs;&longs;endo la quantita continua diui&longs;ibile in infinito, eglie una materia à uoler <lb/>dire, che il &longs;ia impoßibile à dare un corpettino di tanta poca quantita, & grauita, quan <lb/>to che è la differentia che è fra la grauita del corpo.b.nel &longs;ito.i.& quella del corpo.a. <lb/><!-- REMOVE S-->nel &longs;ito.u.<emph.end type="italics"/> N. S<emph type="italics"/>ignore la ragione é quella che ne chiari&longs;&longs;e le co&longs;e dubbio&longs;e, & che ne <lb/>di&longs;cerne il uero dal fal&longs;o.<emph.end type="italics"/> S.A. E<emph type="italics"/>glie il uero.<emph.end type="italics"/> N. S'<emph type="italics"/>eglie il uero, nanti che<emph.end type="italics"/> V.S. <emph type="italics"/>dia <lb/>a&longs;&longs;oluta &longs;ententia alla mia propo&longs;itione quella a&longs;colti prima le mie ragioni.<emph.end type="italics"/> S.A. S<emph type="italics"/>e­<lb/>guitati, & dite cio, che ui pare.<emph.end type="italics"/> N. S<emph type="italics"/>ia e&longs;&longs;empi gratia, la mede&longs;ima libra.a.b.c.della <lb/>precedente propo&longs;itione, nelle istremita, della quale &longs;iano pur appe&longs;i li dui corpi.a. <lb/></s> <s id="s.001915">b.eguali &longs;implicemente in grauita, & &longs;ia abba&longs;&longs;ato con la mano il corpo.a.& elleuato <lb/>il corpo.b.come di &longs;otto appare in figura. </s> <s id="s.001916">Dico che in tal &longs;ito, il corpo.b. <!-- REMOVE S-->è piu ponde­<lb/>ro&longs;o, ouer graue per uigor del &longs;ito del corpo.a.& che la differentia che è fra le grauita <lb/>de questi dui corpi, eglie impoßibile à poterla dar, ouer trouar fra due quantita ine­<lb/>guale, & per dimo&longs;trar questa propo&longs;itione. </s> <s id="s.001917">Tiro le due rette linee.a.h.&.b.d.per­<lb/>pendicolare uer&longs;o il centro del mondo, & tiro anchora le due linee.a.l.&.b.m.contin <lb/>gente il detto cerchio, che de&longs;criue li brazzi della libra, l'una nel ponto.a.& l'altra <lb/>nel ponto.b. </s> <s id="s.001918">Et de&longs;criuo anchora una parte de una circonferentia d'un cerchio, contin <lb/>gente il mede&longs;imo cerchio.a.e.b.in ponto. </s> <s id="s.001919">b.la qual &longs;ia pur d'un cerchio &longs;imile, & e­<lb/>guale al mede&longs;imo cerchio.a. </s> <s id="s.001920">e. <!-- REMOVE S-->b. <!-- REMOVE S-->la qual parte pongo che &longs;ia la.b.z.tal che l'arco.b. <lb/></s> <s id="s.001921">z.uien à e&longs;&longs;er &longs;imile, & eguale all'arco.a.f.& anchora &longs;imilmente po&longs;to, cioe nel me­<lb/>de&longs;imo &longs;ito, ouer luoco, & la linea.b.m.che continge, ouer tocca quello, & perche la <lb/>obliquita dell'arco.a.f. (per quello che fu detto &longs;opra la terza petitione) uien mi&longs;ura­<lb/>ta, ouer con&longs;iderata per meggio dell'angolo contenuto dalla perpendicolar.a.h. </s> <s id="s.001922">& dal <lb/>la circonferentia.a.f. </s> <s id="s.001923">in ponto.a. </s> <s id="s.001924">& la obliquita dell'arco.b.f. </s> <s id="s.001925">uien mi&longs;urata, ouer <lb/>con&longs;iderata per meggio dell'angolo contenuto dalla perpendicolar. </s> <s id="s.001926">b. <!-- REMOVE S-->d. <!-- KEEP S--></s> <s id="s.001927">& dalla <lb/>circonferentia. </s> <s id="s.001928">b. <!-- REMOVE S-->f. <!-- REMOVE S-->in ponto.b. </s> <s id="s.001929">adunque il corpo.b.in tal &longs;ito ueneria ad e&longs;&longs;er tanto <lb/>piu graue del corpo.a.quanto che il detto angolo (contenuto dalla perpendicolar.b.d. <lb/></s> <s id="s.001930">& dalla circonferentia.b.f.in ponto.b.) &longs;ara menore dell'angolo contenuto dalla per­<lb/>pendicolar.a.b. </s> <s id="s.001931">& dalla circonferentia.a.f.in ponto.a. </s> <s id="s.001932">& perche il detto angolo.h.a. <lb/></s> <s id="s.001933">f.è preci&longs;amente eguale all'angolo.d.b.z.& lo detto angolo.d.b.z.uien ad e&longs;&longs;er tanto <lb/>maggiore dell'angolo contenuto dalla detta perpendicolare,b.d.& dalla circonferen-<emph.end type="italics"/><pb pagenum="92" xlink:href="042/01/184.jpg"/><emph type="italics"/><gap/>a.b.f.in ponto.b.quanto che é l'angolo della contingentia delli dui cerchij.b.z.&.b. <lb/></s> <s id="s.001934">f. <!-- REMOVE S-->in ponto. </s> <s id="s.001935">b. <!-- REMOVE S-->& perche il detto angolo della detta contingentia é acutißimo de tutti <lb/>li angoli acuti de linee rette (come per la decima&longs;e&longs;ta del terzo di Euclide facilmente <lb/>&longs;i puo approuare) adunque la differentia, ouer proportione, che ca&longs;ca fra l'angolo. <lb/></s> <s id="s.001936">h.a.f. <!-- REMOVE S-->& l'angolo contenuto dalla perpendicolar.b.d. </s> <s id="s.001937">& della circonferentia.b.f. </s> <s id="s.001938">in <lb/>ponto.b.è menore di qual &longs;i uoglia differentia, ouer proportione, che ca&longs;car po&longs;&longs;a fra <lb/>qual &longs;i uoglia maggiore, & menor quantita, & co&longs;i (per la terza petitione) la diffe­<lb/>rentia della obliquita del de&longs;cen&longs;o.a.f.& del de&longs;cen&longs;o.b.f.& con&longs;equentemente la di&longs;­<lb/>ferentia della detta grauita delli detti dui corpi.a. </s> <s id="s.001939">&.b.&longs;econdo il &longs;ito è menore, del <lb/>quale &longs;i uoglia fra due quantita ineguale, e pero ogni piccola quantita corporea, che <lb/>&longs;ia aggionta &longs;opra il corpo.a.nece&longs;&longs;ariamente in ogni &longs;ito &longs;ara piu graue del corpo.b. <lb/><!-- REMOVE S-->e pero non ce&longs;&longs;ara di de&longs;cendere continuamente <21> fin alla linea direttione, cioe <21> uigor <lb/>fin al ponto.f. </s> <s id="s.001940">& co&longs;i continuamente quello andara elleuando il corpo.b. <!-- REMOVE S-->per fin alla <lb/>detta linea della direttione, cioe per fin al ponto.e.& &longs;e que&longs;to &longs;eguiria in tal &longs;ito, co­<lb/>me che nella &longs;otto&longs;critta figura appare tanto piu &longs;eguiria nel &longs;ito della egualita, nel <lb/>qual &longs;ito, ouer luoco non ui è, ouer &longs;aria alcuna differentia, <21> uigor del &longs;ito, ne <21> uigor <lb/>delli lor de&longs;cen&longs;i, cioe che in tal &longs;ito &longs;ariano egualmente graui, e pero ogni piccola <lb/>quantita di pe&longs;o per minima, che &longs;ia, che ui &longs;ia impo&longs;to dall'una delle bande di qual &longs;i <lb/>uoglia libra (cioe granda, ouer piccola de brazzi eguali) immediate fara declinare <lb/>nece&longs;&longs;ariamente quella da quella mede&longs;ima banda, ouer brazzo, & continuara tal &longs;u<gap/><lb/>declinatione (per le ragioni di &longs;opra adutte) per fin alla linea della direttione, cioe <lb/>per fin al ponto.f.la qual co&longs;a &longs;aria contra à quelle due conclu&longs;ioni, che adduce Ari­<lb/>&longs;totile &longs;opra la &longs;ua prima que&longs;tione Mecanica, delle quale altra uoltane parlai con <lb/>Vo&longs;tra Signoria, delle quale in l'una dice, che &longs;ono alcuni pe&longs;i, li quali impo&longs;ti nel­<lb/>le piccole libre, non &longs;e fanno manife&longs;ti con alcuna inclinatione al &longs;en&longs;o, & che nel­<lb/>le grande libre &longs;e fanno manifesti, la qual conclu&longs;ione, &longs;umendola Mathematica­<lb/>mente, cioe a&longs;tratta da ogni materia, &longs;aria fal&longs;ißima (per le ragioni di &longs;opra adutte) <lb/>perche &longs;i nelle piccole, come nelle grande libre, da quella banda doue &longs;ara po&longs;to quel <lb/>tal pe&longs;o (per piccol che &longs;ia) &longs;ara sforzata à declinar per fina alla detta linea della di­<lb/>rettione, e pero nella declinatione della piccola, & in quella della granda, non &longs;ara <lb/>proportionalmente alcuna differentia, perche in luna, e l'altra la declinatione &longs;ara <lb/>per fina alla linea della direttione, il mede&longs;imo &longs;eguiria dell'altra &longs;ua conclu&longs;ione, <lb/>cioe quando dice, che &longs;ono alcuni pe&longs;i, li quali &longs;ono manife&longs;ti in luna, & l'altra <lb/>&longs;orte de libre, cioe nelle maggiori, & nelle menori, ma molto piu nelle maggiori, <lb/>la qual conclu&longs;ione (per le ragioni di &longs;opra adutte) &longs;aria pur fal&longs;a, perche, come <lb/>detto in luna, & l'altra fara declinare il brazzo della libra per fina alla linea <lb/>della direttione.<emph.end type="italics"/> S. AMBASCIATORE. Q<emph type="italics"/>ue&longs;te uo&longs;tre ragioni, & argo­<lb/>menti &longs;ono ottimi è buoni, nondimeno nelle libre naturale, ouer materiale il &longs;i uede <lb/>pur &longs;eguire la maggior parte delle uolte, come che Ari&longs;totile conchiude, & dice, <lb/>perche &longs;e &longs;opra qual &longs;i uoglia libra (cioe granda, ouer piccola) ui &longs;ara posto <gap/>­<lb/>no grano, ouer &longs;emenza di papauero, o altra &longs;imile piccola quantita, rare libre &longs;e <lb/>ritrouara che per &longs;i poca grauita, &longs;acciano inclinatione &longs;en&longs;ibile, & &longs;i pur ni &longs;e ne ri-<pb xlink:href="042/01/185.jpg"/>trouard alcuna che faccia alcun &longs;en&longs;ibile &longs;egno de declinatione, tamen non procedera <lb/>per fina alla detta linea della direttione, & non &longs;olamente il detto gran de papauero <lb/>non&longs;ara atto à farla declinare per fin alla detta linea della direttione alcuna libra, ma<emph.end type="italics"/><lb/><figure id="id.042.01.185.1.jpg" xlink:href="042/01/185/1.jpg"/><lb/><emph type="italics"/>nanche un gran di formento, qual é molto piu pondero&longs;o, & tutto que&longs;to la &longs;perientia <lb/>lo manife&longs;ta. </s> <s id="s.001941">Si che non &longs;o che mi dire, perche da una banda per le uo&longs;tre ragioni, & ar <lb/>gomenti, uedo, & comprendo che uoi diceti il uero, & dall'altra trouo per i&longs;perientia <lb/>&longs;eguir tutto al contrario.<emph.end type="italics"/> N. I<emph type="italics"/>l tutto procede Signor, dalla materia, perche nelle li­<lb/>bre con&longs;iderate con la mente fuora de ogni materia il &longs;uo &longs;parto, polo, ouer aßis, &longs;e &longs;up <lb/>pone un ponto indiui&longs;ibile, et nelle libre materiale, tal &longs;parto, ouer aßis ha &longs;empre qual <lb/>che corporal gro&longs;&longs;ezza in &longs;e, la qual gro&longs;&longs;ezza, quanto è maggiore tanto men <expan abbr="dilig&etilde;-te">diligen­<lb/>te</expan> redu&longs;&longs;e la detta libra, & &longs;imilmente li brazzi delle libre imaginate (cioe ideale) &longs;e <lb/>&longs;uppongano linee, cioe &longs;enza larghezza, ne gro&longs;&longs;ezza, & nelle libre materiale tai <lb/>brazzi &longs;ono di alcun metallo, ouer di legno, li quali brazzi quanto piu &longs;ono corpulen­<lb/>ti, è großi tanto men diligente reducano tal libre.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.001942">E <emph type="italics"/>ue ho inte&longs;o, &longs;eguitati&longs;e he <lb/>ueti altra propo&longs;itione de adure circa à que&longs;tamateria.<emph.end type="italics"/> NIC. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001943">QVESITO. XXXIIII. PROPOSITIONE VII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001944">Se <emph type="italics"/>li brazzi della libra &longs;aranno ineguali, et che nella i&longs;tremita di cadauno de quelli <lb/>ui &longs;iano appe&longs;i corpi&longs;implicemente eguali in grauita dalla banda del piu <expan abbr="lõgo">longo</expan> braz <lb/>zo tal libra fara declinatione.<emph.end type="italics"/> S. A. Q<emph type="italics"/>ue&longs;ta <lb/>è co&longs;a naturale.<emph.end type="italics"/> N. A<emph type="italics"/>nchor che la &longs;ia co&longs;a na <lb/>turale uolendo procedere rettamente, bi&longs;ogna <lb/>aßignar la cau&longs;a di taleffetto.<emph.end type="italics"/> S.A. S<emph type="italics"/>eguitati.<emph.end type="italics"/><lb/>N. S<emph type="italics"/>ia la uerga, ouer libra.a.c.b.et &longs;iail braz <lb/>zo.a.c.piu longo del.c.b. </s> <s id="s.001945">Dico che e&longs;&longs;endo ap­<lb/>pe&longs;i corpi &longs;implicemente eguali in grauita, nelli <lb/>dui ponti.a.&.b.tal libra declinara dalla par­<lb/>te del.a. </s> <s id="s.001946">Perche e&longs;&longs;endo tirata la perpendicola­<lb/>re.c.f.g. (cioe la linea della direttione) et e&longs;&longs;en<emph.end type="italics"/><lb/><figure id="id.042.01.185.2.jpg" xlink:href="042/01/185/2.jpg"/><pb pagenum="93" xlink:href="042/01/186.jpg"/><emph type="italics"/>do circindle le due quarte parte de circuli, &longs;opra el centro.c.le quale &longs;iano.a.g. </s> <s id="s.001947">&. </s> <s id="s.001948">b. <lb/>f.& e&longs;&longs;endo dutte dal ponto.a.&.b.due linee contingente, le quale &longs;iano.a.e.&.b.d. <lb/></s> <s id="s.001949">Eglie manife&longs;to langolo.e.a.g.della detta contingentia, e&longs;&longs;er menore de langolo. </s> <s id="s.001950">d. <!-- KEEP S--></s> <s id="s.001951">b. <lb/>f.e pero manco obliquo é il de&longs;cen&longs;o fatto per.a.g. </s> <s id="s.001952">del de&longs;cen&longs;o fatto per. </s> <s id="s.001953">b. <!-- REMOVE S-->f, e pero <lb/>(per la terza petitione) piu graue &longs;ara il corpo.a.del corpo.b, in tal &longs;ito, ch'è il pro­<lb/>po&longs;ito.<emph.end type="italics"/> S. A. <!-- KEEP S--></s> <s id="s.001954">E <emph type="italics"/>ue ho inte&longs;o, &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001955">QVESITO. XXXV. PROPOSITIONE VIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001956">Se <emph type="italics"/>li brazzi della libra &longs;aranno proportionali alli pe&longs;i in quella impo&longs;ti, talmen­<lb/>te, che nel brazzo piu corto &longs;ia appe&longs;o il corpo piu graue, quelli tai corpi, ouer <lb/>pe&longs;i &longs;eranno equalmente graui, &longs;econdo tal po&longs;itione, ouer &longs;ito.<emph.end type="italics"/> S.A. D<emph type="italics"/>atime uno e&longs; <lb/>&longs;empio.<emph.end type="italics"/> N. S<emph type="italics"/>ia come prima la regola, ouer libra,a.c.b. </s> <s id="s.001957">& ui &longs;iano appe&longs;i. </s> <s id="s.001958">a.&.b. <!-- REMOVE S-->et <lb/>&longs;ia la proportione del.b.al.a.&longs;i come del brazzo.a.c.al brazzo.b.c. </s> <s id="s.001959">Dico, che tal li­<lb/>bra non declinara in alcuna parte di quella, & &longs;e poßibil fuße (per lauer&longs;ario) che de­<lb/>cl inar pote&longs;&longs;e, poniamo che quella declini dalla parte del b.& che quella di&longs;cenda, & <lb/>tran&longs;i&longs;ca in obliquo, &longs;i come &longs;ta la linea.d.c.e.in luoco della.a.c.b.& attaccatoui.d.co <lb/>me.a.&.e.come.b.& la linea.d.f.de&longs;cenda orthogonalmente, & &longs;imelmente a&longs;cenda <lb/>la.e.h. </s> <s id="s.001960">Hor eglie manife&longs;to (per la. </s> <s id="s.001961">16. &. </s> <s id="s.001962">29. del primo di Euclide) che li dui triango <lb/>li.d.f.c.&.e.h.c.eßer de angoli equali. </s> <s id="s.001963">Onde per la. </s> <s id="s.001964">4. del &longs;e&longs;to di Euclide) quelli &longs;a­<lb/>ranno &longs;imili, & con&longs;equentemente de lati proportionali, adunque la proportione del <lb/>d.c.al.c.e.è &longs;i come del.d.f.al.e.h.& perche &longs;i come del.d.c.al.c.e.co&longs;i è dal pe&longs;o.b. </s> <s id="s.001965">al <lb/>pe&longs;o.a. (dal pre&longs;uppo&longs;ito) adunque la proportione dal.d.f.al.e.b.&longs;ara &longs;i come dal pe­<lb/>&longs;o.b.al. </s> <s id="s.001966">pe&longs;o.a.&longs;ia adunque dal.c.d.tolto la parte.c.l.equale alla.c.b.ouer alla. </s> <s id="s.001967">c. <!-- REMOVE S-->e. <!-- REMOVE S-->& <lb/>&longs;ia po&longs;to. </s> <s id="s.001968">l. <!-- KEEP S--></s> <s id="s.001969">equale al. <!-- REMOVE S-->b. <!-- REMOVE S-->in grauita, & de&longs;cenda el perpendicolo. </s> <s id="s.001970">l. <!-- REMOVE S-->m. <!-- KEEP S--></s> <s id="s.001971">Adunque per­<lb/>che eglie manife&longs;to la. </s> <s id="s.001972">l. <!-- REMOVE S-->m. <!-- REMOVE S-->& la. </s> <s id="s.001973">e. <!-- REMOVE S-->h. <!-- REMOVE S-->e&longs;&longs;er equale, la proportione della. </s> <s id="s.001974">d. <lb/><!-- KEEP S--></s> <s id="s.001975">f. <!-- REMOVE S-->alla. </s> <s id="s.001976">l. <!-- REMOVE S-->m. <!-- REMOVE S-->&longs;ara&longs;i come delle &longs;implice grauita del corpo. <!-- REMOVE S-->b. <!-- REMOVE S-->alla &longs;implice graui­<lb/>ta del corpo. <!-- REMOVE S-->a. <!-- REMOVE S-->ouer della &longs;implice grauita del corpo.l. <!-- REMOVE S-->alla &longs;implice grauita del cor­<lb/>po d. (perche li dui corpi.a.&.d.&longs;ono &longs;uppo&longs;tiuno mede&longs;imo) & &longs;imelmente el cor­<lb/>po.b.&.l.per e&longs;&longs;er &longs;uppo&longs;ta la grauita del. <!-- REMOVE S-->l. <!-- REMOVE S-->equale alla grauita del. <!-- REMOVE S-->b.) e per tanto <lb/>dico, che la proportione di tutta la.d.c.alla.l. </s> <s id="s.001977">c. <!-- REMOVE S-->&longs;ara &longs;i come la grauita del corpo.l. <lb/><!-- REMOVE S-->alla grauita del corpo.d. <!-- KEEP S--></s> <s id="s.001978">Onde &longs;e li detti dui corpi graui, cioe.d.&.l.fu&longs;&longs;eno &longs;implice <lb/>mente equali in grauita, stanti poi in limede&longs;imi &longs;iti, ouer luochi, doue, che al pre&longs;en <lb/>te uengono &longs;uppo&longs;ti, el corpo.d.&longs;aria piu graue del corpo.l.&longs;econdo el&longs;ito (per la. </s> <s id="s.001979">4. <lb/>propo&longs;itione) in tal proportione, qual é di tutto il brazzo.d.c.al brazzo.l.c.& per <lb/>che il corpo.l.è &longs;implicemente (dal pre&longs;uppo&longs;ito) piu graue del corpo.d.&longs;econdo la me <lb/>de&longs;ima proportione (cioe, &longs;i come la proportione del brazzo.d.c.al brazzo.l.c.adun <lb/>que li detti dui corpi.d.&.l.nel &longs;ito della equalita ueneranno ad e&longs;&longs;ere egualmente <lb/>graui, perche per tanto quanto il corpo.d.è piu graue del corpo.l. <!-- REMOVE S-->per uigor del &longs;ito, <lb/>ouer luoco, per quel mede&longs;imo el corpo.l. <!-- REMOVE S-->è &longs;implicemente piu graue del corpo.d.e pe <lb/>vo nel detto &longs;ito della equalita uengono à restare egualmentè graui. </s> <s id="s.001980">Adunque quella <lb/>potentia, ouer grauita, che &longs;ara &longs;ufficiente ad elleuare il corpo.a.dal &longs;ito della equali­<lb/>ta, al ponto, doue che al pre&longs;ente è (cioe per fin al ponto.d.) quella mede&longs;ima &longs;ara&longs;o&longs;a<emph.end type="italics"/><pb xlink:href="042/01/187.jpg"/><emph type="italics"/>ficiente ad elleuare il corpo.l.dal mede&longs;imo &longs;ito della equalita al luoco, doue che al pre <lb/>&longs;ente è. </s> <s id="s.001981">Adunque &longs;el corpo.b. (per lauer&longs;ario) è atto ad elleuare il corpo. <!-- REMOVE S-->a. <!-- REMOVE S-->dal &longs;ito <lb/>della equalita per fin al ponto.d.el mede&longs;imo corpo.b.&longs;aria anchora atto, e &longs;officiente <lb/>ad elleuare il corpo.l.dal mede&longs;imo &longs;ito della equalita per fin al ponto, doue che al pre <lb/>&longs;ente è, el qual con&longs;equente é fal&longs;o, & con­<lb/>tra alla quinta propo&longs;itione, cioe el corpo <lb/>b. (qual è &longs;upposto equale in grauita al <lb/>corpo.l.) elleuaria il detto corpo. <!-- REMOVE S-->l. <!-- REMOVE S-->fuora <lb/>del &longs;ito della equalita, in &longs;iti equali, cioe e­<lb/>qualmente di&longs;tanti dal centro.c.la qual co­<lb/>&longs;a é impoßibile per la detta quinta propo­<lb/>&longs;itione, di&longs;trutto adunque l'oppo&longs;ito, rima <lb/>ne il propo&longs;ito.<emph.end type="italics"/> S. A. Q<emph type="italics"/>uesta è una a&longs;­<lb/>&longs;ai bella propo&longs;itione, ma el me pare, &longs;e <expan abbr="b&etilde;">bem</expan> <lb/>me arricordo, che Archimede Syracu&longs;ano<emph.end type="italics"/><lb/><figure id="id.042.01.187.1.jpg" xlink:href="042/01/187/1.jpg"/><lb/><emph type="italics"/>ne ponga una &longs;imile, ma el non mi pare, che lui la dimo&longs;tri per que&longs;to uo&longs;tro modo.<emph.end type="italics"/><lb/>N. V<emph type="italics"/>o&longs;tra Signoria dice la uerita, anci di tal propo&longs;itione, lui ne fa due propo&longs;itio­<lb/>ni, & que&longs;te &longs;ono la quarta, & quinta di quel libro, doue tratta delli centri delle co&longs;e <lb/>graue, & in effetto tai due propo&longs;itioni lui le dimostra &longs;uccintamente per li &longs;uoi prin <lb/>cipij da lui per auanti po&longs;ti, & demostrati, & perche tai &longs;ui principij, ouer argomen <lb/>ti.non &longs;e conuegnariano in que&longs;to trattato, per eßer materia <expan abbr="alquãto">alquanto</expan> diuer&longs;a da quel­<lb/>la, ne appar&longs;o in questo luoco de dimo&longs;trare tal propo&longs;itioni con altri principij, ouer <lb/>argomenti piu conuenienti in que&longs;to luoco.<emph.end type="italics"/> S.A. E<emph type="italics"/>ue ho inte&longs;o &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.001982">QVESITO XXXVI. PROPOSITIONE IX.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001983">Se <emph type="italics"/>&longs;aranno due &longs;olide uerghe, traui, ouer ba&longs;toni di una &longs;imile, & equal longhez <lb/>za, larghezza, gro&longs;&longs;ezza, & grauita, & che &longs;iano appe&longs;i in una libra talmente <lb/><gap/>he luno &longs;tia equidi&longs;tante al orizonte, & laltro dependi perpendicolarmente, & tal­<lb/>mente anchora, che del termine del dependente, & del mezzo dell'altro &longs;ia una mede <lb/>&longs;ima di&longs;tantia dal centro della libra, &longs;econdo tal&longs;ito, ouer po&longs;itione ueneranno à eßere <lb/>equalmente graui.<emph.end type="italics"/> S.A. N<emph type="italics"/>on ue intendo, e pero datime uno e&longs;&longs;empio.<emph.end type="italics"/> N. E<emph type="italics"/>&longs;&longs;em­<lb/>pi gratia. </s> <s id="s.001984">Siano li termini dellibrazzi della libra.b.&.d.& il &longs;parto, ouer centro di <lb/>quella il ponto.c.& ui &longs;iano attaccati li dui &longs;olidi &longs;imili, & equali, come detto, delli <lb/>quali luno ui &longs;ia attaccato &longs;econdo lordine del bra<emph.end type="italics"/>zz<emph type="italics"/>o della libra, cioe equidistanta­<lb/>mente al orizonte qual &longs;ia.f.e.del qual il &longs;uo ponto di me<emph.end type="italics"/>zz<emph type="italics"/>o &longs;ia el ponto.d.& laltro <lb/>&longs;ia attaccato pendente perpendicolarmente qual &longs;ia.b.g. </s> <s id="s.001985">& &longs;ia il termine del &longs;uo at­<lb/>taccamento il ponto.b.& &longs;ia che la di&longs;tantia del ponto.b.al ponto. </s> <s id="s.001986">c. (centro della li­<lb/>bra) &longs;ia tanto, quanto ch'è dal ponto di mezzo de laltro &longs;olido (cioe dal <expan abbr="põto">ponto</expan>.d.) al me <lb/>de&longs;imo ponto.c. </s> <s id="s.001987">Dico che li detti dui &longs;olidi, in tal &longs;ito, ouer po&longs;itione &longs;ono equalmen­<lb/>te graui, & que&longs;to &longs;e puo dimostrar in piu modi. </s> <s id="s.001988">El primo di quali é que&longs;to, ch'eglie <lb/>manife&longs;to per le co&longs;e dimostrate da Archimede in quello del centro della grauita, che<emph.end type="italics"/><pb pagenum="94" xlink:href="042/01/188.jpg"/><emph type="italics"/>tanto pe&longs;a il &longs;olido.f.e.in tal po&longs;itione nella detta libra, quanto che faria &longs;e quello fu&longs;­<lb/>&longs;e anchora lui appe&longs;o perpendicolarmente in ponto.d.perche in tal ponto. </s> <s id="s.001989">d. <!-- KEEP S--></s> <s id="s.001990">ui &longs;otto <lb/>giace el centro della grauita de tal &longs;olido, & per e&longs;&longs;er li detti dui &longs;olidi equali in gra­<lb/>uita dal pre&longs;uppo&longs;ito, & appe&longs;i equalmente di&longs;tanti dal ponto, ouer centro.c. </s> <s id="s.001991">quelli <lb/>(per la. </s> <s id="s.001992">5. propo&longs;itione) non &longs;e &longs;eparano dal &longs;ito della equalita, ch'é il propo&longs;ito.<emph.end type="italics"/></s> </p> <figure id="id.042.01.188.1.jpg" xlink:href="042/01/188/1.jpg"/> <p type="main"> <s id="s.001993">A<emph type="italics"/>nchora tal propo&longs;itione &longs;i puo demo&longs;trar in que&longs;to altro modo (el quale é piu &longs;ua <lb/>conueniente dimostr atione, perche &longs;e uien à dimo&longs;trare per li &longs;uoi proprij Principij, <lb/>& non per principij alieni. </s> <s id="s.001994">Eglie manife&longs;to, che e&longs;&longs;endo &longs;u&longs;pe&longs;i dui pe&longs;i &longs;implicemen­<lb/>te equali, luno in ponto.f.& laltro in ponto.e.quali poniamo, che &longs;iano.h.<emph.end type="italics"/>k. <emph type="italics"/>& &longs;imel <lb/>mente dui altri equali alli mede&longs;imi in ponto.b.quali &longs;iano.l.m.nelli quali &longs;iti, dico, che <lb/>tai pe&longs;i pe&longs;ar anno equalmente, perche la proportione del pe&longs;o. </s> <s id="s.001995">l. <!-- REMOVE S-->al pe&longs;o.<emph.end type="italics"/> k. <emph type="italics"/>è &longs;i come <lb/>del brazzo.b.c.al brazzo.f.c., per la quarta propo&longs;itione, perche tanto graue &longs;aria <lb/>el corpo.l.&longs;econdo el &longs;ito nel ponto.d.quanto che nel ponto, doue &longs;i troua al pre&longs;ente, <lb/>cioe in ponto.b. (per e&longs;&longs;er.c.d.equale al.c.b.dal pre&longs;uppo&longs;ito) e pero per la detta pro <lb/>po&longs;itione, tal proportione &longs;ara della grauita del corpo. <!-- REMOVE S-->l. <!-- REMOVE S-->al corpo.<emph.end type="italics"/> k. <emph type="italics"/>&longs;econdo el &longs;ito, <lb/>quale &longs;ara del brazzo.d.c.ouer.b.c.al.c.f.& per le mede&longs;ime ragioni tal proportio­<lb/>ne &longs;ara della grauita del corpo.m.alla grauita del corpo.h.&longs;econdo el &longs;ito, quale &longs;ara <lb/>del mede&longs;imo brazzo.c.d.ouer.c.b.al brazzo.c.e.adunque la grauita de ambi dui l<gap/><lb/>corpi.l.m.in&longs;ieme alla grauita de ambi dui licorpi.h.<emph.end type="italics"/>k.<emph type="italics"/>in&longs;ieme &longs;econdo il &longs;ito &longs;ara &longs;i <lb/>come el doppio del brazzo.c.d. </s> <s id="s.001996">ouer del hrazzo.c.b.in&longs;ieme alli dui brazzi.c.f. </s> <s id="s.001997">et.c. <lb/></s> <s id="s.001998">e.pur in&longs;ieme, & perche li detti dui brazzi.c.e.&.c.f.in&longs;ieme &longs;ono preci&longs;amente tan <lb/>to, quanto è il doppio del detto bra<emph.end type="italics"/>zz<emph type="italics"/>o.c.d.ouer.c.b. </s> <s id="s.001999">&longs;eguita anchora, che la graui­<lb/>ta delli detti dui corpi.l.m. </s> <s id="s.002000">&longs;ia equale alla grauita delli dui corpi.h.&.<emph.end type="italics"/>k. <emph type="italics"/>&longs;econdo il &longs;i <lb/>to, ch'è il propo&longs;ito, perche &longs;e del &longs;opradetto &longs;olido.f.e.ne &longs;ara fatto due parti equali, <lb/>appiccandone una di quelle in ponto.f.& laltra in ponto.e.tanto pe&longs;arano co&longs;i &longs;epa­<lb/>rate in tai &longs;iti, &longs;i come faceuano in longo congionte, come di &longs;opra fu &longs;uppo&longs;to, & &longs;i­<lb/>melmente facendo del &longs;olido.b.g.pur due parti, & appiccarle ambe due in el mede&longs;i­<lb/>mo ponto.b.tanto pe&longs;arano co&longs;i &longs;eparate, come che congionte, come, che di &longs;opra &longs;i<gap/><lb/>&longs;uppo&longs;to epero per le co&longs;e detto, & allegate &longs;eguita il propo&longs;ito.<emph.end type="italics"/><pb xlink:href="042/01/189.jpg"/><figure id="id.042.01.189.1.jpg" xlink:href="042/01/189/1.jpg"/><lb/>S.A. V<emph type="italics"/>oria, che me dimo&longs;tra&longs;ti che il brazzo.c.f.in&longs;leme con il.c.e.&longs;ia tanto <expan abbr="quãto">quanto</expan> <lb/>el doppio del brazzo.d.c.ouer.c.b.<emph.end type="italics"/> N. S<emph type="italics"/>ignor eglie manife&longs;to, che tutto il bra<emph.end type="italics"/>zz<emph type="italics"/>o <lb/>c.e.è maggiore del brazzo.c.d.per la parte.e.d.la qual parte.e.d.è equale alla.d.f.di <lb/>remo adunque, che tutta la.c.e.è equal alla.c.d. </s> <s id="s.002001">& anchora alla &longs;ua parte.f.d alla qual <lb/>parte.f.d.giontoui el brazzo.f.c.queste due parti in&longs;teme &longs;e egualiano anchora loro <lb/>alla mede&longs;lma.c.d, e pero tuttala.c.e.in&longs;ieme con la.c.f. </s> <s id="s.002002">&longs;ono preci&longs;amente il doppio <lb/>della.c.d & perche la detta.c.d.è equale (dal pre&longs;uppo&longs;ito) alla.b.c.&longs;eguita, che tutta <lb/>la.c.e.in&longs;ieme con la.c.f.&longs;tano equali al doppio della.c.b. </s> <s id="s.002003">ch'è il propo&longs;ito.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.002004">E <lb/><emph type="italics"/>ue ho inte&longs;o beni&longs;simo, e pero &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.002005">QVESITO XXXVII. PROPOSITIONE X.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002006">Se<emph type="italics"/>l &longs;ara una &longs;olida uerga, traue, ouer ba&longs;tone di una &longs;imile, & equal larghezza, <lb/>gro&longs;&longs;ezza, &longs;o&longs;tantia, & grauita in ogni &longs;ua parte, & che la longhezza di quella <lb/>&longs;la diui&longs;a in due parti inequale, & che nel termine della menor parte ui &longs;la appe&longs;ouno <lb/>altro &longs;olido, ouer corpo graue, el quale faccia &longs;tare la dettauerga, traue, ouer ba&longs;tone <lb/>equidistante al orizonte. </s> <s id="s.002007">La proportione della grauita di tal corpo graue, alla diffe­<lb/>rentia della grauita della maggior parte della detta uerga (traue, ouer ba&longs;tone) alla <lb/>grauita della parte menore, &longs;ara &longs;i come la proportione della <expan abbr="lõghezza">longhezza</expan> di tutta la uer <lb/>ga (traue, ouer ba&longs;tone) al doppio della longhezza della &longs;ua menor parte.<emph.end type="italics"/> S. A. D<emph type="italics"/>a <lb/>time un e&longs;&longs;empio &longs;e uoleti, che ui <expan abbr="int&etilde;da">intenda</expan>.<emph.end type="italics"/> N. S<emph type="italics"/>ia la &longs;olida uerga (traue, ouer ba&longs;tone) <lb/>il &longs;olido.a.b.di una &longs;imile, et equal große<emph.end type="italics"/>zz<emph type="italics"/>a, larghezza, <expan abbr="&longs;o&longs;tãtia">&longs;o&longs;tantia</expan>, et grauita <21> tutto, <lb/>cioe <21> ogni parte, et &longs;ia diui&longs;o <expan abbr="cõ">com</expan> l'intelletto in due parti inequale in <expan abbr="põto">ponto</expan>.c.et &longs;ia &longs;igna <lb/>ta la.c.d.equal alla.a.c.adunque la.d.b. </s> <s id="s.002008"><expan abbr="ui&etilde;">uiem</expan> à e&longs;&longs;ere la <expan abbr="differ&etilde;tia">differentia</expan>, ch'è fra la parte mag <lb/>giore.c.b.et la menore.c.a.della qual <expan abbr="differ&etilde;tia">differentia</expan> &longs;ia trouato il mezzo, qual &longs;ia il pon­<lb/>to.e. </s> <s id="s.002009">Hor <expan abbr="eß&etilde;do">eßendo</expan> &longs;u&longs;pe&longs;o il detto &longs;olido, ouer traue.a.b.nel <expan abbr="põto">ponto</expan>.c.et <expan abbr="eß&etilde;doui">eßendoui</expan> attaccato, <lb/>ouer &longs;u&longs;pe&longs;o nel termine della &longs;ua menor parte un altro &longs;olido (poniamo il &longs;olido.f.) <lb/>qual faccia &longs;tare il primo &longs;olido, ouer traue.a.b.equidi&longs;tãte al <expan abbr="orizõte">orizonte</expan>. </s> <s id="s.002010">Dico, che tal <lb/>proportione hauera la grauita del &longs;olido.f.alla grauita della <expan abbr="differ&etilde;tia">differentia</expan>.d.b. </s> <s id="s.002011">qual hara <lb/>tutta la <expan abbr="lõghezza">longhezza</expan>.a.b.alla.a.d. </s> <s id="s.002012">cioe al doppio della <expan abbr="lõghezza">longhezza</expan> della parte menore.a.c. <lb/></s> <s id="s.002013">Perche tanto pe&longs;a la detta differentia.d.b.m tal po&longs;itione, come che al pre&longs;ente &longs;ta <expan abbr="quã">quam</expan> <lb/>to che faria &longs;e quella fu&longs;&longs;e perpendicolarmente &longs;o&longs;pe&longs;a in ponto.e.e pero (per il con-<emph.end type="italics"/><pb pagenum="95" xlink:href="042/01/190.jpg"/><emph type="italics"/>uer&longs;o della.8.propo&longs;itione) la proportione della grauit à del &longs;olido.f.alla grauita del <lb/>partial &longs;olido, ouer traue.d.b. </s> <s id="s.002014">&longs;ara, &longs;i come la proportione della di&longs;tantia.c.e.alla di­<lb/>&longs;tantia.c.a. </s> <s id="s.002015">Et la proportione, che è della di&longs;tantia.c.e.alla di&longs;tantia.c.a. (per la.15.del <lb/>quinto di Euclide) quella mede&longs;ima &longs;ar a del doppio della di&longs;tantia.c.e. </s> <s id="s.002016">al doppio della <lb/>detta di&longs;tantia.c.a.& perche il doppio della detta di&longs;tantia.c.e.è quanto che è tutta la <lb/>longhezza del &longs;olido.a.b.& il doppio della detta di&longs;tantia.c.a.è quanto che è tutta la <lb/>a.c.d. <!-- REMOVE S-->&longs;eguita (per la.11.del quinto di Euclide) che la proportione della grauita del &longs;o­<lb/>lido.f.alla grauita della pifferentia.d.b.&longs;ia &longs;i come la proportione di tutta la longhez <lb/>za del &longs;olido, ouer uerga.a.b.al doppio della longhezza della parte menore.a.c. (qual <lb/>è la detta.a.c.d.) che è il propo&longs;ito.<emph.end type="italics"/> S.A. P<emph type="italics"/>erche ragione uoleti che il doppio della<emph.end type="italics"/><lb/><figure id="id.042.01.190.1.jpg" xlink:href="042/01/190/1.jpg"/><lb/><emph type="italics"/>di&longs;tantia.c.e.&longs;ia eguale à tutta la longhezza del traue.a.b.<emph.end type="italics"/> N. P<emph type="italics"/>erche la detta di&longs;tan <lb/>tia.c.e.uien à e&longs;&longs;er preci&longs;amente eguale alla mita di tal longhezza.a.b. </s> <s id="s.002017">perche la par­<lb/>ce.d.e. </s> <s id="s.002018">é la mita della parte.d.b.& la.d.c.è la mita dell'altra parte.d.a.adunque le due <lb/>parti.d.e.&.d.c.gionte in&longs;ieme, uengono à e&longs;&longs;ere la mita delle due parti.d.b.&.d.a. <lb/></s> <s id="s.002019">pur gionte in&longs;ieme.<emph.end type="italics"/> S.A. E<emph type="italics"/>ue ho inte&longs;o, e pero &longs;eguitate in altro.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.002020">QVESITO. XXXVIII. PROPOSITIONE XI. <lb/><emph type="italics"/>conuer&longs;a della precedente.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002021">Se <emph type="italics"/>la proportione della grauita d'un &longs;olido &longs;o&longs;pe&longs;o in el termine della menor parte <lb/>di una &longs;imile &longs;olida uerga (traue, ouer ba&longs;tone) diui&longs;a in due parti ineguali, alla dif <lb/>&longs;erentia, che &longs;ara fra la grauita della maggior parte, & quella dellamenore, &longs;ara, &longs;i co <lb/>me la proportione di tutta la longhezza della &longs;olida uerga, traue, ouer ba&longs;tone, al dop­<lb/>pio della longhezza della &longs;ua menor parte. </s> <s id="s.002022">Tal &longs;olida uerga, traue, ouer ba&longs;tone, ne­<lb/>ce&longs;&longs;ariamente &longs;tara equidi&longs;tante all'Orizonte.<emph.end type="italics"/> S.A. C<emph type="italics"/>redo bene che tal precedente <lb/>propo&longs;itione &longs;e conuerti&longs;ca, nondimeno non re&longs;tati da farme la dimostratione.<emph.end type="italics"/> N. <lb/>P<emph type="italics"/>er e&longs;&longs;er que&longs;ta il conuer&longs;o della precedente, per &longs;uo e&longs;&longs;empio &longs;upponeremo la mede­<lb/>&longs;ima di&longs;po&longs;itione, ouer figura, cioe &longs;upponeremo, che la proportione della grauita del <lb/>&longs;olido.f.alla differentia della grauita della maggior parte alla grauita della menore, <lb/>cioe della.d.b.e&longs;&longs;er, &longs;i come la proportione di tutta la longhezza della &longs;olida uerga. <lb/></s> <s id="s.002023">b.al doppio della longhezza della parte menore.a.c. (quale &longs;aria la.a.d.) Dico che <lb/>&longs;tante questo la &longs;olida uerga.a.b.de neceßita &longs;tara equidi&longs;tante all'Orizonte. <!-- KEEP S--></s> <s id="s.002024">Et &longs;e po&longs; <pb xlink:href="042/01/191.jpg"/>&longs;lbil fu&longs;&longs;e (per l'auer&longs;ario) che quella debbia, ouer po&longs;&longs;a declinar da qualche banda, po <lb/>niamo che declini dalla banda uer&longs;o.b.al &longs;olido.f.gli aggiongeremo con lo intelletto <lb/>una tal parte (quale pongo che &longs;ia la parte.g.) che faccia re&longs;tare la detta &longs;olida uerga, <lb/>traue, ouer ba&longs;tone equidi&longs;tante al detto Orizonte. <!-- KEEP S--></s> <s id="s.002025">Adunque, per la precedente, la pro <lb/>portione di tutta la grauita del compo&longs;to delli dui corpi. </s> <s id="s.002026">&longs;i &.g.alla differentia, che è <lb/>fra la grauita della parte maggiore.b.c.& quella della parte menore.a c. (che &longs;aria <lb/>quella della.d.b.) &longs;ara, &longs;i come la proportione di tutta la longhezza.a.b.al doppio <lb/>della longhezza della &longs;ua parte menor.a.c. </s> <s id="s.002027">il qual doppio, &longs;aria la.a.d.& perche il <lb/>&longs;implice &longs;olido.f.ha quella mede&longs;ima proportione,alla mede&longs;ima differentia (dal pre­<lb/>&longs;uppo&longs;ito) &longs;eguitaria (per la.9.del quinto di Euclide) che la grauita del &longs;implice &longs;oli<gap/><emph.end type="italics"/><lb/><figure id="id.042.01.191.1.jpg" xlink:href="042/01/191/1.jpg"/><lb/><emph type="italics"/>do.f.fu&longs;&longs;e eguale alla grauita de tutto il compo&longs;ito di dui &longs;olidi.f.g.la qual co&longs;a è impo&longs; <lb/>&longs;ibile, che la parte &longs;ia eguale al tutto, il mede&longs;imo inconueniente &longs;eguiria quando che lo <lb/>auer&longs;ario &longs;uppone&longs;&longs;e che declina&longs;&longs;e dalla parte.a.perche &longs;egando uia dal &longs;olido.f.una <lb/>tal parte, che il rimanente face&longs;&longs;e re&longs;tare il detto &longs;olido.a.b. </s> <s id="s.002028">equidi&longs;tante all'Orizon­<lb/>te, argomentando, come di &longs;opra fu fatto, &longs;eguiria pur che la grauita del mede&longs;imo re­<lb/>fiduo fu&longs;&longs;e eguale alla grauita di tutto il &longs;olido.f. </s> <s id="s.002029">Adunque non potendo declinare ne <lb/>dalla banda uer&longs;o.b.ne da quella uer&longs;o.a.eglie nece&longs;&longs;ario che stia equidi&longs;tante all'Ori­<lb/>zonte, che è il propo&longs;ito.<emph.end type="italics"/> S.A. S<emph type="italics"/>tabenißimo, hor &longs;eguitati pur.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.002030">QVESITO. XXXIX. PROPOSITIONE XII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002031">Se<emph type="italics"/>l &longs;arauna &longs;olida uerga, trauer ba&longs;tone, come nelle due precedente è &longs;tato detto, <lb/>cioe diuna &longs;imile, & egual gro&longs;&longs;ezza, larghezza, &longs;o&longs;tantia, & grauita, in ogni <lb/>&longs;ua parte, & che di quello ne &longs;ia nota la &longs;ua grauita, & &longs;imilmente la &longs;ua longhezza, et <lb/>che quello &longs;ia diui&longs;o in due parti ineguale pur note. </s> <s id="s.002032">Eglie poßibile di ritrouar un pe&longs;o, <lb/>il quale quando che quello &longs;ara &longs;o&longs;pe&longs;o al termine della &longs;ua menor parte fara stare la <lb/>detta&longs;olida uerga, traue, ouer ba&longs;tone, equidi&longs;tante all'Orizonte.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;to atto <lb/>operatiuo uoglio che mel dichiarati con e&longs;&longs;empio materiale, perche lo uoglio intende­<lb/>rebene.<emph.end type="italics"/> N. S<emph type="italics"/>ia e&longs;&longs;empi gratia la &longs;olida uerga (traue, ouer ba&longs;tone) a.b.&longs;econdo che <lb/>&longs;e propone, cioe di una &longs;imile, & equal gro&longs;&longs;ezza, larghezza, &longs;o&longs;tantia, & grauita <lb/>per ogni&longs;ui banda, ouer parte, & poniamo, che la grauita di tal &longs;olida uerga ne &longs;ia<emph.end type="italics"/><pb pagenum="96" xlink:href="042/01/192.jpg"/><emph type="italics"/>nota, cioe poniamo che tutta pe&longs;i lire. </s> <s id="s.002033">40. et che &longs;imilmente la longhezza di tal uerga, <lb/>ouer ba&longs;tone, ne &longs;ia nota, cioe poniamo che quella &longs;ia longa dui pa&longs;&longs;a, cioe dieci piedi, & <lb/>poniamo anchora che tal uerga &longs;ia diui&longs;a in due parti ineguale in ponto.c.& che le det <lb/>tè partine &longs;ia note, cioe poniamo che la parte.a.c.menore, &longs;ia piedi dui, & che la mag <lb/>gior.c.b.&longs;ta piedi. </s> <s id="s.002034">8. Hor dico, che eglie poßibile di trouare di quante libre uorra e&longs;&longs;er <lb/>quel corpo qual e&longs;&longs;endo &longs;o&longs;pe&longs;o nel ponto.a. (termine della &longs;ua menor parte) faccia &longs;ta <lb/>re la detta uerga, ouer traue equidi&longs;tante all'Orizonte. <!-- KEEP S--></s> <s id="s.002035">Perche (per le co&longs;e dimo&longs;trate <lb/>nelle due precedente propo&longs;itioni) eglie manife&longs;to, che la proportione della grauita di <lb/>quel tal corpo alla grauita di quella differentia che è fra la parte maggiore.c.b.& la <lb/>parte menore.a.c. (la qual differentia uerria à e&longs;&longs;er la.d.b.) &longs;ara, &longs;i come tutta la lon <lb/>ghezza della uerga, ouer traue.a.b. (qual è piedi. </s> <s id="s.002036">10.) al doppio della longhezza della <lb/>partemenor.a.c. (qual è piedi dui) il doppio della quale uerria à e&longs;&longs;er piedi. </s> <s id="s.002037">4. qual <lb/>pongo &longs;ia la.a.d.adunque la grauita di quel tal corpo, alla grauita della partial uerga.d. <lb/></s> <s id="s.002038">b.&longs;ara, &longs;i come la longhezza de tutta la.a.b. (qual è piedi. </s> <s id="s.002039">10.) alla longhezza della.a. <lb/></s> <s id="s.002040">d. (qual è piedi.<emph.end type="italics"/> 4.) O<emph type="italics"/>nde arguendo alcontrario, diremo, chela proportione della.a.d. <lb/>(qual è piedi. </s> <s id="s.002041">4.) à tutta la.a.b. (qual è piedi. </s> <s id="s.002042">10) &longs;ara, &longs;i come la grauita della partial <lb/>uerga.d.b.qual (alla ratta di tutta la.a.b.che libre. </s> <s id="s.002043">40.) uerria ad e&longs;&longs;er libre. </s> <s id="s.002044">24. alla <lb/>grauita del corpo che recercamo, cioe di quello, che appe&longs;o nel ponto.a.debbia man-<emph.end type="italics"/><lb/><figure id="id.042.01.192.1.jpg" xlink:href="042/01/192/1.jpg"/><lb/><emph type="italics"/>tenere la dettauerga, ouer traue equidi&longs;tante all'Orizonte. <!-- KEEP S--></s> <s id="s.002045">Onde per ritrouarlo pro­<lb/>cederemo &longs;econdo l'or dine della regola uolgarmente detta del tre, fondata &longs;opra la. </s> <s id="s.002046">20. <lb/>propo&longs;itione del. <!-- REMOVE S-->7.di Euclide, moltiplicando. </s> <s id="s.002047">10.fia.24.fa.240. & que&longs;to lo parti­<lb/>remo per.4.ne uenira.60.& libre.60.dico che pe&longs;ara, ouer che douera pe&longs;are quel <lb/>tal corpo, qual pongo fia il corpo.f.che è il propofito.<emph.end type="italics"/> S.A. Q<emph type="italics"/>uesto problema me è <lb/>piace&longs;to a&longs;&longs;ai, & l'ho inte&longs;o benißimo, e pero &longs;eguitati &longs;e ci è altro da dire.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.002048">QVESITO. XL. PROPOSITIONE XIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002049">Se<emph type="italics"/>l&longs;e hauerauna uerga, traue, ouer ba&longs;tone, come piu uolte è stato detto, del qual <lb/>ne &longs;ia nota la &longs;ua longhezza, & anchora la &longs;ua grauita, & anchora un corpo pon<lb/>dero&longs;o, del quale ne &longs;ia nota &longs;ua grauita, eglie poßibile à deter minare il luoco doue &longs;e <lb/>hauera da diuidere la data uerga, traue, ouer ba&longs;tone, talmente che appendendo il det-<pb xlink:href="042/01/193.jpg"/>to corpo pondero&longs;o al termine della &longs;ua menor parte faccia &longs;tare la detta uerga, traue, <lb/>uer ba&longs;tone, equidi&longs;tante all'Orizonte.<emph.end type="italics"/> S.A. E<emph type="italics"/>&longs;&longs;emplificatemi questa propo&longs;itione.<emph.end type="italics"/><lb/>N. P<emph type="italics"/>er e&longs;&longs;emplificar que&longs;ta propo&longs;itione, &longs;upponeremo che il &longs;ia pur unauerga, tra­<lb/>ue, ouer ba&longs;tone, come fu la precedente, cioe longa piedi.10.& che la grauita di quella <lb/>fia pur libre.40. (come che nella detta precedente fu &longs;uppo&longs;to.) Et poniamo anchora <lb/>che il &longs;ia un corpo che la grauita di quello &longs;ia libre.80. Dico ch'eglie poßibile à deter <lb/>minare il luoco doue &longs;e debbe diuidere la detta uerga, talmente che appendendo il det­<lb/>to corpo graue al termine della &longs;ua menor parte, faccia &longs;tar quella equidi&longs;tante all'<emph.end type="italics"/>O­<lb/><emph type="italics"/>rizonte. </s> <s id="s.002050">Et quantunque tal problema, &longs;i po&longs;&longs;a ri&longs;oluere per uia di proportioni, nondi­<lb/>meno piu leggiadr amente, &longs;e ri&longs;olue per Algebra, ponendo che la parte menore della <lb/>detta uerga &longs;ia una co&longs;a de pie, onde la parte maggiore ueneria à re&longs;tare piedi.10. <lb/>men.1.co. </s> <s id="s.002051">Duplico la menor parte, cioe.1 co.fa.2.co, & queste.2.co&longs;e le &longs;ottro da tut <lb/>ta la uerga qual è piedi.10.re&longs;ta piedi.10 men.2.co&longs;e, & que&longs;to &longs;ara la differentia, <lb/>che è fra la parte maggiore, & la menore della detta uerga, onde per trouar la graui­<lb/>ta di tal differentia, la moltiplico per.4. (perche pe&longs;ando tutta la uerga libre.40.ue <lb/>neria ogni pie di quella à pe&longs;ar lire.4.) e pero moltiplicando quella per.4. come detto <lb/>ne uenir a libre.40.men.8.co&longs;e. </s> <s id="s.002052">Et perche la proportione di tutta la uerga (qual è pie <lb/>di.10.al doppio della &longs;ua menor parte) il qual doppio &longs;aria.2.co&longs;e (è &longs;i come che la gra<lb/>uita del no&longs;tro corpograue (qual è libre.80.) alla grauita della &longs;opradetta differentia, <lb/>qual fulibre.40.men.8.co. </s> <s id="s.002053">Onde per la.20.del.7.di Euclide (la moltiplicatione della <lb/>prima) che.10.piedi (fia la quarta che è.40.men.8.co&longs;e) qual fara.400.men.80.co <lb/>&longs;e (&longs;ara eguale alla moltiplicatione della terza qual è libre.80.fia la &longs;econda, qual è.2. <lb/>co&longs;e (qual fara.160.co.) e pero haueremo.160.co&longs;e eguale à.400.men.80.co&longs;e, on­<lb/>de ri&longs;torando le parti, & &longs;eguendo il capitolo, trouaremo la co&longs;a ualer.1.e dui terzi, <lb/>& de piedi.1.edui terzi, &longs;e douera &longs;ignar la menor parte della detta uerga, ouer tra­<lb/>ue, onde la maggiore uenira à re&longs;tare de piedi.8.e un terzo, che è il propo&longs;ito.<emph.end type="italics"/> S.A. <lb/>Q<emph type="italics"/>ue&longs;ta è &longs;tata una bella re&longs;olutione, ma &longs;eguitati pur, perche uorria che trahoggi & <lb/>dimane uedeßimo de i&longs;pedire tutto quello, che haueti da proponere &longs;opra di que&longs;ta &longs;cien <lb/>tia, perche uorro poi che me aßignati la cau&longs;a de alcune que&longs;tioni, che ho da dirui.<emph.end type="italics"/> N. <lb/>N<emph type="italics"/>on credo di potermene i&longs;pedire fra diman, e l'altro, perche continuamente me na&longs;ce <lb/>nuoue materie da proponere circa à tal&longs;cientia.<emph.end type="italics"/> S.A. S<emph type="italics"/>e non &longs;e ne potremo i&longs;pedire <lb/>co&longs;i dimane non importa, non perdemo tempo, &longs;eguitati.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <p type="head"> <s id="s.002054">QVESITO. XLI. PROPOSITIONE XIIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002055">La <emph type="italics"/>egualita della declinatione è una mede&longs;ima egualita de pe&longs;o.<emph.end type="italics"/> S.A. D<emph type="italics"/>atemi <lb/>un e&longs;&longs;empio.<emph.end type="italics"/> N. L<emph type="italics"/>a egualita della declinatione uien con&longs;eruata &longs;olamente in <lb/>uia retta. </s> <s id="s.002056">Hor poniamo adunque che la detta uia retta &longs;ia la linea.a.b. </s> <s id="s.002057">& dal ponto.a. <lb/></s> <s id="s.002058">&longs;ia anchor tirata la perpendicolare.a.c.& &longs;upponamo anchor nella detta declinata lie <lb/>nea.a.b.dui diuer&longs;i luochi. </s> <s id="s.002059">Hor poniamo che l'uno &longs;ia il ponto.d.& l'altro il ponto.e. <lb/></s> <s id="s.002060">Hor dico che di&longs;cendendo, qualunque corpo pondero&longs;o, ouer dal ponto.d.ouer dal pon <lb/>to.e.&longs;ara de uno mede&longs;imo pe&longs;o, &longs;econdo il &longs;ito in qual &longs;i uoglia de detti luochi. </s> <s id="s.002061">Per<emph.end type="italics"/><pb pagenum="97" xlink:href="042/01/194.jpg"/><emph type="italics"/>che &longs;e pigliaremo &longs;otto al.d.& al.e.due parti equali nella uia, ouer linea.a.b. </s> <s id="s.002062">Hor po <lb/>niamo, che l'una &longs;ia la parte.d.e.et laltra la.e.g. </s> <s id="s.002063">Dico, che per le dette parti equali ca <lb/>pira equalmente del diretto, cioe della linea.a.c.la qual co&longs;a&longs;e notificara in que&longs;to mo <lb/>do, dalli duiponti.e.&.g.&longs;iano tirate le due linee.e.h.&.g.l. <lb/></s> <s id="s.002064">perpendicolare &longs;opra la linea.a.c.et dalli dui ponti, ouer luo <lb/>chi.d.&.e.le due linee.d.<emph.end type="italics"/>k.<emph type="italics"/>&.e.m. </s> <s id="s.002065">perpendicolare &longs;opra <lb/>le mede&longs;ime.e.h.&.g.l.le qual due perpendicolare, cioe.d.<emph.end type="italics"/><lb/>k.<emph type="italics"/>&.e.m.&longs;aranno fra loro equali, perche adunque il detto <lb/>corpo pondero&longs;o, &longs;i e&longs;&longs;endo nel ponto.d.come nel ponto.e.in <lb/>quantita, ouer de&longs;cen&longs;i equali, capira equalmente del diret­<lb/>to, &longs;ara di una mede&longs;ima grauita in qual &longs;i uoglia de quelli, &longs;e <lb/>condo el &longs;ito, ch'è il propo&longs;ito.<emph.end type="italics"/> S.A. <!-- KEEP S--></s> <s id="s.002066">E <emph type="italics"/>ue ho inte&longs;o, &longs;egui­<lb/>tate pur.<emph.end type="italics"/> N. <!-- KEEP S--></s> </p> <figure id="id.042.01.194.1.jpg" xlink:href="042/01/194/1.jpg"/> <p type="head"> <s id="s.002067">QVESITO XLII. PROPOSITIONE XV.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002068">Se <emph type="italics"/>dui corpi graui de&longs;cendano per uie de diuer&longs;e obliquita, & che la proportio­<lb/>ne delle de clinationi delle due uie, & della grauita de detti corpi &longs;ia fatta una me­<lb/>de&longs;ima, tolta per el mede&longs;imo ordine. </s> <s id="s.002069">Anchora la uirtu de luno, e laltro de detti dui <lb/>corpi graui, in el de&longs;cendere &longs;ara una mede&longs;ima.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;ta propo&longs;itione mi par <lb/>bella, e pero datime anchora un e&longs;&longs;empio chiaro, accio che meglio mipiaccia.<emph.end type="italics"/> N. S<emph type="italics"/>ia <lb/>la linea.a.b.c.equidi&longs;tante al orizonte, & &longs;opra di quella &longs;ia perpendicolarmente e­<lb/>retta la linea.b.d.& dal ponto.d.de&longs;cendano de qua, & de la le due uie, ouer linee.d.a. <lb/></s> <s id="s.002070">&.d.c.& &longs;ia la.d.c.di maggior obliquita. </s> <s id="s.002071">Per la proportione adunque delle lor de­<lb/>clinationi, non dico delli lor angoli, ma delle linee per fina alla equidi&longs;tante re&longs;ecatio­<lb/>ne, in la quale equalmente &longs;ummemo del diretto. </s> <s id="s.002072">Sia <expan abbr="adũque">adunque</expan> la lettera.e.&longs;uppo&longs;ta per <lb/>un corpo graue posto &longs;opra la linea.d.c.& un'altro la lettera.h.&longs;opra la linea.d.a. <lb/></s> <s id="s.002073">& &longs;ia la proportione della &longs;implice grauita del corpo.e.alla &longs;implice grauita del cor <lb/>po.h.&longs;i come quella della.d.c.alla.d.a. </s> <s id="s.002074">Dico li detti dui corpi graui e&longs;&longs;er in tai &longs;iti, o­<lb/>uer luochi diuna mede&longs;ime uirtu, ouer potentia. </s> <s id="s.002075">Et per dimo&longs;trar que&longs;to, tiro la.d.<emph.end type="italics"/>k. <lb/><emph type="italics"/>di quella mede&longs;ima obliquita, ch'è la.d.c.& imagino un corpo graue &longs;opra di quella <lb/>equale a corpo.e.el qual pongo &longs;ia la lettera.g.ma che &longs;ia in diretto con.e.h.cioe e­<lb/>qualmente di&longs;tanti dalla.c.<emph.end type="italics"/>k.H<emph type="italics"/>or &longs;e poßibel è (per lauer&longs;ario) che li detti dui corpi <lb/>e.&.h.non &longs;iano diuna mede&longs;ima, & equal uirtu in tai luochi, adunque luno &longs;ara di <lb/>maggior uirtu, ouer potentia dell'altro, poniamo adunque, che.e. </s> <s id="s.002076">&longs;ia di maggior uir­<lb/>tu, adunque quello &longs;ara atto à di&longs;cendere, & &longs;imelmente à far a&longs;cendere, cioe à tirare <lb/>in &longs;u&longs;o el corpo.h. </s> <s id="s.002077">Hor poniamo (&longs;e poßibel è) che il detto corpo.e.de&longs;cenda per fina <lb/>in ponto.l.& che faccia a&longs;cendere il corpo.h.per fin in ponto.m. </s> <s id="s.002078">& faccio, ouer che <lb/>&longs;egno la.g.n.equale alla.h.m.la quale anchora lei uien à e&longs;&longs;er equale alla.e.l. </s> <s id="s.002079">Et dal <expan abbr="põ">pom</expan> <lb/>to.g.tiro la.g.h.e.la qual &longs;ara perpendicolare &longs;opra la.d.b.per e&longs;&longs;er li detti tre pon­<lb/>ti (ouer corpi) g.h.e.&longs;uppo&longs;ti in diretto, & equalmente distanti dalla.<emph.end type="italics"/> k. <emph type="italics"/>c. <!-- REMOVE S-->& fimel­<lb/>mente dal ponto.l.&longs;ia tiratala.l.t.equidi&longs;tante alla.c.b.qual &longs;ara pur perpendicolare<emph.end type="italics"/><pb xlink:href="042/01/195.jpg"/><emph type="italics"/>&longs;opra la mede&longs;ima.d.b.& dalli tre ponti.n.m.e. </s> <s id="s.002080">&longs;iano tirate le tre perpendicolari.n. <lb/></s> <s id="s.002081">z.m.x.&.e.r. <!-- KEEP S--></s> <s id="s.002082">Et perche la proportione della.n.z.alla.n.g.è &longs;i come quella, che è dall<gap/><lb/>d.y.alla.d.g.e pero &longs;i come anchora quella della.d.b. </s> <s id="s.002083">alla.d.<emph.end type="italics"/>k. <emph type="italics"/>(per e&longs;&longs;er li detti tre <lb/>triangoli &longs;imili.) Simelmente la proportione della.m.x.alla.m.h.è &longs;i come quella, che <lb/>é dalla detta.d.b.alla.d.a. (per e&longs;&longs;er li detti dui triangoli &longs;imili.) Anchora la propor­<lb/>tione della.m.x.alla.n.<emph.end type="italics"/>z. <emph type="italics"/>&longs;ara &longs;i come quella della.d.<emph.end type="italics"/><lb/>k.<emph type="italics"/>alla.d.a.& quella mede&longs;ima (dal pre&longs;uppo&longs;ito) e <lb/>dalla grauita del corpo.g.alla grauita del corpo. <!-- REMOVE S-->h. <lb/><!-- REMOVE S-->perche il detto corpo.g.fu &longs;uppo&longs;to e&longs;&longs;er <expan abbr="&longs;implicem&etilde;">&longs;implicemen</expan> <lb/>te, egualmente graue con el corpo.e. </s> <s id="s.002084">adunque tanto <lb/>quanto, che il corpo.g.è &longs;implicemente piu graue del <lb/>corpo.h.per altro tanto il corpo. <!-- REMOVE S-->h. <!-- REMOVE S-->uien à e&longs;&longs;er piu <lb/>graue per uigor del &longs;ito del detto corpo.g.è pero &longs;i <lb/>uengono ad egualiar in uirtu, ouer potentia, & per <lb/>tanto quella uirtu, ouer potentia, che &longs;ara atta à far <lb/>a&longs;cendere luno de detti dui corpi, cioe à tirarlo in &longs;u <lb/>&longs;o, quella mede&longs;ima &longs;ara atta, ouer &longs;officiente à fare <lb/>a&longs;cendere anchora l'altro, adunque &longs;el corpo.e. (per <lb/>lauer&longs;ario) è atto, & &longs;officiente à far a&longs;cendere il <lb/>corpo.h.per fin in.m.el mede&longs;imo corpo.e.&longs;aria a­<lb/>dunque &longs;officiente à far a&longs;cendere anchora il corpo <lb/>g.à lui equale, & inequale declinatione, la qual co&longs;a<emph.end type="italics"/><lb/><figure id="id.042.01.195.1.jpg" xlink:href="042/01/195/1.jpg"/><lb/><emph type="italics"/>é impoßibile per la precedente propo&longs;itione, adun­<lb/>que il corpo.e.non &longs;ara de maggior uirtu del corpo.h.in tali &longs;iti, ouer luochi, che éil <lb/>propo&longs;ito.<emph.end type="italics"/> S.A. Q<emph type="italics"/>ue&longs;ta è &longs;tata una bella &longs;peculatione, & me è piace&longs;ta a&longs;&longs;ai. </s> <s id="s.002085">Et per <lb/>che uedo e&longs;&longs;er hora tarda, non uoglio, che procedati in altro per hoggi.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002086">F<emph type="italics"/>ine del ottauo libro.<emph.end type="italics"/></s> </p> </subchap1><subchap1> <pb pagenum="98" xlink:href="042/01/196.jpg"/> <p type="head"> <s id="s.002087">LIBRO NONO DELLI <lb/>QVESITI, ET INVENTIONI DIVERSE. <lb/>DE NICOLO TARTAGLIA.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.002088">S<emph type="italics"/>opra la &longs;cientia Arithmetica, Geometrica, & in la Pratica Speculatiua <lb/>de Algebra, & Almucabala, uolgarmente detta Regola de <lb/>la co&longs;a, ouer Arte maggiore, & maßime della <lb/>inuentione de Capitoli de Co&longs;a, e Cubo <lb/>equal à numero, & altri &longs;uoi <lb/>ederenti, et dependenti, <lb/>Et &longs;imelmente de cen&longs;i, e cubi equal à numero, & &longs;uoi <lb/>dependenti, quali dalli Sapienti &longs;ono stati <lb/>giudicati impoßibili.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002089">QVESITO PRIMO FATTO DA MAESTRO <lb/>F<emph type="italics"/>rance&longs;co Feliciano l'anno.1521.in Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002090">MAESTRO FRANCESCO. I<emph type="italics"/>o comprai un pe&longs;ce per lire <lb/>1.p.10.danari.1.& tanti danari lo pagai la lira, quanto, ch'erano <lb/>le lire, che lui pe&longs;aua. </s> <s id="s.002091">Domando quante lire pesò il detto pe&longs;ce.<emph.end type="italics"/><lb/>N. L<emph type="italics"/>ui pesò lire.19.che à danari.19.la lira montaria danari.361. <lb/>che &longs;ariano.p.30.& danari.1.cioe lire.1.§.10. danari.1. che è il <lb/>propo&longs;ito, & tal ragione la ri&longs;oluo in questo modo. </s> <s id="s.002092">10 reduco il <lb/>detto precio, cioe lire.1.p.10.danari.1.tutto in danari, che &longs;aria­<lb/>no danari.361.& di que&longs;ti danari.361.ne cauo la &longs;ua radice, qual è.19.& tante lire <lb/>pesò il detto pe&longs;ce, come di &longs;opra dißi, ch'é facile.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002093">QVESITO SECONDO FATTO DA VN FRA <lb/>R<emph type="italics"/>aphaelle de.<emph.end type="italics"/>S.Z<emph type="italics"/>orzi de Verona, l'anno.<emph.end type="italics"/>1524.</s> </p> <p type="main"> <s id="s.002094">FRA RAPHAELLE. V<emph type="italics"/>no padre ha alquanti figliuoli, & fa te&longs;tamento, <lb/>& fra le altre co&longs;e ha una quantita de ducati in una ca&longs;&longs;a, & da de detti danari <lb/>un ducato al &longs;uo primo figliuolo, & anchora la ottaua parte del rimanente, & al &longs;e­<lb/>condo gli da ducati.2.& la ottaua parte del rimanente, & al terzo gli da ducati.3.et <lb/>pur la ottaua parte del &longs;uo rimanente, & co&longs;i ua procedendo, & accre&longs;cendo con tal <lb/>or dine à cadauno delli altri figliuoli, eccetto à l'ultimo, al qual gli dette tutti quelli, <lb/>che gli erano re&longs;tati, & finalmente tanti ducati &longs;i trouo luno, come laltro. </s> <s id="s.002095">Hor ue adi <lb/>mando quanti ducati haueua in ca&longs;&longs;a il detto padre, & &longs;imelmente quanti figliuoli ha <lb/>ueua.<emph.end type="italics"/> N. I<emph type="italics"/>l detto padre haueua duc.49.in ca&longs;&longs;a, & haueua.7.figliuoli<emph.end type="italics"/> F.R. E<emph type="italics"/><expan abbr="tcõ">tcom</expan> <lb/>che regola ritrouati li detti.49.ducati, &.7.figliuoli.<emph.end type="italics"/> N. I<emph type="italics"/>o cauo quella unita, che <lb/>è &longs;opra la uirgola di quello.1/8.che da à cadauno, di quel.8.ch'e di &longs;otto della <lb/>detta uirgola, & riman.7.& tanti figliuoli conchiudo, che lui haueua, et dapoi qua-<emph.end type="italics"/><pb xlink:href="042/01/197.jpg"/><emph type="italics"/>dro il detto.7.fa.49.& tanti ducati determino, che haueua in ca&longs;&longs;a el detto padre.<emph.end type="italics"/><lb/>F.R. E<emph type="italics"/>t &longs;e in luoco di quello.1/8.lui ui haue&longs;&longs;e dato &longs;empre.1/7.come &longs;e doueria pro­<lb/>cedere.<emph.end type="italics"/> N. P<emph type="italics"/>er lo mede&longs;imo ordine, cioe cauando quella unita, che é &longs;opra la uirgo <lb/>la di quello.7.che é di &longs;otto, et rimaneria.6.& co&longs;i.6.figliuoli haueria il detto padre, <lb/>& dapoi quadrando el detto.6.faria.36.& co&longs;i.36.ducati haueria hauuto in ca&longs;&longs;a.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002096">QVESITO TERZO FATTO DA. VNO MIO DISCI­<lb/><emph type="italics"/>pulo, detto mae&longs;tro Maphio, qual dice e&longs;&longs;erli stato fatto à <lb/>lui in Mantua, l'anno.<emph.end type="italics"/>1526.</s> </p> <p type="main"> <s id="s.002097">MAESTRO MAPHIO. E<emph type="italics"/>glie uno, che impre&longs;ta à uno ducati.300. per <lb/>anni.3.ma non &longs;o à quanto &longs;e conuiene de pagarli de merito ogni anno, ma &longs;o <lb/>ben, che non dandoli ogni anno il merito tra lor conuenuti luiuoleua, che tal merito ui <lb/>fu&longs;&longs;e meritato alla ratta del loro accordo di primi duc.300. Accade, che co&longs;tui non ui <lb/>da co&longs;a alcuna per fin in capo de ditti tre anni, & in capo delli detti tre anni lui lire&longs;e <lb/>fra capital e merito ducati.500.Se adimanda quanto pagò de merito per cento all'an <lb/>no.<emph.end type="italics"/> N. P<emph type="italics"/>agò di merito duc.<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.1666666.2/3.men.100.cioe pagò tanto per <lb/>cento all'anno.<emph.end type="italics"/> M.M. E<emph type="italics"/>t con che regola ritrouati tal merito,<emph.end type="italics"/> N. P<emph type="italics"/>er ritruouare <lb/>tal merito primamente imagino li detti duc.300.in li detti anni tre formar quattro <lb/>termin<gap/> continui proportionali, delli quali quattro termini, li detti duc.300.uengono <lb/>à e&longs;&longs;er el primo, & li dettiduc.500.che lui re&longs;titui&longs;&longs;e, uengono à e&longs;&longs;er el quarto, e pe <lb/>ro bi&longs;ogna ritrouare li dui termini intermedij, oueramente il <expan abbr="&longs;ecõdo">&longs;econdo</expan> (qual ba&longs;ta in que <lb/>&longs;to ca&longs;o) & per ritrouarlo quadro.300.fa.90000. & questo. </s> <s id="s.002098">90000. lo molti­<lb/>plico fia el quarto termine, cioe fia.500.fara.45000000. & la radice cubade dit­<lb/>to.45000000.&longs;aranno ritornati li detti duc.300.tramerito, et capitale in capo del <lb/>primo anno, la qual quantita la diuido per tre (cubando pero el tre per trouar quan­<lb/>to retornara &longs;olamente duc.100.) ne uenira.<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.1666666.2/3.& <expan abbr="tãto">tanto</expan> &longs;aria ritor <lb/>nato duc.100.fra merito, e capitale in capo del primo anno, hor per &longs;apere quanto fu <lb/>el puro merito per cento all'anno, cauo di tal <expan abbr="quãtita">quantita</expan> il capitale, cioe duc.100.rimane <lb/>ra.<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.1666666.2/3.men.100.et tanto dico, che pago de merito per cento all'anno, <lb/>come di &longs;opra dißi.<emph.end type="italics"/> M.M. L<emph type="italics"/>a è piu forte ragione di quello mi pen&longs;aua.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002099">QVESITO QVARTO FATTO DAL MEDESIMO <lb/>M<emph type="italics"/>aestro Maphio, qual dice gli fu propo&longs;to in <lb/>Mantua l'anno.<emph.end type="italics"/>1526.</s> </p> <p type="main"> <s id="s.002100">MAESTRO MAPHIO. T<emph type="italics"/>rouatime duinumeri, che tutte le parti ali­<lb/>quote del primo gionte in&longs;ieme facciano el &longs;econdo, & che &longs;imelmente tutte <lb/>le parti aliquote del &longs;econdo facciano preci&longs;amente elprimo numero.<emph.end type="italics"/> N. L<emph type="italics"/>'uno &longs;a­<lb/>ra. </s> <s id="s.002101">284.& laltro.220.cioe, &longs;e recogliereti tutte le parti aliquote de.284. uoitro­<lb/>uareti, che faranno preci&longs;amente.220.& co&longs;i, &longs;e recogliareti tutte le parti aliquote <lb/><gap/> 220. uoi trouareti, che faranno preci&longs;amente.284.come &longs;e ricerca.<emph.end type="italics"/></s> </p> <pb pagenum="99" xlink:href="042/01/198.jpg"/> <p type="head"> <s id="s.002102">QVESITO QVINTO FATTOMI DA <lb/><emph type="italics"/>un Fiorentino.1526.in Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002103">FIORENTINO. E<emph type="italics"/>gliera un contadino qual e&longs;&longs;endo infermo, & trouan­<lb/>do&longs;i hauer duc.17.1/2. & hauendo trei figliuoli, la&longs;&longs;a che morendo li detti &longs;uoi <lb/>trei figliuoli &longs;e diuide&longs;&longs;ono li detti ducati.17.1/2.egualmente fra loro, cioe che cadau­<lb/>no &longs;e ne piglia&longs;&longs;e la terza parte. </s> <s id="s.002104">Accade che co&longs;tui more, & li detti figliuoli cor&longs;e­<lb/>no alla ca&longs;&longs;a doue erano li detti danari, & cadauno comincio à grapire di quelli meglio <lb/>che pote, cioe che piu, e chimeno diquello &longs;e gli a&longs;pettaua. </s> <s id="s.002105">Ilche inte&longs;o da un &longs;uo bar­<lb/>bano, quel uene, & fece che il figliolo maggiore mette&longs;&longs;e zo&longs;o la mita, & &longs;e retene&longs;&longs;e <lb/>laltra mita de tutti quelli danari, che haueua aggrapiti, & &longs;imelmente fece che laltro <lb/>&longs;econdo fratello mete&longs;&longs;e zo&longs;o liduiterzide detti danari & che &longs;e retene&longs;&longs;e laltro ter <lb/>zo per &longs;e & &longs;imelmente fece che il terzo figliolo mete&longs;&longs;e zo&longs;o litre quarti dedetti de­<lb/>nari, & che &longs;e retene&longs;&longs;e laltro quarto per &longs;e, & tutto quello nnmero de denari, che fu <lb/>po&longs;to zo&longs;o il detto &longs;uo barbano lo diui&longs;e in treparti equali, & a cadauno di loro dete <lb/>una de dette parti, & fatto que&longs;to cadauno di loro &longs;i trouo hauer il &longs;uo douere, cioe tan <lb/>to luno quanto laltro. </s> <s id="s.002106">Hor ue adimando quanti denari tol&longs;e cadauno de loro doppo la <lb/>morte del padre.<emph.end type="italics"/> N. E<emph type="italics"/>l primo tol&longs;e duc. </s> <s id="s.002107">3.8/9.il &longs;econdo duca.5.15/18.il terzo.<emph.end type="italics"/>7.7/9 <lb/>F. <!-- KEEP S--></s> <s id="s.002108">E <emph type="italics"/>con cheregola lo ritrouati.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;ti li ritrouo per la co&longs;a (uero è, che an­<lb/>chor per altre uie &longs;e potriano trouare) cioe pongo, che tutto quello che fu posto giu&longs;o <lb/>da tutti tre fu&longs;&longs;e.1.co&longs;a, & quella diuido in tre parti ne uien.1/3.co, & perche &longs;o che <lb/>con la gionta di que&longs;to. </s> <s id="s.002109">1/3.co.cadauno di loro fece duc.5. 5/6.adunque auanti di quella <lb/>cadauno haueua duc.5.5/6.men.1/3. co.la qual quantita uien à e&longs;&longs;er la mita di quello, che <lb/>nel principio tol&longs;e il primo, & il terzo di quello tol&longs;e il &longs;econdo, & il quarto di quello <lb/>tol&longs;e il tol&longs;e il terzo, e pero moltiplico l'una per.2.l'altra per.3.& l'altra per.4.& <lb/>la &longs;umma di tai moltiplicationi (quale &longs;ara.52.1/2.men.3.co&longs;e) diro che &longs;ia eguale à duc.<emph.end type="italics"/><lb/><gap/>7.1/2.<emph type="italics"/>leuo li &longs;uperflui, & restoro le parti, & &longs;eguito il capitolo, & trouo la co&longs;a ua­<lb/>ler.11.2/3.& tanto fu po&longs;to giu&longs;o da tutti, & que&longs;to lo diuido poi per.3.ne uien.3.8/9. <lb/>qual &longs;ottratto da duc.5.5/6.re&longs;ta duc.1.17/18. & tanto re&longs;to à cadauno dapoi che heb­<lb/>ben po&longs;to giu&longs;o. </s> <s id="s.002110">Et perche que&longs;to duc.1.17/18 uien à e&longs;&longs;er la mita di quello che tol&longs;e, <lb/>nel principio il primo, & il terzo del &longs;econdo, & il <27>uarto del terzo, moltiplico il det <lb/>to duc.1.17/18. per.2.& poi per.3.& poi per.4.& li tre produtti conchiudo e&longs;&longs;er <lb/>quello che cadauno di loro tol&longs;e nel principio, le qual moltiplicationi produranno, co­<lb/>me nel principio fu conchiu&longs;o, cioe il primo tol&longs;e nel principio duc.3.8/9. il &longs;econdo duc. <lb/></s> <s id="s.002111">5.15/18. il terzo duc.<emph.end type="italics"/>7.7/9. F. V<emph type="italics"/>e ringratio a&longs;&longs;ai.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002112">QVESITO SESTO FATTODA VN MAESTRO <lb/>A<emph type="italics"/>loui&longs;e Pirouano Milane&longs;e l'Anno.<emph.end type="italics"/>1529.</s> </p> <p type="main"> <s id="s.002113">MAESTRO ALOVISE. T<emph type="italics"/>rouatemi.2.numeri che li.<emph.end type="italics"/>2/<gap/>.<emph type="italics"/>dell'uno &longs;ia li. <lb/></s> <s id="s.002114">3/7.dell'altro, & che que&longs;ti dui numeri facciano tanto aggionti in&longs;ieme, come <lb/>che moltiplicati l'uno fia l'altro,<emph.end type="italics"/> N. L<emph type="italics"/>'uno de que&longs;ti numeri, cioe il maggiore &longs;ara. <pb xlink:href="042/01/199.jpg"/>2.1/14.& l'altro, cioe il menore &longs;ara.<emph.end type="italics"/>1.14/15. A. E<emph type="italics"/>t come li trouati.<emph.end type="italics"/> N. I<emph type="italics"/>o trouo <lb/>prima &longs;implicemente dui numeri che li.2/5.dell'uno &longs;ia li.3/7.dell'altro, & que&longs;ti li tro­<lb/>uo moltiplicando il denominator dell'uno fia il numerator dell'altro de tai rotti, cioe li <lb/>moltiplico in croce, & di tale moltiplicationine uien.15.&.14.& que&longs;ti &longs;ono quelli, <lb/>che li.2/5.dell'uno fali.3/7.dell'altro, ma non hanno però l'altra conditione, cioe che tan <lb/>to facciano aggionti, come moltiplicati, ma con que&longs;ti però po&longs;&longs;o ritrouar quelli, & <lb/>per ritrouarli &longs;ummo in&longs;ieme que&longs;ti dui numeri fanno.29.et que&longs;to.29.lo parto per <lb/>l'uno, e poiper l'altro di detti dui numeri, cioe per.15.& per.14.& li dui aduenimen <lb/>ti&longs;aranno li dui numeri, che &longs;e ricerca, li quali aduenimenti l'uno &longs;ara.2.1/14.& l'al­<lb/>tro.1.14/15.come di&longs;opra dißi.<emph.end type="italics"/> A. S<emph type="italics"/>ta benißimo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002115">QVESITO SETTIMO FATTO DA VN <lb/>F<emph type="italics"/>rate Beretino del.<emph.end type="italics"/>1526.</s> </p> <p type="main"> <s id="s.002116">FRATE. T<emph type="italics"/>rouatemi un numero che facendone di quello due tal parti, & che à <lb/>moltiplicare li.3/4.dell'una di quelle parti fia li.4/5.dell'altra parte me ne uegna il <lb/>primo numero.<emph.end type="italics"/> N. Q<emph type="italics"/>uesto ca&longs;o &longs;e puo conchiudere in infiniti modi, perche mi po&longs;­<lb/>&longs;o fondar &longs;opra di qual numero mi piace, e&longs;&longs;empi gratia, pigliando.10.per quel tal nu<lb/>mero l'una parte di quello &longs;aria.5.piu<emph.end type="italics"/> <22>.8.1/3.<emph type="italics"/>& l'altra &longs;aria.5.men<emph.end type="italics"/> <22>.8.1/3.<emph type="italics"/>& co&longs;i <lb/>pigliando altro numero quello me daria altre parti.<emph.end type="italics"/> F. E<emph type="italics"/>t come le ritrouate.<emph.end type="italics"/> N. <lb/>I<emph type="italics"/>o cerco di far del detto.10.due tal parti, come ricercate, cioe che li.3/4.dell'una molti <lb/>plicati fia li.4/5.dell'altra mi facciano aponto.10.& per trouar le dette parti, io pon­<lb/>go che l'una &longs;ia una co&longs;a, la &longs;econda per forza &longs;ara 10.men.1.co.piglio li.3/4.de.1.co. <lb/></s> <s id="s.002117">che &longs;aria.3/4.co.& co&longs;i piglio anchora li.4/5.de.10.men.1.co.che &longs;aria.8.men.4/5.co.& <lb/>que&longs;te due quantita, li moltiplico l'una fia l'altra, & fanno.6.co&longs;e men.3/5.cen&longs;i, et que <lb/>sto produtto &longs;ara egual à.10.re&longs;toro le parti, & &longs;eguito il capitolo, & trouo la co&longs;a <lb/>ualer.5.piu<emph.end type="italics"/> <22>.8.1/3.<emph type="italics"/>qual cauo de.10.re&longs;ta.5.men<emph.end type="italics"/> <22>.8.1/3.<emph type="italics"/>& tanto fu l'altra parte, co­<lb/>me di &longs;opra di&longs;&longs;e.<emph.end type="italics"/> F. Q<emph type="italics"/>ue&longs;to uo&longs;tro operar me piace a&longs;&longs;ai.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002118">QVESITO OTTAVO FATTO DA MAESTRO <lb/>F<emph type="italics"/>rance&longs;co Feliciano l'Anno.1526. In Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002119">MAESTRO FRANCESCO. V<emph type="italics"/>no compra una quantita di pernice, & <lb/>&longs;pende in tutte lire.25.de danari, & le porta à Mantoua à reuendere, & tan <lb/>te, come che lui ne haue alla lira, lui li uendete tante lire l'una, & le uendete tutte, ec­<lb/>cetto che.10.& ne cauo lire.75.de danari. </s> <s id="s.002120">Hor ue adimando quante furono tutte le <lb/>dette pernice che compro, & quante n'hebbe alla lira de prima compra.<emph.end type="italics"/> N. L<emph type="italics"/>e per­<lb/>nice che lui compro furono<emph.end type="italics"/> <22>.1900.<emph type="italics"/>piu.5. & n'hebbe per ogni lira de danari per­<lb/>nice<emph.end type="italics"/> <22>.3.2 1/5.<emph type="italics"/>piu.1/5.de prima compra. </s> <s id="s.002121">Et tal que&longs;ito lo ri&longs;oluo in que&longs;to modo, io pon <lb/>go che lui haue&longs;&longs;e una co&longs;a di pernice alla lira, onde hauendo &longs;pe&longs;o (come dite) lire 25. <lb/>de danari, io moltiplico.25.fia.1.co.fa.25.co.de pernice, & de que&longs;te.25.co.de per­<lb/>nice ne cauo le.10.pernice, che lire&longs;to, re&longs;tano.25.co.men.10. & perche diceti che li<emph.end type="italics"/><pb pagenum="100" xlink:href="042/01/200.jpg"/><emph type="italics"/>uendete tante lire l'una, quante che lui n'hebbe alla lira, io moltiplico.1.co.fia.25.co. <lb/></s> <s id="s.002122">men.10.fanno.25.cen&longs;i men.10.co.le quale &longs;aranno eguale à lire.75.che ne cauo, eg­<lb/>guaglio le parti, & poi &longs;chi&longs;&longs;o per.25.& me ne uien.1.cen egual à.2/5.co.piu.3.&longs;egui <lb/>to la regola, & trouo la co&longs;a ualer<emph.end type="italics"/> <22>.3.1/25.<emph type="italics"/>piu.1/5.& tante pernice dico, che hebbe <lb/>per lira, come di &longs;opra dißi, & per &longs;aper quante pernice compro in tutto, dico per la <lb/>regola del.3.&longs;e lire.1.me da pernice<emph.end type="italics"/> <22>.3.1/25.<emph type="italics"/>piu,1/5.che me dara lire.25.che lui &longs;pe­<lb/>&longs;e, onde moltiplicando, & partendo, come uol la regola, trouo che compro pernice<emph.end type="italics"/> <22>. <lb/></s> <s id="s.002123">1900.<emph type="italics"/>piu.5.fatine mo uoi la proua, che la trouareti giu&longs;ta.<emph.end type="italics"/> M.F. Q<emph type="italics"/>ue&longs;to uo&longs;tro o­<lb/>perar a&longs;&longs;ai me piace.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002124">QVESITO NONO FATTO DAL MEDESI­<lb/><emph type="italics"/>mo maestro France&longs;co Feliciano l'Anno.<emph.end type="italics"/>1526.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002125">MAESTRO FRANCESCO. E<emph type="italics"/>glie uno, che me doueua dare una quan­<lb/>tita de ducati & me ne ha dato una parte, talmente che el mi re&longs;ta anchora duc. <lb/></s> <s id="s.002126">300. & &longs;appiati che tolto il.1/5.di quello, che lui me ha dato, & quello moltiplicandolo <lb/>in &longs;e mede&longs;imo fa tanto quanto era il primo debito, ue adimando quanto fu il primo de­<lb/>bito.<emph.end type="italics"/> N. I<emph type="italics"/>l primo debito fu ducati.<emph.end type="italics"/> 400. M.F. E<emph type="italics"/>t con che regola lo ritrouati.<emph.end type="italics"/><lb/>N. A<emph type="italics"/>nchor che per altre uie tal ragione &longs;e potria fare, nondimeno io la ri&longs;oluo per <lb/>Algebra, cioe pongo che li ducati che ue ha dati &longs;iano una co&longs;a, adunque tutto il debito <lb/>fuducati.300.piu una co&longs;a, poi piglio il.1/5.de una co. </s> <s id="s.002127">qual è.1/5.co. </s> <s id="s.002128">& que&longs;to lo mol­<lb/>tiplico in &longs;e mede&longs;imo fa.1/25.de cen&longs;o, & que&longs;to &longs;i è eguale à.1.co.piu.300.ristoro le <lb/>parte, & &longs;eguo il capitolo, & trouo la co&longs;a ualer.100.& ducati.100. ui haueua dati, <lb/>li quali gionti con li ducati.300.che ui re&longs;ta faranno ducati.400.come di &longs;opra ui dißie<emph.end type="italics"/><lb/>M.F. S<emph type="italics"/>ta bene.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002129">QVESITO DECIMO FATTO DA VNO <lb/><emph type="italics"/>maestro Ale&longs;&longs;andro Venetiano l'Anno.1527. <lb/>In Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002130">MAESTRO ALESSANDRO. F<emph type="italics"/>atemi di.10.due tal parti che parti­<lb/>ta la maggior per la menore, & dapoi lamenore per la maggiore, et li dui ad­<lb/>uenimenti aggionti in&longs;ieme facciano.<emph.end type="italics"/>3.1/3. N. L<emph type="italics"/>amaggiore &longs;ara.7.1/2.& la meno­<lb/>re &longs;ara.<emph.end type="italics"/>2.1/2. M.A. E<emph type="italics"/>t come la ri&longs;olueti.<emph.end type="italics"/> N. I<emph type="italics"/>o procedo in que&longs;to modo. </s> <s id="s.002131">Perche <lb/>ogni quantita, che &longs;ia diui&longs;a in due parti, come &longs;i uoglia, partendo la maggiore per la <lb/>menore, & dapoi la menore per la maggiore, li dui aduenimenti moltiplicati l'uno fia <lb/>l'altro &longs;empre &longs;anno aponto.1.Et per tanto in que&longs;to ca&longs;o uolendo ritrouar li detti dui <lb/>aduenimenti, bi&longs;ogna fare del &longs;opradetto.3.1/3.due tal parti, che moltiplicata l'una in <lb/>l'altra faccia.1.La qual parte procedendo per la co&longs;a, ouer per qual uia &longs;i uoglia &longs;i tro <lb/>uara l'una e&longs;&longs;er.3. & l'altra.<emph.end type="italics"/>1/3. E<emph type="italics"/>t dapoi que&longs;to bi&longs;ogna&longs;ar de.10. due tal parti, che <lb/>partendo la maggior per la menor, me ne uenghi.3.ouer che partendo la menor <lb/>per la maggiore, me ne uenghi.1/3, le quale l'una &longs;i trouara e&longs;&longs;ere il quarto <pb xlink:href="042/01/201.jpg"/>de.10.cioe.2.1/2.& l'altra li.3/4.de.10.cioe.7.1/2.come di &longs;opra fu determinato.<emph.end type="italics"/> M.A. <lb/>S<emph type="italics"/>ta benißimo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002132">QVESITO. XI. FATTO DA VNO DETTO <lb/><emph type="italics"/>lo Inzegnero l'Anno.1527. In Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002133">INZEGNERO. F<emph type="italics"/>atemi de.12.due parti tali, che moltiplicando il quadrato <lb/>di luna &longs;ia el quadrato de laltra facciano.<emph.end type="italics"/>130. N.L<emph type="italics"/>una &longs;aria.6.piu<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ali <lb/>de.36.men<emph.end type="italics"/> <22>.130.L<emph type="italics"/>altra&longs;ara.6.men la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale di.36.men<emph.end type="italics"/> <22>. </s> <s id="s.002134">130. INZEG. <lb/>E<emph type="italics"/>t come ritrouati le dette parti.<emph.end type="italics"/> N. P<emph type="italics"/>er &longs;chiuar garbulii de &longs;tranie dignita in pongo <lb/>che una parte &longs;ia.6.men.1.co&longs;a laltra per forza &longs;ara.6. piu.1. co&longs;a, quadro cadauna <lb/>delle dette parti, luna fara.36.men.12.co&longs;e piu.1.cen&longs;o laltra fara36.piu.12. co&longs;e piu <lb/><gap/>. </s> <s id="s.002135">cen&longs;o. </s> <s id="s.002136">Poi multiplico questi dui quadrati luno fia laltro, fanno.1296. men.72.cen&longs;i <lb/>piu.1.cen&longs;o de cen&longs;o et que&longs;to &longs;era equale a.130.re&longs;toro le parti me ne uien.1166. piu <lb/><gap/>.cen&longs;o de cen&longs;o, equal a.72.cen&longs;i &longs;eguito il capitulo, & trouo la co&longs;a ualer radice uni­<lb/>uer&longs;ale de.36.men<emph.end type="italics"/> <22>.130.<emph type="italics"/>donde che luna parte, cloe la maggiore &longs;ara.6.piu<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer <lb/>&longs;ale di.36.men.<emph.end type="italics"/> <22>.130. E<emph type="italics"/>t l'altra, cioe la menore &longs;ara.6.men.<emph.end type="italics"/> <22>.<emph type="italics"/>uniuer&longs;ale.36.men.<emph.end type="italics"/> <22>. <lb/></s> <s id="s.002137">230.<emph type="italics"/>come di &longs;opra fu determinato.<emph.end type="italics"/> I. I<emph type="italics"/>o ue diro la uerita, che io non intendo troppo <lb/>ben que&longs;ta uo&longs;tra conclu&longs;ione, perche que&longs;ta ragione mi fu data a me in Bologna, neio <lb/>laho mai &longs;aputa far, ne <expan abbr="mãco">manco</expan> ho ritrouato, che me la habbia &longs;aputa far, eccetto che uoi <lb/>come credo, che la habbiati ri&longs;olta anchor che io non intenda (come di &longs;opra dißi) tal <lb/>uostra conclu&longs;ione.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002138">QVESITO. XII. FATTOMI DA VNO <lb/>A<emph type="italics"/>rchitettore adi.31.Luio.1527. In Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002139">ARCHITETTORE. I<emph type="italics"/>o faccio far quarelli, ouer piere cotte longhi once. <lb/></s> <s id="s.002140">8.larghi once.4.alti, ouer großi once.2.delli quali ne ua.27.al pie cubo.Do <lb/>mando uolendo far far detti quarelli, ouer piere cotte, che ue ne uada.30.al detto pie <lb/>cubo, & che la &longs;ua longhezza &longs;ia pur doppia alla &longs;ua larghezza, & che &longs;imilmente <lb/>la&longs;ua larghezza &longs;ia doppia alla &longs;ua gro&longs;&longs;ezza, come ch'erano glialtri primi, quanto <lb/>&longs;e doueranno far far longhi, larghi, & großi.<emph.end type="italics"/> N. S<emph type="italics"/>e doueranno far far longhionce<emph.end type="italics"/><lb/><22>.<emph type="italics"/>cuba.458.4/5.larghi once<emph.end type="italics"/> <22>. <emph type="italics"/>cuba.57.3/5. großi once. </s> <s id="s.002141">Radice cuba.<emph.end type="italics"/>7.1/5. A. E<emph type="italics"/>t <lb/>come ritrouate tai mi&longs;ure.<emph.end type="italics"/> N. I<emph type="italics"/>o cubo un piede fatto in once, fara once.1728.cu­<lb/>be, & que&longs;te once.1728.cube le parto per.30. (cioe per li.30.quarelli, ouer piere cog <lb/>te) ne uien.57.3/5.poi trouo tre numeri continui proportionali in proportion dupla, <lb/>che moltiplicati l'uno fia l'altro, & quel produtto fia l'altro facciano.57.3/5. quali pro <lb/>cedendo per la co&longs;a trouo che il maggiore &longs;ara<emph.end type="italics"/> <22>. <emph type="italics"/>cuba.458.4/5.& tante once douera <lb/>e&longs;&longs;er longo il detto quarello, ouer piera cotta, & l'altro &longs;ara Radice cuba.57.3/5.& <lb/>tante once douera e&longs;&longs;er largo, il menore &longs;ara once Radice cuba.7.1/5. & tanto douera <lb/>e&longs;&longs;er gro&longs;&longs;o, come di &longs;opra fu conchiu&longs;o.<emph.end type="italics"/> A. Q<emph type="italics"/>ue&longs;ta ragione è molto piu forte di <lb/>quello mi pen&longs;aua.<emph.end type="italics"/></s> </p> <pb pagenum="101" xlink:href="042/01/202.jpg"/> <p type="head"> <s id="s.002142">QVESITO XIII. FATTO DA MAESTRO ANTONIO <lb/>V<emph type="italics"/>erone&longs;e, Zenero de Mae&longs;tro France&longs;co Feliciano adi. </s> <s id="s.002143">16. <lb/>Settembrio. </s> <s id="s.002144">1527. in Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002145">MAESTRO ANTONIO. Q<emph type="italics"/>ue&longs;ta notte, quando, che non poteua dormi­<lb/>re, me ho imaginato una que&longs;tione a&longs;&longs;ai bella, uero è, che io non ho anchora ritro <lb/>uato el modo da ri&longs;oluerla, & la ho detta anchora al mio &longs;uocero, & ue la uoglio dire <lb/>anchora à uoi, accio, che ui fantasticati anchora uoi &longs;opra.<emph.end type="italics"/> N. D<emph type="italics"/>itela di gratia.<emph.end type="italics"/><lb/>M.A. E<emph type="italics"/>glie una figura Rhombica, che cadauno di &longs;uoi lati è piedi.10.& ha de area <lb/>piedi 72.&longs;uperficiali, domando che proportione é dal diametro maggiore al diame­<lb/>tro menore.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;ta non mipare molto forte questione, perche diuidendo el det <lb/>to Rhombo in dui triangoli, cadauno de detti <expan abbr="triãgoli">triangoli</expan> uenira à e&longs;&longs;er di&longs;uperficie. </s> <s id="s.002146">36. <lb/>& uolendo &longs;apere quanto &longs;ia la ba&longs;a de cadauno, io ponero, che tal ba&longs;a &longs;ia una co&longs;a, <lb/>trouo la &longs;ua perpendicolare, & trouo, che tal perpendicolare è.<emph.end type="italics"/> <22>.<emph type="italics"/>uniuer&longs;ale de.100. <lb/>men un.1/4.de cen&longs;o, & &longs;imelmente ritrouo larea &longs;ua co&longs;i &longs;ordamente quale &longs;ara.<emph.end type="italics"/> <22>. <lb/><emph type="italics"/>uniuer&longs;ale de.25.cen&longs;i, men.1/16.cen&longs;o de cen&longs;o, & que&longs;to &longs;ara equale à. </s> <s id="s.002147">36. quadro <lb/>ambi li termini, me uenira.1296.equal à.25.cen&longs;i, men.1/16. cen&longs;o de cen&longs;o, leuo li <lb/>rotti, & ri&longs;toro le parti, & &longs;eguitc el capitolo, & ritrouo la co&longs;a ualer la.<emph.end type="italics"/> <22>.<emph type="italics"/>uniuer­<lb/>&longs;al de.200 piu.<emph.end type="italics"/> <22>.19264.<emph type="italics"/>& que&longs;to &longs;ara el maggior diametro del detto Rhombo, & <lb/>el menore uenira ad e&longs;&longs;er.<emph.end type="italics"/> <22>. </s> <s id="s.002148">V.200.<emph type="italics"/>men.<emph.end type="italics"/> <22> 19264.<emph type="italics"/>&longs;i che la proportione del diame­<lb/>tro maggior al diametro menor &longs;aria, come, che é dal detto diametro maggiore al det­<lb/>to menore, che é il propo&longs;ito.<emph.end type="italics"/> M.A. V<emph type="italics"/>oi diceti, che tal questione non é molto forte, <lb/>& à me lame pare molto difficile.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002149">QVESITO XIIII. QVAL MI FV MANDATO A <lb/>V<emph type="italics"/>erona da un Mae&longs;tro Zuanne de Tonini da Coi, qual tene­<lb/>ua &longs;chola in Bre&longs;&longs;a, & me lo portò me&longs;&longs;er pre <lb/>Antonio da Cellatica l'anno.<emph.end type="italics"/>1530.</s> </p> <p type="main"> <s id="s.002150">MAESTRO ZVANNE. T<emph type="italics"/>rouatime un numero, qual multiplicato per la <lb/>&longs;ua Radice piu:3.mi faccia.5. Simelmente trouatime.3.numeri, ma chel &longs;e­<lb/>condo &longs;ia.2.piu del primo, & chel terzo &longs;ia pur.2.piu del &longs;econdo, & che multipli­<lb/>cato el primo fia el &longs;econdo, et quel produtto fia el terzo faccia.<emph.end type="italics"/>1000. N. M.Z<emph type="italics"/>uane, <lb/>uoi me haueti <expan abbr="mãdato">mandato</expan> que&longs;ti uostri dui que&longs;iti, come co&longs;e impoßibile da ri&longs;oluere, ouer <lb/>ignorate da uoi, <21>che <expan abbr="proced&etilde;do">procedendo</expan> <21> Algebra, el primo <expan abbr="cõdu&longs;&longs;e">condu&longs;&longs;e</expan> <expan abbr="l'operãte">l'operante</expan>, in.1.cubo piu <lb/>3.c&etilde;&longs;i egual à.5.et il <expan abbr="&longs;ecõdo">&longs;econdo</expan> in.1.cubo piu.6.c&etilde;&longs;i piu.8.co&longs;e equal à.1000.li quali capi <lb/>toli <21> fin à <34>sto <expan abbr="t&etilde;po">tempo</expan> é &longs;tato giudicato da<emph.end type="italics"/> F. L<emph type="italics"/>uca, & altri e&longs;&longs;er impoßibile à ri&longs;oluerli <lb/><21> regola generale, <expan abbr="cred&etilde;doui">credendoui</expan> con tai que&longs;iti di farui cauallero &longs;opra di me, & da farui <lb/>tenere un grandißimo Mathematico, come che ho inte&longs;o, che fati con tutti li altri pro <lb/>fe&longs;&longs;ori di tal &longs;cientia li in Bre&longs;&longs;a, li quali per tema de tai uo&longs;tri Que&longs;iti, non o&longs;&longs;ano à <lb/>parlar conuoi, & for&longs;i meglio intendano in tal faculta di uoi, ma per non e&longs;&longs;er aduer <lb/>titi <expan abbr="tãto">tanto</expan>, che ba&longs;ti, credono, che uoili &longs;appiatire&longs;oluere, e <21> questo ui cedono in tutto.<emph.end type="italics"/><pb xlink:href="042/01/203.jpg"/>O<emph type="italics"/>nde per farui emendar di tal uo&longs;tra uana opinione, & prouocarui, a ricercar di ac­<lb/>quistar ui honor con il &longs;apere, & non con que&longs;tioni da uoi ignorate, ue ri&longs;pondo & di <lb/>co che ui douere&longs;ti aroßire, a proponere da ri&longs;&longs;oluere ad altri, quello che uoi mede&longs;i­<lb/>mo non &longs;apetiri&longs;&longs;oluere. </s> <s id="s.002151">Et per mo&longs;trarui che di que&longs;to ne &longs;on certo me offeri&longs;co à de <lb/>ponere ducati diece contra cinque, <expan abbr="cio&etilde;">cioem</expan> che uoi non &longs;apereti ri&longs;oluere que&longs;ti dui ca&longs;i <lb/>che à me haueti propo&longs;ti con regule generale, & circa cio non uido altra ri&longs;po&longs;ta.<emph.end type="italics"/> M. <lb/>Z. H<emph type="italics"/>o inte&longs;o quanto me haueti &longs;critto, & come che haueti opinione che tai ca&longs;i &longs;iano <lb/>impoßibili, e per tanto ue ri&longs;pondo, che accetto que&longs;ta uostra offerta, cioe che uoi non <lb/>me approuareti che tai ca&longs;i &longs;iano impoßibili<gap/>come che uoidiceti.<emph.end type="italics"/> N. I<emph type="italics"/>o non dico che <lb/>tai ca&longs;i &longs;iano impoßibili anci il primo, cioe quello de cubo é cen&longs;o equal à numero, io me <lb/>per&longs;uado di hauerui trouato la &longs;ua regola generale, ma per al pre&longs;ente la uoglio tace­<lb/>re per piu ri&longs;petti, del &longs;econdo poi, cioe quello de cubi & cen&longs;i, & co&longs;e equale à nume <lb/>ro, confe&longs;&longs;o non hauerui potuto fin à que&longs;ta hora trouar regola generale, ma per que <lb/>&longs;to non dico ne manco uoglio dire ch'el &longs;ia impoßibile a trouaruela anchor che per fina <lb/>à questo tempo la non ue &longs;ia &longs;tata ritrouata. </s> <s id="s.002152">Ma ho detto di uoler deponere li diece do <lb/>cati contra.5.che uoi non &longs;apereti ri&longs;oluere li detti dui que&longs;iti à me mandati con rego­<lb/>le generale, & che circa cioue douere&longs;ti alquanto à roßire à proponere ad altri <lb/>quello, che uoimede&longs;imo non intendeti & fingere de intenderlo per farui reputare <lb/>un gran che.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002153">QVESITO. XV. FATTO DA M. BERNARDIN <lb/>D<emph type="italics"/>ona da Zano lattor in greco l'anno.1530.adi.12.Ottobrio in <lb/>Verona qual di&longs;&longs;e e&longs;&longs;erli &longs;tato propo&longs;to à lui in Bre&longs;&longs;a da <lb/>maestro Zoan de Tonini da Coi.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002154">MISSER BERNARDINO. I<emph type="italics"/>o &longs;on &longs;tato à Bre&longs;&longs;a & me&longs;tato fatto uno <lb/>que&longs;ito da un certo Mae&longs;tro Zuanne da Coi, elquale <expan abbr="&longs;ap&etilde;do">&longs;apendo</expan> haria de caro che <lb/>mel re&longs;olue&longs;ti elqual que&longs;ito dice in questa forma. </s> <s id="s.002155">Voria che nel &longs;otto&longs;critto triango­<lb/>lo.a.b.c.equilatero me gli fu&longs;&longs;e in&longs;critto geometricamente un quadrato.<emph.end type="italics"/> N. Q<emph type="italics"/>ue­<lb/>&longs;to &longs;i puo far in piu modi, ma quello che per al pre&longs;ente mi è uenuto in mente è que&longs;to. <lb/></s> <s id="s.002156">Tiro nel detto triangolo.a.b.c.la &longs;ua <lb/>perpendicolare.a.d.& dal ponto.a.ti <lb/>ro la.a.e.equidi&longs;tãte alla.b.c.& facio <lb/>la detta.a.e equale alla mita della per­<lb/>pendicolare.a.d.& dal ponto.e.tiro <lb/>la.e.d.laqual &longs;ega el lato.a.c.nel <expan abbr="põto">ponto</expan> <lb/>f.dal qual <expan abbr="põto">ponto</expan>.f.tiro la.f.g.per <expan abbr="p&etilde;di-colare">pendi­<lb/>colare</expan> &longs;opra la.b.c.& anchora dal me <lb/>de&longs;imo <expan abbr="põto">ponto</expan>.f.tiro la.f.h. </s> <s id="s.002157"><expan abbr="equidi&longs;tãte">equidi&longs;tante</expan> al <lb/>la.b.c. </s> <s id="s.002158">& dal ponto.h. </s> <s id="s.002159">tiro la linea.h. <lb/></s> <s id="s.002160">i. <!-- REMOVE S-->perpendicolare alla. </s> <s id="s.002161">b.c. <!-- REMOVE S-->& co&longs;i nel<emph.end type="italics"/><lb/><figure id="id.042.01.203.1.jpg" xlink:href="042/01/203/1.jpg"/><lb/><emph type="italics"/>detto triangolo &longs;ara in&longs;critto il quadrilatero.f.g.h.i.qual dico e&longs;&longs;er quadrato, perche<emph.end type="italics"/><pb pagenum="102" xlink:href="042/01/204.jpg"/><emph type="italics"/>il triangolo.a.d.e.è &longs;imile al triangolo.f.g.d.& perch'el lato.a.d è doppio al lato.a.e. <lb/></s> <s id="s.002162"><expan abbr="Simelm&etilde;te">Simelmente</expan> el lato.f.g.&longs;ara doppio al lato.d.g.& perche.f.<emph.end type="italics"/>k.<emph type="italics"/>é equale al.d.g.lo mede <lb/>&longs;imo lato.f.g.&longs;ara anchora doppio al.f.<emph.end type="italics"/>k.<emph type="italics"/>& perche la.f.h.é a nchora lei doppia alla <lb/>mede&longs;ima.f.<emph.end type="italics"/>k <emph type="italics"/>&longs;eguita che il lato.f.h.&longs;ia equale al.f.g.& &longs;imelmente li altri dui lati <expan abbr="cõ">com</expan> <lb/>trapo&longs;iti, (cioe.h.i.&.g.i.) &longs;ono equali alli mede &longs;imi & &longs;imelmente li &longs;uoi quattro <lb/>angoli &longs;ono rettiper e&longs;&longs;er le linee.f.g.& h.i.perpendicolare &longs;opra <gap/>.b.c. </s> <s id="s.002163"><expan abbr="adũque">adunque</expan> tal <lb/>figura è quadrata ch'è il propo&longs;ito.<emph.end type="italics"/> M. B. Q<emph type="italics"/>uesta uo&longs;tra conclu&longs;ion molto mipia <lb/>ce, & uene ringratio a&longs;&longs;ai.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002164">QVESITO XVI. FATTO DA FRATE AMBRO­<lb/><emph type="italics"/>&longs;io da Ferrara del ordine di.s. </s> <s id="s.002165">Maria Organa adi.21. Lu­<lb/>io l'anno.1532. in Verona.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002166">FRATE AMBROSIO. I<emph type="italics"/>o aggio uno triangolo equilatero nel quale ui è <lb/>in&longs;critto dentro un cerchio, & trouo, ouer che &longs;o che il diametro del detto cer­<lb/>chio è la Radice cuba de.16. Hor ue adimando quanto ch'era per fazza el detto tri­<lb/>angolo.<emph.end type="italics"/> N. E<emph type="italics"/>l detto triangolo uenira à e&longs;&longs;er per fazza la Radice cuba della Radi­<lb/>ce quadra de.<emph.end type="italics"/>6912. F. A. E<emph type="italics"/>t perche uia lo ritrouati.<emph.end type="italics"/> N. I<emph type="italics"/>o &longs;uppono uno trian <lb/>golo equilatero à mio piacere, cioe che &longs;ia per fazza quanto mi pare, ma per non abon <lb/>dar in gran numeri in que&longs;to ca&longs;o io pongo che tal triangolo &longs;ia.2.per fazza, ouer <lb/>lato et di que&longs;to tal triangolo ricerco quanto &longs;ia el diametro del maggior cerchio che <lb/>in&longs;criuer &longs;i po&longs;&longs;a in quello, & trouo tal diametro e&longs;&longs;er la Radice quadratade.<emph.end type="italics"/> 1 1/3. <lb/>H<emph type="italics"/>or per la regola uolgarmente detta del tre dico &longs;e.<emph.end type="italics"/> <22>.1.1/3.<emph type="italics"/>de diametro mi da.2. per <lb/>lato del triangolo, che me dara<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.16.de diametro de cerchio multiplico, & par­<lb/>to &longs;econdo l'ordine di tal regola & me ne uien<emph.end type="italics"/> <22>.<emph type="italics"/>q.de<emph.end type="italics"/> <22>. <emph type="italics"/>quadra. </s> <s id="s.002167">6912.come di &longs;opra <lb/>fu da me determinato, & tanto dico fu per fazza el detto triangolo ch'è il propo&longs;ito.<emph.end type="italics"/><lb/>F. A. Q<emph type="italics"/>ue&longs;to uo&longs;tro procedere molto mi piace.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002168">QVESITO XVII. FATTO DA MAESTRO <lb/>A<emph type="italics"/>le&longs;&longs;andro Venetiano l'anno.1533. in Verona <lb/>qual haueua per opinione che fu&longs;­<lb/>&longs;e impoßibile.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002169">MAESTRO ALESSANDRO. E<emph type="italics"/>&longs;&longs;endo io in Fiorenza gia fa quatro <lb/>me&longs;i, & mi fu data una ragione la qual &longs;on certo ch'eglie impoßibile à ri&longs;&longs;ol­<lb/>uerla, come credo che il mede&longs;imo uoi affermareti.<emph.end type="italics"/> N. E<emph type="italics"/>t come dice que&longs;ta uostra <lb/>ragione.<emph.end type="italics"/> M. A. L<emph type="italics"/>a dice in que&longs;ta forma. </s> <s id="s.002170">Eglie uno triangolo de tre lati me qua­<lb/>li, la ba&longs;a del quale è.10.& la &longs;ua perpendicolare è.8.& li altri dui lati tolti in&longs;ieme <lb/>&longs;ono.20. Se domanda quanto era cadauno de dettidui lati per &longs;e mede&longs;tmo.<emph.end type="italics"/> N. I<emph type="italics"/>o <lb/>non uoglio affermare, ne manco negare che tal que&longs;tione &longs;ia impoßibile &longs;e prima non <lb/>tento quanto la pe&longs;a, perche &longs;ono molte que&longs;tioni, che in prima faccia pareno facile, et <lb/>nella re&longs;olutione, &longs;e ritrouano difficile & alcune che in prima faccia pareno difficile,<emph.end type="italics"/><pb xlink:href="042/01/205.jpg"/><emph type="italics"/>& nella re&longs;olutione &longs;i trouano facilißime.<emph.end type="italics"/> M.A. C<emph type="italics"/>o&longs;i me accaduto à me molte uol­<lb/>te, nondimeno que&longs;ta nella re&longs;olutione non ui ritrouo mezzo da poterla concludere, <lb/>e pero haria accaro, che anchora uoi tenta&longs;ti al pre&longs;ente, qua in mia pre&longs;entia, perche <lb/>ho accaro à uedere il uo&longs;tro procedere, & poi io ue diro el mio.<emph.end type="italics"/> N. I<emph type="italics"/>o ue diro per <lb/>ri&longs;oluer que&longs;to ca&longs;o. </s> <s id="s.002171">Io poneria, che il menor lato delli due fu&longs;&longs;e.1.co&longs;a laltro maggior <lb/>de neceßita uerria à e&longs;&longs;er.20.men.1.co&longs;a. </s> <s id="s.002172">Et (per l'ordine della.13.del &longs;econdo di <lb/>Euclide) io aggiongero el quadrato del detto lato menore (el qual quadrato &longs;aria.1. <lb/>cen&longs;o) con el quadrato della ba&longs;a (el qual quadrato &longs;aria.100.) fara.100.piu.1. cen&longs;o, <lb/>& da que&longs;ta &longs;umma ne cauaro el quadrato de laltro maggior lato (el qual quadrato <lb/>&longs;aria.400.piu.1.cen&longs;o, men.40.co&longs;e) & re&longs;tara.40.co&longs;e men.300.et questo parti&longs;co <lb/>per el doppio della ba&longs;a (el qual doppio &longs;aria. </s> <s id="s.002173">20.) & me ne uiene.2.co&longs;e men.15.& <lb/>tanto lontano da langolo doue termina il menor lato con la ba&longs;a, cadera la perpendico <lb/>lare del detto triangolo &longs;opra la ba&longs;a. </s> <s id="s.002174">Onde per uenire alla equatione, io quadraro tal <lb/>di&longs;tantia, cioe.2.co&longs;e men.15.el qual quadrato &longs;ara.4.cen&longs;i men.60.co&longs;e. </s> <s id="s.002175">piu. </s> <s id="s.002176">225. <lb/>& à que&longs;to ui aggiongo el quadrato della perpendicolare, el qual &longs;aria. </s> <s id="s.002177">64. fara in <lb/>&longs;umma.4.cen&longs;i men.60.co&longs;e, piu.289.& que&longs;to (per la penultima del primo di Eu­<lb/>clide) &longs;ara equale al quadrato del menor lato (el qual quadrato &longs;aria.1.cen&longs;o) re&longs;to­<lb/>ro le parti, & &longs;eguito il capitolo, & trouo la co&longs;a ualer.10.men. </s> <s id="s.002178"><22>.3.2/3.& tanto fu <lb/>el lato menore, & el maggiore uenira à e&longs;&longs;ere.10.piu. </s> <s id="s.002179"><22>.3.2/3. della qual conclu&longs;ione, <lb/>&longs;e ne fareti proua, la trouareti e&longs;&longs;er giu&longs;ta, che è il propo&longs;ito.<emph.end type="italics"/> M.A. A<emph type="italics"/>nchora, che <lb/>tutto que&longs;to uo&longs;tro operar &longs;ia &longs;tato bello nondimeno, quel uo&longs;tro &longs;ottrare.400.piu.1. <lb/>cen&longs;o, men.40.co&longs;e de.100.piu.1.cen&longs;o, doue concludeti che resta.40.co&longs;e, men.300. <lb/>eglie &longs;tato il fiore di tutto quanto el uostro operare appre&longs;&longs;o di me. </s> <s id="s.002180">Et quantunque <lb/>habbia detto diuolerui dir il mio procedere nella re&longs;olutione di que&longs;to Que&longs;ito, lo uo­<lb/>glio tacere, perche, per la uia, che io procedeua, io non poteua uenire ad alcuna equa­<lb/>tione, e pero &longs;aria co&longs;a &longs;uperflua à uolerla narrare.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002181">QVESITO XVIII. FATTO CREDO DA MAETSRO <lb/>A<emph type="italics"/>ntonio Maria Fior, qual me porto un gargione &longs;otto <lb/>mano l'anno.1534.in Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002182">GARGIONE. H<emph type="italics"/>aggio una botta piena di uin puro, della quale ne cauo fuo­<lb/>ra dui barili, & la reimpio di acqua, & dapoi alcuni giorni, ne reccauo fuora <lb/>anchora dui altri barili, & la reimpio pur di acqua, & co&longs;i dapoi alcuni altri giorni <lb/>ne reccauo pur fuora dui altri barili, & la reimpio pur di acqua. </s> <s id="s.002183">Et fatto questo, io ri <lb/>trouo, che quel uino, che in ultimo &longs;e ritroua nella detta botta piena é preci&longs;amente la <lb/>mitta uino, & la mitta acqua. </s> <s id="s.002184">Se adimanda quanti barili teneua la detta botta.<emph.end type="italics"/> N. <lb/>Q<emph type="italics"/>ue&longs;to Que&longs;ito non uol dir altro, che trouar quattro quantita continue proportio­<lb/>nale co&longs;i conditionate, che la quarta quantita &longs;ia doppia alla prima perche per la quar <lb/>ta quantita, ouer termine &longs;e intende la tenuta di la botta, & per el primo termine, o­<lb/>uer quantita &longs;e intende per quel uino, che in ultimo riman con lacqua, & che la diffe <lb/>rentla del ter<gap/>o, & quarto termine &longs;ia.2.per li dui barili, che &longs;i caua. </s> <s id="s.002185">Onde per ri&longs;ol-<emph.end type="italics"/><pb pagenum="103" xlink:href="042/01/206.jpg"/><emph type="italics"/>uere tal que&longs;ito fra.1.&.2.ritrouo dui medij continui proportionali, delli quali l'u­<lb/>no &longs;ara Radice cuba.2. (cioe il &longs;econdo termine) l'altro, cioe il terzo termine, &longs;ara<emph.end type="italics"/> <22>. <lb/><emph type="italics"/>q.4.dapoi guardo che differentia è frail terzo, & quarto termine, & trouo che la è. <lb/></s> <s id="s.002186">2.men<emph.end type="italics"/> <22>.<emph type="italics"/>q.4.& io uorrei che fu&longs;&longs;e 2. (come di &longs;opra dißi) e pero con forza di pro­<lb/>portione li po&longs;&longs;o ritrouar in que&longs;to modo, digando &longs;e.2.men<emph.end type="italics"/> <22>.<emph type="italics"/>q.4. (de differentia) <lb/>mi da.2.per il quarto termine, che mi dara.2.de differentia, moltiplicando, & parten <lb/>do &longs;econdo la regola ne uenira.4.piu<emph.end type="italics"/> <22>.<emph type="italics"/>q.32.piu<emph.end type="italics"/> <22>.<emph type="italics"/>q.16.& tanti barili teneua la det <lb/>ta botta.<emph.end type="italics"/> G. E<emph type="italics"/>t io ritrouo che la tiene barili.4.piu<emph.end type="italics"/> <22>.<emph type="italics"/>q.10.men<emph.end type="italics"/> <22>.<emph type="italics"/><expan abbr="q.">que</expan><emph.end type="italics"/>6. N. H<emph type="italics"/>or <lb/>ua, e di à colui, che ti ha mandato, che &longs;e lui proua la &longs;ua, & mia conclu&longs;ione, che lui ri­<lb/>trouara la mia buona & la &longs;ua fal&longs;a, & accio che lui habbia manco fatica, io ti uoglio <lb/>dare li tre re&longs;tanti ordinatamente della detta botta, cioe de uino puro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002187">T<emph type="italics"/>enuta di tutta la botta.4.piu<emph.end type="italics"/> <22>.<emph type="italics"/>q.32.piu<emph.end type="italics"/> <22>.<emph type="italics"/><expan abbr="q.">que</expan><emph.end type="italics"/>16. </s> </p> <p type="main"> <s id="s.002188">L<emph type="italics"/>o primo re&longs;tante &longs;ara<emph.end type="italics"/> <22>.<emph type="italics"/>q.32.piu<emph.end type="italics"/> <22>. <emph type="italics"/>q.16. piu.<emph.end type="italics"/>2. </s> </p> <p type="main"> <s id="s.002189">L<emph type="italics"/>o &longs;econdo re&longs;tante &longs;ara<emph.end type="italics"/> <22>.<emph type="italics"/>q.16 piu.2.piu<emph.end type="italics"/> <22>.<emph type="italics"/><expan abbr="q.">que</expan><emph.end type="italics"/>4. </s> </p> <p type="main"> <s id="s.002190">L<emph type="italics"/>o ultimo re&longs;tante &longs;ara.2.piu<emph.end type="italics"/> <22>.<emph type="italics"/>q.4.piu<emph.end type="italics"/> <22>.<emph type="italics"/><expan abbr="q.">que</expan><emph.end type="italics"/>2. </s> </p> <p type="main"> <s id="s.002191">C<emph type="italics"/>ioe l'ultimo re&longs;tante &longs;ara preci&longs;amente la mita della tenuta di tutta la botta, cioe la mi <lb/>ta del uino, & l'altra mita uenira à e&longs;&longs;er acqua, che è il propo&longs;ito.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002192">QVESITO. XIX. FATTO DAL MAGNIFICO <lb/><emph type="italics"/>me&longs;&longs;er Zuanbattista Memo l'anno ch'io ueni ad ha­<lb/>bitare in Venetia, che fu.<emph.end type="italics"/> 1534.</s> </p> <p type="main"> <s id="s.002193">MAGNIFICO M. ZVAN BATTISTA. H<emph type="italics"/>auetiuoi opinione che il <lb/>&longs;ia poßibile à ritrouare la quadratura del cerchio.<emph.end type="italics"/> N. I<emph type="italics"/>l non &longs;i puo negare, <lb/>che quella co&longs;a che è in e&longs;&longs;er nelle co&longs;e naturale, che il non &longs;ia poßibile anchora à ritro­<lb/>uarla.<emph.end type="italics"/> M.Z. V<emph type="italics"/>oi &longs;eti in errore. </s> <s id="s.002194">Anchora che Ari&longs;totele affermi e&longs;&longs;er poßibile, la <lb/>cau&longs;a è, che fra il diametro del cerchio, & la &longs;ua circon&longs;erentia non ui cade alcuna pro <lb/>portione, perche il diametro non è uniuoco con la cir conferentia (perche il retto, & il <lb/>curuo non &longs;ono uniuoce) e pero non &longs;ono comparabili, et non e&longs;&longs;endo comparabili non <lb/>&longs;i puo dire, che fra loro ue &longs;ia alcuna &longs;pecie di proportione, & quello che non è in nelle <lb/>co&longs;e di natura non è poßibile à poterle ritrouare.<emph.end type="italics"/> N. E<emph type="italics"/>glie ben uero, che la linea ret <lb/>ta non è comparabile alla curua ri&longs;petto à quella qualita del retto, & curuo, ma ri&longs;pet <lb/>to alla <expan abbr="quãtita">quantita</expan>, à me mi pare, che &longs;iano comparabile, perche il predicameuto della quan <lb/>tita è uno, & quello della qualita è un'altro, & che il &longs;ia il uero che &longs;iano comparabili, <lb/>& che ue &longs;ia fra lor proportione, facilmente il &longs;i puo prouare per la quinta diffinitio­<lb/>ne del quinto di Euclide. <!-- KEEP S--></s> <s id="s.002195">Nella quale lui diffini&longs;&longs;e che quelle quantita &longs;e dicono hauer <lb/>proportione fra loro, le quale moltiplicate &longs;i po&longs;&longs;ono eccedere l'una, el altra, & per­<lb/>ch'eglie co&longs;a chiara, che il quadruplo del diametro del cerchio, eccede la <expan abbr="circõfer&etilde;tia">circonferentia</expan> di <lb/>quello, pche il quadruplo del detto diametro di tal cerchio è eguale alli.4.lati del qua­<lb/>dro circon&longs;critto al mede&longs;imo cerchio, & li detti.4.lati, eglie manife&longs;to e&longs;&longs;er molto <lb/>piu della circonferentia del cerchio, adunque potendo&longs;i moltiplicare il diametro del <pb xlink:href="042/01/207.jpg"/>cerchio, talmente che ecceda la detta circonferentia &longs;eguita (per la detta diffinitione) <lb/>che fra il diametro del cerchio, & la circonferentia di quello ue &longs;ia proportione, an­<lb/>chor che tal proportione ne &longs;ia incognita, che è il propo&longs;ito.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002196">QVESITO. XX. FATTO COPERTAMENTE <lb/><emph type="italics"/>da mae&longs;tro zuan de Tonini da Coi, qual mi portò in &longs;critto <lb/>mae&longs;tro Dominico da Vderzo, l'Anno. <!-- REMOVE S-->1535. Adi.12. <lb/>Settembrio, in Venetia, qual di&longs;&longs;e hauerli hauu <lb/>ti da nn Special, che ueniua <lb/>da Bre&longs;&longs;a.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002197">MAESTRO ZVANE. I<emph type="italics"/>o adimandai à uno Pe&longs;catore, che &longs;el mi uoleuæ <lb/>uendere una trutta, che lui haueua, che tante once, come che lei pe&longs;aua, io gli uo <lb/>leua dare tanti danari, ouer pizzoli della lira, & tante lire, come che la pe&longs;aua ancho­<lb/>ra tanti altri danarigli uoleua dar pur della lira, & lui &longs;i contento, & io glidiedi &longs;ol­<lb/>di.7.domando quanto pe&longs;aua la detta trutta.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002198">A<emph type="italics"/>nchorauno me impre&longs;talire.60.de danari à ragion de.5.per cento de utile à l'an­<lb/>no. </s> <s id="s.002199">Et io gli la&longs;&longs;o po&longs;&longs;edere una ca&longs;a qual paga de fitto lire.23.à l'anno. </s> <s id="s.002200">Domando in <lb/>che tempo &longs;ara pagato.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002201">A<emph type="italics"/>nchora &longs;ono trei, che hanno comprato lire. </s> <s id="s.002202">20.di carne, & tante lire ne ha com <lb/>prato uno di loro, che moltiplicato tal numero de lire in &longs;e mede&longs;imo tal produtto è <lb/>eguale alla moltiplicatione delle lire, che hanno comprate glialtri dui, cioe quelle del­<lb/>l'uno fia quelle dell altro, & moltiplicati li due menor quantita de lire l'una fia l'altra <lb/>fanno preci&longs;amente.8.Se adimanda la quantita delle libre di carne, che compro cadau­<lb/>no per &longs;e.<emph.end type="italics"/> N. C<emph type="italics"/>hi uiha dato que&longs;ti que&longs;iti.<emph.end type="italics"/> M.D. E<emph type="italics"/>l me liha dati uno Speciaro qual <lb/>uien da Bre&longs;&longs;a, il qual dice e&longs;&longs;erli &longs;tati dati da uno li in Bre&longs;&longs;a, il qual l'ha pregato, che <lb/>ue li dia far hauer à uoi &longs;otto mane, & ueder da intendere la uo&longs;tra ri&longs;po&longs;ta.<emph.end type="italics"/> N. V<emph type="italics"/>e­<lb/>nendo da Bre&longs;&longs;a, li &longs;ono d'un mae&longs;tro zuan da Coi, qual quando &longs;tantiaua anchora à Ve <lb/>rona l'Anno. <!-- REMOVE S-->1530. me ne mandete dui altri, & qua&longs;i che que&longs;ta mi ra&longs;&longs;omiglia la &longs;ua <lb/>lettera.<emph.end type="italics"/> M.D. P<emph type="italics"/>otria e&longs;&longs;er chi fu&longs;&longs;e quello.<emph.end type="italics"/> N. C<emph type="italics"/>redo che il &longs;e &longs;ia emendato del &longs;uo <lb/>co&longs;tume antico, qual era de proponere alcuni ca&longs;i fanta&longs;tichi, che lui mede&longs;imo non &longs;a­<lb/>peuari&longs;oluere. </s> <s id="s.002203">Perche uedo che il primo de que&longs;ti, è co&longs;a &longs;olubile, & non uol dir altro <lb/>in &longs;o&longs;tantia, &longs;aluo che tante lire, come pe&longs;aua la trutta, tanti &longs;oldi, & tanti danari, ouer <lb/>pizzoli, la uoleua pagar la lira. </s> <s id="s.002204">Onde per a&longs;&longs;oluere tal que&longs;ito.Io ponero che tal trut­<lb/>ta pe&longs;a&longs;&longs;e.1.co&longs;a de lira, adunque la pagai à.1.co&longs;a de &longs;oldo piu.1.co&longs;a de danaro la lira. <lb/></s> <s id="s.002205">Onde moltiplicando.1.co&longs;a de &longs;oldo piu.1.co&longs;a de danaro fia.1.co&longs;a de lira fara.1.cen&longs;o <lb/>de &longs;oldo piu.1.cen&longs;o de danaro. </s> <s id="s.002206">Et questo &longs;ara egual à &longs;oldi.7. Hor reducendo ogni co­<lb/>&longs;a in danari, ouer, pizzoli, à danari.12.al &longs;oldo, uenir anno in tutto.13.cen&longs;i de danaris <lb/>& que&longs;ti &longs;aranno eguali à. </s> <s id="s.002207">84.danari, onde partendo il numero per li cen&longs;i, ne uien.6. <lb/>6/13.& la Radice de.6.6/11.ual&longs;e la co&longs;a, & tante lire pe&longs;o la detta trutta, cioe lire<emph.end type="italics"/> <22>. <lb/></s> <s id="s.002208">6.6/13.<emph type="italics"/>che à &longs;oldi<emph.end type="italics"/> <22>.6.6/13.<emph type="italics"/>piu danari<emph.end type="italics"/> <22>.6.6/13.<emph type="italics"/>la lira montara preci&longs;amente &longs;oldi.7. <lb/>che è il propo&longs;ito.<emph.end type="italics"/></s> </p> <pb pagenum="104" xlink:href="042/01/208.jpg"/> <p type="main"> <s id="s.002209">L<emph type="italics"/>o &longs;econdo anchora che è co&longs;a &longs;olubile, perche meritando le dette lire.60.(rece­<lb/>pute impresto) per uno anno à.5.per cento à l'anno tornar anno tra cauedal è merito <lb/>lire.63.& di que&longs;te bi&longs;ogna cauarne el fitto della ca&longs;a di quell'anno (che &longs;ono lire.23.) <lb/>re&longs;tara anchor debitor de lire.40.in capo del primo anno, hor per il &longs;econdo anno bi <lb/>&longs;ogna pur meritar le dette lire.40.à.5.per cento à l'anno, & tornaranno tra merito, <lb/>& capitale lire.42.& di que&longs;te lire.42.bi&longs;ogna cauarne el fitto della ca&longs;a di quell'an <lb/>no (che &longs;ono lire.23.) re&longs;ta lire. </s> <s id="s.002210">19.& lire.19.uerria à e&longs;&longs;er debitore in capo de detti <lb/>dui anni, hor qui è la difficolta à &longs;aper determinare que parte del terzo anno die po&longs;&longs;e <lb/>dere la ca&longs;a colui à douer re&longs;tare preci&longs;amente &longs;atisfatto, perche eglie co&longs;a chiara, che <lb/>douendo hauer &longs;olamente lire.19.dal patron della ca&longs;a non die po&longs;&longs;edere la detta ca&longs;a <lb/>tutto l'anno, ma &longs;olamente una parte, & per ritrouar quella parte.Io pono che la deb­<lb/>bia po&longs;&longs;edere.1.co&longs;a de giorni, & per tanto tempo merito lire.19.à ragion de.5.per <lb/>cento à l'anno à.365.giorni à l'anno, & per piu breuita moltiplico lire.100.per gior <lb/>ni.365.fanno.36500.fra giorni, & lire di cauedale, & dapoi moltiplico anchora lire. <lb/></s> <s id="s.002211">105.fra utile, & cauedale pur per giorni.365.fanno.38325.fra giorni, & lire de caue <lb/>dal è guadagno, poi moltiplico.1.co&longs;a fia lire.19.fara.19.co&longs;e, dapoi procedo per lare <lb/>gola (uolgarmente detta del tre) digando, &longs;e.36500.mi torna.38325.che me ritorna­<lb/>ranno.19.co&longs;e (cioe quelle lire.19.moltiplicate fia.1.co&longs;a de giorni) operando me ne <lb/>uien.728175/36500.co&longs;e, & questo è fra tempo è danari, & que&longs;to bi&longs;ogna partire per <lb/>lo tempo (qual è.1.co&longs;a de giorni) ne uenira lire.728175/36500.& que&longs;to &longs;aluo da banda, <lb/>dapoi bi&longs;ogna meritar.1.co&longs;a de giorni à lire.23.à l'anno, digando &longs;e giorni.365.uol <lb/>lire.23.che uorra.1.co.operando &longs;econdo la regola uorra.23/365.co&longs;e, & que&longs;to &longs;ara <lb/>egual à.<emph.end type="italics"/>728175/36500.S<emph type="italics"/>eguitando il capitolo &longs;e trouara la co&longs;a ualer.316.55/92.& tanti <lb/>giorni douera star nella detta ca&longs;a à douer e&longs;&longs;er integralmente &longs;atisfatto, oltragli an­<lb/>ni integri, detti di &longs;opra, che è il propo&longs;ito.<emph.end type="italics"/> M.D. C<emph type="italics"/>ertamente li &longs;ono a&longs;&longs;ai belli que <lb/>&longs;iti.<emph.end type="italics"/> N. H<emph type="italics"/>or uedemo un poco que&longs;to terzo qual per quanto uedo, non uol dir altro in <lb/>&longs;o&longs;tantia che fare de.20.tre parti continue proportionale in tal&longs;pecie di proportio­<lb/>ne, che moltiplicando le due menore l'una fia l'altra faccia.8.etiam per quanto po&longs;&longs;o <lb/>co&longs;i all'improui&longs;o con&longs;iderare, dubito che in que&longs;ta faccia delle &longs;ue, & che il non &longs;e&longs;ta <lb/>in tutto emendato, del &longs;uo diffetto pur la uoglio un poco meglio con&longs;iderarla.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002212">QVESITO. XXI. FATTO DA VNO MER­<lb/><emph type="italics"/>cante, qual gli era stato dato à lui da darmi l'anno.1535. <lb/>Adi.16.Ottobrio, in Venetia, & non uol&longs;e <lb/>dir da chi.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002213">MERCANTE. D<emph type="italics"/>ui fanno compagnia, il primo mi&longs;&longs;e ducati.240.& &longs;tette <lb/>me&longs;i.9.l'altro mi&longs;&longs;e una gioia, & &longs;tette me&longs;i.6.& guadagnorno ducati.100. <lb/>à quello della gioia gli tocco fra cauedal eguadagno ducati. </s> <s id="s.002214">150. Domando quan­<lb/>to ual&longs;e la gioia.<emph.end type="italics"/> N. P<emph type="italics"/>er &longs;oluere tal que&longs;ito. </s> <s id="s.002215">Io pongo, che la gioia uaglia.1.co&longs;a, & <lb/>quella moltiplico fia lime&longs;i.6.che &longs;ta in la compagnia fa.6.co&longs;e, poi moltiplico, li <lb/>ducati.240.fia.9.me&longs;i fanno.2160.& que&longs;to &longs;ummo con. </s> <s id="s.002216">6. co&longs;e fanno. </s> <s id="s.002217">2160. <pb xlink:href="042/01/209.jpg"/>piu.6.co&longs;e.Poi dico per regola detta del tre, &longs;e.2160.piu.6.co.me guadagna duc.100. <lb/>la che mi guadagnaran.6.co&longs;e <expan abbr="operãdo">operando</expan> trouo che guadagnariano.600.co. </s> <s id="s.002218">e&longs;imi de. <lb/></s> <s id="s.002219">2160.piu.6.co. </s> <s id="s.002220">& que&longs;to &longs;ara eguale à duc.150.men.1.co. (cioe à quello, che tocco al <lb/>&longs;econdo, de puro guadagno, cioe trattone.1.co&longs;a, che fu il &longs;uo puro capitale) leuando li <lb/>rotti, & &longs;eguitando il capitolo trouo la co&longs;a ualer<emph.end type="italics"/> <22>.78025.<emph type="italics"/>men.155.& tanto ual­<lb/>&longs;e la gioia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002221">QVESITO. XXII. FATTO DA VNO VICENTI <lb/><emph type="italics"/>di Gaffari Adi.13. Ago&longs;to. <!-- REMOVE S-->1536. In Venetia, in la Chie&longs;a di San <lb/>Giouanepolo, in la capella de San Nicolo, i&longs;ponendo io la <lb/>13.propo&longs;itione del terzodecimo di Euclide publica­<lb/>mente, credendo&longs;i lui con tal &longs;uo que&longs;ito di far­<lb/>mi totalmente re&longs;tar confu&longs;o.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002222">VICENTI. C<emph type="italics"/>ertamente uoi haueti i&longs;po&longs;ta que&longs;ta uo&longs;tra lettione, ouer pro­<lb/>po&longs;itione tanto degnamente, quanto dir &longs;i po&longs;&longs;a. </s> <s id="s.002223">Ma uorria, che uoime ri&longs;ol­<lb/>ue&longs;ti anchora que&longs;to que&longs;ito.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002224">S<emph type="italics"/>aggi diece di orc che tenia <lb/>De argento in &longs;e la &longs;ua cuba Radice <lb/>Co&longs;to ducati diece, hor stati al quia <lb/>Che alla ra&longs;on mede&longs;ima &longs;e dice.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002225">D<emph type="italics"/>iece altri &longs;aggi che tenia in&longs;erto <lb/>De argento in &longs;e la &longs;ua quadra Radice <lb/>Co&longs;ta ducati nuoue intendi il merto<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002226">P<emph type="italics"/>roportionatamente, qual dimanda <lb/>Che ual&longs;e il &longs;aggio di cia&longs;cun incerto<emph.end type="italics"/><lb/>A <emph type="italics"/>uoi &longs;pirto gentil questa &longs;i manda <lb/>Et perche hormai &longs;i &longs;panda <lb/>La fama di colui che l'ha compo&longs;ta <lb/>Di Gaffari Vicenti, è la propo&longs;ta.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002227">NIC. Q<emph type="italics"/>uando che uno uol arguire contra ad alcuno, che legga publicamente in qual <lb/>che &longs;cientia, lui de &longs;empre arguire &longs;opra alle co&longs;e da lui lette, & dichiarate, nella &longs;ua <lb/>lettione, ouer i&longs;po&longs;itione, & non in altre particolarita fuora di tal propo&longs;ito, & &longs;e pur <lb/>alcuno temerario (per mo&longs;trar anchora lui di &longs;apere) ui propone&longs;&longs;e, ouer parla&longs;&longs;e di <lb/>qualche altra particolarita fuora di tal propo&longs;ito (come che haueti fatto uoi) il letto­<lb/>re puo con &longs;uo honore, recu&longs;are di darui ri&longs;po&longs;ta, come co&longs;a fuora di propo&longs;ito, nondi­<lb/>meno allegramente, eccetto que&longs;to uo&longs;tro que&longs;ito, con que&longs;to patto però, che anchora <lb/>uoi ne acettati un'altro da me.<emph.end type="italics"/> V. M<emph type="italics"/>ade uolontiera.<emph.end type="italics"/> N. H<emph type="italics"/>auendo uoi tanto lauda <lb/>ta la miai&longs;po&longs;itione, eglie da credere, che uoi l'habbiati rettamente inte&longs;a, & perche <lb/>non me ritrouo co&longs;i all'improui&longs;o alcuno piu famigliar que&longs;ito, che la pre&longs;ente propo­<lb/>&longs;itione da me i&longs;posta, ue impongo, che uoi di nuouo qui publicamente la i&longs;poneti, & in <lb/>que&longs;to meggio, mandaro à tuor penna, & inchio&longs;tro, & uiri&longs;oluero il uostro que&longs;ito.<emph.end type="italics"/><pb pagenum="105" xlink:href="042/01/210.jpg"/><emph type="italics"/>&longs;e&longs;apero.<emph.end type="italics"/> VICENTI. I<emph type="italics"/>o ue diro io non intendo Geometria, ma el mio que&longs;ito è <lb/>in numeri, ouer in Algebra &longs;i che preponetime un que&longs;ito in numeri, ouer in Alge­<lb/>bra, che io lo accettaro & ue lo ri&longs;oluero &longs;ubito.<emph.end type="italics"/> N. S<emph type="italics"/>on contento &longs;e uenereti à lal­<lb/>tra mia lettione ue lo portero.<emph.end type="italics"/> VICENTI. V<emph type="italics"/>eniro &longs;enza fallo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002228">QVESITO XXIII. FATTO DAPOI LAL­<lb/><emph type="italics"/>tralettione al detto Vicenti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002229">NICOLO. I<emph type="italics"/>n fin de l'altra mialettione, me&longs;&longs;er Vicenti. </s> <s id="s.002230">Voi me prepone&longs;ti <lb/>quel uo&longs;tro que&longs;ito che &longs;appeti, & io lo accettai con que&longs;ta conditione che <lb/>uoi ne doue&longs;ti anchora uoi accettarne un'altro da me et uoi ue contenta&longs;ti di accettar­<lb/>lo domente che talmio que&longs;ito, fu&longs;&longs;e in numeri, ouer per Algebra. <!-- KEEP S--></s> <s id="s.002231">Et co&longs;i ue l'ho por <lb/>tato elqual è que&longs;to, trouatime uno numero, che multiplicato fia la &longs;ua Radice piu. <lb/></s> <s id="s.002232">6.faccia à ponto.<emph.end type="italics"/>100. VICENTI. B<emph type="italics"/>enlo ri&longs;oluero. </s> <s id="s.002233">Ma ditime haueti ri&longs;olto il <lb/>mio che io ui dedi.<emph.end type="italics"/> N. M<emph type="italics"/>e&longs;&longs;er &longs;i che io l'ho re&longs;olto, & tal uostro que&longs;ito è molto <lb/>bello, & ingenio&longs;o, ma <expan abbr="nõ">non</expan> è uo&longs;tra farina. </s> <s id="s.002234">Perche uoi confe&longs;&longs;a&longs;ti, quando mel de&longs;ti che <lb/>uoi non haueui, ouer intendeui geometria, & tal uo&longs;tro que&longs;ito (anchor che &longs;ia pro­<lb/>po&longs;to &longs;otto ombra de numeri) è co&longs;a geometrica, ma uoi el doueti hauer ritrouato, <lb/>&longs;critto &longs;opra qualche libro, da qualche per&longs;ona dotta, & con tal particolarita, ue re­<lb/>putati e&longs;&longs;ere un gran huomo in tal faculta, ma colui che co&longs;i po&longs;itiuamente &longs;e ucste di <lb/>panni d'altri pre&longs;to &longs;e ne &longs;poglia. </s> <s id="s.002235">Hor per uenire alla conclu&longs;ione, dico che'l &longs;aggio <lb/>del uo&longs;tro ero ual&longs;e ducati.1.1/90.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.1/72900.piu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba quadra.1/53144100000. <lb/>piu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba quadra.1/5314410.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.1/7290.piu<emph.end type="italics"/> <22>. <emph type="italics"/>quadra<emph.end type="italics"/>1/810 <lb/>E<emph type="italics"/>t el &longs;aggio de l'argento ual&longs;e ducati.9/10.men<emph.end type="italics"/> <22>.1/10.<emph type="italics"/>piu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba.1/100.piu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba <lb/>quadra<emph.end type="italics"/> 1/100000. H<emph type="italics"/>or guardati &longs;el ui pare che tal uostro que&longs;ito &longs;ia ben re&longs;olto.<emph.end type="italics"/><lb/>VICENTI. S<emph type="italics"/>el &longs;e incontra, con que&longs;to che ade&longs;&longs;o, ade&longs;&longs;o ui mo&longs;traro &longs;un que&longs;to <lb/>mio libro lui &longs;ara ben re&longs;olto, & e&longs;&longs;endo altramente, lui &longs;ara fal&longs;o.<emph.end type="italics"/> N. E<emph type="italics"/>t io di­<lb/>co che &longs;e la conclu&longs;ione di quello che haueti &longs;ul detto uo&longs;tro libro &longs;e incontrara con la <lb/>mia, la uostra &longs;ara bona, & e&longs;&longs;endo altramente, la &longs;ara fal&longs;a.<emph.end type="italics"/> VICENTI. H<emph type="italics"/>or in <lb/>contramole un puoco, la &longs;e incontra benißimo.<emph.end type="italics"/> N. A<emph type="italics"/>dunque confirmati, che la &longs;ta <lb/>bene.<emph.end type="italics"/> VICENTI. L<emph type="italics"/>a &longs;ta ben per certo.<emph.end type="italics"/> N. H<emph type="italics"/>or &longs;u à laltra lettione ui a&longs;petto <lb/>con la re&longs;olution del mio.<emph.end type="italics"/> VICENTI. V<emph type="italics"/>eniro.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.002236">QVESITO XXIIII. FATTO DAL NOSTRO <lb/><emph type="italics"/>amicißimo mi&longs;&longs;er Hieronimo Triui&longs;ano, dapoi <lb/>laltra lettione.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002237">MISSER HIERONIMO. M<emph type="italics"/>olto mi allegro<emph.end type="italics"/> M. N. <emph type="italics"/>carißimo chel <lb/>Vicenti non habbia &longs;aputo ri&longs;oluere il uo&longs;tro que&longs;ito, & e&longs;&longs;er re&longs;tato total­<lb/>mente confu&longs;o, come meritaua la &longs;ua audacia, qual &longs;e per&longs;uadeua con tal &longs;ua que&longs;tione <lb/>di farue restare publicamente confu&longs;o, & fu uolta ch'io dubitai che uoi non la &longs;ape&longs;ti <lb/>re&longs;oluere perche lui ha giurato non hguer mai ritrouato huomo, che ge l'habbia &longs;apu-<emph.end type="italics"/><pb xlink:href="042/01/211.jpg"/><emph type="italics"/>ta ri&longs;oluere. </s> <s id="s.002238">Et per che in effetto tal ragione mi piace uoria che per uo&longs;tra gentilez­<lb/>za mi mostra&longs;ti il modo da ri&longs;oluerla.<emph.end type="italics"/> N. M<emph type="italics"/>olio uolentera &longs;appiati che per ri&longs;olue <lb/>re tal ragione, ouer que&longs;ito bi&longs;ogna con&longs;iderar que&longs;to. </s> <s id="s.002239">Che quello ducato che monta <lb/>de piu li primi &longs;aggi.10.é per e&longs;&longs;er in quello piu oro che non è nelli altri &longs;econdi &longs;aggi. <lb/></s> <s id="s.002240">10.& manco argento, & quel oro è tanto quanto che è la differentia ch'è fra la Radi­<lb/>ce cuba di.10.& la Radice quadra de.10.laqual differentia, è<emph.end type="italics"/> <22>.10.<emph type="italics"/>men<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.10.& <lb/>que&longs;to re&longs;iduo de oro ual uno ducato de più, che &longs;el fu&longs;&longs;e argento, cioe un tal re&longs;iduo <lb/>a'oro ualeria de piu de un tal re&longs;iduo di argento, uno docato à ponto. </s> <s id="s.002241">Adunque bi&longs;o­<lb/>gna uedere che ualeria alla ratta<emph.end type="italics"/> <22>. <emph type="italics"/>cuba.10.de oro puro, digando &longs;e<emph.end type="italics"/> <22>.10.<emph type="italics"/>men<emph.end type="italics"/> <22>. <emph type="italics"/>cu­<lb/>ba.10 dioro ual ducati.1.che ualeria<emph.end type="italics"/> <22>.<emph type="italics"/>q.10.di oro operando haueremo<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.10.da <lb/>partir per<emph.end type="italics"/> <22>.10.<emph type="italics"/>men<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.10.& per trouar el partitore rationale, multiplicare­<lb/>mo el detto<emph.end type="italics"/> <22>.10.<emph type="italics"/>men<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.10.per.10.piu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba quadra.100000. piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.100. <lb/>ne uenira<emph.end type="italics"/> <22>.1000.<emph type="italics"/>men.10.& questo re&longs;iduo, lo remultiplicaremo per el&longs;uo binomio, <lb/>cioe per<emph.end type="italics"/> <22>.1000.<emph type="italics"/>piu.10.produra.900.à ponto (che numero rationale) & questo &longs;er <lb/>uaremo per no&longs;tro partitore. </s> <s id="s.002242">Dapoi multiplicaremo la co&longs;a da partire, (cioe<emph.end type="italics"/> <22>.<emph type="italics"/>cu. <lb/></s> <s id="s.002243">10.per la detta quantita trinomiale, et dapoi per quella binomiale, cioe prima per.10. <lb/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cuba quadra 100000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.100 fara<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.10000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cuba quadra. <lb/></s> <s id="s.002244">10000000.piu.10. Dapoi bi&longs;ogna anchora multiplicar que&longs;to produtto per el bino­<lb/>mio, cioe per.<emph.end type="italics"/> <22>.1000.<emph type="italics"/>piu.10.fara.100.piu.<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.10000000. piu<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.quadra. <lb/></s> <s id="s.002245">10000000000000.piu<emph.end type="italics"/> <22>. <emph type="italics"/>cu.qua.100000000000000000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.100000000000 <lb/>00000.piu<emph.end type="italics"/> <22>. </s> <s id="s.002246">100000. E<emph type="italics"/>t que&longs;ta quantita de &longs;ei nomi, bi&longs;ogna partirla per el no­<lb/>&longs;tro partitor &longs;aluato, cioe per.900. & ne uenira.1/1.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.10/729.piu<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.002247">qua. <lb/></s> <s id="s.002248">10/531441.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.100000/531441.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.10000/531441.piu<emph.end type="italics"/> <22>.0/81.E<emph type="italics"/>t tan <lb/>to ual&longs;e<emph.end type="italics"/> <22>.<emph type="italics"/>cu.10.de oro piu de altro tanto argento. </s> <s id="s.002249">Onde <expan abbr="aggiung&etilde;do">aggiungendo</expan><emph.end type="italics"/> <22>.<emph type="italics"/>cu.10.in luo <lb/>co de lo argento alla prima uirga cioe à &longs;aggi.10.men<emph.end type="italics"/> <22>.<emph type="italics"/>cu.10.faranno &longs;aggi.10.de <lb/>oro puro elqual oro puro montaria piu di primi ducati.10.la &longs;opra &longs;critta quantita <lb/>de &longs;ei nomi compo&longs;ta, cioe ualeriano ducati.10.1/9.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.11/729.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.qua. <lb/></s> <s id="s.002250">10/531441.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.100000/531441.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.10000/531441.piu<emph.end type="italics"/> <22>.10/81.D<emph type="italics"/>a­<lb/>poi uolendo &longs;aper che ual&longs;e il &longs;aggio, bi&longs;ogna partire li &longs;opra &longs;critti. </s> <s id="s.002251">6.nomi per li.10 <lb/>&longs;aggine uenira ducati. </s> <s id="s.002252">1.1/90.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.10/729000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.10/531441000000. <lb/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua. </s> <s id="s.002253">10000/531441000000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.10000/531441000000. <lb/>piu<emph.end type="italics"/> <22>.10/8100.<emph type="italics"/>& tanto ual&longs;e el &longs;aggio del detto oro puro ch'é il primo propo&longs;i­<lb/>to. </s> <s id="s.002254">Ma bi&longs;ogna notare che li detti rotti &longs;e po&longs;&longs;ono la maggior parte &longs;chi&longs;&longs;are & &longs;chi­<lb/>&longs;andoli &longs;econdo il bi&longs;ogno &longs;e trouarano ducati.1.1/90.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cuba.1/72900.piu.<emph.end type="italics"/> <22>. <lb/><emph type="italics"/>cu qua.1/53144100000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qu.1/5314410.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.1/53144100. <lb/>piu<emph.end type="italics"/> <22>.1/810.<emph type="italics"/>& tanto ual&longs;e il detto &longs;aggio del detto oro puro. </s> <s id="s.002255">Anchor bi&longs;ogna <lb/>notare, che quel penultimo nome, cioe<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.1/53144100. é numero quadra <lb/>to, onde cauandone la radice &longs;e trasferiria in<emph.end type="italics"/> <22>.<emph type="italics"/>cu.1/7290.& &longs;aria piu breue & ele­<lb/>gante ri&longs;po&longs;ta à dire che il &longs;aggio del detto oro puro ual&longs;e du.1 1/90. piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.1/72900. <lb/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.1/53144100000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu. </s> <s id="s.002256">qua.1/5314410.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cuba <lb/>1/7290.piu.<emph.end type="italics"/> <22>.1/810. H<emph type="italics"/>or per &longs;apere quanto ual&longs;e il &longs;aggio del argento, bi&longs;ogna ari <lb/>cordar&longs;i di quello che di &longs;opra fu <expan abbr="cõclu&longs;o">conclu&longs;o</expan>, cioe che.<emph.end type="italics"/> <22>.10 <emph type="italics"/>men.<emph.end type="italics"/> <22>.<emph type="italics"/>cu. </s> <s id="s.002257">10.dioro ual duc.<emph.end type="italics"/><pb pagenum="106" xlink:href="042/01/212.jpg"/>1.<emph type="italics"/>di piu di altro tanto argento, adunque altro tanto argento, cioe<emph.end type="italics"/> <22>.10.<emph type="italics"/><expan abbr="m&etilde;">men</expan>.<emph.end type="italics"/> <22>.<emph type="italics"/>cu. </s> <s id="s.002258">10 <lb/>d'argento ual un duc. </s> <s id="s.002259">manco di altro tanto oro & per tanto diremo &longs;e<emph.end type="italics"/> <22>.10. <emph type="italics"/>men.<emph.end type="italics"/><lb/><22>.<emph type="italics"/>cuba. </s> <s id="s.002260">10. di argento, ual duc.1.manco di altro tanto oro che ualera &longs;aggi.10.men.<emph.end type="italics"/><lb/><22>.10.<emph type="italics"/>di argento, operando come prima, cioe multiplicando duc.1.fia &longs;aggi.10.men.<emph.end type="italics"/><lb/><22>.10.<emph type="italics"/>fara pur &longs;aggi.10.men.<emph.end type="italics"/> <22>.10.<emph type="italics"/>qual bi&longs;ogna pur partir per<emph.end type="italics"/> <22>.10. <emph type="italics"/>men.<emph.end type="italics"/> <22>. <emph type="italics"/>cu.10 <lb/>trouando per prima un partitor rationale come di &longs;opra fu fatto, cioe multiplicando <lb/>el detto partitor de<emph.end type="italics"/> <22>.10.<emph type="italics"/>men.<emph.end type="italics"/> <22>.<emph type="italics"/>cu.10.per.10.piu.<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.100000.piu.<emph.end type="italics"/> <22>.<emph type="italics"/>cu.100 <lb/>fara<emph.end type="italics"/> <22>.1000.<emph type="italics"/>men.10.& que&longs;to mede&longs;imo multiplicandolo per el &longs;uo binomio fara. <lb/></s> <s id="s.002261">900. come prima qual bi&longs;ogna &longs;eruar da banda per nostro partitore. </s> <s id="s.002262">Dapoi bi&longs;ogna <lb/>multiplicare la nostra co&longs;a da partire, cioe &longs;aggi.10.me<emph.end type="italics"/> <22>.10.<emph type="italics"/>per lo mede&longs;imo trino <lb/>mio & binomio, ma comenzar prima per el binomio, cioe per.<emph.end type="italics"/> <22>.1000.<emph type="italics"/>piu.10. (per­<lb/>che comenzando dal trinomio &longs;e ueniria in gran confu&longs;ion de nomi) adunque multi­<lb/>plicandolo prima per<emph.end type="italics"/> <22>.1000.<emph type="italics"/>piu.10 far.<emph.end type="italics"/> <22>.100000.<emph type="italics"/>men.<emph.end type="italics"/> <22>.1000. <emph type="italics"/>qual multiplican <lb/>dolo anchora per el trinomio, cioe per.10.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu qua.100000.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.100. fara.<emph.end type="italics"/><lb/><22>.10000000.<emph type="italics"/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.100000000000000000000.piu.<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qu.<emph.end type="italics"/>10000000000-­<lb/>000000000.<emph type="italics"/>men<emph.end type="italics"/> <22>.100000.<emph type="italics"/>men<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.100000000000000.m&etilde;<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.<emph.end type="italics"/>10000-­<lb/>000000000.<emph type="italics"/>& que&longs;to tal produtto bi&longs;ogna partirlo per el no&longs;tro partitore, cioe per. <lb/></s> <s id="s.002263">900.ma per abreuiar li detti &longs;ei nomi bi&longs;ogna uedere s'eglie alcune de detta quantita, <lb/>che &longs;iano communicante, & quelle &longs;umarle, ouer &longs;otrarle &longs;econdo il bi&longs;ogno il che fa <lb/>cendo &longs;e trasferira quelli tanti nomi in<emph.end type="italics"/> <22>.8100000.<emph type="italics"/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.<emph.end type="italics"/>53144100000000-­<lb/>000000.<emph type="italics"/>piu<emph.end type="italics"/> R.<emph type="italics"/>cu.qua.5314410000000000000.& que&longs;to tal trinomio bi&longs;ogna par­<lb/>tirlo per el &longs;opradetto.900.recando &longs;empre el partitore alla natura della dignita che <lb/>&longs;i uol partire il che <expan abbr="fac&etilde;do">facendo</expan> ne uenira<emph.end type="italics"/> <22>.10.<emph type="italics"/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.10.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.10. & <expan abbr="tãti">tanti</expan> duc. <lb/></s> <s id="s.002264">manco ual &longs;aggi.10.men.<emph.end type="italics"/> <22>. </s> <s id="s.002265">10. <emph type="italics"/>de argento puro de altro tante oro, onde cauandolo <lb/>de duc.9.lo rimanente &longs;ara el ualor de &longs;aggi.10.di argento puro, el qual rimanente <lb/>&longs;ara duc.9.men questo trinomio, cioe<emph.end type="italics"/> <22>.10.<emph type="italics"/>piu.<emph.end type="italics"/> <22>.<emph type="italics"/>cu.10.piu<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.002266">qua.10.& tanto <lb/>ual&longs;e &longs;aggi.10.di argento puro, lo qual ualor partendolo per.10.ne uenira duc.9/10. <lb/>men que&longs;to trinomio<emph.end type="italics"/> <22>.1/10.<emph type="italics"/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.1/100.piu<emph.end type="italics"/> R.<emph type="italics"/>cu.qua.1/100000.et tanto ual <lb/>&longs;e el&longs;aggio del <expan abbr="arg&etilde;to">argento</expan> puro, & accio che meglio lo poßiati <expan abbr="cõ&longs;iderare">con&longs;iderare</expan> qua de &longs;otto ue <lb/>lo uoglio distintamente notare. </s> <s id="s.002267">El &longs;aggio de l'oro ual&longs;e ducati.1.1/90.piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.1/12900. <lb/>piu<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.1/53144100000.piu<emph.end type="italics"/> R.<emph type="italics"/>cu.qua.1/5314410.piu<emph.end type="italics"/> R.<emph type="italics"/>cuba. <lb/></s> <s id="s.002268">1/7290.piu<emph.end type="italics"/> <22>. </s> <s id="s.002269">11/810. E<emph type="italics"/>l &longs;aggio de l'argento ual&longs;e ducati.9/10.men<emph.end type="italics"/> R.1/10.<emph type="italics"/>piu<emph.end type="italics"/> R.<emph type="italics"/>cu. <lb/></s> <s id="s.002270">1/100.piu.<emph.end type="italics"/> <22>.<emph type="italics"/>cu.qua.<emph.end type="italics"/>1/100000. M. H. Q<emph type="italics"/>uesta é una delle piu forte ragioni che <lb/>mai uede&longs;&longs;e in mia uita, et ui è molte co&longs;e nella uostra operatione lequale <expan abbr="nõ">non</expan> le ho trop <lb/>po ben inte&longs;e, ma per al pre&longs;ente non ui uoglio dar altro fa&longs;tidio perche mi pare che <lb/>habbiati fatto a&longs;&longs;ai, ma la &longs;tudiaro un puoco da mia po&longs;ta, &longs;e <gap/>i<gap/>rouaro co&longs;a ch'io non <lb/>intenda ritornaro da uoi.<emph.end type="italics"/> N. S<emph type="italics"/>on &longs;empre parato à farue à piacere.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002271">QVESITO XXV. FATTO DA M. ZVANNE DI TONI­<lb/><emph type="italics"/>ni da Coi per&longs;onalmente l'anno. </s> <s id="s.002272">1536. adi. </s> <s id="s.002273">10. Decembre in Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002274">MISSER ZV ANNE. H<emph type="italics"/>o inte&longs;o che za molti giorni uoi uenesti in di­<lb/>&longs;puta con Mae&longs;ero Antoniomaria fior. </s> <s id="s.002275">Et che finalmente ue conneni&longs;ti<emph.end type="italics"/><pb xlink:href="042/01/213.jpg"/><emph type="italics"/>in que&longs;to che lui ui doue&longs;&longs;e proponere.30.que&longs;iti in &longs;critto &longs;otto bolla realmente diuer <lb/>&longs;i in mane de<emph.end type="italics"/> M. <emph type="italics"/>pre Iacomo di zambelli notaro, & che &longs;imelmente uoi ne propone­<lb/>re&longs;ti altri.30. à lui realmente diuer&longs;i & co&longs;i face&longs;ti, & aßigna&longs;ti.40.ouer.50.giorni <lb/>di termine à cadauno di uoi per &longs;oluere li detti que&longs;iti, & determina&longs;ti che quello di <lb/>uoi, che al detto termine &longs;i troua&longs;&longs;e hauer a&longs;&longs;olto piu numero di detti.30.receputi que <lb/>&longs;iti re&longs;ta&longs;&longs;e con l'honore oltra no&longs;oche puoco di &longs;cotto che limita&longs;ti per ogni que&longs;ito. <lb/></s> <s id="s.002276">Et me &longs;tato referto, & accertado per fina à Bre&longs;&longs;a che uoi re&longs;olue&longs;ti tutti li &longs;uoi.30.in <lb/>termine di due, hore laqualco&longs;a mi par dura da credere.<emph.end type="italics"/> N. E<emph type="italics"/>glie il uero quanto ue <lb/>&longs;tato detto, ouer referto. </s> <s id="s.002277">Et la cau&longs;a che io re&longs;ol&longs;e li &longs;uoi.30.con tanta breuita è que&longs;ta <lb/>che lui propo&longs;e tutti li detti &longs;uoi.30.que&longs;iti, che conduceuano l'operante per Algebra <lb/>in co&longs;a, é cubo equal à numero, credendo&longs;i che de quelli non ne doue&longs;&longs;e ri&longs;oluere alcu­<lb/>no, perche frate Luca nella &longs;ua opera afferma e&longs;&longs;er impoßibile à ri&longs;oluere tal capito­<lb/>lo con Regola generale, & io che permia bona &longs;orte, &longs;olamente.8.giorni auanti al ter <lb/>mine di portar li.30.&.30.que&longs;iti &longs;otto bolla dal notaro. </s> <s id="s.002278">Io haueua ritrouata la re­<lb/>gola general a tal capitolo. </s> <s id="s.002279">Onde per e&longs;&longs;er tal inuentione co&longs;i di fre&longs;co, mella trouai <lb/>molto prompta, & famigliar, & per que&longs;to io lire&longs;ol&longs;e tutti.30. contanta celerita, <lb/>ouer pre&longs;tezza.<emph.end type="italics"/> M. ZV ANNE. C<emph type="italics"/>he ue indu&longs;&longs;e co&longs;i à recercare à quel tempo <lb/>la regola di tal capitulo.<emph.end type="italics"/> N. L<emph type="italics"/>ui mede&longs;imo, perche lui &longs;i andaua uantando per far­<lb/>me paura hauer trouata tal, regola, uero è che in principio non gli credena questa co <lb/>&longs;a, perche lui non haueua &longs;cientia, ma &longs;olamente gran pratica, & per la pura pratica, <lb/>io comprendeua chel non era atto ne&longs;officiente à poter hauer ritrouata tal regolaper <lb/>&longs;e mede&longs;mo. </s> <s id="s.002280">Ma lui per farme credere che haue&longs;&longs;e tal pa&longs;&longs;o, & che doue&longs;&longs;e temere di <lb/>lui, anchor che non haue&longs;&longs;e theorica, &longs;e auantaua che gia trenta anni tal &longs;ecreto gli era <lb/>&longs;tato mo&longs;trato da un gran mathematico, il che mifece dubitar, che'l fu&longs;&longs;e il uero, e per <lb/>que&longs;to io po&longs;i ogni mio &longs;tudio, cura & arte per ritrouar regola à tal capitolo, & co&longs;i <lb/>per mia bona &longs;orte (come di &longs;opra è detto) la ritrouai.8.giorni auanti al termine de <lb/>dar li detti.30.que&longs;iti &longs;otto bolla al notaro, & que&longs;to fu l'anno pa&longs;&longs;ato, cioe del.1535. <lb/>adi.12.di.Febraro (uero è che in Venetia ueneua à e&longs;&longs;er del.1534.) et per alcuni aui<gap/><lb/>& accidenti di tal inuentione il giorno &longs;eguente ritrouai anchora regola generale al <lb/>capitolo de co&longs;e, & numero equal à cubo.<emph.end type="italics"/> M. Z. V<emph type="italics"/>oi haue&longs;ti una gran &longs;orte à ri­<lb/>trouar tal pa&longs;&longs;o co&longs;i al improui&longs;o, perche &longs;e uoi non lo haue&longs;ti ritrouato uoi re&longs;taui ui <lb/>tuperato appre&longs;&longs;o al uolgo de gli ignoranti, non gia appre&longs;&longs;o delli intelligenti, perche <lb/>uno particolar &longs;ecreto, non da la &longs;cientia à l'huomo, perche la &longs;cientia uer&longs;a &longs;opra <lb/>le co&longs;e generale, & non &longs;opra le particolare perche li partico'ari &longs;ono infiniti, & pe <lb/>ro non è poßibile hauer cognitione de ogni particolare. </s> <s id="s.002281">Ma ditime un puoco in che <lb/>materia prepone&longs;ti li uo&longs;tri.30.que&longs;iti à lui.<emph.end type="italics"/> N. I<emph type="italics"/>o ge li propo&longs;i tutti realmente di­<lb/>uer&longs;i, & que&longs;to feci per mo&longs;trarli che io era uniuer&longs;ale, & chel mio fondamento, non <lb/>era in una, ne in due, ne in tre mie particolar inuentioni, ouer &longs;ecreti, anchor che à <lb/>pre&longs;&longs;o di me li haue&longs;&longs;e hauuti per &longs;icurißimi, & che &longs;opra di quelli ui haue&longs;&longs;e potuto <lb/>formar. </s> <s id="s.002282">10000. ca&longs;i non che. </s> <s id="s.002283">30. anci li uol&longs;i proponere (come detto) tutti <lb/>realmenle diuer&longs;i, per mo&longs;trarli che io non lo &longs;timaua ne temeua in conto alcuno.<emph.end type="italics"/> M. <lb/>ZV ANNE. E<emph type="italics"/>t quanti ne re&longs;ol&longs;elo lui di uo&longs;tri.<emph.end type="italics"/> NICOLO. D<emph type="italics"/>e niun mai poteti<emph.end type="italics"/><pb pagenum="107" xlink:href="042/01/214.jpg"/><emph type="italics"/>hauerne ri&longs;po&longs;ta, uero é, che lui &longs;e andaua auantando, che gli baucua ri&longs;olti, ma el <lb/>non me li uol&longs;e mai la&longs;&longs;ar uedere tai &longs;ue re&longs;olutioni, ma per couerzer la co&longs;a, lui uole­<lb/>ua, che &longs;e elegge&longs;&longs;e alcuni &longs;uoi amici, che giudica&longs;&longs;eno &longs;e lui gli haueua ben ri&longs;olti, ouer <lb/>non, la qual co&longs;a uedendo, che da ogniun era giudicato per perdente, io gli feci publi­<lb/>camente un pre&longs;ente del precio giocato.<emph.end type="italics"/> M.Z. D<emph type="italics"/>i gratia datemi in &longs;critto li detti. <lb/></s> <s id="s.002284">30.que&longs;iti, che lui ui propo&longs;e, con le &longs;ue &longs;olutioni, & &longs;imilmente li uo&longs;tri. </s> <s id="s.002285">30.che pro <lb/>pone&longs;ti à lui.<emph.end type="italics"/> N. Q<emph type="italics"/>uando che haue&longs;&longs;e tempo da coppiarli, io ue daria ben li detti que <lb/>&longs;iti, ma non le mie re&longs;olutioni, perche ogni uolta, che uoi uede&longs;ti lemie re&longs;olutioni, imme <lb/>diate intender esti la regola, ma &longs;e pur uoleti li detti &longs;implici que&longs;iti, andati dal notaro, <lb/>& donategli una gentilezza, che ue ne dara la coppia immediate. </s> <s id="s.002286">Aui&longs;andoui anchora <lb/>che de li mei.30. che gli propo&longs;e à lui, io non ho coppia alcuna, perche, &longs;i come gli heb <lb/>bi notati, io li portai di &longs;ubito &longs;otto bolla al notaro, & non ne tenni altramente coppia, <lb/>talmente che non ue li &longs;apria dire la mita de quelli, &longs;e io non anda&longs;&longs;e dal notaro à far­<lb/>mene dar coppia.<emph.end type="italics"/> M.Z. D<emph type="italics"/>itemene un poco tre, ouer quattro de quelli, che uoi gli <lb/>proponesti à lui.<emph.end type="italics"/> N. I<emph type="italics"/>l primo que&longs;ito delli miei.30.che io gli propo&longs;i à lui, &longs;e ben <lb/>me aricordo, diceua in que&longs;ta forma. <lb/> Trouatemi una quantita che &longs;ia irrationale, che moltiplicata &longs;ia la &longs;ua radice piu. <lb/></s> <s id="s.002287">40. faccia numero rationale, & di&longs;ereto. La &longs;econda. <lb/> Trouatemi una quantita, che &longs;la irratienale, la qual moltiplicata fia.30.men la ra <lb/>dice di detta quantita, faccia numero rational, & di&longs;creto. La terza. <lb/> Trouatemi una quantita, qual gionta con il quadruplo della &longs;ua radice cuba <lb/>faccia.13. La quarta.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002288">T<emph type="italics"/>rouatemi una quantita, che &longs;ottratone.5.delle &longs;ue radice cube re&longs;ti.<emph.end type="italics"/>10. </s> </p> <p type="main"> <s id="s.002289">E<emph type="italics"/>t quantunque que&longs;te quattro uarieta de equationi, ouer capitoli, da me ritrouati. <lb/></s> <s id="s.002290">Io gli haue&longs;&longs;e per fortißimi paßi, nondimeno non ui uol&longs;e proponere, &longs;aluo che un &longs;ol <lb/>que&longs;ito per cadauno capitolo, per mo&longs;trarli, come di &longs;opra dißi, che lo non mi &longs;onda­<lb/>ua, ne &longs;peraua di conuencerlo con una, ne due, ne tre, ne quattro particolar inuentioni, <lb/>ouer &longs;egreti, anci tutti li miei.30.que&longs;iti eranotutti uarij, &longs;i in Geometria, come in el <lb/>operar de Algebra, che longo &longs;aria à uolerueli narrare à uno per uno.<emph.end type="italics"/> M.Z. P<emph type="italics"/>er <lb/>quanto uedo il primo uo&longs;tro que&longs;ito conduce l'operante in cubo, e cen&longs;i egual à qualub <lb/>que numero &longs;i uoglia, pur che dia la co&longs;a irrationale, & lo &longs;econdo conduce in cubo, <lb/>& numero egual à cen&longs;i. </s> <s id="s.002291">Il terzo poi in cubo é co&longs;a egual à numero, & lo quarto in co <lb/>&longs;e è numero egual à cubo. </s> <s id="s.002292">Adunque uoi haueti ritrouato anchora regola al capitolo <lb/>de cubo é cen&longs;o egual à numero, & à quello de cubo, e numero egual à cen&longs;i.<emph.end type="italics"/> N. Q<emph type="italics"/>ue <lb/>&longs;to trouai per fin dell'anno. </s> <s id="s.002293">1530. quando &longs;tantiaua à Verona, & quella uo&longs;tra ra­<lb/>gione, che mi manda&longs;ti per me&longs;&longs;er pre Antonio da Cellatica, fu cau&longs;a di farme ritro­<lb/>uar regola à tai capitoli.<emph.end type="italics"/> M.Z. E<emph type="italics"/>t che ragion fu gia quella.<emph.end type="italics"/> N. L<emph type="italics"/>e furno due, ma <lb/>in una. </s> <s id="s.002294">Voi me adimandaui, che ui troua&longs;&longs;e un numero, che moltiplicato per la &longs;ua ra­<lb/>dice piu.3.face&longs;&longs;e.5.qual que&longs;ito conduce l'operante, come &longs;apeti in.1.cubo piu.3.cen­<lb/>&longs;i egual à.5.& io ue re&longs;crißi, che uoi non &longs;apre&longs;ti ri&longs;oluere tai dui que&longs;iti à me man­<lb/>dati, cioe quello in&longs;ieme con quell'altro, che me mandasti in&longs;ieme con quello, & che cir <lb/>ca cio. </s> <s id="s.002295">Io me offeriua di giocare duc.10.contra.<emph.end type="italics"/>5. M.Z. E<emph type="italics"/>me ne aricordo.<emph.end type="italics"/> N. R<emph type="italics"/>e-<pb xlink:href="042/01/215.jpg"/>plico <expan abbr="adũque">adunque</expan>, che tal uo&longs;tro que&longs;ito fu cau&longs;a di farme ritrouar la regola di tal capitolo <lb/>de cubo è cen&longs;o egual à numero, & ritrouato quello il giorno &longs;eguente ritrouai regola <lb/>all'altro, cioe à quello de cubo è numero egual à cen&longs;i, perche l'uno tira l'altro. </s> <s id="s.002296">Et co&longs;i <lb/>mae&longs;tro Antoniomaria Fiore per auantar&longs;e di hauer quello di co&longs;a è cubo egual à nu­<lb/>mero (o fu&longs;&longs;e il uero, o no) non &longs;olamente mi fece à quel tempo ritrouare tal capitolo, <lb/>ma anchora immediate quello di co&longs;e à numero egual à cubo, con le quale inuentioni, da <lb/>poi alquanti giorni, ritrouai molte altre regoli, & capitoli, & uolendoli &longs;tudiar &longs;opra <lb/>à tal materia &longs;e ne potria trouar infiniti, perche una regola apre gliocchi in molte al­<lb/>tre, come poteti con&longs;iderare, ma per e&longs;&longs;er hora tarda, non uoglio, che parlamo piu di <lb/>queste materie, anci uoglio andare à cena, & uoglio, che restati à cena con meco.<emph.end type="italics"/><lb/>M.Z. I<emph type="italics"/>o &longs;ono a&longs;pettato da uno mio cugino, che &longs;tantia qua in Venetia.<emph.end type="italics"/> N. A<emph type="italics"/>&longs;petti <lb/>quanto uoglia, che uoglio, che re&longs;tati.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002297">QVESITO. XXVI. FATTO DAL MEDE­<lb/><emph type="italics"/>&longs;imo Me&longs;&longs;er zuane de Tonini da Coi, l'Anno.<emph.end type="italics"/><!-- REMOVE S-->1536. A<emph type="italics"/>di.15.Decembrio.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002298">I<emph type="italics"/>n Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002299">MAESTRO ZVANE. M<emph type="italics"/>e&longs;&longs;er Nicolo, mi uoglio partire per ritornarme­<lb/>ne à Bre&longs;&longs;a, uero è, che fra pochi giorni ritornaro, ma nanti, che mi parta ue uor <lb/>ria pregare, che uoi me de&longs;ti uno di quelli uostri quattro que&longs;iti ri&longs;olto.<emph.end type="italics"/> N. V<emph type="italics"/>oi do­<lb/>ueti &longs;apere Me&longs;&longs;er zuane, che le inuentioni &longs;ono difficili, & lo aggiongergli è facile. <lb/></s> <s id="s.002300">Et per tanto e&longs;&longs;endomi molto affaticato per ritrouare tai particolarita, il non mi pare <lb/>licito, che io li debbia co&longs;i facilmente publicare, & maßime doue non me ne reufi&longs;ca al­<lb/>cuno honore, ne utilita, eglie ben uero, che il non è nanche licito à uoler tenere tai in­<lb/>uentioni totalmente &longs;epolte, ma &longs;appiati, che la mia intentione non è di uolerle tener <lb/>oppre&longs;&longs;e, ma de publicar le à ogni huomo, & come che habbia &longs;pedito alcune mie altre <lb/>gia principiate fatiche, &longs;pero de e&longs;&longs;equir tal mia buona intentione, & accio che uoi <lb/>non pen&longs;a&longs;ti che tai inuentioni &longs;iano da me piu i&longs;timate del douere, io mi ue offeri&longs;co, <lb/>ogni uolta che uoi me &longs;apereti formar uno, ouer piu que&longs;iti, che io non ue li &longs;appia ri&longs;ol <lb/>uere, di barattar con uoi à capo per capo, cioe à uno per uno, ilche non è poco à offe­<lb/>rirue una co&longs;a generale (&longs;opra della quale non &longs;olamente &longs;e puo formare infiniti ca&longs;i, <lb/>ma &longs;e puo con facilita ritrouare regola à molti altri capitoli) per un particolare.<emph.end type="italics"/><lb/>M.<gap/>. </s> <s id="s.002301">Q<emph type="italics"/>ue&longs;ta uo&longs;tra mi par una hone&longs;ta oblatione. </s> <s id="s.002302">Et per tanto ue uoglio propone­<lb/>re dui belli que&longs;iti, li quali non &longs;apendoli ri&longs;oluere, io ue li in&longs;ignaro, & uoi me in&longs;i­<lb/>gnareti la regola di detti uo&longs;tri capitoli, & maßime quella di co&longs;a è cubo egual à nu­<lb/>mero, il primo di quai que&longs;iti è que&longs;to.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002303">E<emph type="italics"/>glie il triangolo rettangolo, poniamo lo.a.b.c.del qual l'angolo.c.è retto, & nel <lb/>detto triangolo ui è i&longs;critto il cerchio.e.f.d.il cui diametro è. </s> <s id="s.002304">2. & trouo che la linea. <lb/></s> <s id="s.002305">a.c.gionta con la.c.b.tal &longs;umma &longs;ara &longs;empre eguale alla linea.a.b. </s> <s id="s.002306">gionta con il dia­<lb/>metro de cerchio (qual come detto è.<emph.end type="italics"/>2.) H<emph type="italics"/>or ue adimando la cau&longs;a di que&longs;to.<emph.end type="italics"/></s> </p> <pb pagenum="108" xlink:href="042/01/216.jpg"/> <figure id="id.042.01.216.1.jpg" xlink:href="042/01/216/1.jpg"/> <p type="main"> <s id="s.002307">S<emph type="italics"/>econdariamente, eglie il triangolo.a.b.c.che il lato.a.b. </s> <s id="s.002308">é.13.a.c.15.b.c.14.& la <lb/>&longs;ua perpendicolare e la.a.d. </s> <s id="s.002309">& dall'angolo.b.tiro la linea.b.f.e. </s> <s id="s.002310">la qual &longs;ega dalla li­<lb/>uea.a.d.la.f.d.la qual è.3.&longs;e adimanda la quantita delle due parti.a.e.&.e.c.<emph.end type="italics"/></s> </p> <figure id="id.042.01.216.2.jpg" xlink:href="042/01/216/2.jpg"/> <p type="main"> <s id="s.002311">H<emph type="italics"/>or guardati &longs;el ui pare di mo&longs;trarmi quella uostra regola de cen&longs;o é cubo egual à nu­<lb/>mero, io ui mo&longs;traro il modo di ri&longs;oluere que&longs;ti dui que&longs;iti, quali in uero &longs;ono belli, & <lb/>forti.<emph.end type="italics"/> N. Q<emph type="italics"/>ue&longs;ti egli ho per co&longs;e facile, perche &longs;e mi dati tempo un'hora, io ue li da­<lb/>ro ri&longs;olti. </s> <s id="s.002312">Ma fati una co&longs;a ch'io ui diro, l'anno pa&longs;&longs;ato mi furono portatitre uo&longs;tri <lb/>que&longs;iti, quali me porto Maestro Dominico da Vderzo, fra li quali uno ue ne era, qual <lb/>diceua in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002313">S<emph type="italics"/>ono trei, che hanno comprato lire.20.di carne, & tante lire ne ha comprate uno <lb/>di loro, che moltiplicato tal numero de lire in &longs;e mede&longs;imo, tal produtto è eguale alla <lb/>moltiplicatione delle lire, che hanno comprato glialtri dui, cioe quelle dell'uno fia quel <lb/>le dell'altro, & moltiplicate anchor le due menor quantita de lire, l'una &longs;ia l'altra <lb/>fanno preci&longs;amente.8. &longs;e adimanda la quantita delle lire della carne, che compro cadau <lb/>no per &longs;e, il qual que&longs;ito non uol dire altro in &longs;o&longs;tantia, che far de.20.tre parti conti­<lb/>nue proportionale, in tal &longs;pecie di proportione, che moltiplicando le due menore, l'u­<lb/>na fia l'altra facciano.8.hor mo&longs;tratemi à &longs;oluere questo tal que&longs;ito con regola ge­<lb/>nerale, che io me offeri&longs;co à mo&longs;trarui il modo, & regola generale da ri&longs;oluere, quala <lb/>equatione ui pare di &longs;opradetti quattro capitoli.<emph.end type="italics"/> A <emph type="italics"/>benche &longs;o, che uoi non accettareti <lb/>que&longs;to partito, perche uoi mede&longs;imo non &longs;apeti ri&longs;oluere tal que&longs;ito. </s> <s id="s.002314">Et è gran co&longs;a, <lb/>che non ui poßiati in tutto rimouere del vo&longs;tro u&longs;o antico.<emph.end type="italics"/> M.Z. <!-- KEEP S--></s> <s id="s.002315">E <emph type="italics"/>ue diro il non é <lb/>manco bello il &longs;apere dimo&longs;trare la impoßibilita d'un ca&longs;o irre&longs;olubile, quanto che è <lb/>à ri&longs;oluezne uno &longs;olubile.<emph.end type="italics"/> NIC. Q<emph type="italics"/>ue&longs;ta uo&longs;tra &longs;cu&longs;a non è buona, perche uoi <pb xlink:href="042/01/217.jpg"/>non me lo haueti propo&longs;to per impoßibile, anci me lo haueti propo&longs;to, come co a, che <lb/>uoi non intendeti, ne &longs;apreti ri&longs;oluere, ne manco me &longs;apreti dimo&longs;trar che il &longs;ia impo&longs;­<lb/>&longs;ibile, perche à me mi ba&longs;taria l'animo di formar.1000.che uoi ne altri li &longs;apra ri&longs;ol­<lb/>uere, ne manco, ne uoi, ne altri mi potra con ragione dimostrare che il &longs;ia impoßibile <lb/>à darli ri&longs;olutione. </s> <s id="s.002316">Anci è uoglio dire, che tal uo&longs;tro que&longs;ito non &longs;olamente è l'ho per <lb/>poßibile, ma i&longs;pedito alcune mie facende &longs;pero trouarui regola generale, come feci an­<lb/>chora à quello, che me manda&longs;ti à Verona.<emph.end type="italics"/> M.Z. F<emph type="italics"/>areti a&longs;&longs;ai &longs;e la ritrouareti. </s> <s id="s.002317">Hor <lb/>perche il &longs;e appre&longs;&longs;a l'hora da douermi partire, ui prego che per uo&longs;tra gentilezza <lb/>uogliati darme almen uno di quelli uo&longs;tri quatro que&longs;iti a&longs;&longs;olto che ui prometto come <lb/>&longs;on gionto à bre&longs;&longs;a di &longs;criuerui & di mandarue qualche bello que&longs;ito qual &longs;el non &longs;ape <lb/>reti ri&longs;oluere mi offero à mandarue anchora la re&longs;olutione, & &longs;e haueti anchora qual­<lb/>che altra comuna que&longs;tione fuora di que&longs;ti uo&longs;tri capitolinoui ui prego me le uoglia­<lb/>ti dar, che &longs;apendola ri&longs;oluere ui mandaro anchora la &longs;ua re&longs;olutione in &longs;critto.<emph.end type="italics"/> N. L<emph type="italics"/>e <lb/>uo&longs;tre parole mi hann a&longs;tretto à compiacerui alquanto et per tanto ui uoglio dar a&longs;&longs;ol <lb/>to el primo, cioe quello che dice trouatime una quantita che &longs;ia irrationale, che molti­<lb/>ta fia la &longs;ua radice piu.40.faccia numero rational & di&longs;creto, anchor che &longs;on certo <lb/>che ui trouareti regola generale, o uer particolare alla re&longs;olutione di &longs;imili que&longs;iti.<emph.end type="italics"/><lb/>E <emph type="italics"/>per tanto dicoche la detta quantita &longs;e puo conchiudere in infiniti modi per e&longs;&longs;er l'o­<lb/>perante in liberta de eguagliar&longs;e à che numero li piace, nondimeno io mi uoglio egua­<lb/>gliar à.2888.perche la co&longs;a miuerra un re&longs;iduo &longs;implice, onde la detta quantita ue­<lb/>nira à e&longs;&longs;er.78.men<emph.end type="italics"/> <22>.308.<emph type="italics"/>la radice della quale uien à e&longs;&longs;er<emph.end type="italics"/> <22>.77.<emph type="italics"/>men.1.aggiongen­<lb/>doli.40.fara.39.piu<emph.end type="italics"/> <22>.77.<emph type="italics"/>qual moltiplicata fia la detta quantita, cioe fia.78.men<emph.end type="italics"/><lb/><22>.308.<emph type="italics"/>fara preci&longs;e.2888.che il propo&longs;ito.<emph.end type="italics"/> M.Z. <!-- KEEP S--></s> <s id="s.002318">A <emph type="italics"/>che fin gli propone&longs;ti la co&longs;a <lb/>tanto larga di poter&longs;i eguagliar à che numero li pare&longs;&longs;e, pur che de&longs;&longs;e la co&longs;a irra­<lb/>tionale.<emph.end type="italics"/> N. I<emph type="italics"/>o il fece per due cau&longs;e. </s> <s id="s.002319">La prima fu, che &longs;e per ca&longs;o lui haue&longs;&longs;e hauuto <lb/>opinione, che io non haue&longs;&longs;e &longs;aputo ri&longs;oluere tal capitolo, e&longs;&longs;endo tal que&longs;ito &longs;otto co&longs;i <lb/>larga forma, &longs;empre mi po&longs;&longs;o eguagliar à tal numero, che il ualor della co&longs;a me ueni­<lb/>ra un &longs;implice re&longs;iduo, come di &longs;opra haueti ui&longs;to, che la co&longs;a ual&longs;e<emph.end type="italics"/> <22>.77.<emph type="italics"/>men.1.il qual <lb/>re&longs;iduo è una quantita facile da maneggiar, per poterne far la proua alla improui&longs;a, il <lb/>che non accade co&longs;i facile in altre &longs;ue equationi. </s> <s id="s.002320">La &longs;econda fu, che per tal ri&longs;olutione, <lb/>non &longs;i puo co&longs;i facilmente apprendere la regola generale da ri&longs;oluere &longs;imili capitoli, <lb/>come &longs;e apprendaria, quando che tal ri&longs;olutione ueni&longs;&longs;e da.4.ouer.5.nomi.<emph.end type="italics"/> M.Z. <!-- KEEP S--></s> <s id="s.002321">E <lb/><emph type="italics"/>ue ho inte&longs;o. </s> <s id="s.002322">Hor &longs;e hauesti qualche altra bella ragione da darmi, mi fareti à piacere.<emph.end type="italics"/><lb/>N. I<emph type="italics"/>o ue ne uoglio dar una quala mi fu propo&longs;ta gia fa.4.me&longs;i, in San zuanepolo, <lb/>i&longs;ponendo io la.13.propo&longs;itione del.13.di Euclide, qual dice in que&longs;ta forma. </s> <s id="s.002323">Eglie una <lb/>uerga, che pe&longs;a &longs;aggi.10.di oro, qual tien di argento la Radice cuba de.10.& ual duc. <lb/></s> <s id="s.002324">10.Et eglie anchora un'altra uerga, qual pe&longs;a altri &longs;aggi.10.pur di oro, qual tien di ar <lb/>gento la Radice quadra de.10.& alla proportione del primo que&longs;to ual &longs;olamente du <lb/>cati. </s> <s id="s.002325">9.&longs;e adimanda che ual&longs;e il &longs;aggio del oro puro, & &longs;imilmente quello dell'argento <lb/>puro.<emph.end type="italics"/> M.Z. Q<emph type="italics"/>ue&longs;ta mi pare a&longs;&longs;ai bella que&longs;tione. </s> <s id="s.002326">Hora ue uoglio la&longs;&longs;are, come &longs;ia <lb/>gionto à Bre&longs;&longs;a ue &longs;criuero, me arricomando.<emph.end type="italics"/> N. A<emph type="italics"/>ndati in buon'hora, arricoman­<lb/>datemi à Me&longs;&longs;er Pre Antonio da Cellatica.<emph.end type="italics"/></s> </p> <pb pagenum="109" xlink:href="042/01/218.jpg"/> <p type="head"> <s id="s.002327">QVESITO XXVII. FATTO DA M. HIERONI­<lb/><emph type="italics"/>mo Treui&longs;ano.1536.adi.16. Decembrio in Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002328">MESSER HIERONIMO. E<emph type="italics"/>ue ho da dir de nouo.<emph.end type="italics"/> N. C<emph type="italics"/>he co&longs;a ui é <lb/>accaduto me&longs;&longs;er Hieronimo.<emph.end type="italics"/> M. H. H<emph type="italics"/>ieri el mi fu à ritrouar un certo <expan abbr="grã">gram</expan> <lb/>don, qual dice e&longs;&longs;er anchora lui Bre&longs;&longs;ano, el qual &longs;i fa molto piu grande nelle mathema <lb/>tice di quello ch'è la grandezza della &longs;ua per&longs;ona, et fra le altre co&longs;e gli ho uoluto dir <lb/>di uoi, & come che haueti letto publicamente il terzodecimo di Euclide in &longs;an Zuanne <lb/>polo. </s> <s id="s.002329">Lui me ha ri&longs;po&longs;to che uoi haueti letto el detto.13.libro & che non intendeti <lb/>il decimo. </s> <s id="s.002330">Et chel non cono&longs;ce huomo, che ben intenda el detto decimo di Euclide ac­<lb/>cetto che lui.<emph.end type="italics"/> N. E<emph type="italics"/>glie ben stato qua da me due uolte & è andato uia per fin da hie <lb/>ri alla uolta de Bre&longs;&longs;a, ma el mi dole che uoi non mi habbiati rifferto que&longs;ta &longs;ua bra­<lb/>uata auanti che lui &longs;e fu&longs;&longs;e partito perche gli hauria dato quella debbita ri&longs;po&longs;ta che <lb/>à tal &longs;ua arrogantia &longs;i conuenia. </s> <s id="s.002331">Et al pre&longs;ente mi auedo che lui era uenuto qua per <lb/>uenire con meco alle conte&longs;e, ma lui per quanto po&longs;&longs;o con&longs;iderare) &longs;e ha me&longs;&longs;o paura di <lb/>quella mia inuentioni de capitoli Algebratici quali mi ricer caua con tanta i&longs;tantia.<emph.end type="italics"/> M. <lb/>H. A<emph type="italics"/>dunque le &longs;tato qua da uoi à ricercarue de quelli uo&longs;tri noui capitoli trouati.<emph.end type="italics"/> N. <lb/>E<emph type="italics"/>l cie stato due uolte.<emph.end type="italics"/> M. H. E<emph type="italics"/>t che glihaueti ri&longs;posto.<emph.end type="italics"/> N. I<emph type="italics"/>o gli ho ri&longs;po&longs;to che <lb/>ogni uolta che lui proponerauno, ouer piu ca&longs;i che io non li &longs;appia ri&longs;oluere mi offe­<lb/>ri&longs;co à baratar con lui. </s> <s id="s.002332">Et co&longs;i lui me ne proponete dui, ma io gli dißi, che tai &longs;uoi ca­<lb/>&longs;t io li haueua per co&longs;a facile & che &longs;e lui mi da&longs;eua termine una hora che io me gli of­<lb/>ferriua à dargeli ambidui ra&longs;olti.<emph.end type="italics"/> M. H. E<emph type="italics"/>t come dicano quelli ca&longs;i.<emph.end type="italics"/> N. E<emph type="italics"/>l pri­<lb/>mo dice in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002333"><gap/>E<emph type="italics"/>glie il triangolo rettangolo.a.b.c.del quale langolo.e.é retto & nel detto triango <lb/>lo ui è in &longs;critto il cerchio.e.f.d. </s> <s id="s.002334">il cui diametro è.2. & trouo che la linea.a.c.gionta <lb/>con la.c.b.tal &longs;umma &longs;ara &longs;empre equal alla lmea.a.b. </s> <s id="s.002335">gionta con el diametro del cer­<lb/><gap/>hio, qual (come detto) è.2.&longs;e adimanda la cau&longs;a di que&longs;to.<emph.end type="italics"/></s> </p> <figure id="id.042.01.218.1.jpg" xlink:href="042/01/218/1.jpg"/> <p type="main"> <s id="s.002336">M. H. L<emph type="italics"/>a me par difficile.<emph.end type="italics"/> N. A<emph type="italics"/>nci la è facilißima & il tutto &longs;i conclude & di­<lb/>mo&longs;tra per la penultima del terzo di Euelide per la qual &longs;e uerifica le due linee.a.e. <lb/></s> <s id="s.002337">&.a.d.e&longs;&longs;er fra loro equale, & &longs;imelmente le due.b.d.&.b.f.e&longs;&longs;er pur fra loro equa­<lb/>le & &longs;imelmente le due.c.e.&.c.f.& que&longs;te due ultime, cioe.c.e.et.c.f.non <expan abbr="&longs;olam&etilde;te">&longs;olamente</expan> <lb/>&longs;ono &longs;ra loro equale, ma per e&longs;&longs;er l'angolo.c. </s> <s id="s.002338">retto cadauna de loro uien a e&longs;&longs;er equale<emph.end type="italics"/><pb xlink:href="042/01/219.jpg"/><emph type="italics"/>alla mita del diametro del detto cerchio tal che ambedue in&longs;ieme uerano à e&longs;&longs;ere equa <lb/>le à tutto il diametro del detto cerchio, onde per concludere tal que&longs;ito arguiremo in <lb/>que&longs;to modo, per e&longs;&longs;er la partial linea.a.e.equale alla partial.a.d.& &longs;imelmente la <lb/>partial.b.f.e&longs;&longs;er equale alla partial.b.d.&longs;eguita che le due partiale linee.a.e.&.b.f. <lb/></s> <s id="s.002339">e&longs;&longs;er equale à tutta la linea.a.b.onde aggiongendo da luna è laltra banda equalmente <lb/>el diametro del detto cerchio (per comuna&longs;ententia) le dette due &longs;umme &longs;aranno an­<lb/>chora equale, & perche le due linee.c.e.&.c.f.(come di &longs;opra fu detto) &longs;ono equale <lb/>à tutto il diametro del detto cerchio, &longs;eguita adunque che le due linee.a.c.&.c.b.&longs;ia­<lb/>no equale alla linea.a.b.gionta con el diametro del detto cerchio ch'è il propo&longs;ito.<emph.end type="italics"/> M. <lb/>H. S<emph type="italics"/>ta bene. </s> <s id="s.002340">Hor ditime un puoco l'altra.<emph.end type="italics"/> N. L'<emph type="italics"/>altra dice in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002341">E<emph type="italics"/>glie il triangolo.a.b.c. </s> <s id="s.002342">che il lato.a.b.è 13. & lo.a.c. </s> <s id="s.002343">15. & lo.b.c. </s> <s id="s.002344">14. & la &longs;ua <lb/>perpendicolare è la.a.d. </s> <s id="s.002345">& da l'angolo.b.tiro la linea.b.f.e.la qual &longs;egha dalla linea. <lb/></s> <s id="s.002346">a.d.la.f.d.la qual è. </s> <s id="s.002347">3. &longs;e adimanda la quantita delle due parti.a.e.&.e.c.<emph.end type="italics"/></s> </p> <figure id="id.042.01.219.1.jpg" xlink:href="042/01/219/1.jpg"/> <p type="main"> <s id="s.002348">M. H. Q<emph type="italics"/>ue&longs;to mipar piu difficile, di l'altro.<emph.end type="italics"/> N. A<emph type="italics"/>nci ch'eglie a&longs;&longs;ai piu facile, per <lb/>che &longs;e dal ponto.c.&longs;ia tirata la.c.h.equidi&longs;tante alla perpendicolar.a.d.& che &longs;ia slon <lb/>gata la linea.b.e.per fina à tanto che quella &longs;eghila.c.h.in ponto.g. </s> <s id="s.002349">Et perche (per la. <lb/></s> <s id="s.002350">13. del &longs;econdo di Euclide) la perpendicolare.a.d.uien à e&longs;&longs;er. </s> <s id="s.002351">12. & la linea.b.d.uien <lb/>à e&longs;&longs;er. </s> <s id="s.002352">5. Et perche (per la&longs;econda del &longs;e&longs;to di Euclide) la proportione della.g.c.à tut <lb/>ta la.b.c. (quala è. </s> <s id="s.002353">14. ) è &longs;i come quella della.d.f. (quala è. </s> <s id="s.002354">3. )alla.d.b. (quala é. </s> <s id="s.002355">5.) <lb/>onde la.c.g.ueneria ad e&longs;&longs;er.<emph.end type="italics"/> 8. 2/5. E<emph type="italics"/>t perche il triangolo.f.a.e.é&longs;imile al triangolo.g. <lb/></s> <s id="s.002356">e.c. (per e&longs;&longs;er fra linee <expan abbr="equidi&longs;tãte">equidi&longs;tante</expan>) la proportione del lato.a.f. (qual è. </s> <s id="s.002357">9. al lato.g.c <lb/>(qual è. </s> <s id="s.002358">8. 2/5. &longs;ara &longs;i come quella dalla.a.e.alla.e.c.& (per la. </s> <s id="s.002359">18. del quinto di Euclide) <lb/>la proportione del conglonto della.a.f.&.g.c. (qual congionto &longs;aria. </s> <s id="s.002360">17. 2/5. )alla.g.c. <lb/>(qual é. </s> <s id="s.002361">8. 2/5. )&longs;ara &longs;i come la proportione del congionto della.a.e.et.e.c. (qual è.<emph.end type="italics"/> 15.) <emph type="italics"/>alla.e.c. </s> <s id="s.002362">Onde procedendo per laregola &longs;e trouara la.c.c.e&longs;&longs;er. </s> <s id="s.002363">7. 7/29. & la.a.e.il re­<lb/>&longs;tante per fin in. </s> <s id="s.002364">15. che &longs;aria. </s> <s id="s.002365">7. 22/29. ch'é il propo&longs;ito.<emph.end type="italics"/> M. H. L<emph type="italics"/>a non è &longs;tata tanto <lb/>difficile, come che mi pen&longs;aua. </s> <s id="s.002366">Ma diteme non gliuoleti mandar que&longs;te uo&longs;tre due re <lb/>&longs;olutioni acc io ch'el non &longs;i creda che uoi non li habbiate &longs;aputeri&longs;&longs;oluere.<emph.end type="italics"/> N. A<emph type="italics"/>nci <lb/>non uoglio mandaruene alcuna. </s> <s id="s.002367">Perche comprendo che lui ha animo di uoler ueniro <lb/>ud habitar qua, & me ha prome&longs;&longs;o de ritornar fra pochi giornie pero non lo uoglio<emph.end type="italics"/><pb pagenum="110" xlink:href="042/01/220.jpg"/><emph type="italics"/>de&longs;inanimare, perche non dandoui ri&longs;po&longs;ta lui &longs;i pen&longs;ara che io <expan abbr="nõ">non</expan> li &longs;appia re&longs;&longs;oluere, <lb/>& non &longs;e deffidara del uenire & uenendoui ui uoglio lauar il capo d'altro che di &longs;apo­<lb/>ne, u&longs;ando pero termini, ouer parole non con conueniente, come che &longs;o che lui haue­<lb/>ria fatto quando che lui non &longs;i fu&longs;&longs;e &longs;paurito per quelle mie inaentioni de capitoli, anci <lb/>&longs;on certo che lui me &longs;criuera, & me mandara qualche altro que&longs;lto per meglio ta&longs;tar <lb/>me, ma de niuno non li uoglio dar ri&longs;po&longs;ta.<emph.end type="italics"/> M. H. E<emph type="italics"/>ue ho inte&longs;o.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002368">QVESITO. XXVIII. FATTO DA M. ZV ANNE <lb/><emph type="italics"/>di Tonini da Coi con una &longs;ua lettera quale me portò Bene­<lb/>detto caualaro l'anno. </s> <s id="s.002369">1537. adi. </s> <s id="s.002370">8. Genaro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002371">MAESTRO ZV ANNE. Q<emph type="italics"/>uando da uoi mi &longs;comiai Me&longs;&longs;er Nicolo ca­<lb/>rißimo, uoi &longs;apete ch'io ui dißi che &longs;critto ue harrei, & hora per pagar el de­<lb/>bito che in cio teneua con uoihouui la pre&longs;ente &longs;critta. </s> <s id="s.002372">Nellaqual primieramente ui <lb/>&longs;criuo la re&longs;olution (&longs;e io non &longs;ono errato) di quella domanda, che dice eglie una uer­<lb/>zella di oro qual pe&longs;a &longs;aggi. </s> <s id="s.002373">10. & tien di argento la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba di. </s> <s id="s.002374">10. & ual duc. </s> <s id="s.002375">10. & <lb/>eglie anchora un'altra uerga pur di oro che pe&longs;a pur &longs;aggi. </s> <s id="s.002376">10. & tien di argento la <lb/>Radice quadra de. </s> <s id="s.002377">10. & alla proportion del primo ual &longs;olamente duc. </s> <s id="s.002378">9. &longs;e adiman­<lb/>da che ual&longs;e el &longs;aggio del oro puro & &longs;imelmente quello del argento puro. </s> <s id="s.002379">Io ue dico <lb/>cheloro della primaual<emph.end type="italics"/> <22>. <emph type="italics"/>qua. </s> <s id="s.002380">1000. piu<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.002381">72. 9/10. <expan abbr="m&etilde;">men</expan><emph.end type="italics"/> <22> <emph type="italics"/>cu. </s> <s id="s.002382">7290. <expan abbr="m&etilde;">men</expan><emph.end type="italics"/> <22>. <emph type="italics"/>cu.qua. <lb/></s> <s id="s.002383">100000. Et <expan abbr="l'arg&etilde;to">l'argento</expan> ual la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de<emph.end type="italics"/> <22>. <emph type="italics"/>qua. </s> <s id="s.002384">100000. men<emph.end type="italics"/> <22>. <emph type="italics"/>cu 7. 2. 9/10. <expan abbr="m&etilde;">men</expan><emph.end type="italics"/> <22> <emph type="italics"/>cuba. </s> <s id="s.002385">10 <lb/>Et quella che tìen di argento la<emph.end type="italics"/> <22>. <emph type="italics"/>qua.di. </s> <s id="s.002386">10. l'oro ual<emph.end type="italics"/> <22>. <emph type="italics"/>qua. </s> <s id="s.002387">1000. men. </s> <s id="s.002388">10. men<emph.end type="italics"/> <22>. <emph type="italics"/>cu. <lb/></s> <s id="s.002389">7290. piu<emph.end type="italics"/> <22>. <emph type="italics"/>qua.de<emph.end type="italics"/> <22>. <emph type="italics"/>cu.<emph.end type="italics"/> 53144100000/7000000. E<emph type="italics"/>t l'argento ual. </s> <s id="s.002390">10. men<emph.end type="italics"/> <22>. <emph type="italics"/>qua. </s> <s id="s.002391">de<emph.end type="italics"/><lb/><22>. <emph type="italics"/>cu'a. </s> <s id="s.002392">53144100000/1000000. men<emph.end type="italics"/> <22>. <emph type="italics"/>qua. </s> <s id="s.002393">10. La proua di que&longs;ta ragione è a&longs;&longs;ai bella <lb/>& la co&longs;a ual<emph.end type="italics"/> <22> 10. <emph type="italics"/>men<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.002394">7. 29/100. men.<emph.end type="italics"/> 1. (N. P<emph type="italics"/>er mia fe che costui ri&longs;ponde <lb/>a&longs;&longs;aiben à propo&longs;ito.)<emph.end type="italics"/> M. Z. L'<emph type="italics"/>altra uo&longs;traragione che dice trouatime un numero <lb/>che &longs;tairrationale che multiplicato uia la &longs;ua Radice piu. </s> <s id="s.002395">40. faccia numero rationa <lb/>le a trouarlo &longs;i dupla il. </s> <s id="s.002396">40. & del duplato &longs;i tra due & re&longs;ta. </s> <s id="s.002397">78. & di que&longs;to ne ca­<lb/>namo uno resta. </s> <s id="s.002398">77. & que&longs;to per. </s> <s id="s.002399">4. &longs;e multiplica & del prodotto &longs;i prende la Radi­<lb/>ce che &longs;ara<emph.end type="italics"/> <22>. <emph type="italics"/>qua. </s> <s id="s.002400">308. & co&longs;i aduiene in tutti. </s> <s id="s.002401">Et perche co&longs;i dobbiamo fare ho tro­<lb/>uata la cagione. </s> <s id="s.002402">Et &longs;i diremo trouame uno numero che multiplicato per la &longs;ua Radice <lb/>piu. </s> <s id="s.002403">8. faccia numero rationale. </s> <s id="s.002404">Questo &longs;ara. </s> <s id="s.002405">14. men.<emph.end type="italics"/> <22>. </s> <s id="s.002406">52. <emph type="italics"/>& la &longs;ua<emph.end type="italics"/> <22>. <emph type="italics"/>è.<emph.end type="italics"/> <22>. </s> <s id="s.002407">13. <emph type="italics"/>men <lb/>1. Et giongendoli. </s> <s id="s.002408">8. re&longs;tara<emph.end type="italics"/> <22>. </s> <s id="s.002409">13. <emph type="italics"/>piu. </s> <s id="s.002410">7. & que&longs;to binomio multiplicato <expan abbr="cõ">com</expan> que&longs;to re <lb/>ci&longs;o. </s> <s id="s.002411">14. men.<emph.end type="italics"/> <22>. </s> <s id="s.002412">52. <emph type="italics"/>fara. </s> <s id="s.002413">72. Et&longs;e not diremo, multiplicato per la &longs;ua Radice men. </s> <s id="s.002414">8. <lb/>faremo dir il. </s> <s id="s.002415">52. piu.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002416">H<emph type="italics"/>ora &longs;e a uoipare di mandarme la &longs;olutione delle no&longs;tre due oueramente di quelle che <lb/>ni trouarete hauer fatte uoi mi farete in cio tanto appiacer <expan abbr="quãto">quanto</expan> che io mi credo che <lb/>riceuer pote&longs;&longs;e giamai, maio uorrei che in&longs;leme <expan abbr="cõloro">colloro</expan> mi mandaste que&longs;te due etian <lb/>dio &longs;ciolte delle quale la prima. </s> <s id="s.002417">Et che mi trouate tre quantita continue proportio­<lb/>nale, che la maggiore &longs;ia. </s> <s id="s.002418">700. & il prodotto delle due menore luna in l'altra multi­<lb/>plicato in &longs;e produca<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.002419">10000. La &longs;econda que&longs;tione che io uorrei che uci fo <lb/>ste contento ditrouar una quantita che multiplicata in &longs;e & il produtto multiplicato<emph.end type="italics"/><pb xlink:href="042/01/221.jpg"/><emph type="italics"/>anchora per la detta quantita, & al prodotto giontoui la inuenta quantita faccia. </s> <s id="s.002420">8. <lb/>in que&longs;ta domanda <expan abbr="uol&etilde;do">uolendo</expan> noi adoperar lalgebra per trouarla, poneremo questa quan <lb/>tita e&longs;&longs;er una co&longs;a, laqual multiplicata in &longs;e fara uno cen&longs;o & que&longs;to cen&longs;o multiplica <lb/>to per una co&longs;a fara uno cubo, & à que&longs;to cubo aggiungerli la co&longs;a che prima noi po­<lb/>neßimo haueremo un cubo & una co&longs;a equal al numero. </s> <s id="s.002421">8. Quando io ui domandai <lb/>me&longs;&longs;er Nicolo che una domanda di que&longs;ta manier a mi de&longs;ti fatta. </s> <s id="s.002422">Parmiche poco &longs;a­<lb/>uiamente face&longs;ti quando uoi del tutto à me la nega&longs;ti <expan abbr="hau&etilde;domi">hauendomi</expan> (<expan abbr="quãdo">quando</expan> à trouar la pri <lb/>ma uolta ui uenni) mo&longs;trata tanta beniuolenza. </s> <s id="s.002423">Et u&longs;andomi quella amicheuole cor­<lb/>te&longs;ia, che uoi miu&longs;a&longs;te à farmi quella &longs;era qua&longs;i per uiua forza uenir à cena con uoi. <lb/></s> <s id="s.002424">Ma dapoiche mi haue&longs;ti u&longs;ata quell'altra corte&longs;ia nouamente in darmi quella a&longs;&longs;o<gap/><lb/>che &longs;apeti (de cen&longs;o è cubo equal à numero) mi parue che'l error, che fatto haueuate <lb/>in non uolermi quell'altra, che ui adimandai &longs;oluere, qua&longs;i in tutto emendato haueste, <lb/>& perche di legiero uoipotre&longs;ti dire, per qual cagione, uoi&longs;auiamente non ragiona&longs;t­<lb/>all'hora che mi nega&longs;te di non uoler quella domanda &longs;oluere piacemi in que&longs;ta charta <lb/>al pre&longs;ente dinarraruela in bona parte, uoi&longs;apete me&longs;&longs;er Nicolo che <expan abbr="incontan&etilde;te">incontanente</expan> che <lb/><gap/>o ui domandai quel ca&longs;o uoi me dice&longs;ti, che le inuentioni &longs;ono difficile, & lo aggiun­<lb/>gergliè co&longs;a facile, & che per e&longs;&longs;erui molto affaticato per ritrouare tale, & tai capi­<lb/>toli, chel non ui pareua co&longs;a molto licita à douerli co&longs;t facilmente publicare à ognipar <lb/>ticolar per&longs;ona, & maßime doue non ue ne reu&longs;i&longs;ca alcunbonore, ne utilita, & per <lb/>tanto dico che il tener caro quello che in uoi &longs;olo non è ne pur di uo&longs;tri amici, <expan abbr="manife-&longs;tam&etilde;te">manife­<lb/>&longs;tamente</expan> à ogn'uno ui pale&longs;ate di hauerne grandißima cara&longs;tia, laqualco&longs;a e&longs;&longs;endo io <lb/>della <expan abbr="pfeßiõe">pfeßione</expan> uo&longs;tra auoi la&longs;&longs;o il giudicio qual è piu, ò il bia&longs;mo ò l'honor che ne porta <lb/>te, & &longs;e premio di cio cercate & <expan abbr="nõ">non</expan> honore parmi che quello debba e&longs;&longs;er pochißimo, et <lb/>mi&longs;erißimo, e&longs;&longs;endo uero quello che me fureferto, (come <expan abbr="ueram&etilde;te">ueramente</expan> <expan abbr="t&etilde;go">tengo</expan> che &longs;ia) che <lb/>30. ca&longs;i, ouer que&longs;iti di que&longs;ta &longs;orte in due hore dauoierano &longs;tati a&longs;&longs;olti à mae&longs;tro Gio <lb/>uanantonio Maria fior uo&longs;tro riuallo, parmi che farebbestato il premio a&longs;&longs;ai gra&longs;&longs;o <lb/>bauendoui dato &longs;oldi. </s> <s id="s.002425">5. per cia&longs;cun deßi, ma &longs;e for&longs;e uole&longs;ti dire che non tanto é il pre <lb/>mio che domandate della fatica quanto è quello della inuentione, et del modo da &longs;oluer <lb/>gli&longs;ecreto, il che non &longs;i puo con uerita dire che il modo &longs;ia &longs;ecreto, ne etiandio che la &longs;ia <lb/>propria inuentione &longs;apendolo nanti il uo&longs;tro aduer&longs;ario. </s> <s id="s.002426">Hor &longs;e uogliamo dir della <lb/>muentione, non &longs;apeti uoi che &longs;olamente le prime inuentioni &longs;ono lodate & premiate <lb/>da color che &longs;anno, & che premio & che loda uore&longs;ti uoi che merita&longs;&longs;e un huomo che <lb/>mai non haue&longs;&longs;e da niuno apparata Geometria, ne mai haue&longs;&longs;e ueduto Euclide, & che <lb/>da&longs;e &longs;te&longs;&longs;o ne compone&longs;&longs;e uno, nel qual tutte quelle co&longs;e dice&longs;&longs;e, chel detto autor ha­<lb/>dette nel &longs;uo. </s> <s id="s.002427">Io non &longs;o gia con tutto que&longs;to che loda potre&longs;ti dar à co&longs;tui, ne che pre­<lb/>mio, ma uolendolo incio bia&longs;imare à uoi &longs;arebbe ageuolißimo, con&longs;iderando che egli <lb/>haue&longs;&longs;e gettato uia tutto il tempo della &longs;uauita in co&longs;e che de niente non fo&longs;&longs;ero, ne &longs;a­<lb/>rebbe mai gioueueuole à niun <expan abbr="uiu&etilde;te">uiuente</expan>, et &longs;e à uoi era di me&longs;tiero per e&longs;&longs;eruime&longs;&longs;o à con <lb/>tendere <expan abbr="cõ">com</expan> quel mae&longs;tro che <21> in&longs;egna tenea le corone, o da &longs;oluer li oda re&longs;tar in <expan abbr="grã">gram</expan> <lb/>parte &longs;uergognato appre&longs;&longs;o aluolgo, <expan abbr="nõ">non</expan> gia appre&longs;&longs;o à gli huomini, dotti et <expan abbr="intellig&etilde;ti">intelligenti</expan> <lb/>di que&longs;te &longs;cientie, ba&longs;taui adunque per premio della fatica che uoi hauete fatta in tro­<lb/>uar la <expan abbr="inu&etilde;tione">inuentione</expan> da &longs;oluerei detti. </s> <s id="s.002428">30. ca&longs;i, l'honor & fauor, che per lei haueti hauuto<emph.end type="italics"/><pb pagenum="111" xlink:href="042/01/222.jpg"/><emph type="italics"/>in far quelmae&longs;tro re&longs;tar uinto, & &longs;uperato da uoi. </s> <s id="s.002429">Et che il fu&longs;&longs;e ben fatto per trarne <lb/>premio, ouer honore à far que&longs;te co&longs;e stampare, come uoi me dice&longs;ti, non e&longs;&longs;endo co&longs;e <lb/>qua&longs;i in parte alcuna gioueuoli al mondo, io tengo fermamente, che niuno che diritta­<lb/>mente giudichi non lo e&longs;timera giamai. </s> <s id="s.002430">Et che &longs;tara in pen&longs;iero, che di quegli non &longs;i tro­<lb/>uino, che diranno, che per la uilta, & maluagita dell'animo uostro, non ui cur ate di pia <lb/>cere à glihuomini, ne in gentilezza, ne in beniuolenza, ne in corte&longs;ia alcuna, que&longs;ta uil <lb/>ta non credo, ne credero di leggeri, che in uoi alberghi, ne albergar po&longs;&longs;a giamai per <lb/>hauerui cono&longs;ciuto pieno d'amoreuolezza, pieno di gentilezza, pieno di lealta, pieno <lb/>di corte&longs;ia, & in fine pieno d'ogni hone&longs;ta, & gentil conuer&longs;atione, per ilche io non &longs;to <lb/>in dubbio, che uoi diciate, che io me affatichi à trouare il modo da &longs;oluerle, &longs;i come uoi <lb/>anchor a haueti fatto, & quando pur dice&longs;ti que&longs;to, que&longs;ta fatica non uoglio, ne debbo <lb/>farla per fuggir quel bia&longs;mo, che &longs;i darebbe à colui, che una opera &longs;imile à quella di Eu <lb/>clide, compone&longs;&longs;e nuouamente, & &longs;e pur miueni&longs;&longs;e talento di far qualche fatica d'in­<lb/>torno à una &longs;imil co&longs;a, io la farei in bia&longs;mare, & uituperare la mente uile, & maluag­<lb/>gia di colui, che una tanta a&longs;inaria u&longs;a&longs;&longs;e, perche &longs;ei dotti huomini per adictro &longs;tai, que <lb/>&longs;to haue&longs;&longs;ero o&longs;&longs;eruato, ne Euclide, ne tanti altri dignißimi autori hoggi da niun uiuen <lb/>te non &longs;arebbono cono&longs;ciuti. </s> <s id="s.002431">Hora non &longs;o gia à che altro ui uogliate ne poßiate tenere <lb/>di non e&longs;&longs;er in cio altro, che liberale, &longs;e for&longs;e non uole&longs;te dire, che &longs;e à uoi fu&longs;&longs;e di me­<lb/>&longs;tieri di contendere con un'altro mae&longs;tro di cio ui&longs;eruire&longs;ti, ilche appena mi &longs;t la&longs;&longs;acre <lb/>dere, che uoi pur il pen&longs;ate, perche &longs;e uoi con&longs;iderate, che que&longs;to modo per il quale &longs;i <lb/>&longs;oluono que&longs;ta maniera de domande non è &longs;aputo da uoi &longs;olamente, maetiandio è &longs;tato <lb/>inanzi da uoi &longs;aputo da colui, che malui uole, & non credete uoi, che &longs;e egli&longs;ape&longs;&longs;e, che <lb/>uoi contende&longs;ti, ch'egli &longs;i ingegnarebbe di dare ogni aiuto à uo&longs;tri auer&longs;arij, che per lui <lb/>&longs;i pote&longs;&longs;e il maggiore, & non che premio di cio à lor domanda&longs;&longs;e, magli pregarebbe <lb/>che ne di lui ne del&longs;uo hauere in cio ponto non lo &longs;parmia&longs;&longs;e per tentare di uendicar&longs;e <lb/>della uergogna, & dishonore, che uoi gli haueti fatto, & &longs;i cio mae&longs;tro Nicolo non cre <lb/>dete mal credete, & che uolete che altro d'intorno à que&longs;ta materia ui &longs;criua, di cio che <lb/>mae&longs;tro Antoniomaria Fior mi offer&longs;i (&longs;i come &longs;aggio) di darmi una di quelle. </s> <s id="s.002432">30. do­<lb/>mande che à lui &longs;oluesti, ma per che tanto piu mi piace la uo&longs;tra amicitia della &longs;ue quan <lb/>to che è la uostra uirtu della &longs;ua maggiore. </s> <s id="s.002433">Et anche per e&longs;&longs;er della patria, io mi uenni <lb/>prima à trouarui uoi, & con quella instantia ue gli domandai che uoi i&longs;te&longs;&longs;o &longs;apete, & <lb/>perche uoi mi de&longs;ti quello uo&longs;tro ca&longs;o a&longs;&longs;olto che &longs;apeti, io non uol&longs;i ritornar piu da lui <lb/>à richiederglilo per non obligarmegli altrimente, & perche anchora mi dice&longs;ti all'ho­<lb/>ra che&longs;e io ue ne daua à uoi alcuni che non &longs;ape&longs;ti ri&longs;oluere, che altritanti ne daresti à <lb/>me, quanto all'hora il uostro parlar mi piacque, io non uel potrei dire di qui à un'anno <lb/>compiutamente, matanto in cio &longs;olamente ui dico, che adueni&longs;&longs;e (ch'io non m'il credo) <lb/>che uoi non haue&longs;te tanti ca&longs;i co&longs;i accommodati da mandarmi, quanti nell'animo ne ha­<lb/>ue&longs;ti di domandarmene. </s> <s id="s.002434">Non uoglio percio che in parte alcuna ui retignate di non chie <lb/>dere tutti quelli, che nel uo&longs;tro animo ui &longs;corge&longs;&longs;e di chiedermi. </s> <s id="s.002435">Et non &longs;olamente ca&longs;t, <lb/>maogn'altra co&longs;a che ui piaccia, che in balia &longs;ta dime, io co&longs;iuolontieri, per uoi me&longs;&longs;er <lb/>Nicolo quanto che per cia&longs;cuno buomo che uiua lo faro certamente. </s> <s id="s.002436">Horauenendo al <lb/>fine di que&longs;ta &longs;crittura, la qual per la maggior parte d'altro non ragiona (come uoi uc-<pb xlink:href="042/01/223.jpg"/>der poteti) che di quel capitolo di co&longs;a, & cubo, egual à numero, mo&longs;trando che à me <lb/>nou fia di&longs;diceuole il chiederuelo, ne il concederlo mi à uoi, altre&longs;i, & &longs;e in lei trouare­<lb/>te aggionta alcuna uoce, & de altre in tutto ca&longs;&longs;e, & altre in tutto mutate, questi&longs;ono <lb/>gli inditij, che lei dimo&longs;trino e&longs;&longs;er &longs;tata &longs;critta di&longs;contiamente, & benche io acconcio, <lb/>& adaggiato &longs;ia non &longs;criua bene, non dico giai caratteri, che cura alcuna in eßi non <lb/>ho po&longs;ta, come uoi &longs;te&longs;&longs;o ueder potete, ma dico nel &longs;tile, & per cio &longs;e in lei troua&longs;te uo­<lb/>ce, che ui &longs;piace&longs;&longs;ero, uaglia il perdonare, che &longs;e mailettra fu di&longs;conciamente &longs;critta, <lb/>credo che que&longs;ta &longs;ia una d'e&longs;&longs;e, dico di&longs;conciamente per hauerla &longs;critta in cinque gior­<lb/>ni, hora in un luoco, hora in un'altro, & di cio ne potrebbe e&longs;&longs;er buon te&longs;timonio mae <lb/>&longs;tro Battista, che &longs;taua in ca&longs;a del Conte Nicolo de Lodron, il quale. </s> <s id="s.002437">& io altre&longs;i à uoi <lb/>molto &longs;e aricomandiamo, & uorrei che al Frate, che &longs;ta in Fricciaria me aricomanda­<lb/>&longs;ti, ma primieramente uorrei, che letta che harete la lettra, che incontanente nota&longs;ti i <lb/>ca&longs;i, che all hora all'hora piu ageuolmente uoi potrete, ma per mio contento piacciaui <lb/>di notar per il primo quello di co&longs;a, è cubo, egual à numero, & all'hora all hora man­<lb/>darmeli &longs;el fu&longs;&longs;e poßibile uia piu che digaloppo, & c. <!-- REMOVE S-->à. </s> <s id="s.002438">5. di Genaro.<emph.end type="italics"/> 1537. </s> </p> <p type="main"> <s id="s.002439">G<emph type="italics"/>iouanni di Tonini uostro à gui&longs;a di buon fratello.<emph.end type="italics"/><lb/>NICOLO. Q<emph type="italics"/>ue&longs;ta &longs;ua gran retorica non uoglio che habbia ri&longs;po&longs;ta da me. </s> <s id="s.002440">Ma pur <lb/>uoglio con&longs;iderar que&longs;to &longs;uo que&longs;ito, nel qual lui uole, che io gli troui tre quantita con <lb/>tinue proportionale, che la maggior &longs;ia. </s> <s id="s.002441">700. & che il produtto delle due menore, l'u <lb/>na fia l'altra, moltiplicato poi in &longs;e mede&longs;imo produca la Radice cuba de. </s> <s id="s.002442">10000. <lb/>Qual credo, che &longs;ia facile, uero è, che per ri&longs;oluerlo bi&longs;ogna notar, che moltiplicando <lb/>la prima ditre quantita continue proportionale fia la &longs;<17>conda, & quel produtto fia la <lb/>terza, quell'ultimo produtto &longs;empre &longs;ara eguale al cubo della &longs;econda, e per tunto &longs;e il <lb/>quadrato delle due menore l una fia l'altra fanno<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.002443">10000. adunque il puro pro <lb/>dutto fu la<emph.end type="italics"/> <22>. <emph type="italics"/>quadra della<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de. </s> <s id="s.002444">10000. cioe il fu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.002445">100. & que&longs;to molti­<lb/>plicandolo fia la terza, che &longs;u.<emph.end type="italics"/> 700. (<emph type="italics"/>cubando prima.<emph.end type="italics"/> 700.) <emph type="italics"/>fara<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.002446">34300000000. <lb/>& la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba di questo produtto &longs;ara lo &longs;econdo termine, cioe<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. <lb/></s> <s id="s.002447">34300000000. Hor per trouar il primo termine quadro il &longs;econdo, cioe<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de<emph.end type="italics"/> <22>. <lb/><emph type="italics"/>cuba. </s> <s id="s.002448">34300000000. & quel tal quadrato lo parto per lo terzo, cîoe per. </s> <s id="s.002449">700. (re­<lb/>cando. </s> <s id="s.002450">700. à cubo de cubo) ne uenira<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.002451">117049/4035360700. & que­<lb/>&longs;to &longs;ara il primo termme, che è il propo&longs;ito.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002452">QVESITO. XXIX. FATTO DAL MEDESIMO <lb/>M<emph type="italics"/>e&longs;&longs;er Zuane de Tonini da Coi, con una &longs;ua lettera alli. </s> <s id="s.002453">17. <lb/>di Febraro. <!-- KEEP S--></s> <s id="s.002454">1537. In Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002455">MESSER ZVANE. M<emph type="italics"/>e&longs;&longs;er Nicolo il me ha detto Benedetto cauallaro, <lb/>che uoi haueti hauuta la no&longs;tra lettera, & che gli hauete detto, che uoi me ha­<lb/>ueti à cio ri&longs;po&longs;to, ilche à me pare molto duro à douerlo credere, con&longs;iderando ch'egli <lb/>è me&longs;&longs;o molto da fidar&longs;e, & che all'uno, & a l'altro di noi &longs;erue uolontieri. </s> <s id="s.002456">Et che non <lb/>mi hauete uoluto per lui mandar mi lettra niuna la, onde non &longs;to gia in pen&longs;iero, che <lb/>uoi re&longs;tar non doueuate, perche ui manca&longs;&longs;e la carta, o per non &longs;aper &longs;criuere, o per<emph.end type="italics"/><pb pagenum="112" xlink:href="042/01/224.jpg"/><emph type="italics"/>fuggir la fatica (che cio uo&longs;tro co&longs;tume non é) o per non &longs;apere con belli carattere <lb/>&longs;criuermi, perche io co&longs;i habbia &longs;critto à uoi, che cio non è &longs;tato u&longs;ato da me in parte <lb/>ueruna à uoi. </s> <s id="s.002457">Ma &longs;olamente &longs;to in pen&longs;iero che uoi re&longs;tate, o per il &longs;criuermi To&longs;cana­<lb/>mente, o per non uolermi mandar quel ca&longs;o &longs;ciolto de co&longs;a, & cubo egual à numero, <lb/>qual con tanta in&longs;tanza ui ho adimandato. </s> <s id="s.002458">Io non a&longs;petto, che To&longs;canamente mi &longs;cri­<lb/>uiate, ne etiandio che mi mandate quel ca&longs;o &longs;e à uoi non ui piace. </s> <s id="s.002459">Ma ben di cio ui pre­<lb/>go che ui uogliati degnar di &longs;criuermi o poco, o a&longs;&longs;ai, che ui piaccia, & &longs;e cio me&longs;&longs;er <lb/>Nicolo non fate io tenero per fermo, che uoi poca &longs;tima fareti di me, & della mia <lb/>amicitia, alli. </s> <s id="s.002460">14. Febraro.<emph.end type="italics"/> 1537. </s> </p> <p type="main"> <s id="s.002461">G<emph type="italics"/>iouanni di Tonini uo&longs;tro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002462">NICOLO. M<emph type="italics"/>e&longs;&longs;er Zuane ho riceuuto due uo&longs;tre, & hoggi un'altra, che &longs;ono tre <lb/>delle quale le due ultime &longs;ono &longs;olamente ammonitorie, che ui debbia dar ri&longs;posta alla <lb/>prima uo&longs;tra, uer amente haueua deliberato, che &longs;olamente il mio tacere ui fu&longs;&longs;e ri&longs;po­<lb/>sta per molte ragioni, la prima è, che uolendo dar particolar ri&longs;po&longs;ta à ogni uo&longs;tra ri­<lb/>chie&longs;ta, & ragioni da uoi allegate, bi&longs;ognaria &longs;criuere un quinterno di carta, ilche le <lb/>occupationi diurne, & notturne, non mel conciedono. </s> <s id="s.002463">La &longs;econda è, che dapoi la parti­<lb/>ta uo&longs;tra da Venetia me&longs;&longs;er Hieronimo Triui&longs;ano, & anchora quel mae&longs;tro Dominico <lb/>da Vderzo (che mi portò quelle uo&longs;tre.3.dimande) me hanno riferto tante uo&longs;tre bra <lb/>uate, che longo &longs;aria à narrarle, ma molto mi dol&longs;e con cadauno de loro, perche non mi <lb/>feceno intendere tal co&longs;e auanti la partita uo&longs;tra. </s> <s id="s.002464">Che haueria fatto qualche &longs;perien­<lb/>tia diuoi, & uoi di me, & comprendo che uoi eriuenuto à po&longs;ta per tal effetto, ma ue <lb/>teme&longs;ti per quelli capitoli da me trouati, li quali me ricercati con tanta in&longs;tantia, alla <lb/>qual richie&longs;ta breuiter ri&longs;pondo, che hauendoui dato a&longs;&longs;olto quello de cen&longs;o, e cubo <lb/>egual à numero (per mia gentilezza) ue douere&longs;ti alquanto arroßire à richiedermi <lb/>anchora quell'altro, e&longs;&longs;endo quell'buomo, che ue teneti, & maßime hauendoui fatto <lb/>quella oblatione, che ogni uolta che me proponereti un ca&longs;o, & che il non &longs;appia ri­<lb/>&longs;oluere di barattar conuoi, la qual offerta non è poco à offerire una co&longs;a generale per <lb/>una particolare, ilche mi fa credere uoi non e&longs;&longs;ere quello, che mi credeua, non ba&longs;tan­<lb/>doui l'animo di componere un ca&longs;o, ouer que&longs;ito, che io non lo &longs;appia ri&longs;oluere, ma per <lb/>che non uoglio, che fati piu &longs;perientia di me, ne che piu me tediate con uo&longs;tre dimande, <lb/>ouer que&longs;iti, uoglio annullar tal oblatione, perche mi bi&longs;ogna attendere ad altro, che <lb/>&longs;tar tutto il giorno a&longs;&longs;oluere uo&longs;tri que&longs;iti &longs;enza alcun frutto, ne honore, ne ancho­<lb/>ra ue uoglio dar tal ca&longs;o a&longs;&longs;olto, per gentilezza, e&longs;&longs;endo di poco ualore appre&longs;&longs;o di <lb/>uoi, perche poca &longs;aria la mia gentilezza, e&longs;&longs;endo &longs;timato da uoi &longs;oldi cinque per ca&longs;o, <lb/>che in uero piu non ualeria, premiandomi, come &longs;e fanno gli facchini, ouer manuali, <lb/>che lauorano à tanto al giorno, la qual propo&longs;ta è molto ridicolo&longs;a appre&longs;&longs;o de ogni <lb/>intelligente. </s> <s id="s.002465">Et perche diceti (per calonniar tal mia inuentione) che &longs;olamente le pri­<lb/>me inuentioni &longs;ono laudate appre&longs;&longs;o di color, che &longs;anno, & che tal mia inuentione non <lb/>è propria inuentione, &longs;apendola il mio auer&longs;ario auanti di me. </s> <s id="s.002466">Et che poca laude meri­<lb/>taria un'huomo, che mai haue&longs;&longs;e imparato Geometria, ne mai haue&longs;&longs;e ueduto Eucli­<lb/>de, & che da &longs;ei&longs;ie&longs;&longs;o compone&longs;&longs;e un'altra opera &longs;imile à quella di Euclide, ma uo­<lb/>lendolo in cio bia&longs;imare &longs;arebbe ageuolißimo, con&longs;iderando che egli haue&longs;&longs;e gettato <pb xlink:href="042/01/225.jpg"/>uia tutto il tempo della &longs;ua uita in co&longs;e, che de niente fu&longs;&longs;ero, ne &longs;arebben mai gioueuo <lb/>le à niun uiuente, circa alla prima parte ri&longs;pondo, & dico, che uoi non hauetì altra cer <lb/>tezza, ouer indicio, che il mio auer&longs;ario haue&longs;&longs;e tal &longs;ecreto, &longs;aluo per hauermi co&longs;i pro <lb/>posti tutti li &longs;uoi. </s> <s id="s.002467">30. ca&longs;i, che mi conduceuano à tal difficulto&longs;o pa&longs;&longs;o, la qual co&longs;a non <lb/>ui fa certo, che lui haue&longs;&longs;e, ouer &longs;ape&longs;&longs;e tal &longs;ecreto, perche molti &longs;ogliono &longs;pe&longs;&longs;euolte, <lb/>per confutar il &longs;uo auer&longs;ario proponere delle que&longs;tioni, che loro mede&longs;iminon le inten <lb/>dono, ne le &longs;apriano ri&longs;oluere, &longs;i come fe&longs;ti uoi à me, quando che io &longs;tantiaua à Verona <lb/>con quelle due dimande, che mi manda&longs;ti per Me&longs;&longs;er Pre Antonio. </s> <s id="s.002468">Ma &longs;upponendo an­<lb/>chor che il detto mio auer&longs;ario gli&longs;ape&longs;&longs;e ri&longs;oluere auanti di me, & hauendola io ritro <lb/>uata da me &longs;enza aiuto di alcun autore, la &longs;e puo chiamare mia propria inuentione, per <lb/>che circa à quell'altra parte che uoi diceti, che poca laude meritaria uno, che compo­<lb/>ne&longs;&longs;e da&longs;e un'altra opera &longs;imile à quella di Euclide, anchor che non haue&longs;&longs;e mai ui&longs;to <lb/>Euclide, ne imparato Geometria. <!-- KEEP S--></s> <s id="s.002469">Et io dico, che quando il &longs;i &longs;ape&longs;&longs;e di certo, lui non ha <lb/>uer ui&longs;to l opera di Euclide, ne cauato da quello, ne d'altri, che meritaria mille uolte <lb/>piu laude di Euclide, perche non hauemo certezza, che Euclide non habbia cauato d'al <lb/>tri anciani di lui. </s> <s id="s.002470">Et accio che non crediati, come diceti, che ui nega tai mie inuentioni, <lb/>ne che le tenga accare per contendere con qualche altro. </s> <s id="s.002471">Le ben la uerita, che di tal co­<lb/>&longs;a (accadendo) me ne potria &longs;eruire, nientedimeno accio non pen&longs;ati, che ogni mio fon­<lb/>damento &longs;ia in tai mie particolarita. </s> <s id="s.002472">Quando che alcuno di&longs;idera&longs;&longs;e di uenire al cimen <lb/>to con meco, & che non haue&longs;&longs;e altra temenza di me, &longs;aluo che delli detti capitoli di co <lb/>&longs;a, e cubo egual à numero, & di cen&longs;o è cubo egual à numero, & delli &longs;uoi ederenti uo­<lb/>lendo giocare un precio condecente per un meggio &longs;cudo me obligaro à non propo­<lb/>nerui ca&longs;o alcuno, che conduca l'operante in alcuno de detti capitoli, & &longs;uoi ederenti, <lb/>& lo faro &longs;icuro di que&longs;to. </s> <s id="s.002473">Oltra di que&longs;to uoi me ammonite con grande i&longs;tantia, che <lb/>ui uoglia mandare quelli ca&longs;i, che mi trouo hauer ri&longs;olti de quelli, che uoi mi la&longs;cia&longs;ti in <lb/>&longs;critto, & di quelli che me haueti rimandati, & &longs;imilmente quel mae&longs;tro Dominico, <lb/>che mi portò quelli altri tre uo&longs;tri me ha riferto qualmente uoi gli fe&longs;tiuna grandißi­<lb/>ma&longs;tantia, che doue&longs;&longs;e uenir à domandarme, quelli, & perche lui ui di&longs;&longs;e (come il ue­<lb/>ro) che io ne haueua a&longs;&longs;olti dui &longs;ubito ch'io gli hebbi riceuuti alla &longs;ua pre&longs;entia, dice <lb/>che uoiue ne ridesti, come che il non &longs;u&longs;&longs;e il uero. </s> <s id="s.002474">Et perche cono&longs;co, che que&longs;to uo&longs;tro <lb/><expan abbr="tõto">tonto</expan> proponere non è altro, che un uoler ta&longs;tarme doue &longs;ia di&longs;armato, ouer mco forte, <lb/>per ilche ho deliberato di non uoler ri&longs;pondere ad alcuna uostra propo&longs;ta fina a tanto <lb/>che uoi uenereti à Venetia per&longs;onalmente, come me promette&longs;ti al partir uo&longs;tro diuo <lb/>ler ritornare à quell'hora, poi ui daro la <expan abbr="re&longs;olutiõe">re&longs;olutione</expan> di quelle, che hauero &longs;aputo &longs;oluere <lb/>& quelle che non hauero &longs;aputo &longs;oluere me le in&longs;ignareti, pagandoue però, non altro. <lb/></s> <s id="s.002475">Iddio da mal ui guardi. </s> <s id="s.002476">In Venetia alli. </s> <s id="s.002477">3. di Marzo.<emph.end type="italics"/> 1537. </s> </p> <p type="main"> <s id="s.002478">N<emph type="italics"/>icolo Tartaglia Bri&longs;ciano.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002479">QVESITO. XXX. FATTO DA MESSER <lb/>H<emph type="italics"/>ieronimo Triui&longs;ano, qual gliera sta fatto a lui <lb/>l'Anno. <!-- REMOVE S-->1537. Adi. <!-- REMOVE S-->25. Ago&longs;to.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.002480">I<emph type="italics"/>n Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <pb pagenum="113" xlink:href="042/01/226.jpg"/> <p type="main"> <s id="s.002481">MESSER HIERONIMO. V<emph type="italics"/>orria me&longs;&longs;er Nicolo caro che me mostra­<lb/>&longs;ti à ri&longs;oluere uno que&longs;ito che mi fu datto hieri da uno mercante qual dice in <lb/>que&longs;ta forma. </s> <s id="s.002482">Doi fanno compagnia, el primo me&longs;&longs;e duc. </s> <s id="s.002483">240. e &longs;tette me&longs;i. </s> <s id="s.002484">9. l'altro <lb/>mi&longs;&longs;e una gioia & &longs;tette me&longs;i. </s> <s id="s.002485">6. & guadagnorono duc. </s> <s id="s.002486">100. a quello della gioia gli toc <lb/>co fra cauedal é guadagno duc. </s> <s id="s.002487">150. domanda quanto ual&longs;e la gioia, cioe quanto la &longs;u <lb/>apprecciata nella compagnia.<emph.end type="italics"/> N. P<emph type="italics"/>er ri&longs;oluere questa domanda bi&longs;ogna poner che <lb/>la gioia uaglia una co&longs;a, & multicarla fia li me&longs;i. </s> <s id="s.002488">6. (che ste nella compagnia el &longs;econ <lb/>do) fara. </s> <s id="s.002489">6 co. </s> <s id="s.002490">poi el &longs;i die multiplicar li duc. </s> <s id="s.002491">240. fia li. </s> <s id="s.002492">9. me&longs;i (che &longs;tete nella compa <lb/>gnia el primo) fara. </s> <s id="s.002493">2160. & que&longs;te due multiplicationi. </s> <s id="s.002494">bi&longs;ogna &longs;umarle in&longs;ieme & <lb/>faranno in &longs;omma. </s> <s id="s.002495">6. co&longs;e piu. </s> <s id="s.002496">2160. Dapoi bi&longs;ogna procedere per la regola del tre <lb/>digando &longs;e. </s> <s id="s.002497">6. co.piu. </s> <s id="s.002498">2160. me guadagnano duc. </s> <s id="s.002499">100. che mi guadagnara. </s> <s id="s.002500">6. co&longs;e ope <lb/>rando &longs;econdo che uol la detta regola &longs;e trouara che guadagnariano. </s> <s id="s.002501">600. co&longs;e e&longs;lmi <lb/>de. </s> <s id="s.002502">2160. piu. </s> <s id="s.002503">6. co&longs;e & que&longs;to rotto &longs;ara equal à ducati. </s> <s id="s.002504">150. men. </s> <s id="s.002505">1. co&longs;a (cioe à quello <lb/>che tocco al <expan abbr="&longs;ecõdo">&longs;econdo</expan> d<gap/> puro guadagno, cioe trattone. </s> <s id="s.002506">1. co&longs;a che fu el &longs;uo capitale) onde <lb/>de leuando el rotto, & &longs;eguitando el capitolo &longs;e trouara la co&longs;a ualer<emph.end type="italics"/> <22>. </s> <s id="s.002507">78025. <emph type="italics"/>men. <lb/></s> <s id="s.002508">155. & tanto ual&longs;e la gioia.<emph.end type="italics"/> M. H. V<emph type="italics"/>e ringratio.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002509">QVESITO XXXI. FATTO DA M. ZVANAN­<lb/><emph type="italics"/>tonio libraro, per nome d'un me&longs;&longs;er Hieronimo Cardano, Medico <lb/>& delle Mathematice lettor publico in Milano, <lb/>adi. </s> <s id="s.002510">2. Genaro.<emph.end type="italics"/> 1539.</s> </p> <p type="main"> <s id="s.002511">ZVANANTONIO. M<emph type="italics"/>e&longs;&longs;er Nicolo el me ha drizzato da uoi un huomo da <lb/>bene Medico da Millano chiamato mi&longs;&longs;er Hieronimo Cardano elquale é un gran <lb/>dißimo Mathematico, & legge publicamente Euclide li in Millano, & al pre&longs;ente fa <lb/><gap/><expan abbr="tãpare">tampare</expan> una &longs;ua oper a in la pratica di Arithmetica & Geometria & in Algebra che <lb/>&longs;ara una bella co&longs;a. </s> <s id="s.002512">Et per che egli ha inte&longs;o uoi e&longs;&longs;er &longs;tato in una di&longs;puta con maestro <lb/>Antoniomaria fiore, & che uoi romane&longs;ti daccordo di proponere. </s> <s id="s.002513">30. ca&longs;i, ouer que <lb/>&longs;tioni, per uno, & che co&longs;i face&longs;ti, & &longs;ua eccellentia ha inte&longs;o che il detto maestro An­<lb/>toniomaria, ui propo&longs;e tutti li &longs;uoi. </s> <s id="s.002514">30. che ui conduceuano in Algebra in un capito­<lb/>lo di co&longs;a è cubo equal à numero. </s> <s id="s.002515">Et che uoi troua&longs;ti regola generale à tal capitolo, <lb/>& per uigore di tal uo&longs;tra inuentione uoi ri&longs;olue&longs;ti tutti li detti. </s> <s id="s.002516">30. ca&longs;i à uoi propo­<lb/>&longs;ti in termine de due hore. </s> <s id="s.002517">Et per tanto &longs;ua eccellentia ui prega che uoi gli uogliati <lb/>mandare di gratia tal regola da uoi trouata, & s'el ui pare lui la dara fora in la pre­<lb/>&longs;ente &longs;ua opera &longs;otto uostro nome, & &longs;e anchor el non ui pare, che lui la dia fora, la te­<lb/>nera&longs;ecreta.<emph.end type="italics"/> N. D<emph type="italics"/>iceti à &longs;ua eccellentia, che quella mi perdona, che quando uoro pu <lb/>blicar tal mia inuentione la uoro publicar in opere mie, & non in opere de altri, &longs;i che <lb/>&longs;ua eccellentia mi habbia per i&longs;cu&longs;o.<emph.end type="italics"/> Z. N<emph type="italics"/>on uolendoli dar tal uo&longs;tra inuentione &longs;ua <lb/>eccellentia mi ha or dinato che uiprega che gli uogliati almen dar li detti. </s> <s id="s.002518">30. ca&longs;i che <lb/>lui ui propo&longs;e, con la uo&longs;tra re&longs;olutione, & &longs;ime <expan abbr="lm&etilde;te">lmente</expan> li uo&longs;tri. </s> <s id="s.002519">30. che gli proponefti <lb/>a lui.<emph.end type="italics"/> N. M<emph type="italics"/>anco questo &longs;arin perche ogni uolta che lui haue&longs;&longs;e uno de detti ca&longs;t con <lb/>la &longs;ua &longs;olutione &longs;ubito &longs;ua eccellentia intendaria la regola da me rnrouata con laquale<emph.end type="italics"/><pb xlink:href="042/01/227.jpg"/><emph type="italics"/>molte altre regole &longs;e potria ritrouare, &longs;opra à tal materie.<emph.end type="italics"/> Z. S<emph type="italics"/>ua eccellentia mi ha <lb/>dato. </s> <s id="s.002520">8. que&longs;tioni, ouer que&longs;iti da darue pregandoui che ge li uogliati ri&longs;oluere liquai <lb/>que&longs;iti &longs;ono que&longs;ti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002521">P<emph type="italics"/>artime diece in quatro parti continue proportionale che la prima, &longs;ia.<emph.end type="italics"/> 2. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002522">P<emph type="italics"/>artime diece in. </s> <s id="s.002523">4. parti continue proportionale che la &longs;econda parte &longs;la.<emph.end type="italics"/> 2. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002524">T<emph type="italics"/>rouatime. <!-- KEEP S--></s> <s id="s.002525">4. numeri continui proportionali che il primo &longs;ia. </s> <s id="s.002526">2. & el &longs;econdo é. </s> <s id="s.002527">4. <lb/>gionti in&longs;ieme faciano.<emph.end type="italics"/> 10. </s> </p> <p type="main"> <s id="s.002528">T<emph type="italics"/>rouatime. <!-- KEEP S--></s> <s id="s.002529">4. numeri continui proportionali ch'el primo &longs;ia. </s> <s id="s.002530">2. & il terzo è quarto <lb/>gionti in&longs;iema facciano.<emph.end type="italics"/> 10. </s> </p> <p type="main"> <s id="s.002531">T<emph type="italics"/>rouatime. <!-- KEEP S--></s> <s id="s.002532">4. quantita continue proportionale che la &longs;econda &longs;ia. </s> <s id="s.002533">2. & la prima & <lb/>quarta gionte in&longs;ieme facciano.<emph.end type="italics"/> 10. </s> </p> <p type="main"> <s id="s.002534">F<emph type="italics"/>atime de. </s> <s id="s.002535">10. tre parti continue proportionale che multiplicata la prima nella &longs;econ <lb/>da facia.<emph.end type="italics"/> 8. </s> </p> <p type="main"> <s id="s.002536">T<emph type="italics"/>rouatime uno numero che multiplicato nella &longs;ua radice piu. </s> <s id="s.002537">3. facia.<emph.end type="italics"/> 21. </s> </p> <p type="main"> <s id="s.002538">NICOLO. Q<emph type="italics"/>ue&longs;ti que&longs;iti &longs;ono de me&longs;&longs;er Zuanne da Coi. <!-- KEEP S--></s> <s id="s.002539">Et <expan abbr="nõ">non</expan> d'altri, perche li co­<lb/>no&longs;co à que&longs;te due ultime perche una &longs;imile à que&longs;ta &longs;esta mi mando gia fa dui anni et <lb/>tal ragione gli feci confe&longs;&longs;are che lui mede&longs;imo non la intendeua ne la &longs;apeua ri&longs;olue­<lb/>re & una &longs;imile à que&longs;ta ultima (quale induce l'oper ante in cen&longs;o è cubo equal à nume <lb/>ro) glidei per gentilezza a&longs;&longs;olta non è anchora un'annno, & pertal &longs;olutione trouo <lb/>una regola particolare &longs;opra &longs;imili que&longs;iti. </s> <s id="s.002540">z. <!-- KEEP S--></s> <s id="s.002541">Io &longs;o ben mi che que&longs;ti que&longs;iti el me li <lb/>ba dati la detta eccellentia de me&longs;&longs;er Hieronimo Cardano & non altro.<emph.end type="italics"/> N. A<emph type="italics"/>dun­<lb/>que il detto me&longs;&longs;er zuanne da Coi debbe e&longs;&longs;er uenuto à Millano & ge li ha propo&longs;ti à <lb/>&longs;ua eccellentia & quella per non &longs;aperli ri&longs;oluere melli ha mandati da ri&longs;oluere à me <lb/>& <27>&longs;to tengo per certo <21>che il detto me&longs;&longs;er <expan abbr="zuãne">zuanne</expan> me promi&longs;&longs;e gia fa un'anno da uo­<lb/>ler uenire à &longs;tar qua à Venetia, & tamen il non ui é mai uenuto, e pero credo chel &longs;i &longs;ia <lb/><expan abbr="p&etilde;tito">pentito</expan> da uenir à Venetia, & ch'el &longs;e &longs;ia uoltato alla uolta de Millano.<emph.end type="italics"/> z. <!-- KEEP S--></s> <s id="s.002542">N<emph type="italics"/><expan abbr="õ">om</expan> <expan abbr="p&etilde;&longs;ati">pen&longs;ati</expan> <lb/>che &longs;ua <expan abbr="eccell&etilde;tia">eccellentia</expan> ui manda&longs;&longs;e que&longs;te que&longs;tioni &longs;e la non li <expan abbr="int&etilde;de&longs;&longs;e">intende&longs;&longs;e</expan>, et &longs;ape&longs;&longs;e ri&longs;oluere <lb/>ouer che fu&longs;&longs;ero de altra per&longs;ona, perche &longs;ua eccellentia é di primi di Millano di dot­<lb/>trina, & il Marche&longs;e dal Va&longs;to gliha dato una gran proui&longs;ione per la &longs;ua &longs;ufficien­<lb/>tia.<emph.end type="italics"/> N. N<emph type="italics"/>on nego che &longs;ua eccellentia non &longs;ia per&longs;ona dottißima, & &longs;ufficientißima. <lb/></s> <s id="s.002543">Ma ben dico che quella non &longs;apera ri&longs;oluere que&longs;ti. </s> <s id="s.002544">7. que&longs;iti ch'ella mi ha mandato à <lb/>me dari&longs;oluere con regole generale. </s> <s id="s.002545">Perche &longs;e &longs;ua eccellentia non &longs;a ri&longs;oluere quel­<lb/>lo di co&longs;a, é cubo equal à numero (che me haueti ricercato con tante preghere) come <lb/>&longs;aprala ri&longs;oluere la maggior parte di que&longs;tiliquali conducano l'operante in molto piu <lb/>&longs;tranie &longs;orte de capitoli di quello di co&longs;a, e cubo equal à numero, e pero &longs;e quella &longs;ape&longs;­<lb/>&longs;e ri&longs;oluere tutti que&longs;ti, molto piu facilmente &longs;aperia anchora ri&longs;oluere quello di co&longs;a <lb/>è cubo equal à numero, & &longs;apendolo ri&longs;oluere &longs;on certo che la non lo and aria <expan abbr="m&etilde;dican">mendican</expan> <lb/>dolo ne <expan abbr="cercãdolo">cercandolo</expan>. </s> <s id="s.002546">z. <!-- KEEP S--></s> <s id="s.002547">Io <expan abbr="nõ">non</expan> &longs;o che <expan abbr="ri&longs;põderui">ri&longs;ponderui</expan> perche <expan abbr="nõ">non</expan> me <expan abbr="int&etilde;do">intendo</expan> di que&longs;te co&longs;e, ma <lb/><expan abbr="quãdo">quando</expan> che parla&longs;ti <expan abbr="cõ">com</expan> lui credo che ui &longs;apria <expan abbr="ri&longs;põdere">ri&longs;pondere</expan>, ma la&longs;&longs;amo andar tutte que&longs;te <lb/>co&longs;e, accioche <expan abbr="nõ">non</expan> &longs;ia uenuto in darno datime <expan abbr="alm&etilde;">almen</expan> la coppia delli&longs;implici. </s> <s id="s.002548">30. ca&longs;i che <lb/>il detto mae&longs;tro Antonio Maria fior ui propo&longs;&longs;e à uoi et &longs;e pote&longs;ti anchora darmi la <lb/>coppia di uostri. </s> <s id="s.002549">30. che uoi prepone&longs;ti à lui me fare&longs;ti &longs;ummo appiacer.<emph.end type="italics"/>N. D<emph type="italics"/>elli &longs;uoi<emph.end type="italics"/><pb pagenum="114" xlink:href="042/01/228.jpg"/><emph type="italics"/>anchor che habbia care&longs;tia del tempo) ue ne daro coppia, ma delli mei, non ue la po&longs;&longs;o <lb/>dar perche io non ho coppia alcuna appre&longs;&longs;o di me ne <expan abbr="mãco">manco</expan> me li aricordo co&longs;i preci­<lb/>&longs;e tutti perche erano tutti uarii, ma &longs;e andati dal notaro lui ue ne potra dar coppia.<emph.end type="italics"/><lb/>Z. M<emph type="italics"/>or&longs;u datime li &longs;uoi.<emph.end type="italics"/> N. S<emph type="italics"/>ono questi preci&longs;e come che luile &longs;cri&longs;&longs;e.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002550">L<emph type="italics"/>aus deo. </s> <s id="s.002551">1534. adi. </s> <s id="s.002552">22. Febraro in Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.002553">Q<emph type="italics"/>ue&longs;te &longs;ono le. </s> <s id="s.002554">30. ra&longs;one propo&longs;te per mi Antoniomaria <lb/>fior à uoi Mae&longs;tro Nicolo Tartaglia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002555">1 T<emph type="italics"/>rouame uno numero che azontoli la &longs;ua radice cuba uenghi &longs;ie, cioe.<emph.end type="italics"/> 6. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002556">2 T<emph type="italics"/>rouame. </s> <s id="s.002557">2. numeri in dupla proportione che il quadrato del mazor numero mul <lb/>tiplicato, per el menore, & à quella multiplicatione zontoli li. </s> <s id="s.002558">2. primi numeri <lb/>uenga quaranta, cioe.<emph.end type="italics"/> 40. </s> </p> <p type="main"> <s id="s.002559">3 T<emph type="italics"/>rouame uno numero che cubiccato, & &longs;opra quella cubicatione azontoli el det­<lb/>to numero uenghi cinque.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002560">4 T<emph type="italics"/>rouatime. <!-- KEEP S--></s> <s id="s.002561">3. numeri in tripla proportione chel quadrato del menore multiplica <lb/>to per el numero mazore & a quella multiplicatione azontoli el numero mezza­<lb/>no uenghi &longs;ette.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002562">5 D<emph type="italics"/>oi huomini fanno compagnia, & die mettere de cauedal tra tutti duoi ducati no­<lb/>uecento con que&longs;ta conditione che uno metta la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del altro domandando che <lb/>die mettere cadauno in detta compagnia.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002563">6 D<emph type="italics"/>oi huomini hanno guadagnato ducati cento, & die partire ditto uadagno in que­<lb/>&longs;ta forma, che luno dieba hauere la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del altro, domando che tocca per uno de <lb/>ditto guadagno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002564">7 T<emph type="italics"/>rouame un numero che azontolile due &longs;ue<emph.end type="italics"/> <22>. <emph type="italics"/>cube uenghi trede&longs;e.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002565">8 T<emph type="italics"/>rouame un numero che azontolile tre &longs;ue<emph.end type="italics"/> <22>. <emph type="italics"/>cube uenghi quinde&longs;e.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002566">9 T<emph type="italics"/>rouame un numero che azontoli le &longs;ue quatro<emph.end type="italics"/> <22>. <emph type="italics"/>cube uenga di&longs;ette.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002567">10 F<emph type="italics"/>ame de. </s> <s id="s.002568">14. doi parti che luna parte fia la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de l'altra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002569">11 F<emph type="italics"/>ame de. </s> <s id="s.002570">20. doital parte che una parte &longs;ia la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de laltra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002571">12 V<emph type="italics"/>no zoielero uende due zoie per duc.mille & nouecento zoe uno diamante, et uno <lb/>rebino, et lo robino, fu <expan abbr="u&etilde;duto">uenduto</expan> la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.002572">del diamente, <expan abbr="domãdo">domando</expan> che ual&longs;e el robino.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002573">13 V<emph type="italics"/>no zudio impresta à uno dinari non &longs;o quanti con que&longs;ta conditione che in capo <lb/>de uno anno li debba dar de u&longs;ura la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del &longs;uo capitale in capo de l'anno haue <lb/>il zudio fra capital è guadagno ducati ottocento domando quanto fuel capital del <lb/>zudio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002574">14 F<emph type="italics"/>ame de. </s> <s id="s.002575">13. due parte che <expan abbr="tãto">tanto</expan> fazza à multiplicare una parte per laltra, come fa <lb/>ra el quadrato della menore multiplicato in &longs;e mede&longs;imo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002576">15 V<emph type="italics"/>no uende uno Safil per ducati. </s> <s id="s.002577">500. & ha guadagnato la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del &longs;uo capitale <lb/>domando quanto fu el guadagno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002578">16 E<emph type="italics"/>glie uno riangolo orthogonio.a.b.c.la linea.a.b.& la linea.b.c.zonte in&longs;ieme <lb/>&longs;ono brazza&longs;eite & la linea.a.b.é<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de.b.c.domando la linea.a.c.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/229.jpg"/> <figure id="id.042.01.229.1.jpg" xlink:href="042/01/229/1.jpg"/> <p type="main"> <s id="s.002579">17 E<emph type="italics"/>glie uno arboro alto &longs;opra terra brazza. </s> <s id="s.002580">12. il quale le rompete in dui pezzi iu <lb/>tal luogo che quello che rima&longs;e in pie fu la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba di quello fu &longs;egato uia, doman­<lb/>do quanto fu quello pezzo, che rima&longs;e in pie.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002581">18 E<emph type="italics"/>glie una linea longa brazza. </s> <s id="s.002582">9 la qual uoglio diuidere in due parti ineguale in tal <lb/>luoco, che la linea menore fia la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba della maggiore, domando la quantita del­<lb/>le parte menore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002583">19 S<emph type="italics"/>ono dui triangoli equilateri, che le loro &longs;uper ficie gionte in&longs;ieme &longs;ono brazza. </s> <s id="s.002584">25. <lb/>& la menore è la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba della maggiore, domando la &longs;uperficie del menore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002585">20 S<emph type="italics"/>ono dui quadrati che le lor &longs;uperficie gionte in&longs;teme &longs;ono. </s> <s id="s.002586">26. e la menore &longs;uper­<lb/>ficie è<emph.end type="italics"/> <22>. <emph type="italics"/>cuba della maggiore, domando la &longs;uperficie del maggiore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002587">21 S<emph type="italics"/>ono dui penthagoni equilateri, che le loro &longs;uperficie gionte in&longs;ieme &longs;ono brazza. <lb/></s> <s id="s.002588">28. la menore è la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba della maggiore, domando la &longs;uperficie menore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002589">22 S<emph type="italics"/>ono dui e&longs;&longs;agoni equilateri che le loro &longs;uperficie gionte in&longs;ieme &longs;ono brazza. </s> <s id="s.002590">27. <lb/>& lo e&longs;&longs;agono menore è la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del maggiore, <expan abbr="domãdo">domando</expan> la &longs;uperficie del menore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002591">23 S<emph type="italics"/>ono dui ottagoni equilateri che le lor &longs;uperficie gionte in&longs;ieme &longs;ono brazza. </s> <s id="s.002592">29. <lb/>la menor è la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba della maggior, domando quanto è la&longs;uperfioie maggior.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002593">24 S<emph type="italics"/>ono dui triangoli equilateri, che li loro cateti gionti in&longs;ieme &longs;ono brazza. </s> <s id="s.002594">34. il <lb/>cateto menore é la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del maggiore, domando il cateto menore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002595">25 S<emph type="italics"/>ono dui triangoli equilateri, che le loro fazze gionte in&longs;ieme &longs;ono brazza. </s> <s id="s.002596">12. la <lb/>fazza menore è la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba della maggior, <expan abbr="domãdo">domando</expan> la fazza del triangolo maggiore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002597">26 S<emph type="italics"/>ono dui corpi cubi che la loro Aree &longs;ono in tutto brazza cento, & la area cor­<lb/>poral del menor è<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del maggior, domando l'area menor.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002598">27 S<emph type="italics"/>ono dui corpi de quattro ba&longs;e triangolari che le loro aree corporale &longs;ono braz­<lb/>za. </s> <s id="s.002599">140. l'area corporal del menor è<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del maggior, domando l'area del <lb/>maggior.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002600">28 S<emph type="italics"/>ono dui corpi de otto ba&longs;e triangolari equilateri che le loro aree corporale &longs;ono <lb/>brazza. </s> <s id="s.002601">300. & l'area corporal del menore è<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del maggior, domando l'a­<lb/>rea menor.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002602">29 S<emph type="italics"/>ono dui corpi de. </s> <s id="s.002603">12. ba&longs;e penthagonale che le loro aree corporale gionte in&longs;ieme <lb/>&longs;ono brazza. </s> <s id="s.002604">810. l'area corporal del menore è<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del maggior, domando l'a­<lb/>rea maggior.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002605">30 S<emph type="italics"/>ono dui corpi de. </s> <s id="s.002606">20. ba&longs;e triangolare che le loro aree corporal gionte in&longs;ieme &longs;o <lb/>no brazza. </s> <s id="s.002607">700. & l'area del menor è<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del maggior, <expan abbr="domãdo">domando</expan> l'area menor. <lb/></s> <s id="s.002608">Io Antoniomaria Fior del.q.maestro Pelegrino &longs;cri&longs;&longs;e.<emph.end type="italics"/></s> </p> <pb pagenum="115" xlink:href="042/01/230.jpg"/> <p type="main"> <s id="s.002609">H<emph type="italics"/>or que&longs;ti &longs;ono li delti. </s> <s id="s.002610">30. ca&longs;i che mi propo&longs;e el detto mae&longs;tro Antoniomaria fior. </s> <s id="s.002611">li <lb/>quali tutti conducono l'operante in el capitolo de co&longs;a é cubo el qual capitolo per ha <lb/>uerui trouato circa giorni. </s> <s id="s.002612">8. auanti la regola generale che uoi me ricercati. </s> <s id="s.002613">Io li re­<lb/>&longs;ol&longs;i tutti. </s> <s id="s.002614">30. in cermine de hore due &longs;i che toleti que&longs;ta coppia.<emph.end type="italics"/> Z. V<emph type="italics"/>e ringratio <gap/><lb/>recomando.<emph.end type="italics"/> N. A<emph type="italics"/>ndati in bon'hora.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002615">QVESITO XXXII. FATTO CON VNA LET­<lb/><emph type="italics"/>tera dalla eccellentia de me&longs;&longs;er Hieronimo Cardano l'anno <lb/>1539. adi. </s> <s id="s.002616">12. Febraro.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002617">MISSER HIERONIMO. M<emph type="italics"/>imar auiglio molto Me&longs;&longs;er Nicolo caro de &longs;i <lb/>di&longs;conueneuole ri&longs;po&longs;ta haueti data à uno Zuanantonio da Ba&longs;&longs;ano libraro el qua <lb/>le da mia parte ui ha pregato li uole&longs;ti dare la ri&longs;po&longs;ta di &longs;ette, ouer otto <27>&longs;tioni le qua­<lb/>le ui mandai, & la coppia delle propo&longs;te fatte trauoi & mae&longs;tro Antoniomaria fior <lb/>con le &longs;ue &longs;olutioni alle quale non ui è ba&longs;tato di non mandarmene niuna&longs;aluo che quelle <lb/>de mae&longs;tro Antoniomaria lequale &longs;ono. </s> <s id="s.002618">30. propo&longs;te ma reuera qua&longs;t una &longs;ola &longs;ostan­<lb/>tia, cioe cubo è co&longs;a equal à numero, pero mi doglio tra l'altre di&longs;gratie di que&longs;ta arte <lb/>che quelli li danno opera&longs;ono tanto di&longs;corte&longs;i è tanto pre&longs;umeno di &longs;e &longs;te&longs;&longs;o, che non <lb/>&longs;enza cagion &longs;ono iudicati dal uulgo apre&longs;&longs;o che pazzi à cio ui caui for a de que&longs;ta <lb/>fanta&longs;ta della quale cauai nouamente me&longs;&longs;er zuanne da Coi, cioe d'e&longs;&longs;ere il primo ho­<lb/>mo del mondo donde &longs;e partito da Millano per di&longs;perato, ue uoglio &longs;criuere amo­<lb/>reuolmente & trarui fori di fanta&longs;ia che uoi ui crediati e&longs;&longs;ere &longs;i grande ui faro co­<lb/>no&longs;cere con amoreuole admonitioni per le uo&longs;tre parole mede&longs;ime che &longs;eti piu apre&longs;&longs;o <lb/>a la ualle che alla &longs;umita del monte, potria ben e&longs;&longs;ere che in altra co&longs;a fo&longs;ti piu e&longs;er­<lb/>citato, & ualente che non dimo&longs;trati per la ri&longs;po&longs;ta & prima ui aui&longs;o pero che io ue <lb/>ho hauuto in bon conto & &longs;ubito ariuo li uo&longs;tri libri &longs;oprale artegliarie ne <expan abbr="cõprai">comprai</expan> dui <lb/>che &longs;olo porto zuanantonio delli quali uno ne dette al Signor Marche&longs;e, & l'altro ten <lb/>ne per mi, & oltra cio ui laudai molto al Signor Marche&longs;e pen&longs;ando fosti piu gen­<lb/>til recono&longs;citore, & piu humano, & piu corte&longs;e, & piu &longs;ufficiente de Me&longs;&longs;er zuan­<lb/>ne qual uoi allegati, ma mi pare poca differentia da luno à laltro &longs;e altro non mo­<lb/>strati hora peruenire a fatti ue accu&longs;o in quatro co&longs;e de momento. </s> <s id="s.002619">La prima è <lb/>che uoi diceti che le mie interrogatione non e&longs;&longs;er mie ma de me&longs;&longs;er zuanne Colle qua­<lb/>&longs;i uolendo dire che <expan abbr="nõ">non</expan> &longs;ia huomo in Millano che &longs;ape&longs;&longs;e fare tale interrogatione, me&longs;&longs;er <lb/>mio li ualentomini <expan abbr="nõ">non</expan> &longs;i cono&longs;cono a le propo&longs;te come uoi pen&longs;ati, ma alle ri&longs;po&longs;te pero <lb/>peecati di pro&longs;umptione grauißima, ce &longs;ono in Millano molti che le &longs;anno, et io le &longs;ape <lb/>ua auanti che me&longs;&longs;er <expan abbr="zuãne">zuanne</expan> &longs;ape&longs;&longs;e numerare &longs;in à. </s> <s id="s.002620">10. &longs;e lui è co&longs;i giouine come &longs;i fa. <lb/></s> <s id="s.002621">La <expan abbr="&longs;ecõda">&longs;econda</expan> è che uoi haueti detto al libraro che &longs;olta una delle que&longs;tioni de maestro An <lb/>toniomaria &longs;ariano &longs;olte tutte le mie, ui domando di gratia <expan abbr="cõ">com</expan> che credetì parlare con <lb/>li uo&longs;tri &longs;colari, ouer con huomini, doue troua&longs;ti uoimai che la inuentione de la radi­<lb/>ce pronicamedia, la qual è il fondamento de la &longs;olutione de tutte le. </s> <s id="s.002622">30. que&longs;tioni de <lb/>mae&longs;tro Antoniomaria, laqual è fondata &longs;opra l'ottaua del &longs;e&longs;to di Euclide poßi e&longs;&longs;ere <lb/>la re&longs;ulutione duna que&longs;tione di cubo è numero equal à <expan abbr="c&etilde;&longs;o">cen&longs;o</expan> fopra elqual capitolo &longs;i fon <pb xlink:href="042/01/231.jpg"/>da la propo&longs;ta, che dice. </s> <s id="s.002623">Trouami quattro quantita continue proportionale, che la &longs;eo <lb/>conda &longs;ia. </s> <s id="s.002624">2. & che la prima, e quarta gionte in&longs;ieme &longs;acciano. </s> <s id="s.002625">10. co&longs;i dico delle al­<lb/>tre, &longs;i che mentre&longs;eti uoluto dimo&longs;tr arui mir acolo&longs;o nell'arte uo&longs;tra con un libraro, ui <lb/>&longs;eti dimostrato un grande ignorante appre&longs;&longs;o à quelli, che intendono, ne pero per que <lb/>&longs;to ui e&longs;istimo ignorante, ma troppo pro&longs;ontuo&longs;o, come ch'era me&longs;&longs;er Zuane da Coi, <lb/>qual pen&longs;ando di far credere che il &longs;ape&longs;&longs;e quello, che il non &longs;apeua, fece credere, che il <lb/>non &longs;ape&longs;&longs;e quello, che il &longs;apeua.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002626">L<emph type="italics"/>a terza è, che uoi haueti detto al libraro, che &longs;olta una delle mie que&longs;tioni &longs;ono <lb/>&longs;olte tutte, la qual co&longs;a è fal&longs;ißima, & è una ingiuria coperta de dire, che pen&longs;ando man <lb/>darui. </s> <s id="s.002627">7. questioni ue ne habbia mandato una, ilche arguirebbe in me un gran tra&longs;cor­<lb/>&longs;o di mente, e certo s'io fu&longs;&longs;e dell'arte io uorrei deponere. </s> <s id="s.002628">100. &longs;cudi &longs;opra que&longs;to pa&longs;­<lb/>&longs;o, cioe che non &longs;i ponno redurre, ne in una, ne in due, ne in tre que&longs;tioni, & pur quando <lb/>li uole&longs;ti mettere, to non li rifiutaria, et ueniro à Venetia à posta, e daro &longs;icurta de ban <lb/>co qua de accettare, &longs;e uoi uoleti uenir qua, ouer datila uoi la in Venetia ch'io ueniro, <lb/>ne per que&longs;to fo la profeßione, pen&longs;ati che fareti con quelli, che la fanno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002629">L<emph type="italics"/>a quarta è uno errore troppo manife&longs;to nel uo&longs;tro libro, detto &longs;cientia nuoua de <lb/>artegliarie, nel qual uoleti alla quinta propo&longs;itione del primo, che niuno corpo egual­<lb/>mente graue poßi and are per alcuno &longs;pacio di tempo, ouer di luoco di moto naturale, <lb/>& uiolente in&longs;ieme mi&longs;to, la quale è fal&longs;ißima, & contra ogni ragione, & i&longs;perientia <lb/>naturale. </s> <s id="s.002630">Il uo&longs;tro fondamento con che lo prouati è piu &longs;torno a&longs;&longs;ai, che non è la ri&longs;po <lb/>sta, che haueti data al libraro, non &longs;apeti uoi che il non è inconueniente nel di&longs;cendere <lb/>una co&longs;a &longs;i moua piu uelocemente, & nel procedere uadi piu tardo, &longs;i come uedemo nel <lb/>la i&longs;pertentia nel trare d'una pietra, la quale, come piu de&longs;cende, piu uiene ueloce à ter <lb/>ra, e pur procedendo ua piu tardo, dalla qual conclu&longs;ione faceti na&longs;cere altre ragioni, <lb/>molto strane in detto libro, &longs;i che pen&longs;ati bene, che gli huomini da bene non &longs;ono al ri­<lb/>prendere &longs;i facili. </s> <s id="s.002631">Ch'io ue ho hauuto per i&longs;cu&longs;ato in uolerui riprendere, perche trat­<lb/>tando de artegliaria, ch'era poco uo&longs;tro me&longs;tiero, ue &longs;iti pero ingegnato di dire qual­<lb/>che bella co&longs;a, ma accio non pen&longs;ati, che &longs;ia &longs;imile à uoi, & à me&longs;&longs;er Zuan Colle ui man <lb/>do due que&longs;tioni con le &longs;ue &longs;olutioni, ma le &longs;olutioni &longs;aranno &longs;eparate dalle que&longs;tioni, & <lb/>il me&longs;&longs;o le portara &longs;eco, & &longs;e uoi non le &longs;apreti &longs;oluere lui ue dara &longs;ubito hauendola, <lb/>pero &longs;ieco à una, à una, accio non crediate l'habbia mandate per impararle, & non <lb/>per donaruele, ma ritorra prima le uo&longs;tre in drieto, accio non gli da&longs;e&longs;ti intendere ha­<lb/>uerle &longs;olte, & non le haue&longs;ti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002632">O<emph type="italics"/>ltra di cio dignareteui di mandarme le propo&longs;te fatte per uoi à mae&longs;tro Antonio <lb/>maria Fior, & &longs;e non uoleti mandar le &longs;olutioni, tenetile per uoi, poi che ne &longs;eti co&longs;i ca <lb/>restio&longs;o, & &longs;e il ui piace riceuendo le &longs;olutioni delle dette mie questioni, &longs;enza che uoi <lb/>le &longs;appiati &longs;oluere, dapoi che &longs;eti chiaro le mie &longs;ette que&longs;tioni e&longs;&longs;er diuer&longs;e, mandar­<lb/>mene la &longs;olutione di qualche una di loro mi fareti &longs;ingolarißimo appiacer, piu per la <lb/>amicitia, & per cono&longs;cere il uostro grande ingegno, che per altro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002633">L<emph type="italics"/>a prima questione feme de. </s> <s id="s.002634">10. quattro quantita continue proportionale, che li <lb/>loro quadrati gionti in&longs;ieme facciano. </s> <s id="s.002635">60. una &longs;imile pone Frate Luca, ma non <lb/>la &longs;olue.<emph.end type="italics"/></s> </p> <pb pagenum="116" xlink:href="042/01/232.jpg"/> <p type="main"> <s id="s.002636">L<emph type="italics"/>a &longs;econda, duifeceno compagnia, & po&longs;&longs;eno non &longs;o quanti ducati, & guadagnor­<lb/>no il cubo dellà decima parte del &longs;uo capitale, & &longs;e haue&longs;&longs;ero guadagnato. </s> <s id="s.002637">3. meno di <lb/>quello che guadagnorno haueriano guadagnato tanto quanto fuil &longs;uo capitale aponto <lb/>&longs;e domanda il &longs;uo capital è guadagno, non altro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002638">H<emph type="italics"/>ieronimo Cardano Medico.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002639">NICOLO. E<emph type="italics"/>ccellentißimo me&longs;&longs;er Hieronimo ho riceuuto una uo&longs;tra, nella quale <lb/>dite che molto ue mar auigliati de &longs;i di&longs;conueneuole ri&longs;po&longs;ta per me data à une Zuanan <lb/>tonio da Ba&longs;&longs;ano Libraro, per hauergli negato di dare la maggior parte di quello mi <lb/>richiedeua da parte di uo&longs;tra Eccellentia, per ilche quella u&longs;a de molte braue, arro­<lb/>gante, & ingiurio&longs;e parole, che à uolerle replicare, & ri&longs;pondere à una per una, <lb/>ui andaria da &longs;criuere a&longs;&longs;ai, fra le quale uoi dite, che me accu&longs;ate in quattro co&longs;e <lb/>di momento.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002640">L<emph type="italics"/>a prima è, che uoi diceti, che io ho detto al libraro, che quelle &longs;ette interrogatio­<lb/>ni à me mandate non e&longs;&longs;er uo&longs;tre, ma d'un me&longs;&longs;er Zuane da Coi, qua&longs;i uolendo dire, che <lb/>il non &longs;ia huomo in Millano, che &longs;ape&longs;&longs;e &longs;oluere tale interrogationi, con cio che &longs;ugue. <lb/></s> <s id="s.002641">Circa à que&longs;ta uo&longs;tra prima accu&longs;a ui ri&longs;pondo, & dico, che eglie il uero, che io ho det <lb/>to, che tale que&longs;tioni erano di me&longs;&longs;er Zuane da Coi, perche gia fa un'anno è meggio à <lb/>me, me ne propo&longs;e una &longs;imile alla penultima di quella (ma &longs;otto altre parole) la quale à <lb/>lui mede&longs;imo gli feciconfe&longs;&longs;are qua in Venetia, che non la intendeua, & non la &longs;apeua <lb/>ri&longs;oluere, &longs;i che per tal ragione, & altri inditij giudicai tale questioni e&longs;&longs;er &longs;ue, et che <lb/>lui proprio me le manda&longs;&longs;e &longs;otto nome uo&longs;tro, ma quando che il libraro me acerto ha­<lb/>uerle hauute da uo&longs;tra Eccellentia, giudicai che il detto me&longs;&longs;er Zuane da Coi fu&longs;&longs;e ue­<lb/>nuto à Millano, & che gli haue&longs;&longs;e proposte à quella (come che anchor giudico, & ten <lb/>go per fermo) & che quella per non &longs;aperle ri&longs;oluere me le habbia mandate dari&longs;ol­<lb/>uere à me per le ragioni, che di &longs;otto &longs;e dira.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002642">S<emph type="italics"/>econdariamente quella dice, che mi accu&longs;a, che ho detto al detto libraro, che &longs;olta <lb/>una delle que&longs;tioni di<emph.end type="italics"/> M. A<emph type="italics"/>ntoniomaria &longs;ariano &longs;olte tutte le uo&longs;tre. </s> <s id="s.002643">7. à me mandate.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002644">T<emph type="italics"/>ertio quella dice, che mi accu&longs;a anchora, che io ho detto al &longs;opradetto libraro, che <lb/>a&longs;&longs;olta una delle uo&longs;tre. </s> <s id="s.002645">7. que&longs;tioni à me mandate, &longs;ariano ri&longs;olte tutte, & &longs;eguitando <lb/>dite, che que&longs;ta è una co&longs;a fal&longs;ißima, & che &longs;opra à que&longs;to pa&longs;&longs;o uoleti deponere. </s> <s id="s.002646">100. <lb/>&longs;cudi, cioe che tale. </s> <s id="s.002647">7. que&longs;tioni non &longs;i ponno ridurre ne in una, ne in due, ne in tre que­<lb/>&longs;tioni, & quando che mi pare&longs;&longs;e di uoler deponere gli detti. </s> <s id="s.002648">100. &longs;cudi &longs;opra à que&longs;to <lb/>pa&longs;&longs;o, che quella uenira à Venetia à posta, & chi quella dara &longs;icurta de banco la in Mil <lb/>lano uolendo io uenia la à Millano di accettare, oueramente che io debbia dare la detta <lb/>&longs;icurta qua in Venetia, che quella uenira qua à Venetia, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002649">E<emph type="italics"/>t per tanto circa à que&longs;ta uo&longs;tra &longs;econda, & terza accu&longs;a ue ri&longs;pondo, & dico, <lb/>che credo che uoi ue habbiati in&longs;oniato que&longs;te uostre zance. </s> <s id="s.002650">Eglie ben uero, che io ho <lb/>detto al detto libraro, che uo&longs;tra Eccellentia non &longs;aperia ri&longs;oluere le dette. </s> <s id="s.002651">7. que­<lb/>stioni à me mandate con regole generale, & accio che il non pare&longs;&longs;e, che io dice&longs;&longs;e tal <lb/>co&longs;a &longs;enza qualche ragione, gli di&longs;&longs;e, che &longs;e quella non &longs;a ri&longs;oluere il capitolo de co&longs;a è <lb/>cubo egual à numero (qual me ricercati con tanta i&longs;tantia) manco &longs;apereti ri&longs;oluere <lb/>quelle uo&longs;tre. </s> <s id="s.002652">7. à me mandate, le quale conducano l'operante in piu &longs;tranie equationi, <pb xlink:href="042/01/233.jpg"/>ouer capitoli di quello di co&longs;a, e cubo egual à numero. </s> <s id="s.002653">Et che &longs;e pur quella li &longs;ape&longs;&longs;e ri­<lb/>&longs;oluere, che molto piu facilmente &longs;oluere&longs;ti il capitolo di co&longs;a è cubo egual à numero, <lb/>& que&longs;to è quanto che ho detto al libraro. </s> <s id="s.002654">Ma per quanto po&longs;&longs;o con&longs;iderare uo&longs;tra Ec <lb/>cellentia molto de&longs;idera di far cono&longs;cere con meco la &longs;ua &longs;officientia, ilche e&longs;&longs;endo, &longs;e io <lb/>fu&longs;&longs;e ben certo di re&longs;tar perdente, non uoglio rifiutare tal inuito, cioe di deponere cir­<lb/>ca cio li detti ducati. </s> <s id="s.002655">100. & ueniro per&longs;onalmente per fina à Millano, &longs;e quella non <lb/>uorra uenire à Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002656">Q<emph type="italics"/>uarto quella dice, che mi accu&longs;a d'uno errore fra glialtritroppo manifesto, nel <lb/>mio libro, detto nuoua &longs;cientia, nella quinta propo&longs;itione del primo libro, perche in <lb/>quella conchiudo, che niun corpo egualmente graue, poßi andare per alcuno &longs;pacio di <lb/>tempo, ouer di luoco, di moto naturale, & uiolente in&longs;ieme mi&longs;to, & dite che tal pro­<lb/>po&longs;itione è fal&longs;ißima, & contra ogni ragione, & i&longs;perientia naturale, & che il mio <lb/>fondamento con il quale approuo la detta propo&longs;itione, uoi dite, ch'eglie piu &longs;torno <lb/>a&longs;&longs;ai, che non fu la ri&longs;po&longs;ta, che io deti al libraro, circa à cio quella adduce molte &longs;ue <lb/>ragioni contra à tal mia propo&longs;itione.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002657">E<emph type="italics"/>t per tanto circa à que&longs;ta uo&longs;tra quarta accu&longs;a ue ri&longs;pondo, & dico, che le uo&longs;tre <lb/>ragioni, & argomenti per uoi adutti à de&longs;truttione di tal mia quinta propo&longs;ltione &longs;ono <lb/>tanto deboli, & mal conditionati, che una femina inferma &longs;aria &longs;officiente à sbatterli <lb/>per terra, perche &longs;e la conclu&longs;ione della detta mia quinta propo&longs;itione è fal&longs;a, eglie ne­<lb/>ce&longs;&longs;ario, che li &longs;uoi primi principij &longs;tano fal&longs;i, ouer amente che alcuna delle &longs;ue preme&longs;­<lb/>&longs;e propo&longs;itioni, con le quale &longs;e dimo&longs;tra la detta quinta &longs;ia fal&longs;a, la qual co&longs;a e&longs;&longs;endo uoi <lb/>doueti pur &longs;apere, che l'officio del perito medico &longs;i è de inue&longs;tigare con &longs;omma diligen­<lb/>tia la cau&longs;a principale de ogni infirmita, che gli occorra alle mani, & ritrouata quella, <lb/>anchora con &longs;omma diligentia di cercare piu di opponere, ouer di curare la detta cau&longs;a <lb/>principale, che di opponere, ouer di cur are li &longs;uoi tristi effetti, perche rimo&longs;&longs;a che &longs;ia <lb/>la cau&longs;a de neceßita, &longs;aranno rimoßi anchora tutti li &longs;uoi tri&longs;ti effetti.<emph.end type="italics"/> E <emph type="italics"/>pero uo­<lb/>lendo uo&longs;tra Eccellentia opponere, ouer arguìre contra à tal mia quinta propo&longs;itione <lb/>quella doueua primamente opponere, ouer arguire &longs;opra alli &longs;uoi primi principij, oue­<lb/>ramente &longs;opra ad alcuna di quelle prome&longs;&longs;e propo&longs;itioni, con le quale io conchiudo la <lb/>detta quinta propo&longs;itione (come fondamento, & cau&longs;a principale di tal effetto) per­<lb/>che &longs;e uoi haue&longs;ti potuto di&longs;truggere il fondamento con qualche &longs;ofi&longs;tice ragioni tutta <lb/>la fabrica &longs;aria andata per terra, mauoi credendoui di dimostrarue à me miracolo&longs;o <lb/>con tale uo&longs;tre ridicolo&longs;e oppo&longs;itioni, ue &longs;eti dimo&longs;trato, non uoglio dire, un grande <lb/>ignorante, come haueti detto à me, ma un'huomo di poco giudicio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002658">E<emph type="italics"/>t perche<emph.end type="italics"/> V. E<emph type="italics"/><expan abbr="ccell&etilde;tia">ccellentia</expan> dice, che me ha per i&longs;cu&longs;o, trattando de artegliarie, che è po <lb/>co mio me&longs;tiero, anchor che me &longs;ia ingegnato di dire circa a tal arte qualche bella co&longs;a.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002659">C<emph type="italics"/>irca à que&longs;ta particolarita ue ri&longs;pondo, & dico, che me diletto de nuoue inuentio­<lb/>ni, & di trattare, & parlare de co&longs;e, che altri non habbia trattato, ne parlato, & non <lb/>me diletto di far, come fanno alcuni, che empiono li &longs;uoi uolumi di co&longs;e robate da que­<lb/>sto, & da quell'altro autore. </s> <s id="s.002660">Et quantunque à parlare delle artegliarie, et lor tiri non <lb/>&longs;ia co&longs;a molto honoreuole in &longs;e, pur per e&longs;&longs;er una materia nuoua, & di non poca &longs;pecu <lb/>latione, me appar&longs;o di parlarne alquanto, & circa cio al pre&longs;ente dago fuora due &longs;or-<emph.end type="italics"/><pb pagenum="117" xlink:href="042/01/234.jpg"/><emph type="italics"/>te de in&longs;trumenti circa à tal arte, cioe una &longs;quadra per regolar li tiri delle dette arte­<lb/>gliarie, & anchora per liuellare, & inue&longs;tigare ogni altezza. </s> <s id="s.002661">Et uno altro in&longs;tru­<lb/>mento, per inue&longs;tigare ogni di&longs;tantia in piano, con l'a&longs;petto, liquali in&longs;trumenti anda <lb/>rano con el detto mio libro de artegliaria. </s> <s id="s.002662">Et perche me haueti &longs;critto che uoi com­<lb/>pera&longs;ti dui de detti mei libri, delli quali uno ne de&longs;ti alla eccellentia del Signor Mar­<lb/>che&longs;e, & laltro tene&longs;ti per uoi, me appar&longs;o anchora dimandarue, quatro delli detti in <lb/><expan abbr="&longs;trum&etilde;ti">&longs;trumenti</expan> & li ho dati alla Signoria de me&longs;&longs;er Ottauian Scotto che ueda da farueli por <lb/>tar per qualche me&longs;&longs;o che uegna à quelle bande, delli quali quatro instrumenti, dui ne <lb/>donareti alla eccellentia del Signor, Marche&longs;e, & li altri dui tenereti per uoi, uo&longs;tra <lb/>eccellentia anchora me &longs;criue, che accio che io non pen&longs;a che quella &longs;ia &longs;imile à me & <lb/>à me&longs;&longs;er Zuan Colle che quella me manda due que&longs;tioni con le &longs;ue &longs;olutioni, ma che il <lb/>me&longs;&longs;o tenera le dette &longs;olutioni &longs;eparate dalle dette questioni, & che &longs;e io non le &longs;apro <lb/>ri&longs;oluere che il detto me&longs;&longs;o me le dara &longs;ubito <expan abbr="hau&etilde;dole">hauendole</expan>, pero &longs;eco à una <21> una accio che <lb/>io <expan abbr="nõ">non</expan> creda, che quella me le habbia <expan abbr="mãdate">mandate</expan> per impararle, & <expan abbr="nõ">non</expan> per darmele ma che <lb/>il detto me&longs;&longs;o retora prima le mie &longs;olutioni in drío <expan abbr="nãti">nanti</expan> che me dia le uo&longs;tre accioche io <lb/>non li de&longs;&longs;e ad intendere di hauer le a&longs;&longs;olte, & chel non fu&longs;&longs;e il uero. </s> <s id="s.002663">della qualco&longs;a me <lb/>ne ho ride&longs;to a&longs;&longs;ai & la cau&longs;a de tal mio ridere &longs;e narrara &longs;opra alla &longs;olutione della uo <lb/>&longs;tra &longs;econda questione.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002664">H<emph type="italics"/>or per ri&longs;pondere alla uo&longs;tra prima <expan abbr="que&longs;tiõe">que&longs;tione</expan> quale dice, che ui debbia far de. </s> <s id="s.002665">10. <lb/>quattro quantita continue proportionale, che li loro quadr ati gionti in&longs;ieme facciano. <lb/></s> <s id="s.002666">60. io ue ri&longs;pondo che le dette parti &longs;ono le &longs;otto &longs;critte cioe.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002667">L<emph type="italics"/>a prima &longs;ara. </s> <s id="s.002668">6. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002669">7. 1/4. <emph type="italics"/>meno la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002670">49. 1/2. <expan abbr="m&etilde;">men</expan><emph.end type="italics"/> <22>. </s> <s id="s.002671">1225. 1/4. <emph type="italics"/>men <lb/>que&longs;to e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002672">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002673">9396. <emph type="italics"/>men. </s> <s id="s.002674">288. e&longs;imo de<emph.end type="italics"/> <22>. </s> <s id="s.002675">116. <emph type="italics"/>piu. </s> <s id="s.002676">4. cioe <lb/>da partire per el detto<emph.end type="italics"/> <22>. </s> <s id="s.002677">116. <emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002678">L<emph type="italics"/>a &longs;econda &longs;ara<emph.end type="italics"/> <22>. </s> <s id="s.002679">7. 1/4. <emph type="italics"/>men. </s> <s id="s.002680">1. 1/2. men la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002681">9. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002682">65. 1/4 <emph type="italics"/>men que­<lb/>&longs;to e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002683">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002684">9396. <emph type="italics"/>men. </s> <s id="s.002685">288. e&longs;imo, cioe da partire per<emph.end type="italics"/> <22>. <lb/></s> <s id="s.002686">116. <emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002687">L<emph type="italics"/>a terza &longs;ara<emph.end type="italics"/> <22>. </s> <s id="s.002688">7. 1/4. <emph type="italics"/>men. </s> <s id="s.002689">1. 1/2. piu la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002690">9. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002691">65. 1/4. <emph type="italics"/>men que&longs;to <lb/>e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002692">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002693">9396. <emph type="italics"/>men. </s> <s id="s.002694">288. da partire per<emph.end type="italics"/> <22>. </s> <s id="s.002695">116. <emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002696">L<emph type="italics"/>a quarta &longs;ara. </s> <s id="s.002697">6. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002698">7. 1/2. <emph type="italics"/>piu la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002699">49. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002700">1225. 1/4. <emph type="italics"/>men <lb/>questo e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002701">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002702">9396 <emph type="italics"/>men. </s> <s id="s.002703">288. da partire per<emph.end type="italics"/> <22>. </s> <s id="s.002704">116. <emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002705">E<emph type="italics"/>t que&longs;te tai parti le ritrouo in que&longs;to modo. </s> <s id="s.002706">Prima <expan abbr="tõ&longs;idero">ton&longs;idero</expan> che &longs;e &longs;ar anno. </s> <s id="s.002707">4. quan <lb/>tita continue proportionale delle quale la &longs;econda & terza in&longs;ieme ne &longs;ian note, et che <lb/>la prima & quarta in&longs;ieme ne &longs;ian note eglie poßibile à potere ritrouare quanto &longs;ia <lb/>cadauna delle dette quantita feparatamente, perche chi partira el cubo della &longs;umma <lb/>della <expan abbr="&longs;ecõda">&longs;econda</expan> & terza, per el <expan abbr="cõpo&longs;to">compo&longs;to</expan> di tutte quattro & del doppio della &longs;umma della <lb/>&longs;econda & terza l'aduenimento &longs;ara equale alla multiplicatione della &longs;econda nella ter <lb/>za, ouer della prima nella quarta (ch'è il mede&longs;imo) per ílche <expan abbr="fac&etilde;do">facendo</expan> due tal parti della <lb/>&longs;umma della &longs;econda, & terza, ouer della prima & quarta, che multiplicata luna fia <lb/>l'altra faccia lo detto aduemmento &longs;eguir a il propo&longs;ito. </s> <s id="s.002708">Hor con tal euidentia io po <lb/>so che la &longs;econda & terza ínfleme &longs;iano. </s> <s id="s.002709">1. co&longs;a adunque, la prima, & quarta in&longs;ieme <lb/>por &longs;orza&longs;arano. </s> <s id="s.002710">10. men.i.co&longs;a, cubo la co&longs;a fa. </s> <s id="s.002711">1. cubo el qual parto per. </s> <s id="s.002712">10. piu el<emph.end type="italics"/><pb xlink:href="042/01/235.jpg"/><emph type="italics"/>doppio della &longs;econda & terza, cioe per. </s> <s id="s.002713">10. piu. </s> <s id="s.002714">2. co&longs;e ne uien. </s> <s id="s.002715">1. cu.e&longs;imo de. </s> <s id="s.002716">10. piu <lb/>2. co&longs;e, et <27>sto &longs;ara il pdutto della &longs;econda nella terza, ouer della prima nella. </s> <s id="s.002717">4. Adun <lb/>que per trouar cadauna &longs;eparatamente faccio di. </s> <s id="s.002718">1. co. </s> <s id="s.002719">due tal parti che multiplicata <lb/>luna fia l'altra faccia. </s> <s id="s.002720">1. cu. </s> <s id="s.002721">e&longs;imo de. </s> <s id="s.002722">10. piu. </s> <s id="s.002723">2. co&longs;e, <expan abbr="operãdo">operando</expan> come bi&longs;ogna trouo che <lb/>la menore è. </s> <s id="s.002724">1/2. co.men<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->1/4. ce.m&etilde;. </s> <s id="s.002725">1. cubo.e&longs;imo de. </s> <s id="s.002726">10. piu. </s> <s id="s.002727">2. co&longs;e et la maggiore <lb/>&longs;ara. </s> <s id="s.002728">1/2. co.piu<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->1/4. ce.m&etilde;. </s> <s id="s.002729">1. cubo e&longs;imo de. </s> <s id="s.002730">10. piu. </s> <s id="s.002731">2. co&longs;e, & co&longs;i <expan abbr="&longs;ordam&etilde;te">&longs;ordamente</expan> haro <lb/>trouata la &longs;econda & terza <expan abbr="&longs;eparatam&etilde;te">&longs;eparatamente</expan>. </s> <s id="s.002732">Simelmente trouaro la prima & quarta fa <lb/><expan abbr="c&etilde;do">cendo</expan> de. </s> <s id="s.002733">10. <expan abbr="m&etilde;">men</expan>. </s> <s id="s.002734">1. co.due tal parti che multiplicata luna fia l'altra facia. </s> <s id="s.002735">1. cu.e&longs;imo de. <lb/></s> <s id="s.002736">10. piu, 2. co&longs;e, <expan abbr="operãdo">operando</expan> come bi&longs;ogna trouo che la prima &longs;ara. </s> <s id="s.002737">5. <expan abbr="m&etilde;">men</expan>. </s> <s id="s.002738">1/2. co.m&etilde;<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->25. <lb/><expan abbr="m&etilde;">men</expan>. </s> <s id="s.002739">5. co piu. </s> <s id="s.002740">14. ce <expan abbr="m&etilde;">men</expan>. </s> <s id="s.002741">1. cubo e&longs;imo de. </s> <s id="s.002742">10. piu: 2. co&longs;e (cioe la menor) la quarta cioe la <lb/>maggiore &longs;ara. </s> <s id="s.002743">5. men. </s> <s id="s.002744">1/2. co.piu<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->25. men. </s> <s id="s.002745">5. co.piu. </s> <s id="s.002746">1/4. ce.m&etilde;. </s> <s id="s.002747">1 cubo.e&longs;imo de. </s> <s id="s.002748">10. <lb/>piu. </s> <s id="s.002749">2. co&longs;e, & co&longs;i li haueremo tutte quatro &longs;eparate come di &longs;otto appare.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002750">P<emph type="italics"/>rima &longs;ara. </s> <s id="s.002751">5. men. </s> <s id="s.002752">1/2. co.men<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->25. men. </s> <s id="s.002753">5. co.piu. </s> <s id="s.002754">1/4. ce.men. </s> <s id="s.002755">1. cubo e&longs;imo de. </s> <s id="s.002756">10. <lb/>piu. </s> <s id="s.002757">2. co. </s> <s id="s.002758">El quadrato della qual quantita &longs;ara. </s> <s id="s.002759">50. men. </s> <s id="s.002760">10. co.piu. </s> <s id="s.002761">1/2. cen&longs;o men. <lb/></s> <s id="s.002762">1. cubo. </s> <s id="s.002763">e&longs;imo de. </s> <s id="s.002764">10. piu. </s> <s id="s.002765">2. co.men, anchora el doppio del dutto de luna par­<lb/>te in laltra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002766">L<emph type="italics"/>a &longs;econda &longs;ara. </s> <s id="s.002767">1/2. co.men<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->1/4. ce.men. </s> <s id="s.002768">1. cubo e&longs;imo de. </s> <s id="s.002769">10. piu. </s> <s id="s.002770">2. co&longs;e. </s> <s id="s.002771">Et el &longs;uo <lb/>quadrato &longs;ara. </s> <s id="s.002772">1/2. ce.men. </s> <s id="s.002773">1. cu.e&longs;imo de. </s> <s id="s.002774">10 piu. </s> <s id="s.002775">2. co.men, anchora el doppio de lu <lb/>na parte in l'altra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002776">L<emph type="italics"/>aterza &longs;ara. </s> <s id="s.002777">1/2. co.piu<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->1/4. ce.men.u.cu.e&longs;imo de. </s> <s id="s.002778">10. piu. </s> <s id="s.002779">2. co. </s> <s id="s.002780">Et il quadrato de <lb/>tal quantita &longs;ara. </s> <s id="s.002781">1/2. ce.men. </s> <s id="s.002782">1. cu.e&longs;imo de. </s> <s id="s.002783">10. piu. </s> <s id="s.002784">2. co.piu, anchora il doppio de <lb/>luna parte in l'altra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002785">L<emph type="italics"/>a quarta&longs;ara. </s> <s id="s.002786">5. men. </s> <s id="s.002787">1/2. co.piu<emph.end type="italics"/> <22>. <emph type="italics"/>u. <!-- REMOVE S-->25. men. </s> <s id="s.002788">5. co.piu. </s> <s id="s.002789">1/4. ce.men. </s> <s id="s.002790">1. cu.e&longs;imo de. </s> <s id="s.002791">10. <lb/>piu. </s> <s id="s.002792">2. co. </s> <s id="s.002793">Et il quadrato de questa quantita &longs;ara. </s> <s id="s.002794">50. men. </s> <s id="s.002795">10. co.piu. </s> <s id="s.002796">1/2. ce.men. </s> <s id="s.002797">1. <lb/>cu.e&longs;imo de. </s> <s id="s.002798">10. piu. </s> <s id="s.002799">2. co.piu anchora el doppio de luna parte in l'altra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002800">E<emph type="italics"/>t dapoi &longs;ummo li detti quatro quadr ati et fanno in &longs;umma. </s> <s id="s.002801">100. men. </s> <s id="s.002802">20. co.piu. </s> <s id="s.002803">2. ce. <lb/></s> <s id="s.002804">men. </s> <s id="s.002805">4. cubi e&longs;imi de. </s> <s id="s.002806">10. piu. </s> <s id="s.002807">2. co.& questa &longs;umma &longs;ara equale à. </s> <s id="s.002808">60. egualio le par <lb/>ti & ri&longs;toro li diminuti & leuo li rotti & in ultimo me ne peruene. </s> <s id="s.002809">6. co.piu. </s> <s id="s.002810">1. ce. </s> <s id="s.002811">e­<lb/>gual à. </s> <s id="s.002812">20. &longs;eguito el capitolo & trouo la co&longs;a ualer<emph.end type="italics"/> <22>. </s> <s id="s.002813">29. <emph type="italics"/>men. </s> <s id="s.002814">3. & tanto dico che <lb/>fu la &longs;umma della &longs;econda, & terza quantita. </s> <s id="s.002815">Onde che la &longs;umma della príma et quan <lb/>ta de neceßita &longs;ara. </s> <s id="s.002816">13. men<emph.end type="italics"/> <22>. </s> <s id="s.002817">29. <emph type="italics"/>cioe el <expan abbr="restãte">restante</expan> per fina in. </s> <s id="s.002818">10. Hor per trouar le par <lb/>te &longs;eparate bi&longs;ogna procedere come fuproce&longs;&longs;o &longs;ordamente, cioe trouando el produt­<lb/>to della &longs;econda in la terza, ouer della prima nella quarta, el qual <expan abbr="uol&etilde;dolo">uolendolo</expan> trouar cu­<lb/>bo<emph.end type="italics"/> <22>. </s> <s id="s.002819">29. <emph type="italics"/>men. </s> <s id="s.002820">3. fa.in &longs;umma<emph.end type="italics"/> <22>. </s> <s id="s.002821">41876. <emph type="italics"/>men. </s> <s id="s.002822">288. piu<emph.end type="italics"/> <22>. </s> <s id="s.002823">9396. <emph type="italics"/>et que&longs;to parto per. <lb/></s> <s id="s.002824">10. piu el doppio de<emph.end type="italics"/> <22>. </s> <s id="s.002825">29. <emph type="italics"/>men. </s> <s id="s.002826">3. cioe per<emph.end type="italics"/> <22>. </s> <s id="s.002827">116. <emph type="italics"/>piu. </s> <s id="s.002828">4. mene uiene<emph.end type="italics"/> <22>. </s> <s id="s.002829">41876. <emph type="italics"/>piu<emph.end type="italics"/><lb/><22>. </s> <s id="s.002830">9396. <emph type="italics"/><expan abbr="m&etilde;">men</expan>. </s> <s id="s.002831">288. e&longs;imo de<emph.end type="italics"/> <22>. </s> <s id="s.002832">116. <emph type="italics"/>piu. </s> <s id="s.002833">4. & questo &longs;ara equale al produtto della &longs;e <lb/><expan abbr="cõda">conda</expan> nella terza, ouer della prima nella quarta. </s> <s id="s.002834">Hor per trouare cadauno <expan abbr="&longs;eparatam&etilde;-te">&longs;eparatamen­<lb/>te</expan> procedendo <expan abbr="&longs;ecõdo">&longs;econdo</expan> il &longs;olito trouo che la &longs;econda è<emph.end type="italics"/> <22>. </s> <s id="s.002835">7. 1/4. <emph type="italics"/><expan abbr="m&etilde;">men</expan>. </s> <s id="s.002836">1. 1/2. <expan abbr="m&etilde;">men</expan> la<emph.end type="italics"/> <22>. <emph type="italics"/>u.de. <!-- REMOVE S-->9. <lb/>1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002837">65. 1/2. <emph type="italics"/><expan abbr="m&etilde;">men</expan> anchora<emph.end type="italics"/> <22>. </s> <s id="s.002838">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002839">9396. <emph type="italics"/><expan abbr="m&etilde;">men</expan>. </s> <s id="s.002840">288. e&longs;imo.de<emph.end type="italics"/> <22>. </s> <s id="s.002841">116. <emph type="italics"/><expan abbr="m&etilde;">men</expan>. </s> <s id="s.002842">4. <lb/>La terza uera à e&longs;&longs;ere la mede&longs;ima<emph.end type="italics"/> <22>. </s> <s id="s.002843">7. 1/4. <emph type="italics"/>me.<emph.end type="italics"/> 1/2. M<emph type="italics"/>a piu la &longs;opra&longs;critta<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer <lb/>&longs;ale de. </s> <s id="s.002844">9. 1/2. men.<emph.end type="italics"/> <22>. </s> <s id="s.002845">65. 1/4. <emph type="italics"/>men, anchora la<emph.end type="italics"/> <22>. </s> <s id="s.002846">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002847">9396, <emph type="italics"/>men. </s> <s id="s.002848">288. e&longs;imo <lb/>de<emph.end type="italics"/> <22>. </s> <s id="s.002849">116. <emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <pb pagenum="118" xlink:href="042/01/236.jpg"/> <p type="main"> <s id="s.002850">H<emph type="italics"/>or per ritrouar la prima & quarta &longs;eparatamente procedero, come di &longs;opra fa <lb/><expan abbr="c&etilde;do">cendo</expan> de. </s> <s id="s.002851">13. men<emph.end type="italics"/> <22>. </s> <s id="s.002852">29. <emph type="italics"/>due tal parti che multiplicata luna in l'altra facia pur il &longs;opra <lb/>&longs;critto e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002853">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002854">9396. <emph type="italics"/>men. </s> <s id="s.002855">288. e&longs;imo de<emph.end type="italics"/> <22>. </s> <s id="s.002856">116. P<emph type="italics"/>iu. </s> <s id="s.002857">4. onde <lb/>operando <expan abbr="&longs;ecõdo">&longs;econdo</expan> il &longs;olito trouo che la prima (cioe la menore) &longs;ara preci&longs;amente. </s> <s id="s.002858">6. <lb/>1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002859">7. 1/4. <emph type="italics"/>men la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002860">49. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002861">1225. 1/4. <emph type="italics"/><expan abbr="m&etilde;">men</expan> que&longs;to e&longs;imo, cioe<emph.end type="italics"/><lb/><22>. </s> <s id="s.002862">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002863">9396. <emph type="italics"/><expan abbr="m&etilde;">men</expan>. </s> <s id="s.002864">288. e&longs;imo de<emph.end type="italics"/> <22>. </s> <s id="s.002865">116. <emph type="italics"/>piu. </s> <s id="s.002866">4. et la maggiore cioe la quar <lb/>ta&longs;ara. </s> <s id="s.002867">6. 1/2. <expan abbr="m&etilde;">men</expan><emph.end type="italics"/> <22>. </s> <s id="s.002868">7 1/4. <emph type="italics"/>piu la &longs;opra &longs;critta<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale. </s> <s id="s.002869">Onde le dette quatro parti <lb/>del detto. </s> <s id="s.002870">10. adimandate dauo&longs;tra eccellentia &longs;arano come di&longs;otto appare.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002871">L<emph type="italics"/>a prima &longs;ara. </s> <s id="s.002872">6. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002873">7. 1/4. <emph type="italics"/>men la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002874">49. 1/2. men.<emph.end type="italics"/> <22>. </s> <s id="s.002875">1225. 1/4. <lb/><emph type="italics"/>men que&longs;to e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002876">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002877">9396. <emph type="italics"/>men. </s> <s id="s.002878">288. e&longs;imo de<emph.end type="italics"/> <22>. </s> <s id="s.002879">116. <emph type="italics"/>piu. </s> <s id="s.002880">4. <lb/>cioe da partire per<emph.end type="italics"/> <22>. </s> <s id="s.002881">116. <emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002882">L<emph type="italics"/>a &longs;econda &longs;ara<emph.end type="italics"/> <22>. </s> <s id="s.002883">7. 1/4. <emph type="italics"/>men. </s> <s id="s.002884">1. 1/2. men la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002885">9. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002886">65. 1/4. <emph type="italics"/>men <lb/>que&longs;to e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002887">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002888">9396. <emph type="italics"/>men. </s> <s id="s.002889">288. da partire per.<emph.end type="italics"/> <22>. </s> <s id="s.002890">116 <lb/><emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002891">L<emph type="italics"/>a terza &longs;ara<emph.end type="italics"/> <22>. </s> <s id="s.002892">7. 1. 1/4. <emph type="italics"/>men. </s> <s id="s.002893">1. 1/2. piu.la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002894">9. 1/2. men<emph.end type="italics"/> <22>. </s> <s id="s.002895">65. 1/4. <emph type="italics"/>men que <lb/>&longs;to e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002896">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002897">9396. <emph type="italics"/>men. </s> <s id="s.002898">288. da partire per<emph.end type="italics"/> <22>. </s> <s id="s.002899">116. <emph type="italics"/>piu.<emph.end type="italics"/> 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002900">L<emph type="italics"/>a quarta &longs;ara. </s> <s id="s.002901">6. 1/2. <expan abbr="m&etilde;">men</expan><emph.end type="italics"/> <22>. </s> <s id="s.002902">7. 1/4. <emph type="italics"/>piu la<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale de. </s> <s id="s.002903">49. 1/2. men.<emph.end type="italics"/> <22>. </s> <s id="s.002904">1225. 1/4. <emph type="italics"/>men <lb/>que&longs;to e&longs;imo, cioe<emph.end type="italics"/> <22>. </s> <s id="s.002905">41876. <emph type="italics"/>piu<emph.end type="italics"/> <22>. </s> <s id="s.002906">9396. <emph type="italics"/>men. </s> <s id="s.002907">288. e&longs;imo de<emph.end type="italics"/> <22>. </s> <s id="s.002908">116. <emph type="italics"/>piu. </s> <s id="s.002909">4. come <lb/>che nel principio fu conclu&longs;o.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002910">C<emph type="italics"/>irca à l'altra uostra &longs;econda questione, quala dice che &longs;ono doi che feceno compagnia <lb/>& po&longs;eno non &longs;o quanti ducati & guadagnorno el cubo della decima parte del &longs;uo ca <lb/>pitale & che &longs;e haue&longs;&longs;ero guadagnato. </s> <s id="s.002911">3. meno de quello che guadagnorono, haueria­<lb/>no guadagnato tanto quanto fu il &longs;uo capitale aponto, &longs;e adimanda il &longs;uo capitale & <lb/>guadagno. </s> <s id="s.002912">Certamente di que&longs;ta come di &longs;opra dißi me ne &longs;on ride&longs;to a&longs;&longs;ai, perche ue­<lb/>do che uostra eccellentia cerca di uoler giocare con meco à trapola, oueramente al gio <lb/>co della corrigiola, come co&longs;tumano li cingheni & &longs;i crede di uolermi agabare con di­<lb/>re di hauermi mandato la &longs;alutione di que&longs;ta ragione &longs;e io non la &longs;apero ri&longs;oluere. </s> <s id="s.002913">La <lb/>qual ragione procedendo per Algebra (come credo che &longs;apeti) condu&longs;&longs;e l'operante in <lb/>el capitolo de co&longs;e, et numero equal à cubo Et la regola da ri&longs;oluere tal capitolo, affer <lb/>mo e&longs;&longs;er totalmente ignorata da uoi, & per mo&longs;trarue che di que&longs;to ne &longs;on certißi­<lb/>mo me offeri&longs;co à deponere circa cio ducati diece contra uno, & accio non crediate <lb/>ch'io parli auentura dico che dapoi che io hebbe ritrouato la regola del capitolo de co <lb/>&longs;a è cubo equal à numero, per alcuni aui&longs;i di tal inuentione il giorno &longs;eguente ritrouai <lb/>regola general anchora à que&longs;to di co&longs;e et numero equal à cubo, la cur regola gia mai <lb/>haueria potuta inue&longs;tigare &longs;enza la prima, cioe &longs;enza quella di co&longs;a è cubo equal à nu<lb/>mero, & perche tal regola è da uoi ignorata, tanto piu ui è occulta que&longs;ta di co&longs;e, & <lb/>numero equale, a cubo, la quale con cautela ue credeui di cauarmela da le mani con di­<lb/>re che haueui data la &longs;ua &longs;olutione al me&longs;&longs;o, la qual bogia mi fa dubitare che uoi non <lb/>&longs;appiati ri&longs;oluere nanche la uo&longs;tra prima qual ui mando re&longs;olta.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002914">O<emph type="italics"/>ltra di que&longs;to mi pregati ch'io ui <expan abbr="mãda">manda</expan> le propo&longs;te per me fatte à mae&longs;tro Anto <lb/>niomaria fiore et che &longs;e non ui uoglio mandar le &longs;ue &longs;olutioni che le debbia ritener per <lb/>me.<emph.end type="italics"/> E <emph type="italics"/>per <expan abbr="tãto">tanto</expan> ue faccio <expan abbr="int&etilde;dere">intendere</expan> che le dette m<gap/>. <!-- REMOVE S-->30. que&longs;tioni &longs;ono digran &longs;crittura<emph.end type="italics"/><pb xlink:href="042/01/237.jpg"/><emph type="italics"/>& à douerucle regi&longs;trare tutte ue andaria da &longs;criuere a&longs;&longs;ai & &longs;i mal me ritrouaioe­<lb/>cupato me ritrouo al pre&longs;ente & la cau&longs;a é che ho posto fuora alcuni cartelli publici <lb/>qualmente dominica proßima uoglio principiare à i&longs;ponere publicamente in &longs;an zuan <lb/>nepolo, la &longs;cientia di pe&longs;i & mostr are alcune co&longs;e operatiui &longs;opra la pratica delle co­<lb/>&longs;e per me ritrouate &longs;opra li tiri delle artegliarie con altre uarie particolarita. </s> <s id="s.002915">Et ac­<lb/>cio che uo&longs;tra eccellentia non &longs;i creda che que&longs;ta &longs;ia una finta per non uolerui &longs;eruire à <lb/>mandarue le dette mie. </s> <s id="s.002916">30. que&longs;tioni ui mando la coppia del cartello che ho po&longs;to fuo­<lb/>ra gia fa dui giorni, & per mo&longs;trarui che ho uolonta de &longs;eruirui (anchor che &longs;ia occu <lb/>pato) ue ne mando, per al pre&longs;ente noue che mi &longs;ono re&longs;tati in memoria delle dette mie <lb/>questioni (perche in uero) io non ne fece de quelli nota ne memorria alcuna da tener ap <lb/>pre&longs;&longs;o di me, ma ce&longs;&longs;ato che me &longs;ia que&longs;te mie occupationi di leggere publico, ne anda­<lb/>ro à cauar la coppia dal notaro, & ue la mandaro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002917">E<emph type="italics"/>l primo de detti que&longs;iti &longs;e ben me aricordo fu &longs;opra il capitolo de cen&longs;o è cubo e­<lb/>qual à numero, & ue lo propo&longs;i largamente da poter&longs;i egualiar à che numero liparea <lb/>pur che de&longs;&longs;ela co&longs;a irrationale. </s> <s id="s.002918">Qual diceua in que&longs;to modo trouatime una quantita <lb/>che &longs;ia irrationale che multiplicata fia la &longs;ua radice piu. </s> <s id="s.002919">40. faccia numero rationale <lb/>è di&longs;creto, & ue la propo&longs;i co&longs;i larga di poter&longs;i egualiar à che numero gli parea per un <lb/>certo mio ri&longs;petto, et non ue ne detti altro &longs;opra à tal capitolo, uero è che me&longs;&longs;er zuan <lb/>ne da Coi mi prego che ui de&longs;&longs;e que&longs;to ca&longs;o a&longs;&longs;olto & io ge lo dedi ri&longs;olto in uno &longs;impli <lb/>ce reci&longs;o qual &longs;u&longs;e <expan abbr="b&etilde;">bem</expan> me aricordo. </s> <s id="s.002920">78. men<emph.end type="italics"/> <22>. </s> <s id="s.002921">308. <emph type="italics"/>et per tal &longs;olutione lui ui trouo una <lb/>certa regola da &longs;oluere tutti &longs;imili, e pero piu non mi fidaria à proporli &longs;otto tal for­<lb/>ma, ma tal, &longs;ua regola non &longs;erue &longs;aluo in quelli numeri, ouer &longs;olutioni, che &longs;e ri&longs;olueno <lb/>in un re&longs;iduo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002922">E<emph type="italics"/>l &longs;econdo que&longs;ito fu &longs;opra il capitolo de cen&longs;o é numero equal à cubo & non ue ne <lb/>detti &longs;imelmente altro che uno &longs;opra tal capitolo. </s> <s id="s.002923">Ma &longs;opra al capitolo de cubo, e nu­<lb/>mero equal à cen&longs;i non ue ne dette elcuno perche co&longs;i al improui&longs;o non potei trouar re <lb/>gola à tal capitolo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002924">E<emph type="italics"/>l terzo poi fu &longs;opra il capitolo de co&longs;a è cubo equal à numero & ge lo detti pur <lb/><expan abbr="largam&etilde;te">largamente</expan> da poter&longs;i egualiare à che numero gli parea pur che de&longs;&longs;e la co&longs;a irrationa <lb/>le, et <expan abbr="nõ">non</expan> ue ne ppo&longs;i altro &longs;opra à tal capitolo, ma <expan abbr="nõ">non</expan> me aricordo come diceua preci&longs;e.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002925">E<emph type="italics"/>l quarto fu &longs;opra el capitolo de co&longs;e, e numero equal à cubo ne piu ue ne uol&longs;i pro <lb/>ponere &longs;opro à tal capitolo, et &longs;opra al capitolo de cubo, é numero equal à co&longs;e <expan abbr="nõ">non</expan> ue ne <lb/>propo&longs;i alcuno perche co&longs;i al improui&longs;a <expan abbr="nõ">non</expan> potetitrouare la regola de tal capitolo. <lb/></s> <s id="s.002926">Del quinto <expan abbr="nõ">non</expan> me aricordo, come dice&longs;&longs;e ne manco de li altri <expan abbr="ordinariam&etilde;te">ordinariamente</expan>, ma &longs;o ben <lb/>che io gli propo&longs;e fra le altre co&longs;e che mi doue&longs;&longs;e ritrouar una quantita, qual multipli <lb/>cata per<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.002927">24. piu<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.002928">6. piu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.002929">1. 1/2. face&longs;&longs;e numero rationale, et di&longs;creto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002930">A<emph type="italics"/>nchora io gli propo&longs;i una linea retta et gli adimandai che me la &longs;ega&longs;&longs;e geometri <lb/>camente in. </s> <s id="s.002931">3. tal parti che facendo di quelle parti un triangolo quel fu&longs;&longs;e retangolo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002932">A<emph type="italics"/>nchora io gli propo&longs;iuna piramide troncata & gli adimandai che geometrica­<lb/>mente, me la &longs;ega&longs;&longs;e in. </s> <s id="s.002933">3. parti equali per trauer&longs;o.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002934">A<emph type="italics"/>nchora gli propo&longs;i uno <expan abbr="triãgolo">triangolo</expan> de tre lati inequale et gli adimandai che in quel­<lb/>lo geometricamente me gli in&longs;criue&longs;&longs;e un quadrato.<emph.end type="italics"/></s> </p> <pb pagenum="119" xlink:href="042/01/238.jpg"/> <p type="main"> <s id="s.002935">A<emph type="italics"/>nchora io gli propo&longs;i la &longs;otto&longs;critta questione per e&longs;&longs;ermene &longs;tata propo&longs;ta qua&longs;i <lb/>una &longs;imile &longs;otto mane da lui qual tenea <21> ragion fortißima, ma <expan abbr="l'agun&etilde;tai">l'agunentai</expan> in difficult<gap/><emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002936">H<emph type="italics"/>aggio una botta piena de uino puro, della quale ne cauo dui &longs;ecchi, & la riempio <lb/>di acqua, & dapoi que&longs;to ne recauò fuora dui altri&longs;ecchi, & la reimpio di acqua, & da <lb/>poi que&longs;to ne recauo pur fuora dui &longs;ecchi, & la riempio di acqua, & co&longs;iuado faccian <lb/>do per fin al numero de. </s> <s id="s.002937">6. uolte & fatto que&longs;to in ultimo ritrouo, che in la detta bot­<lb/>ta era la mita uino, & la mita acqua, & gli adimandaua la tenuta della botta.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002938">Q<emph type="italics"/>uattro altri que&longs;iti gli propo&longs;i anchora in Algebra communa, quali non me ari­<lb/>cordo, come preci&longs;amente diceuano. </s> <s id="s.002939">Molti ue ne propo&longs;e de a&longs;&longs;oluere geometrice, per <lb/>che lui non haueua alcuna &longs;cientia in tal operare, ma&longs;olamente pratica nelli numeri, li <lb/>quali non gli ho allamente, ma un'altra uolta con piu commodita, come detto, ue li man <lb/>daro, perche li andaro à tuor dal notaro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002940">A<emph type="italics"/>nchora uo&longs;tra Eccellentia mi prega, che ui uoglia mandar la &longs;olutione di qualche <lb/>una delle uostre prime. </s> <s id="s.002941">7. que&longs;tioni, che mi portò il libraro. </s> <s id="s.002942">Certamente molto mi ma­<lb/>rauiglio, & &longs;tupi&longs;co, hauendo quella hauuto tanto per male, per hauer io detto al li­<lb/>braro, che uo&longs;tra Eccellentia non &longs;aperia ri&longs;oluere tai propo&longs;itioni, & hauendo&longs;i poi <lb/>quella con tanta arrogantia auantato, che lei li &longs;apeua ri&longs;oluere auanti, che mae&longs;tro <lb/>Zuane &longs;ape&longs;&longs;e numerar fina à. </s> <s id="s.002943">10. & che anchora me richiedeti, che ue le debbia ri&longs;ol­<lb/>uere, ma tengo, che uoi non ue aricordati di quello, che hauueti detto nel principio del <lb/>la uo&longs;tra lettera, non altro. </s> <s id="s.002944">In Venetia alli. </s> <s id="s.002945">18. Febraro.<emph.end type="italics"/> 1539. </s> </p> <p type="main"> <s id="s.002946">N<emph type="italics"/>icolo Tartaglia<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002947">QVESITO. XXXIII. FATTO CON VNA <lb/><emph type="italics"/>lettera dalla eccellentia de me&longs;&longs;er Hieronimo Cardano <lb/>l'Anno. <!-- REMOVE S-->1539. Adi. <!-- REMOVE S-->19. Marzo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002948">MESSER HIER ONIMO. M<emph type="italics"/>e&longs;&longs;er Nicolo mio carißimo ho riceuuto <lb/>una uo&longs;tra lettera a&longs;&longs;ai longa, la quale quanto piu è &longs;tata longa, tanto piu me <lb/>piacciuta, & uorria fu&longs;&longs;e &longs;tata doppia, tanto ne ui pen&longs;ate, che le mie mordente paro­<lb/>le &longs;iano procedute, ne da odio non e&longs;&longs;endogli cau&longs;a, ne da maligna natura facendo io be <lb/>ne doue po&longs;&longs;o, piu pre&longs;to, che male, e&longs;&longs;endo a&longs;&longs;ueto nell e&longs;&longs;ercitio mio del medicare, <lb/>che porta que&longs;to, ne manco &longs;on mo&longs;&longs;o da inuidia, perche &longs;e uoi&longs;eti, o eguale, o menore, <lb/>non ne ho cau&longs;a &longs;e &longs;eti maggiore in que&longs;t'arte debbo cercare di agguagliarue, & non <lb/>de dirne male, oltra di cio l'inuidio&longs;o maledice in ab&longs;entia, & non in pre&longs;entia, ma io <lb/>&longs;cri&longs;&longs;e que&longs;to per e&longs;citarui à re&longs;criuere, giudicandoui di pelegrino ingegno, come &longs;eti <lb/>per relatione de me&longs;&longs;er zuan Colle, il quale è &longs;tato qua, & hauendolo io molto fauori­<lb/>giato, & fattogli appiacere, &longs;econdo il mio potere, donde che lui ui faceua a&longs;&longs;ai bene, <lb/>& haueua anchora in di&longs;&longs;egno di la&longs;&longs;arui una mia lettura, ma lui &longs;i portò ingratamen­<lb/>te, dicendo male priuatamente, & publicamente, & inuitandomi fuora di propo&longs;ito, <lb/>con cartelli, & &longs;critture, la qual co&longs;a non riu&longs;cendoli à &longs;uo modo, che di una petitione <lb/>hebbe. </s> <s id="s.002949">3. &longs;olutioni, una di Euclide, l'altra di Ptolomeo, l'altra di zebber, &longs;i confu&longs;e tal­<lb/>mente, che &longs;i parti per di&longs;perato, & la&longs;&longs;o una &longs;cuola de for&longs;i. </s> <s id="s.002950">60. &longs;colari, dilche me ne <pb xlink:href="042/01/239.jpg"/>dol&longs;e a&longs;&longs;ai, &longs;i che &longs;e ue ho &longs;critto a&longs;per amente l'ho fatto uolontieri, pen&longs;ando di far &longs;e­<lb/>guire quello, che ne &longs;eguito, cioe di hauere la ri&longs;po&longs;ta uo&longs;tra con l'amicitia di co&longs;i &longs;in­<lb/>golar huomo in que&longs;t'arte à quel giudico per le co&longs;e &longs;critte nella uo&longs;tra lettera, &longs;i che <lb/>ho fatto un peccato di che non me ne uoglio pentire.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002951">H<emph type="italics"/>ora doueti &longs;apere, che oltra la lettera uo&longs;tra, ho riceuuto uno cartello delle co&longs;e, <lb/>che al pre&longs;ente &longs;eti per leggere publicamente in San Zuanepolo, il qual cartello mi è <lb/>&longs;ommamente piacciuto, & oltra di cio mi prometteti duii&longs;tromenti per dare al<emph.end type="italics"/> S.M<emph type="italics"/>ar <lb/>che&longs;e, & dui per me, et il<emph.end type="italics"/> S. O<emph type="italics"/>ttauiano &longs;criue ne manda quattro pur &longs;in al pre&longs;ente non <lb/>ho hauuto ne dui, ne quattro, ma dice, ch'io li hauero con certi libri, che mi manda uo­<lb/>lontieri, gli hauerei hauuti da dare al<emph.end type="italics"/> S.M<emph type="italics"/>arche&longs;e, come gli hauero ue li daro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002952">Q<emph type="italics"/>uanto alla ri&longs;po&longs;ta delle quattro mie accu&longs;e mi acca&longs;ca &longs;olo ri&longs;ponderui à due, l'u­<lb/>na &longs;i è della accu&longs;atione della uostra quinta propo&longs;itione dell'arte nuoua l'altra è dal ue <lb/>nire al cimento con uoi, che &longs;ia piu ualente huomo in que&longs;t'arte.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002953">Q<emph type="italics"/>uanto à que&longs;ta &longs;econda uoglio piu pre&longs;to uiuere un poco poltrone, che morire ua <lb/>lent'huomo, dapoi che gia ui rendeti, dicendo che Zuanantonio ha mal inte&longs;o, &longs;i che fac <lb/>cio fine à que&longs;to combattimento, &longs;pero uerreti à Millano, & uoi me cono&longs;cereti &longs;enza <lb/>il depo&longs;ito di. </s> <s id="s.002954">100. ducati, perche reuera io ue cono&longs;co per ualent'huomo, & co&longs;i co­<lb/>no&longs;cendo&longs;i tutti dui poi potremo deliberare.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002955">C<emph type="italics"/>irca alla di&longs;putatione della uostra quinta propo&longs;itione certo uoi fati bene à u&longs;ar <lb/>parole braue, & difendere la uo&longs;tra co&longs;a gia diuulgata Et certo uenendo (come &longs;pero <lb/>piacendo à Dio) uoi à Millano ne parlaremo piu adaggio, et tanto piu ch'io hebbe le uo <lb/>&longs;tre lettere hier&longs;era, & hoggi me bi&longs;ognato re&longs;criuerui per commandamento del Sig. <lb/><!-- REMOVE S-->Marche&longs;e, &longs;i che non ho potuto hauer con&longs;ideratione delle altre uostre propo&longs;itioni, <lb/>pregoui mandati, ouer portati quel re&longs;to delle uo&longs;tre. </s> <s id="s.002956">30. conclu&longs;ioni, che de&longs;ti à mae­<lb/>&longs;tro Antoniomaria ad ogni modo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002957">S<emph type="italics"/>e mi manda&longs;ti qualche &longs;olutione delle uo&longs;tre, cioe regole, ouer mi dareti, uenendo <lb/>l'hauero &longs;ommo appiacere, perche doueti &longs;apere, ch'io me diletto de ogni gentilezza, <lb/>& ch'io ho dato fuora una opera pur di pratica di Geometria, & di Arithmetica, & <lb/>di Algebra, della quale &longs;in à que&longs;t'hora è &longs;tampato piu della mita, & &longs;e uoleti, dando­<lb/>mene ch'io la daga fuora &longs;otto uo&longs;tro nome, io le daro fuora in fin dell'opera, come ho <lb/>fatto de tutti glialtri me hanno dato qualche co&longs;a di bello, & ui ponero uoi per l'inuen <lb/>tore, & &longs;é uoleti ch'io le tenghi occulte, faro come uorreti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002958">I<emph type="italics"/>o aui&longs;ai la eccellentia del<emph.end type="italics"/> S.M<emph type="italics"/>arche&longs;e de gli i&longs;tromenti quali gli mandati (anchor <lb/>che non &longs;iano per fina hora gionti) et gli dißi del cartello, et &longs;ua eccellentia mi <expan abbr="cõmando">commando</expan> <lb/>lo legge&longs;&longs;e, et tutte queste uo&longs;tre co&longs;e, piacque grandemente à &longs;ua eccellentia. </s> <s id="s.002959">Et mi <expan abbr="cõ-mando">con­<lb/>mando</expan> di &longs;ubito ui &longs;criue&longs;&longs;e la pre&longs;ente con grande i&longs;tantia in nome &longs;uo, aui&longs;andoui che <lb/>ui&longs;ta la pre&longs;ente doue&longs;ti uenir à Millano &longs;enza fallo, che uorria parlar con uoi. </s> <s id="s.002960">Et co&longs;i <lb/>ue e&longs;&longs;orto à douer uenire &longs;ubito, et non pen&longs;arui &longs;u, perche il detto<emph.end type="italics"/> S.M<emph type="italics"/>arche&longs;e è &longs;i gen <lb/>til remuneratore delli uirtuo&longs;i, &longs;i liberale, et &longs;i magnamimo che niuna per&longs;ona chi&longs;erue <lb/>&longs;ua eccellentia, mentre &longs;ia da qualche co&longs;a, re&longs;ta <expan abbr="di&longs;cont&etilde;ta">di&longs;contenta</expan>. </s> <s id="s.002961">Si che non re&longs;tati de uenire, <lb/>et uenireti à logiare in ca&longs;a mia, <expan abbr="nõ">non</expan> altro. </s> <s id="s.002962">Chri&longs;to da mal ui guardi alli. </s> <s id="s.002963">13. marzo.<emph.end type="italics"/> 1539. </s> </p> <p type="main"> <s id="s.002964">H<emph type="italics"/>ieronimo Cardano medico.<emph.end type="italics"/><pb pagenum="120" xlink:href="042/01/240.jpg"/>NICOLO. P<emph type="italics"/>er co&longs;tui &longs;on ridutto à un &longs;tranio pa&longs;&longs;o, perche &longs;enon uado à Millano <lb/>il<emph.end type="italics"/> S.M<emph type="italics"/>arche&longs;e il potria hauer per male, & qualche male me potria riu&longs;cire, & mal u<gap/><lb/>lontiera ui uado, pur ui uoglio andare.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002965">QVESITO. XXXIIII. FATTO PERSONAL­<lb/><emph type="italics"/>mente dalla eccellentia del mede&longs;imo me&longs;&longs;er Hieronimo Car <lb/>dano in Millano in ca&longs;a &longs;ua Adi. <!-- REMOVE S-->25. Marzo.<emph.end type="italics"/> 1539.</s> </p> <p type="main"> <s id="s.002966">MESSER HIERONIMO. H<emph type="italics"/>o molto accaro che uoi&longs;iati uenuto in que <lb/>&longs;ta, che la eccellentia del<emph.end type="italics"/> S.M<emph type="italics"/>arche&longs;e è caualcato per fina à Vegeuene, perche <lb/>haueremo commodita di poter&longs;e galdere, et ragionare in&longs;ieme delle co&longs;e no&longs;tre per fin <lb/>che torni. </s> <s id="s.002967">Certamente uoi &longs;eti &longs;tato pur troppo di&longs;corte&longs;e à non hauermi uoluto da­<lb/>re quella regola da uoi ritrouata &longs;opra il capitolo di co&longs;a, e cubo egual à numero, et ma&longs; <lb/>&longs;ime hauendouene tanto pregato.<emph.end type="italics"/> N. I<emph type="italics"/>o ue diro, io non fazzo tanto il care&longs;tio&longs;o, per <lb/>il &longs;implice capitolo, ne per le co&longs;e ritrouate per lui, ma per quelle, che per notitia di <lb/>quello &longs;i po&longs;&longs;ono ritrouare, perche eglie una chiaue, che ne apre la uia à potere inue&longs;ti­<lb/>gare infiniti altri capitoli, & &longs;e il non fu&longs;&longs;e che al pre&longs;ente io &longs;on occupato nella tradut <lb/>tione di Euclide, in uolgare (& per fin à que&longs;t'hora l'ho tradutto per fin al &longs;uo. </s> <s id="s.002968">13. li­<lb/>bro) à molti altri capitoli haueria gia trouato regola generale, ma &longs;pedito che habbia <lb/>que&longs;ta mia fatica di Euclide gia principiata, ho de&longs;ignato di <expan abbr="cõponere">componere</expan> un'opera di pra­<lb/>tica, & in&longs;ieme con quella, una nuoua Algebra, nella quale non &longs;olamente ho deliberato <lb/>di publicare ad ogni huomo tutte le dette mie inuentioni de capitoli nuoui, ma molti al <lb/>tri, che &longs;pero di ritrouare, & anchora uoglio mo&longs;trare la regola di poterne inue&longs;tigar <lb/>ne infiniti altri qual&longs;pero, che la &longs;ara una co&longs;a utile, & bella, & que&longs;ta é la cau&longs;a, che <lb/>me glifa negar ad ogniuno, per che io al pre&longs;ente non ui pongo alcuna cura &longs;opra di <lb/>loro (per e&longs;&longs;er, come detto, occupato &longs;opra Euclide) & in&longs;ignandoli ad alcuno &longs;pecu­<lb/>latiuo (come che è uo&longs;tra eccellentia) facilmente potria con tal euidentia trouar altri <lb/>capitoli (per e&longs;&longs;er facile lo aggiongere alle co&longs;e trouate) & publicarli, come inuento­<lb/>re, ilche facendo mi gua&longs;taria ogni mio di&longs;&longs;egno. </s> <s id="s.002969">Si che questa è la principal cau&longs;a, che <lb/>mi ha fatto e&longs;&longs;er tanto di&longs;corte&longs;e con uo&longs;tra Eccellentia, & tanto piu facendo al pre&longs;en <lb/>te imprimere quella &longs;ua opera in &longs;imil materia, & hauendomi anchor &longs;critto di uoler <lb/>dar fuora tai mie inuentioni &longs;otto mio nome, & farmene inuentore La qual co&longs;a in ef­<lb/>fetto non mi piace in conto alcuno, perche tale mie <expan abbr="inu&etilde;tioni">inuentioni</expan> le uoglio publicare in ope <lb/>re mie, et non in opere de altra per&longs;ona.<emph.end type="italics"/> M.H. E<emph type="italics"/>ue ho pur &longs;critto anchora che &longs;e uoi <lb/>non ui contentati, che io ue le dia fuora, che io le reteniro &longs;ecrete.<emph.end type="italics"/> N. B<emph type="italics"/>a&longs;ta che in que <lb/>&longs;ta parte non ui ho uolesto credere.<emph.end type="italics"/> M.H. I<emph type="italics"/>o ui giuro, ad&longs;acra Dei euangelia, & da <lb/>real gentil'huomo, non &longs;olamente da non publicar giamai tale uo&longs;tre inuentioni, &longs;e me <lb/>le in&longs;ignate. </s> <s id="s.002970">Ma anchora ui prometto, et impegno la fede mia da real Christiano, da no <lb/>tarmele in zifera, accio che dapoi la mia morte alcuno non le po&longs;&longs;a intendere, &longs;e me il <lb/>uoleti mo credere credetilo, &longs;e non la&longs;&longs;atilo &longs;tare.<emph.end type="italics"/> N. N<emph type="italics"/>on uolendo io pre&longs;tar fede à <lb/>tanti uo&longs;tri giur amenti io meritaria certamente da e&longs;&longs;er giudicato huomo &longs;enza fede, <lb/>ma perche ho deliberato caualcare per fina à Vegeuene à ritrouar la eccellentia del<emph.end type="italics"/> S. <lb/>M<emph type="italics"/>arche&longs;e, perche eglie hormai tre giorni ch'io &longs;on qua, & me rincre&longs;&longs;e lo a&longs;pettare <pb xlink:href="042/01/241.jpg"/>tanto, ritornato che &longs;ia ui prometto di mo&longs;trarui il tutto.<emph.end type="italics"/> M.H. D<emph type="italics"/>apoi che haueti <lb/>deliberato da uolere adogni modo caualcare per fina à Vegeuene dal<emph.end type="italics"/> S. M<emph type="italics"/>arche&longs;e, ni <lb/>uoglio dar una lettera da dar à &longs;ua Eccellentia, accio che quella &longs;appia, che uoi &longs;eti, ma <lb/>nanti che ue parteti, uoglio che mi mo&longs;trati la regola di que&longs;ti uostri capitoli, come che <lb/>me haueti prome&longs;&longs;o.<emph.end type="italics"/> N. I<emph type="italics"/>o &longs;on contento, ma uoglio che &longs;appiati, che per potermi ari <lb/>cordare in ogni mia improui&longs;a occorrentia tal modo operatiuo, io l'ho redutto in uno <lb/>capitolo in rima, perche &longs;e io non haue&longs;&longs;e u&longs;ato questa cautella &longs;pe&longs;&longs;o me &longs;aria u&longs;cito di <lb/>mente, & quantunque tal mio dire in rima non &longs;ia molto ter&longs;o non mi ho curato, per­<lb/>che mi basta che mi&longs;erua à ridurme in memoria tal regola ogni uolta, che io il dica, il <lb/>qual capitolo ue lo uoglio &longs;criuere de mia mano, accio che &longs;iati &longs;icuro, che ui dia tal <lb/>inuentione giu&longs;ta, & buona.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002971">Q<emph type="italics"/>uando chel cubo con le co&longs;e appre&longs;&longs;o <lb/>Se agguaglia à qualche numero di&longs;creto <lb/>Trouan dui altri differenti in e&longs;&longs;o.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002972">D<emph type="italics"/>apoi terrai que&longs;to per con&longs;ueto <lb/>Che'llor produtto &longs;empre &longs;ia eguale <lb/>Alterzo cubo delle co&longs;e neto,<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002973">E<emph type="italics"/>l re&longs;iduo poi &longs;uo generale <lb/>Delli lor lati cubi ben &longs;ottratti <lb/>Varra la tua co&longs;a principale.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002974">I<emph type="italics"/>n el &longs;econdo de cote&longs;tiatti <lb/>Quando che'l cubo re&longs;ta&longs;&longs;e lui &longs;olo <lb/>Tu o&longs;&longs;eruarai que&longs;t'altri contratti,<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002975">D<emph type="italics"/>el numer farai due tal part'à uolo <lb/>Che l'una in l'altra &longs;i produca &longs;chietto <lb/>El terzo cubo delle co&longs;e in &longs;tolo<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002976">D<emph type="italics"/>elle qual poi, per communprecetto <lb/>Torrai li lati cubi in&longs;ieme gionti <lb/>Et cotal &longs;omma &longs;ara il tuo concetto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002977">E<emph type="italics"/>l terzo poi de que&longs;ti no&longs;tri conti <lb/>Se &longs;olue col &longs;econdo &longs;e ben guardi <lb/>Che per natura &longs;on qua&longs;i congionti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002978">Q<emph type="italics"/>ue&longs;ti trouai, & non con paßi tardi <lb/>Nel mille cinquecentè, quatroe trenta <lb/>Con fondamenti ben &longs;ald'è gagliardi<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002979">N<emph type="italics"/>ella citta dal mar'intorno centa.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002980">I<emph type="italics"/>l qual capitolo parla tanto chiaro, che &longs;enz'altro e&longs;&longs;empio credo che uo&longs;tra Eccel <lb/>lentia intendera il tutto.<emph.end type="italics"/> M.H. C<emph type="italics"/>ome &longs;e lo intendero, e l'ho qua&longs;i inte&longs;o per fina el­<lb/>pre&longs;ente, andati pur, che, come &longs;areti ritornato, ue faro poi uedere &longs;e l hauero inte&longs;o.<emph.end type="italics"/><lb/>N. H<emph type="italics"/>or uo&longs;tra Eccellentia &longs;e aricordi mo à non mancar della prome&longs;&longs;a fede, perche <lb/>&longs;e per mala &longs;orte quella me manca&longs;&longs;e, <gap/> che me de&longs;&longs;e fuora que&longs;ti capitoli, o &longs;ia in<emph.end type="italics"/><pb pagenum="121" xlink:href="042/01/242.jpg"/><emph type="italics"/>que&longs;ta opera che fatti imprimere al pre&longs;ente, ouer in altra anch or che quella li de&longs;&longs;e <lb/>fora &longs;atto mio nome, & che mi face&longs;&longs;e il proprio inuentore, ui prometto, & giuro di <lb/>&longs;arne &longs;tampare immediate drio un'altra, laqual non ui &longs;ara molto agrata.<emph.end type="italics"/> M. H. <lb/>N<emph type="italics"/>on ue dubitati che quello che ui ho prome&longs;&longs;o ue lo attendaro, andati è &longs;tati &longs;icuro to­<lb/>le, dareti que&longs;ta mia lettera al Signor Marche&longs;e da mia parte.<emph.end type="italics"/> N. H<emph type="italics"/>or &longs;ume arrico <lb/>mando.<emph.end type="italics"/> M. H. A<emph type="italics"/>ndati in bon'hora.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002981">N. P<emph type="italics"/>er la fede mia che non uoglio andare altramente à Vigeuene, ancime uoglio <lb/>uoltare alla uolta di Venetia, uada la co&longs;a come &longs;i uoglia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.002982">QVESITO XXXV. FATTO DALLA ECCELLEN­<lb/><emph type="italics"/>tia del mede&longs;imo<emph.end type="italics"/> M. H<emph type="italics"/>ieronimo Cardano, con una lettera fatta <lb/>alli. </s> <s id="s.002983">9. Aprile. <!-- KEEP S--></s> <s id="s.002984">1539. mandatame in Venetia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002985">MESSER HIERONIMO. M<emph type="italics"/>e&longs;&longs;er Nicolo mio carißimo mi &longs;ono molto <lb/>mar auigliato della uo&longs;tra partita co&longs;i al improui&longs;ta &longs;enza parlare al Signor <lb/>Marche&longs;e qual <expan abbr="u&etilde;ne">uenne</expan> el &longs;abbato Santo, & non pote hauer li uo&longs;tri in&longs;tromenti per fin <lb/>al marti dapo Pa&longs;qua & con grandißima difficulta, pur gli hebbi & li conzai & ge <lb/>li appre&longs;entai il medemo martidi de &longs;era, certo io pen&longs;o che fala&longs;ti à non farui cono&longs;ce <lb/>re da &longs;ua eccellentia, perche eglie Principe liber alißimo & grande amatore de uirtu, <lb/>& fautore, & hebbe molto à caro li uostri instromenti, & li uol&longs;e intendere, & io li <lb/>mo&longs;trai &longs;ucitamente la &longs;ua ualuta, hor que&longs;to ba&longs;ta potria anchor uenir tempo che ui <lb/>giouaria l'e&longs;&longs;ere cono&longs;ciuto dal<emph.end type="italics"/> S. M<emph type="italics"/>arche&longs;e, anchor ch'io &longs;o perche cau&longs;a ue &longs;iti par <lb/>tito perche coloro che ui con&longs;igliorono me lo di&longs;&longs;ero.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002986">Q<emph type="italics"/>uanto à l'opera mia pen&longs;o &longs;era fornita la &longs;ettimana che uiene che non li manta <lb/>&longs;aluo che tre fogli à fornirla. </s> <s id="s.002987">Quanto alla que&longs;tione del uo&longs;tro capitolo di co&longs;a é cubo <lb/>equal à numero ui ringratio a&longs;&longs;ai che mi da&longs;e&longs;ti tal capitolo, & ui faro cono&longs;cere ch'io <lb/>non ui&longs;aro ingrato. </s> <s id="s.002988">Ma pero io confe&longs;&longs;o il mio errore di non hauer hauuto tanto inge <lb/>gno che io lo habbia potuto anchora intendere, e pero ui &longs;upplico per l'amor che mi <lb/>portati, & per l'amicitia ch'è tra noi che &longs;pero durara fin che uiueremo che mi man­<lb/>dati &longs;ciolta que&longs;ta que&longs;tione. </s> <s id="s.002989">1. cubo piu. </s> <s id="s.002990">3. co&longs;e, equal à. </s> <s id="s.002991">10. & &longs;pero che mandandome <lb/>la ue ne trouareti &longs;i contento quanto io di hauerla riceuuta non altro Chri&longs;to da mal <lb/>ui guardi in Millano alli. </s> <s id="s.002992">9. Aprile.<emph.end type="italics"/> 1539. </s> </p> <p type="main"> <s id="s.002993">H<emph type="italics"/>ieronimo Cardano medico tutto uo&longs;tro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002994">NICOLO. H<emph type="italics"/>onorando me&longs;&longs;er Hieronimo ho riceputa una uo&longs;tra di. </s> <s id="s.002995">9. Aprile <lb/>& ho inte&longs;o il tenor di quella, la cau&longs;a della mia co&longs;i improui&longs;a et tacita partita da Mi <lb/>lano &longs;enza parlare alla eccellentia del Signor Marche&longs;e è que&longs;ta che quando me par­<lb/><gap/>eti da Venetia per uenir à Milano io promißi alli mei amici di e&longs;&longs;er qua infalante à <lb/>Pa&longs;qua & con&longs;ider ando che &longs;e io &longs;ta&longs;eua niente piu di quello ch'io &longs;teti à partirme da <lb/>Millano egliera forza à re&longs;tar mendace, perche uenendo uia à &longs;taffetta hebbi fatica ad <lb/>e&longs;&longs;er qua el &longs;ebbo Santo &longs;i che non incolpati alcun che mi habbia con&longs;igliato.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002996">C<emph type="italics"/>irca alla uo&longs;tra opera molto de&longs;idero che la&longs;e forni&longs;ca presto, & di uederla, per­<lb/>che per fin che <expan abbr="nõ">non</expan> la uedo &longs;to &longs;u&longs;petto&longs;o che quella non mi manchi di &longs;ede, cioe che quel-<emph.end type="italics"/><pb xlink:href="042/01/243.jpg"/><emph type="italics"/>la non ue interponga, li mei capitoli.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002997">C<emph type="italics"/>irca al detto mio capitolo de co&longs;a è cubo equal à numero molto mi marauiglio che <lb/>uo&longs;tra <expan abbr="eccell&etilde;tia">eccellentia</expan> <expan abbr="nõ">non</expan> habbia inte&longs;o maßime che io parlo chiaro nel detto mio capitolo, <lb/>ma ho pen&longs;ato che uoi ui &longs;iati ingannato in quel ditto, che dice al terzo cubo delle co&longs;e <lb/>netto, cioe pen&longs;o che uoi habbiati tolto il terzo del cubo delle co&longs;e, et bi&longs;ogna tor il cu <lb/>bo del terzo delle co&longs;e e&longs;&longs;empi gratia à uoler ri&longs;oluere quella equatione de. </s> <s id="s.002998">1. cubo piu. <lb/></s> <s id="s.002999">3. co&longs;e equal à. </s> <s id="s.003000">10. che uo&longs;tra <expan abbr="eccell&etilde;tia">eccellentia</expan> mi ha mandata dico che bi&longs;ogna trouar dui nu<lb/>meri (ouer quantita) che la differentia de luno à laltro &longs;ia. </s> <s id="s.003001">10. (cioe tanto quanto è <lb/>il no&longs;tro numero) & che il produtto de que&longs;te due quantita multiplicate luna fia l'al­<lb/>tra facciamo à ponto. </s> <s id="s.003002">1. cioe el cubo della terza parte delle co&longs;e, liquali dui numeri, <lb/>ouer quantita, operando per Algebra, ouer per qual altra uia para piu commoda &longs;e <lb/>trouara luna de loro, cioe la menore e&longs;&longs;er<emph.end type="italics"/> <22>. </s> <s id="s.003003">26. <emph type="italics"/>men. </s> <s id="s.003004">5. & laltra, cioe la maggiore<emph.end type="italics"/> <22><lb/>26. <emph type="italics"/>piu. </s> <s id="s.003005">5. Hor de cadauna di que&longs;te due quantita bi&longs;ogna trouar il &longs;uo lato cubo, cioe <lb/>la &longs;ua<emph.end type="italics"/> <22>. <emph type="italics"/>cuba, & quella della menor &longs;ara<emph.end type="italics"/> <22>. <emph type="italics"/>uniuerr&longs;ale cuba de<emph.end type="italics"/> <22>. </s> <s id="s.003006">26. <emph type="italics"/>men. </s> <s id="s.003007">5. & quel­<lb/>la della maggiore &longs;ara<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale cuba de<emph.end type="italics"/> <22>. </s> <s id="s.003008">26. <emph type="italics"/>piu. </s> <s id="s.003009">5. Hor bi&longs;ogna &longs;ottrare il lato <lb/>menore del maggiore, et il re&longs;tante &longs;ara el ualore della no&longs;tra co&longs;a principale, el qual <lb/><expan abbr="restãte">restante</expan> uenira à e&longs;&longs;er el re&longs;iduo di quelle due<emph.end type="italics"/> <22>. <emph type="italics"/>uniuer&longs;ale cu.cioe &longs;ara<emph.end type="italics"/> <22>. <emph type="italics"/>u.cu.<emph.end type="italics"/> <22>. </s> <s id="s.003010">26. <lb/><emph type="italics"/>piu. </s> <s id="s.003011">5. men<emph.end type="italics"/> <22>.<emph type="italics"/>u.cuba<emph.end type="italics"/> <22>. </s> <s id="s.003012">26. <emph type="italics"/>me. </s> <s id="s.003013">5. & tanto ual&longs;e la no&longs;tra co&longs;a principale, la qual con­<lb/>clu&longs;ione, oltra che la i&longs;perienza ne renda bona testimonianza, cioe cubando la detta <lb/>quantita, ouer co&longs;a, & à tal cubo giongendoui il triplo di detta quantita tal &longs;umma fa <lb/>ra preci&longs;amente. </s> <s id="s.003014">10. come &longs;e propone, ma anchora <expan abbr="Geometricam&etilde;te">Geometricamente</expan> facilmente &longs;e di <lb/>mo&longs;tra la bonta et cau&longs;a di tal operare, & <expan abbr="quãdo">quando</expan> chel fu&longs;&longs;e. </s> <s id="s.003015">1. cubo piu. </s> <s id="s.003016">1. co&longs;a equal <lb/>à. </s> <s id="s.003017">11. bi&longs;ognaria pur trouar dui numeri, ouer quantita, che luna fu&longs;&longs;e. </s> <s id="s.003018">11. piu de laltra, <lb/>& che il produtto de luna in laltra faccia. </s> <s id="s.003019">1/27. cioe il cubo del terzo delle co&longs;e, onde <lb/><expan abbr="operãdo">operando</expan> come di&longs;opra fu fatto &longs;e trouara la no&longs;tra co&longs;a ualer<emph.end type="italics"/> <22>. <emph type="italics"/>u.cuba<emph.end type="italics"/> <22>. </s> <s id="s.003020">30.31/108. <lb/><emph type="italics"/>piu. </s> <s id="s.003021">5. 1/2. men<emph.end type="italics"/> <22>.<emph type="italics"/>u.cuba<emph.end type="italics"/> <22>. </s> <s id="s.003022">30.31/108. <emph type="italics"/>men, 5. 1/2. non altro Iddio da mal ui guardi in Ve <lb/>netia alli. </s> <s id="s.003023">23. di Aprile. <!-- KEEP S--></s> <s id="s.003024">1539. aricordatiue della prome&longs;&longs;a.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003025">N<emph type="italics"/>icolo Tartaglia<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.003026">QVESITO. XXXVI FATTO DALLA ECCEL­<lb/><emph type="italics"/>lentia de me&longs;&longs;er Hieronimo Cardano con una &longs;ua lettera <lb/>fatta all. </s> <s id="s.003027">12. di Mazzo.<emph.end type="italics"/> 1539.</s> </p> <p type="main"> <s id="s.003028">MESSER HIER ONIMO. I<emph type="italics"/>n ri&longs;po&longs;ta de una uo&longs;tra delli. </s> <s id="s.003029">23. d'Aprile, <lb/>hauuta non hieri l'altro, me&longs;&longs;er Nicolo carißimo, ui ri&longs;pondero &longs;ucintamente à <lb/>partita per partita, & prima, quanto alla e&longs;cu&longs;atione del e&longs;&longs;er partito, &longs;enza andar à <lb/>Vigeueno. </s> <s id="s.003030">Io non uoglio &longs;aluo quello che uoleti uoi, me rincre&longs;&longs;e l'habbiati pigliato <lb/>que&longs;ta fatica per cau&longs;a della mia amicitia &longs;enza frutto alcuno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003031">Q<emph type="italics"/>anto à l'opera che &longs;ia fornita per cauarui di &longs;o&longs;petto ue ne mando una e ue la <lb/>mando disligata che non ho uoluto farla battere per e&longs;&longs;er troppo fre&longs;ca,<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003032">Q<emph type="italics"/>uanto al capitolo uostro & al mio ca&longs;o per uoi a&longs;&longs;olto ue ne ringratio <expan abbr="&longs;ingola-rißimam&etilde;te">&longs;ingola­<lb/>rißimamente</expan>, & laudo il uo&longs;tro ingegno &longs;opra tutti quelli che ho cono&longs;ciuti, & me &longs;ta-<emph.end type="italics"/><pb pagenum="122" xlink:href="042/01/244.jpg"/><emph type="italics"/>to accaro piu che &longs;e mi hauesti donato duc. </s> <s id="s.003033">100. & ui cono&longs;co per mìo amicißimo & <lb/>ne ho fatto proua & l'ho trouato generalißimo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003034">Q<emph type="italics"/>uanto al dubbio che uoi haueti che non ui faccia &longs;tampare tai uostre inuentioni, <lb/>la mia fede che ui ho data con giuramento, ui doueua ba&longs;tare, perche la &longs;peditione del <lb/>mio libro non faceua niente à que&longs;to, perche &longs;empre che mi pare gli po&longs;&longs;o &longs;empre ag­<lb/>giongere, ma ue ho per e&longs;cu&longs;o che la dignita della co&longs;a, non ui la&longs;&longs;a fondare &longs;opra quel <lb/>lo che ui doueti fondare, cioe &longs;opra la fede d'un gentilhuomo & ui fondati &longs;opra una <lb/>co&longs;a che non ual niente, cioe &longs;opra il finir d'un libro al quale &longs;i potria &longs;empre agion­<lb/>gere capitulum nouum. </s> <s id="s.003035">ouer capitula noua, & ui é. </s> <s id="s.003036">1000. altriremedij, ma el ponto é <lb/>qua chel non è mazor tradimento che à e&longs;&longs;er mancator di fede, & far di&longs;piacere à chi <lb/>ha fatto appiacere, & &longs;e me e&longs;perimentareti trouareti &longs;e io ui &longs;aro amico, ouer nò, <lb/>& &longs;e hauero grato l'amicitia uo&longs;tra, & li piaceri che me haueti fatti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003037">V<emph type="italics"/>e aui&longs;o anchora, et caramente ui prego che di que&longs;te mie opere &longs;tampate per amo <lb/>re di quello che li ha <expan abbr="&longs;tãpate">&longs;tampate</expan> qual ne <expan abbr="mãdara">mandara</expan> iui da uendere, che ge ne facciati &longs;pazzar <lb/>piu che poßibel &longs;ia per mio amore che, &longs;e fu&longs;&longs;ero &longs;tampate à mie &longs;pe&longs;e <expan abbr="nõ">non</expan> ue ne diria pa <lb/>rola perche &longs;on piu caldo del ben di mei amici che del mio, <expan abbr="nõ">non</expan> altro Dio da mal ui guar <lb/>di in Milano alli. </s> <s id="s.003038">12. di Marzo.<emph.end type="italics"/> 1539. </s> </p> <p type="main"> <s id="s.003039">H<emph type="italics"/>ieronimus Cardanus Medicus totus ue&longs;ter.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003040">NICOLO. H<emph type="italics"/>onorandißimo me&longs;&longs;er Hieronimo ho riceputo una uo&longs;tra in&longs;ieme <lb/>con una delle uo&longs;tre, opere della quale ue ne ringratio, & quantunque al pre&longs;ente non <lb/>habbia tempo di poterla uedere ordinnariamente come &longs;i de, &longs;i per e&longs;&longs;er molto occupa <lb/>to nella i&longs;peditione di Euclide &longs;i per e&longs;&longs;er anchora mezzo amalato, nondimeno ui ho <lb/>dato una occchiata co&longs;i disligata, & ho guardato quel uo&longs;tro modo di formar el rotto <lb/>di quello re&longs;iduo che rimane nella e&longs;tratione della radice cuba al. <!-- REMOVE S-->23 capi.alla carta &longs;i­<lb/>gnata<emph.end type="italics"/> D.<emph type="italics"/>iiij.doue che uostra eccellentia uole che &longs;i metta quel detto re&longs;iduo che auan <lb/>za nella e&longs;tratione delle radice cube, &longs;opra una uirgula per numeratore, & di &longs;otto di <lb/>tal uirgulaquella uole che &longs;i ue metta el treppio del quadrato della radice per denomin­<lb/>tore nella qual co&longs;a uo&longs;tra eccellentia err a tanto de gro&longs;&longs;o che me ne &longs;tupi&longs;co, perche <lb/>cadauno che haue&longs;&longs;e &longs;olamente mezzo un'occhio lo potria uedere, & &longs;el non fu&longs;&longs;e che <lb/>quella con e&longs;&longs;empij la ua replicando io haueria giudicato che fu&longs;&longs;e errore di &longs;tampa, <lb/>& che el &longs;ia eluero che tal uo&longs;tra regola &longs;ia fal&longs;ißima &longs;e puo cono&longs;cere uolendo cauar <lb/>la Radice cuba propinqua de. </s> <s id="s.003041">24. la quale primamente &longs;aria. </s> <s id="s.003042">2. & auanzaria. </s> <s id="s.003043">16. el­<lb/>qual. </s> <s id="s.003044">16. <expan abbr="part&etilde;dolo">partendolo</expan> per el treppio del quedrato del.<emph.end type="italics"/> 2. (<emph type="italics"/>qual&longs;aria.<emph.end type="italics"/> 12.) <emph type="italics"/>ne uenira. </s> <s id="s.003045">1. 1/3. <lb/>qual gionto con la prima radice, cioe con. </s> <s id="s.003046">2. fara. </s> <s id="s.003047">3. 1/3. & co&longs;i &longs;econdo tal uo&longs;tra rego <lb/>la la radice cu. </s> <s id="s.003048">propinqua de. </s> <s id="s.003049">24. &longs;aria. </s> <s id="s.003050">3. 1/3. co&longs;a molto rediculo&longs;a, perche il cubo de. <lb/></s> <s id="s.003051">3. 1/3. &longs;aria. </s> <s id="s.003052">37. 1/72. co&longs;a molto <expan abbr="lõtana">lontana</expan> dalla uerita, della qualco&longs;a molto me ne rincre&longs;ce <lb/>per honor uo&longs;tro <expan abbr="nõ">non</expan> altro Iddio da mal ui guardi in Venetia alli. </s> <s id="s.003053">27. di Mazzo.<emph.end type="italics"/> 1539. </s> </p> <p type="main"> <s id="s.003054">N<emph type="italics"/>icolo Tartaglia tutto uo&longs;tro.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.003055">QVESITO XXXVII. FATTO DA MAESTRO <lb/>M<emph type="italics"/>aphio Poueiani gia no&longs;tro di&longs;cipulo qual stantiaua à Ber <lb/>gamo, con una lettera de di. </s> <s id="s.003056">10. Luio.<emph.end type="italics"/> 1539.</s> </p> <pb xlink:href="042/01/245.jpg"/> <p type="main"> <s id="s.003057">MAESTRO MAPHIO. H<emph type="italics"/>onorando me&longs;&longs;er mae&longs;tro &longs;aluti &c. </s> <s id="s.003058">Pre­<lb/>go uo&longs;tra eccellentia mi uoglia chiarire questa <expan abbr="ragiõcella">ragioncella</expan>, la quale io non la &longs;o <lb/>ne per po&longs;itione ne per altra regola ri&longs;oluere. </s> <s id="s.003059">Hor guardati &longs;e io &longs;on un cauallo, qual <lb/>ragione dice à que&longs;to modo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003060">E<emph type="italics"/>glie uno che uorebbe comprar un pe&longs;&longs;e, & <expan abbr="domāda">domanda</expan> quanto ne uoi tu della lira gro&longs; <lb/>&longs;a da once. </s> <s id="s.003061">30. come qui in Bergamo &longs;iu&longs;a, & colui ri&longs;ponde & dice, ne uoglio tanti de <lb/>nari della lira con quante once pe&longs;a tutto il pe&longs;&longs;e, et co&longs;i à quel mercato fu pe&longs;ato il det <lb/>to pe&longs;ce qual monto &longs;oldi. </s> <s id="s.003062">8. &longs;e adimanda quante lire pe&longs;aua tutto il pe&longs;ce. </s> <s id="s.003063">Et ue de­<lb/>gnareti di darmene aui&longs;o & perdonatime &longs;e ogni tratto ue dago di&longs;turbo con qualche <lb/>chimera di poco &longs;ugo certo ui poteti accorgere che io dago poca opera al &longs;tudio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003064">A<emph type="italics"/>nchora ui ho da aui&longs;arue que&longs;to de nouo, che uno mio amico da Milano m'ha &longs;crit <lb/>to come che il Medico Cardano compone un'altra opera, in Algebra, &longs;opra certi ca­<lb/>pitoli nouamente trouati, onde pen&longs;o che le &longs;iano le co&longs;e che gia me dice&longs;ti hauerli in­<lb/>&longs;egnate &longs;i che mi dubito che ui uoglia gabbare non altro à uoimol to mi aricomando, <lb/>& offero in Bergamo alli. </s> <s id="s.003065">10. di Luio.<emph.end type="italics"/> 1339. </s> </p> <p type="main"> <s id="s.003066">M<emph type="italics"/>aphio Poueiani uo&longs;tro di&longs;cepolo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003067">NICOLO. M<emph type="italics"/>ae&longs;tro Maphio carißimo ho riceuuto la uo&longs;tra alla qual breuemen <lb/>te ri&longs;pondo, & dico che il detto pe&longs;&longs;e pe&longs;aua once<emph.end type="italics"/> <22>. </s> <s id="s.003068">2880. <emph type="italics"/>lequal once le ritrouo in <lb/>questo modo. </s> <s id="s.003069">Io pongo chel pe&longs;&longs;e pe&longs;a&longs;&longs;e. </s> <s id="s.003070">1. co&longs;a di once, adunque fu po&longs;to la lira una <lb/>co&longs;a de danari diro adunque &longs;e onci. </s> <s id="s.003071">30. ual una co.de danari, che ualera. </s> <s id="s.003072">1. co&longs;a de on­<lb/>ce multiplico. </s> <s id="s.003073">1. co&longs;a.de once fia. </s> <s id="s.003074">1. co&longs;a de danari fara. </s> <s id="s.003075">1. cen&longs;o de danari da partir <lb/>per. </s> <s id="s.003076">30. qual partendolo me ne uien. </s> <s id="s.003077">1. cen&longs;o, e&longs;imo de. </s> <s id="s.003078">30. & que&longs;to tal rotto &longs;ara equa <lb/>le à danari. </s> <s id="s.003079">96. cioe à &longs;oldi. </s> <s id="s.003080">8. fatto in danari, leuo li rotti et feguito el capitolo trouo la <lb/>co&longs;a ualer<emph.end type="italics"/> <22>. </s> <s id="s.003081">2880. <emph type="italics"/>& tante once pe&longs;aua el detto pe&longs;&longs;e, come di &longs;opra dißi, & ancho <lb/>ra tanti danari fu posto la lira à once. </s> <s id="s.003082">30. per lira, onde facendo el <expan abbr="cõto">conto</expan> montaria pre <lb/>ci&longs;amonte danari. </s> <s id="s.003083">96. cioe &longs;oldi. </s> <s id="s.003084">8. ch'è il propo&longs;ito.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003085">C<emph type="italics"/>irca alla noua che me &longs;criueti hauer inte&longs;o del Medico Cardano da Mila no, cer <lb/>tamente ne ho riceuuto fa&longs;tidio a&longs;&longs;ai, perche s'eglie il uero che lui dice di uo ler darfo <lb/>ra capitoli nouamente ritrouati, el non puo e&longs;&longs;er altramente di quello che haueti det­<lb/>to, e pero il prouerbio <expan abbr="nõ">non</expan> <expan abbr="m&etilde;ti&longs;&longs;e">menti&longs;&longs;e</expan>, qual dice. </s> <s id="s.003086">Quello che tu non uoi che &longs;i &longs;appia nol dir <lb/>ad alcuno, stati attento &longs;e intendereti altro &longs;opra di que&longs;to datimene aui&longs;o non altro <lb/>Iddio da mal ui guardi in Venetia alli. </s> <s id="s.003087">19. di. </s> <s id="s.003088">Luio.<emph.end type="italics"/> 1539. </s> </p> <p type="head"> <s id="s.003089">QVESITO. XXXVIII. FATTO CON VNA <lb/><emph type="italics"/>lettera dalla eccellentia de me&longs;&longs;er Hieronimo Cardano <lb/>riceputa alli. </s> <s id="s.003090">4. di Ago&longs;to.<emph.end type="italics"/> 1539.</s> </p> <p type="main"> <s id="s.003091">MESSER HIERONIMO. P<emph type="italics"/>er aui&longs;o del no&longs;tro ben &longs;tare, & de molte <lb/>altre lettere quale ue ho &longs;critte anchor non ue &longs;iati dignato di re&longs;criuermi, & <lb/>tanto piu io ue ho mandato adomandare la re&longs;olutione de diuer&longs;i que&longs;iti alli quali non <lb/>mi haueti ri&longs;po&longs;to, & tra li altri quello di cubo equale à co&longs;e, e numero, eglie ben <lb/>uero che ho inte&longs;o tal regola, ma quando che il cubo della terza parte delle co&longs;e ec-<emph.end type="italics"/><pb pagenum="123" xlink:href="042/01/246.jpg"/><emph type="italics"/>cede il qu adrato della mita del numero, all'hora non po&longs;&longs;o farli &longs;eguir la equatione, <lb/>come appare, pero haueria appiacere me &longs;olue&longs;ti que&longs;ta. </s> <s id="s.003092">1. cubo egual à. </s> <s id="s.003093">9. eo&longs;e piu. <lb/></s> <s id="s.003094">10. & di que&longs;to mi fareti &longs;ommo appiacere.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003095">V<emph type="italics"/>i prego anchora che mi uogliati mandarme quel uostro modo da de&longs;criuere Geo­<lb/>metrice uno quadrato in un triangolo de lati diuer&longs;i, pero che circa à tal co&longs;a me gli&longs;o <lb/>no affaticato a&longs;&longs;ai, & mai ho potuto ritrouar modo da &longs;aperlo fare, offerendomi an­<lb/>chora mi per uoi, &longs;e po&longs;&longs;o, e uaglio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003096">V<emph type="italics"/>e aui&longs;o anchora qualmente io indrizzai da uoi il signor Don Diego de Mendo­<lb/>cia Amba&longs;ciatore della maesta dell'Imper atore, qual &longs;e diletta di queste &longs;cientie, qual <lb/>pen&longs;o non ui &longs;ara inutile, & gli dißi dell'altezza delle uirtu uo&longs;tre, come meritati.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003097">Q<emph type="italics"/>uanto alla proßimatione della Radice, & della formatione del &longs;uo rotto, nelli re­<lb/>&longs;idui delli numeri, che non &longs;ono cubi. </s> <s id="s.003098">Dico che ne &longs;ono due altre regole buone po&longs;te nelle <lb/>detta opera, & in quella non ui ca&longs;ca errore, &longs;aluo che nel detto e&longs;&longs;empio de<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. <lb/></s> <s id="s.003099">24. perche la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba del detto. </s> <s id="s.003100">24. reuera &longs;arebbe circa. </s> <s id="s.003101">2. 1/4. ouer parlando piu <lb/>preci&longs;amente &longs;aria. </s> <s id="s.003102">2. 20/81. non altro. </s> <s id="s.003103">Chri&longs;to da mal ui guardi.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003104">H<emph type="italics"/>ieronymus Cardanus medicus totus ue&longs;ter.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003105">NICOLO. S<emph type="italics"/>to in fanta&longs;ia di non dar ri&longs;po&longs;ta à questa, &longs;i come che ho fatto ancho <lb/>ra alle altre due, pur ui uoglio ri&longs;pondere, & farli intendere quello, che ho inte&longs;o di <lb/>lui. </s> <s id="s.003106">Et dapoi che uedo, che ua &longs;o&longs;pettando &longs;opra la retta uia della regola del capitolo di <lb/>co&longs;e, e numero, egual à cubo, uoglio tentare&longs;e gli pote&longs;&longs;e cambiare li dati che ha in ma <lb/>ne, cioe remouerlo di tal uia retta, & farlo entrare in qualche altra, à benche credo <lb/>non ui &longs;ara meggio, nondimeno il tentar non nuoce.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003107">M<emph type="italics"/>e&longs;&longs;er Hieronimo ho riceuuta una uo&longs;tra, nella quale me &longs;criueti qualmente haue­<lb/>ti inte&longs;o il capitolo de cubo, eguale à co&longs;e, & numero, ma che quando il cubo della ter­<lb/>za parte delle co&longs;e, eccede il quadrato della mita del numero, che all'hora non poteti <lb/>fargli &longs;eguir la equatione, & che per tanto me pregati, che ue dia ri&longs;olto que&longs;to capi­<lb/>tolo de. </s> <s id="s.003108">1. cubo, eguale à. </s> <s id="s.003109">9. co&longs;e piu.<emph.end type="italics"/> 10. </s> </p> <p type="main"> <s id="s.003110">E<emph type="italics"/>per tanto ue ri&longs;pondo, & dico, che uoi non haueti appre&longs;a la buona uia per ri&longs;ol­<lb/>uere tal capitolo, anci dico, che tal uo&longs;tro procedere è in tutto fal&longs;o, circa al darui que­<lb/>&longs;to capitolo, che me haueti mandato ri&longs;olto, ue dico, che molto me rincre&longs;ce di quello, <lb/>che per fina à quest'hora ui ho dato, attento che ho inte&longs;o da per&longs;one degne di fede, <lb/>che uoi &longs;eti per dar fuora un'altra opera in Algebra, & che ue andati auantando per <lb/>Millano hauer trouato nuoui capitoli in Algebra, ma auertite, che &longs;e uoi mancareti di <lb/>fede à me, che certamente io non ui mancaro à uoi (per non e&longs;&longs;er mio co&longs;tume) anci ui <lb/>prometto di attenderui piu di quello, che ui ho prome&longs;&longs;o.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003111">A<emph type="italics"/>nchora me pregati, che ui uoglia mandare il modo da de&longs;criuere in uno triangolo <lb/>de lati diuer&longs;i Geometricamente uno quadrato. </s> <s id="s.003112">Per mo&longs;tr arui che ho fatto qua in Ve­<lb/>netia qualche buon di&longs;cipulo, ue aui&longs;o qualmente ho proposto que&longs;to ca&longs;o à dui miei di <lb/>&longs;cepoli, delli quali l'uno ha nome me&longs;&longs;er Ricardo Ventuorthe gentil'huomo Ingle&longs;e, & <lb/>l'altro è un me&longs;&longs;er Zuanantonio di Ru&longs;coni qua di Venetia, & cadauno di loro à con­<lb/>correntia dell'altro, la mattina &longs;eguente à buon'hora mi porto tal ca&longs;o a&longs;&longs;olto. </s> <s id="s.003113">& lauia <lb/>del procedere dell'uno è molto differente di quella dell'altro, & anchor della mia, & <pb xlink:href="042/01/247.jpg"/>accio che quella &longs;ia certa di que&longs;to, ho uole&longs;to che cadauno di loro ui manda tal &longs;olutlo­<lb/>ne &longs;critta de &longs;ua mano, le quale &longs;ono le inchiu&longs;e in que&longs;ta, & &longs;e nella ri&longs;olutione di me&longs;­<lb/>&longs;er Ricardo, ui trouareti qualche uocabolo, ouer parola mal proferta per non hauer <lb/>la retta pronontia della lingua Italiana uoi l'hauereti per i&longs;cu&longs;o, tamen &longs;o che per di­<lb/>&longs;crettione quella intendera il tutto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003114">C<emph type="italics"/>irca all'errore per quella comme&longs;&longs;o, ouer fatto doue che in&longs;egna à formar il rot­<lb/>to delli re&longs;idui, che auanzano nella e&longs;tratione della radice cuba, nelli numeri non cubi, e <lb/>quella &longs;e &longs;cu&longs;a, et dice primamente che in la detta opera ue ne &longs;ono due altre regole buo <lb/>ne, ma non dice in che capitolo, ouer à quante carte &longs;iano.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003115">C<emph type="italics"/>irca questa particolarita ri&longs;pondo ch'io non ho guardata da quella uolta in qua al <lb/>tramente la detta uo&longs;tra opera, ne manco l'ho fatta, anchora ligare ne manco ho tem­<lb/>po di uederla al pre&longs;ente per e&longs;&longs;er (come piu uolte ho detto, e &longs;critto) occupato, circa <lb/>la traduttione di Euclide, e pero non &longs;o che ri&longs;pondere, de quelle altre due uostre re­<lb/>gole, quale dite che &longs;ono buoue. </s> <s id="s.003116">Ma ben ui dico (e&longs;&longs;endo come haueti detto) che il mi pa­<lb/>re il uo&longs;tro procedere molto di&longs;ordinato, & di&longs;regolato, & non &longs;o doue che quella <lb/>habbia tolto tal ordine, à dar regola à una mede&longs;ima particolarita in tre diuer&longs;i luo­<lb/>chi in una mede&longs;ima opera.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003117">M<emph type="italics"/>a me ho poi pen&longs;ato che for&longs;i quella non ha datta fuora tal opera, come co&longs;e com­<lb/>poste da &longs;ua te&longs;ta, ma come co&longs;e elette raccolte, & copiate de diuer&longs;i libri à penna, & <lb/>in diuer&longs;i tempi, &longs;i come che gli&longs;ono uenuti alle mani. </s> <s id="s.003118">Perche &longs;e quelle fu&longs;&longs;eno co&longs;e com <lb/>po&longs;te, & ordinate di &longs;ua te&longs;ta. </s> <s id="s.003119">Certamente io giudicaria in quella piu pre&longs;to ignoran­<lb/>tia, che intelligentia perche la &longs;officientia dell'huomo nella compo&longs;itione d'un'opera &longs;i <lb/>cono&longs;ce nell'ordine &longs;uo, & non nella altezza della materia di che tratta. </s> <s id="s.003120">Et che il &longs;ia il <lb/>uero, il &longs;i uede che l'altezza delle co&longs;e di che ha trattato Euclide, non &longs;ono quelle, che <lb/>ui habbiano dato &longs;i gran nome, perche la maggior parte di quelle erano note à cadau­<lb/>no Philo&longs;ofo, perche molti altri anciani haueuano di tal materie abbondantemente <lb/>trattato. </s> <s id="s.003121">Auanti di Euclide, ma &longs;olamente per hauerle co&longs;i con tanto mirabil ordine <lb/>raccolte, a&longs;&longs;ettate, & ordinate.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003122">S<emph type="italics"/>econdariamente quella &longs;ottogionge, & dice, che in quella tal &longs;ua regola da me tan­<lb/>&longs;ata, non ui ca&longs;ca errore, &longs;aluo che nel detto e&longs;&longs;empio de Radice cuba. </s> <s id="s.003123">24. Et io dico, <lb/>che in cadauno rotto formato con tal uo&longs;tro ordine &longs;empre ui ca&longs;cara errore, & non <lb/>poco, ma io ui diedi lo e&longs;&longs;empio co&longs;i &longs;opra la Radice cuba de. </s> <s id="s.003124">24. per farui piu eui­<lb/>dente tal errore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003125">T<emph type="italics"/>ertio quella concede che nel detto e&longs;&longs;empio de Radice cuba de. </s> <s id="s.003126">24. cauato &longs;econ­<lb/>do la regola per lei po&longs;ta, e&longs;&longs;er fal&longs;o, & credendo&longs;i di hauerlo cono&longs;ciuto, & emen­<lb/>dato dice, che reuera non &longs;arebbe, &longs;aluo circa. </s> <s id="s.003127">2. 1/4. ouer parlando piu preci&longs;amente, <lb/>che quella &longs;aria. </s> <s id="s.003128">2. 20/81. della qual conclu&longs;ione me ne ho ride&longs;to a&longs;&longs;ai, perche quella cre­<lb/>dendo&longs;i di emendare il &longs;uo primo errore, ne ha comme&longs;&longs;o dui altri maggiori, dicendo <lb/>che reuera, la Radice cuba propinqua del detto. </s> <s id="s.003129">24. &longs;aria circa. </s> <s id="s.003130">2. 1/4. & che parlan­<lb/>do piu preci&longs;amente, che quella &longs;aria.<emph.end type="italics"/> 2. 20/81. P<emph type="italics"/>erche il cubo de. </s> <s id="s.003131">2. 1/4. &longs;aria &longs;olamente.<emph.end type="italics"/><lb/>11.25/<gap/>4. <emph type="italics"/>il qual cubo il &longs;i uede quanto ch'eglie menore, ouer lontano dal no&longs;tro. </s> <s id="s.003132">24. & <lb/>perche. </s> <s id="s.003133">2. 20/81. è alquanto menore de. </s> <s id="s.003134">2. 1/4. &longs;enz'altra proua, ouer i&longs;perientia, eglie co-<emph.end type="italics"/><pb pagenum="124" xlink:href="042/01/248.jpg"/><emph type="italics"/>&longs;a chiara, che il &longs;uo cubo &longs;ara anchora menore del cubo de. </s> <s id="s.003135">2. 1/4. cioe menor de. </s> <s id="s.003136">11. 25/64. <lb/>e pero &longs;ara anchora piu lontano del no&longs;tro. </s> <s id="s.003137">24. & quella uole che &longs;ta piu preci&longs;e, co&longs;a <lb/>come che ho detto, molto ridicolo&longs;a. </s> <s id="s.003138">Eglie ben uero, che il non è da marauigliar&longs;i mol­<lb/>to quando che un'huomo erra in qualche particolarita (per e&longs;&longs;er lo errare co&longs;a huma <lb/>na) ma ben eglie da marauigliar&longs;i, & da &longs;tupir&longs;i, quando che lui è stato auertito del &longs;uo <lb/>errore, & che quello non &longs;olamente non&longs;e &longs;ia &longs;aputo emendare, ma che quello &longs;ia incor <lb/>&longs;o in un'altro maggiore, come che quella ha fatto. </s> <s id="s.003139">Et me aricordo quando ch'era à M<gap/><lb/>lano in ca&longs;a uo&longs;tra, che quella me di&longs;&longs;e, che la non haueua mai tentato de ritrouare il ca <lb/>pitolo di co&longs;a, e cubo egual à numero da me trouato, perche Frate Luca haueua detto, <lb/>ch'egliera impoßibile, qua&longs;i uolendo dire, che &longs;e uoi ui fu&longs;ti me&longs;&longs;o à ricercarlo, che l'ha <lb/>uere&longs;ti ritrouato, della qual co&longs;a al pre&longs;ente me ne rido, perche uedo ch'eglie horamai <lb/>dui me&longs;i, che ui ho aui&longs;ato del uo&longs;tro error comme&longs;&longs;o nella e&longs;tratione della Radice cu­<lb/>ba, il qual atto è qua&longs;i uno di primi principij che &longs;e in&longs;egna à un &longs;colaro, che uoglia dar <lb/>principio à l'Algebra, & &longs;e in tanto tempo non haueti &longs;aputo ritrouar medicina da <lb/>medicare il detto uo&longs;tro errore (che è una co&longs;a minima) hor pen&longs;ati mo &longs;e uoi eri &longs;offi <lb/>ciente à ritrouare il detto capitolo. </s> <s id="s.003140">Et certamente il fu gia, che ui haueua in buon con­<lb/>to, ma al pre&longs;ente uedo, che me ingannaua de gro&longs;&longs;o, non altro. </s> <s id="s.003141">Iddio ui con&longs;erui, in <lb/>Venetia alli. </s> <s id="s.003142">7. Ago&longs;to.<emph.end type="italics"/> 1539. </s> </p> <p type="main"> <s id="s.003143">N<emph type="italics"/>icolo Tartaglia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.003144">QVESITO. XXXIX. FATTO DALLA ECCEL­<lb/><emph type="italics"/>lentia del mede&longs;imo me&longs;&longs;er Hieronimo Cardano, con una <lb/>lettera de di. </s> <s id="s.003145">18. Ottobrio.<emph.end type="italics"/> 1539.</s> </p> <p type="main"> <s id="s.003146">MESSER HIERONIMO. H<emph type="italics"/>o riceuuto una uo&longs;tra, me&longs;&longs;er Nicolo o&longs;&longs;er­<lb/>uandißimo, nella quale me pare &longs;iati u&longs;cito di uoi à dire, che io non ho inte&longs;o la <lb/>regola del capitolo de cubo, egual à co&longs;e è nuuiero, & che tal mia uia è in tutto fal&longs;a, <lb/>onde credo, che uoi zauariati, & che &longs;iati u&longs;cito di ceruello for&longs;i per il troppo uostro <lb/>&longs;tudiare, ouer leggere, onde ui e&longs;&longs;orto à torne un poco meno con menor utilita, perche <lb/>certo uoi u&longs;cireti del &longs;enno, o della uita, & per que&longs;to non mi marauiglio de gli impro­<lb/>perij fuora di propo&longs;ito, che me &longs;criueti, che io ui &longs;on uo&longs;tro grande amico, & ui ho <lb/>laudato fina al Cielo &longs;enza inuidia di alcuno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003147">A <emph type="italics"/>quel che me &longs;criueti della uia del &longs;cioluere il capitolo de cubo egual à co&longs;e è nume <lb/>ro. </s> <s id="s.003148">Dico che &longs;ta benißimo, & &longs;e uoletimettere. </s> <s id="s.003149">25. &longs;cudi, ne ponero. </s> <s id="s.003150">100. all'incontro, <lb/>& ui mando la &longs;olutione de. </s> <s id="s.003151">1. cubo eguale à. </s> <s id="s.003152">12. co&longs;e piu. </s> <s id="s.003153">20. Dico che la co&longs;a ual&longs;e<emph.end type="italics"/> <22>. <lb/><emph type="italics"/>cuba. </s> <s id="s.003154">16. piu<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.003155">4. & il cubo ual&longs;e<emph.end type="italics"/> <22>. <emph type="italics"/>cuba. </s> <s id="s.003156">27648. piu<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.003157">6912. piu. </s> <s id="s.003158">20. la <lb/>qual co&longs;a prouandola la trouareti buona. </s> <s id="s.003159">Se uoleti mo dire, che ue &longs;ia altro modo piu <lb/>generale di questo non contendo con uoi.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003160">A<emph type="italics"/>nchora circa all'altra parte dico, che zauariati à dire, che haueti inte&longs;o, che uo­<lb/>glio dar fuora l'atre magna, & che uoglio dar fuora li uo&longs;tri capitoli. </s> <s id="s.003161">Ma pen&longs;o ue ra <lb/>degati de me&longs;&longs;er Ottauiano Scotto, quanto all'opera de My&longs;terijs æternitatis, che ui <lb/>pen&longs;ati &longs;ia l'arte magna, che io uoglia dar fuora.<emph.end type="italics"/></s> </p> <pb xlink:href="042/01/249.jpg"/> <p type="main"> <s id="s.003162">Q<emph type="italics"/>uanto al pentirue hauermi dato quel uostro capitolo per questo non mi mouo, <lb/>per uostre parole à niuna co&longs;a contra la fede ui promi&longs;es.,<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003163">D<emph type="italics"/>apoi doueti &longs;apere, che nella mia opera ho ritrouati molti errori di &longs;car&longs;o, e non <lb/>di arte, li quali daro fuora, come habbi un poco di tempo, non altro. </s> <s id="s.003164">Iddio da mal ui <lb/>guardi in Millano alli. </s> <s id="s.003165">18. Ottobrio.<emph.end type="italics"/> 1539. </s> </p> <p type="main"> <s id="s.003166">H<emph type="italics"/>ieronymus Cardanus medicus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003167">NIC. D<emph type="italics"/>apoi che il <expan abbr="nõ">non</expan> miha giouato lamia cautella, io <expan abbr="nõ">non</expan> ui uoglio dar altra ri&longs;po&longs;ta.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.003168">QVESITO. XL. FATTO DALLA ECCELL EN­<lb/><emph type="italics"/>tia del mede&longs;imo me&longs;&longs;er Hieronimo Cardano, con una <lb/>lettera de di. </s> <s id="s.003169">5. Genaro.<emph.end type="italics"/> 1540.</s> </p> <p type="main"> <s id="s.003170">MESSER HIER ONIMO. M<emph type="italics"/>e&longs;&longs;er Nicolo quanto fratello, aui&longs;oui qual <lb/>mente eglie ritornato qui quel diauolo de me&longs;&longs;er Zuane Colle, il qual è uenuto <lb/>per hauere inte&longs;o, che io era contento renontiarli una delle mie letture, cioe quella di <lb/>Arithmetica, trouando che lui fu&longs;&longs;e ualent'huomo, & in que&longs;to lo prouato, & non tro <lb/>uo, che lui &longs;ia quello, che il &longs;i pen&longs;a ne &longs;i dimostra, aui&longs;oui che lui ha il uo&longs;tro capitolo <lb/>de co&longs;a, e cubo egual à numero, & quello de co&longs;a è numero egual à cubo, lo <gap/>dato <lb/>come haueua hauuti detti capitoli, me ri&longs;po&longs;e, che e&longs;&longs;endo lui à Venetia, operò talmente <lb/>che ui po&longs;e un'altra uolta alle mani con mae&longs;tro Antoniomaria & che per tal uia gli <lb/>auenne cio, che cercaua, perche contra&longs;tando inte&longs;e la natura della equatione, & tan­<lb/>dem per diuer&longs;e conietture trouò detti capitoli in&longs;ieme con un &longs;uo compagno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003171">D<emph type="italics"/>apoi &longs;appiati che lui troua regola de cauare la Radice cuba de <22>. </s> <s id="s.003172">108. piu. </s> <s id="s.003173">10. <lb/>per regola generale in tutti quelli bin omi, che hanno detta Radice cuba, & co&longs;i dice, <lb/>come è il uero, che la è <22>. </s> <s id="s.003174">3. piu. </s> <s id="s.003175">1. & co&longs;i dice, che la Radice cuba de <22>. </s> <s id="s.003176">108. men. </s> <s id="s.003177">10. é <lb/><22>. </s> <s id="s.003178">3. men. </s> <s id="s.003179">1. adunque la <22>. </s> <s id="s.003180">cuba de <22>. </s> <s id="s.003181">108. piu. </s> <s id="s.003182">10. men la <22>. </s> <s id="s.003183">cuba de <22>. </s> <s id="s.003184">108. men. </s> <s id="s.003185">10. è <lb/>la <22>. </s> <s id="s.003186">3. piu. </s> <s id="s.003187">1. men <22>. </s> <s id="s.003188">3. men. </s> <s id="s.003189">1. che è. </s> <s id="s.003190">2. &longs;o che le il uero que&longs;to, ma non ho hauuto tempo <lb/>di trouar tal regola, e per tanto ui prego uogliati ueder di trouarla, & contentarui <lb/>dell'honore, anchora mi non re&longs;taro di cercarla, & &longs;e io la trouaro auanti di uoi ue <lb/>la mandaro anchora mi à uoi.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003191">A<emph type="italics"/>ui&longs;oui anchora che lui ha certo la &longs;olutione di tal que&longs;tione fame di. </s> <s id="s.003192">10. tre parti <lb/>continue proportionale, che la prima moltiplicata nella <expan abbr="&longs;ecõda">&longs;econda</expan> facia. </s> <s id="s.003193">8. perche il me la <lb/>uole&longs;ta in&longs;ignar &longs;e io gli uoleua renontiar la lettura, e pero uorria che uoi uedesti di tro <lb/>uarla, et co&longs;i faro anchora io, et chi piu pre&longs;to la troua la <expan abbr="cõmunichi">communichi</expan> al <expan abbr="cõpagno">compagno</expan>. </s> <s id="s.003194">An­<lb/>chora uorria che uoi uede&longs;ti da trouar que&longs;ta, la quale lui <expan abbr="cõfe&longs;&longs;a">confe&longs;&longs;a</expan> à non &longs;aperla &longs;oluere.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003195">T<emph type="italics"/>rouatemi tre quantita continue proportionale. </s> <s id="s.003196">che la prima <expan abbr="cõ">com</expan> la terza facia. </s> <s id="s.003197">10. <lb/>& la prima nella &longs;econda moltiplicata facia. </s> <s id="s.003198">7. ma lui non l'ha, &longs;i che <expan abbr="&longs;ap&etilde;do">&longs;apendo</expan> che &longs;i puo <lb/>&longs;oluere certo, & lui non è piu de huomo, cercatela ui prego, & co&longs;i faro anchora io, et <lb/>chi la troua la <expan abbr="cõmunichi">communichi</expan> al compagno, cioe tra noi, perche ello confe&longs;&longs;a, che &longs;i troua <21><lb/>un certo andare. </s> <s id="s.003199">Dice anchora hauer la dimo&longs;tr atione qualmente il cerchio è di mag­<lb/>gior contenuta d'ogn'altra figura, et che detta dimo&longs;tr atione è in Greco à &longs;tampa for&longs;i <lb/>è in proclo, ouero in theone, & che un me&longs;&longs;er Phileno da Bologna gli l'ha in&longs;ignata, et <lb/>dice, che gli la dette per co&longs;a grande. </s> <s id="s.003200">L'altra domanda che lui ha è que&longs;ta.<emph.end type="italics"/></s> </p> <pb pagenum="125" xlink:href="042/01/250.jpg"/> <p type="main"> <s id="s.003201">E<emph type="italics"/>glie uno paralellogramo.a.c.che.a.b.e. </s> <s id="s.003202">2. &.b.c.è 3. et &longs;i &longs;egna dentro el centro <lb/>d. <!-- KEEP S--></s> <s id="s.003203">et &longs;i trazeno due linee.d.f.&.d.e.equale ita ch'el ponto.e.&.f.con el ponto.g.&longs;ono <lb/>in linea una, cioe.e.g.f.&longs;e adimanda quanta è la linea.d.e. </s> <s id="s.003204">Vedeti ui prego di mandar­<lb/>ne qualcuna di queste a&longs;ciolte, non altro ricomandatime al Signor Amba&longs;ciatore et ba <lb/>&longs;ciateli la mano in Milano alli. </s> <s id="s.003205">5. Zenaro.<emph.end type="italics"/> 1540. </s> </p> <figure id="id.042.01.250.1.jpg" xlink:href="042/01/250/1.jpg"/> <p type="main"> <s id="s.003206">NICOLO. I<emph type="italics"/>n piu co&longs;e cono&longs;co costui e&longs;&longs;er molto piu tondo di quello che io i&longs;ti <lb/>maua, et prima lo dimo&longs;tra nel parlare, nel quale dice alcune co&longs;e che <expan abbr="nõ">non</expan> <expan abbr="hãno">hanno</expan> alcuna <lb/>co&longs;onantia, cioe dice prima ch'eglie ritornato quel diauolo de<emph.end type="italics"/> M. Z<emph type="italics"/><expan abbr="uãne">uanne</expan> Colle per ha <lb/>uer inte&longs;o che lui li uol renonciar la lettura de Arithmetica trouando che lui fu&longs;&longs;e ua <lb/>lent'huomo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003207">A<emph type="italics"/>nci credo che gli &longs;ia ritornato per torge la detta lettura contra il &longs;uo uolere. </s> <s id="s.003208">Poi <lb/>dice ch'el l'ha prouato & che non lo ritroua che lui &longs;ia quello ch'el &longs;i pen&longs;a. </s> <s id="s.003209">Et per <lb/><expan abbr="quãto">quanto</expan> uedo lui trema di paura di lui. </s> <s id="s.003210">Dapoi uedo che lui &longs;i la&longs;&longs;a dar ad intender al detto<emph.end type="italics"/><lb/>M. Z<emph type="italics"/>uanne che ha li mei capitoli di co&longs;a è cubo equal à numero, & de co&longs;e, e nume <lb/>ro equal à cubo la qual co&longs;a non è uera ma&longs;i la&longs;&longs;a infenocchiare da lui. </s> <s id="s.003211">Dapoi dice chel <lb/>detto<emph.end type="italics"/> M.Z.<emph type="italics"/>ha ritrouato la regola generale de cauar la radice cu.de<emph.end type="italics"/> <22> 108. <emph type="italics"/>piu. </s> <s id="s.003212">10. & <lb/>co&longs;i in tutti li altri binomi che hanno la detta<emph.end type="italics"/> <22>. <emph type="italics"/>cu.& li pare che questo &longs;ia una gran <lb/>co&longs;a maßime nelli binomi cubi, perche tal &longs;ua radice &longs;e puo trouar, ouer cauare &longs;ola­<lb/>mente de luno di &longs;uoi nomi qual &longs;i uoglia, cioe uolendola cauar del &longs;opradetto<emph.end type="italics"/> <22>. </s> <s id="s.003213">108. <lb/><emph type="italics"/>piu. </s> <s id="s.003214">10. per maggior mia commodita la trouaria &longs;opra el. </s> <s id="s.003215">10. (per e&longs;&longs;er piu facile da <lb/>maneggiare nel &longs;lmplice numero che nelle radice) e per cauarla que&longs;ta é la &longs;ua pro­<lb/>priaregola, bi&longs;ogna far del detto. </s> <s id="s.003216">10. due tal parti, che luna di quelle &longs;ia numero cubo, <lb/>& che l'altra &longs;ia diui&longs;ibile in tre parti equali &longs;enza rotto, & per trouarli &longs;ottro del <lb/>detto. </s> <s id="s.003217">10. luno de quelli numeri cubi contenuti dal detto. </s> <s id="s.003218">10. liquali &longs;ono. </s> <s id="s.003219">1. &. </s> <s id="s.003220">8. & ue <lb/>do qual di loro mi da il rimanente diui&longs;ibile (come detto) in tre parti equali & troua­<lb/>remo che &longs;ara. </s> <s id="s.003221">1. et <expan abbr="nõ">non</expan> lo. </s> <s id="s.003222">8. hor dico che la<emph.end type="italics"/> <22>. <emph type="italics"/>cu. </s> <s id="s.003223">de. </s> <s id="s.003224">1. qual è pur. </s> <s id="s.003225">1. &longs;ara el menor nome <lb/>della detta radice binomiale, et laltro &longs;ara la radice quadra del <expan abbr="aduenim&etilde;to">aduenimento</expan> che perue <lb/>nira a partire la terza parte del &longs;opradetto <expan abbr="riman&etilde;te">rimanente</expan> partita <21> el detto nostro menor <lb/>nome, cioe&longs;ottrato el detto numero cu. </s> <s id="s.003226">1. de. </s> <s id="s.003227">10. roman. </s> <s id="s.003228">9. del qual. </s> <s id="s.003229">9. <expan abbr="piglãdone">piglandone</expan> la &longs;ua <lb/>terza parte qual è. </s> <s id="s.003230">3. et quella partiremo per la<emph.end type="italics"/> <22>. <emph type="italics"/>cu.del nostro numero cubo. </s> <s id="s.003231">1. qual <lb/>&longs;ara pur. </s> <s id="s.003232">1. ne uenira del detto partimento pur. </s> <s id="s.003233">3. & la radice quadra de. </s> <s id="s.003234">3. &longs;ara el mag <lb/>gior nome del no&longs;tro radical binomio, cioe che la radice cuba. </s> <s id="s.003235">de de<emph.end type="italics"/> <22>. </s> <s id="s.003236">108. <emph type="italics"/>piu. </s> <s id="s.003237">10. <lb/>&longs;ara<emph.end type="italics"/> <22>. </s> <s id="s.003238">3. <emph type="italics"/>piu. </s> <s id="s.003239">1. ch'è il propo&longs;ito, & de<emph.end type="italics"/> <22>. </s> <s id="s.003240">108. <emph type="italics"/>men. </s> <s id="s.003241">10. la &longs;aria<emph.end type="italics"/> <22>. </s> <s id="s.003242">3. <emph type="italics"/>men. </s> <s id="s.003243">1. Et que&longs;ta<emph.end type="italics"/><pb xlink:href="042/01/251.jpg"/><emph type="italics"/>medema radice &longs;e puo anchora trouar &longs;opra el maggior nome, cioe &longs;opra<emph.end type="italics"/> <22>. </s> <s id="s.003244">108. <emph type="italics"/>per <lb/>el mede&longs;imo modo, ma la radice cu. </s> <s id="s.003245">del no&longs;tro numero cubo &longs;ara el maggior nome del­<lb/>la no&longs;tra binomial radice, ouer re&longs;iduale e&longs;&longs;endo re&longs;iduo e&longs;&longs;empi gratia, faremo, pur <lb/>de<emph.end type="italics"/> <22>. </s> <s id="s.003246">108 <emph type="italics"/>&longs;implicemente due tal parti, che luna &longs;ia<emph.end type="italics"/> <22>. <emph type="italics"/>de un numero cubo & che l'al­<lb/>tra &longs;ia diui&longs;ibile per. </s> <s id="s.003247">3. come radice, cioe per el quadrato de. </s> <s id="s.003248">3. ch'è. </s> <s id="s.003249">9. Onde <expan abbr="inue&longs;tigãdo">inue&longs;tigando</expan> <lb/>come di &longs;opra fu fatto &longs;opra li numeri cubi &longs;e ritrouara che tal<emph.end type="italics"/> <22>. <emph type="italics"/>de numero cubo &longs;a <lb/>ra la<emph.end type="italics"/> <22>. </s> <s id="s.003250">27. <emph type="italics"/>hor dico che la radice cu.de<emph.end type="italics"/> <22>. </s> <s id="s.003251">27. (<emph type="italics"/>qual è<emph.end type="italics"/> <22>. </s> <s id="s.003252">3.) <emph type="italics"/>&longs;ara el maggior nomè <lb/>del no&longs;tro Radical binomio, (ouer re&longs;iduo) &longs;e fu&longs;&longs;e re&longs;iduo & que&longs;ta parte de<emph.end type="italics"/> <22>. </s> <s id="s.003253">27. <lb/><emph type="italics"/><expan abbr="&longs;ottrah&etilde;do">&longs;ottrahendo</expan> la del tutto, cioe de<emph.end type="italics"/> <22>. </s> <s id="s.003254">108. <emph type="italics"/>re&longs;tara pur<emph.end type="italics"/> <22>. </s> <s id="s.003255">27. <emph type="italics"/>della quale <expan abbr="pigliãdone">pigliandone</expan> la &longs;ua <lb/>terza parte, come radice, (che &longs;ara la nona) ne uenira<emph.end type="italics"/> <22>. </s> <s id="s.003256">3. <emph type="italics"/>& que&longs;ta <expan abbr="part&etilde;dola">partendola</expan> per el <lb/>no&longs;tro primo nome, (cioe <21> la<emph.end type="italics"/> <22>. <emph type="italics"/>cu.della no&longs;tra<emph.end type="italics"/> <22>. </s> <s id="s.003257">27. <emph type="italics"/>qual è pur<emph.end type="italics"/> <22>. </s> <s id="s.003258">3.) <emph type="italics"/>de tal parti <lb/><expan abbr="m&etilde;to">mento</expan> ne uenira. </s> <s id="s.003259">1. et la<emph.end type="italics"/> <22>. <emph type="italics"/>de. </s> <s id="s.003260">1. qual è pur. </s> <s id="s.003261">1. &longs;ara el menor nome del no&longs;tro radical bi­<lb/>nomio ouer re&longs;iduo, cioe che la radice cu.de<emph.end type="italics"/> <22>. </s> <s id="s.003262">108. <emph type="italics"/>piu. </s> <s id="s.003263">10. &longs;aria<emph.end type="italics"/> <22>. </s> <s id="s.003264">3. <emph type="italics"/>piu. </s> <s id="s.003265">1. e de<emph.end type="italics"/> <22>. </s> <s id="s.003266">108 <lb/><emph type="italics"/>men. </s> <s id="s.003267">10 la &longs;aria<emph.end type="italics"/> <22>. </s> <s id="s.003268">3. <emph type="italics"/>men. </s> <s id="s.003269">1. &longs;i come fu anchor a determinato, ouer trouato &longs;opra el. </s> <s id="s.003270">10. <lb/>& per tal uia &longs;i puo anchora cono&longs;cere &longs;e uno binomio, ouer re&longs;iduo propo&longs;to è cubo, <lb/>ouer non cubo, perche s'eglie cubo bi&longs;ogna che il nostro operare &longs;e incontri in luno et <lb/>laltro nome et non potendoli far incontrare, tal binomio, ouer re&longs;iduo non &longs;aria cubo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003271">D<emph type="italics"/>apoi uedo anchora che lui &longs;e la&longs;&longs;a dar ad intendere dal detto<emph.end type="italics"/> M. Z<emph type="italics"/>uane, che lui <lb/>habbia ritrouato il modo, ouer regola di &longs;oluere quella que&longs;tione, che dice, fame di. </s> <s id="s.003272">10. <lb/>tre parti continue proportionale, che la prima moltiplicata nella &longs;econda faccia. </s> <s id="s.003273">8. Et <lb/>gli crede fermamente per hauerli fatto offerta de in&longs;ignarglila &longs;e gli renoncia la lettu­<lb/>ra, et non &longs;i auede il poueretto, che il non gli fa tal oblatione &longs;e non per fargli credere, <lb/>che habbia detta regola, accio che habbia tema di lui, perche lui&longs;a bene, che non ui re­<lb/>nontiaria la lettura per in&longs;ignargli la regola di ri&longs;oluere tal ragione, non tanto per la <lb/>lettura, ma per la uergogna, che gli ne &longs;eguiria, e pero uedo che eglie di poco ingegno.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003274">D<emph type="italics"/>apoi dice, che il detto<emph.end type="italics"/> M.Z<emph type="italics"/>uane confe&longs;&longs;a non &longs;aper &longs;oluere quell'altra &longs;ua propo­<lb/>&longs;ta ragione, et che la è &longs;olubile, perche il detto<emph.end type="italics"/> M.Z<emph type="italics"/>uane gli ha detto, che la &longs;e ri&longs;olue <lb/>per un certo andare, et non &longs;e auede, che lui dice due co&longs;e contrarie, cioe che il non la &longs;a <lb/>ri&longs;oluere, et che la &longs;e ri&longs;olue per un certo andar, perche &longs;e il non la &longs;a ri&longs;oluere manco <lb/>el puo &longs;apere perche uia, ouer perche andar la&longs;e ri&longs;olue. </s> <s id="s.003275">Dapoi dice che lui ha la de­<lb/>mo&longs;tratione <expan abbr="qualm&etilde;te">qualmente</expan> il cerchio é di maggior contenuta de ogni altra figura, & li pa <lb/>re a lui che que&longs;to &longs;ia troppo gran co&longs;a, la quale quantunque alcun autor non haue&longs;&longs;e <lb/>mai parlato, &longs;e potria trouar di dimostrarla in piu modi, cioe ch'eglie piu capace de <lb/>ogni figura i&longs;operimetra per le co&longs;e dimostrate da Archimede, & anchora dal Cardi <lb/>nal de Cu&longs;a. </s> <s id="s.003276">In quello de tra&longs;mutatiouibus Geometricis, e per que&longs;to cono&longs;co che con­<lb/>tien poco &longs;ugo. </s> <s id="s.003277">Dapoi uedendo anchora che lui non &longs;a ri&longs;oluere quella ultima que&longs;tio <lb/>ne geometrica ch'é una co&longs;a facile, (perche la maggior difficulta che occorra nella ri <lb/>&longs;olution di quella é à &longs;aper ritrouar le due partiale linee.c.e.et.a.f.le quale &longs;on medie <lb/>continua proportionalita fra li dui lati del paralellogramo.a.c. </s> <s id="s.003278">delli quali luno é. </s> <s id="s.003279">2. <lb/>& laltro. </s> <s id="s.003280">3. dal pre&longs;uppo&longs;ito & trouate quelle con facilita &longs;e ritrouara la quanti­<lb/>ta de la linea.d.e.ouer.d.f.) lo giudico di poco di&longs;cor&longs;o. </s> <s id="s.003281">Et per que&longs;to non li uo­<lb/>glio dar altrari&longs;po&longs;ta, perche è non ui ho piu affetione à lui che à me&longs;&longs;er Zuanne, e<emph.end type="italics"/><pb pagenum="126" xlink:href="042/01/252.jpg"/><emph type="italics"/>pero li uoglio la&longs;&longs;ar ar tra loro, ma me la uedo che lui é per&longs;o de animo, non &longs;o mo <lb/>come la andara.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.003282">QVESITO XLI. FATTO DA MAESTRO MA­<lb/><emph type="italics"/>phio Poueiani, con una lettera de di. </s> <s id="s.003283">15. Aprile.<emph.end type="italics"/> 1540.</s> </p> <p type="main"> <s id="s.003284">MAESTRO MAPHIO. E<emph type="italics"/>ccellente me&longs;&longs;er Mae&longs;tro &longs;aluti infiniti &c. <lb/></s> <s id="s.003285">Sono molti giorni che ho hauuto de&longs;iderio di domandarui uno apiacere, ma <lb/>con&longs;iderando le uo&longs;tre occupationi non mi è mai dato il core, temendo di non efferui <lb/>mole&longs;to, pur ca&longs;&longs;ando ogni ri&longs;petto me è appar&longs;o de &longs;criuerloui ogni modo fareti poi <lb/>il parer uostro &c. </s> <s id="s.003286">La co&longs;a che ue uoria domandar &longs;i é que&longs;ta, che haueria &longs;ingolar <lb/>appiacer che me manda&longs;te una nota di quel mi&longs;urar di terre alla Venetiana, ouer &longs;econ <lb/>do il co&longs;tume di là, cioe &longs;el &longs;i ua à campi, ouer à tornidure, & quante tauole fa un cam <lb/>po, & &longs;e ue dago fa&longs;tidio perdonatime, ui haueria de aui&longs;are de molti mae&longs;tri che mi &longs;o <lb/>no capitati inanti mentre &longs;taua in Bergamo, come é el figliuolo del Tagliente, & tra li <lb/>altri mae&longs;tro zuanne da Coi doue tra noi fu alquante parole in fin fatti amici gli par­<lb/>&longs;e per &longs;ua gratia di laudarmi, & di&longs;&longs;e che uifaceua honore, al fin el &longs;e parti da Berga <lb/>mo quantunque el fu&longs;&longs;e partito da Bre&longs;&longs;a per uenir à &longs;tantiar in Bergamo, & an à <lb/>Millano con tanta importunita che non uoleua la&longs;&longs;ar far bene quelli mae&longs;tri, tenu­<lb/>to &longs;chola che ghe hebbe alquanti me&longs;i &longs;e ne partete con &longs;ua grandißima ignominia, <lb/>ma ritrouandomi que&longs;ti giorni pa&longs;&longs;ati in Milano, trouai chel ghe era ritornato, & <lb/>non &longs;o per qual cau&longs;a gli habbiano tolto la lettura al Cardano (gia amico uo&longs;tro) <lb/>& data à lui, cioe al detto maestro zuanne, a benche for&longs;i el poteti hauer inte&longs;o pri­<lb/>mache ade&longs;&longs;o, pur me appar&longs;o di daruene aui&longs;o ca&longs;o che nol &longs;ape&longs;ti, non altro &longs;e <lb/>non che con tutto il core humilmente me aricomando et offero, a quo benignum et gra<lb/>tio&longs;um expecto ri&longs;pon&longs;um. </s> <s id="s.003287">Di Trento adi. </s> <s id="s.003288">15. Aprile.<emph.end type="italics"/> 1540. </s> </p> <p type="main"> <s id="s.003289">D<emph type="italics"/>iuostra eccellentia &longs;eruitor & di&longs;cipulo Maphio Poueiani.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003290">NICOLO. M<emph type="italics"/>ae&longs;tro Maphio carißimo ho riceputo una uo&longs;tra & inte&longs;o quan <lb/>to me &longs;criueti, & per tanto ue aui&longs;o qualmente &longs;ul Treui&longs;ano li terreni &longs;e uendeno et <lb/>comprano à campi & un campo é de tauole. </s> <s id="s.003291">1250. & una tauola (per quanto ho in­<lb/>te&longs;o) è un quadretto di terra de una pertega de mi&longs;ura per fazza, el campo poi Pado <lb/>uano è <expan abbr="&longs;olam&etilde;te">&longs;olamente</expan> de tauole. </s> <s id="s.003292">840. Et co&longs;i el Vi&longs;entino, uero é che la pertega Padouano <lb/>credo che la&longs;la alquanto piu <expan abbr="lõga">longa</expan> della Triui&longs;ana, el <expan abbr="cãpo">campo</expan> Verone&longs;e e de tauole. </s> <s id="s.003293">720. <lb/>in Mantoana el terreno &longs;e uende à biolchi et il biolco è de tauole. </s> <s id="s.003294">100. ma la tauola é <lb/>uno quadretto di terra de dui cauezzi per fazza elqual cauezzo è una mi&longs;ura lon­<lb/>ga. </s> <s id="s.003295">6. brazza tal che la tauola ueneria à e&longs;&longs;er uno quadretto di terra de brazza. </s> <s id="s.003296">12. <lb/>per fazza, a Bre&longs;&longs;a poi el detto terreno &longs;e uende à pio, el qual pio é pur de tauole. </s> <s id="s.003297">100 <lb/>&longs;i come il Mantouano, & &longs;imelmente la &longs;ua tauola è pur uno quadretto di terra de dui <lb/>cauezzi per fazza, liquali cauezzi &longs;ono pur longhi brazza. </s> <s id="s.003298">6. luno &longs;i come el Man­<lb/>touan. <!-- KEEP S--></s> <s id="s.003299">Sul Bergama&longs;co el detto terreno &longs;e uende à perteghe & una pertegha de terra <lb/>&longs;i è di tauole. </s> <s id="s.003300">24. Et la tauola è &longs;i come la tauola Bre&longs;&longs;ana, cioe de dui cauezzi, ouer <lb/>de. </s> <s id="s.003301">12. brazza per fazza. </s> <s id="s.003302">Sul Millane&longs;e, <expan abbr="&longs;imilm&etilde;te">&longs;imilmente</expan> &longs;e <expan abbr="u&etilde;de">uende</expan> el terreno à perteghe &longs;i co <lb/>me &longs;ul Bergama&longs;co et la detta pertica é pur de tauole. </s> <s id="s.003303">24. et la detta tauola è pur uno<emph.end type="italics"/><pb xlink:href="042/01/253.jpg"/><emph type="italics"/>quadretto de due mi&longs;ure longhe. </s> <s id="s.003304">6. brazza luna per fazza, cioe brazza. </s> <s id="s.003305">12. in tutto <lb/>per fazza.<emph.end type="italics"/> A <emph type="italics"/><expan abbr="b&etilde;che">benche</expan> &longs;o che quelle pratiche di Bergamo et da Milano ui debbiano e&longs;&longs;er <lb/>note nondimeno ui mando la coppia de una nota che me ritrouo apre&longs;&longs;o di me circa al <lb/>aui&longs;o del medico Cardano da Milano, a me é co&longs;a noua, che gli&longs;ia &longs;tata tolta la lettura, <lb/>& data a<emph.end type="italics"/> M. z<emph type="italics"/>uanne, eglie <expan abbr="b&etilde;">bem</expan> uero, che per lettere del Cardano mi haueua antiueduto <lb/>tal co&longs;a non altro Iddio ui con&longs;erui di Venetia alli. </s> <s id="s.003306">24. Aprile.<emph.end type="italics"/> 1540. </s> </p> <p type="head"> <s id="s.003307">QVESITO. XLII. FATTO DAL MIO HONORANDO <lb/><emph type="italics"/>compare<emph.end type="italics"/> M. R<emph type="italics"/>icardo Ventuorthe gentil'huomo Ingle&longs;e l'anno.<emph.end type="italics"/> 1541.</s> </p> <p type="main"> <s id="s.003308">MESSER RICAR. C<emph type="italics"/>ompar carißimo io &longs;on al pre&longs;ente per partirme da <lb/>uoi, & ritornarmene in Inghilterra. </s> <s id="s.003309">& hauendome mo&longs;trata la regola del ca <lb/>pitolo de co&longs;a, et cubo equal à numero, & delli altri dui &longs;oi <expan abbr="cõpagni">compagni</expan> uoria piacendoui, <lb/>che fe&longs;ti la co&longs;a <expan abbr="cõpita">compita</expan>, cioe che mi mo&longs;tra&longs;ti anchora la Regola del capitolo de cen&longs;o, <lb/>e cubo equal à numero, & &longs;imelmente delli altri dui &longs;uoi <expan abbr="cõpagni">compagni</expan>.<emph.end type="italics"/> N. M<emph type="italics"/>e&longs;&longs;er compa <lb/>re <expan abbr="certam&etilde;te">certamente</expan> è non me ritrouo co&longs;a, qual e&longs;&longs;endoui agrata giamai ui pote&longs;&longs;e ne doue&longs;&longs;e <lb/>negare, per le molte obligationi, che ho con uoi. </s> <s id="s.003310">Ma perche ho deliberato, &longs;ubito cho <lb/>habbia i&longs;pedito di tradur Euclide, & di correggere le figure, & altrierrori fatti da <lb/>&longs;crittori & traduttori &longs;opra Archimede Sir acu&longs;ano, di <expan abbr="cõponere">componere</expan> una opera in la pra <lb/>tica di Arithmetica, et Geometria, et in&longs;ieme con quella una noua Algebra, nella quale <lb/>non <expan abbr="&longs;olam&etilde;te">&longs;olamente</expan> uoglio ponere tutte le regole per me ritrouate &longs;opra li detti capitoli con <lb/>tutte le &longs;ue ragioni, & fondamenti, ma molte altre, che &longs;pero per loro euidentie de ri­<lb/>trouare & quella dadicaruela à uoi, per due cau&longs;e luna per &longs;atisfare imparte alli detti <lb/>molti oblighi ho <expan abbr="cõ">com</expan> uoi, laltra come à per&longs;ona piu atta cauar di lei co&longs;trutto di qualun <lb/>que altra, per &longs;uo mirabile & profondo ingegno. </s> <s id="s.003311">Et per tanto <expan abbr="mo&longs;trãdoui">mo&longs;trandoui</expan> al pre&longs;ente, <lb/>quello che nella detta opera offerirue intendo, &longs;aria un degradare la reputatione della <lb/>detta opera appre&longs;&longs;o di uoi, e per questa cau&longs;a uoglio che per al pre&longs;ente me habbiate <lb/>per i&longs;cu&longs;o, & che non ue &longs;ia graue lo a&longs;pettare perche hauereti poi la co&longs;a meglio dige <lb/>&longs;ta.<emph.end type="italics"/> M. R. D<emph type="italics"/>apoi che uoleti che a&longs;petti a&longs;pettaro, ma uoglio che me dati almen dui, <lb/>ouer treica&longs;i a&longs;&longs;olti &longs;opra à tal materia de capitoli, per che in que&longs;to mezzo me uoglio <lb/>e&longs;&longs;ercitare, & tentare &longs;e per mezzo de tai &longs;olutioni &longs;ape&longs;&longs;e trouar per me le dette re­<lb/>gole, ouer parti de quelle. </s> <s id="s.003312">Et fra li altriuoglio che mi dati a&longs;&longs;olto quel ca&longs;o, ouer que­<lb/>&longs;tione che prepone&longs;ti al uicenti in &longs;an zuannepolo, perche me li &longs;ono affaticato a&longs;&longs;ai <lb/>per ri&longs;oluerla, & mai ho potuto.<emph.end type="italics"/> N. E<emph type="italics"/>t come diceua tal que&longs;tione.<emph.end type="italics"/> M. R. L<emph type="italics"/>a di <lb/>ceua in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003313">T<emph type="italics"/>rouatime una quantita che multiplicata fiala &longs;ua Radice piu. </s> <s id="s.003314">6. faccia aponto. <lb/></s> <s id="s.003315">100 Onde ponendo che tal quantita &longs;ia un cen&longs;o, la &longs;ua Radice &longs;aria una co&longs;a alla qua <lb/>le giontoui. </s> <s id="s.003316">6. faria. </s> <s id="s.003317">1. co.piu. </s> <s id="s.003318">6. qual multiplicandola fia. </s> <s id="s.003319">1. cen&longs;o faria. </s> <s id="s.003320">1. cubo piu. </s> <s id="s.003321">6. <lb/>cen&longs;i et que&longs;to &longs;aria equal à.<emph.end type="italics"/> 100. N. I<emph type="italics"/>n que&longs;to ca&longs;o la co&longs;a ualeua<emph.end type="italics"/> <22>. <emph type="italics"/>u.cu. <!-- REMOVE S-->42. piu<emph.end type="italics"/> <22>. <lb/></s> <s id="s.003322">17000. <emph type="italics"/>piu<emph.end type="italics"/> <22>. <emph type="italics"/>u.cu. <!-- REMOVE S-->42. <expan abbr="m&etilde;">men</expan><emph.end type="italics"/> <22>. </s> <s id="s.003323">17000. <emph type="italics"/><expan abbr="m&etilde;">men</expan> el terzo di cen&longs;i cioe men.<emph.end type="italics"/> 2. M.R.A <emph type="italics"/>uoler <lb/>far la proua di que&longs;ta uo&longs;tra conclu&longs;ione, la &longs;araue molto, fatico&longs;a & di&longs;&longs;icile.<emph.end type="italics"/> N. I<emph type="italics"/>n <lb/>effetto la non è molto facile.<emph.end type="italics"/> M R. N<emph type="italics"/>on me ne potre&longs;ti dar un'altro &longs;imile ri&longs;olto,<emph.end type="italics"/><pb pagenum="127" xlink:href="042/01/254.jpg"/><emph type="italics"/>che mi de&longs;&longs;e il ualor della co&longs;a di un'altra quantita piu facile da maneggiare.<emph.end type="italics"/> N. S<emph type="italics"/>t <lb/>bene, perche mi po&longs;&longs;o &longs;empre eguagliare à tal numero che mi dara el ualor della co&longs;a <lb/>in un &longs;implice re&longs;iduo. </s> <s id="s.003324">E&longs;&longs;empi gratia &longs;e io baue&longs;&longs;e detto trouatime una quantita che <lb/>multiplicata fia la &longs;ua<emph.end type="italics"/> <22>. <emph type="italics"/>piu. </s> <s id="s.003325">9. faccia à ponto. </s> <s id="s.003326">100. apponendo&longs;i come di &longs;opra uoi fe <lb/>&longs;ti &longs;e perueneria in 1. cubo piu. </s> <s id="s.003327">9. cen&longs;i equal à. </s> <s id="s.003328">100. & in que&longs;to ca&longs;o la co&longs;a ualeria<emph.end type="italics"/><lb/><22>. </s> <s id="s.003329">24 <emph type="italics"/>men. </s> <s id="s.003330">2. & la adimondata quantita &longs;aria el quadrato de<emph.end type="italics"/> <22>. </s> <s id="s.003331">24. <emph type="italics"/>men. </s> <s id="s.003332">2. elqual <lb/>quadrato &longs;aria. </s> <s id="s.003333">26. men<emph.end type="italics"/> <22>. </s> <s id="s.003334">384 M. R. Q<emph type="italics"/>uesta re&longs;olutione mi piace molto piu de <lb/>l'altra, perche piu facilmente ne po&longs;&longs;o far la proua. </s> <s id="s.003335">perche &longs;e alla co&longs;a, cioe à<emph.end type="italics"/> <22>. </s> <s id="s.003336">24. <lb/><emph type="italics"/>men. </s> <s id="s.003337">2. gli aggiongo. </s> <s id="s.003338">9. fara<emph.end type="italics"/> <22>. </s> <s id="s.003339">24. <emph type="italics"/>piu. </s> <s id="s.003340">7. qual &longs;umma multiplicata fia. </s> <s id="s.003341">26. men<emph.end type="italics"/> <22>. <lb/></s> <s id="s.003342">384. <emph type="italics"/>fa preci&longs;amente. </s> <s id="s.003343">100. come &longs;e <expan abbr="adimãda">adimanda</expan> hor uoria che me ne de&longs;ti dui altri &longs;imili.<emph.end type="italics"/><lb/>NICO. Q<emph type="italics"/>uando che. </s> <s id="s.003344">1. cubo piu. </s> <s id="s.003345">3. cen&longs;i fu&longs;&longs;e equal à. </s> <s id="s.003346">2. la co&longs;a ualeria<emph.end type="italics"/> <22>. </s> <s id="s.003347">3. <emph type="italics"/>men. <lb/></s> <s id="s.003348">1. Et co&longs;i quando che. </s> <s id="s.003349">1. cubo piu. </s> <s id="s.003350">7. cen&longs;i fu&longs;&longs;e equale à. </s> <s id="s.003351">50. la co&longs;a ualeria.<emph.end type="italics"/> <22>. </s> <s id="s.003352">11. <emph type="italics"/><expan abbr="m&etilde;">men</expan>.<emph.end type="italics"/> 1. <lb/>M.R. B<emph type="italics"/>a&longs;ta circa à que&longs;to capitolo, hor datemene anchora dui altri &longs;olti &longs;opra il ca­<lb/>pitolo de cubo, e numero egual à cen&longs;i, & &longs;e poßibile é proponeteli, che diano il ualor <lb/>della co&longs;a in quantita facile da maneggiare, accio che io ne po&longs;&longs;a far la proua.<emph.end type="italics"/> N. <lb/>Q<emph type="italics"/>uando che il fu&longs;&longs;e. </s> <s id="s.003353">1. cubo piu. </s> <s id="s.003354">4. egual à. </s> <s id="s.003355">5. cen&longs;i la co&longs;a ualcria<emph.end type="italics"/> <22>. </s> <s id="s.003356">8. <emph type="italics"/>piu.<emph.end type="italics"/> 2. M.R. <lb/>A<emph type="italics"/>nchora que&longs;ta ri&longs;olutione me piace, perche la po&longs;&longs;o prouare facilmente, perche &longs;e la <lb/>co&longs;a ual<emph.end type="italics"/> <22>. </s> <s id="s.003357">8. <emph type="italics"/>piu. </s> <s id="s.003358">2. il cen&longs;o ualera. </s> <s id="s.003359">12. piu<emph.end type="italics"/> <22>. </s> <s id="s.003360">128. <emph type="italics"/>& il cubo ualera. </s> <s id="s.003361">56. piu<emph.end type="italics"/> <22>. </s> <s id="s.003362">3200. <lb/><emph type="italics"/>al qual cubo giontoli. </s> <s id="s.003363">4. fara. </s> <s id="s.003364">60. piu<emph.end type="italics"/> <22>. </s> <s id="s.003365">3200. <emph type="italics"/>& que&longs;to è preci&longs;amente eguale à. </s> <s id="s.003366">5. <lb/>cen&longs;i, cioe à. </s> <s id="s.003367">5. fia. </s> <s id="s.003368">12. piu<emph.end type="italics"/> <22>. </s> <s id="s.003369">128. <emph type="italics"/>qual fa mede&longs;imamente. </s> <s id="s.003370">60. piu<emph.end type="italics"/> <22>. </s> <s id="s.003371">3200. <emph type="italics"/>che é il <lb/>propo&longs;ito hor datemene anchora un'altro.<emph.end type="italics"/> N. Q<emph type="italics"/>uando che. </s> <s id="s.003372">1. cubo piu. </s> <s id="s.003373">6. fu&longs;&longs;e egua <lb/>le à. </s> <s id="s.003374">7. cen&longs;i la co&longs;a ualeria<emph.end type="italics"/> <22>. </s> <s id="s.003375">15. <emph type="italics"/>piu.<emph.end type="italics"/> 3. M.R. L<emph type="italics"/>auoglio prouare. </s> <s id="s.003376">Se la co&longs;a ual<emph.end type="italics"/> <22>. <lb/></s> <s id="s.003377">15. <emph type="italics"/>piu. </s> <s id="s.003378">3. il cen&longs;o ualera. </s> <s id="s.003379">24. piu<emph.end type="italics"/> <22>. </s> <s id="s.003380">540. <emph type="italics"/>& il cubo. </s> <s id="s.003381">162. piu<emph.end type="italics"/> <22>. </s> <s id="s.003382">26460. <emph type="italics"/>al qual cubo <lb/>giontoli. </s> <s id="s.003383">6. fara. </s> <s id="s.003384">168. piu<emph.end type="italics"/> <22>. </s> <s id="s.003385">26460 <emph type="italics"/>hor&longs;e. </s> <s id="s.003386">7. fia. </s> <s id="s.003387">24. piu<emph.end type="italics"/> <22>. </s> <s id="s.003388">540. <emph type="italics"/>fara quel mede&longs;i­<lb/>mo la &longs;tara benißimo, in effetto trouo che la fa quel mede&longs;imo, &longs;i che &longs;ta benißimo, hor­<lb/>&longs;u credo che que&longs;ti me ba&longs;tara.<emph.end type="italics"/> N. M<emph type="italics"/>e&longs;&longs;er Compare anchor che per uo&longs;tra &longs;atisfat­<lb/>tione ue habbia dati li &longs;opra&longs;critti capitoli ri&longs;olti, ue e&longs;&longs;orto à non &longs;tare à perder tem­<lb/>po, ne à romperue la te&longs;ta in uolere con i&longs;perientie de numeri (per meggio delle dette <lb/>mie ri&longs;olutioni) ritrouar la regola generale ad alcuno de detti capitoli, perche credo, <lb/>che uoi ue affaticareti in darno, la cau&longs;a è, che tutti tai capitoli riceueno due diuer&longs;e ri­<lb/>&longs;po&longs;te, & for&longs;i piu, onde &longs;eguita, che habbiano, ouer riceuano due diuer&longs;e regole, e for <lb/>&longs;i piu, & l'una piu difficulto&longs;a dell'altra, la qual co&longs;a fondandoui &longs;opra la &longs;perientia <lb/>de numeri ue fara zauariar a&longs;&longs;ai, et in ultimo credo, che non trouareti niente che uaia, <lb/>perche questi tai capitoli uogliono e&longs;&longs;er ricercati &longs;peculatiuamente, & non con i&longs;pe­<lb/>rientie de numeri, e per tanto ui e&longs;&longs;orto ad hauer patientia per fin che ue manda le det <lb/>te regole con li &longs;uoi fondamenti dimostrartiui, & prima di quelli de co&longs;a, e cubo egual <lb/>à numero con glialtri dui &longs;uoi compagni, dalle quale regole &longs;e caua le regole dimo&longs;tra <lb/>tiue de tutti glialtri perche tutte &longs;ono in&longs;ieme concatenate, dico quelle de cen&longs;o, e cubo <lb/>egual à numero, & &longs;uoi compagni, à quelle de co&longs;a, e cubo egual à numero, et &longs;uoi com <lb/>pagni, come à luoco é tempo ui faro uedere.<emph.end type="italics"/> M.R. I<emph type="italics"/>l me pare di&longs;tranio di quello, che <lb/>haue ti detto, cioe che tutti tai capitoli riceuano due diuer&longs;e ri&longs;po&longs;te, & for&longs;i piu, et che <lb/>per tal cau&longs;a riceueno due diuer&longs;e regole, & for&longs;i piu, la qual co&longs;a mi pare dura da <pb xlink:href="042/01/255.jpg"/>credere.<emph.end type="italics"/> N. L<emph type="italics"/>a è certo co&longs;a dura da credere, & certamente &longs;e la &longs;perientia non me <lb/>ne face&longs;&longs;e testimonianza, qua&longs;i che non il crederei, perche &longs;e io dice&longs;&longs;e trouatemi un <lb/>numero, ouer quantita, che gionta con tre delle &longs;ue radice cube faccia. </s> <s id="s.003389">14. Eglie co&longs;a <lb/>chiara, che il numero. </s> <s id="s.003390">8. fara questo, che &longs;e adimanda, perche la &longs;ua radice cuba è. </s> <s id="s.003391">2. <lb/>& tre &longs;ue radice cube &longs;aranno. </s> <s id="s.003392">6. quale gionte con il detto. </s> <s id="s.003393">8. faranno. </s> <s id="s.003394">14. come &longs;e ri­<lb/>cerca, hor dico, che chi ri&longs;oluera tal capitolo de. </s> <s id="s.003395">1. cu.piu. </s> <s id="s.003396">3. co&longs;e egual à. </s> <s id="s.003397">14. &longs;econdo <lb/>la regola da me ritrouata, &longs;e ritrouara la co&longs;a ualer<emph.end type="italics"/> <22>. <emph type="italics"/>u.cuba. <!-- REMOVE S-->7. piu<emph.end type="italics"/> <22>. </s> <s id="s.003398">41. <emph type="italics"/>men<emph.end type="italics"/> <22>. <emph type="italics"/>u. <lb/><!-- REMOVE S-->cuba. </s> <s id="s.003399">7. men<emph.end type="italics"/> <22>. </s> <s id="s.003400">41. <emph type="italics"/>la qual co&longs;a treplicandola, & tal treplicatione aggiongerla al &longs;uo <lb/>cubo fara mede&longs;imamente. </s> <s id="s.003401">14. &longs;i come fa anchora ualendo la co&longs;a &longs;implicemente.<emph.end type="italics"/> 2. <lb/>E <emph type="italics"/>pero eglie co&longs;a manife&longs;ta, che il capitolo de co&longs;a, e cubo egual à numero riceue due <lb/>regole, cioe l'una (che nel &longs;opr adetto capitolo) me doueria dar il ualor della co&longs;a ra­<lb/>tionale, cioe. </s> <s id="s.003402">2. & l'altra è la no&longs;tra qual me da la co&longs;a irrationale, come di&longs;opra &longs;i è <lb/>uisto. </s> <s id="s.003403">Et da qui è na&longs;ciuto, che coloro che per auanti di me hanno ricercato regola à tal <lb/>capitolo, credendo&longs;i che tal capitolo non riceue&longs;&longs;e altro, che una &longs;ol regola, cioe una <lb/>che &longs;erue&longs;&longs;e &longs;i nelle conclu&longs;ioni rationale, come nelle irrationale loro la ricercauano <lb/>&longs;olamente con la i&longs;perientia de numeri rationali apo&longs;tati, come di&longs;opra per noi fu fat­<lb/>to de. </s> <s id="s.003404">1. cubo piu. </s> <s id="s.003405">3. co&longs;e egual à. </s> <s id="s.003406">14. del qual capitolo gia &longs;apemo che la co&longs;a ual. </s> <s id="s.003407">2. & <lb/>la regola de ritrouar, che la co&longs;a uaglia. </s> <s id="s.003408">2. eglie da pen&longs;are che la ue &longs;ia, anchor che da <lb/>gli no&longs;tri anciani la non &longs;ia stata ritrouata.<emph.end type="italics"/> L'<emph type="italics"/>alira regola da me ritrouata con dimo­<lb/>&longs;trationi Geometrice &longs;e cono&longs;ce la &longs;ua bontà, & &longs;i cono&longs;ce anchora che da me la non fu <lb/>ricercata con numeri apo&longs;tati (come for&longs;ihanno fatto coloro, che ui &longs;e &longs;ono affaticati <lb/>auanti di me) ma con la pura &longs;peculatione, & que&longs;te due uarie ri&longs;po&longs;te &longs;e ritrouara non <lb/>&longs;olamente in tutte le &longs;orte de equationi de co&longs;e é cubi eguali à numero, doue acca&longs;chi la <lb/>co&longs;a e&longs;&longs;er rationale (come fu nel &longs;opra datto e&longs;&longs;empio del.<emph.end type="italics"/> 14.) <emph type="italics"/>ma anchora il mede&longs;i­<lb/>mo &longs;eguira nel capitolo de co&longs;a è numero egual à cubo, & in quello de cubo, e numero <lb/>egual à co&longs;e, & in quello de cen&longs;o è cubo egual à numero, & in quello de cubo egual à <lb/>cen&longs;o è numero, & finalmente in quello de cubo, è numero egual à cen&longs;i, e pero eglie da <lb/>credere che riceuono anchora due uarie regole, & in alcuni de loro per certe &longs;ue ua­<lb/>riationi, & accidenti mi fanno qua&longs;i certo riceuere piu di due regole, come che in bre­<lb/>ue, piacendo à Iddio, &longs;e dimo&longs;trara. </s> <s id="s.003409">& pero me&longs;&longs;er Compare non &longs;tati à durar fatica <lb/>in ricercar tale regole con i&longs;perientie, che in breue le hauereti con le &longs;ue ragioni, & <lb/>fondamenti chiare, & nette.<emph.end type="italics"/> M.R. E<emph type="italics"/>uoglio far quello, che me con&longs;igliati, & maßi­<lb/>me che uedo in alcune equationi &longs;eguitar ri&longs;olutione de certe quantita de molto &longs;trania <lb/>irrationalita, & molto difficile, & fa&longs;tidio&longs;e da maneggiare in pratica, & &longs;e in queste <lb/>&longs;orte de capitoli de co&longs;e, cubi, cen&longs;i, enumero ui ca&longs;ca co&longs;i &longs;tranie conclu&longs;ioni, che &longs;e­<lb/>guiria poi nelle altre dignita, cioe doue interueni&longs;&longs;e il primo relato, oueramente cen&longs;o <lb/>de cubo, ouer amente il &longs;econdo relato, e per tanto credo, che in tal pratica di Algebra, <lb/>uoi &longs;iati peruenuto per fin doue &longs;ia poßibile à peruenire, perche il &longs;e entraria in un <lb/>Chaos à uoler tentar piu oltra de tai capitoli per uoi trouati.<emph.end type="italics"/> N. A<emph type="italics"/>nci ui uoglio di­<lb/>re, che nelle equationi di alcune altre piu alte dignita, non &longs;eguiria for&longs;i nella &longs;ua con­<lb/>clu&longs;ione quantita de co&longs;i &longs;trania irrationalita, quanto che &longs;eguita nelli predetti capito­<lb/>li, & que&longs;to procede per la &longs;ua di&longs;proportionalita, ch'è &longs;trania Anci me aricordo che<emph.end type="italics"/><pb pagenum="128" xlink:href="042/01/256.jpg"/><emph type="italics"/>l'anno. </s> <s id="s.003410">1536. la notte de &longs;an Martin, laqual fe&longs;ta fu in &longs;abbo, fanta&longs;ticando in letto quan <lb/>do che non potea dormire trouai la regola generale allo capitolo de cen&longs;o de cubo; & <lb/>cubi, equal à numero & &longs;imelmente alli altri dui &longs;uoi compagni, nella mede&longs;ima notte, <lb/>il che non me fu difficile anchor che fu&longs;&longs;eno compo&longs;ti di piu alte dignita di co&longs;a è cubo <lb/>equal à numero, per e&longs;&longs;er di megliore proportionalita & la &longs;ua regola è piu facile, & <lb/>di piu amena conclu&longs;ione & piu uniuer&longs;ale, perche quella ne &longs;erue &longs;i nelle <expan abbr="cõclu&longs;ioni">conclu&longs;ioni</expan> ra<lb/>tionale come nelle irrationale.<emph.end type="italics"/> M.R. H<emph type="italics"/>or queste hauero molto accaro de intende­<lb/>re nanti che me parta da uoi et for&longs;i piu di quelle di <expan abbr="c&etilde;&longs;i">cen&longs;i</expan> è cubo equal à numero, et delli <lb/>altri dui &longs;uoi compagni, per e&longs;&longs;er, come haueti detto, di piu amena conclu&longs;ione, e pe <lb/>ro datemene una nota.<emph.end type="italics"/> N. P<emph type="italics"/>igliati la penna, & &longs;criueti in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003411">Q<emph type="italics"/>uando li cen&longs;i de cubi in&longs;ieme con li cubi &longs;e eguagliarano al numero reccareti la <lb/>equatione à un cen&longs;o de cubo. </s> <s id="s.003412">Dapoi smezzareti li cubi, & tal mita multiplicareti in <lb/>&longs;e mede&longs;ima & à tal quadrato aggiongereti el numero & di quella &longs;umma cauaretine <lb/>la Radice quadrata & di tal radice quadrata cauaritene la mita di cubi & la radice cu <lb/>ba del rimanente ualera la co&longs;a. </s> <s id="s.003413">E&longs;&longs;empio in numeri di&longs;creti per uo&longs;tra maggior intel <lb/>ligentia, (elqual e&longs;&longs;empio non &longs;e potria dar in el capitolo de co&longs;a è cubo equal à nume <lb/>ro, & altri &longs;uoi ederenti, ne in quello de cen&longs;o, e cubo equal à numero, & &longs;uoi edderen <lb/>ti<emph.end type="italics"/>). 1. <emph type="italics"/>cubo de cen&longs;o piu. </s> <s id="s.003414">4. cubi equal à. </s> <s id="s.003415">96. &longs;mezzo li cubi mene uien. </s> <s id="s.003416">2. lo quadro fa. <lb/></s> <s id="s.003417">4. gli agiongo el numero fa. </s> <s id="s.003418">100. ne cauo la radice quadra qual é. </s> <s id="s.003419">10. et di que&longs;to. </s> <s id="s.003420">10. <lb/>ne cauo, la mita del numero di cubi qual è. </s> <s id="s.003421">2. re&longs;ta. </s> <s id="s.003422">8. & la radice cuba de. </s> <s id="s.003423">8. qual e. <!-- REMOVE S-->2. <lb/>ual la no&longs;tra co&longs;a el &longs;imile o&longs;&longs;eruareti quando che fu&longs;&longs;eno quantita irrationale. </s> <s id="s.003424">Hor <lb/>per el &longs;econdo &longs;criueti in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003425">Q<emph type="italics"/>uando li cen&longs;i de cubi, &longs;e eguagliano alli cubi, & al numero, fareti come di &longs;opra, <lb/>cioe reccareti tutta la equatione à un cen&longs;o de cubo, dapoi &longs;mezzati li cubi & tal mita <lb/>multiplicati in &longs;e & à tal multiplicatione, ouer quadrato aggiongereti el numero, & <lb/>di tal &longs;umma cauaretine la<emph.end type="italics"/> <22>. <emph type="italics"/>quadra alla qual<emph.end type="italics"/> <22>. <emph type="italics"/>quadra aggiongereti la mita di cubi <lb/>& la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba di tal &longs;umma ualera la co&longs;a. </s> <s id="s.003426">E&longs;&longs;empio in numeri di&longs;creti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003427">S<emph type="italics"/>ia. </s> <s id="s.003428">1. cubo de cen&longs;o egual à. </s> <s id="s.003429">4. cubi piu. </s> <s id="s.003430">32. &longs;mezzo li. </s> <s id="s.003431">4. cubi ne uien. </s> <s id="s.003432">2. lo quadro <lb/>fa. </s> <s id="s.003433">4. gli aggiongo il numero, cioe. </s> <s id="s.003434">32. fa. </s> <s id="s.003435">36. ne piglio la<emph.end type="italics"/> <22>. <emph type="italics"/>quadra qual è. </s> <s id="s.003436">6. alla qual <lb/>gli aggiongo la mita di cubi, che é. </s> <s id="s.003437">2. fa. </s> <s id="s.003438">8. & la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de. </s> <s id="s.003439">8. qual è. </s> <s id="s.003440">2. ualera la co&longs;a, <lb/>& per &longs;imil modo &longs;e doueria procedere quando che ne ri&longs;ulta&longs;&longs;e quantita irrationale. <lb/></s> <s id="s.003441">Hor per el terzo &longs;criueti in que&longs;ta forma.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.003442">Q<emph type="italics"/>uando li cen&longs;i de cubi piu numero, &longs;e eguagliano alli cubi, reccareti la equatione <lb/>tutta à un cen&longs;o di cubo. </s> <s id="s.003443">Dapoi &longs;mezzareti li cubi & tal mita multiplicareti in &longs;e, & <lb/>di quel produtto, ouer quadrato ne cauareti el numero, & del rimanente ne trouareti <lb/>la<emph.end type="italics"/> <22>. <emph type="italics"/>quadra, & à tal radice quadra gli aggiongereti, ouer cauareti la mita di cubi, & <lb/>la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba di tal &longs;umma, ouer re&longs;to ualera la co&longs;a. </s> <s id="s.003444">E&longs;&longs;empio.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.003445">S<emph type="italics"/>ia. </s> <s id="s.003446">1. cubo de cen&longs;o piu. </s> <s id="s.003447">48. egual à. </s> <s id="s.003448">14. cubi, &longs;mezzo li cubi. </s> <s id="s.003449">14. ne uien. </s> <s id="s.003450">7. quadro <lb/>questo. </s> <s id="s.003451">7. fa. </s> <s id="s.003452">49. & de questo. </s> <s id="s.003453">49. ne cauo il numero (cioe. </s> <s id="s.003454">48.) re&longs;ta. </s> <s id="s.003455">1. & di que&longs;to <lb/>ne cauo la<emph.end type="italics"/> <22>. <emph type="italics"/>quadra qual è pur. </s> <s id="s.003456">1. al qual gli aggiongo, ouer cauo la mita di cubi che è. <lb/></s> <s id="s.003457">7. & perche in que&longs;to ca&longs;o il detto. </s> <s id="s.003458">7. è maggior de. </s> <s id="s.003459">1. Io non lo po&longs;&longs;o &longs;e non aggionge­<lb/>re, & fara. </s> <s id="s.003460">8. & la<emph.end type="italics"/> <22>. <emph type="italics"/>cuba de. </s> <s id="s.003461">8. ualera la co&longs;a, cioe. </s> <s id="s.003462">2. & bi&longs;ogna notar, che que&longs;to <pb xlink:href="042/01/257.jpg"/>capitolo alcuna fiata dara ri&longs;po&longs;ta in dui modi, alcun'altra &longs;olamente in un modo &longs;olo, <lb/>come accaduto in que&longs;to &longs;opra&longs;critto, cioe che la mita di cubi non&longs;e puo &longs;e non aggion­<lb/>gere alla radice di quel rimanente, che fu. </s> <s id="s.003463">1. ma quando &longs;e fu&longs;&longs;e potuto aggiongere, & <lb/>cauare for&longs;i, che l'uno, e l'altro haueriano dato perfetta ri&longs;po&longs;ta, ma per una ri&longs;po&longs;ta <lb/>&longs;empre la dara, o in el aggiongere, ouer nel cauare, et mai falla, ma alcuna uolta ri&longs;pon<lb/>dera all'uno, e l'altro medo.<emph.end type="italics"/> M.R. Q<emph type="italics"/>ue&longs;ti tre capitoli certamente non gli ho manco <lb/>accari di quello hauero quelli de cen&longs;o è cubo egual à numero con glialtri dui &longs;uoi com­<lb/>pagni, quando che me li mandareti, hor&longs;u ui uoglio la&longs;&longs;are Compare, gionto che &longs;ia in <lb/>Inghilterra ue &longs;criuero.<emph.end type="italics"/> N. A<emph type="italics"/>ndati me&longs;&longs;er Compare, che Iddio ue dia il buon uiag­<lb/>gio, & ui prego che me &longs;criueti &longs;ubito, che ui &longs;eti aggionto, come haueti detto.<emph.end type="italics"/> M.R. <lb/>F<emph type="italics"/>aro &longs;enza fallo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.003464">F<emph type="italics"/>ine delli Que&longs;iti, & Inuentioni diuer&longs;e de Nicolo Tartaglia.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.003465">REGISTRO.</s> </p> <p type="head"> <s id="s.003466">ABCDEFGHIKLMNOPQRSTVXYZ <lb/>AA BB CC DD EE FF GG HH II.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.003467">T<emph type="italics"/>utti &longs;ono Duerni.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.003468">I<emph type="italics"/>n Venetia per Nicolo de Ba&longs;carini, ad in&longs;tantia & requi&longs;itione, <lb/>& à proprie &longs;pe&longs;e de Nicolo Tartaglia Autore.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.003469">N<emph type="italics"/>ell'anno di no&longs;tra &longs;alute.<emph.end type="italics"/> M D LIIII.<!-- KEEP S--></s> </p> </subchap1> </chap> </body> <back/> </text> </archimedes>