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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <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></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"></pb> <p type="head"> <s id="s.000001">QVESITI ET INVEN<lb></lb><emph type="italics"></emph>TIONI DIVERSE <emph.end type="italics"></emph.end><lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.000002">DI NOVO RESTAMPATI CON VNA <lb></lb>GIONTA AL SESTO LIBRO, NULLA <lb></lb><emph type="italics"></emph>quale ſi moſtra duoi modi di redur una Citta ineſpugnabile.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000003">LA DIVISIONE ET CONTINENTIA DI TVTTA <lb></lb>l'opra nel ſeguente foglio ſi 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"></figure> <p type="head"> <s id="s.000005">APPRE<emph type="italics"></emph>SS<emph.end type="italics"></emph.end>O DE L'AVTTORE <lb></lb>MD LIIII.</s> </p> </subchap1><subchap1> <pb xlink:href="042/01/002.jpg"></pb> <p type="head"> <s id="s.000006">LA PRESENTE OPERA E DI<lb></lb><emph type="italics"></emph>uiſa in noue libri, la continentia di ciaſcun di loro <lb></lb>ſummariamente di ſotto ſi narra.<emph.end type="italics"></emph.end><lb></lb><emph type="italics"></emph>Nel primo libro ſi tratta, delli tiri & effetti delle artegliarie, ſecondo le ſue va-<lb></lb> rie elleuationi, & ſecondo la uaria poſition delle mire con altri ſuoi ſtrani <lb></lb> accidenti. a car. </s> <s id="s.000007">5 <lb></lb>Nel ſecondo ſi manifeſta la differentia, che occorre fra li tiri, & effetti fatti con balle di <lb></lb> piombo, di ferro, ouer di pietra, con altre ſotilita circa la proportion peſo & miſura <lb></lb> delle dette balle. a car. </s> <s id="s.000008">32 <lb></lb>Nel tertio ſe notifica le ſpecie di ſalnitri, & le uarie compoſitioni delle poluere uſata da <lb></lb> noſtri antichi & moderni ſperimentatori. a car. </s> <s id="s.000009">73 <lb></lb>Nel quarto ſi da el modo di ſaper ordinar li eſſerciti in battaglia ſotto uarie & diuerſe <lb></lb> forme, con un modo di faper tramutar in un ſubito una ordinanza in forma quadra di <lb></lb> gente, in una forma cunea ſenza deſordinar la prima ordinanza & altre. </s> <s id="s.000010">a char. </s> <s id="s.000011">43 <lb></lb>Nel quinto libro ſe inſegna il modo di mettere rettamente il diſegno con el Boſſolo, li ſiti, <lb></lb> Paeſi, & le piante delle Città, con el modo de fabicar il detto Boſſolo in dui modi. <lb></lb> a carte. </s> <s id="s.000012">55 <lb></lb>Nel ſeſto libro ſi narra, il modo, che ſi doueria oſſeruar nel fortificar le Città a queſti tem<lb></lb>pi per ouiar alli uigoroſi colpi delle artegliarie per uigor della forma. a car. </s> <s id="s.000013">64 <lb></lb>Nella gionta del detto ſeſto libro ſi moſtra dui modi de fortificar una Città, luno di quali <lb></lb> per ſe la reduſſe ineſpugnabile, et che non potra eſſer battuta ne daneggiata da nemici <lb></lb> <expan abbr="cõ">com</expan> le artegliarie, ne potra eſſer minata, ne ìpite le foſſe, et l'altro ſara tale, che <expan abbr="ruuinã">ruuinam</expan> <lb></lb> dogli le mura ſi fara quaſi piu forte che con le mura, <expan abbr="cõ">com</expan> altre particolarita. a car. </s> <s id="s.000014">71 <lb></lb>Nel ſettimo libro ſi manifeſta alcuni dubbij, che mouer ſi poſſeno ſopra li principij delle <lb></lb> queſtioni Mecanice de Ariſtotile, per acuir li pelegrini in gegni. </s> <s id="s.000015">a car. </s> <s id="s.000016">78 <lb></lb>Nel ottauo libro ſi tratta della ſcientia di Peſi demoſtratiuamente, per mezzo della qual <lb></lb> ſcientia non ſolamente ſi puo conoſcere & ſapere la forza de l'huomo, ma anchora <lb></lb> trouar modo, di augumentar quella con artificioſi iſtrumenti in infinito. </s> <s id="s.000017">a car. </s> <s id="s.000018">83 <lb></lb>Nel nono libro ſi da regola & modo di ſaper riſoluere uarij & diuerſi caſi, ouer que<lb></lb>ſtioni in Arithmetica, in Geometria, & in la Pratica ſpeculatiua de l'arte Magna, <lb></lb> detta Algebra & almucabala, uolgarmente detta la Regola della coſa, & maßime <lb></lb> ſopra le Regole de coſe e cubi eguali a numero, dal preſente Autor ritrouate, & ſimel <lb></lb> mente de cenſi e cubi & altri ſuoi edderenti, li quali da ſapienti erano giudicati im<lb></lb>poßibili. a car.<emph.end type="italics"></emph.end> 98 </s> </p> </subchap1><subchap1> <pb xlink:href="042/01/003.jpg"></pb> <p type="head"> <s id="s.000019"><emph type="italics"></emph>TAVOLA DE CIO CHE <emph.end type="italics"></emph.end><lb></lb>SI CONTIEN PARTICOLARMEN<lb></lb>TEIN CIASCVNLIBRO.</s> </p> <p type="head"> <s id="s.000020"><emph type="italics"></emph>El ſoggetto delli Queſiti del primo libro.<emph.end type="italics"></emph.end><lb></lb>Di <emph type="italics"></emph>che ſoſtantia ſia la notitia della proportione delli tiri lontani e propinqui. </s> <s id="s.000021">a car<lb></lb>te. </s> <s id="s.000022">5. al Queſito primo <lb></lb>Come che una artegliaria fara maggior effetto nelli tiri elleuati che nelli aliueliati. </s> <s id="s.000023">a car<lb></lb>te. </s> <s id="s.000024">7. al Queſito ſecondo <lb></lb>Come the una balla tirata da una artegliaria mai ua per linea retta eccetto che rettamente <lb></lb> in ſuſo uerſo el cielo, ouer rettamĕte in zoſo uerſo el centro del <expan abbr="mõdo">mondo</expan>. </s> <s id="s.000025">a car.<emph.end type="italics"></emph.end> 11. <expan abbr="q.">que</expan> 3 <lb></lb>C<emph type="italics"></emph>ome che tirando un pezzo due uolte luna drieto l'altra in un medeſimo uerſo, tirara <lb></lb> piu alla ſeconda uolta che alla prima. a carte. </s> <s id="s.000026">23. al Queſito. 4 <lb></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"></emph.end> <expan abbr="q.">que</expan> 5 <lb></lb>D<emph type="italics"></emph>onde procede che da gando piu poluer a un pezzo dara piu alto da quel ſegno doue con <lb></lb> men poluere ue tiraua rettamente de mira. </s> <s id="s.000029">a car. </s> <s id="s.000030">14. al Queſito. 6. <lb></lb>De tutti li effetti, ouer botte cha puo occorrere nel tirar de mira quando che la mira da<lb></lb>uanti del pezzo e egualmente alta a quella da drio, o ueramente piu alta o ueramente <lb></lb> piu baſſa del ſuo douere. a carte. </s> <s id="s.000031">14. al Queſito. 7. <lb></lb>De tutti li effetti, ouer botte che puo occorrere nel tirar de mira quando che la mira dauan<lb></lb>ti non e tanto piu corta di quella de drio quanto biſognaria. a car. </s> <s id="s.000032">16. al<emph.end type="italics"></emph.end> <expan abbr="q.">que</expan> 8. <lb></lb>D<emph type="italics"></emph>e tutti li effetti, ouer botte che puo occorrere nel tirar de mira quando che la mira dauan<lb></lb>ti ha la ſua conueniente baſſezza reſpetto a quella de drio. </s> <s id="s.000033">a car. </s> <s id="s.000034">17. al Queſito. 9. <lb></lb>Donde puo proceder la cauſa quando che un pezzo da molto coſtero nel tirar de mira. <lb></lb> a carte. </s> <s id="s.000035">17. al Queſito. 10. <lb></lb>Come che el non e generale queſta regola che quanto che un pezzo e piu longo di canna <lb></lb> tanto piu tiri lontano, & come che nel far colobrine molto longhe è un error troppo <lb></lb> manifeſto & di molto danno. a car. </s> <s id="s.000036">18. al Queſito. 11. <lb></lb>Della longhezza de tutte le ſpecie de pezzi, & della quantita del metallo, che <expan abbr="cõmunamĕ-">communamĕ<lb></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. c. 19. al<emph.end type="italics"></emph.end> <expan abbr="q.">que</expan> 11. <lb></lb>D<emph type="italics"></emph>i quanta longhezza doueria eſſer la canna de cadaun pezzo a douer eſſer ben propor<lb></lb>tionata la longhezza. a car. </s> <s id="s.000038">20. al Queſito. 22. <lb></lb>Come de neceſsita eglie un certo termine, ouer miſura nel dar della poluere nel qual <lb></lb> daendo piu, ouer men poluer al pezzo di quella tal miſura ſempre tal pezzo tirara <lb></lb> manco. a car. </s> <s id="s.000039">20. al Queſito. 13. <lb></lb>Qual ſia meglio calcar benißimo la poluer nel pezzo ouer laſſarla alquanto rara. </s> <s id="s.000040">a car<lb></lb>te. </s> <s id="s.000041">22. al Queſito. 14. <lb></lb>Qual è la cauſa che con un ſchioppo ſe tiri piu lontan de mira che non ſi fa con un ar<lb></lb>chibuſo & tamen lo archibuſo fara maggior paſſata in un comun tramite del ſchiop-<emph.end type="italics"></emph.end><pb xlink:href="042/01/004.jpg"></pb> <emph type="italics"></emph>po. </s> <s id="s.000042">a car. </s> <s id="s.000043">22. al Queſito. 15. <lb></lb>Donde procede che una artegliaria non fa tanto effetto percotendo in una naue ouer ga<lb></lb>lia in mare quanto faria percottendo in una muraglia. </s> <s id="s.000044">a car. </s> <s id="s.000045">22. al Queſito. 16. <lb></lb>Come ſe potria diſchiodare al improuiſo una multitudine de artegliarie che fuſſeno ſtate <lb></lb> inchiodate. a car. </s> <s id="s.000046">23. al Queſito. 17. <lb></lb>Doue naſce la cauſa che una artegliaria fa manco effetto nella coſa doue ſe tira, a ſtarui <lb></lb> molto propinquo che a ſtarui alquanto di lontano. </s> <s id="s.000047">a car. </s> <s id="s.000048">23. al Queſito. 18. <lb></lb>In quanta diſtantia una artegliaria faria el maggior effetto, che far poſſa. </s> <s id="s.000049">a carte. </s> <s id="s.000050">24. <lb></lb> al Queſito. 29. <lb></lb>Perche cauſa ſe mette quelli ſtroppaioni di fieno, ouer di ſtoppa auanti alla balla & da <lb></lb> poi. a car. </s> <s id="s.000051">24. al Queſito. 20 <lb></lb>La cauſa d'un certo caſo rediculoſo di una artegliaria che ſorbete dentro nella canna un <lb></lb> cagnolino. a car. </s> <s id="s.000052">24. al Queſito. 21. <lb></lb><expan abbr="Dõde">Donde</expan> procede che de tutte le artegliarie che creppano, creppano la maggior parte de drio, <lb></lb> ouer nella bocca, & rare uolte nel mezzo. a carte. </s> <s id="s.000053">25. al Queſito. 22 <lb></lb>Come ſe potria conoſcere ſe una artegliaria tirara li ſuoi tiri retti ſenza tirarla altra<lb></lb>mente. a carte. </s> <s id="s.000054">26. al Queſito. 23. <lb></lb>La cauſa d'un'altro accidente di una artegliaria che ſorbette ſuſo gran quantita di ſabbia <lb></lb> a Lio. a car. </s> <s id="s.000055">27. al Queſito. 24. <lb></lb>Come che quelle mire che ſeruono per tirar in piano, non ſeruono coſi preciſamente per <lb></lb> tirar a l'alta, ouer al baſſo. a car. </s> <s id="s.000056">27. al Queſito. 25 &. </s> <s id="s.000057">26. <lb></lb>Come che quelle mire che fanno dar la botta di ſopra dal ſegno in maggior diſtantia la <lb></lb> faranno dar molto piu di ſopra dal ſegno. a car. </s> <s id="s.000058">28. al Queſito. 27. <lb></lb>Come che quelle mire che fanno dar la botta de ſotto dal ſegno in maggior diſtantia puo <lb></lb> far uarij effetti. a car. </s> <s id="s.000059">28. al Queſito. 28. <lb></lb>Donde procede che ogni Schioppettero, & anche Bombardero, generalmente quanto <lb></lb> che e piu propinquo al ſegno tolto de mira tanto piu è atto a far piu bella botta. <lb></lb> a car. </s> <s id="s.000060">29. al Queſito. 29. <lb></lb>Donde procede che<gap></gap>urando de continuo a un ſe gno de mira con un medeſimo ſchioppo alle <lb></lb> uolte ſe da molto di ſopra, alle uolte molto di ſotto, alle uolte molto costero del ſegno <lb></lb> tolto de mira & alle uolte nel ſegno. a car. </s> <s id="s.000061">31. al Queſito.<emph.end type="italics"></emph.end> 30 </s> </p> <p type="head"> <s id="s.000062"><emph type="italics"></emph>Elſoggetto delli Queſiti del Secondo libro.<emph.end type="italics"></emph.end><lb></lb>Q<emph type="italics"></emph>ual andara piu lontaro (& quanto) una balla di Piombo, ouer di Ferro, ouer di Pie<lb></lb>tra, & prima con equal quantita di Poluere, & da poi con la ſua poluere ordinaria. <lb></lb> a car. </s> <s id="s.000063">32. al Queſito. 1. 2. 3. &. </s> <s id="s.000064">4. <lb></lb>Qual fara maggior effetto in una diſtantia comuna, una balla di Piombo, ouer di Ferro, <lb></lb> ouer di Pietra, & prima con equal quantita di poluere, & dapoi con la ſua poluere <lb></lb> ordinaria. a car. </s> <s id="s.000065">33. al Queſito. 5. &. </s> <s id="s.000066">6. <lb></lb>Donde procede che eſſendo tirato ad alcuni guaſtadori in Rodi, alla prima uolta la balla <pb xlink:href="042/01/005.jpg"></pb> ziffolana molto forte per aere, & alle altri tiri la balla ui ueniua tacita & quieta. <lb></lb> a car. </s> <s id="s.000067">33. al Queſito. 7. <lb></lb>Qual andara piu lontano una balla graue, ouer legera. </s> <s id="s.000068">a car. </s> <s id="s.000069">34. al Queſito. 8. <lb></lb>Certe regole, che per la notitia del diometro & peſo di una balla ſe puol determinare el <lb></lb> peſo, ouer el diametro di qualunque altra. </s> <s id="s.000070">a car. </s> <s id="s.000071">34. al Queſito. 9. & 10. <lb></lb>La determinatione del diametro de piu ſorte balle per linea ritrouati geometrice per la no <lb></lb> titia d'un diametro dato. a car. </s> <s id="s.000072">35. al Queſito. 11. &<emph.end type="italics"></emph.end> 12. </s> </p> <p type="head"> <s id="s.000073"><emph type="italics"></emph>Elſuggetto delli Queſiti del Terzo libro.<emph.end type="italics"></emph.end><lb></lb>Q<emph type="italics"></emph>ualmente la notitia del Salnitrio & la natura ſua è antiquißima & come ne ſono de ua<lb></lb>rie ſpecie. a car. </s> <s id="s.000074">37. al Queſito. 1. & 2. <lb></lb>Perche cauſa li antiqui non ſepeno componer la poluere delle artegliarie. </s> <s id="s.000075">a carte 38. <lb></lb> al Queſito. 3. <lb></lb>Che uirtu, ouer officio particolare ha cadauno di tre ſimplici, ouer materiali, cioe Salnitrio, <lb></lb> Solphere et Carbone nella compoſitione della poluere. </s> <s id="s.000076">a car. </s> <s id="s.000077">38. al Queſito. 4. <lb></lb>Chi fu inuentor della poluere, & con che ragione fu determinata la proportione della quan <lb></lb> tita de cadauno de detti tre materiali. a car. </s> <s id="s.000078">39. al Queſito. 5. <lb></lb>Delli uarij ordeni ſi antiqui come moderni uſitadi nella compoſitione delle poluere groſſe <lb></lb> & fine. a car. </s> <s id="s.000079">39. al Queſito. 5. <lb></lb>Come ſe puol conoſcere una poluere eſſer piu potente de un'altra. </s> <s id="s.000080">a car. </s> <s id="s.000081">41. al Queſito. 6. <lb></lb>Come ſi puo augumentar la poluere in uirtu, ouer potentia. </s> <s id="s.000082">a car. </s> <s id="s.000083">41. al Queſito. 7. <lb></lb>Se egli è neceſſario a limitar la compoſitione della poluere delle artegliarie groſſe da quel <lb></lb> la delle ſotile & da quella delli archibuſi & Schioppi. </s> <s id="s.000084">a car. </s> <s id="s.000085">42. al Queſito. 8. <lb></lb>Perche cauſa ſi da la grana alla poluere delli archibuſi, & non a quella delle artegliarie. <lb></lb> a car. </s> <s id="s.000086">42. al Queſito. 9. &<emph.end type="italics"></emph.end> 10. </s> </p> <p type="head"> <s id="s.000087"><emph type="italics"></emph>Elſuggetto delli Queſiti del Quarto libro.<emph.end type="italics"></emph.end><lb></lb>C<emph type="italics"></emph>ome ſi de procedere, a uoler redure una quantità de fanti, ouer un eſſercito in Batta<lb></lb>glia quadra di gente & a quanti per fila ſi debbono far caminar per uiaggio, ouer ca<lb></lb>mino accio che occorrendo el biſogno con facilità ſi poteſſeno mettere ſubito in orde<lb></lb>nanza. a car. </s> <s id="s.000088">43. al Queſito. 1. &. </s> <s id="s.000089">2. <lb></lb>Come ſe debbe procedere a uoler far una ordinanza ſimile a una data in ogni quantità <lb></lb> de fanti. a car. </s> <s id="s.000090">46. al Queſito. 3. <lb></lb>Come ſi de procedere uolendo redur una quantità de fanti, ouer un eſſercito in una Batta<lb></lb>glia quadra di terreno. a car. </s> <s id="s.000091">47. al Queſito 4. <lb></lb>Come ſi de procedere de una quantita de fanti a uolerne formar el cuneo, ouer la forfice. <lb></lb> a car. </s> <s id="s.000092">47. al Queſito. 5. & 6. <lb></lb>Di che auantaggio ſaria un'eſſercito formato in forma cunea, quando che li nemici non <lb></lb> ſapeſſeno conſtituir la forſice. a car. </s> <s id="s.000093">48. al Queſito. 7. <lb></lb>Come ſe doueria procedere uolendo de una quantità de fanti formar la Serra, ouer Segha. <lb></lb> a car. </s> <s id="s.000094">49. al Queſito.<emph.end type="italics"></emph.end> 8. <pb xlink:href="042/01/006.jpg"></pb>C<emph type="italics"></emph>ome ſe doueria procedere uolendo redur una quantita de fanti in figura Rhombica di <lb></lb> gente. a car. </s> <s id="s.000095">49. al Queſito. 9. <lb></lb>Come ſe poteria ordinar una quantita de fanti, ouer un eſſercito in una battaglia cor<lb></lb>nuta. a car. </s> <s id="s.000096">50. al Queſito. 10. <lb></lb>Come non e licito uno eſſercito offeſo dalle artegliarie nemiche, a reſtringerſi inſieme, ne <lb></lb> manco a caminare ſecondo che ſi troua. a car. </s> <s id="s.000097">52. al Queſito. 11. <lb></lb>Come ſe doueria procedere uolendo in un ſubito ridure una ordinanza in forma quadra <lb></lb> di gente, in una forma cunea ſenza deſordinare la prima ordinanza. a carte. </s> <s id="s.000098">52. <lb></lb> al Queſito. 22. <lb></lb>Con ragion ſe approua come che eglie poßibile a ritrouar col frequente ſtudio modi di <lb></lb> ordinar un eſſercito quaſi di che fattion, ouer autorita ſi uoglia. </s> <s id="s.000099">a car. </s> <s id="s.000100">53. &.<emph.end type="italics"></emph.end> 54. </s> </p> <p type="head"> <s id="s.000101"><emph type="italics"></emph>Elſoggetto delli Queſiti del quinto libro.<emph.end type="italics"></emph.end><lb></lb>C<emph type="italics"></emph>ome ua fabricato il Boſſolo per tor in diſegno li ſiti paeſi & le piante delle Città. <lb></lb> a carte. </s> <s id="s.000102">55. al Queſito primo <lb></lb>Come ſe de proceder a, uoler tor in diſegno un ſito, ouer paeſe contenuto da linee rette. <lb></lb> a carte. </s> <s id="s.000103">56. al Queſito ſecondo <lb></lb>Come ſe de procedere uolendo tor in diſegno un paeſe contenuto da linee corue & rette. <lb></lb> a carte. </s> <s id="s.000104">79. &. </s> <s id="s.000105">60. al Queſito. 3. &. </s> <s id="s.000106">4. <lb></lb>Come ſi de procedere uolendo tor in diſegno la pianta de una Città. </s> <s id="s.000107">a car. </s> <s id="s.000108">61. al<emph.end type="italics"></emph.end> <expan abbr="q.">que</expan> 5. <lb></lb>C<emph type="italics"></emph>ome ſe de procedere uolendo formar un Boſſolo per ſe medeſimo & con puoco artefi<lb></lb>cio & ſpeſa. a carte. </s> <s id="s.000109">61. al Queſito.<emph.end type="italics"></emph.end> 6. </s> </p> <p type="head"> <s id="s.000110">ALLI LETTORI.</s> </p> <p type="main"> <s id="s.000111">C<emph type="italics"></emph>hi Brama di ueder noue inuentioni, <lb></lb>Non tolte da Platon, ne da Plotino, <lb></lb>Ne d'alcun altro Greco, ouer Latino, <lb></lb>Ma ſol da Larte, miſura, e Ragioni.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000112">L<emph type="italics"></emph>ega di queſto le interrogationi, <lb></lb>Fatte da Pietro, Pol, Zuann', e Martino<emph.end type="italics"></emph.end><lb></lb>(S<emph type="italics"></emph>i come, l'occorea ſera, e Matino<emph.end type="italics"></emph.end>) <lb></lb>E<emph type="italics"></emph>t ſimelmente, le reſponſioni.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000113">Q<emph type="italics"></emph>ui dentr'intendara, sè non m'inganno, <lb></lb>De molti effetti aſſai ſpeculatiui, <lb></lb>La cauſa propinqua del ſuo danno,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000114">A<emph type="italics"></emph>nchor de molti atti operatiui, <lb></lb>Se uedera eſſequir con puoc'affanno<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000115"><emph type="italics"></emph>Nell'arte della guerra Profittiui. <lb></lb></s> <s id="s.000116">Et molto defenſui.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000117">C<emph type="italics"></emph>on altre coſe di magno ualore,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000118">E<emph type="italics"></emph>t inuentioni nell'arte maggiore.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/007.jpg"></pb> <p type="head"> <s id="s.000119"><emph type="italics"></emph>AL CLEMENTISSIMO, ET <emph.end type="italics"></emph.end><lb></lb>INVITTISSIMO HENRICO, OTTAVO, <lb></lb>PERLA DIO GRATIA RE DE ANGLIA, DE <lb></lb>FRANCIA, ET DE HIB ERNIA, ETC.</s> </p> <figure id="id.042.01.007.1.jpg" xlink:href="042/01/007/1.jpg"></figure> <p type="head"> <s id="s.000120"><emph type="italics"></emph>NICOLO TARTAGLIA.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000121">Le <emph type="italics"></emph>Dimande, Queſiti, ouer Interrogationi Maeſtà <lb></lb>Serenißima, & Illuſtrißima, fatte da Saui, & <lb></lb>Prudenti Domandatori, fanno molte uolte conſi<lb></lb>derare allo interrogato molte coſe, & anchora co<lb></lb>noſcerne molte altre, le quale ſenza eſſerne adi<lb></lb>mandato giamai harebbe conoſciute, ne conſiderate. <lb></lb></s> <s id="s.000122">Queſto dico per me, qual mai feci profeßione, <lb></lb>ouer dilettai de tirare di alcuna ſorte, Arteglia<lb></lb>ria, Archibuſo, Bombarda, ne Schioppo, (ne <lb></lb>manco tirar intendo) & un ſol queſito fattomi da <lb></lb>un perito Bombardero, l'anno<emph.end type="italics"></emph.end> MDXXXI. <lb></lb><emph type="italics"></emph>in Verona, mi fece à quel tempo conſiderare, & inueſtigare ſpeculatiuamente l'ordine, <lb></lb>& proportione di tiri propinqui, & lontani, ſecondo le uarie elleuationi de tale ma<lb></lb>chine tormentarie, alle qual coſe giamai haueria poſto cura, ſe tal Bombardero, con <lb></lb>tal ſuo queſito non mi haueſſe in tal materia ſueggiato. </s> <s id="s.000123">Ma piu ſentendo io l'anno <emph.end type="italics"></emph.end><lb></lb>MDXXXVII. <emph type="italics"></emph>con quanto gran preparamente ſi moueua Soliman Impera<lb></lb>tor de Turchi, per infeſtare la noſtra Chriſtiana Religione, Compoßi con gran celeri<lb></lb>tà ſopra à tal materia una operina, & quella publicai. </s> <s id="s.000124">Accioche tai mie particolar in<lb></lb>uentioni ſi haueſſeno à ſperimentare, uedere, & conſiderare ſe di quelle ſi poteua caua<lb></lb>re qualche buon coſtrutto in beneficio & difenſion di quella, & quantunque di tal coſa <lb></lb>non ne ſeguitaſſe altro (per uari accidenti, ne manco io me ne curai, perche tal guerra <lb></lb>in fummo ſi riſolſe,) nondimeno tal mia operina, ha prouocato uarie qualità di perſo<lb></lb>ne, & maggior parte non uolgare, ma di ſupremo, & alto ingegno) à trouagliarmi <lb></lb>di nouo con altri uarij Queſiti, ouer interrogationi, & non ſolamente ſopra à tal ma<lb></lb>teria di Artegliarie, Balle, Salnitrio, & Poluere. </s> <s id="s.000125">Ma anchora ſopra di nouo me han<lb></lb>no fatto non ſolamente conſiderare tai particolarità da loro adimandate, ma anchora co<lb></lb>noſcerne, & ritrouarne (com'e detto) molte altre, lequale ſenza tai ſuoi Queſiti, <lb></lb>ouer interrogationi, forſi giamai haueria conoſciute, ne conſiderate. </s> <s id="s.000126">Dapoi fra me <lb></lb>penſando, che non puoco biaſino merita quel huomo, qual, ouer per ſcientia, ouer per ſua <lb></lb>induſtria, ouer per ſorte ritroua qualche notabil particolarità, & chi ſolamente lui ſolo<emph.end type="italics"></emph.end><pb xlink:href="042/01/008.jpg"></pb><emph type="italics"></emph>ne uoglia eſſer poſſeſſore, perche ſe tutti li noſtri anciani il medeſimo haueſſeno oſſer<lb></lb>uato, poco dalli animali irrationali al preſente ſareßimo differenti adunque per non in<lb></lb>correre in queſto biaſimo. </s> <s id="s.000127">Ho deliberato di uolere tai mei queſiti, ouer inuentioni man<lb></lb>dar al tutto in luce, & per dar principio ad eſſequire tal mio bon uolere, ne ho raccolto <lb></lb>per al preſente una parte da un mio memoriale nel qual ſempre per bona memoria tutti <lb></lb>li notabili, che me ueneuan ſatti de mia man notaua, & queſta parte la ho diſtribuita in <lb></lb>nuoue libri diſtinti ſecondo la qualità delle materie conforme de tai Queſiti. </s> <s id="s.000128">Dapoi ue<lb></lb>nendomi ad aricordare, che ragionando un giorno, con el noſtro honorando compare, <lb></lb>meſſer Ricardo Ventuorth, gentil'huomo di uoſtra Sacra Maeſtà, elqual predicandomi <lb></lb>della Magnificentia, Magnanimità, Liberalità, Generoſità, Humanità, & Clemen<lb></lb>tia di uoſtra Altezza, mi diſſe anchora, qualmente uoſtra Celſitudine ſi dilettaua gran<lb></lb>damente di tutte le coſe alla guerra pertinente. </s> <s id="s.000129">Il che penſando, ini ha datto ardire<emph.end type="italics"></emph.end><lb></lb>( Q<emph type="italics"></emph>uantunque in me non ſia quella eloquentia, & ornato dire, che ſe rechiederia al<lb></lb>l'udito di uoſtra Serenità) di douere tai mei Queſiti, ouer interrogationi, con le ſue ri<lb></lb>ſolute riſpoſte à quella offerire, & dedicare, non come coſa conueniente à uoſtra Subli<lb></lb>mità (perche in uero le coſe di profondißima dottrina, narrate, & eſplicate con elle<lb></lb>gante, & terſo ſtile, non potriano aggiungere al primo grado di uoſtra altezza, non <lb></lb>che queſte noſtre, che ſono coſe Mechanice, e plebee, & ſimilmente dette. </s> <s id="s.000130">& prononcia<lb></lb>te con rozzo & baſſo ſtile.) Ma ſolamente come coſe nuoue à quella le offeriſco, & de<lb></lb>dico, come ſi coſtuma à fare delli primi frutti, che al principio di ſua ſtagione uengono <lb></lb>ritrouati, liquait (anchor che ſiano alquanto immatturi, & di puoca ſoſtantia, & men <lb></lb>ſapore) ſempre ſe ſogliono appreſentare à perſone Magnifiche & ſignorile, non per <lb></lb>la qualita della materia, ma per la nouità di quella, perche le coſe nuoue naturalmente ſo<lb></lb>ghono aggradire al intelletto humano, & cio mi ha dato à credere, tai noſtre inuentioni <lb></lb>non douere à uoſtra Clementia in tutto diſpiacere anzi aggradirli alquanto, il che eſſen<lb></lb>do (come deſidero) mi darà animo di douere per l'auenire piu oltra tentare, alli piedi <lb></lb>della quale, proſtrato in terra con le man gionte, & capo chino humilmente mi racco<lb></lb>mando.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb pagenum="5" xlink:href="042/01/009.jpg"></pb> <p type="head"> <s id="s.000131">IL PRIMO LIBRO DELLI <lb></lb>QVESITI, ET INVENTIONI DIVERSE <lb></lb>DE NICOLO TARTAGLIA, <lb></lb>SOPRA GLI TIRI DELLE ARTIGLIERIE, <lb></lb>ET ALTRI SVOI VARII <lb></lb>ACCIDENTI.</s> </p> <figure id="id.042.01.009.1.jpg" xlink:href="042/01/009/1.jpg"></figure> <p type="head"> <s id="s.000132">QVESITO PRIMO FATTO DALL'ILLVSTRISS. <lb></lb>S<emph type="italics"></emph>ignor Franceſco Maria Duca Eccellentißimo di Vrbino.<emph.end type="italics"></emph.end><lb></lb>L'A<emph type="italics"></emph>nno.<emph.end type="italics"></emph.end> M. D. XXXVIII. <lb></lb>IN VENETIA.</s> </p> <p type="main"> <s id="s.000133">Dvca. </s> <s id="s.000134">C<emph type="italics"></emph>he ragioniſono quelle che dicete hauer trouato, nel uo<lb></lb>ſtro libro à me intitolato, ſopra al tirare delle artiglierie.<emph.end type="italics"></emph.end> NI<lb></lb>COLO. L<emph type="italics"></emph>a proportione, & ordine de i tiri lontani, & pro<lb></lb>pinqui di qual ſi uoglia pezzo, & con qual ſiuoglia ſorte di balla.<emph.end type="italics"></emph.end><lb></lb>S. D. I<emph type="italics"></emph>o non u'intendo parlatemi piu chiaro, & datemi un'eßem <lb></lb>pio.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>olendo eſſemplificar queſta noſtra inuentione à uo<lb></lb>stra Eccellentia, ſono astretto à parlar prima di quello istrumen<lb></lb>to materiale, da noi ritrouato, figurato nel principio del detto noſtro libretto à quella <lb></lb>intitolato: il qual iſtrumento è una ſquadra di legno, ouer di alcun mettallo fatta con di<lb></lb>ligentia, alla ſimilitudine della ſotto ſcritta figura. </s> <s id="s.000135">b. a. c. la quale ha interchiuſo uno <lb></lb>quadrante, cioè una quarta parte di un cerchio, alla ſimiliuudine della figura. </s> <s id="s.000136">h. i. g. k. <lb></lb>la qual figura, ouer quadrante. </s> <s id="s.000137">h. i. g. k. ſi deſcriue con un compaſſo ſopra il centro. </s> <s id="s.000138">h. <lb></lb>cioè ponendo il pede immobile del detto compaſſo, in el detto ponto. </s> <s id="s.000139">h. (angolo intrin<lb></lb>ſtco di tal ſquadra, & l'altro piede mobile girandolo per. </s> <s id="s.000140">i. g.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>formando il detto la<lb></lb>to curuo. </s> <s id="s.000141">i. g.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>del detto quadrante, & dapoi reſtringere alquanto el detto compaßo, <lb></lb>& deſcriuere un'altra linea curua, equidiſtante alla prima, quale ſia la linea. </s> <s id="s.000142">e. f. et tut <lb></lb>to quel ſpatio, che è fra queſte due linee curue, cioè fra el lato curuo. </s> <s id="s.000143">i. g.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>et la curua <lb></lb>e. f. uuol eſſer diuiſo, prima in dodici parte equali, le quai diuiſioni uogliono eſſer tirate <lb></lb>con una rega, che uenga dal ponto. </s> <s id="s.000144">h. (centro del quadrante) à ciaſcheduna di dette di <lb></lb>uiſioni, accioche ciaſcheduna diuiſione riſguardi il detto centro. </s> <s id="s.000145">h. come in la figura <lb></lb>appare, & queſte dodici parte le chiameremo ponti.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/010.jpg"></pb> <figure id="id.042.01.010.1.jpg" xlink:href="042/01/010/1.jpg"></figure> <p type="main"> <s id="s.000146">An<emph type="italics"></emph>chora cadauna di queste tai parti, ouero ponti uuol eſſer anchora diuiſa in'al<lb></lb>tre dodici parti equali, con il medeſimo ordine, le qual diuiſioni non ho uoluto <lb></lb>tirare in queſta figura piccola, perche generarebbeno confuſione, ma in una ſqua<lb></lb>dra di commune grandezza, coſi, come ho detto, uuol eſſer diuiſa, tal che tutto il det<lb></lb>to quadrante. </s> <s id="s.000147">e. f. i. g.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>nenira à eſſer diuiſo in. </s> <s id="s.000148">144. parti equali, le qual parti chia<lb></lb>meremo minuti, & questi minuti ſe ſegnano con lineette alquanto piu corte di quel<lb></lb>le delli ponti, perche ſono poi piu facili da eſſer numerati per mezzo de i ponti (con <lb></lb>maggior lince depinti) per ſaper gia che ogni ponto contiene. </s> <s id="s.000149">12. minuti. </s> <s id="s.000150">Fatto que<lb></lb>sto biſogna ficcare un pironcino di ferro, ouero di ottone preciſamente in ponto. </s> <s id="s.000151">h. <lb></lb>(centro del quadrante) & à quel tal pironcino attaccarui uno perpendicolo girabi<lb></lb>le, cioè uno fil di ſeta (ò d'altro) con uno piombino dacapo alla ſimilitudine del per<lb></lb>pendicolo. </s> <s id="s.000152">h. g. d. </s> <s id="s.000153">& coſi con tal iſtrumento habbiamo conſiderato tutte le uarie poſi<lb></lb>tioni, ouero elleuationi, che occorrer poſſa in qual ſi uoglia pezzo di artiglieria. </s> <s id="s.000154">Et <lb></lb>la prima poſitione di cadauno pezzo ſe intende quando, che quello è aliuello, cioè tal<lb></lb>mente aſſettato, che ponendoui la gamba piu longa della detta noſtra ſquadra in boc<lb></lb>ca diſteſa rettamente per el fondo del uacuo della canna, el per pendicolo caſchi preci<lb></lb>ſamente ſopra ellato. </s> <s id="s.000155">h. f.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>del quadrante, come di ſotto appare nella prima figura, <lb></lb>Et ſimilmente uno pezzo ſe intende eſſer elleuato un ponto quando che quello ſia tal<lb></lb>mente aſſettato, che ponendoui la detta gamba piu longa della detta noſtra ſquadra <lb></lb>in bocca diſteſa rettamente per el fondo del uacuo della canna (come prima) el per<lb></lb>pendicolo <expan abbr="caſchipreciſamẽte">caſchi preciſamente</expan> ſu la diuiſione del primo ponto, come di ſotto appar nel<lb></lb>la ſeconda figura: Et coſi un pezzo ſe intende eſſere elleuato due ponti, quando che el <lb></lb>detto perpendicolo caſchi preciſamente ſopra la diuiſione del detto ſecondo ponto, & <lb></lb>coſi al terzo quando caſcara ſopra la divſion del terzo, el medeſimo ſe intende del <lb></lb>quarto, quinto, & ſeſto. </s> <s id="s.000156">Et quando che uno pezzo è elleuato al ſeſto ponto (cioè co-<emph.end type="italics"></emph.end><pb pagenum="6" xlink:href="042/01/011.jpg"></pb><emph type="italics"></emph>me di ſotto appare nella terza figura) ſe intende alla maggiore elleuatione, che elleuar <lb></lb>ſi poſſa.<emph.end type="italics"></emph.end> (D<emph type="italics"></emph>ico un pezzo d'artigliaria perche li mortari poi ſe poſſono elleuare in <lb></lb>tutti li altri ſeguenti per fin al duodecimo ponto.<emph.end type="italics"></emph.end>) E<emph type="italics"></emph>t queſto che habbiamo detto de i <lb></lb>ponti, ſe debbe anchora intendere de i minuti, cioè, che quando, che uno pezzo ſia tal <lb></lb>mente elleuato, che el perpendicolo caſchi preciſamente ſopra la diuiſione del pri<lb></lb>mo minuto, cioè ſopra la duodecima parte del primo ponto, tal pezzo s'intende eſ<lb></lb>ſer elleuato uno minuto, & quando caſchara ſopra alli due minuti, s'intendera eſſere <lb></lb>elleuato duoi minuti, il medefimo s'intendera de tutti li altri, per fin alla maggior el<lb></lb>leuatione cioè alla elleuatione del ſeſto <expan abbr="põto">ponto</expan>, ouero ſettantadue minuti, come nella det<lb></lb>ta terza figura appare: Li altri minuti che ſeguita per fino in capo, ſono per le elle<lb></lb>uationi di mortari.<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.011.1.jpg" xlink:href="042/01/011/1.jpg"></figure><lb></lb><figure id="id.042.01.011.2.jpg" xlink:href="042/01/011/2.jpg"></figure></s> </p> <pb xlink:href="042/01/012.jpg"></pb> <figure id="id.042.01.012.1.jpg" xlink:href="042/01/012/1.jpg"></figure> <p type="main"> <s id="s.000157">S. DVCA. C<emph type="italics"></emph>he uolete inferir per queſto.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>rimamente uoglio inferir que <lb></lb>ſto, che tirando un pezzo alla elleuatione del primo ponto, tir ara molto piu lontano di <lb></lb>quello che fara ſtando aliuello, & tirandolo alla elleuatione del ſecondo ponto, tirara <lb></lb>molto piu lontano di quello, che fara alla elleuatione del primo ponto, & coſi alla elle<lb></lb>uatione del terzo ponto tirara piu lontano, che alla elleuatione del ſecondo, & coſi alla <lb></lb>elleuation del quarto tirara anchora aſſai piu lontano di quello, che fara alla elleuatio<lb></lb>ne del terzo, & ſimilmente alla elleuatione del quinto tirara alquanto piu, che alla elle <lb></lb>uatione del quarto, & coſi alla ultima elleuatione, cioè al ſeſto ponto, con balla di piom<lb></lb>bo tirara alquanto piu, che alla elleuation del quinto, ma poco piu, per che la ragion ne <lb></lb>dimostra, che queſti que tiri, cioè tirati al quinto, & ſeſto ponto ſono tanto uicini, o<lb></lb>uer tanto poco differenti, che ogni poco d'auantaggio, che ſi trouaſſe nel quinto, ò per <lb></lb>uigor di poluere, ouer per altro, al detto quinto, ſe tiraria <expan abbr="tãto">tanto</expan>, quanto al ſeſto, et forſi <lb></lb>piu. </s> <s id="s.000158">Et chi poteſſe elleuar tal pezzo come ſe fanno li mortari, cioè al ſettimo ponto, <lb></lb>ſenza dubbio al detto ſettimo ponto tirara alquanto manco, che al detto ſeſto, & coſi <lb></lb>all'ottauo pento tirara aſſai manco, che al detto ſettimo, & ſimilmente, al nono tirara <lb></lb>molto manco, che all'ottauo, & coſi al decimo tirara molto manco, che al nono, et coſi <emph.end type="italics"></emph.end><pb pagenum="7" xlink:href="042/01/013.jpg"></pb><emph type="italics"></emph>al undecimo, tirara molto manco, che al decimo, & ſimelmente al duodecimo, cioc al <lb></lb>ultimo ponto tirara molto e molto manco che al undecimo anci in tal ultima elleuatio<lb></lb>ne per raſon naturale la balla doueria retornar a dare preciſamente nella bocca di tal <lb></lb>pezzo, ma per molti <expan abbr="accidtiẽ">accidtiem</expan> che ui puo occorrere nel diſca<gap></gap>agarſi, tal balla <expan abbr="nõ">non</expan> ui ritor <lb></lb>nara coſi preciſe, ma bennon andara a dare molto lontana dal detto pezzo.<emph.end type="italics"></emph.end> S. D. <lb></lb>E<emph type="italics"></emph>glie coſa conſonante quaſi tutto quello che haueti detto, ma che uoleti inferire per <lb></lb>queſto.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oglio ſecondariamente inferir queſto, che noi habbiamo ritrouato in <lb></lb>che ſpecie di proportione, ouer ordine uanno augumentando li detti tiri in ogni elleua<lb></lb>tione, & non ſolamente a ponto per ponto della detta nostra ſquadra, ma anchora a mi <lb></lb>nuto per m<gap></gap>uto per fin alla elleuatione del ſeſto ponto, ouer di. </s> <s id="s.000159">72. minuti, & in ogni <lb></lb>ſorte balla, cioe di piombo, ferro, ouer di pietra. </s> <s id="s.000160">Et ſimelmente chi poteſſe elleuare li <lb></lb>pezzi oltra al detto ſesto ponto (come ſe fanno li mortari) hauemo anchora ritrouato <lb></lb>in che proportione andaranno calando li ſuoi tiri, & non ſolamente a ponto per pon<lb></lb>to, ma anchora (come detto) a minuto per minuto per fin al fine di tutta la ſquadra, <lb></lb>cioe per fin in capo de tutti li 12. ponti, ouer. </s> <s id="s.000161">144. minuti.<emph.end type="italics"></emph.end> S.D. Q<emph type="italics"></emph>ue coſtrutto ſe <lb></lb>puo cauar de tal uoſtra inuentione.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>l coſtrutto de tal inuentione è questo, che <lb></lb>per la notitia de unſol tiro di qual ſi uoglia pezzo, poſſo formar una tauola de tutti li <lb></lb>tiri che tirara quel tal pezzo in ogni elleuatione, cioe a ponto per ponto, et a minutop <lb></lb>minuto della noſtraſquadra, la qual tauola ſara di tal <expan abbr="ſoſtãtia">ſoſtantia</expan>, ouer proprieta, che qua <lb></lb><expan abbr="lũque">lunque</expan> pſona la hauera a preſſo diſe, <expan abbr="nõ">non</expan> <expan abbr="ſolamẽte">ſolamente</expan> ſapra tirare, ma ſapra far tirare ogni <lb></lb>groſſo bombardero con tal ſorte pezzi di lontano quanti paſſa li parira (pur che non <lb></lb>ſla piu lontano del maggior tiro di tal pezzo) & che non hauera la detta noſtra tauo<lb></lb>la, non potra imparare alcuna particolarita di tal inuentione, ma tal ſecreto reſtara ſo <lb></lb>lamente a preſſo di colui che hauera tal tauola, & non ad altri.<emph.end type="italics"></emph.end> S.D. M<emph type="italics"></emph>o ſi colui che <lb></lb>hauera tal uoſtra tauola non uora tirare lui medeſimo, ma uora far tirare a un'altra <lb></lb>ſeconda perſond, non ſara neceſſario che tal ſeconda perſona impari tal ſecreto.<emph.end type="italics"></emph.end> N. <lb></lb>N<emph type="italics"></emph>on Signor Eccellentißimo, anci tal ſeconda perſona reſtara come restano li garzo<lb></lb>ni di ſpeciari de medicine, li quali <expan abbr="continuamẽte">continuamente</expan> <expan abbr="cõponeno">componeno</expan> medicine, <expan abbr="ſecõdo">ſecondo</expan> che gli uen <lb></lb>gono or dinate dalli medici, & tamen mai imparano a ſaper medicare.<emph.end type="italics"></emph.end> S.D. Q<emph type="italics"></emph>ueſta <lb></lb>mi pare una coſa molto dura da credere, & tanto piu che nel noſtro libretto (a me inti<lb></lb>tulato) uoi diceti che mai tiraſti di artegliaria, ne di ſchioppo, & colui che ſa un giudi <lb></lb>cio di una coſa, della quale non habbia uiſto lo effetto, ouer iſperientia, lamaggior par<lb></lb>te delle uolte ſe inganna, perche ſolamente l'occhio è quello che ne rende uera testimo<lb></lb>nianza delle coſe immaginate.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie benuero che il ſenſo iſteriore, ne dice la ue<lb></lb>rita nelle coſe particolare, ma non nelle uniuerſale, perche le coſe uniuerſale ſono ſot<lb></lb>topoſte ſolamente al intelletto, & non ad alcun ſenſo.<emph.end type="italics"></emph.end> S.D. B<emph type="italics"></emph>aſta ſe me fareti ueder <lb></lb>queſto (coſa che non credo) el me parera un miracolo.<emph.end type="italics"></emph.end> N. T<emph type="italics"></emph>utte le coſe che accade<lb></lb>no per natura, ouer per arte pareno de grande ammiratione, quando che di quelle non <lb></lb>ſi ſala cauſa, mapreſto uoſtra Eccellentia ſe ne potrachiarire, facendone far laiſpe<lb></lb>rientia con un pezzo.<emph.end type="italics"></emph.end> S.D. V<emph type="italics"></emph>oglio andare per fina à Peſaro, ſubito che ſia ritor<lb></lb>nato, certo la uoglio uedere.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/014.jpg"></pb> <p type="head"> <s id="s.000162">QVESITO SECONDO FATTO <lb></lb><emph type="italics"></emph>dal medeſimo Illust. Sig. Duca conſequentemente <lb></lb>al precedente.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000163">DVCA. M<emph type="italics"></emph>a ditemi un poco per qual uerſo credete uoi che una <lb></lb>Artegliaria <lb></lb>fara maggior effetto, ouer paſſata nella coſa doue ſe tira, tirandoui con quel<lb></lb>la aliuellata, ouer elleuata <expan abbr="dauãti">dauanti</expan>.<emph.end type="italics"></emph.end> N. </s> <s id="s.000164">A <emph type="italics"></emph>uoler reſoluere queſto queſito ſenza repren<lb></lb>ſione, egliè neceſſario, che uoſtra Eccellentia, me proponga tal queſito per eſſempio, <lb></lb>ouer figura, con la quantita della diſtantia de tal Artegliaria, & la qualita del luoco <lb></lb>doue ſe tira.<emph.end type="italics"></emph.end> S.D. P<emph type="italics"></emph>ongo per <expan abbr="eßẽpio">eßempio</expan>, che il mi occorreſſe di far battere una fortez<lb></lb>za che fuſſe in cima di una colina, ouer monticello, alto paſſa. </s> <s id="s.000165">60. & che lontano paſ<lb></lb>ſa. </s> <s id="s.000166">100. da quella tal colina, ouer monticello, ui fuſſe un'altra còlina, ouer monticel<lb></lb>lo, alto alla equalita di detta fortezza, cioè pur paſſa. </s> <s id="s.000167">60. (come di ſotto appare in <lb></lb>figura) & poniamo che ſopra la cima di queſto ſecondo monticello, ui ſe poteſſe sta<lb></lb>re commodamente con la artegliaria à battere queſta tal fortezza, la quale arteglia<lb></lb>ria in tal luoco ueneria à tirare in quella retto tramite, cioè con la detta artegliaria <lb></lb>aliuellata (come di ſotto appare in figura) & poniamo anchora che tal fortezza, ſl <lb></lb>poteſſe commodamente battere ſtando con la artegliaria nel piano (cioè ſtando da <lb></lb>banda nel pie del detto ſecondo monticello in quella medeſima diſtantia) cioè ſtando <lb></lb>lontano dal pie del monte, doue è la fortezza pur paſſa. </s> <s id="s.000168">100. nel qual luoco, la detta <lb></lb>artegliaria uerria à tirare in quella stante molto elleuata dauanti, cioè tiraria in quel<lb></lb>la di ſotto in ſuſo (come di ſotto appare in figura.) Hor ue adimando, in qual luoco <lb></lb>penſati che tale artegliaria faria maggiore effetto, ouer paſſata in detta fortezza,<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.014.1.jpg" xlink:href="042/01/014/1.jpg"></figure><pb pagenum="8" xlink:href="042/01/015.jpg"></pb><emph type="italics"></emph>eioè ſtando in cima del detto monticello, ouer ſtando iui da banda nel pie di quello.<emph.end type="italics"></emph.end><lb></lb>N. S<emph type="italics"></emph>enza dubbio, che ſtando nel piano, cioè nel pie del monte, faria mag<lb></lb>giore effetto, ouer paſſata in detta fortezza, di quello faria ſtando nella ſommita del <lb></lb>monte.<emph.end type="italics"></emph.end> S.D. E<emph type="italics"></emph>t lo giudicarei, & giudico eſſer tutto al <expan abbr="cõtrario">contrario</expan>, perche quelle che ti<lb></lb>rar anno dalla ſommita del monte ſaranno molto piu propinque alle muraglie di quel<lb></lb>la tal fortezza, di quello che ſaranno quelle che tirar anno dal pie del monte, & quan<lb></lb>to che la coſa doue ſe tira è piu propinqua alla artegliaria, per ragion naturale, la <lb></lb>balla douria far maggiore effetto in lei.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph><expan abbr="uãdo">uando</expan> che un'artegliaria tiraſſe egual<lb></lb>mente per ogni uerſo ſegueria quello, che dice uoſtra Eccellentia. </s> <s id="s.000169">Ma per efficace ra<lb></lb>gioni ritrouo tutto all'oppoſito, cioè che ogni ſorte di artegliaria neceſſariamente ti<lb></lb>rara manco per line a retta, ſtante aliuellata di quello faria in qualunque altro modo <lb></lb>aſſettata, o per dir meglio, che ogni ſorte di artegliaria neceſſariamente tirara pile <lb></lb>per linea retta ſtante alquanto elleuata dauanti di quello fara ſtante quella à liuello, <lb></lb>& quanto piu ſtara elleuata tanto piu tirara per retta linea, il medeſimo ſi debbe in<lb></lb>tendere eſſendo abbaſſata, cioè che molto piu tir ara per linea retta ſtante quella al<lb></lb>quanto abbaſſata dauanti, di quello fara ſtante à liuello, & quanto piu ſtara abbaſ<lb></lb>ſata, <expan abbr="tãto">tanto</expan> piu tirara per linea retta.<emph.end type="italics"></emph.end> S.D. Q<emph type="italics"></emph>ueſto che uoi dite, me pare una coſa mol<lb></lb>to ſtrania da credere, cioè à dire, che una medeſima quantita, e poſſanza di poluere, <lb></lb>debbia ſpingere piu uigoroſamente una medeſima grauita di balla, per un uerſo, che <lb></lb>per un'altro, e pero haria à caro, che uoi me aßignaſti la ragione, e cauſa di questa uo<lb></lb>ſtra openione.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a ragion di questo lo dimoſtr amo (per li accidenti accadenti nelli <lb></lb>ſuoi tiri) nella ultima propoſitione del Secondo libro della noſtra nuoua ſcientia, ue<lb></lb>ro è, che in tal dimoſtratione, non ſe aſſegna la cauſa propinqua di tale effetto, la qual <lb></lb>coſa in tal luoco pretermeßi, per non faſtidiar uostra Eccellentia, perche tal cauſa <lb></lb>propinqua, ſe dimoſtra con la ſcientia di peſi, la quale è una ſcientia di non poca ſpe<lb></lb>culatione, per eſſer quella ſubalternata, ſi dalla Geometria, come dalla natural Filo<lb></lb>ſophia. </s> <s id="s.000170">Ma quando non ſia graue à quella lo aſcoltarme, io mi sforzaro di dimostrar<lb></lb>la al preſente.<emph.end type="italics"></emph.end> S.D. S<emph type="italics"></emph>eguitatipur, ma ſotto breuita.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er dimoſtrar queſta coſa <lb></lb>rettamente ſono astretto uolendo eſſere inteſo à <expan abbr="mãdare">mandare</expan> auanti la diffinitione de alcu<lb></lb>ni termini opportuni, etiam alcune ſuppoſitioni, come ſi coſtuma in ciaſcuna ſcientia, <lb></lb>& perche tutte le coſe meglio ſe apprendono per eſſempio, che per parole. </s> <s id="s.000171">Pongo <lb></lb>per eſſempio 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></lb>centro, ſopra del qual lei gira, ſia il detto ponto.c.& nelle eſtremita di detti dui braz<lb></lb>zi ſlano congionti dui corpi egualmente graui, li quali nominaremo dalle medeſime <lb></lb>lettere, cioè.a.&.b. </s> <s id="s.000175">li quali dui corpi, per eſſere eguali in grauita, dal preſuppoſito, <lb></lb>& appeſi in longhezze eguali, cioè à gli detti dui brazzi.a.c.&.c.b. </s> <s id="s.000176">della propo<lb></lb>ſta libra, qual ſouo ſta ſuppoſti eſſere egualmente longhi, per la prima petitione adut<lb></lb>ta da Archimede, nel libro che fa del centro della grauita, quelli inclinar anno egual<lb></lb>mente, cioè che ſtaranno in equilibra, come di ſotto appare in figura.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/016.jpg"></pb> <figure id="id.042.01.016.1.jpg" xlink:href="042/01/016/1.jpg"></figure> <p type="main"> <s id="s.000177">An<emph type="italics"></emph>chora ſta deſcritto ſopra il centro.c.un cerchio, ſecondo la quantita dell'u<lb></lb>no di brazzi della libra, ouer bilanza qual ſla il cerchio.e.a.f.b. </s> <s id="s.000178">la circonfe<lb></lb>rentia del quale ſupponeremo per il uiaggio che fariano li centri di detti corpi, gi<lb></lb>rando à torno la detta bilanza ſopra il ſuo centro.c.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000179">D<emph type="italics"></emph>iffinitione Prima.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000180">S<emph type="italics"></emph>tando adunque li detti dui corpi in equilibra, come in figura appare, in tal luoco <lb></lb>li detti dui corpi, ſe dicono eſſer nel ſito della equalita.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000181">D<emph type="italics"></emph>iffinitione Seconda.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000182">A<emph type="italics"></emph>nchor tirando dalla ſommita una perpendicolare paſſante per il centro. </s> <s id="s.000183">c. <lb></lb>(quala ſia la linea.e.c.f.) tal linea uien detta la linea della direttione.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.016.2.jpg" xlink:href="042/01/016/2.jpg"></figure> <p type="head"> <s id="s.000184">S<emph type="italics"></emph>uppoſitione Prima.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000185">An<emph type="italics"></emph>chora biſogna notare qualmente un corpo graue ſe ſuppone eſſer tanto piu <lb></lb>graue, nel luoco doue ſe ritroua quanto che il diſcender di quello è manco obli<lb></lb>quo, cicè manco curuo, in el medeſimo ſito, ouer luoco. </s> <s id="s.000186">Lo eſſempto di queſta ſuppo<lb></lb>ſitione ſe adura nella ſeguente figuratione.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000187">S<emph type="italics"></emph>uppoſitione Seconda.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000188">E<emph type="italics"></emph>t il diſcender d'un corpo graue, ſe ſuppone eſſer tanto piu obliquo, quanto che <lb></lb>nel ſuo diſcender capiſſe manco del diretto, in medeſima quantita, cioe che capiſſe man <lb></lb>co parte della linea della direttione, ouer di una altra a quella equidiſtante, in la mede<lb></lb>ſima quanlita, cioe in medeſima quantita di cir conferentia del cerchio doue gira, ouer <lb></lb>ua, & queſto nella figuration ſequente meglio ſe intendera.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="9" xlink:href="042/01/017.jpg"></pb> <p type="main"> <s id="s.000189">Sv<emph type="italics"></emph>pposte adunque le ſopradette ſuppoſitione, adduco questa propoſitione, & dico <lb></lb>che ogni librato peſo partendoſl dal ſito, ouer luoco della equalita, quel ſi fa piu le <lb></lb>ue, & tanto piu quanto piu ſara lontano dal detto luoco della equalita. </s> <s id="s.000190">Et per eſſeme <lb></lb>pio di questa propoſitione ſia la libra.a.b. (della figura precedente) girabile ſopra el <lb></lb>detto centro.c. </s> <s id="s.000191">con li dui medeſimi corpi.a.&.b. (equali) appeſi, ouer congionti alle <lb></lb>due eſtremita di ambi dui li brazzi della detta libra, & ſtiano nel medeſimo ſito della <lb></lb>equalita (come di ſopra fu ſuppoſto) hor dico, che remouando l'uno, & l'altro de detti <lb></lb>corpi dal detto ſito della equalita (cioè arbaſſandone uno, & elleuando l'altro) l'uno, <lb></lb>e l'altro de quelli ſara fatto piu leue ſecondo el luoco, & tanto piu leui, quanto che piu <lb></lb>ſaranno allontanati dal detto luoco della equalita. </s> <s id="s.000192">Et per dimoſtrar queſto ſia arbaſſa <lb></lb>to el corpo.a. (della detta figura precedente) per fina al <expan abbr="põto">ponto</expan>.u. (come nella ſotto ſcrit<lb></lb>ta figura appare, & l'altro ſuo oppoſito (cioè el corpo.b.) uerra à eſſerſe elleuato per <lb></lb>in fina al ponto.i.& ſia diuiſo l'uno, e l'altro di dui archi.a.u.&.i.b. </s> <s id="s.000193">in quante parti <lb></lb>ſi 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.ſ. <lb></lb>& dalli trei ponti.n.l.i.ſiano tirate le tre linee.n.o.l.m.&.i.<emph.end type="italics"></emph.end>k <emph type="italics"></emph>equidiſtante al diame<lb></lb>tro.b.a.le quale ſegarano la linea.e.f.della direttione nelli trei ponti.z.y.x.ſimelmen <lb></lb>te dalli trei ponti.q.s.u. </s> <s id="s.000195">ſiano tirate le tre linee.q.p.s.r. </s> <s id="s.000196">&.u.t.pur equidiſtante alla <lb></lb>medema linea.a.b. </s> <s id="s.000197">le quale ſegarano la medema linea della direttione nelli tre ponti, <lb></lb>&.<36><gap></gap>. </s> <s id="s.000198">Onde per queste coſe coſi deſpoſite ueniremo ad hauer diuiſo tutto el decenſo <lb></lb>a.u.fatto dal detto corpo.a.nel diſcender in ponto.u.in trei decenſi, ouer parti equa<lb></lb>li, le quale ſono.a.q.q.s.&.s.u. </s> <s id="s.000199">Et ſimelmente tutto el decenſo.i.b. </s> <s id="s.000200">qual faria el detto <lb></lb>corpo.b. nel diſcendere, ouer ritornare al ſuo primo luoco (cioè in ponto.b.) uerra à eſ <lb></lb>ſer diuiſo in trei decenſi, ouer in tre parti equali, le quali ſono.i.l.l.n.&.n.b.& cadau <lb></lb>no de queſti tre, & tre partiai decenſi capiſſe una parte della linea della direttione, <lb></lb>cioè el decenſo dal.a.al.q. </s> <s id="s.000201">piglia, ouer capiſſe dalla linea della direttione la parte.c.&. <lb></lb></s> <s id="s.000202">lo decenſo.q.s.piglia, ouer capiſſe la parte, &.<36>. </s> <s id="s.000203">& lo decenſo.s.u. </s> <s id="s.000204">capiſſe la parte <36>. <lb></lb><gap></gap>.& perche la parte.c.&. </s> <s id="s.000205">emaggiore della parte.&.<36>. (come facilmente geometri <lb></lb>ce ſe puo prouare) onde (per la ſeconda ſuppoſitione) el decenſo.q.s. </s> <s id="s.000206">uerra à eſſer piu <lb></lb>obliquo del decenſo.a.q. </s> <s id="s.000207">onde piu leue ſara el detto corpo.a. (per la ſuppoſitione) ſtan <lb></lb>te quello in ponto. </s> <s id="s.000208">q di quello ſara, ſtante quello in ponto.a. </s> <s id="s.000209">Simelmente perche la par <lb></lb>te.<36>.<gap></gap>. (della linea della direttione) è menore della parte. </s> <s id="s.000210">&.<36>. </s> <s id="s.000211">el decenſo.s.u. (per la <lb></lb>medeſima ſeconda ſuppoſitione ſara piu obliquo del decenſo.q.s.& conſequentemen<lb></lb>te) per la prima ſuppoſitione piu leue ſara el detto corpo.a ſtante quello in ponto.s. </s> <s id="s.000212">di <lb></lb>quello ſaraſtante in ponto.q. </s> <s id="s.000213">Et tutto queſto, & per li medeſimi modi ſe demoſtrara <lb></lb>nella oppoſita parte del corpo.b. cioè chel decenſo di quello dal ponto.i. </s> <s id="s.000214">al ponto. </s> <s id="s.000215">l. è <lb></lb>piu obliquo di quello, che è dal ponto.l. </s> <s id="s.000216">al ponto.n. (per la detta ſeconda ſuppoſitione) <lb></lb>perche la parte.x.y. </s> <s id="s.000217">che capiſſe della linea della direttione, è menore della parte y.z. <lb></lb>onde per la detta prima ſuppoſitione piu leue ſara el detto corpo ſtante quello in pon<lb></lb>to.i.di quello ſara ſtante quello in ponto.l. </s> <s id="s.000218">& per le medeſime ragioni piu leue ſara <lb></lb>ſtante quello in ponto.l.di quello ſara ſtante in ponto.n. </s> <s id="s.000219">& ſimelmente piu leue ſara <lb></lb><expan abbr="stãte">stante</expan> in <expan abbr="põto">ponto</expan>.n. </s> <s id="s.000220">di quello ſara ſtante in <expan abbr="põto">ponto</expan>.b. (ſito della equalita) che è il propoſito.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/018.jpg"></pb> <figure id="id.042.01.018.1.jpg" xlink:href="042/01/018/1.jpg"></figure> <p type="main"> <s id="s.000221">S. DVCA. C<emph type="italics"></emph>he uoleti inferir per queſto.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oglio inferir queſto, che ogni arti <lb></lb>gliaria eſſendo aliuellata, la ſe intende eſſer nel ſito della equalita, & la balla tirata da <lb></lb>quella, in tal ſito uſciſſe del pezzo piu graue, che in qualunque altro modo elleuata, <lb></lb>ouer ſeparata da quel ſito della equalita (per le ragioni di ſopra adutte) e pero in tal <lb></lb>ſito la balla ua con piu difficultà, & molto piu preſto comincia à declinar al baſſo, cioè <lb></lb>uerſo terra, & in maggior quantita lei ua declinando, che in qualunque altro modo el <lb></lb>leuata, cioè che lei ua (come fra bombardieriſe dice) molto manco per linea retta, che <lb></lb>in qualunque altro modo elleuata, e pero li effetti di tiri fatti in tal ſito ſaranno men ui <lb></lb>goroſi, ouer di menor effetto, che in qualunque altro uerſo. </s> <s id="s.000222">Vero è, che uoſtra Eccellen<lb></lb>tia potria dire, & ragioneuolmente, per queſte tue ragioni ſon chiaro, che in diſtantia <lb></lb>equale lei fara <expan abbr="mãco">manco</expan> effetto, ma in distantie inequale reſto dubbioſo, perche nel noſtro <lb></lb>Queſito ſi uede, che quelle artegliarie, che ſono nel piano, ouer nel pie del monte, ſono <lb></lb>molto piu diſtante, dalla fortezza, di quelle, che ſon nella ſommita del monte, talmente <lb></lb>che tal differentia potria eſſer molto maggiore della differentia del ſuo tirar per li<lb></lb>nea retta, ouer della differentia de ſuoi effetti in diſtantie equale, & eſſendo coſi quelle <lb></lb>de la ſommita del monte, uerriano à far maggior effetto, di quelle poſte in piano, cir<lb></lb>ca al qual dubbio riſpondo, che gliè ben uero, che la diſtantia di quelle, che ſtano in pia <lb></lb>no, potria eſſer alle uolte tanto grandemente differente da quella, di quelle, che ſono ne <lb></lb>la ſommita del monte, che ſeguiria quello, che di ſopra hauemo detto, ouer dubitato.<emph.end type="italics"></emph.end><lb></lb>S.D. D<emph type="italics"></emph>atime <expan abbr="un'eßẽpio">un'eßempio</expan> in figura, ſe uoleti, che ue intenda.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er uoler eſſemplifi <lb></lb>care figuralmente queſta coſa ſupponeremo una colobrina da lire. </s> <s id="s.000223">20. di balla, laqual <lb></lb>colobrina (per quella ſperientia, che fu fatta à Verona, narrata nel principio della no <lb></lb>ſtra noua ſcientia à uoſtra Eccellentia) io trouo, che tal colobrina nel ſito della equali<lb></lb>ta (cioè ſtando aliuellata) tirara de mira, ouer per linea retta circa paſſa. </s> <s id="s.000224">200. & alla <lb></lb>elleuatione de. </s> <s id="s.000225">45. gradi, cioè al ſeſto ponto, ouer alli. </s> <s id="s.000226">72. minuti della noſtra ſquadra <lb></lb>tal colobrina (per le ragioni adutte nella ultima propoſitione del <expan abbr="ſecõdo">ſecondo</expan> libro della no <lb></lb>stra noua ſcientia) tirara de mira, ouer per linea retta, in quel uerſo, circa paſſa.<emph.end type="italics"></emph.end> 800. <lb></lb>S.D A<emph type="italics"></emph>dunque <expan abbr="tirãdo">tirando</expan> la detta colobrina à tal elleuatione tirara circa paſſa. </s> <s id="s.000227">800. per <lb></lb>linea retta, & tirandola poi aliuellata, non tirara ſaluo che circa paſſa.<emph.end type="italics"></emph.end> 200 N. C<emph type="italics"></emph>o <lb></lb>ſi ne afferma la ragione.<emph.end type="italics"></emph.end> S.D. L<emph type="italics"></emph>a me pare una grah differentia.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uesto pro<lb></lb>cede per eſſer anchora tal ellcuatione molto differente dal ſito della equalita, perche ſe<emph.end type="italics"></emph.end><pb pagenum="10" xlink:href="042/01/019.jpg"></pb><emph type="italics"></emph>condo che la ſi ua elleuando de minuto in minuto, coſi de minuto in minuto lei ua ancho <lb></lb>ra augumentando il ſuo tirar per linea retta, il medeſimo fara etiam nelli ponti, & in <lb></lb>maggior quantita, cioè, che elleuata al primo ponto della ſquadra tirara molto piu <lb></lb>per linea retta, di quello fara nel ſito della equalita, cioè aliuellata, & elleuata poi al ſe <lb></lb>condo ponto di detta ſquadra, molto piu tirara per linea retta, di quello fara elleuata al <lb></lb>primo ponto, & coſi elleuata al terzo ponto, tirara piu pur per linea retta, di quello <lb></lb>fara al ſecondo, & coſi ſucceßiuamente al quarto, tirara piu, che al terzo & al quin<lb></lb>to piu che al quarto, & al ſeſto (detto di ſopra) tirara piu che al quinto, & ſe piu ol<lb></lb>tra la ſi poteſſe elleuare gradatamante andaria augumentando il ſuo tirare per linea <lb></lb>retta, cioè, che al. 7. ponto, tirara piu per linea retta, che al. 6. & al. 8. piu che al. 7. <lb></lb>& al. 9. piu che al. </s> <s id="s.000228">8. & al. 10. piu che al. 9. & al. 11. piu che al. 10. & al. 12. piu che <lb></lb>al. 11. & à queſto. </s> <s id="s.000229">12. tutto il ſuo tiro ſara per linea retta, perche ſara perpendicola<lb></lb>re ſopra all'orizonte, & queſto tale ſara piu perfettamente retto de cadauno delli an<lb></lb>teditti, perche in uero il tranſito, ouer moto uiolente d'un corpo egualmente graue, <lb></lb>che ſia fora della perpendicolar del orizonte, mai pol hauere alcuna parte, che ſia per <lb></lb>fettamente retta (come fu detto ſopra la ſeconda ſuppoſitione del ſecondo libro della <lb></lb>noſtra noua ſcientia.<emph.end type="italics"></emph.end> S.D. P<emph type="italics"></emph>erche diceti adunque per linea retta, non eſſendo per<lb></lb>fettamente retta.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er eſſer inteſo dal uolgo, perche quella parte, che è quaſi in<lb></lb>ſenſibelmente curua, la chiamamo retta, & quella che è euidentamente curua, li dico<lb></lb>no curua.<emph.end type="italics"></emph.end> S.D. S<emph type="italics"></emph>eguitati.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>or per ritornare al noſtro propoſito, dico adun<lb></lb>que, che ſe la altezza della predetta ſortezza foſſe tanta, che da quella à le arteglia<lb></lb>rie, che fuſſeno nel piano del monte, fuſſe. </s> <s id="s.000230">760. paſſa, & che dalla medema fortezza <lb></lb>à quelle artegliarie, che fuſſeno nella ſummita del monte, fuſſe ſolamente paſſa. </s> <s id="s.000231">130. in <lb></lb>questo caſo dico, che la ſopra detta colobrina faria mazzor effetto nelle muraglie di <lb></lb>detta fortezza, stante quella ne la ſommita del monte, di quello faria, ſtante nel pie dil <lb></lb>monte. </s> <s id="s.000232">La cauſa è, perche la detta colobrina (ſtante aliuellata) tira circa paſſa. </s> <s id="s.000233">200. <lb></lb>per linea retta (come di ſopra fu detto) Eſſendo adunque da quella à la muraglia paſ<lb></lb>ſa. </s> <s id="s.000234">130. (come fu ſupposto) lei ueneria à percuotere ne la detta muraglia circa per. </s> <s id="s.000235">70. <lb></lb>paſſa auanti al termine dil ſuo andar per linea retta: Ma ſtante quella nel pie dil mon<lb></lb>te (dal qual luoco alla detta muraglia è ſta ſuppoſto eſſer diametralmente paſſa. </s> <s id="s.000236">760.) <lb></lb>& elleuandola alla elleuatione de. </s> <s id="s.000237">45. gradi (cioè al. 6. ponto della noſtra ſquadra) ti<lb></lb>rara circa paſſa. </s> <s id="s.000238">800. per linea retta (come di ſoprafu detto) onde lei ueneria à per<lb></lb>cuotere nella detta muraglia ſolamente circa per paſſa. </s> <s id="s.000239">40. auanti il termine del ſuo <lb></lb>andar per linea retta, cioè auanti la ſua ſenſibil declinatione. </s> <s id="s.000240">Et perche quella balla che <lb></lb>nel ſuo percotere hauera à tranſire per piu longo ſpatio (non trouando reſiſtcntta) fa <lb></lb>ra maggior effetto in tal reſistente (per le ragioni adutte ſopra la. </s> <s id="s.000241">4. propoſitione del <lb></lb>primo libro della noſtra noua ſcientia) perche adunque la halla tirata da la ſommita <lb></lb>del monte nel ſuo percottere haueria anchora à andare paſſa. </s> <s id="s.000242">70. per linea retta. </s> <s id="s.000243">Et <lb></lb>quella tirata dal piano, nel ſuo percottere haueria à procedere ſolamente paſſa. </s> <s id="s.000244">40. <lb></lb>per linea retta, & per queſte ragiom ſe <expan abbr="cõchiuderia">conchiuderia</expan> in tal caſo, che maggior effetto fa <lb></lb>ria la detta colobrina in detta muraglia, ſtante quella ne la ſommita del monte di quel<lb></lb>lo faria ſtante nel piano, ouero pie dil monte alla elleuatione del detto. </s> <s id="s.000245">6 ponto della<emph.end type="italics"></emph.end><pb xlink:href="042/01/020.jpg"></pb><emph type="italics"></emph>noſtra ſquadra), & ſe alla detta elleuatione dil. </s> <s id="s.000246">6. ponto lei fara manco effetto, molto <lb></lb>meno lei lo faria ad alcuna altra piu baſſa elleuatione. </s> <s id="s.000247">Ma ſe per caſo la distantia de <lb></lb>detta fortezza alle artegliarie, che fuſſeno nel piano fuſſe paſſa. </s> <s id="s.000248">600. cioè diametral<lb></lb>mente, & che dalla medema à quelle che fuſſeno nella ſommita del monte fuſſe paſſa <lb></lb>150. in tal caſo dico, che la detta colobrina fara molto maggiore effetto nella detta mu <lb></lb>raglia stante nel piano (ouer pie dil monte alla elleuatione del detto. </s> <s id="s.000249">6. ponto.) di quel<lb></lb>lo faria ſtante nella ſommita del monte, perche stante nel piano le balle tirate da quel<lb></lb>ia ueniranno à percuottere nella detta muraglia circa à paſſa. </s> <s id="s.000250">200. auanti il termine <lb></lb>dil ſuo procedere per linea retta, Et quelle tirate dalla ſommita del monte ueneriano <lb></lb>à percuotere ſolamente à paſſa. </s> <s id="s.000251">50. auanti al termine del ſuo andar per linea retta, & <lb></lb>perche la differentia de detti effetti, cioè dalli. </s> <s id="s.000252">50. paſſa, alli. </s> <s id="s.000253">200. (che feriſcono <expan abbr="auã">auam</expan> <lb></lb>ti la ſua ſenſibel declinatione) è circa paſſa. </s> <s id="s.000254">150. e per tanto la detta colobrina non ſo<lb></lb>lamente alla elleuatione del ſeſto ponto della noſtra ſquadra ma anchora alla elleuatio<lb></lb>ne del quinto ponto, fara maggior el detto effetto: ma di queſto non uoglio star à far<lb></lb>ne dimoſtratione, perche ſo che ueneria in faſtidio à quella. </s> <s id="s.000255">Adunque, ſe in una coſt <lb></lb>grande altezza (quala in queſto ultimo caſo hauemo ſuppoſta) la detta colobrina fa<lb></lb>ria maggior effetto (stante quella nel piano alla elleuatione del. 6. & etiam del. 5. pon<lb></lb>to) di quello faria ſtante la medema nella ſommita del monte, molto piu euidentamen<lb></lb>te ſeguiria tal effetto nel primo caſo propoſto da<emph.end type="italics"></emph.end> V. E<emph type="italics"></emph>c. nel quale fu ſuppoſto il <expan abbr="mõte">monte</expan>, <lb></lb>et etiam la fortezza, eſſere egualmente alti ſolamente paſſa. </s> <s id="s.000256">60. & la diſtantia delle <lb></lb>radice delli dui monti, ouer le cime de quelli eſſer paſſa. </s> <s id="s.000257">100. onde la linea diametrale, <lb></lb>ouer diagonale, cioè la distantia de detta fortezza al luoco à coſto alla radice del mon <lb></lb>te, doue ſe ſuppone el ſtar delle artegliarie in piano, per la penultima del primo di Eu<lb></lb>clide ſara circa paſſa. </s> <s id="s.000258">116. (laſſando li rotti) è per tanto, le balle tirate dalla detta no<lb></lb>ſtra colobrina, ſtante quella nella ſommita del monte, ueriano à percuottere nella det<lb></lb>ta muraglia circa à paſſa. </s> <s id="s.000259">140. auanti al termine del ſuo procedere per linea retta, & <lb></lb>quelle tirate dalla medeſima ſtante quella nel piano alla elleuatione del. 6. ponto uene<lb></lb>riano à percottere nella detta mur aglia, circapaſſa. </s> <s id="s.000260">684. auanti al termine del ſuo an <lb></lb>dar per linea retta, & perche tal differentia è grandißima, cioè da. </s> <s id="s.000261">140. paſſa à. </s> <s id="s.000262">684. <lb></lb>paſſa, che feriſcono auanti al termine del ſuo andar per linea retta. </s> <s id="s.000263">Eglie coſa euiden<lb></lb>te, e chiara, in queſto caſo, che non ſolamente alla elleuatione del. 6. ponto, la detta colo <lb></lb>brina ſtante nel pie del monte, fara maggior effetto in detta fortezza di quello faria <lb></lb>ſtante nella ſommita. </s> <s id="s.000264">Ma anchora alla elleuatione di qual ſiuoglia ponto, che ſia elleua <lb></lb>ta, che è il propoſito.<emph.end type="italics"></emph.end> S.D. M<emph type="italics"></emph>e haueti riſolto aſſai bene queſto Queſito.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000265">QVESITO TERZO FATTO DAL MEDESIMO <lb></lb>I<emph type="italics"></emph>lluſtrißimo Signor Duca conſequentemente.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000266">DVCA. M<emph type="italics"></emph>a nel uoſtro arguire me haueti reduto in un'altra maggior <lb></lb>difficul<lb></lb>ta, ouer dubitatione <21>che ſe <expan abbr="bẽ">bem</expan> ui aricordati, haueti detto, che la balla sboccata <lb></lb>che ſia d'un pezzo maiua parte alcuna del ſuo motto <21> linea retta, ſaluo che <expan abbr="tirãdola">tirandola</expan> <lb></lb><expan abbr="rettamẽte">rettamente</expan> in ſuſo uerſo il cielo.<emph.end type="italics"></emph.end> N. O<emph type="italics"></emph>uer <expan abbr="rettamẽte">rettamente</expan> in zoſo uerſo il centro dil <expan abbr="mõdo">mondo</expan>?<emph.end type="italics"></emph.end><pb pagenum="11" xlink:href="042/01/021.jpg"></pb>S.D. Q<emph type="italics"></emph>ueſto ui <expan abbr="cõcedo">concedo</expan> ben, cioe che <expan abbr="tirãdo">tirando</expan> o <expan abbr="rettamẽte">rettamente</expan> in ſuſo uerſo il cielo, ouer retta <lb></lb>mente in zoſo uerſo il centro del mondo, che il tranſito, ouer moto di tal balla, ſia total <lb></lb>mente retto, & anchora ui concedo che in tai dui uerſi tal balla uada molto piu per li<lb></lb>nea retta che in qual ſiuoglia altra elleuatione, ouer in qual ſi uoglia altro uerſo. </s> <s id="s.000267">Ma <lb></lb>che in ogni altro uerſo delli detti dui in fuora la non uada parte alcuna del ſuo moto ret <lb></lb>tamente, cioe per retta lunea, la non mi pare coſa da credere, ne io la credo, perche ſe <lb></lb>ben ue aricordati di ſopra diceſti che per quelli dui tiri a Verona tirati, uoi trouaſti <lb></lb>che la detta colobrina da lire. </s> <s id="s.000268">20. tiraua de mira, cioe per retta linea in quanto al ſen<lb></lb>ſo, circa paſſa. </s> <s id="s.000269">200. eſſendo aliuellata, hor ſe tal tramito de paſſa. </s> <s id="s.000270">200. uoi trouati <lb></lb>poi con ragione non eſſer totalmente retto, cioe totalmente per linea retta, io uel cre<lb></lb>do, et uel concedo. </s> <s id="s.000271">Ma ſe tal pezzo non puol tirare per retta linea li detti paſſa. </s> <s id="s.000272">200. <lb></lb>non uoleti concedere che una tal machina ne tiri al manco la mita, cioe paſſa. </s> <s id="s.000273">100. & <lb></lb>ſe non. </s> <s id="s.000274">100. al men.<emph.end type="italics"></emph.end> 50. N. N<emph type="italics"></emph>on ſolamente la non tirara li detti paſſa. </s> <s id="s.000275">50. per linea <lb></lb>perfettamente retta, ma la non tirara un paſſo ſolo.<emph.end type="italics"></emph.end> S.D. E<emph type="italics"></emph>glie una pacia la uoſtra.<emph.end type="italics"></emph.end><lb></lb>N. L<emph type="italics"></emph>a ragione è quella che acquieta lo intelletto delli huomini, per che quella, ne di<lb></lb>ſcerne il uero dal falſo.<emph.end type="italics"></emph.end> S.D. E<emph type="italics"></emph>glie il uero.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>apoi adunque che la opinione di <lb></lb>uoſtra Eccellentia è che la balla tirata da tal colobrina aliuellata, debbia andare una <lb></lb>parte del ſuo tranſito, ouer moto uiolente per linea retta, & il reſtante poi per linea <lb></lb>curua ſtante che queſto fuſſe il uero, uoria ſapere da quella, qual è la cauſa propria <lb></lb>che tal balla uada coſi per linea retta, in quella parte, doue che quella ſuppone che uada <lb></lb>coſi rettamente, & quala ſia medeſimamente la cauſa che lei uada coſi per linea curua, <lb></lb>in quella parte, doue ſuppone uostra Eccellentia che uada coſi curuamente.<emph.end type="italics"></emph.end> S.D. L<emph type="italics"></emph>a <lb></lb>grandißima uelocita che ſe ritroua nel moto di tal balla, nel uſcir della bocca del pez<lb></lb>zo è la propria cauſa che tal balla per un poco di tempo, ouer ſpacio uada rettamen<lb></lb>te per aere, ma dapoi mancando alquanto in quella il uigore, & la uelocita comincia <lb></lb>pói ad alentarſe & ad abbaſſarſe ſucceßiuamente uerſo terra, & coſi ua continuando <lb></lb>per fin che percuote ſopra quella.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>ertamente uoſtra Eccellentia non potea ri<lb></lb>ſponder meglio di quello ha riſpoſto, cioe a dire che la gran uelocita è la propria cau<lb></lb>ſa, di redure il moto di tal balla (ſe poßibil è) alla rettitudine, & ſimilmente, il mancar <lb></lb>della uelocita in quella, e la propria cauſa di farla tendere & declinare nel ſuo moto <lb></lb>curuamente uerſo terra, & quanto piu ua mancando in quella la detta uelocita, tanto <lb></lb>piu fa maggiore la ſua declinatione, ouer curuita, & tutto queſto procede, perche ogni <lb></lb>corpo graue ſpinto uiolentemente per acre, quanto piu ua ueloce, tanto piu in tal mo<lb></lb>to ſe fa men graue, e pero ua piu rettamente per aere, perche lo aere piu facilmente ſo<lb></lb>stenta un corpo quanto piu eglie leue, tamen nel far di ſuoi effetti in tal moto aſſum<lb></lb>me molto maggior grauita della ſua propria, e pero quanto piu un corpo graue ua ue<lb></lb>loce (nel moto uiolente) tanto maggior effetto fa in ogni reſiſtente. </s> <s id="s.000276">Similmente quan<lb></lb>to piu ua mancando in quello la uelocita, tanto piu in tal moto gli ua creſcendo la gra<lb></lb>uita, la qual grauita, continuamente lo ua ſtimulando, & tirando uerſo terra. </s> <s id="s.000277">Ma nel <lb></lb>far de ſuoi effetti in tal moto aſſumme maggior leuita, ouer minor grauita, e pero fa <lb></lb>minor effetto.<emph.end type="italics"></emph.end> S.D. Q<emph type="italics"></emph>ueſto uoſtro diſcorſo non me diſpiace, e pero ſeguitate.<emph.end type="italics"></emph.end> N. <lb></lb>D<emph type="italics"></emph>ico adunque che da queſte coſe dette, & per ragion naturale approbate, naſce que-<pb xlink:href="042/01/022.jpg"></pb>ſta concluſione, che doue è maggior uelocita nella balla tir ata uio lentemente per aere, <lb></lb>in quella è manco grauita, & econuerſo, cioe che doue che in quella è menor uelocita iui<lb></lb>è maggior grauita in quella.<emph.end type="italics"></emph.end> S. D. E<emph type="italics"></emph>glie il uero.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nchor dico, che doue che in <lb></lb>quella è maggior grauita, iui è maggior ſtimulatione di quella in tirare la detta balla <lb></lb>uerſo il centro del mondo, cioe uerſo la terra.<emph.end type="italics"></emph.end> S. D. E<emph type="italics"></emph>glie coſa credibile.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>or <lb></lb>per conchiuder il nostro'propoſito, ſup poneremo che tutto il tranſito, ouer uiaggio che <lb></lb>debbia far, ouer che habbia fatto la balla tirata dalla ſopradetta colobrina ſia tutta la <lb></lb>linea. </s> <s id="s.000278">a. b. c. d. </s> <s id="s.000279">& ſe poßibil è che in quello ſia alcuna parte che ſia perſettamente retta, <lb></lb>poniamo che quella ſia tutta la parte. </s> <s id="s.000280">a. b. la qual ſia diuiſa in due parti eguali in ponto <lb></lb>e. & perche la balla tranſira piu ueloce per il ſpacio. </s> <s id="s.000281">a. e. (per la terza propoſitione <lb></lb>del primo, della noſtra nuoua ſcientia) di quello fara per il ſpacio. </s> <s id="s.000282">e. b. </s> <s id="s.000283">Adunque la det<lb></lb>ta balla andara piu rettamente, per le ragioni di ſopra adutte, per il ſpacio. </s> <s id="s.000284">a. e. di quel <lb></lb>lo fara per il ſpacio. </s> <s id="s.000285">e. b. onde la linea. </s> <s id="s.000286">a. e. ſaria piu retta della. </s> <s id="s.000287">e. b. la qual coſa è impoſ <lb></lb>ſibile, perche ſe tutta la. </s> <s id="s.000288">a. b. è ſuppoſta eſſer perfettamente retta, la mitade di quella <lb></lb>non puol eſſer ne piu ne men retta dell'altra mitade, & ſe pur l'una mitade ſara piu ret<lb></lb>ta dell'altra ſeguita neceſſariamente quell'altra mitade non eſſer retta, e pero ſegui<lb></lb>ta de neceßita, la parte. </s> <s id="s.000289">e. b. non eſſer perfettamente retta.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.022.1.jpg" xlink:href="042/01/022/1.jpg"></figure> <p type="main"> <s id="s.000290">E<emph type="italics"></emph>t ſe pur alcuno haueſſe anchora opinione che la parte. </s> <s id="s.000291">a. e. fuſſe pur <21> <expan abbr="fettamẽte">fettamente</expan> retta, <lb></lb>tal opinione ſe reprobara per falſa, per li medeſimi modi, e uie, cioe diuidendo la detta <lb></lb>parte. </s> <s id="s.000292">a. e. pur in due parti eguali in ponto. </s> <s id="s.000293">f. & per le medeſime ragioni di ſopra adut<lb></lb>te, ſera manifeſto la parte. </s> <s id="s.000294">a. f. eſſer piu retta della parte. </s> <s id="s.000295">f. e. adunque la detta parte. </s> <s id="s.000296">f. <lb></lb>e. de neceßita non ſara perfettamente retta, ſimilmente che diuideſſe anchora la. </s> <s id="s.000297">a. f. <lb></lb>in due parti eguali, con le medeſime ragioni ſe manifeſta la mita di quella uerſo. </s> <s id="s.000298">a. eſſer <lb></lb>piu retta di quella che uerſo. </s> <s id="s.000299">f. & coſi chi diuideſſe quella mita pur in altre due parti <lb></lb>eguali il medeſimo ſeguira, cioe la parte terminante in a. eſſer piu retta dell'altra, & <lb></lb>perche queſto procedere è infinito ſeguita di neceßita che non ſolamente tutta la. </s> <s id="s.000300">a. b. <lb></lb>non è perfettamente retta, ma che alcuna minima parte di quella non puo eſſer perfet<lb></lb>tamente retta, che è il propoſito. </s> <s id="s.000301">Si uede adunque qualmente la balla tirata da detta co <lb></lb>lobrina in tal uerſo non ua alcuna minima parte del ſuo moto, ouer tranſito per linea <lb></lb>perfettamente retta (uſciſca pur con qual grandißima uelocita ſi uoglia) perche la ue<lb></lb>locita (per granda che la ſia) mai è ſufficiente, in ſimili uerſi, a farla andar per linea <lb></lb>retta, uero è che quanto piu ua ueloce in ſimili uerſi tanto piu col moto ſuo ſe appro<lb></lb>pinqua al moto retto, cioe all'andar per retta linea, tamen mai puo arriuar a tal ſegno, <lb></lb>e pero piu conueniente è a dire in ſimil caſo, che quanto piu la detta balla ua ueloce, fa<emph.end type="italics"></emph.end><pb pagenum="12" xlink:href="042/01/023.jpg"></pb><emph type="italics"></emph>il moto ſuo men curuo.<emph.end type="italics"></emph.end> S. D. D<emph type="italics"></emph>oue procede adunque che molte uolte ſe uiſto per<lb></lb>cuotere uno preciſamente nel luoco tolto de mira, la qual coſa non potria occorrere ſe <lb></lb>tal balla non fuſſe andata rettamente.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor queſto non ne fa certi che la balla <lb></lb>uada rettamente, perche anchora molte uolte ſe uiſto percuotere di ſopra dal ſegno <lb></lb>tolto de mira, la qual coſa, eſſendo le mire eguale, è impoßibile, cioe che la balla ſeghi <lb></lb>la linea uiſuale equidiſtante alla canna di tal pezzo, ma tai effetti non procedeno, per<lb></lb>che la balla uada rettamente, ne perche quella aſcenda oltra la rettitudine, ma proce<lb></lb>dano totalmente dalle mire, ouer dal traſguardante. </s> <s id="s.000302">Eglie ben uero, che chi poteſſe ue<lb></lb>der la balla, nel moto ſuo ſenza dubbio giudicarebbe tal balla per un commun ſpacio <lb></lb>eſſer andata rettißima, perche il noſtro ſenſo non è atto, ne ſufficiente a diſcerner tale <lb></lb>obliquita, ſi come occorre, guardando l'acqua del mare quando è quieto, la quale per <lb></lb>una gran diſtantia ne pare perfettamente piana, & nondimeno, per meggio della ra<lb></lb>gione ſapemo eſſer all oppoſito, cioe ſpherica, e pero nelli giudici fatti ſecondo il ſenſo <lb></lb>del uedere, molte uolte ſe ingannamo.<emph.end type="italics"></emph.end> S. D. L<emph type="italics"></emph>e ragioni uoſtre ſon buone certo, pur <lb></lb>mi pare molto distranio a dire, che una balla tirata da una tal machina, & con tanta <lb></lb>uehementia, non uada alquanto per linea retta, ma pur conſider ando anchor che in tal <lb></lb>obliquo uerſo la grauita della balla è molto piu atta a far declinar, ouer a tirare la det <lb></lb>ta balla uerſo terra, che in ogni altra elleuatione, mi fa credere che uoi diciate il uero. <lb></lb></s> <s id="s.000303">Ma tir ando quella alquanto elleuata dauanti, penſo & tengo per fermo che quella deb <lb></lb>ba andar per alquanto rettamente per aere, perche la grauita di tal balla tirandola in <lb></lb>ſimei uerſi elleuati è manco atta a far declinar la balla uerſo terra di quello che è tiran <lb></lb>dola a liuello.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oſtra Eccellentia dice ben il uero, che la grauita della balla non è <lb></lb>tanto atta a ouiar il moto di quella, nelli tiri elleuati, quanto che nelli tiri equidiſtanti <lb></lb>all'orizonte, cioe aliuellati, ouer de ponto in bianco (come dicono li bombarderi) per <lb></lb>due cauſe, l'una perche in talſito (come nel principio fu approuato) ui è maggior graui <lb></lb>ta, l'altra perche la detta grauita tira la balla perpendicolarmente ſopra il moto, ouer <lb></lb>tranſito di quella uerſo terra, il qual modo da tirare è piu uigoroſo, e gagliardo, che <lb></lb>in ogni altra elleuatione, perche elleuandola gradatamente, etiam gradatamente la det <lb></lb>ta grauita, ſi ua accostando uerſo il ſuo tranſito, cioe che non ui cade coſi perpendico<lb></lb>lare ſopra il detto moto, ouer tranſito, anci ſempre ſi ua piu restringendo uerſo quello: <lb></lb>ilche la fa men uigoroſa, ouer men gagliarda a tirar detta balla fuora del uiaggio, ouer <lb></lb>moto ſuo, & oltra di queſto (come in principio fu dimoſtrato) quanto piu ſi ua elleuan <lb></lb>do tanto piu lí tiri ſuoiſono ben men curui, tamen mai ponno eſſer per alcuna ſua par<lb></lb>te perfettamente retti, eccetto nelli ſopradetti duoi uerſi, cioe rettamente in ſuſo uerſo <lb></lb>il cielo, ouer rettamente in gioſo uerſo il centro del mondo, <21> che in ogni uerſo ui é alc<gap></gap><lb></lb>na parte de grauita quala ſempre tira la detta balla fuora del ſuo uiaggio, ouer fuora <lb></lb>del ſuo tranſito, ouer moto, eccetto che nelli predetti dui uerſi, cioe rettamente uerſo il <lb></lb>cielo, ouer <expan abbr="rettamẽte">rettamente</expan> in giuſo uerſo il <expan abbr="cẽtro">centro</expan> del <expan abbr="mõdo">mondo</expan>, nelli quali dui uerſi la detta graui <lb></lb>ta (ſe pur <gap></gap> è grauita) uien a tirare la detta balla <expan abbr="rettamẽte">rettamente</expan> <expan abbr="ſecõdo">ſecondo</expan> l'or dine del ſuo uiag <lb></lb>gio, ouer moto, et <expan abbr="nõ">non</expan> fuora di quello, come <21> la ſottoſcritta figura <expan abbr="facilmẽte">facilmente</expan> ſenza altra <lb></lb><expan abbr="lõga">longa</expan> dimostratione ſi puo <expan abbr="cõprẽdere">comprendere</expan>, et coſi nelli tiri abbaſſati, come nelli elleuati, <expan abbr="ſup-penẽdo">ſup<lb></lb>penendo</expan>. </s> <s id="s.000304">a. la bocca del pezzo, doue ſia uſcita la balla. </s> <s id="s.000305">b. et la grauita di tal balla. </s> <s id="s.000306">b. la ſup <pb xlink:href="042/01/024.jpg"></pb>poneremo in forma del <21> <expan abbr="pẽdicolo">pendicolo</expan>. </s> <s id="s.000307">c. il <expan abbr="q̃l">qual</expan> <expan abbr="<21>pẽdicolo"><21>pendicolo</expan>, ouer gra<lb></lb>uita. </s> <s id="s.000308">c. in ogni uerſo ſempre <expan abbr="uatirãdo">uatirando</expan> la detta balla uerſo il <expan abbr="cẽ">cem</expan> <lb></lb>tro del <expan abbr="mõdo">mondo</expan>, cioe <21> <expan abbr="pẽdicolarmẽte">pendicolarmente</expan> uerſo terra, onde <expan abbr="argumẽ">argumen</expan> <lb></lb><expan abbr="tãdo">tando</expan>, come nel tiro aliuellato ſu fatto, ſara manifeſto <expan abbr="qualmẽ">qualmen</expan> <lb></lb>te in nullo altro uerſo che nelli dui ſopra detti, la balla tirata <lb></lb>da detta colobrina, ouer d'altro pezzo, non puo andare alcu <lb></lb>na minima parte del ſuo moto per linea perfettamente retta, <lb></lb>che è il propoſito.<emph.end type="italics"></emph.end> S. D. V<emph type="italics"></emph>oi haueti ben difeſa la uoſtra ra<lb></lb>gione, & questo baſta per hoggi, come ſia ritornato da Peſa<lb></lb>ro uoro che ſi faccia la iſperientia di queſte uoſtre inuentioni.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.024.1.jpg" xlink:href="042/01/024/1.jpg"></figure> <p type="head"> <s id="s.000309">QVESITO QVARTO FATTO DAL SIGNOR <lb></lb>G<emph type="italics"></emph>abriel Tadino da Martinengo Cauallier de Rodi, <lb></lb>& Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000310">PRIORE. T<emph type="italics"></emph>irando un pezzo di artegliaria due uolte l'una drieto a l'altra, <lb></lb>a <lb></lb>una medeſima elleuatione, & uerſo uno medeſimo luoco, et cargato ſempre egual <lb></lb>mente, domando ſe queſti dui tiri ſar anno eguali.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio ſaranno in eguali, <lb></lb>perche tirara piu lontano alla ſeconda uolta che alla prima.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>erche ragione.<emph.end type="italics"></emph.end> N. <lb></lb>P<emph type="italics"></emph>er due ragioni, la prima è queſta, che al primo tiro la balla ritrouara l'aere quieto, et <lb></lb>nel ſecondo lo ritrouara non ſolamente tutto commoſſo dalla balla tirata dal primo ti<lb></lb>vo, ma anchora molto tendente, ouer ſcorrente uerſo al luoco doue ſe tira. </s> <s id="s.000311">Et perche <lb></lb>eglie piu facile a mouere etiam a penetrare una coſa gia commoſſa & penetrata, che <lb></lb>una che ſtia ripoſata & quieta. </s> <s id="s.000312">Seguita che la balla tirata alla ſeconda uolta (per ritro <lb></lb>uare men ostacolo nel ſuo moto della prima) andara molto piu lontano di quella tirata <lb></lb>alla prima uolta. </s> <s id="s.000313">La ſeconda ragione è queſta, che al primo tiro la poluere poſta nel <lb></lb>pezzo, ſpeſſe uolte ritroua la canna alquanto humida, maßime quando che quel tal pez <lb></lb>zo non fuſſe ſtato tirato gia alquanti giorni, per la qual coſa, la detta poluere non bru<lb></lb>ſara coſi preſto, come faria trouando tal luoco arido, & alquanto caldo d'una calidita <lb></lb>temperata: la qual calidita ſuga alquanto la poluere de ogni humidita che in lei fuſſe: il<lb></lb>che la fa piu preſta, e potente nell'abbruſiare, & per tanto non operara coſi uigoroſa<lb></lb>mente nel primo tiro, come fara nel ſecondo, ſi che anchora per questa ſeconda ra<lb></lb>gione alla ſeconda uolta douera tirar piu lontano che alla prima.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſte uoſtre <lb></lb>ragioni molto mi piaceno, & uoglio che baſti per queſta ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000314">QVESITO QVINTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo. </s> <s id="s.000315">Sig. Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000316">PRIORE. H<emph type="italics"></emph>ierſera uoi concludeſti, & con buone ragioni naturali <lb></lb>approua<lb></lb>sti, che tirando un pezzo due uolte l'una drieto l'altra a una medeſima elleua<lb></lb>tione, & uerſo uno medeſimo luoco, & etiam egualmente cargato, molto piu tirara la <lb></lb>ſeconda uolta, che la prima, hor ue adimando, che continuaſſe per longo tempo a tira-<emph.end type="italics"></emph.end><pb pagenum="13" xlink:href="042/01/025.jpg"></pb><emph type="italics"></emph>re ìl detto pezzo à tal elleuatione, & uerſo il medeſimo luoco, ſe contìnuamente anda <lb></lb>ria augmentando li ſuoi tiri.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on ſignore, chel non ſeguiria queſto.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o <lb></lb>perche uoi diceſti pur hierſera, che per trouare lo aere commoſſo, & alquanto ſcor<lb></lb>rente uerſo el luoco doue ſe tira, etiam perche la poluere posta nel pezzo, troua el <lb></lb>luoco piu arido, & ſutto, & alquanto caldo, che alla ſeconda uolta tiraria piu, che alla <lb></lb>prima, e per tanto quanto piu ſi ua <expan abbr="tirarãdo">tirarando</expan>, tanto piu la balla uien à ritrouare l'aere <lb></lb>piu commoſſo, e penetrato, etiam piu ſcorrente uerſo al luoco doue ſe tira (per cauſa <lb></lb>delli tiri anciani) & ſimelmente la poluere, che ſe ua recargando, ouer remettendo nel <lb></lb>pezzo, continuamente ua ritrouando il luoco (cioè la canna del pezzo) continuamen<lb></lb>te piu arida, & ſutta, & piu calda, la qual calidita (come uoi diceſti hierſera) ſuga la <lb></lb>poluere de ogni humidita, che in lei fuſſe, per il che tal poluere ſi fa piu preſta nel ab<lb></lb>bruſiare: la qual preſtezza la uien à far piu potente del ſolito.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie ben uero <lb></lb>tutto quello, che dice uostra Signoria, ma ui occorre un'altro accidente molto contra<lb></lb>rio, el quale è questo: che per el continuo tirare el pezzo continuamente piu ſe ua ſcal<lb></lb>dando, & quanto piu è caldo, tanto piu la canna di quello ſi fa attrattiua, cioè, ſi come <lb></lb>una uentoſa, quando èſcaldata per la ſtoppa abbruſiata dentro in quella, & perche la <lb></lb>balla non è ſpulſata, ouer ſpinta da altro, che dalla eſſalatione aerea, ouer uentoſa, cau<lb></lb>ſata dal ſalnitrio, onde facendoſi tal pezzo continuamente piu attrattiuo, come ho det <lb></lb>to, per el maggior caldo, quel medemo uiene à ſorbere, & à retenere, & continuamen <lb></lb>te piu di quella uentoſita, che doueria ſeruire al ſpingere la balla, e pero ſcemando (& <lb></lb>continuamente piu) la uirtu eſpulſiua nel detto pezzo, raſoneuolmente la balla conti<lb></lb>nuamente debbe uſcire men ueloce, ouer piu debile, & conſequentemente andar conti<lb></lb>nuamente men lontano.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſta uoſtra ragione mi conſona molto<emph.end type="italics"></emph.end>: <emph type="italics"></emph>ma chi ſa, che <lb></lb>quelli dui accidenti primi, che dano fauore, & aiuto al moto della balla, cioe la gran <lb></lb>combuſtione, ouer ſcorrentia del aere uerſo al luoco doue continuamente ſe tira, & lo <lb></lb>uigore, che ſe augumenta nella poluere, per cauſa del caldo, non ſiano ſofficienti à ſup<lb></lb>plire à quel difetto attratiuo cauſato dalla gran calidita del pezzo et forſi piu, la qual <lb></lb>coſa eſſendo coſi, ſeguiria, che el detto pezzo tiraſſe ſempre à uno medeſimo modo eſ<lb></lb>ſendo tanto quello, che ui aggiongeſſe li detti dui primi accidenti, quanto quello, che ui <lb></lb>robaſſe el terzo, oueramente che tiraſſe continuamente piu, eſſendo piu la augmenta<lb></lb>tione di ditti dui primi accidenti, della detrattione del terzo.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>ertamente el non <lb></lb>ſi puo negare, che quelli dui primi accidenti (cioe el rompimento dell'aere, & quel ui<lb></lb>gor che accreſſe nella poluere) non diano grande aiuto e ſußidio al moto della balla, el <lb></lb>qual aiuto, e ſußidio, eglie da credere, che per alquanto tempo ſuppliſca (& ſorſi da<lb></lb>uantaggio) per quella uirtu expulſiua, che continuamente ua robando, ouer ſorbendo <lb></lb>el pezzo, ſecondo che fi ua ſcaldando, talmente che forſi el terzo, & quarto tiro ſaran <lb></lb>no quaſi pari in bilancia, con el ſecondo, ouer poco differenti, nondimeno à longo anda<lb></lb>re, eglie da tenere, che li detti dui accidenti non potranno ſupplire al difetto del terzo <lb></lb>accidente, per la augmentatione del grandißimo caldo, che continuamente ſi ua cauſan <lb></lb>do in quel tal pezzo, per il che el detto pezzo, come di ſopra è detto, ſi fa continua<lb></lb>mente piu attrattiuo, e pero continuamente ua robando, ouero ſorbendo piu di quella <lb></lb>eſſalatione, che doueria ſpingere la balla, & per tanto queſto terzo accidente à longo<emph.end type="italics"></emph.end><pb xlink:href="042/01/026.jpg"></pb><emph type="italics"></emph>andare uien à reſtar ſuperiore alli detti dui primi, et per queſto à longo andar talpez <lb></lb>zo uien à tirare molto manco del ſolito.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o chi reffreddaſſe tal pezzo, con ac<lb></lb>qua (cioè gettandoui dell'acqua nella canna) non credeti chel tiraraue piu uerſo il me<lb></lb>deſimo luoco.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubio che tiraraue piu, quando che tal pezzo reſtaſſe per<lb></lb>fettamente fredo, & aſciuto, ma raffredandolo coſi con acqua, el metallo che è caldo, <lb></lb>ſorbe di quella acqua, & ſorbendola la riſolue in uapore aereo, el qual uapore non po<lb></lb>tendo stare nella canna è sforzato à uſcir di quella pian piano, el qual uapore, quando <lb></lb>chel non portaſſe con ſeco alcuna humidita, & chel pezzo restaſſe di dentro ben aſciu <lb></lb>to, tal uapore doueria piu preſto augumentar il tiro in tal pezzo, che ſcemarlo: per<lb></lb>che de attrattiuo, che era tal pezzo, per lo continuo uſcire di tal uapore ſaria fatto <lb></lb>eſpulſiuo, ma perche tal uapore è tutto humidità, onde recargando tal pezzo, quan<lb></lb>tunque para aſciuto nel metterui la poluere, el non puo eſſere che tal uapore humido, <lb></lb>non humidiſca alquanto la poluere, per il che non fara <expan abbr="tãto">tanto</expan> uigoroſo il ſuo effetto, <expan abbr="quã">quam</expan> <lb></lb>to faria ſe tal pezzo ſi laſſaße raffredare per ſe ſteſſo ſenza metterui acqua.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>oi <lb></lb>me haueti molto ſatisfatto queſta ſera, ma <21> eſſer hora tarda, uoglio, che questo baſti.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000317">QVESITO SESTO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000318">PRIORE. Q<emph type="italics"></emph>ual è la cauſa, che dandoſi piu quantita di poluere del <lb></lb>ſolito à un <lb></lb>pezzo di artegliaria quella percuottera piu alto del ſegno, doue che prima con <lb></lb>men poluere ui tiraua rettamente de mira.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto procede, che il moto, ouero <lb></lb>tranſito di tal balla tirata con piu poluere, è manco curuo, che quel di quella tirata con <lb></lb>men poluere, & la differentia di queſte due curuita piu ſe dimoſtra, ouer che piu ſi fa <lb></lb>apparente nel fin del moto, che in ogni altro luoco, pero che quel tranſito, ouer moto, <lb></lb>che è men curuo, ſempre ſe iſtende, & procede di ſopra à quello, che è piu curuo, & <lb></lb>quanto piu è longo el tiro, tanto piu la percußione del <expan abbr="mẽ">men</expan> curuo ſara piu alta di quella <lb></lb>del piu curuo, perche il tranſito, ouer moto men curuo piu ſi accosta al tranſito, ouero <lb></lb>moto retto, di quello. </s> <s id="s.000319">che fa lo piu curuo, & perche el tramito, ouer tranſito retto, <lb></lb>cioe quello, che ſe iſtende rettamente ſecondo la rettitudine della canna del pezzo in <lb></lb>qual ſi uoglia uerſo, èſempre ſuperiore à tutti li moti, ouer tranſiti obliqui di qual ſi <lb></lb>uoglia balla, che uiolentemente uſciſca di quel pezzo in qual ſi uoglia uerſo.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>pero <lb></lb>quel moto, ouer tranſito, che piu ſi accoſta al detto retto, ſempre uien à eſſer ſuperiore <lb></lb>à quello, che men ui ſi accoſta, & perche la balla tirata con piu poluere uſciſſe, & ua <lb></lb>piu ueloce di quella tirata con men poluere, e pero fa el moto ſuo piu retto, ouer men <lb></lb>curuo di l'altra, e per tanto la ſua percußione è ſuperiore à quella di l'altra.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o <lb></lb><expan abbr="nõ">non</expan> bene <expan abbr="intẽdo">intendo</expan> queſto che uoi diceti, che el tiro fatto con piu poluere ua men curuo di <lb></lb>quello fatto con men poluere. </s> <s id="s.000320">Non uoleti uoi, che una balla tirata con un pezzo car<lb></lb>gato con la ſua debita, & conſueta miſura di poluere uada rettamente al luoco, ouer ſe <lb></lb>gno tolto de mira, in una mediocre diſtantia.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci queſto il nego, cioe, che tal <lb></lb>balla uada per linea retta alſegno tolto de mira, & queſto medemo paſſo fu da me di<lb></lb>ſputato un'altra uolta auanti della buona memoria della Eccellentia del Duca di Vrbi-<emph.end type="italics"></emph.end><pb pagenum="14" xlink:href="042/01/027.jpg"></pb><emph type="italics"></emph>no padre di questo, cioe, che una balla tirata con qual ſi uoglia pezzo di artegliaria, <lb></lb>& per qual ſi uoglia uerſo mai ua, ne puo andare alcuna minima parte del ſuo moto, <lb></lb>ouer tranſito per linea perfettamente retta, ſaluo che non la tiraſſe rettamente uerſo <lb></lb>el cielo, ouer rettamente uerſo el centro del mondo.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>omprendo, che uoi diti la <lb></lb>uerita, perche ſe quella andaſſe alla prima rettamente al ſegno, per darui poi piu quan <lb></lb>tita di poluere, raſoneuolmente non doueria dar de ſopra del ſegno, anzi doueria pur <lb></lb>dar nel medeſimo loco, doue che prima con men poluere percuoteua, & per queſto ui <lb></lb>ho fatto lo preſente Queſito, perche mi pareua di ſtranio, che per darui piu poluere <lb></lb>la balla doueſſe aſcendere di ſopra alla rettitudine, nondimeno doman di ſera uoro che <lb></lb>diſputamo meglio queſta materia, perche la me piace.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000321">QVESITO SETTIMO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000322">PRIORE. H<emph type="italics"></emph>ierſera uoi concludesti, & con buone ragioni naturale uoi dimo <lb></lb>ſtraſti qualmente una balla tirata da una artegliaria, mai ua per linea retta in <lb></lb>parte alcuna, ſaluo che rettamente uerſo il cielo, ouer rettamente uerſo il centro del <lb></lb>mondo. </s> <s id="s.000323">Hor ue dimando donde procede, che tirandoſe ad alcun ſegno de mira, alcuna <lb></lb>fiata ſi da preciſamente in brocca, cioe nel ſegno tolto de mira, alcun'altra fiata ſi da di <lb></lb>ſotto, & alcun'altra di ſopra dal ſegno.<emph.end type="italics"></emph.end> N. T<emph type="italics"></emph>utto queſto procede dalle mire, perche <lb></lb>ſe la mira dauanti é preciſamente tanto alta, quanto quella de drio, cioe, che l'una, & <lb></lb>l'altra ſiano egualmente lontane dal fondo del uacuo della canna di tal pezzo, & che <lb></lb>colui, che uol tirare ad alcun ſegno, incontri col ſuo occhio preciſamente el detto ſegno <lb></lb>con le due mire, cioe con le iſtremita di quelle ſempre in tal caſo dara alquanto di ſotto <lb></lb>dal ſegno, & quanto piu il detto ſegno ſara lontano, tanto piu baſſa ſara la botta, & é <lb></lb>conuerſo, cioé, che quanto piu ſara propinquo il detto ſegno, tanto men baſſa ſara la <lb></lb>detta botta. </s> <s id="s.000324">Queſto medeſimo, & con maggior differentia, ſeguiria quando che la mi <lb></lb>ra de drio fuſſe piu baſſa, ouero piu corta di quella dauanti, dico piu corta in reſpetto <lb></lb>al fondo del uacuo della canna del pezzo.<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>on ue intendo.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>ccio meglio <lb></lb>me intendiati uoglio ponere figuralmente la ſottoſcritta artegliaria con le due mire <lb></lb>e. &. </s> <s id="s.000325">d. </s> <s id="s.000326">le qual due mire poniamo in queſto caſo, che ſiano equale, cioe, che le due istre<lb></lb>mita di quelle (cioe. </s> <s id="s.000327">c. &. </s> <s id="s.000328">d.) ſiano egualmente diſtante dal fondo del uacuo della can<lb></lb>na, & con queſte due mire ſia incontrato el ponto. </s> <s id="s.000329">e. cioe ſupponemo, chel ponto. </s> <s id="s.000330">e. ſia <lb></lb>el ſegno, che hauemo tolto de mira per tirarui, hor dico in queſto caſo, che neceſſa<lb></lb>riamente ſempre ſe dara alquanto piu baſſo del ſegno, & ſia tal ſegno lontano, ouero <lb></lb>propinquo quanto ſi uoglia. </s> <s id="s.000331">Perche la noſtra linea uiſuale (qual ſia la. </s> <s id="s.000332">c. d. </s> <s id="s.000333">e.) <lb></lb>ſempre procedera, ouero ſe eſtendera egualmente diſtante al uacuo della canna, o<lb></lb>uero alla linea, che ſia protratta rettamente in longo, ſecondo l'ordine del uacuo <lb></lb>della canna, ouero centro di quella, la quale in queſto caſo pongo ſia la linea. </s> <s id="s.000334">f. g. <lb></lb>et perche il ponto. </s> <s id="s.000335">g. é neceſſario eſſer piu baſſo del ponto. </s> <s id="s.000336">e. per tanto quanto che é dal <lb></lb>ponto. </s> <s id="s.000337">d al centro della canna, ſi uede adunque, che ſe la balla andaſſe perfettamente <lb></lb>per linea retta, in queſto caſo lei percuotteria de ſotto dal ſegno, cioe in ponto. </s> <s id="s.000338">g. ma<emph.end type="italics"></emph.end><pb xlink:href="042/01/028.jpg"></pb><emph type="italics"></emph>per eſſer ſtato dimoſtrato, che in ſimei tiri la balla mai ua per linea perfettamenteret <lb></lb>ta, ma ſempre per obliqua, ouer curua ſeguita di neceßita, che tal balla dia, ouer dara <lb></lb>di ſotto dal ponto. </s> <s id="s.000339">g. come ſaria à dire in ponto. </s> <s id="s.000340">i. & perche ogni commune intelletto, <lb></lb>ſenza altra dimostratione, confirmara in queſto caſo, che quanto piu ſara lontano el <lb></lb>detto ſegno. </s> <s id="s.000341">e. tanto piu baſſo ſara el ponto. </s> <s id="s.000342">i. perche el tranſito, ouer moto curuo con <lb></lb>tinuamente ſi ua piu curuando uerſo terra, che è il primo propoſito.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.028.1.jpg" xlink:href="042/01/028/1.jpg"></figure> <p type="main"> <s id="s.000343">E<emph type="italics"></emph>l ſecondo propoſito (cioè, che ſe la mira dauanti ſara piu alta, che quella de drio, <lb></lb>che ſimelmente la botta ſempre dara piu baſſa del ſegno, & in ogni uerſo, & molto <lb></lb>piu baſſo di quello faria con le mire eguale, & queſto ſenza altra dimoſtratione è ma <lb></lb>nifeſto, come per la figura ſottoſcritta ſenſibelmente ſi uede, e pero ſopra di cio non di <lb></lb>ro altro, ſaluo che queſti dui eſſempi, quantunque ſiano dati nel tirar aliuello ſi debbe <lb></lb>intendere il medeſimo ſuccedere in ogni altro uerſo.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.028.2.jpg" xlink:href="042/01/028/2.jpg"></figure> <p type="main"> <s id="s.000344">PRIORE. Q<emph type="italics"></emph>ueſti dui uoſtri eſſempi, gli ho inteſo benißimo, ſi che uegnamo <lb></lb>pur all'altra parte, cioè doue naſce, che molte uolte ſi da in brocca, & alcuna fiata di <lb></lb>ſotto dal ſegno.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>etta la conditione, & qualita delle botte, che occorre, quando <lb></lb>che le due mire ſono eguale, & etiam quando, che la mira dauanti è piu alta di quella <lb></lb>de drio (cioè, che in l'una, & l'altra ſempre de neceßita ſi da di ſoto dal ſegno.) Hor <lb></lb>reſta ſolamente à narrare le conditione, & qualita delle botte, che puo occorrere <expan abbr="quã">quam</expan> <lb></lb>do che la mira dauanti ſia alquanto piu baſſa, cioè alquanto piu corta di quella de drio, <lb></lb>& questo piu baſſa, ouer piu corta ſi debbe intendere ſempre (come di ſopra fu detto) <lb></lb>in riſpetto al fundo del uacuo della canna del detto pezzo. </s> <s id="s.000345">Dico adunque, che quando <lb></lb>la mira dauanti ſara alquanto piu baſſa di quella de drio in tal caſo puo occorrere, che <lb></lb>alcuna fiata ſe dia in brocca, & alcun'altra, che ſe dia di ſopra, & alcun'altra di ſotto <lb></lb>dal ſegno.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>erche ragione.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a ragione è queſta, che ogni uolta, che la mi<lb></lb>ra dauanti ſia alquanto piu baſſa di quella de drio (per la quinta petitione di Eucli<lb></lb>de) la nostra linea uiſuale è neceſſario concorrere con la linea retta, che procede<emph.end type="italics"></emph.end><pb pagenum="15" xlink:href="042/01/029.jpg"></pb><emph type="italics"></emph>qettamente ſecondo lo aßis del uacuo della canna, & perche il tranſito, ouer viaggio, <lb></lb>qual debbe far la balla (quantunque il non ſia retto, ne che uada realmente per la detta <lb></lb>linea che procede rettamente ſecondo l'ordine del aßis del uacuo della canna del pez<lb></lb>zo) tamen per molto ſpacio ua quafi contiguo con quella, ouer poco lontano da quella.<emph.end type="italics"></emph.end><lb></lb>E <emph type="italics"></emph>per tanto tal ſegamento puo eſſer in tal luoco che la medeſima linea uiſuale ſeghera <lb></lb>anchora il tranſito, ouer uiaggio qual debbe far la balla. (Et queſto accadera quando <lb></lb>che la mira dauanti ſara piu baſſa del douere riſpetto a quella de drio) & puo anchora <lb></lb>eſſer in tal luoco, che non ſolamente la detta linea uiſuale non ſeghera il detto tranſito, <lb></lb>ouer uiaggio, ma anchora non lo toccata, & questo accadera quando che la mira da<lb></lb>uanti non ſara a ſufficientia piu baſſa di quella de drio. </s> <s id="s.000346">Anchora puo eſſer in tal luoco <lb></lb>che tal linea uiſuale ſara contingente con il detto tranſito, ouer uiaggio qual debbe far <lb></lb>la balla, & queſto occorrera quando che la mira dauanti hauera la ſua debita & conue <lb></lb>niente baſſezza riſpetto alla mira de drio, ſe per ſorte adunque la noſtra linea uiſua<lb></lb>le ſeghera il detto tranſito, ouer uiaggio qual debbe far la balla, & che per ſorte an<lb></lb>chora il ſegno che ſe tuol de mira, ſia preciſamente nel ponto di tal interſecatione ſen<lb></lb>za dubbio la balla dara preciſamente in brocca, ma ſe per caſo il detto ſegno ſara di den <lb></lb>tro da tal interſeccatione, cioe piu in uerſo il pezzo, tal balla dara ſempre alquanto di <lb></lb>ſotto dal ſegno, cioe dalla brocca di quello, & quanto piu il detto ſegno ſara remoto, <lb></lb>ouer lontano datal interſeccatione, cioe piu uerſo il pezzo, tanto piu baſſo dal ſegno, <lb></lb>ouer dalla brocca di quello, dara la detta balla. </s> <s id="s.000347">Ma ſe per caſo il detto ſegno ſara alquan <lb></lb>to fuora della detta interſeccatione, cioe alquanto piu alta de tal interſeccatione, tal <lb></lb>balla dara di ſopra dal detto ſegno, & quanto piu ſara da quello lontano (per un certo <lb></lb>ſpacio) tanto piu dara di ſopra da quello.<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>on ue intendo troppo bene.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>o<lb></lb>niamo per figura la ſottoſcritta artegliaria, & le due mire di quella ſiano. </s> <s id="s.000348">c. &. </s> <s id="s.000349">d. </s> <s id="s.000350">& <lb></lb>ſta la mira. </s> <s id="s.000351">d. </s> <s id="s.000352">piu baſſa della mira. </s> <s id="s.000353">c. & ſia la linea che procede rettamente ſecondo l'or <lb></lb>dine del aßis del uacuo della canna, la. </s> <s id="s.000354">f. g. & il tranſito, ouer uiaggio qual debbe far la <lb></lb>balla la linea. </s> <s id="s.000355">h. i. & la noſtra linea uiſuale quella che procede rettamente ſecondo l'or<lb></lb>dine delle due iſtreme ponte delle due mire. </s> <s id="s.000356">c. &. </s> <s id="s.000357">d. </s> <s id="s.000358">la quale neceſſariamente (come è det <lb></lb>to) ſeghera la linea. </s> <s id="s.000359">f. g. & per tanto poniamo anchor che quella ſeghi la detta linea. </s> <s id="s.000360">h. <lb></lb>i. in ponto.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>(come di ſotto appar in figura) hor dico, che ſe il ſegno che ſe tuol de mi<lb></lb>ra ſara preciſamente in ponto.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>tal balladara preciſamente in brocca, & ſe per caſo il <lb></lb>detto ſegno fuſſe di dentro di tal interſeccatione, cioe in uerſo del pezzo, come ſaria a <lb></lb>dire in ponto. </s> <s id="s.000361">m. tal balla dara ſempre alquanto di ſotto dalla brocca del detto ſegno, <lb></lb>perche per tutto tal luoco, ouer ſpacio il tranſito della balla paſſa ſempre di ſotto dalla <lb></lb>noſtra linea uiſuale, & quanto piu remoto ſara il detto ſegno dal ponto.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>cioe quanto <lb></lb>piu ſara uerſo il pezzo, tanto piu baſſa ſara la detta noſtra botta, niente dimeno tal <lb></lb>baſſezza in un ſimil caſo mai puo eſſer eguale alla differentia, che è dalla iſtremita della <lb></lb>mira dinanti, cioe dal ponto. </s> <s id="s.000362">d. </s> <s id="s.000363">al centro del foro del pezzo, ouer uacuo della canna, la <lb></lb>qual differentia è circa alla mita della groſſezza del pezzo nella parte de drio, cioe <lb></lb>nella culatta, e per tanto, eſſendo il ſegno doue ſe tira de mira di qua da tal interſecca<lb></lb>tione, il bombardiero è ſoggietto a poco errore (per conto delle mire.) Ma quando tal <lb></lb>ſegno fuſſe alquanto fuora da tal interſeccatione, come ſaria a dire in ponto. </s> <s id="s.000364">l. tal balla <pb xlink:href="042/01/030.jpg"></pb>dara di ſopra dal ſegno, per che per un longo tramito, ouer ſpacio, il tranſito della balla <lb></lb>paſſa di ſopra dalla linea uiſuale, e pero quanto piu lontano ſara il detto ſegno dal pon<lb></lb>to.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>per un longo ſpacio, tanto piu alta ſara la botta, uero è, che à longo andare la bal<lb></lb>la con il tranſito ſuo curuo, ouer naturale ritornera à ſegare un'altra uolta la noſtra li <lb></lb>nea uiſuale, perche la noſtra linea uiſuale. </s> <s id="s.000365">c. d.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>l. procede in infinito rettamente, & la <lb></lb>balla per il tranſito. </s> <s id="s.000366">h.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>i. non procede in infinito, anci con tempo ua mancando, & ſi <lb></lb>ua curuando uerſo il centro del mondo, & finalmente ſe redrizza rettamente di moto <lb></lb>naturale (non trouando reſistentia) uerſo il detto centro del mondo, e pero eglie neceſ<lb></lb>ſario che a longo andare che la ritorni con il tranſito ſuo à interſeccarſe un'altra uolta <lb></lb>con la nostra linea uiſuale, e pero ſe il detto ſegno fuſſe tanto, & tanto lontano, cioe tan <lb></lb>to oltra la prima interſeccatione fatta in ponto.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>& che per ſorte fuſſe anchora pre<lb></lb>ciſamente in quella altra ſeconda interſeccatione, ſenza dubbio in tal luoco coſi lontano <lb></lb>ſe daria preciſamente in brocca, perche ogni uolta che la noſtra linea uiſuale ſeghi il <lb></lb>tranſito della balla, eglie neceſſario che la ſeghi quello in dui lochi, l'uno de quali, cioe il <lb></lb>primo, non puo eſſer molto lontano, ma l'altro, cioe il ſecondo è neceſſario che ſia mol<lb></lb>to, e molto lontano, cioe quaſi in fine del ſuo moto uiolente, & tal hora potria eſſer nel <lb></lb>ſuo moto, ouer tranſito naturale, e pero in tal caſo eſſendo il ſegno che ſe tuol de mira, <lb></lb>in qual ſi uoglia de queſti dui lochi, ouer iterſeccationi, <expan abbr="neceſſariamẽte">neceſſariamente</expan> ſe daria i brocca.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.030.1.jpg" xlink:href="042/01/030/1.jpg"></figure> <p type="main"> <s id="s.000367">PRIORE. Q<emph type="italics"></emph>ueſta Speculatione molto mi piace, & è molto bella, ma non ho trop<lb></lb>po ben inteſa questa ultima particularita che mi haueti detta, cioe che in dui ſegni poſti <lb></lb>in dui diuerſi luoghi, ui ſi poſſa tirar, & dar de mira, e pero datime un'eſſempio ſe poſ <lb></lb>ſi<gap></gap>il è in figura, perche à mi me pare che tal coſa non ſia poßibile.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia eſſem pi <lb></lb>gratia la ſottoſcritta artegliaria con le due mire. </s> <s id="s.000368">c. &. </s> <s id="s.000369">d. </s> <s id="s.000370">ſecondo il propoſito, cioe <lb></lb>che la mira. </s> <s id="s.000371">d. </s> <s id="s.000372">ſia talmente piu baſſa della mira. </s> <s id="s.000373">c. che la noſtra linea uiſuale ſeghi il <expan abbr="trã">tram</expan> <lb></lb>ſito, ouer uiaggio qual debbe far la balla, & ſia tutto il tranſito, ouer uiaggio che hab<lb></lb>bia fatto, ouer che faria la balla (non trouando reſistentia) di moto uiolente tutta la li<lb></lb>nea. </s> <s id="s.000374">h. i.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>l. m. & la linea. </s> <s id="s.000375">m. n. ſia parte del tranſito, ouer uiaggio che quella habbia <lb></lb>fatto, ouer faria de moto naturale, hor dico, che ſe la noſtra linea uiſuale (procedente <lb></lb>per le iſtremita delle due mire. </s> <s id="s.000376">c. &. </s> <s id="s.000377">d.) Seghara il detto tranſito, ouer uiaggio. </s> <s id="s.000378">h. i.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>l. <lb></lb>m. n. et quella procedendo rettamente in in infinito (per le ragion di ſopra aditte) eglie <lb></lb>neceſſario che la interſeghi tal tranſito, ouer uiaggio in dui lochi, cioe uno nella parte <lb></lb>retta (ouer men curua.) h. i.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>& l'altro nella parte curua.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>l. m. ouer nel tranſito na <lb></lb>turale. </s> <s id="s.000379">m. n. hor ſupponamo che nella parte retta. </s> <s id="s.000380">h. i.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>la la ſeghi in ponto. </s> <s id="s.000381">i. & nella <lb></lb>curua in ponto, l. (come nella figura appare) conchiudo adunque che ſe il ſegno tolto de<emph.end type="italics"></emph.end><pb pagenum="16" xlink:href="042/01/031.jpg"></pb><emph type="italics"></emph>mira, ſara in qual ſi uoglia delle dette due interſeccationi, cioe in ponto. </s> <s id="s.000382">i. ouer in pon <lb></lb>to. </s> <s id="s.000383">l. </s> <s id="s.000384">neceſſariamente la balla dara preciſamente in brocca, & quando che il detto ſegno <lb></lb>ſara piu in fuora della prima interſeccatione, cioe dal ponto. </s> <s id="s.000385">i. per fin al ponto.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>tan<lb></lb>to piu alta ſara la detta botta, ma quanto piu oltra al detto ponto.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>per fin al ponto. </s> <s id="s.000386">l. <lb></lb></s> <s id="s.000387">ſara il detto ſegno tanto men alta ſara la detta botta, ma quando che il detto ſegno fuſſe <lb></lb>per alquanto oltra al ponto. </s> <s id="s.000388">l. </s> <s id="s.000389">tal botta neceſſariamente dara di ſotto dal ſegno, & <expan abbr="quã">quam</expan> <lb></lb>do tal ſegno ſara molto oltra al ponto. </s> <s id="s.000390">l. </s> <s id="s.000391">la detta balla non potra arriuare al ſegno, co<lb></lb>me (per ragion naturale) credo, che quella poſſa facilmente comprendere.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>om<lb></lb>prendo che eglie troppo il uero. </s> <s id="s.000392">Et <expan abbr="certamẽte">certamente</expan> questa è ſtata una bella Speculatione, e pe <lb></lb>ro non uoglio che piu ue affaticati per queſta ſera, diman de ſera direti poi il restante.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.031.1.jpg" xlink:href="042/01/031/1.jpg"></figure> <p type="head"> <s id="s.000393">QVESITO OTTAVO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> S. P<emph type="italics"></emph>rior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000394">PRIORE. H<emph type="italics"></emph>or ſeguitamo la materia de hierſera.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>ierſera (ſe ben mi ari <lb></lb>cordo) fu detto tutti gli effetti, ouer botte che puo occorrere, quando che per la <lb></lb>molta cortezza, ouer baſſezza della mira denanti riſpetto à quella de drio, la nostra <lb></lb>linea uiſuale ſeghera il tranſito, ouer uiaggio qual debbe far la balla. </s> <s id="s.000395">Et queſta ſera uo<lb></lb>glio dichiarire tutti gli effetti, ouer botte, che puo occorrere, quando che la detta mi<lb></lb>ra de nanti non è talmente piu corta, ouer baſſa della mira de drio, quanto ui ſi conue<lb></lb>gneria, per la qual cauſa, la noſtra linea uiſuale non procede tanto al baſſo che ſi poſſa <lb></lb>congiongere con il tranſito, ouer uiaggio qual debbe far la balla, e pero in ſimil caſo, <lb></lb>ſempre la balla dara di ſotto dal ſegno, perche per tutto tal luoco, ouer ſpacio, il tran<lb></lb>ſito della balla paſſa di ſotto della noſtra linea uiſuale, uero è, che ui è un certo luoco, nel <lb></lb>quale la noſtra linea uiſuale piu ſe appropinqua al detto tranſito della balla che in ogni <lb></lb>altro luoco, e per tanto, ſe per caſo il ſegno doue ſe tira de mira ſara nel detto luoco, a <lb></lb>ben che la balla dara di ſotto da quello pur ui dara piu propinquo che in ogni altro luo <lb></lb>co eſſempi gratia ſia per figura lo ſottoſcritto pezzo di artegliaria: le due mire delqua <lb></lb>le fiamo. </s> <s id="s.000396">c. &. </s> <s id="s.000397">d. </s> <s id="s.000398">& ſia il tranſito della balla la linea. </s> <s id="s.000399">h. i.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>& ſia pur la mira denanti, <lb></lb>cioe la. </s> <s id="s.000400">d. </s> <s id="s.000401">alquanto piu corta, ouer piu baſſa della. </s> <s id="s.000402">c. ma in tanta poca quantita che la li<lb></lb>nea uiſuale che <expan abbr="trãſtra">tranſtra</expan> p le iſtremita di quelle (quala ſia la linea. </s> <s id="s.000403">c. d. </s> <s id="s.000404">m. l.) non tocchi lo <lb></lb>detto <expan abbr="trãſito">tranſito</expan>. </s> <s id="s.000405">h. i.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>et ſia il <expan abbr="põto">ponto</expan>. </s> <s id="s.000406">m. il luoco di tal linea piu propinquo al detto <expan abbr="trãſito">tranſito</expan> di <pb xlink:href="042/01/032.jpg"></pb>qualunque altro, hor dico, che ſe per caſo il ſegno che ſe tuol de mira ſara in ponto. </s> <s id="s.000407">m. <lb></lb>la balla dara pur di ſotto dal ſegno, cioe daria in ponto. </s> <s id="s.000408">n. ma pur ui dara piu propin<lb></lb>quo che in qualunque altro luoco, perche ſe tal ſegno fuſſe piu de la dal ponto. </s> <s id="s.000409">m. (come <lb></lb>ſaria a dire in ponto. </s> <s id="s.000410">l.) ouer di qua (come ſaria a dire in ponto. </s> <s id="s.000411">o.) ſempre dara piu <lb></lb>baſſo, uero è che eglie ſuggetto a maggior errore di la, che di qua dal detto ponto. </s> <s id="s.000412">m. <lb></lb>(come dì ſotto nella figura appare.)<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>on piu che ue ho inteſo benißimo, circa a <lb></lb>queſta parte.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.032.1.jpg" xlink:href="042/01/032/1.jpg"></figure> <p type="head"> <s id="s.000413">QVESITO NONO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> S. P<emph type="italics"></emph>rior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000414">PRIORE. H<emph type="italics"></emph>or ſeguitati la ultima parte di queſta propoſta materia, cioe <expan abbr="quã">quam</expan> <lb></lb>do che la mira dauanti hauera la ſua conueniente cortezza, ouer baſſezza ri<lb></lb>ſpetto a quella de drio.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uando che la mira dauanti ſara talmente piu ſcarſetta, <lb></lb>ouer piu baſſa di quella de drio, che la noſtra linea uiſuale che tranſira per le iſtremita <lb></lb>delle ponte di quelle, nel tuor la mira delle coſe, uada ſolamente a toccare, e non ſegare <lb></lb>il tranſito, ouer uiaggio qual debbe far la balla (come nella ſottoſcritta figura appare <lb></lb>in ponto. </s> <s id="s.000415">m.) & tutta la diſtantia che ſara dalla bocca de tal pezzo al ponto de tal toc <lb></lb>camento che nella ſottoſcritta figura ſaria la linea. </s> <s id="s.000416">h. m. tanto ſe potra dire con ragio<lb></lb>ne, che tal pezzo tiri de mira, perche ſe per caſo il ſegno che ſe tuol de mira ſe trouara <lb></lb>à eſſere nel ponto di tal toccamento, la balla dara preciſamente in brocca, ma eſſendo <lb></lb>fuora di tal toccamento, cioe fuora del ponto. </s> <s id="s.000417">m. la balla ſempre dara alquanto di ſotto <lb></lb>di tal ſegno, cioe di ſotto dalla brocca di quello, & tanto piu quanto piu ſara remoto il <lb></lb>detto ſegno dal detto ponto del toccamento. </s> <s id="s.000418">o. ſia de là, ouer de quà da quello. </s> <s id="s.000419">Vero è, <lb></lb>che eſſendo de quà, cioe uerſo il pezzo, tal balla non puo dar molto baſſa, perche tal <lb></lb>baſſezzamai ſe puo agguagliare alla altezza della mira de drio, che puo eſſere circa <lb></lb>allamita della groſſezza del pezzo nella culattade drio (come fu detto anchora in fi<lb></lb>ne del Settimo queſito) e pero in tal caſo ſe è ſuggetto à poco errore in riſpetto à quello <lb></lb>che potria occorrer quando che il ſegno fuſſe de la dal ponto del detto toccamento, co<lb></lb>me ogni commun intelletto puo conſiderare.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>erche uoleti coſi attribuire alla di<lb></lb>ſtanua del ſopradetto ponto del toccamento che ſia il tirar de mira di tal pezzo, et non <lb></lb>alla diſtantia del ponto della interſeccatione, nel quale eſſendoui il ſegno, la balla da me <lb></lb>deſimamente in brocca, ſi come fa nel ponto del toccamento, come fu dimoſtrato nel <lb></lb>Settimo queſito.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>erche il ponto della interſeccatione non ha luoco determinato,<emph.end type="italics"></emph.end><pb pagenum="17" xlink:href="042/01/033.jpg"></pb><emph type="italics"></emph>ma puo occorrere in infiniti luochi, ſecondo li infiniti modi, che la mira dauanti puo eſ <lb></lb>ſer di ſoperchio piu corta di quella de drio, ma el ponto del toccamento non puo occor <lb></lb>rere, ſaluo che in un luoco ſolo, el qual luoco è il piu lontano della bocca del pezzo de <lb></lb>qual ſi uoglia altro, doue concorrer poſſa la noſtra linea uiſuale con el tranſito, ouer <lb></lb>uiaggio qual debbe far la balla, eſſendo adunque el piu lontano concorſo de cadauno de <lb></lb>li altri concorſi, che ſe interſecano, & el manco uariabile: per tale ragioni à mi me pa <lb></lb>re, che piu meritamente à quel ſi debbia atribuire tal dignita, che ad alcuno di ponti <lb></lb>delle interſecationi.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>oi hauetiragione, & queſta con le due paſſate ſono state <lb></lb>tre belle lettioni.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.033.1.jpg" xlink:href="042/01/033/1.jpg"></figure> <p type="head"> <s id="s.000420">QVESITO DECIMO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000421">PRIORE. F<emph type="italics"></emph>in qua me haueti fatto chiaro, donde procede la cauſa, <expan abbr="quãdo">quando</expan> che <lb></lb>uno tirando de mira à uno ſegno alle uolte da in brocca, alle uolte di ſopra, et alle <lb></lb>uolte di ſotto del detto ſegno, hor uoria ſapere da che procede, che alcune uolte da mol <lb></lb>to costero dal detto ſegno tolto de mira.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto puo procedere per due cauſe, l'u<lb></lb>na è per le mire, le quale alle uolte l'una, ouer ambe due non ſara preciſamente nella <lb></lb>mezzara del pezzo, cioè nel mezzo della parte ſuperiore del pezzo, per il che tal <lb></lb>pezzo èsforzato à percuottere coſtero, perche ſe la mira de drio ſara fora del detto <lb></lb>ponto di mezzo: poniamo uerſo la noſtra man deſtra, etiam el detto pezzo dara coſte <lb></lb>ro alla medeſima banda deſtra del ſegno, che ſe tol de mira, & ſe la detta mira de drio <lb></lb>ſara fora del ponto di me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & uerſo la man ſiniſtra, etiam el detto pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o percuote <lb></lb>ra coſtero, & uerſo la medeſima parte ſiniſtra.<emph.end type="italics"></emph.end> P. </s> <s id="s.000422">A <emph type="italics"></emph>me pare, che doueria eſſer al <lb></lb>contrario di quello che haueti detto, cioè che ſe la mira de drio ſia fora del ponto di <lb></lb>me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & uerſo la banda destra, che il detto pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o ueria tirar costero uerſo la ban<lb></lb>da ſiniſtra.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on Signore, anci eglie, come hauemo detto, & accioche quella <lb></lb>per ragione ne ſia certa, poniamo eßempi gratia, lo ſotto ſcritto pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, che la mira de <lb></lb>drio. </s> <s id="s.000423">c. ſia alquanto fora del ponto di me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & uerſo man deſtra, & che la mira. </s> <s id="s.000424">d. <lb></lb></s> <s id="s.000425">dauanti ſia iuſtamente nel ponto de me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & il ſegno incontrato, ouer tolto de mira <lb></lb>con le dette due mire, poniamo ſia el ponto. </s> <s id="s.000426">e. el qual ponto. </s> <s id="s.000427">e. eglie neceſſario, che ſia <lb></lb>diſcrepante, ouer diſcoſto dal uiaggio, che debbe far la balla, & uerſo la banda ſini<lb></lb>stra, come di ſotto in figura appare, ſupponendo che la linea f. g. ſia el uiaggio, che de <lb></lb>ue far la balla. </s> <s id="s.000428">Eſſendo adunque elſegno. </s> <s id="s.000429">e. diſcoſto à <expan abbr="bãda">banda</expan> ſinistra del uiaggio, che de-<emph.end type="italics"></emph.end><pb xlink:href="042/01/034.jpg"></pb><emph type="italics"></emph>ue far la balla, ſeguita chel uiaggio che deue far la detta balla paßi diſcoſto dal detto <lb></lb>ſegno, & uerſo la banda destra di quello, come nello ſotto ſcritto eſſempio ſi puo uede <lb></lb>re, & molto piu ſeguiria tal effetto ſe la mira. </s> <s id="s.000430">d. </s> <s id="s.000431">dauanti fuſſe anchora lei fuora del det <lb></lb>to ponto di mezzo, ma uerſo l'altra banda, cioe uerſo la banda ſinistra.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.034.1.jpg" xlink:href="042/01/034/1.jpg"></figure> <p type="main"> <s id="s.000432">LA<emph type="italics"></emph>ſeconda cauſa, che puo cauſar tal effetto, ouer inconueniente puo procedere <lb></lb>del uacuo della canna, el quale molte uolte non è triuellato, ouer gettato dretta<lb></lb>mente nel me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o del mettallo, cioe, che tal foro non è perfettamente nel mezzo del <lb></lb>mettallo, anci da una banda ui è piu ſottile, ouer piu groſſo, che non è dall'altra, talmen <lb></lb>te, che ſe ben le due mire fuſſeno collocate, & aſſettate perfettamente nelli ponti di <lb></lb>me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o di la parte ſuperiore del mettallo, tal pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o neceſſariamente tirara coſtero, <lb></lb>perche ſe ben le mire ſono nelli ponti del me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o del ſuperior mettallo non ſono ſopra <lb></lb>la me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>ara del foro, & per queſta cauſa da coſtero, onde per remediar à tal inconue <lb></lb>niente, eglie neceſſario <expan abbr="cõ">com</expan> induſtria ritrouare doue batte la mezzara del foro ſi de drio <lb></lb>come dauanti, & iui aſſettaruile mire: & leuaraßi tal inconueniente al detto pezzo, <lb></lb>per trouar la me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>aria del detto foro, li bombardieri coſtumano à retrouarla (per <lb></lb>quanto ho inteſo da alcuni) con due liſte, ouer cantinelle egualmente larghe, & rettißi <lb></lb>me, & una ne cazano nel pezzo rettamente per ilfondo della canna, & l'altra di fo<lb></lb>ra ſopra il pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & incontrano una parte di quella di ſopra el pezzo <expan abbr="cõ">com</expan> quella par <lb></lb>te, che auanza fora della bocca del pezzo di quella, che ua per dentro el pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & <lb></lb>coſi doue batte el mezzo di quella di foraſopra il pezzo ſi de drio, come dauanti ui <lb></lb>pongono l'una, & l'altra mira, el qual modo per eſſer aſſai ſpediente, & di poco artifi <lb></lb>cio, non è da biaſmare, quantunque per altre uie ſe potriano inueſtigare.<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>on ſe <lb></lb>potria truouare el mo do di agiuſtar le dette mire ſenza altra induſtria de dette liſte, <lb></lb>maſolamente nel tirar continuamente el pezzo.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>e potria ſi, cioe ſel pezzo deſ <lb></lb>ſe coſtero, poniamo uerſo la banda deſtra del ſegno, ſpingendo la mira de drio alquan<lb></lb>to uerſo la parte ſiniſtra, & ſe per caſo lui percoteſſe coſtero uerſo la banda ſinistra <lb></lb>del ſegno, ſpingere alquanto la detta mira de drio uerſo la banda deſtra, & coſi andar <lb></lb><expan abbr="facẽdo">facendo</expan>, tanto che ſe ritroui il perfetto luoco di tal mira, & ritrouato che ſia far in tal <lb></lb>luoco un ſegno ſtabile (ſe tal mira fuſſe coſa mobile) accioche un'altra uolta non ſi hab <lb></lb>bia cauſa à ricercar tal luoco.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>e ho inteſo benißimo, & basta per queſta ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000433">QVESITO VNDECIMO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000434">PRIORE. P<emph type="italics"></emph>erche cauſa uno pezzo di artegliaria quanto è piu <expan abbr="lõgo">longo</expan> di <expan abbr="cãna">canna</expan>,<emph.end type="italics"></emph.end><pb pagenum="18" xlink:href="042/01/035.jpg"></pb><emph type="italics"></emph>tanto piu tira lontano.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſta uoſtra propoſitione non è generale, cioe che <expan abbr="quã">quam</expan> <lb></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></lb>ner per fermo, che ogni ſpecie di pezzo, ui ſia una ſua certa, & determinata longhez <lb></lb>za, coſi debitamente proportionata alla poluere, & balla che porta quello tal pezzo, <lb></lb>la quale ogni uolta che ſia preterita (in qual modo ſi uoglia) tal pezzo ſempre deb<lb></lb>bia tirar manco, e per tanto dico, che poteſſe hauer perfetta cognitione di queſta ſua <lb></lb>proportionata longhezza in ogni ſpecie di pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o non accaderia à fare pezzi <expan abbr="lõghi">longhi</expan>, <lb></lb>& pezzi corti di canna (ſaluo per neceßità) perche ogni uolta che una ſpecie di pez<lb></lb>zo fuſſe fatto piu <expan abbr="lõgo">longo</expan> di quella ſua proportionata <expan abbr="lõghe">longhe</expan><emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a, ouer piu corto tal pez <lb></lb>zo ſempre tirariamanco (dico con una medeſima quantita di poluere.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>redo che <lb></lb>uoi diciati el uero, perche uedo che à tutte le ſpecie de canoni, & altri pezzi corti, per <lb></lb>tirarli ordinariamente ui danno di poluere li dui terzi di quello, che peſa la balla. </s> <s id="s.000436">Ma <lb></lb>à tutte le ſpecie di colobrine, per eſſer pezzi piu longhi di canna à cadauna ordinaria <lb></lb>mente per tirarla ui danno li quatro quinti di quello peſa la balla, & tutto questo cre<lb></lb>do chel facciano, perche daendoli ſolamente li dui terzi, come ſi coſtuma dar alli cano<lb></lb>ni forſi che la non tiraria tanto, come fanno li canoni.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto è una coſa certa<lb></lb>mente, che io non ſapeua, & eſſendo coſi ho molto à caro hauerla inteſa.<emph.end type="italics"></emph.end> P. A<emph type="italics"></emph>nci <lb></lb>queſta è una coſa, che è notißima ad ogni minimo bombardiero.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>redo, che eſſen <lb></lb>do coſi ui debbia eſſer nota à cadauno di loro. </s> <s id="s.000437">Ma io non ſo che materia ſia queſta, & <lb></lb>molto mi marauiglio di Principi, che fanno gettar tai pezzi con uno difetto tanto eui <lb></lb>dente per uoler poi medicar quel tal effetto con ſuo gran <expan abbr="diſcõmodo">diſcommodo</expan>, & ſpeſa.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>a <lb></lb>ſe ben queſte colobrine uiſi da piu poluere di quello, che ſe fa alli canoni, tirano poi an <lb></lb>chora piu di quello fanno li canoni.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>e ha mai fatto far iſperientia uoſtra Signo<lb></lb>ria di queſto.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o non ho mai fatto far queſta ſperientia, nondimeno io ho per fer<lb></lb>mo, che ſia coſi, perche etiam tutti li <expan abbr="bõbardieri">bombardieri</expan> <expan abbr="hãno">hanno</expan> <expan abbr="uniuerſalmẽte">uniuerſalmente</expan> queſta opinione, <lb></lb>& non puo eſſer altramente, perche eſſendo la colobrina piu <expan abbr="lõga">longa</expan> di canna del canone, <lb></lb>& daendoli poi anchor piu poluere di quello ſi fa al canone, el <expan abbr="nõ">non</expan> puo eſſer altramen<lb></lb>te, che la non tiri aſſai piu di quello che fa il canone, & la ſpeſa <expan abbr="nõ">non</expan> è tanto grande, come <lb></lb>uoi la fati, perche in uno canone da libre. </s> <s id="s.000438">20. di balla ui ſi da ordinariamente per ti<lb></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 ſi da <lb></lb>ordinariamente per tirarla lire. </s> <s id="s.000442">16. di poluere, che ſaria ſolamente lire. </s> <s id="s.000443">2. onze.<emph.end type="italics"></emph.end> S. <emph type="italics"></emph>de <lb></lb>piu, ſi che queſta ſpeſa de lire. </s> <s id="s.000444">2. onze. </s> <s id="s.000445">8. de poluere de piu è una miſeria.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o <expan abbr="nõ">non</expan> uo <lb></lb>glio affermare, che la colobrina debbia tirar piu, ouer meno del ſuo canone <21> <expan abbr="nõ">non</expan> eſſer <lb></lb>tal coſa molto chiara, <21> <expan abbr="nõ">non</expan> hauerſi perfetta notitia della ſua proportionata <expan abbr="lõghezza">longhezza</expan> <lb></lb>(detta di ſopra) ma ſe eglie il uero, che la colobrina <expan abbr="cargãdola">cargandola</expan> ſolamente con tanta pol <lb></lb>uere, quanta ſi da al ſuo canone, la non tiritanto quanto fa el ſuo canone, io ſon certißi <lb></lb>mo, che à uoler che la tiri preciſamente tanto, <expan abbr="quãto">quanto</expan> fa el ſuo canone, eglie neceſſario à <lb></lb>porui <expan abbr="dẽtro">dentro</expan> piu poluere di quello ſi fa al canone, & tanto piu poluere ui uora, quanto <lb></lb>maggior ſara la <expan abbr="differẽtia">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></lb>do chel potria eſſer <expan abbr="facilmẽte">facilmente</expan>, che <expan abbr="tirãdo">tirando</expan> la ſopra detta colobrina da. </s> <s id="s.000446">20. <expan abbr="cõ">com</expan> la poluere <lb></lb>che <expan abbr="ordinariamẽte">ordinariamente</expan> ui ſi da de piu del canone, che quella tal poluere <expan abbr="nõ">non</expan> ſara forſi <expan abbr="ſoffi-ẽte">ſoffi<lb></lb>ente</expan> à farla arriuare à quel ſegno, che tira el canone, uero è chel potria eſſer anchora<emph.end type="italics"></emph.end><pb xlink:href="042/01/036.jpg"></pb><emph type="italics"></emph>che da quelli primi, che determinorono, che ui ſe doueſſe dare li detti quattro quinli di <lb></lb>quello, che peſa la balla, ui la proportionarono forſi talmente con la iſperientia, che la <lb></lb>tiraſſe tanto, quanto ſa el ſuo canone, & forſi piu, ma tal coſa non ſi potria affermare, <lb></lb>ne negare ſenza qualche particolar iſperientia, nondimeno ſia come ſi uoglia ſe la det <lb></lb>ta colobrina, con la medeſima poluere, che ſi da al canone non tira tanto, quanto fa el <lb></lb>ſuo canone. </s> <s id="s.000447">Eglie un'error euidentißimo, & è una coſa rediculoſa, à dir poi di uoler re <lb></lb>mediare à tal errore con dire: metteremo, ouer daremo alquanto piu quantita de polue <lb></lb>re alla detta colobrina, accioche la tiri tanto, quanto fa detto ſuo canone, ouer piu di <lb></lb>quello, la qual poluere, che ui ſi da di piu, che la deſſe medeſimamente al detto canone <lb></lb>forſi che tiraria molto piu della detta colobrina. </s> <s id="s.000448">Circa alla ſpeſa, che ui ua de piu, qua<lb></lb>la uostra Signoria dice eſſer una miſeria. </s> <s id="s.000449">Dico eſſer molto maggiore di quello, che uo <lb></lb>ſtra Signoria ſi penſa: perche, ſe non me inganno, facendoſi le dette colobrine piu lon<lb></lb>ghe delli canom, la ragion uole, che ſi facciano anchor piu groſſe di metallo. </s> <s id="s.000450">Il che eſ<lb></lb>ſendo, ui intra molto piu metallo, che in uno canone, & conſequentemente debbeno eſ<lb></lb>ſer molto piu graue delli ſuoi canoni, et eſſendo piu graue, uogliono anchora (per con <lb></lb>durle) piu numero de buoui, ouer caualli, di quello uoleno li canoni, & maggior molti<lb></lb>tudine de huomini, che gouerni quelli, & maggior quantita di uettouaglia ſi per li ani <lb></lb>mali, come per li huomini, che gouernan quelli oltra il <expan abbr="ſtipẽdio">ſtipendio</expan>, che à quelli ui ſi da per <lb></lb>ordinario ò dal principe, ouer da quelli communi, che li manda per comandamento del <lb></lb>principe, ſi uede adunque da un picciolo errore fatto nel principio quanti ne ſeguita <lb></lb>nel fine, & ſe tali errori ſono aſſai in una colobrina da lire. </s> <s id="s.000451">20. di balla, molto piu ſe <lb></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 inteſo da bom <lb></lb>bardieri, che ſe coſtumano.<emph.end type="italics"></emph.end> P. S<emph type="italics"></emph>enza dubbio, che piu metallo intra in le colobrine, <lb></lb>che nelli canoni, & conſequentamente per condurle, ui ua piu animali, & di queſto ne <lb></lb>azzo una notta in un mio memoriale ſi del mettallo che ui intra, & della ſua longhez<lb></lb>za di cadauna ſorte pezzo, come delli animali, che gliua à condurle.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>i gratia <lb></lb>uoſtra ſignoria me ne dia la coppia, perche di queſte particolarita ne potria forſi ca<lb></lb>uar con tempo qualche coſtrutto.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>olto uolentieri, portame qua quel mio me<lb></lb>moriale, che è in la mia caſſa.<emph.end type="italics"></emph.end> SERVO. E<emph type="italics"></emph>ccolo Signore.<emph.end type="italics"></emph.end> P. H<emph type="italics"></emph>or ſcriueti coſi. <lb></lb></s> <s id="s.000454">Vn falconetto da lire tre di balla di piombo ua longo piedi cinque e meggio, & di met<lb></lb>tallo ui intra com munamente lire quatrocento, & à condurlo ui uuol caualli pa<lb></lb>ra uno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000455">V<emph type="italics"></emph>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></lb>lo caualli para.<emph.end type="italics"></emph.end> 2. </s> </p> <p type="main"> <s id="s.000459">A<emph type="italics"></emph>ſpidi 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></lb>condurli caualli para.<emph.end type="italics"></emph.end> 3. </s> </p> <p type="main"> <s id="s.000463">S<emph type="italics"></emph>acri da lire. </s> <s id="s.000464">12. de longhezza de pie.<emph.end type="italics"></emph.end> S. <emph type="italics"></emph>uuol di mettallo lire. </s> <s id="s.000465">1400. & per condurli <lb></lb>caualli para.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.000466">S<emph type="italics"></emph>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></lb>caualli para.<emph.end type="italics"></emph.end> 5. </s> </p> <p type="main"> <s id="s.000470">S<emph type="italics"></emph>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></lb>caualli para.<emph.end type="italics"></emph.end> 3. </s> </p> <pb pagenum="19" xlink:href="042/01/037.jpg"></pb> <p type="main"> <s id="s.000474">C<emph type="italics"></emph>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></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"></emph.end> 5. </s> </p> <p type="main"> <s id="s.000479">P<emph type="italics"></emph>aſſauolante 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></lb>durlo buoui para.<emph.end type="italics"></emph.end> 5. </s> </p> <p type="main"> <s id="s.000483">C<emph type="italics"></emph>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></lb>per condurla buoui para.<emph.end type="italics"></emph.end> 5. </s> </p> <p type="main"> <s id="s.000487">C<emph type="italics"></emph>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></lb>durla buoui para.<emph.end type="italics"></emph.end> 7. </s> </p> <p type="main"> <s id="s.000491">V<emph type="italics"></emph>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></lb>durlo buoui para.<emph.end type="italics"></emph.end> 5. </s> </p> <p type="main"> <s id="s.000495">V<emph type="italics"></emph>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></lb>lo buoui para. </s> <s id="s.000499">5. in. </s> <s id="s.000500">6. <lb></lb>Vna colobrina da lire. </s> <s id="s.000501">30. di longhezza piedi uol di metallo lire & <lb></lb> per condurla buoui para. </s> <s id="s.000502">8. <lb></lb>Vn canon da lire. </s> <s id="s.000503">30. di longhezza piedi uol di metallo lire & per <lb></lb> condurlo buoui para.<emph.end type="italics"></emph.end> 6. </s> </p> <p type="main"> <s id="s.000504">V<emph type="italics"></emph>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></lb>& per condurla buoui para.<emph.end type="italics"></emph.end> 12. </s> </p> <p type="main"> <s id="s.000508">E<emph type="italics"></emph>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></lb>& per condurla buoui para.<emph.end type="italics"></emph.end> 14. </s> </p> <p type="main"> <s id="s.000512">V<emph type="italics"></emph>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></lb>per condurlo para. </s> <s id="s.000516">9. de buoui.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000517">V<emph type="italics"></emph>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></lb>& per condurlo buoui para.<emph.end type="italics"></emph.end> 18. </s> </p> <p type="main"> <s id="s.000521">C<emph type="italics"></emph>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></lb>durli buoui para.<emph.end type="italics"></emph.end> 25. </s> </p> <p type="main"> <s id="s.000525">C<emph type="italics"></emph>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></lb>condurle buoui para.<emph.end type="italics"></emph.end> 28. </s> </p> <p type="main"> <s id="s.000529">N. V<emph type="italics"></emph>oſtra Signorla non me ne dica piu, perche mi bastaua della mita di questi che ho <lb></lb>notati.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>e ne resta de dirui ſolamente ſei altri, e pero compiteli, cioe ui ſono an<lb></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></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"></emph.end></s> </p> <p type="main"> <s id="s.000535">A<emph type="italics"></emph>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></lb>ui para.<emph.end type="italics"></emph.end> 12. </s> </p> <p type="main"> <s id="s.000539">A<emph type="italics"></emph>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></lb>buoui para.<emph.end type="italics"></emph.end> 11. </s> </p> <p type="main"> <s id="s.000543">A<emph type="italics"></emph>ltre pur da lire. </s> <s id="s.000544">100. longhe ſolamente piedi. </s> <s id="s.000545">8. e meggio, che uol di metallo lire. <lb></lb></s> <s id="s.000546">4500. & per condurle buoui para.<emph.end type="italics"></emph.end> 9. </s> </p> <p type="main"> <s id="s.000547">A<emph type="italics"></emph>nchora ui ſono 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></lb>& per condurli buoui para.<emph.end type="italics"></emph.end> 5. </s> </p> <p type="main"> <s id="s.000551">V<emph type="italics"></emph>n'altra ſorte 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></lb></s> <s id="s.000554">1600. & per condurli buoui para. </s> <s id="s.000555">3. & coſi faremo fine.<emph.end type="italics"></emph.end><pb xlink:href="042/01/038.jpg"></pb>N. L<emph type="italics"></emph>e ſopra annotate lire ſono alla ſottile, ouer alla groſſa, & ſimilmente li piedi ſo<lb></lb>no piedi alia miſura di Venetia, ouer maggiore, ouer menore di quella.<emph.end type="italics"></emph.end> P. L<emph type="italics"></emph>e lire cre <lb></lb>do ſtano tutte alla ſottile, delli piedi non uel ſaprei dire, ma perche queſta nota mi fu da <lb></lb>ta à Barletta, potria eſſer che fuſſeno piedi à miſura di quelle bande, pur credo ſiano <lb></lb>egualt à questi.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>or non importa hauer la coſa tanto per ſottile, ma me baſta ha <lb></lb>uer inieſo 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></lb>Et le colc brine pur da. </s> <s id="s.000559">50. ui ne una ſorte longa piedi. </s> <s id="s.000560">12. che uol di metallo lire. </s> <s id="s.000561">6600. <lb></lb>che ſarian 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></lb>di quello uol il canone, & li detti cinque para de buoui credo uorranno cinque huomini <lb></lb>che li gouerni, hor guardati ſe queſto importa à longo andare, oltra la ſpeſa della pol<lb></lb>uere che uole de piu à ogni colpo che la ſe tira.<emph.end type="italics"></emph.end> P. L<emph type="italics"></emph>a importa ſi in una, ma molto <lb></lb>piu importa in molte, & certamente ſe fuſſe ſano ne uorria ueder la iſperientia per eſ<lb></lb>ſer coſa molto importante.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000564">QVESITO DVODECIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> S. P<emph type="italics"></emph>rior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000565">PRIORE. H<emph type="italics"></emph>ierſera fu aſſai diſputato qualmente à ogni artegliaria lo eſſer <lb></lb>troppo longa di canna, & etiam lo eſſer troppo cortanoce alli tiri di quella, hor <lb></lb>uorria ſapere di quanta longhezza ſe potria con ragion naturale determinare che do<lb></lb>ueſſe eſſer la ſua canna, à douer eſſer debitamente proportionata alla ſua conueniente <lb></lb>miſura di poluere, & balla.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a ſua longhezza uorria eſſer tanta che in quello <lb></lb>iſtante che tutta la poluere compiſſe di eſſer riſolta in fuoco, in quello medeſimo la bal <lb></lb>la ſe ritroui eſſer peruenuta preciſamente nella iſtremita della canna, cioe preciſamente <lb></lb>alla bocca del pezzo, perche in tal iſtante tutta la uirtu iſpulſiua della poluere uiene à <lb></lb>operare nella balla nel colmo della ſua furia, ouer poſſanza, & dapoi che tal uirtu ha <lb></lb>operato nella detta balla, la detta balla non ritroua coſa alcuna, che ui impediſca, ouer <lb></lb>che gli interrompa il moto eccetto che l'aere, e pero debbe andar piu in tal longhezza, <lb></lb>che ſe tal canna fuſſe piu longa, ouer piu corta, perche ſe la canna fuſſe piu corta, la bal <lb></lb>la uſciſſe della bocca del pezzo auanti che ſia compita di eſſer riſolta in fuoco tutta la <lb></lb>poluere, e pero tutta la uirtu iſpulſiua della poluere non uiene à operare nella balla, an <lb></lb>ci parte di quella reſta una, & puo accadere facilmente, che molta poluere uſciſca ſa<lb></lb>na fuora del pezzo inſieme con la balla, cioe poluere non tocca dal fuoco. </s> <s id="s.000566">Ma quando <lb></lb>poi che la detta canna fuſſe piu longa, in quello iſtante che compiſſe da eſſer riſolta in <lb></lb>ſuoco tutta la poluere, la balla in quel medeſimo non ſi troua coſi preciſamente alla boc <lb></lb>ca del pezzo, ma alquanto piu in dentro, e per tanto la detta balla nel colmo della ſua ue <lb></lb>locita, ſcorrendo per quella poca parte di canna che ui reſtaua à compire, la detta can<lb></lb>na grandemente ue interrompe il ſuo moto, perche ogni uolta che un corpo immobile <lb></lb>tocchi alcun corpo che ſi moua ſempre ui interrompe il moto, & tanto piu, quanto che <lb></lb>maggior parte, ouer per maggior tempo ua toccando quello.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>e ho inteſo beniſ<lb></lb>ſimo, & queſte uoſtre ragioni me piaceno molto, ne uoglio che procedemo in altro per <lb></lb>queſta ſera.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="20" xlink:href="042/01/039.jpg"></pb> <p type="head"> <s id="s.000567">QVESITO DECIMOTERTIO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di <lb></lb>Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000568">PRIORE. H<emph type="italics"></emph>ierſera uoi dimoſtraſti con buone ragioni di quanta longhezza ſe <lb></lb>potria con ragione determinare che doueſſe eſſer la longhezza della canna d'un <lb></lb>pezzo di Artegliaria ad eſſere debitamente proportionata alla conueniente miſura <lb></lb>della poluere, & balla che ſi coſtuma à dare à un tal pezzo, la qual miſura conueniente <lb></lb>il ſe ſuppone che ſia li dui terzi di quello che peſa la balla. </s> <s id="s.000569">Hor ſe il fuſſe uno pezzo <lb></lb>(poniamo uno canon da. </s> <s id="s.000570">20.) che per ſorte haueſſe quella ſua debita & proportiona<lb></lb>ta longhezza che ui ſi conuiene alli dui terzi poluere di quello peſa la balla, che gli deſ <lb></lb>ſe poi piu poluere, cioe piu delli detti dui terzi di quello che peſa la balla, ue adimando <lb></lb>ſe tal pezzo tirara piu del ſolito.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio che lui tirara alquanto piu delſo <lb></lb>lito.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>uesto ſaria contra alle ragioni da uoi hierſera adutte, perche in queſto caſo <lb></lb>la balla ſara uſcita della bocca del pezzo auanti che tutta la detta poluere ſia compita di <lb></lb>riſoluerſi in fuoco, e pero quella parte de uigore, che ſara cauſato da quella tal parte de <lb></lb>poluere di piu, dapoi che ſara uſcita la balla della bocca del pezzo ſara fruſta è uana, <lb></lb>e pero tal pezzo non doueria tirar piu, per tal poluer dataui de piu (reſtando il uigor <lb></lb>di quella in tutto uano è fruſto) anci doueria tirare ſolamente ſecondo il ſolito.<emph.end type="italics"></emph.end> N. <lb></lb>Q<emph type="italics"></emph>uel uigore uentoſo, che generara quella parte di poluer dataui de piu (dapoi che la <lb></lb>balla ſara uſcita dalla bocca del pezzo) à benche lui non potra operare nella detta balla <lb></lb>mentre che quella ſara dentro della canna del pezzo, il non reſtara pero da operare <lb></lb>in quella, dapoi che ſara uſcita dalla bocca del pezzo, cioe in aere, perche tutto quel <lb></lb>uento che uien cauſato dalla poluere nella detta canna ſempre ſeguita per alquanto uni<lb></lb>tamente la balla, anchor che la balla ſia uſcita per alquanto fuora della bocca del pez<lb></lb>zo, e pero ui augumenta alquanto il moto, uero è che tal uigor uentoſo non operara <lb></lb>tanto nel ſpingere la detta balla (per trouarla coſi fuora della detta canna) come faria <lb></lb>ſe la trouaſſe dentro nella canna, cioe che tal ſuo operare non ſara proportionale à <lb></lb>quella quantita di poluere poſtaui di piu, anei ſara molto lontano di tal proportione.<emph.end type="italics"></emph.end><lb></lb>P. I<emph type="italics"></emph>o non intendo queſto operar poportionale.<emph.end type="italics"></emph.end> N. O<emph type="italics"></emph>perar proportionale ſe in<lb></lb>tende in queſto modo, poniamo eſſempi gratia che queſto noſtro canon da lire uenti, ti<lb></lb>randolo à una data elleuatione con li dui terzi poluere di quello peſa la balla, tiri paſſa <lb></lb>1000. tirandolo poi con tanta poluere quanto peſa la balla, la qual poluere ueneria à <lb></lb>eſſere un tanto è meggio di quello era prima (cioe dalli dui terzi) hor dico, che ſe que<lb></lb>ſta poluere che ui fuſſe aggionta de piu operaſſe proportionalmente nella balla, tal <lb></lb>pezzo doueria lirare alla medeſima elleuatione preciſamente paſſa. </s> <s id="s.000571">1500. cioe un tan <lb></lb>to è meggio di quello fece con li dui terzi poluere. </s> <s id="s.000572">Et io dico, che il pezzo in ſimil ca<lb></lb>ſo non ſolamente il non tiraria li detti paſſa. </s> <s id="s.000573">500. de piu, ma forſi che il non tiraria <lb></lb>manco la mita di piu, cioe paſſa. </s> <s id="s.000574">250. Ma ſupponemo che lui tiraſſe li detti paſſa. <lb></lb></s> <s id="s.000575">250. de piu (che in ſumma ſaria paſſa. </s> <s id="s.000576">1250.) Anchora dico, che tiraſſe il me<lb></lb>deſimo canone con uno altro terzo di poluere de piu, cioe con tanta poluere quan<lb></lb>to peſa la balla, & un terzo piu, che ſaria quattro terzi queſto ſecondo terzo non <pb xlink:href="042/01/040.jpg"></pb>accreſceria il detto tiro tanto quanto fece il primo terzo, cioe chel non accreſcera quel <lb></lb>li paſſa. </s> <s id="s.000577">250. che fu ſuppoſto che faceſſe il primo terzo, ma creſceria molto manco de <lb></lb>dettipaſſa. </s> <s id="s.000578">250. & ſimilmente, che ui aggiongeſſe anchora un'altro terzo di poluere di <lb></lb>piu queſt'altro terzo accreſceria pur il tiro, ma molto manco di quello hauera fatto lo <lb></lb>ſecondo terzo, che fu aggionto, ſi che ogni accreſcimento di poluere andaria per fina à <lb></lb>un certo termine ſempre accreſcendo alquanto il tiro, ma tal creſcere andaria ſempre <lb></lb>ſminuendo del ſuo anciano per fina al detto termine, ma da quello termine in ſuſo che ui <lb></lb>aggiongeſſe piu poluere non faria accreſcere piuil detto tiro, anci potria eſſer tanto lo <lb></lb>accreſcimento della poluere che non ſolamente la non faria creſcere, ma faria calare aſ <lb></lb>ſai il detto tiro.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>oi diceti una coſa, che non mi conſona molto, cioe à dire che ui ſe <lb></lb>potria aggiongere, ouer accreſcerui tanta poluere oltra à un certo termine, che non ſo <lb></lb>lamente la non faria accreſcere il tiro à tal pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, ma che lo faria callare, la qual coſa <lb></lb>me pare molto fuora diragione.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci è ragioneuole per commun prouerbio: qual <lb></lb>dice, che ogni ſuperchio rompe il coperchio, & per chiarire ben queſto dubbio biſo<lb></lb>gna uenir alli eſtremi. </s> <s id="s.000579">Et per tanto dico, che chicargaſſe queſto tal pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o con tanta <lb></lb>poluere quanto puo tener la canna, laſſandoui ſolamente nella iſtremita di detta canna <lb></lb>tanto diuacuo quanto è il diametro della balla, cioe tanto che ui ſt poteſſe mettere la bal <lb></lb>la à pena, & tir arlo poi in tal modo cargato, adimando à uoſtra Signoria, ſe quella cre <lb></lb>de, che quello tiraria piu, ouer meno di quello faria à cargarlo ſecondo l'ordinario, cioe <lb></lb>con dui terzi poluere di quello peſa la balla.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o credo che chi il tiraſſe in tal modo <lb></lb>cargato che tal pezzo crepparia, & che uer amente il ſuperchio di detta poluere, rom <lb></lb>peria il coperchio (come dice il uoſtro prouerbio) cioe che romperia il detto pezzo.<emph.end type="italics"></emph.end><lb></lb>N. N<emph type="italics"></emph>on uoglio ſtare à diſputare che in un tal caſo, tal pezzo doueſſe ragioneuolmen <lb></lb>te creppare, ouer non creppare, perche longa ſaria tal diſputta, ma ſuppoǹiamo pur, <lb></lb>che tal pezzo non creppaſſe.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>n queſto caſo che gli poneſſe una balla che ui entraſ <lb></lb>ſe talmente ſtretta, che fuſſe neceſſario à farla entrar per forza di ma<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>ate. </s> <s id="s.000580">Io ten<lb></lb>go per fermo che tiraria molto lontano.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n tutte le coſe che ſono ſtate dette, et che <lb></lb>ſe hanno da dire, circa alle coſe di tiri delle artegliarie, ſempre ſe ſuppone (non ſpecifi<lb></lb>cando altro) che le balle ſiano, eguale ſi in grandezza, come di peſo, etiam che ſiano <lb></lb>egualmente rotonde, perche ciaſcuno di questi accidenti fanno uarìar li tiri.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per tan<lb></lb>to in queſto noſtro caſo dico, che ſe debbe intendere, che la balla che ſe ha datir are conla <lb></lb>canna piena di poluer ſia di quella medeſima qualita di peſo, miſura, & rotondita, che <lb></lb>quella che ſe ha da tirare ſecondo l'ordinario, cioe con li dui terzi poluere di quello pe <lb></lb>ſa la balla.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>igliandola per il modo che uoi diceti, in effetto la coſa è dubbioſa.<emph.end type="italics"></emph.end> N. <lb></lb>N<emph type="italics"></emph>on ui è dubbio alcuno, anci è coſa certa che tirandola conla canna piena di poluere ti <lb></lb>rara molto, & molto manco di quello faria con la poluere ordinaria.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>erche ra<lb></lb>gione.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>aragion è queſta, che ognipoluere (per fina che la ſia) abbruſa in tem<lb></lb>po, cioe che prima abbruſa quella che ſe ritroua nel luoco doue ui ſe da fuoco, di quella <lb></lb>che è alquanto remota dal detto luoco, & quella, che è piu propinqua al detto luoco ſe <lb></lb>abbruſa alquanto auanti di quella, che ui è men propinqua, ouer che ui è piu remota, <lb></lb>ſtante adunque queſta propoſitione, eglie manifeſto che qual ſi uoglia parte di quella tal <lb></lb>poluere, che ſe ritroua nella canna del detto pezzo, che ſia piu propinqua al foro doue<emph.end type="italics"></emph.end><pb pagenum="21" xlink:href="042/01/041.jpg"></pb><emph type="italics"></emph>ſe gli da el fuoco, ſe abbruſa auanti di quella, che glie piu remota, & per eſſer me<lb></lb>glio inteſo, diuidamo con la mente tutta la longhezza della poluere, che ſe ritroua in <lb></lb>detta canna in quattro parti equali. </s> <s id="s.000581">Dico adunque, che quella quarta parte, che termi <lb></lb>na al buſo, doue che ui ſtda el fuoco, ſe abbruſa auanti dell' altra conſe quente parte, & <lb></lb>bruſiando genera tanta gran quantita di eſſalation uentoſa, che diece luochi equali al <lb></lb>luoco della poluere abbruſata non ſariano capaci per la detta eſſalatione, & per tan<lb></lb>to ſecondo che la detta eſſalatione continuamente ſe ua cauſando, per la poluere, che <lb></lb>continuamente ſe ua abbruſando. </s> <s id="s.000582">Anchora eglie neceſſario à quella tal eſſalatione con <lb></lb>tinuamente andarſe acquiſtando per forza luoco maggiore aſſai, di quello della polue <lb></lb>re, da che eglie cauſata, & questo luoco la nol puol acquiſtare, ſaluo che per due uie. <lb></lb></s> <s id="s.000583">La prima è ſpingendo per forza auanti il reſtante della poluere, non abbruſata, che è <lb></lb>uerſo la bocca del pezzo inſteme con la balla, oueramente far crepare il pezzo, & <lb></lb>perche eglie da credere, che piu facil ui ſia à ſpingere fuora la detta poluere inſieme <expan abbr="cõ">com</expan> <lb></lb>la balla, che à far creppar il pezzo, & maßime per eſſer la balla nella iſtremita della <lb></lb>canna, diremo adunque, che la prima quarta parte de ditta noſtra poluere, che prima <lb></lb>ſe abbruſa, bruſando continuamente ua ſpingendo auanti l'altra poluere, che ſi ua tro<lb></lb>uando auanti di ſe, & conſequentemente quella ſpenge la balla, et per eſſer la balla coſi <lb></lb>propinquißima all'uſcita alla prima, & minima urtata, che nel principio ſente, quella <lb></lb>uſciſſe del pezzo ſubito, ſpinta ſolamente dalla poluer ſana (come detto) & non dalla <lb></lb>propria eſſalatione della poluere abbruſata, lo qual ſpengimento (per eſſer fatto coſi <lb></lb>nel principio) non puo eſſer ſe non dabole nella balla, dico debole riſpetto à quello che <lb></lb>ſaria, <expan abbr="quãdo">quando</expan> che quella fuſſe ſpinta dalla propria eſſalatione uentoſa, et nel colmo della <lb></lb>gran furia di quella<emph.end type="italics"></emph.end>: E<emph type="italics"></emph>t oltra di queſto, la balla nell'uſcire del pezzo è ſeguitata (per <lb></lb>alquanto) dalla poluere ſana, la qual poluere dali à un puoco cade in terra, la qual pol <lb></lb>uere nel andar per aere, & poi nel cader in terra, molto interrompe el moto di quel<lb></lb>la eſſalatione uentoſa, che dapoiſeguita la balla, il che non poco nuoce al moto di quel<lb></lb>la Si che per queſte ragionital balla (in ſimel caſo) non andara molto da lontano: ma <lb></lb>che ricargaſſe tal pezzo con alquanto men poluer ſenza dubbio lui tirar aue aſſai piu <lb></lb>di quello faria, eſſendo coſi piena la canna, perche ſe in queſto ſecondo modo ui mancaſ <lb></lb>ſe à impire tutta la canna dui diametri di balla, cargato che ſia la balla, non ſe ritroua<lb></lb>ra coſi nella istremita della bocca del pezzo, ma piu in dentro, & pero quella non uſci <lb></lb>ra coſi della bocca del pezzo alla prima, & minima urtata dalla poluere, anci reſiſte<lb></lb>ra per un poco piu dell'altra, nel qual tempo, molto piu poluere ſara abbruſata, et con <lb></lb>ſequentemente maggior quantita de eſſalatione uentoſa ſara cauſata, & tal balla da <lb></lb>maggior impeto, ouer furore ſara urtata, & ſpinta, dico urtata, & ſpinta pur dalla <lb></lb>poluere, & non dalla propria eſſalatione uentoſa, ſi come dell'altro tiro fu detto, & co <lb></lb>ſi per tale euidente ragioni, in questo ſecondo tiro con men poluere, conchiudemo che <lb></lb>tirara piu lontano di quello, faria al primo con quaſitutta la canna piena di poluere, et <lb></lb>ſimelmente, che recargaſſe tal pezzo anchor con men poluere, cioè poniamo con tan<lb></lb>ta poluere, che ui mancaſſe à impire tutta la canna tre diametri di balla, dico che in tal <lb></lb>caſo lui tiraria piu di quello faria cargandolo, ſecondo che di ſopra fu detto, cioè ſola<lb></lb>mente per dui diametri manco, & coſi chel cargaſſe per quattro diametri manco tira<emph.end type="italics"></emph.end><pb xlink:href="042/01/042.jpg"></pb><emph type="italics"></emph>ra piu che <expan abbr="cõ">com</expan> li tre manco, et coſi con cinque manco tirara piu che con quattro <expan abbr="mãco">manco</expan>, et <lb></lb>coſi andaria <expan abbr="procedẽdo">procedendo</expan> per fin à un certo termine medio fra queſti dui eſtremi, el qual <lb></lb>termine <expan abbr="giõto">gionto</expan> che ui ſe fuſſe haueria queſta dignita in ſe, che chi cargaſſe poi tal pez<lb></lb>zo <expan abbr="cõ">com</expan> <expan abbr="mẽ">men</expan> poluere lui tir araue <expan abbr="mãco">manco</expan>, et <expan abbr="ſimelmẽte">ſimelmente</expan> che ui daße piu poluere, anchora ti<lb></lb>rar aue <expan abbr="mãco">manco</expan>.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph><expan abbr="ertamẽte">ertamente</expan> questa è una bella ſpeculatione, et molto mi piace, per<lb></lb>che in uero conoſco, che fra dui iſtremi diuerſi in proprieta eglie neceſſario eſſerui un <lb></lb>perſetto me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o.<emph.end type="italics"></emph.end> SERVO. S<emph type="italics"></emph>ignor el paſſa l'hora da cena.<emph.end type="italics"></emph.end> P. H<emph type="italics"></emph>orſu chel ſe ceni.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000584">QVESITO DECIMO QVARTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000585">PRIORE. Q<emph type="italics"></emph>ual credeti ſia meglio à calcar benißimo la poluere in un pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o <lb></lb>ouer à laſſarla alquanto diſperſa, erara.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n tutti gli iſtremi contrari biſo <lb></lb>gna fondarſe ſul me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, cioè, che la non uuol eſſer molto calcata, ne molto diſperſa, <lb></lb>perche la poluere molto, e molto calcata fa maggior reſiſtentia al ingreſſo del fuoco, <lb></lb>di quello faria eſſendo alquanto rara, & per tanto la poluere molto, e molto calcata <lb></lb>pena piu tempo ad eſſer conſumata dal fuoco, di quello faria, ſe quella fuſſe <expan abbr="alquãto">alquanto</expan> ra <lb></lb>ra, & quanto piu tempo pena una poluere ad eſſer conſumata dal fuoco, tanto piu de<lb></lb>boli ſegue li ſuoi effetti, & é conuerſo, cioe, che quanto piu preſto uien riſolta in fuoco <lb></lb>tanto piu uigoroſamente ſpinge la balla, perche la ſua uirtu, ouer poſſanza piu unita<lb></lb>mente opera. </s> <s id="s.000586">Il medeſimo quaſi ſeguita, eſſendo molto diſperſa, & rara, & maßime in <lb></lb>forma longa, come ſi uede ſeguir nelle ſementelle, che ſi coſtumano per uoler dar fuoco <lb></lb>à qualche coſa ſtando da lontano, delle qual ſementelle prima abbruſa quella parte, <lb></lb>che ſe ritroua nel capo di tal ſementalla doue ui ſi da fuoco, & ſucceßiuamente ua con<lb></lb>tinuando, cioè abbruſando di mano in mano, per fin chel fuoco aggionge all'altro ca<lb></lb>po, & quanto piu è longa tal ſementella, tanto piu tempo pena tal poluere ad eſſer to <lb></lb>talmente conſumata dal fuoco. </s> <s id="s.000587">Il medeſimo uoglio inferire delle artegliarie, che quan<lb></lb>to piu ſe laſſa la poluere diſperſa, & rara quella occupa piu della canna, cioè tal for<lb></lb>ma di poluere uien à eſſer piu longa, e pero piu tempo ui uuol ad eſſer totalmente con<lb></lb>ſumata dal fuoco, e per tanto li ſuoi effetti non ſaranno coſi uigoroſi. </s> <s id="s.000588">Concludeſi adun <lb></lb>que, che la poluere molto e molto calcata nel pezzo, ouer molto diſperſa e rara inde<lb></lb>biliſſe gli effetti di tel pezzo, e pero biſogna fondarſe nel termine di mezzo (come di <lb></lb>ſopra e detto) & non nelli iſtremi, cioe, che quella ſia non molto colcata, ne molto ra<lb></lb>ra.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſta uostra openione molto mi conſona.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000589">QVESITO DECIMO QVINTO FATTO DAL <lb></lb><emph type="italics"></emph>detto Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000590">PRIORE. Q<emph type="italics"></emph>ual è la cauſa che con un ſchioppo ſe tira piu rettamente, & piu <lb></lb>lontano de mira, che non ſe fa con uno archibuſo, et <expan abbr="tamẽ">tamen</expan> lo archibuſo fara mag <lb></lb>gior effetto, ouer paſſata m un commun tramite del ſehioppo.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uesto procede, <lb></lb>che le balle delli ar chibuſi debbono eſſer forſi piu groſſe di quelle di ſchioppi, & la<emph.end type="italics"></emph.end><pb pagenum="22" xlink:href="042/01/043.jpg"></pb><emph type="italics"></emph>grauita della balla offende aſſai piu della uelocita di quella, eſſenipi gratia eſſendo un <lb></lb>ſchioppo, che tiri di lontano retto tramite paſſa. </s> <s id="s.000591">400. con una balla di peſo di mezza <lb></lb>onza, & un archibuſo, che retto tramite tiri ſolamente paſſa. </s> <s id="s.000592">300. ma con una balla, <lb></lb>che peſiuna onza, hor dico, che in un tramite di. </s> <s id="s.000593">100. ouer. </s> <s id="s.000594">150. paſſa, lo archibuſo fa<lb></lb>ra maggior paſſata del ſchioppo, quantunque in tal luoco la balla del ſchioppo uada <lb></lb>piu ueloce per le ragioni adutte nella quarta propoſitione del primo libro della noſtra <lb></lb>noua ſcientia, di quella del archibuſo. </s> <s id="s.000595">Et pero eſſendo, come dice uoſtra ſignoria, di ra <lb></lb>gione la balla dello archibuſo debbeno eſſe piu groſſe, che quelle de ſchioppi.<emph.end type="italics"></emph.end> P. S<emph type="italics"></emph>en <lb></lb>za dubbio, che gli archibuſt portano generalmente maggior balla de ſchioppi, uero è, <lb></lb>che ſono alcune ſorte de ſchioppi, che portano balle alla equalita de alcuni archibuſt.<emph.end type="italics"></emph.end><lb></lb>N. M<emph type="italics"></emph>a quando fuſſe un ſchioppo, che portaſſe tanta balla, quanto che faceſſe un ar<lb></lb>chibuſo, & che tal ſchioppo tiraſſe piu rettamente, ouer piu lontano di mira, di quello <lb></lb>tal archibuſo, ſenza dubbio in <expan abbr="diſtãtie">diſtantie</expan> equale, lo ſchioppo fara maggior paſſata del ar <lb></lb>chibuſo.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſto è coſaraſoneuole, & basta per queſta ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000596">QVESITO DECIMOSESTO FATTO DAL <lb></lb><emph type="italics"></emph>detto Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000597">PRIORE. D<emph type="italics"></emph>onde procede la cauſa, che percuotendo con una artegliaria in <lb></lb>unanaue, ouer galia in mare, el pare che tal artegliaria faccia puoco effetto, o<lb></lb>uer paſſata reſpetto à quello che ſolita à far <expan abbr="tirãdo">tirando</expan> in una mur aglia, perche eſſendo co <lb></lb>me ſi ſame ſi ſa ogni naue, ouer galia di tabule di legname onde eſſendo due, ouer tre <lb></lb>naue uni appreſſo laltra, el pare, che tirando un pezzo groſſo in quelle, reſpetto à <lb></lb>quello, che faria tal pezzo in una groſſa muraglia, ragioneuolmente le doueria pene <lb></lb>trar tutte tre dabanda à banda con tutte le bagaglie che ritrouaſſe per quelle, per eſ<lb></lb>ſer ognicoſa di legname, & tamen rare uolte accade, che ne poſſa penetr ar una ſola da <lb></lb>banda à banda, anci la maggior parte delle uolte le balle reſtano nellanaue, ouer galia.<emph.end type="italics"></emph.end><lb></lb>N. E<emph type="italics"></emph>glie manifeſto per ragion naturale, che quella coſa, che piu impediſce il moto, <lb></lb>piu uien ſpenta, urtata, ouer offeſa dalla coſa mobile, ouer percotente per eſſer adun<lb></lb>que la muraglia una coſa ſtabile, & ſoda, & che piu impediſſe el moto della balla del<lb></lb>la artegliaria di quello fa una naue, ouer galia eſſendo quella in el mare, mobile, la qual <lb></lb>mobilita fa che la detta naue ouer galia conſente alquanto al moto, ouer alla percußio <lb></lb>ne della balla, per il che la balla non fa quel uigoroſo effecto, ouer paſſata, che faria ſe <lb></lb>tal naue, ouer galia fuſſe ben aſſettata in terra ferma, ſi come ſono le muraglie. </s> <s id="s.000598">Si che <lb></lb>per tal ragione, piu gagliardo effetto fauna artegliaria in una muraglia, ouer in una <lb></lb>altra coſa ferma e ſiſſa in terra ſoda, che non fa in una naue, ouer galia, nel mare mobi<lb></lb>le. </s> <s id="s.000599">Ma molto maggior effetto fara la detta artegliaria in una naue, ouer galia, che gli <lb></lb>uegna alincontro, di quello faria in una, che gli fuggiſſe dauanti, perche quella, che gli <lb></lb>uien alincontro uien contra al moto della balla, & pero la ballo debbe far maggior ef <lb></lb>fetto in quella, che non farta ſtando quella ferma in mare. </s> <s id="s.000600">Et quella, che gli fuggie da<lb></lb>uanti, molto piu ua conſentendo alla percußion della balla, di quello faria, ſe quella ſt<gap></gap>ſ <lb></lb>ſe in mare ſerma, & quteta.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>e ho inteſo benißimo.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/044.jpg"></pb> <p type="head"> <s id="s.000601">QVESITO DECIMOSETTIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000602">PRIORE. D<emph type="italics"></emph>iteme un poco, ſe per caſo in qualche improuiſo aſſalto ne ſuſſe <lb></lb>inchiodate le artegliarie, ſaria poßibile à ritrouar un modo, che fuſſe ſpediente <lb></lb>& preſto di poter ipſo facto, cioe de ſubito diſchiodar le dette artegliarie, dico de ſubi <lb></lb>co, perche moliti dicono ſaper far, & fanno certa acqua, ouer olio, qual ponendolo ſo<lb></lb>pra el ſoro inchiodato corode quel ferro talmente, che diſchiodano quel tal pezzo. <lb></lb></s> <s id="s.000603">Alcuni altri ho inteſo, che fanno el medeſimo con un trappano, cioe per el modo che u<lb></lb>ſano à farui il primo buſo, nondimeno cadauno di queſti modi uoleno tempo aſſai, & <lb></lb>maßime eſſendoui molto numero de pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>i da deſchiodare, & io uoria ritrouar un mo <lb></lb>do, ſe poßit el fuſſe, di poterle diſchiodar con cellerita, & preſtezza.<emph.end type="italics"></emph.end> N. </s> <s id="s.000604">A <emph type="italics"></emph>me mi <lb></lb>pare, che tal coſa ſe potria fare (ſe non me inganno) à recargare tutte le dette arteglia <lb></lb>ria, con balle alquanto ſcarſette, cioe, che non uadano molto ſerrate nel pezzo, & da <lb></lb>poi che ſono cargate, metterle à ſegno uerſo al luoco doue potria occorrer il biſogno, <lb></lb>cioe come proprio ſe faria, quando che loro non fuſſeno inchiodate, & dapoi farui una <lb></lb>ſementella di poluere nel fondo della <expan abbr="cãna">canna</expan>, che uada dalla bocca del pezzo, per fin alla <lb></lb>balla di cadauna artegliaria, & per non tirarle fruſtamente aſpettar la occaſtione, & <lb></lb>occorrendo la occaſione da tirarle, darui il ſuoco per la bocca, onde oltra che faranno <lb></lb>li ſuoi effetti ordinarij, tutte nel diſcargarſe penſo ſe diſchioderanno, & getteranno <lb></lb>fuora quel chiodo, ouer ponta di ferro con che furono inchiodate: & coſi facendo de <lb></lb>tal inchiodatura ſe uenira à non patirne alcun ſenistro ouer diſconzo.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>erto que <lb></lb>sto è bello, e molto ſpediente, & non credo, che ſi poteſſe ritrouar modo meglio di que <lb></lb>ſto, domente che nel diſcargarſe facciano questo effetto, che haueti detto di gettarne <lb></lb>quel chiodo, ouer ponta di ferro, con che furno inchiodate.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio lo git<lb></lb>taranno.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>t ſe per caſo alcuna non lo gettaſſe, per eſſcrui forſi piu fiſſamente po<lb></lb>sto delle altre, che rimedio ui ſi potria aggiongere.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>argarla, & tirarla un'al<lb></lb>tra uolta per el medeſimo modo, uero è che ui gettaſſe ſopra la inchiodatura un poco <lb></lb>di oglio caldißimo ſcaldando anchora prima el luoco doue è la inchiodatura con car<lb></lb>bon acceſo, poi con creda farui ſopra un uaſetto attorno el buſo, che ritenga quello olio <lb></lb>caldo, che ui ſi ponera, il che facendo el buco con quel ferro interpoſto, per la ſua cali<lb></lb>dita, ſorbiranno quello olio caldo, la qual coſa fara quel tal ferro piu lubricoſo ad uſci <lb></lb>re. </s> <s id="s.000605">Anchora ſe dapoi che ſi hauera poſta, & aſſettata la poluere nel mezzo (innanti <lb></lb>che ui ſe ponga la balla) ſara fatto uno buſo con una aſta nella detta poluere, el quale <lb></lb>penetri per fin in fondo della canna del ditto pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, cioe che uada à referire appreſ<lb></lb>ſo al detto buſo inchiodato, tal cautella <expan abbr="nõ">non</expan> ſara fora di propoſito in questo caſo: Et cre <lb></lb>do, che <34>ſta ſupplira ſenza operar <expan abbr="altramẽte">altramente</expan> olio caldo.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſto credo anchora <lb></lb>mi, perche nel diſcargarſe, la furia del fuoco troua tutte le comiſſure mal comeſſe, & <lb></lb>pero non credo che uiſta debiſogno à preparar la materia con olio caldo, ne fredo, al<lb></lb>tramente. </s> <s id="s.000606">Et perche credo ſta hora da'cena, non uoglio proccdiamo piu oltra, et pla<lb></lb>uenire, <expan abbr="nõ">non</expan> uoglio che piu parlamo della artegliaria, ma che intramo in qual che altra in <lb></lb>genioſa materia, perche circa alle coſe della artegliaria, io non ſo piu che <expan abbr="adimãdarui">adimandarui</expan>.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="23" xlink:href="042/01/045.jpg"></pb> <p type="head"> <s id="s.000607">QVESITO DECIM'OTTAVO FATTOMI <lb></lb><emph type="italics"></emph>dal Signor Iacomo de Achaial' Anno.<emph.end type="italics"></emph.end> 1542.</s> </p> <p type="head"> <s id="s.000608">I<emph type="italics"></emph>n Venetia qual ui <expan abbr="uẽne">uenne</expan> alla Senſa.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000609">SIGNOR IACOMO. I<emph type="italics"></emph>o ho uiſto per iſperientia che tirando con una Arte<lb></lb>gliaria in una muraglia standoui molto propinquo non ui fa coſi gagliardo effet<lb></lb>to, ouer paſſata quanto fa à starui alquanto piu di lontano, et per leragioni da uoi aduc<lb></lb>te nella uoſtra nuoua ſcientia, doueria ſeguir tutto al contrario, perche la balla tirata <lb></lb>da ogni artegliaria quanto piu ſe allontana dalla bocca del pezzo tanto piu ſe allenta di <lb></lb>uelocita, come uoi approuate, cioe che quella ua men ueloce, & doue ua men ueloce, iui <lb></lb>fa menor effetto. </s> <s id="s.000610">Adunque quanto piu ſi sta propinquo al luoco doue ſe tira tanto mag <lb></lb>gior effetto doueria far tal balla nel luoco doue percuote, di quello faria ſtandoui piu <lb></lb>lontano, perche tal balla feriſſe di moto piu ueloce, & tamen, come diſopra ho detto. <lb></lb></s> <s id="s.000611">Io trouo con la iſperientia riuſcir tutto al contrario, è per tanto ui adimando la cauſa <lb></lb>di queſto inconueniente.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er ben riſoluere queſto dubbio biſogna notare qual<lb></lb>mente ogni coſa moſſa moue ſempre qualche altra coſa. </s> <s id="s.000612">Et pero quando che la balla <lb></lb>uien moueſta da quella uentoſita cauſata dal ſalnitrio, la medeſima balla inſteme con la <lb></lb>medeſima uentoſita, moue anchora in quel medeſimo iſtante quel aere à ſe conterminale <lb></lb>nella canna, & quel medeſimo aere moue & ſpinge l'altro aere à ſe conſequentemente <lb></lb>conterminale, & coſi l'altro ſpinge l'altro talmente che la detta balla uien à ſpingere, <lb></lb>& à mandare auanti di ſe una gran quantita di aere di forma molto longa, la qual for<lb></lb>ma, quantunque la ſia de aere, per uigor del moto, tal aere ſumme grauita in ſe talmen<lb></lb>te, che per un certo poco ditempo ua penetrando l'altro aere che per iluiaggio ſuo ri<lb></lb>troua, come ſe fuſſe quaſi un trauo di legno, ma tal ſuo penetrar non procede molto <expan abbr="lõ">lom</expan> <lb></lb>tano, perche tal figura aerea, per un poco di tempo, ouer ſpacio procede auanti della <lb></lb>balla, ma perche la balla è di materia graue piu facilmente penetra lo aere, di quello fa <lb></lb>la detta figura aerea, & pero la balla uien a eſſer di moto molto piu uelocißima della <lb></lb>detta figura aerea, & per tanto in breuißimo tempo la detta balla uien à laſciarſe de <lb></lb>drio da ſe quella tal fignra aerea (che prima andaua auanti diſe) hor per tornare al no <lb></lb>ſtro primo propoſito, quando che con una artegliariaſe tira in una coſa, che kiſia mol<lb></lb>to propinquißima, quella figura aerea, che è ſpinta auanti della balla detta di ſopra) <lb></lb>per cuotera prima in quella coſa doue ſe tira, dellaballa, & per non eſſer tal figura ae<lb></lb>rea atta à penetrar quella coſa, eglie neceſſario, che quella prima, & iſtrema parte di <lb></lb>tal figura, che prima percuote, à refflettere, & ritornar in drio, in contra alla mede<lb></lb>ſima figura, & alla balla, che ſeguita (maßime quando tal tiro ſia tirato con il pezzo <lb></lb>aliuellato) la qual reffleßione (continua) nell'aggiongere della balla con il reſiduo di tal <lb></lb>figura aerea che è contigua alla balla fanno uno contraſto grandißimo, cioe il reſiduo <lb></lb>della figura aereauol proceder auanti, & non puo parte, per non eſſer atto (come di <lb></lb>ſopra è detto) à penetrar quella coſa doue ſe tira, & parte par cauſa di quell'altra par <lb></lb>te che è sforzata à ritornar in drio, la qual combustione da un grande impedimento al <lb></lb>moto della balla, talmente che la balla non puo far sutto quello effetto, che doueria fa<lb></lb>re. </s> <s id="s.000613">Ma quando che il luoco doue ſe tira è d'una mediocre diſtantia, la bala per la ſua <pb xlink:href="042/01/046.jpg"></pb>uelocita laſſa de drio daſe la detta figura aerea, & ſe non tutta almeno la maggior par <lb></lb>te, talmente che in tal luoco di mediocre distantia la balla ui fara maggior effetto di <lb></lb>quello faria nel luoco piu propinquo, perche tal balla nel fare il ſuo effetto non ritroua <lb></lb>tanto impedimento di reffleßione ne combuſtion di aere.<emph.end type="italics"></emph.end> S. IACO MO. Q<emph type="italics"></emph>ueſtauo <lb></lb>straragione ne conſona molto, & comprendo che non puo procedere da altra coſa.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000614">QVESITO DECIMONONO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Iacomo <lb></lb>de Achaia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000615">SIGNOR IACOMO. M<emph type="italics"></emph>a un'altro dubbio uorria che me chiareſti, il qual <lb></lb>è queſto, ſe per ſtar troppo propinquo con la artegliaria alla coſa doue ſe tira, gli <lb></lb>effetti di tal artegliaria, non ſono coſi uigoroſi quanto ſariano in una mediocre diſtan<lb></lb>tia, per le ragioni per uoi adutte, è per le ſperientie per me fatte, ſimilmente per ſtar<lb></lb>ui troppo di lontano (per commune opinione) ſeguitail medeſimo, cioe che per ſtarui <lb></lb>molto di lontano non fa coſi gagliardo effetto, nella coſa doue percuote quanto faria <lb></lb>in una mediocre diſtantia, hor ui adimando doue ſe potria con ragione determinare il <lb></lb>luoco doue che la balla di tal artegliaria faria il piu gagliardo, ouer uigoroſo effetto, <lb></lb>che far poteſſe in tutto il tranſito, ouer uiaggio che far debbe, ouer che faria, quella tal <lb></lb>balla, non trouando alcuno impedimento.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n quello iſtante che la balla peruiene, <lb></lb>ouer aggionge nella iſtrema parte di quella figura aerea (detta nel precedente queſi<lb></lb>to) trouando in tal luoco un reſistente, in quel tal luoco ui faria maggiore, ouer pue <lb></lb>uigoroſo effetto, che in qualunque altro luoco, perche ſe tal reſiſtente fuſſe piu in uer<lb></lb>ſo la bocca del pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, in quel tale reſiſtente prima ui percuoteria la detta figura aerea <lb></lb>che la balla (come nel precedente queſito fu detto) & dapoi la per cußione immediate <lb></lb>refflettaria in drio incontra alla medeſima figura aerea, & alla balla, ouiando alquan<lb></lb>to il moto di quella (come fu detto nel precedente queſito.) Et ſe tal reſiſtente ſara piu <lb></lb>lontano di tal luoco, ſubito che la balla uſciſſe totalmente di quella figura aerea, cioe la <lb></lb>ſciando quella de drio da ſe immediate ritroua lo aere quaſi quieto, onde tal balla uiene <lb></lb>ad hauer alquanto piu difficulta à penetr ar tal aere quieto, che non haueua à penetra<lb></lb>re quello della detta figura aerea, per eſſer quello di detta figura medeſimamente in <lb></lb>corſo, & uerſo il medeſimo luoco doue ua la balla. </s> <s id="s.000616">Et per tanto uſcita la balla di tal fi<lb></lb>gura continuamente ui andara mancando il uigore, & tanto piu quanto piu ſe andara <lb></lb>allontanando, e pero conſequentemente tanto piu deboli fara li ſuoi affetti ſi che per <lb></lb>queſte due ragioni, la detta balla doueria far piu gagliardo effetto in un reſitente tro<lb></lb>uando quello preciſamente nello uſcire della iſtremita della ſopradetta figura aerea, <lb></lb>che in qualunque altro luoco piu lontano, ouer propinquo.<emph.end type="italics"></emph.end> S.I. E<emph type="italics"></emph>glie da credere che <lb></lb>ſia coſi, perche in effetto comprendo che in tal luoco la balla feriſſe ſenza impedimen<lb></lb>to direſſleßione de aere, ne per fina allhora non è stata impedita da aere quieto, come <lb></lb>ſaria impedita per lo auenire ſe procedeſſe piu oltra.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="24" xlink:href="042/01/047.jpg"></pb> <p type="head"> <s id="s.000617">QVESITO VIGESIMO FATTO DA VNO <lb></lb>C<emph type="italics"></emph>apo de Bombardieri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000618">BOMBARDIERO. P<emph type="italics"></emph>erche cauſa credete uoiche ſi metta quelli dui ſtrope <lb></lb>paioni de ſieno, ouer de ſtoppa, ogni uolta che ſi carga una artegliaria, cioe uno <lb></lb>dapoi che ui ſe ha poſta la poluere, cioe auanti che ui ſi metta la balla, & l'altro dapoi <lb></lb>che ui ſi ha poſta la detta balla.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>ertamente che io non ſapeua queſta coſa, che uoi <lb></lb>me haueti detto, cioe che auanti che ſi metta la balla nel pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o ui ſi metta uno ſtrop<lb></lb>paion de fieno, ouer de ſtoppa, & coſi un'altro dapoi che ui ſe ha poſta la balla, ma eſ<lb></lb>ſendo coſi (come al preſente credo) à me mi pare, che piu ſe conuegnaria che io ui adi<lb></lb>mandaſſe à uoi la cauſa di tal cautella, cha che uoi l'adimandaſti à me, perche ſe uoi uſa <lb></lb>ti di far tal coſa ogniuolta che uoi cargati un pezzo, uoi douereſti pur ſapere à che fin <lb></lb>il fati, perche l'arte biſogna che la imiti lanatura in questo, che tutte le coſe, che quella <lb></lb>fa, le faccia à qualche fine.<emph.end type="italics"></emph.end> B. M<emph type="italics"></emph>aue dirò, io non ho grammatica, & ſe pur uſo di far <lb></lb>queſta coſa, lo faccio, perche ho uiſto che tutti glialtrilo fanno.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto ſi coſtu<lb></lb>ma in molti, & in molte arte, ſi mecanice come liberale, e pero non me mar auiglio di <lb></lb>uoi, ne manco uibiaſimo, anci ue laudo à ricercar la cauſa di quelle coſe che ſi coſtuma <lb></lb>difare nell'arte uostra, ilche doueria far ogniuno, perche il ſapere non è altro che co<lb></lb>noſcere la coſa per la cauſa, hor tornando al noſtro propoſito, il primo ſtroppaione, <lb></lb>cioe quello che diceti che ſi mette drio alla poluere, auanti che ui ſe metta la balla, non <lb></lb>poſſo penſare che ui ſi metta per altro, ſaluo che per ſpazzar, & condure tutta quella <lb></lb>poluere (che nel cargare il pezzo fuſſe rimasta per la canna) inſieme con l'altra, & à <lb></lb>tenerla dapoi unita al ſuo luoco, dou'è ſtata aſſettata. </s> <s id="s.000619">Ma il ſecondo ſtroppaione, cioe <lb></lb>quello che uoi diceti che metteti drio alla balla, biſogna penſare, che colui, che prima co <lb></lb>mincio à porui tal stroppaione fu aſtretto da qualche neceßita, la qual neceßita non ui <lb></lb>puo eſſer occorſa, ſaluo che lui doueua eſſere in qualche luoco doue gli conuenia tirare <lb></lb>albaſſo, cioe tirar de ſuſo in giuſo, la qual coſa <expan abbr="uolẽdola">uolendola</expan> eſſequire ſenza porui tal ſtrop<lb></lb>paione, nell'abbaſſare il pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o dauanti per metterlo à ſegno, la balla ſaria uſcita del <lb></lb>pezzo, e pero accio che tal balla non uſcideſſe, fu sforzato à porui tal ſtroppione.<emph.end type="italics"></emph.end> B. <lb></lb>Q<emph type="italics"></emph>ueſte uoſtre ragioni ſono bonißime, ma e uedo che tal stroppaione uc lo ponemo an<lb></lb>chora quando che uolemo tirare all'alta, cioe di giuſo in ſuſo, doue non è quel pericolo <lb></lb>che diceti, cioe che la balla uſciſca del pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o nel metterlo à ſegno, e pero uorria ſapere <lb></lb>la cauſa di questo.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a cauſa di queſto è la ignorantia, perche ſe uoi ſapeſti la cauſa <lb></lb>di tal attione, uoi non ui ponereſti tal ſtroppaione, ſaluo quando che la neceßita, accio <lb></lb>ue aſtringeſſe.<emph.end type="italics"></emph.end> B. C<emph type="italics"></emph>ertamente comprendo che uoi diceti troppo il uero.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000620">QVESITO VIGESIMOPRIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Capo de Bombardieri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000621">BOMBARDIERO. V<emph type="italics"></emph>euoglio raccontar una nouella, della quale ſoncerto <lb></lb>ue ne marauigliarcti molto, la qual è queſta. </s> <s id="s.000622">Rurouandomi una uolta à fare una <lb></lb>ba<gap></gap>la, & dapoi moluuri, accadete che per uno certo diſconcio, il pezzo nel di-<pb xlink:href="042/01/048.jpg"></pb>ſcargarſe ſe elleu<gap></gap> talmente che andete con la bocca in terra, & in tanto che io tende<lb></lb>ua à ragunar facchini con ſtanghe per ritornar tal pezzo al ſuo luoco un cagnolino <lb></lb><gap></gap>olſe andar (come accade) à naſare la bocca di tal pezzo, & ſubito che il detto cagno<lb></lb>lino fu gionto alla bocca di tal pezzo, immediate lo detto pezzo lo tiro dentro della <lb></lb>canna, la qual coſa uista dalli circoſtanti, alcuni corſe per aiutare il detto cagnolino, & <lb></lb>lo trouorno eſſer stato tirato quaſt in capo della canna, cioe quaſt in capo del uacuo del <lb></lb>la canna di tal pezzo, pur lo cauorno, come morto, non ſo quello che dapoi ſeguiſſe <lb></lb>de lui, ma credo che moriſſe, hor cheue pare di queſto.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>i queſta coſa non <lb></lb>me ne mar auiglio, perche un pezzo per il molto tirar, diuenta caldo, & per tal cal<lb></lb>dezza (come fu detto nel quinto queſito) quel tal pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o ſi fa attrattiuo, cioe alla ſimi<lb></lb>litudine di una uentoſa, quando ui è arſa di dentro la stoppa.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>pero non è marauiglia, <lb></lb>che ſorbeſſe ſuſo quel tal cagnolino, anci credo, che quando un tal pezzo è molto caldo <lb></lb>ſeuno ui andaſſe ad appoggiar la pancia nuda alla bocca di quello, colui in tal luoco ui <lb></lb>reſtaria talmente appreſo, che con difficulta ui ſe diſtaccaria. </s> <s id="s.000623">Et molto piu attrattiuo <lb></lb>tal pezzo diuentaria in tal caſo, che ui atturaſſe, ouer aſtroppaſſe quel buſetto doue ſe <lb></lb>gli da il fuoco.<emph.end type="italics"></emph.end> B. Q<emph type="italics"></emph>ueſta uoſtra ragione mi conſona molto.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000624">QVESITO VIGESIMOSECVNDO FATTO <lb></lb><emph type="italics"></emph>da uno Gettador di Artegliaria.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000625">GETTADORE. D<emph type="italics"></emph>onde procede che di tutte le artegliarie che creppano, la <lb></lb>maggior parte creppano, de drio doue ſta la poluere, ouer alla bocca, & rare <lb></lb>uolte nel meggio, uero è che del creppar nella parte de drio doue ſta la poluere non me <lb></lb>ne marauiglio, perche in tal luoco la poluere ui moſtra ogni ſua poſſanza, ma del crep <lb></lb>pare in bocca ne ſtago molto ammir atiuo, perche à me mi pare che piu preſto doueria <lb></lb>creppar nel meggio della canna che alla bocca, perche la eſſalatione del ſalmitrio alla <lb></lb>bocca uitroua luoco largo da sborare, coſa che non troua coſi di dentro nel meggio del <lb></lb>la canna.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>irca à questa coſa biſogna penſare, che ogni mouente puo riceuere <lb></lb>due difficulta, ouer nocumenti nel mouere un corpo rotondo graue che stia ripoſato é <lb></lb>quieto nel mouerlo per traſuerſo la prima è à mouerlo nel principio, perche dapoi che <lb></lb>moſſo ſia non ui ha tanta difſiculta à mantenerlo continuamente in moto, l'altra diffi<lb></lb>culta che puo riceuere tal mouente è queſta, che dapoi che ha moueſto quel tal corpo <lb></lb>rotondo, e graue, e quel redutto in moto continuo, ouer ſucceßiuo per trauerſo ritro<lb></lb>uando poialcuno repentino oſtacolo, ouer, teſiſtente à tal moto, tal mouente riceue no <lb></lb>cumento aſſai. </s> <s id="s.000626">Et per tanto dico, che à quella eſſalatione di uento cauſata dal ſalnitrio, <lb></lb>dapoi che e generata nel pezzo ui occorre due gran difficulta, la prima è à mouere co <lb></lb>ſi repentmamente la balla ripoſſante quieta, e pero in tal accidente ſubitano trouandoſi <lb></lb>il pezzo in tal luoco debole di metallo, ouer di metallo, nel getto mal conſolidato, ouer <lb></lb>piu ſottile da una banda che dall'altra, facilmente in tal luoco creppa, ma ſe per caſo il <lb></lb>metallo di tal luoco reſiſta gagliardamente tanto che tal eſſalatione moue la balla, moſ<lb></lb>ſa che ſia dal ſuo luoco, non ui è piu pericolo in tal parte di creppare (ſaluo ſe à tal balla <lb></lb>non ui occorreſſe dentro dal pezzo qualche ſtrano accidente (come in fine ſe dira,)<emph.end type="italics"></emph.end><pb pagenum="25" xlink:href="042/01/049.jpg"></pb><emph type="italics"></emph>perche ſubito, che la balla ſia in moto con facilita tal eſſalatione ue landaria mantenen <lb></lb>do, non occorrendoui altro impedimento, ma ſubito, come la balla aggionge alla bocca <lb></lb>del pezzo iui truoua tutto lo aere eſtrinſico: el quale, quanto che <expan abbr="cõ">com</expan> piu maggiore pre <lb></lb>stezza uien la balla inſieme con la detta eſſalatione, che la ſpinge ad aſſaltarlo <expan abbr="tãto">tanto</expan> piu <lb></lb>unitamente, et con maggiore uigoroſita ui ſi oppone gagliardamente all'incontro, per <lb></lb>reſiſtere à tal moto ſubitano, onde in tal luoco ui ſe uiene à cauſare un'altra difficulta, <lb></lb>ouer riſſa fra la eſſalatione intrinſica (che ſpinge la balla) & laere eſtrinſico, cioe lun <lb></lb>uoria uſcire, & laltro non uoria che uſcideſſe, pur ſinalmente lo intrinſico per eſſer di <lb></lb>maggior poſſanza, e uigore uſciſſe con uittoria rompendo, & ſpezzando el ſuo nemi <lb></lb>co, nel quale rompimento ſe cauſa quel coſi gran ſuono, perche ogni ſuono dalli Sapien <lb></lb>tiſe diffiniſſe non eſſer altro, che la percußione fatta de dui corpi inanimati, inſieme, e <lb></lb>pero in queſto caſo non puo procedere da altro, che dalla percußione fatta da quella <lb></lb>eſſalatione, cauſata dentro dal pezzo, con lo acre eſtrinſico, trouandoſe <expan abbr="adũque">adunque</expan> la boc <lb></lb>ca del pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o quaſi nel mezzo di tal abbattimento, uiene à patire grandamente in ge<lb></lb>nerale, e queſta è la cauſa, che in tal luoco el pezzo non hauendoui la ſua conueniente <lb></lb>groſſezza, ouer eſſendoui qualche occulto diffetto cauſato nel gettarlo, <expan abbr="facilmẽte">facilmente</expan> cre <lb></lb>pa.<emph.end type="italics"></emph.end> G. Q<emph type="italics"></emph>ueſte due uoſtre ragioni molto me quadrano, ma reſta un'altro dubbio, el <lb></lb>quale è queſto, che quantunque la maggior parte delle uolte creppano (come di ſopra è <lb></lb>detto) nella parte de drio doue ſta la poluere, ouer nella bocca, pur alcune uolte crep<lb></lb>pano anchora nel mezzo, e pero haria à caro, che me aßignaſti la cauſa di queſto.<emph.end type="italics"></emph.end> N. <lb></lb>L<emph type="italics"></emph>e due cauſe di ſopra per me aßignate, ſono cauſe generale, che ſempre per ordinario <lb></lb>fanno patire generalmente ogni ſpecie di pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o nelli preditti dui luochi piu che in al<lb></lb>tro luoco, ma oltra le dette cauſe generale, biſogna penſare, & credere, che per acci<lb></lb>dente ue ne poſſa occorrere molte altre, le quale non ſolamente puono <expan abbr="augumẽtar">augumentar</expan> paſ <lb></lb>ſion al pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o nelli medemi dui luochi, cioe de drio, & nella bocca, ma anchora nel mez <lb></lb>zo della canna, eſſempigratia, ſe per mala ſorte la balla nel ſcorrere per la canna tro<lb></lb>uaſſe qualche piccìol pieretta in ſorma di cuneo, ouer altro corpetto duro, & che per <lb></lb>ſorte la balla ui ſcorreſſe per di ſopra tal pieretta, ouer corpetto interromperia neceſ <lb></lb>ſariamente el moto, ouer corſo della balla, per il che la balla ſariasforzata in tal luoco <lb></lb>à far de due coſe luna, ò à intertener ſi (& queſto ſeguiria quando la balla andaſſe mol<lb></lb>to ſerrata nel pezzo) ouer tal balla nel paſſarui ſopra faceße un ſalteto, & questo po<lb></lb>tria far, quando la canna del pezzo fuſſe alquanto piu larga della groſſezza della bal <lb></lb>la, ſe per caſo adunque la balla fuße intertenuta da tal pieretta, ouer corpetto in for<lb></lb>ma de cuneo, per tal intertenimento (eſſendo gaiardo) ſariasforzato tal pezzo di cre <lb></lb>pare, & ſe tal cuneo fuſſe trouato dalla balla nel principio del ſuo moto, tal pezzo cre <lb></lb>paria pur nella parte doue ſta la poluere, & ſe tal cuneo fuſſe trouato nel mezzo della <lb></lb>canna, & nel mezzo della canna <expan abbr="naturalmẽte">naturalmente</expan> crepparia, & ſe fuſſe trouato appreßo <lb></lb>alla bocca, & nella bocca crepperia. </s> <s id="s.000627">Maſe per caſo la balla hauera luoco di poßer paſ <lb></lb>ſar di ſopra à tal corpetto, nel paßarui (come di ſopra dißi neceßariamente fara un ſal <lb></lb>tetto, nel qual ſaltetto percottera nella ſummita della canna, & rebattera poi nel fon<lb></lb>do, la qual percußione, & repercußion, non puo eßer tanto debile, che non ſia atta à <lb></lb>fa creppare el pezzo in tal luoco, et queſta è una delle cauſe accidentale, che è atta à<emph.end type="italics"></emph.end><pb xlink:href="042/01/050.jpg"></pb><emph type="italics"></emph>far creppar el pezzo quaſi in ogni luoco. </s> <s id="s.000628">Anchora quando che una balla non è egual <lb></lb>mente tonda, ouer che haueſſe qualche parte piu elleuata in un luoco, che in un'altro, <lb></lb>potria alle uolte far accadere un tal inconueniente uerſo la bocca del pezzo. </s> <s id="s.000629">Anchora <lb></lb>quando, che el pezzo è molto caldo per el lungo tirare, è molto piu atto al crep<lb></lb>pare, che eſſendo freddo (eſſendo pero di bronzo) perche el bronzo è di tal na<lb></lb>tura, che per il caldo ſe fa frangibile. </s> <s id="s.000630">Anchora un pezzo quanto piu tira in alto <lb></lb>tanto piu patiſſe di quello fa tirandolo in piano. </s> <s id="s.000631">Anchora nel gettare il pezzo, ui ſe <lb></lb>puo cauſar alcune comeſſure, & cauernoſita parte occulte al ſenſo, & parte paleſe: ma <lb></lb>per eſſer di dentro dal pezzo non ſi poſſono uedere, le quale fanno piu debile in tal luo <lb></lb>co el pezzo di quello ui ſi conuiene, e per queſto alle uolte ſenza altro particolar acci<lb></lb>dente, in talluoco creppa, ò ſia de drio, ouer dauanti, ouer in mezzo. </s> <s id="s.000632">Alcuna fiata an<lb></lb>chora el foro del pezzo <expan abbr="nõ">non</expan> paſſa preciſamente per mezzo dil mettallo, ma tende piu <lb></lb>da una banda, che dall'altra: per il che il mettallo uien à restare da una banda piu ſotti <lb></lb>le, & dall'altra piu groſſo del ſuo douere, e per tanto da quella banda doue che el met <lb></lb>tallo è piu ſottile, et debile del ſuo douere el pezzo alle uolte creppa, et questo è quan<lb></lb>to che alle cauſe del creppare, uiſo dire<emph.end type="italics"></emph.end>, G. V<emph type="italics"></emph>oime haueti largamenta di mei dub<lb></lb>bij ſatisfatto.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000633">QVESITO VIGESIMOTERZO FATTO DA <lb></lb>M. A<emph type="italics"></emph>lberghetto di Alberghetti gettadore de artegliaria.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000634"><emph type="italics"></emph>l'anno. </s> <s id="s.000635">1545. adi Aprile. </s> <s id="s.000636">In Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000637">ALBER GHETTO. S<emph type="italics"></emph>aria poßibel di poter ſapere, de una artegliaria noua <lb></lb>uamente incaſſata, ouer fornita, & non mai tirata ſe quella tirara li ſuoi tirirct <lb></lb>ti, ouer coſteri, ouer in ſgalembro, ſenza tirarla altramente.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uesto uostro que <lb></lb>ſito in ſoſtantia non uuol dir altro, che ſapere conoſcere ſe el foro di tal pezzo giace <lb></lb>rettamente nel me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o del mettallo, ouer non, & non giacendo in mezzo del detto met <lb></lb>tallo ſapere determinare in qual uerſo pende tal foro: la qual coſa non ho per difficile, <lb></lb>& conſidero che eglie una coſa, che per molte uie ſe potria inuestigare, & ſapere: ma <lb></lb>à uoler dare un modo, che ſia iſpediente e facile, biſogneria penſarui alquanto.<emph.end type="italics"></emph.end> A. P<emph type="italics"></emph><expan abbr="ẽ">em</expan> <lb></lb>ſatigli un poco, perche ho addimandato questo dubbio à molti, che fanno profeßione <lb></lb>de ingegno, & non ho ritrouato alcun, che me habbia ſaputo dar reſolutione.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o <lb></lb>ho penſato ſopra queſta materia, & ritrouo in effetto tal coſa poterſi inueſtigar per <lb></lb>piu uie: ma à uolerlo ſapere con una coſa ſpediente, et di poco artiſicio el ſi die tuor due <lb></lb>aſte, ouer dui baſtoni drittißimi, ouer due cantinelle, ouer liſte ben pianate, & egual<lb></lb>mente larghe, longhe quanto che è la canna de tal pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & anchora uno brazzo di <lb></lb>piu, & in quel brazzo di piu metterui, & inchiodar ui dui trauerſi longhi quanto che <lb></lb>è la mitta della culatta del pezzo uel circa (e nanti piu che meno) & lontani luno da <lb></lb>l'altro circa un bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, accio ſiano piu atti à conſeruar li dette due aſte, ouer canti<lb></lb>nelle, ouer liſte egualmente diſtante, e dapoi ficare luna di quelle aſte, ouer liſte nella <lb></lb>canna, ouero foro de tal pezzo, & laltra andara de fuora uia. </s> <s id="s.000638">Et uolendo ſapere ſe <lb></lb>tal pezzo è piu groſſo di mettallo in un luoco, che in un'altro, procederemo in queſto<emph.end type="italics"></emph.end><pb pagenum="26" xlink:href="042/01/051.jpg"></pb><emph type="italics"></emph>modo. </s> <s id="s.000639">La aſta, che ua per dentro uia prima la diſtendaremo, & giuſtaremo rettamen <lb></lb>te per la parte ſuperiore del uacuo de detta canna, & fatto queſto miſuraremo, ouer <lb></lb>che faremo miſurare ſottilmente quanto che ſara diſtante dal mettallo la iſtrema par<lb></lb>te, cioe il capo di quella asta, ouer liſta, che procede de fuora uia, fatto queſto el ſi de uol <lb></lb>tar alquanto dalla banda del detto uacuo della canna la detta aſta, ouer liſta, che ua per <lb></lb>dentro, cioe mutarui alquanto luoco, & in queſto ſecondo luoco far come primà, cioe <lb></lb>far guardare, & miſurare con diligentia quanto che ſara diſtante dal mettallo la detta <lb></lb>eſtrema parte, ouer capo di quella aſta, ouer liſta, che procede de fuora uia, & ſe in que <lb></lb>ſto ſecondo luoco lui ſara preciſamente tanto lontano dal mettallo, quanto che eranel<lb></lb>la prima poſitione, ſe potra concluder el mettallo eſſer nelli detti dui luochi egualmen <lb></lb>te groſſo, maſe ſara piu lontano, ſe potra concludere in queſto ſecondo luoco eſſerui <lb></lb>piu ſottile el mettnllo, che nel primo, & tanto piu ſottile, quanto che la detta lontanan <lb></lb>za dal detto mettallo in queſta ſeconda poſitione ſara maggiore della prima. </s> <s id="s.000640">Et ſimel<lb></lb>mente, ſe per caſo in queſta ſeconda poſitione el detto capo della detta aſta, ouer liſta ſa <lb></lb>ra piu propinquo al mettallo della prima, ſeguira tutto al contrario, cioe, che in queſto <lb></lb>ſecondo luoco ui ſara piu groſſo el mettollo, che nel primo, & con tal ordine proceden <lb></lb>do de in parte in parte, ouer de banda in banda d'intorno à tutto el pezzo con tal eui<lb></lb>dentiaſe conoſcera ſel detto foro ſara preciſamente, ouer rettamente in me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o del <lb></lb>mettallo, ouer non, perche ſel mettallo ſe trouara egualmente groſſo, ſe potra conclude <lb></lb>re tal foro eſſer rettamente in mezzo del mettallo, & tirara etiam li ſuoi tiri retta<lb></lb>mente, ſecondo la <expan abbr="apparẽtia">apparentia</expan> di tutto el pezzo: & ſe per caſo ſe trouara eſſer piu groſ <lb></lb>ſo e<gap></gap> mettallo da una banda, che dall'altra, ſe potra concludere, tal foro non eſſer retta <lb></lb>mente in mezzo del mettallo, & conſequentemente non tirara li ſuoi tiri retti, ſecon<lb></lb>do la apparentia de tutto el pezzo: ma li tirara ſempre pendenti, ouer obliqui uerſo à <lb></lb>quella banda doue che ſar a piu groſſo el mettallo, cioe ſi tal groſſe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a ſara dalla ban<lb></lb>da deſtra lui tirara coſtero uerſo lv medeſima parte, ouer banda deſtra, & è conuerſo: <lb></lb>& ſe tal groſſezza ſara in ſgalembro poniamo fra la parte, ouer banda deſtra, & la <lb></lb>parte ſuprema del pezzo luitirara <expan abbr="medeſimamẽte">medeſimamente</expan> li detti ſuoitiri in ſgalembro, cioe <lb></lb>obliqui, ouer <expan abbr="pẽdẽtiiſuſo">pendentiiſuſo</expan>: ma uerſo la medema <expan abbr="bãda">banda</expan> doue è tal groſſezza, et coſi ſi deb <lb></lb>be <expan abbr="intẽder">intender</expan>, et <expan abbr="cõcludere">concludere</expan> in qual ſi uoglia <expan abbr="bãda">banda</expan>, che fuſſe tal maggior groſſezza di met <lb></lb>tallo. </s> <s id="s.000641">Et p eßer meglio inteſo ſotto breuita <expan abbr="põgo">pongo</expan> p <expan abbr="eßẽpio">eßempio</expan> figurale, che ſialo ſotto ſcrit <lb></lb>to pezzo di artegliaria, et che in quello uogliamo inueſtigare <34>llo, che di ſopra fu pro <lb></lb>poſto, cioe ſelſuo foro, ouer uacuo della <expan abbr="cãna">canna</expan> giace <expan abbr="rettamẽte">rettamente</expan> in mezzo dil mettallo, <lb></lb>hor p uoler inueſtigar tal coſa, dico, che el ſi die pigliar due aſte dritte, et eguale, ouer <lb></lb>due liſtette, come ſono le due. </s> <s id="s.000642">a.b. &. </s> <s id="s.000643">c.d. & con dui trauerſi daun capo, ouer ſopra un <lb></lb>brazzo de tabula inchiodaruele, che ſtiano <expan abbr="equidiſtãte">equidiſtante</expan>, et <expan abbr="lõtane">lontane</expan> luna dallaltra <expan abbr="alquãto">alquanto</expan> <lb></lb>piu di <34>llo, che é la mitta della groſſe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a di tutto el pezzo nella parte de drio, et <expan abbr="lõghe">longhe</expan> <lb></lb><expan abbr="tãto">tanto</expan> piu del uacuo della <expan abbr="cãna">canna</expan> di tal pezzo, <expan abbr="quãto">quanto</expan> che biſogna per mettere in li dui tra <lb></lb>uerſi, ouer tabula, et dapoi cazzar luna de dette aſte, ouer liſte (poniamo la. </s> <s id="s.000644">d.c.) p il <lb></lb>ſoro, ouer uacuo della canna, talmente che stia uniuerſalmente per longo contingente <lb></lb>con la parte ſuperiore del foro, ouer uacuo de detta canna, come in queſta prima figu<lb></lb>ra appare, e dapoi miſurare, ouer far miſurar ſottilmente la <expan abbr="diſtãtia">diſtantia</expan>, che è dal <expan abbr="põto">ponto</expan>. </s> <s id="s.000645">a.<emph.end type="italics"></emph.end><pb xlink:href="042/01/052.jpg"></pb><figure id="id.042.01.052.1.jpg" xlink:href="042/01/052/1.jpg"></figure><lb></lb><emph type="italics"></emph>(capo de laſta, ouer liſta) al mettallo de tal pezzo in tal luoco, & poniamo che tal di<lb></lb>ſtantia ſia preciſe quanto, che è la lineetta. </s> <s id="s.000646">e. & fatto queſto, el ſi de tramutar tai aſte, <lb></lb>ouer liſte in uno altro luoco, ouer banda di tal pezzo, hor traſmutamola (per far la dif <lb></lb>ferentia piu ſenſibile) nella parte oppoſita, come in queſta altra figura appare, et coſi <lb></lb>in tal luoco miſuraremo pur (ouer faremo miſur are) in tal luoco la distantia, che ſa<lb></lb>ra dal medeſimo ponto. </s> <s id="s.000647">a. (capo de lasta) al pezzo ouer mettallo, la qual diſtantia ſup <lb></lb>ponamo, che la ſta quanto e la linea f. hor dico, che ſe per caſo la linea. </s> <s id="s.000648">f. fuſſe ſtata e<lb></lb>quale alla linea. </s> <s id="s.000649">e. el mettallo di tal pezzo ſaria stato equalmente groſſo ſi de ſopra, co <lb></lb>me di ſotto di tal pezzo: ma perche in questo caſo ſenſibelmente trouamo la linea. </s> <s id="s.000650">f.<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.052.2.jpg" xlink:href="042/01/052/2.jpg"></figure><lb></lb><emph type="italics"></emph>eſſer molto maggiore della linea. </s> <s id="s.000651">e. e per tanto concluderemo eſſer molto piu groſſo el <lb></lb>mettallo diſopra, che di ſotto in tal pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o, & tanto piu groſſo, quanto che la linea. </s> <s id="s.000652">f. <lb></lb>ſara piu longa della linea. </s> <s id="s.000653">e. & contal ordine, e modo ſe die procedere dalla banda de<lb></lb>ſtra, & dalla ſiniſtra etiam in tutte le altre parte, ouer bande a torno a torno di tal pez <lb></lb>zo notando ſempre le dette diſtantie per linee, & con tai linee ſe conoſcera minuta<lb></lb>mente la groſſezza, & ſottigliezza del mettallo à torno à torno del foro di tal pe<emph.end type="italics"></emph.end>z<lb></lb><emph type="italics"></emph>zo, etiam per qual uerſo, ouer banda penderanno li ſuoi tiri per le ragioni, per auanti <lb></lb>dette, che è il propoſito.<emph.end type="italics"></emph.end> A. Q<emph type="italics"></emph>ueſto uostro modo è molto <expan abbr="ſpediẽte">ſpediente</expan>, et me piace aſſai.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000654">QVESITO VIGESIMO QVARTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo<emph.end type="italics"></emph.end> M. A<emph type="italics"></emph>lberghetto.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000655">ALBER GHETTO V<emph type="italics"></emph>n'altro dubbio ue uoglio <expan abbr="addimãdare">addimandare</expan>. </s> <s id="s.000656">Accadete una <lb></lb>uolta, che prouandoſi alcuni pezzi à lio, uno de ditti pezzi dapoi alcuni tiri <lb></lb>nel diſcargarſe, andete con la teſta dauanti in terra, cioe con la bocca, et ſubito che tal <lb></lb>pezzo ſu <expan abbr="giõto">gionto</expan> <expan abbr="cõ">com</expan> la detta bocca in terra (doue era molta ſabbia, ouer ſabbione) tiro<emph.end type="italics"></emph.end><pb pagenum="27" xlink:href="042/01/053.jpg"></pb><emph type="italics"></emph>gran quantita della detta ſabbia dentro da ſi, cioe dentro dal ſoro della <expan abbr="cãna">canna</expan>, hor ue ad <lb></lb>mando la cauſa di tal effetto.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>n caſo ſimil à queſto, etiam alquanto piu fantaſti<lb></lb>co, mi fu ricercato da uno Bombardiero (come appare in queſto al. 21. queſito) il quale, <lb></lb>ſi come nel uoſtro, il pezzo tiro gran quantita di ſabbia dentro dal uacuo della canna, <lb></lb>nel ſuo, tal pezzo ue tiro dentro uno cagnolino, coſa aſſai ridicoloſa, e pero queſto uo<lb></lb>ſtro dubbio lo riſolueremo, ſi come riſolueßimo quello, cioe che per tir ar il pezzo, tal <lb></lb>pezzo neceſſariamente ſe ſcalda, & ſubito che il ſia alquanto caldo, ſubito ſi fa alquan <lb></lb>to attrattiuo alla ſimilitudine d'una uentoſa, e tanto piu, quanto piu ſi troua caláo, e pe <lb></lb>ro non è marauiglia ſe tal pezzo traſſe tal ſabbia dentro da ſe.<emph.end type="italics"></emph.end> A. Q<emph type="italics"></emph>ueſta uoſtra <lb></lb>ragion molto mi conſona.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000657">QVESITO VIGESIMOQVINTO FATTO DA <lb></lb><emph type="italics"></emph>uno Schioppettero, & etiam Bombardiero.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000658">SCHIOPPETIERO. H<emph type="italics"></emph>auendo io un ſchioppo con la ſua mira tanto ben ac<lb></lb>concia, che tirando à un ſegno poſto in piano, in una certa mia conueniente diſtan<lb></lb>tia quaſi la maggior parte delle uolte, dia preciſamente in brocca, cioe nella coſa tolta <lb></lb>de mira per picciola che la ſia. </s> <s id="s.000659">Ve adimando ſe tal mira coſi ben acconcia me ſeruira à <lb></lb>tirare à un ſegno, o altra picciola coſa, che ſia poſta in àlto, in quella medeſima diſtan<lb></lb>tia.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie coſa chiara, che tal mira non ue ſeruira coſi preciſamente tirando al<lb></lb>l'alta, & in quella medeſima diſtantia.<emph.end type="italics"></emph.end> S. M<emph type="italics"></emph>a percheragione.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a ragione è que <lb></lb>sta, ſe tirando in piano in quella uoſtra commune distantia uoi date la maggior parte <lb></lb>preciſamente in brocca, neceſſariamente in quella tal diſtantia, & in tal luoco, ui ſe con <lb></lb>gionge, ouer concorre la uoſtra linea uiſuale, o per contingentia, ouer per interſeccatio <lb></lb>ne, con il tranſito, ouer uiaggio qual debbe far la balla. </s> <s id="s.000660">Et perche nelli tiri elleuati, la <lb></lb>balla ua molto piu per linea retta, ouer linea men curua di quello ua nelli tiri fatti in <lb></lb>piano, cioe con il pezzo, ouer ſchioppo aliuellato, come fu diſputato ſopra al ſecondo <lb></lb>queſito, e perche quanto che piu rettamente ſe iſtende il tranſito, ouer uiaggio, qual deb <lb></lb>ba far la balla (tirando all'alta) di quello faceua tirando in piano, tanto piupreſto uien <lb></lb>à concorrere, & à interſeccarſe, il detto tranſito, ouer uiaggio, con la detta linea uiſua <lb></lb>le, di quello faceua tirando in piano. </s> <s id="s.000661">Facendoſi adunque tal interſeccatione piu propin<lb></lb>qua (per tirar coſiin alto) la coſa à chi ſe tira uien à reſtare oltra à tal interſeccatione <lb></lb>(per eſſer quella nella medeſima prima distantia) & eſſendo fuora di tal interſeccatio<lb></lb>ne è impoßibile à dar preciſamente in brocca per ragion delle mire.<emph.end type="italics"></emph.end> S. I<emph type="italics"></emph>o non inten<lb></lb>do troppo bene queſte uoſtre ragioni, ne manco uoglio che ue affaticati à darmele ad in <lb></lb>tendere, perche credo, che uoi ui hauereſti difficulta ma conchiudetemi pur ſe tir ando <lb></lb>à tal ſegno poſto in alto, & nella medeſima prima diſtantia io daro piu alto, ouer piu <lb></lb>baſſo di tal ſegno.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>onchiudo che uoi dariti piu alto, perche ogni uolta che la li<lb></lb>neauiſuale ſe interſecca con il tranſito, ouer uiaggio qual debbe far la balla, & che la <lb></lb>coſa, ouer ſegno à che ſe tira ſia oltra à tal interſeccatione, ſempre la balla percuotera <lb></lb>alquanto di ſopra del ſegno, & tanto piu alto quanto che il detto ſegno, ſara piulon<lb></lb>tano dalla detta interſeccatione.<emph.end type="italics"></emph.end> S. C<emph type="italics"></emph>ertamente uoihaueti detto la uerita, et ſappiati <pb xlink:href="042/01/054.jpg"></pb>che io ho morto alli miei giorni. </s> <s id="s.000662">2000. uccelli (dico di piccioli) & la mia longa iſpe<lb></lb>rientia mi hafatto chiaro di quello che uoi me haueti detto, e pero ogni uolta che mioc<lb></lb>corre à tirare ad alcuno uccello che ſia ſopra à qualche alboro nella mia conſueta <expan abbr="di-ſtãtia">di<lb></lb>ſtantia</expan>, io toglio ſempre la mira alli piedi di tal uccello, ma eſſendo tal uccello in piano, io <lb></lb>toglio la mira <expan abbr="preciſamẽte">preciſamente</expan> nel corpo di tal uccello, ilche <expan abbr="facẽdo">facendo</expan> rare uolte tiro in fallo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000663">QVESITO VIGESIMOSESTO FATTO <lb></lb><emph type="italics"></emph>dal medeſimo Schioppettiero.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000664">SCHIOPPETTIERO. A<emph type="italics"></emph>nchora ui uoglio <expan abbr="adimãdarui">adimandarui</expan> un'oltro paſſo, qual <lb></lb>è queſto. </s> <s id="s.000665">Se con il detto mio ſchioppo uoglio tirare à un ſegno poſto al baſſo, ma <lb></lb>pur nella medeſima diſtantia (detta diſopra) ue adimando ſe tal mia mir a mi ſeruira, ſi <lb></lb>come fa in piano, cioe ſe io daro in brocca, ouer di ſopra, ouer di ſotto dal detto ſegno.<emph.end type="italics"></emph.end><lb></lb>N. S<emph type="italics"></emph>enza dubbio che tal mira nonue ſeruiria in quella medeſima diſtantia, per le me<lb></lb>deſime ragioni dette di ſopra, ma uoi dareti pur anchora piu alto del ſegno, cioe di ſo<lb></lb>pra dal detto ſegno.<emph.end type="italics"></emph.end> S. V<emph type="italics"></emph>oi dite pur anchor la uerita, perche ogni uolta che io tiro à <lb></lb>alcun uccello che ſia in qualche baſſura, ouer diſmontata, la longa ſperientia miha fat<lb></lb>to cauto che ſempre piglio la mira pur nelli piedi di detto uccello, come faccio anchora <lb></lb>à quelli che ſono all'alta, cioe ſopra à qualche arboro, ouer torre, & coſi facendo rare <lb></lb>uolte tiro in fallo.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ho molto à caro, che la uostra longa iſperientia ui habbia <lb></lb>dato buona teſtimonianza, di quello che con ragioni naturale, ui ho conchiuſo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000666">QVESITO VIGESIMOSETTIMO <lb></lb><emph type="italics"></emph>fatto dal medeſimo <lb></lb>Schioppettiero.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000667">SCHIOPPETIERO. V<emph type="italics"></emph>n'altro paſſo ui ho anchora di adimandarui qual è <lb></lb>questo, tir andoſt con un ſchioppo à un berſaglio, ouer ad altro ſegno, de mira, & <lb></lb>che per ſorte la botta dia di ſopra dal ſegno, traſportando poi il detto ſegno alquanto <lb></lb>piu lontano, ouer ritir andoſi il ſchioppettero alquanto piu in drio, & ritir ando poi an <lb></lb>chora de mira al detto ſegno, ſe adimandaſe con tal tiro ſi dara piu alto, ouer piu baſſo <lb></lb>dell'altro tiro.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n un ſimil caſo alla ſeconda uolta ſi dara molto piu di ſopra dal ſe <lb></lb>gno di quello ſi fece alla prima.<emph.end type="italics"></emph.end> S. V<emph type="italics"></emph>oi haucti detto la uerita, perche me accaduto à <lb></lb>me uolendo inuestigare quanto tiraua de mira uno ſchioppo nuouo non piu tirato qual <lb></lb>in una certa commune diſtantia mi daſeua diſopra dalſegno, et facendo traſportar piu <lb></lb>di lontano il detto ſegno, cioe circa. </s> <s id="s.000668">10. paſſa con ſperanza de dar in brocca, & ritiran <lb></lb>do al medeſimo ſegno, io percoßi molto piu di ſopra dal ſegno alla ſeconda uolta che al<lb></lb>la prima, la qual coſa, mi parue tanto fuora diragione quanto dir ſe poſſa, perche à mi <lb></lb>me parea, è pare anchora che allontanando il ſegno ſe doueria battere piu baſſo, di quel <lb></lb>lo ſi faceua ſtandoui piu appreſſo, e per tanto haueria molto accaro à intendere la cau<lb></lb>ſa di queſto inconueniente.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto non è inconueniente, anci è coſa conueniente à <lb></lb>far quello che diragion de fare, & inconueniente grandißimo ſariaſe ſeguitaſſe ſecon-<emph.end type="italics"></emph.end><pb pagenum="28" xlink:href="042/01/055.jpg"></pb><emph type="italics"></emph>do il detto uoſtro parere, perche ogni uolta che un ſchioppetiero, ouer bombardicro <lb></lb>tiri de mira à un ſegno, & che per uigor, ouer difetto delle due mire lui dia di ſopra dal <lb></lb>ſegno. </s> <s id="s.000669">Eglie manifeſio che la linea uiſuale interſecca, il tranſito, ouer uiaggio qual deb<lb></lb>be far la balla, & che tal interſeccatione che fa la detta linea uiſuale con il detto uiaggio <lb></lb>qual debbe far la balla, ſe fa de qua dal ſegno (per le ragioni adutte nel. </s> <s id="s.000670">7. queſito) & <lb></lb>perche per un molto longo ſpacio, quanto piu il ſegno doue ſe tira ſia piu oltra la detta <lb></lb>interſeccatione, tanto piu la percoſſa dara di ſopra dalſegno, traſportando adunque il <lb></lb>detto ſegno, per alquanto piu lontano, ſimilmente per alquanto piu lontano ſara traſ<lb></lb>ferido dalla dalla medeſima interſeccatione, et per tanto la botta dara piu alta, ouer piu <lb></lb>di ſopra dal ſegno dell'altra, & tanto piu quanto che piu lontano per fin à un certo ter <lb></lb>mine ſara trasſerito, ouer traſportato il detto ſegno il medeſimo ſeguiria ſeil ſchiop<lb></lb>petiero, ouer bombardiero ſe ritiraſſe per alquan<gap></gap>o in drio, & tutto queſto che ho det<lb></lb>to ſe debbe intendere quando che la botta è alta per difetto delle due mire, & non per di <lb></lb>fetto de colui che tira, perche ſe per difetto de colui che tira, cioe che nel diſcargare il <lb></lb>ſchioppo lui faceſſe alcun mouimento, & che per tal mouimento lui deſſe diſopra, ouer <lb></lb>diſotto, ouer coſter dal ſegno, tal inconueniente non ſi comprende nel noſtro ragiona<lb></lb>mento, ma <expan abbr="ſolamẽte">ſolamente</expan> quando che tal effetto occorre per difetto delle due mire delſchiop <lb></lb>po. </s> <s id="s.000671">Anchor biſogna auertire, che il detto ſegno ſe potria traſportar tanto, & tanto lon <lb></lb>tano dalla prima poſitione, che non ſolamente ſe potria dar piu propinquo alſegno del<lb></lb>la prima botta, ma anchora ſe potria dar nel proprio ſegno, per le ragioni adutte nel fi <lb></lb>ne del. 7. queſito, cioe ſe per ſorte ſe traſportaſſe tanto, & tanto lontano il detto ſegno, <lb></lb>& che per ſorte ſe metteſſe nel luoco doue che la nostra linea uiſuale fa la ſeconda in<lb></lb>terſeccatione, <expan abbr="cõ">com</expan> il <expan abbr="trãſito">tranſito</expan> della balla ſenza dubbio ſe daria in brocca (come fu detto ſo <lb></lb>pra al detto. </s> <s id="s.000672">7. queſito) & ſe p caſo <expan abbr="nõ">non</expan> fuſſe coſi preciſe in tal ſeconda interſeccatione, <lb></lb>ma propinquo, tal botta non dara coſi preciſamente in brocca, ma ben ui dara propin<lb></lb>quo, cioe ſe tal ſegnó ſara alquanto di qua da tal interſeccatione, dar a alquanto diſopra <lb></lb>dal ſegno, & ſe ſara alquanto de la, dara alquanto di ſotto dal detto ſegno, & tutto que <lb></lb>sto facilmente ſe apprendera dalle ragioni adutte per figura in fine del detto. </s> <s id="s.000673">7. queſi<lb></lb>to. </s> <s id="s.000674">Vero è, che il detto ſegno ſe potria traſportar tanto di la della detta ſeconda inter<lb></lb>ſeccatione che la balla non potria aggiongere à quello, come per ragion naturale fa<lb></lb>cilmente ſi puo comprendere.<emph.end type="italics"></emph.end> S. H<emph type="italics"></emph>o inteſo benißimo la uoſtra ragione, & la bo <lb></lb>molto accara.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000675">QVESITO VIGESIMO OTTAVO <lb></lb><emph type="italics"></emph>fatto dal medeſimo <lb></lb>Schioppettiero.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000676">SCHIOPPETIERO. D<emph type="italics"></emph>al ſopradetto queſito me ne uenuto un'altro in men <lb></lb>te, qual è queſto, ſe <expan abbr="tirãdo">tirando</expan> <expan abbr="cõ">com</expan> il detto mio ſchioppo pur à un ſegno de mira, et che p <lb></lb>diſetto delle due mire io deſſe di ſotto dalſegno, <expan abbr="traſportãdo">traſportando</expan> anchora il detto ſegno al<lb></lb>quanto piu lontano, ouer <expan abbr="ritirãdomi">ritirandomi</expan> alquanto in drio, & ritir ando al medeſimo ſegno <lb></lb>de mira, ue adimando ſe questa ſeconda botta ſara piu alta, ouer piu baſſa della prima.<emph.end type="italics"></emph.end><pb xlink:href="042/01/056.jpg"></pb>N. I<emph type="italics"></emph>n queſto caſo puo far uarie mutationi, perche la mira dauanti puo eſſere <gap></gap>gual<lb></lb>mente alta alla mira de drio, & puo eſſere anchora piu alta, & anchora piu baſſa di <lb></lb>quella, ſe per caſo adunque la mira <expan abbr="dauãti">dauanti</expan> ſara eguale, ouer maggiore di quella de drio <lb></lb>(per le ragioni adutte nel principio del. 7. queſito) quanto piu ſe traſportara tal ſegno <lb></lb>di lontano, tanto piu baſſa ſara la botta. </s> <s id="s.000677">Ma ſe la mira dauanti ſara piu baſſa di quella <lb></lb>de drio, & che per ſorte la ſia talmente piu baſſa di quella, che la noſtra linea uiſuale <lb></lb>uada realmente à ſegare il tranſito, ouer uiaggio qual debbe far la balla, come ſe dimo<lb></lb>ſtra in fine del. 7. queſito, in tal caſo, la ſeconda botta neceſſariamente ſara di ſopra della <lb></lb>prima, uero è che la puo eſſer anchor lei pur di ſotto dalſegno, cioe fra il ſegno, & la <lb></lb>prima botta, & puol eſſer anchora preciſamente nel proprio ſegno, cioe in brocca, & <lb></lb>anchor puol eſſer diſopra dal ſegno, perche ogni uolta che la detta mira dauanti ſia tal <lb></lb>meute piu baſſa di quella de drio, che la noſtra linea uiſuale uada realmente à ſegare il <lb></lb>detto tranſito, ouer uiaggio qual debbe far la balla, come di ſopra è detto, & che in un <lb></lb>ſimil caſo alcuno ſchioppettero, ouer bombardiero tiri de mira à un ſegno, & che per <lb></lb>uigore delle dette due mire (et <expan abbr="nõ">non</expan> p ſuo difetto) lui dia diſotto del ſegno, eglie manife<lb></lb>ſto che la interſeccatione, che fa la linea uiſuale, conil tranſito, ouer uiaggio che debbe <lb></lb>far la bella, per le ragioni adutte in fine del ſettimo queſito, ſara de la dal ſegno, cioe che <lb></lb>il ſegno ſara fra la detta interſeccatione, & colui che tira. </s> <s id="s.000678">Et per tanto, ſe il luoco doue <lb></lb>ſara traſportato il detto ſegno, ſia anchora di qua da tal interſeccatione, neceſſaria<lb></lb>mente la detta ſeconda botta ſara di ſotto dal ſegno, uero è che ui ſara piu propinqua <lb></lb>della prima, cioe ſara fra il ſegno, & la prima botta, ma ſe la traſportatione del ſegno <lb></lb>ſara per ſorte nel luoco della propria interſeccatione, al detto ſecondo tiro ſi dara pre<lb></lb>ciſamente in brocca, cioe nel detto ſegno tolto de mira, ma ſe per ſorte il detto ſegno ſa<lb></lb>ra traſportato oltra la detta interſeccatione neceſſariamente la detta ſeconda botta da <lb></lb>ra diſopra dal ſegno, & tanto piu dara di ſopra quanto che piu oltra la detta interſec<lb></lb>catione ſara traſportato detto ſegno, per fin à uno certo termine (come in fine del pre<lb></lb>cedente queſito anchor fu detto) ma ſe la detta mira dauanti ſara pur alquanto piu baſ<lb></lb>ſa di quella de drio, ma che tal ſua baſſezza ſia tanto poca, che nonſia atta di condure la <lb></lb>noſtra linca uiſuale tanto baſſa che ſi poſſa congiongere con il uiaggio, ouer tranſito, <lb></lb>qual debbe far la balla, anchora in queſto caſo in ogni traſportatione del detto ſegno, la <lb></lb>botta dara pur di ſotto dal ſegno, uero è, che tal ſeconda botta potria dar di ſopra, & <lb></lb>anchor di ſotto della prima, & anchora in quella medeſima, perche ſe la prima poſition <lb></lb>del ſegno ſara per ſorte nel luoco doue che la linea uiſuale paſſa piu propinquo al tran <lb></lb>ſito, ouer uiaggio qual debbe far la balla (come ſe dimoſtra nel. </s> <s id="s.000679">8. queſito) traſportan<lb></lb>do poi il detto ſegno oltra al detto luoco ſenza dubbio la ſeconda botta ſara piu baſſa <lb></lb>della prima, il medeſimo ſeguiria quando, che la poſitione del ſegno fuſſe oltra al detto <lb></lb>luoco. </s> <s id="s.000680">Ma quando che la detta prima poſitione de ſegno fuſſe de qua da tal luoco (piu <lb></lb>propinquo traſportando poi il detto ſegno piu appreſſo à tal luoco, la detta ſeconda <lb></lb>botta ſara di ſopra della prima, ma pur ſara di ſotto dal ſegno, cioe ſara fra la prima <lb></lb>botta, & il ſegno. </s> <s id="s.000681">Ma quando tal ſegno fuſſe traſportado di la di tal luoco propinquo <lb></lb>potria eſſer tanto poco di la che pur la detta ſeconda botta ſara fra la prima, & il ſe<lb></lb>gno, & potria eſſer anchor tanto di la che la detta ſeconda botta dara di ſotto della pri-<emph.end type="italics"></emph.end><pb pagenum="29" xlink:href="042/01/057.jpg"></pb><emph type="italics"></emph>ma, & potrìa anchor eſſer coſi proportionalmente di la, che la detta ſeconda botta da <lb></lb>ria preciſamente nel luocho della prima, & tutto queſio, che ben conſiderara la figu<lb></lb>ratione del ottauo quæſito, ſar a manifeſto. </s> <s id="s.000682">Ma quando che la mira dauanti haueſſe per <lb></lb>ſorte la ſua debita & conueniente baſſezza reſpetto à quella de drio, laqual coſa acca <lb></lb>de rare uolte, cioe che la linea uiſuale andaſſe preciſamente à toccare, ma non ſegare, <lb></lb>el tranſito, ouer uiaggio: qual debbe far la balla. </s> <s id="s.000683">Et che in un ſimel caſo alcun ſcioppet<lb></lb>tero, ouer bombardiero tiraſſe de mira ad alcun ſegno, & che per uigore delle dette <lb></lb>due mire & non per ſuo diffetto, lui deſſe di ſotto dal ſegno, per le coſe dette & dimo<lb></lb>strate nel. </s> <s id="s.000684">9. queſito, puo occorrer che tal ſegno ſia di qua etiam di la dal toccamento <lb></lb>delle dette due linee, perche coſi eſſendo di qua, come di la da tal toccamento ſempre da <lb></lb>ra di ſotto dal ſegno, come ſopra alla figura del detto. </s> <s id="s.000685">9. Queſito facilmente ſe appren<lb></lb>de, uero è, che quando tal prima botta fuſſe molto baſſa, ſaria da giudicare che tal ſe<lb></lb>gno fuſſe di la dal detto toccamento, perche eſſendo de qua tal botta, non puo eſſer mol <lb></lb>to baſſa, per le ragioni adutte nel detto nono Queſito, ſe tal ſegno adunque ſara de la <lb></lb>dal detto toccamento, & traſportando poi tal ſegno anchor piu in la, cioe piu lontano <lb></lb>dal detto toccamento, ſenza dubbio la ſeconda botta ſara molto piu baſſa della prima. <lb></lb></s> <s id="s.000686">Ma quando che tal ſegno fuſſe di qua dal detto toccamento, traſportandolo poi piu in <lb></lb>la, puo occorrere che tal ſegno in tal ſeconda poſitione, ſia anchor di qua dal detto toc <lb></lb>camento, & puo accadere, che ſia nel proprio toccamento, & puo eſſer anchor che ſia <lb></lb>di la da tal toc camento. </s> <s id="s.000687">Sel ſegno adunque in tal ſeconda poſitione ſara de qua dal toc <lb></lb>camento, la ſecouda botta ſara de ſopra della prima, uero è, che ſara pur de ſotto dal <lb></lb>ſegno, cioe ſara fra el ſegno, & la prima botta. </s> <s id="s.000688">Ma ſel detto ſegno in tal ſeconda poſi<lb></lb>tione ſara p ſorte nel <expan abbr="põto">ponto</expan> del detto toccamento, la detta <expan abbr="ſecõda">ſeconda</expan> botta dara preciſamen <lb></lb>te in brocca. </s> <s id="s.000689">Ma ſel detto ſegno in tal ſeconda poſitione ſara de la dal detto toccamen<lb></lb>to, puo eſſer tanto de la, che la detta ſeconda botta ſara piu baſſa della prima, & puo eſ <lb></lb>ſer anchora coſi poco di la da tal toccamento, che la detta ſeconda botta ſara di ſopra <lb></lb>della prima, ma pur di ſotto dal ſegno, cioe fra il ſegno e la prima botta, & puo eſſere <lb></lb>anchora coſi proportionalmente di la, che la detta <expan abbr="ſecõda">ſeconda</expan> botta dara preciſamente nel <lb></lb>luoco della prima.<emph.end type="italics"></emph.end> S. Q<emph type="italics"></emph>ueste uoſtre ragioni certamente me ingraſſano, & queſto <lb></lb>procede, perche le comenzo à intendere, e per queſto mio intendere, <expan abbr="quãdo">quando</expan> che mi cre <lb></lb>deua di por fine à mei Queſiti, le uoſtre argumentationi me inducono nuoue chimere <lb></lb>uella mente mia, ouer nuoui dubbij de addimandarui, ma dubito de non farui faſtidio.<emph.end type="italics"></emph.end><lb></lb>N. S<emph type="italics"></emph>eguitati pur, che non mi fatti faſtidio alcuno.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000690">QVESITO VIGESIMONONO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Schioppettero.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000691">SCHIOPPETTERO. P<emph type="italics"></emph>er quanto poſſo conſiderare per le uoſtre argumen <lb></lb>tationi do ſopra adutte, la openione uoſtra è, che ſe il ſegno doue ſe tira de mira <expan abbr="nõ">non</expan> <lb></lb>ſe imbatte per ſorte à eſſer nel ponto doue concorre la lineauiſuale con el tranſito, o<lb></lb>uer uiaggio qual debbe far la balla, non ſi poſſa dare preciſamente in brocca. </s> <s id="s.000692">La qual <lb></lb>coſa, da una <expan abbr="bãda">banda</expan> p <expan abbr="ragiõ">ragiom</expan> naturale <expan abbr="cõſidero">conſidero</expan>, che eglie neceßario coſi eßer, ma da laltra<emph.end type="italics"></emph.end><pb xlink:href="042/01/058.jpg"></pb><emph type="italics"></emph>banda, la mia longa iſperientia pare, che non correſponda preciſamente à questo: ma <lb></lb>innanti che io ue dica in que conto la non me correſponda, uoglio che me chiariti que<lb></lb>ſto altro dubbio, cioe. </s> <s id="s.000693">Donde procede, che ogni ſchioppettero, & anchor bombar die<lb></lb>ro generalmente quanto piu ſta propinquo à un ſegno tolto de mira, tanto piu è atto <lb></lb>à darui dentro, ouer à far piu bella botta, & in ogni qualita de mire.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er riſol<lb></lb>uere regolatamente queſto uostro dubbio, in tutte le ſorte, ouer qualita de differentie <lb></lb>che occorrer poſſa nelle due mire. </s> <s id="s.000694">Incominciaremo prima, <expan abbr="quãdo">quando</expan> che per ſorte la mi <lb></lb>ra dauanti fuſſe preciſamente di quella medeſima altezza, che è quella de drio. </s> <s id="s.000695">Dico <lb></lb>adunque, che quando la mira dauanti ſara egualmente alta à quella de drio in tal caſo, <lb></lb>quanto piu colui, che tirara stara propinquo al ſegno, tanto piu ſara atto à darui den<lb></lb>tro, ouer à far piu bella botta, & queſto ſeguita per due cauſe. </s> <s id="s.000696">La prima è, perche ſem <lb></lb>pre (come fu detto ſopra el ſettimo Queſito) tal ſchioppo, ouer pezzo dara di ſotto <lb></lb>dal ſegno, che ſe tol de mira, & tanto piu baſſa ſara tal botta, quanto che piu lontano <lb></lb>ſara dal detto ſegno, & è conuerſo, quanto che piu propinquo ſara al ſegno, tanto men <lb></lb>baſſa ſara tal botta, & la menor baſſe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a, che ui poſſa occorrere in ſimel caſo, ſaria <lb></lb>quella, quando, che ſe ſteſſe tanto propinquißimo alſegno, che la iſtremita della mira <lb></lb>de nanti, toccaſſe quaſi el detto ſegno, che ſi tol de mira, la qual baſſezza puo eſſer cir <lb></lb>ta à tanto, quanto che è la diſtantia, che è dalla iſtremita de l'una, e l'altra mira al ua<lb></lb>cuo della canna, la quale puo eſſer poco piu della groſſezza del mettallo del pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o ne <lb></lb>la parte de drio, che in un ſchioppo puo eſſer circa à tanto, quanto è la groſſezza di <lb></lb>un dedo, & in un pe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o groſſo tanto piu, quanto piu ſara groſſo di mettallo nella par <lb></lb>te de drio. </s> <s id="s.000697">Et <expan abbr="quãtunque">quantunque</expan> la balla ſubito, che è uſcita della bocca del ſchicppo, ouer pez <lb></lb>zo, uada continuamente declinando al baſſo (come ſi dimoſtra nel terzo Queſito) ta<lb></lb>men per un poco di tempo, ouer ſpatio, quando che tal balla ſi poteſſe uedere tal ſuo de<lb></lb>clinare non ſaria ſenſibile, cioe chel noſtro occhio non lo potria diſcernere, e pero in <lb></lb>un corto ſpatio, per conto delle dette mire, tal ſchioppo puo dar poco piu baſſo del ſe<lb></lb>gno tolto de mira di quella groſſezza d'un dedo, detta di ſopra, dico per uigor delle mi <lb></lb>re, e non per difetto di colui che tira, perche li difetti, & accidenti, che puo occorrere <lb></lb>per difetto di colui che tira, non ſe comprendono nelli noſtrir agionamenti, & queſta <lb></lb>é la prima cauſa, che un ſchioppettero, & anchor bombardiero, quando che la mira da <lb></lb>uanti è di quella medeſima alte<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a, che è quella de drio, quanto piu stara propinquo <lb></lb>al ſegno tolto de mira, tanto piu ſara atto à darui dentro, ouer à far piu bella botta di <lb></lb>quello fara à ſtarui piu lontano, et per queſta medeſima cauſa occorreria el medeſimo, <lb></lb>quando che la mira de nanti fuſſe alquanto piu alta di quella de drio, perche in ſimel ca <lb></lb>ſo, come fu detto nel detto ſettimo Queſito, ſempre tal pezzo dara di ſotto dal ſegno <lb></lb>tolto de mira, & tanto piu di ſotto, qoanto che piu ſara lontano dal detto ſegno, & la <lb></lb>menor baſſezza che ui poßi occorrere in tal caſo puo eſſer circa à tanto, quanto che <lb></lb>ſara dalla iſtremita della mira dauanti, al uacuo della canna de tal ſchioppo, ouer arte<lb></lb>gliaria, ouer poco piu, la qual coſa, quando chel ſegno fuſſe, come di ſopra dißi, propin <lb></lb>quißimo alla bocca del ſchioppo potria eſſer poco piu dell'altra, cioe poco piu della <lb></lb>groſſezza dun dedo, uero é che in diſtantie equale daria alquanto piu baſſo dell altra, <lb></lb>detta di ſopra, ma poco piu baſſo, maßime in una piccola diſtantia, ſi che, come di ſo-<emph.end type="italics"></emph.end><pb pagenum="30" xlink:href="042/01/059.jpg"></pb><emph type="italics"></emph>pra è detto, queſta è la prima cauſa, che un ſchioppettero, & anchor bombardiero, <lb></lb>quando che la mira dauanti fuſſe ben alquanto piu alta di quella de drio, quanto piu <lb></lb>ſtara propinquo al ſegno tolto de mira, tanto piu ſara atto à darui dentro, ouer à fare <lb></lb>piu bella botta di quello ſaria à ſtarui piu lontano. </s> <s id="s.000698">Ma oltra à queſta prima cauſa io re <lb></lb>puto, che la ragion naturale ne inſegni una altra al detto bombardiero, ouer ſchioppet <lb></lb>tero, la qual è queſta, che ogni uolta, che lui è molto propinquo al ſegno doue uol tira <lb></lb>re, che lui non pigli la mira nel proprio ſegno, ma alquanto di ſopra dal ſegno, perche <lb></lb>el die comprendere per diſcretione naturale, che le istremita delle due mire ſono <expan abbr="alquã">alquam</expan> <lb></lb>to piu ad alto della bocca del pezzo, doue uſciſſe la balla, la qual coſa facendo, uiene à <lb></lb>medicare quel poco errore, detto di ſopra, che doueria far in baſſezza quel tal tiro, <lb></lb>il che lo fa piu atto à dar preciſamente in brocca. </s> <s id="s.000699">Et per tanto dico, ſe quando la mi<lb></lb>ra dauanti è equalmente alta, & anchor alquanto piu alta di quella de drio, el bombar <lb></lb>diero, ouer ſchioppettero è tanto piu atto à dar nel ſegno doue tira, ouer à far piu bel<lb></lb>la botta, quanto piu ui sta propinquo, per le due ragioni di ſopra adutte, molto mag<lb></lb>giormente, per le medeſime ragione, ſeguiria el medeſimo, quando che la mira dauanti <lb></lb>ſara alquanto piu baſſa di quella de drio, & ſia tal ſua baſſezza troppo, ouer poco à <lb></lb>ſufficienza: perche in qual ſi uoglia modo, che la ſia piu baſſa, la uien à unir piu la linea <lb></lb>uiſuale con el uiaggio qual debba far la balla, et continuamente piu per fina al luoco do <lb></lb>ue che tal linea uisuale ſega, ouer tocca, ouer che paßa piu propinqua al detto tranſi<lb></lb>to, ouer uiaggio, qual debbe far la balla di quello ſi fa nelle due poſitione dette di ſopra, <lb></lb>perche in quella la detta linea uisuale continuamente ſi ua discostando dal detto tranſi<lb></lb>to, ouer uiaggio, che debbe far la balla, & in queſte continuamente la ui ſi ua piu acco<lb></lb>ſtando, per fin al luoco detto diſopra, & quantunque anchora in queſta ſeconda poſi<lb></lb>tione de mire quanto piu el ſegno, che ſe tuol de mira, sara de qua dal luoco doue con<lb></lb>correra la linea uiſuale con el detto tranſito, ouer uiaggio, ouer dal luoco, doue che piu <lb></lb>tranſiranno uicine, ouer propinque, dette linee, tanto piu baſſa sara la botta, come ſe <lb></lb>dimoſtra nel ſettimo, ottauo, & nono Queſito, tamen la baſſezza puo eſſer poca, co<lb></lb>me fu detto ſopra li predetti Queſiti, pche la maggiore che ui poſſa occorrere saria <lb></lb>quella, che nelle altre due prime era la maggiore, cioe quando chel segno, che ſe tol de <lb></lb>mira fuſſe propinquißimo alla mira dauanti, cioe alla bocca del ſchioppo, ouer pez<lb></lb>zo, la qual di sopra determinaßimo in un ſchioppo poter eſſer poco piu della groſſez <lb></lb>za dun dedo, se la maggior baſſezza adunque é poco piu dun dedo in un ſchioppo ſtan <lb></lb>do al segno propinquißimo alla bocca di quello. </s> <s id="s.000700">Eſſendo adunque tal ſegno alquanto <lb></lb>lontano da detta bocca, neceſſariamente men baſſa ſara la ſua botta, cioe men di quella <lb></lb>groſſe<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a dun dedo, & tanto men baſſa, quanto che ſara piu lontano dalla bocca del <lb></lb>ſchioppo, pur che non ſia oltra alla detta intersecatione, ouer toccamento che fa la det <lb></lb>ta linea uisuale con el tranſito della balla, ouer alla maggior propinquita di quelle, <expan abbr="eßẽ">eßem</expan> <lb></lb>do adunque tal segno lontano al men diece paſſa della detta bocca del ſchioppo, quaſi <lb></lb>che la baſſezza de tal botta non ſaria ſenſibile, oltra che, come di ſopra dißi, <expan abbr="quãdo">quando</expan> che <lb></lb>colui, che tira è molto propinquo al ſegno doue tira, credo per una certa deſcretione <lb></lb>naturale, che lui non pigli la mira preciſamente nella brocca, ma una minima coſa piu <lb></lb>alto, perche lui die comprendere per ragion naturale, come di ſopradißi, che la iſtre-<emph.end type="italics"></emph.end><pb xlink:href="042/01/060.jpg"></pb><emph type="italics"></emph>mita delle due mire ſono alquanto piu alte della brocca del ſchioppo doue uſciſſe la bal<lb></lb>la. </s> <s id="s.000701">la qual coſa facendo (come credo che faccia) ueneria ad annular quel poco errore, <lb></lb>che doueria far in baſſezza la detta balla, & per queſte due cauſe tal ſchioppettero, <lb></lb>ouer bombardero con tal ſorte di mire generalmente ſara molto piu atto à dar nel ſe<lb></lb>gno, ouer à far piu bella botta in un luoco propinquo di quello ſaria con le due prime <lb></lb>qualita de mire dette nel principio di queſto Queſito, perche in queſta qualita la linea <lb></lb>uiſuale per molto ſpatio ua quaſi congionta, ouer poco diſtante dal tranſito della balla, <lb></lb>e pero in tutto quel ſpacio che è fra la bocca del ſchioppo, & el luoco doue concorano <lb></lb>le dette due linee, ouer doue che ſono piu propinque, non ſe è ſuggetto quaſi ad alcuno <lb></lb>errore per le ragion dette di ſopra, dico ad alcuno errore p conto delle mire.<emph.end type="italics"></emph.end> S. C<emph type="italics"></emph>er <lb></lb>tamente con queſto uoſtro ragionamento uoi me haueti ſatisfatto in tutto, e per tutto, <lb></lb>perche da una banda io teneua, per le ragioni da uoi adutte nel precedente Queſito, <lb></lb>che fuſſe impoßibile à dar in un ſegno tolto de mira, quando che tal ſegno non fuſſe pre <lb></lb>ciſamente nel ponto della interſecatione, ouer del toccamento delle due linee concor<lb></lb>rente, cioe della linea uiſuale, & del tranſito della balla, & dell'altra banda, me parcua <lb></lb>che la mia longa iſperientia non correſpondeſſe à questo, perche con el mio ſchioppo <lb></lb>ho tirato, & morto infiniti uccelli, alcuni à ſtarui competentamente da lontano, alcu<lb></lb>ni altri à ſtarui coſi <expan abbr="mediocremẽte">mediocremente</expan> di lontano, et alcuni altri ſtarui molto propinquo, <lb></lb>la qual coſa non potria accadere, eſſendo, come prima tenea (perche ſe le mire del detto <lb></lb>mio ſchioppo ſono tale, che mi facciano concorrere la mia linea uiſuale con el tranſito <lb></lb>della balla, el ponto di tal <expan abbr="cõcorſo">concorſo</expan> eglie da credere, che ſempre ſi faccia quaſi in una me <lb></lb>deſima diſtantia (maßime tir ando per un medeſimo uerſo, e cargandolo ſempre à uno <lb></lb>medeſimo modo) e per tanto eſſendo ſtata la coſa à che ſe tira piu, ouer men distante di <lb></lb>quella tal determinata diſtantia, ſaria ſtato impoßibile à imbroccar la detta coſa tol<lb></lb>ta de mira, e gia (come di ſopra ho detto) per iſperientia ritrouaua al contrario, cioe <lb></lb>che in diſtantie commune, & mediocre, & propinque, & in un medeſimo uerſo me oc<lb></lb>corſo molte uolte à dar imbrocca con el mio ſchioppo, la qual coſa mi faceua ſtar mol <lb></lb>to ambiguo, ma uoi me haueti ottimamente da ogni dubbio fatto chiaro, & maßime <lb></lb>che ogni uolta che mi occorre à tirare à qualche uccello, che me ſia molto propinquo, <lb></lb>io coſtumo come di ſopra dicesti, cioe à pìgliar la mira talmente piu alto, che la bocca <lb></lb>del mio ſchioppo uenga à <expan abbr="cõuerzerme">conuerzerme</expan> lo uccello, il che <expan abbr="facẽdo">facendo</expan> rare uolte tiro in fallo.<emph.end type="italics"></emph.end><lb></lb>N. M<emph type="italics"></emph>i piace aſſai, che la uoſtra longa ſperientia ui renda bona teſtimonianza di quel <lb></lb>lo, che per ragion naturale, e geometrica la mia mente ſente.<emph.end type="italics"></emph.end> S. Q<emph type="italics"></emph>uantunque del mio <lb></lb>dubbio me habbiati fatto chiaro, nondimeno penſando ſoprala uoſtra argumentatio<lb></lb>ne, me ne occorſo nouamente un'altro in mente, ma dubito <expan abbr="dinõ">dinon</expan> farui faſtidio.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>e <lb></lb>guitati pur che non mi fatte fastidio alcuno, anci me fatti appiacere.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000702">QVESITO TRIGESIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Schioppetero.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000703">SCHIOPPETTERO N<emph type="italics"></emph>ella argumentatione per uoi fatta ſopra al <expan abbr="precedẽ">precedem</expan> <lb></lb>te Queſito, <expan abbr="cõ">com</expan> bonißime ragionihauete dimoſtrato <expan abbr="qualmẽte">qualmente</expan> un ſchioppettero in<emph.end type="italics"></emph.end><pb pagenum="31" xlink:href="042/01/061.jpg"></pb><emph type="italics"></emph>un ſegno propinquo è <expan abbr="sẽpre">sempre</expan> ſuggetto à dar <expan abbr="alquãto">alquanto</expan> di ſotto dal ſegno, cioe piu baſſo del <lb></lb>ſegno, & che tal baſſezza non puo eccedere la groſſezza d'un dedo, o poco piu, & lo <lb></lb>ho uiſto molti, che con uno medeſimo ſchioppo, in una non molto longa diſtantia tir an<lb></lb>do de continuo à un ſegno hauer dato talhora molto di ſopra dal ſegno, & talhora mol <lb></lb>to di ſotto, & talhora molto coſtero, & talhora nel proprio ſegno, e per tanto ue adi<lb></lb>mando la cauſa di queſto inconueniente, il quale me pare eſſer molto diſcordante à tutte <lb></lb>le uostre ragioni adutte in tutte le uoſtre argumentationi.<emph.end type="italics"></emph.end> N. B<emph type="italics"></emph>iſogna ſapere, che tut <lb></lb>ti gli errori occorrenti nel tirar de ſchioppo, alcuni ponno eſſer cauſati ſolamente dal<lb></lb>le mire, & alcuni altri ſolamente per difetto da colui che tira, & alcuni altri per difet<lb></lb>to dell'uno, & dell'altro, cioe & dalle mire, & da colui che tira. </s> <s id="s.000704">Gli errori adunque, del <lb></lb>li quali nelle precedente noſtre argumentationi hauemo parlato, ſono quelli che ſola<lb></lb>mente dalle mire ponno eſſer cauſati, non interponendoui alcuno minimo difetto de co<lb></lb>lui, che tira (come piu uolte alli ſuoi lochi è ſtato detto) perche gli errori che proce<lb></lb>deno ſimplicemente dalle due mire hanno in ſe regola è miſura, come alli ſuoi lochi è ſta <lb></lb>to detto, ma quelli che ſimplicemente procedeno per difetto di colui che tira, non hanno <lb></lb>in ſe alcun ordine, ouer regolarita, perche la maggior parte de tai errori, procedeno <lb></lb>per cauſa de qualche <expan abbr="mouimẽto">mouimento</expan>, che ha fatto con il ſchioppo colui che tira dapoi che ha <lb></lb>preſa la mira, ouer nel diſcargar del ſchioppo, perche ogniminimo moto fatto in quel <lb></lb>lo iſtante, che ſe diſcarga il detto ſchioppo puo cauſar grande errore al luoco, ouer al ſe <lb></lb>gno doue ſe tira de mira, & tanto piu quanto piu tal ſegno ſara lontano, & perche tal <lb></lb>mouimento del ſchioppo (qual puo occorrere, per il menar del fiato, ouer per il batter <lb></lb>del polſo, ouer per tremar della mano) non ha in ſi regolarita alcuna e per tanto quan<lb></lb>do che il ſegno fuſſe ben preciſamente nel ponto doue concorre la linea uiſuale con il <lb></lb>uiaggio qual doueria far la balla (nel qual luoco alla ragion delle mire lui doueria dar <lb></lb>preciſamente in brocca) nondimeno quel tale, mouendo il ſchioppo lui é ſoggetto à er<lb></lb>rare in tutti i uerſi, cioe che eglie ſoggetto ſi à dar diſopra, come di ſotto dalſegno, & <lb></lb>coſi anchora à dar coſtero ſi dalla banda deſtra, come dalla ſiniſtra, uero è, che eglie <lb></lb>etiam ſoggetto à dar per ſorte in brocca, & tutti questi medeſimi accidenti gli puo ac<lb></lb>caſare quando che il ſegno fuſſe di qua, ouer di la di tal concorſo, uero è, che quando il <lb></lb>detto ſegno fuſſe di la da tal concorſo, glierrori ſi cauſano maggiori (per la gran di<lb></lb>ſtantia) di quello fariano eſſendo di qua, per eſſer piu propinquo, perche in uero quan<lb></lb>to piu il ſegno è propinquo à colui, che tira, tanto piu ogni ſpecie di errore ſe ſminuiſſe <lb></lb>in lui, e pero tanto piu ſe è ſoggetto à darui dentro, ouer à far piu bella botta, come ſu<lb></lb>detto nel precedente queſito; & à tutti queſti medeſimi accidenti, anchora è ſoggetto <lb></lb>quando che nelle mire fuſſe qualche difetto, cioe che per il mouimento del detto ſchiop <lb></lb>po lui è ſoggetto à dare ſi di ſopra, come di ſotto del ſegno, & etiam coſtero. </s> <s id="s.000705">Anchora <lb></lb>eglie ſoggetto à dar preciſamente in brocca, perche quel moto del ſchioppo potria per <lb></lb>ſorte eſſer tale che medicaria il difetto delle mire, & darla in brocca, uero è, che non ſa <lb></lb>riu per ſuo ſapere, maſolamente per ſorte.<emph.end type="italics"></emph.end> S. N<emph type="italics"></emph>on piu, che ue ho inteſo benißimo, et <lb></lb>queſta uoſtra argumentatione, me ha certamente da ogni mio ſcropoloſo dubbio ret<lb></lb>camente chiarito.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000706">I<emph type="italics"></emph>l fine del Primo Libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/062.jpg"></pb> <p type="head"> <s id="s.000707">LIBRO SECVNDO DE LI <lb></lb>QVESITI ET INVENTION DIVERSE.</s> </p> <p type="head"> <s id="s.000708">DE NICOLO TARTAGLIA, <lb></lb>S<emph type="italics"></emph>opra la differentia, che occorre nelli tiri, & effetti <lb></lb>fatti con balla de Piombo, ouer di Ferro, ouer <lb></lb>di Pietra, & altre uarie particola<lb></lb>rita, circa la proportione, <lb></lb>peſo, & miſura delle <lb></lb>dette balle.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000709">QVESITO PRIMO FATTO DAL SIGNOR <lb></lb>G<emph type="italics"></emph>abriel Tadino Cauallier de Rodi, & Prior <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000710">PRIORE. D<emph type="italics"></emph>apoi che non ſappiamo piu che dire, per al preſen<lb></lb>te ſopra le qualita di tiri, & altri accidenti delle Artegliarie, per <lb></lb>non ſtar otioſi dapoi la lettione di Euclide, uoglio che parlamo al<lb></lb>quanto delle qualita, & accidenti delle diuerſita delle balle.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per <lb></lb>tanto, ditemi un poco, qual credeti che andara piu lontano, & quan <lb></lb>to una balla di piombo, ouer di ferro, tirate con una iſteſſa arte<lb></lb>gliaria, & à una isteſſa elleuatione, & con egual quantita di polue<lb></lb>re.<emph.end type="italics"></emph.end> N. B<emph type="italics"></emph>iſogna che quella me dica, con quanta quantita di polue<lb></lb>re.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>oniamo con li dui terzi di quello peſara la balla di piombo.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dub <lb></lb>bio la balla di ferro andara piu lontano.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>uanto piu.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>elli tiri baßi, cioe <lb></lb>con il pezzo aliuellato andara quaſi un terzo de piu, ma alla elleuatione d'un ponto, an <lb></lb>dara alquanto meno d'un terzo piu, & quanto piu la ſe andara elleuando tanto piu an<lb></lb>dara ſcemando di tal proportione, talmente che tirandola alla elleuatione del quinto, <lb></lb>ouer ſeſto ponto, tal balla de ferro andara piu lontano di quella di piombo ſolamente <lb></lb>poco piu d'un quinto, & accio che<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>meglio me intenda, poniamo che la balla di <expan abbr="piõ">piom</expan> <lb></lb>bo, ſtando il pezzo aliuellato, uada di lontano paſſa. </s> <s id="s.000711">300. dico che la balla di ferro (ti<lb></lb>rata con quella medeſima quantita di poluere con che fu tir ata quella de piombo (cioe <lb></lb>con li dui terzi di quello peſa la detta balla di piombo) andara di lontano quaſi paſſa. <lb></lb></s> <s id="s.000712">400. cioe quaſi in ſeſquitertia proportione, ma ſe tal balla de piombo alla elleuatione <lb></lb>del quinto, ouer ſesto ponto andaſſe di lontano poniamo paſſa. </s> <s id="s.000713">3000. dico che la balla <lb></lb>di ferro à tal elleuatione, con la medeſima poluere, andara di lontano poco piu di paſſa. <lb></lb></s> <s id="s.000714">3600. cioe poco piu che in ſequi quinta proportione.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>erche ragione ſeguita tal <lb></lb>coſa, cioe che coſi nelli tiri elleuati, non eccede ſecondo la mede ſima proportione che fa <lb></lb>nelli baßi.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>erche lo aere fa maggior reſistentia <expan abbr="proportionalmẽte">proportionalmente</expan> al corpo men <lb></lb>graue, ſecondo laſpecie, di quello fa al piu graue, & tanto piu <expan abbr="quãto">quanto</expan> piu la ritroua quel <lb></lb>lo men ueloce, ouer piu lento, e laſſo. </s> <s id="s.000715">Et perche nelli tiri baßi, non pertranſiſſe per aere <lb></lb>ſaluo che nella ſua piu uigoroſa uelocita, perche preſto ritroua la terra che ue impe-<emph.end type="italics"></emph.end><pb pagenum="32" xlink:href="042/01/063.jpg"></pb><emph type="italics"></emph>diſſe il moto, e pero non ui ſe moltiplica tanto la offenſione dell'aere, quanto che fanelli <lb></lb>tiri elleuati, perche in quelli pertranſiſſe aſſai piu tempo per l'aere, & maßime nella <lb></lb>ſua laßitudine, nella qual laßitudine (come di ſopra dißi) lo aere ui ha proportional<lb></lb>mente maggior potesta, & dominatione di quello ha nelli tiri baßi, & per tanto la det <lb></lb>ta balla di ferro non eccede tanto la balla di piombo nelli tiri elleuati (proportional<lb></lb>mente) quanto fa nelli tiri baßi.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>e ho inteſo benißimo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000716">QVESITO SECONDO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000717">PRIORE. Q<emph type="italics"></emph>ual credeti poi che andara piu lontano, o la detta balla di piom<lb></lb>bo, ouer di ferro, tirate pur con una iſteſſa artegliaria, & à una iſteſſa elleuatio <lb></lb>ne, ma ciaſcaduna con la ſua poluere ordinaria, cioe con li dui terzi di quello peſa cia<lb></lb>ſcaduna balla per ſe.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>elli tiri baßi, cioe aliuellati, ouer poco elleuati non ui ſara <lb></lb>gran differentia, ma nelli tiri molto elleuati, come ſaria à dire alla elleuatione del terzo, <lb></lb>quarto, quinto, & ſesto ponto, la balla de piombo andara aſſai piu lontano di quella di <lb></lb>ferro, & tutto questo procedera per le ragioni adutte nel precedente queſito.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o <lb></lb>haueua in animo di uolerui adimandare, quando che cadauna di dette balle fuſſe tirata <lb></lb>con li dui terzi poluere di quello peſa la balla di ferro, qual ſaria andata piu lontano, <lb></lb>ma per le ragion di ſopra adutte comprendo che la balla di ferro andaria piu lontano.<emph.end type="italics"></emph.end><lb></lb>N. C<emph type="italics"></emph>oſi è.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000718">QVESITO TERZO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Priore <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000719">PRIORE. Q<emph type="italics"></emph>ual credeti poi che andara piu lontano, & quanto una balla di fer<lb></lb>ro, ouer una di pietra pur tirate con una iſteſſa artegliaria, & à una iſteſſa elleua<lb></lb>tione, & con egual quantita di poluere, cioe con li dui terzi poluere di quello peſa la <lb></lb>balla di ferro.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza alcun dubbio la ragion ne dimostra che nelli tiri baßi, et nel <lb></lb>la maggior parte delli elleuati, la balla di pietra andara piu lontano di quella di ferro.<emph.end type="italics"></emph.end><lb></lb>P. E<emph type="italics"></emph>t quanto andara piu lontano.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>elli tiri baßi (poniamo dal ſito della equali<lb></lb>ta, per fina alla elleuation de un ſol ponto) la balla de pietra andara piu lontano, circa à <lb></lb>un quarlo piu di quello ſara andata, ouer che andaria la balla di ferro, & inanti piu che <lb></lb>manco, ma poi nelli tiri piu elleuati, non creſſaria tanto, & tanto meno quanto piu ſa<lb></lb>ranno elleuati, & talmente andara ſcemando che alla elleuatione del quarto ponto ui ſa <lb></lb>ra pochißima differentia, cioe che à tal elleuatione andara quaſi tanto lontano la balla <lb></lb>di ferro quanto quella di pietra, ma alla elleuatione del quinto, & ſeſto ponto la balla <lb></lb>di ferro andara poi alquanto piu lontano di quella di pietra, & tutto queſto procede <lb></lb>per le ragioni adutte ſopra il primo queſito.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>ertamente le ſono coſe belle da <lb></lb>conſiderare.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/064.jpg"></pb> <p type="head"> <s id="s.000720">QVESITO QVARTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000721">PRIORE. Q<emph type="italics"></emph>ual credeti poi che andara anchora piu <expan abbr="lõtano">lontano</expan>, o la detta balla di <lb></lb>ferro, o quella di pietra, pur tirate <expan abbr="cõ">com</expan> una iſteſſa artegliaria, et à una iſteſſa elle <lb></lb>uatione, ma con la ſua poluere ordinaria, cioe tirando la balla di ferro con li dui terzi, <lb></lb>poluere di quello peſa la balla, & quella di pietra con un terzo di quello peſa la medeſi <lb></lb>ma balla di pietra.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a determination di queſto non è molto facile per il uariar <lb></lb>della proportione del peſo di cadauna balla alla ſua poluere, nondimeno conchiudo che <lb></lb>la balla di ferro andara piu lontano di quella di pietra in ogni elleuatione, uero è, che <lb></lb>quanto piu il tiro ſara elleuato, tanto piu andara piu lontano la detta balla di ferro pro <lb></lb>portionalmente di quella di pietra, & econuerſo, cioe che quanto piu il tiro ſe accoſte<lb></lb>ra al ſito della equalita, ui occorrera menor differentia<emph.end type="italics"></emph.end>. </s> <s id="s.000722">P. C<emph type="italics"></emph>omprendo adunque che <lb></lb>quelli primi che determinorno che alla balla di pietra ui ſi doueſſe dar ſolamente il ter<lb></lb>zo poluere, di quello peſa la balla, il ferno, perche forſi con con la ſperientia trouaro <lb></lb>quello che uoi diceti, cioe che ſe agguagliaua à quella di ferro.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000723">QVESITO QVINTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000724">PRIORE. Q<emph type="italics"></emph>ual teneti che fara maggior effetto, ouer paſſata (in una egual di <lb></lb>ſtantia) una balla di piombo, ouer di ferro tirate con una iſteſſa artegliaria, & à <lb></lb>una iſteſſa elleuatione, & prima con egual quantita di poluere, cioe con li dui terzi di <lb></lb>quello peſa la balla de piombo) & dapoi con la ſua poluere ordinarìa.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>i ſopra <lb></lb>nel primo queſito fu conchiuſo che la balla di ferro in ogni elleuatione andara piu lon<lb></lb>tano di quella di piombo (eſſendo pero ambedue tirate con quella detta egual quantita <lb></lb>di poluere) e pero ſe la coſa doue ſe tira fuſſe tanto lontano che la balla di piombo non <lb></lb>ui poteſſe arriuare, & che quella di ferro ui arriuaſſe, cadauno ſapra far queſto giudi<lb></lb>cio ſenza che io il dica, ma ſe la detta coſa doue ſe tiraſara in una diſtantia conueniente <lb></lb>all uno, e l'altro tiro, & che la detta coſa non ſia di tal durezza che ſia atta à ſmac care <lb></lb>la balla de piombo, ſenza dubbio la balla de piombo fara molto maggior effetto, ouer <lb></lb>paſſata di quello fara la balla di ferro, per cauſa della ſua maggior grauita, perche mol <lb></lb>to piu opera la grauita che la uelocita (come ſopra al. 16. queſito del primo anchor fu <lb></lb>detto) uero è, che quando la detta coſa doue ſe tira fuſſe di tal durezza che fuſſe atta à <lb></lb>ſmaccar la detta balla di piombo, uiſaria da dubitare, che la balla di ferro doueſſe pene <lb></lb>trare alquanto piu di quella di piombo, uero è, che ſe ben la balla di piombo non pene<lb></lb>traſſe tanto quanto quella di ferro, il non reſtara ch'ella non conquaßimolto piu la det <lb></lb>ta coſa percoſſa di quello fara la detta balla di ferro, per cauſa della ſua maggior gra<lb></lb>uita, & tutto queſto che ſe detto di tai balle tirate, con la detta egual quantita di polue<lb></lb>re meglio ſe uerificara tir andole con la ſua poluere ordinaria, cioe con li dui terzi di <lb></lb>quello chi peſa cadauna balla per ſe, cioe che nelle coſe che non ſiano atte per ſua durez <lb></lb>za à ſmaccare la balla de piombo molto piu ſara di maggior effetto, ouer paſſata la<emph.end type="italics"></emph.end><pb pagenum="33" xlink:href="042/01/065.jpg"></pb><emph type="italics"></emph>detta balla di piombo di quella di ferro, di quello era tirandole cadauna con la ſopra <lb></lb>detta equal quantita di poluere, & ſimelmente in quelle coſe, che per la ſua durezza <lb></lb>ſiano atte à ſmaccar la balla de piombo, quantunque forſi la balla di ferro potria eßer <lb></lb>che penetraſſe alquanto piu, nondimeno molto maggior botta, & <expan abbr="conquaſſamẽto">conquaſſamento</expan> fara <lb></lb>la balla di piombo di quella di ferro.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>glie coſa, che aſſai mi conſona.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000725">QVESITO SESTO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Priore di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000726">PRIORE. Q<emph type="italics"></emph>ual credeti poi che fara maggior effetto, ouer paſſata (in equal <lb></lb>diſtantia) una balla di ferro, ouer di pietra, tir ate con una iſteſſa artegliaria, & <lb></lb>a una iſteſſa elleuatione, & prima con equal quantita di poluere, cioe con li dui terzi <lb></lb>di quello peſa la balla di ferro, & dapoi con la ſua poluere ordinaria.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n queſta <lb></lb>non ui è alcun dubbio, che la balla di ferro fara molto maggior effetto, ouer paſſata, et <lb></lb>in ogni qualita di materia, di quello fara la balla di pietra, domente che la coſa doue ſe <lb></lb>tira non fuſſe tanto lontana, che la balla di ferro non ui poteſſe arriuare, & che quel<lb></lb>la di pietra ui arriuaſſe (come fu detto anchoraſopra la balla di piombo, & di ferro <lb></lb>nel precedente Queſito) & ſe adunque la balla di ferro fara maggior effetto, ouer paſ <lb></lb>ſata, della balla di pietra tirandole ambe due con quella equal quantita di poluere, mol <lb></lb>to maggior effetto, ouer paſſata fara la poi tirandole ambe due con la ſua poluere ordi <lb></lb>naria, cioe la balla di ferro con li dui terzi di quello peſa la detta balla, & quella di pie <lb></lb>tra con un ſolterzo di quello peſa detta balla di pietra.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o ho ſempre tenuto, che <lb></lb>coſi fuſſe, come uoi hauete detto, & determinato.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000727">QVESITO SETTIMO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000728">PRIORE. E<emph type="italics"></emph>ſſendo io à Rhodi al tempo, che il Turco ui era à torno, & eſſen <lb></lb>do io andato in una certa parte della terra con molti guaſtadori per far fare al <lb></lb>cuni ripari, accadete, che ne fu tirato da Turchi con una artegliaria, & la balla con el <lb></lb>ſuo ciffolare ſe fece ſentire tanto di lontano, che ogn uno hebbe aſſai commodita di po<lb></lb>ter dar luoco alla detta balla, & ſchiuarſi da quella, & coſi ogn'un fece. </s> <s id="s.000729">Et dapoi che <lb></lb>la detta balla hebbe fatto il ſuo effetto fruſtatorio, ogniuno retornorno à lauorare ſicu <lb></lb>ramente confidandoſi, che ſe ben ue retirauano piu di ſaluarſi ſempre al auiſo della bal <lb></lb>a, cioe alſuo ciffolare, hor accadete, che ue retirorno un'altra uolta, & la detta balla <lb></lb>uenne tanto quietamente, che alcun non la ſentete, ſaluo nel aggiongere, ouer nel far el <lb></lb>ſuo effetto, talmente che quella ucciſe quattro guaſtadori, hor ue adimando la cauſa di <lb></lb>tal ſuo uenir coſi tacito, & quieto, & maßime, che ue retirorno molte altre nolte, & <lb></lb>faceua el medeſimo.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a cauſa di tal effetto procede, per le ragioni adutte nel. </s> <s id="s.000730">4. <lb></lb>Queſito del primo libro, cioe, perche la prima uolta, che ui fu tirato, tal balla ritrouo <lb></lb>lo aere quieto, per la qual quietitudine, fa maggior reſiſtentia al moto della balla di <lb></lb>quello faria eſſendo commoſſo, per la qual reſiſtentia ſe cauſa quelſuo ſi <expan abbr="grã">gram</expan> ciffolare,<emph.end type="italics"></emph.end><pb xlink:href="042/01/066.jpg"></pb><emph type="italics"></emph>cioe, che tal ciffolare, naſſe dalla gran difficulta, che ritroua la detta balla in penetrar <lb></lb>tal aere ripoſante, e quieto: ma perche alla <expan abbr="ſecõda">ſeconda</expan> uolta tal balla, non ſolamente la ritro <lb></lb>uo tal aere tutto commoſſo, rotto, & conquaſſato, dalla prima balla tirata, ma ancho<lb></lb>ra molto tendente, ouer ſcorrente uerſo al luoco doue ſe tira, cioe ſecondando el moto <lb></lb>della detta halla, per le qual coſe la detta balla, per non ritrouar quell'ostacolo alla ſe <lb></lb>conda uolta, che fece alla prima, la non ciffolaua coſi forte, come fece alla prima uolta, <lb></lb>& per le medeſime ragioni molto meno doueua ciffolare nelli altri tiri, eſſendo pero ti <lb></lb>rati conſequentemente.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſta uoſtra ragione mi conſona aſſai.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000731">QVESITO OTTAVO FATTO DAL <lb></lb>M<emph type="italics"></emph>agnifico<emph.end type="italics"></emph.end> M. B<emph type="italics"></emph>ernardo Segreo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000732">MAGN. M. BERNARDO Q<emph type="italics"></emph>ual credeti che andara piu <expan abbr="lõtano">lontano</expan>, una balla <lb></lb>graue, ò una leggiera, <expan abbr="tirãdo">tirando</expan> l'una e laltra <expan abbr="cõ">com</expan> una iſteſſa artegliaria, et à una iſteſ <lb></lb>ſa elleuatione, & con equal quantita di poluere.<emph.end type="italics"></emph.end> N. </s> <s id="s.000733">A <emph type="italics"></emph>queſto non ui ſi puo dare de<lb></lb>terminata reſpoſta, che non diſtingue la differentia della lor grauita, & la quantita de <lb></lb>la poluere, perche, & la grauita della coſa, & la leuita ſe é uista fruſtare la uirtu del <lb></lb>mouente, perche la coſa tirata puo eſſer di tal leuita, che à pena, ouer poco lontano dal <lb></lb>la bocca del pezzo ſara ſpenta, ouer tirata, & ſimelmente potria eßer di tanta gran <lb></lb>grauita (riſpetto alla poca quantita della poluere) che ſeguitaria el medeſimo inconue <lb></lb>niente, e pero eglie neceßario à diſtinguere la differentia della lor grauita, etiam di <lb></lb>che materia ſia cadauna balla, etiam la quantita della poluere, perche ſe l'una fuſſe de <lb></lb>piombo, & l'altra di ferro, ouer di pietra, & tirandole con i dui terzi di poluerè di <lb></lb>quello peſa la balla de piombo, eglie coſa chiara (per le ragioni adutte di ſopra nel pri<lb></lb>mo, & terzo Queſito) che la balla di ferro, ouer di pietra andara piu lontano di quel <lb></lb>la di piombo, ma ſe l'una de dette balle fuſſe di piombo, ouer di ferro, et l'altra di legno <lb></lb>leggiero, ouer di quel ſuore, che ſi mette nelli ſubri, ouer zocoli delle donne, eglie da <lb></lb>credere che la balla graue, cioe quella di piombo, ouer di ferro (tirata con la ſua pol<lb></lb>uere or dinaria) andara molto piulontano, della balla leue (cioe di quella balla di le<lb></lb>gno leggiero, ouer diſuore) tirate anchor quelle con la medeſima quantita di polue<lb></lb>re. </s> <s id="s.000734">Ma uoltando carta, che uoleſſe tirare una balla de piombo da lire cento con un ca<lb></lb>non da cento, & ſimelmente una balla di legno di quella medeſima grandezza, ouer <lb></lb>groſſezza, che é quella di piombo, ma tirare l'una, e l'altra ſolamente con una lira, <lb></lb>ouer due di poluere, eglie da credere in queſto caſo, che la balla di legno andara piu <expan abbr="lõ">lom</expan> <lb></lb>tano di quella di piombo, la qual coſa ne auertiſſe qualmente eglie neceſſario, che tra <lb></lb>la grauita della coſa tirata, & la uirtu della coſa mouente (ouer che ſpenge) ui caſca <lb></lb>una ſua limitata proportione.<emph.end type="italics"></emph.end> M. B. Q<emph type="italics"></emph>ueſto uoſtro diſcorſo non me diſpiace, & <lb></lb>ſappiati, che una uolta mi uolſi chiarire di queſto dubbio, & feci far una balla, pur di <lb></lb>mettallo, ma buſa, cioe uacua di dentro, & la feci tirare, & quella ando aſſai meno del <lb></lb>la balla or dinaria di ferro.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="34" xlink:href="042/01/067.jpg"></pb> <p type="head"> <s id="s.000735">QVESITO NONO FATTO DAL MAGNIFICO <lb></lb>S<emph type="italics"></emph>ignor Giulio Sauorgnano.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000736">SIGNOR GIVLIO E<emph type="italics"></emph>glie una balla, che per diametro è onze quatro di mi <lb></lb>ſura, & peſa lire otto, hor ue adimando quanto peſaria unaltra, che fuſſe per dia <lb></lb>metro onze.<emph.end type="italics"></emph.end> 6. N. L<emph type="italics"></emph>a peſaria lire.<emph.end type="italics"></emph.end> 27. S. G. C<emph type="italics"></emph>ome è poßibile, che una balla, che <lb></lb>ſia per diametro onze. </s> <s id="s.000737">6. de miſura (che ſaria mezzo pie) non peſi piu de lire. </s> <s id="s.000738">27. an <lb></lb>zi tengo, che debbia peſare piu de lire.<emph.end type="italics"></emph.end> 60. N. E<emph type="italics"></emph>glie il uero, che ſe tal balla fuſſe di <lb></lb>ferro, et che per diametro la fuſſe onze. </s> <s id="s.000739">6. de miſura ordinaria (che ſaria me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o pie) <lb></lb>ſenza dubbio tengo, che peſaria circa à dette lire.<emph.end type="italics"></emph.end> 60. S. G. P<emph type="italics"></emph>erche diceti adunque <lb></lb>che la peſara ſolamente lire.<emph.end type="italics"></emph.end> 27. N. I<emph type="italics"></emph>o dico, che la peſara lire. </s> <s id="s.000740">27. stante, che quella <lb></lb>che è di diametro onze quattro peſi ſolamente lire otto: maſe tal balla fuſſe de ſerro, <lb></lb>& che de diametro la fuſſe (come è detto) onze quattro de miſura ordmaria (cioe un <lb></lb>terzo dun pie) la peſaria piu de lire. </s> <s id="s.000741">18. uel circa, e pero io ho riſposto ſecondo la pro <lb></lb>poſta.<emph.end type="italics"></emph.end> S. G. E<emph type="italics"></emph>t come haueti trouato quelle lire.<emph.end type="italics"></emph.end> 27. N. I<emph type="italics"></emph>o le ho ritrouate in que<lb></lb>ſto modo, io ho cubato quelle onze. </s> <s id="s.000742">4. (diametro della prima balla) el cubo delle quale <lb></lb>è. </s> <s id="s.000743">64. & <expan abbr="ſimelmẽte">ſimelmente</expan> ho cubato quelle. </s> <s id="s.000744">6. onze (diametro della <expan abbr="ſecõda">ſeconda</expan> balla) el cubo del <lb></lb>le quale è. </s> <s id="s.000745">216. et dapoi per la regola del tre, dico: ſe. </s> <s id="s.000746">64. peſa lire. </s> <s id="s.000747">8. che peſara. </s> <s id="s.000748">216. <lb></lb>multiplico, & parto ſecondo l'ordine di tal regula, & mene uenuto le dette lire. </s> <s id="s.000749">27. e <lb></lb>pero ho concluſo, che la detta ſeconda balla peſaria lire. </s> <s id="s.000750">27. ſtante che la prima peſaſ<lb></lb>ſe ſolamente lire.<emph.end type="italics"></emph.end> 8. S. G. V<emph type="italics"></emph>eho inteſo benißimo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000751">QVESITO DECIMO FATTO DA M. ZANAN<lb></lb><emph type="italics"></emph>tonio di Ruſconi Pittor, & Architettor.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000752">ZANANTONIO E<emph type="italics"></emph>glie una balla, che per diametro è. </s> <s id="s.000753">5. deda ui <lb></lb>adimando <lb></lb>come faro io aritrouare quanto che ſia el diametro duna altra balla che ſia dop<lb></lb>pia à questa.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oi doueti cubar quelli cinque deda de diametro, el qual cubo ſara <lb></lb>125. & questo. </s> <s id="s.000754">125. uoi lo adoppiareti, fara. </s> <s id="s.000755">250. & la radice cuba di queſto. </s> <s id="s.000756">250. ſa<lb></lb>ra el diametro di quella <expan abbr="ſecõda">ſeconda</expan> balla (doppia alla prima) la qual radice cuba de 250. <lb></lb>cauandola per el modo, che ui ho moſtrato uoi trouareti, che la ſara alquanto piu de <lb></lb>ſei deda, cioe ui auanzara. </s> <s id="s.000757">34. rotti.<emph.end type="italics"></emph.end> Z. C<emph type="italics"></emph>ome mi debbio gouernare con quello. </s> <s id="s.000758">34. <lb></lb>che mi auanza per formar il conueniente rotto da accompagnar con quelli ſei deda.<emph.end type="italics"></emph.end><lb></lb>N. L<emph type="italics"></emph>a bona regola di formar el rotto di quel reſiduo, che auanza nella eſtratione <lb></lb>della radice cuba (nelli numeri non cnbi) per fin à queſta hora maiho ritrouato in al<lb></lb>cun Autore, che di tal materia habbia trattato, che l'habbia rettamente inteſa, & que <lb></lb>ſto procede (ſe non me inganno) perche el retto modo da cauar la detta radice cuba, <lb></lb>dalla maggior parte è ignorato, <expan abbr="nõ">non</expan> dico ignorato, che quelli tali <expan abbr="nõ">non</expan> la ſappiano caua <lb></lb>re, ouer che le regole da lor poſte, non ſeruino per cauarla, ma uoglio dire, che tai <lb></lb>ſue regole non procedeno per la uera, & retta uia naturale, perche ſe queſti tali proce <lb></lb>deſſeno per la ſua rettauia nel cauar la detta radice cuba, & che intendeßino po<gap></gap>la <lb></lb>cauſa di tal ſuo operare, facile ui ſaria ad aßignare con ragione la uera regola da<emph.end type="italics"></emph.end><pb xlink:href="042/01/068.jpg"></pb><emph type="italics"></emph>ſormar el ſuo rotto, nelli reſidui restanti nel ſuo operare.<emph.end type="italics"></emph.end> Z. L<emph type="italics"></emph>a retta uia da cauare <lb></lb>la detta radice cuba, non eglie quella, che uoime baueti moſtrata.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uella pro<lb></lb>pria.<emph.end type="italics"></emph.end> Z. D<emph type="italics"></emph>apoi che uoi me haueti moſtrata tal regola, uoi me moſtrareti pur ancho <lb></lb>ra el modo da formar rettamente el detto rotto.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er al preſente uoi hareti pa<lb></lb>tientia, ma ben ui prometto, che in breue con alcune altre coſe inſieme ue le faro uede<lb></lb>re à uoi, et alli altri.<emph.end type="italics"></emph.end> Z. N<emph type="italics"></emph>on potendo far altro haro patientia per fin a quel <expan abbr="tẽpo">tempo</expan>.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000759">QVESITO VNDECIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> M. Z<emph type="italics"></emph>anantonio di Ruſconi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000760">ZANANTONIO. C<emph type="italics"></emph>on che regola, ouer uia determina adunque Vetruuio <lb></lb>la proportione delle pietre, che ſe hanno da mettere al forame della Balista.<emph.end type="italics"></emph.end> N. <lb></lb>A<emph type="italics"></emph>deſſo me aricordo, che la ragione, che uoi me adimandaſti nel precedente Queſito é <lb></lb>proprio quella medeſima, che pone il detto Vittruuio al. 17. capitulo del ſuo decimo li<lb></lb>bro, nel qual luoco lui conclude, che ſelſaſſo qual debbe tirare la baliſta ſara dui peſi, <lb></lb>cioè de due libre) che el forame del ſuo capitello ſara de. </s> <s id="s.000761">5. digiti, ouer dedi, e che ſe tal <lb></lb>ſaſſo ſara de. </s> <s id="s.000762">4. libre, dice chel detto forame ſia fatto de. </s> <s id="s.000763">6. digiti, ouer dedi, la qual de <lb></lb>terminatione é ſimile alla noſtra fatta nel precedente Queſito reſpetto al numero ſa<lb></lb>no, cioe al ſeſto, ma non al rotto, perche quello. </s> <s id="s.000764">34. che in tal luoco ne auanzo ne <expan abbr="riſpõ">riſpom</expan> <lb></lb>de aſſai piu dun quarto de digito, cioe, che tal forame doueria eſſer alquanto piu de di<lb></lb>giti. </s> <s id="s.000765">6. c un quarto.<emph.end type="italics"></emph.end> Z. P<emph type="italics"></emph>otria eſſer, che il fuſſe ſtato mal tradutto.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>l medeſi<lb></lb>mo ſi trouanel Latino.<emph.end type="italics"></emph.end> Z. V<emph type="italics"></emph>edeti mo, ſe nelle altre ſue determinationi, che ſeguitano <lb></lb>in tal luoco, ſono giuſtamente <expan abbr="cõcluſe">concluſe</expan>.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio ui è qualche errore, ma piu <lb></lb>in una, che nell'altra, & credo tutto queſto proceda per ignorare quella regola da noi <lb></lb>ritrouata (detta nel precedente Queſito) di ſapere formare el ſuo conueniente rotto <lb></lb>di quel reſiduo, che auanza nelle eſtrationi delle radice cube, nelli numeri non cubi, & <lb></lb>che el ſia eluero, lui conclude, che ſelſaſſo, che ſe ha da tirare ſara de. </s> <s id="s.000766">7. libre, che el fo <lb></lb>rame del capitello de detta baliſta ſi debbia far de digiti. </s> <s id="s.000767">7. & per el rotto, che debbe <lb></lb>eſſer de piu de detti digiti. </s> <s id="s.000768">7. lui mette noue ponti in forma quaſi circulare.<emph.end type="italics"></emph.end> Z. C<emph type="italics"></emph>he <lb></lb>ſa, che quelli. </s> <s id="s.000769">9. ponti non ſignificano el conueniente rotto, ouer parte de digiti, che uol <lb></lb>eſſer el detto forame de piu delli detti. </s> <s id="s.000770">7. digiti, quantunque che noi non intendamo el <lb></lb>ſigniſicato de detti noue ponti, per eſſer coſa antiqua.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uando coſi fuſſe neceſ<lb></lb>ſariamente ſeguitaria, che in qualunque luoco doue ſono poſti quelli tali noue ponti, ui <lb></lb>repreſentaſſono uno medeſimo rotto, la qual coſa non è uera, perche nelli detti luochi <lb></lb>ui occorre rottimolto diuerſi in quantita, eſſempi gratia, al detto ſaſſo de ſeilibre, el <lb></lb>detto forame uora eſſer de. </s> <s id="s.000771">7. digiti, & circa a uno ottauo de digito, cioe uol eſſer al<lb></lb>quanto ſcarſo de. </s> <s id="s.000772">7. digiti, & uno ottauo de digito. </s> <s id="s.000773">Et per tanto quellinoue ponti, in <lb></lb>tal luoco ueneriano a ſignificare alquanto manco de uno ottauo de digito. </s> <s id="s.000774">Et nel ſaſſo <lb></lb>de diece libre lui conclude, che el detto forame uora eſſer de. </s> <s id="s.000775">8. digiti, & piu el ſignifi<lb></lb>cato de detti noue ponti, & noi procedendo per l'ordine dato nel precedente Queſito, <lb></lb>ritrouamo che el detto ſaſſo de diece libre, uora di forame alquanto piu de digiti otto e <lb></lb>mezzo, per il che ſeguitaria, che li detti noue ponti nel detto luoco ſignificaſſono al-<emph.end type="italics"></emph.end><pb pagenum="35" xlink:href="042/01/069.jpg"></pb><emph type="italics"></emph>quanto piu d'un mezz digito, & gia di ſopra trouaßimo, che ſignificauano manco d'un <lb></lb>ottauo de digito, la qual coſa ne manifeſta qualmente li detti nuoue ponti non hanno al<lb></lb>cuna regolata ſignificatione, & ſimilmente ne aduertiſſe qualmente Vitruuio non haue <lb></lb>uaregola di ſapere formare rettamente il rotto di quel reſiduo che ſoprauanza nelle <lb></lb>eſtrattioni delle radice, cube, nelli numeri non cubici (che di ſopra nel precedente que<lb></lb>ſito diceßimo hauer ritrouata) la qual diceßimo anchora eſſer ſtata ignorata da quanti <lb></lb>Autori habbiamo letto, che di tal materia habbiam trattato.<emph.end type="italics"></emph.end> Z. N<emph type="italics"></emph>on poſſo credere, <lb></lb>che Vitruuio ignoraſſe tal coſa, ma la cauſa debbe eſſer proceſſa dalli traduttori.<emph.end type="italics"></emph.end> N. <lb></lb>I<emph type="italics"></emph>l medeſimo è nelli antichißimi in lingua Latina, ma piu che nel ſaſſo de. </s> <s id="s.000776">20. libre, lui <lb></lb>determina che il detto forame uorra eſſer de digiti diece, & piu il ſignificato di detti <lb></lb>nuoue ponti, & noi ritrouamo, che tal forame uorra eſſer de digiti diece, & piu de tre <lb></lb>quarti d'un' altro digito, onde in queſto luoco li detti nuoue ponti ueneriano à ſignifi<lb></lb>care piu de tre quarti d'un digito, & coſi ua procedendo, & errando quaſi in tutte le <lb></lb>altre ſue determinationi che ſeguitano.<emph.end type="italics"></emph.end> Z. M<emph type="italics"></emph>e ſtupiſco che tal huomo habbia erra<lb></lb>to in ſimil caſo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000777">QVESITO DVODECIMO FATTO DAL <lb></lb>S<emph type="italics"></emph>ignor lacomo di Achaia, Con una ſua lettera <lb></lb>mandata da Lezze.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000778">SIGNOR IACOMO. I<emph type="italics"></emph>o ui prego di gratia, che per il lattor della preſente, <lb></lb>me uogliati mandar in diſſegno quanto ſia, ouer debbia eſſere il diametro di una <lb></lb>palla di uno rotulo à peſo, & coſi quello di una, di dui rotuli, & ſimilmente datre, da <lb></lb>quattro, da cinque, da ſei, & coſi procedendo per fina à quella maggior quantita de <lb></lb>rotuli, che à uoi parera.<emph.end type="italics"></emph.end> N. </s> <s id="s.000779">A <emph type="italics"></emph>douer ſatisfare alla dimanda di uostra Signoria, eglie <lb></lb>neceſſario che quella me dia notitia del diametro, & del peſo di una balla con ſomma di <lb></lb>ligentia miſurata, & peſata, cioe ueder di trouare una balla, & quanto piu è groſſa tan <lb></lb>to è meglio, & quella peſarla ſottilmente, come ſe fuſſe di argento, & dapoi trouar dili<lb></lb>gentemente quanto è per diametro, cioe quanto è per linea, & dapoi mandarme in diſ<lb></lb>ſegno la longhezza di tal diametro, etiam la quantita del peſo di tal balla, & darmi an <lb></lb>chor notitia, ouer inſormatione che peſo ſia un rotulo, & come ſe diuide, cioe quante li <lb></lb>re, ouer onze ſia, perche tal ſorte de peſo non ſe coſtuma in queſte bande, & facendo <lb></lb>questo ſatisfaro alla petitione, ouer queſito de uoſtra Signoria.<emph.end type="italics"></emph.end> S.I. M. N<emph type="italics"></emph>icolo cariſ<lb></lb>ſimo ho riceuuta la uoſtra, & inteſo il tutto, e per tanto ui auiſo qualmente la ſottoſcrit <lb></lb>ta linea è il diametro di una balla di ferro, qual peſa preciſamente. </s> <s id="s.000780">9. rotuli, & ſappiati <lb></lb>che un rotulo è un certo peſo che ſi uſa qua in Lezze, il qual rotulo è onze. </s> <s id="s.000781">33. e un ter <lb></lb>zo di on za, cioe onze. </s> <s id="s.000782">100. ſono tre rotuli.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor Iacomo honor andißimo ho ri<lb></lb>ceuuta la uostra inſieme con il diametro di una balla de rotuli. </s> <s id="s.000783">9. con il qual diametro <lb></lb>ue ho ritrouato il diametro delle ſottoſcritte, & piu ue ne haria ritrouato, ma mi ho <lb></lb>penſato, che queſti debbano eſſer à ſufficientia, per quello deſidera uoſtra Signoria, & <lb></lb>per piu commune ſatisfattione ho uoluto tirar tal peſo de rotuli al peſo de queste ban<lb></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"></pb>ghi che non poteuduo capire nel foglio, ui ho notato ſolamente la mitade di tal diame<lb></lb>tro, come quella potra uedere, & ſe il diametro, che quella me ha mandato è giuſto, an<lb></lb>chora questida me geometricamente ritrouati, ſar anno giuſti, & ſe quella hauera <expan abbr="cõ-meſſo">con<lb></lb>meſſo</expan> alcuno errore, nel detto diametro à me mandato, anchor li miei non ſaranno ſen-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.070.1.jpg" xlink:href="042/01/070/1.jpg"></figure><pb pagenum="36" xlink:href="042/01/071.jpg"></pb><emph type="italics"></emph>zamenda, ſimilmente ſe il uoſtro rotulo è giuſtamente onze. </s> <s id="s.000785">33. e un terzo, & le lire <lb></lb>da me determinate ſopra detti diametri ſtar anno bene à ragion de onze. </s> <s id="s.000786">12. per lira, <lb></lb>& ſi taluoſtre onze ſaranno eguale alle noſtre onze qua da Venetia, anchora le dette <lb></lb>balle ſe uerificaranno al noſtro peſo da Venetia, altr amente non.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.071.1.jpg" xlink:href="042/01/071/1.jpg"></figure> <pb xlink:href="042/01/072.jpg"></pb> <p type="main"> <s id="s.000787">VERO <emph type="italics"></emph>è, che tutte le balle gettate in una medeſima forma non <lb></lb>ſaranno pre<lb></lb>ciſamente d'un medeſimo peſo, perche in una il metallo ui ſe congella alle uol<lb></lb>te piu fiſſo, ouer piu poroſo che nell'altra per molte cauſe le quale non uoglio al pre<lb></lb>ſente ſtar à narrarle, ma ſolamente me apparſo de aduertirui, accio che ſe la nostra de<lb></lb>terminatione, non ui riſpondeſſe coſi preciſamente, come habbiamo determinato, che <lb></lb>quella non ſe ne debbia ſcandalizzare, perche tutte le coſe operate in materia, mai pon <lb></lb>no eſſer fatte coſiuere è preciſe, che ſempre le <expan abbr="nõ">non</expan> poßano eſſere piu uere, et piu preciſe.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000788">ANCHORA V<emph type="italics"></emph>ostra Signoria aduertiſca, che ſe il detto diametro <lb></lb>à me man<lb></lb>dato fu di una balla di ferro (come me haueti ſcritto) tutti li noſtri ſe debbono <lb></lb>intendere ſolamente ſopra balle di ferro, & non di piombo, ma uolendoli etiam adat<lb></lb>tare alle balle di piombo, biſogna augumentarui il ſuo peſo per la ſua mita, cioe ſelo <lb></lb>detto diametro è di balla di ferro, & che quella peſi, come detto rotuli.<emph.end type="italics"></emph.end> 9 (<emph type="italics"></emph>ouer lire.<emph.end type="italics"></emph.end><lb></lb>25.) <emph type="italics"></emph>dico che un'altra di piombo gettata in quella medeſima forma peſara, circa à un <lb></lb>tanto è me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>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></lb>bo, al ferro in grauita ſta quaſi in ſeſquialtera proportione, & coſi ſi debbe intendere <lb></lb>in tutti glialtri. </s> <s id="s.000791">Et che ne uoleſſe farne far de pietra commune ſopra la miſura di alcu<lb></lb>no di detti diametri, tal balla peſara circa la quarta parte di quello peſaria quella de <lb></lb>piombo, cioe che la proportione della pietra marmorina al piombo in ponderoſita é <lb></lb>quaſi ſubquadrupla, & con il ferro è quaſi come da. </s> <s id="s.000792">15. à. </s> <s id="s.000793">38. per la qual notitia ſe po<lb></lb>tra trouar la grauita di qual ſiuoglia balla, ſopra qual ſi uoglia diametro aßignato, & <lb></lb>accio che meglio quella lo poſſa tener in memoria qua di ſotto ui ho notata la detta lor <lb></lb>proportione diſtintamente.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000794">I<emph type="italics"></emph>l piombo al ferro è quaſi come. </s> <s id="s.000795">30. à. </s> <s id="s.000796">19. cioe quaſi ſeſquialtera.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000797">I<emph type="italics"></emph>l piombo al pietra marmorina è quaſi come. </s> <s id="s.000798">4. à.<emph.end type="italics"></emph.end> 1. </s> </p> <p type="main"> <s id="s.000799">I<emph type="italics"></emph>l ferro alla pietra è quaſi come. </s> <s id="s.000800">38. à.<emph.end type="italics"></emph.end> 15. </s> </p> <p type="head"> <s id="s.000801">I<emph type="italics"></emph>l fine del Secondo Libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb pagenum="37" xlink:href="042/01/073.jpg"></pb> <p type="head"> <s id="s.000802">LIBRO TERZO DELLI <lb></lb>QVESITI ET INVENTIONI DIVERSE, <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.000803">S<emph type="italics"></emph>opra del Salnitrio, & delle uarie compoſitioni della poluere delle arte<lb></lb>gliarie, & della proprietà, ouer particular officio, che ha <lb></lb>cadauno di ſuoi tre materiali in tal compoſitione, <lb></lb>& altre particolarita.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000804">QVESITO PRIMO FATTO DAL SIGNOR <lb></lb>G<emph type="italics"></emph>abriel Tadino Priore di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000805">PRIORE. N<emph type="italics"></emph>on é da mar auigliarſi, che gli autiqui non haueſſero <lb></lb>notitia del ſalnitrio, qual à noi moderni è fatto tanto famigliare.<emph.end type="italics"></emph.end><lb></lb>N. A<emph type="italics"></emph>nzi la notitia di tal ſimplice è antiquißima, perche el ſi uede <lb></lb>tutti li antiqui Phyſici, ouer naturali farne mentione, uero è che al <lb></lb>cuni (& maßime Auicenna) l'hanno chiamata, Baurach, perche co <lb></lb>ſi in lingua Arabica è nominato, & alcuni altri gli dicono, Afro<lb></lb>nitrum, perche da Greci coſi è detto, & altri poi (& maßime Sera <lb></lb>pione, Diaſcoride, & Plinio) lo chiamano Nitro, ouer ſpuma ni<lb></lb>tri, perche in lingua Latina coſi è nominato, & nelle Pandete ſe affermale ſpecie del <lb></lb>nitro, ouer ſalnitri, eſſer due, cioe minerale, & artificiale, & del minerale, dicono eſ<lb></lb>ſeruen di. </s> <s id="s.000806">4. ſorte, cioe Armeno, Affricano, Romano, & Egyptio. </s> <s id="s.000807">Et Serapione dice, <lb></lb>che le minere del ſalnitrio, ſono come le minere de ſali, perche di quello ſe ne troua, che <lb></lb>ſono acque ſcorrente, le quale acque ſe congellano, et ſi condenſano quaſi, come pietra, <lb></lb>& queſto medeſimo afferma Plinio, & ſe ne troua anchora, che nella ſua minera è co<lb></lb>me pietra, & chiamaſi ſal petroſo, anchor dice, che di queſto ſalnitrio ſe ne troua de <lb></lb>bianco, de roſſo, & de molti colori, & per tanto aſſerma le ſpecie di quello eſſer molte, <lb></lb>non ſolamente per la diuerſita del colore, ma perche ui ſe ne troua prima una ſpecie, <lb></lb>che è molto ſpongoſo, cioe pieno de forami, & un'altra poi che uiene in lamine frangi <lb></lb>bìle, & de molte altre qualita, che longo ſaria à starle à narrare à una per una: delle <lb></lb>quale una è piu mordente, & potente dell'altra, del Artificiale poi non accade à par<lb></lb>larne, per eſſer à queſti tempi piu cognito, che la herba Betonica.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>erto credeua <lb></lb>che la notitia ſua fuſſe moderna.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000808">QVESITO SECONDO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000809">PRIORE. D<emph type="italics"></emph>itime un poco, ſe gli antiqui bebbero cognitione del ſalnitrio ſi <lb></lb>del naturale, come del artificiale (come di ſopra haueti approuato) per autori<lb></lb>ta de antiqui Phyſici, hebbero poi notitia che quello ardeſſe abbruſaſſe coſi uigoroſa<lb></lb>mente come fa.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>ertamente liſopradetti antiqui naturali non fanuo mentione,<emph.end type="italics"></emph.end><pb xlink:href="042/01/074.jpg"></pb><emph type="italics"></emph>ſaluo di quelle proprietà, che in luiſe ritruoua, alla medicina neceſſarie, & non d'al<lb></lb>tro: ma molti altri antiqui autori, ne fanno certißimi, che lor ſeppero, che abbruſaua, <lb></lb>perche loro ſe ne ſeruiuano nelle compoſitioni de alcuni fuochi, per abbruſare le teſtu <lb></lb>dine, ouer ariete, & le ellepoli, & altre torre portatile, che nelle iſpugnationi delle cit <lb></lb>ta à quel tempo ſi uſaua: Et ſimilmente per abbruſare le armate nauale, uero e che in <lb></lb>tai compoſitioni alcuni el chiamano ſal ardente, altri el chiamano ſal petroſo, altri el <lb></lb>chiamano ſal praticha, & altri el chiamano proprio, ſalnitrio.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>irca di queſio ui <lb></lb>ho da adimandarui un'altro dubbio: ma perche el mi dole alquanto la teſta, lo uoglio re <lb></lb>mettere à doman de ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000810">QVESITO TERZO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000811">PRIORE. S<emph type="italics"></emph>e gli antiqui hebbero cognitione, chel ſalnitrio bruſaua, & arde<lb></lb>ua con quella uigoroſita che fa, perche non ſeppero far la poluere delle arte<lb></lb>gliarie di tanta importanza nell'arte militare, come noi moderni.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſta con<lb></lb>ſe que ntia non è bona, à dire, che ſe li antiqui hebbero notitia del ſalnitrio, & che ſa<lb></lb>peſſono, che ardeua, ouer bruſaua, che de neceßita doueſſono ſaper componere la pol <lb></lb>uere delle artegliarie, perche la detta poluere non ſi fa de ſalnitrio puro, anzi ſe com <lb></lb>pone de tre materiali (come credo, che quella ſappia) cioe di ſalnitrio, ſolfere, & car <lb></lb>bone. </s> <s id="s.000812">Et pero eglie coſa credibile, chel ſia poßibile hauer <expan abbr="cognītione">cognintione</expan> del ſalnitrio, <lb></lb>& della natura di quello, & ignorare la compoſitione della detta poluere.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>oi <lb></lb>haueti ragione.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000813">QVESITO QVARTO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000814">PRIORE. C<emph type="italics"></emph>on che ragione, ouer perche cauſa la detta poluere delle arteglia <lb></lb>rie, ſe compone coſi de queſti tre materiali, cioe de ſalnitrio, ſolfere, et carbone, <lb></lb>& non de altri ſimplici, & que uirtu, ouer officio particolare ha cadauno di detti tre <lb></lb>materiali, ouer ſimplici per ſe in tal compoſitione, & que effetto faria ogni dui di lo <lb></lb>ro ſenza el terzo.<emph.end type="italics"></emph.end> N. T<emph type="italics"></emph>al poluere ſe compone coſi de detti tre materiali, perche ca <lb></lb>dauno loro medica, & ſuppliſſe ad alcun difetto de alcun delli altri dui, perche el ſol<lb></lb>fere è piu atto di accendere il fuoco con fiamma (eſſendo alquanto tocco da quello) de <lb></lb>alcun delli altri dui, el qual fuoco con fiamma é molto piu atto à introdur in fuoco el <lb></lb>ſalnitrio di qualunque altro fuoco, & perche el detto ſalnitrio bruſando ſe riſolue in <lb></lb>eſſalatione uentoſa, la quale è tanto potente, che ſubito amorzarebbe la fiamma gia <lb></lb>introdutta nel ſolfere, & conſequentemente quella introduta (per quella del ſolfere) <lb></lb>nel medemo ſalnitrio, & perche la natura del ſolfere, & ſimelmente quella del ſalni<lb></lb>trio è tale, che morta la fiamma, non ui reſta alcuna minima inſegna di fuoco, & per <lb></lb>tanto componendo inſieme ſolamente ſalnitrio, & ſolfere ottimamente piſti, & acco<lb></lb>ſtandoui el fuoco, immediate tal fuoco ui ſe accendera, & immediate ui ſe deſtuara,<emph.end type="italics"></emph.end><pb pagenum="38" xlink:href="042/01/075.jpg"></pb><emph type="italics"></emph>per le ragioni di ſopra dette, cioe, che tal fuoco non continuera per fina che ſia conſu<lb></lb>mata, ouer abbruſata tutta la materia, ma ſolamente ne abbruſara un poco, & lo re<lb></lb>ſtante reſtara non offeſa dal detto fuoco, onde per medicare queſto difetto, uiſe mcſco <lb></lb>la con ambidui el carbone ottimamente poluerizato, perche el carbone è di tal natu<lb></lb>ra, che tocco dalla fiamma del fuoco ſubito ſi accende, & ſi conuerte in fuoco ſenza <lb></lb>fiamma, el qual fuoco ſenza fiamma, quanto piu è ueſſado dalcun uento, tanto piuſi ac <lb></lb>cende, & conſerua per fina à tanto, che ogni ſua ſoſtantia ſia conuerſa in cenere, e per <lb></lb>tanto, toccando tal compoſitione con el fuoco immediate el ſolfere ſi apprende <expan abbr="cõ">com</expan> <expan abbr="fiã-ma">fian<lb></lb>ma</expan> (come detto) la qual fiamma non ſola nente mtroduſſe immediate fuoco e fiamma <lb></lb>nel ſalnitrio, ma etiam in quello iſtante introduſſe fuoco ſenza fiamma nel carbone, el <lb></lb>qual fuoco, per alcun uento non ſe eſtingue, anzi ſe augmenta, & pero quel uento cau<lb></lb>ſato dal ſalnitrio, non è atto à poter ammorzar quel fuoco ſenza fiamma, che é nel car <lb></lb>bone anzi, come ho detto lo augmenta, & perche il ſolfer eſſendo contiguo con el fuo <lb></lb>co, ò ſia con fiamma, ouer ſenza fiamma, non puo ſtar ſenza fiamma la qual fiamma, <lb></lb>come detto infiamma el ſalnitrio, e pero queſtitre materiali piſti, & miſti ottimamen <lb></lb>te inſieme, & in tal miſtur a introdutoui el fuoco tal fuoco uien à eſſere ineſtinguibile, <lb></lb>per fin che non ſia conſumata ogni ſostantia (ſaluo ſe in alcuno de detti materiali non <lb></lb>fuſſe qualche accidental diſetto, ò de humidita, ouer che fuſſeno tolti molto differenti <lb></lb>di la ſua conueniente proportione) & pero ſe conclude, che lo officio del ſolfere in tal <lb></lb>compoſitione è ſolamente per apprendere il fuoco con fiamma, & introdurlo nelli al<lb></lb>tri dui materiali, & quello del carbone è ſolamente de mantenere el detto fuoco ſenza <lb></lb>fiamma, gia introdutoui dal ſolfere, & maßime contra quel gran uento, che cauſa el <lb></lb>ſalnitrio, ma lo officio poidel detto ſalnitrio è ſolamente per cauſar quella coſi gran<lb></lb>dißima eſſalatione di uento, perche in quel tal uento conſiſte tutta la uirtu, et proprie <lb></lb>ta di la poluere, perche quello è ſolamente quello, che fpmge coſt uigoroſamente ogni <lb></lb>balla, & per tanto ſe conclude, che ſolamente dal ſalnitrio depende tutta la uirtu, e <lb></lb>poſſanza della poluere, & li altri dui ſimplici, ouer materiali, cioe el ſolfere, & el car <lb></lb>bone uiſe pongono ſolamente per riſoluere in fuoco, e uento el detto ſalnitrio, e non <lb></lb>per altro, perche chi componeſſe poluere ſolamente de ſolfere, e carbone, & che di <lb></lb>quella ſe ne cargaſſe una artegliaria à gran misura, dico che in tal ſorte di poluere in<lb></lb>troducendoui el fuoco, la non ſaria atta à ſpingere fora di detta artegliaria un minime <lb></lb>legnetto, ouer una paglia, & queſto procede, perehe tutta quella utrtu eſpulſiua de<lb></lb>pende ſolamente dal puro ſalnitrio, & non da altro, e per tanto elſe potria piu preſto <lb></lb>concludendo dire eſſer piu poßibile à fare poluere de artegliaria, ſenza carbone, & <lb></lb>ſolfere, che ſenza ſalnitrio, perche eglie da credere eſſer piu poßibile à trouar altri <lb></lb>materiali, che faceſſeno lo officio del ſolfere in apprendere el fuoco con fiamma, & <lb></lb>ſimelmente del carbone in mantenerui el detto fuoco ſenza fiamma, che à ritrouarne <lb></lb>uno altro, che fuſſe atto à cauſar tanto grande, & impetuoſo uento, come fa el detto ſal <lb></lb>nitrio.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>glie da credere che ſia piu preſto poßibile à componere poluere buona <lb></lb>ſenza carbone eſolfere, che ſenza ſalnitrio, perche tutta la uirtu e poſſanza della pol <lb></lb>uere (come di ſopra haueti detto) depende dal puro ſalnitrio, & non da altro, ma per <lb></lb>ßer hora tarda, uoglio facciamo fine.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/076.jpg"></pb> <p type="head"> <s id="s.000815">QVESITO QVINTO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Priore di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000816">PRIORE. H<emph type="italics"></emph>ierſerauoi aßignaſtila cauſa, perche la poluere ſe compone coſi <lb></lb>coſi di quelli tre materiali, & che officio ha cadauno de dittimateriali, in tal <expan abbr="cõ">com</expan> <lb></lb>poſitione, hor ue adimando, che fu inuentor di tal poluere, & con che ragione fu de<lb></lb>terminata da quello, la proportione della quantita di cadauno materiale conueniente à <lb></lb>tal compoſitione.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>he fuſſe inuentor di queſta poluere, & della artegliaria, fra <lb></lb>el uulgo è ſparto, per autorita del Cornazano, qual dice, che futrouata à caſo da un <lb></lb>Todeſco Alchimista, ma io ſon di openione, che di tal compoſitione Archimede Sira<lb></lb>cuſano<emph.end type="italics"></emph.end> (P<emph type="italics"></emph>hiloſopho, & Mathematico peritißimo) ne fuſſe inuentore (& di queſta me <lb></lb>dema opinione è il commentator di Vitruuio ſopra el primo libro à carte.<emph.end type="italics"></emph.end> 8.) <emph type="italics"></emph>perche <lb></lb>di lui ſi troua in molti luochi in ſcritto (come narra Valturio nel decimo libro de remi<lb></lb>litare) qualmente lui trouo una certa ſpecie di machina di ferro, con la quale lui traſe <lb></lb>ua uerſo lo eſſercito terreſto ſaßi di grandißimo peſo, e grandezza, & con uno incre<lb></lb>dibel ſuono, la qual coſa ne da ad intendere, che fuſſe una machina ſimile à una arteglia <lb></lb>ria, ma che tir aſſe balle di pietra großißime, come che anchor a non è molto tempo, che <lb></lb>fra moderniſi coſtumaua, & maßime per quel incredibel ſuono, che nel tirarla ui oc<lb></lb>corre, el qual ſuono, in altraſorte di machina da tirar, à me non pare, che uiſe poſſa <lb></lb>cauſare, ſaluo che in una ſimile alla artegliaria, uero é, che à quel tempo io tengo, che <lb></lb>fuſſeno molto difforme, & piu diſconze di quelle, che alli preſenti tempi ſi coſtuma, <lb></lb>perche ſempre le prime inuentioni teneno del rustico, ma con el tempo ſe uanno meglio <lb></lb>rando, per eſſer coſa facile aggiongere alle coſe trouate, & il medeſimo dico della pol <lb></lb>uere, cioe, che al principio, che la fu trouata (ò da Archimede, ouer da chi ſi uoglia) <lb></lb>eglie da credere, che in quel tempo la nonſe componeſſe con tal ordine e proportione, <lb></lb>come che al preſente ſi coſtuma, anzi giudico, che da quel tempo in qua ſe ſia uariato <lb></lb>l'ordine da componerla quaſi infiniti modi, & che el ſia el uero, io ho ritrouato ſopra <lb></lb>alcuni libri non molto antiqui certi modi, & ordinida componerla, molto differenti <lb></lb>dalli piu moderni.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>itime un poco, che proportion oſſeruamo, & oſſeruauano.<emph.end type="italics"></emph.end><lb></lb>N. I<emph type="italics"></emph>o ho ritrouato in alcuni piu antiqui libri, che à uoler far poluere di bombarda uo <lb></lb>leuano, che ſe pigliaſſe de cadauno di ſopra detti tre materiali parte equale, cioe tanto <lb></lb>de l'uno, quanto de l'altro. </s> <s id="s.000817">Et alcuni altri dapoi uoleuano che ſe pigliaſſe parte. </s> <s id="s.000818">3. di <lb></lb>ſalnitrio, & parte. </s> <s id="s.000819">2. di ſolfere, & parte. </s> <s id="s.000820">2. di carbone. </s> <s id="s.000821">Alcuni altri poi uoleuano, che <lb></lb>per far la detta poluere di bombarda ſe toglieſſe lire. </s> <s id="s.000822">10. di ſalnitrio, & lire. </s> <s id="s.000823">3. di ſolfe <lb></lb>re, & lire. </s> <s id="s.000824">3. di carbone. </s> <s id="s.000825">Et alcuni altri uoleuano, che ſe pigliaſſe lire. </s> <s id="s.000826">12. di ſalnitrio, <lb></lb>& lire. </s> <s id="s.000827">3. di ſolfere, & lire. </s> <s id="s.000828">2. di carbone. </s> <s id="s.000829">Altriuoleuano che ſi toglieſſe parte. </s> <s id="s.000830">9. di ſal <lb></lb>nitrio, & parte. </s> <s id="s.000831">2. di ſolfere, e parte. </s> <s id="s.000832">3. di carbone, et alcuni altri piu moderni per far <lb></lb>la per ſchioppiuoleuano, che ſe pigliaſſe parti. </s> <s id="s.000833">4. de ſalnitrio, & parte una di ſolfere, <lb></lb>& parte. </s> <s id="s.000834">1. di carbone: alcuni altri han detto, che per far poluere groſſaſi doueſſe pi<lb></lb>gliare parti. </s> <s id="s.000835">20. di ſalnitrio, et parti. </s> <s id="s.000836">3. di ſolfere, et parti. </s> <s id="s.000837">10. di carbon, & <21> farla al <lb></lb>quanto piu fina per ſchioppi <expan abbr="hãno">hanno</expan> detto, che ſi doueſſe tore parti. </s> <s id="s.000838">100. di ſalnitrio, & <lb></lb>parti. </s> <s id="s.000839">10. di ſolfe re, et parti. </s> <s id="s.000840">36. di carbone, altri dicono che <21> far poluere groſſa, che<emph.end type="italics"></emph.end><pb pagenum="39" xlink:href="042/01/077.jpg"></pb><emph type="italics"></emph>ſi debbiatuor parti. </s> <s id="s.000841">100. di ſalnitrio, et parti. </s> <s id="s.000842">20. di ſolfere, et parti. </s> <s id="s.000843">37. dicarbone. </s> <s id="s.000844">Et <lb></lb><21> farla fina parti. </s> <s id="s.000845">9. ſalnitrio, parti. </s> <s id="s.000846">3. ſolfere, et parti. </s> <s id="s.000847">6. de fior de mirochea (cioe <expan abbr="hã-no">han<lb></lb>no</expan> tentato di farla ſenza carbone, anchor che tal herba à me ſia incognita, perche tal <lb></lb>nome di herba mai ho potuto ritrouare, ne in le Pandete, ne in Auicenna, ne in alcun <lb></lb>herbolario) alcuni altri piu moderni poi hanno detto, che per fare la poluer groſſa ſe <lb></lb>debbia pigliare ſalnitrio parti. </s> <s id="s.000848">2. ſolfere parti. </s> <s id="s.000849">1. carbon de ſalice parti. </s> <s id="s.000850">1. Et per far <lb></lb>quella de archibuſi dicono che ſi debbia pigliare ſalnitrio parti. </s> <s id="s.000851">3. carboni de rami di ſa <lb></lb>lice giouani, parte. </s> <s id="s.000852">1. ſolfere parti. </s> <s id="s.000853">1. Et à far la poluer fina de ſchioppo dicono, che ſe <lb></lb>debbia pigliare ſalnitrio raffinato piu uolte parti. </s> <s id="s.000854">5. ſolfere parti. </s> <s id="s.000855">1. carbone de uerghet <lb></lb>te di Auellane, ouer nocelle giouine de un'anno parti. </s> <s id="s.000856">1. alcuni altri dicono, che per far <lb></lb>poluer groſſa, che ſi debbia tuor parti. </s> <s id="s.000857">3. de ſalnitrio raffinato, & parti. </s> <s id="s.000858">1. di ſolfere, et <lb></lb>parti. </s> <s id="s.000859">2. di carbon de ſalice, & per fare la poluere mezzana dicono, che ſi debbia pi<lb></lb>gliare parti. </s> <s id="s.000860">10. di ſalnitrio raffinato, & parti. </s> <s id="s.000861">2. di ſolfere, & parti. </s> <s id="s.000862">3. di carbon de ſa <lb></lb>lice, & per farla fina de archibuſi dicono, che ſe debbia pigliar parti. </s> <s id="s.000863">10. di ſalnitrio <lb></lb>raffinato ſolfer 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></lb>migliore, eioe per ſchioppo, uogliono che ſe toglia parti. </s> <s id="s.000866">27. de ſalnitrio raffinato ſol<lb></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></lb>per farla piu gagliarda che ſi debbia tuore ſalnitro raffinato lire. </s> <s id="s.000869">7. ſolfere lire. </s> <s id="s.000870">1. car<lb></lb>bon de uerzella de nizola monde lire. </s> <s id="s.000871">1. altri per farla molto migliore uoleno che ſi to <lb></lb>glia ſalnitrio raffinato parti. </s> <s id="s.000872">8. ſolfere parte. </s> <s id="s.000873">1. carbon de uerzelle de uizola gioueni, <lb></lb>& monde parte. </s> <s id="s.000874">1. alcuni per farla piu forte hanno uoluto aggiongere dell'argento ui <lb></lb>uo, alcuni acqua de uitta, alcuni ſal armoniaco, alcuni canfora, alcuni farla con carboni <lb></lb>de torſi de uerzi, alcuni con carbone de gionchi, ouer di tela di lino bruſiata, alcuni han <lb></lb>no tentato à farla in uari colori ſenza carboni, cioe bianca, roſſa, biaua, ponendoui alcu <lb></lb>ni fiori di herbe ſecche in poluere che faceuano lo officio del carbone, & chi ue daſe<lb></lb>uano quel tal colore, le qual coſe, à uolerle deſcriuere à una per una ci haueria da dire <lb></lb>per fin à diman da mattina, & accio che quella poſſa uedere la differentia, che ſia fra <lb></lb>queſti modi li uoglio deſcriuere qua ſotto a uno per uno diſtintamente, ſecondo che di <lb></lb>ſopra gliho recitati, & de molti altri non recitati per piu breuita. <lb></lb> Poluere di bombarda al modo piu an<lb></lb> tico. <lb></lb></s> <s id="s.000875">1 Salnitrio parte.1. <lb></lb> Solfere parte.1. <lb></lb> Carbone parte.1. <lb></lb> Poluer di bombarda al modo non tanto <lb></lb> antico. <lb></lb></s> <s id="s.000876">2 Salnitrio parti.3. <lb></lb> Solfere parti.2. <lb></lb> Carbone parti.2. <lb></lb> Poluer di bombarda al modo non tan<lb></lb> to antico. <lb></lb></s> <s id="s.000877">3 Salnitrio parti.10. <lb></lb> Solfere parti.3. <lb></lb> Carbone parti.3. <lb></lb> Poluer di bombarda al modo non tan<lb></lb> to antico. <lb></lb></s> <s id="s.000878">4 Salnitrio parti.12. <lb></lb> Solfere parti.3. <lb></lb> Carbone parti.2. <pb xlink:href="042/01/078.jpg"></pb> Poluer di bombarda al modo non trop <lb></lb> po antico. <lb></lb></s> <s id="s.000879">5 Salnitrio pari.9.. <lb></lb> Solfere partti.2 <lb></lb> Carbone parti.3. <lb></lb> Poluer aſſai moderna de ſchioppo. <lb></lb> Salnitrio parti.4. <lb></lb>6 Solfere parte.1. <lb></lb> Carbone parte.1. <lb></lb> Poluer di bombarda al modo piu mo<lb></lb> derno. <lb></lb> Salnitrio parti.20. <lb></lb>7 Solfere parti.3. <lb></lb> Carbone parti.10. <lb></lb> Poluer di bombarda al modo piu mo<lb></lb> derno. <lb></lb></s> <s id="s.000880">8 Salnitrio parti.100. <lb></lb> Solfere parti.10. <lb></lb> Carbone parti.36. <lb></lb> Poluer groſſa al modo moderna. <lb></lb> Salnitrio parti.100. <lb></lb>9 Solfere parti.20. <lb></lb> Carbone parti.37. <lb></lb> Poluer fina non molto antica. <lb></lb> Salnitrio parti.9. <lb></lb>10 Solfere parti.3. <lb></lb> Pior de mirochea parti.6. <lb></lb> Poluer groſſ a piu moderna. <lb></lb> Salnitrio parti.2. <lb></lb> Solfere parte.1. <lb></lb>11 Carbone deſalice parte.1. <lb></lb> Poluer di archibuſo piu moderna. <lb></lb> Salnitrio parti.3. <lb></lb>12 Solfere parti.1. <lb></lb> Carbone de rami de ſalice giouani <lb></lb> parte.1. <lb></lb> Poluer fina piu moderna. <lb></lb></s> <s id="s.000881">13 Salnitrio raffinato piu uolte parti.5. <lb></lb> Solfere parte.1. <lb></lb> Carbone de uerga de auolane gioue<lb></lb> ni parte.1. <lb></lb> Poluer groſſa piu moderna. <lb></lb> Salnitrio raffinato parti.3. <lb></lb>14 Solfere parte.1. <lb></lb> Carbone di ſalice parti.2, <lb></lb> Poluer mezzana piu moderna. <lb></lb> Salnitrio raffinato parti.10. <lb></lb>15 Solfere parti.2. <lb></lb> Carbone de ſalice parti.3. <lb></lb> Poluer di archibuſo moderno. <lb></lb> Salnitrio raffinato piu uolte parti.10. <lb></lb>16 Solfere parte.1. <lb></lb> Carbone de uerzelle di nizola mon<lb></lb> de parte.1. <lb></lb> Poluer de ſchioppo piu moderna. <lb></lb> Salnitrio raffinato parti.27. <lb></lb>17 Solfere parti.3. <lb></lb> Carbone de uerzelle de nizola mon<lb></lb> de parti.4. <lb></lb> Poluer de ſchioppo piu gagliarda, & <lb></lb> piu moderna. <lb></lb> Salnitrio raffinato parti.7. <lb></lb>18 Solfere parte.1. <lb></lb> Carbone de uerzelle de nizola mon<lb></lb> de è giouene parte.1. <lb></lb> Poluer de ſchioppo piu fina è ga<lb></lb> gliarda. <lb></lb> Salnitrio raffinato piu uolte <lb></lb> parti6. <lb></lb>19 Solfere parte.1. <lb></lb> Carbone de uerzelle de nizo la gioue<lb></lb> ne è monde parte.<emph.end type="italics"></emph.end>1. <pb pagenum="40" xlink:href="042/01/079.jpg"></pb> P<emph type="italics"></emph>oluer groſſa moderna <lb></lb> Salnitrio parti.4. <lb></lb>20 Solfere parte.1. <lb></lb> Carbone de ſalice parte.1. <lb></lb> Poluer groſſa moderna. <lb></lb> Salnitrio parti.20. <lb></lb>21 Solfere parti.4. <lb></lb> Carbone de ſalice parti.5. <lb></lb> Poluer de ſchioppo moderna. <lb></lb> Salnitrio raffinato à ſecco parti.48. <lb></lb>22 Solfero cetrino parti.7. <lb></lb> Carbone de nizolaro, ouer de legni <lb></lb> del caneuo ſecchi parti.8. <lb></lb> Poluer da ſchioppo moderna. <lb></lb> Salnitrio raffinato parti.18. <lb></lb>23 Solfere parti.2. <lb></lb> Carbon de legno de nizolaro parti.<emph.end type="italics"></emph.end>3. </s> </p> <p type="main"> <s id="s.000882">P<emph type="italics"></emph>er fare qual ſi uoglia delle ſopraſcritte ſorte di poluere, biſogna notare, che à uoler <lb></lb>che la ſia buona, ſecondo la qualita ſua, eglie neceſſario, che il ſalnitrio ſia puro, e netto, <lb></lb>& potente (la qual coſa ſi conoſce da pratici à bruſarne un poco) ſimilmente che il ſol<lb></lb>fere ſia netto di terra, & da altre ſporcitie, che in eſſo ſi troua, & che il carbone an<lb></lb>chora non ſia ſuboido per stare in luoco humido, ouer che il non ſia miſto con poluere, <lb></lb>ouer terra, ultimamente bijogna aduertire, che tal poluere ſia ottimamente peſta, & <lb></lb>li detti tre materiali inſieme ben incorpor ati ilche facendo tal poluere non mancara di <lb></lb>ſuoi effetti ſecondo la ſpecie di quella, domente, che anchora ſia da ogni humidita bene <lb></lb>eßicata, e pero la non uol eſſer tenuta in luoco humido ma in luoco ſutto. </s> <s id="s.000883">Anchora per <lb></lb>un'altra ragione uol ſtar in luoco ſutto, che la humidita riſolue il ſalnitrio in acqua, & <lb></lb>riſolto che ſia diſcende pian piano uerſo il fondo del uaſo doue reposta tal poluere, per <lb></lb>ilche nella poluere del fondo uien à eſſer piu ſalnitrio, che in quella che ſtanella parte <lb></lb>di ſopra del detto uaſo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000884">HOR V<emph type="italics"></emph>oſtra Reuerentia puo uedere in quanti uarij modi è <lb></lb>ſtato determinato <lb></lb>l'ordine, ouer la proportione della quantita di ſopradetti tre materiali nella <lb></lb>compoſitione della detta poluere.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>ertamente eglie da marauigliare de tante ua<lb></lb>rie mutationi de ordini, & non poſſo penſare con che ragione quelli tali ſe ſiano moßi à <lb></lb>determinar tai ordmi.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a prima inuentione (quantunque alcuni dicono che la fu <lb></lb>trouata à caſo) io tengo che la fuſſe ritrouata con ragion naturale, ſpeculatiuamente, <lb></lb>cioe che tai tre materiali ben piſti, & meſcolati inſieme doueſſeno eſſer atti à formar <lb></lb>un fuoco coſi gagliardo, & ineſtinguibile, per fin che ogni materia non fuſſe conſu<lb></lb>mata, perche ui ſono le ragionuiue coſi douer eſſer, ma à determinare la proportione <lb></lb>della quantita de detti materiali, credo che con la iſperientia ſe ſiano conſigliati, per<lb></lb>che nel primo ordine ſe fondorno ſu la proportion della equalita, perche il ſiuede, <lb></lb>che pigliauano tanto de l un materiale quanto che dell'altro, & quantunque tal pol<lb></lb>uere in gran quantita faceſſe forſi qualche buon effetto, nondimeno conſiderando che <lb></lb>tal effetto procedeua dal ſalnitrio, ſecero un'altro ordine, cioe <expan abbr="pigliãdo">pigliando</expan> maggior parte <lb></lb>de ſalmtrio di quello faceano de cadauno delli altri, et ritrouorno tal poluer piu <expan abbr="potẽte">potente</expan> <pb xlink:href="042/01/080.jpg"></pb>della prima, et coſi con tai auiſi ragioneuoli, alcuni ſono andati uariando tal ordine per <lb></lb>fin à queſtitempi, uero è, che ui ſo no alcuni ordini delli ſopra notati, che con poca ra<lb></lb>gion, & manco giudicio ſono ſtati ordinati, anzi credo che ſtano ſtati alcuni, che per <expan abbr="nõ">non</expan> <lb></lb>uoler far, come faceuano gli altri) per moſtrar diſaper piu di loro) ſenza altra ragio<lb></lb>ne hanno uoluto formar nuoui ordini, cioe creſcendo il carbone, & ſminuendo il ſolfe<lb></lb>re, altri in creſcere il ſolfere, & ſminuire il carbone, altri uariando tutti tre li detti ma <lb></lb>teriali in certe ſtranie proportioni, accio che para con maggior ſapientia, & ſottilita <lb></lb>ritrouato.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>glie queſto, ſi come ſono anchora quelli compoſitori, che non ſanno <lb></lb>dire, ne fare, ſe non quello, che hanno detto, ouer fatto gli altri, ma perche ſi uergogna <lb></lb>no alle uolte apparere che habbiano imparato, ouer tolto da quelli tali ſe sforzan di ua <lb></lb>riar alquanto il modo, ouer il parlare.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>oſi è preciſo.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſto ragionamen<lb></lb>to è ſtato molto longo, e pero uoglio che facciamo fine.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000885">QVESITO SESTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo<emph.end type="italics"></emph.end> S. P<emph type="italics"></emph>rior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000886">PRIORE. H<emph type="italics"></emph>ierſerauoi dimoſtraſti in quanti modi (da non molto <expan abbr="tẽpo">tempo</expan> in qua) <lb></lb>è ſtato uariato l'ordine, ouer la proportione della quantita di tre materiali nel <lb></lb>componere la poluere, hor ue adimando, qual di ſopra notati ordini (ſi di piu antichi, <lb></lb>come di piu moderni) giudicati eſſer migliore, cioe che ne dia piu perfetta, & piu ga<lb></lb>gliarda, ouer potente poluere.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio quella poluere ſe de giudicar eſſer <lb></lb>piu gagliarda, & potente che contien maggior parte de ſalnitrio, dico maggior parte <lb></lb>riſpetto al tutto. </s> <s id="s.000887">Eſſempi gratia, il primo ordine di ſopra annotati, cioe quello doue ſi <lb></lb>tuol de cadauno materiale parte una, tal compoſitione uenira à tener un terzo ſalnitrio <lb></lb>& li dui terzifraſolfere è carbone, & lo ſecondo conſequente à quello, cioe quello do<lb></lb>ue ſe tuol ſalnitrio parte. </s> <s id="s.000888">3. ſolfere parte. </s> <s id="s.000889">2. e carbone parte. </s> <s id="s.000890">2. ueniria à tener li tre <lb></lb>ſettimi ſalnitrio, & li quattro ſettimi fraſolfere, e carbone, & perche li tre ſettimi è <lb></lb>maggior parte de un terzo, e pero diremo che la poluere del detto ſecondo ordine ſara <lb></lb>piu gagliarda, e potente di quella del primo ordine, ſimilmente la poluere del terzo or <lb></lb>dine ſara piu potente di quella del ſecondo, perche quella del detto terzo ordine tien li <lb></lb>cinque ottaui ſalnitrio, li quai cinque ottaui ſono molto maggior parte de tre ſettimi, <lb></lb>& il quarto uien à tener li dodeci. </s> <s id="s.000891">17. eßimi ſalnitrio, & perche dodeci. </s> <s id="s.000892">17. eßimi è <lb></lb>maggior de cinque ottaui, e pero diremo, che la poluere del detto quarto ordine è piu <lb></lb>gagliarda di quella del terzo, & il quinto ordine uien à tener li nuoue. </s> <s id="s.000893">14. eßimi ſal<lb></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></lb>poluer del detto quinto ordine eſſer peggiore, ouer men potente di quella del quarto, <lb></lb>& il ſeſto ordine uien à tener li dui terzi ſalnitrio, & perche li dui terzi è maggior <lb></lb>delli nuoue. </s> <s id="s.000896">14. eßimi, diremo che la poluere del ſeſto ordine eſſer migliore, ouer piu <lb></lb>potente di quella del quinto, & con tal modo procedendo in tutti glialtri conſequenti <lb></lb>ordini (à che non ignorara lo operar, & cognition di rotti) con facilita conoſcera <lb></lb>qual ordine ſia migliore, ouer peggiore, cioe qual poluere ſara piu gagliarda è poten<lb></lb>te, & econuerſo, intendendo pero in una iſteſſa ſorte di ſalnitrio, & coſiſe potra far<emph.end type="italics"></emph.end><pb pagenum="41" xlink:href="042/01/081.jpg"></pb><emph type="italics"></emph>comparatione di quelle groſſe, ouer de artegliarie alle altre ſue ſimile, et coſt delle fine, <lb></lb>ouer deſchioppo, alle altre ſue ſimile, perche ſaria coſa longa à uoler dare eſſempio à <lb></lb>tutti li ſapra detti ordini à uuo per uno.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>oncludetemi al manco de tutti li ſopra <lb></lb>notati or dini qual ſara la piu gagliarda é <expan abbr="potẽte">potente</expan> de tutte le altre.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uella del. 16. <lb></lb>ordine ſara la piu potente, & gagliarda de tutte le ſopra notate (cioe quella doue ſe tol <lb></lb>ſalnitrio raffmato piu uolte parte. </s> <s id="s.000897">10. ſolfere parte. </s> <s id="s.000898">1. carbon de uerzelle de nizola <lb></lb>giouene e monde parte. </s> <s id="s.000899">1. & queſta ſara la piu potente per due cauſe. </s> <s id="s.000900">La prima è, per <lb></lb>che tal poluere uien à tener li cinque ſeſti ſalnitrio, el qual cinque ſeſti è maggiore di <lb></lb>qual ſi uoglia parte occorrente in qual ſi uoglia delli altri ſopra notati ordini. </s> <s id="s.000901">La ſe<lb></lb>conda cauſa è, che tal ſalnitrio ua raffinato piuuolte, che lo fa piu perfetto etiam ui <lb></lb>concorre piu perfetto carbone, perche in effetto quanto piu el carbone è di materia le<lb></lb>ue, e dolce, eglie piu atto à riceuere, & mantenere piu facilmente il fuoco, e pero tan<lb></lb>to piu è perfetto, per eſſer piu atto, & diſpoſto à far con celerita lo officio ſuo.<emph.end type="italics"></emph.end> P. <lb></lb>Q<emph type="italics"></emph>ueſta uostra openione mi conſona molto, ma mi resta un dubbio di adimandarui, ma <lb></lb>per eſſer tardi lo uoglio laſſar à diman di ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000902">QVESITO SETTIMO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000903">PRIORE. H<emph type="italics"></emph>ierſera uoi concludeſti, che quella del decimoſeſto ordine, eſſer la <lb></lb>piu fina, & piu potènte, ouer gagliarda poluere de cadauno altro di ſopra nota <lb></lb>ti ordini, perche contien ma ggior parte de ſalnitrio, de cadauno delli predetti ordeni <lb></lb>la qual parte è li cinque ſesti del tutto, hor ue adimando ſe la non ſaria aſſai piu ga<lb></lb>gliarda, e potente, che la faceſſe con maggior parte de detti cinque ſeſti del medeſimo <lb></lb>ſalnitrio, & menor parte de un ſeſto fra ſolfere, e carbon, cioe carbon della medeſima <lb></lb>ſorte.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio, che la ſaria piu gagliarda, e potente, domente, che tal mini <lb></lb>ma parte de ſolfere, & carbone fuſſe atta, & ſofficiente à far quelſuo officio, che uiſe <lb></lb>aſpetta, cioe ad apprendere con prestezza el fuoco, etiam à introdurlo, & mantener<lb></lb>lo nel ſalnitrio per fina che ſia totalmente riſſolto in fuoco, perche ſel fuſſe tanto poca <lb></lb>la quantita, ouer parte del detto ſolfere, & carbone, che la non fuſſe atta, e ſofficiente <lb></lb>à far tal officio, tal compoſitione reſtaria inutile, & quaſi de niun ualore, e pero biſo<lb></lb>gna ſopra questo molto ben aduertire, perche ſel fuſſe poßibile à far tal poluere de pu <lb></lb>ro, e perfetto ſalnitrio, ſenza dubbio quella ſaria piu potentißima, ouer gagliardißima <lb></lb>di qualunque altra compoſta de medeſimo ſalnitrio con ſolfere, & carbone: ma petche <lb></lb>el detto ſalnitrio per ſe ſolo non é atto ne ſofficiente ad apprendere con tal cellerita el <lb></lb>ſuoco con uiua fiamma, come fa el ſolfere, ne etiam à conſeruarlo per fina à tanto, che <lb></lb>fuſſe totalmente arſo, & diſtrutto (come fa el carbone) e pero eglie neceſſario à dargli <lb></lb>la compagnia delli altri dui, cioe ſolfere, & carbone, & tanta quantita, che ſia atta, e <lb></lb>ſofficiente à fare quel tal ſuo officio, che uiſe aſpetta (detto di ſopra.)<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>ue ho in<lb></lb>teſo benißimo, & uoglio, che queſto baſti per queſta ſera.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/082.jpg"></pb> <p type="head"> <s id="s.000904">QVESITO OTTAVO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Priore di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000905">PRIORE. H<emph type="italics"></emph>ierſera uoi determinaſti, che quella poluere, che <expan abbr="cõtien">contien</expan> maggior <lb></lb>parte de ſalnitrio, et menor parte fraſolfere e carbone (domente che talſolfere, <lb></lb>& carbone ſia ſofficiente à far clſuo officio) e migliore, e piu potente di qualunque al <lb></lb>tra compoſta della medeſima ſorte di ſalnitrio, ſolfere, e carbone, ma con menor parte <lb></lb>del detto ſalnitrio, & maggiore fra ſolfere e carbone (et queſto credo anchor a io) ma <lb></lb><expan abbr="cõfidero">confidero</expan>, che tal regola <expan abbr="nõ">non</expan> è generale à ogni ſpecie di artegliaria, perche el ſe ſa commu <lb></lb>namente che li ſchioppi, la uogliono piu fina delli archibuſt, & li archibuſt la uogliono <lb></lb>piu fina delli moſchetti, et falconetti, & li falconetti la uogliono megliore delle altre <lb></lb>ſor te de artegliarie groſſe, & per tanto ue adimando ſel non ui pare, che el ſianeceſſa <lb></lb>rio à limitare questa ſua compoſitione. </s> <s id="s.000906">& finezza ſecondo la ſorte di pezzi.<emph.end type="italics"></emph.end> N. </s> <s id="s.000907">A <lb></lb><emph type="italics"></emph>me non pare, che tal coſa ſia neceſſaria, anchor che laſe coſtumi, anzi ho una openio<lb></lb>ne, che queſto ſia un errore aſſai maggiore di quello fu detto delle collobrine, & ſuoi <lb></lb>canoni al. </s> <s id="s.000908">11. Queſito del. 1. libro.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o come uoreſti uoi, che ſi faceſſe.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>lpre <lb></lb>ſente <expan abbr="nõ">non</expan> uoglio coſi <expan abbr="abſolutamẽte">abſolutamente</expan> dar determinata riſpoſta à <27>sta materia, <21>che la uo <lb></lb>glio un poco conſider arla meglio, et ſpero di farui conoſcere un errore in <27>ſta coſa, el <lb></lb>quale ſe ne tira drio molri altri de piu diſcomodita, interreſſo, et ſpeſa di quello <expan abbr="fãnole">fannole</expan> <lb></lb>dette colobrine riſpetto alli ſuoi canoni (come ſi fece conoſcere ſopra lo detto. </s> <s id="s.000909">11. Que <lb></lb>ſito del. 1. libro.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>onſideratila un poco bene, perche le ſono coſe che importano aſ <lb></lb>ſai à longo andare, & tal hora aſſai piu di quello che l'huom ſi penſa.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000910">QVESITO NONO FATTO DA VN HIERONIMO <lb></lb><emph type="italics"></emph>qual diſſe eſſer ſotto capo de bombar dieri nella iſola de Cipri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000911">HIERONIMO. P<emph type="italics"></emph>erche cauſa credeti, che ſe dia la grana alla poluere fina, <lb></lb>(cioe à quella de ſchioppo, & de archibuſo) & non alla groſſa (cioe à quella del <lb></lb>le artegliarie.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ſo bene, che la cauſa di queſta tal particolarita non è da uoiigno <lb></lb>rata, & che non me adimiandati tal coſa, perche non la ſappiati: ma ſolamente per far <lb></lb>iſperientia di me.<emph.end type="italics"></emph.end> H. A<emph type="italics"></emph>nziue la adimando per saperla, & non per far iſperientia di <lb></lb>uoi: perche non solamente conſeſſo non ſaper tal cauſa, cioe perche ragione ui ſe dia. <lb></lb></s> <s id="s.000912">tal grana, ma ui giuro da real Chriſtiano, che ho ricer cato queſta tal cosa da molti che <lb></lb>fanno poluere, dico prouiſionati dalla ſignoria per far poluere d'ogni ſorte, & niuno <lb></lb>me ne ha ſaputo aßignar ragion alcuna, ſaluo quello che lauora qua in larſenale di Ve<lb></lb>netia, el quale me ha riſpoſto, che per darui la detta grana tal poluere ſi fa, ouer diuen<lb></lb>ta piu gagliarda, e potente, la qual ſua ragione mi conſona alquanto ma non tanto che <lb></lb>baſti, e pero ſon uenuto da uoi per chiarirme meglio, e per uedere ſe la uoſtra openio<lb></lb>ne é ſimile alla ſua.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uaſi che non poſſo credere queſto, che uoime dite, perche el <lb></lb>mi pare quaſi impoßibile, che uno artiſta faccia alcuna coſa, ſenza ſapere à che fine el <lb></lb>la faccia, & maßime di quelle coſe, che lui fa de continuo, perche el biſogna che larte <lb></lb>imiti la natura in queſto, che tutte le coſe che lei ſa, la lifaccia à qualche fine. </s> <s id="s.000913">Et pero<emph.end type="italics"></emph.end><pb pagenum="42" xlink:href="042/01/083.jpg"></pb><emph type="italics"></emph>non poſſo credere, che coſtui del Arſenale (qual me haueti detto, che è prouiſionate <lb></lb>dalla ſignoria per far poluere ſi fina come groſſa) non ſappia à que fine ſe dia coſi la <lb></lb>grana alla poluere de ſchioppo, e de archibuſo, & non à quella dalle artegliarie, et maſ<lb></lb>ſime facendone continuam ente ogni giorno.<emph.end type="italics"></emph.end> H. I<emph type="italics"></emph>o ui ſo dir certo, che non ui ſa aßi<lb></lb>gnare altra meglior ragione di quella, che ui ho detta.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>nanti che di questa cosa <lb></lb>ue dica la mia opinione, uoglio che ritornati da lui, & pregarlo di gratia, che ue di<lb></lb>ca realmente, perche ragione ui da tal grana.<emph.end type="italics"></emph.end> H. N<emph type="italics"></emph>on accade che ui uada altramen<lb></lb>te, perche io ſon certo, che mi replicara el medeſimo, cioe, che tal grana la fa diuentar <lb></lb>piu gagliarda, e potente.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>e pur el ue replica queſto, reſpondetegli in queſto mo <lb></lb>do, ſe tal grana fala poluere piu gagliarda, e potente, mo non ſaria benfatto à ingra<lb></lb>nire anchora quella groſſa (cioe quella delle artegliarie) per farla diuentare piu ga<lb></lb>gliarda e potente.<emph.end type="italics"></emph.end> H. L<emph type="italics"></emph>aſſatifar à me, che ui uoglio ritornare (& forſi hoggi) & <lb></lb>diman ue refferiro quello me hauera riſpoſto.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000914">QVESITO DECIMO FATTO DAL MEDESIMO <lb></lb>H<emph type="italics"></emph>ieronimo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000915">HIERONIMO. D<emph type="italics"></emph>apoi che fui partito da uoi hieri, io andai ſubito in lar<lb></lb>ſenale, & andai à ritrouar l'amico, & lo pregai de nouo, che ſe lui haueua al<lb></lb>tra ragione di quella, che lui me haueua detta, che non me la uoleſſe cellare, che di cio <lb></lb>ſempre gline reſteria obligatißimo, lui me giuro, che non ſapeua altra ragione di quel <lb></lb>la, che gia me haueua detta, cioe, che la ſe ingraniua per augumentarla in uirtu, & poſ <lb></lb>ſanza, cioe per farla piu gagliarda, & potente, & io gli dißi quello, che me ordinaſti, <lb></lb>cioe ſel non ſaria buono à ingr anire anchora la poluere delle artegliarie, cioe la groſ <lb></lb>ſa, per farla anchor lei piu gagliarda, e potente di quello che la é, lui me riſpoſe, che ſi <lb></lb>andaria à pericolo di far creppar li pezzi, et coſi meriſolſe.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oi gli doueui pur <lb></lb>riſpondere, che ſe potriano poi cargare tai pezzi con manco poluere del ſolito, & tan <lb></lb>to ſaria auanzato, ouer amente ponerui dentro alquanto manco ſalnitrio del ſolito.<emph.end type="italics"></emph.end><lb></lb>H. I<emph type="italics"></emph>o non ho hauuto tanto auiſo di ſaperui far tal riſpoſta, ma che credeti, tutti que<lb></lb>ſti che fanno poluere, uanno facendo ſecondo, che hanno uiſto far alli altri, ouer ſecon <lb></lb>do, che gli è ſtato inſegnato, & non ſi curano di cercare, ne manco di ſapere la cauſa <lb></lb>delle coſe, che loro fanno, cioe à che fin le faceiano. </s> <s id="s.000916">Et uoi dir di me, che anchora mi ho <lb></lb>fatto della poluere groſſa, e fina, & quando ne faceua de fina, io la ingraniua anchora <lb></lb>mi, anchor che non ſapeſſe, ne anchor ſo à que fine la ſe ingraniſcha, & queſto faceua, <lb></lb>perche haueua uisto che tuttili altri coſi faceuano.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>redo, che ſia, come uoi di<lb></lb>ceti.<emph.end type="italics"></emph.end> H. D<emph type="italics"></emph>i gratia ditime la uoſtra opinione circa à queſta coſa.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>auendoui <lb></lb>quaſi promeſſo de diruela, eglie il douer ch'io ui attenda, & per tanto dico, che da<lb></lb>poi, che hieri ui partiſti da me, ho conſiderato ſopra di tal coſa, & in effetto ho ritro<lb></lb>uato, che ſolamente la neceßita, ouer commoditaha indutto gli huomini à inueſtigar <lb></lb>il modo de ingranire la detta poluere de ſchioppo, & de archibuſo, & non quella de <lb></lb>artegliaria, perche la detta poluere granita e molto piu ſcorrente, de la non gra<lb></lb>nita alla ſimilitudine, che ſaria uno pugno di ſrcmento, de un pugno de farina,<emph.end type="italics"></emph.end><pb xlink:href="042/01/084.jpg"></pb><emph type="italics"></emph>cioe ponendo ſopra una tabula piana un pugno di fromento, & ſeparatamente un pu<lb></lb>gno di farina, & inclinando poi al quanto da una banda la detta tabula, ſenza dubbio <lb></lb>piu facilmente ſcorrera el detto fromento zoſo della detta tabula, di quello fara la det <lb></lb>ta farina, ma tal farina restara amaccata, & piu immobile, & ſe pur anchora lei ui <lb></lb>ſcorreſſe per la molta dependetia di tal tabula, la ui ſcorrera quaſi tutta in un colpo, <lb></lb>& il frumento ui ſcorrir a à parte a parte, cioe piu diſgregatamente.<emph.end type="italics"></emph.end> H. </s> <s id="s.000917">E <emph type="italics"></emph>ue ho in<lb></lb>teſo benißimo, ma che mi gioua quella ſua ſcorrentia.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>o <expan abbr="nõ">non</expan> ſapeti, che uolendo <lb></lb>portar un ſchioppo, ouer un'archibuſo per ſeruirſene alli biſogni, eglie neceſſario an<lb></lb>chora portarſe drio della poluere, per poterlo cargar ad ogni ſuo piacere, & che tal <lb></lb>poluere ſe porta nelle fiaſche, & per cargarli con miſura in quelle tai fiaſche uiſe fa <lb></lb>uſcire, come ſapeti, un certo canoncino atto a riceuere tanta poluere, quanta ui ſi con<lb></lb>uiene a cargare quel tal ſchioppo, ouer archibuſo con un certo ingegno da rechiuderlo <lb></lb>poi di dentro uia, quando che e pieno, accioche tal poluere non poſſa uſcire fora del ca <lb></lb>noncino, & ritornar nella fiaſcha.<emph.end type="italics"></emph.end> H. I<emph type="italics"></emph>o ſo tutte queſte particolarita, ſi che non <lb></lb>accade che uoi me le dicate.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nchor che ſo, che uoi le ſapeti meglio di me, ue le <lb></lb>ho uolute dire, accioche meglio me intendiati per l'auenire. </s> <s id="s.000918">Et per tanto concludo, <lb></lb>che ſe la poluere, che ſi mette nelle dette fiaſche, non fuſſe granita, con difficulta ſe po<lb></lb>tria fare impire quel tal canoncino, perche nel riuoltar la fiaſcha per far impire <lb></lb>quel tal canoncino la poluere che fuſſe nella detta fiaſcha, caſcaria quaſi tutta in un <lb></lb>tratto ſopra alla intrata di tal canoncino, chiudendo, ouer reſſer ando in quello quaſi <lb></lb>tutto quello aere, che in quello ſi trouaſſe, per eſſer uodo, el qual aereueneria a impedi <lb></lb>re lo ingreſſo alla poluere, talmente, che tal canoncino la maggior parte delle uolte ſi <lb></lb>trouaria quaſi uacuo, ouer molto ſcemo, la qual coſa non ui occorrera coſi, ſe la detta <lb></lb>poluere ſara granita, perche tal poluere granita ſcorrera nel detto canoncino piu di<lb></lb>ſgregatamente (come fu detto del <expan abbr="fromẽto">fromento</expan>, et della farina) la qual diſgregatione dara <lb></lb>adito a quello aere, che ſi ritrouara nel detto <expan abbr="canõcino">canoncino</expan> da poter uſcire, et de intrare ne <lb></lb>la fiaſca a impire quel loco che occupaua quella poluere, che intrara nel detto <expan abbr="canõci-no">canonci<lb></lb>no</expan>, e pero el detto <expan abbr="canõcino">canoncino</expan> la maggior parte delle uolte ſe trouara pieno, come ſi <expan abbr="cõuie">conuie</expan> <lb></lb>ne, et coſi <21> queſta cauſa li huomini ſono ſtati aſtretti a inuiſtigar el modo de ingranire <lb></lb>la detta poluere de ſchioppo, & de archibuſo, & <expan abbr="nõ">non</expan> quella di artegliaria, perche nelle <lb></lb>artegliarie ui ſe mette la poluere <expan abbr="cõ">com</expan> una cazza, come ſapeti, et <expan abbr="cõ">com</expan> quella la ui ſe porta <21><lb></lb>fin nel fondo della ſua canna, et pero <expan abbr="nõ">non</expan> importa che tal poluere ſia <expan abbr="ſcorrẽte">ſcorrente</expan>, ò <expan abbr="nõ">non</expan> ſcor <lb></lb>rente, anzi ſaria coſa ſuperflua a ingranire quella delle artigliarie, ma piu, che per ine <lb></lb>ſcar quel buſettino doue ſe da el fuocho alli ſchioppi, & alli archibuſi ſe costuma por<lb></lb>tar. </s> <s id="s.000919">come ſapeti, un fia ſchettino piccolino pieno di poluer finißima, la qual poluere, ſe <lb></lb>per ſorte non fuſſe menutamente granita, la non uoria, ne potria uſcire di quel tal buſo <lb></lb>coſi piccolino, <21> le ragioni di ſopra dette, e pero fu neceſſario a farla <expan abbr="minutamẽte">minutamente</expan> grani <lb></lb>ta, la qual coſa <expan abbr="nõ">non</expan> accade nelle artegliarie, perche, <21> quanto ho inteſo, uoi ue la metteti <lb></lb><expan abbr="cõ">com</expan> la mano.<emph.end type="italics"></emph.end> H. E<emph type="italics"></emph>glie coſi, & certamente queſte uostre ragioni ſono lo euangelio, ne <lb></lb>mai haria penſato, che per ſimel cauſa ui ſe li deſſe tal grana, & queſta coſa la ho acca <lb></lb>ro piu di dieci ſcudi, & pero di queſto ue ne ringratio grandamente.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000920">I<emph type="italics"></emph>l fine del terzo libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb pagenum="43" xlink:href="042/01/085.jpg"></pb> <p type="head"> <s id="s.000921">LIBRO QVARTO DELLI <lb></lb>QVESITI ET INVENTIONI DIVERSE, <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.000922">S<emph type="italics"></emph>opra l'ordinar delle ſchiere, ouer eſſerciti in battaglia ſotto <lb></lb>uarie & diuerſe forme, & del modo de far caminar <lb></lb>quelli, con altre uarie particolarita.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000923">QVESITO PRIMO FATTO DAL <lb></lb>C<emph type="italics"></emph>onte Hieronimo da Piagnano.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000924">CONTE HIERONIMO. V<emph type="italics"></emph>olendo io redure una quantita <lb></lb>de Fanti, ouer un eſſercito in una battaglia quadra di gente, ue do<lb></lb>mando in che modo, ouer con che regola potria ſapere quanti Fan<lb></lb>ti ſe doueria mettere per fila.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>igliando la radice quadrata <lb></lb>di quel tal numero de Fanti, e tanto quanto ſara quella tal radice, <lb></lb>tanti Fanti ſe ne douera mettere per fila.<emph.end type="italics"></emph.end> C.H. D<emph type="italics"></emph>atime uno eſ<lb></lb>ſempio in uno piccolo numero, perche ue intendero meglio.<emph.end type="italics"></emph.end> N. <lb></lb>P<emph type="italics"></emph>oniamo che ſia. </s> <s id="s.000925">100. Fanti, dico che uolendoli mettere in una ordinanza, ouer batta<lb></lb>glia quadra di <expan abbr="gẽte">gente</expan>, il ſe debbe cauare la radice quadra de. </s> <s id="s.000926">100. quala come, ſapeti è. <lb></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></lb>fila, le quale. </s> <s id="s.000931">10. file aſſettandole ordinatamente l'una drieto all'altra, talmente che tut <lb></lb>ti li interualli che ſara fra Fante, è Fante, ſi dalle bande, come dauanti, & de drio ſia<lb></lb>no equali, tai. </s> <s id="s.000932">100. Fanti formaranno una figura quadrata, ſi di <expan abbr="gẽte">gente</expan>, come diterre<lb></lb>no, come di ſotto appare in figura.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.085.1.jpg" xlink:href="042/01/085/1.jpg"></figure> <p type="main"> <s id="s.000933">MA <emph type="italics"></emph>perche in effetto li Fanti poſti in ordinanza non stanno, ne caminano, come <lb></lb>di ſopra è sta ſupposto, cioe in eguale diſtantie, perche ogni Fante (come aſ<lb></lb>ſerma Vegetio) uol per larghezza piedi tre, cioe daſpalla, à ſpalla, & per longhez<lb></lb>za picdi. </s> <s id="s.000934">7. cioe piedi. </s> <s id="s.000935">3. dauanti di ſe, & piedi. </s> <s id="s.000936">3. de drio, & un piede uol che occupi la <lb></lb>ſua perſona, per la qual coſa la ſopraſcritta or dinanza, ſtando li Fanti ſecondo le det-<pb xlink:href="042/01/086.jpg"></pb>te diſtantie ordinarie, non ſara quadrata di terreno anci occupara in longhezza piedi. <lb></lb></s> <s id="s.000937">70. & in larghezza ſolamente piedi. </s> <s id="s.000938">30. onde che all'oc chio parera piu che bislonga, <lb></lb>come di ſotto appare in figura.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.086.1.jpg" xlink:href="042/01/086/1.jpg"></figure> <p type="main"> <s id="s.000939">CONTE HIERONIMO. V<emph type="italics"></emph>e ho inteſo benißimo in quanto à questo, ma <lb></lb>quando, che tal numero de fanti non fuſſe coſi quadrato, come ſaria ſe fuſſeno. <lb></lb></s> <s id="s.000940">200. fanti, la radice di quali, ſe non me inganno, ſaria. </s> <s id="s.000941">14. ma auanzaria. </s> <s id="s.000942">4. fanti, hor <lb></lb>come doueria fare in tal caſo.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n queſto caſo uoi ne douereſti pur mettere. </s> <s id="s.000943">14. per <lb></lb>fila, & ueneria pur la detta battaglia quadra di gente, ſi come la precedente, cioe ſara <lb></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></lb>nanza, li quali il Sargente li aſſetta doue à lui pare, fuora di tal ordinanza, ouer che li <lb></lb>pone forſi nella coda de tal ordinanza.<emph.end type="italics"></emph.end> C.H. A<emph type="italics"></emph>nchor queſta parte ho inteſa benißi<lb></lb>mo, ma ſe il fuſſe un grande eſſercito, che mi occorreſſe di mettere pur in forma quadra <lb></lb>di gente, come doueria procedere.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er il medeſimo modo, eſſempi gratia, ponia<lb></lb>mo che tal eſſercito ſia de fanti. </s> <s id="s.000947">35000. dice che di questi. </s> <s id="s.000948">35000. fanti uoi ne douetica <lb></lb>uar la radice quadrata per l'ordine che ue ho inſignato, & trouareti quella eſſer. </s> <s id="s.000949">187. <lb></lb>& auanzara fanti. </s> <s id="s.000950">31. e per tanto ſe douera mettere fanti. </s> <s id="s.000951">187. per fila, & tal eſſercito <lb></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></lb>che ui auanzara quelli fanti. </s> <s id="s.000954">31. detti di ſopra, li quali il Sargente li accommoda doue li <lb></lb>pare, ma io tengo che tai reſidui ſempre li pongano nella coda di tal eſſercito.<emph.end type="italics"></emph.end> C. H. <lb></lb>C<emph type="italics"></emph>oſi credo anchora io.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.000955">QVESITO SECONDO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> C. H<emph type="italics"></emph>ieronimo da Piagnano.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000956">CONTE HIERONIMO. M<emph type="italics"></emph>o occorrendomi à douer condure una quan<lb></lb>tita de fanti, ouer uno eſſercito in uiaggio, ouer per camino, ue adimando, come <lb></lb>ſe potria ſapere à quanti fanti per fila li ſe doueria far caminare, accio che occor<lb></lb>rendo il biſogno, ſe poteſſono mettere in un ſubijo in battaglia quadra di gente, & che<emph.end type="italics"></emph.end><pb pagenum="44" xlink:href="042/01/087.jpg"></pb><emph type="italics"></emph>la bandera ſe ueniſſe à ritrouare nel meggio de tal ordinanza, ouer battaglia.<emph.end type="italics"></emph.end> N. <lb></lb>P<emph type="italics"></emph>er ſaper far questa coſa con preſtezza, ſubito pigliati la radice quadra di quella tal <lb></lb><expan abbr="quãtita">quantita</expan> de fanti, et ſe tal radice ſara diuiſibile per tre, <expan abbr="tãto">tanto</expan> <expan abbr="quãto">quanto</expan> ſara la detta terza par <lb></lb>te di tal radice, à tanti per fila ſe douera far caminar li detti fanti per camino.<emph.end type="italics"></emph.end> C.H. <lb></lb>D<emph type="italics"></emph>e gratia datime un eſſempio, & in piccol numero, perche meglio ue intendero, in uno <lb></lb>numero piccolo, che in uno grande.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>oniamo per eſſempio, che li fanti, che ſe ha <lb></lb>da condur, ſiano fanti. </s> <s id="s.000957">81. dico che il ſi debbe tuor la radice de. </s> <s id="s.000958">81. la qual è. </s> <s id="s.000959">9. & per<lb></lb>che queſta tal radice è diuiſibile per tre, & la ſua terza parte è tre, e per tanto dico che <lb></lb>li detti fanti. </s> <s id="s.000960">81. ſi debbono far caminar per uiaggio à tre fanti per fila, & far anno in <lb></lb>tutto file. </s> <s id="s.000961">27. come qui ſotto appare.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.087.1.jpg" xlink:href="042/01/087/1.jpg"></figure> <p type="main"> <s id="s.000962">E<emph type="italics"></emph>t quando l'occorreſſe el biſogno di uolerli redure in battaglia quadra tutte queſte. </s> <s id="s.000963">27. <lb></lb>file ſi debbono ſmembrare in tre parti eguale, come dimoſtra. </s> <s id="s.000964">a.b. & c.d. che in ogni <lb></lb>parte uenira à reſtare. </s> <s id="s.000965">9. file à tre fanti per fila, & dapoi il ſi debbe far fermar la pri<lb></lb>ma parte uerſo la fronte, & che le altre due procedano auanti dalla banda deſtra, ouer <lb></lb>ſiniſtra della prima (gia fermata) per fina à tanto che la teſta, ouer fronte della ſecon<lb></lb>da parte ſe uniſca con la teſta, ouer fronte della prima, & iui fermarſe, & fermata la <lb></lb>prima, & ſeconda parte ſi debbe far il medeſimo con la terza parte, cioe farla camina<lb></lb>re, e procedere à canto della ſeconda parte (gia fermata) per fina à tanto che la ſua te<lb></lb>ſta, ouer fronte ſe uniſca con la testa, ouer fronte della prima, & ſeconda (come nella <lb></lb>ſottoſcritta figura.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.087.2.jpg" xlink:href="042/01/087/2.jpg"></figure> <p type="main"> <s id="s.000966">L<emph type="italics"></emph>e qual tre parti coſi redutte, & aſſettate, haueranno redutta tal battaglia in forma <lb></lb>quadra di gente, come di ſotto appare in figura, & per far che la bandiera caſchinel <lb></lb>meggio di tal battaglia ſempre la ſe debbe aſſettar nel meggio della ſeconda parte, co<lb></lb>me diſopra appare in ponto.<emph.end type="italics"></emph.end> B. E<emph type="italics"></emph>t biſogna auertire che anchor che tal figura ſia qua<lb></lb>dra di terreno, come ſenſibilmente ſi uede, nondimeno in atto proprio tal figura ſe <lb></lb>trouora occupare per longhezza predi. </s> <s id="s.000967">63. & per larghezza piedi uentiſette, <pb xlink:href="042/01/088.jpg"></pb>(per le ragion adutte nel preſente queſito) le qual diſtantie <lb></lb>non hauemo oſſeruate, ne anchora ſe oſſeruara nella mag<lb></lb>gior parte delle figure che hanno da uenire, per che occupa<lb></lb>riano troppo gran ſpacio.<emph.end type="italics"></emph.end> C.H. Q<emph type="italics"></emph>ueſto non me impor<lb></lb>ta, ma ditemi pur, come ſe potra ſaper, ouer conoſcer li luo<lb></lb>chi doue ſe debbia ſmembrare le dette. </s> <s id="s.000968">27. file in tre parte <lb></lb>eguale, ſenza ſtare à numerare le dette file à. </s> <s id="s.000969">9. per che quan <lb></lb>do che il fuſſe una gran quantita de fanti ſaria coſa molto lon <lb></lb>ga.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ho inteſo che ogni quantita de fanti ui ſe li da una<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.088.1.jpg" xlink:href="042/01/088/1.jpg"></figure><lb></lb><emph type="italics"></emph>fila de archibuſeri nella fronte, & un'altra nelle ſpalle che in queſti ſopraſcritti fanti. <lb></lb></s> <s id="s.000970">81. ui uorria. </s> <s id="s.000971">18. archibuſeri, cioe 9. nella fronte, &. </s> <s id="s.000972">9. nella coda, & per tanto nelli luo <lb></lb>chi doue ſe doueria far la diuiſione ui metteria due file de archibuſeri, come diſotto ap <lb></lb>pare in figura, intendendo li archibuſeri per queſta lettera o.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.088.2.jpg" xlink:href="042/01/088/2.jpg"></figure> <p type="main"> <s id="s.000973">L<emph type="italics"></emph>i quali archibuſeri ui auertir anno ſempre delli luochi doue ſe douer anno ſmembr are <lb></lb>le dette file. </s> <s id="s.000974">27. & coſi in ogni altro maggior numero.<emph.end type="italics"></emph.end> C.H. E<emph type="italics"></emph>ue ho inteſo beſiißi<lb></lb>mo, fin qua, ma uorria che me dicesti, come ſe doueria procedere quando che la radice <lb></lb>de detti fanti non ſi poteſſe diuidere in tre partieguale.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uando che tal radice <lb></lb>non è diuiſibile in tre parti eguali, io non ſo come ſe procedano li periti Sargenti, ma <lb></lb>ben ue diro in che modo in tal caſo, ſe potria procedere, il qual modo, ſe il ſara per ca<lb></lb>ſo ſimil à quello che lor coſtumano, io lo hauero accaro, & ſe per caſo il ſara meglio di <lb></lb>quello che lor coſtumano, io lo hauero molto piu accaro, & ſe per caſo il ſara peggio<lb></lb>re, imputareti la mia poca pratica, ouer iſperientia di tal eſſercitio. </s> <s id="s.000975">Dico adunque che <lb></lb>quando la radice di detti fanti non ſia diuiſibile in tre parti eguali, neceſſariamente in <lb></lb>tal diuiſione auanzara uno, ouer dui, hor pigliamo prima per eſſempio quella che auan <lb></lb>za ſolamente uno, come ſaria ſe fuſſeno 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></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></lb>tre, à tre (cioe tante file quanto è il numero della radice) & altre diece file, à quattro, <lb></lb>à quattro, & altre diece pur à tre, à tre, come qui ſotto appare con li ſuoi. </s> <s id="s.000981">20. archi<lb></lb>buſi oltra li detti. </s> <s id="s.000982">100. fanti.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.088.3.jpg" xlink:href="042/01/088/3.jpg"></figure> <p type="main"> <s id="s.000983">E<emph type="italics"></emph>t queste tre parti, quando l'occorreſſe di uolerli redur in battaglia quadra di gente, <lb></lb>ſe procedaria, ſi come di ſopra, cioe far affermar la prima parte uerſo la fronte, &<emph.end type="italics"></emph.end><pb pagenum="45" xlink:href="042/01/089.jpg"></pb><emph type="italics"></emph>fermata che ſia far procedere auanti la ſeconda anchor la terza per fina à tanto che la <lb></lb>teſta, ouer fronte della ſeconda parte ſe ſia unita con la teſta, ouer fronte della prima, <lb></lb>& coſi fermata la detta ſeconda parte, far procedere auanti, per el medeſimo modo an <lb></lb>chor la terza parte, la qual coſa <expan abbr="facẽdo">facendo</expan> ſe uedera eſſer redutta tal battaglia in forma <lb></lb>quadra di gente, come di ſotto appare con li ſuoi archibuſeri alla fronte, et alle ſpalle.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.089.1.jpg" xlink:href="042/01/089/1.jpg"></figure> <p type="main"> <s id="s.000984">M<emph type="italics"></emph>a quando che nel partire la detta radice auanzaſſe. </s> <s id="s.000985">2. come ſaria, quando che li fan <lb></lb>ti fuſſeno. </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></lb>auanza. </s> <s id="s.000989">2. (come habbiamo detto) dico che in queſto caſo, & in altri ſimili io faria ca <lb></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></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 ſotto appar in figura <expan abbr="cõ">com</expan> <lb></lb>li ſuoi. </s> <s id="s.000996">22. archibuſeri oltra li detti fanti. </s> <s id="s.000997">121. li quali fanti ogni uolta che ſe uoleſſeno<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.089.2.jpg" xlink:href="042/01/089/2.jpg"></figure><lb></lb><emph type="italics"></emph>redure in battaglia quadra di gente ſe procederia, come di ſopra fu fatto.<emph.end type="italics"></emph.end> C.H. Q<emph type="italics"></emph>ue <lb></lb>ſto uoſiro diſcorſo non me diſpiace, anchor che tai tre parti per eſſere diſeguale, par <lb></lb>che diſdicano aſſai, ma diteme un poco queſta regola ſeruila coſi in ogni gran numero <lb></lb>de fanti.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio, che la ſeruira in ogni numero, ſi quadrato, come <expan abbr="nõ">non</expan> qua<lb></lb>drato.<emph.end type="italics"></emph.end> C.H. D<emph type="italics"></emph>atime un'eſſempio in parole ſolamente.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>oniamo per eſſempio, <lb></lb>che ſiano fanti. </s> <s id="s.000998">3969. delli quali uolendo uoiſapere à quanti fanti per fila uoi li debbia<lb></lb>ti far caminar per camino, accioche ſiano commodi à poterli in un ſubito mettere in <lb></lb>battaglia quadra di gente, dico che de queſti tai fanti uoi debbiati pigliar la radice qua <lb></lb>drata (per el, modo che ui ho inſignato) quala trouareti eſſer. </s> <s id="s.000999">63. &. </s> <s id="s.001000">63. fanti ſara per <lb></lb>fila tutta la battaglia in quadro di gente, & perche questa radice (cioè. </s> <s id="s.001001">63.) è diuiſibi<lb></lb>le in tre parti equale, ne pigliareti el terzo (per regola ferma) qual ſara. </s> <s id="s.001002">21. & coſi à <lb></lb>21. fante per fila uoi li douete far caminare in camino.<emph.end type="italics"></emph.end> C.H. M<emph type="italics"></emph>o quante file potro <lb></lb>io ſapere che ſiano in tutto coſi à. </s> <s id="s.001003">21. fante per fila.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>empre ſar anno el treppio<emph.end type="italics"></emph.end><pb xlink:href="042/01/090.jpg"></pb><emph type="italics"></emph>della uoſira radice, cioe el treppio de ſeſſantatre, che ſaria. </s> <s id="s.001004">189. et. </s> <s id="s.001005">189. file à fanti. </s> <s id="s.001006">21. <lb></lb>per fila ue ne peruenira.<emph.end type="italics"></emph.end> C.H. D<emph type="italics"></emph>oue ſapro io doue ſe debbia mettere quelle due, & <lb></lb>due file de archibuſeri, per cognoſcere el luoco doue ſe debbia ſmembrare in tre par<lb></lb>te per metter li in battaglia quadra di gente.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a uoſtra radice (cioe ſeſſantatre) <lb></lb>ui da el tutto, cioe, che tal diuiſione ſe fa alle. </s> <s id="s.001007">63. &. </s> <s id="s.001008">63. file talmente, che la prima par<lb></lb>te ſara de ſeſſantatre file, & coſi etiam la ſeconda, & la terza.<emph.end type="italics"></emph.end> C.H. V<emph type="italics"></emph>e ho inteſo be <lb></lb>nißimo in quanto a questa parte, e pero ſeguitate.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>aſe nel partire la uoſtra ra<lb></lb>dice per tre ui auanzaſſe uno (come accaderia ſe li propoſti fanti fuſſeno. </s> <s id="s.001009">5776. che la <lb></lb>radice di quelli ſaria ſettantaſei, la qual radice diuidendola per tre, ne ueneria. </s> <s id="s.001010">25. & <lb></lb>auanzeria uno: hor dico, che tutte le file, che reuſciran de queſti tai fanti ſar anno pur <lb></lb>el treppio della radice, cioe el treppio de ſettantaſei, che ſaria. </s> <s id="s.001011">228. & perche tutta <lb></lb>queſta fila de file ua diuiſa ſempre in tre parti (come diſopra fu detto, etiam fatto) a <lb></lb>ſettanta ſei file per parte (cioe tanto quanto e la noſtraradice) hor dico, che la prima, <lb></lb>& la ultima de queſte tre parte, ſi debbano far caminar a uinticinque fanti per fila, <lb></lb>cioe quanto che é il terzo della noſtra radice, & perche el ne auanzo uno (come di ſo<lb></lb>pra appare) dico che quel tal. </s> <s id="s.001012">1. ſi debbe mettere ſempre nella ſeconda parte, cioe in <lb></lb>quella di mezzo, cioe facendo caminar quelli della detta ſeconda parte à. </s> <s id="s.001013">26. fanti per <lb></lb>fila, talmente, che la prima, & la ultima parte della gran fila delle file, ſaranno à. </s> <s id="s.001014">25. <lb></lb>fanti per fila, & la ſeeonda parte ſara de fanti. </s> <s id="s.001015">26. per fila, & il medeſimo ſi debbe fa <lb></lb>re in ogni altra radice, che partita per. </s> <s id="s.001016">3. ue auanzi ſolamente. </s> <s id="s.001017">1. ma quando l'auan<lb></lb>zaſſe. </s> <s id="s.001018">2. ſeguita tutto al contrario, cioe, che la prima, & la ultima parte uuol eſſer de <lb></lb>uno fante de piu, di quello ſara el terzo della nostra radice, come, eſſempi gratia ſe li <lb></lb>detti fanti fuſſeno. </s> <s id="s.001019">2809. la ſua radice ſara. </s> <s id="s.001020">53. la qual partita per tre, ne uien. </s> <s id="s.001021">17. & <lb></lb>auanza. </s> <s id="s.001022">2. e per <expan abbr="tãto">tanto</expan> dico, che tai fanti ſe ne formara file.<emph.end type="italics"></emph.end> 159. (<emph type="italics"></emph>cioe el treppio de.<emph.end type="italics"></emph.end> 53.) <lb></lb><emph type="italics"></emph>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></lb>la radice, & la prima, & terza parte uol eſſer de uno fante de piu del terzo della no<lb></lb>ſtra radice, cioe uoleno eſſer de fanti. </s> <s id="s.001025">18. per fila, & la ſeconda parte, cioe la parte de <lb></lb>mezzo, uol eſſer puramente el terzo della nostra radice, cioe de fanti. </s> <s id="s.001026">17. per fila tal<lb></lb>mente, che de tutte le. </s> <s id="s.001027">159. file, le prime. </s> <s id="s.001028">53. file, & coſi le ultime. </s> <s id="s.001029">53. file uoranno eſſer <lb></lb>de fanti. </s> <s id="s.001030">18. per fila, & le. </s> <s id="s.001031">53. file di mezzo uoranno eſſer ſolamente de fanti. </s> <s id="s.001032">17. per <lb></lb>fila. </s> <s id="s.001033">Et in quella che nel partire la radice per. </s> <s id="s.001034">3. auanza ſolamente uno ua al contrario <lb></lb>di queſta, cioe, che la prima, & terza parte della detta gran fila delle file, uoleno ſem<lb></lb>pre tanti fanti per fila, quanto ſara la terza parte integra della nostra radice, & la <lb></lb>parte di mezzo, cioe la ſeconda uora uno fante de piu del ditto terzo della nostra radi <lb></lb>ce. </s> <s id="s.001035">Et perche mai puo auanzar piu che uno, ouer dui, à partire la detta noſtra radice <lb></lb>per. </s> <s id="s.001036">3. le dette nostre regole ue ſatisfar anno in ogni quantita de fanti ſi quadrata, ouer <lb></lb>non quadrata, perche, come di ſopra fu detto, nelle quantita, ouer numerinon quadra<lb></lb>ti, ſempre ſe piglia la radice propinqua di quel tal numero, & di quella ſe ne ſerue, co <lb></lb>me di ſopra è ſtato detto, & de quello reſiduo, ouer ſuperfluo de fanti, che ſoperchiaſ<lb></lb>ſeno el quadrato di tal radice el ſargente li aſſetta ſecondo el ſuo parere, eſſempi gra<lb></lb>tia, ſe li detti fanti fuſſeno quattromilla, el qual numero non è quadrato, nondimeno di <lb></lb>co, che di quello ſe debbia cauar la ſua radice propinqua, la quale ſara<emph.end type="italics"></emph.end> 63. (<emph type="italics"></emph>uero è, che<emph.end type="italics"></emph.end><pb pagenum="46" xlink:href="042/01/091.jpg"></pb><emph type="italics"></emph>auanzara fanti.<emph.end type="italics"></emph.end> 31.) <emph type="italics"></emph>& di tal radice ſeruirſene ſecondo il ſuo uolere, eſſempi gratia, uo <lb></lb>lendoli de ſubito mettere in btttaglia quadra di gente, ſe ne doueria mettere ſeſſanta<lb></lb>tre fanti per fila, & tal battaglia uenira quadra di gente, come nel primcipio fa det<lb></lb>to, uero è, che ui auanzaria fora di tal ordinanza quelli fanti. </s> <s id="s.001037">31. li quali il ſargente li <lb></lb>aſſettara ſecondo el ſuo uolere, ſimilmente uolendo mettere li detti fanti quattro mille <lb></lb>in camino ſe die pur tore la detta ſua radice propinqua, la quale, come detto è ſeſſanta <lb></lb>tre, la qual partendola per tre, ne uien. </s> <s id="s.001038">21. & non auanza coſa alcuna, e per tanto gli <lb></lb>detti fanti ſi debbouo far caminare à fanti. </s> <s id="s.001039">21. per fila, & partire le dette file in tre <lb></lb>parte à. </s> <s id="s.001040">63. file per parte, uero é, che la ultima parte uerra à eſſer de. </s> <s id="s.001041">64. file, & an<lb></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></lb>detto) reſtar anno fora della ordinanza, ſecondo il parere del ſargente, & per lo me<lb></lb>deſimo modo ſe procedaria, quando che la radice di tal numero non quadrato non re<lb></lb>ceueſſe la perfetta diuiſion per tre, cioe, ſel auanzaſſe uno, procedere, come di ſopra <lb></lb>dißi, cioe dar uno fante de piu per fila alla parte di mezzo, & alle altre due parti, <lb></lb>cioe alla prima, & alla terza porui ſolamente tanti fanti per fila, quanto ſara la ter<lb></lb>za parte della nostra radice, & quando auanzaſſe. </s> <s id="s.001044">2. procedere al contrario, cioe <lb></lb>dar uno fante per fila de piu alla prima, & alla terza parte, & alla ſeconda porui ſola <lb></lb>mente tanti fanti per fila, quanto ſara el terzo della noſtra radice, & quelli fanti che <lb></lb>fuſſeno auanzati nel cauar della radice in principio, aſſettarli, come di ſopra è ſtato <lb></lb>detto.<emph.end type="italics"></emph.end> C.H. N<emph type="italics"></emph>on procedati piu oltra, che ue ho inteſo benißimo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001045">QVESITO TERZO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> C.H<emph type="italics"></emph>ieronimo da Piagnano.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001046">CONTE HIERONIMO. I<emph type="italics"></emph>o adimandai una uolta à uno famoſo Sargen<lb></lb>te, come ordinaria una battaglia de. </s> <s id="s.001047">1000. fanti, lui me riſpoſe, che lui faria el fi <lb></lb>le de fanti. </s> <s id="s.001048">49. per teſta, hor ue adimando, uolendo io ordinare una battaglia ſimile à <lb></lb>queſta de una altra maggiore, ouer menore quantita de fanti, come me doueria gouer<lb></lb>nare.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uadrati quello numero de. </s> <s id="s.001049">49. cioe multiplicatilo in ſe medeſimo, che fara <lb></lb>2401. & queſto. </s> <s id="s.001050">2401. moltiplicareti fia quella quantita de fanti, che uoreti mettere <lb></lb>in battaglia, & quel produtto, partiritele per el uoſtro. </s> <s id="s.001051">1000. & la radice di queſto <lb></lb>aduenimento ſara nel numero di fanti, che douereti metter in cadauna fila per teſta, <lb></lb>eſſempigratia, ſe quelli fanti, che deſiderareti di mettere in una battaglia ſimile fuſ<lb></lb>ſeno. </s> <s id="s.001052">2500. multiplicati queſti 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></lb>ra. </s> <s id="s.001056">8403500. & queſto tal produtto, partireti per el uoſtro. </s> <s id="s.001057">1000. ne uenira. </s> <s id="s.001058">8403. <lb></lb>(laſſando el rotto, perche uno huomo non ſi puo ſpezzare, che non periſca el tutto,) <lb></lb>& di queſto. </s> <s id="s.001059">8403. ne cauareti la radice, la qual ſara. </s> <s id="s.001060">91. & auanzara. </s> <s id="s.001061">112. & fanti <lb></lb>91. douereti mettere in cadauna fila per teſta, & per fianco ne uerra à eſſer fanti. </s> <s id="s.001062">38. <lb></lb>uero è che anchor ne auanzara fora fanti. </s> <s id="s.001063">42. quali non compir anno la ultima fila de <lb></lb>drio. </s> <s id="s.001064">Et con ſimel ordine uoi procedareti in ogni altra maggior, ouer menor quantita.<emph.end type="italics"></emph.end><lb></lb>C.H. V<emph type="italics"></emph>eho inteſo benißimo, & questa uoſtra regola la ho piu accara, che coſa, che <lb></lb>me habbiati inſegnato, perche me gli ſon affaticato molti giorni, per trouarui rego<lb></lb>la, & mai ue la ho potuta ritrouare.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/092.jpg"></pb> <p type="head"> <s id="s.001065">QVESITO QVARTO FATTO DAL SARGENTE <lb></lb><emph type="italics"></emph>maggiore del Duca di Vrbino.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001066">SARGENTE. C<emph type="italics"></emph>ome ordinareſti una battaglia quadra di terreno, & non di <lb></lb>gente.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>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></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></lb>uol che occupi la ſua perſona, che in ſumma ſarian piedi. </s> <s id="s.001073">7. in lungo, et da ſpalla à ſpal <lb></lb>la uol che occupi piedi. </s> <s id="s.001074">3. come di ſopra è detto, io procedaria in queſto modo multipli <lb></lb>carei quella quantita de fanti, che deſideraſſe di metter in battaglia, per el quadrato <lb></lb>de ſette. </s> <s id="s.001075">cioe per. </s> <s id="s.001076">49. & quel produtto parteria per. </s> <s id="s.001077">21. & quanto fuſſe la radice di <lb></lb>tal aduenimento, tantifanti mettaria in cadauna fila per teſta, eſſempi gratia, ſel fuſſe <lb></lb>fanti. </s> <s id="s.001078">3600. li quali deſideraßi di mettere in battaglia quadra di terreno, & non di <lb></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></lb>176400. & queſto produtto lo parteria per. </s> <s id="s.001082">21. del qual partimento ne ueneria <lb></lb>8400. & di queſto <expan abbr="aduenimẽto">aduenimento</expan> ne cauaria la radice, laqnal ſaria.<emph.end type="italics"></emph.end> 91. (<emph type="italics"></emph>uero è che auan <lb></lb>zaria.<emph.end type="italics"></emph.end> 119.) <emph type="italics"></emph>& de fanti. </s> <s id="s.001083">91. faria le file per teſta, uero è che la maggior parte delle uol <lb></lb>te nella coda ui reſtara una fila non compita, cioe imperfetta, perche li numeri rare <lb></lb>uolte ne ſeruano preciſamente ſecondo el noſtro intento, ſi, come anchora occorre nel <lb></lb>fare le battaglie quadre di gente, cioe, che la maggior parte delle uolte ne <expan abbr="auãza">auanza</expan> qual <lb></lb>che fante de piu, tamen una fila de piu, ouer de manco, non fa error troppo apparente.<emph.end type="italics"></emph.end><lb></lb>S. D<emph type="italics"></emph>oue cauati quel. </s> <s id="s.001084">21. con el quale uoi parteti quella uoſtra multiplicatione.<emph.end type="italics"></emph.end> N. <lb></lb>I<emph type="italics"></emph>o imagino una battaglia de tre file a fanti. </s> <s id="s.001085">7. per fila, la qual batt aglia ſaria quadra di <lb></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></lb>dauanti, & de drio con quel piede, che occupa ogni fila, & ſimelmente li fanti. </s> <s id="s.001088">7. in lar <lb></lb>ghezza uoranno medeſimamente piedi. </s> <s id="s.001089">21. di terreno a piedi. </s> <s id="s.001090">3. per fante, ondeſe tal <lb></lb>battaglia occupa piedi. </s> <s id="s.001091">21. di terreno in ogni uerſo la ſara quadra di terreno, & tutta <lb></lb>tal battaglia contenera fanti. </s> <s id="s.001092">21. & queſti fanti. </s> <s id="s.001093">21. me ne ſeruo per partitore nella ſo <lb></lb>praſcritta mia operatione.<emph.end type="italics"></emph.end> S. S<emph type="italics"></emph>ta benißimo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001094">QVESITO QVINTO FATTO DAL S. GABRIEL <lb></lb>T<emph type="italics"></emph>admo da Martinengo, Cauallier de Rhodi, <lb></lb>e Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001095">PRIORE. D<emph type="italics"></emph>apoi che ſopra la compoſitione della poluere non ui habbiamo <lb></lb>altro che dire, per non star ocioſi dapoi la noſtra lettione di Euclide, uoglio che <lb></lb>ragionamo un poco del modo de ordinare li eſſerciti in battaglia, & maßime in alcu<lb></lb>ne ingenioſe forme, uſitate da noſtri antiqui, el qual modo, alli preſenti tempi, par ſia <lb></lb>totalmente perſo, & anullato, per non trouarſe alcuno autore antiquo, ne moderno, <lb></lb>che ne dia el modo, ouer regola di ſaperli ordinare, & queſte tai figure, ouer forme ſo <lb></lb>no el cuneo, la forfice, la ſerra, el <expan abbr="rhũbo">rhumbo</expan>, el cerchio, et la forma lunare, uero è che el ual <lb></lb>lo ha posto alcune str anie ſorme di battaglie, ma rare di quelle è che ſia atta a poter ca <lb></lb>minare, che <expan abbr="nõ">non</expan> ui ſegua immediate diſordine, <21> che ogni ordinata battaglia ſe la debbe<emph.end type="italics"></emph.end><pb pagenum="47" xlink:href="042/01/093.jpg"></pb><emph type="italics"></emph>eſſer atta à poter caminare in quel tal ordine eglie neceſſario che ogni fante habbia uno <lb></lb>altro fante in debita diſtantia, che ui camini auanti di ſe, eccetto quelli della prima fron <lb></lb>te, & coſi un'altro per banda, eccetto quelli che ſono nei fianchi, et coſi un'altro de drio <lb></lb>eccetto la ultima fila, perche ogni fante nel caminare ſe regge dal ſuo compagno che gli <lb></lb>camina auanti di ſe, eccetto quelli della prima fila, e pero ſe una ordinanza uorra cami <lb></lb>nare, & che tutti li fanti non habbiano un'altro fante, che gli camini auanti di ſe nella <lb></lb>ſua debita diſtantia, accettuando quelli della prima fronte, ſubito tal ordinanza uerra <lb></lb>in confuſione.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>redo che ſia coſi, perche ogni fante piglia la meta nel ſuo cami<lb></lb>nare pian, e forte, dal compagno che gli camina auanti, eccetto quelli che ſono nella pri <lb></lb>ma fila della fronte, li quali non ſi reggono da niuno nel caminare, ancitutte le altre fi<lb></lb>le ſe reggono da quella ſola.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>oſi è, hor dapoi che uedo che haueti inteſo la mia o<lb></lb>pinione, ue adimando, come ſe douera procedere, uolendo ordinare una quantita de fan <lb></lb>ti, ouer uno eſſercito in forma cunea, ouer triangolare talmente che fuſſeno atti à po<lb></lb>ter caminare uerſo la ponta de tal cuneo, cioe che tal ordinanza poſſa caminare con la <lb></lb>ponta di tal cuneo uerſo li nemici.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſta forma di ordinanza, ouer di battaglia <lb></lb>naſce, ouer ſe forma dalla progreßione aſcendente per numero binario, cominciando <lb></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></lb></s> <s id="s.001099">9. & dapoi. </s> <s id="s.001100">11. & coſi andar procedendo, & accreſcendo ſempre dui fanti de piu, per <lb></lb>fina à tanto che non ui ſia piu fanti, uero è, che potria eſſer tal numero de fanti, che in <lb></lb>ultimo non potranno, ouer non ſaranno ſofficienti à compir la ultima fila, ilche eſſen<lb></lb>do ſe potriano laſſar coſi fuora della ordinanza da ſeruirſene ſecondo parera al buon <lb></lb>Sargente, perche tal coſa occorre la maggior parte delle uolte, & in ogni ſpecie de or<lb></lb>dinanza, cioe che ſempre ui reſta qualche fante fuora di tal ordinanza.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>redo <lb></lb>queſto che uoi diceti, ma datime uno eſſempio in figura ſopra tal materia, & in piccol <lb></lb>numero, perche nelli numeri piccoli meglio ſe intende la coſa.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>oniamo che li fan <lb></lb>ti che deſideriamo di mettere in battaglia cunea ſiano. </s> <s id="s.001101">100. dico che prima ſe ne pon<lb></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. & coſi andar procedendo ſempre <lb></lb>mettendoui. </s> <s id="s.001107">2. fanti de piu per fina à tanto che ue ſia fanti, come di ſotto appare in fi<lb></lb>gura, onde la ultima fila, in queſto caſo uenira à eſſer de fanti. </s> <s id="s.001108">19. & non ui auanzara <lb></lb>alcun fante, & queſto è, perche il numero delli fanti (cioe il. </s> <s id="s.001109">100.) è numero quadrato,<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.093.1.jpg" xlink:href="042/01/093/1.jpg"></figure><pb xlink:href="042/01/094.jpg"></pb><emph type="italics"></emph>& coſi in ogni altro numero, che ſia quadrato ſe formara il detto cuneo ſenza alcuno <lb></lb>ſoprauanzamento de fanti, ma ſe il detto numero de fanti non ſara numero quadrato <lb></lb>ſempre ui auanzara tanti fanti, quanto che il detto numero de fanti auanzara il mag<lb></lb>gior numero quadrato contenuto da quello, eſſempi gratia ſe gli propoſti fanti da far <lb></lb>il cuneo fuſſeno. </s> <s id="s.001110">120. dico che ui auanzara. </s> <s id="s.001111">20. fanti fuora della ordinanza del cuneo, <lb></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></lb>quello) che ſaria pur. </s> <s id="s.001114">20. ma fe gli detti fanti fuſſeno. </s> <s id="s.001115">123. ui auanzaria ſolamente fan <lb></lb>ti. </s> <s id="s.001116">2. perche il maggior numero quadrato contenuto da. </s> <s id="s.001117">123. ſaria. </s> <s id="s.001118">121. e pero. </s> <s id="s.001119">123. <expan abbr="auã">auam</expan> <lb></lb>za il detto. </s> <s id="s.001120">121. nel detto. </s> <s id="s.001121">2. & questo medeſimo ſi debbe intendere in ogni gran nu<lb></lb>mero.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>ue ho inteſo benißimo, & me baſta aſſai per queſta ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001122">QVESITO SESTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001123">PRIORE. C<emph type="italics"></emph>ome ſe potria formar quella figura chiamata la forfice, la quale <lb></lb>uſauano gliantichi per opponere alla forma cunea.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a forfice ſe costituiſ <lb></lb>ſe con due forme cunee congionte per tuor la detta figura cunea in meggio.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>ati<lb></lb>me uno eſſempio figurale, & in piccol numero.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>o eſſempio di questa lo uoglio <lb></lb>adure nel medeſi no numero de fanti. </s> <s id="s.001124">100. con che fu fatto il cuneo, accio che quella <lb></lb>poſſa far giudicio, ſe il fuſſe dui eſſerciti eguali de quantita de fanti, & che l'uno for<lb></lb>maſſe il cuneo, & l'altro la forfice, qual de loro haueria auantaggio, dico adunque che <lb></lb>eſſendo fanti. </s> <s id="s.001125">100. & uolendo de quelli formare la forfice, li ſe debbono diuidere in due <lb></lb>parti eguali, che ne ueneria. </s> <s id="s.001126">50. per parte, & de cadauna de queſte parti ſe ne debbe<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.094.1.jpg" xlink:href="042/01/094/1.jpg"></figure><pb pagenum="48" xlink:href="042/01/095.jpg"></pb><emph type="italics"></emph>ſormar uno cuneo, ſecondo il modo di ſopra detto, & congionger li inſieme, come di <lb></lb>ſopra appare in figura con le ſue ponte uerſo delli nemici, cioe ner ſo del cuneo per tor <lb></lb>lo in meggio, & biſogna notare qualmente nella formatione di queſti dui cunei, ui auan <lb></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></lb>ro quadrato, & auanza il maggior numero quadrato contenuto da quello (qual è.<emph.end type="italics"></emph.end> 49.)<emph type="italics"></emph><lb></lb><21> un fante ſolo, cioe fra tutti dui ui <expan abbr="auãzaria">auanzaria</expan> dui fanti, come di ſopra appare in figura.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001128">PRIORE. C<emph type="italics"></emph>ertamente non è huomo che non reputaſſe che li fanti che ſono <lb></lb>in quelli dui cunei che formano la detta forfice, non fuſſeno piu d'un tanto, e meg <lb></lb>gio de quelli, che ſono nel primo cuneo, & ſe io non gli haueſſe numerati, io non lo cre<lb></lb>derei che fuſſeno eguali, e per tanto, io giudicarei, in dui eſſerciti coſi ordinati, eſſer <lb></lb>maggior auantaggio nella forfice, che nel cuneo, perche la forfice piglia in meggio il <lb></lb>detto cuneo, & quello ha da tendere nel combattere dall'una é l'altra banda, & li dui <lb></lb>cunei della forfice non hanno da tendere nel combattere, ſaluo che da una banda ſola <lb></lb>cadauno de loro.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>oſi è da giudicare.<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>on uoglio che intramo in altra ma<lb></lb>teria per questa ſera, ma diman de ſera uoglio che diſputamo la proprieta di queſta fi<lb></lb>gura cunea, quando che il nemico non ſapeſſe formar la detta forfice.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001129">QVESITO SETTIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barleata.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001130">PRIORE. B<emph type="italics"></emph>en quando ſe ordinaſſe uno eſſercito in forma cunea, & che li ne<lb></lb>mici non haueſſono l'arte di ſaper far la forfice, che auantaggio ſe potria giudi<lb></lb>care per quella ſorte figura, maßime hauendo tanta gente l'una parte quanto l'altra.<emph.end type="italics"></emph.end><lb></lb>N. Q<emph type="italics"></emph>uando che la contraria parte uoleſſe opponerſe à tal figura cunea, con una for<lb></lb>ma quadra di terreno, come al preſente ſi coſtuma, à tutte le ragion del mondo restara<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.095.1.jpg" xlink:href="042/01/095/1.jpg"></figure><pb xlink:href="042/01/096.jpg"></pb><emph type="italics"></emph>rotto è ſbezzato.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>erche ragione.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a ragion ue la diro, ſia eſſempi gra<lb></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></lb>poſition del detto cuneo, come di ſotto appare in figura, & perche l'ordine del ferir <lb></lb>del cuneo, e queſto che tutti quelli che tirano de alcuna ſorte iſtrumento, come ſono ar<lb></lb>tegliarie, archibuſi, dardi, archi, ouer baleſtre, tutti debbono tendere à tirare, & à ſe<lb></lb>rire ſolamente in quel luoco doue ua à inferire la ponta del cuneo, cioe in ponto. </s> <s id="s.001133">a. on<lb></lb>de li fanti che in quel luoco ſe ritrouar anno, ui ſara neceſſario, o a morire, ouer à dar <lb></lb>luoco alla ponta del detto cuneo, per la grande moltitudine delle archibuſate, & friz<lb></lb>zate tutte in quel ſolo luoco tirate, intrando adunque dentro la ponta del detto cu<lb></lb>neo in tal luoco, continuamente andara preforando, & penetrando tutta quella or <lb></lb>dinanza da banda, à banda, perche tutti archibuſeri, & arceri che reſtano di fuora, <lb></lb>non debbono ceſſar de tirare in quel iſteſſo luoco, & non altroue, la qual coſa facendo <lb></lb>eglie impoßibile che non ui ſia dato luoco al detto cuneo da penetrare, et penetrato che <lb></lb>ſia tal eſſercito è rotto ſenza alcun remedio.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſta coſa è chiara, che ſe il detto <lb></lb>cuneo penetra tutta la detta ordinanza quella ſenza dubbio reſta rotta, e fracaſſata, et <lb></lb>è quaſi impoßibile che non gli uenga ad efſetto, perche tutta la poſſanza & uirtu de <lb></lb>quel tal cuneo uien à operare in quel luoco ſolo, e pero eglie quaſi impoßibile che in <lb></lb>quel tal luoco ui poſſano durare anchor, che fuſſeno molto piu in tal <expan abbr="ordinãza">ordinanza</expan>, de quel<lb></lb>li che fuſſeno nel detto cuneo, perche tal luoco non puo eſſer ſoccorſo da alcuno de quel <lb></lb>li di tal ordinanza, perche ſe quelli che ſono uerſo. </s> <s id="s.001134">b. ouer uerſo. </s> <s id="s.001135">c. uoleſſeno uenire à <lb></lb>dar ſoccorſo à quel tal luoco, ſaria forza à deſordinarſe, & deſordinati che fuſſono, <lb></lb>incorrariano nel medeſimo ſcandolo, cioe reſtariano rottitotalmente, & reſtando nel <lb></lb>ſuo luoco la ſua uirtu, ouer poſſanza, reſta quaſi morta, perche niun de loro la puo mo <lb></lb>ſtrare per ualente che ſia, & hor comprendo di quanta importantia ſia queſta forma <lb></lb>cunea, à chinon ui ſapeßi, trouar laſua medicina, ouer rimedio.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio che <lb></lb>onv buona forma alle uolte è di tal autorita quanto che è la ſua materia, & anchor piu.<emph.end type="italics"></emph.end><lb></lb>P. C<emph type="italics"></emph>ertamente queſta uoſtra opinione mi è piaceſta aſſai, et mi baſta per queſta ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001136">QVESITO OTTAVO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001137">PRIORE. C<emph type="italics"></emph>ome ſe potria formare, de una quantita de fanti, ouer di uno eſſer <lb></lb>cito, quella forma, ouer figura di battaglia dalli antichi chiamata la Serra.<emph.end type="italics"></emph.end> N. <lb></lb>Q<emph type="italics"></emph>ueſta forma di battaglia, ſecondo la qualita del ſuo nome, à mi me pare che debbia <lb></lb>eſſere dentata, ſi come è la ſega con che ſe coſtuma ſegar li traui, e per tanto uolendo re <lb></lb>dure una quantita de fanti, ouer uno eſſercito in tal forma. </s> <s id="s.001138">biſogna conſiderare due co <lb></lb>ſe, l'una de quanti dentiſe uol far queſta Serra, ouer ſega, & ſe oltra tai denti ui ſi uol <lb></lb>altra ordinanza da ſostentar quelli denti, ouer non.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>atime uno eſſempio in figu <lb></lb>raſopra quello che uoleti in ferire, ma in poco numero de fanti, perche meglio appren <lb></lb>dero la coſa.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>oniamo che li fanti delli quali ſe uol formare li puri denti della det<lb></lb>ta Serra ſiano. </s> <s id="s.001139">100. hor queſti. </s> <s id="s.001140">100. fanti ſi debbono diuidere nel numero delli denti che <lb></lb>ſi uol dar à queſta Serra, & de cadauna de quelle parti formarne un cuneo, per la re-<emph.end type="italics"></emph.end><pb pagenum="49" xlink:href="042/01/097.jpg"></pb><emph type="italics"></emph>gola data nel. </s> <s id="s.001141">5. Queſito, & quelli tai cunei, congiongerli in diretto, ſecondo che fu fat <lb></lb>to di quelli dui nel formar la forfice, eſſempi gratia, poniamo, che delli detti fanti cen <lb></lb>to ſe uoglia far quattro denti di una ſerra, dico, che li detti fanti <expan abbr="cẽto">cento</expan> li ſe debbono par <lb></lb>tire in quattro parti, del qual partimento ne uenira fanti. </s> <s id="s.001142">25. per parte, hor di cadau <lb></lb>na di queste parti ſe ne debbe formar un cuneo ſecondo lordine dato nel detto. </s> <s id="s.001143">5. Que <lb></lb>ſito, & queſti quattro cunei congiongerli in diretto, come diſotto appar in figura, & <lb></lb>queſto è in quanto al far delli puri denti, ma ſe per caſo ſe uoleſſe mettere una altra or <lb></lb>dinanza drio alli detti quattro denti, biſognaria prima determinare de quanti fanti <lb></lb>tal ordinanzaſe uora fare, & quella cauarla de per ſe, & del resto formar li denti, &<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.097.1.jpg" xlink:href="042/01/097/1.jpg"></figure><lb></lb><emph type="italics"></emph>de drio de detti denti ponerui quella quantita de fanti, che prima fu cauata, & ordi<lb></lb>narli à tanti fanti per fila, quanti fanti ſe trouara direttamente in longo eſſere in tutte <lb></lb>le baſe delli denti formati, eſſempi gratia, poniamo che ſiano fanti. </s> <s id="s.001144">244. et che de fan <lb></lb>ti. </s> <s id="s.001145">100. de quelli ſe uoglia fare quattro denti di una ſerra, & delli altri. </s> <s id="s.001146">144. ſe uoglia <lb></lb>fare una ordinanza ſuſtentante li detti quattro denti, dico, che redutti li fanti cento in <lb></lb>quattro denti, come di ſopra fu detto, conſequentemente drieto à quelli ui ſe debbe aſſet <lb></lb>tar quelli cento quar antaquattro fanti à fanti trentaſei per fila, perche in tutte quat<lb></lb>tro le baſe de detti quattro denti ui ſono fanti trentaſei, come nella ſotto ſcritta figura <lb></lb>appare, & coſi con tal modo, & ordine ſe potra ordinare, ſe fuſſeno bene cento milia <lb></lb>fanti deſtinguendo, come di ſopra ſe fatto in quel poco numero.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>eho inteſo be<lb></lb>nißimo, & baſta per queſtaſera.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.097.2.jpg" xlink:href="042/01/097/2.jpg"></figure> <p type="head"> <s id="s.001147">QVESITO NONO FATTO DAL MEDESIMO <lb></lb>S<emph type="italics"></emph>ignor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001148">PRIORE. C<emph type="italics"></emph>ome ſe potria redure una quantita de fanti, ouer uno eſſercito in <lb></lb>figura Rhombica di gente, che fuſſeno atti à poter caminar con uno angolo uer-<emph.end type="italics"></emph.end><pb xlink:href="042/01/098.jpg"></pb><emph type="italics"></emph>ſo li nemici.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>on la regola che ſi fa el cuneo, con quella medeſima quaſi ſi fa el <expan abbr="rhõ">rhom</expan> <lb></lb>bo, perche diuidendo tutti quei fanti, ouer quello eſſercito con, che ſi uuol formar el <lb></lb>detto rhombo in due parti equali, & di quella mita formar el cuneo, & formato che le <lb></lb>ſopra el me deſimo ultimo lato, uiſe debbe andar aſſettando l'altra mita de fanti, ouer <lb></lb>del aſſercito con file, che continuamente andaſſeno declinando per dui fanti <expan abbr="mãco">manco</expan>, cioe <lb></lb>al contrario di quello ſe fa comenzandolo dalla unita, cioe comenzando à far la ponta <lb></lb>del cuneo, nel qual ſi ua continuamente accreſcendo le file per dui fanti piu, ma biſo<lb></lb>gna aduertire, che ſe nella fabricatione del primo cuneo, ui ananzaſſe qualche fanti, <lb></lb>che non fuſſeno à ſofficienza de farui un'altra fila, quella medeſima fila ſe debbe pur <lb></lb>compire con li fanti dell'altra mita de fanti, perche uno di queſti dui cunei congionti, <lb></lb>uiene a eſſer de una fila piu de l'altro.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>atime un'eſſempio in figura ma in picciol <lb></lb>numero.<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.098.1.jpg" xlink:href="042/01/098/1.jpg"></figure><pb pagenum="50" xlink:href="042/01/099.jpg"></pb>N. P<emph type="italics"></emph>oniamo, eſſempi gratia, che li fanti, con li quali ſe deſidera di uoler ſormar el <lb></lb>rhombo ſiano. </s> <s id="s.001149">320. dico, che ſi debbono partire in due parti equali, che de tal partinen <lb></lb>to ne uenira fanti. </s> <s id="s.001150">160. per parte, & de l'una di queſte partiſe ne debbe far uno cuneo <lb></lb>ſecondo l'ordine datto nel quinto Queſito, el qual fatto ſi trouara auanzar fanti. </s> <s id="s.001151">16. <lb></lb>(per le ragioni adutte nel detto quinto Queſito) cioe ui mancara fanti noue à compi<lb></lb>re la detta ultima fila de tal primo rhombo, hor dico, che tal fila ſi debbe compire con <lb></lb>li fanti dell'altra mita, cioe pigliarne quelli fanti. </s> <s id="s.001152">19. che ui manca, che nel detto primo <lb></lb>rhombo uenira à eſſer fanti. </s> <s id="s.001153">169. & nell'altra parte uenira à reſtare ſolamente fanti <lb></lb>151. coni quali formandone l'altro rhombo, ſopra la ultima fila del primo, la qual ulti <lb></lb>ma fila ſara de fanti uinticinque, onde biſognara ſopra di quella aſſettaruene un'altra <lb></lb>fila de dui fanti manco, cioe de fanti uimitre, & di ſopra à quella de detti fanti uintitre <lb></lb>aſſettaruene un'altra de fanti uintiuno, & ſopra à quella de fanti uintiuno, un'altra <lb></lb>de fanti deſnoue, & ſopra à quella de fanti deſnoue un'altra de fanti dieciſette, & coſi <lb></lb>andar procedando ſempre con dui fanti manco, per fina à tanto che ſe peruenira alla fi <lb></lb>la dun fante ſolo (come di ſopra appar in figura) uero è, che ſi trouara in ultimo auan<lb></lb>zar fantiſette, li quali il ſacente Sargente li aſſettara ſecondo il ſuo parere, & coſi con <lb></lb>tal modo, & ordine ſe potra redure in una ſimel ordinanza ogni grande eſſercito, & <lb></lb>potranno uoltarſe, & caminar facendo deſpalle fronte, & ſimelmente de qual ſi uo<lb></lb>glia fianco.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o ue ho inteſo ottimamente, & chel ſia el uero, uoi uoleti primamen <lb></lb>te, che ſe aduertiſca, come chel primo cuneo ui à eſſer de una fila di fanti de piu del ſe<lb></lb>condo, e pero eſſendo diuiſo lo eſſercito in due parti equali, & ponendo poi quelli fan<lb></lb>ti deſnoue, che auanzano nella formation del primo cuneo, inſieme <expan abbr="cõ">com</expan> quelli fanti. </s> <s id="s.001154">160. <lb></lb>dell'altra mita fariano poi fanti cento ſettantanoue, delli quali uolendone poi formar <lb></lb>l'altro cuneo ſopra la ultima fila del detto primo cuneo, laquale ſaria ſolamente de fan <lb></lb>ti uintitre, & cominciando poi el ſecondo cuneo de fanti uintiuno (cioe per dui fanti <lb></lb>manco) & coſi andar procedendo (per duo fanti meno) per fin al compimento di que <lb></lb>ſto ſecondo cuneo, ne uenira auanzar fanti cinquantacinque, & uoi per far auanzar <lb></lb>men fanti uoleti, che quella ultima fila (imperfetta del primo cuneo, quala è ſolamente <lb></lb>di fanti deſnoue, che la ſe compiſca delli fanti dell'altra mita (cioe pigliando quelli fan<lb></lb>ti noue che ui manca) il che facendo, & procedendo poi come di ſopra fudetto, inul<lb></lb>tima ui uenira auanzar ſolamente fanti ſette, come di ſopra fu detto, et dapoiſotto <expan abbr="giõ">giom</expan> <lb></lb>geti qualmente queſta figura rhombica ha quella poteſia, che ſe ritroua nelle ordinan <lb></lb>ze quadre di gente, ouer diterreno, cioe, che ella è atta à uoltarſe, & far de ſpalle <expan abbr="frõ">from</expan> <lb></lb>te, & caminar etiam per queluerſo, & ſimelmente è atta à far da qual ſi uoglia fianco <lb></lb>teſta, uero è, che ui occorre in taiuerſi à douerſi reſtringer per un uerſo, & allargar<lb></lb>ſe per un'altro, come medemamente, occorre anchora nelle dette ordinanze qua<lb></lb>dre di gente, ouer di terreno.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on altro che queſto uolemo inferire.<emph.end type="italics"></emph.end> P. A<emph type="italics"></emph>dun <lb></lb>que ue ho inteſo, e pero al preſente non uoglio che procedamo piu oltra <21> queſta ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001155">QVESITO DECIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/100.jpg"></pb> <p type="main"> <s id="s.001156">PRIORE. <emph type="italics"></emph>Come ſe potria ordinare una quantita de fanti, ouer uno eſſercito <lb></lb>in una battaglia cornuta, che fuſſe atta à poter caminare in tal ordine contra à <lb></lb>li <expan abbr="nemicī">nemicim</expan>, & chi fuſſe anchora atta occorrendo il biſogno à poter allongar i corni, cioe <lb></lb>buttarli in fuora etiam à tirarli in dentro (come ſuol far la lumaca, ouer bouolo) ſen <lb></lb>za alcum pericolo de alcun deſordine.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>olendo eſſeguir tal coſa, io diuideria tut <lb></lb>ti quelli fanti, ouer tutto quel eſſercito in tre partiequali, & una di quelle parti redu<lb></lb>ria in battaglia quadr a diterreno, & cadauna delle altre due le reduria in battaglia <lb></lb>quadra di gente, & <expan abbr="nõ">non</expan> di terreno, et una di queſte due battaglie, la mettaria alla <expan abbr="bãda">banda</expan> <lb></lb>deſtr a della prima battaglia (gia fatta in forma quadra di gente) & l'altraue la pone <lb></lb>ria alla banda ſiniſtra, non continuate con quella, ma alquanto diſtante: accio poßino <lb></lb>caminar piu preſto, ouer piutardi di quella di mezzo (occorrendo el biſogno) ſenzæ <lb></lb>interrompere l'andare, ouer el ſtare della detta battaglia di mezzo.<emph.end type="italics"></emph.end> P. </s> <s id="s.001157">E <emph type="italics"></emph>ue ho quaſt <lb></lb>inteſo, nondimeno datime uno eſſempio in figura, ma ſopra tutto in poca quantita de <lb></lb>fanti, perche molto meglio ſe apprende la coſa nelli numeri piccoli, che nelli numeri <lb></lb>grandi.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>oniamo, che tutti li noſtri fanti fuſſeno trecento, li quali uolendo li re<lb></lb>dure in quella forma di battaglia, che me adimanda uoſtra<emph.end type="italics"></emph.end> R <emph type="italics"></emph>euerentia, dico, che li diui <lb></lb>deria in tre parti equali, che in cadauna ſaria fanti cento, & l'una di queſte partiredu <lb></lb>ria in battaglia quadra di terreno (per el modo dato nel quarto Queſito) & cadauna <lb></lb>delle altre due reduria in battaglia quadra di gente (per el modo dato nel primo Que<lb></lb>ſito) & fra queste due battaglie, gli aſſettaria la prima battaglia detta di ſopra, cioe <lb></lb>quella quadra diterreno, talmente, che fuſſe alquanto diſtinta, ouer diſgionta da quel<lb></lb>le, come di ſotto appar in figura, accio che occorrendo à uoler far procedere auanti<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.100.1.jpg" xlink:href="042/01/100/1.jpg"></figure><lb></lb><emph type="italics"></emph>uno, ouer ambidue li corni, chel ſi poſſa fare ſenza diſtur bar la ordinauza dimezzo, <lb></lb>ouer amente occorrendo à uoler retir are uno, ouer ambidui di ditti corni in drio, che <lb></lb>medeſimamente el ſi poſſa fare ſenza impedimento della detta ordinanza di mezzo.<emph.end type="italics"></emph.end><lb></lb>P. C<emph type="italics"></emph>redeti che tai ſorte de corni fuſſeno quelli, che uſauano li antiqui in alcune ſue <lb></lb>battaglie.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on uiſaprei dire di certo ſe fuſſeno ſun queſta forma, ma quſtea ſor<lb></lb>te me la ho imaginata da me, perche la me par hauer in ſe tutto quello che mi ba ri<lb></lb>cercato<emph.end type="italics"></emph.end> V.R. P. B<emph type="italics"></emph>aſta che la non me diſpiace, anchor che la non fuſſe ſimile à questo <lb></lb>che uſauano li antichi.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="51" xlink:href="042/01/101.jpg"></pb> <p type="head"> <s id="s.001158">QVESITO VNDECIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001159">PRIORE. E<emph type="italics"></emph>ſſendo uno eſſercito ordinato in qual ſi uoglia forma, & che per <lb></lb>ſorte li nemici inuistideſſono dentro con le ſue artegliarie, talmente che amaz<lb></lb>zaſſeno molti de quelli fanti di tal eſſercito, ſe adimanda qual ſaria meglio che tal eſſer <lb></lb>cito caminaſſe ſecondo che lui ſe ritrouaſſe, cioe laſſando quelli lochi coſi uacui di quel <lb></lb>le perſone morte dalle artegliarie, ouer à restringerſi inſieme per impire quelli tali <lb></lb>lochiuacui.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>ll'uno modo mi par male, & all'altro peggio, perche laſſando quel <lb></lb>li lochi coſi uacui, & maßime nella fronte, ſi da facilita <expan abbr="grãdißima">grandißima</expan> alli nemici di entrar <lb></lb>nella detta ordinanza, & diromperla, & facendo poirestringere la detta ordinanza <lb></lb>per empir li detti lochi, neceſſariamente tal or dinanza ſe diſordina totalmente, & ſe <lb></lb>reduſſe quaſi in confuſione, perche eglie da credere, che le dette artegliarie, non conſu <lb></lb>mano alcuna fila de fanti integralmente da un capo all altro per longo, ma ſolamente <lb></lb>una parte di queſta, & una parte di quell'altra, & alcune reſtano illeſe, ouer non offe<lb></lb>ſe, ma intiere, & ſane, onde uolendole far reſtringere per empir li detti lochiuacui, <lb></lb>eglie neceſſario à diſconciar le file acconcie, per integrar le diſconcie, tal che tal ordi<lb></lb>nanza uerra à restar con piu numero de file de fanti (al longo)nella coda, che nella fron <lb></lb>te, la qual coſa, ſe tal ordinanza uorra caminare, eglie neceſſario che immediate uenghi <lb></lb>in confuſione, per cauſa di quelle file imperfette per longo.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>glie coſa conſonan<lb></lb>te, ma come uorresti che ſe faceſſe altramente.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o laudarei che ſe amaeſtraſſe li <lb></lb>fanti in ſimil caſo, à non reſtar maiſenza compagno auanti diſe, eccetto che nella fron <lb></lb>te, cioe auertir cadauno de loro, che ſe per caſo gli ueniſſe à manco quello fante che gli <lb></lb>camina auanti di ſe, ouer piu, che ſubito, & con gran preſtezza debbia caminare tan<lb></lb>to auanti che ritroui un'altro compagno nella conſueta distantia auanti di ſe, & ſe <21><lb></lb>caſo non ui ne ritrouaſſe alcuno auertirli, come debbiano procedere per fin alla teſta, <lb></lb>ouer fronte, et in tal luoco fermarſe, ouer caminare ſecondo che fara tal fila della teſta, <lb></lb>ouer della fronte.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>oglialtri che ſaranno nella medeſima fila de drio da quel tal <lb></lb>compagno, per longo, che uorreti che facciano.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>ßendo queſtaregola ferma che <lb></lb>ogni fante piglia la miſura del ſuo caminar pian, e forte dal ſuo compagno che gli ca<lb></lb>mina dauanti, & non da quelli che gli ſono dalle bande, e per tanto tutti quelli fanti che <lb></lb>ſe ritrouaranno in quella medeſima fila de drio da quel tal fante à che ſara mancato il <lb></lb>ſuo compagno, ouer piu compagni dauanti, ſaranno sforzati à correre, ouer camina<lb></lb>re à longhi paßiſecondo che caminara quel tal compagno, la qual coſa eßendo oßerua <lb></lb>ta da tutti, tal or dinanza, ouer battaglia ſe trouara ſempre nella fronte integra, eſana, <lb></lb>& quelli ſpaci uacui, delli ucciſi fanti, ſe traſportar anno nella coda, nel qual luoco non <lb></lb>ſaranno quaſi de alcuno pericolo.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>e gratia datime uno eßempio, & in poco nu<lb></lb>mero de fanti, per non mi confonder lo intelletto.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>oniamo per eßempio che in <lb></lb>una nostra battaglia de fanti. </s> <s id="s.001160">144. in forma quadra di <expan abbr="gẽte">gente</expan>, linemici ui habbiano mor <lb></lb>to fanti.12.come per li ſuoilochiuacuati nella ſottoſcritta figura appare, dico che ha<lb></lb>uendo auertito cadaun fante à far quanto che di ſopra habbiamo narrato, cioe che ogni <lb></lb>uolta che ui mancaße il ſuo compagno che glicamina dauanti (ouer piu) ſubito debbia <pb xlink:href="042/01/102.jpg"></pb>à longare i paßi, & con quella preſtezza che à lui ſia poßibile, non de ceſſare de cami<lb></lb>nare tanto auanti, che ritroua un'altro compagno nella conſueta diſtantia, che gli ca<lb></lb>mini auanti diſe, et ſe per caſo in quella tal fila per longo non ue ne trouaſſe alcuno, deb <lb></lb>ba procedere tanto, che peruenga alla ultima fila uerſo la fronte, cioe nella fila della<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.102.1.jpg" xlink:href="042/01/102/1.jpg"></figure><lb></lb><emph type="italics"></emph>fronte, & li affermarſe, ouer caminar ſecondo l'ordine di detta fila, & ſimilmente <lb></lb>ſi debbe auertire cadauno, che nel ſuo caminare piano, e forte, ſi debbia regge<lb></lb>re ſempre dal ſuo compagno che gli camina dauanti, & non da alcuno de quelli <lb></lb>che gli è dalle bande, la qual coſa eſſendo oſſeruata, nella ſopraſcritta figurata or<lb></lb>dinanza quella ſe tr as ferira in queſt'altra forma, che qui diſotto appar, cioe che quel-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.102.2.jpg" xlink:href="042/01/102/2.jpg"></figure><lb></lb><emph type="italics"></emph>li dodecilochi uacui ſaranno traslatati nella coda, come ſenſibilmente ſipuo uedere, nel <lb></lb>qual luoco non ſaranno quaſi de alcun pericolo, ouer diſordine.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſta uoſtra <lb></lb>opinione è bonißima, & non credo che la ſi poſſa megliorare in ſimil caſo.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="52" xlink:href="042/01/103.jpg"></pb> <p type="head"> <s id="s.001161">QVESITO DVODECIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001162">PRIORE. D<emph type="italics"></emph>itemi un poco, ſaria poßibile di potere traſmutar con preſtrez<lb></lb>za uno eſſercito in forma quadra di gente, in una forma cunea, ſenza diſordi<lb></lb>nar la prima ordinanza, & ſenza pericolo di confuſione.<emph.end type="italics"></emph.end> N. T<emph type="italics"></emph>roppo ſaria poßibi<lb></lb>le.<emph.end type="italics"></emph.end> P. </s> <s id="s.001163">E <emph type="italics"></emph>come.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>econdo che con il ſuono, ouer con uoce uoi ue fati intendere <expan abbr="quã">quam</expan> <lb></lb>do che uoleti che quelli ſi uoltano con la faccia uerſo la banda deſtra, ouer ſiniſtra, ouer <lb></lb>à ſpalle, con un diuerſo ſuono, ouer con la uoce uoglio che ſiano auertiti, & amaeſtrati <lb></lb>à ſaperſi uoltare in quel uerſo, che è fra la fronte, & il fianco deſtro, ouer il ſiniſtro, <lb></lb>& ſimilmente in quello che è fra il fianco deſtro, ouer il ſiniſtro, & le ſpalle, & dapoi <lb></lb>che ſaranno ben informati di queſta particolarita, uoglio che anchora ſiano ben auer<lb></lb>titi di quello fu detto nel precedente queſito, cioe de auertire, & amaestr are cadauno <lb></lb>fante, che ogni uolta che fuſſe fatto uoltare in alcun di ſopradetti uerſi, et che non ſi tro <lb></lb>uaſſe hauer compagno nella conſueta <expan abbr="diſtãtia">diſtantia</expan> auanti di ſe, che quel debbia con gran pre <lb></lb>ſtezza procedere, ouer caminare tanto rettamente auanti, che ritroui un compagno <lb></lb>nella conſueta diſtantia auanti di ſe, delle qual coſe eſſendo tutti ben informati, & amae <lb></lb>ſtrati, in uno batter d'occhio ſe potra eſſequire quello ricerca Voſtra Signoria, cioe uo <lb></lb>lendo traſmutare uno eſſercito che ſia in forma quadra di gente, in una forma cunea, et <lb></lb>uolendo che l'angolo deſtro della fronte reſti la ponta della detta forma cunea, dico che <lb></lb>facendo uoltar con il ſuono, ouer con uoce, tutti li fanti di tal eſſercito con la faccia in <lb></lb>quel uerſo, che è fra la fronte, & il fianco deſtro, & ſubito uoltati che ſiano, oſſeruan<lb></lb>do cadauno l'ordine detto di ſopra, cioe che tutti quelli che non ſi trouaranno hauer <lb></lb>compagno nella conſueta diſtantia auanti di ſe, procedino rettamente auanti tanto che <lb></lb>ne ritrouano uno, la qual coſa eſſequida, ſe trouara eſſer trasformata la detta forma <lb></lb>guadrata di gente in una forma cunea, & la ponta di tal figura cunea uerra à eſſer lo <lb></lb>detto angolo deſtro della fronte della prima figura.<emph.end type="italics"></emph.end> PRIORE. Q<emph type="italics"></emph>ueſta uoſtra <lb></lb>regola me par molto bellißima, e preſta, ma non la ho ben capita, e pero ui prego <lb></lb>che me dati uno eſſempio in figura, ma ſopra tutto in poco numero, perche la<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.103.1.jpg" xlink:href="042/01/103/1.jpg"></figure><pb xlink:href="042/01/104.jpg"></pb><emph type="italics"></emph>me par molto difficile da intendere.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a non è coſi difficile, come la pare, & che il <lb></lb>ſia il uero, ſia eßempi gratia fanti.25.in forma quadra digente, come diſopra appare <lb></lb>in figura, & per eßer meglio inteſo me apparſo di formar tal figura co n.25.lettere <lb></lb>del noſtro alphabeto, hor uolendo traſmutare cal figura quadrata di gente, in una fi<lb></lb>gura cunea, primamente gli faccio uoltar tutti con la faccia in quel uerſo che è fra la <lb></lb>fronte, & quel fianco doue mi pare di uoler coſtituire la ponta del cuneo, eßempi gra<lb></lb>tia uolendo che la ponta di tal figura cunea ſia l'angolo.e.faro che tutti ſi uoltano con<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.104.1.jpg" xlink:href="042/01/104/1.jpg"></figure><lb></lb><emph type="italics"></emph>la faccia per quel uerſo che è fra la fronte, & il fianco deſtro, cioe uerſo l'angolo.e.la <lb></lb>qual coſa eßequida tal figura uerra à ſtare, come quiſotto appare, nella qual figura il ſi <lb></lb>uede che ui ſono molti fanti che non hanno compagno nella conſueta diſtantia auanti di <lb></lb>ſe, uero che hanno ben compagno rettamente auanti di ſe, ma molto piu lontano del ſo<lb></lb>lito, cioe il doppio del ſolito, come appare al.f.il qual harettamente auanti di ſe il.b. <lb></lb></s> <s id="s.001164">ma la diſtantia che è dal detto.f.al detto.b.è il doppio della diſtantia conſueta, onde ſel <lb></lb>.f.uorra oßeruare li precetti di ſopra adutti, ſubito che hauera uoltato la faccia uerſo <lb></lb>tal uerſo immediate ſe andara ad approßimarſe al detto.b.nella conſueta diſtantia, il<lb></lb>che facendo ſe cacciara fra.a.et.g.uero è, che il detto.g.non reſtara nel ſuo luoco pre <lb></lb>ſente, ma ſe trasferira appreßo al.c.in distantia conſueta, & nel luoco doue prima era <lb></lb>il.g.ui conueneria uenir.l.tal chel.f.ſe trouara fra.a.&.l.& coſi ſe tutti glialtri pro <lb></lb>cederanno auanti ſecondo il detto ordine, cioe per fina che trouano compagno in <expan abbr="diſtã">diſtam</expan> <lb></lb>tia conſueta auanti di ſe la.h.ſe andara ad approßimarſe al.d.& lo.m.ſeguitara la det <lb></lb>ta.h.& il.q.ſeguitara drio al detto.m.tutti per fina alla conſueta diſtantia, & coſilo.i. <lb></lb></s> <s id="s.001165">ſeapproßimara al.e.& lo.n.ſeguitara lo.i.& lo.r.ſeguitara lo.n.& lo.x.ſeguitara il <lb></lb>detto.r.tutti per fin alla conſueta diſtantia ſimilmente lo.o.ſe approßimara al.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>& lo. <lb></lb></s> <s id="s.001166">ſ.ſeguitara lo.o.&.y.ſeguitara.ſ.pur per fin à diſtantia conſueta, & coſi.t.ſe approßi<lb></lb>mara al.p.&.z.ſeguitara.t.pur per fin alla conſueta diſtantia, & ſimilmente, & ſe ap<lb></lb>proßimata al.u.pur nella detta conſueta diſtantia, la qual coſa oßeruata tal ordinan<lb></lb>za quadra di gente ſe ſara traſmutata in una ordinanza cunea, come di ſotto appare in <lb></lb>figura, & la ponta di tal figurauerra à eßer l'angolo.e.& con tal ordine ſe procede<lb></lb>riaſe tal eßercito fuße ben de.100000.fanti, pur che li detti fanti ſiano ben auertiti, <lb></lb>& amaeſtrati di quanto diſopra èſtato detto, ſi del ſaperſi uoltar, come del caminare.<emph.end type="italics"></emph.end><lb></lb>P. Q<emph type="italics"></emph>ueſta è una bella inuentione, & dimolta importantia, perche reducendo coſi al-<emph.end type="italics"></emph.end><pb pagenum="53" xlink:href="042/01/105.jpg"></pb><emph type="italics"></emph>Pimprouiſo uno eßereito in forma cunea, eglie quaſi impoßibile che linemici poßano, <lb></lb>oueſappiano formar la forfice da opponerui, talmente cheſe ueniria ad hauer gran-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.105.1.jpg" xlink:href="042/01/105/1.jpg"></figure><lb></lb><emph type="italics"></emph>de auantaggio, come ſe uerifico diſopra nel ſettimo Queſito, perche à mi me pare che <lb></lb>una battaglia cunea ſia ſempre atta e ſofficiente à rompere ogni altra battaglia in <lb></lb>forma quadra di terreno, come che al preſente ſi costuma, anchor che quella fuſſe di <expan abbr="gẽ">gem</expan> <lb></lb>te, ouer de fanti un tanto e mezzo de piu, domente, che quelli della forma cunea ſiano <lb></lb>ben istrutti del modo del ferire (detto nel ſettimo Queſito.)<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001167">QVESITO DECIMOTERZO FATTO DAL MEDESIMO <lb></lb><emph type="italics"></emph>Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001168">PRIORE. I<emph type="italics"></emph>o ho penſato aſſai queſta notte ſopra à quella traſmutatione de <lb></lb>hierſera, & à tutte quelle altre uarieta di forme, di che hauemo fin à queſta ho<lb></lb>ra parlato, & certamente el non ſi puo negare, che le non ſiano coſe molto ingenioſe, <lb></lb>& atte à dare alle uolte honor atamente una uittoria, anchor che li nimici fuſſeno un <expan abbr="tã">tam</expan> <lb></lb>to e mezzo piu di noſtri, come dißi anchor hierſera, nondimeno non ſono di tanta au<lb></lb>torita, quanto che à questitempi biſognaria, perche contra à una <expan abbr="potẽtia">potentia</expan>, come è quel <lb></lb>la del Turco, comprendo, che alcuna de loro non ſaria ſofficiente a darli noia, la cauſa <lb></lb>è che quello è ſempre atto a fare, & fa continuamente (come ſapeti) uno eſſercito di <lb></lb>tre, & quattro tanta moltitudine de fanti de noi Christiani, delli caualli poi non ne par <lb></lb>lo, che ſempre ne ha una infinita, da non comparare alli noſtri.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>pero uolendo eſſere <lb></lb>ſicuri di poterſi opporre ſitur amente a quello in campagna, el biſognaria inueſtigare <lb></lb>qualche altro artificioſo modo di ordinare uno eſſercito de fantaria, che fuſſe at<lb></lb>to, & ſicuro di poter reſistcre in una nuda campagna a uno altro eſſercito almen ditre <lb></lb>tanta moltitudine ac, anti, & che anchora el fuſſe ſicuro di non poter eſſer turbato,<emph.end type="italics"></emph.end><pb xlink:href="042/01/106.jpg"></pb><emph type="italics"></emph>ne offeſo da alcuna moltitudine de caualli, & circa cio ui ho ſtudiato molti giorni, & <lb></lb>meſt, ma finalmente per certe ragioni ho compreſo non eſſer poßibile, perche una coſa <lb></lb>ſola mi guaſta ogni diſegno.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie il uero, che tal coſa non é molto facile, nondime <lb></lb>no el non è da concludere coſi abſolutamente, che la ſia impoßibile, perche ſecondo, che <lb></lb>lo ingegno de l'huomo ha ritrouato (con ragion & arte) che uno ſolhuomo leui, ouer <lb></lb>conduca tal peſo, che quattro, e piu huomini natur almente per ſe non ſariano atti ad <lb></lb>alleuarlo, ouer condurlo, coſi anchora eglie da penſare, che con ragion, & arte ſia poſ <lb></lb>ſibile di ritrouare tal modo, eforma di ordinare uno eſſercito che ſia atto, & ſicuro à <lb></lb>ſuperare, & rompere ogni altro eſſercito, quantunque el fuſſe di tre, & anchor de <lb></lb>quattro tanta moltitudine di genſè di piu, & in qualſi uoglia forma.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>l potria eſ <lb></lb>ſer queſto, che uoi diceti, quando che el non uiſe interponeſſe artegliarie, archibuſi, et <lb></lb>archi, perche in uero doue è maggior eſſercito à queſti tempi, eglie da giudicare, che <lb></lb>iuiſia anchor maggior numero de tai bellici iſtrumenti, per la autorita de guali, & <expan abbr="nõ">non</expan> <lb></lb>per altro el detto Turco riportò honor at a uittoria contra el Sophi, al qual Sophi non <lb></lb>li giouò hauer uno eſſercito tutto de huomini generoſi, & honoratamente armati, & <lb></lb>con mir abel ordine ordinati, perche, come cominciorno ad eſſer ſalutati dalle arte<lb></lb>gliarie, archibuſi, & archi Turcheſchi ogniſuo ordine diuento uano. </s> <s id="s.001169">Et me arricor<lb></lb>do quando, chel Turco uenne all'impreſa de Rhodi, che io uolſi andare con una bona <lb></lb>banda de ottimi fanti, ad aſſaltare una grande moltitudine de Turchi, che erano uenu<lb></lb>ti in un certo luoco non molto lontano dalla terra:maſcoperti, che nui fuſſemo à quelſi <lb></lb>ſu <expan abbr="tãta">tanta</expan> la moltitudine delle frizze, che ne incominciorno à piouere ſoprala testa, che <lb></lb>fuſſemo sforzati immediate à ritornar nella terra, uero è, ohe erano piu di tre tanti de <lb></lb>noi, & nondimeno ſe la tanta moltitudine delle ſue frizze non fuſſe ſtata, & che ſe fuſ <lb></lb>ſemo potesti approßimar à quelli con le noſtre picche, & ſpade, ſenza dubbio li ha<lb></lb>uereßimo ſbaratati, & maßime, che non haueuano artegliaria con loro, per eſſer gen <lb></lb>teche andaſeuano robando, & depredando per l'iſola: ſi che uoglio inferire, che ſe tai <lb></lb>machine non fuſſe, credo chel ſe potria ritrouare de or dinare uno eſſercito con tal ar<lb></lb>tificioſo modo, che fuſſe atto a rompere un'altro eſſercito molto maggior di lui, come <lb></lb>fudetto ſopra al cuneo, ma quando, che la parte contraria habbia gran coppia de arte <lb></lb>gliarie, archibuſi, & archí, non credo che la natura, ne l'arte ui poteſſe fare equiualen <lb></lb>te riparo, ſaluo, che con altre tante, ouer con maggior quantita di quelle, perche à tai <lb></lb>machine, & maßime alle artegliarie, non ui ſi puo trouar ingegno, che ui duri, ne me<lb></lb>dicina, che ui uaglia, & ſe queſte tai machine fuſſeno ſtate al tempo antiquo, li elephan <lb></lb>ti haueriano perſala ſcrimia, & li carri falcati ui ſariano ſtati di poco giouemento, <lb></lb>ouer profitto.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie da tener per fermo, che la natura mai creaſſe, ne crea alcun <lb></lb>ſi crudo ueleno, che anchor immediate non creaſſe, ouar crei la ſua propria medecina, <lb></lb>quantunque coſi immediate la non ſia conoſciuta dalli huomini, ſimelmente dico, che <lb></lb>l'arte mai ritrouo; ne puo ritrouare coſa coſi noceuole all'huomo, che quella non ſia an <lb></lb>chor atta à ritrouarui immediate ilſuo conueniente rimedio, anchor che la ignorantia <lb></lb>delli huomini non lo ſappia alle uolte coſi all'improuiſo immaginare, ouer ritrouare.<emph.end type="italics"></emph.end><lb></lb>P. I<emph type="italics"></emph>o non credero mai, che l'arte ſia atta à poter ouiare, che le artegliarie non ſiano <lb></lb>ſempre atte à dannificare ogni eſſercito ordinato in campagnaſecondo el ſolito, & ſia<emph.end type="italics"></emph.end><pb pagenum="54" xlink:href="042/01/107.jpg"></pb><emph type="italics"></emph>pur tal eſſercito ordinato in forma quadrata, cunea; ouer come ſi uoglia, ſaluo che non <lb></lb>circondaſſe tal eſſercito de großißime mura, ouer baſtioni, come ſi coſtuma alli preſen <lb></lb>ti tempi nelli alloggiamenti, ma uolendo poi uenir alla frontera, eglie forza uſcir de <lb></lb>quelli, ſi che nel atto del combattere, io non credo, ne reputo, che ue ſia alcun meglior ri <lb></lb>medio a uoler uinzere, & ſuperchiar el nemico, che hauere gente, artegliarie, archibu<lb></lb>ſi, & archi piu di lui, & perſone pratiche, & eſſercitate nella guerra.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto, <lb></lb>che conclude uoſtra Signoria, ſe intende natur almente coſi douer ſeguire, cioe non ui <lb></lb>ſe interponendo alcuna artificialita, perche eglie coſa naturale, che el numero maggio <lb></lb>re in ogni attione ſuperi el menore, cioe che lo eſſercito maggiore ſuperi el menore, et <lb></lb>che el maggior numero de artegliarie, archibuſi, & archi, ſiano de molta maggior fac <lb></lb>cione, che non ſara el menore: ma nelle coſe fatte, & ordinate con arte non ſeguita ſeni <lb></lb>pre queſto, perche l'arte tende ſempre a l'uno de queſti dui fini, oueramente ad emitar <lb></lb>la natura ad ogni ſuo potere, oueramente a ſupplire alli diffetti di eſſanatura, cioe a fa <lb></lb>re quelle coſe, che la natura non puo fare, ouer che natur almente non ſi poſſono eſſe<lb></lb>quire (coſa certamente magnanima, & generoſa)e pero non è da concludere, ne da di <lb></lb>re, che con arte non ſia poßibile a ſuperare quelle coſe, che per natura ſiamo uenti.<emph.end type="italics"></emph.end><lb></lb>P. D<emph type="italics"></emph>apoi che haueti queſta tal openione, che uia ui pare, che ſi potria tenere, ouer <expan abbr="cõ">com</expan> <lb></lb>che mezzo credeti, che tal coſa poteſſe fare.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>irca cio biſognaria penſarui <expan abbr="alquã">alquam</expan> <lb></lb>to.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>enſatigli un poco (dico con ſumma diligentia) perche eglie una coſa molto <lb></lb>importantißima, & neceſſaria a questi tempi, & in cio conoſcero quanto ualeti, per<lb></lb>che nelle infirmita, che ſono giudicate incurabile, ſi conoſce la ſufficienza del medico.<emph.end type="italics"></emph.end><lb></lb>N. I<emph type="italics"></emph>o certamente ui penſaro, ma molto piu con diligentia, quando preſentiro approſ <lb></lb>ſimarſi el biſogno.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001170">I<emph type="italics"></emph>l fine del quarto libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/108.jpg"></pb> <p type="head"> <s id="s.001171">LIBRO QVINTO DELLI <lb></lb>QVESITI, ET INVENTIONI DIVERSE, <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.001172"><emph type="italics"></emph>Sopra el mettere, ouer tuore rettamente in diſegno con el boſſolo, li ſiti, <lb></lb>paeſi, & ſimelmente le piante delle citta, con el modo de ſa<lb></lb>pere fabricare el detto boſſolo, & in diuerſi <lb></lb>modi, la cui ſcientia da Ptolomeo è <lb></lb>detta Chorografia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001173">QVESITO PRIMO FATTO DAL MIO HONO<lb></lb><emph type="italics"></emph>rando Compare.<emph.end type="italics"></emph.end> M. R<emph type="italics"></emph>ichardo Ventuorth, gentil'huomo <lb></lb>della Maeſtà del Re d'inghilterra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001174">RICHARDO. C<emph type="italics"></emph>ompare carißimo haria molto accaro, che me <lb></lb>dichiaraſti, come ſe poteria mettere in diſegno rettamente un ſito<lb></lb>ouer un particolar paeſe, & ſimelmente la pianta di una citta, la <lb></lb>cui pratica da Ptolomeo, come ſapeti nella ſua Geographia, è det<lb></lb>ta Chorographia.<emph.end type="italics"></emph.end> N. T<emph type="italics"></emph>al coſa ſi puo ſare con un boſſolo artifi<lb></lb>cialmente fatto con la ſua calamita, che ſia giuſto.<emph.end type="italics"></emph.end> R. V<emph type="italics"></emph>i prego <lb></lb>me dicati in che forma uol eſſer fatto queſto boſſolo.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a for <lb></lb>ma di tal boſſolo ſi puo far in dui modi.<emph.end type="italics"></emph.end> L'<emph type="italics"></emph>uno, qual è il piu communo, ſi é à farlo con <lb></lb>una dioptra, ouer traſguar do mobile, cioe, che ſi puol girare à torno per poter traſ<lb></lb>guardare in ogni uerſo ſecondo che occorre il biſogno.<emph.end type="italics"></emph.end> L'<emph type="italics"></emph>altro ſi fa da poterſeneſer<lb></lb>uireſenza quella tal dioptra, ouer traſguardo mobile, il che è molto accommodo, e di <lb></lb>menor artificio, ma ben ui oceorre un boſſolo con una lancetta molto longa.<emph.end type="italics"></emph.end> R. M<emph type="italics"></emph>o <lb></lb>stratime pur per al preſente ſolamente quella forma, che é piu in uſo, cioe quella che <lb></lb>piu ſi coſtuma. </s> <s id="s.001175">perche quando ſaro in Inghilterra me ne ſappia far far uno.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a <lb></lb>piu frequentata ſi fa in queſto modo. </s> <s id="s.001176">Primaſe fa far un tondo di lama di rame, ouer di <lb></lb>ottone groſſa una coſta di cortello uel circa el diametro, del qual tondo non uoria eſſer <lb></lb>men de unaſpanna, perche quanto piu tal iſtrumento è maggiore, tanto piu eglie men <lb></lb>fallace, uero è, che eglie poi piu diſcommodo da portarſe drio, & per questa cauſamol <lb></lb>ti lo coſtumano piu piccolo aſſai per eſſer piu commodo, & queſto tal tondo di lama <lb></lb>ſe fa ſpianar bemßimo alla mola, & dapoi, che é ben ſpianato ſopra el centro del mede <lb></lb>ſimo tondo ui ſi deſcriue prima un cerchio piu ſcarſo una coſta di corteilo del tondo di <lb></lb>detta lama et anchora un'altro piu piccolo di queſto <36> due bone coſte di cortello, et tut <lb></lb>ta la <expan abbr="circõferẽtia">circonferentia</expan> del primo cerchio, primaſe diuide <expan abbr="cõſumma">conſumma</expan> <expan abbr="diligẽtia">diligentia</expan> in quatro par <lb></lb>ti equali, et à una di queſte diuiſione ui ſeſcriue <expan abbr="Leuãte">Leuante</expan>, et all'altra à queſta oppoſicaui <lb></lb>ſe ſcriue <expan abbr="Ponẽte">Ponente</expan>, & à quella diuiſione, che é fra queste due uerſo <expan abbr="Tramõtana">Tramontana</expan>, uiſeſcri <lb></lb>ue Tramontana, & à quella che è uerſo Oſtro, ui ſeſcriue Ostro, & coſi la <expan abbr="circõferen-tia">circonferen<lb></lb>tia</expan> del detto primo cerchio uenira a eſſer diuiſa in le dette quattro parti equali, delle <lb></lb>quali una uenira à eſſer fra <expan abbr="Leuãte">Leuante</expan>, et <expan abbr="Tramõtana">Tramontana</expan>, et una fra <expan abbr="Tramõtana">Tramontana</expan>, & <expan abbr="Ponẽte">Ponente</expan>,<emph.end type="italics"></emph.end><pb pagenum="55" xlink:href="042/01/109.jpg"></pb><emph type="italics"></emph>& una fra Ponente, & Oſtro, & una fra Oſtro, & Leuante. </s> <s id="s.001177">Anchora cadauna di que <lb></lb>ſte quattro parti ſe diuide pur in due parti eguali, & quella diuiſione che fra Leuan<lb></lb>te, & Tramontana, ui ſeſcriue Grego, & à quella che è fra Tramontana, e Ponente, <lb></lb>ui ſe ſcriue Maiſtro, & à quella che é fra Ponente, & Ostro, ui ſe ſcriue Gar<lb></lb>bino. </s> <s id="s.001178">Et à quella, che è fra Oſtro, e Leuante, ui ſe ſcriue Sirocco, & coſi la cir<lb></lb>conferentia di tal primo cerchio uenira à eſſer diuiſa in otto parti eguali, & cadaun<lb></lb>di quelle diuiſioni ſe chiama uento, e pero tal circonferentia ſera diuiſa in otto uenti, <lb></lb>& cadauno de quelli ſi chiama, come di ſopra è ſtato detto, nondimeno per abbreuia<lb></lb>ſcrittura in luoco di Leuante, ui ſe ſcriue un.<emph.end type="italics"></emph.end> L.<emph type="italics"></emph>et in luoco di Ponente, ui ſe ſcriue un.<emph.end type="italics"></emph.end> P. <lb></lb><emph type="italics"></emph>& in luoco di Tramontana, ui ſe ſcriue un.<emph.end type="italics"></emph.end> T.<emph type="italics"></emph>& in luoco di Oſtro, ui ſe ſcriue un.<emph.end type="italics"></emph.end> O. <lb></lb><emph type="italics"></emph>& in luoco di Grego, uiſe ſcriue un.<emph.end type="italics"></emph.end> G.<emph type="italics"></emph>& in luoco di Garbino, uiſe ſcriue un'altro.<emph.end type="italics"></emph.end> G. <lb></lb><emph type="italics"></emph>& in luoco di Maiſtro, ui ſe ſcriue un.<emph.end type="italics"></emph.end> M.<emph type="italics"></emph>& in luoco de Sirocco, ui ſe ſcriue un.<emph.end type="italics"></emph.end> S.<emph type="italics"></emph>co<lb></lb>me di ſotto nella figura appare. </s> <s id="s.001179">Anchora ſe diuide cadauna di quelle ottaue parti di det <lb></lb>ta circonſerentia, primamente in tre partieguali, & cadauna di quelle terze parti ſe <lb></lb>diuide anchora in altre tre partieguali, & cadauna di queste ultime parti (eſſendo lo <lb></lb>detto tondo di lamma, di competente grandezza) ſi debbono ultimamente diuidere in <lb></lb>tinque parti eguali, il che facendo ſe trouara tutta la circonferentia del detto primo ce<gap></gap><lb></lb>chio eſſer diuiſa in.360.parti eguali (ſecondo l'ordine, & diuiſione delli antichi cho<lb></lb><gap></gap>ographi) & cadauna di queſte tal partiſe chiama grado, & accio che tai diuiſioni, ſia <lb></lb>no apparente ſe ſegnano cadauna con una linceta long a una meggia coſta di cortello, et <lb></lb>queſte tai lineete (accio che tutte tendano al centro di tal cerchio) ſe deſcriuono con <lb></lb>unaregagiuſtando talrega con il centro di tal cerchio, & con il ponto di quella diuiſio <lb></lb>ne che ſi uol ſignare nella detta circonferentia, & accio che tai diuiſioni ſi poſſano con <lb></lb>facilita numer are (occorrendo il biſogno) à ogni cinque de tai diuiſioni piccole ui ſe ſa <lb></lb>una diuiſiont che trauerſi tutto quel ſpacio che è fra la circonferentia del detto primo <lb></lb>cerchio, & la circonferentia del ſecondo. </s> <s id="s.001180">Ma ſe per caſo il ſopradetto tondo di lamma, <lb></lb>fuſſe talmente piccolo, che quelle ultime terze partinon fuſſeno atte, per la ſua picco<lb></lb>lezza, à eſſer diuiſe nelle ſopradette cinque parti eguali, ſe laſſariano ſtar coſi, per il<lb></lb>che la circonferentia del detto primo cerchio ueneria à eſſer diuiſa ſolamente in.72. <lb></lb>partieguali, onde facendo tai.72.parti, apparente con il tirarui quella lineeta per fi<lb></lb>na alla circonſerentia del menor cerchio ſecondo l'ordine detto diſopra, cioe che tutte <lb></lb>le dette lineete <expan abbr="tendanõ">tendanon</expan> al centro delli detti cerchij, ſi come appare nella figura ſotto<lb></lb>ſcritta, ma biſognanotare che ſi ben la circonferentia di tallamma, per la ſua piccoleæ <lb></lb>za, ſara diuiſaſolamente nelle ſopradette.72.partieguali, come nella detta ſottoſcrita <lb></lb>figura appare, nondimeno tutta la detta circonferentia con lo intelletto ſe debbe inten<lb></lb>dere eſſer diuiſa pur nelle dette.360.partieguali, cioe in.360.gradi, & pero nel com<lb></lb>putar le ſottoſcritte.72.diuiſioni, per cadauna di quelle, ui ſe computa cinque gradi, <lb></lb>perche.5.fia.72.uien à fare li detti.360.gradi, & dapoi che ſe haueran fatte tutte <lb></lb>queſte coſe, ouer diuiſioni, ui ſe debbe far aſſaldare una armilla della medeſima ſorte di <lb></lb>banda di ottone, ouer di rame à torno al centro, cioe uno cerchio della detta banda lar<lb></lb>ga almen dul dedi, qual uenghi affare à modo di una ſcatolina à torno al detto centro <lb></lb>della detta prima lamma circolare, talmente che ſia concentrica con quella, & nel cen-<pb xlink:href="042/01/110.jpg"></pb>tro poiui ſe de far aſſettar una ponta alta circa per la mita della detta ſcatolina, e que<lb></lb>ſta ponta è per metterui ſuſo la lanzetta acconcia con la calamita, alla ſimilitudine di <lb></lb>quelle, che hanno quelli horologietti, che uengono de Alamagna, ma alquanto piu gran<lb></lb>da, & nel fondo di questa ſcatola ui ſe de ſegnar una linea quaſi alla ſimilitudine della <lb></lb>lanzetta che uada da. </s> <s id="s.001181"><expan abbr="Tramõtana">Tramontana</expan> uerſo Oſtro rettamente, accio che ſi poſſa conoſcere <lb></lb>quando che il boſſolo ſia ben aſſettato (perche il <lb></lb>boſſolo ſe intende eſſer ben aſſettato, quando che <lb></lb>la ponta della dettalanzetta guarda rettamente <lb></lb>uerſo la Tramontana (ſi come nella figura appa<lb></lb>re) la qual coſa facilmente ſi conoſce per meggio <lb></lb>della detta linea, cioe come ſe fa preciſo con li ſo<lb></lb>pradetti horologietti quando ſe uol ſaper quan<lb></lb>te hore ſono, & fatto queſto uiſe de poner la det <lb></lb>ta lanzetta acconcia (come è detto) con la cala<lb></lb>mita, & dapoi ſi fa un coperchio alla detta ſca<lb></lb>tolina de uitrio chiaro, come ſe coſtuma alli boſ-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.110.1.jpg" xlink:href="042/01/110/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſoli da nauicare, accio ſi poſſa uedere il ſtar, & l'andar della detta lanzetta, & dopo <lb></lb>queſto uiſe de metter una dioptra, ouer traſguardo, la qual dioptra, ouer traſguardo <lb></lb>ſolea coſtumarſi alla ſimilitudine della prima figura.a.b.con quelli dui bracci.c.d.&.e. <lb></lb></s> <s id="s.001182">ſ.il qual modo <21> mettere in diſſegno un paeſe era <expan abbr="ſofficiẽte">ſofficiente</expan> aſſai, ma <21> mettere in diſſe <lb></lb>gno la <expan abbr="piãta">pianta</expan> de una citta era <expan abbr="alquãto">alquanto</expan> <expan abbr="diſcõmodo">diſcommodo</expan>, onde <21> farlo piu <expan abbr="accõmodo">accommodo</expan>, & genera <lb></lb>le ui ſe coſtuma à ponerui un'altro traſuerſo in croce, <21> <expan abbr="fettamẽte">fettamente</expan> ſquadra <expan abbr="eßẽpi">eßempi</expan> gratia <lb></lb>à quella armilla uacua.a.b.ui ſe aſſalda prima nelli dui bracci.c.d.et.e.f.della principal <lb></lb>dioptra, ouer traſguardo, con quelle due lamette in alto elleuate nelle istremita di quel<lb></lb>la, con uno buſettino in cadauna da traſguardare, per quelli le coſe che accadera, à ben <lb></lb>che anchor due pontine acute ſeruiriano, ſi come quelli dui buſettini, & forſi meglio, <lb></lb>& dapoi ui ſe ſalda anchora quelli altri dui brazzetti.g.h.&.i.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>per fettamente in cro <lb></lb>ce, cio perfettamente à ſquara ſopra la principal dioptra, & nel capo dell'un de questi <lb></lb>ſecondi bracciui ſi aſſetta, ouer ſalda quell'altro brazzetto.l.m.pur à ſquadra, come <lb></lb>nella ſeconda figur a appare, & la forma di quala ſi uoglia delle due ſottoſcritte ſorte <lb></lb>de dioptreuol eſſere totalmente fabricata che la detta armilla.a.b.ſia de tal grandez-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.110.2.jpg" xlink:href="042/01/110/2.jpg"></figure><pb pagenum="56" xlink:href="042/01/111.jpg"></pb><emph type="italics"></emph>za che ui poſſa entrare ſazzatamente quell'altra armilla, ouer ſcatolina del ſopra<lb></lb>ſcritto noſtro <expan abbr="istromẽto">istromento</expan>, et che quelli dui, ouer quattro bracci, cioe.c.d.e.f.g.b.&.i.<emph.end type="italics"></emph.end>k. <lb></lb><emph type="italics"></emph>ſiano talmente fabricati che dall'una, & l'altra banda dimoſtrino giustamente li gradi <lb></lb>ſepra la prima lamma circolare gia ſignati, & li dui principali, cioe.c.d.&.e.f.uoleno <lb></lb>eſſer di tanta longhezza che dall'una, & l'altra banda ufciſcano alquanto fuora del <lb></lb>cerchio della noſtra prima lamma circolare, & nella istremita dell'uno, & l'altro de <lb></lb>queſti dui bracci ui ſe ſalda le ſopradette due lamette, ouer figure quadrangole in alte <lb></lb>elleuate di tal altezza che ſopra auanzano la altezza della ſcatolina del noſtro boſſo<lb></lb>lo, & talmente larghe, che facendoli uno buſettino in meggio di cadauna di quelle, cioe <lb></lb>in quella parte che ſoperchia di ſopra del detto boſſolo, uno rettamente oppoſito all al <lb></lb>tro, talmente che traſguardando per li detti dui buſettini la noſtra linea uiſuale tranſi<lb></lb>ſca preciſamente ſopra al centro del cerchio del detto noſtro iſtromento, & dapoi tal <lb></lb>dioptra ſi debbe con diligentia incaſſare ſopra al detto noſtro boſſolo, cioe ſopra à quel <lb></lb>la armilla, ouer ſcatolina, che interchiude il detto boſſolo, ilche facendo il detto noſtro <lb></lb>iſtromento ſtara preciſamente, come di ſotto appare in figura, & la dioptra, ouer traſ <lb></lb>guardo, ſara girabile, cioe che la ſe potragir are per ogniuerſo à torno à torno, et per <lb></lb>quelli dui buſettini, che ſar anno in quelle due lamette quadrangole in alto elleuate, ſe po<lb></lb>tratraſguardar con un'occhio li ſegni, & termini, che ſi uorra uedere, come per l'aue<lb></lb>nire per eſſempio ſe moſtrara, uero è, che in luoco de quelli dui buſettini à me mi pia-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.111.1.jpg" xlink:href="042/01/111/1.jpg"></figure><lb></lb><emph type="italics"></emph>ce, & me pare anchora piu ſpediente due pontine acute, come diſopra dißi.<emph.end type="italics"></emph.end> R. Q<emph type="italics"></emph>ue<lb></lb>ſta forma de iſtromento molto mi piace, dimane parlaremo poi del modo di operarlo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001183">QVESITO SECONDO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> M.R<emph type="italics"></emph>ichardo Ventuorth.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001184">RICHARDO. H<emph type="italics"></emph>or uorria Compare che ſotto breuita me dichiar asti il <lb></lb>modo <lb></lb>di operare l'iſtromento, che hieri me inſignaſti à fare.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er uoler operar <lb></lb>tal iſtromento à uoler mettere in diſſegno qualche ſito, ouer paeſe, biſogna hauere un <lb></lb>baſtone longo, circa piedi tre, & che tal baſione in un di capi habbia un ferro ap<lb></lb>pontito, per poter lo piantare in terra, & dall'altro capo un tondo di legno alla gran<lb></lb>dezza dello iſtromento con un poco di orlo, che ſia atto à tener tale iſtromento <pb xlink:href="042/01/112.jpg"></pb>incaſſato, & fermo in cima de quel tal bastone, come diſotto appare in figura, & che <lb></lb>cal orlo ſia tanto baſſo che il non impediſca il poter girar la dioptra in ogni uerſo.<emph.end type="italics"></emph.end> R. <lb></lb>N<emph type="italics"></emph>on ſe potria far ſaldar un canon di banda buſo ſotto à tal iſtromento per ſicar dentro <lb></lb>tal baſtone, ouer una ponta da poterlo piantar in cima di tal baſtone, facendo prima un <lb></lb>buſo nella cima di tal bastone.<emph.end type="italics"></emph.end> N. L'<emph type="italics"></emph>uno è l'altro de queſti, daria impedimento per <lb></lb>mettere tal diſſegno in carta, come alli ſuoiluochi ſi potra giudicare.<emph.end type="italics"></emph.end> R. S<emph type="italics"></emph>eguitati.<emph.end type="italics"></emph.end><lb></lb>N. I<emph type="italics"></emph>nteſo adunque tutte queſte coſe biſogna notare, che per mettere in diſſegno un ſi<lb></lb>to, ouer un paeſe, ſi puo procedere in dui modi, l'uno è <lb></lb>à ſtare in meggio, cioe dentro dal detto ſito, ouer pae<lb></lb>ſe con il detto iſtromento piantato, fermo è ſtabile, & <lb></lb>l'altro é à andare à torno, à torno per la circonferen<lb></lb>tia di tal ſito, ouer paeſe.<emph.end type="italics"></emph.end> R. Q<emph type="italics"></emph>ual è meglio de queſti <lb></lb>dui modi.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>ertamente piu giusto, ouer men fal<lb></lb>lace riuſcira tal diſſegno à ſtare fermo è fiſſo nel meg<lb></lb>gio, cioe dentro di tal ſito, ouer luoco, perche in ogni <lb></lb>traſmutatione che ſi fa del detto buſſolo nel traſpor<lb></lb>tario da un luoco in un'altro ſempre ſe incorre in qual<lb></lb>che poco di errore, & perche à tuor in diſſegno un luo <lb></lb>co, ouer ſito andando per la circonferentia di quello ſe <lb></lb>famolte traſmutationi, del detto boſſolo, come per lo<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.112.1.jpg" xlink:href="042/01/112/1.jpg"></figure><lb></lb><emph type="italics"></emph>auenire ſe potrauedere, e pero delli molti pochi errori ſe ne uiene à cauſare poila mag <lb></lb>gior parte delle uolte, in fine uno maggiore.<emph.end type="italics"></emph.end> R. M<emph type="italics"></emph>oſtratime adunque quello che de <lb></lb>ſtar dentro in meggio, perche l'altro eſſendo coſi fallace non me ne curo.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci é <lb></lb>neceſſario, che uoi intendiati l'uno è l'altro modo perche non ſempre ſi puo tuor in diſ<lb></lb>ſegno un ſito, ouer paeſe à star dentro nel detto ſito, perche ſpeſſe uolte ui ſe troua del <lb></lb>li arbori, monticelli, caſamenti, & altre coſe, che impediſcono il poter uedere tutti li <lb></lb>termini di tal ſito, alcuna fiata per la grandezza ſua non ſi potra eſſequire tal effetto à <lb></lb>star coſi fermo nel meggio anchor che non ui fuſſe arbori, ne altri impedimenti, come <lb></lb>che uoleſſe mettere in diſſegno uno grandißimo paeſe, che per la ſua grandezza in al<lb></lb>cun luoco dentro di quello non ſi poteſſe uedere tutti li ſuoitermini, e pero quantunque <lb></lb>il modo di quelluor in diſſegno à ſtar dentro di tal ſito, ouer luoco ſia piu giuſto, ouer <lb></lb>men fallace dell'altro, nondimeno l'altro è poi piu generale, perche con quello ſe puo <lb></lb>operare, ſi nelli paeſi grandi, come nelli piccoli, o con arbori, monti, & caſamenti, co<lb></lb>me eſſendo piani, & con questo tale ſi puol tuor in diſſegno, non ſolamente le piante del <lb></lb>le citta, ma anchora tutto il territorio di quelle, et ſimilmente Iſole, prouincie, & altre <lb></lb>coſe ſimile.<emph.end type="italics"></emph.end> R. A<emph type="italics"></emph>dunque me li dichiarereti ambi dui. </s> <s id="s.001185">tamen cominciatemi prima à di <lb></lb>chiarire quel primo modo, cioe à ſtar dentro nel meggio di tal ſito, ouer paeſe, & da<lb></lb>poi me dichiarereti l'altro.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>ccio che meglio me intendiati, ſupponeremo che il <lb></lb>ſia uno paeſetto de cinque fazze, ouer lati, alla ſimilitudine della ſottoſcritta figura. <lb></lb></s> <s id="s.001186">a.b.c.d.e.& che ſia di tal qualita, che ſtando dentro in meggio, ouer circa al meggio di <lb></lb>quella, & che facendo poi piantar una bacchetta in cadauno di quelli cinque angoli, <lb></lb>ouer cantoni che tai bacchette ſi poſſano uedere à una per una, hor dico, che à uoler<emph.end type="italics"></emph.end><pb pagenum="57" xlink:href="042/01/113.jpg"></pb><emph type="italics"></emph>metter rottamente in diſegnoſopra à uno foglio di carta un'altra figura ſimile alla <lb></lb>propoſia.a.b.c.d.e.el ſi debbe far piantare una bacchettina per ciaſcaduno delli detti <lb></lb>cinque angoli, ouer <expan abbr="cãtoni">cantoni</expan>.a.b.c.d.e.& dapoiel ſi debbe intrare nel detto ſito, ouer lo <lb></lb>co, & andare nel mezzo di quello, ouer cir ca al mezzo (perche piue manco del mez<lb></lb>zo non importa, & iui piantarui quel baſtone con el detto noſtro boſſolo in cima, et da <lb></lb>poi che ſara piantato biſognara torzerlo, & fermarlo talmente, che el detto boſſolo <lb></lb>ſtia ben aſſettato, cioe, che la lenguella della calamita stia giuſta ſecondo el ſuo ordine, <lb></lb>come fu detto di ſopra, cioe, che la ponta di detta lenguella, ouer lanzetta guardi retta <lb></lb>mente uerſo la Tramontana del detto iſtrumento, il che ſi conoſce facilmente per mez <lb></lb>zo di quella linea, che ua da Tramontana al Oſtro, di ſotto della detta lenguella, ouer <lb></lb>lanzetta, cioe, come ſe coſtuma in aſſettar quelli horologietti, che uien de Alemagna, <lb></lb>quando ſe uol ſaper quante hore ſono, con el ſole, & dapoi che tal iſtrumento ſara tal <lb></lb>mente aſſettato, el ſi de girar la dioptra, ouer traſguardo del detto iſtrumento, <expan abbr="talmẽ">talmen</expan> <lb></lb>te che cignando con uno occhio per quelli dui buſettini della detta dioptra (ſe tal dio<lb></lb>ptra hauera detti buſettini) chel ſi ueda una di quelle.5.bacchette piantate, ouer amente <lb></lb>ſe la detta dioptra non hauer a li detti dui buſettini, ma che haueſſe quelle due pontine <lb></lb>acute, come di ſopra fu detto, le qual due pontine à me mi pareno molto pin accommo <lb></lb>de che li huſi, el ſi de guardare una di dette bacchette, & uoltar tanto la detta dioptra, <lb></lb>che la line a uiſuale ſe incontri con le dette due pontine de detta dioptra, & con quella <lb></lb>bacchetta che ſi guardara, & fatto questo el ſi de annotare ſopra una policetta, per <lb></lb>qual grado (de quelli.360.ſe ſaranno.360.oueramenta de quelle.72.parti ſel detto i<lb></lb>ſtrumento ſara diuiſo in.72.parti à gradi.5.per parte, paſſara la detta linea uiſuale (il <lb></lb>qual grado la dioptra lo fara manifeſto) & per eſſer impoßibile à dar in un piccol ſpa<lb></lb>tio perfetto eſſempio in figura à queſta materia, ſe sforzaremo al men con parole di <lb></lb>ſupplire à quello, che non ſi puo dar in figura, hor poniamo che à traſguardare quella <lb></lb>bacchetta poſta in <expan abbr="põto">ponto</expan>.a.la noſtra linea uiſuale paßi alli.3.gradi de Sirocco uerſo<emph.end type="italics"></emph.end> O<lb></lb><emph type="italics"></emph>ſtro, fatto queſto, el ſi de miſurare, ouer far miſurare <expan abbr="quãto">quanto</expan> è dal pede del noſtro iſtru<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.113.1.jpg" xlink:href="042/01/113/1.jpg"></figure><pb xlink:href="042/01/114.jpg"></pb><emph type="italics"></emph>mento alla detta bacchetta poſta in ponto.a.hor poniamo che ui ſia paſſa.54.hor dico, <lb></lb>che di tutto queſto ſe ne debbe far memoriaſopra una policetta in queſta forma, cioe à <lb></lb>gradi tre de Sirocco uerſo Ostro paſſa.54.fatto queſto, el ſi de uoltar la detta dioptra <lb></lb>(stando pero lo iſtrumento ſempre fermo e fiſſo ſecondo el ſuo ordine) talmente, che <lb></lb>per el medeſimo modo el ſi ueda l'altra bacchetta che ſeguita, poniamo quella poſta in <lb></lb>ponto.b.& uiſto, et notato el grado, etiam la diſtantia, che ſara dal pie del noſtro iſtru <lb></lb>mento per fin al ponto.b.ſopra la nostra polizetta alla ſimilitudine dell'altra, & con <lb></lb>tal modo, e uia ſi de procedere à cadauna delle altre tre bacchette poste nelli altri tre <lb></lb>angoli, ouer cantoni.c.d, &.e.& per abbreuiar ſcrittura, poniamo che le dette cinque <lb></lb>diſtantie annotate ſopra alla detta polizetta uadano, & ſiano tanto quanto qua di ſot <lb></lb>to appare, perche coſi debbono eſſer notate.<emph.end type="italics"></emph.end><lb></lb>A <emph type="italics"></emph>gradi. </s> <s id="s.001187">3. de Siroccouerſo Oſtro paſſa.<emph.end type="italics"></emph.end> 54. <lb></lb>A <emph type="italics"></emph>gradi. </s> <s id="s.001188">29. de Greco uerſo Leuante paſſa.<emph.end type="italics"></emph.end> 63. <lb></lb>A <emph type="italics"></emph>gradi. </s> <s id="s.001189">28. de Tramontana uerſo Greco paſſa.<emph.end type="italics"></emph.end> 81. <lb></lb>A <emph type="italics"></emph>gradi. </s> <s id="s.001190">9. de Maiſtro uerſo Ponente paſſa.<emph.end type="italics"></emph.end> 72. <lb></lb>A <emph type="italics"></emph>gradi. </s> <s id="s.001191">5. de Garbino uerſo Oſtro paſſa.<emph.end type="italics"></emph.end> 62. </s> </p> <p type="main"> <s id="s.001192">H<emph type="italics"></emph>or fatto queſto, ſe de cauare lo istrumento, & andarſene à caſa con la ſopradetta ſua <lb></lb>poliza, & quando lí pare di uoler mettere in diſſegno quella tal figura de paeſe ſopra <lb></lb>una carta, ouer tela primamente el ſi debbe diſtendere quella tal carta, ouer tela ſopra <lb></lb>una tabula pianißima, & ſopra à quella imbroccaruela, ouer taccaruela con cera tal<lb></lb>mente, che la non ſi poſſa muouere, & dapoi tirare una linea retta, in mezzo di quella <lb></lb>tal carta, ouer tela alla ſimilitudine della ſottoſcritta linea.a.b.& al mezzo di quella <lb></lb>aſſettarui el detto nostro istrumento, talmente, che la detta linea uenghi à paſſar per <lb></lb>el centro del detto iſtrumento, & che anchor el detto iſtrumento ui ſtia ſopra ben agiu <lb></lb>stato, cioe, che la ſua lanzetta ſtia ſecondo el ſuo debito ordine (piu uolte detto) & da <lb></lb>poi da l'una e l'altra parte del detto iſtrumento el ſe die diſtinguere quella parte della <lb></lb>detta linea.a.b.che uien à eſſer ſotto al iſtrumento (cioe coperta da quello) da quella, <lb></lb>che é diſcoperta con dui piccoli ponti, qualiſiano li dui ponti.c.&.d.et questo ſi fa per <lb></lb>poter ritrouar con facilita el luoco, doue ſe ripoßi el centro del detto iſtrumento, per<lb></lb>che la detta parte.c.d.uien à eſſer equal al diametro del detto iſtrumento, & pero nel <lb></lb>mezzo di quella, cioe in ponto.e.ſe ripoſara el centro del detto iſtrumento. </s> <s id="s.001193">Dapoi che <lb></lb>ſe hauera fatte queſte coſe, el ſi de ſignar.5.ponti ſopra alla detta carta à torno del i-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.114.1.jpg" xlink:href="042/01/114/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſtrumento ſecondo l'ordine della noſtra polizetta, cioe uno à dirimpetto alli.3.gradi <lb></lb>de Sirocco uerſo Oſtro, & coſi un'altro à derimpetto delli.29.gradi de Greco uerſo <lb></lb>Leuante, coſi un'altro à dirimpetto delli.28.gradi de Tramontana uerſo Greco, & <lb></lb>un'altro alli.9.gradi de Maiſtro uerſo Ponente, & un'altro alli.5.gradi di Garbino <lb></lb>uerſo Oſtro el giuſto loco da ſegnar li ſopradetti.5.ponti ſi troua per mezzo della dio <lb></lb>ptra, cioe uoltando prima la detta dioptra talmente, che la ſe ripoßi giustamente alli <lb></lb>detti.3.gradi de Sirocco uerſo Oſtro, & ſecondo l'ordine di quel poco brazzo della <lb></lb>detta dioptra, che paſſa fuora del iſtrumento, ſignar el detto ponto ſu la carta perpen<emph.end type="italics"></emph.end><pb pagenum="58" xlink:href="042/01/115.jpg"></pb><emph type="italics"></emph>dicolarmente ſotto al loco doue procede la noſtra linea uiſuale per quelli dui buſetti<lb></lb>ni, ouer per quelle due ponte, & ſignato quel tal ponto, uoltar la detta dioptra, & <lb></lb>giuſtarla alli.29.gradi di Greco uerſo Leuante, come parla la polizetta, & ſiguar el <lb></lb>ſecondo ponto, & coſi andar procedendo alli.28.gradi di Tramontana uerſo Greco, <lb></lb>& alli.9.gradi di Maiſtro uerſo Ponente, & ultimamente alli.5.gradi di Garbino uer <lb></lb>ſo Oſtro, come con lo intelletto facilmente ſi puo comprender ſopra la figura ſequen<lb></lb>te, & dapoi che ſe hauera ſignati li detti ponti, ſe potra leuar lo detto iſtrumento, & <lb></lb>ſignar el luoco doue ſe ripoſſauael centro di quello (come di ſopra dißi eſſer nella mit<lb></lb>ta della ſopradetta partial linea.c.d.in ponto.e.) & dal detto centro, con una rega, <lb></lb>ouer una regola tirar.5.linee de indiffinita quantita, che paßino per li detti.5.ponti, <lb></lb>cioe la prima dal detto centro al primo ponto, cioe a quello ſignato alli.3.gradi de Si<lb></lb>rocco uerſo Oſtro, & quella tirarla de longo ſenzafarui termine, & coſi procedere <lb></lb>alli altri quattro ponti, & dapoi che ſe haueran tirate le dette.5.linee, di cadauna di <lb></lb>quelle biſognara cauarne com un compaſſo una parte de <expan abbr="tãte">tante</expan> miſurette, ouer apriture <lb></lb>di compaſſo, quanto ſaranno li paßi della ſua relatiua nella noſtra polizetta, <expan abbr="comenzã">comenzam</expan> <lb></lb>do pero ſempre à miſurare à quel loco, doue ſe ripoſſaua el centro del nostro istrumen <lb></lb>to, cioe à quel ponto.e. (di ſopra detto) eſſempi gratia, da quella linea, che paſſara per <lb></lb>li.3.gradi di Sirocco uerſo Oſtro, ſe ne douer a miſurar fora.54.apriture di compaßo, <lb></lb>per eſſer la ſua relatiua nella polizetta paſſa.54.et in capo delle dette.54.apriture di <lb></lb>compaſſo, ui ſe douera far un ponto fermo <expan abbr="terminãte">terminante</expan> detta linea, & coſi ſenza mouere <lb></lb>il <expan abbr="cõpaſſo">compaſſo</expan>, cioe <expan abbr="cõ">com</expan> la medeſima apritura, ſi debbe miſurare fuora à cadauna delle altre <lb></lb>quattro linee, <expan abbr="tãte">tante</expan> apriture, quanto ſara el numero di paſſa della ſua relatiua nella no <lb></lb>ſtra polizetta, cioe à quella che paſſa per li.29.gradi di Greco uerſo <expan abbr="Leuãte">Leuante</expan>, <21> eſſere <lb></lb>la ſua relatiua paſſa.63.ſe ne miſurara fuora.63.apriture di <expan abbr="cõpaſſo">compaſſo</expan>, et in fine di <34>lla <lb></lb>farui un ponto fermo, & coſi <21> non abondar in parole, de l'altra conſequente ſe ne do <lb></lb>uer a miſurar fuora.81 & far ponto, & de l'altra.72.& della ultima.62.emezzo, <lb></lb>& in fine di cadauna di quelle farui un ponto fermo (come di ſopra fu detto) & fatto <lb></lb>queſto, el ſi de congiongere li detti.5.ponti fermi con.5.linee rette, le quale.5.linee ti<lb></lb>rate, che ſiano, repreſentaranno li.5.lati del noſtro ſito, ouer paeſe proportionalmen<lb></lb>te, come di ſotto appare in figura, cioe, che tal piccol diſegno, ouer figura ſara ſimile à <lb></lb>quella figura del noſtro paeſe, ouer ſito, & langolo.a.della ſottoſcritta figura ſara re <lb></lb>latiuo, & equale a langolo.a.della figura del noſtro paeſe, & langolo.b.a langolo.b. <lb></lb></s> <s id="s.001194">& coſi tutti li altri al ſuo relatiuo. </s> <s id="s.001195">Et biſogna notar, che quantunque io habbia ti<lb></lb>rate quelle.5.linee, che uien dal centro à ciaſcun angolo del noſtro diſſegno, tutte ap<lb></lb>parente (come nella figura appare) nondimeno uoleno eſſer tirate occulte, cioe ſenza <lb></lb>inchioſtro, perche guaſtano la figura, ma coſi le ho tirate, accio che uoi intendiate me<lb></lb>glio la coſa. </s> <s id="s.001196">Anchor biſogna notar, che per miſurar fora delle ſopra ſcritte.5.linee <lb></lb>quelle apriture di <expan abbr="cõpaßo">compaßo</expan> che biſogna, <expan abbr="cõ">com</expan> piu breuita, ſe puo ſignar dacanto una lineet <lb></lb>ta de.100.apriture di <expan abbr="cõpaßo">compaßo</expan>, ouer de piu, <expan abbr="ſecõdo">ſecondo</expan> che tal paeſe ſara <expan abbr="grãde">grande</expan>, ouer picco <lb></lb>lo, et <34>lla tal lineetta diuiderla <expan abbr="ĩ">im</expan> parte a.10.apritura <21> parte, et queſta tal linea ſe chia <lb></lb>ma ſchala della noſtra miſura, et quando poi occorreße de miſurare ſora da una data <lb></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.paſſa,<emph.end type="italics"></emph.end><pb xlink:href="042/01/116.jpg"></pb><figure id="id.042.01.116.1.jpg" xlink:href="042/01/116/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſe tal noſtraſcala ſara ſuppoſta poniamo de cento apriture di compaſſo, le quale repre <lb></lb>ſentaſſe.100.paſſa, prima con un compaſſo largo alla equalita di tal ſcala, ſe miſurara <lb></lb>fora ſette apriture di quel tal compaſſo, le quale denotaranno.700.paſſa, dapoi ſe re <lb></lb>ſtringera el detto compaſſo alla equalita de una decima parte de tal ſcala, la quale re<lb></lb>preſentara dieci paſſa, & <expan abbr="cõ">com</expan> tal apritura ſe miſurara fora anchora.9.e meggio di tal <lb></lb>apriture, & coſi ſe hauera miſurato fuora li ſopradetti paſſa ſettecento nouantacin<lb></lb>que, & questo ſi fa, perche ſaria coſa molto longa à uoler ſtare à miſur are una tanta <lb></lb>gran quantita di paſſa, con una apritura di compaſſo che repreſentaſſe un ſol paſſo, & <lb></lb>maßime, che tal hora el diſſegno ſi uora far tanto piccolo, che un paſſo nonſaria quan<lb></lb>tita ſenſibile, & per queſto ſempre ſi coſtuma far la detta linea (chiamata ſcala) & <lb></lb>quella ſe ſuppone de quanti paſſa pare all'operante, nondimeno la maggior parte la <lb></lb>ſuppone de cento paſſa nelle diſcretion piccole, ma nelle grande in Geographia ſe ſup<lb></lb>pongano de milliari, & non de paſſa, cioe de cento, ouer piu milliari. </s> <s id="s.001197">Anchora biſogna <lb></lb>notar, che quella prima linea, che di ſopra fu detto, che ſi debbe tirare in mezzo della <lb></lb>carta, doue ſe uol deſcriuere el nostro diſſegno (cioe quella linea.a.b.) la ſe puo fuppo<lb></lb>nere, che uada rettamente da Leuante à Ponente, ouer da Oſtro à Tramontana, il che <lb></lb>ſupponendola, biſogna poi giuſtar la medeſima del noſiro istrumento ſopra à quella, <lb></lb>& dapoitorcere talmente la tabula, che la lancetta della calamita ſe uada à giuſtar (in <lb></lb>tal poſitione) ſecondo el ſuo ordine, & dapoi procedere, come di ſopra fu detto.<emph.end type="italics"></emph.end> R. <lb></lb>E<emph type="italics"></emph>ue ho inteſo benißimo, & baſta per hoggi.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001198">QVESITO TERZO FATTO DAL MEDESIMO <lb></lb>M. R<emph type="italics"></emph>ichardo Ventuorth.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001199">RICHARDO. H<emph type="italics"></emph>or uoria, che uoi mi dichiaraſti un poco quando che li lati <lb></lb>del detto paeſe non fuſſeno perfettamente retti, come ſe doueria procedere.<emph.end type="italics"></emph.end><lb></lb>N. Q<emph type="italics"></emph>uando che quello paeſe, che ſe deſideraſſe da mettere in diſſegno fuſſe contenu <lb></lb>to parte da linee curue, & parte da rette, ouer amente tutto da linee curue, eglie ne<lb></lb>ceſſario à formar in tal figura curuilinea una figura rettilinea de molti lati per acco<lb></lb>ſtarſe piu che ſia poßibile à quelle linee curue, & mettere in diſſegno quella figura<emph.end type="italics"></emph.end><pb pagenum="59" xlink:href="042/01/117.jpg"></pb><emph type="italics"></emph>rettilinea in ſcritta in quella curuilinea, & darui poi alli ſuoi debiti luochi alquanto di <lb></lb>curuita per pratica, cioe à deſcrittione, & per eſſor meglio inteſo, ſupponeremo che il <lb></lb>ſia uno paeſe contenuto la maggior parte da linee curue, come di ſotto appare in figu<lb></lb>ra. </s> <s id="s.001200">Dico à uoler metter in diſſegno questa tal figura, etaltre ſimile piantato, che ſe hab <lb></lb>bia il detto nostro iſtromento in meggio del detto ſito, uel circa, come di ſotto appare, <lb></lb>& quello agiuſtato, ouer aſſettato ſecondo il ſuo ordine el ſi de far piantar molte bac<lb></lb>chette per la circonferentia di quelle curaita, & doue è maggior curuita piantarui mol <lb></lb>to piu ſpeſſe le dette bacchette per poter ſi con linee rette piu approßimarſe à quella <lb></lb>curuita, come di ſotto appare, & ſupponer che quelle differentie che è da bacchetta à <lb></lb>bacchetta ſiano lati de una figura rettelinea in ſcritta in quella figura curuilinea, e per <lb></lb>tanto el ſi debbe andar traſguardando con la noſtra dioptra cadauna di dette bacchet<lb></lb>te, & notare nella pollicetta per qual grado paſſara cadauna linea uiſuale con la ſua <lb></lb>quantìta di paſſa, che ſara dal piede dell'iſtromento à cadauna bacchetta, & fatto que<lb></lb>sto, ilſe debbe far un qualche ſegno, ouer nota per memoria de quelle ſue curuita, cioe <lb></lb>ſe tai curuita danno in fuora, ouer ſe ſe incarnano in dentro della figura, & dapoi ca<lb></lb>uar l iſtromento, & andarſene à caſa, & uolendo poi mettere tal diſſegno in carta, <lb></lb>ouer in tela, diſteſa quella ſopra una tauola ſecondo il ſolito, il ſi de prima mettere in <lb></lb>diſſegno quella figura rettelinea in ſcritta (ma non tirar li ſuoi lati per linea retta, ma <lb></lb>andar congiongendo le istremita di quelle linee (terminate con il ſolito ponto fermo) <lb></lb>con una linea alquanto curuata in fuora, ouer in dentro ſecondo che dinotara quel ſe<lb></lb>gno che gia fu annotato per memoria, ilche facendo ſe fara una figura ſimile à quella di <lb></lb>quel tal paeſe. </s> <s id="s.001201">ouer ſito, granda, ouer piccola ſecondo che ſiuorra, cioe uolendola far <lb></lb>granda ſe fara anchora la noſtra ſcala (detta nel precedente queſito) de.100.paſſa al<lb></lb>quanto longa, & uolendola piccola, ſe fara la detta ſcala alquanto curta, & biſognano <lb></lb>tare, che quantunque io habbia tirate quelle.25.linee nel noſtro diſſegno tutte appa<lb></lb>rente, et l'haggio fatto, accio che piu euidentemente ſi ueda il modo de procedere per<lb></lb>che le dette.25.linee ſono relatiue à quelli.25.interualli, che ſono dal piede del noſtro<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.117.1.jpg" xlink:href="042/01/117/1.jpg"></figure><pb xlink:href="042/01/118.jpg"></pb><emph type="italics"></emph>ſtromento à cadauna bacchetta piantata nel <expan abbr="cõtorno">contorno</expan> del nostro ſito, ouer pae e, le qual <lb></lb>bacchette, ſe non me inganno, ſono <gap></gap>r.25.tamen in fatto proprio non uoleno eſſer ti <lb></lb>rate apparente (come diſopra nell'altro diſſegno fu anchor detto) perche guaſtano la <lb></lb>figura deſignata, ma ſolamente quelle del contorno uoleno eſſer tirate apparente, per<lb></lb>che quelle ſono che ne rappreſentano la figura, & queſte tale, che uoleno eſſer tirate, <lb></lb>non le ho uoleſte tirare, ma ſolamente ui ho annotato li ponti fermi, accio meglio ſi ap <lb></lb>prenda il modo operatiuo, li quali ponti fermi, che li congiongera con una linea retta.<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.118.1.jpg" xlink:href="042/01/118/1.jpg"></figure><lb></lb><emph type="italics"></emph>ouer curua, conueſſa, ouer concaua, ſecondo il biſogno, ſe uedera rappreſentarſe una <lb></lb>figuretta ſimile à quella del noſtro ſito, ouer paeſe.<emph.end type="italics"></emph.end> R. A<emph type="italics"></emph>nchora questa parte l'ho <lb></lb>inteſa benißimo, & uoglio che baſti per hoggi.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001202">QVESITO QVARTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> M. R<emph type="italics"></emph>ichardo Ventuorth.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001203">RICHARDO. H<emph type="italics"></emph>or uorria Compare che me dichiaraſti quel ſecondo modo <lb></lb>de tuor in diſſegno, che in principio diceſti, cio procedendo, ouer andando per <lb></lb>la circonferentia, ouer contorno di tal ſito, ouer paeſe.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>auendo uoi ben inteſo il <lb></lb>primo modo, uoi ueniti hauer anchor a inteſo piu della mita di queſto ſecondo, perche <lb></lb>ſimilmente uolendo proceder per la circonferentia di tal ſito, ouer paeſe, eſſendo quel <lb></lb>lo contenuto de lati, ouer linee rette nelli angoli de quello, ui biſogna pur mettere una <lb></lb>bacchetta, ouer qualche altro ſignale da potere traſguardare, & dapoi piantare il det <lb></lb>to noſtro iſtromento in uno di ſuoi angoli, & quello aſſettarlo ſecondo l'ordine piu uol <lb></lb>te detto, & dapoitraſguardare quella bacchetta, o altro ſignale, che ſia nell'altro ango <lb></lb>lo auanti di ſe, & girare talmente la dioptra che la linea uiſuale paßi per quelli dui bu<lb></lb>ſettini (hauendo dettibuſettini) ouer amente che la ſe incontri con quelle due ponte (ha <lb></lb>uendo dette ponte, quale à me mi pareno piu ſpediente) & dapoi notar ſopra una pol<lb></lb>licetta il uento, & numero di gradi per donde paſſara la detta linea uiſuale (ilche la <lb></lb>dioptra fara manifeſto) & dapoi far miſurare quanto è dal piede dell'iſtromento à <lb></lb>quella bacchetta, o altro ſignale, che ſara ſu l'altro angolo: & tal quantita de paſſa, à <lb></lb>notarli ſu la pollicetta conſequentemente drio à quello uento, & numero de gradi per<emph.end type="italics"></emph.end><pb pagenum="60" xlink:href="042/01/119.jpg"></pb><emph type="italics"></emph>auanti annotati (ſi come nella precedente operatione fu anchor fatto) & dapoi cauar <lb></lb>il detto iſtromento di quell angolo, & andarlo à piantare in ſu quell'altro (doue è quel <lb></lb>la bacchetta, ouer ſignale, gia traſguardato) et con il medeſimo modo traſguardar quel <lb></lb>la bacchetta, o altro ſignale che ſara ſu l'altro terzo angolo, & annotar ſimilmente <lb></lb>nella pollicetta per qual uento, & numero de gradi paſſara la linea uiſuale, & conſe<lb></lb>quentemente à notarui drio il numero di paſſa, che ſara dal piede del noſtro iſtromen<lb></lb>to per fina al detto ſegno, & coſi con tal ordine ſi debbe andar procedendo per fin che <lb></lb>ſi hauera totalmente circondato quel tal paeſe grande, ouer piccolo che ſia, ilche ſe ha<lb></lb>uera totalmente circondato, quando ſe ſara peruenuto à traſguardare quel ſegno poſto <lb></lb>in ſu quel angolo, ouer cantone, doue che nel principio fu piantato la prima uolta lo <lb></lb>iſtromento, & fatto queſto il ſi puo cauar lo ſuo iſtromento, & andarſene à caſa, & <lb></lb>quando ſe uorra mettere tal paeſe in diſſegno, in carta, ouer in tela, il ſi debbe proce<lb></lb>der quaſi, come nell'altra deſcrittione, cioe distendere tal carta, ouer tela, ſoprauna <lb></lb>tauola piana, & da quella banda, che parera piu conuenire al primo lato del noſtro pae <lb></lb>ſe, & non nel meggio de tal carta, come nell'altra fu fatto, ſe douera aſſettare il detto <lb></lb>nostro iſtromento talmente che la lancetta del boſſolo ſtia ſecondo l'ordine ſuo, & da<lb></lb>poi aſſettare anchora la dioptra à quel uento, & numero de gradi annotati nella prima <lb></lb>partita della nostra pollicetta, & aſſettata che ui ſia, il ſi debbe ſignar dui pontini ſu la <lb></lb>càrta piccolißimi (con un'ago, ouer altra coſa pontita) cioe l'uno da l'un capo della dio<lb></lb>ptra, & l'altro dall'altro per pendicolarmente ſotto al luoco doue ſuol procedere ret<lb></lb>tamente la nostra linea uiſuale, & queſto facilmente ſe puo conoſcere per meggio de <lb></lb>quella poca parte della dioptra che uſciſſe fuora dell'iſtromento (come nell'altro que<lb></lb>ſito anchor fu detto) & dapoi che ſe hauera ſignati li detti dui ponti, il ſi debbe leuar <lb></lb>uia l'iſtromento, & con una rega il ſi debbe tirare, ouer ſignare una linea retta de indif <lb></lb>finita quantita, la qual paßi preciſamente per li detti dui pontini, & di queſta tal linea <lb></lb>il ſi ne debbe miſurar fuora con il compaſſo (con l'ordine della noſtra ſcala) tanti paſ<lb></lb>ſa quanti dira la noſtra pollicetta, & principiare à miſurare doue ne parera piu con<lb></lb>ueniente nella detta linea, & nel principio, & fine di tal parte miſurata ui ſe debbe far <lb></lb>un ponto fermo, fatto queſto il ſi debbe giuſtar la dioptra, à quel uento, & numero de <lb></lb>gradi, che ſi contiene nella ſeconda partita della noſtra pollicetta (cioe nella ſeconda sta<lb></lb>tione) & dapoi giuſt arlo al capo de drio di detta dioptra à quel ponto fermo, che fu ſi<lb></lb>gnato in fine della noſtra prima linea, & agiustato, che uiſia, il ſi debbe torcere tanto <lb></lb>in qua, & in la il detto iſtromento inſieme con la dioptra, che la lancetta del boſſolo ua <lb></lb>da al ſuo ſegno ſenza che la dioptra ſi muoua dell' or dine, che fu prima aſſettata, ma ſo<lb></lb>lamente girare à torno à quel ponto fermo, come ſuo centro, talmente che queſte tre <lb></lb>coſe ſi accordano, cioe che la lancetta ſtia giuſta al ſuo ſegno, & che la dioptra ſtia al <lb></lb>ſuo uento, & numero de gradi, & che anchora la detta dioptra con il capo da drio <lb></lb>uenghi à terminare preciſamente à quel ponto fermo della prima linea ſignata, & <lb></lb>quando che queſte tre coſe ſiano ben accordate, il ſi debbe ſignare uno pontino dal<lb></lb>l'altro capo della dioptra con uno ago, ouer altra coſa appontita, cioe ſotto al luoco do <lb></lb>ue paſſa, ouer ſuol paſſare la noſtra linea uiſuale, et ſignato tal pontino, il ſi debbe leuar <lb></lb>uia lo iſtromento, & con una rega il ſi debbe tirare una linea retta, che paßi per <pb xlink:href="042/01/120.jpg"></pb>quel ponto fermo, & anchora per quello pontino, & di queſta ſeconda linea il ſe ne <lb></lb>debbe con un compaſſo (ſecondo l'ordine della noſtra ſcala) miſurar fuora tanti paſſa, <lb></lb>quanti dira la ſeconda partita della noſtra pollicetta, & principiare à miſurare à quel <lb></lb>ponto fermo, terminante la prima linea, & in capo de tal commenſuratione, farui pur <lb></lb>un ponto fermo ſecondo il ſolito, & de nuouo il ſi debbe agiuſtar la dioptra à quel uen<lb></lb>to, & numero de gradi, come ſe contien nella terza partita della noſtra pollicetta, & <lb></lb>agiuſtarla à tal ponto fermo, & accordar quelle tre coſe (dette di ſopra) & ſignare <lb></lb>quel pontino, dall'altro capo della dioptra, & leuar l'iſtromento, & miſurar fuora <lb></lb>(con il compaſſo) da tal linea, tanti paſſa (con l'ordine della noſtra ſcala) quanti dira la <lb></lb>detta terzapartita della noſtra pollicetta, & coſi andar procedendo per fin che ſe hab <lb></lb>bia circondato, ouer ſerrato tutto tal diſſegno, & ſe per caſo ſe hauera commeſſo qual <lb></lb>che errore, ſe ne accorgera nell'ultimo lato, ouer linea, che compira di ſerrare tal diſ<lb></lb>ſegno, perche quellaſara neceſſario à tirarla ſenza miſurarla altramente con il com<lb></lb>paſſo, perche quella ſe tirara dal ponto fermo, terminante il penultimo lato, ouer linea <lb></lb>di tal diſſegno, al ponto fermo, doue principiara lo primo lato, ouer linea, che prima fu <lb></lb>tirata, cioe doue fupoſto lo iſtromento nel principio, cioe la prima uolta, & ſe per ca<lb></lb>ſo, dapoi che la ſe hauera tirata la ſe ritrouara, con il compaſſo à eſſer de tanti paßa, <lb></lb>(ſecondo l'ordine della noſtra ſcala) quanto che ſara not ato nella ultima partita della <lb></lb>noſtra pollicetta (ilcherare uolte accade) dinotara non eßerſi commeßo alcuno mini<lb></lb>mo errore in tutto quanto il noſtro operare, ma ſe per caſo il detto ultimo lato, ouer <lb></lb>linea, del noſtro dißegno ſe trouara de piu, ouer men apriture di compaßo di quello ſa<lb></lb>ra il numero di paßa, annotati nella pollicetta, di tal ſuo relatiuo lato del noſtro ſito, <lb></lb>ouer paeſe, dinotara eßerſi fatto errore nell'operare, & tanto maggior quanto mag<lb></lb>gior differentia ſi trouara fra quelli, & ſe il ui pare ue ne daro uno eßempio in figura.<emph.end type="italics"></emph.end><lb></lb>R. N<emph type="italics"></emph>on accade che uoi me dati altro eßempio, perche ue ho inteſo benißimo, & ba<lb></lb>sta per hoggi.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001204">QVESITO QVINTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo.<emph.end type="italics"></emph.end> M. R<emph type="italics"></emph>ichardo <lb></lb>Ventuorth.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001205">RICHARDO. A<emph type="italics"></emph>nchor che quaſi comprenda, come ſe doueria procedere qun <lb></lb>do che tal ſito fuſſe contenuto da linee, ouer lati curui, ouer montuoſi, nondime <lb></lb>no hauero accaro à intendere la uoſtra opinione per uedere ſe la mia ſe conforma con <lb></lb>la uoſtra.<emph.end type="italics"></emph.end> N. B<emph type="italics"></emph>iſogna procedere pur, come fu detto nel terzo queſito, cioe nella cur<lb></lb>uita de tai lati piantarui de molte bacchette, et tanto piu ſpeſſe quanto che piu ſono cur <lb></lb>ui, & dapoi procedere, come ſe fece nel precedente queſito, cioe procedere propria<lb></lb>mente, come ſe tal figura fuſſe contenuta de tante linee, ouer lati retti, quante ſaranno <lb></lb>quelle differentie, che ſara da bacchetta, à bacchetta, ma nel diſſegnarli poi, biſogna <lb></lb>darui un poco del curuo in fuora, ouer in dentro, ſecondo che con qualche ſegno ue ne <lb></lb>haucti fatto memoria nella pollicetta.<emph.end type="italics"></emph.end> R. C<emph type="italics"></emph>oſi preciſamente haueua in opinione, che <lb></lb>ſi doueſſe fare, e pero non uoglio, che per hoggi entramo in altro.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="61" xlink:href="042/01/121.jpg"></pb> <p type="head"> <s id="s.001206">QVESITO SESTO FATTO DAL MEDESIMO <lb></lb>M. R<emph type="italics"></emph>ichardo Ventuorth.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001207">RICHARDO. P<emph type="italics"></emph>er le ragioni dette nelli precedenti dui Queſiti à me mi pa<lb></lb>re, che ſenza alcun uoſtro auiſo io ſaperia anchor tor in diſegno la pianta de <lb></lb>una citta.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>i bene, ma in questo biſogna conſiderar, che li lati di una citta ſono <lb></lb>muraglie, & perche nel proprio loco, doue che è la detta muraglia non ui ſi puo anda <lb></lb>re, ne piantarui el noſtro iſtromento, ne etiam le bacchette, ouer ſignali, perche la det <lb></lb>ta muragliane impediſſe, e per tanto biſogna procedere per l'uno de dui modi, el pri<lb></lb>mo di quali è <expan abbr="q́ueſto">queſto</expan>: che el ſi puo procedere per el medeſimo modo, ma andando egual <lb></lb>mente diſtante à cadauna muraglia, cioe piantare el noſtro iſtromento alquanto lonta <lb></lb>no dalla detta muraglia, come ſaria à dire tre piedi, & coſi ſe de far piantare la bac<lb></lb>chetta, che ſi uuol traſguardare, medeſimamente lontana dalla detta muraglia li detti <lb></lb>tre piedi, onde traſguardando la detta bacchetta ſecondo l'ordinario, & annotar nel <lb></lb>la policetta, per qual uento, & numero de gradi paſſara la noſtra linea uiſuale, & da <lb></lb>poi far miſur are la longhezza di quella tal muraglia, ouer cortina, & tal numero de <lb></lb>paſſa annotarlo nella policetta conſequentemente drio à quel uento, et numero de gra <lb></lb>di, che prima fu annotati, & coſi con tal ordine andar procedendo in cadauna corti<lb></lb>na, & ſe per ſorte in alcuna di dette muraglie, ouer cortine ui fuſſe qualche porta, ba <lb></lb>luardo, ouer torrione, biſogna farne un poco di memoria nella policetta, cioe à quan<lb></lb>ti paſſa ſara della detta cortina, etiam di quanti paſſa ſara la ſua larghezza, per po<lb></lb>terli, & ſaper li poi mettere, ouer deſignare nel noſtro diſegno alli ſuoi debiti luochi, <lb></lb>& con le ſue debite miſure, & queſto medeſimo modo ſe douera anchora oſſeruare, <lb></lb>quando l'occorreſſe à uoler mettere in diſegno un paeſe, doue fuſſe neceſſario à pro<lb></lb>ceder per la circonferentia, ouer contorno di quello, & che nella detta ſua circonfe<lb></lb>rentìa, ouer contorno ui fuſſe qualche foſſo, cieſe, ouer qualche altra coſa, che ne im<lb></lb>pedideße il poter andare à piantar el noſtro iſtromento, & le bacchette da traſguar<lb></lb>dare, in la uera circonferentia di tal ſito, ouer paeſe, cioe, chel ſi doueria procedere <expan abbr="e-quīdiſtantemente">e<lb></lb>quindiſtantemente</expan> à quel tal lato, cioe ſel tal nostro iſtromento, ſaremo sforzati à pian <lb></lb>tarlo lontano dal uero lato de tal ſito, poniamo paſſa.4.ouer piu, altertanti anchora <lb></lb>ſe douera piantar lontano la bacchetta dall'altro capo di tal lato.<emph.end type="italics"></emph.end> R. E<emph type="italics"></emph>ue ho inteſo <lb></lb>benißimo circa à queſto primo modo, hor diteme pur l'altro modo.<emph.end type="italics"></emph.end> N. L'<emph type="italics"></emph>altro mo <lb></lb>do certamente è molto piu eſpediente, & presto, perche in quello non ui occorre à far <lb></lb>piantar bacchette, ne metter altriſignali, perche quel brazzetto, ouer trauerſo.l.m. <lb></lb></s> <s id="s.001208">che fu poſto a ſquadra nella iſtremita di quello brazzo.g.h. </s> <s id="s.001209">ne caua de tal faſtidio, <lb></lb>perche uolendo ſapere per qual uento, & grado proceda, ouer ſtia una cortina, ouer <lb></lb>muraglia di tal citta, baſta ſolamente a tuor el detto noſtro iſtromento in mani, & an<lb></lb>dare adappozzare quel tal brazzo, ouer trauerſo.l.m.in un luoco piano di tal corti<lb></lb>na, ouer muraglia, & dapoi girarui fotto lo detto iſtromento, ouer boſſolo, per fina a <lb></lb>tanto, che la lenguella, ouer lancetta ſtia ſecondo el ſuo ordine, & fatto questo biſogna <lb></lb>notare nella noſtra policetta, per qual uento, e numero de gradi paſſara, ouer che di<lb></lb>ſcouerzera la noſtra principal dioptra, perche, per quel medeſimo procedera ancho-<emph.end type="italics"></emph.end><pb xlink:href="042/01/122.jpg"></pb><emph type="italics"></emph>ra quella tal cortina, ouer muraglia (per eſſer la detta principal dioptra in tal poſi<lb></lb>tione equidistante à tal cortina, ouer muraglia, & dapoi far miſurare tal cortina, o<lb></lb>uer muraglia, & tal ſua quantita de paſſa annotarli conſequentemente drio à quel <expan abbr="uẽ">uem</expan> <lb></lb>to, & numero de gradi, gia annotati, & coſi andar facendo à cadauna dell'altre corti <lb></lb>ne (facendo memoria delli luochi delle ſue porte, & baluardi (come di ſopra fu det<lb></lb>to) & fatto queſto andarſene à caſa, & quando ſe uora poi mettere in diſegno la pian <lb></lb>ta di tal citta, ſe potra procedere preciſamente, come fu fatto di quel paeſe nel.4.Que <lb></lb>ſito, uero è, che ſe potria tirar anchora le linee, ſecondo l'ordine di quel brazzo.l.m. <lb></lb></s> <s id="s.001210">cioe aſſettato, che ſe habbia tal noſtro iſtromento ſu la carta da quella banda, doue pa<lb></lb>re piu conuegnirſe alla prima cortina di tal citta, & agiuſtato la dioptra à quel uento,<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.122.1.jpg" xlink:href="042/01/122/1.jpg"></figure><lb></lb><emph type="italics"></emph>& numero de gradi, come parlara la prima partita della noſtra policetta, & fatto <lb></lb>queſto, tir are una linea retta de indiffinita quantita, ſecondo l'ordine del detto braz<lb></lb>zetto.l.m.& datal linea cauarne, ouer miſurarne fora con el compaſſo, tanti paßa (ſe <lb></lb>condo l'ordine della noſtra ſcala) come parlara la detta prima partita della noſtra po <lb></lb>licetta, & nel principio, & fine di tal linea farui un ponto fermo, come piu uolte è ſta <lb></lb>to detto, & dapoi reconzar la dioptra al uento, & grado, come parlara la ſeconda <lb></lb>partita della nostra policetta, & con tal poſitione aſſettarla quel brazzetto.l.m. </s> <s id="s.001211">à <lb></lb>quel ponto fermo gia fatto nel fin della detta prima linea, con tal modo, & forma che <lb></lb>ſe accorda quelle tre coſe dette nel precedente Queſito, cioe, che la lancetta della cala<lb></lb>mita, ſtia ſecondo el ſuo ordine, & che la dioptra ſtia à quel uento, & nomero de gr<lb></lb>di, come parla la dettaſeconda partita della policetta terzo, & ultimo, che el detto <lb></lb>brazzetto.l.m.termini preciſamente à quel ponto fermo, terminante la prima linea, <lb></lb>& accordate queſte tre coſe, tirate un'altra linea de indeffinita quantita, ſecondo l'or <lb></lb>dine del detto brazzetto.l.m.la qual paßi per el detto ponto fermo, terminante la pri <lb></lb>ma linea, & di queſta ſeconda linea, con el compaſſo ſe ne debbe pur miſurar fuora tan <lb></lb>ti paſſa (ſecondo l'ordine della noſtraſeala) quanti ſara notati nella detta ſeconda par <lb></lb>tita della noſtra policetta, comenzando pero à miſurare al detto ponto fermo, termi<lb></lb>ne della prima linea, & principio della ſeconda, & in fine farui pur un ponto fermo, <lb></lb>& coſi con tal modo, & ordine ſe douera andar procedendo, per fin che ſe hauera <expan abbr="cõ-pito">con<lb></lb>pito</expan> da deſignare la <expan abbr="piãta">pianta</expan> di cadauna cortina di tal citta, et chi uoleße ſapere che <expan abbr="uẽto">uento</expan><emph.end type="italics"></emph.end><pb pagenum="62" xlink:href="042/01/123.jpg"></pb><emph type="italics"></emph>percoteße <expan abbr="perpĕdicolarmẽte">perpĕdicolarmente</expan> ſopra à cadauna cortina, ſempre el brazzo.g.h. </s> <s id="s.001212">lo fara <lb></lb>manifeſto.<emph.end type="italics"></emph.end> R. V<emph type="italics"></emph>oi me haueti certamenti molto ſatisfatto, uero è, che el me è occor<lb></lb>ſo un'altra particolarita de <expan abbr="adimãdarui">adimandarui</expan>, ma per eſſer tardi, la uoglio laſſar à dimane.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001213">QVESITO SETTIMO FATTO DAL MEDESIMO <lb></lb>M. R<emph type="italics"></emph>ichardo Ventuorth.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001214">RICHARDO. A<emph type="italics"></emph>nchor che me habbiati<emph.end type="italics"></emph.end> (C<emph type="italics"></emph>ompar carißimo) molto ſatisfat <lb></lb>to in tutto quello, che nel principio ue richieſe, nondimeno penſando poi, che in <lb></lb>ogni luoco, ouer citta, <expan abbr="nõ">non</expan> potero forſi trouare maeſtro, che mi poteſſe, ouer ſapeſſe ſer <lb></lb>uire in farmi tal <expan abbr="iſtromẽto">iſtromento</expan>, ouer boſſolo, per eſſer quello, ſecondo el mio parere, di <expan abbr="nõ">non</expan> <lb></lb>poco artificio, & per tanto uiprego, che ſel fuſſe poßibile de immaginare una qualche <lb></lb>altra forma, che fuſſe de tal facilita, che fuſſe ſicuro di poter in ognicitta ritrouare <lb></lb>maeſtri, che me poteſſono, ouer ſapeſſono fare.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ue ne uoglio inſignare à for<lb></lb>marne uno di legno, el quale non ſolamente in ogni cittauoi trouareti molte perſone, <lb></lb>che uel ſapranno, & potrauno fare, ma anchora per uoi medeſimo aun biſogno lo ſa<lb></lb>pereti, & potreti fare.<emph.end type="italics"></emph.end> R. V<emph type="italics"></emph>oi non mi potreſti fare coſa piu grata, ma dubito aſſai <lb></lb>che tal coſa non ſia el uero, & la cauſa, che mi fa dubbitare è questa, che ſolamente in <lb></lb>le citta maritime, ſe ritroua perſone, che ſappiano far li boſſoli, & temperare quella <lb></lb>ſua lancetta, la qual è il timone, che gouerna la naue di questa noſtra pratica.<emph.end type="italics"></emph.end> N. E<lb></lb><emph type="italics"></emph>glie ben il uero, che in ogni citta non ſi troua coſi perſone, che ſiano atte a far tal coſa, <lb></lb>ma non me potretinegare, che in ogni citta non ui ſi troua di quelli horologietti, che <lb></lb>uengono dalla Lemagna, con li quali alſole ſe pol ſapere quante hore ſono, & ſi uendo <lb></lb>no tre, ouer quattro ſoldi luno.<emph.end type="italics"></emph.end> R. C<emph type="italics"></emph>he de quelli, che hanno una Tramontanella pic <lb></lb>cola, cioe poco piu della ungia del dedo groſſo.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>roprio de quelli.<emph.end type="italics"></emph.end> R. S<emph type="italics"></emph><expan abbr="ẽza">enza</expan> dub <lb></lb>bio, che de tali horologiettiſe ne ritroua per egni citta.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>t con uno de quelli ue <lb></lb>uoglio inſignare a far ui uno iſtrumento, & con gran facilita, con el quale ue ne potre<lb></lb>ti ſeruir in tutte queſte prasiche, di che hauemo fin hora parlato.<emph.end type="italics"></emph.end> R. E<emph type="italics"></emph>come.<emph.end type="italics"></emph.end> N. <lb></lb>I<emph type="italics"></emph>o uoglio, che uoi diſegnati con un compaſſo ſopra a un foglio di carta <expan abbr="alquãto">alquanto</expan> großa <lb></lb>e ferma, e <expan abbr="bẽ">bem</expan> lißa, una figura ſimile a quella, che <expan abbr="ĩ">im</expan> principio ui moſtrai di far ſopra quel <lb></lb>la <expan abbr="lãma">lamma</expan> di ottone, cioe quelli medeſimi circuli, <expan abbr="cõ">com</expan> le me deſime diuiſioni de uenti, & de <lb></lb>gradi, come che anchora di ſotto appar in figura, ma farlo, che <21> diametro ſia al men <lb></lb>una <expan abbr="ſpãna">ſpanna</expan>, accio che la ſua circonferentia poſſa eſſer diuiſa in.360.gradi, et dapoi che <lb></lb>baueriti fatto queſto tal diſegno in carta, uoglio che tal diſegno l'incollati ſopra ad un <lb></lb>quadretto di tabula di legno <expan abbr="bẽ">bem</expan> piana, et di legno <expan abbr="bẽ">bem</expan> ſecco, groſſa circa a un dedo, & ſe <lb></lb>poßibil fuſſe farla far de legno d'ancipreſſo (perche tal legno <expan abbr="nõ">non</expan> fa mutatione ſenſibile <lb></lb>ne ſe ſtorge <21> <expan abbr="tẽpo">tempo</expan>) & far che el detto quadretto di tabula habbia nel mezzo de un di <lb></lb>ſuoi lati un'altro quadrettino congionto di <expan abbr="tãta">tanta</expan> <expan abbr="grãdezza">grandezza</expan>, che ſia capace di poterui ſo <lb></lb>pra di quello incaſſarui, & incollarui uno delli ſopradetti horologietti, che uengono <lb></lb>da Allemagna, ma biſogna aduertire ne l'incollar el detto diſegno, & el detto horolo<lb></lb>gietto di far, che la <expan abbr="Tramõtana">Tramontana</expan> del detto diſegno, et <expan abbr="ſimilmẽte">ſimilmente</expan> quella del detto horolo <lb></lb>gietto guardino rettamente per uno medeſimo uerſo, come di ſotto appar in figura.<emph.end type="italics"></emph.end><pb xlink:href="042/01/124.jpg"></pb>E <emph type="italics"></emph>dapoì queſto, biſogna farui una dio<lb></lb>ptra pur li legno d'ancipreſſo (ſe poßi<lb></lb>bil è) ouer di qualche altro, che ſia ben <lb></lb>ſecco, talmente, che per tempo non fac<lb></lb>cia mutatione, che in cio l'ancipreſſo lau <lb></lb>piu de tutti. </s> <s id="s.001215">Et per far queſta dioptra, <lb></lb>che ſia giuſtißima, biſogna far fare una <lb></lb>reghetta, ouer liſtetta del detto legno, <lb></lb><expan abbr="lõga">longa</expan> circa un brazzo, e mezzo, & lar <lb></lb>ga circa a un dedo, & groſſa circa a <lb></lb>una coſta di cortello, & queſta tal ri-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.124.1.jpg" xlink:href="042/01/124/1.jpg"></figure><lb></lb><emph type="italics"></emph>ghetta uol eſſer rettißima, & giuſtißima, & per conoſcere ſe tal regha ſara giuſta, <lb></lb>ſe potra conoſcere per quel modo poſto nel terzo libro della noſtra nouaſcientia, & <lb></lb>dapoi fatta queſta tal regha, di quella biſogna ſegarne fuora otto pezzetti, cioe quat<lb></lb>tro maggiori, & quattro menori, li quattro maggiori uoleno eſſer di tal longhezza, <lb></lb>che ſopragionti, & incolati, come di ſotto appar in ponto.e.&.f. </s> <s id="s.001216">ſiano alquanto piu <lb></lb>del diametro del detto istromento. </s> <s id="s.001217">Et biſogna notar, che tal ſopragiontion uol eſſer <lb></lb>fatta per groſſezza, & uol eſſer tanta, quanto che è la ſua larghezza, & con tal mo-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.124.2.jpg" xlink:href="042/01/124/2.jpg"></figure><lb></lb><emph type="italics"></emph>do, & ordine, che queſti dui par de pezzi (coſi congionti, & incolati) ponendoli luno <lb></lb>ſopra l'altro in perfetta croce, cioe perfetta linea a ſquadra (come di ſopra appar in <lb></lb>figura) <expan abbr="uẽgono">uengono</expan> a fare, ouer a formare nella ſua <expan abbr="cõgiontione">congiontione</expan> uno quadretto (come nella <lb></lb>detta ſottoſcritta figura appare) el qual quadretto uenghia cauſar un angolo in pon<lb></lb>to.g.& un altro a quel oppoſito in ponto.h. </s> <s id="s.001218">Et coſi queſti dui par de pezzi uogliono <lb></lb>eſſer perfettamente incolati in tal poſitione, cioe, come nella dettaſottoſcritta figura <lb></lb>appare. </s> <s id="s.001219">Gli altri.4.pezzetti menori, li quali po <lb></lb>niamo che ſiano li ſopra notati <21>.a.b.c.d.uoglio <lb></lb>no eſſer piu corti delli altri.4.maggiori, tanto <lb></lb>quanto è la larghezza de cadauno de loro, <21> che <lb></lb>de quelli uoglio che ſe ne ſerui <21> redure la ſopra <lb></lb>ſcritta croce tutta piana, e ſolida, <21> che eglie ma<lb></lb>nifesto, che li dui brazzi.i.h.g.<emph.end type="italics"></emph.end> k <emph type="italics"></emph><21> eſſer ſopra <lb></lb>posti alli altri dui, <expan abbr="nõ">non</expan> toccano el piano doue ſeri<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.124.3.jpg" xlink:href="042/01/124/3.jpg"></figure><lb></lb><emph type="italics"></emph>poſſa li detti altri dui brazzi a <34>lli ſottopoſti, anci <expan abbr="ſtãno">ſtanno</expan> in aere, cioe <expan abbr="lõtani">lontani</expan> dal detto <lb></lb>piano <expan abbr="tãto">tanto</expan> <expan abbr="quãto">quanto</expan> è la groſſezza de cadauno de loro, e pero <21> impir quel uacuo uoglio,<emph.end type="italics"></emph.end><pb pagenum="63" xlink:href="042/01/125.jpg"></pb><emph type="italics"></emph>che otto à cadauno de detti dui bracci.i.h.g.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>ui ſia incollato uno de quelli.4.pezzi <lb></lb>menori.a.b.c.d.detti di ſopra, li quali ueniranno à empire perfettamente quelli duiua<lb></lb>cui, perche ſe conueneranno preciſamente in quelli, & coſi ſera redutta tal croce piana <lb></lb>dalla parte di ſotto uerſo il piano, ma non di ſopra, perche quelli dui primi bracci poſti <lb></lb>in piano non aſcendono alla altezza delli dui ſopra poſti, cioe de.i.h.<emph.end type="italics"></emph.end> g.k.<emph type="italics"></emph>anci ui manca <lb></lb>tanto quanto è la groſſezza de cadauno de loro, e pero per empir quel uacuo, uoglio <lb></lb>che ui ſia incollato ſopra à cadauno de loro uno de quelli altri dui pezzi menori giare<lb></lb>ſtati, li quali uenir anno à empire perfettamente quel uacuo, perche ſe conueniranno <lb></lb>preciſamente in quelli, & fatto queſto, tal croce ſara redutta tutta ſolida, & piana da <lb></lb>ambe le bande, e ſara fortificata, perche ſara fatta tutta doppia, et tutto queſto meglio <lb></lb>ſe uedera nel fabricarla, che per figura. </s> <s id="s.001220">Et dapoi queſto nel capo de dui di detti bracci <lb></lb>oppoſiti, biſogna incollarui un'altro pezzetto dellamedeſima liſtetta pur doppia, co<lb></lb>me di ſotto appare in ponto.a.& in ponto.b.& in l'uno, el'altro de queſti dui lochi ui <lb></lb>douera piantar una ponta acuta, come ſaria una ponta de ago, che ſeruino per traſ<lb></lb>guardar, in luoco delli dui buſi. </s> <s id="s.001221">Et ſe piu ag-gradara li buſi che tai due ponte, in tai me<lb></lb>deſimi lochi ui ſe potra incaſſar, & incollar <lb></lb>dui quadratini in alto elleuati con li detti dui <lb></lb>buſi, ma piu mi piace le due ponte, che li bu <lb></lb>ſi. </s> <s id="s.001222">Et per poterſi ſeruire di queſto tal istro<lb></lb>mento per tuor in diſſegno le piante delle cit <lb></lb>ta, nella iſtremita del braccio.c.d.ui ſe potra <lb></lb>incaſſar, & incollar il brazzetto.e.f.à ſqua<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.125.1.jpg" xlink:href="042/01/125/1.jpg"></figure><lb></lb><emph type="italics"></emph>dra, come nella ſopraſcritta figura appare. </s> <s id="s.001223">Et dapoi queſto nel centro di tal dioptra bi <lb></lb>ſogna farui un buſettino, & con un pironcino di ferro, ouer di ottone piantare tal dio<lb></lb>ptra nel centro di tal iſtromento, la qual coſa facendo tal iſtromento ſtara preciſe, come <lb></lb>me di ſotto appare in figura, & di queſto ue ne potretiſeruire, ſi come di quello di ot<lb></lb>tone.<emph.end type="italics"></emph.end> R. Q<emph type="italics"></emph>uesto mi pare una coſa molto facile, & di poco artificio, & quaſi di niu<lb></lb>na ſpeſa, perche tutta la ſpeſa che ui entrara non credo che aſcendera à un marcello, ma <lb></lb>dubito che il <expan abbr="nõ">non</expan> ſara di quella medeſima giuſtezza che ſara quello di ottone.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>n <lb></lb>ci per molte ragioni, eglie neceſſario, che queſto ſia molto piu giuſto di quello di ot-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.125.2.jpg" xlink:href="042/01/125/2.jpg"></figure><pb xlink:href="042/01/126.jpg"></pb><emph type="italics"></emph>tone, perche in quello di ottone, oltra che ui occorre maggior difficolta in far quelli dui <lb></lb>bracci della ſua dioptra, che ſiano rettißimi (per eſſer di metallo) di quello, che occorre <lb></lb>nelli dui bracci della ſopraſcritta dioptra.a.b. (per eſſer piu facile da lauorar con la <lb></lb>piona il legno del metallo) ma poniamo anchora che gli detti bracci di ottone (per la <lb></lb>buona diligentia del maeſtro fuſſeno fatti di tanta giuſtezza, quanto quelli di legno) <lb></lb>dico che eglie difficile aſſai ad aſſettarli poi in quella ſua armilla, che ſi incontr ano ret<lb></lb>tamente, & non in contrando ſi tal iſtromento ſaria falſo, & oltra di questo, eglie an<lb></lb>chora molto difficoltoſo, che tal armilla uada, ouer intraga talmente giuſta, ouer ſaz<lb></lb>zadamente, in quella altra armilla ſaldata à torno del boſſolo, che non ſcantini piu in <lb></lb>un luoco, che in un'altro, ilche facendo tal dioptra non riſpondera il uero grado, ilche <lb></lb>facendo tal <expan abbr="iſtromẽto">iſtromento</expan> ſaria falſo. </s> <s id="s.001224">Et oltra di queſto, non è molto facile ad aſſaldare quel <lb></lb>la prima armilla à torno al centro di tal iſtromento di ottone, che ſia perfettamente <expan abbr="cõ">com</expan> <lb></lb>centrica con il detto iſtromento, & non eſſendo concentrica tal iſtromento ſaria falſo, <lb></lb>e per tanto dico, che à far tal dioptra di legno per il modo dato di ſopranon ui occorre <lb></lb>alcune delle ſopr adette difficolta, ma ſolamente biſogna eſſer diligente in far, che quel<lb></lb>la prima righetta, ouer liſtetta ſia giuſtißima (ilche facilmente per lo ſopradetto mo<lb></lb>do da noi poſto nel Terzo libro detto Nuona Scientia) ſi puo conoſcere, & uedere.<emph.end type="italics"></emph.end> R. <lb></lb>C<emph type="italics"></emph>onſidero che eglie il uero quello, che uoi diceti, ma eglie ſe non una coſa, che quel qua<lb></lb>dretto doue uoleti che ui ſe incaßt il detto horologietto, par che molto diſdica coſi con<lb></lb>gionto in quel lato, de fuor a uia.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>ir ca à queſto, ui ſe gli potria rimediare in piu mo <lb></lb>di, l'uno di quali è questo, il ſe potria da tal horologietto ſegarui, ouer tagliarui fuora <lb></lb>quel poco boſſoletto, cioe quella tramontanella, & tal tramontanella incaſſar la in uno <lb></lb>de quelli ſpaci uacui de quelli angoli del quadrato, che conterminorno con il medeſimo <lb></lb>lato doue che è congionto tal quadretto, cioe in quel ſpacio doue é ſignato.o.ouer nel<lb></lb>l'altro, mabiſogna auertire nell'incaſſar tal boſſoletto, ouer tramontanella, in tal luo<lb></lb>co de far che la Tramontana de tal boſſoletto, guardi per quel medeſimo uerſo, che <lb></lb>guardara quella del noſtro diſſegno, cioe che la linea che ua da Oſtro à Tramontana <lb></lb>nel boſſoletto ſtia equidiſtante à quella, che medeſimamente ua da Oſtro à Tramonta<lb></lb>na del noſtro diſſegno, il qual boſſoletto eſſendo coſi aſſettato, tanto ui ſeruira, come ſe <lb></lb>quel fuſſe, come era prima, cioe congionto con quel lato de fuor a uia.<emph.end type="italics"></emph.end> R. </s> <s id="s.001225">A <emph type="italics"></emph>queſto <lb></lb>modo sta molto meglio, & molto piu mi piace dell'altro. </s> <s id="s.001226">Nondimeno ho à caro di ba<lb></lb>uer inteſo l'uno, e l'altro, & per al preſente non ui uoglio dare altro faſtidio. </s> <s id="s.001227">Ma un'al <lb></lb>tra uolta con piu uoſtro, & mia commodita, uorro poi che anchora mi dichiarati di <lb></lb>quell'altra forma de iſtromento, ouer boſſolo, che ſerue ſenza dioptra.<emph.end type="italics"></emph.end> N. O<emph type="italics"></emph>gni uol <lb></lb>ta che ui ſia accommodo ſon ſempre apparato à farui appiacere. </s> <s id="s.001228">Ma una coſa ui ho da <lb></lb>ricordare, ogni uolta che uoleti operare tal iſtromento auertir, che non ui ſta propin<lb></lb>quo ferro diſorte alcuna, perche il boſſolo, ouer calamita, non ui riſponderia il uero, e <lb></lb>pero in tal negocio non ſi debbe portar ſpada, ne pugnal cinto, perche il pomo ſpeſſe <lb></lb>uolte ui faria errare, & non di poco.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001229">I<emph type="italics"></emph>l fine del Quinto Libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb pagenum="64" xlink:href="042/01/127.jpg"></pb> <p type="head"> <s id="s.001230">LIBRO SESTO DELLI <lb></lb>QVESITI, ET IN VENTIONI DIVERSE, <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.001231">S<emph type="italics"></emph>opra il modo di fortificar le Citta <lb></lb>riſpetto alla forma.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001232">QVESITO PRIMO FATTO DAL S. GABRIEL <lb></lb>T<emph type="italics"></emph>adino, Cauallier de Rodi, & Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001233">PRIORE. N<emph type="italics"></emph>on credeti uoi che lo ingegno dell'huomo al preſente <lb></lb>ſia peruenuto à quel ſublime grado doue ſia poßibile à peruenire, <lb></lb>per fortificare una citta.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>i queſto non ui ſaprei riſpondere, <lb></lb>perche non ſolamente ho praticato poco per Italia, & manco fuor <lb></lb>de Italia, ma da dodeci anni in qua mai ſon ſtato fuora di Venetia, <lb></lb>ſaluo una uolta che andai à Verona per un mio negocio quaſi à ſtaf<lb></lb>fetta.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o non uedeſti Padoua, & Verona, non haueti ancho<lb></lb>ra uiſto Breſſa uoſtra Patria.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>adoua ho uiſto per tranſito ſim <lb></lb>plicemente in trauerſarla per andare alle barche dal Fraßine, ma non conſiderata. </s> <s id="s.001234">Si<lb></lb>milmente ho uiſto Verona, & ſtantiato per diece anni in quella, ma mai la circondai, <lb></lb>ne manco conſiderai, la figura del contorno di quella. </s> <s id="s.001235">La canſa fu che à quel tempo non <lb></lb>mi dilettaua de tai particolarita, ne mai hebbi in animo di dilettarmene in conto alcu<lb></lb>no, ma queſti ſoſpetti, & mouimenti Turcheſchi me hanno dato nuouamente occaſione <lb></lb>di ponerui alquanto cura, come coſa utile, & neceſſaria, & quello che ho detto di Ve<lb></lb>rona, il medeſimo dico di Breſſa<emph.end type="italics"></emph.end> (P<emph type="italics"></emph>atria mia) & ſimilmente di Crema, Bergamo, & <lb></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></lb>conſiderata la forma delle mura di alcuna di quelle, eglie ben uero, che quando stantia<lb></lb>ua à Verona, io fui alcune uolte à San Georgio, & uidi à quella porta eſſerui princi<lb></lb>piati alcuni fondamenti dimura di una iſmiſurata groſſezza, & ſimilmente me aricor <lb></lb>do hauer uiſto à cadauna delle altre porte certi baſtioni, torrioni, ouer baluardi, alcuni <lb></lb>ſolamente principiati, alcuni meggi fatti, & alcuni compiti, di una groſſezza ineſtima <lb></lb>bile, ma come ho detto, mai poßicura alla forma del contorno di quella, il medeſimo di<lb></lb>co hauer uiſto Breſſa<emph.end type="italics"></emph.end> (P<emph type="italics"></emph>atria mia) & stantiato per tutta la mia pueritia, in quella, & <lb></lb>me aricordo delli ſuoi großißimi terrai, muri, et torrioni, ma non della forma.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o <lb></lb>hauendo uiſto quelli ſondamenti de mura, & torrioni coſi großißimi di Verona, et quel <lb></lb>li großißimi terrai, mura, & torrioni, che circonda Breſſa, non poteti far giudicio del <lb></lb>laſua fortezza.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>o ingegno dell'huomo, nel fortificar una citta (ſecondo il mio <lb></lb>parere) ſe conoſce per la forma, & non per la materia, perche à fortificare una citta <lb></lb>ſimplicemente per uigore, & forza de materia. </s> <s id="s.001238">La non mi pare coſa molto ingenio<lb></lb>ſa, ne di molte laude degna.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o non ue intendo troppo bene.<emph.end type="italics"></emph.end> NIC. I<emph type="italics"></emph>o dico, <lb></lb>che à fortificare una Citta ui concorre la materia, & la forma, & che lo inge<lb></lb>gno dillo huomo ſe approua per la forma delle ſue mura, & non per la materia, <pb xlink:href="042/01/128.jpg"></pb>cioe per la groſſezza de quelle. </s> <s id="s.001239">Et per tanto quantunque habbia uiſto la groſſezza del <lb></lb>le mura, et torrioni de tai citta, non hauendo conſiderata la ſua forma non poſſo far giu <lb></lb>dicio di quello, che me ha adimandato<emph.end type="italics"></emph.end> V.S.<emph type="italics"></emph>perche quella (ſe ben me aricordo) me ha adi <lb></lb>mandato, ſe à me mi pare che lo ingegno dell'huomo ſia peruenuto à quel ſublime gra<lb></lb>do doue ſia poßibile de peruenire, nel fortificare una citta. </s> <s id="s.001240">Onde ſe lo ingegno dell huo <lb></lb>mo, in ſimil caſo (come di ſopra è detto) ſe approua per la forma, & non hauendo io <lb></lb>conſiderato alcuna forma non poſſo far alcun giudicio.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>oman de ſera ui uoglio <lb></lb>moſtrar il diſſegno d'una citta de Italia, la qual è giudicata ineſpugnabile, uorro poi <lb></lb>che ſopra la forma di quella me dicati la uoſtra opinione, cioe ſe la ſara ingenioſa<lb></lb>mente fabricata.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001241">QVESITO SECONDO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001242">PRIORE. V<emph type="italics"></emph>edeti qua, queſto è il diſſegno della pianta de <lb></lb>Turino, qual da gli <lb></lb>huomini de ingegno è giudicato eſſer ineſpugnabile. </s> <s id="s.001243">Hor che diceti di queſta figu <lb></lb>ra.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n questa tal figura, non ui dicerno alcuna gran ſottilita d'ingegno.<emph.end type="italics"></emph.end> P. </s> <s id="s.001244">O <emph type="italics"></emph>uoi <lb></lb>ſeti, non ſolamente contra alla opinione d'ogn'uno, ma anchora contra à tutto quello, <lb></lb>che per ſperientia ſe è ueduto, toccato, e palpato.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on dico, ne manco uoglio di<lb></lb>re, che Turino non ſia forte, & forſi fortiſ<lb></lb>ſimo, perche una citta puo eſſere alle uolte <lb></lb>forte per la natura del luoco doue che la ſe <lb></lb>ritroua, & alle uolte ſolamente per artificio <lb></lb>dell'huomo, & alle uolte per l'uno, e per l'al <lb></lb>tro. </s> <s id="s.001245">Quelle che ſono forte ſolamente per la <lb></lb>natura del luoco (cioe quando che quella fuſ<lb></lb>ſe cinta, ouer cir <expan abbr="cõdata">condata</expan> da acque, fiumi, ouer <lb></lb>paludi) io non ne parlo, perche il laude di tal <lb></lb>ſua fortezza ſi debbe attribuire piu preſto <lb></lb>alla natura, che all'ingegno dell'huomo. </s> <s id="s.001246">Ma <lb></lb>quelle che ſono forte ſolamente per artificio <lb></lb>dell'huomo, tal ſua fortezza puo accadere<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.128.1.jpg" xlink:href="042/01/128/1.jpg"></figure><lb></lb><emph type="italics"></emph>in dui modi, cioe tal hora puo eſſer forte, piu per uigor della pura materia, che della for <lb></lb>ma, cioe piu per uigor delle ſue groſſe mura, baſtioni, larghe & profonde foſſe, che dal <lb></lb>la forma di quella, il qual modo, anchor che faccia quaſi lo effetto diſiderato, à me non <lb></lb>pare che ſia de molto ingegno.<emph.end type="italics"></emph.end> L'<emph type="italics"></emph>altro modo è, che talhora una citta puo eſſer forte piu <lb></lb>per uigore della forma, che della materia, cioe che la forma delle mura del circuito de <lb></lb>tal citta, potria eſſer alle uolte di tal ſorte, che quella non ſaria di menor impedimento, <lb></lb>ouer ostacolo alli nemici, di quello che ſaria le ſue groſſe mura, bastioni, larghe et pro<lb></lb>fonde foſſe, la qual coſa eſſendo, giudicareital opraeſſer compoſta, ouer ordinata da <lb></lb>non mediocre ingegno.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>auoglio che ſappiati qualmente la detta citta è fortißi<lb></lb>ma, & nonſolamente per la pura materia, ma anchora per la buona forma, & accio<emph.end type="italics"></emph.end><pb pagenum="65" xlink:href="042/01/129.jpg"></pb><emph type="italics"></emph>meglio intendiati il tutto, questa tal citta è di forma quadrangola, come in el ſottoſcrit <lb></lb>to diſegno appare, & la fazzata, che ua da Leuante à Ponente, uerſo Septentrione é <lb></lb>circa paſſa.360.el medeſimo è l'altra fazzata à queſta oppoſita. </s> <s id="s.001247">Le altre due faz<lb></lb>zate, ouer teſte ſono alquanto piu corte, cioe <lb></lb>meno de detti paſſa.360.& in cadauno delli <lb></lb>quattro angoli di queſta citta ui è un Baluar<lb></lb>do, ouer baſtione de iſmiſurata groſſezza. <lb></lb></s> <s id="s.001248">La fazzata de fora uia, cioe la coſta.a.b.o<lb></lb>uer.b.c.de cadauno de quelli, me ſta referto <lb></lb>eſſer paſſa.40.Le quattro fazze di queſta <lb></lb>citta con li detti baluardi, ouer baſtioni ſono <lb></lb>ſtati fatti modernamente, cioe di muraglia no <lb></lb>ua großißima, & hanno ſerrato dentro da ſe <lb></lb>tutta la muraglia uecchia, con <expan abbr="alquãto">alquanto</expan> de in<lb></lb>teruallo fra la muraglia noua, & la muraglia <lb></lb>uecchia, & cadauno di quattro baluardi ha <lb></lb>due canonere di dentro della noua muraglia,<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.129.1.jpg" xlink:href="042/01/129/1.jpg"></figure><lb></lb><emph type="italics"></emph>che guardano quel ſpacio, ouer interuallo, che è fra la muraglia noua, e la uecchia <lb></lb>(detto di ſopra.) Anchora fra baluardo, e baluardo, cioe nel mezzo di cadauna faz<lb></lb>zata ui é una forma piatta, ouer caualliero, le quale guardano li baluardi, & cadauna <lb></lb>di queste forme piatte ha due canonere di dentro della noua muraglia oppoſite à quel<lb></lb>le di baluardi, che guardano quel detto ſpatio, che è fra la muraglia noua, & la mura<lb></lb>gliauecchia. </s> <s id="s.001249">Le foſſe poi che cercondano questa citta nel fondo ſono larghe paſſa.14. <lb></lb>& nella ſommita, ouer bocca paſſa.16.& alte paſſa.4.hor ue adimando, ſel non ui pa <lb></lb>re, che queſta tal citta ſia fortißima, ſi ſecondo la forma, come ſecondo la materia.<emph.end type="italics"></emph.end><lb></lb>N. I<emph type="italics"></emph>o confirmo, che la é forte reſpetto alla materia, cioe in quanto alle ſue groſſe mu <lb></lb>ra, baluardi, cauallieri, profonde, & larghe foſſe. </s> <s id="s.001250">Ma in quanto alla forma delle dette <lb></lb>ſue mura, non ui diſcerno alcuna artificioſa particolarita.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>t à me mi pare, che <lb></lb>la forma di tal ſuo contorno, ouer mura non potria eſſer megliore, & credo chel ſia <lb></lb>quaſi impoßibile à poterla megliorare in conto alcuno.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n queſto uoſtra Reue<lb></lb>rentia ſe inganna grandemente.<emph.end type="italics"></emph.end> P. H<emph type="italics"></emph>aro de caro, che mel fatti conoſcere, ma per <lb></lb>eſſer hora tarda, ucglio che la remettiamo à diman de ſera.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001251">QVESITO TERZO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001252">PRIORE. V<emph type="italics"></emph>oi <expan abbr="cõchiudeſti">conchiudeſti</expan> hierſera, che la detta citta de <lb></lb>Turino, <expan abbr="nõ">non</expan> ha in ſe <lb></lb>gran fortezza, per uigor della forma delle ſue mura, ma ſolamente per uigore <lb></lb>della groſſezza de quelle, et delle ſue profonde, & larghe foſſe hor uoria, che me dice <lb></lb>ſti, le <expan abbr="cõditioni">conditioni</expan>, qualita, ouer particularita, che à uoi par, che ſe doueria fare, ouer che <lb></lb>doueria hauere la ſorma delle mura de una citta à douer eſſer forte per uigor di tal for <lb></lb>ma, accio ch'io ſappia in che riprendeti, ouer in che coſa pecca, ouer manca la forma<emph.end type="italics"></emph.end><pb xlink:href="042/01/130.jpg"></pb><emph type="italics"></emph>de Turino.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>e <expan abbr="cõditioni">conditioni</expan>, qualita, & particolarita, che douria hauere, ouer cheſt <lb></lb>potria adattare, alla forma, & mura de una citta, ſi per reſiſtere à queſti tempi alli ui<lb></lb>goroſi colpi delle artegliarie, come anchora per potere confacilita, rebattere, & of <lb></lb>fendere in uarij modi li nimici in ogni lor impetuoſo aſſalimento, eglie da credere, che <lb></lb>ſiano molti. </s> <s id="s.001253">Ma quelle, che coſi per al preſente me ho imaginate, ſono ſolamente ſei, <lb></lb>& perche queſte ſei ſe poſſono alterare, & uariare in uarij, & diuerſi modi, ſecondo <lb></lb>uarij, & diuerſi riſpetti, à me ſarianeceſſario (à uolere à ſofficienza ben dechiarire, <lb></lb>& con ragione dimoſtrare di cadauna di quelle particolarmente ſua ualuta) à deſigna <lb></lb>re, uarie, & diuerſe piante, ouer à fabricare materialmente uarij, & diuerſi modelli, <lb></lb>la qual coſa non ſi puo fare coſi all'improuiſo, anci ui uol tempo, & non poco, & maßi<lb></lb>me à me, che nel operar manuale non ſon molto iſperto.<emph.end type="italics"></emph.end> P. A<emph type="italics"></emph>nchor, che coſi al im<lb></lb>prouiſo non poßiati deſignare le dette piante, ne fabricar materialmente li detti mo<lb></lb>delli, non poteti almen ſotto breuita narrare la conditione, & proprieta di queſte uo<lb></lb>stre ſei imaginate particolarita, & dapoi deſignare con uoſtra commodita le dette <expan abbr="piã">piam</expan> <lb></lb>te, ouer modelli.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>e poſſo dir ſi.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o ditteli adunque conſequentemente <lb></lb>l'una dietro l'altra, perche in effetto à me mi pare, che ſia quaſi impoßibile di poter <lb></lb>taſſare la forma de Turino de unſolo non che de ſei diffetti.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a prima coſa, che <lb></lb>à me mi pare, che doueria hauere la forma delle mura de una citta, ouer che ui ſe do<lb></lb>ueria fare, uolendo à questi tempi fortificar quella è queſta, che mai in conto alcuno ſe <lb></lb>doucria far pala de alcuna ſua cortina, ouer muraglia, talmente, che li nemici ui poteſ<lb></lb>ſono percotere, ouer tirare <21> pendicolarmente con le artegliarle, perche, ogni mura<lb></lb>glia cede molto piu facilmente alle <21>cußioni delle balle, che feriſcono <21> pendicolermen <lb></lb>te ſopra à quella, di quello fa à quelle, che gli feriſcono obliquamente, cioe in ſguinzo, <lb></lb>& quanto piu ueneranno, ouer feriranno obliquamente, cioe in ſguinzo, tanto menor <lb></lb>nocumento faranno in detta cortina, ouer muraglia. </s> <s id="s.001254">La cauſa è, che ogni <expan abbr="cõmuna">communa</expan> per <lb></lb>coſſa fatta perpendicolarmente ſopra à una muraglia è molto piu riſentita in tutte le <lb></lb>parte di tal muraglia, di quello ſara ogni altra molto maggiore, che percottera obli<lb></lb>quamente, ouer in ſguinzo ſopra alla medeſima.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>redo questo, che uoi diceti, per <lb></lb>che delle per cußioni fatte coſi obliquamente, ouer in ſguinzo, la muraglia non riceue <lb></lb>tutta la botta, ma ſolamente parte di quella, la qual parte tanto ſara menore, quanto <lb></lb>che piu obliquamente, ouer in ſguinzo tal balla ferira ſopra à quella.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>dunque <lb></lb>la forma de Turino incorre in queſto errore, perche cadauna delle ſue quattro mura<lb></lb>glie, ouer cortine, che la circonda, ſono aſſettate di tal ſorte (come ſi uede nel ſuo diſe<lb></lb>gno) che li nemici ui potranno ageuolmente tir are perpendicolarmente in cadauna di <lb></lb>quelle.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>uando, che tal uostra opinione ſi poteſſe mandar ad eſſecutione in ogni <lb></lb>cortina, el non ſe potria negare, che la non fuſſe una coſa molto ingenioſa, & utile. <lb></lb></s> <s id="s.001255">Ma non ſolamente dubito, che uoi non ue ingannati. </s> <s id="s.001256">Ma tengo, che tal coſa ſta impoßi <lb></lb>bile, perche de quante citta ho pratticate, & uiſte mai, ne bo uiſto alcuna (che batter ſi <lb></lb>poſſa) che in ogni ſua cortina, non uiſe poſſa tirare per pendicolarmente con le arte<lb></lb>gliarie.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>apoi, che noi haueremo compito da narrare tutte queſte nostre ſei ima <lb></lb>ginate qualita, ouer conditioni, non ſolamente faro conoſcere, & uedere à uoſtra Si<lb></lb>gnoria in figura (ouer con modelli) qualmente eglie poßibile di mandar ad effetto tal<emph.end type="italics"></emph.end><pb pagenum="66" xlink:href="042/01/131.jpg"></pb><emph type="italics"></emph>noſtra imaginata qualita, ouer particolarita in ogni cortina. </s> <s id="s.001257">Ma che anchora eglie <lb></lb>poßibile à farlo in tre diuerſi modi, & forſi piu.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſto bauero molto a caro, <lb></lb>di uedere.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001258">QVESITO QVARTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo ſignor Priore <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001259">PRIORE. H<emph type="italics"></emph>or ſeguitati anchora la ſeconda qualita, ouer particolarita.<emph.end type="italics"></emph.end><lb></lb>N. <lb></lb>L<emph type="italics"></emph>a ſeconda qualita, ouer conditione e queſta, che biſogna ben antiuedere di aſſet <lb></lb>tar tutte le ſue cortine, & baluardi, con tal modo e forma, che li nimici non poſſano <lb></lb>trouar luoco alcuno di poter piantare le ſue artegliarie, che ſempre non ſia menor di <lb></lb>ſtantia di alcuno di baluardi di tal citta al detto luoco, di quella, che ſara dal detto loco <lb></lb>à quella cortlna, che deſiderar anno da battere. </s> <s id="s.001260">Il che facendo, li detti nimici non po<lb></lb>tranno piantare le dette ſue artegliarie per battere detta citta, ſe non conſuo gran di<lb></lb>ſauantaggio. </s> <s id="s.001261">Et di queſta qualita, ouer <expan abbr="cõditione">conditione</expan>, manca anchora la forma di Turino, <lb></lb>perche el ſi uede, che in qualunque luoco ſi uora aſſettar li nemici con le artegliarie <lb></lb>per battere tal citta ſempre ſara maggior diſtantia di qual ſtuoglia baluardo al detto <lb></lb>luoco, che non ſara dal medeſimo luoco à quella cortina, che deſiderar anno da battere.<emph.end type="italics"></emph.end><lb></lb>P. Q<emph type="italics"></emph>ueſto mi par quaſi impoßibile.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o non diria una coſa a uoſtra Signoria, che <lb></lb>fuſſe impoßibile di fare. </s> <s id="s.001262">Anci in fine à quella faro non ſolamente figur almente uedere <lb></lb>qualmente tal coſa ſia poßibile, ma che eglie poßibile à farlo in uarij, & diuerſt modi.<emph.end type="italics"></emph.end><lb></lb>P. D<emph type="italics"></emph>i queſto ne hauero appiacer grandißimo. </s> <s id="s.001263">Et ui uoglio dire, che con queſta uoſtra <lb></lb>ſeconda conditione mi haueti auerto lo intelletto talmente, che ſpero fra pochi giorni <lb></lb>di farue uedere una pianta deſignata de mia mano, che hauera in ſe queſte uoſtre due <lb></lb>dette conditioni.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ſon certißimo, che ſe uoſtra Signoria ui penſara alquan<lb></lb>to ſopra, facilmente le ritrouara, & deſignera: perche ogni commun ingegno, che <lb></lb>di tai particolarita ſia auertito, facilmente ritruouara il tutto, tanto piu uoſtra <lb></lb>Signoria, che è colma de ingegno.<emph.end type="italics"></emph.end> P. H<emph type="italics"></emph>or ſu per queſta ſera, non uoglio, che <lb></lb>procedamo in altro.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001264">QVESITO QVINTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001265">PRIORE. H<emph type="italics"></emph>or uegnamo alla terza conditione, ouer particolarita.<emph.end type="italics"></emph.end> N. <lb></lb>L<emph type="italics"></emph>a <lb></lb>terza conditione è queſta, che el biſogna, che la forma di tal citta ſia talmente di <lb></lb>ſpoſita, che ſe li nemici deliberaſſeno di darui una battaglia ordinata, chel non ſi troui <lb></lb>alcuna parte di quella tal citta, che poſſa eſſer aſſaltata da nemici, che quelli non poßa <lb></lb>no ſempre eſſer offeſi da quelli dalla terra almen da quattro diuerſe bande con le arte <lb></lb>gliarie (& da piu bande ſe eglie poßibile) della qual coſa manca la ditta citta <lb></lb>de Turino, perche ogni uolta, che li nemici aſſaltaſſero tal citta in una (qual ſi uoglia)<emph.end type="italics"></emph.end><pb xlink:href="042/01/132.jpg"></pb><emph type="italics"></emph>delle ſue quattro fazzate, ouer cortine, quelli non potranno eſſer offeſi, da quelli dalla <lb></lb>terra, con lartegliaria, ſaluo che da due bande, cioe dalli dui baluar di, che guardano <lb></lb>quella tal cortina, ouer mur aglia, perche la forma piatta, ouer caualliero, <expan abbr="nõ">non</expan> debbe po<lb></lb>ter tirar tanto baſſo, che poſſa offendere li nemici, che ſiano ſotto alle mura.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>i <lb></lb>questa particolarita manca anchora ogni altra fortificata citta de Italia, & anchora <lb></lb>fuor de Italia, perche de quante ne ho uiste maine ho uiſta alcuna, che le ſue cortine <lb></lb>ſtano guardate, ſaluo che da due bande, cioe da dui baluar di. </s> <s id="s.001266">Et quando, che queſta uo <lb></lb>ſtra particolarita ſi poteſſe condur ad effetto in ogni cortina, certo la ſaria una coſa <lb></lb>di molto profitto, ma ui dubito grandemente.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n fine di queſti noſtri ragiona<lb></lb>menti (ſi come ho promeſſo) faro ueder à quella il tutto in figura, & quando, che uo<lb></lb>ſtra ſignoria hauera uiſto el diſegno di tal pianta, ſon certo, che quella non ui hauera <lb></lb>dubbio alcuno, & tanto piu, che gli farò uedere, tal coſa poterſi far in piu modi.<emph.end type="italics"></emph.end> P. <lb></lb>Q<emph type="italics"></emph>ueſto hauero molto accaro.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001267">QVESITO SESTO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001268">PRIORE. H<emph type="italics"></emph>or ſeguitati anchora la quarta qualita, perche eglie à <lb></lb>buon'ho<lb></lb>ra.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a quarta conditione, che ſi conuien nel fortificar una citta, reſpetto <lb></lb>alla forma delle mura è queſta. </s> <s id="s.001269">Che nelfar fabricar, et in alzar le ſue mura, ouer corti <lb></lb>ne. </s> <s id="s.001270">Biſogna fra le altre coſe eſſer cauto de farle in alzar con tal modo eforma, che ſe <lb></lb>per caſo quelle fuſſeno ruinate da nemici con le artegliarie, che tai mura coſi ruinate, <lb></lb>rendano quaſi maggior difficultà, & pericolo alli dettinemici, uolendo quelli intrare <lb></lb>nella detta citta, di quello che faceuano, quando, che quelle erano intiere, & ſane. </s> <s id="s.001271">De <lb></lb>la qual coſa ſon certo, che manca la forma di Turino.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>ueſta non me pare coſa <lb></lb>da credere, perche ſe tal coſa fuſſe poßibile, ſeguiria, che tal citta fuſſe quaſi piu for<lb></lb>te ſenza le mura, che con le mura.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto è uero, che la ſaria quaſi piu forte, <lb></lb>perche ſe le mura cadute, & ruinate cauſar anno quaſi maggior difficulta, & pericolo <lb></lb>alli nimici à uoler intrar dentro della detta citta, di quello fariano eſſendo intiere, & <lb></lb>ſane. </s> <s id="s.001272">Seguira de neceßita, che la detta cittaſia piu forte con le mura ruinate, che con <lb></lb>quelle intiere eſane.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>o non poſſo quaſi credere questa coſa.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uando che uo <lb></lb>ſtra Reuerentia hauera uiſto el modello de tal forma de mura, ſon certo, che quella af<lb></lb>fermera tutto quello, che hauemo detto. </s> <s id="s.001273">Ma piu, che gli faro uedere, & con ragion <lb></lb>toccare, poterſi tal particolarita condur ad effetto in tre diuerſi modi.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>uando <lb></lb>che queſto fuſſe la uerita, le artegliarie haueriano perſo la mita della ſua reputatione, <lb></lb>nelle iſpugnation delle citta. </s> <s id="s.001274">Et ui uo dire, che coſi ragionando, & tutta uia penſando <lb></lb>ſopra à queſta uoſtra particolarita, e me ho quaſi imaginato, come ſe potria far que<lb></lb>ſta tal coſa, ma la uoglio un poco meglio conſiderare, & farne un modelletto, perche <lb></lb>nel far di modelli meglio ſe delucida la coſa, dapoi uoro uedere ſe la mia opinione ſara <lb></lb>ſimile alla uostra.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ſon certißimo, che ſe uoſtra Signoria ui penſara alquanto <lb></lb>ſopra, quella ritrouara il tutto, auanti che ueda altramente gli miei modelli, perche<emph.end type="italics"></emph.end><pb pagenum="67" xlink:href="042/01/133.jpg"></pb><emph type="italics"></emph>ogni commun ingegno (come di ſopra dißi) che di tai particolarita ſia auertito facil<lb></lb>mente da ſe le ritrouara, non che Voſtra Reuerentia.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>onſidero ueramente, che <lb></lb>il molto praticare, ragionare, & diſputare de una materia, fa ritrouar molte coſe, cir <lb></lb>ca à quella, perche nel praticare, ragionare, et diſputare, l huomo uien ſempre auerti<lb></lb>to de qualche nuoua particolarita, et dapoi ch eglie auertito, et ſopra à quella <expan abbr="pẽſando">penſando</expan> <lb></lb>facilmente la ritroua.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001275">QVESITO SETTIMO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001276">PRIORE. S<emph type="italics"></emph>eguitati anchora la quinta particolarita, ouer conditione, per <lb></lb>fin <lb></lb>che uenga hora da cena.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a quinta qualita, ouer conditione, che debbe ha<lb></lb>uer una citta è queſta, che ſempre ſi debbe adattare qualche particolare, & ſicuro in<lb></lb>gegno alla guardia de cadauna cortina, ouer muraglia, che occorrendo che li nemici ue <lb></lb>niſſono per ſcalarla con ſcale, che con facilita ui ſi poteſſe rompere totalmente ogni ſuo <lb></lb>diſſegno, & con ſuo grandißimo danno, et uergogna, della qual coſa ſon certo, che man <lb></lb>ca le cortine, ouer mura de Turino.<emph.end type="italics"></emph.end> P. A<emph type="italics"></emph>nci di questa tal particolarita, non ſolamen<lb></lb>te, non manca la citta de Turino, ma nanche alcun'altra citta de Italia, perche ſempre <lb></lb>ui ſe mette dui, & tal hora quattro pezzi di artegliaria per banda in cadauno baluar <lb></lb>do, li quali guardano, & defendano tal cortina da chi la uoleſſe ſcalare.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>l non bi<lb></lb>ſogna <expan abbr="totalmẽte">totalmente</expan> aßicurarſe ſopra dui, ne quattro pezzi di artegliaria, che fuſſeno per <lb></lb>banda in cadauno baluardo, ne tenere, che quelli ſiano ſofficienti à difendere tal corti<lb></lb>na, da uno impetuoſo, & grandißimo aſſalimento, perche anchor che le artegliarie ſia <lb></lb>no de gran terrore, & de mirabile effetto (doue che percuoteno) nondimeno tai ſuoi <lb></lb>effettila maggior parte delle uolte, ouer che uanno totalmente falliti, ouer che manca<lb></lb>no aſſai di quello, che le perſone ſe iſtimano, ouer penſano, perche le lor balle paſſano <lb></lb>ſempre per ſtretto luoco, e pero offendono li nemici ſolamente in particolare (cioe à <lb></lb>chi la tocca per ſorte) & non in generale. </s> <s id="s.001277">Et per tanto dico, che biſogna prepar arui <lb></lb>coſe che offendono li detti nemici in generale cioe di tal qualita che ſubito che li nemici <lb></lb>cominciaſſeno ad aggiongere nella ſommita di tal cortina, che non ſolamente fuſſeno <lb></lb>atte di ributtare in drio generalmente tutti quelli, che fuſſeno peruenuti nella ſommi<lb></lb>ta di tal cortina, inſteme con quelli, che ſu per tai ſcale ſt trouaſſeno. </s> <s id="s.001278">Ma che anchora <lb></lb>offendeſſono generalmente tutti quelli altri, che ſopra à tai ſcale ſteſſono per aſſalire.<emph.end type="italics"></emph.end><lb></lb>P. Q<emph type="italics"></emph>uando che il non fuſſe le artegliarie. </s> <s id="s.001279">Credo ben che facilmente ſe potria trouar <lb></lb>qualche particolar ingegno chi faceſſe in gran parte quello, che haueti detto. </s> <s id="s.001280">Ma uo<lb></lb>glio che ſappiati, che quando li nemici deliberano di dare l'aſſalto, ouer battaglia à una <lb></lb>citta, ſempre cercano da daruela da tal banda, ouer in tal luoco, che con le ſue arteglia <lb></lb>rie lor poßino leuare facilmente quelli della terra dalle diffeſe & doue che le arteglia<lb></lb>rie poſſono giuocare, non credo che ſia poßibile di accommodarui alcuna ſorte de inge <lb></lb>gno, che da quelle non ſia immediate rotto, & dißipato, come dißi anchora ſopra il far <lb></lb>delle ordinanze.<emph.end type="italics"></emph.end> N. O<emph type="italics"></emph>gni dritto ha il ſuo rouerſo, baſta che in fine nel far di noſtri <lb></lb>modelli, ſecondo la promeſſa, faro uedere à<emph.end type="italics"></emph.end> V.R. <emph type="italics"></emph>& con ragion toccare, che non ſola-<pb xlink:href="042/01/134.jpg"></pb>mente eglie poßibile di far una tal particolarita ad ogni cortina. </s> <s id="s.001281">Mache eglie poßibile <lb></lb>à far la in tre diuerſi modi, & che eglie una coſa facile, & dur abile, & di pochißimo ar <lb></lb>teficio, & manco ſpeſa. </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 ſaran<lb></lb>no ſofficientißimi à difendere. </s> <s id="s.001285">150. paſſa di cortina, ouer muraglia da ogni grandißma <lb></lb>moltitudine de nemici, che con ſcale la uenißono per ſcalare, ouer che la haueßono gia <lb></lb>ſcalata (come diſopra è detto) & tal particolarita ſara ſicura dalle artegliarie nemi<lb></lb>che.<emph.end type="italics"></emph.end> P. Q<emph type="italics"></emph>uando che queſto fuße la uerita, ne ſeguiria due cofe digrandißimo momen <lb></lb>to, & utilita l'una è, che con pochißima gente, et conſe quentemente con pochißima ſpe <lb></lb>ſa ſi faria guardar una tal citta.<emph.end type="italics"></emph.end> (A<emph type="italics"></emph>nchor che fuße molto granda<emph.end type="italics"></emph.end>) <emph type="italics"></emph>l'altra è, che una cit <lb></lb>ta da poca gente guardata, con difficolta, puo eßer aßediata, ilche importa aßai.<emph.end type="italics"></emph.end> N. <lb></lb>E<emph type="italics"></emph>glie ben uero, che una citta da poca gente guardata, ui uol molto piu tempo à douerla <lb></lb>aßediare, di quello uorria, quando che quella fuße di gente molto piena, nondimeno à <lb></lb>questi tempi questo non ſatisfa tanto che baſti, perche<emph.end type="italics"></emph.end> V.R. <emph type="italics"></emph>ſa la poſſanza del Turco, <lb></lb>per la difenſion del quale, hauemo inueſtigato, tutto quello, che per fina à queſta hora <lb></lb>hauemo detto, & diſputato. </s> <s id="s.001286">Et per tanto dico, quando che di quel ſe dubitaſſe, ouer de <lb></lb>altra, poſſanza ſimile, che fuſſe atta à mantenere longamente l'aſſedio à tal citta, accio <lb></lb>che à longo andare tal citta non incorreſſe in tal errore. </s> <s id="s.001287">Il ſarianeceſſario à fargli al<lb></lb>tra prouiſione, come nella ſeguente ſeſta particolarita, ouer conditione ſi narrara, la <lb></lb>quale per eſſer hora tarda la laſſaremo à diman de ſera.<emph.end type="italics"></emph.end> P. H<emph type="italics"></emph>orſu doman ui aſpetto, <lb></lb>& ueniti à bon'hora.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001288">QVESITO OTTAVO FATTO DAL <lb></lb><emph type="italics"></emph>medeſimo Signor Prior <lb></lb>di Barletta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001289">PRIORE. H<emph type="italics"></emph>orſu ſeguitati la ſeſta qualita, ouer particolarita.<emph.end type="italics"></emph.end> N. <lb></lb>L<emph type="italics"></emph>a ſeſta <lb></lb>qualita, ouer conditione è queſta. </s> <s id="s.001290">Quando che la citta, che ſe ha da fortificare, ſe <lb></lb>dubitaſſe del Turco (come dißi hierſera) ouer de qualche altra potentia ſimile, cioe che <lb></lb>fuſſe atta, & ſofficiente à mantenerui molti anni l'aſſedio. </s> <s id="s.001291">Biſognaria al tutto auertire <lb></lb>di dar una tal forma, alle mura, & circuito di quella, talmente che quelli di detta citta <lb></lb>poteſſono ſicur amente andare, ouer mandare à lauorare, ſeminare, & raccogliere, al <lb></lb>men tanto terreno, che fuſſe atto, & ſofficiente à dargli quaſi il uiuere, cioe che li ne<lb></lb>mici (per großi che fuſſeno) non ui poteſſono uenire, ne ſcorrere in conto alcuno à <lb></lb>danneggiare li raccolti, ne gli lauoranti, ouer raccoglienti quelli.<emph.end type="italics"></emph.end> P. S<emph type="italics"></emph>enza dubbio <lb></lb>che queſto ſaria una coſa ottima, & ſanta, & credo anchora che il ſe potria fare, maue <lb></lb>entraria una troppo gran ſpeſazza.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci io ho opinione che à fortificare, & aſ<lb></lb>ſicurare il paeſe di una citta per un commun ſpacio à torno, ui entraria molto manco <lb></lb>ſpeſa di quello che entraria à fortificare la ſimplice citta.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o ditemi un poco, non <lb></lb>uoleti che prima ſe fortifichi la ſimplice citta, auanti che ſe fortifichi il paeſe.<emph.end type="italics"></emph.end> N. F<emph type="italics"></emph>or <lb></lb>tificando il paeſe non accade à fortificare altramente la citta, perche la detta citta ſara <lb></lb>fatta forte per la fortezza del paeſe, perche ſe tal paeſe ſara fatto forte (poniamo)<emph.end type="italics"></emph.end><pb pagenum="68" xlink:href="042/01/135.jpg"></pb><emph type="italics"></emph>per. </s> <s id="s.001292">200. ouer piu paſſa da lontano à torno à torno di talcitta, & che ſia fortificato <lb></lb>di tal ſorte, che dentro di tai termini alcun eſſercito (per groſſo che ſia) non ſolamen<lb></lb>te non ſia atto, ne ſofficiente à poter penetrare, ma nanche per altri. </s> <s id="s.001293">100. paſſa oltra <lb></lb>à tai termini poſſa ſicuramente piantar la ſua artegliaria, per battere detta citta. </s> <s id="s.001294">Sen<lb></lb>za dubbio tal citta uenira ad eſſer ſicura da non poter eſſer danneggiata da nemici con <lb></lb>le artegliarie. </s> <s id="s.001295">Et per tanto eſſendo ſicura detta citta da non poter eſſer battuta con <lb></lb>le artegliarie danemici, non ui occorrer a à farui altra ſpeſa in fortificarla. </s> <s id="s.001296">Ma ui ba<lb></lb>ſtara una ſimplice muraglia per una battaglia da mano per buonriſpetto.<emph.end type="italics"></emph.end> P. I<emph type="italics"></emph>n ef<lb></lb>fetto ogni uolta che ſi poteße aßicurare una citta, da non poter eßer battuta da nemi<lb></lb>ci con le artegliarie, la non puo eßer ſe non fortißima, quantunque haueße le mura niol <lb></lb>to debole, perche le artegliarie (à questitempi) ſono il uerbo principale per debel<lb></lb>lare una citta. </s> <s id="s.001297">Et quando che il fuße poßibile à condure ad effetto queſto che uoi haue<lb></lb>ti detto, anchor che ui entraße il doppio ſpeſa, di quello che entraria à fortificar la ſim <lb></lb>plice citta, la ſaria una coſa molto laudabile, & degna, & le artegliarie nelle iſpugna<lb></lb>tioni de tai citta haueriano perſo tutto il credito. </s> <s id="s.001298">Ma per non ue dir bugia, non credo <lb></lb>che il ſia poßibile di far una tal coſa (come di ſopra dißi) ſaluo, che con una grandißi<lb></lb>ma, & intolerabil ſpeſa.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uando che uoſtra Reuerentia hauera uisto in diße<lb></lb>gno la forma delle piante, oueramente li modelli di tai ſorte de fortificationi, & ſopra <lb></lb>de quelli calculata la ſpeſa che ui entrara, ſpero che quella ritrouara entrarui manco <lb></lb>ſpeſa di quello, che di ſopra dißi.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o quando uoleti dar principio à far queſte uo<lb></lb>stre piante, ouer modelli.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>artito che ſia da uoſtra Signoria non tendaro ad altro.<emph.end type="italics"></emph.end><lb></lb>P. D<emph type="italics"></emph>itemiun poco, in queſti uoſtri modelli non gli fareti li ſuoi baluar di, & cauallie<lb></lb>ri, ouer forme piatte, & ſimilmente le ſue foße.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio. </s> <s id="s.001299">Anci uolendo io <lb></lb>dimoſtrare con ragioni ſenſibili, la proprieta, & ualuta di cadauna di dette forme, <lb></lb>ſono aſtretto à farui großo modo tutte queſte coſe.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>itemi anchora haueti pra<lb></lb>tica, ouer notitia della forma, & miſura di baluardi, cauallieri, ouer forme piatte, che <lb></lb>al preſente ſi coſtuma nelle moderne fortificationi, cioe di quanta longhezza, larghez <lb></lb>za, & altezza ſi formino, & ſimilmente di quanta großezza, & altezza ſi fac<lb></lb>ciano li loro mura, & parapetti, & ſimilmente, di quanta longhezza, altezza, & <lb></lb>großezza, ſi faccia cadauna cortina, & par apetti di quelle, & ſimilmente di quan<lb></lb>ta larghezza, & altezza, ſi coſtumano, far le foße.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>eramente che di questo <lb></lb>non ue ne ſaperia dire alcuna minima particolarita, ne per alduta, ne manco per ue<lb></lb>duta, perche (come nel principio dißi à uoſtra Signoria) giamai ho praticato in luo<lb></lb>co doue ſe fortificaſſe, ne manco ho conuerſato con alcuno che di tal coſa habbia no<lb></lb>titia.<emph.end type="italics"></emph.end> P. M<emph type="italics"></emph>o di queſta materia ue ne ſapro rendere buon conto, la qual coſa, ui po<lb></lb>tra giouare, per far li ſopradetti uoſtri modelli ben proportionati, ſecondo il coſtu<lb></lb>me moderno.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o hauero molto accaro di hauerne notitia. </s> <s id="s.001300">Anchor che di tal <lb></lb>coſa non credo di ſeruirmene molto, nondimeno hauero ſommo appiacere ad inten<lb></lb>dere il tutto, per piuriſpetti.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>oglio incominciare dalle cortine. </s> <s id="s.001301">Hor ſappiati, <lb></lb>che alli preſenti tempi, ſi coſtuma di far le cortine nel fondo communamente di groſ<lb></lb>ſezza piedi ſette, & coſi le fanno andar procedendo per fina alla altezza de piedi <lb></lb>diece, & da li in ſuſo ſe fanno ſolamente de piedi dui, ma ui fanno poi li contrafortide <pb xlink:href="042/01/136.jpg"></pb>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></lb>la altezzadi detta cortine, ſi coſtuma far de piedi. </s> <s id="s.001304">34 cominciando dal pian del foſſo. <lb></lb></s> <s id="s.001305">La <expan abbr="lõghezza">longhezza</expan> di dette cortine ſi fa tal hora de paſſa. </s> <s id="s.001306">250. tal hora de paſſa. </s> <s id="s.001307">300. et tal <lb></lb>hora de piu <expan abbr="ſecõdo">ſecondo</expan> il biſogno, come haueti inteſo, ſopra la <expan abbr="piãta">pianta</expan> di Turino, che due del <lb></lb>le ſue cortine ſon de paſſa. </s> <s id="s.001308">360. l'una, & l'altre poco meno. </s> <s id="s.001309">Libaluardi poi nel fondo ſi <lb></lb>fanno di groſſezza de piedi. </s> <s id="s.001310">8. ma per fin alla altezza de piedi. </s> <s id="s.001311">10. ſe uanno reſtringen <lb></lb>do talmente che ſe reduce in piedi. </s> <s id="s.001312">6. (per il retirar della ſcarpa, la qual ſe ua retiran<lb></lb>do in ogni. </s> <s id="s.001313">5. piedi, un piede. </s> <s id="s.001314">Et da quel in ſuſo ſe fa de piedi. </s> <s id="s.001315">2. Ma ui fanno poi li con<lb></lb>traforti, di groſſezza de piedi. </s> <s id="s.001316">2. & longhinel fondo piedi. </s> <s id="s.001317">27. ma in cima ſolamente <lb></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 groſſezza, & di que<lb></lb>sta groſſezzaſe ne fa il parapetto de piedi. </s> <s id="s.001321">18. & il corritore de piedi.<emph.end type="italics"></emph.end> 6. L'<emph type="italics"></emph>altezza di <lb></lb>baluardi ſe fa de piedi. </s> <s id="s.001322">37. che uien ad auanzare piedi. </s> <s id="s.001323">3. di ſopra alle cortine. </s> <s id="s.001324">Le pri<lb></lb>me piazze da baſſo delli detti baluardi ſono alte dal pian del foſſo piedi. </s> <s id="s.001325">17. & coſi le <lb></lb>lor canonere, & lor parapettide piedi. </s> <s id="s.001326">24. di groſſezza. </s> <s id="s.001327">Il merlon ſe fa di altezza <lb></lb>piedi. </s> <s id="s.001328">8. dal pian delle canonere. </s> <s id="s.001329">Et le dette canonere, ſe fanno de piedi. </s> <s id="s.001330">10. in bocca, & <lb></lb>in meggio de piedi. </s> <s id="s.001331">5. La retirata della piazza da baſſo ſi fa di paſſa. </s> <s id="s.001332">10. & la larghez <lb></lb>zaſe fa de paſſa. </s> <s id="s.001333">11. Del piano della piazza di ſotto, à quello della piazza diſopra, ſe <lb></lb>fapiedi. </s> <s id="s.001334">13. di altezza. </s> <s id="s.001335">La piazza granda in ſu la entrata ſe fa di larghezza paſſa. </s> <s id="s.001336">16. <lb></lb>& nel meggio paſſa. </s> <s id="s.001337">28. & di larghezza paſſa. </s> <s id="s.001338">25. & piede uno, cioe piedi. </s> <s id="s.001339">126. & <lb></lb>coſicon tal ordine, e miſura ſe fanno quaſi tutti li baluardi. </s> <s id="s.001340">Li cauallieri, ouer forme <lb></lb>piatte, ſe fanno nel meggio delle cortine, & tai cauallieriſe fanno alcuni di longhez<lb></lb>za paſſa. </s> <s id="s.001341">32. (cioe ſecondo l'andar della cortina) & di larghezza paßa. </s> <s id="s.001342">18. Alcuni al<lb></lb>tri ſi 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></lb>cauallieri ſe fanno communamente de piedi. </s> <s id="s.001345">44. che ueneria ad aſcendere piedi. </s> <s id="s.001346">10. di <lb></lb>ſopra la cortina. </s> <s id="s.001347">Li parapetti de detti cauallieri ſe fanno di groſſezza de piedi. </s> <s id="s.001348">24. Et <lb></lb>coſi con tal ordine, e miſura ſe fanno quaſi tutti li cauallieri, ouer forme piatte. </s> <s id="s.001349">Il foßo <lb></lb>poi nel fondo ſi 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></lb>& coſi con tal ordine, & miſura ſi fa communamente tutte le foße. </s> <s id="s.001353">La contramina poi <lb></lb>ſe fa di larghezza piedi. </s> <s id="s.001354">3. e meggio, & di altezza piedi. </s> <s id="s.001355">7. & ha li ſuoi ſoratori, & ui <lb></lb>ſi fanno anchora due porte per uſcir li fanti, & queſta contramina la fanno ſotto ter<lb></lb>ra, per non indebelir il muro. </s> <s id="s.001356">Et coſi con tal ordine, e miſura ſe procede generalmente <lb></lb>quaſi in tutte le moderne fortificationi.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uinti pezzi di artegliaria ſi coſtuma à <lb></lb>mettere per ogni baluardo.<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>ella prima piazza da baßo ui ſe ne mette dui pez<lb></lb>zi per banda, & queſti tali ui ſe pongono ſolamente per guardia delle cortine, & del <lb></lb>foßo. </s> <s id="s.001357">Et ſimilmente nella piazza di ſopra ui ſe aßetta per quanto ho inteſo nuouamen<lb></lb>te dui, & tal hora tre altri pezzi per banda in cadaun baluardo, & queſti tali guar<lb></lb>dano pur anchorale cortine, e parte del foßo, & credo, che guardano anchora l'altro <lb></lb>baluardo, & maßime uno de detti pezzi.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>t ſopra li cauallieri quanti pezzi ui ſi <lb></lb>coſtuma tenere.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>inque communamente, cioe dui per banda, li quali guardano li <lb></lb>baluardi, & uno che per faccia guarda la campagna.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>i che qualita ſono queſti <lb></lb>tai pezzi, ſi di baluardi, come di cauallieri.<emph.end type="italics"></emph.end> P. A<emph type="italics"></emph>lcuni ſono da. </s> <s id="s.001358">20. alcuni da. </s> <s id="s.001359">30. al<lb></lb>cunida. </s> <s id="s.001360">50. & alcuni da. </s> <s id="s.001361">100. lire di balla.<emph.end type="italics"></emph.end> N. </s> <s id="s.001362">A <emph type="italics"></emph>me non pare, che nelli cauallieri, ne<emph.end type="italics"></emph.end><pb pagenum="69" xlink:href="042/01/137.jpg"></pb><emph type="italics"></emph>ſimilmente nelli baluardi ui ſi conuengono coſi großi pezzi, perche li pezzi großiſo<lb></lb>no (ſecondo il mio parere) ſolamente per rouinar le mura delle citta, & non per tirar <lb></lb>nelli eſſerciti, & li pezzi piccoli, & meggiani, ſono per tirare nelle ordinanze, ouer <lb></lb>nelli eßerciti, & non per rouinar le mura delle citta, perche un pezzo piccolo, ouer un <lb></lb>meggiano, à me mi pare eſſer di tanta faccione, per tirare in una banda de fantaria che <lb></lb>ueniſſe ſotto à tal citta, quanto che ſaria un canon da. </s> <s id="s.001363">50. ouer da. </s> <s id="s.001364">100. & forſi piu.<emph.end type="italics"></emph.end><lb></lb>P. Q<emph type="italics"></emph>ueſta uoſtra opinione non me diſpiace, perche un ſacro, & altri pezzi ſimili, <lb></lb>nel tempo che uorra uno di detti pezzi großi à tirarlo due uolte, ſe potranno tirare <lb></lb>tre uolte, & forſipiu, & tanto effetto fara forſi l'uno, quanto l'altro per cadauna uol <lb></lb>ta.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>oſi è da credere, oltra che ſariano di molto menor ſpeſa, et occupariano man <lb></lb>co luoco.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>ertamente penſando ſopra di uoi ſtago ſtupefatto, che non hauendo uoi <lb></lb>mai tirato, ne dilettato da tirare di artegliaria, archibuſo, ne ſchioppo, ne eſſerui gia<lb></lb>mai eſſercitato, nell'arte militare, ne praticato doue ſe fortifichi alcuna citta, ouer for<lb></lb>tezza. </s> <s id="s.001365">Et che ui baſti l'animo non ſolamente di parlare, ma ditrattar di queste coſe.<emph.end type="italics"></emph.end><lb></lb>N. I<emph type="italics"></emph>l non è da mar auigliarſi di queſto, perche l'occhio mentale uede piu intrinſeca<lb></lb>mente nelle coſe generale, di quello, che fa l'occhio corporale, nelle particolare.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>i <lb></lb>temi un poco, ue aricordati hauermi conoſciuto, quando che io ſtantiaua à Breſſa.<emph.end type="italics"></emph.end><lb></lb>N. M<emph type="italics"></emph>e ne ariccordo ſi, <expan abbr="quãtunque">quantunque</expan> à quel tempo io fuſſe molto piccolo, & per tal ſi<lb></lb>gnale uoſtra Signoria stantiaua in quella contrata, che è fra li Carmini, & Santo Chri <lb></lb>ſtofolo, ouer Santa Chiara nuoua.<emph.end type="italics"></emph.end> P. V<emph type="italics"></emph>oi diceti la uerita: Ditemi anchora, come ſe <lb></lb>chiamaua uoſtro padre.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>io padre hebbe nome Michele. </s> <s id="s.001366">Et perche la natura <lb></lb>non gli fu manco auara in dare à ſua perſona grandezza conneniente, di quello, che fu <lb></lb>la fortuna in farlo partecipe di ſuoi beni, fu chiamato Micheletto.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>ertamente ſe <lb></lb>la natura fu alquanto auara, in dare alla perſona di uoſtro padre grandezza conuenien <lb></lb>te, nanche con uoi è ſtata molto liberale.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o me ne allegro, perche l'eſſer di perſo <lb></lb>na coſi piccolo, mi fa teſtimoniaza che ueramente fui ſuo figlio, perche anchor che il <lb></lb>non mi laſciaſſe al mondo, à me con un'altro mio fratello, & due ſorelle, quaſi ſaluo, che <lb></lb>l'eſſer per buona memoria de lui, mi baſta hauer ſentito à dire da molti che il conoſceua <lb></lb>& praticaua, che egliera huomo da bene, della qual coſa molto piu me ne contento, & <lb></lb>allegro di quello haueria fatto ſe mi haueſſe laſciato di molta facolta con un triſto no<lb></lb>me.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>he eſſercitio faceua uoſtro padre.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>io padre teneua un cauallo, & con <lb></lb>quello correua alla poſta ad iſtantia di Cauallari da Breſſa, cioe portando lettere della <lb></lb>Illuſtrißima Signoria, da Breſſa, à Bergamo, à Crema, à Verona, & altri luochi ſimili.<emph.end type="italics"></emph.end><lb></lb>P. D<emph type="italics"></emph>i che caſataſe chiamaua.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er Dio che io non ſo, ne me aricordo de altra ſua <lb></lb>caſata ne cognome, ſaluo che ſempre il ſentei da piccolino chiamar ſimplicemente Mi <lb></lb>cheletto Cauallaro, potria eſſer che haueſſe hauuto qualche altra caſata, ouer cogno<lb></lb>me, ma non che io ſappia, la cauſa è, che il detto mio padre mi morſe eſſendo io di eta de <lb></lb>anni ſei, uel circa, & coſi restai io, & un'altro mio fratello (poco maggior di me) & <lb></lb>una mia ſorella (menora di me) inſieme con nostra madre uedoua, & liquida di beni <lb></lb>della fortuna, con la quale, non poco dapoi fuſſemo dalla fortuna conquaſſati, che à uo <lb></lb>lerlo raccontar jaria coſa longa, la qual coſa mi dete da penſare in altro, che de inque<lb></lb>rire di che caſata ſe chiamaſſe mio padre.<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>on ſapendo di che caſata ſi chiamaſſe<emph.end type="italics"></emph.end><pb xlink:href="042/01/138.jpg"></pb><emph type="italics"></emph>uoſto o padre, perche ue chiamati coſt Nicolo Tartaglia.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ue diro, quando che <lb></lb>li Frarceſi ſaccheggiorno Breſſa (nel qual ſacco fu preſo la bona memoria del Magni <lb></lb>fico meſſer Andrea Gritti (à quel tempo Proueditore) & fu menato in Franza, oltra <lb></lb>che ne fu ſualiſata la caſa (anchor che poco uifuſſe) ma piu, che eſſendo io fuggito nel <lb></lb>domo di Breſſa inſieme con mia madre, & miaſorella, & molti altri huomini, & don<lb></lb>ne della noſtra contrata, credendone in tal luoco eſſer ſalui almen della perſona, ma tal <lb></lb>penſier ne ando falito, perche in tal chieſa, alla preſentia di mia madre mi fur date cin <lb></lb>que ferite mortale, cioe tre ſu la testa (che in cadauna la panna del ceruello ſi uedeua) <lb></lb>& due ſu la fazza, che ſe la barba non me le occultaſſe, io pareria un mostro, frale <lb></lb>quale una ue ne haueua à trauerſo la bocca, & denti, la qual della maſſela, & palato <lb></lb>ſuperiore me ne fece due parti, & el medeſimo della inferiore: per la qual ferita, non <lb></lb>ſolamente io non poteua parlare (ſaluo, che in gorga, come fanno le gazzole) ma nan <lb></lb>che poteua manzare, perche io non poteua mouere la bocca, nelle maſſele in conto al<lb></lb>cuno, per eſſer quelle (come detto) inſteme con li denti tutte fraccaſſate, talmente, che <lb></lb>biſognaua cibarme ſolamente con cibi liquidi, & con grande induſtria. </s> <s id="s.001367">Ma piu forte <lb></lb>che à mia madre, per non hauer coſi il modo da comprar li unguenti (non che da tuor <lb></lb>medico) fu aſtretta à medicarme ſempre di ſua propria mano, & non con unguenti, <lb></lb>ma ſolamente con el tenermi nettate le ferite ſpeſſo, & tolſe tal eſſempio dalli cani, <lb></lb>che quando quelli ſi trouano feriti, ſi ſanano ſolamente con el tenerſi netta la ferita con <lb></lb>la lingua. </s> <s id="s.001368">Con la qual cautella, in termine di pochi meſi me riduſſe à bon porto, hor <lb></lb>per tornare al noſtro propoſito, eſſendo io quaſi guarrito di tale, et tai ferite, ſtetti un <lb></lb>tempo, che io non poteua ben proferire parole, ma ſempre balbutaua nel parlare, per <lb></lb>cauſa di quella ferita à trauerſo della bocca, & denti (non anchor ben <expan abbr="cõſolidata">conſolidata</expan>) per <lb></lb>il che li putti della mia eta con chi conuerſaua, me impoſero per ſopra nome Tarta<lb></lb>glia. </s> <s id="s.001369">Et perche tal cognome me duro molto tempo, per bona memoria di tal mia di<lb></lb>ſgratia, me apparſo de uolermi chiamare p Nicolo Tartaglia.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>iche eta erate uoi <lb></lb>à quel tempo.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>e anni. </s> <s id="s.001370">12. uel circa.<emph.end type="italics"></emph.end> P. C<emph type="italics"></emph>ertamente la fu coſa molto crudele à <lb></lb>ferire un putto di quella eta, auiſandoui, che mi mar auigliaua di tal uoſtro str anio co <lb></lb>gnome, pche à me mi pareua di <expan abbr="nõ">non</expan> hauer mai alduto ne ſentito à nominar una tal caſa<lb></lb>ta in Breſſa.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a coſa sta preciſamente, come ho narrato à uoſtra Reuerentia.<emph.end type="italics"></emph.end><lb></lb>P. C<emph type="italics"></emph>he fu uoſtro precettore.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>uanti, che mio padre moriſſe, fui mandato al<lb></lb>quanti meſi à ſcola di leggere, ma perche à quel tempo io era molto piccolo, cioe di <lb></lb>eta de anni cinque in ſei, <expan abbr="nõ">non</expan> me aricordo el nome di tal maeſtro, uero è, che eſſendo poi <lb></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 ſcola de ſcriuere <lb></lb>da uno chiamato maeſtro Franceſco, nel qual tempo imparaia fare la.<emph.end type="italics"></emph.end> A.<emph type="italics"></emph>b.c.per fin al<emph.end type="italics"></emph.end><lb></lb>k. <emph type="italics"></emph>de lettra mer canteſca.<emph.end type="italics"></emph.end> P. P<emph type="italics"></emph>erche coſi per fina al.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>& non piu oltra.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er<lb></lb>che li termini del pagamento (con el detto maeſtro) erano di darui cl terzo <expan abbr="auãti">auanti</expan> trat <lb></lb>to, & un'altro terzo quando che ſapeua fare la detta.<emph.end type="italics"></emph.end> A.<emph type="italics"></emph>b.c.per fina al.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>& el reſto <lb></lb>quando, che ſapeua fare tutta la detta.<emph.end type="italics"></emph.end> A.<emph type="italics"></emph>b.c. </s> <s id="s.001374">& perche al detto termine non mi troua <lb></lb>ua coſi li danari de far el debito mio (& deſideroſo de imparare) cercai di hauere alcu <lb></lb>ni diſuoi Alphabeti compiti, & eſſempi de lettera ſcritti di ſua mano, & piu non ui <lb></lb>tornai, perche ſopra de quelli imparai da mia poſta, & coſi da quel giorno in qua, mai<emph.end type="italics"></emph.end><pb pagenum="70" xlink:href="042/01/139.jpg"></pb><emph type="italics"></emph>piu fui, ne andai da aleun'altro precettore, ma ſolamente in compagnia di una figlia di <lb></lb>pouerta, chiamata Induſtria. </s> <s id="s.001375">Soprale opere de gli huomini defonti continuamente mi <lb></lb>ſon trauagliato. </s> <s id="s.001376">Quantunque della età d'anni uinti in qua ſempre ſla ſtato da non poca <lb></lb>cura famigliare straniamente impedito. </s> <s id="s.001377">Et finalmente poi la crudel morte mi ha fatto <lb></lb>reſtare nouamente poco men che ſolo.<emph.end type="italics"></emph.end> P. N<emph type="italics"></emph>on haueti fatto poco, hauendo hauuto cu <lb></lb>ra famigliare a frequentar el ſtudio.<emph.end type="italics"></emph.end> SERVO. S<emph type="italics"></emph>ignor, eglie ſonato cinque hore.<emph.end type="italics"></emph.end><lb></lb>P. Q<emph type="italics"></emph>ueſto nostro ragionamento é ſtato molto piu longo del ſolito, e pero uoglio fac<lb></lb>ciamo fine, ui prego, che piu preſto, che poteti, me fatti quelli modelli, perche molto de <lb></lb>ſidero di uedergli.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on mancaro de ſolicitudine.<emph.end type="italics"></emph.end> P. D<emph type="italics"></emph>itemi un poco, uolendo <lb></lb>far queſti modelli, non deſignareti prima le ſue piante.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio della mag<lb></lb>gior parte deſignaro prima le ſue piante, & dapoi ſopra a quelle andaro eleuando le <lb></lb>ſue cortine, & baluardi, ſecondo, che occorrera.<emph.end type="italics"></emph.end> P. H<emph type="italics"></emph>auero molto accaro, che co<lb></lb>me hauereti deſignate le dette piante, ſubito me le fatte uedere, & deſignatele tutte <lb></lb>pur ſopra la pianta de Turino, perche a mi me pare, che tal forma de Turino (come <lb></lb>nel principio ue dißi) non ſi poſſa megliorare.<emph.end type="italics"></emph.end> N. F<emph type="italics"></emph>aro molto uolentiera, & di que<lb></lb>ſto in breue me ne iſpedirò, perche le piante ſe <expan abbr="deſignarã">deſignaram</expan> preſto.<emph.end type="italics"></emph.end> P. E<emph type="italics"></emph>t queſto è quel <lb></lb>lo, che uoglio dire, che le iſpedireti piu preſto. </s> <s id="s.001378">Et ſpeſſe uolte tanto ſe intende la coſa <lb></lb>ſopra della pianta, quanto che ſopra un modello de releuo.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>oſiè, & ſe pur ui ſa <lb></lb>ra qualche particolarita, che nella pura pianta non ſi poſſa dimoſtrare, cercaremo de <lb></lb>delucidarla con parole, & ſe per caſo con quelle non potro ſodisfare uostra Signoria, <lb></lb>la faremo poi de releuo.<emph.end type="italics"></emph.end> P. A<emph type="italics"></emph>lla buon'hora ſia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001379">I<emph type="italics"></emph>l fine del ſesto Libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/140.jpg"></pb> <p type="head"> <s id="s.001380">LA GIONTA DEL SESTO <lb></lb>LIBRO DI QVESITI, ET INVENTIONI DIVERSE <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.001381">N<emph type="italics"></emph>ella quale ſi dimoſtra un primo modo diredure una citta ineſpugnabi<lb></lb>le, & che non potra eſſer battuta, ne danneggiata da nemici <lb></lb>con le artegliarie, con altre particolar <lb></lb>ſottilita.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001382">QVESITO PRIMO FATTO DAL MAGNIFICO, <lb></lb><emph type="italics"></emph>& Clarißimo Signor Marc' Antonio Moroſini Dottor, <lb></lb>& Philoſopho Eccellentißimo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001383">SIGNOR MARC'ANTONIO. S<emph type="italics"></emph>on molto deſideroſo <lb></lb>ſier Nicolo di uedere in diſegno, ouer in figura quelle piante de <lb></lb>fortificationi, che gia prometteſti di mostrare al Prior di Barlet <lb></lb>ta, cioe con quelle ſei qualita, ouer conditioni, che nel uoſtro ſeſto <lb></lb>libro preponete: perche tutte me paiono coſe ingenioſe, <expan abbr="nõ">non</expan> piu au <lb></lb>dite, ne uedute, ne conſiderate d'alcuno altro, & ſe poßibel é di po<lb></lb>terle mandar à eſſecutione (come credo) ſara coſa utilißima, & <lb></lb>maßime quella uostra terza qualita, ouer conditione, nella quale diceti, che uoleti, che <lb></lb>la forma delle mura di una citta ſia talmedte diſpoſita, che ſe per ſorte li nemici delibe<lb></lb>raſſeno di darui la battaglia generale, chel non ſi troui alcuna parte di quella, che poſ <lb></lb>ſa eſſer aſſaltata da nemici, che quelli non poßino eſſer ſempre offeſi da quelli dalla <lb></lb>terra, al men da quattro bande con le artegliarie: il che potendoſi fare, me pareria co<lb></lb>ſa grande, e pero queſta tal qualita, ouer conditione haueria piu accaro di uedere de <lb></lb>qual ſi uoglia delle altre cinque.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oſtra Eccellentia, Signor Magnifico, ſa, che <lb></lb>mi puo comandare, & per tanto non ſolamente le predette ſei qualita moſtraro in di<lb></lb>ſegno à Voſtra Magnificentia, ma molte altre inueſtigate dapoi: perche (come dice il <lb></lb>prouerbio) di coſa ſempre naſce coſa, cioe trouata che ſia una coſa, ſempre ui ſi troua <lb></lb>di megliorarla, & di farla molto meglio. </s> <s id="s.001384">Ma biſogna notare, che tutte tai qualita, <lb></lb>ouer conditioni non ſi conuengono in una medeſima forma de fortificatione, anci par<lb></lb>te ſe conuengono in una, & parte in un'altra: & perche le forme de fortificare da me <lb></lb>immaginate, & ritrouate ſono molte, ſecondo uarij reſpetti delle quale alcune ſi difen <lb></lb>dono con baluardi, & cauallieri, ſecondo, che communamente ſi coſtuma nelle moder<lb></lb>ne fortificationi, ma ſotto altra forma. </s> <s id="s.001385">Altre poi ſi difendono per altri uarij, & inge<lb></lb>nioſi modi, l'uno molto piu ſicuro, & di molto manco ſpeſa dell'altro: Ma perche à uo<lb></lb>ler moſtr are in diſegno tutte le dette forme in un tratto generariano confuſione à Vo<lb></lb>ſtra Eccellentia, e pero li andaro mostrando à una per una, & uoglio cominciare dalla <lb></lb>piu triſta, come coſtumano li botegheri nel moſtrar le ſue merce, che tengono da uen<lb></lb>dere. </s> <s id="s.001386">Et queſto tal modo, ouer formaſara di maggior ſpeſa de tutti li altri: perche ſara <lb></lb>diſeſo con baluardi, & cauallieri, ſi come, che alli preſenti tempi ſi coſtuma, ma ſotto<emph.end type="italics"></emph.end><pb pagenum="71" xlink:href="042/01/141.jpg"></pb><emph type="italics"></emph>altra forma & con altre particolarita de piu. </s> <s id="s.001387">Et queſto tal modo, ouer forma nonſo <lb></lb>lamente hauera in ſe quella noſtra terza qualita, ouer conditione, che Voſtra Magni<lb></lb>ficentia tanto deſidera di uedere: ma hauera anchora in ſe la ſeconda, & terza, & <lb></lb>piu, che la non potra eßer danneggiata da nemici con le artegliarie, come, che ſopra <lb></lb>il diſegno de due ſole cortine intiere, & parte de due altre inſieme congionte con le ſue <lb></lb>foſſe, baluardi, & cauallieri alli ſuoi conſueti luochi, à quella faro uedere, & toccare.<emph.end type="italics"></emph.end><lb></lb>S.M. Q<emph type="italics"></emph>ueſto hauero ben accaro di uedere.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto ſotto ſcritto, Signor Clariſ <lb></lb>ſimo, è il diſegno di quelle cortine di ſopra narrate à Voſtra Magnificentia, ſecondo la <lb></lb>forma delle quale, uoglio, che ſiano fatte tutte le cortine, foſſe, baluardi, & cauallieri, <lb></lb>che circondano tal citta, cioe far, che ogni due cortine uadino à ingolfarſi con dui capi <lb></lb>uerſo il corpo della citta, formando un angolo ottuſo, ſi come fanno le ſotto ſcritte due <lb></lb>a.b.&.c.b. in ponto. </s> <s id="s.001388">b. & che li altri dui capi ſe iſtendino in fuora, cauſando con le al <lb></lb>tre due circonſtante cortine dui alti angoli ottuſi, uerſo la campagna, come fanno le <lb></lb>medeſime ſottoſcritte.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></lb>in ciaſcun de detti angoli ui ſe gli debbe conſtituir un baluardo, ſecondo, che nelle det<lb></lb>te moderne fortificationi ſi coſtuma <expan abbr="cõ">com</expan> le ſue canonere nella piazza da baſſo, che guar <lb></lb>dino non ſolamente le due circostante cortine, & foſſe, ma anchora li dui circoſtanti <lb></lb>baluardi: male canonere della piazza di ſopra parte debbono guardare pur le due <lb></lb>circoſtante cortine, foſſe, & baluardi, et parte guardino minutamente quel ſpatio in<lb></lb>golfato dentro dalle lettere.o.y.<emph.end type="italics"></emph.end> 4.z.<emph type="italics"></emph>m.l.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>h.i.n.o.& anchora la campagna di fuora <lb></lb>dalle lettere.o.y.<emph.end type="italics"></emph.end>z.<emph type="italics"></emph>m.& maßime li dui baluardi.a.&.c.non ſolamente debbono guar <lb></lb>dar la campagna, ma l'uno debbe guardar l'argine, che è oppoſito all'altro, cioe il ba<lb></lb>luardo.a.debbe guardar quel ſpacio, che è di fora dil ponto.o. </s> <s id="s.001391">& il baluardo. </s> <s id="s.001392">c. debbe <lb></lb>guardare quel ſpacio, che è di fora del ponto. </s> <s id="s.001393">m. & il baluardo. </s> <s id="s.001394">b. non ſolamente deb<lb></lb>te guardar per tutto il detto ſpatio, dentro delle dette lettere.o.y. </s> <s id="s.001395">4. z.m.l.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>h.i.n.o. <lb></lb>& anchora di fora da dette lettere: ma particolarmente debbe guardare à longo, do<lb></lb>ue ſono.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>l.m. </s> <s id="s.001396">&. </s> <s id="s.001397">i.n.o. </s> <s id="s.001398">Et fatto queſto, uolendo ſeguir il moderno uſo di fortificare, <lb></lb>ſi debbe far nel meggio della ſummita de ciaſcuna cortina un caualleretto, ſi come ſo<lb></lb>no li dui.f.g.nou molto larghi, ne longhi, ma ſolamente di tal capacita, che ui poſſa ſtar <lb></lb>ſuſo dui, ouer tre ſacri, per cadauno, & l'officio de questi dui caualleretti ſia princi<lb></lb>palmente di guardar li dui circoſtanti baluardi: & oltra di queſto uoglio, che guardi<lb></lb>no quel ſpatio ingolfato, & anchora la campagna istrinſeca, uero è, che il caualliero <lb></lb>f. forſi con difficulta potra guardare quella riuera de fora della foſſa, che procede ſe<lb></lb>condo le lettere.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>l.m.per eſſer troppo ſotto di lui: ma tal riuera.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>l.m.ſara commo<lb></lb>damente guardata dall'altro caualleretto. </s> <s id="s.001399">g. & dal baluardo. </s> <s id="s.001400">b. & il detto caualliero <lb></lb>f.inſieme con el detto baluardo. </s> <s id="s.001401">b. <expan abbr="guardarãno">guardaranno</expan> commodamente la riuera, ouer argine, <lb></lb>che procede ſecondo le lettere.i.n.o. </s> <s id="s.001402">Oltra di queſto uoglio, che da l'una, et l'altra ban <lb></lb>da del baluardo. </s> <s id="s.001403">b. ſia fatto un caualleretto piccolo quadrangolo (ſi come ſono li dui.f. <lb></lb></s> <s id="s.001404">&.g.) oueramente tondo nella ſummita, ſi come ſono li dui ſignati per. </s> <s id="s.001405">2. & 3. di tal ca <lb></lb>pacita, che ui ſe poſſa accommodar ſopra, pur dui, ouer tre ſacri da. </s> <s id="s.001406">12. lire di balla p<lb></lb>ciaſcadun de loro, & uoglio, che ciaſcaduno de loro ſia talmente aſſettato, che poſſa <lb></lb>guardare l'uno, & l'altro di dui baluardi. </s> <s id="s.001407">a. &. </s> <s id="s.001408">c. la qual coſa ſi potra fare facilmente <pb xlink:href="042/01/142.jpg"></pb>perche ſenſibilmente ſi uede, che il cauallero. </s> <s id="s.001409">2. puo guardare, et difendere la banda. u.<lb></lb>x, del baluardo. </s> <s id="s.001410">c. & ſimilmente la banda.s.t.del baluardo. </s> <s id="s.001411">a. & quelle medeſime puol <lb></lb>guardar anchora lo cauallero. </s> <s id="s.001412">3. Et oltra di queſto uoglio che guardino per longo uia <lb></lb>tutto quel ſpacio ingolfato per fin nella campagna iſtrinſeca, & maßime uoglio, che <lb></lb>guardino quelle riuere, ouer ſpacij arginati, che procedono ſecondo le lettere.i.n.o.&<emph.end type="italics"></emph.end><lb></lb>k.<emph type="italics"></emph>l.m.ilche commodamente far anno, uero è, che diſcommodamente potr anno guar da<lb></lb>re il ſpacio, che procede ſecondo le lettere.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>h.i.per eſſer forſi troppo ſotto de loro, ma <lb></lb>tal parte potra eſſer facilmente guardata, & difeſa dalli dui baluardi. </s> <s id="s.001413">a. &. </s> <s id="s.001414">c. & dalli <lb></lb>dui caualleri. </s> <s id="s.001415">f. &. </s> <s id="s.001416">g. & da molte altre bande, come nel noſtro proceſſo ſe intendera. <lb></lb></s> <s id="s.001417">Perche uoglio anchora, che nella ſommita di ciaſc aduna cortina (per longo uia) ſia fat<lb></lb>to contr auetti piantati, & buone tauole molte parianette alte alquanto piu dell'altez<lb></lb>za de un'huomo, le quai parianette trauerſino tutta la ſommita della detta cortina, ma <lb></lb>che tal trauerſamento non uadi ad angolo retto ſopra alla detta cortina, anci uoglio, <lb></lb>che procedano con la parte di fuora alquanto uerſo la citta, & conla parte di dentro <lb></lb>obliquarſi in fuora uerſo la campagna, come ſi uede deſignato nella preſente figura, ue <lb></lb>ro è, che le dette parianette uogliono eſſer alquanto piu oblique di quello che moſtra la <lb></lb>figura per le ragioni, che di ſotto ſe dira, fatto queſto, uoglio che dalla banda che guar <lb></lb>da uerſo la campagna di ciaſcaduna di dette parianette ue ſia fatto un'arginetto di ter<lb></lb>ra (come ſi uede nelle due parianette. </s> <s id="s.001418">p.&.r.) di tanta groſſezza, che non poſſa eſſer <lb></lb>danneggiato da nemici con le ſue artegliarie, & ſotto à ciaſcaduno de detti argenetti, <lb></lb>uoglio che ui ſia aſſettato, ouer poſto un falconetto da. </s> <s id="s.001419">6. ouer da. </s> <s id="s.001420">3. lire di balla, & per <lb></lb>queſto uoglio che le dette parianette, & argenetti ſiano alti alquanto piu de un'huomo, <lb></lb>accio che facciano ſcudo à ciaſcun de detti falconetti, che non poſſano eſſer danneggiati <lb></lb>da nemici con le ſue artegliarie, & uoglio anchora che tai argenetti ſtiano alquanto <lb></lb>obliqui con la parte dauanti uerſo la citta, accio che li nemici non poßino uedere ne ti<lb></lb>rare per la parte dauanti ſotto alli detti argenetti, cioe nel luoco doue ſta li detti falco<lb></lb>netti, perche il proprio officio de tutti queſti falconetti, uoglio che ſia di guardare mi<lb></lb>nutamente tutto quel ſpacio ingolfato fra le gia dette lettere.o.y.z.m.l.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>h.i.n. </s> <s id="s.001421">& al<lb></lb>quanto piu in fuora del angolo.o.&.m.cioe cercar de far che gli falconetti della cor<lb></lb>tina.a.b.tutti poßino tirare, & guardare ſtanti ſotto al ſuo arginetto, per otto, ouer <lb></lb>dieci paſſa piu in fuora del ponto.o.& quelli della cortina.c.b. </s> <s id="s.001422">guardino il medeſimo <lb></lb>piu in fuora del ponto.m.accio che niun ſia ſicuro ſotto alli argini di terra, che ſar an<lb></lb>no di fuora del foſſo à de rimpetto delli dui baluardi.a.&.c.perche nel far delli foßi, <lb></lb>ouer foſſe, uoglio che la mitta della terra, che ſene caua ſia gettata di dentro della citta <lb></lb>per far li argeni de drio alle cortine con li ſuoi contraforti, come ſi coſtuma nelle mo<lb></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 foſ<lb></lb>ſa di fuora uia ſia fatto un muro commune ſecondo l'andar della detta foſſa, alto circa <lb></lb>dui piedi manco della cortina di dentro, & à quel tal muro di fuora uia farui li ſuoi con <lb></lb>traforti, & fra quelli contr aforti gettarui quella mitta della terra, che ſe caua della gia <lb></lb>detta foſſa, facendo con tal terra ungroſſo argine di fuora uia di tal muro il qual argi<lb></lb>ne uada procedendo ſecondo le lettere.m.l.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>h.i.n.o. </s> <s id="s.001425">& diſcendendo à ſcarpa uerſo lo <lb></lb>ingolfato ſpacio, che è diſuora uia, il qual argine oltra che uenira à far ſcudo quaſi à tut<emph.end type="italics"></emph.end><pb xlink:href="042/01/143.jpg"></pb><figure id="id.042.01.143.1.jpg" xlink:href="042/01/143/1.jpg"></figure><pb pagenum="72" xlink:href="042/01/144.jpg"></pb><emph type="italics"></emph>ta la cortina, et à tutti li baluardi <21>che de <27>lli <expan abbr="nõ">non</expan> potra eſſer uisto ne battuto da nemici <lb></lb><expan abbr="cõ">com</expan> le ſue artegliarie, eccetto che <27>lla ſoprema parte de dui piedi, cheſe laſcera ſcoperiæ <lb></lb><21> poter tirar di fuora <expan abbr="cõ">com</expan> le artegliarie della citta. </s> <s id="s.001426">Et <27>l ſpacio largo. </s> <s id="s.001427">12. piedi, uel cir <lb></lb>ca (laſciato fra la foſſa, et lo detto argine di fuora) formara una uia coperta, ouer ſe<lb></lb>creta, <21> laquale potra andare <expan abbr="ſecretamẽte">ſecretamente</expan> caualli, et fanti, et altri ſicuramente à torno <lb></lb>atorno di fuora uia di tal citta, cioe atorno della foſſa di fuora uia, et ſe douera laſciar al <lb></lb>cune aperture <expan abbr="penetrãte">penetrante</expan> il muro, quaſi tutto l'argine, cheſe dicono porte falſe fatte di <lb></lb>muro ſempio, cioe duna piera, coperte difuora uia <expan abbr="leggiermẽte">leggiermente</expan> di terra, accio che <21> tut <lb></lb>to ui paia argine, le quai porte falſe ſi poßino <expan abbr="facilmẽte">facilmente</expan> rouinare <21> poter uſcir <expan abbr="tacitamẽ">tacitamen</expan> <lb></lb>te la notte, & andare à far qualche ſtrettagema, ouer iprouiſoaſſalto alli nemici, le quai <lb></lb>porte falſe ſe 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 ſimili lo <lb></lb>chi, uero è, che tal uia ſecreta, o uogliam dir coperta non ſi diſcernera nella noſtra figu <lb></lb>ra, perche la non ui è stata poſta, perche <expan abbr="uolẽdola">uolendola</expan> far à miſura ſaria da ſe coſa inſenſibi <lb></lb>le, et reſtaria in tutto coperta dal noſtro argine, e pero biſogna che <expan abbr="cõ">com</expan> la pura imaginæ <lb></lb>tiua ſia uiſta, et inteſa. </s> <s id="s.001428">Et queſta tal uia uenira à eſſer ottimamente guardata, et difeſa, <lb></lb>non ſolamente 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="ſtarã">ſtaram</expan> <lb></lb>no ſotto à quelli argenetti della ſua oppoſita cortina, ma anchora piu minutamente ſaræ <lb></lb>guardata, et difeſa da quelli archibuſeri, che <expan abbr="ſarãno">ſaranno</expan> ſotto alli medeſimi arginetti, <21>che <lb></lb>tal uia uoglio che la ſia totalmente diſcoperta uerſo la citta, la qual uia hauera anchora <lb></lb>queſt'altra proprieta, cheſe nella foſſa non ui fuſſe acqua, et che li nemici per ſorte con <lb></lb>trincere penetr aſſono nella detta foſſa, per minare, ouer ſcalare le mura, ouer corti<lb></lb>ne di tal citta quelli della terra <expan abbr="potrãno">potranno</expan> uenire <expan abbr="ſicuramẽte">ſicuramente</expan> per tal uia à offendere li det <lb></lb>ti nemici nella ſchena con archibuſi, balestre, archi, et altre coſe ſimili. </s> <s id="s.001431">Dico oltra à quel <lb></lb>lo, che <expan abbr="farãno">faranno</expan> poi li baluardi, caualleri, falconetti, et archibuſi, che <expan abbr="ſarãno">ſaranno</expan> ſu la cortina <lb></lb>di <expan abbr="dẽtro">dentro</expan> della citta. </s> <s id="s.001432">Et coſi ſara <expan abbr="cõpita">compita</expan> <27>ſta noſtra prima forma de fortificare, la qual <lb></lb>forma ſe trouara bauere in ſe non ſolamente tutte quelle. </s> <s id="s.001433">3. qualita, ouer <expan abbr="cõditioni">conditioni</expan> det <lb></lb>te, nel. </s> <s id="s.001434">3. 4. et. </s> <s id="s.001435">5. queſito del noſtro. </s> <s id="s.001436">6. libro (come che.<emph.end type="italics"></emph.end> V.M. <emph type="italics"></emph><expan abbr="cõ">com</expan> il ſuo ſano intelletto puo <lb></lb><expan abbr="facilmẽte">facilmente</expan> <expan abbr="cõprẽdere">comprendere</expan>) ma ui ba anchora queſto de piu, che tal citta (come fu detto diſo<lb></lb>pra) <expan abbr="nõ">non</expan> puo eſſer <expan abbr="dãneggiata">danneggiata</expan> da nemici <expan abbr="cõ">com</expan> le artegliarie, la qual coſa di <expan abbr="quãta">quanta</expan> autorita, <lb></lb>et importantia la ſta, à<emph.end type="italics"></emph.end> V.M. <emph type="italics"></emph>ne laſſo il giudicio. </s> <s id="s.001437">Poi di quella uia coperta, o <expan abbr="uogliã">uogliam</expan> dir <lb></lb>ſecreta, <expan abbr="nõ">non</expan> uoglio ſtar à narrare di <expan abbr="quãta">quanta</expan> <expan abbr="cõmodita">commodita</expan>, et utilita, la ſia à quelli della terra, <lb></lb>et de <expan abbr="dãno">danno</expan> et terrore alli nemici <21> cauſa delli improuiſi <expan abbr="aſſalimẽii">aſſalimenii</expan>, che di notte gli <expan abbr="uerrã">uerram</expan> <lb></lb>no fatti da diuerſe <expan abbr="bãde">bande</expan> <21> uia di quelle porte falſe. </s> <s id="s.001438">Et accio che<emph.end type="italics"></emph.end> V.M. <emph type="italics"></emph>poſſa groſſo mo<lb></lb>do <expan abbr="intẽdere">intendere</expan>, le miſure, et <expan abbr="diſtãtie">diſtantie</expan> di tal noſtra forma ui ho deſcritta la ſcala, da noi uſata <lb></lb>nella deſignation di quella, la qual ſcala è la linea.<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph><expan abbr="lõga">longa</expan> paſſa. </s> <s id="s.001439">120. uero che nelle ma <lb></lb>terie piccole <expan abbr="nõ">non</expan> ui ſe è oſſeruato le ſue debite miſure.<emph.end type="italics"></emph.end> S.M. N<emph type="italics"></emph><expan abbr="õ">om</expan> me importa à uederla <lb></lb><expan abbr="tãto">tanto</expan> p ſottile, mi baſta aſſai, che gli uedo quella uostra. </s> <s id="s.001440">3. qualita, ouer <expan abbr="cõditione">conditione</expan> da me <lb></lb>deſider ata di uedere, et molto maggiore di quello preponeti nel. </s> <s id="s.001441">5. queſito. </s> <s id="s.001442">Perche ue<lb></lb>do chiaramente, che ſe li nemici deliberaßeno di dar una battagia generale à tal citta <lb></lb>ſubito, che quelli ſar anno entrati in quello ingolfato piano, cioe di dentro da quelle <lb></lb>lettere m.z. 4. y.o.nõ ſolamente ſar anno offeſi da quelli della terra da quattro ban<lb></lb>de con le artegliarie, ma da piu de. </s> <s id="s.001443">20. bande, perche conoſco, che non ſolamente ſa<lb></lb>ranno offeſi 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"></pb>falconetti, che ſar anno ſot<lb></lb>to à quelli argenetti per lon <lb></lb>go all'una, e l'altra cortina, <lb></lb>e perche comprendo eſſere <lb></lb>impoßibile da potere eſſere <lb></lb>ouiate tai difeſe da nemici, <lb></lb>non credo che ſariano coſi <lb></lb>pazzi, per großi che fuſſe<lb></lb>no che ſe metteßono à tal im <lb></lb>preſa, cioe à uoler dar batta <lb></lb>glia à una citta, talmente for <lb></lb>tificata, eglie <expan abbr="bẽ">bem</expan> uero, che tal <lb></lb>forma è alquanto moſtruoſa <lb></lb>dauedere, nel reſto poi la <expan abbr="cõ">com</expan> <lb></lb>mendamo aſſai.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor <lb></lb>Clarißimo, ſe la natura ha<lb></lb>ueſſe principiato, & ſempre <lb></lb>continuato à far tutti glihuo <lb></lb>mini ſenza naſo, et ſenzao<lb></lb>recchie, et che dapoi per ſor <lb></lb>te ne faceſſe uno con il naſo, <lb></lb>et orecchie, certamente à tut <lb></lb>ti glialtri huomini pareria <lb></lb>coſa moſtruoſa da uedere, il <lb></lb>medeſimo dico di questa no<lb></lb>ſtra forma de fortificatione, <lb></lb>la quale per eſſer molto di<lb></lb>uerſa dall'uſo <expan abbr="cõmune">commune</expan>, à quel <lb></lb>la pare, & à molti altri pa<lb></lb>rera mostruoſa coſa da ue<lb></lb>dere, pur ſia, come ſi uoglia, <lb></lb>doue, che è neceſſario la for <lb></lb>tezza, non ſi debbe far con<lb></lb>to di bellezza.<emph.end type="italics"></emph.end> S. M. E<lb></lb><emph type="italics"></emph>glie il uero.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.145.1.jpg" xlink:href="042/01/145/1.jpg"></figure> <pb pagenum="73" xlink:href="042/01/146.jpg"></pb> <p type="head"> <s id="s.001447">QVESITO SECONDO FATO CONSEQ VENTE<lb></lb><emph type="italics"></emph>mente dal medeſimo Magnifico, & Eccellentißimo <lb></lb>Dottor, Signor Marc' Antonio <lb></lb>Moroſini.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001448">SIGNOR MARC'ANTONIO. M<emph type="italics"></emph>a ditime un pnco, uolendo uoi, che <lb></lb>tutte le cortine, che hanno da circondare tal citta procedano ſecondo l'ordine de <lb></lb>le predette, doue uorete poi, che ſiano fatte le porte neceſſarie à tal citta.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor <lb></lb>Magnifico tutte le porte neceſſarie à tal citta, uoglio, che ſiano fatti in quelli angoli <lb></lb>ingolfati uerſo la citta, cioe, doue, che nella figura paſſata fu fatto il baluardo. </s> <s id="s.001449">b. per<lb></lb>cha tai angoli, ouer luochi ſono le piu ſicure parti di tutto il contorno di tal citta. </s> <s id="s.001450">Ma <lb></lb>biſogna farle far con tal modo, e forma, che dalla banda deſtra, & ſiniſtra di quella ui <lb></lb>ſe gli poſſa accommodar dui, ouer tre ſacri, che guardino non ſolamente l'una, e l'altra <lb></lb>cortina, & ſimelmente li dui circostanti baluardi, inſiene <expan abbr="cõ">com</expan> el foſſo, ma anchora quel<lb></lb>la uia coperta dal argine, cioe, che fu laſſata fra l'argine, & il foſſo, ouer foſſa, la qual <lb></lb>coſa ſara facilißima da fare, et <expan abbr="ſimelmẽte">ſimelmente</expan>, far ſopra alla detta porta, cioe nella ſummita <lb></lb>de la cortina, fra li dui caualleretti, un luoco di poterui aſſettar tre, ouer quattro ſa<lb></lb>cri, che poßino tirare, & guardare à <expan abbr="lõgo">longo</expan> per tutto quel ſpacio ingolfato, & maßime <lb></lb>per longo alli argini, cioe doue procedono le lettere.m.l.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>i.n.o. </s> <s id="s.001451">& anchora per quel <lb></lb>la uia coperta, & nella campagna iſteriore, uero è, che lo ingreſſo di andare alla det<lb></lb>ta porta non uoglio, che ſi faccia nel argine.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>h.i. </s> <s id="s.001452">Anci uoglio, che tal ingreſſo ſia fat <lb></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. &. </s> <s id="s.001454">o. <lb></lb>& tal ingreſſo, ouer intrata ſi debbe far con una porta ſoda. </s> <s id="s.001455">ouer con un ponte leuato <lb></lb>re, che habbia un poco di foſſettaſotto, & coſi tal ingreſſo ſara ſicurißimo, perche tut <lb></lb>ti quelli, che uor anno intrar dentro di tal citta, ò ſiano carri, caualli, ouer pedoni, ſara <lb></lb>neceſſario, che per un pezzo camineno per quella uia coperta à quelli di fuora, ma tut <lb></lb><gap></gap> diſcoperta à quelli, che ſar anno ſopra le cortine della citta ſotto à quelli argenetti <lb></lb>piu uolte detti, nelli quali luochi, oltra li falconetti, ui puo ſtare ſicur amente molti ar<lb></lb>chibuſeri, come fu detto nel principio, e pero ſe li nemici con qualche inganno pigliaße <lb></lb>no tal ingreſſo, porta, ouer ponte, nanti che poteſſono peruenir alla principal porta, <lb></lb>da piu bande ſaranno rebattuti, & mal trattati, & la detta porta principale hauera <lb></lb>commodita, & tempo abondante da eſſer ſerrata, & quella ſerrata, che ſia, li nemici <lb></lb>ſar anno sforzati (ſe non uor anno morire) à torſe fuora di tal uia, & ritornarſene alli <lb></lb>ſuoi alloggiamenti conſuo grandißimo danno, & uergogna per eſſer tal uia in ogni lo <lb></lb>co diſcoperta à quelli, che ſar anno ſopra la ſummita della cortina, & anchora alli ba<lb></lb>luardi, et cauallereti, come di ſopra fu detto, uero é, che tal uia dal primo ingreſſo per <lb></lb>fin alla porta principale della citta uuol eſſer tanto larga, che incontr andoſi dui carri <lb></lb>carghi l'uno poſſa dar luoco all'altro di paſſare.<emph.end type="italics"></emph.end> S.M. C<emph type="italics"></emph>ertamente, che queſta uo<lb></lb>ſtra prima forma è molto artificioſamente compoſta, tal che à me pare eſſer ineſpu<lb></lb>gnabile. </s> <s id="s.001456">Et uoi dite, che la è la piu triſta de tutte le altre, & io non poſſo imaginare, co <lb></lb>me ſia poßibile de megliorarla, ma per eſſer bora tarda, uoglio, che poniamo fine à tal <lb></lb>ragionamento.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>l piacer di quella.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/147.jpg"></pb> <p type="head"> <s id="s.001457">QVESITO TERZO FATTO DAL MEDESIMO <lb></lb>M<emph type="italics"></emph>agnifico, & Eccellentißimo Dottor, Signor <lb></lb>Marc' Antonio Moroſini.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001458">SIGNOR MARC'ANTONIO. N<emph type="italics"></emph>on ſaria buona coſa à far far ancho<lb></lb>ra quel tal argine, & quella uia coperta alle citta, che ſono gia fortificate, accio, <lb></lb>che li nemici non le poteßino battere con le artegliarie, accettuando in quella poca par <lb></lb>te apparente di ſopra di tai argini.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on ſignor Magnifico, perche le forme, che <lb></lb>ſi costuma à dare à tai fortificationi nol comportano, anci ſaria tai argini molto noci<lb></lb>ui à quelli della citta: perche ſotto de quelli (cioe dalla banda de fora) ui potria ſicura<lb></lb>mente ſtar li nemici, & quelli con trincere potriano penetrar in diuerſi luochi li detti <lb></lb>argini, & anchora intrar nella foſſa, con el farui larghe, & profonde aperture, e per <lb></lb>quelle battere in diuerſi luochi ſicuramente le mura, ouer cortine di tal citta, la qual <lb></lb>coſa non puo occorrere nella noſtra forma, perche ſe quella ben ſe arricorda, la parte <lb></lb>de fora dello detto argine, ouer argini (cioe, doue ſono le lettere.m.l.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>h.i.n.o.è otti<lb></lb>mamente guardata, & difeſa da uarie, & diuerſe bande.<emph.end type="italics"></emph.end> S.M. M<emph type="italics"></emph>e ne arricordo, et <lb></lb>comprendo, che uoi diceti il uero. </s> <s id="s.001459">Questo debbe eſſere quel modo de fortificare, <lb></lb>che preponeti nello ottauo Queſito del uoſtro ſesto Libro: Perche uedo, che quelli <lb></lb>della terra potr anno andare ſicuramente à lauorare, ſeminare, e riccogliere per <lb></lb>tutti quelli ſpacij di terreno, che ſe <expan abbr="ingoifarãno">ingoifaranno</expan> à torno al circuito di tal citta, ſimili à <lb></lb>quello, che è dentro delle lettere.m.z. </s> <s id="s.001460">4. y.o. ma anchora molto piu in fora delle det<lb></lb>te lettere: & oltra di queſto tal citta non potra eſſer battuta, ne danneggiata da nemi<lb></lb>ci con le artegliarie, come ſe prepone del detto Queſito.<emph.end type="italics"></emph.end> 8. N. N<emph type="italics"></emph>on ſignor Magnifico, <lb></lb>che tal modo non è queſto, anci quello aßicurara tal paeſe, per piu di tre tanto lontano <lb></lb>dalle mura di tal citta, & con molto e molto <expan abbr="mãco">manco</expan> ſpeſa, di quello intrara in queſtaſor <lb></lb>te de fortificatione, & queſto moſtraro da far per due diuerſe uie, come, che in fine à <lb></lb>uoſtra Eccellentia gli faro uedere.<emph.end type="italics"></emph.end> S.M. C<emph type="italics"></emph>erto gran coſa me parera, ſe uoi me fare <lb></lb>tiucder una tal opra con ſi pocaſpeſa.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001461">QVESITO QVARTO FATTO DAL MEDESIMO <lb></lb>M<emph type="italics"></emph>agnifico, & Eccellentißimo Dottor, Signor <lb></lb>Marc' Antonio Moroſini.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001462">SIGNOR MARC'ANTONIO. M<emph type="italics"></emph>ireſta da dirui, perche cauſa uoleti <lb></lb>coſi, che langolo fatto delle due cor tine in ponto.b.ſia ottuſo, & non retto, ne acu <lb></lb>to.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>erche ſe langolo.b.foſſe retto, ouer acuto (uolendo procedere regolatamen <lb></lb>te) ſaria neceſſario à far li angoli.a.&.c.di quella medeſima qualita, & nelli angoli <lb></lb>retti, ouer ottuſi non ui ſe puo far baluardo, che uaglia, & queſto procede, perche lan <lb></lb>golo del baluardo è neceſſario à farlo menore del angolo delle dette cortine, perche, <lb></lb>che lo faceſſe equale, ouer maggior di quello, el ſaria impoßibile tal baluardo à poter <lb></lb>eſſer guardato da alcun delli altri dui circoſtanti baluardi. </s> <s id="s.001463">Et ſaria anchora impoßi<lb></lb>bile à poter far in alcun luoco ſopra l'una, & l'altra cortina un cauallero, che lo po-<emph.end type="italics"></emph.end><pb pagenum="74" xlink:href="042/01/148.jpg"></pb><emph type="italics"></emph>teſſe guardare: onde facendo <expan abbr="lãgolo">langolo</expan> di tal baluardo acuto, ueneria debelißimo, tal che <lb></lb>con facilita potria eſſer ruinato da nemici con le artegliarie.<emph.end type="italics"></emph.end> S.M. P<emph type="italics"></emph>erche cauſa ſe<lb></lb>guitaria, cheſe langolo del baluardo fuſſe eguale, ouer maggiore del angolo compreſo <lb></lb>dalle due cortine, eſſer impoßibile à poter eſſer guardato dalli dui circoſtanti baluar<lb></lb>di, & manco da alcun cauallero, che fuſſe ſopra à l'una, e l'altra cortina.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor <lb></lb>Magnifico, per aßignar la cauſa di queſto, ſupponamo, che langolo compreſo da due <lb></lb>cortine ſia langolo.a.b.c.& che le dette due cortine, ouer che la iſtenſion di quelle ſia <lb></lb>ſecondo le due linee.a.b.&.b.c.hor uolendo conſtituir rettamente un baluardo ſopra <lb></lb>à tal angolo.a.b.c.diuideremo tal angolo in due partiequali (ſecondo l'ordine dato de <lb></lb>Euclide nella nona del primo) con la linea.d.b.e.f.& in qual ponto ne parera nella li<lb></lb>nea iſtrinſica.b.e.f.conſtituiremo un angolo (per la. </s> <s id="s.001464">31. del primo di Eutlide) equale ſi <lb></lb>quel angolo, che ne parera di fare langolo del noſtro baluardo, ma farlo contal condi<lb></lb>tione, che tal angolo ſia diuiſo pur in due parti equali dalla detta linea.b.e.f. </s> <s id="s.001465">& queſto <lb></lb>ſi fara facendo la mita di tal angolo da una banda, & l'altra mita dall'altra di detta li <lb></lb>nea, hor ſupponemo, che questo tal angolo ſia langolo.g.e.h.hor dico, che ſe tal angolo <lb></lb>g.e.h.ſara equale, ouer maggiore del angolo.a.b.c. </s> <s id="s.001466">eſſer impoßibile à poter fare in al <lb></lb>cun luoco della cortina.a.b. </s> <s id="s.001467">una canonera, che poſſa uedere, ne tirare, ne difendere lo <lb></lb>lato.g.e.del detto baluardo. </s> <s id="s.001468">Il medeſimo dico della cortina.c.b.cioe eſſer impoßibile di <lb></lb>fare in aleun luoco di quella una canonera, ouer bombardera, che poſſa uedere, ne tira <lb></lb>re, ne difendere l'altro lato.e.h.del detto baluardo, la qual coſaſe dimoſtra in questo <lb></lb>modo, ſe 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"></emph.end><lb></lb><figure id="id.042.01.148.1.jpg" xlink:href="042/01/148/1.jpg"></figure><lb></lb><emph type="italics"></emph>(per communa ſcientia) ſara eguale alla mitta de l'altro, e pero langolo.g.e.b. </s> <s id="s.001470">ſara e<lb></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></lb></s> <s id="s.001473">ſaranno equidiſtante, & per le medeſime ragioni la linea. </s> <s id="s.001474">e.h.ſara equidistante alla li-<emph.end type="italics"></emph.end><pb xlink:href="042/01/149.jpg"></pb><emph type="italics"></emph>nea.b.c.per la qual coſa il nostro primo propoſito uenera à eſſer manifeſto: perche, ſe <lb></lb>la linea.e.g. (lato del baluardo) non puo concorrere con la linea.a.b.eglie coſa chiara <lb></lb>che in alcun luoco di detta linea, ouer cortina.a.b.poter eſſer fatto una canonera, che <lb></lb>poſſa ueder, ne tirar, ouer difendere il detto lato.g.e.di tal baluardo, et <expan abbr="cõ">com</expan> le medeſime <lb></lb>ragioniſe approuara, l'altro lato.e.h.dal detto baluardo eſſer equidiſtante alla linea, <lb></lb>ouer cortina.b.c.e <21> questo eſſer impoßibile poterſi far una canonera in alcun luoco di <lb></lb>detta cortina.b.c. </s> <s id="s.001475">che poſſa guardare il lato.e.h.dil detto baluardo. </s> <s id="s.001476">Et molto piuſegui <lb></lb>ria tal impoßibilita, <expan abbr="quãdo">quando</expan>, che tutto langolo.g.e.h.del detto baluardo fuſſe maggior <lb></lb>del angolo.a.b.c.perche ſeguiria, che anchora la mitta di tal angolo fuſſe anchor mag <lb></lb>giore della mitta del angolo della cortina, cioe, che <expan abbr="lãgolo">langolo</expan>.g.e.b.fuſſe maggiore del an <lb></lb>golo.a.b.d. </s> <s id="s.001477">Et perche lo detto angolo.a.b.d.inſieme con langolo.a.b.e. (per la. </s> <s id="s.001478">13. del <lb></lb>primo di Euclide) ſar anno eguali à dui angoli retti, per il che li dui angoli.a.b.e.&.g. <lb></lb></s> <s id="s.001479">e.b.ſar anno maggiori di dui angoli retti, onde (per lo conuerſo modo della quinta pe<lb></lb>titione del noſtro Euclide) protratta la linea.e.g. </s> <s id="s.001480">dalla banda dal.g. </s> <s id="s.001481">continuamente ſe <lb></lb>andara allargando, & alluntanando dalla cortina.b.a.e pero molto piu euidente ſe ma<lb></lb>nifeſta la ſopra detta impoßibilita, & <21> le medeſime ragioni ſe dimoſtrara dell'altro la <lb></lb>to e.h.con la cortina.b.c. </s> <s id="s.001482">Ma ſe lo detto angolo.g.e.h.del baluardo ſara menore del an <lb></lb>golo.a.b.c.della cortina, ſeguira, che <expan abbr="lãgolo">langolo</expan>.g.e.b.ſia anchor minore del angolo.a.b.d. <lb></lb></s> <s id="s.001483">& ſimelmente (per la detta. </s> <s id="s.001484">13. del primo di Euclide) ſeguira, che li dui angoli.g.e.b. <lb></lb></s> <s id="s.001485">&. </s> <s id="s.001486">e.b.a.ſiano menori de dui angoli retti, onde (per la detta quinta petitione) protrat <lb></lb>ta la linea.e.g.inſieme con la linea.b,a.eglie neceſſario, che concorreno inſieme, e pero <lb></lb>tutte le canonere fatte à canto al luoco di tal concorſo, quelle guardar anno rettamen<lb></lb>te il detto lato.g.e.& queſto medeſimo ſeguira nella cortina.b.c.cioe, che quella <expan abbr="cõcor">concor</expan> <lb></lb>rera con la linea.e.h.eſſendo protratta in diretto uerſo.c.et coſi tutte le canonere, che <lb></lb>ſar an fatte à canto al luoco di tal concorſo, ò ſiano di ſopra, ouer di ſotto di tal luoco, <lb></lb>cioe, ò ſiano de baluardi, ouer de caualleri guardar anno rettamente il detto lato.e.h. <lb></lb></s> <s id="s.001487">del baluardo. </s> <s id="s.001488">Et aiſogna notar, che quanto piu ſara menore langolo del baluardo del <lb></lb>angolo delle cortine, tanto piu propinquo al detto baluardo ſe fara tal concorſo, et tan <lb></lb>to piu debile ſara tal baluardo, & per il contrario, quanto manco ſminuera langolo del <lb></lb>detto baluardo del angolo delle due cortine, tanto piu lontano dal detto baluardo ſe fa<lb></lb>ra tal concorſo, & piu gagliardo, ouer forte ſara tal baluardo, e per tanto dico, che uo <lb></lb>lendo far un baluardo ſopra à un angolo retto de due cortine, eglie neceſſario (uolen<lb></lb>do far, che tal baluardo ſia guardato da altri baluardi, ouer caualleri) à far tal ba<lb></lb>luardo de angolo acuto, & ogni baluardo de angolo acuto uien à eſſer debole, & <lb></lb>tanto piu debole ſara, quanto piu acuto angolo contenera: e pero, quando, che <lb></lb>langolo contenuto dalle due cortine ſara poiacuto, de neceßita molto piu acuto biſogna <lb></lb>ra far langolo del detto baluardo, & conſe quentemente molto piu debole uenira à eſ<lb></lb>ſer tal baluardo.<emph.end type="italics"></emph.end> S.M. E<emph type="italics"></emph>ho ben inteſo da molti pratici fortiſicatoride citta eſſer <lb></lb>difficulto ſißimo à poter fortificar un angolo retto de una citta, & molto piu un ango<lb></lb>lo acuto, & quantunque la iſperienza ne faccia chiaridi queſto, nondimeno con queſte <lb></lb>uostre Euclidiane argumentationi, me haueti fatto perfettamente conoſcere la cauſa <lb></lb>propinqua de tali effetti.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor Magnifico non ſolamente l'hanno per difficul<emph.end type="italics"></emph.end><pb pagenum="75" xlink:href="042/01/150.jpg"></pb><emph type="italics"></emph>toßßimo: ma un certo meſſer Ceſare Napolitano zotto (qual faceua gran proſeßione <lb></lb>de fortificar citta) me affermo eſſer impoßibil edi poter fortificare l'angolo retto, & <lb></lb>manco l'acuto, della qual coſa fra me molto me ne riſi, ma allui finſi da credere tal ſua <lb></lb>concluſione.<emph.end type="italics"></emph.end> S.M. A<emph type="italics"></emph>dunque haueti opinione, che li detti angoli ſi poſſano ſicuramen <lb></lb>te fortificare.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>enza dubbio Signor Magnifico, che ſi poſſono fortificare.<emph.end type="italics"></emph.end> S.M. <lb></lb>Q<emph type="italics"></emph>ueſto hauero ben accaro di uedere.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>n'altra uolta di cio ſatisfaro Voſtra Ma<lb></lb>gnificentia, perche al preſente è hora tarda de intrar in tal ragionamento.<emph.end type="italics"></emph.end> S.M. <lb></lb>M<emph type="italics"></emph>orſu diman ui aſpetto.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ueniro Signor Magnifico.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001489">QVESITO QVINTO FATTO DAL MEDESIMO <lb></lb>M<emph type="italics"></emph>agnifico, & Eccellentißimo Dottor. </s> <s id="s.001490">Signor <lb></lb>Marc' Antonio Moroſini.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001491">SIGNOR MARC'ANTONIO. H<emph type="italics"></emph>or narratime un poco queſto uoſtro <lb></lb>modo de fortificare un'angolo retto, ouer acuto de unacitta.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſto ſi fa<lb></lb>ra Signor Magnifico, facendo prima di ſopra al detto angolo, o uogliamo dir cantone <lb></lb>uno cauallero, il qual cauallero trauerſi da una cortina all'altra, ma che tal cauallero ſia <lb></lb>molto in dentro dal detto angolo, retto, ouer acuto, perche ſe tal cauallero fuſſe fatto <lb></lb>terminare con alcuna parte di quello ſopra al detto angolo facil coſa ſaria alli nemici à <lb></lb>rouinare tal angolo con le ſue artegliarie (per eſſer debile) onde ſe tal angolo fuſſe fon <lb></lb>dameuto del detto cauallero, ueneria à rouinare il detto cauallero inſieme con tal ango <lb></lb>lo, la qual coſa non poco pericolo cauſaria à quelli della citta, perche tal rouinazzo ca <lb></lb>deria nella foſſa, & ueneria à far ſcala alli nemici di poter aſcendere, & entrare per <lb></lb>tal luoco dentro della citta.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per queſto uoglio, che tal cauallero trauerſi rettamente <lb></lb>da una cortina all'altra molto in dentro di tal angolo, & perche tal angolo retto, ouer <lb></lb>acuto (anchor che ſopra di quello non ui fuſſe il detto cauallero) potria pur eſſer roui <lb></lb>nato da nemici ad ogni ſuo piacer, etmaßime tutta quella parte, che fuſſe <expan abbr="apparẽte">apparente</expan> di ſo <lb></lb>pra dalla foſſa, e pero meglio è à fare di uolonta quello, che li nemici (parendogli) ne <lb></lb>potriano far per forza, & con noſtro maggior pericolo, perche rouinando ſimplice<lb></lb>mente tal angolo per forza tal luoco rouinato inſieme con il rouinazzo, che caderia <lb></lb>nel foſſo (come è detto) ueneriano pur à far ſcala alli nemici di aſcendere, & entrare <lb></lb>nel cauallero, & nella detta citta.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per tanto uoglio, che tutto tal angolo, ouer canton <lb></lb><expan abbr="apparẽte">apparente</expan> dalla foſſa in ſuſo ſia <expan abbr="totalmẽte">totalmente</expan> tagliato, ouer ſmuſſato à ſcarpa per fin à <expan abbr="cãto">canto</expan> <lb></lb>del <expan abbr="fondamẽto">fondamento</expan> del cauallero, la qual coſa <expan abbr="facẽdo">facendo</expan> tal loco uenira à reſtar aſſai gagliardo, <lb></lb>eforte. </s> <s id="s.001492">Oltra di queſto uoglio, che circa al meggio dell'una, & l'altra cortina ſia fatto <lb></lb>un baluardo, <expan abbr="cõ">com</expan> tal ordine, che li lati, che ſono dalla <expan abbr="bãda">banda</expan> uerſo il detto cauallere dell'<gap></gap><lb></lb>no, e l'altro de quelli, ſiano <expan abbr="rettamẽte">rettamente</expan> ſignoreggiati, & guardati dal detto cauallero, ol <lb></lb>tra di queſto uoglio che <expan abbr="acã">acam</expan><gap></gap>o dell'uno, e l'altro baluardo, dalla <expan abbr="bãda">banda</expan> uerſo l'angolo, ret <lb></lb>to, ouer acuto ſia fatto un caualleretto (qua<gap></gap>r <expan abbr="ãgolo">angolo</expan>, ouer <expan abbr="tõdo">tondo</expan>, ouer ouale) di tal capa <lb></lb>cita, che ſopra all'uno, & l'altro de quelli ui ſe poſſa <expan abbr="accõmodare">accommodare</expan>. </s> <s id="s.001493">3. ouer. </s> <s id="s.001494">4. falconetti <lb></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. ſacri, & che li detti caualleretti ſiano ſituati di <lb></lb>ſorte, che poßino <expan abbr="rettamẽte">rettamente</expan> difendere, et guardar tal angolo.<emph.end type="italics"></emph.end> S.M. E<emph type="italics"></emph>ui ho <expan abbr="ottimamẽ-te">ottimamen<lb></lb>te</expan> inteſo, nondimeno fatime un poco di eſſempio in figura.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor clarißimo, per <pb xlink:href="042/01/151.jpg"></pb>ſatlsfar meglio<emph.end type="italics"></emph.end> V. M<emph type="italics"></emph>ag. </s> <s id="s.001498">ho portato in diſſegno un modelletto di tal ſorte angolo forti<lb></lb>ficato, qual è queſto ſottoſcritto, cioe l'angolo.a.è l'angolo terreo contenuto dalle due <lb></lb>cortine, retto, ouer acuto. </s> <s id="s.001499">Et.b.è lo cauallero fatto ſopra di quello, & lo triangolo.c. <lb></lb></s> <s id="s.001500">d.e.è il taglio, ouer ſmuſſatura à ſcarpa, dell'angolo, ouer cantone, che era apparente <lb></lb>di ſopra della foſſa, che gia conteneua le due cortine, et la linea.a.e.è il restante dell'an <lb></lb>golo contenuto pur dalle dette due cortine, il quale uien à eßere alto, quanto è alta la foſ <lb></lb>ſa, cioe la linea.a.e. </s> <s id="s.001501">debbe eßer eguale alla detta altezza della foſſa, la qual foßa non <lb></lb>ue la ho uoluta deſignare, accio meglio ſi ueda il tutto, l'uno, e l'altro baluardo ſono.f. <lb></lb></s> <s id="s.001502">&. </s> <s id="s.001503">g. Et li dui caualleretti ſono.h.&.i.le qual coſe <expan abbr="difenderãno">difenderanno</expan> honoratamente tal ſpe <lb></lb>cie di angolo, & lo far anno gagliardo, & forte, uero è, che io laudarei, che ſopra à <lb></lb>l'un, e l'altro di dui baluardi (ſi nella piazza di ſopra, come in quella da baßo) ui ſe gli <lb></lb>metteße piu preſto pezzi piccoli, che großi, cioe ſacri, ouer falconetti da. </s> <s id="s.001504">6. & met-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.151.1.jpg" xlink:href="042/01/151/1.jpg"></figure><lb></lb><emph type="italics"></emph>teruene tanto piu numero.<emph.end type="italics"></emph.end> S.M. M<emph type="italics"></emph>e piace aßai questa uoſtra opinione, pur penſo, <lb></lb>che conſiderando ben questa coſa ui ſe ritrouera molte coſe da poterui opponere, e pe <lb></lb>ro uoglio che rimettemo à diſputar meglio queſta uoſtra opinione à un'altra fiata<emph.end type="italics"></emph.end><lb></lb>N. C<emph type="italics"></emph>ome pare à uoſtra Magnificentia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001505">QVESITO SESTO FATTO DAL MEDESIMO <lb></lb>M<emph type="italics"></emph>agnifico, & Eccellentißimo Dottor, Signor <lb></lb>Marc' Antonio Moroſini.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001506">SIGNOR MARC'ANTONIO. N<emph type="italics"></emph>el Sesto Queſito del uostro Seſto li<lb></lb>bro, uoi diceti, che à uoler fortificar una citta, che ſi debbe dar tal forma alle mu<lb></lb>ra, ouer cortine di quella, che ſe per ſorie quelle tai mura, ouer cortine fuſſeno roui-<emph.end type="italics"></emph.end><pb pagenum="76" xlink:href="042/01/152.jpg"></pb><emph type="italics"></emph>nate da nemici con le artegliarie, che tal citta ſia quaſi piu forte con tai mura rouina<lb></lb>te, che ſi quelle fuſſeno intiere, & ſane, della qual coſa molti ſe ſono ſcandalizzati di <lb></lb>uoi.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor clarißimo, credo uer amente, che molti ſe ne ſiano ſcandalizzati, pen <lb></lb>ſando loro, che io uoglia forſi dire, che rouinate le dette mura per fin alli fondamenti, <lb></lb>ma io non uoglio dir coſi, anciuoglio dire, che rouinata quella parte apparente di ſo<lb></lb>pra al horo della foſſa (come ſi coſtuma communamente nelle batterie) che ne ſeguiria <lb></lb>poi quello, che hauemo detto nel detto Seſto Queſito del noſtro Seſto libro, cioe che tal <lb></lb>citta ſaria quaſi piu forte con tai parti de mura rouinate di quello ſaria eſſendo intiere, <lb></lb>e ſane.<emph.end type="italics"></emph.end> S.M. I<emph type="italics"></emph>ntendetela mo, come uoleti, che per qual modo ſi uoglia la me par co<lb></lb>ſa granda, & ſe poßibil fuſſe di farme intendere con parole la qualita di tal uoſtra for <lb></lb>ma de mura, me fareſti coſa gratißima, delle altre coſe poi, che me haueti promeſſo a<lb></lb>ſpettaro fin che uorreti uoi, accio le poſſate far con uostra commodita.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor <lb></lb>Magnifico, eglie coſa chiara per ragion naturale, che quando li nemici uogliono bat<lb></lb>tere una citta còn le artegliarie non cercano da battere, ne darouinare quella parte de <lb></lb>te de mura, ouer cortina, che non uedono, ma ſolamente quella parte, che è apparente <lb></lb>di ſopra al horo della foſſa, perche rouinata che ſia tal parte apparente, cadendo tal <lb></lb>rouinamento nella foſſa gli uien à far una ſcala di poter aſcendere, & da entrare com<lb></lb>modamente nella detta citta.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per tanto nel fabricar le dette mura, ouer cortine, quan <lb></lb>do che ſono elleuate quaſi alla altezza del horo della foſſa, uorria, che quella parte, <lb></lb>che gli manca à compirle in altezza, fuſſeno fabricate piuin dentro uerſo la citta tal<lb></lb>mente, che uenghi à reſtar de fuora uia un ſpacio nella ſommita del primo muro, il qual <lb></lb>ſpacio uoglio cheſia di <expan abbr="tãta">tanta</expan> capacita, che ſta atto à riceuere, & tenere ſopra di ſe quaſi <lb></lb>tuttoil rouinazzo, di quella <expan abbr="ſecõda">ſeconda</expan> parte di cortina (fatta piu <expan abbr="idẽtro">identro</expan>) ſe rouinata fuſſe <lb></lb>da nemici con le artegliarie (o poco manco) uero è, che biſogna auertire nel far li bal<lb></lb>uardi di farli con tal modo, e miſura, che habbiano almen due, ouer tre canonere per <lb></lb>banda, cherettamente poſſano tirare à longo per tutto quel tal ſpacio, ma dico con l'u <lb></lb>no, & l'altro di dui baluardi, poſti alla guardia di quella tal cortina, la qual coſa facen<lb></lb>do tal forma de cortina hauera in ſe la detta noſtra qualita, perche ſe quella ſeconda <lb></lb>parte di cortina (fatta piu in dentro) apparente di ſopra lo horo della foſſa ſara per <lb></lb>ſorte rouinata da nemici, con le artegliarie. </s> <s id="s.001507">Quel rouinazzo di tal cortina reſtara aſ<lb></lb>ſunato ſopra di quel ſpacio (gia laſciato per tal effetto) & perche ogni uolta, che tal <lb></lb>parte apparente di una tal cortina uenga rouinata da nemici con le artegliarie, non la <lb></lb>rouinar anno mai totalmente, ma rouinar anno ſolamente quella parte compoſta di pie <lb></lb>tre, & malta, ma quella parte poi che è di terra fra quelli contraforti (che noi chiama<lb></lb>mo argine) non reſtara, mai totalmente rouinata, ma de quella ne rouinara ſolamente <lb></lb>unacerta parte, che ſe tirara drio la cortina di pietre, e malta, nel cader chi fara, & <lb></lb>reſtara poi una certa diſceſa, ouer montata di terra inſieme con certe reliquie di quel<lb></lb>li contr aforti gia fatti de drio à tal cortina fatta de pietre, e malta, la qual diſceſa, ouer <lb></lb>montata non ſara molto facile di aſcendere.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per tanto ſe li nemici dapoi che hauer an<lb></lb>no rouinata tal muraglia ouer cortina, deliberar anno di uoler entrare in tal citta, pri <lb></lb>ma gliſara neceſſario à portar ſcale di poter aſcendere dal fondo della foſſa per fin à <lb></lb>quel <gap></gap> acio doueſe ripoſſara quel rouinamento, il qual ſpacio per eſſer tutto occupa-<pb xlink:href="042/01/153.jpg"></pb>to, et <expan abbr="piẽ">piem</expan> di pietre, oltra che nell'appogiar le dette ſcale molte pietre ſi <expan abbr="farãno">faranno</expan> rouinar <lb></lb>à doſſo, ma li primi, che <expan abbr="aſcenderãno">aſcenderanno</expan> uolendo montare poi ſuſo per quel monte de pie<lb></lb>tre non poche de tai pietre ne far anno non ſolamente rouinar à doſſo de quelli, che ſu <lb></lb>per le dette ſcale conſequentemente aſcender anno, ma anchora à quelli, che nella foſſa <lb></lb>ſtar anno per aſcendere de mano in mano, oltra che le canonere delle piazze da baſſo <lb></lb>dell'uno, o l'altro baluardo romperanno molte de quelle ſcale, & uccider anno molti de <lb></lb>quelli, che aſcender anno, & che staranno per aſcendere per le dette ſcale. </s> <s id="s.001508">Ma piu che <lb></lb>le canonere della piazza di ſopra pur dell'uno, e l'altro baluardo inſieme con quelle, <lb></lb>che gia furno aſſettate dall'una, e l'altra banda per guardar à longo per tutto quel ſpa <lb></lb>cio doue ſe repoſſer anno le dette pietre della cortina rouinata, ſenza comparatione fa <lb></lb>ranno piu effetto, & danno nelli detti nemici, per cauſa de tal rouinamento de cortina, <lb></lb>cheſe tal cortina fuſſe intiera, & ſana, perche tirando in quelli fanti, che ſuſo per quel <lb></lb>le amontonate pietre aſcenderanno, oltra che amazzar anno, & ſtroppiar anno con le <lb></lb>pure balle gran parte de quelli, li quali cadendo per quelle amontonate pietre redola<lb></lb>ranno, & far anno redolar quelle pietre giuſo per la teſta de quelli, che aſcender anno, <lb></lb>& ſtar anno per aſcendere ſu per dette ſcale. </s> <s id="s.001509">Ma le balle tirate ſu per quelle tai pietre <lb></lb>sbroffar anno quelle per tutte le parti di tal foſſa, & non ui è dubbio, che li dettinemici <lb></lb>riceuer anno infinite uolte piu danno, & offenſione dalle pure pietre, che dalle pure bal <lb></lb>le tirate dall'un, e l'altro baluardo, & canonere.<emph.end type="italics"></emph.end> S.M. S<emph type="italics"></emph>enza dubbio che li detti ne<lb></lb>mici ſar anno piu offeſi, & mal trattati dalle dette pietre, che dalle pure balle, & que<lb></lb>ſta uoſtra opinion me piace aſſai, perche comprendo che tai pietre rouinate coſtitue<lb></lb>ranno, & formar anno un'altra altezza de pietre rouinate ſopra della prima fonda<lb></lb>mental cortina, oltra quella diſceſa, ouer montata di quel argine di terra miſto, & col<lb></lb>ligato con le reliquie di contr aforti gia fatti nell'arginar la cortina rouinata, la qual <lb></lb>altezza à uolerla aſcendere li nemici trouar anno de molte difficolta, e forſi molto piu, <lb></lb>cheſe tal cortina fuſſe intiera, e ſana. </s> <s id="s.001510">Ma ditemi un poco, quel tal ſpacio uoleti che ſia <lb></lb>per fettamente quadrangolo, & rettangolo.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on Signor magnifico, anci uoglio <lb></lb>che tal ſpacio dall'uno, e l'altro capo uada tondezando in uerſo la citta, cioe ſcanſando, <lb></lb>& annullando l'uno, e l'altro de quelli dui angoli che doueriano formar ſi uerſo la detta <lb></lb>citta, tal che il detto ſpacio uenira à formar una figura biangola quaſi alla ſimilitudine <lb></lb>di quella figura, che fa la Luna <expan abbr="quãdo">quando</expan> è in quadrato con il Sole, dico dalli capi di tal ſpa <lb></lb>cio, cioe che l'un, e l'altro uengano à formar un'angolo ſolo quaſi contiguo con il bal<lb></lb>uardo à ſe conterminale dall'uno, & dall'altro capo.<emph.end type="italics"></emph.end> S.M. E<emph type="italics"></emph>ue ho inteſo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001511">QVESITO SETTIMO FATTO DAL MEDESIMO <lb></lb>M<emph type="italics"></emph>agnifico, & Eccellentißimo Dottor, Signor <lb></lb>Marc' Antonio Moroſino.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001512">SIGNOR MARC'ANTON. S<emph type="italics"></emph>o che doueti ſaper <expan abbr="minutamẽte">minutamente</expan>, come ſi fan <lb></lb>no al preſente li baluardi di dentro uia, cioe la piazza da baſſo, & quella di ſopra <lb></lb>& ſo, che doueti hauer trouato qualche bella ſottilita ſopra la coſtrution de quelli, e <lb></lb>per non ſtare otioſi fina à hora da cena, uorria, che di cio ne ragionaßimo un poco.<emph.end type="italics"></emph.end><pb pagenum="77" xlink:href="042/01/154.jpg"></pb>N. A<emph type="italics"></emph>nci eglie tutto al contrario Signor Magnifico, che delle ſue particolarita non <lb></lb>gli ne ho altraſpecial cognitione, che quello, che mi fu narrato in parole dal<emph.end type="italics"></emph.end> S. P<emph type="italics"></emph>rior <lb></lb>di Barletta, quaſi in fine del ottauo Queſito del mio ſeſto libro, perche gia mai fui in <lb></lb>luoco, che poteſſe uedere realmente la piazza di ſopra, ne manco quella da baſſo de al<lb></lb>cun baluardo, & la cauſa di queſto fu da me narrata al detto Signor Priore nel primo, <lb></lb>& anchora in fine del ottauo Queſito del detto noſtro ſeſto libro, eglie ben uero, che <lb></lb>ho compreſo, come ſia fatta l'una, e l'altra piazza, per uigor de un diſegno retratto <lb></lb>da un baluardo de una citta maritima, el qual è queſto.<emph.end type="italics"></emph.end> S.M. S<emph type="italics"></emph>eti ſtato per mare.<emph.end type="italics"></emph.end><lb></lb>N. S<emph type="italics"></emph>on ſtato fina à lio Signor Magnifico, quando, che la Illuſtrißima Signoria ua a<lb></lb>ſpoſar el mare, & non piu oltra.<emph.end type="italics"></emph.end> S.M. C<emph type="italics"></emph>ome cauaſti adunque il ritratto di tal ba-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.154.1.jpg" xlink:href="042/01/154/1.jpg"></figure><lb></lb><emph type="italics"></emph>luardo da tal citta maritima.<emph.end type="italics"></emph.end> N. T<emph type="italics"></emph>al ritratto non fu da me cauato, ma mi fu dato da <lb></lb>un mio diſcipulo Pittore eccellente.<emph.end type="italics"></emph.end> S.M. S<emph type="italics"></emph>apeti come ſtia, ouer come ſia fatta la <lb></lb>piazza da baſſo di tal baluardo, & altri ſimili.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>i ueduta non ui ſaprei dire, ne <lb></lb>di questo, ne manco de altri ſimili, come di ſopra ho detto. </s> <s id="s.001513">ma diro bene, come iſtimo, <lb></lb>che ſia fatta. </s> <s id="s.001514">Penſo, che tal piazza da baſſo ſia fatta in uolti ſopra, de großi, & ga<lb></lb>gliardi pilaſtroni, & che la intrata di andar, & condur le artegliarie in tal piazza da <lb></lb>baſſo ſia doue ſiuede il <expan abbr="põto">ponto</expan>.a.et che quelle feneſtrelle, che ſono per el piano della piaz <lb></lb>za diſopra ſiano fatte per dar luce alla detta piazza da baſſo.<emph.end type="italics"></emph.end> S.M. V<emph type="italics"></emph>oi non haueti <lb></lb>in tutto mal penſato, ma molto me marauiglio di uoi, che non ue ſiati dilettato de anda <lb></lb>re à uedere minutamente tai particolarita.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on ho tempo Signor Eccellentiß. di <lb></lb>andar à cercar di uedere tai coſe, & maßime, che io <expan abbr="nõ">non</expan> mi curo, ne tengo conto di quel <lb></lb>le coſe, che molti le ſanno fare, anchor, che ſiano da me ignorate (come che nel ſuppli<lb></lb>mento della nostra trauagliata inuentione da me fu anchor detto) ma ſolamente di quel <lb></lb>le coſe che niuno le ſanno eſſequire molto me diletto, & curo ditrouare. </s> <s id="s.001515">Io non uo di<lb></lb>re, che quando fuſſe uno de detti baluardi qua in Venetia, & appreſſo della mia <expan abbr="ſtãtia">ſtantia</expan>,<emph.end type="italics"></emph.end><pb xlink:href="042/01/155.jpg"></pb><emph type="italics"></emph>che non lo andaſſe qualche uolta à uedere, ma non con altro mio maggior diſconzo.<emph.end type="italics"></emph.end><lb></lb>S.M. C<emph type="italics"></emph>redo, che ſiati molto occupato nel eſſercitio uostro. </s> <s id="s.001516">Dimane ſon per andare <lb></lb>alla uilla, doue ſtaro alquanti giorni, per certe mie occorrentie. </s> <s id="s.001517">In questo mezzo pre<lb></lb>parareti quelle altre forme de fortificationi, accio ſiano in ordine alla tornata mia. </s> <s id="s.001518">Et <lb></lb>maßime quella, che preponetinel. </s> <s id="s.001519">7. Queſito del uoſtro ſeſto Libro, cioe di fare quel <lb></lb>uoſtro particolar ingegno di accommodar à ogni cortina, che ſicur amente potra eſſer <lb></lb>guardata, & difeſa da. </s> <s id="s.001520">25. ouer. </s> <s id="s.001521">30. fanti al piu, contra à ogni grandißimo aßalimen<lb></lb>to, che con ſcale la uoleſſeno ſcalare. </s> <s id="s.001522">Et preparate anchora quel modo de fortificar el <lb></lb>paeſe atorno de una citta (come, che preponeti nell'ottauo Queſito) talmente, che quel <lb></lb>li della citta poſſeno ſicuramente andare à lauorare, ſeminare, & raccogliere quaſi <expan abbr="tã">tam</expan> <lb></lb>to, che ſia atto à dar il uiuere à quelli della citta, perche ſon molto deſideroſo de ueder <lb></lb>tal uoſtra inuentione, perche la me par coſa granda à farlo con coſi poca ſpeſa, come di <lb></lb>ceti.<emph.end type="italics"></emph.end> N. F<emph type="italics"></emph>aro Signor Magnifico.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001523">F<emph type="italics"></emph>ine della Gionta del ſeſto Libro delli Queſiti, & Inuentioni <lb></lb>diuerſe de Nicolo Tartaglia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001524">CON <emph type="italics"></emph>gratia, & priuilegio dall'Illustrißimo Senato Veneto, che niuno ardiſca, ne <lb></lb>preſuma di ſtampar, ne far ſtampare la preſente Gionta, ne ſtampate altroue uen<lb></lb>dere, ne far uendere in Venetia, ne in alcuno altro luoco, ò terra del Dominio Ve<lb></lb>neto, per anni diece, ſotto pena de duc. </s> <s id="s.001525">300. & perdere le opere in qual ſi uoglia lo <lb></lb>co, che ſar anno trouate, el terzo della qual pena pecuniaria ſia applicata all'Arſe<lb></lb>nale, & un terzo ſia del Magiſtrato, doue ſe fara la eſſecutione, & l'altro terzo ſia <lb></lb>del denonciante, & le opere ſiano del preſence Autore, come che nel priuilegio ſi <lb></lb>contiene.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb pagenum="78" xlink:href="042/01/156.jpg"></pb> <p type="head"> <s id="s.001526">LIBRO SETTIMO DELLI <lb></lb>QVESITI, ET INVENTIONI DIVERSE, <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.001527">S<emph type="italics"></emph>opra gli principij delle Queſtioni Mechanice di <lb></lb>Ariſtotile.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001528">QVESITO PRIMO FATTO DAL ILLVSTRISS. <lb></lb>S<emph type="italics"></emph>ignor Don Diego Hurtado di Mendozza, Ambaſciator <lb></lb>Ceſareo in Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001529">SIGNOR AMBASCIATORE. T<emph type="italics"></emph>artaglia, dapoi, che <lb></lb>noi deßimo uacatione alle lettioni di Euclide, ho ritrouato coſe <lb></lb>nuoue ſopra le Mathematice.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>he coſa ha ritrouato uoſtra <lb></lb>Signoria.<emph.end type="italics"></emph.end> S.A. L<emph type="italics"></emph>e Queſtioni Mechanice di Ariſtotile, Grece, <lb></lb>& Latine.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie tempo aſſai che io le uidi, maßime Lati<lb></lb>ne.<emph.end type="italics"></emph.end> S.A. C<emph type="italics"></emph>he ue ne pare.<emph.end type="italics"></emph.end> N. B<emph type="italics"></emph>enißimo, & certamente le ſo <lb></lb>no coſe ſuttilißime, & di profonda dottrina.<emph.end type="italics"></emph.end> S.A. A<emph type="italics"></emph>nchora io <lb></lb>le ho ſcorſe, & inteſo di quelle la maggior parte, nondimeno me resta molti dubbij ſo<lb></lb>pra di quelle, li quali uoglio, che me li dichiarati.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignore, ui ſono dubbij aſſai, che <lb></lb>à uolergli à ſofficienza delucidare, à me ſaria neceſſario prima à dechiarare à uoſtra <lb></lb>Signoria li principij della ſcientia di peſi.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.001530">A <emph type="italics"></emph>me mi pare, che Ariſtotile dimo<lb></lb>ſtri il tutto, ſenza procedere, ouer intendere altramente la ſcientia di peſi.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie <lb></lb>ben uero, che lui approua cadauna de dette queſtioni, parte con ragioni, & argomenti <lb></lb>naturali, & parte con ragioni, & argomenti Mathematici. </s> <s id="s.001531">Ma alcuni di quelli ſuoi <lb></lb>argomenti naturali, con altri argomenti naturali ui ſi puol opponere. </s> <s id="s.001532">Et alcuni altri <lb></lb>con argomenti Mathematici (mediante la ſcientia di peſi detta diſopra) ſe poſſono re <lb></lb>probar per falſi. </s> <s id="s.001533">Et oltra di questo lui pretermette, ouer tace una questione ſopra del<lb></lb>le libre, ouer bilanze di non poca importanza, ouer ſpeculatione, & queſto è proceſ<lb></lb>ſo (per quanto poſſo conſiderare) perche di tal queſtione, non ſi puo aßignar la cauſa <lb></lb>per ragion naturale, ma ſolamente con la detta ſcientia di peſi.<emph.end type="italics"></emph.end> S.A. N<emph type="italics"></emph>on credo, che <lb></lb>queſto ſia la uerita, cioe, che alcuna ſua argumentatione patiſca oppoſitione, perche <lb></lb>Ariſtotile non fu uu'ocha, ne manco credo, che lui habbia pretermeſſo, ouer taciuto <lb></lb>queſtione alcuna ſopra delle libre, che ſia de importantia.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci eglie troppoel ue <lb></lb>ro, <21>che <expan abbr="uolẽdo">uolendo</expan> <expan abbr="cõſiderare">conſiderare</expan>, giudicare, et dimoſtrare la cauſa della ſua prima <27>stione, ſi <lb></lb>come naturale, cioe <expan abbr="cõ">com</expan> <27>lli ultimi <expan abbr="argomẽti">argomenti</expan> naturali, che lui aduce ſopra le libre ouer bi <lb></lb><expan abbr="lãce">lance</expan> materiale. </s> <s id="s.001534"><expan abbr="Medeſimamẽte">Medeſimamente</expan> <expan abbr="cõ">com</expan> altri <expan abbr="argomẽti">argomenti</expan> naturali (come di ſopra dißi) ſi puo ap <lb></lb>prouare, che ſeguita tutto al <expan abbr="cõtrario">contrario</expan> di <27>llo, che in tal <27>ſtione <expan abbr="cõclude">conclude</expan>, ouer ſuppone. <lb></lb></s> <s id="s.001535">Et <expan abbr="uolẽdo">uolendo</expan> poi <expan abbr="cõſiderare">conſiderare</expan>, & giudicare tal Queſtione, ſi come Mathematico, & <expan abbr="cõ">com</expan> ar <lb></lb><expan abbr="gomẽti">gomenti</expan> Mathematici ſi puo medeſimamente li detti ſui argomenti reprobar per falſi, <lb></lb>mediante la ſcientia di peſi detta di ſopra.<emph.end type="italics"></emph.end> S.A. C<emph type="italics"></emph>ome ſe conſiderano, & giudicano <lb></lb>le coſe, ſi come natura le, & come ſe conſiderano, & giudicano, ſi come Mathematico.<emph.end type="italics"></emph.end><pb xlink:href="042/01/157.jpg"></pb>N. E<emph type="italics"></emph>l naturale <expan abbr="cõſidera">conſidera</expan>, giudica, et determina le coſe, <expan abbr="ſecõdo">ſecondo</expan> el ſenſo, & <expan abbr="apparẽtia">apparentia</expan> di <lb></lb>quelle in materia. </s> <s id="s.001536">Ma el Mathematico le conſidera, giudica, & determina, non ſecon <lb></lb>do el ſenſo, ma ſecondo la ragione (aſtrate da ogni materia ſenſibile) come che<emph.end type="italics"></emph.end> V. S<emph type="italics"></emph>ig. <lb></lb>ſa, che coſtuma Euclide.<emph.end type="italics"></emph.end> S.A. C<emph type="italics"></emph>irca di queſto non ſo che riſpondere, perche io non <lb></lb>me arricordo coſi all'improuiſo il ſoggetto di tal ſua prima queſtione, e pero ditime. <lb></lb></s> <s id="s.001537">come, che quella parla, & dice.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a dice, & parla preciſamente in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001538">P<emph type="italics"></emph>erche cauſa le maggior libre, ouer bilanze, ſono piu diligente delle menore.<emph.end type="italics"></emph.end><lb></lb>S.A. B<emph type="italics"></emph>en? </s> <s id="s.001539">che uoleti dire ſopra di tal queſtione.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oglio dir queſto, che ſumen<lb></lb>dola, ouer conſiderandola, ſi come Mathematico (cioe astrata da ogni materia) ſenza <lb></lb>alcun dubbio tal queſtione è uniuerſalmente uera, ſi per le ragioni da lui adutte per <lb></lb>auanti, come, che per molte altre, che nella ſcientia di peſi addur ſe potria. </s> <s id="s.001540">Perche quel <lb></lb>la linea, che con la ſua mobile iſtremita piu ſe allontana dal centro d'un cerchio, moue<lb></lb>sta dauna medeſima uirtu, ouer potentia (in tal ſua iſtremita) piu facilmente, & con <lb></lb>maggior celerita, ouer preſte<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a ſaramoſſa, ſpenta, ouer portata, di quella, che <expan abbr="cõ">com</expan> la <lb></lb>detta ſua iſtremita men ſe alluntanara dal detto centro, & per tal ragione le libre, o<lb></lb>uer bilanze maggiori, ſe uerificano eſſer piu diligente delle menore. </s> <s id="s.001541">Ma uolendo poi <lb></lb>conſiderare, & approuare tal queſtione in materia, & con argomenti naturali, co<lb></lb>me, che in ultimo lui conſidera, & approua, cioe per el ſenſo del uedere in eſſe libre, <lb></lb>ouer bilanze materiale. </s> <s id="s.001542">Dico, che con tai ſorte de argomenti non ſe uerifica general<lb></lb>mente tal queſtione, anzi ſe trouara ſeguir tutto al contrario, cioe le libre, ouer bilan <lb></lb>ze menori eſſer piu diligente delle maggiori, & che questo ſia el uero nelle libre, ouer <lb></lb>bilanze materiale, la ſperientia lo fa manifeſto: perche ſe de uno ducato ſcarſo uoremo <lb></lb>ſapere de quani grani lui ſia ſcarſo, con una libra, ouer bilanza granda, cioe con una <lb></lb>de quelle, che adoprano li ſpeciali per peſar ſpecie, zuccaro, zenzero, e canella, & al <lb></lb>tre coſe ſimile, malamente ſe ne potremo chiarire, ma con una di quelle librette, ouer <lb></lb>bilancette piccole, che oprano li bancheri, or efici, & gioieleri, ſenza dubbio ſe ne po<lb></lb>tremo totalmente certificare. </s> <s id="s.001543">Per il che ſeguitaria tutto al contrario, di quello, che in <lb></lb>tal queſtione ſe conchiude, & dimoſtra, cioe, che tai bilancette piu piccole ſiano piu di <lb></lb>ligente, delle piu grande, perche piu diligentemente, ouer ſottilmente dimoſtrano la <lb></lb>differentia di peſi. </s> <s id="s.001544">Et la cauſa di queſto inconueniente non procede da altro, che dalla <lb></lb>materia, perche le coſe costrutte, ouer fabricate in quella, mai ponno eſſer coſi preci<lb></lb>ſamente fatte, come, che con la mente uengono imaginate fuora di eſſa materia, per il <lb></lb>che tal hor ſe uien à cauſar in quelle alcuni effetti molto contr arij alla ragione. </s> <s id="s.001545">Et per <lb></lb>questo, & altri ſimili reſpetti, el Mathematico non accetta, ne conſente alle dimoſtra<lb></lb>tioni, ouer probationi fatte per uigor, & autoritadi ſenſi in materia, ma <expan abbr="ſolamẽte">ſolamente</expan> à <lb></lb>quelle fatte <21> demostrationi, et <expan abbr="argomẽti">argomenti</expan> aſtrati da ogni materia ſenſibile. </s> <s id="s.001546">Et <21> questa <lb></lb>cauſa, le diſcipline Mathematice. </s> <s id="s.001547">non ſolamente ſono giudicate dalli ſapienti eſſer piu <lb></lb>certe delle naturale, ma quelle eſſer anchora nel primo grado di certezza. </s> <s id="s.001548">Et pero <lb></lb>quelle queſtioni, che con argomenti Mathematici ſe poſſono dimoſtrare, non è coſa <lb></lb>conueniente ad approbarle con argomenti naturali. </s> <s id="s.001549">Et ſimelmente quelle, che ſo<lb></lb>no gia dimoſtrate con argomenti Mathematici (che ſono piu certi) non é da ten<lb></lb>tare, ne da perſuader ſi de certificarle meglio con argomenti naturali, li quali ſono<emph.end type="italics"></emph.end><pb pagenum="79" xlink:href="042/01/158.jpg"></pb><emph type="italics"></emph>men certi.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.001550">A <emph type="italics"></emph>me mi pare che lui uoglia, in tal prima queſtione, che quella resti <lb></lb>ot timamente chiarita (come è il uero) per le ragioni, & argomenti per auanti adutti, <lb></lb>& dimoſtrati, le quale ragioni, ouer argomenti ſcno tutti Mathematici, & non natu<lb></lb>rali, perche parte de quelli ſe uerificano per la. </s> <s id="s.001551">23. del Seſto di Euclide, & parte per <lb></lb>la quarta del medeſimo.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oſtra Signoria inſieme con lui dice la uerita, che tal que <lb></lb>ſtione è manifeſta per le ſue ragioni adutte per auanti, & questo medeſimo anchoraio <lb></lb>di ſopra lo affermai, perche tai antecedentiſono ſtati da lui dimoſtrati con argomenti <lb></lb>Mathematici, ma in fine de tai buone argomentationi, ui ſottogionge due altre con<lb></lb>cluſioni, la prima delle quale dice preciſamente in queſta forma. </s> <s id="s.001552">Et certamente ſono <lb></lb>alcuni peſi, li quali poſti nelle piccol libre, non ſono manifesti al ſenſo, & nelle grande <lb></lb>ſono manifesti. </s> <s id="s.001553">La qual concluſione, uolendola conſiderare, giudicare, & approuare, <lb></lb>ſi come naturale, cioe per uigore, & autorita del ſenſo del uedere, nelle libre materia<lb></lb>le, ſenza dubbio tal ſua concluſione patiſſe oppoſitioni aſſai, perche nelle dette libre, <lb></lb>ouer bilanze materiale, la maggior parte delle uolte ſe trouara ſeguir tutto al contra<lb></lb>rio, cioe che ſono alcuni peſi, li quali poſti, nelle libre, ouer bilanze grande, non ſe fa<lb></lb>ranno con alcuna inclinatione manifeſti al ſenſo del uedere. </s> <s id="s.001554">Et nelle bilanzette piccole <lb></lb>ſe manifestar anno, cioe che far anno inclinatione uiſibile, & tutto questo, la ſperien<lb></lb>tia lo manifeſta. </s> <s id="s.001555">Perche ſe ſopra una di quelle ſopradette bilanze grande de Speciali, ui <lb></lb>ſara posto un grano di formento. </s> <s id="s.001556">Eglie coſa chiara, che nella maggior parte di quelle, <lb></lb>non fara alcuna uiſibil inclinatione. </s> <s id="s.001557">Et nella maggior parte di quelle piccolette che uſa <lb></lb>no li Banchieri, far anno inclinatione molto cuidente. </s> <s id="s.001558">Ma uolendo poi conſiderare, <lb></lb>giudicare, & dimoſtrare tal ſua queſtione, ouer concluſione, ſi come Mathematico, <lb></lb>cioe fuora de ogni materia, ſenza dubbio tal ſua concluſione ſaria falſa, perche ogni <lb></lb>piccol peſo poſto in qual ſe uoglia libra fara inclinar quella continuamente per fina <lb></lb>all'ultimo, ouer piu baſſo luoco, che inclinar ſe poſſa, & tutto queſto nelli principij del<lb></lb>la ſcientia di peſi à Voſtra Signoria, lo faro manifeſto. </s> <s id="s.001559">Dapoi lui ſottogionge anchora <lb></lb>queſt'altra concluſione, & dice in queſta forma. </s> <s id="s.001560">Et certamente ſono alcuni peſi, le <lb></lb>quali ſono manifeſti nell'una, & l'altra ſorte de libre (cioe nelle maggiori, & nelle me <lb></lb>nori) ma molto piu nelle maggiori, perche molto piu granda inclinatione, uien fatta dal <lb></lb>medeſimo peſo nelle maggiori. </s> <s id="s.001561">La qual concluſione, uolendolo conſiderare, giudicare, <lb></lb>& approuare, ſi come naturale (come fu detto dell'altra) cioe per uigore, & autorita <lb></lb>del ſenſo del uedere, nelle dette libre materiale, certamente queſta non patira men op<lb></lb>poſitioni dell'altra, per le medeſime ragioni in quella adutte. </s> <s id="s.001562">Et ſimilmente, <expan abbr="uolẽdo">uolendo</expan> poi <lb></lb>conſiderare, giudicare, & dimoſtrare tal concluſione, come Mathematico, cioe fuora <lb></lb>de ogni materia medeſimamente talſua concluſione ſaria falſa, perche ogni ſorte di pe <lb></lb>ſo poſto in qual ſi uoglia ſorte de libra, fara inclinar quella de continuo per fina à tan <lb></lb>to che quella ſia gionta all'ultimo, ouer piu baſſo luoco, che quella inclinar ſi poſſa, & <lb></lb>tutto queſto, nelli detti principij della ſcientia di peſi dimostr atiuamente à quella ſi fara <lb></lb>manifeſto.<emph.end type="italics"></emph.end> S.A. A<emph type="italics"></emph>nchor che tutte queste uoſtre oppoſitioni, & argomenti naturali, <lb></lb>habbiano del ueriſimile non poſſo credere, che il non ue ſia altre ragioni, & argo<lb></lb>menti, ſi naturali, come Mathematici da poter difendere, & ſaluare, tal ſua questione <lb></lb>inſieme con quell altre due concluſioni. </s> <s id="s.001563">Anci è ho ferma opinione che chi ſtudiaſſe con <pb xlink:href="042/01/159.jpg"></pb><expan abbr="diligẽtia">diligentia</expan> ſopra à tal materia, ritrouaria tutte <expan abbr="q̃lle">qualle</expan> particolarita materiale, che ſono cais <lb></lb>ſa, che tal queſtione, & <expan abbr="cõcluſioni">concluſioni</expan> <expan abbr="nõ">non</expan> ſe uerificano in materia, come che l'autor <expan abbr="cõchiu">conchiu</expan> <lb></lb>de, et dice. </s> <s id="s.001564">Et dapoi che quelle fuſſeno ritrouate, et conoſciute, <expan abbr="tẽgo">tengo</expan> che ſaria coſa facile <lb></lb>à rimediarli, & fare che ſe uerificaſſeno in materia preciſamente, come che l'autor <lb></lb>propone.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oſtra Signoria non è di uana opinione, perche in effetto tutte quelle <lb></lb>coſe che nella mente ſono conoſciute uere, & maßime per dimoſtrationi aſtratte da o<lb></lb>gni materia, ragioneuolmente ſi debbono anchora uerificare al ſenſo del uedere in ma<lb></lb>teria (altramente le Mathematice ſariano in tutto uane, & dinullo giouamento, ouer <lb></lb>profitto all'huomo, & ſe per caſo quelle non ſe uerificano, comc che nelle ſopradette li <lb></lb>bre, ouer bilance maggior, & menor, e ſtato detto, & diſputato. </s> <s id="s.001565">Eglie da credere, anci <lb></lb>da tener per fermo, che il tutto proceda dalla diſproportionalita, & inequalita delle <lb></lb>parti, & membri materiali, dalli quali uengono compoſte, cioe che le dette parti, & <lb></lb>memibri dell'una piu ſe diſcoſtano, ouer allontanano da quelle conſiderate fuora de ogni <lb></lb>materia, di quello che fanno quelli dell'altra.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per tanto uolendo difendere, & ſalua<lb></lb>re tal queſtione Aristotelica, cioe far che quella ſempre ſe uerifichi in materia, & in <lb></lb>ogni qualita de libre, ouer bilance ſi grande, come piccole. </s> <s id="s.001566">Biſogna agguagliar le dette <lb></lb>parti, ouer membri dicadauna di quelle, talmente che quelli ſiano egualmente diſtanti <lb></lb>da quelle conſiderate fuora de ogni materia ſenſibile. </s> <s id="s.001567">Ilche <expan abbr="facẽdo">facendo</expan> non ſolamente ſe ue <lb></lb>rificara tal ſua queſtione al ſenſo in materia, cioe nelle dette libre, ouer bilance materia <lb></lb>le, ma anchora ſe uerificaranno quelle altre due concluſioni, che ſottogionſe in fine.<emph.end type="italics"></emph.end><lb></lb>S.A. I<emph type="italics"></emph>o ho accaro che la mia opinione ſe ſia uerificata.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001568">QVESITO SECONDO FATTO CONSEQ VEN<lb></lb><emph type="italics"></emph>temente dal medeſimo Illustrißimo Signor Don <lb></lb>Diego Ambaſciator <lb></lb>Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001569">SIGNOR AMBASCIATORE. M<emph type="italics"></emph>a per non hauer troppo ben inteſo le <lb></lb>ragioni da uoi allegate, uorria che un'altra uolta, & piu chiar amente me le repli <lb></lb>casti.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>ico Signore, che la cauſa che le ſopradette libre, ouer bilance maggiore, <lb></lb>& menore, non riſpondeno ſecondo che l'autor conchiude, & dimoſtra, non procede <lb></lb>d'altro, che dalla inequalita delle parti, ouer membrimateriali, dalli quali uengono com <lb></lb>poſte, le quai parti, ouer membri, ſono li dui bracci, & anchora il ſparto (cioe quel <lb></lb>axis ouer centro, ſopra del qual girano li detti bracci in cadauna de loro, perche li <lb></lb>detti bracci, & ſparto nelle libre, ouer bilance maggiore ſono molto piu großi, & cor <lb></lb>pulenti di quelle delle menore. </s> <s id="s.001570">Et perche li bracci di quelle libre, ouer bilance che uen<lb></lb>gono conſiderate, come Mathematico, cioe fuora de ogni materia, ſono conſiderati, et <lb></lb>ſuppoſti, come ſimplice linee, cioe ſenza larghezza, ne groſſezza, & il ſparto, ouer <lb></lb>axis di quelle uien conſiderato, & ſuppoſto un ſimplice ponto indiuiſibile, le qual ſorte <lb></lb>de libre, ouer <expan abbr="bilãce">bilance</expan>. </s> <s id="s.001571"><expan abbr="Quãdo">Quando</expan> che poßibil foſſe à darne una coſi realmente ſpogliata, & <lb></lb>nuda de ogni materia ſenſibile, come che con la <expan abbr="mẽte">mente</expan> uengono conſiderate, ſenza alcun<emph.end type="italics"></emph.end><pb pagenum="80" xlink:href="042/01/160.jpg"></pb><emph type="italics"></emph>dubbio quella ſaria agilißima, & diligentißima ſopra à tutte lelibre, ouer bilance ma <lb></lb>teriale, di quella medeſima grandezza, perche quella ſaria totalmente libera da ogni <lb></lb>material impedimento. </s> <s id="s.001572">Et per tanto conchiudendo dico, che quanto piu le parti, ouer <lb></lb>membri di una libra, ouer bilanza materiale, ſe accoſtano, ouer appropinquano alle <lb></lb>parti, ouer membri della non materiale (qual è la originale, ouer ideale di tutte le mate <lb></lb>riale) tanto ſara piu agile, & diligente di quelle che men ui ſe accostaranno, ouer ap<lb></lb>propinquaranno (di quella medeſima grandezza') Et perche le parti, ouer membri di <lb></lb>quelle bilancette, che adoprano li Bancheri, & Gioieleri (diſopra allegate) molto piu <lb></lb>ſe accoſtano, ouer appropinquano alle parti, ouer membri della detta ſua ideale, di <lb></lb>quello che fanno le parti, ouer membri di quelle libre, ouer bilance maggiori, che ado<lb></lb>prano li Speciali (diſopra allegate) perche li brazzetti delle dette bilancette piccole <lb></lb>ſono ſottilißimi, & quelli delle grande ſono piu großi. </s> <s id="s.001573">Onde li ſottili piu ſe accoſtano <lb></lb>alla ſimplice linea (quale manca de larghezza, & groſſezza) di quello fanno li piu <lb></lb>großi, & corpulenti, & ſimilmente il ſparto, ouer axis delle dette librette, ouer bilan<lb></lb>cette piccole, è piccolino, & ſottile, & quello delle grande, è piu grande, & groſſo. <lb></lb></s> <s id="s.001574">Onde il detto ſparto delle dette bilancette piccole piu ſe accosta, ouer appropinqua al <lb></lb>ſparto della ſua ideale (qual è un ponto indiuiſibile) di quello fa il ſparto delle dette bi<lb></lb>lance grande per eſſer piu grande, & groſſo. </s> <s id="s.001575">Et queſta è la principal cauſa che le ſopra <lb></lb>dette librette, ouer bilancette menori, ſe dimoſtrano al ſenſo piu diligente delle mag<lb></lb>giori, cofa totalmente contraria alla ſopra allegata Ariſtotelica queſtione.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001576">QVESITO TERZO FATTO CONSE<lb></lb><emph type="italics"></emph>quentemente dal medeſimo Illuſtrißimo <lb></lb>Signor Don Diego Ambaſcia<lb></lb>tor Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001577">SIGNOR AMBASCIAT ORE. B<emph type="italics"></emph>en in che modo ſi puo difendere, & <lb></lb>ſaluare talſua queſtione, cioe far che quella ſe uerifichi al ſenſo in materia ſecon<lb></lb>do che lui propone, ouer conchiude.<emph.end type="italics"></emph.end> N. B<emph type="italics"></emph>iſogna fondarſe ſopra le libre, ouer bilan<lb></lb>ce ideale, cioe ſopra quelle che uengono conſiderate con la mente aſtratte da ogni mate<lb></lb>ria, & uedere in che coſale maggiore ſiano differente dalle menore, la qual coſa eſſen <lb></lb>do oſſeruata nelle libre, ouer bilance materiale ſara difeſa, & ſaluata tal queſtione Ari <lb></lb>ſtotelica, cioe che quella ſempre ſe uerificara al ſenſo nelle dette libre materiale.<emph.end type="italics"></emph.end> S. A. <lb></lb>N<emph type="italics"></emph>on ue intendo parlatime piu chiaro.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>ico Signore, che à uoler difendere, & <lb></lb>ſaluare tal queſtione, biſogna fondarſe, ouer reggerſi per le libre, ouer bilance idea<lb></lb>le, cioe per quelle, che con la mente uengono conſiderate fuora de ogni materia, & <lb></lb>uedere in che coſa le maggiori ſiano differente dalle menori, ſopra la qual coſa con<lb></lb>ſiderando, & guardando, ſe trouara, che le dette libre, ouer bilance maggiori, nen <lb></lb>ſono differente dalle menori, eccetto che nella longhezza di ſuoi bracci, & in tut<lb></lb>te le altre coſe ſe agguagliano, perche anchor che li bracci delle libre maggiori ſia<lb></lb>no piu longhi de quelli delle menori, tamen non ſono ne piu großi, ne piu ſotti<lb></lb>li de quelli, perche, ſi nelle maggiori, come nelle menori, ſono conſiderati, <pb xlink:href="042/01/161.jpg"></pb>come ſtmplice linee, le quale mancano dilarghezza, & groſſezza, e pero in larghez<lb></lb>za, & groſſezza non ui è alcuna differentia. </s> <s id="s.001578">Et ſimilmente li ſparti, ouer axi delle li<lb></lb>bre, ouer bilance maggiori ſono eguali alli ſparti, ouer axi delle menori, perche ſi nelle <lb></lb>maggiori, come nelle menori ſono conſiderati, come ſimplici ponti, li quali ponti per eſ<lb></lb>ſer tutti indiuiſibili, ſono eguali, le qual coſe eſſendo diligentemente oſſeruate nelle li<lb></lb>bre, ouer bilance materiale, cioe che le maggiore non ſiano differente dalle menore, ec<lb></lb>cetto che nella longhezza di ſuoi bracci, ma che in larghezza, et groſſezza ſiano egua <lb></lb>li, & coſi li lor ſparti materiali ſenza dubbio in quelle, non ſolamente ſe uerificara al <lb></lb>ſenſo quello, che Aristotile nella detta ſua queſtione conchiude. </s> <s id="s.001579">Ma anchora ſe uerifica <lb></lb>ranno, quelle altre due concluſioni che ui ſottogionſe in fine.<emph.end type="italics"></emph.end> (A<emph type="italics"></emph>nchor che in aſtratto, <lb></lb>cioe fuora de ognimateria, ambedue falſe ſiano, come che per li principij della ſcientia <lb></lb>di peſi à<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>faro manifeſto.<emph.end type="italics"></emph.end>) E<emph type="italics"></emph>t ſiano le dette libre, ouer bilance di che qualita, mate<lb></lb>ria, & condition fi uoglia, pur che oſſeruino la detta egualita nella groſſezza di detti <lb></lb>bracci, & ſpartiloro.<emph.end type="italics"></emph.end> S.A. C<emph type="italics"></emph>ertamente che queſto uoſtro diſcorſo me piace aſſai.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001580">QVESITO QVARTO FATTO CONSE<lb></lb><emph type="italics"></emph>quentemente dal medeſimo Illuſtrißimo Signor <lb></lb>Don Diego Ambaſciator Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001581">SIGNOR AMBASCIATORE. M<emph type="italics"></emph>a ſe ben me aricordo uoi dicesti an<lb></lb>chora nel principio del noſtro ragionamento, che Ariſtotile pretermette, ouer ta <lb></lb>ce una queſtione ſopra delle dette libre di non poca importantia, ouer ſpeculatione, hor <lb></lb>ditemi, che queſtione è queſta.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>e<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>ben ſe aricorda della ſua ſeconda queſtione, <lb></lb>in quella lui mterrogatiuamente adimanda, & conſequentemente dimoſtra, perche cau <lb></lb>ſa quando che <gap></gap> ſparto ſera diſopra della libra, & che l'uno di bracci di qu<gap></gap>lla da qual<lb></lb>che peſo ſia portato, ouer ſpinto à baſſo, remoſſo cheſia, ouer leuato uia quel tal peſo, <lb></lb>la detta libra di nuouo reaſcende, & ritorna al ſuo primo luoco. </s> <s id="s.001582">Et ſe il detto ſparto é <lb></lb>di ſotto della detta libra, & che medeſimamente l'uno di ſuoi bracci ſia da qualche peſo <lb></lb>pur portato, ouer ſpinto à baſſo remoſſo, ouer leuato che ſia uia quel tal peſo la detta li <lb></lb>bra non reaſcende, ne ritorna al ſuo primo luoco (come che fa nell'altra poſitione) ma <lb></lb>rimane diſotto, cioe à baſſo. </s> <s id="s.001583">Hor dico, che lui pretermette, ouer tace un'altra queſtio<lb></lb>ne, che in queſto luoco ſe conueneria, di molta maggior ſpcculatione di cadauna delle ſo<lb></lb>pradette, la qual queſtione è queſta. </s> <s id="s.001584">Perche cauſa quando che il ſparto è preciſamente <lb></lb>in eſſa libra, et che l'un di bracci di quella ſta da qualche peſo portato, ouer urtato à baſ <lb></lb>ſo, remoſſo, ouer ieuato che ſia uia quel tal peſo, la detta libra di nuouo reaſcende al ſuo <lb></lb>primo luoco, ſi come che fa anchora quella, che ha il ſparto di ſopra da lei.<emph.end type="italics"></emph.end> S. A. <lb></lb>Q<emph type="italics"></emph>ueſta mi pare una bella queſtione, & molto piu remota dal noſtro intelletto natu<lb></lb>rale che le due ſopradette, & molto hauero accaro ad intendere la cauſa di tal effetto, <lb></lb>ma prima noglio che me chiariti un dubbio, che nella mente me intona ſopra delle ſopra <lb></lb>allegate queſiioni, il quale è queſto.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="81" xlink:href="042/01/162.jpg"></pb> <p type="head"> <s id="s.001585">QVESITO QVINTO FATO CONSE QVENTE<lb></lb><emph type="italics"></emph>temente dal medeſimo Illustrißimo Signor Don Diego, <lb></lb>Ambaſciator Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001586">SIGNOR AMBASCIATORE. D<emph type="italics"></emph>oue ſe troua una libra, ouer bilanza <lb></lb>materiale, che il ſuo ſparto ſia di ſopra, ouer di ſotto di quella, anci à me mi pare, <lb></lb>che il detto ſparto in tutte ſia preciſamente in eſſe libre, come, che nella uoſtra terza <lb></lb>question ſe ſuppone, & non di ſopra, ne manco di ſotto.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nchor, che di tal ſorte <lb></lb>bilance non ſi faccia, ouer ſi troui el non reſta pero, chel non ſe ne poteſſe fare.<emph.end type="italics"></emph.end> S.A. <lb></lb></s> <s id="s.001587">A <emph type="italics"></emph>me mi pare una materia, à mouer queſtione ſopra à <expan abbr="cōſe">conſe</expan>, che non ſi costumano, ne ſi <lb></lb>trouino in eßere.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>l tutto ſifa Signore, perche tutti li artificioſi iſtromenti, che <lb></lb>per augumentare le forze del huomo ſe oprano, in qual ſi uoglia arte Mechanica ſe re <lb></lb>feriſcono à una delle ſopradettetre ſpecie de libre, ouer bilance, et coſi in ogni dubbio, <lb></lb>ouer queſtione, che ſopra ad alcuno de tai iſtromenti naſcer poteſſe, uolendone conoſce <lb></lb>re, ouer aßignare la intrinſica cauſa. </s> <s id="s.001588">Eglie neceſſario prima uenir a quella ſorte libra, <lb></lb>ouer bilanza, alla qual piu ſe referiſſe quel tal iſtromento, & dalla detta libra, ouer bi <lb></lb>lanza ſe uien al cerchio, per la mirabil uirtu, & potentia del qnale ſe riſolue il tutto, <lb></lb>come, che nella ſcientia di peſi ſi fara manifeſto.<emph.end type="italics"></emph.end> S. A. E<emph type="italics"></emph>ſſendo adunque coſe di tan<lb></lb>ta importantia, uoglio, che me replicati, & dimoſtrati figuralmente cadauna de det <lb></lb>te tre Queſtioni, ouer parti a una per una: perche le uoglio ben intendere, & comin<lb></lb>ciati alla prima.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er dimoſtrar in figura la prima parte di tal Queſtione. </s> <s id="s.001589">Sia la <lb></lb>libra. </s> <s id="s.001590">a. b. el ſparto della quale ſia el ponto. </s> <s id="s.001591">c. (qual ſparto ſia alquanto di ſopra del<lb></lb>la detta libra.a. </s> <s id="s.001592">b. come nella figura appare) & ſia che per la impoſitione del peſo. </s> <s id="s.001593">e. <lb></lb>el ſuo brazzo. </s> <s id="s.001594">a. d. </s> <s id="s.001595">ſia da quel tirato a baſſo, come che di ſotto appare in detta figu <lb></lb>ra: hor dico, che chileuaſſeuia el detto peſo.e.tal brazzo. </s> <s id="s.001596">a. d. </s> <s id="s.001597">reaſcendaria, &<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.162.1.jpg" xlink:href="042/01/162/1.jpg"></figure><lb></lb><emph type="italics"></emph>retornaria al ſuo primo, & condecente luoco, el qual luoco ſaria nel ponto, ouer <lb></lb>ſito.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>& coſi l'altro brazzo. </s> <s id="s.001598">d. </s> <s id="s.001599">b. deſcendaria per fina al ponto, ouer ſito. </s> <s id="s.001600">l. </s> <s id="s.001601">& <lb></lb>tutto queſto procede: perche nel traſportar el detto brazzo. </s> <s id="s.001602">a. d. </s> <s id="s.001603">a baſſo, piu del<lb></lb>la mitta di tutto el fuſto della detta libra. </s> <s id="s.001604">a. b. ſe uien a trasferrirſi in alto, cioe <lb></lb>oltra la perpendicolar.n.m. </s> <s id="s.001605">paſſante per il ſparto.c.la qual perpendicolar ſe chiama<emph.end type="italics"></emph.end><pb xlink:href="042/01/163.jpg"></pb><emph type="italics"></emph>la lined della direttione, cioe, che la parte.b.d. </s> <s id="s.001606">g. in alto elleuata uien à eſſer tan<lb></lb>to piu della mita de tutto el fuſto.a.b.quanto che è dal.d.al.g.& la reſtante parte.a.g. <lb></lb></s> <s id="s.001607">ridutta al baſſo uien à eſſer tanto manco della mita di tutto el detto fuſto.a.b. </s> <s id="s.001608">quanto <lb></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></lb>molto maggiore del restante brazzo.a.g.al baſſo trasferto, leuandoſe uia el detto pe<lb></lb>ſo.e.la detta parte.a.g. (piu debole) uien à eßer urtata, & ſpinta dall'altra maggior <lb></lb>parte.b.d.g.in alto elleuata (per eſſer di lei piu potente) per fin à tanto, che la detta li <lb></lb>nea della direttione caſchi perpendicolarmente ſopra el detto fuſto, ouer libra.a.b. </s> <s id="s.001610">& <lb></lb>che ſeghi quello in due parti equali in ponto.d.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſtaragion è quaſi ſimile à <lb></lb>quella che aduce Ariſtotile, ma è alquanto piu chiara, & miglior figura.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001611">QVESITO SESTO FATTO CONSE<lb></lb><emph type="italics"></emph>quentemente dal medeſimo Illuſtrißimo Signor <lb></lb>Don Diego Ambaſciator Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001612">SIGNOR AMBASCIATORE. H<emph type="italics"></emph>or ſeguitati la ſeconda parte.<emph.end type="italics"></emph.end> N. <lb></lb>P<emph type="italics"></emph>er dimoſtrare la ſeconda à uoſtra Signoria. </s> <s id="s.001613">Pongo ſia la libra.a. </s> <s id="s.001614">b. la qual hab<lb></lb>bia il ſparto (cioe quel ponto, ouer polo, ſopra del qual lei gira) alquanto di ſotto, cioe <lb></lb>diſotto dal fuſto.a.b.come diſotto appar in ponto.c. </s> <s id="s.001615">& ſia anchor, che per la impoſi<lb></lb>tion del peſo.e.el ſuo brazzo.a.d.ſia da quel tirato à baſſo, come che di ſotto nella figu <lb></lb>ra appar, hor dico, che chi leuaſſe uia el detto peſo.e.tal brazzo nonreaſcenderia ne ri <lb></lb>tornaria al ſuo primo luoco, cioe in ponto.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>(come, che fa in quella, che ha il ſparto di <lb></lb>ſopra) ma rcſtaria coſi inclinato à baſſo, & la cauſa di queſto procede, perche nel tra <lb></lb>ſportarſe el detto brazzo.a.d.al baſſo piu della mitta di tutto el fuſto, ouer libra.a.b.<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.163.1.jpg" xlink:href="042/01/163/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſi uien à trasferire drio à quello, oltra la linea della direttione, cioe oltra la perpendi<lb></lb>colar.n.m.qual paſſa per il ſparto.c.tal che tutta la parte.a.g. </s> <s id="s.001616">al baſſo ridutta, uien à <lb></lb>eſſer 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></lb></s> <s id="s.001618">b. in alto elleuata uien à reſtare tanto meno della detta mitta, quanto, che è dal detto.d. <lb></lb></s> <s id="s.001619">al detto.g.per eſſer adunque la elleuata parte.g.b.di menor quantita della inelinata.a. <lb></lb></s> <s id="s.001620">g.uien à eſſer piu debole, ouer men potente di lei, e pero, non é atta, ne <expan abbr="ſofficiẽte">ſofficiente</expan> à po-<emph.end type="italics"></emph.end><pb pagenum="82" xlink:href="042/01/164.jpg"></pb><emph type="italics"></emph>terla urtare, & sforzare à farla aſcendere al ſuo primo luoco in.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>come fece nella paſ <lb></lb>ſata, anci quella restara coſi inclinata al baſſo, & la retenera lei coſi in aere clleuata, <lb></lb>che è il propoſito.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueste due parti quaſi, che il noſtro intelletto le apprende <lb></lb>per ragion naturale, ſenza altra dimoſtratione.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>oſt è Signore.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001621">QVESITO SETTIMO FATTO CONSEQ VENTEMEN<lb></lb><emph type="italics"></emph>te dal medeſimo Illustrißimo Signor Don Diego, <lb></lb>Ambaſciator Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001622">SIGNOR AMBASCIATORE. H<emph type="italics"></emph>or ſeguitati mo la terza parte, quale <lb></lb>diceti, che manca in queſto luoco, cioe doue naſce la cauſa, che quando el ſparto de <lb></lb>una libra ſara preciſamente nel mezzo di eſſa, cioe ne di ſotto, ne di ſopra, ma nel me<emph.end type="italics"></emph.end>z <lb></lb><emph type="italics"></emph>zo di quella, come, che ſono tutte le libre, ouer bilance, che communamente ſe oprano, <lb></lb>& che l'uno di bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>i di quella ſia da qualche peſo (ouer dalla noſtra mano) urtato à <lb></lb>baſſo, leuado, che ſia uia quel tal peſo (ouer mano) immediate tal bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o riaſcende, et <lb></lb>ritorna al ſuo primo luoco ſi come che anchor fa <expan abbr="q̃lla">qualla</expan> libra, qual <expan abbr="tiẽ">tiem</expan> il ſparto di ſopra <lb></lb>da eſſa libra. </s> <s id="s.001623">Perche in effetto la cauſa di queſto ultimo effetto mi par molto piu remo <lb></lb>ta dal noſtro intelletto de cadauna delle altre due.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>ho detto à uoſtra Signoria, <lb></lb>che à uoler dimostrare la cauſa di tal effetto à me è neceßario à diffinire, & dechiari<lb></lb>re prima à uoſtra Signoria alcuni termini, & principij della ſcientia di peſi.<emph.end type="italics"></emph.end> S.A. S<emph type="italics"></emph>o <lb></lb>no coſa longa questi principij, che ui biſogna dechiarare.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er <expan abbr="quãto">quanto</expan> aſpetta à uo <lb></lb>ler demoſtr are ſimplicemente queſta particolarita ſara coſa breuißima, uero è, che <lb></lb>quando, che uoſtra ſignoria uoleſſe intendere ordinariamente tutti li principij di tal <lb></lb>ſcientia, ui ſaria da dire aſſai.<emph.end type="italics"></emph.end> S.A. B<emph type="italics"></emph>enſa, che uoglio intendere il tutto <expan abbr="ordinariamẽ">ordinariamen</expan> <lb></lb>te, come ſi de.<emph.end type="italics"></emph.end> N. L'<emph type="italics"></emph>hora è tarda Signore per far queſto effetto.<emph.end type="italics"></emph.end> S.A. B<emph type="italics"></emph>en andati, <lb></lb>& ritornati dimane da mattina.<emph.end type="italics"></emph.end> N. R<emph type="italics"></emph>itornaro Signore.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001624">I<emph type="italics"></emph>l fine del ſettimo Libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb xlink:href="042/01/165.jpg"></pb> <p type="head"> <s id="s.001625">LIBRO OTTAVO DELLI <lb></lb>QVESITI, ET INVENTIONI DIVERSE, <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.001626">S<emph type="italics"></emph>oprala Scientia di Peſi.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001627">QVESITO PRIMO FATTO DAL ILLVSTRISS.S<emph type="italics"></emph>ignor Don Diego Hurtado di Mendozza, Ambaſciator <lb></lb>Ceſareo in Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001628">SIGNOR AMBASCIATORE. H<emph type="italics"></emph>or uoria Tartaglia, <lb></lb>che me incomenciasti à dechiarire ordinariamente quella ſcien<lb></lb>tia de peſi, di che me parlaſti hiæri. </s> <s id="s.001629">Ma, perche conoſco tal ſcien <lb></lb>tia non eſſer ſemplicemente per ſe (per non eſſer le arte liberale, <lb></lb>ſaluo che ſette) ma ſubalternata, uoria che prima me diceſti, da <lb></lb>che ſcientia, ouer diſciplina quella deriui, & naſci.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor <lb></lb>Clarißimo parte di queſtaſcientia naſce, ouer deriua dalla Geo<lb></lb>metria, & parte dalla Natur al Philoſophia: perche, parte delle ſue concluſioni ſe dimo <lb></lb>ſtrano Geometricamente, & parte ſe approuano Phyſicalmente, cioe naturalmente.<emph.end type="italics"></emph.end><lb></lb>S.A. </s> <s id="s.001630">E <emph type="italics"></emph>ue ho inteſo circa questa particolarita.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001631">QVESITO SECONDO FATTO CONSEQ VEN<lb></lb><emph type="italics"></emph>temente dal medeſimo Illustrißimo Signor Don <lb></lb>Diego Ambaſciator <lb></lb>Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001632">SIGNOR AMBASCIATORE. M<emph type="italics"></emph>a ditime anchora, che coſtrutto ſi puo <lb></lb>cauar di tal ſcientia.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>i coſtrutti, che di tal ſcientia ſi potriano cauare, ſa<lb></lb>ria quaſi impoßibile à poterli à uoſtra Signoria iſprimere, ouer connumerare, nondi<lb></lb>meno io ue referiro quelli, che per al preſente à me ſono manifeſti. </s> <s id="s.001633">Et per tanto dico, <lb></lb>che primamente per uigore di tal ſcientia, eglie poßibile à conoſcere, & miſurare con <lb></lb>ragione la uirtu, & potentia di tutti queſti iſtromenti Mechanici, che da noſtri anti<lb></lb>qui ſono ſtati ritrouati, per augumentare la forza de l'huomo, nel elleuare, condurre, <lb></lb>ouer ſpingere auanti ogni graue peſo cioe in qual ſi uoglia grandezza, che quelli ſiano <lb></lb>conſtituidi, ouer fabricati, ſecondariamente per uirtu di tal ſcientia, non ſolamente <lb></lb>eglie poßibile di poter con ragion conoſcere, & miſurare ſimplicemente la forza de <lb></lb>l'huomo, ma anchora eglie poßibile di trouar el modo di augumentar quella in infini<lb></lb>to, & in uarij modi, & coſi in qual ſi uoglia modo eglie poßibile à conoſcere l'ordine, <lb></lb>& proportione di tal augumentatione, come, che in fine con uarij iſtromenti Mecha<lb></lb>nici à Voſtra Signoria faro conoſcere, & uedere.<emph.end type="italics"></emph.end> S. A. Q<emph type="italics"></emph>uesto hauero molto <lb></lb>accaro.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="83" xlink:href="042/01/166.jpg"></pb> <p type="head"> <s id="s.001634">QVESITO TERZO FATTO CONSE<lb></lb><emph type="italics"></emph>quentemente dal medeſimo Illuſtrißimo Signor <lb></lb>Don Diego Ambaſcia <lb></lb>tor Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001635">SIGNOR AMBASCIAT ORE. H<emph type="italics"></emph>or ſeguitati, come ui pare circa à tal <lb></lb>ſcientia.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er procedere regolatamente, hoggi diffiniremo ſolamente alcuni <lb></lb>termini, & modi di parlare occorrenti in queſta ſcientia, accio che il frutto della intel <lb></lb>ligentia di quella,<emph.end type="italics"></emph.end> V.S.<emph type="italics"></emph>piu facilmente apprenda. </s> <s id="s.001636">Dimane poi dichiariremo li principij <lb></lb>di tal ſcientia, cioe quelle coſe che in tal ſcientia non ſi poſſono dimoſtrare, perche (co <lb></lb>me che<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>ſa) ogni ſcientia ha li ſuoi primi princpij indemoſtrabili, li quali eſſendo <lb></lb>do conceßi, ouer ſuppoſti per lor meggio ſi diſputa, & ſoſtenta tutta la ſcientia, dapoi <lb></lb>queſto andaremo preponendo uarie propoſitioni, ouer concluſioni ſopra di tal ſcien<lb></lb>tia, & parte de quelle dimostraremo à<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>con argomenti Geometrici, & parte ap<lb></lb>prouaremo con ragioni naturali, come di ſopra dißi. </s> <s id="s.001637">Et dapoi questo,<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>preponera <lb></lb>tutti quei dubbij, ouer queſtioni che à quella gli parera, nelle coſe Mecanice, & maßi<lb></lb>me ſopra li mir abili effetti delli ſopradetti iſtromenti materiali che augumentano la <lb></lb>forza dell'huomo, che per le coſe dette, & approbate, nella detta ſcientia de peſi, tutte <lb></lb>ſe reſolueranno.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſto uoſtro procedere coſi regolatamente molto mi piace.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001638">QVESITO QVARTO FATTO CONSE<lb></lb><emph type="italics"></emph>quentemente dal medeſimo Illuſtrißimo Signor Don <lb></lb>Diego Ambaſciator Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001639">SIGNOR AMBASCIATORE. H<emph type="italics"></emph>or ſeguitate adunque le dette diffini<lb></lb>tioni conſequentemente.<emph.end type="italics"></emph.end> N. </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"></emph>corpiſe dicono di grandezza eguali, quando che quelli occupano, ouer empi<lb></lb>no luochi eguali.<emph.end type="italics"></emph.end> S.A. D<emph type="italics"></emph>atemi qualche material eſſempio.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>ſſempi gra <lb></lb>tia, doi corpi ſpherici gettati, ouer prontati in una medeſima forma, ouer in forme e<lb></lb>guale, ſe diriano eguali di grandezza, anchor che fuſſeno di materia diuerſa, cioe che <lb></lb>l'uno fuſſe di piombo, & l'altro di ferro, ouer di pietra, & coſi ſi debbe intendere in <lb></lb>qual ſi uoglia altra diuerſita di forma.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.001642">E <emph type="italics"></emph>ue ho inteſo, ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.001643">QVESITO. V. DIFFINITIONE II.</s> </p> <p type="main"> <s id="s.001644">Si<emph type="italics"></emph>milmente li corpi ſe dicono di grandezza diuerſi, ouer ineguali, quando che <lb></lb>quelli occupano, ouer empino luochi diuerſi, ouer ineguali. </s> <s id="s.001645">Et maggiore ſe in<lb></lb>tende quello, che occupa maggior luoco.<emph.end type="italics"></emph.end> S. AMBASCIA. </s> <s id="s.001646">E <emph type="italics"></emph>ue ho inteſo, <lb></lb>ſeguitati.<emph.end type="italics"></emph.end> NIC. </s> </p> <pb xlink:href="042/01/167.jpg"></pb> <p type="head"> <s id="s.001647">QVESITO. VI. DIFFINITIONE TERZA.</s> </p> <p type="main"> <s id="s.001648">La <emph type="italics"></emph>uertu d'un corpo graue ſe intende, & piglia per quella potentia, che lui ha da <lb></lb>tendere, ouer di andare al baſſo, & anchora da reſiſtere al moto contrario, cioe <lb></lb>à che il uoleſſe tirar in ſuſo.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>uando che non ui dico altro ſeguitati, perche col <lb></lb>mio tacere, e ue dinoto hauerui inteſo, & che debbiati ſeguitare.<emph.end type="italics"></emph.end> N. </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"></emph>corpi ſe dicono de uertu, ouer potentia, equali, quando che quelli in tempi egua <lb></lb>li di moto pertranſiſcono ſpacij eguali.<emph.end type="italics"></emph.end></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"></emph>corpi ſe dicono de uertu, ouer potentia diuerſa, quando che quelli in tempi di<lb></lb>uerſi, pertranſiſcono di moto, ſpacij eguali, ouer che in tempi eguali pertranſi<lb></lb>ſcono interualli ineguali.<emph.end type="italics"></emph.end></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"></emph>uertu, ouer potentia de corpi diuerſi, quella ſe intende eſſer maggiore, la qua <lb></lb>le nel pertranſire uno medeſimo ſpacio ſumme manco tempo. </s> <s id="s.001655">Et menor quella <lb></lb>che ſumme piu tempo, ouer amente quella che in tempi eguali pertranſiſſe mag<lb></lb>gior ſpacio.<emph.end type="italics"></emph.end></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"></emph>elli corpi ſe dicono eſſere di uno medeſimo genere, quando che ſono di egual <lb></lb>grandezza, & che ſono anchora di egual uertu, ouer potentia.<emph.end type="italics"></emph.end></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"></emph>ellicorpi ſe dicono eſſere de diuerſi generi, quando che ſono di egual gran<lb></lb>dezza, & che non ſono di egual uertu, ouer potentia.<emph.end type="italics"></emph.end></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"></emph>elli corpi ſe dicono eſſere ſimplicemente eguali in grauita, li quali ſono real<lb></lb>mente di egual peſo, anchor che fuſſeno dimateria diuerſa.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001662">QVESITO. XIII. DIFFINITIO<lb></lb>NE DECIMA.</s> </p> <pb pagenum="84" xlink:href="042/01/168.jpg"></pb> <p type="main"> <s id="s.001663">Vn <emph type="italics"></emph>corpo ſe dice eſſere ſiinplicemente piu graue d'un'altro, quando che quello <lb></lb>è realmente piu ponderoſo di quello, anchor che fuſſe di materia diuerſa.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001664">QVESITO. XIIII. DIFFINITIONE XI.</s> </p> <p type="main"> <s id="s.001665">Vn <emph type="italics"></emph>corpo ſe dice eſſere piu graue d'un'altro ſecondo la ſpecie, quando che la ſo<lb></lb>ſtantia material di quello è piu ponderoſa della ſoſtantia material dell'altro, co<lb></lb>me che è il piombo del ferro, & altri ſimili.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001666">QVESITO. XV. DIFFINITIONE XII.</s> </p> <p type="main"> <s id="s.001667">Vn <emph type="italics"></emph>corpo ſe dice eſſere piu, ouer men graue d'un'altro nel deſcendere, quando <lb></lb>che la rettitudine, obliquita, ouer dependentia del luoco, ouer ſpacio doue de<lb></lb>ſcende lo fa deſcendere piu, ouer men graue dell'altro, & ſimilmente piu, ouer menue<lb></lb>loce dell'altro, anchor che ſiano ambidui ſimplicemente eguali in grauita.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001668">QVESITO. XVI. DIFFINITIONE XIII.</s> </p> <p type="main"> <s id="s.001669">Vn <emph type="italics"></emph>corpo ſi dice eſſere piu graue, ouer men graue d'un'altro, ſecondo il luoco, <lb></lb>ouer ſito, quando che la qualita del luoco doue che lui ſeripoſa, & giace, lo fa <lb></lb>eſſere piu graue dell'altro anchor che fuſſeno ſimplicemente egualmente gr aui.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001670">QVESITO. XVII. DIFFINITIONE XIIII.</s> </p> <p type="main"> <s id="s.001671">La <emph type="italics"></emph>grauita d'un corpo ſe dice eſſerenota, quando che il numero delle libre, che <lb></lb>lui peſane ſia noto, ouer altra denomination de peſo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001672">QVESITO. XVIII. DIFFINITIONE XV.</s> </p> <p type="main"> <s id="s.001673">Li <emph type="italics"></emph>bracci de una libra, ouer bilancia ſe dicono eſſere nel ſito, ouer luoco della e<lb></lb>qualita, quando che quelli ſtanno equidiſtanti al piano dell'Orizonte.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001674">QVESITO. XIX. DIFFINITIONE XVI.</s> </p> <p type="main"> <s id="s.001675">La <emph type="italics"></emph>linea della diretttione é una linearetta imaginata uenire perpendicolarmen<lb></lb>te da alto al baſſo, & paſſare per il ſparto, polo, ouer aßis de ogni ſorte libra, <lb></lb>ouer bilancia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001676">QVESITO. XX. DIFFINITIONE XVII.</s> </p> <p type="main"> <s id="s.001677">Pi<emph type="italics"></emph>u obliquo ſe dice eſſere quel deſcenſo, d'un corpo graue, il quale in una medeſi<lb></lb>ma quantita, capiſſe manco della linea della direttione, oueramente del deſcenſo <pb xlink:href="042/01/169.jpg"></pb>vetto uerſo il centro del mondo.<emph.end type="italics"></emph.end> S. A. I<emph type="italics"></emph>n queſta non ue intendo troppo bene. </s> <s id="s.001678">e pero <lb></lb>datemi uno eſſempio.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er eſſemplificare queſta diffinitione ſia il corpo.a. & il <lb></lb>retto deſcenſo di quello uerſo il centro del mondo ſia la linea.a.b. </s> <s id="s.001679">& ſia anchora li de<lb></lb>ſcenſi.a.c. </s> <s id="s.001680">&. </s> <s id="s.001681">a.d. & de queſti dui ne ſia ſignati le due quantita, ouer parti.a.e. </s> <s id="s.001682">&. </s> <s id="s.001683">a.f. <lb></lb>eguale, & dalli dui ponti.e. </s> <s id="s.001684">&. </s> <s id="s.001685">f. ſiano tirate le <lb></lb>due linee.e.g. </s> <s id="s.001686">&. </s> <s id="s.001687">f.h. equidiſtanti al piano del<lb></lb>l'Orizonte, e perche la parte.a.b.è menore della <lb></lb>parte.a.g. </s> <s id="s.001688">il deſcenſo.a.f.d.ſe dira eſſer piu obli <lb></lb>quo del deſcenſo.a.e.c.perche lui capiſſe manco <lb></lb>del deſcenſo retto, cioe della linea.a.b.in una me <lb></lb>deſima quantita. </s> <s id="s.001689">Et queſto medeſimo ſi debbe in<lb></lb>tendere in tutti li deſcenſi che poteſſe fare il det<lb></lb>to corpo.a. (ouer altro ſimile) ſtante appeſo al <lb></lb>al braccio di alcuna libra, cioe che quel deſcenſo <lb></lb>ſe dira eſſer piu obliquo, che per lo medeſimo mo <lb></lb>do capira manco della linea della direttione, in <lb></lb>una medeſima quantita de deſcenſo.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.001690">E <emph type="italics"></emph>ue<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.169.1.jpg" xlink:href="042/01/169/1.jpg"></figure><lb></lb><emph type="italics"></emph>ho inteſo àſofficientia, e pero ſeguitati ſe haueti altra coſa da diffinire.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignore <lb></lb>queſta é la ultima coſa che habbiamo da diffinire ſopra à queſta materia. </s> <s id="s.001691">Dimane poi <lb></lb>dichiariremo li principij di queſta ſcientia, <expan abbr="ſecõdo">ſecondo</expan> la promeſſa.<emph.end type="italics"></emph.end> S.A. A<emph type="italics"></emph>lla bon'hord.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001692">QVESITO. XXI. FATTO CONSE<lb></lb><emph type="italics"></emph>quentemente dal medeſimo Illuſtrißimo Signor <lb></lb>Don Diego Ambaſciator Ceſareo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001693">SIGNOR AMBASCIATORE. H<emph type="italics"></emph>or ſeguitati Tartaglia questi uoſtri <lb></lb>principij.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>iprincipij de qual ſi uoglia ſcientia alcuni uogliano che ſiano det <lb></lb>ti dignita, perche quelli approuano altri, & loro non ponno eſſere approuati da altri, <lb></lb>alcuni le chiamano ſuppoſitioni, perche ſe ſuppongono per ueri in detta ſcientia, altri <lb></lb>piacque chiamarli petitioni, perche uolendo diſputare tal ſcientia, & quella ſoſtentare <lb></lb>con dimoſtrationi, biſogna prima adimandar e all'auerſario la conceßione de quelli, <lb></lb>perche ſe lui non li uoleſſe concedere (ma negare) ſaria negata tutta la ſcientia, ne ui <lb></lb>occorreria à diſputarla altr amente. </s> <s id="s.001694">Et perche queſta ultima opinione mi piace alqnan<lb></lb>to piu delle altre due, petitioni le chiamaremo, & coſi anchora in forma de petitioni <lb></lb>li proferiremo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001695">QVESITO. XXII. PETITIONE PRIM A.</s> </p> <p type="head"> <s id="s.001696"><emph type="italics"></emph>&<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001697">Ad<emph type="italics"></emph>imandamo che ne ſia conceſſo, che il mouimento natur ale de ogni corpo pon<lb></lb>deroſo, e graue ſia rettamente uerſo il centro del mondo.<emph.end type="italics"></emph.end> S. AMB. Q<emph type="italics"></emph>ueſto <lb></lb>non è da negare.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="85" xlink:href="042/01/170.jpg"></pb> <p type="head"> <s id="s.001698">QVESITO XXIII. PETITIONE II.</s> </p> <p type="main"> <s id="s.001699">Si<emph type="italics"></emph>melmente adimandamo, che naſia conceſſo quel corpo, ch'è di maggior potentia <lb></lb>debbia anchora diſcendere piu uelocemente, et nelli moti contrarij, cioe nelli <expan abbr="aſcẽ-ſi">aſcen<lb></lb>ſi</expan>, aſcendere piu pigramente, dico nella libra.<emph.end type="italics"></emph.end> S.A. D<emph type="italics"></emph>atime uno eſſempio materiale <lb></lb>ſopra di queſta petitione, ſe uoleti, che ue intenda.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia, eſſempi gratia, le due li<lb></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. &. </s> <s id="s.001703">b.c.ſiano equali alli dui braz <lb></lb>zi.d.e. </s> <s id="s.001704">&. </s> <s id="s.001705">e.ſ. & li lor ſparti, ouer centriſiano.b. </s> <s id="s.001706">&. </s> <s id="s.001707">e. & nella iſtremita del brazzo. <lb></lb></s> <s id="s.001708">b.a.ui ſia appeſo il corpo.a.poniamo de libre due in grauita, & nella iſtremita de l'al<lb></lb>tro brazzo, cioe in ponto.c.non ui ſia alcuna altra grauita, & coſi nella iſtremita del <lb></lb>brazzo.e.d.ai ſia appeſo el corpo.d.poniamo di una libra ſola in grauita, & nellà i<lb></lb>ſtremita dell'altro brazzo, cioe in ponto.f.non ui ſia alcuna grauita, & ſiano li detti <lb></lb>dui corpi, coſi congionti elleuati con la mano in alto egualmente, come che di ſotto ap<lb></lb>par in figura: hor adimando, che me ſia conceſſo, laſciando andare cadauno de detti dui <lb></lb>corpi coſi in alto elleuati, che il corpo.a. (per eſſer piu graue) diſcenda piu ueloce-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.170.1.jpg" xlink:href="042/01/170/1.jpg"></figure><lb></lb><emph type="italics"></emph>mente al baſſo del corpo.d.cioe, che il detto corpo.a. ſumara manco tempo à pertran <lb></lb>ſire il curuo ſpacio.a.g.di quello fara il detto corpo. d o pertranſire il curuo ſpatio.d. <lb></lb></s> <s id="s.001709">h.li quali ſpacij uengono à eſſer eguali, perche li brazzi de dette libre ſono eguali dal <lb></lb>preſuppoſito, e pero li detti dui ſpacij, ouer deſcenſi curui, uengono à eſſer <expan abbr="circõferen">circonferen</expan> <lb></lb>tie di cerchij eguali. </s> <s id="s.001710">Et é conuerſo, quando, che li detti <expan abbr="corpiſarãno">corpiſaranno</expan> diſceſinel ſuo in<lb></lb>mo, ouer piu baſſo luoco, cioe l'uno in ponto.g. </s> <s id="s.001711">& l'altro in ponto.h.adimando, che me <lb></lb>ſia conceſſo, che quella uirtu, ouer potentia, la qual oſſendo appeſa nell'altro brazzo <lb></lb>della libra in ponto.c.ſara atta ad elleuare el detto corpo.a.per fin al luoco, doue, che <lb></lb>al preſente ſe ritroua nella figura ſuperiore, quella medeſima ſia atta ad alleuar piu ue <lb></lb>locemente il corpo.d.eſſendo appeſa nell'altro brazzo della ſua libra, cioe in <expan abbr="põto">ponto</expan>.f.<emph.end type="italics"></emph.end><lb></lb>S.A. Q<emph type="italics"></emph>uesto ui concedo, perche la ſperientia ne rende buona <expan abbr="teſtimoniãza">teſtimonianza</expan>.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>a <lb></lb>uoſtra Signoriaſappia, che quello, che hauemo detto, & adimandato delli detti dui cor <lb></lb>pi, delli quali l'uno é ſimplicemente piu potente dell'altro, il medeſimo adimandamo de <lb></lb>dui corpi ſimplicemente eguali in potentia ma inequali per uigor della lor poſitione, <lb></lb>ouer ſito nel brazzo de una medeſima libra, eſſempigratia, ſe nel brazzo.a.b. </s> <s id="s.001712">della<emph.end type="italics"></emph.end><pb xlink:href="042/01/171.jpg"></pb><emph type="italics"></emph>libra.a.b.c. </s> <s id="s.001713">ue ſia appeſo li dui corpi.a. </s> <s id="s.001714">&. </s> <s id="s.001715">d.ēguali ſimplicemente in potentia, cioe, <lb></lb>luno in ponto.a. </s> <s id="s.001716">& l'altro in ponto.d.come di ſotto appar in figura, anchor, che ſiano <lb></lb>ſimplicemente egualmente potenti, nondimeno il corpo.a. in tal poſitione per la. </s> <s id="s.001717">13. <lb></lb>diffinitione ſe dira eſſer piu grauedel corpo.d. come per lauenire ſe fara manifeſto, <lb></lb>perche in queſto luoco non ſi puo aßignar la ragioue per le coſe dette, ma per laueni<lb></lb>re ſe prouara el corpo.a. in ſimel ſito eſſer piu graue del corpo.d.e pero. </s> <s id="s.001718">eſſendo quelli <lb></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="eßẽdo">eßendo</expan> ambi dui abandonati, dico, <lb></lb>che il corpo.a.diſcẽdera piu ueloce del corpo.d. & é <expan abbr="cõuerſo">conuerſo</expan>, eſſendo luno, e l'altro di <lb></lb>ſceſi nelli loro infimi luochi, cioe luno in ponto.f. </s> <s id="s.001721">& laltro in ponto. </s> <s id="s.001722">h. quella potentia <lb></lb>che ſara atta in ponto.c.ad elleuare il corpo.a.dal ponto.f.per fina al ponto.e. </s> <s id="s.001723">quella <lb></lb>medeſima ſara atta ad elleuare nel medeſimo luoco, molto piu uelocemente il corpo.d.<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.171.1.jpg" xlink:href="042/01/171/1.jpg"></figure><lb></lb><emph type="italics"></emph>dal ponto.h.per fi al ponto.g.<emph.end type="italics"></emph.end> S. A. A<emph type="italics"></emph>nchora queſta è coſa chiara, ma uoria inten<lb></lb>dere due coſe da uoi. </s> <s id="s.001724">la prima é, che uoria intendere, perche non fingeti la ſopraſcritta <lb></lb>figura de libra, con quelle ſue due tazzette appeſe luna da un capo, & laltra da laltro <lb></lb>(come nelle material libre ſi coſtuma) per imponeruili peſi, ouer campioni in luna, & <lb></lb>nell'altra le coſe, che ſe hanno da ponderare; la ſeconda è, che uoria ſapere ſe queſto eſ <lb></lb>ſempio de libra ſi debbe intendere di quelle, che hanno il lor ſparto di ſopra, ouer di <lb></lb>quelle, che l'hanno di ſotto, ouer di quelle, che non l'hanno, ne di ſopra, ne di ſotto, ma <lb></lb>in eſſe libre proprie.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>irca alla prima, riſpondo, che la pura libra ſe intende per <lb></lb>quella pura <expan abbr="lõghezza">longhezza</expan>, che fcrma quelli dui brazziluno di qua, laltro di la dal ſparto, <lb></lb>ò ſiano li detti bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>iequali tra loro, ouer inequali, & quelle due tazzette, che dice<emph.end type="italics"></emph.end><lb></lb>V.S. <emph type="italics"></emph>non ſono parte della libra, ma ui ſe aggiongono per commodita del ponder ante, <lb></lb>per imponerui li campioni, & peſi, che ha da ponderare, ſi come ch'è anchora la ſella <lb></lb>dun cauallo, la quale non è parte del cauallo, ma una coſa aggionta per <expan abbr="cõmodita">commodita</expan> di co <lb></lb>lui, che l'ha da caualcare, e perche meglio ſi uede, & comprende uno cauallo nudato <lb></lb>della ſua ſella, che <expan abbr="cõ">com</expan> laſella, et <expan abbr="ſimelmẽte">ſimelmente</expan> una libra nudata di quelle ſue due tazzette, <lb></lb>che con le tazzette ſenza tazzette la eßemplificamo. </s> <s id="s.001725">Circa alla ſeconda particolari <lb></lb>ta, dico, che la preſente libra, & ſimelmente tutte quelle, che per lauenir ſi proponera <lb></lb>(non ſpecificando altro) ſi debbono intendere di quelle, che hanno il ſparto in lor me<lb></lb>defime, come nelle materiale ſi costuma.<emph.end type="italics"></emph.end> S.A. E<emph type="italics"></emph>ue ho inteſo, ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <pb pagenum="86" xlink:href="042/01/172.jpg"></pb> <p type="head"> <s id="s.001726">QVESITO. XXIIII. PETITIONE III.</s> </p> <p type="main"> <s id="s.001727">An<emph type="italics"></emph>chora adimandamo, che ne ſia conceſſo un corpo graue eſſer in el diſcendere <lb></lb>tanto piu graue, quanto che il moto di quello è piu retto al centro del mondo.<emph.end type="italics"></emph.end><lb></lb>S.A. D<emph type="italics"></emph>atime anchora uno qualche material eſſempio ſopra à queſt'altra petitione <lb></lb>ſe uoleti, che ui intenda.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia, eßempi gratia, il corpo graue.a. </s> <s id="s.001728">& poniamo, che le <lb></lb>quattro linee.a.b.a.c.a.d.a.e.ſiano <expan abbr="quattrō">quattrom</expan> luochi, ouer ſpacij da poter deſcendere el <lb></lb>detto corpo.a. & poniamo anchora, che la linea. </s> <s id="s.001729">a.b. ſtail rettißimo, & perpendico<lb></lb>lar deſcenſo uerſo il <expan abbr="cẽtro">centro</expan> del mondo, onde la linea.a. </s> <s id="s.001730">d.ueneria ad eßer piu retta uer <lb></lb>ſo il detto centro del mondo della linea.a.e. </s> <s id="s.001731">& per tanto in queſto caſo adimandamo, <lb></lb>chene ſia conceſſo ildetto corpo.a. eſſer piu graue nel diſcendere per la linea a.d. </s> <s id="s.001732">che <lb></lb>per la linea.a.e.per eſſer (come detto) piu retta di quella al centro del mondo, & ſi<lb></lb>melmente per la linea.a.c.deſcendere piu graue, che per la linea.a.d.per eſſer tal linea <lb></lb>a.c.piu retta al centro del mondo della detta tinea.a.d. </s> <s id="s.001733">& coſt quanto piu el detto cor <lb></lb>po.a.ſe andara accoſtando alla detta linea. </s> <s id="s.001734">a. b. nel ſuo deſcendere ſe ſuppone tanto <lb></lb>piu graue deſcendere, perche quel tranſito, ouer deſcenſo, che forma piu acuto angolo <lb></lb>con la linea.b.a.in ponto.a.ſe intende eßer piu retto al centro del mondo, di quello, che <lb></lb>lo forma men acuto. </s> <s id="s.001735">Onde per la linea.a.b.uien à diſcendere piu graue, che per qual ſi <lb></lb>uoglia altro uerſo.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.172.1.jpg" xlink:href="042/01/172/1.jpg"></figure> <p type="main"> <s id="s.001736">E<emph type="italics"></emph>t queſto, che hauemo detto, & adimandato dal ſopradetto corpo. a. ſeparato <lb></lb>da ogni libra, il medeſimo adim andamo de quelli, che deſcendono appeſi al brazzo di <lb></lb>qualche libra. </s> <s id="s.001737">Eſſempi gratia, ſia anc hora el detto corpo.a. appeſo al brazzo della <lb></lb>libra.a.b.c. </s> <s id="s.001738">giranteſopra al ſparto, ouer centro.b. </s> <s id="s.001739">oueramente al brazzo della libræ <lb></lb>a.d.e.girante ſopra al ſparto, ouer centro. </s> <s id="s.001740">d. </s> <s id="s.001741">& ſia el perpendicolar deſcenſo uerſo il <lb></lb>centro del <expan abbr="mõdo">mondo</expan> la linea retta.a.f. </s> <s id="s.001742">& el deſcenſo, che faria el detto corpo.a. <expan abbr="cõ">com</expan> el braz <lb></lb>zo.a.b.della libra.a.b.c.ſopra elcentro.b.la linea curua.a.g. </s> <s id="s.001743">Et el deſcenſo, che faria <lb></lb>el medeſimo corpo.a.con el brazzo.a.d.della li<gap></gap>ra.a.d.e. </s> <s id="s.001744">ſopra el centro.d. </s> <s id="s.001745">la linea <lb></lb>curua.a.h. </s> <s id="s.001746">Hor dico, & adimando, che ne ſia conceſſo il detto corpo.a.eſſer piu graue <lb></lb>nel deſcendere per il deſcenſo.a<gap></gap>h. </s> <s id="s.001747">che p el deſcenſo.a g. </s> <s id="s.001748">per eſſere el detto deſcenſo <lb></lb>a. h. piu retto al centro del mondo del deſcenſo. </s> <s id="s.001749">a. g. perche el detto deſenſo. </s> <s id="s.001750">a. h.<emph.end type="italics"></emph.end><pb xlink:href="042/01/173.jpg"></pb><emph type="italics"></emph>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></lb>quello fa lo decenſo.a.g.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.173.1.jpg" xlink:href="042/01/173/1.jpg"></figure> <p type="main"> <s id="s.001752">S.A. </s> <s id="s.001753">E <emph type="italics"></emph>ue ho inteſo benißimo, & tal petitione non è da negare, e pero ſeguitati nel<lb></lb>l'altra.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.001754">QVESITO. XXV. PETITIONE IIII.</s> </p> <p type="main"> <s id="s.001755">An<emph type="italics"></emph>chora adimandamo, che ne ſia conceſſo quelli corpi eſſer egualmente graui, <lb></lb>ſecondo el ſito, ouer poſitione, quando che li lor deſcenſi in tai ſiti ſono <expan abbr="egualmẽ">egualmen</expan> <lb></lb>te obliqui, & piu graue eſſer quello, che nel ſuo ſito, ouer luoco doue ſe ripoſa, ouer gia <lb></lb>ce ha il deſcenſo manco obliquo.<emph.end type="italics"></emph.end> S.A. A<emph type="italics"></emph>nchora questa <expan abbr="uiẽ">uiem</expan> a eſſer manifeſta per quello <lb></lb>fu detto nella precedente, & anchora ſopra la ſeconda petitione, e pero ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.001756">QVESITO. XXVI. PETITIONE V.</s> </p> <p type="main"> <s id="s.001757">Si<emph type="italics"></emph>melmente adimandamo, che neſta conceſſo quel corpo eſſer men graue dun altro <lb></lb>ſecondo el ſito, ouer luoco, <expan abbr="quãdo">quando</expan> che per el <expan abbr="deſcẽſo">deſcenſo</expan> di quello altro, nell'altro braz <lb></lb>zo della libra in lui ſeguita il moto contrario, cioe, che da lui uien elleuato inſuſo uerſo <lb></lb>il ciclo, & é conuerſo.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſta è coſa troppo chiara da concedere.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.001758">QVESITO. XXVII. PETITIONE VI.</s> </p> <p type="main"> <s id="s.001759">An<emph type="italics"></emph>chora adimandamo, che ne ſia conceſſo, niun corpo eſſer graue in ſe medeſi<lb></lb>mo.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſta uostra petitione non intendo.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>ioe, che l'acqua nella <lb></lb>acqua, il uino nel uino, l'olio nel olio, & l'aere nel aere non eſſere di alcuna grauita.<emph.end type="italics"></emph.end><lb></lb>S.A. </s> <s id="s.001760">E <emph type="italics"></emph>ue ho inteſo, & è coſa conceßibile, perche la ſperientia nel manifesta, ſi che, ſe <lb></lb>guitati.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on ci è altra coſa da adimandare à.<emph.end type="italics"></emph.end> V. S. <emph type="italics"></emph>diman, piacendo à Iddio, in<lb></lb>traremo nelle propoſitioni.<emph.end type="italics"></emph.end> S. A. S<emph type="italics"></emph>aranno propoſitiom aſſai.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on troppo <lb></lb>ſignore.<emph.end type="italics"></emph.end> S. A. C<emph type="italics"></emph>redeti, che leſpediremo dimane.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph><expan abbr="õ">om</expan> credo Signore, che le ſpe <lb></lb>diremo <expan abbr="nãche">nanche</expan> fra diman, e l'altro.<emph.end type="italics"></emph.end> S.A. B<emph type="italics"></emph><expan abbr="ẽ">em</expan> andate, ritornate da mattina à bon'hora.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="87" xlink:href="042/01/174.jpg"></pb> <p type="head"> <s id="s.001761">QVESITO. XXVIII. PROPOSITIONE <lb></lb>PRIMA.</s> </p> <p type="main"> <s id="s.001762">SIGNOR AMBASCIATORE. H<emph type="italics"></emph>or ſeguitati Tartaglia queſte uoſtre <lb></lb>propoſitioni, ouer concluſioni conſequentemente l'una drieto all'altra, & ſotto <lb></lb>breuita.<emph.end type="italics"></emph.end> NICOLO. </s> </p> <p type="main"> <s id="s.001763">La <emph type="italics"></emph>proportione della grandezza di corpi de un medeſimo genere, & quella del<lb></lb>la lor potentia è una medeſima.<emph.end type="italics"></emph.end> S.A. D<emph type="italics"></emph>atemi uno eſſempto.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>iano li dui <lb></lb>corpì.a.b. </s> <s id="s.001764">&. </s> <s id="s.001765">c. de uno medeſimo genere, & ſia.a.b. </s> <s id="s.001766">maggiore, & ſia la potentia del <lb></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></lb>corpo.a.b.al.corpo.c. quella medeſima è della potentia.d.e.alla potentia.f. </s> <s id="s.001768">Et ſe poßi<lb></lb>bile è eſſer altramente (per l'auerſario) ſia che la proportione del corpo.a.b.al corpo. <lb></lb>c. ſia menore di quella della potentia.d.e.alla potentia.f. </s> <s id="s.001769">Hor ſta del corpo.a.b. (mag<lb></lb>giore) compreſo una parte eguale al corpo.c.menore, quale ſia la parte.a. </s> <s id="s.001770">& perche <lb></lb>la uertu, ouer potentia del compoſito è compoſta dalla uertu di componenti. </s> <s id="s.001771">Sia adun<lb></lb>que la uertu, ouer potentia della parte.a.la.d. </s> <s id="s.001772">& la uertu, ouer potentia del re ſiduo. </s> <s id="s.001773">b <lb></lb>de neceßita ſara la reſtante potentia.e.et perche <lb></lb>la parte.a.è tolta egual al.c.la potentia.d. (per <lb></lb>il conuerſo della. </s> <s id="s.001774">7. diffinitione) ſara eguale alla <lb></lb>potentia.f.& la proportione de tutto il corpo. <lb></lb>a.b.alla ſua parte.a. (per la ſeconda parte della. <lb></lb></s> <s id="s.001775">7. del quinto di Euclide) ſara, ſi come quella del <lb></lb>medeſimo corpo. a. b.al corpo.c. (per eſſer.a. <lb></lb></s> <s id="s.001776">egual al.c.) & ſimilmente la proportione della <lb></lb>potentia.d.e.alla potentia.f.ſara, ſi come quella <lb></lb>della detta potentia.d. </s> <s id="s.001777">e. alla ſua parte.d. (per<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.174.1.jpg" xlink:href="042/01/174/1.jpg"></figure><lb></lb><emph type="italics"></emph>eſſer la.d.egual alla.f.) Adunque la proportione de tutto il corpo.a.b.alla ſua parte. <lb></lb></s> <s id="s.001778">a.ſara menore di quella di tutta la potentia.d.e.alla ſua parte.d. </s> <s id="s.001779">Adunque euerſamente <lb></lb>(per la. </s> <s id="s.001780">30. del quinto di Euclide) la proportione del medeſimo corpo.a.b. al reſiduo <lb></lb>corpo.b. ſara maggiore di quella di tutta la potentia.d.e. </s> <s id="s.001781">alla reſtante potentia. </s> <s id="s.001782">e. la <lb></lb>qual coſa ſaria inconueniente, & contra la opinion dell'auerſario, il qual uol che la <lb></lb>proportione del maggior corpo al menore ſia menore, di quella della ſua potentia alla <lb></lb>potentia del detto menore. </s> <s id="s.001783">Adunque deſtrutto l'oppoſito rimane il propoſito.<emph.end type="italics"></emph.end> S. A. <lb></lb>S<emph type="italics"></emph>ta bene, ſeguitati.<emph.end type="italics"></emph.end> NIC. </s> </p> <p type="head"> <s id="s.001784">QVESITO. XXIX. PROPOSITIONE <lb></lb>SECONDA.</s> </p> <p type="main"> <s id="s.001785">La <emph type="italics"></emph>proportione della potentia di corpi graui de uno medeſimo genere, & quella <lb></lb>della lor uelocita (nelli deſcenſi) ſe conchiude eſſer una medeſima, anchor quel-<pb xlink:href="042/01/175.jpg"></pb>la delli lor moti contr arij (cioe delli lor aſcenſi) ſe conchiude eſſer la medeſima, ma traſ <lb></lb>mutatiuamente.<emph.end type="italics"></emph.end> S.A. E<emph type="italics"></emph>ſſemplificatemi tal propoſitione.<emph.end type="italics"></emph.end> NIC. </s> </p> <p type="main"> <s id="s.001786">Si<emph type="italics"></emph>a anchora li dui corpi.a.b.&.c.de uno medeſimo genere, & di grandezza diuer <lb></lb>ſa, & ſia lo.a.b.maggiore, & ſia la potentia del.a.b.la.d.e.& del.c.la.f. </s> <s id="s.001787">& per<lb></lb>che il corpo di potentia, ouer grauita maggiore (per la ſeconda petitione) deſcende piu <lb></lb>uelocemente, ſia adunque la uelocita nel deſcender del corpo.a.b.la.g.h. & quella del <lb></lb>corpo.c.la.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>hor dico, che la proportione della potentia. </s> <s id="s.001788">d. e. alla potentia. </s> <s id="s.001789">f. & quella <lb></lb>della uelocita.g.h.alla uelocita.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>eſſer una medeſima, & quella delli lor moti contrarij <lb></lb>eſſer quella medeſima, ma traſmutatiuamente, cioe che la proportione della uelocita <lb></lb>del corpo.a.b.alla uelocita del corpo.c.nel moto contrario (cioe nell'aſcendere) eſſer, <lb></lb>ſi come quella della potentia.f.alla potentia.d.e.ouer, come del corpo.c.al corpo.a.b. <lb></lb>la qual coſa ſe dimoſtra per il medeſimo modo, che fu dimoſtrata la precedente, cioe <lb></lb>ſe la proportione della potentia.d.e.alla po<lb></lb>tentia.f.non è (per l'auerſario) ſi come quel <lb></lb>la della uelocita.g.h.alla uelocita.<emph.end type="italics"></emph.end>k. <emph type="italics"></emph>neceſſa <lb></lb>riamente la ſara maggiore, ouer menore, <lb></lb>hor poniamo che la ſia menore, della poten<lb></lb>tia.d.e.ne aßignaremo la parte.d.eguale al<lb></lb>la.f.& coſi della uelocita.g.h.ne aßignare<lb></lb>mo la parte.g.eguale alla.<emph.end type="italics"></emph.end>k. <emph type="italics"></emph>& arguiremo, <lb></lb>come nella <expan abbr="precedẽte">precedente</expan>, <expan abbr="dicẽdo">dicendo</expan> che la pportio <lb></lb>ne di tutta la potentia.d.e.alla ſua parte.d. <lb></lb></s> <s id="s.001790">ſara (per la ſeconda parte della. </s> <s id="s.001791">7. del quin-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.175.1.jpg" xlink:href="042/01/175/1.jpg"></figure><lb></lb><emph type="italics"></emph>io di Euclide) ſi come quella della medeſima potentia.d.e.alla potentia.f. (per eſſer la <lb></lb>d.&.f.eguale) & ſimilmente la proportione de tutta la uelocita.g.h.alla ſua parte.g. <lb></lb></s> <s id="s.001792">eſſer, ſi come quella della medeſima.g.h.alla.<emph.end type="italics"></emph.end>k. </s> <s id="s.001793">A<emph type="italics"></emph>dunque la proportione di tutta la po<lb></lb>tentia.d.e.alla ſua parte.d.ſara menore di quella di tutta la uelocita.g.h.alla ſua par<lb></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 medeſima po<lb></lb>tentia.d.e.al ſuo reſiduo.e.hauera maggior proportione, che tutta la uelocita.g.h.al <lb></lb>ſuo reſiduo.h.la qual coſa ſaria contra la opinione dell'auerſario qual <expan abbr="ſupponē">ſupponem</expan>, che la <lb></lb>proportione della maggior potentia alla menore eſſer menore di quella della maggior <lb></lb>uelocita alla menore. </s> <s id="s.001796">Et con li medeſimi argomentiſe procederia quando che quel ſup<lb></lb>poneſſe che la proportione della maggior potentia alla menore fuſſe maggiore di quel <lb></lb>la della maggior uelocita alla menore, diſtrutto adunque l'oppoſito rimane il propoſi<lb></lb>to, hor per la ſeconda parte della noſtra concluſione, dico, che la proportione della ue<lb></lb>locita delli deſcenſi, & delli contrari moti, cioe delli aſcenſi de detti corpi è una medeſi<lb></lb>ma, ma traſmutatiuamente, cioe che la proportione della uelocita del corpo.a.b. eſſen <lb></lb>do da qualche altra uertu impoſta nell'altro braccio della libra in alto elleuato (ponia<lb></lb>mo per fin alla linea della direttione) alla uelocita del corpo.c.dalla medeſima uertu, <lb></lb>pur in alto elleuato per fin all medeſima linea della direttione ſara, ſi come quella del<lb></lb>la uelocita.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>alla uelocita.g.h.ouer della potentia.f.alla petentia.d.e.ouer del cor-<emph.end type="italics"></emph.end><pb pagenum="88" xlink:href="042/01/176.jpg"></pb><emph type="italics"></emph>po.c.al corpo.a.b.perche quanta uertu, ouer potentia ha uncorpo graue per deſcen<lb></lb>dere al baſſo, tantane ha anchora per reſiſtere al moto contrario, cioe à che il uoleſſe <lb></lb>tirare, ouer à leuare in alto adunque la potentia del corpo.a.b. per reſiſtere à che il uo <lb></lb>leſſe elleuare in alto, ſaratanto quanto la ſopradetta.d.e.& quella del corpo.c.ſara <lb></lb>tanto quanto la ſopradetta.f. </s> <s id="s.001797">Adunque quella uertu che nell'altro braccio della libra <lb></lb>ſara atta ad elleuare coſi à pena il detto corpo.a.b.per fin alla linea della direttione, <lb></lb>quella medeſima ſara atta ad elleuare il detto corpo.c.tanto piu uelocemente (per fin <lb></lb>alla detta linea della direttione) quanto che la ſua reſiſtentia ſara proportionalmente <lb></lb>menore di quella del corpo.a.b.& perche la detta reſiſtentia del detto corpo.c. </s> <s id="s.001798">e tan<lb></lb>to menore della reſiſtentia del corpo.a.b.quanto che la ſua potentia.f.della potentia. <lb></lb></s> <s id="s.001799">d.e. </s> <s id="s.001800">Adunque la uelocita del corpo.c. (nel moto contrario) alla uelocita del corpo.a. <lb></lb>b.ſara, ſi come la potentia.e.d.alla potentia.f.ouer come che il corpo.a.b.al corpo. <lb></lb>c. che il propoſito.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001801">CORRELARIO.</s> </p> <p type="main"> <s id="s.001802">Da <emph type="italics"></emph>qui ſe manifeſta qualmente la proportione della grandezza di corpi di uno <lb></lb>medeſimo genere, & quella della lor potentia, & quella della lor uelocita nelli <lb></lb>lor deſcenſi eſſer una medeſima. </s> <s id="s.001803">Et ſimilmente quella della lor uelocita nelli moti <lb></lb>contrarij, ma traſmutatiuamente.<emph.end type="italics"></emph.end> S. AMBASCIATORE. </s> <s id="s.001804">E <emph type="italics"></emph>ue ho inteſo, <lb></lb>ſeguitati pur.<emph.end type="italics"></emph.end> NICOLO. </s> </p> <p type="head"> <s id="s.001805">QVESITO XXX. PROPOSITIONE III.</s> </p> <p type="main"> <s id="s.001806">Se <emph type="italics"></emph>ſaranno dui corpi ſimplicemente eguali di grauita, ma ineguali per uigor del <lb></lb>ſito, ouer poſitione, la preportione della lor potentia, & quella della lor ueloci<lb></lb>ta neceſſariamente ſara una medeſima. </s> <s id="s.001807">Ma nelli lor moti contrarij, cioe nelli aſceo<lb></lb>ſi, la proportione della lor potentia, & quella della lor uelocita ſe afferma eſſer la <lb></lb>medeſima, ma traſmutatiuamente.<emph.end type="italics"></emph.end> S. AMB ASCIA. F<emph type="italics"></emph>atemi la dimoſtratione di <lb></lb>queſto.<emph.end type="italics"></emph.end> NICOLO. </s> </p> <p type="main"> <s id="s.001808">SIANO L<emph type="italics"></emph>i dui corpi.a.&.b. </s> <s id="s.001809">ſimplicemente eguali di grauita, & ſia la libra. <lb></lb></s> <s id="s.001810">c. d. </s> <s id="s.001811">il cui centro, ouer ſparto il ponto. </s> <s id="s.001812">e. & ſia nella ſtrema parte del braz<lb></lb>zo.e.c.cioe in ponto.c.appeſo, & ſoſtentato il corpo.a.& in uno altro luoco piu pro<lb></lb>pinquo al ſparto nel medeſimo brazzo, hor ſia in ponto.f.ui ſia ſoſtentato il corpo.b. <lb></lb>Et à ben che queſti dui corpi ſtano ſimplicemente eguali di grauita, nondimeno (per <lb></lb>la quarta petitione) il corpo.a. ſara (per uigor del luogo) piu graue del corpo. b. <lb></lb>perche il deſcenſo di quello qual ſia lo.c.h. </s> <s id="s.001813">e manco obliquo del deſcenſo del corpo.b. <lb></lb>qual ſia lo.f.g. (per la terza, & quarta petitione) eſſendo adunque il corpo.a. piu <lb></lb>graue, ſecondo il ſito del corpo.b.ſara etiom piu potente, & eſſendo piu potente (per <lb></lb>la ſeconda petitione) nelli deſcenſi deſcendera piu uelocemente del corpo.b. & nelli <lb></lb>moti contr arij, cioe nelli aſcenſipiu tardamente. </s> <s id="s.001814">Dico adunque che la proportione <lb></lb>della lor uelocita nelli deſcenſi eſſer ſimile à quella della loro potentia, & quella delli lo-<pb xlink:href="042/01/177.jpg"></pb>ro aſcenſi eſſer pur la medeſima, ma traſmutatiuamente, et per dimoſtrar la prima par <lb></lb>te, ſia la potentia del corpo.a.la.l. & quella del corpo.b.la.m. </s> <s id="s.001815">& la uelocita del corpo <lb></lb>a. (nelli deſcenſi) 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></lb>ta.n.alla uelocita.o.eſſer, ſi come quella della potentia.l.alla potentia.m.la qual coſa ſe <lb></lb>dimostra, ſi come la precedente, cioe ſe poßibil fuſſe, che la proportione della poten<lb></lb>tia.l.alla potentia.m. (per l'auerſario) poteſſe eſſer menore di quella della uelocita.n. <lb></lb></s> <s id="s.001818">alla uelocita.o.ſumendo della potentia.l.la parte.p.eguale alla.m. </s> <s id="s.001819">& della uelocita.n.la <lb></lb>parte.q.eguale alla.o.& arguendo, come nella precedente, cioe che la proportione di <lb></lb>tutta la potentia.l. </s> <s id="s.001820">alla ſua parte.p. (per la. </s> <s id="s.001821">7. del quinto di Euclide) ſara menore di <lb></lb>quella di tutta la uelocita.n. <lb></lb></s> <s id="s.001822">alla ſua parte.q. </s> <s id="s.001823">Onde (per <lb></lb>la. </s> <s id="s.001824">30. del quinto di Euclide) <lb></lb>la proportione della medeſi <lb></lb>ma potentia. </s> <s id="s.001825">l. </s> <s id="s.001826">all'altra ſua <lb></lb>parte, ouer reſiduo.r.haue<lb></lb>ra maggior proportione di <lb></lb>quello, che hauera tutta la <lb></lb>uelocita.n.all'altra ſua par <lb></lb>te, ouer reſiduo.s.la qual co <lb></lb>ſa ſaria <expan abbr="inconuemẽte">inconuemente</expan>, et con <lb></lb>tra la opinione dell'auerſa<lb></lb>rio, qual ſuppone che la pro <lb></lb>porclone della maggior po<lb></lb>tentia alla menore, eſſer me <lb></lb>nore di quella dellamaggior <lb></lb>uelocita, alla menore, & il <lb></lb>medeſimo inconueniente ſe-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.177.1.jpg" xlink:href="042/01/177/1.jpg"></figure><lb></lb><emph type="italics"></emph>guiria quando che l'auerſario, ſupponeſſe che la proportione della potentia.l.al<lb></lb>la potentia.m. </s> <s id="s.001827">fuſſe maggiore di quella della uelocita.n.alla uelocita.o. </s> <s id="s.001828">distrutto adun <lb></lb>que l'oppoſito rimane il propoſito. </s> <s id="s.001829">La ſeconda parte ſe riſolue, ouer arguiſſe, ſi come <lb></lb>nella precedente, cioe che quella potentia, che nell'altro brazzo della libra (poniamo <lb></lb>in ponto.d.) ſara atta ad ellcuare il corpo.a.per fin alla linea della direttione, cioe in <lb></lb>ponto.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>quella medeſima ſara atta ad elleuare tanto piu uelocemente il corpo.b.per fi <lb></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></lb>potentia del corpo.b. (qual'è la.l.) perche quanto che la potentia d'un corpo è menore <lb></lb>tanto men reſiſte al moto contrario, & econuerſo, adunque la uelocita del corpo.b. à <lb></lb>quella del corpo.a. (nelli aſcenſi) ſara, ſi come quella della potentia.l.alla potentia. </s> <s id="s.001831">m. <lb></lb>che è il ſecondo propoſito.<emph.end type="italics"></emph.end> S. AMB. Q<emph type="italics"></emph>ueſta è stata aſſai bella propoſitione, ma <lb></lb>ſeguitati pur.<emph.end type="italics"></emph.end> NIC. </s> </p> <pb pagenum="89" xlink:href="042/01/178.jpg"></pb> <p type="head"> <s id="s.001832">QVESITO XXXI. PROPOSITIONE IIII.</s> </p> <p type="main"> <s id="s.001833">La <emph type="italics"></emph>proportione della potentia di corpiſimplicemente equali in grauita, ma ine<lb></lb>quali per uigor delſito, ouer poſitione, & quella delle lor diſtantie dal ſparto, <lb></lb>euer centro della libra, ſe approuano eſſer equali.<emph.end type="italics"></emph.end> S.A. D<emph type="italics"></emph>atime uno eſſempio.<emph.end type="italics"></emph.end> N. </s> </p> <p type="main"> <s id="s.001834">Si<emph type="italics"></emph>ano li dui corpi.a.&.b.della figura precedente ſimplicemente equali in grauita <lb></lb>& ſia la libra.c.e.d.el centro, ouer ſparto della quale ſia el ponto.e.& ſia appeſo <lb></lb>el corpo.a. in ponto.c.& lo corpo.b.nel ponto.f.come nella figura precedente appa<lb></lb>re. </s> <s id="s.001835">Dico, che la proportione della potentia del corpo.a. (quale ſia la.l.) alla potentia <lb></lb>del corpo.b. (quale ſia la.m.) eſſer ſimile à quella, ch'è dalla diſtantia, ouer brazzo.e. <lb></lb></s> <s id="s.001836">c.alla distantia, ouer brazzo.e.f.& tutto queſto ſi approuaſecondo lordine della pre <lb></lb>cedente, cioe, ſe la proportione della diſtantia, ouer brazzo. </s> <s id="s.001837">c. e. alla distantia, ouer <lb></lb>brazzo.f.e.non è (per lauerſario, ſi come quella, ch'é dalla potentia.l.alla poteutia.m. <lb></lb></s> <s id="s.001838">adunque neceſſariamente ſara maggiore, ouer minore, hor ſia prima (ſe poßibil è) me <lb></lb>nore ſia del brazzo, ouer diſtantia.c.e.maggiore cauato el brazzo, ouer distantia.e. <lb></lb></s> <s id="s.001839">f.menore dalla banda uerſo.c.quale ſia la.c.x.& dalla potentia.l.ne ſia cauata la par<lb></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></lb>distantia, ouer brazzo.e.c.alla ſua parte.c.x.hauera menor proportione, di quello, <lb></lb>che hauera tutta la potentia.l.alla ſua parte. </s> <s id="s.001842">p. </s> <s id="s.001843">Onde per la. </s> <s id="s.001844">30. del quinto di Euclide) <lb></lb>la proportione del brazzo, ouer distantia.c.e.alla restante diſtantia, ouer bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o. </s> <s id="s.001845">e. <lb></lb>x.hauera maggior proportione di quello hauera la potentia.l.alla reſtante <expan abbr="potẽtia">potentia</expan>.r. <lb></lb></s> <s id="s.001846">la qual potentia.r.uerria ad eſſer la potenza del medeſimo corpo.b. ſtante nel ponto <lb></lb>x.la qual coſa ſaria inconueniente, perche, ſe la proportione della maggiore diſtantia <lb></lb>dal ſparto alla menore (per lauerſario) hauera maggior proportione, che la maggior <lb></lb>potentia alla menore, queſto doueria ſeguire in ogni poſitione, & tamenſe uede occor<lb></lb>rere al contrario, cioe, che la proportione della diſtantia.c.e.alla diſtantia.e. </s> <s id="s.001847">x. ſaria <lb></lb>maggiore di quella della potentia.l.alla potentia del corpo.b.nel ſito, ouer luoco, do<lb></lb>ue.x.diſtrutto adunque lo oppoſito rimane il propoſito.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001848">CORRELARIO.</s> </p> <p type="main"> <s id="s.001849">Da<emph type="italics"></emph>lle coſe dette, & dimostrate, ſe manifeſta non ſolamente la proportione delle <lb></lb>diſtantie dal ſparto nel bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o della libra, & quella delle <expan abbr="potẽtie">potentie</expan> di cor pi ſim <lb></lb>plicementi equali in grauita, in taiſiti, ouer luochi, & ſimelmente la uelocita de quelli <lb></lb>nelli dcſcenſi eſſer una medeſima, ma anchora li lor deſcenſi, & anchora li loro <expan abbr="aßcẽſi">aßcenſi</expan> <lb></lb>oßeruano la medeſima, perche qual proportione è dal bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o.e.c.al brazzo.e.f.tala <lb></lb>è dal curuo deſcenſo.c.h.al curuo deſcenſo.f.g.& <expan abbr="ſimelmẽte">ſimelmente</expan> del curuo aſſenſo. </s> <s id="s.001850">c.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>al <lb></lb>curuo aſſcenſo.f.i.pche li dette deſcenſi, & aſſcenſi uengono à eſſer cadauno de loro la <lb></lb>quarta parte della circonferentia de dui ceochij. </s> <s id="s.001851">delli quali el ſemidiametro del mag<lb></lb>giore uerria à eſſer el brazzo, ouer diſtantia.e.c.et del menore el brazzo, ouer <expan abbr="diſtã">diſtam</expan> <lb></lb>tia.e.f.<emph.end type="italics"></emph.end> S.A. A<emph type="italics"></emph>nchor queſta é ſtata una bella propoſitione ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <pb xlink:href="042/01/179.jpg"></pb> <p type="head"> <s id="s.001852">QVESITO XXXII. PROPOSITIONE V.</s> </p> <p type="main"> <s id="s.001853">Qv<emph type="italics"></emph>ando, che la poſitione de una libra de brazzi equali ſta nel ſito della equali<lb></lb>ta, & nella iſtremita de l'uno, e l'altro brazzo ui ſiano appeſi corpi ſimplice<lb></lb>mente equali in grauita, tal libra non ſe ſeparara dal detto ſito della equalita, & ſe per <lb></lb>caſo la ſia da qualche altro peſo in luno de detti bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>i impoſto ſeparata dal detto ſi<lb></lb>to della equalita, oueramente con la mano, remoſſo quel tal peſo, ouer mano, tal libra <lb></lb>de neceßita ritornara al detto ſito della equalita.<emph.end type="italics"></emph.end> S. A. Q<emph type="italics"></emph>ueſta è quella Queſtione, <lb></lb>della quale uoi dite, che manca Ariſtotile nelle ſue Queſtioni Mechanice.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>oſi è <lb></lb>Signore.<emph.end type="italics"></emph.end> S.A. M<emph type="italics"></emph>olto haro à caro à intendere la cauſa di tal effetto, e pero ſeguita<lb></lb>te.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia eſſempi gratia la libra.a.c.b.el centro della quale ſia il ponto. </s> <s id="s.001854">c. & ſia el <lb></lb>bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o.a.c.equale al bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o.b.e.& stia nel ſito della equalita, come ſe prepone. </s> <s id="s.001855">Et <lb></lb>che nella iſtremita de luno, e laltro bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o uiſia appeſo uno corpo (poniamo el cor<lb></lb>po.a.&.a.) li quali corpiſiano ſimplicemente equali in grauita. </s> <s id="s.001856">Dico che la detta li<lb></lb>bra (per la impoſitione de detti corpi) non ſe ſeparara dal detto ſico della equalita, & <lb></lb>ſe pur quella fuſſe ſeparata dal detto ſito, ò per la impoſitione di qualche altro peſo, <lb></lb>ouer con la mano, remoſſo che ſia quel tal imposto peſo, ouer mano, tal libra de neceßi <lb></lb>ta ritornara al detto ſito della equalita. </s> <s id="s.001857">La prima parte è manifeſta, perche li detti dui <lb></lb>corpi ſono ſimplicemente di equal grauita (dal pre <lb></lb>ſuppoſito) et <expan abbr="ſimelmẽte">ſimelmente</expan> ſono equalmente graui per <lb></lb>uigor del ſito, per la quarta petitione (per eſſer li <lb></lb>loro deſcenſi equalmente obliqui) e pero eſſendo <lb></lb>quelli ſi per uigor del ſito, come che <expan abbr="ſimplicemẽte">ſimplicemente</expan> <lb></lb>duna equal grauita, e potentia, e pero niun de loro <lb></lb>fara atto à poter elleuar l'altro, cioe à farlo aſcen <lb></lb>dere di moto contrario, e pero restaranno nel me<lb></lb>deſimo ſito della equalita.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſto ue credo <lb></lb>& ue lo haueria largamente conceſſo ſenza altra<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.179.1.jpg" xlink:href="042/01/179/1.jpg"></figure><lb></lb><emph type="italics"></emph>demonſtratione, per eſſer coſa naturale. </s> <s id="s.001858">Ma ſeguitati la ſeconda parte, la qual me pare <lb></lb>molto piu aſtrata, ouer lontana dal noſiro intelletto naturale dell'altra.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er la ſe <lb></lb>condu parte ſia pur anchora la libra.a.c.b.de braz <lb></lb>zi equali et nella iſtremita de quelli ſiano pur ap<lb></lb>peſi li dui corpi.a.et.b.ſimplicemente equali in gra<lb></lb>uita, la qual librap le ragioni di ſopra adutte ſtara <lb></lb>nel ſito della equalita, come di ſotto appar <expan abbr="ĩ">im</expan> figura.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.179.2.jpg" xlink:href="042/01/179/2.jpg"></figure> <p type="main"> <s id="s.001859">HOR <emph type="italics"></emph>eſſendo ſpinto el brazzo.a.c.al baſſo con la mano, ouer per la impoſitio <lb></lb>ne di qualche altro peſo ſopra el corpo.a.remoſſo uia la mano, ouer quel tal <lb></lb>peſo, el brazzo di tal libra reaſcendera, & ritornera al ſuo primo luoco della <gap></gap>quali<lb></lb>ta, & per aßignar la cauſa propinqua di tal effetto, fla deſcritto ſopra el centro.c. </s> <s id="s.001860">el <lb></lb>cerchio.a.c.b.f. </s> <s id="s.001861">per el uiazzo, che fariano li detti dui corpi alzando, ouer arbaſſando <lb></lb>li brazzi della detta libra, & ſia tirata la linea della direttione, quale ſia la.e.f. </s> <s id="s.001862">& ſia <lb></lb>diuiſo l'arco.a.f.in quanti parti equali ſi uoglia (hor ſia in quattro) nelli trei ponti,<emph.end type="italics"></emph.end><pb pagenum="90" xlink:href="042/01/180.jpg"></pb><emph type="italics"></emph>q.ſ.u.& in altre tante ſla anchor diuiſo l'arco.e.b. </s> <s id="s.001863">nelli trei ponti.i.l.n. </s> <s id="s.001864">& dalli detti <lb></lb>trei ponti.n.l.i.ſiano tirate le tre linee.n.o.l.m.&.i.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>equidiſtante alſito della equa<lb></lb>lita, cioe al diametro, ouer linea.a.b.le quale ſegaranno la linea.e.f. </s> <s id="s.001865">della direttione ne <lb></lb>li tre ponti.z y.x. </s> <s id="s.001866">Simelmente dalli tre ponti.q.ſ.u.ſiano tirate le tre linee.q.p.ſ.r.&. <lb></lb></s> <s id="s.001867">u.t.pur equidiſtante alla medeſima linea.a.b.le quale ſegaranno la medeſima linea del <lb></lb>la direttione.e.f.nelli trei ponti.&.<emph.end type="italics"></emph.end><36>.<38>. </s> <s id="s.001868">E<emph type="italics"></emph>t dapoi ſia arbaſſato con la mano il corpo.a. <lb></lb>(ouer con la impoſitione di qualche altro peſo) per fin al ponto.u. </s> <s id="s.001869">& laltro corpo.b. <lb></lb>(à quel oppoſito) in tal poſitione ſe trouar a eſſer aſſeſo de moto contrario per fin al <lb></lb>ponto.i. </s> <s id="s.001870">Onde per queste coſe coſi diſpoſite ueniremo ad hauer diuiſo tutto el deſcenſo <lb></lb>a.u.fatto dal detto corpo.a.nel diſcendere in ponto.u.in tre deſcenſi, ouer parti equa <lb></lb>li, le qualeſono.a.q.q.ſ.&.ſ.u.& ſimelmente tutto el deſcenſo.i.b. </s> <s id="s.001871">qual faria il detto <lb></lb>corpo.b.nel diſcendere, ouer ritornare alſuo primo luoco (cioe in ponto.b.) uerra ad <lb></lb>eßer diuiſo in trei deſcenſi, ouer in tre parti equalile quali ſono.i.l.l. </s> <s id="s.001872">n. &.n.b. </s> <s id="s.001873">& ca<lb></lb>dauno de queſti tre, & tre partiai deſcenſi capiſſe una parte della linea della direttio<lb></lb>ne, cioe il deſcenſo dal.a.al.q.piglia, ouer capiſſe della linea della direttione la parte.e. <lb></lb></s> <s id="s.001874">&.& lo deſcenſo.q.ſ.capiſſe la parte.&.<emph.end type="italics"></emph.end><36>. <emph type="italics"></emph>& lo deſcenſo.ſ.u.capiſſe la parte.<emph.end type="italics"></emph.end> <36>. </s> <s id="s.001875"><38>. <lb></lb><emph type="italics"></emph>& laltro deſcenſo, che reſta à deſcendere al detto corpo.a.cioe el deſcenſo. </s> <s id="s.001876">u.f.capiße <lb></lb>la linea, ouer parte.<emph.end type="italics"></emph.end><38>.<emph type="italics"></emph>f. </s> <s id="s.001877">Et ſimelmente el deſcenſo del corpo.b. dal ponto.i. </s> <s id="s.001878">al ponto.l. <lb></lb></s> <s id="s.001879">capiſſe della medeſima linea della direttione la parte.x.y.& nel deſcenſo dal ponto.l. <lb></lb></s> <s id="s.001880">al ponto.n.capiſſe la parte.y.z.& dal ponto.n.al ponto.b.capiſſe la parte.z.c.et tue <lb></lb>te queſte partiſono 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></lb>y.della.y.x.& la.y.x.della.x.e.& ſimelmente la parte. </s> <s id="s.001883">c. &. </s> <s id="s.001884">è maggiore della par<lb></lb>te.&.<emph.end type="italics"></emph.end><36>.<emph type="italics"></emph>& la parte.&.<emph.end type="italics"></emph.end><36>.<emph type="italics"></emph>della parte.<emph.end type="italics"></emph.end><36>.<38>.<emph type="italics"></emph>& la.<emph.end type="italics"></emph.end><36>.<38>.<emph type="italics"></emph>della.<emph.end type="italics"></emph.end><38>.<emph type="italics"></emph>f.& tutto queſto facil<lb></lb>mente Geometrice ſi puo prouare, & ſimelmente ſe puo prouare, la parte.<emph.end type="italics"></emph.end> <38>.<emph type="italics"></emph>f. </s> <s id="s.001885">eſſere <lb></lb>equale alla porte.e.x.& la parte.<emph.end type="italics"></emph.end><38>.<36>.<emph type="italics"></emph>alla parte.x.y.& la parte.<emph.end type="italics"></emph.end><36>.<emph type="italics"></emph>&.alla parte.y.z. <lb></lb></s> <s id="s.001886">& la parte.&.c.alla parte.z.c. </s> <s id="s.001887">Hor per tornare al noſtro propoſito. </s> <s id="s.001888">Dico, che il cor <lb></lb>po.b.ſtante quel nel ponto.i.uien à eſſer piu graue, ſecondo il ſito del corpo. a. stante <lb></lb>quello in ponto.u. (come diſotto appar in figura) perche il deſcenſo del detto corpo <lb></lb>b.dal ponto.i.nel ponto.l. </s> <s id="s.001889">è piu retto del deſcenſo del corpo.a. dal ponto. </s> <s id="s.001890">u. nel ponto <lb></lb>f. (per la ſeconda parte della quarta petitione) perche capiſſe piu della linea della di<lb></lb>rettione, cioe, che nel deſcendere il detto corpo.b. dal ponto. </s> <s id="s.001891">i. nel ponto.l. </s> <s id="s.001892">lui capiſſe, <lb></lb>ouer piglia della linea della direttione, la parte.x.y.& il corpo.a. nel diſcendere dal <lb></lb>ponto.u.nel ponto.f.lui caperia della detta linea della direttione, la parte.<emph.end type="italics"></emph.end><38>.<emph type="italics"></emph>f.& per<lb></lb>che la parte.x.y. </s> <s id="s.001893">é maggiore della linea, ouer parte.<emph.end type="italics"></emph.end><38>.<emph type="italics"></emph>f. (per la. </s> <s id="s.001894">17. diffinitione) piu <lb></lb>obliquo ſara il deſcenſo dal ponto.u.al ponto.f.di quello dal ponto.i.al ponto.l. </s> <s id="s.001895">Onde <lb></lb>(per la ſeconda parte della quarta petitione) il corpo.b.in tal poſitione ſara piu gra<lb></lb>ue ſecondo il ſito del corpo.a.eßendo adunque piu graue, leuando uia lo impoſto peſo, <lb></lb>ouer la mano dal corpo.a. (per il conuerſo della quinta petitione) lui fara reaſcende<lb></lb>re di moto contrario il detto corpo. a.dal ponto.u.al ponto.ſ. </s> <s id="s.001896">& lui deſcendera dal <lb></lb>ponto.i.nel ponto.l.nel qual ponto.l. </s> <s id="s.001897">lui uenira à trouarſe anchora piu graue del det <lb></lb>to corpo.a.ſecondo el ſito, perche il detto corpo.a. ſtante nel ponto. </s> <s id="s.001898">ſ. hauera il de<lb></lb>ſcenſo.ſ.u.piu obliquo del deſcenſo.l. </s> <s id="s.001899">n. del corpo. b. perche capiſſe men parte della<emph.end type="italics"></emph.end><pb xlink:href="042/01/181.jpg"></pb><emph type="italics"></emph>detta linea della direttione, cioe, che la parte.<emph.end type="italics"></emph.end><36>.<38>. <emph type="italics"></emph>è menore della parte.y.z. </s> <s id="s.001900">Onde per <lb></lb>le ragioni di ſopra adutte, el detto corpo.b.fara elleuare il detto corpo.a. & aſcende<lb></lb>re nel ponto.q.& lui deſcendera nel ponto.n.nel qual ponto.n.el medeſimo corpo. b. <lb></lb>ſi trouara pur piu graue anchora, ſecondo il ſito del corpo.a.perche il deſcenſo dal.q. <lb></lb></s> <s id="s.001901">in.s.è piu obliquo del defcenſo dal ponto.n.nel ponto.b. </s> <s id="s.001902">per eſſer la parte.z.c.maggio <lb></lb>re della parte.&.<emph.end type="italics"></emph.end><36>. </s> <s id="s.001903">E <emph type="italics"></emph>pero (per le ragioni di ſopra adutte) el detto corpo.b.fara re<lb></lb>aſcendere il detto corpo.a.al ponto.a. (ſuo primo, & condecente luoco) & lui medeſi <lb></lb>mamente deſcendara nel ponto.b.pur ſuo primo, <lb></lb>& condecente luoco, cioe nel ſito della equalita, <lb></lb>nel qual ſito li detti dui corpiſe trouar anno (per <lb></lb>le ragioni aduttenella prima parte di queſta) e<lb></lb>gualmente graui ſecondo el ſito, & perche ſono <lb></lb>anchora ſimplicemente egualmente graui, ſe con <lb></lb>ſeruarano nel detto luoco, come di ſopra fu det<lb></lb>to, & approuato, che è il noſtro propoſito.<emph.end type="italics"></emph.end><lb></lb>S. A. Q<emph type="italics"></emph>ueſta è ſtata una bella demostratione, <lb></lb>maſe ben me arricordo, uoi diceſti anchor ſopra <lb></lb>la detta prima queſtion Mechanica de Ariſtoti<lb></lb>le, che quelle ſue due concluſioni, che lui ui aduce <lb></lb>in fine eßer falſe.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie il uero.<emph.end type="italics"></emph.end> S.A. P<emph type="italics"></emph>er<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.181.1.jpg" xlink:href="042/01/181/1.jpg"></figure><lb></lb><emph type="italics"></emph>che ragione.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a ragione di tal particolarita, ouer oppoſitioni ſe uerifica<lb></lb>ranno nella ſequente propoſitione, mediante alcuni correlarij, che dalle coſe dette, & <lb></lb>dimostrate nella precedente ſi manifeſtano, delli quali il primo è queſto.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001904">CORRELARIO.</s> </p> <p type="main"> <s id="s.001905">Da<emph type="italics"></emph>lle coſe dette, et dimostrate di ſopra, ſe manifeſta qualmente un corpo graue in <lb></lb>qual ſi uoglia parte, che luiſe parta, ouer remoui dal ſito della equalita lui ſi fa <lb></lb>piu leue, ouer leggiero ſecondo el ſito, ouer luoco, & tanto piu, <expan abbr="quãto">quanto</expan> piuſara remoßo <lb></lb>da tal ſito, eſſempi gratia. </s> <s id="s.001906">El corpo.a.ſi trouara eſſer piu leue nel ponto.u.chi nel <expan abbr="põ">pom</expan> <lb></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.ſito della equali<lb></lb>ta, <21> cauſa della uarieta di deſcenſi, cioe, che luno è piu obliquo dell'altro, cioe el deſcen <lb></lb>ſo.u f.uiẽ à eßer piu obliquo del <expan abbr="deſcẽſo">deſcenſo</expan>.ſ.u.perche la parte.f.<emph.end type="italics"></emph.end><38>.<emph type="italics"></emph>della direttione, è me <lb></lb>nore della.<emph.end type="italics"></emph.end><38>.<36>.<emph type="italics"></emph>et coſi el <expan abbr="deſcẽſo">deſcenſo</expan>.ſ.u.uiẽ à eßer piu obliquo del <expan abbr="deſcẽſo">deſcenſo</expan>.q.s. </s> <s id="s.001907"><21>che la par <lb></lb>te.<emph.end type="italics"></emph.end><38>.<36>.<emph type="italics"></emph>è menore della parte.<emph.end type="italics"></emph.end><36>.<emph type="italics"></emph>&.& lo <expan abbr="deſcẽſo">deſcenſo</expan>.q.ſ.uiẽ à eſſer piu obliquo del deſcen<lb></lb>ſo.a.q.perche la parte.<emph.end type="italics"></emph.end><36>.<emph type="italics"></emph>&.è menore della parte.&.c.& per le medeſime ragioni ſi <lb></lb>manifeſta del corpo.b.cioe, che quello ſara piu leue nel <expan abbr="põto">ponto</expan>.i.che nel <expan abbr="põto">ponto</expan>.l.& nel po<lb></lb>to.l.che nel ponto.n.& nel ponto.n.che nel ponto.b.ſito della equalita.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.001908">CORRELARIO SECONDO.</s> </p> <p type="main"> <s id="s.001909">An<emph type="italics"></emph>chora per le coſe dette, & dimostrate ſe manifeſta, che remuouendoſi li detti <lb></lb>dui corpi dal detto ſito della equalita, cioe luno <expan abbr="ĩ">im</expan> giuſo, et laltro inſuſo, anchor<emph.end type="italics"></emph.end><pb pagenum="91" xlink:href="042/01/182.jpg"></pb><emph type="italics"></emph>che l'uno, e l'altro ſia fatto piu leue ſecondo il ſito, tamen in ogni poſitìone men leue ſi <lb></lb>trouara quello che ſara in alto elleuato di quello, che ſi trouara al baſſo oppreſſo, & <lb></lb>queſto é manifeſto per la argomentatione di ſopra adutta, cioe che il corpo.b.nel ſito, <lb></lb>ouer ponto.i.eſſer piu graue del corpo.a.nel ſito, ouer ponto.u.& coſi nelli altri ſiti <lb></lb>ſuperiori ſi trouara piu graue del corpo.a.nelli ſiti inferiori, ſimili.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.001910">E <emph type="italics"></emph>ue ho <lb></lb>inteſo, ſeguitati.<emph.end type="italics"></emph.end> NICOLO. </s> </p> <p type="head"> <s id="s.001911">QVESITO. XXXIII. PROPOSITIONE VI.</s> </p> <p type="main"> <s id="s.001912">Qv<emph type="italics"></emph>ando che la poſitione d'una libra de bracci eguali ſia nel ſito della egualita, & <lb></lb>che nella iſtremita dell'uno è l'altro brazzo ui ſiano appeſi corpi ſimplicemen <lb></lb><gap></gap>e ineguali di grauita, dalla parte doue ſara il piugraue ſara sforzata à declinare per <lb></lb>fin alla linea della direttione.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.001913">A <emph type="italics"></emph>me non pare che queſta uoſtra propoſitione poſ <lb></lb>ſa eſſer uniuerſalmente uera, & queſto uoglio che uoi medeſimo il confeſſati perche uoi <lb></lb>ſapeti che nel Correlario precedente haueti conchiuſo, che remouendoſi li detti dui cor <lb></lb>pi.a.&.b. (dalla figura della precedente propoſitione) dal ſito della egualita, cioe l'u<lb></lb>no in giuſo, & l'altro inſuſo, anchor che l'uno è l'altro ſia fatto piu leue, ouer leggero, <lb></lb>ſecondo il ſito, tamen in ogni poſitione men leue ſi trouara quello, che ſara in alto elle<lb></lb>uato di quello, che ſi trouara quello, che ſara à baſſo inclinato.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie il uero Si<lb></lb>gnore.<emph.end type="italics"></emph.end> S.A. S<emph type="italics"></emph>e queſto è uero, eglie da credere, anci da tener per fermo, che chi impo <lb></lb>neſſe ſopra al corpo.a.à baſſo inclinato, un'altro corpetto qual in grauita fuſſe eguale <lb></lb>à quella differentia, che il corpo elleuato è piu graue, ſecondo il ſito del corpo à baſſo <lb></lb>inclinato, che cadauno de loro reſtaria nel proprio luoco doue ſi trouaſſe, & accio me<lb></lb>glio me intendiati, uoi ſapeti che il corpo.b.della figura della precedente propoſitione, <lb></lb>ſtante elleuato per fin al ponto.i. (come in quello appare) & il corpo.a.à baſſo inclina <lb></lb>to per fin al ponto.u.uoi approuaſti il detto corpo.b.in tal ſito eſſer piu graue del cor <lb></lb>po.a.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignore eglie il uero.<emph.end type="italics"></emph.end> S.A. A<emph type="italics"></emph>dunque conchiudo che chi imponeſſe in tal <lb></lb>ſito un'altro corpetto ſopra alcorpo.a.qual fuſſe preciſamente di tanta grauita, quan <lb></lb>to, che è la <expan abbr="differẽtia">differentia</expan>, che è fra li detti dui corpi.a.&.b.in tal poſitione li detti dui cor <lb></lb>pireſtariano fermi, & ſtabili in tal poſitione, perche in talſito ſe trouariano egualmen <lb></lb>te potenti, cioe il corpo.b.non ſaria ſofficiente à far reaſcendere il detto corpo.a.al ſi<lb></lb>to della egualita, per eſſer il detto corpo.a. (per uigor di quel corpetto aggionto) tan<lb></lb>to graue è potente quanto lui, cioe che per quel tanto che il detto corpo.b. è piu poten<lb></lb>te, ouer graue per uigor del ſito del corpo.a.per quel tanto ſara piu graue il detto cor <lb></lb>po.a.del detto corpo.b.per uigore della grauita di quel ſimplice corpetto aggiontoui <lb></lb>ſopra, per ilche il detto corpo.b.non ſara atto à far reaſcendere il detto corpo.a.al ſi<lb></lb>to della egualita, & manco il corpo.a.ſara atto à potere piu elleuare il detto corpo.b. <lb></lb>del ſito.i.e pero l'uno è l'altro de neceßita non ſe potra partire di tal ſuo luoco, cioe il <lb></lb>corpo.a.con la gionta di quell'altro corpo, non potra reaſcendere al ſito della eguali<lb></lb>ta, ne manco potra deſcendere alla linea della direttione, cioe al ponto.f.come ſe con<lb></lb>chiude nella uostra propoſitione, & pur il detto corpo.a.inſieme con quell'altro cor<lb></lb>petto aggionto, ſaria ſimplicemente piu graue del corpo.b.e per tanto non poteti ne-<pb xlink:href="042/01/183.jpg"></pb>gare che tal uoſtra propoſitione non ſia falſa in quanto al generale, eglie ben uero, che <lb></lb>ſe la grauita di quel corpetto che fuſſe aggionto ſopra al detto corpo.a.fuſſe maggiore <lb></lb>della grauita, nella quale il corpo.b.è piu graue per uigor del ſito del corpo.a. ſeguiria <lb></lb>quello che nella detta uoſtra propoſitione ſe conchiude, & ſe per caſo tal grauita di cor <lb></lb>petto fuſſe menore di detta differentia, tal corpo.b.faria aſcendere il detto corpo.a.in <lb></lb>un'altro ſito piu alto del ponto.u. </s> <s id="s.001914">ſecondo che piu, ouer men ſcarſezaſſe la grauita di <lb></lb>tal corpetto della detta differentia che è fra loro per uigor del ſito.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſta oppo <lb></lb>ſitione di<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>certamente è molto ſpeculatiua, & bella, nondimeno auertiſco quella, <lb></lb>che ſe ben il corpo.b.in tal ſito.i.ſia piu graue del corpo.a.nel ſito.u.la differentia di <lb></lb>queſte due grauita ineguale è tanto piccola, ouer minima, ch'eglie impoßibile à potere <lb></lb>ritrouare una coſi piccola, ouer minima differentia fra due quantita ineguale.<emph.end type="italics"></emph.end> S. A. <lb></lb>Q<emph type="italics"></emph>uesto che haueti detto mi pare una coſa molto abſorda da dire, & manco da crede<lb></lb>re, perche eſſendo la quantita continua diuiſibile in infinito, eglie una materia à uoler <lb></lb>dire, che il ſia impoßibile à dare un corpettino di tanta poca quantita, & grauita, quan <lb></lb>to che è la differentia che è fra la grauita del corpo.b.nel ſito.i.& quella del corpo.a. <lb></lb>nel ſito.u.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignore la ragione é quella che ne chiariſſe le coſe dubbioſe, & che ne <lb></lb>diſcerne il uero dal falſo.<emph.end type="italics"></emph.end> S.A. E<emph type="italics"></emph>glie il uero.<emph.end type="italics"></emph.end> N. S'<emph type="italics"></emph>eglie il uero, nanti che<emph.end type="italics"></emph.end> V.S. <emph type="italics"></emph>dia <lb></lb>aſſoluta ſententia alla mia propoſitione quella aſcolti prima le mie ragioni.<emph.end type="italics"></emph.end> S.A. S<emph type="italics"></emph>e<lb></lb>guitati, & dite cio, che ui pare.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia eſſempi gratia, la medeſima libra.a.b.c.della <lb></lb>precedente propoſitione, nelle istremita, della quale ſiano pur appeſi li dui corpi.a. <lb></lb></s> <s id="s.001915">b.eguali ſimplicemente in grauita, & ſia abbaſſato con la mano il corpo.a.& elleuato <lb></lb>il corpo.b.come di ſotto appare in figura. </s> <s id="s.001916">Dico che in tal ſito, il corpo.b. è piu ponde<lb></lb>roſo, ouer graue per uigor del ſito del corpo.a.& che la differentia che è fra le grauita <lb></lb>de questi dui corpi, eglie impoßibile à poterla dar, ouer trouar fra due quantita ine<lb></lb>guale, & per dimoſtrar questa propoſitione. </s> <s id="s.001917">Tiro le due rette linee.a.h.&.b.d.per<lb></lb>pendicolare uerſo il centro del mondo, & tiro anchora le due linee.a.l.&.b.m.contin <lb></lb>gente il detto cerchio, che deſcriue li brazzi della libra, l'una nel ponto.a.& l'altra <lb></lb>nel ponto.b. </s> <s id="s.001918">Et deſcriuo anchora una parte de una circonferentia d'un cerchio, contin <lb></lb>gente il medeſimo cerchio.a.e.b.in ponto. </s> <s id="s.001919">b.la qual ſia pur d'un cerchio ſimile, & e<lb></lb>guale al medeſimo cerchio.a. </s> <s id="s.001920">e. b. la qual parte pongo che ſia la.b.z.tal che l'arco.b. <lb></lb></s> <s id="s.001921">z.uien à eſſer ſimile, & eguale all'arco.a.f.& anchora ſimilmente poſto, cioe nel me<lb></lb>deſimo ſito, ouer luoco, & la linea.b.m.che continge, ouer tocca quello, & perche la <lb></lb>obliquita dell'arco.a.f. (per quello che fu detto ſopra la terza petitione) uien miſura<lb></lb>ta, ouer conſiderata per meggio dell'angolo contenuto dalla perpendicolar.a.h. </s> <s id="s.001922">& dal <lb></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 miſurata, ouer <lb></lb>conſiderata per meggio dell'angolo contenuto dalla perpendicolar. </s> <s id="s.001926">b. d. </s> <s id="s.001927">& dalla <lb></lb>circonferentia. </s> <s id="s.001928">b. f. in ponto.b. </s> <s id="s.001929">adunque il corpo.b.in tal ſito ueneria ad eſſer tanto <lb></lb>piu graue del corpo.a.quanto che il detto angolo (contenuto dalla perpendicolar.b.d. <lb></lb></s> <s id="s.001930">& dalla circonferentia.b.f.in ponto.b.) ſara menore dell'angolo contenuto dalla per<lb></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></lb></s> <s id="s.001933">f.è preciſamente eguale all'angolo.d.b.z.& lo detto angolo.d.b.z.uien ad eſſer tanto <lb></lb>maggiore dell'angolo contenuto dalla detta perpendicolare,b.d.& dalla circonferen-<emph.end type="italics"></emph.end><pb pagenum="92" xlink:href="042/01/184.jpg"></pb><emph type="italics"></emph><gap></gap>a.b.f.in ponto.b.quanto che é l'angolo della contingentia delli dui cerchij.b.z.&.b. <lb></lb></s> <s id="s.001934">f. in ponto. </s> <s id="s.001935">b. & perche il detto angolo della detta contingentia é acutißimo de tutti <lb></lb>li angoli acuti de linee rette (come per la decimaſeſta del terzo di Euclide facilmente <lb></lb>ſi puo approuare) adunque la differentia, ouer proportione, che caſca fra l'angolo. <lb></lb></s> <s id="s.001936">h.a.f. & l'angolo contenuto dalla perpendicolar.b.d. </s> <s id="s.001937">& della circonferentia.b.f. </s> <s id="s.001938">in <lb></lb>ponto.b.è menore di qual ſi uoglia differentia, ouer proportione, che caſcar poſſa fra <lb></lb>qual ſi uoglia maggiore, & menor quantita, & coſi (per la terza petitione) la diffe<lb></lb>rentia della obliquita del deſcenſo.a.f.& del deſcenſo.b.f.& conſequentemente la diſ<lb></lb>ferentia della detta grauita delli detti dui corpi.a. </s> <s id="s.001939">&.b.ſecondo il ſito è menore, del <lb></lb>quale ſi uoglia fra due quantita ineguale, e pero ogni piccola quantita corporea, che <lb></lb>ſia aggionta ſopra il corpo.a.neceſſariamente in ogni ſito ſara piu graue del corpo.b. <lb></lb>e pero non ceſſara di deſcendere continuamente <21> fin alla linea direttione, cioe <21> uigor <lb></lb>fin al ponto.f. </s> <s id="s.001940">& coſi continuamente quello andara elleuando il corpo.b. per fin alla <lb></lb>detta linea della direttione, cioe per fin al ponto.e.& ſe queſto ſeguiria in tal ſito, co<lb></lb>me che nella ſottoſcritta figura appare tanto piu ſeguiria nel ſito della egualita, nel <lb></lb>qual ſito, ouer luoco non ui è, ouer ſaria alcuna differentia, <21> uigor del ſito, ne <21> uigor <lb></lb>delli lor deſcenſi, cioe che in tal ſito ſariano egualmente graui, e pero ogni piccola <lb></lb>quantita di peſo per minima, che ſia, che ui ſia impoſto dall'una delle bande di qual ſi <lb></lb>uoglia libra (cioe granda, ouer piccola de brazzi eguali) immediate fara declinare <lb></lb>neceſſariamente quella da quella medeſima banda, ouer brazzo, & continuara tal ſu<gap></gap><lb></lb>declinatione (per le ragioni di ſopra adutte) per fin alla linea della direttione, cioe <lb></lb>per fin al ponto.f.la qual coſa ſaria contra à quelle due concluſioni, che adduce Ari<lb></lb>ſtotile ſopra la ſua prima queſtione Mecanica, delle quale altra uoltane parlai con <lb></lb>Voſtra Signoria, delle quale in l'una dice, che ſono alcuni peſi, li quali impoſti nel<lb></lb>le piccole libre, non ſe fanno manifeſti con alcuna inclinatione al ſenſo, & che nel<lb></lb>le grande libre ſe fanno manifesti, la qual concluſione, ſumendola Mathematica<lb></lb>mente, cioe aſtratta da ogni materia, ſaria falſißima (per le ragioni di ſopra adutte) <lb></lb>perche ſi nelle piccole, come nelle grande libre, da quella banda doue ſara poſto quel <lb></lb>tal peſo (per piccol che ſia) ſara sforzata à declinar per fina alla detta linea della di<lb></lb>rettione, e pero nella declinatione della piccola, & in quella della granda, non ſara <lb></lb>proportionalmente alcuna differentia, perche in luna, e l'altra la declinatione ſara <lb></lb>per fina alla linea della direttione, il medeſimo ſeguiria dell'altra ſua concluſione, <lb></lb>cioe quando dice, che ſono alcuni peſi, li quali ſono manifeſti in luna, & l'altra <lb></lb>ſorte de libre, cioe nelle maggiori, & nelle menori, ma molto piu nelle maggiori, <lb></lb>la qual concluſione (per le ragioni di ſopra adutte) ſaria pur falſa, perche, come <lb></lb>detto in luna, & l'altra fara declinare il brazzo della libra per fina alla linea <lb></lb>della direttione.<emph.end type="italics"></emph.end> S. AMBASCIATORE. Q<emph type="italics"></emph>ueſte uoſtre ragioni, & argo<lb></lb>menti ſono ottimi è buoni, nondimeno nelle libre naturale, ouer materiale il ſi uede <lb></lb>pur ſeguire la maggior parte delle uolte, come che Ariſtotile conchiude, & dice, <lb></lb>perche ſe ſopra qual ſi uoglia libra (cioe granda, ouer piccola) ui ſara posto <gap></gap><lb></lb>no grano, ouer ſemenza di papauero, o altra ſimile piccola quantita, rare libre ſe <lb></lb>ritrouara che per ſi poca grauita, ſacciano inclinatione ſenſibile, & ſi pur ni ſe ne ri-<pb xlink:href="042/01/185.jpg"></pb>trouard alcuna che faccia alcun ſenſibile ſegno de declinatione, tamen non procedera <lb></lb>per fina alla detta linea della direttione, & non ſolamente il detto gran de papauero <lb></lb>nonſara atto à farla declinare per fin alla detta linea della direttione alcuna libra, ma<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.185.1.jpg" xlink:href="042/01/185/1.jpg"></figure><lb></lb><emph type="italics"></emph>nanche un gran di formento, qual é molto piu ponderoſo, & tutto queſto la ſperientia <lb></lb>lo manifeſta. </s> <s id="s.001941">Si che non ſo che mi dire, perche da una banda per le uoſtre ragioni, & ar <lb></lb>gomenti, uedo, & comprendo che uoi diceti il uero, & dall'altra trouo per iſperientia <lb></lb>ſeguir tutto al contrario.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>l tutto procede Signor, dalla materia, perche nelle li<lb></lb>bre conſiderate con la mente fuora de ogni materia il ſuo ſparto, polo, ouer aßis, ſe ſup <lb></lb>pone un ponto indiuiſibile, et nelle libre materiale, tal ſparto, ouer aßis ha ſempre qual <lb></lb>che corporal groſſezza in ſe, la qual groſſezza, quanto è maggiore tanto men <expan abbr="diligẽ-te">diligen<lb></lb>te</expan> reduſſe la detta libra, & ſimilmente li brazzi delle libre imaginate (cioe ideale) ſe <lb></lb>ſuppongano linee, cioe ſenza larghezza, ne groſſezza, & nelle libre materiale tai <lb></lb>brazzi ſono di alcun metallo, ouer di legno, li quali brazzi quanto piu ſono corpulen<lb></lb>ti, è großi tanto men diligente reducano tal libre.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.001942">E <emph type="italics"></emph>ue ho inteſo, ſeguitatiſe he <lb></lb>ueti altra propoſitione de adure circa à queſtamateria.<emph.end type="italics"></emph.end> NIC. </s> </p> <p type="head"> <s id="s.001943">QVESITO. XXXIIII. PROPOSITIONE VII.</s> </p> <p type="main"> <s id="s.001944">Se <emph type="italics"></emph>li brazzi della libra ſaranno ineguali, et che nella iſtremita di cadauno de quelli <lb></lb>ui ſiano appeſi corpiſimplicemente eguali in grauita dalla banda del piu <expan abbr="lõgo">longo</expan> braz <lb></lb>zo tal libra fara declinatione.<emph.end type="italics"></emph.end> S. A. Q<emph type="italics"></emph>ueſta <lb></lb>è coſa naturale.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nchor che la ſia coſa na <lb></lb>turale uolendo procedere rettamente, biſogna <lb></lb>aßignar la cauſa di taleffetto.<emph.end type="italics"></emph.end> S.A. S<emph type="italics"></emph>eguitati.<emph.end type="italics"></emph.end><lb></lb>N. S<emph type="italics"></emph>ia la uerga, ouer libra.a.c.b.et ſiail braz <lb></lb>zo.a.c.piu longo del.c.b. </s> <s id="s.001945">Dico che eſſendo ap<lb></lb>peſi corpi ſimplicemente eguali in grauita, nelli <lb></lb>dui ponti.a.&.b.tal libra declinara dalla par<lb></lb>te del.a. </s> <s id="s.001946">Perche eſſendo tirata la perpendicola<lb></lb>re.c.f.g. (cioe la linea della direttione) et eſſen<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.185.2.jpg" xlink:href="042/01/185/2.jpg"></figure><pb pagenum="93" xlink:href="042/01/186.jpg"></pb><emph type="italics"></emph>do circindle le due quarte parte de circuli, ſopra el centro.c.le quale ſiano.a.g. </s> <s id="s.001947">&. </s> <s id="s.001948">b. <lb></lb>f.& eſſendo dutte dal ponto.a.&.b.due linee contingente, le quale ſiano.a.e.&.b.d. <lb></lb></s> <s id="s.001949">Eglie manifeſto langolo.e.a.g.della detta contingentia, eſſer menore de langolo. </s> <s id="s.001950">d. </s> <s id="s.001951">b. <lb></lb>f.e pero manco obliquo é il deſcenſo fatto per.a.g. </s> <s id="s.001952">del deſcenſo fatto per. </s> <s id="s.001953">b. f, e pero <lb></lb>(per la terza petitione) piu graue ſara il corpo.a.del corpo.b, in tal ſito, ch'è il pro<lb></lb>poſito.<emph.end type="italics"></emph.end> S. A. </s> <s id="s.001954">E <emph type="italics"></emph>ue ho inteſo, ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.001955">QVESITO. XXXV. PROPOSITIONE VIII.</s> </p> <p type="main"> <s id="s.001956">Se <emph type="italics"></emph>li brazzi della libra ſaranno proportionali alli peſi in quella impoſti, talmen<lb></lb>te, che nel brazzo piu corto ſia appeſo il corpo piu graue, quelli tai corpi, ouer <lb></lb>peſi ſeranno equalmente graui, ſecondo tal poſitione, ouer ſito.<emph.end type="italics"></emph.end> S.A. D<emph type="italics"></emph>atime uno eſ <lb></lb>ſempio.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia come prima la regola, ouer libra,a.c.b. </s> <s id="s.001957">& ui ſiano appeſi. </s> <s id="s.001958">a.&.b. et <lb></lb>ſia la proportione del.b.al.a.ſi come del brazzo.a.c.al brazzo.b.c. </s> <s id="s.001959">Dico, che tal li<lb></lb>bra non declinara in alcuna parte di quella, & ſe poßibil fuße (per lauerſario) che de<lb></lb>cl inar poteſſe, poniamo che quella declini dalla parte del b.& che quella diſcenda, & <lb></lb>tranſiſca in obliquo, ſi come ſta la linea.d.c.e.in luoco della.a.c.b.& attaccatoui.d.co <lb></lb>me.a.&.e.come.b.& la linea.d.f.deſcenda orthogonalmente, & ſimelmente aſcenda <lb></lb>la.e.h. </s> <s id="s.001960">Hor eglie manifeſto (per la. </s> <s id="s.001961">16. &. </s> <s id="s.001962">29. del primo di Euclide) che li dui triango <lb></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 ſeſto di Euclide) quelli ſa<lb></lb>ranno ſimili, & conſequentemente de lati proportionali, adunque la proportione del <lb></lb>d.c.al.c.e.è ſi come del.d.f.al.e.h.& perche ſi come del.d.c.al.c.e.coſi è dal peſo.b. </s> <s id="s.001965">al <lb></lb>peſo.a. (dal preſuppoſito) adunque la proportione dal.d.f.al.e.b.ſara ſi come dal pe<lb></lb>ſo.b.al. </s> <s id="s.001966">peſo.a.ſia adunque dal.c.d.tolto la parte.c.l.equale alla.c.b.ouer alla. </s> <s id="s.001967">c. e. & <lb></lb>ſia poſto. </s> <s id="s.001968">l. </s> <s id="s.001969">equale al. b. in grauita, & deſcenda el perpendicolo. </s> <s id="s.001970">l. m. </s> <s id="s.001971">Adunque per<lb></lb>che eglie manifeſto la. </s> <s id="s.001972">l. m. & la. </s> <s id="s.001973">e. h. eſſer equale, la proportione della. </s> <s id="s.001974">d. <lb></lb></s> <s id="s.001975">f. alla. </s> <s id="s.001976">l. m. ſaraſi come delle ſimplice grauita del corpo. b. alla ſimplice graui<lb></lb>ta del corpo. a. ouer della ſimplice grauita del corpo.l. alla ſimplice grauita del cor<lb></lb>po d. (perche li dui corpi.a.&.d.ſono ſuppoſtiuno medeſimo) & ſimelmente el cor<lb></lb>po.b.&.l.per eſſer ſuppoſta la grauita del. l. equale alla grauita del. b.) e per tanto <lb></lb>dico, che la proportione di tutta la.d.c.alla.l. </s> <s id="s.001977">c. ſara ſi come la grauita del corpo.l. <lb></lb>alla grauita del corpo.d. </s> <s id="s.001978">Onde ſe li detti dui corpi graui, cioe.d.&.l.fuſſeno ſimplice <lb></lb>mente equali in grauita, stanti poi in limedeſimi ſiti, ouer luochi, doue, che al preſen <lb></lb>te uengono ſuppoſti, el corpo.d.ſaria piu graue del corpo.l.ſecondo elſito (per la. </s> <s id="s.001979">4. <lb></lb>propoſitione) in tal proportione, qual é di tutto il brazzo.d.c.al brazzo.l.c.& per <lb></lb>che il corpo.l.è ſimplicemente (dal preſuppoſito) piu graue del corpo.d.ſecondo la me <lb></lb>deſima proportione (cioe, ſi come la proportione del brazzo.d.c.al brazzo.l.c.adun <lb></lb>que li detti dui corpi.d.&.l.nel ſito della equalita ueneranno ad eſſere egualmente <lb></lb>graui, perche per tanto quanto il corpo.d.è piu graue del corpo.l. per uigor del ſito, <lb></lb>ouer luoco, per quel medeſimo el corpo.l. è ſimplicemente piu graue del corpo.d.e pe <lb></lb>vo nel detto ſito della equalita uengono à restare egualmentè graui. </s> <s id="s.001980">Adunque quella <lb></lb>potentia, ouer grauita, che ſara ſufficiente ad elleuare il corpo.a.dal ſito della equali<lb></lb>ta, al ponto, doue che al preſente è (cioe per fin al ponto.d.) quella medeſima ſaraſoſa<emph.end type="italics"></emph.end><pb xlink:href="042/01/187.jpg"></pb><emph type="italics"></emph>ficiente ad elleuare il corpo.l.dal medeſimo ſito della equalita al luoco, doue che al pre <lb></lb>ſente è. </s> <s id="s.001981">Adunque ſel corpo.b. (per lauerſario) è atto ad elleuare il corpo. a. dal ſito <lb></lb>della equalita per fin al ponto.d.el medeſimo corpo.b.ſaria anchora atto, e ſofficiente <lb></lb>ad elleuare il corpo.l.dal medeſimo ſito della equalita per fin al ponto, doue che al pre <lb></lb>ſente è, el qual conſequente é falſo, & con<lb></lb>tra alla quinta propoſitione, cioe el corpo <lb></lb>b. (qual è ſupposto equale in grauita al <lb></lb>corpo.l.) elleuaria il detto corpo. l. fuora <lb></lb>del ſito della equalita, in ſiti equali, cioe e<lb></lb>qualmente diſtanti dal centro.c.la qual co<lb></lb>ſa é impoßibile per la detta quinta propo<lb></lb>ſitione, diſtrutto adunque l'oppoſito, rima <lb></lb>ne il propoſito.<emph.end type="italics"></emph.end> S. A. Q<emph type="italics"></emph>uesta è una aſ<lb></lb>ſai bella propoſitione, ma el me pare, ſe <expan abbr="bẽ">bem</expan> <lb></lb>me arricordo, che Archimede Syracuſano<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.187.1.jpg" xlink:href="042/01/187/1.jpg"></figure><lb></lb><emph type="italics"></emph>ne ponga una ſimile, ma el non mi pare, che lui la dimoſtri per queſto uoſtro modo.<emph.end type="italics"></emph.end><lb></lb>N. V<emph type="italics"></emph>oſtra Signoria dice la uerita, anci di tal propoſitione, lui ne fa due propoſitio<lb></lb>ni, & queſte ſono la quarta, & quinta di quel libro, doue tratta delli centri delle coſe <lb></lb>graue, & in effetto tai due propoſitioni lui le dimostra ſuccintamente per li ſuoi prin <lb></lb>cipij da lui per auanti poſti, & demostrati, & perche tai ſui principij, ouer argomen <lb></lb>ti.non ſe conuegnariano in queſto trattato, per eßer materia <expan abbr="alquãto">alquanto</expan> diuerſa da quel<lb></lb>la, ne apparſo in questo luoco de dimoſtrare tal propoſitioni con altri principij, ouer <lb></lb>argomenti piu conuenienti in queſto luoco.<emph.end type="italics"></emph.end> S.A. E<emph type="italics"></emph>ue ho inteſo ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.001982">QVESITO XXXVI. PROPOSITIONE IX.</s> </p> <p type="main"> <s id="s.001983">Se <emph type="italics"></emph>ſaranno due ſolide uerghe, traui, ouer baſtoni di una ſimile, & equal longhez <lb></lb>za, larghezza, groſſezza, & grauita, & che ſiano appeſi in una libra talmente <lb></lb><gap></gap>he luno ſtia equidiſtante al orizonte, & laltro dependi perpendicolarmente, & tal<lb></lb>mente anchora, che del termine del dependente, & del mezzo dell'altro ſia una mede <lb></lb>ſima diſtantia dal centro della libra, ſecondo talſito, ouer poſitione ueneranno à eßere <lb></lb>equalmente graui.<emph.end type="italics"></emph.end> S.A. N<emph type="italics"></emph>on ue intendo, e pero datime uno eſſempio.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>ſſem<lb></lb>pi gratia. </s> <s id="s.001984">Siano li termini dellibrazzi della libra.b.&.d.& il ſparto, ouer centro di <lb></lb>quella il ponto.c.& ui ſiano attaccati li dui ſolidi ſimili, & equali, come detto, delli <lb></lb>quali luno ui ſia attaccato ſecondo lordine del bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o della libra, cioe equidistanta<lb></lb>mente al orizonte qual ſia.f.e.del qual il ſuo ponto di me<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o ſia el ponto.d.& laltro <lb></lb>ſia attaccato pendente perpendicolarmente qual ſia.b.g. </s> <s id="s.001985">& ſia il termine del ſuo at<lb></lb>taccamento il ponto.b.& ſia che la diſtantia del ponto.b.al ponto. </s> <s id="s.001986">c. (centro della li<lb></lb>bra) ſia tanto, quanto ch'è dal ponto di mezzo de laltro ſolido (cioe dal <expan abbr="põto">ponto</expan>.d.) al me <lb></lb>deſimo ponto.c. </s> <s id="s.001987">Dico che li detti dui ſolidi, in tal ſito, ouer poſitione ſono equalmen<lb></lb>te graui, & queſto ſe puo dimostrar in piu modi. </s> <s id="s.001988">El primo di quali é queſto, ch'eglie <lb></lb>manifeſto per le coſe dimostrate da Archimede in quello del centro della grauita, che<emph.end type="italics"></emph.end><pb pagenum="94" xlink:href="042/01/188.jpg"></pb><emph type="italics"></emph>tanto peſa il ſolido.f.e.in tal poſitione nella detta libra, quanto che faria ſe quello fuſ<lb></lb>ſe anchora lui appeſo perpendicolarmente in ponto.d.perche in tal ponto. </s> <s id="s.001989">d. </s> <s id="s.001990">ui ſotto <lb></lb>giace el centro della grauita de tal ſolido, & per eſſer li detti dui ſolidi equali in gra<lb></lb>uita dal preſuppoſito, & appeſi equalmente diſtanti dal ponto, ouer centro.c. </s> <s id="s.001991">quelli <lb></lb>(per la. </s> <s id="s.001992">5. propoſitione) non ſe ſeparano dal ſito della equalita, ch'é il propoſito.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.188.1.jpg" xlink:href="042/01/188/1.jpg"></figure> <p type="main"> <s id="s.001993">A<emph type="italics"></emph>nchora tal propoſitione ſi puo demoſtrar in queſto altro modo (el quale é piu ſua <lb></lb>conueniente dimostr atione, perche ſe uien à dimoſtrare per li ſuoi proprij Principij, <lb></lb>& non per principij alieni. </s> <s id="s.001994">Eglie manifeſto, che eſſendo ſuſpeſi dui peſi ſimplicemen<lb></lb>te equali, luno in ponto.f.& laltro in ponto.e.quali poniamo, che ſiano.h.<emph.end type="italics"></emph.end>k. <emph type="italics"></emph>& ſimel <lb></lb>mente dui altri equali alli medeſimi in ponto.b.quali ſiano.l.m.nelli quali ſiti, dico, che <lb></lb>tai peſi peſar anno equalmente, perche la proportione del peſo. </s> <s id="s.001995">l. al peſo.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>è ſi come <lb></lb>del brazzo.b.c.al brazzo.f.c., per la quarta propoſitione, perche tanto graue ſaria <lb></lb>el corpo.l.ſecondo el ſito nel ponto.d.quanto che nel ponto, doue ſi troua al preſente, <lb></lb>cioe in ponto.b. (per eſſer.c.d.equale al.c.b.dal preſuppoſito) e pero per la detta pro <lb></lb>poſitione, tal proportione ſara della grauita del corpo. l. al corpo.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>ſecondo el ſito, <lb></lb>quale ſara del brazzo.d.c.ouer.b.c.al.c.f.& per le medeſime ragioni tal proportio<lb></lb>ne ſara della grauita del corpo.m.alla grauita del corpo.h.ſecondo el ſito, quale ſara <lb></lb>del medeſimo brazzo.c.d.ouer.c.b.al brazzo.c.e.adunque la grauita de ambi dui l<gap></gap><lb></lb>corpi.l.m.inſieme alla grauita de ambi dui licorpi.h.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>inſieme ſecondo il ſito ſara ſi <lb></lb>come el doppio del brazzo.c.d. </s> <s id="s.001996">ouer del hrazzo.c.b.inſieme alli dui brazzi.c.f. </s> <s id="s.001997">et.c. <lb></lb></s> <s id="s.001998">e.pur inſieme, & perche li detti dui brazzi.c.e.&.c.f.inſieme ſono preciſamente tan <lb></lb>to, quanto è il doppio del detto bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o.c.d.ouer.c.b. </s> <s id="s.001999">ſeguita anchora, che la graui<lb></lb>ta delli detti dui corpi.l.m. </s> <s id="s.002000">ſia equale alla grauita delli dui corpi.h.&.<emph.end type="italics"></emph.end>k. <emph type="italics"></emph>ſecondo il ſi <lb></lb>to, ch'è il propoſito, perche ſe del ſopradetto ſolido.f.e.ne ſara fatto due parti equali, <lb></lb>appiccandone una di quelle in ponto.f.& laltra in ponto.e.tanto peſarano coſi ſepa<lb></lb>rate in tai ſiti, ſi come faceuano in longo congionte, come di ſopra fu ſuppoſto, & ſi<lb></lb>melmente facendo del ſolido.b.g.pur due parti, & appiccarle ambe due in el medeſi<lb></lb>mo ponto.b.tanto peſarano coſi ſeparate, come che congionte, come, che di ſopra ſi<gap></gap><lb></lb>ſuppoſto epero per le coſe detto, & allegate ſeguita il propoſito.<emph.end type="italics"></emph.end><pb xlink:href="042/01/189.jpg"></pb><figure id="id.042.01.189.1.jpg" xlink:href="042/01/189/1.jpg"></figure><lb></lb>S.A. V<emph type="italics"></emph>oria, che me dimoſtraſti che il brazzo.c.f.inſleme con il.c.e.ſia tanto <expan abbr="quãto">quanto</expan> <lb></lb>el doppio del brazzo.d.c.ouer.c.b.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ignor eglie manifeſto, che tutto il bra<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>o <lb></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></lb>remo adunque, che tutta la.c.e.è equal alla.c.d. </s> <s id="s.002001">& anchora alla ſua parte.f.d alla qual <lb></lb>parte.f.d.giontoui el brazzo.f.c.queste due parti inſteme ſe egualiano anchora loro <lb></lb>alla medeſlma.c.d, e pero tuttala.c.e.inſieme con la.c.f. </s> <s id="s.002002">ſono preciſamente il doppio <lb></lb>della.c.d & perche la detta.c.d.è equale (dal preſuppoſito) alla.b.c.ſeguita, che tutta <lb></lb>la.c.e.inſieme con la.c.f.ſtano equali al doppio della.c.b. </s> <s id="s.002003">ch'è il propoſito.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.002004">E <lb></lb><emph type="italics"></emph>ue ho inteſo beniſsimo, e pero ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.002005">QVESITO XXXVII. PROPOSITIONE X.</s> </p> <p type="main"> <s id="s.002006">Se<emph type="italics"></emph>l ſara una ſolida uerga, traue, ouer baſtone di una ſimile, & equal larghezza, <lb></lb>groſſezza, ſoſtantia, & grauita in ogni ſua parte, & che la longhezza di quella <lb></lb>ſla diuiſa in due parti inequale, & che nel termine della menor parte ui ſla appeſouno <lb></lb>altro ſolido, ouer corpo graue, el quale faccia ſtare la dettauerga, traue, ouer baſtone <lb></lb>equidistante al orizonte. </s> <s id="s.002007">La proportione della grauita di tal corpo graue, alla diffe<lb></lb>rentia della grauita della maggior parte della detta uerga (traue, ouer baſtone) alla <lb></lb>grauita della parte menore, ſara ſi come la proportione della <expan abbr="lõghezza">longhezza</expan> di tutta la uer <lb></lb>ga (traue, ouer baſtone) al doppio della longhezza della ſua menor parte.<emph.end type="italics"></emph.end> S. A. D<emph type="italics"></emph>a <lb></lb>time un eſſempio ſe uoleti, che ui <expan abbr="intẽda">intenda</expan>.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia la ſolida uerga (traue, ouer baſtone) <lb></lb>il ſolido.a.b.di una ſimile, et equal große<emph.end type="italics"></emph.end>zz<emph type="italics"></emph>a, larghezza, <expan abbr="ſoſtãtia">ſoſtantia</expan>, et grauita <21> tutto, <lb></lb>cioe <21> ogni parte, et ſia diuiſo <expan abbr="cõ">com</expan> l'intelletto in due parti inequale in <expan abbr="põto">ponto</expan>.c.et ſia ſigna <lb></lb>ta la.c.d.equal alla.a.c.adunque la.d.b. </s> <s id="s.002008"><expan abbr="uiẽ">uiem</expan> à eſſere la <expan abbr="differẽtia">differentia</expan>, ch'è fra la parte mag <lb></lb>giore.c.b.et la menore.c.a.della qual <expan abbr="differẽtia">differentia</expan> ſia trouato il mezzo, qual ſia il pon<lb></lb>to.e. </s> <s id="s.002009">Hor <expan abbr="eßẽdo">eßendo</expan> ſuſpeſo il detto ſolido, ouer traue.a.b.nel <expan abbr="põto">ponto</expan>.c.et <expan abbr="eßẽdoui">eßendoui</expan> attaccato, <lb></lb>ouer ſuſpeſo nel termine della ſua menor parte un altro ſolido (poniamo il ſolido.f.) <lb></lb>qual faccia ſtare il primo ſolido, ouer traue.a.b.equidiſtãte al <expan abbr="orizõte">orizonte</expan>. </s> <s id="s.002010">Dico, che tal <lb></lb>proportione hauera la grauita del ſolido.f.alla grauita della <expan abbr="differẽtia">differentia</expan>.d.b. </s> <s id="s.002011">qual hara <lb></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></lb></s> <s id="s.002013">Perche tanto peſa la detta differentia.d.b.m tal poſitione, come che al preſente ſta <expan abbr="quã">quam</expan> <lb></lb>to che faria ſe quella fuſſe perpendicolarmente ſoſpeſa in ponto.e.e pero (per il con-<emph.end type="italics"></emph.end><pb pagenum="95" xlink:href="042/01/190.jpg"></pb><emph type="italics"></emph>uerſo della.8.propoſitione) la proportione della grauit à del ſolido.f.alla grauita del <lb></lb>partial ſolido, ouer traue.d.b. </s> <s id="s.002014">ſara, ſi come la proportione della diſtantia.c.e.alla di<lb></lb>ſtantia.c.a. </s> <s id="s.002015">Et la proportione, che è della diſtantia.c.e.alla diſtantia.c.a. (per la.15.del <lb></lb>quinto di Euclide) quella medeſima ſar a del doppio della diſtantia.c.e. </s> <s id="s.002016">al doppio della <lb></lb>detta diſtantia.c.a.& perche il doppio della detta diſtantia.c.e.è quanto che è tutta la <lb></lb>longhezza del ſolido.a.b.& il doppio della detta diſtantia.c.a.è quanto che è tutta la <lb></lb>a.c.d. ſeguita (per la.11.del quinto di Euclide) che la proportione della grauita del ſo<lb></lb>lido.f.alla grauita della pifferentia.d.b.ſia ſi come la proportione di tutta la longhez <lb></lb>za del ſolido, ouer uerga.a.b.al doppio della longhezza della parte menore.a.c. (qual <lb></lb>è la detta.a.c.d.) che è il propoſito.<emph.end type="italics"></emph.end> S.A. P<emph type="italics"></emph>erche ragione uoleti che il doppio della<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.190.1.jpg" xlink:href="042/01/190/1.jpg"></figure><lb></lb><emph type="italics"></emph>diſtantia.c.e.ſia eguale à tutta la longhezza del traue.a.b.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>erche la detta diſtan <lb></lb>tia.c.e.uien à eſſer preciſamente eguale alla mita di tal longhezza.a.b. </s> <s id="s.002017">perche la par<lb></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></lb>parti.d.e.&.d.c.gionte inſieme, uengono à eſſere la mita delle due parti.d.b.&.d.a. <lb></lb></s> <s id="s.002019">pur gionte inſieme.<emph.end type="italics"></emph.end> S.A. E<emph type="italics"></emph>ue ho inteſo, e pero ſeguitate in altro.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.002020">QVESITO. XXXVIII. PROPOSITIONE XI. <lb></lb><emph type="italics"></emph>conuerſa della precedente.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002021">Se <emph type="italics"></emph>la proportione della grauita d'un ſolido ſoſpeſo in el termine della menor parte <lb></lb>di una ſimile ſolida uerga (traue, ouer baſtone) diuiſa in due parti ineguali, alla dif <lb></lb>ſerentia, che ſara fra la grauita della maggior parte, & quella dellamenore, ſara, ſi co <lb></lb>me la proportione di tutta la longhezza della ſolida uerga, traue, ouer baſtone, al dop<lb></lb>pio della longhezza della ſua menor parte. </s> <s id="s.002022">Tal ſolida uerga, traue, ouer baſtone, ne<lb></lb>ceſſariamente ſtara equidiſtante all'Orizonte.<emph.end type="italics"></emph.end> S.A. C<emph type="italics"></emph>redo bene che tal precedente <lb></lb>propoſitione ſe conuertiſca, nondimeno non reſtati da farme la dimostratione.<emph.end type="italics"></emph.end> N. <lb></lb>P<emph type="italics"></emph>er eſſer queſta il conuerſo della precedente, per ſuo eſſempio ſupponeremo la mede<lb></lb>ſima diſpoſitione, ouer figura, cioe ſupponeremo, che la proportione della grauita del <lb></lb>ſolido.f.alla differentia della grauita della maggior parte alla grauita della menore, <lb></lb>cioe della.d.b.eſſer, ſi come la proportione di tutta la longhezza della ſolida uerga. <lb></lb></s> <s id="s.002023">b.al doppio della longhezza della parte menore.a.c. (quale ſaria la.a.d.) Dico che <lb></lb>ſtante questo la ſolida uerga.a.b.de neceßita ſtara equidiſtante all'Orizonte. </s> <s id="s.002024">Et ſe poſ <pb xlink:href="042/01/191.jpg"></pb>ſlbil fuſſe (per l'auerſario) che quella debbia, ouer poſſa declinar da qualche banda, po <lb></lb>niamo che declini dalla banda uerſo.b.al ſolido.f.gli aggiongeremo con lo intelletto <lb></lb>una tal parte (quale pongo che ſia la parte.g.) che faccia reſtare la detta ſolida uerga, <lb></lb>traue, ouer baſtone equidiſtante al detto Orizonte. </s> <s id="s.002025">Adunque, per la precedente, la pro <lb></lb>portione di tutta la grauita del compoſto delli dui corpi. </s> <s id="s.002026">ſi &.g.alla differentia, che è <lb></lb>fra la grauita della parte maggiore.b.c.& quella della parte menore.a c. (che ſaria <lb></lb>quella della.d.b.) ſara, ſi come la proportione di tutta la longhezza.a.b.al doppio <lb></lb>della longhezza della ſua parte menor.a.c. </s> <s id="s.002027">il qual doppio, ſaria la.a.d.& perche il <lb></lb>ſimplice ſolido.f.ha quella medeſima proportione,alla medeſima differentia (dal pre<lb></lb>ſuppoſito) ſeguitaria (per la.9.del quinto di Euclide) che la grauita del ſimplice ſoli<gap></gap><emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.191.1.jpg" xlink:href="042/01/191/1.jpg"></figure><lb></lb><emph type="italics"></emph>do.f.fuſſe eguale alla grauita de tutto il compoſito di dui ſolidi.f.g.la qual coſa è impoſ <lb></lb>ſibile, che la parte ſia eguale al tutto, il medeſimo inconueniente ſeguiria quando che lo <lb></lb>auerſario ſupponeſſe che declinaſſe dalla parte.a.perche ſegando uia dal ſolido.f.una <lb></lb>tal parte, che il rimanente faceſſe reſtare il detto ſolido.a.b. </s> <s id="s.002028">equidiſtante all'Orizon<lb></lb>te, argomentando, come di ſopra fu fatto, ſeguiria pur che la grauita del medeſimo re<lb></lb>fiduo fuſſe eguale alla grauita di tutto il ſolido.f. </s> <s id="s.002029">Adunque non potendo declinare ne <lb></lb>dalla banda uerſo.b.ne da quella uerſo.a.eglie neceſſario che stia equidiſtante all'Ori<lb></lb>zonte, che è il propoſito.<emph.end type="italics"></emph.end> S.A. S<emph type="italics"></emph>tabenißimo, hor ſeguitati pur.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.002030">QVESITO. XXXIX. PROPOSITIONE XII.</s> </p> <p type="main"> <s id="s.002031">Se<emph type="italics"></emph>l ſarauna ſolida uerga, trauer baſtone, come nelle due precedente è ſtato detto, <lb></lb>cioe diuna ſimile, & egual groſſezza, larghezza, ſoſtantia, & grauita, in ogni <lb></lb>ſua parte, & che di quello ne ſia nota la ſua grauita, & ſimilmente la ſua longhezza, et <lb></lb>che quello ſia diuiſo in due parti ineguale pur note. </s> <s id="s.002032">Eglie poßibile di ritrouar un peſo, <lb></lb>il quale quando che quello ſara ſoſpeſo al termine della ſua menor parte fara stare la <lb></lb>dettaſolida uerga, traue, ouer baſtone, equidiſtante all'Orizonte.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſto atto <lb></lb>operatiuo uoglio che mel dichiarati con eſſempio materiale, perche lo uoglio intende<lb></lb>rebene.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia eſſempi gratia la ſolida uerga (traue, ouer baſtone) a.b.ſecondo che <lb></lb>ſe propone, cioe di una ſimile, & equal groſſezza, larghezza, ſoſtantia, & grauita <lb></lb>per ogniſui banda, ouer parte, & poniamo, che la grauita di tal ſolida uerga ne ſia<emph.end type="italics"></emph.end><pb pagenum="96" xlink:href="042/01/192.jpg"></pb><emph type="italics"></emph>nota, cioe poniamo che tutta peſi lire. </s> <s id="s.002033">40. et che ſimilmente la longhezza di tal uerga, <lb></lb>ouer baſtone, ne ſia nota, cioe poniamo che quella ſia longa dui paſſa, cioe dieci piedi, & <lb></lb>poniamo anchora che tal uerga ſia diuiſa in due parti ineguale in ponto.c.& che le det <lb></lb>tè partine ſia note, cioe poniamo che la parte.a.c.menore, ſia piedi dui, & che la mag <lb></lb>gior.c.b.ſta piedi. </s> <s id="s.002034">8. Hor dico, che eglie poßibile di trouare di quante libre uorra eſſer <lb></lb>quel corpo qual eſſendo ſoſpeſo nel ponto.a. (termine della ſua menor parte) faccia ſta <lb></lb>re la detta uerga, ouer traue equidiſtante all'Orizonte. </s> <s id="s.002035">Perche (per le coſe dimoſtrate <lb></lb>nelle due precedente propoſitioni) eglie manifeſto, che la proportione della grauita di <lb></lb>quel tal corpo alla grauita di quella differentia che è fra la parte maggiore.c.b.& la <lb></lb>parte menore.a.c. (la qual differentia uerria à eſſer la.d.b.) ſara, ſi come tutta la lon <lb></lb>ghezza della uerga, ouer traue.a.b. (qual è piedi. </s> <s id="s.002036">10.) al doppio della longhezza della <lb></lb>partemenor.a.c. (qual è piedi dui) il doppio della quale uerria à eſſer piedi. </s> <s id="s.002037">4. qual <lb></lb>pongo ſia la.a.d.adunque la grauita di quel tal corpo, alla grauita della partial uerga.d. <lb></lb></s> <s id="s.002038">b.ſara, ſi come la longhezza de tutta la.a.b. (qual è piedi. </s> <s id="s.002039">10.) alla longhezza della.a. <lb></lb></s> <s id="s.002040">d. (qual è piedi.<emph.end type="italics"></emph.end> 4.) O<emph type="italics"></emph>nde arguendo alcontrario, diremo, chela proportione della.a.d. <lb></lb>(qual è piedi. </s> <s id="s.002041">4.) à tutta la.a.b. (qual è piedi. </s> <s id="s.002042">10) ſara, ſi come la grauita della partial <lb></lb>uerga.d.b.qual (alla ratta di tutta la.a.b.che libre. </s> <s id="s.002043">40.) uerria ad eſſer libre. </s> <s id="s.002044">24. alla <lb></lb>grauita del corpo che recercamo, cioe di quello, che appeſo nel ponto.a.debbia man-<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.192.1.jpg" xlink:href="042/01/192/1.jpg"></figure><lb></lb><emph type="italics"></emph>tenere la dettauerga, ouer traue equidiſtante all'Orizonte. </s> <s id="s.002045">Onde per ritrouarlo pro<lb></lb>cederemo ſecondo l'or dine della regola uolgarmente detta del tre, fondata ſopra la. </s> <s id="s.002046">20. <lb></lb>propoſitione del. 7.di Euclide, moltiplicando. </s> <s id="s.002047">10.fia.24.fa.240. & queſto lo parti<lb></lb>remo per.4.ne uenira.60.& libre.60.dico che peſara, ouer che douera peſare quel <lb></lb>tal corpo, qual pongo fia il corpo.f.che è il propofito.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>uesto problema me è <lb></lb>piaceſto aſſai, & l'ho inteſo benißimo, e pero ſeguitati ſe ci è altro da dire.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.002048">QVESITO. XL. PROPOSITIONE XIII.</s> </p> <p type="main"> <s id="s.002049">Se<emph type="italics"></emph>lſe hauerauna uerga, traue, ouer baſtone, come piu uolte è stato detto, del qual <lb></lb>ne ſia nota la ſua longhezza, & anchora la ſua grauita, & anchora un corpo pon<lb></lb>deroſo, del quale ne ſia nota ſua grauita, eglie poßibile à deter minare il luoco doue ſe <lb></lb>hauera da diuidere la data uerga, traue, ouer baſtone, talmente che appendendo il det-<pb xlink:href="042/01/193.jpg"></pb>to corpo ponderoſo al termine della ſua menor parte faccia ſtare la detta uerga, traue, <lb></lb>uer baſtone, equidiſtante all'Orizonte.<emph.end type="italics"></emph.end> S.A. E<emph type="italics"></emph>ſſemplificatemi questa propoſitione.<emph.end type="italics"></emph.end><lb></lb>N. P<emph type="italics"></emph>er eſſemplificar queſta propoſitione, ſupponeremo che il ſia pur unauerga, tra<lb></lb>ue, ouer baſtone, come fu la precedente, cioe longa piedi.10.& che la grauita di quella <lb></lb>fia pur libre.40. (come che nella detta precedente fu ſuppoſto.) Et poniamo anchora <lb></lb>che il ſia un corpo che la grauita di quello ſia libre.80. Dico ch'eglie poßibile à deter <lb></lb>minare il luoco doue ſe debbe diuidere la detta uerga, talmente che appendendo il det<lb></lb>to corpo graue al termine della ſua menor parte, faccia ſtar quella equidiſtante all'<emph.end type="italics"></emph.end>O<lb></lb><emph type="italics"></emph>rizonte. </s> <s id="s.002050">Et quantunque tal problema, ſi poſſa riſoluere per uia di proportioni, nondi<lb></lb>meno piu leggiadr amente, ſe riſolue per Algebra, ponendo che la parte menore della <lb></lb>detta uerga ſia una coſa de pie, onde la parte maggiore ueneria à reſtare piedi.10. <lb></lb>men.1.co. </s> <s id="s.002051">Duplico la menor parte, cioe.1 co.fa.2.co, & queste.2.coſe le ſottro da tut <lb></lb>ta la uerga qual è piedi.10.reſta piedi.10 men.2.coſe, & queſto ſara la differentia, <lb></lb>che è fra la parte maggiore, & la menore della detta uerga, onde per trouar la graui<lb></lb>ta di tal differentia, la moltiplico per.4. (perche peſando tutta la uerga libre.40.ue <lb></lb>neria ogni pie di quella à peſar lire.4.) e pero moltiplicando quella per.4. come detto <lb></lb>ne uenir a libre.40.men.8.coſe. </s> <s id="s.002052">Et perche la proportione di tutta la uerga (qual è pie <lb></lb>di.10.al doppio della ſua menor parte) il qual doppio ſaria.2.coſe (è ſi come che la gra<lb></lb>uita del noſtro corpograue (qual è libre.80.) alla grauita della ſopradetta differentia, <lb></lb>qual fulibre.40.men.8.co. </s> <s id="s.002053">Onde per la.20.del.7.di Euclide (la moltiplicatione della <lb></lb>prima) che.10.piedi (fia la quarta che è.40.men.8.coſe) qual fara.400.men.80.co <lb></lb>ſe (ſara eguale alla moltiplicatione della terza qual è libre.80.fia la ſeconda, qual è.2. <lb></lb>coſe (qual fara.160.co.) e pero haueremo.160.coſe eguale à.400.men.80.coſe, on<lb></lb>de riſtorando le parti, & ſeguendo il capitolo, trouaremo la coſa ualer.1.e dui terzi, <lb></lb>& de piedi.1.edui terzi, ſe douera ſignar la menor parte della detta uerga, ouer tra<lb></lb>ue, onde la maggiore uenira à reſtare de piedi.8.e un terzo, che è il propoſito.<emph.end type="italics"></emph.end> S.A. <lb></lb>Q<emph type="italics"></emph>ueſta è ſtata una bella reſolutione, ma ſeguitati pur, perche uorria che trahoggi & <lb></lb>dimane uedeßimo de iſpedire tutto quello, che haueti da proponere ſopra di queſta ſcien <lb></lb>tia, perche uorro poi che me aßignati la cauſa de alcune queſtioni, che ho da dirui.<emph.end type="italics"></emph.end> N. <lb></lb>N<emph type="italics"></emph>on credo di potermene iſpedire fra diman, e l'altro, perche continuamente me naſce <lb></lb>nuoue materie da proponere circa à talſcientia.<emph.end type="italics"></emph.end> S.A. S<emph type="italics"></emph>e non ſe ne potremo iſpedire <lb></lb>coſi dimane non importa, non perdemo tempo, ſeguitati.<emph.end type="italics"></emph.end> N. </s> </p> <p type="head"> <s id="s.002054">QVESITO. XLI. PROPOSITIONE XIIII.</s> </p> <p type="main"> <s id="s.002055">La <emph type="italics"></emph>egualita della declinatione è una medeſima egualita de peſo.<emph.end type="italics"></emph.end> S.A. D<emph type="italics"></emph>atemi <lb></lb>un eſſempio.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a egualita della declinatione uien conſeruata ſolamente in <lb></lb>uia retta. </s> <s id="s.002056">Hor poniamo adunque che la detta uia retta ſia la linea.a.b. </s> <s id="s.002057">& dal ponto.a. <lb></lb></s> <s id="s.002058">ſia anchor tirata la perpendicolare.a.c.& ſupponamo anchor nella detta declinata lie <lb></lb>nea.a.b.dui diuerſi luochi. </s> <s id="s.002059">Hor poniamo che l'uno ſia il ponto.d.& l'altro il ponto.e. <lb></lb></s> <s id="s.002060">Hor dico che diſcendendo, qualunque corpo ponderoſo, ouer dal ponto.d.ouer dal pon <lb></lb>to.e.ſara de uno medeſimo peſo, ſecondo il ſito in qual ſi uoglia de detti luochi. </s> <s id="s.002061">Per<emph.end type="italics"></emph.end><pb pagenum="97" xlink:href="042/01/194.jpg"></pb><emph type="italics"></emph>che ſe pigliaremo ſotto al.d.& al.e.due parti equali nella uia, ouer linea.a.b. </s> <s id="s.002062">Hor po <lb></lb>niamo, che l'una ſia la parte.d.e.et laltra la.e.g. </s> <s id="s.002063">Dico, che per le dette parti equali ca <lb></lb>pira equalmente del diretto, cioe della linea.a.c.la qual coſaſe notificara in queſto mo <lb></lb>do, dalli duiponti.e.&.g.ſiano tirate le due linee.e.h.&.g.l. <lb></lb></s> <s id="s.002064">perpendicolare ſopra la linea.a.c.et dalli dui ponti, ouer luo <lb></lb>chi.d.&.e.le due linee.d.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>&.e.m. </s> <s id="s.002065">perpendicolare ſopra <lb></lb>le medeſime.e.h.&.g.l.le qual due perpendicolare, cioe.d.<emph.end type="italics"></emph.end><lb></lb>k.<emph type="italics"></emph>&.e.m.ſaranno fra loro equali, perche adunque il detto <lb></lb>corpo ponderoſo, ſi eſſendo nel ponto.d.come nel ponto.e.in <lb></lb>quantita, ouer deſcenſi equali, capira equalmente del diret<lb></lb>to, ſara di una medeſima grauita in qual ſi uoglia de quelli, ſe <lb></lb>condo el ſito, ch'è il propoſito.<emph.end type="italics"></emph.end> S.A. </s> <s id="s.002066">E <emph type="italics"></emph>ue ho inteſo, ſegui<lb></lb>tate pur.<emph.end type="italics"></emph.end> N. </s> </p> <figure id="id.042.01.194.1.jpg" xlink:href="042/01/194/1.jpg"></figure> <p type="head"> <s id="s.002067">QVESITO XLII. PROPOSITIONE XV.</s> </p> <p type="main"> <s id="s.002068">Se <emph type="italics"></emph>dui corpi graui deſcendano per uie de diuerſe obliquita, & che la proportio<lb></lb>ne delle de clinationi delle due uie, & della grauita de detti corpi ſia fatta una me<lb></lb>deſima, tolta per el medeſimo ordine. </s> <s id="s.002069">Anchora la uirtu de luno, e laltro de detti dui <lb></lb>corpi graui, in el deſcendere ſara una medeſima.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſta propoſitione mi par <lb></lb>bella, e pero datime anchora un eſſempio chiaro, accio che meglio mipiaccia.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ia <lb></lb>la linea.a.b.c.equidiſtante al orizonte, & ſopra di quella ſia perpendicolarmente e<lb></lb>retta la linea.b.d.& dal ponto.d.deſcendano de qua, & de la le due uie, ouer linee.d.a. <lb></lb></s> <s id="s.002070">&.d.c.& ſia la.d.c.di maggior obliquita. </s> <s id="s.002071">Per la proportione adunque delle lor de<lb></lb>clinationi, non dico delli lor angoli, ma delle linee per fina alla equidiſtante reſecatio<lb></lb>ne, in la quale equalmente ſummemo del diretto. </s> <s id="s.002072">Sia <expan abbr="adũque">adunque</expan> la lettera.e.ſuppoſta per <lb></lb>un corpo graue posto ſopra la linea.d.c.& un'altro la lettera.h.ſopra la linea.d.a. <lb></lb></s> <s id="s.002073">& ſia la proportione della ſimplice grauita del corpo.e.alla ſimplice grauita del cor <lb></lb>po.h.ſi come quella della.d.c.alla.d.a. </s> <s id="s.002074">Dico li detti dui corpi graui eſſer in tai ſiti, o<lb></lb>uer luochi diuna medeſime uirtu, ouer potentia. </s> <s id="s.002075">Et per dimoſtrar queſto, tiro la.d.<emph.end type="italics"></emph.end>k. <lb></lb><emph type="italics"></emph>di quella medeſima obliquita, ch'è la.d.c.& imagino un corpo graue ſopra di quella <lb></lb>equale a corpo.e.el qual pongo ſia la lettera.g.ma che ſia in diretto con.e.h.cioe e<lb></lb>qualmente diſtanti dalla.c.<emph.end type="italics"></emph.end>k.H<emph type="italics"></emph>or ſe poßibel è (per lauerſario) che li detti dui corpi <lb></lb>e.&.h.non ſiano diuna medeſima, & equal uirtu in tai luochi, adunque luno ſara di <lb></lb>maggior uirtu, ouer potentia dell'altro, poniamo adunque, che.e. </s> <s id="s.002076">ſia di maggior uir<lb></lb>tu, adunque quello ſara atto à diſcendere, & ſimelmente à far aſcendere, cioe à tirare <lb></lb>in ſuſo el corpo.h. </s> <s id="s.002077">Hor poniamo (ſe poßibel è) che il detto corpo.e.deſcenda per fina <lb></lb>in ponto.l.& che faccia aſcendere il corpo.h.per fin in ponto.m. </s> <s id="s.002078">& faccio, ouer che <lb></lb>ſegno la.g.n.equale alla.h.m.la quale anchora lei uien à eſſer equale alla.e.l. </s> <s id="s.002079">Et dal <expan abbr="põ">pom</expan> <lb></lb>to.g.tiro la.g.h.e.la qual ſara perpendicolare ſopra la.d.b.per eſſer li detti tre pon<lb></lb>ti (ouer corpi) g.h.e.ſuppoſti in diretto, & equalmente distanti dalla.<emph.end type="italics"></emph.end> k. <emph type="italics"></emph>c. & fimel<lb></lb>mente dal ponto.l.ſia tiratala.l.t.equidiſtante alla.c.b.qual ſara pur perpendicolare<emph.end type="italics"></emph.end><pb xlink:href="042/01/195.jpg"></pb><emph type="italics"></emph>ſopra la medeſima.d.b.& dalli tre ponti.n.m.e. </s> <s id="s.002080">ſiano tirate le tre perpendicolari.n. <lb></lb></s> <s id="s.002081">z.m.x.&.e.r. </s> <s id="s.002082">Et perche la proportione della.n.z.alla.n.g.è ſi come quella, che è dall<gap></gap><lb></lb>d.y.alla.d.g.e pero ſi come anchora quella della.d.b. </s> <s id="s.002083">alla.d.<emph.end type="italics"></emph.end>k. <emph type="italics"></emph>(per eſſer li detti tre <lb></lb>triangoli ſimili.) Simelmente la proportione della.m.x.alla.m.h.è ſi come quella, che <lb></lb>é dalla detta.d.b.alla.d.a. (per eſſer li detti dui triangoli ſimili.) Anchora la propor<lb></lb>tione della.m.x.alla.n.<emph.end type="italics"></emph.end>z. <emph type="italics"></emph>ſara ſi come quella della.d.<emph.end type="italics"></emph.end><lb></lb>k.<emph type="italics"></emph>alla.d.a.& quella medeſima (dal preſuppoſito) e <lb></lb>dalla grauita del corpo.g.alla grauita del corpo. h. <lb></lb>perche il detto corpo.g.fu ſuppoſto eſſer <expan abbr="ſimplicemẽ">ſimplicemen</expan> <lb></lb>te, egualmente graue con el corpo.e. </s> <s id="s.002084">adunque tanto <lb></lb>quanto, che il corpo.g.è ſimplicemente piu graue del <lb></lb>corpo.h.per altro tanto il corpo. h. uien à eſſer piu <lb></lb>graue per uigor del ſito del detto corpo.g.è pero ſi <lb></lb>uengono ad egualiar in uirtu, ouer potentia, & per <lb></lb>tanto quella uirtu, ouer potentia, che ſara atta à far <lb></lb>aſcendere luno de detti dui corpi, cioe à tirarlo in ſu <lb></lb>ſo, quella medeſima ſara atta, ouer ſofficiente à fare <lb></lb>aſcendere anchora l'altro, adunque ſel corpo.e. (per <lb></lb>lauerſario) è atto, & ſofficiente à far aſcendere il <lb></lb>corpo.h.per fin in.m.el medeſimo corpo.e.ſaria a<lb></lb>dunque ſofficiente à far aſcendere anchora il corpo <lb></lb>g.à lui equale, & inequale declinatione, la qual coſa<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.195.1.jpg" xlink:href="042/01/195/1.jpg"></figure><lb></lb><emph type="italics"></emph>é impoßibile per la precedente propoſitione, adun<lb></lb>que il corpo.e.non ſara de maggior uirtu del corpo.h.in tali ſiti, ouer luochi, che éil <lb></lb>propoſito.<emph.end type="italics"></emph.end> S.A. Q<emph type="italics"></emph>ueſta è ſtata una bella ſpeculatione, & me è piaceſta aſſai. </s> <s id="s.002085">Et per <lb></lb>che uedo eſſer hora tarda, non uoglio, che procedati in altro per hoggi.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002086">F<emph type="italics"></emph>ine del ottauo libro.<emph.end type="italics"></emph.end></s> </p> </subchap1><subchap1> <pb pagenum="98" xlink:href="042/01/196.jpg"></pb> <p type="head"> <s id="s.002087">LIBRO NONO DELLI <lb></lb>QVESITI, ET INVENTIONI DIVERSE. <lb></lb>DE NICOLO TARTAGLIA.</s> </p> <p type="head"> <s id="s.002088">S<emph type="italics"></emph>opra la ſcientia Arithmetica, Geometrica, & in la Pratica Speculatiua <lb></lb>de Algebra, & Almucabala, uolgarmente detta Regola de <lb></lb>la coſa, ouer Arte maggiore, & maßime della <lb></lb>inuentione de Capitoli de Coſa, e Cubo <lb></lb>equal à numero, & altri ſuoi <lb></lb>ederenti, et dependenti, <lb></lb>Et ſimelmente de cenſi, e cubi equal à numero, & ſuoi <lb></lb>dependenti, quali dalli Sapienti ſono stati <lb></lb>giudicati impoßibili.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002089">QVESITO PRIMO FATTO DA MAESTRO <lb></lb>F<emph type="italics"></emph>ranceſco Feliciano l'anno.1521.in Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002090">MAESTRO FRANCESCO. I<emph type="italics"></emph>o comprai un peſce per lire <lb></lb>1.p.10.danari.1.& tanti danari lo pagai la lira, quanto, ch'erano <lb></lb>le lire, che lui peſaua. </s> <s id="s.002091">Domando quante lire pesò il detto peſce.<emph.end type="italics"></emph.end><lb></lb>N. L<emph type="italics"></emph>ui pesò lire.19.che à danari.19.la lira montaria danari.361. <lb></lb>che ſariano.p.30.& danari.1.cioe lire.1.§.10. danari.1. che è il <lb></lb>propoſito, & tal ragione la riſoluo in questo modo. </s> <s id="s.002092">10 reduco il <lb></lb>detto precio, cioe lire.1.p.10.danari.1.tutto in danari, che ſaria<lb></lb>no danari.361.& di queſti danari.361.ne cauo la ſua radice, qual è.19.& tante lire <lb></lb>pesò il detto peſce, come di ſopra dißi, ch'é facile.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002093">QVESITO SECONDO FATTO DA VN FRA <lb></lb>R<emph type="italics"></emph>aphaelle de.<emph.end type="italics"></emph.end>S.Z<emph type="italics"></emph>orzi de Verona, l'anno.<emph.end type="italics"></emph.end>1524.</s> </p> <p type="main"> <s id="s.002094">FRA RAPHAELLE. V<emph type="italics"></emph>no padre ha alquanti figliuoli, & fa teſtamento, <lb></lb>& fra le altre coſe ha una quantita de ducati in una caſſa, & da de detti danari <lb></lb>un ducato al ſuo primo figliuolo, & anchora la ottaua parte del rimanente, & al ſe<lb></lb>condo gli da ducati.2.& la ottaua parte del rimanente, & al terzo gli da ducati.3.et <lb></lb>pur la ottaua parte del ſuo rimanente, & coſi ua procedendo, & accreſcendo con tal <lb></lb>or dine à cadauno delli altri figliuoli, eccetto à l'ultimo, al qual gli dette tutti quelli, <lb></lb>che gli erano reſtati, & finalmente tanti ducati ſi trouo luno, come laltro. </s> <s id="s.002095">Hor ue adi <lb></lb>mando quanti ducati haueua in caſſa il detto padre, & ſimelmente quanti figliuoli ha <lb></lb>ueua.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>l detto padre haueua duc.49.in caſſa, & haueua.7.figliuoli<emph.end type="italics"></emph.end> F.R. E<emph type="italics"></emph><expan abbr="tcõ">tcom</expan> <lb></lb>che regola ritrouati li detti.49.ducati, &.7.figliuoli.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o cauo quella unita, che <lb></lb>è ſopra la uirgola di quello.1/8.che da à cadauno, di quel.8.ch'e di ſotto della <lb></lb>detta uirgola, & riman.7.& tanti figliuoli conchiudo, che lui haueua, et dapoi qua-<emph.end type="italics"></emph.end><pb xlink:href="042/01/197.jpg"></pb><emph type="italics"></emph>dro il detto.7.fa.49.& tanti ducati determino, che haueua in caſſa el detto padre.<emph.end type="italics"></emph.end><lb></lb>F.R. E<emph type="italics"></emph>t ſe in luoco di quello.1/8.lui ui haueſſe dato ſempre.1/7.come ſe doueria pro<lb></lb>cedere.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er lo medeſimo ordine, cioe cauando quella unita, che é ſopra la uirgo <lb></lb>la di quello.7.che é di ſotto, et rimaneria.6.& coſi.6.figliuoli haueria il detto padre, <lb></lb>& dapoi quadrando el detto.6.faria.36.& coſi.36.ducati haueria hauuto in caſſa.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002096">QVESITO TERZO FATTO DA. VNO MIO DISCI<lb></lb><emph type="italics"></emph>pulo, detto maeſtro Maphio, qual dice eſſerli stato fatto à <lb></lb>lui in Mantua, l'anno.<emph.end type="italics"></emph.end>1526.</s> </p> <p type="main"> <s id="s.002097">MAESTRO MAPHIO. E<emph type="italics"></emph>glie uno, che impreſta à uno ducati.300. per <lb></lb>anni.3.ma non ſo à quanto ſe conuiene de pagarli de merito ogni anno, ma ſo <lb></lb>ben, che non dandoli ogni anno il merito tra lor conuenuti luiuoleua, che tal merito ui <lb></lb>fuſſe meritato alla ratta del loro accordo di primi duc.300. Accade, che coſtui non ui <lb></lb>da coſa alcuna per fin in capo de ditti tre anni, & in capo delli detti tre anni lui lireſe <lb></lb>fra capital e merito ducati.500.Se adimanda quanto pagò de merito per cento all'an <lb></lb>no.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>agò di merito duc.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.1666666.2/3.men.100.cioe pagò tanto per <lb></lb>cento all'anno.<emph.end type="italics"></emph.end> M.M. E<emph type="italics"></emph>t con che regola ritrouati tal merito,<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er ritruouare <lb></lb>tal merito primamente imagino li detti duc.300.in li detti anni tre formar quattro <lb></lb>termin<gap></gap> continui proportionali, delli quali quattro termini, li detti duc.300.uengono <lb></lb>à eſſer el primo, & li dettiduc.500.che lui reſtituiſſe, uengono à eſſer el quarto, e pe <lb></lb>ro biſogna ritrouare li dui termini intermedij, oueramente il <expan abbr="ſecõdo">ſecondo</expan> (qual baſta in que <lb></lb>ſto caſo) & per ritrouarlo quadro.300.fa.90000. & questo. </s> <s id="s.002098">90000. lo molti<lb></lb>plico fia el quarto termine, cioe fia.500.fara.45000000. & la radice cubade dit<lb></lb>to.45000000.ſaranno ritornati li detti duc.300.tramerito, et capitale in capo del <lb></lb>primo anno, la qual quantita la diuido per tre (cubando pero el tre per trouar quan<lb></lb>to retornara ſolamente duc.100.) ne uenira.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.1666666.2/3.& <expan abbr="tãto">tanto</expan> ſaria ritor <lb></lb>nato duc.100.fra merito, e capitale in capo del primo anno, hor per ſapere quanto fu <lb></lb>el puro merito per cento all'anno, cauo di tal <expan abbr="quãtita">quantita</expan> il capitale, cioe duc.100.rimane <lb></lb>ra.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.1666666.2/3.men.100.et tanto dico, che pago de merito per cento all'anno, <lb></lb>come di ſopra dißi.<emph.end type="italics"></emph.end> M.M. L<emph type="italics"></emph>a è piu forte ragione di quello mi penſaua.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002099">QVESITO QVARTO FATTO DAL MEDESIMO <lb></lb>M<emph type="italics"></emph>aestro Maphio, qual dice gli fu propoſto in <lb></lb>Mantua l'anno.<emph.end type="italics"></emph.end>1526.</s> </p> <p type="main"> <s id="s.002100">MAESTRO MAPHIO. T<emph type="italics"></emph>rouatime duinumeri, che tutte le parti ali<lb></lb>quote del primo gionte inſieme facciano el ſecondo, & che ſimelmente tutte <lb></lb>le parti aliquote del ſecondo facciano preciſamente elprimo numero.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>'uno ſa<lb></lb>ra. </s> <s id="s.002101">284.& laltro.220.cioe, ſe recogliereti tutte le parti aliquote de.284. uoitro<lb></lb>uareti, che faranno preciſamente.220.& coſi, ſe recogliareti tutte le parti aliquote <lb></lb><gap></gap> 220. uoi trouareti, che faranno preciſamente.284.come ſe ricerca.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="99" xlink:href="042/01/198.jpg"></pb> <p type="head"> <s id="s.002102">QVESITO QVINTO FATTOMI DA <lb></lb><emph type="italics"></emph>un Fiorentino.1526.in Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002103">FIORENTINO. E<emph type="italics"></emph>gliera un contadino qual eſſendo infermo, & trouan<lb></lb>doſi hauer duc.17.1/2. & hauendo trei figliuoli, laſſa che morendo li detti ſuoi <lb></lb>trei figliuoli ſe diuideſſono li detti ducati.17.1/2.egualmente fra loro, cioe che cadau<lb></lb>no ſe ne pigliaſſe la terza parte. </s> <s id="s.002104">Accade che coſtui more, & li detti figliuoli corſe<lb></lb>no alla caſſa doue erano li detti danari, & cadauno comincio à grapire di quelli meglio <lb></lb>che pote, cioe che piu, e chimeno diquello ſe gli aſpettaua. </s> <s id="s.002105">Ilche inteſo da un ſuo bar<lb></lb>bano, quel uene, & fece che il figliolo maggiore metteſſe zoſo la mita, & ſe reteneſſe <lb></lb>laltra mita de tutti quelli danari, che haueua aggrapiti, & ſimelmente fece che laltro <lb></lb>ſecondo fratello meteſſe zoſo liduiterzide detti danari & che ſe reteneſſe laltro ter <lb></lb>zo per ſe & ſimelmente fece che il terzo figliolo meteſſe zoſo litre quarti dedetti de<lb></lb>nari, & che ſe reteneſſe laltro quarto per ſe, & tutto quello nnmero de denari, che fu <lb></lb>poſto zoſo il detto ſuo barbano lo diuiſe in treparti equali, & a cadauno di loro dete <lb></lb>una de dette parti, & fatto queſto cadauno di loro ſi trouo hauer il ſuo douere, cioe tan <lb></lb>to luno quanto laltro. </s> <s id="s.002106">Hor ue adimando quanti denari tolſe cadauno de loro doppo la <lb></lb>morte del padre.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>l primo tolſe duc. </s> <s id="s.002107">3.8/9.il ſecondo duca.5.15/18.il terzo.<emph.end type="italics"></emph.end>7.7/9 <lb></lb>F. </s> <s id="s.002108">E <emph type="italics"></emph>con cheregola lo ritrouati.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſti li ritrouo per la coſa (uero è, che an<lb></lb>chor per altre uie ſe potriano trouare) cioe pongo, che tutto quello che fu posto giuſo <lb></lb>da tutti tre fuſſe.1.coſa, & quella diuido in tre parti ne uien.1/3.co, & perche ſo che <lb></lb>con la gionta di queſto. </s> <s id="s.002109">1/3.co.cadauno di loro fece duc.5. 5/6.adunque auanti di quella <lb></lb>cadauno haueua duc.5.5/6.men.1/3. co.la qual quantita uien à eſſer la mita di quello, che <lb></lb>nel principio tolſe il primo, & il terzo di quello tolſe il ſecondo, & il quarto di quello <lb></lb>tolſe il tolſe il terzo, e pero moltiplico l'una per.2.l'altra per.3.& l'altra per.4.& <lb></lb>la ſumma di tai moltiplicationi (quale ſara.52.1/2.men.3.coſe) diro che ſia eguale à duc.<emph.end type="italics"></emph.end><lb></lb><gap></gap>7.1/2.<emph type="italics"></emph>leuo li ſuperflui, & restoro le parti, & ſeguito il capitolo, & trouo la coſa ua<lb></lb>ler.11.2/3.& tanto fu poſto giuſo da tutti, & queſto lo diuido poi per.3.ne uien.3.8/9. <lb></lb>qual ſottratto da duc.5.5/6.reſta duc.1.17/18. & tanto reſto à cadauno dapoi che heb<lb></lb>ben poſto giuſo. </s> <s id="s.002110">Et perche queſto duc.1.17/18 uien à eſſer la mita di quello che tolſe, <lb></lb>nel principio il primo, & il terzo del ſecondo, & il <27>uarto del terzo, moltiplico il det <lb></lb>to duc.1.17/18. per.2.& poi per.3.& poi per.4.& li tre produtti conchiudo eſſer <lb></lb>quello che cadauno di loro tolſe nel principio, le qual moltiplicationi produranno, co<lb></lb>me nel principio fu conchiuſo, cioe il primo tolſe nel principio duc.3.8/9. il ſecondo duc. <lb></lb></s> <s id="s.002111">5.15/18. il terzo duc.<emph.end type="italics"></emph.end>7.7/9. F. V<emph type="italics"></emph>e ringratio aſſai.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002112">QVESITO SESTO FATTODA VN MAESTRO <lb></lb>A<emph type="italics"></emph>louiſe Pirouano Milaneſe l'Anno.<emph.end type="italics"></emph.end>1529.</s> </p> <p type="main"> <s id="s.002113">MAESTRO ALOVISE. T<emph type="italics"></emph>rouatemi.2.numeri che li.<emph.end type="italics"></emph.end>2/<gap></gap>.<emph type="italics"></emph>dell'uno ſia li. <lb></lb></s> <s id="s.002114">3/7.dell'altro, & che queſti dui numeri facciano tanto aggionti inſieme, come <lb></lb>che moltiplicati l'uno fia l'altro,<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>'uno de queſti numeri, cioe il maggiore ſara. <pb xlink:href="042/01/199.jpg"></pb>2.1/14.& l'altro, cioe il menore ſara.<emph.end type="italics"></emph.end>1.14/15. A. E<emph type="italics"></emph>t come li trouati.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o trouo <lb></lb>prima ſimplicemente dui numeri che li.2/5.dell'uno ſia li.3/7.dell'altro, & queſti li tro<lb></lb>uo moltiplicando il denominator dell'uno fia il numerator dell'altro de tai rotti, cioe li <lb></lb>moltiplico in croce, & di tale moltiplicationine uien.15.&.14.& queſti ſono quelli, <lb></lb>che li.2/5.dell'uno fali.3/7.dell'altro, ma non hanno però l'altra conditione, cioe che tan <lb></lb>to facciano aggionti, come moltiplicati, ma con queſti però poſſo ritrouar quelli, & <lb></lb>per ritrouarli ſummo inſieme queſti dui numeri fanno.29.et queſto.29.lo parto per <lb></lb>l'uno, e poiper l'altro di detti dui numeri, cioe per.15.& per.14.& li dui aduenimen <lb></lb>tiſaranno li dui numeri, che ſe ricerca, li quali aduenimenti l'uno ſara.2.1/14.& l'al<lb></lb>tro.1.14/15.come diſopra dißi.<emph.end type="italics"></emph.end> A. S<emph type="italics"></emph>ta benißimo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002115">QVESITO SETTIMO FATTO DA VN <lb></lb>F<emph type="italics"></emph>rate Beretino del.<emph.end type="italics"></emph.end>1526.</s> </p> <p type="main"> <s id="s.002116">FRATE. T<emph type="italics"></emph>rouatemi un numero che facendone di quello due tal parti, & che à <lb></lb>moltiplicare li.3/4.dell'una di quelle parti fia li.4/5.dell'altra parte me ne uegna il <lb></lb>primo numero.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uesto caſo ſe puo conchiudere in infiniti modi, perche mi poſ<lb></lb>ſo fondar ſopra di qual numero mi piace, eſſempi gratia, pigliando.10.per quel tal nu<lb></lb>mero l'una parte di quello ſaria.5.piu<emph.end type="italics"></emph.end> <22>.8.1/3.<emph type="italics"></emph>& l'altra ſaria.5.men<emph.end type="italics"></emph.end> <22>.8.1/3.<emph type="italics"></emph>& coſi <lb></lb>pigliando altro numero quello me daria altre parti.<emph.end type="italics"></emph.end> F. E<emph type="italics"></emph>t come le ritrouate.<emph.end type="italics"></emph.end> N. <lb></lb>I<emph type="italics"></emph>o cerco di far del detto.10.due tal parti, come ricercate, cioe che li.3/4.dell'una molti <lb></lb>plicati fia li.4/5.dell'altra mi facciano aponto.10.& per trouar le dette parti, io pon<lb></lb>go che l'una ſia una coſa, la ſeconda per forza ſara 10.men.1.co.piglio li.3/4.de.1.co. <lb></lb></s> <s id="s.002117">che ſaria.3/4.co.& coſi piglio anchora li.4/5.de.10.men.1.co.che ſaria.8.men.4/5.co.& <lb></lb>queſte due quantita, li moltiplico l'una fia l'altra, & fanno.6.coſe men.3/5.cenſi, et que <lb></lb>sto produtto ſara egual à.10.reſtoro le parti, & ſeguito il capitolo, & trouo la coſa <lb></lb>ualer.5.piu<emph.end type="italics"></emph.end> <22>.8.1/3.<emph type="italics"></emph>qual cauo de.10.reſta.5.men<emph.end type="italics"></emph.end> <22>.8.1/3.<emph type="italics"></emph>& tanto fu l'altra parte, co<lb></lb>me di ſopra diſſe.<emph.end type="italics"></emph.end> F. Q<emph type="italics"></emph>ueſto uoſtro operar me piace aſſai.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002118">QVESITO OTTAVO FATTO DA MAESTRO <lb></lb>F<emph type="italics"></emph>ranceſco Feliciano l'Anno.1526. In Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002119">MAESTRO FRANCESCO. V<emph type="italics"></emph>no compra una quantita di pernice, & <lb></lb>ſpende in tutte lire.25.de danari, & le porta à Mantoua à reuendere, & tan <lb></lb>te, come che lui ne haue alla lira, lui li uendete tante lire l'una, & le uendete tutte, ec<lb></lb>cetto che.10.& ne cauo lire.75.de danari. </s> <s id="s.002120">Hor ue adimando quante furono tutte le <lb></lb>dette pernice che compro, & quante n'hebbe alla lira de prima compra.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>e per<lb></lb>nice che lui compro furono<emph.end type="italics"></emph.end> <22>.1900.<emph type="italics"></emph>piu.5. & n'hebbe per ogni lira de danari per<lb></lb>nice<emph.end type="italics"></emph.end> <22>.3.2 1/5.<emph type="italics"></emph>piu.1/5.de prima compra. </s> <s id="s.002121">Et tal queſito lo riſoluo in queſto modo, io pon <lb></lb>go che lui haueſſe una coſa di pernice alla lira, onde hauendo ſpeſo (come dite) lire 25. <lb></lb>de danari, io moltiplico.25.fia.1.co.fa.25.co.de pernice, & de queſte.25.co.de per<lb></lb>nice ne cauo le.10.pernice, che lireſto, reſtano.25.co.men.10. & perche diceti che li<emph.end type="italics"></emph.end><pb pagenum="100" xlink:href="042/01/200.jpg"></pb><emph type="italics"></emph>uendete tante lire l'una, quante che lui n'hebbe alla lira, io moltiplico.1.co.fia.25.co. <lb></lb></s> <s id="s.002122">men.10.fanno.25.cenſi men.10.co.le quale ſaranno eguale à lire.75.che ne cauo, eg<lb></lb>guaglio le parti, & poi ſchiſſo per.25.& me ne uien.1.cen egual à.2/5.co.piu.3.ſegui <lb></lb>to la regola, & trouo la coſa ualer<emph.end type="italics"></emph.end> <22>.3.1/25.<emph type="italics"></emph>piu.1/5.& tante pernice dico, che hebbe <lb></lb>per lira, come di ſopra dißi, & per ſaper quante pernice compro in tutto, dico per la <lb></lb>regola del.3.ſe lire.1.me da pernice<emph.end type="italics"></emph.end> <22>.3.1/25.<emph type="italics"></emph>piu,1/5.che me dara lire.25.che lui ſpe<lb></lb>ſe, onde moltiplicando, & partendo, come uol la regola, trouo che compro pernice<emph.end type="italics"></emph.end> <22>. <lb></lb></s> <s id="s.002123">1900.<emph type="italics"></emph>piu.5.fatine mo uoi la proua, che la trouareti giuſta.<emph.end type="italics"></emph.end> M.F. Q<emph type="italics"></emph>ueſto uoſtro o<lb></lb>perar aſſai me piace.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002124">QVESITO NONO FATTO DAL MEDESI<lb></lb><emph type="italics"></emph>mo maestro Franceſco Feliciano l'Anno.<emph.end type="italics"></emph.end>1526.</s> </p> <p type="main"> <s id="s.002125">MAESTRO FRANCESCO. E<emph type="italics"></emph>glie uno, che me doueua dare una quan<lb></lb>tita de ducati & me ne ha dato una parte, talmente che el mi reſta anchora duc. <lb></lb></s> <s id="s.002126">300. & ſappiati che tolto il.1/5.di quello, che lui me ha dato, & quello moltiplicandolo <lb></lb>in ſe medeſimo fa tanto quanto era il primo debito, ue adimando quanto fu il primo de<lb></lb>bito.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>l primo debito fu ducati.<emph.end type="italics"></emph.end> 400. M.F. E<emph type="italics"></emph>t con che regola lo ritrouati.<emph.end type="italics"></emph.end><lb></lb>N. A<emph type="italics"></emph>nchor che per altre uie tal ragione ſe potria fare, nondimeno io la riſoluo per <lb></lb>Algebra, cioe pongo che li ducati che ue ha dati ſiano una coſa, adunque tutto il debito <lb></lb>fuducati.300.piu una coſa, poi piglio il.1/5.de una co. </s> <s id="s.002127">qual è.1/5.co. </s> <s id="s.002128">& queſto lo mol<lb></lb>tiplico in ſe medeſimo fa.1/25.de cenſo, & queſto ſi è eguale à.1.co.piu.300.ristoro le <lb></lb>parte, & ſeguo il capitolo, & trouo la coſa ualer.100.& ducati.100. ui haueua dati, <lb></lb>li quali gionti con li ducati.300.che ui reſta faranno ducati.400.come di ſopra ui dißie<emph.end type="italics"></emph.end><lb></lb>M.F. S<emph type="italics"></emph>ta bene.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002129">QVESITO DECIMO FATTO DA VNO <lb></lb><emph type="italics"></emph>maestro Aleſſandro Venetiano l'Anno.1527. <lb></lb>In Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002130">MAESTRO ALESSANDRO. F<emph type="italics"></emph>atemi di.10.due tal parti che parti<lb></lb>ta la maggior per la menore, & dapoi lamenore per la maggiore, et li dui ad<lb></lb>uenimenti aggionti inſieme facciano.<emph.end type="italics"></emph.end>3.1/3. N. L<emph type="italics"></emph>amaggiore ſara.7.1/2.& la meno<lb></lb>re ſara.<emph.end type="italics"></emph.end>2.1/2. M.A. E<emph type="italics"></emph>t come la riſolueti.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o procedo in queſto modo. </s> <s id="s.002131">Perche <lb></lb>ogni quantita, che ſia diuiſa in due parti, come ſi uoglia, partendo la maggiore per la <lb></lb>menore, & dapoi la menore per la maggiore, li dui aduenimenti moltiplicati l'uno fia <lb></lb>l'altro ſempre ſanno aponto.1.Et per tanto in queſto caſo uolendo ritrouar li detti dui <lb></lb>aduenimenti, biſogna fare del ſopradetto.3.1/3.due tal parti, che moltiplicata l'una in <lb></lb>l'altra faccia.1.La qual parte procedendo per la coſa, ouer per qual uia ſi uoglia ſi tro <lb></lb>uara l'una eſſer.3. & l'altra.<emph.end type="italics"></emph.end>1/3. E<emph type="italics"></emph>t dapoi queſto biſognaſar de.10. due tal parti, che <lb></lb>partendo la maggior per la menor, me ne uenghi.3.ouer che partendo la menor <lb></lb>per la maggiore, me ne uenghi.1/3, le quale l'una ſi trouara eſſere il quarto <pb xlink:href="042/01/201.jpg"></pb>de.10.cioe.2.1/2.& l'altra li.3/4.de.10.cioe.7.1/2.come di ſopra fu determinato.<emph.end type="italics"></emph.end> M.A. <lb></lb>S<emph type="italics"></emph>ta benißimo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002132">QVESITO. XI. FATTO DA VNO DETTO <lb></lb><emph type="italics"></emph>lo Inzegnero l'Anno.1527. In Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002133">INZEGNERO. F<emph type="italics"></emph>atemi de.12.due parti tali, che moltiplicando il quadrato <lb></lb>di luna ſia el quadrato de laltra facciano.<emph.end type="italics"></emph.end>130. N.L<emph type="italics"></emph>una ſaria.6.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſali <lb></lb>de.36.men<emph.end type="italics"></emph.end> <22>.130.L<emph type="italics"></emph>altraſara.6.men la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale di.36.men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002134">130. INZEG. <lb></lb>E<emph type="italics"></emph>t come ritrouati le dette parti.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er ſchiuar garbulii de ſtranie dignita in pongo <lb></lb>che una parte ſia.6.men.1.coſa laltra per forza ſara.6. piu.1. coſa, quadro cadauna <lb></lb>delle dette parti, luna fara.36.men.12.coſe piu.1.cenſo laltra fara36.piu.12. coſe piu <lb></lb><gap></gap>. </s> <s id="s.002135">cenſo. </s> <s id="s.002136">Poi multiplico questi dui quadrati luno fia laltro, fanno.1296. men.72.cenſi <lb></lb>piu.1.cenſo de cenſo et queſto ſera equale a.130.reſtoro le parti me ne uien.1166. piu <lb></lb><gap></gap>.cenſo de cenſo, equal a.72.cenſi ſeguito il capitulo, & trouo la coſa ualer radice uni<lb></lb>uerſale de.36.men<emph.end type="italics"></emph.end> <22>.130.<emph type="italics"></emph>donde che luna parte, cloe la maggiore ſara.6.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuer <lb></lb>ſale di.36.men.<emph.end type="italics"></emph.end> <22>.130. E<emph type="italics"></emph>t l'altra, cioe la menore ſara.6.men.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>uniuerſale.36.men.<emph.end type="italics"></emph.end> <22>. <lb></lb></s> <s id="s.002137">230.<emph type="italics"></emph>come di ſopra fu determinato.<emph.end type="italics"></emph.end> I. I<emph type="italics"></emph>o ue diro la uerita, che io non intendo troppo <lb></lb>ben queſta uoſtra concluſione, perche queſta ragione mi fu data a me in Bologna, neio <lb></lb>laho mai ſaputa far, ne <expan abbr="mãco">manco</expan> ho ritrouato, che me la habbia ſaputa far, eccetto che uoi <lb></lb>come credo, che la habbiati riſolta anchor che io non intenda (come di ſopra dißi) tal <lb></lb>uostra concluſione.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002138">QVESITO. XII. FATTOMI DA VNO <lb></lb>A<emph type="italics"></emph>rchitettore adi.31.Luio.1527. In Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002139">ARCHITETTORE. I<emph type="italics"></emph>o faccio far quarelli, ouer piere cotte longhi once. <lb></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></lb>mando uolendo far far detti quarelli, ouer piere cotte, che ue ne uada.30.al detto pie <lb></lb>cubo, & che la ſua longhezza ſia pur doppia alla ſua larghezza, & che ſimilmente <lb></lb>laſua larghezza ſia doppia alla ſua groſſezza, come ch'erano glialtri primi, quanto <lb></lb>ſe doueranno far far longhi, larghi, & großi.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>e doueranno far far longhionce<emph.end type="italics"></emph.end><lb></lb><22>.<emph type="italics"></emph>cuba.458.4/5.larghi once<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba.57.3/5. großi once. </s> <s id="s.002141">Radice cuba.<emph.end type="italics"></emph.end>7.1/5. A. E<emph type="italics"></emph>t <lb></lb>come ritrouate tai miſure.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o cubo un piede fatto in once, fara once.1728.cu<lb></lb>be, & queſte once.1728.cube le parto per.30. (cioe per li.30.quarelli, ouer piere cog <lb></lb>te) ne uien.57.3/5.poi trouo tre numeri continui proportionali in proportion dupla, <lb></lb>che moltiplicati l'uno fia l'altro, & quel produtto fia l'altro facciano.57.3/5. quali pro <lb></lb>cedendo per la coſa trouo che il maggiore ſara<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba.458.4/5.& tante once douera <lb></lb>eſſer longo il detto quarello, ouer piera cotta, & l'altro ſara Radice cuba.57.3/5.& <lb></lb>tante once douera eſſer largo, il menore ſara once Radice cuba.7.1/5. & tanto douera <lb></lb>eſſer groſſo, come di ſopra fu conchiuſo.<emph.end type="italics"></emph.end> A. Q<emph type="italics"></emph>ueſta ragione è molto piu forte di <lb></lb>quello mi penſaua.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="101" xlink:href="042/01/202.jpg"></pb> <p type="head"> <s id="s.002142">QVESITO XIII. FATTO DA MAESTRO ANTONIO <lb></lb>V<emph type="italics"></emph>eroneſe, Zenero de Maeſtro Franceſco Feliciano adi. </s> <s id="s.002143">16. <lb></lb>Settembrio. </s> <s id="s.002144">1527. in Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002145">MAESTRO ANTONIO. Q<emph type="italics"></emph>ueſta notte, quando, che non poteua dormi<lb></lb>re, me ho imaginato una queſtione aſſai bella, uero è, che io non ho anchora ritro <lb></lb>uato el modo da riſoluerla, & la ho detta anchora al mio ſuocero, & ue la uoglio dire <lb></lb>anchora à uoi, accio, che ui fantasticati anchora uoi ſopra.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>itela di gratia.<emph.end type="italics"></emph.end><lb></lb>M.A. E<emph type="italics"></emph>glie una figura Rhombica, che cadauno di ſuoi lati è piedi.10.& ha de area <lb></lb>piedi 72.ſuperficiali, domando che proportione é dal diametro maggiore al diame<lb></lb>tro menore.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſta non mipare molto forte questione, perche diuidendo el det <lb></lb>to Rhombo in dui triangoli, cadauno de detti <expan abbr="triãgoli">triangoli</expan> uenira à eſſer diſuperficie. </s> <s id="s.002146">36. <lb></lb>& uolendo ſapere quanto ſia la baſa de cadauno, io ponero, che tal baſa ſia una coſa, <lb></lb>trouo la ſua perpendicolare, & trouo, che tal perpendicolare è.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>uniuerſale de.100. <lb></lb>men un.1/4.de cenſo, & ſimelmente ritrouo larea ſua coſi ſordamente quale ſara.<emph.end type="italics"></emph.end> <22>. <lb></lb><emph type="italics"></emph>uniuerſale de.25.cenſi, men.1/16.cenſo de cenſo, & queſto ſara equale à. </s> <s id="s.002147">36. quadro <lb></lb>ambi li termini, me uenira.1296.equal à.25.cenſi, men.1/16. cenſo de cenſo, leuo li <lb></lb>rotti, & riſtoro le parti, & ſeguitc el capitolo, & ritrouo la coſa ualer la.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>uniuer<lb></lb>ſal de.200 piu.<emph.end type="italics"></emph.end> <22>.19264.<emph type="italics"></emph>& queſto ſara el maggior diametro del detto Rhombo, & <lb></lb>el menore uenira ad eſſer.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002148">V.200.<emph type="italics"></emph>men.<emph.end type="italics"></emph.end> <22> 19264.<emph type="italics"></emph>ſi che la proportione del diame<lb></lb>tro maggior al diametro menor ſaria, come, che é dal detto diametro maggiore al det<lb></lb>to menore, che é il propoſito.<emph.end type="italics"></emph.end> M.A. V<emph type="italics"></emph>oi diceti, che tal questione non é molto forte, <lb></lb>& à me lame pare molto difficile.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002149">QVESITO XIIII. QVAL MI FV MANDATO A <lb></lb>V<emph type="italics"></emph>erona da un Maeſtro Zuanne de Tonini da Coi, qual tene<lb></lb>ua ſchola in Breſſa, & me lo portò meſſer pre <lb></lb>Antonio da Cellatica l'anno.<emph.end type="italics"></emph.end>1530.</s> </p> <p type="main"> <s id="s.002150">MAESTRO ZVANNE. T<emph type="italics"></emph>rouatime un numero, qual multiplicato per la <lb></lb>ſua Radice piu:3.mi faccia.5. Simelmente trouatime.3.numeri, ma chel ſe<lb></lb>condo ſia.2.piu del primo, & chel terzo ſia pur.2.piu del ſecondo, & che multipli<lb></lb>cato el primo fia el ſecondo, et quel produtto fia el terzo faccia.<emph.end type="italics"></emph.end>1000. N. M.Z<emph type="italics"></emph>uane, <lb></lb>uoi me haueti <expan abbr="mãdato">mandato</expan> queſti uostri dui queſiti, come coſe impoßibile da riſoluere, ouer <lb></lb>ignorate da uoi, <21>che <expan abbr="procedẽdo">procedendo</expan> <21> Algebra, el primo <expan abbr="cõduſſe">conduſſe</expan> <expan abbr="l'operãte">l'operante</expan>, in.1.cubo piu <lb></lb>3.cẽſi egual à.5.et il <expan abbr="ſecõdo">ſecondo</expan> in.1.cubo piu.6.cẽſi piu.8.coſe equal à.1000.li quali capi <lb></lb>toli <21> fin à <34>sto <expan abbr="tẽpo">tempo</expan> é ſtato giudicato da<emph.end type="italics"></emph.end> F. L<emph type="italics"></emph>uca, & altri eſſer impoßibile à riſoluerli <lb></lb><21> regola generale, <expan abbr="credẽdoui">credendoui</expan> con tai queſiti di farui cauallero ſopra di me, & da farui <lb></lb>tenere un grandißimo Mathematico, come che ho inteſo, che fati con tutti li altri pro <lb></lb>feſſori di tal ſcientia li in Breſſa, li quali per tema de tai uoſtri Queſiti, non oſſano à <lb></lb>parlar conuoi, & forſi meglio intendano in tal faculta di uoi, ma per non eſſer aduer <lb></lb>titi <expan abbr="tãto">tanto</expan>, che baſti, credono, che uoili ſappiatireſoluere, e <21> questo ui cedono in tutto.<emph.end type="italics"></emph.end><pb xlink:href="042/01/203.jpg"></pb>O<emph type="italics"></emph>nde per farui emendar di tal uoſtra uana opinione, & prouocarui, a ricercar di ac<lb></lb>quistar ui honor con il ſapere, & non con queſtioni da uoi ignorate, ue riſpondo & di <lb></lb>co che ui douereſti aroßire, a proponere da riſſoluere ad altri, quello che uoi medeſi<lb></lb>mo non ſapetiriſſoluere. </s> <s id="s.002151">Et per moſtrarui che di queſto ne ſon certo me offeriſco à de <lb></lb>ponere ducati diece contra cinque, <expan abbr="cioẽ">cioem</expan> che uoi non ſapereti riſoluere queſti dui caſi <lb></lb>che à me haueti propoſti con regule generale, & circa cio non uido altra riſpoſta.<emph.end type="italics"></emph.end> M. <lb></lb>Z. H<emph type="italics"></emph>o inteſo quanto me haueti ſcritto, & come che haueti opinione che tai caſi ſiano <lb></lb>impoßibili, e per tanto ue riſpondo, che accetto queſta uostra offerta, cioe che uoi non <lb></lb>me approuareti che tai caſi ſiano impoßibili<gap></gap>come che uoidiceti.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o non dico che <lb></lb>tai caſi ſiano impoßibili anci il primo, cioe quello de cubo é cenſo equal à numero, io me <lb></lb>perſuado di hauerui trouato la ſua regola generale, ma per al preſente la uoglio tace<lb></lb>re per piu riſpetti, del ſecondo poi, cioe quello de cubi & cenſi, & coſe equale à nume <lb></lb>ro, confeſſo non hauerui potuto fin à queſta hora trouar regola generale, ma per que <lb></lb>ſto non dico ne manco uoglio dire ch'el ſia impoßibile a trouaruela anchor che per fina <lb></lb>à questo tempo la non ue ſia ſtata ritrouata. </s> <s id="s.002152">Ma ho detto di uoler deponere li diece do <lb></lb>cati contra.5.che uoi non ſapereti riſoluere li detti dui queſiti à me mandati con rego<lb></lb>le generale, & che circa cioue douereſti alquanto à roßire à proponere ad altri <lb></lb>quello, che uoimedeſimo non intendeti & fingere de intenderlo per farui reputare <lb></lb>un gran che.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002153">QVESITO. XV. FATTO DA M. BERNARDIN <lb></lb>D<emph type="italics"></emph>ona da Zano lattor in greco l'anno.1530.adi.12.Ottobrio in <lb></lb>Verona qual diſſe eſſerli ſtato propoſto à lui in Breſſa da <lb></lb>maestro Zoan de Tonini da Coi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002154">MISSER BERNARDINO. I<emph type="italics"></emph>o ſon ſtato à Breſſa & meſtato fatto uno <lb></lb>queſito da un certo Maeſtro Zuanne da Coi, elquale <expan abbr="ſapẽdo">ſapendo</expan> haria de caro che <lb></lb>mel reſolueſti elqual queſito dice in questa forma. </s> <s id="s.002155">Voria che nel ſottoſcritto triango<lb></lb>lo.a.b.c.equilatero me gli fuſſe inſcritto geometricamente un quadrato.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ue<lb></lb>ſto ſi puo far in piu modi, ma quello che per al preſente mi è uenuto in mente è queſto. <lb></lb></s> <s id="s.002156">Tiro nel detto triangolo.a.b.c.la ſua <lb></lb>perpendicolare.a.d.& dal ponto.a.ti <lb></lb>ro la.a.e.equidiſtãte alla.b.c.& facio <lb></lb>la detta.a.e equale alla mita della per<lb></lb>pendicolare.a.d.& dal ponto.e.tiro <lb></lb>la.e.d.laqual ſega el lato.a.c.nel <expan abbr="põto">ponto</expan> <lb></lb>f.dal qual <expan abbr="põto">ponto</expan>.f.tiro la.f.g.per <expan abbr="pẽdi-colare">pendi<lb></lb>colare</expan> ſopra la.b.c.& anchora dal me <lb></lb>deſimo <expan abbr="põto">ponto</expan>.f.tiro la.f.h. </s> <s id="s.002157"><expan abbr="equidiſtãte">equidiſtante</expan> al <lb></lb>la.b.c. </s> <s id="s.002158">& dal ponto.h. </s> <s id="s.002159">tiro la linea.h. <lb></lb></s> <s id="s.002160">i. perpendicolare alla. </s> <s id="s.002161">b.c. & coſi nel<emph.end type="italics"></emph.end><lb></lb><figure id="id.042.01.203.1.jpg" xlink:href="042/01/203/1.jpg"></figure><lb></lb><emph type="italics"></emph>detto triangolo ſara inſcritto il quadrilatero.f.g.h.i.qual dico eſſer quadrato, perche<emph.end type="italics"></emph.end><pb pagenum="102" xlink:href="042/01/204.jpg"></pb><emph type="italics"></emph>il triangolo.a.d.e.è ſimile al triangolo.f.g.d.& perch'el lato.a.d è doppio al lato.a.e. <lb></lb></s> <s id="s.002162"><expan abbr="Simelmẽte">Simelmente</expan> el lato.f.g.ſara doppio al lato.d.g.& perche.f.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>é equale al.d.g.lo mede <lb></lb>ſimo lato.f.g.ſara anchora doppio al.f.<emph.end type="italics"></emph.end>k.<emph type="italics"></emph>& perche la.f.h.é a nchora lei doppia alla <lb></lb>medeſima.f.<emph.end type="italics"></emph.end>k <emph type="italics"></emph>ſeguita che il lato.f.h.ſia equale al.f.g.& ſimelmente li altri dui lati <expan abbr="cõ">com</expan> <lb></lb>trapoſiti, (cioe.h.i.&.g.i.) ſono equali alli mede ſimi & ſimelmente li ſuoi quattro <lb></lb>angoli ſono rettiper eſſer le linee.f.g.& h.i.perpendicolare ſopra <gap></gap>.b.c. </s> <s id="s.002163"><expan abbr="adũque">adunque</expan> tal <lb></lb>figura è quadrata ch'è il propoſito.<emph.end type="italics"></emph.end> M. B. Q<emph type="italics"></emph>uesta uoſtra concluſion molto mipia <lb></lb>ce, & uene ringratio aſſai.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002164">QVESITO XVI. FATTO DA FRATE AMBRO<lb></lb><emph type="italics"></emph>ſio da Ferrara del ordine di.s. </s> <s id="s.002165">Maria Organa adi.21. Lu<lb></lb>io l'anno.1532. in Verona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002166">FRATE AMBROSIO. I<emph type="italics"></emph>o aggio uno triangolo equilatero nel quale ui è <lb></lb>inſcritto dentro un cerchio, & trouo, ouer che ſo che il diametro del detto cer<lb></lb>chio è la Radice cuba de.16. Hor ue adimando quanto ch'era per fazza el detto tri<lb></lb>angolo.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>l detto triangolo uenira à eſſer per fazza la Radice cuba della Radi<lb></lb>ce quadra de.<emph.end type="italics"></emph.end>6912. F. A. E<emph type="italics"></emph>t perche uia lo ritrouati.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ſuppono uno trian <lb></lb>golo equilatero à mio piacere, cioe che ſia per fazza quanto mi pare, ma per non abon <lb></lb>dar in gran numeri in queſto caſo io pongo che tal triangolo ſia.2.per fazza, ouer <lb></lb>lato et di queſto tal triangolo ricerco quanto ſia el diametro del maggior cerchio che <lb></lb>inſcriuer ſi poſſa in quello, & trouo tal diametro eſſer la Radice quadratade.<emph.end type="italics"></emph.end> 1 1/3. <lb></lb>H<emph type="italics"></emph>or per la regola uolgarmente detta del tre dico ſe.<emph.end type="italics"></emph.end> <22>.1.1/3.<emph type="italics"></emph>de diametro mi da.2. per <lb></lb>lato del triangolo, che me dara<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.16.de diametro de cerchio multiplico, & par<lb></lb>to ſecondo l'ordine di tal regola & me ne uien<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.de<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>quadra. </s> <s id="s.002167">6912.come di ſopra <lb></lb>fu da me determinato, & tanto dico fu per fazza el detto triangolo ch'è il propoſito.<emph.end type="italics"></emph.end><lb></lb>F. A. Q<emph type="italics"></emph>ueſto uoſtro procedere molto mi piace.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002168">QVESITO XVII. FATTO DA MAESTRO <lb></lb>A<emph type="italics"></emph>leſſandro Venetiano l'anno.1533. in Verona <lb></lb>qual haueua per opinione che fuſ<lb></lb>ſe impoßibile.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002169">MAESTRO ALESSANDRO. E<emph type="italics"></emph>ſſendo io in Fiorenza gia fa quatro <lb></lb>meſi, & mi fu data una ragione la qual ſon certo ch'eglie impoßibile à riſſol<lb></lb>uerla, come credo che il medeſimo uoi affermareti.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>t come dice queſta uostra <lb></lb>ragione.<emph.end type="italics"></emph.end> M. A. L<emph type="italics"></emph>a dice in queſta forma. </s> <s id="s.002170">Eglie uno triangolo de tre lati me qua<lb></lb>li, la baſa del quale è.10.& la ſua perpendicolare è.8.& li altri dui lati tolti inſieme <lb></lb>ſono.20. Se domanda quanto era cadauno de dettidui lati per ſe medeſtmo.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o <lb></lb>non uoglio affermare, ne manco negare che tal queſtione ſia impoßibile ſe prima non <lb></lb>tento quanto la peſa, perche ſono molte queſtioni, che in prima faccia pareno facile, et <lb></lb>nella reſolutione, ſe ritrouano difficile & alcune che in prima faccia pareno difficile,<emph.end type="italics"></emph.end><pb xlink:href="042/01/205.jpg"></pb><emph type="italics"></emph>& nella reſolutione ſi trouano facilißime.<emph.end type="italics"></emph.end> M.A. C<emph type="italics"></emph>oſi me accaduto à me molte uol<lb></lb>te, nondimeno queſta nella reſolutione non ui ritrouo mezzo da poterla concludere, <lb></lb>e pero haria accaro, che anchora uoi tentaſti al preſente, qua in mia preſentia, perche <lb></lb>ho accaro à uedere il uoſtro procedere, & poi io ue diro el mio.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ue diro per <lb></lb>riſoluer queſto caſo. </s> <s id="s.002171">Io poneria, che il menor lato delli due fuſſe.1.coſa laltro maggior <lb></lb>de neceßita uerria à eſſer.20.men.1.coſa. </s> <s id="s.002172">Et (per l'ordine della.13.del ſecondo di <lb></lb>Euclide) io aggiongero el quadrato del detto lato menore (el qual quadrato ſaria.1. <lb></lb>cenſo) con el quadrato della baſa (el qual quadrato ſaria.100.) fara.100.piu.1. cenſo, <lb></lb>& da queſta ſumma ne cauaro el quadrato de laltro maggior lato (el qual quadrato <lb></lb>ſaria.400.piu.1.cenſo, men.40.coſe) & reſtara.40.coſe men.300.et questo partiſco <lb></lb>per el doppio della baſa (el qual doppio ſaria. </s> <s id="s.002173">20.) & me ne uiene.2.coſe men.15.& <lb></lb>tanto lontano da langolo doue termina il menor lato con la baſa, cadera la perpendico <lb></lb>lare del detto triangolo ſopra la baſa. </s> <s id="s.002174">Onde per uenire alla equatione, io quadraro tal <lb></lb>diſtantia, cioe.2.coſe men.15.el qual quadrato ſara.4.cenſi men.60.coſe. </s> <s id="s.002175">piu. </s> <s id="s.002176">225. <lb></lb>& à queſto ui aggiongo el quadrato della perpendicolare, el qual ſaria. </s> <s id="s.002177">64. fara in <lb></lb>ſumma.4.cenſi men.60.coſe, piu.289.& queſto (per la penultima del primo di Eu<lb></lb>clide) ſara equale al quadrato del menor lato (el qual quadrato ſaria.1.cenſo) reſto<lb></lb>ro le parti, & ſeguito il capitolo, & trouo la coſa ualer.10.men. </s> <s id="s.002178"><22>.3.2/3.& tanto fu <lb></lb>el lato menore, & el maggiore uenira à eſſere.10.piu. </s> <s id="s.002179"><22>.3.2/3. della qual concluſione, <lb></lb>ſe ne fareti proua, la trouareti eſſer giuſta, che è il propoſito.<emph.end type="italics"></emph.end> M.A. A<emph type="italics"></emph>nchora, che <lb></lb>tutto queſto uoſtro operar ſia ſtato bello nondimeno, quel uoſtro ſottrare.400.piu.1. <lb></lb>cenſo, men.40.coſe de.100.piu.1.cenſo, doue concludeti che resta.40.coſe, men.300. <lb></lb>eglie ſtato il fiore di tutto quanto el uostro operare appreſſo di me. </s> <s id="s.002180">Et quantunque <lb></lb>habbia detto diuolerui dir il mio procedere nella reſolutione di queſto Queſito, lo uo<lb></lb>glio tacere, perche, per la uia, che io procedeua, io non poteua uenire ad alcuna equa<lb></lb>tione, e pero ſaria coſa ſuperflua à uolerla narrare.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002181">QVESITO XVIII. FATTO CREDO DA MAETSRO <lb></lb>A<emph type="italics"></emph>ntonio Maria Fior, qual me porto un gargione ſotto <lb></lb>mano l'anno.1534.in Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002182">GARGIONE. H<emph type="italics"></emph>aggio una botta piena di uin puro, della quale ne cauo fuo<lb></lb>ra dui barili, & la reimpio di acqua, & dapoi alcuni giorni, ne reccauo fuora <lb></lb>anchora dui altri barili, & la reimpio pur di acqua, & coſi dapoi alcuni altri giorni <lb></lb>ne reccauo pur fuora dui altri barili, & la reimpio pur di acqua. </s> <s id="s.002183">Et fatto questo, io ri <lb></lb>trouo, che quel uino, che in ultimo ſe ritroua nella detta botta piena é preciſamente la <lb></lb>mitta uino, & la mitta acqua. </s> <s id="s.002184">Se adimanda quanti barili teneua la detta botta.<emph.end type="italics"></emph.end> N. <lb></lb>Q<emph type="italics"></emph>ueſto Queſito non uol dir altro, che trouar quattro quantita continue proportio<lb></lb>nale coſi conditionate, che la quarta quantita ſia doppia alla prima perche per la quar <lb></lb>ta quantita, ouer termine ſe intende la tenuta di la botta, & per el primo termine, o<lb></lb>uer quantita ſe intende per quel uino, che in ultimo riman con lacqua, & che la diffe <lb></lb>rentla del ter<gap></gap>o, & quarto termine ſia.2.per li dui barili, che ſi caua. </s> <s id="s.002185">Onde per riſol-<emph.end type="italics"></emph.end><pb pagenum="103" xlink:href="042/01/206.jpg"></pb><emph type="italics"></emph>uere tal queſito fra.1.&.2.ritrouo dui medij continui proportionali, delli quali l'u<lb></lb>no ſara Radice cuba.2. (cioe il ſecondo termine) l'altro, cioe il terzo termine, ſara<emph.end type="italics"></emph.end> <22>. <lb></lb><emph type="italics"></emph>q.4.dapoi guardo che differentia è frail terzo, & quarto termine, & trouo che la è. <lb></lb></s> <s id="s.002186">2.men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.4.& io uorrei che fuſſe 2. (come di ſopra dißi) e pero con forza di pro<lb></lb>portione li poſſo ritrouar in queſto modo, digando ſe.2.men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.4. (de differentia) <lb></lb>mi da.2.per il quarto termine, che mi dara.2.de differentia, moltiplicando, & parten <lb></lb>do ſecondo la regola ne uenira.4.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.32.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.16.& tanti barili teneua la det <lb></lb>ta botta.<emph.end type="italics"></emph.end> G. E<emph type="italics"></emph>t io ritrouo che la tiene barili.4.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.10.men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end>6. N. H<emph type="italics"></emph>or <lb></lb>ua, e di à colui, che ti ha mandato, che ſe lui proua la ſua, & mia concluſione, che lui ri<lb></lb>trouara la mia buona & la ſua falſa, & accio che lui habbia manco fatica, io ti uoglio <lb></lb>dare li tre reſtanti ordinatamente della detta botta, cioe de uino puro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002187">T<emph type="italics"></emph>enuta di tutta la botta.4.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.32.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end>16. </s> </p> <p type="main"> <s id="s.002188">L<emph type="italics"></emph>o primo reſtante ſara<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.32.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>q.16. piu.<emph.end type="italics"></emph.end>2. </s> </p> <p type="main"> <s id="s.002189">L<emph type="italics"></emph>o ſecondo reſtante ſara<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.16 piu.2.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end>4. </s> </p> <p type="main"> <s id="s.002190">L<emph type="italics"></emph>o ultimo reſtante ſara.2.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.4.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end>2. </s> </p> <p type="main"> <s id="s.002191">C<emph type="italics"></emph>ioe l'ultimo reſtante ſara preciſamente la mita della tenuta di tutta la botta, cioe la mi <lb></lb>ta del uino, & l'altra mita uenira à eſſer acqua, che è il propoſito.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002192">QVESITO. XIX. FATTO DAL MAGNIFICO <lb></lb><emph type="italics"></emph>meſſer Zuanbattista Memo l'anno ch'io ueni ad ha<lb></lb>bitare in Venetia, che fu.<emph.end type="italics"></emph.end> 1534.</s> </p> <p type="main"> <s id="s.002193">MAGNIFICO M. ZVAN BATTISTA. H<emph type="italics"></emph>auetiuoi opinione che il <lb></lb>ſia poßibile à ritrouare la quadratura del cerchio.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>l non ſi puo negare, <lb></lb>che quella coſa che è in eſſer nelle coſe naturale, che il non ſia poßibile anchora à ritro<lb></lb>uarla.<emph.end type="italics"></emph.end> M.Z. V<emph type="italics"></emph>oi ſeti in errore. </s> <s id="s.002194">Anchora che Ariſtotele affermi eſſer poßibile, la <lb></lb>cauſa è, che fra il diametro del cerchio, & la ſua circonſerentia non ui cade alcuna pro <lb></lb>portione, perche il diametro non è uniuoco con la cir conferentia (perche il retto, & il <lb></lb>curuo non ſono uniuoce) e pero non ſono comparabili, et non eſſendo comparabili non <lb></lb>ſi puo dire, che fra loro ue ſia alcuna ſpecie di proportione, & quello che non è in nelle <lb></lb>coſe di natura non è poßibile à poterle ritrouare.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie ben uero, che la linea ret <lb></lb>ta non è comparabile alla curua riſpetto à quella qualita del retto, & curuo, ma riſpet <lb></lb>to alla <expan abbr="quãtita">quantita</expan>, à me mi pare, che ſiano comparabile, perche il predicameuto della quan <lb></lb>tita è uno, & quello della qualita è un'altro, & che il ſia il uero che ſiano comparabili, <lb></lb>& che ue ſia fra lor proportione, facilmente il ſi puo prouare per la quinta diffinitio<lb></lb>ne del quinto di Euclide. </s> <s id="s.002195">Nella quale lui diffiniſſe che quelle quantita ſe dicono hauer <lb></lb>proportione fra loro, le quale moltiplicate ſi poſſono eccedere l'una, el altra, & per<lb></lb>ch'eglie coſa chiara, che il quadruplo del diametro del cerchio, eccede la <expan abbr="circõferẽtia">circonferentia</expan> di <lb></lb>quello, pche il quadruplo del detto diametro di tal cerchio è eguale alli.4.lati del qua<lb></lb>dro circonſcritto al medeſimo cerchio, & li detti.4.lati, eglie manifeſto eſſer molto <lb></lb>piu della circonferentia del cerchio, adunque potendoſi moltiplicare il diametro del <pb xlink:href="042/01/207.jpg"></pb>cerchio, talmente che ecceda la detta circonferentia ſeguita (per la detta diffinitione) <lb></lb>che fra il diametro del cerchio, & la circonferentia di quello ue ſia proportione, an<lb></lb>chor che tal proportione ne ſia incognita, che è il propoſito.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002196">QVESITO. XX. FATTO COPERTAMENTE <lb></lb><emph type="italics"></emph>da maeſtro zuan de Tonini da Coi, qual mi portò in ſcritto <lb></lb>maeſtro Dominico da Vderzo, l'Anno. 1535. Adi.12. <lb></lb>Settembrio, in Venetia, qual diſſe hauerli hauu <lb></lb>ti da nn Special, che ueniua <lb></lb>da Breſſa.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002197">MAESTRO ZVANE. I<emph type="italics"></emph>o adimandai à uno Peſcatore, che ſel mi uoleuæ <lb></lb>uendere una trutta, che lui haueua, che tante once, come che lei peſaua, io gli uo <lb></lb>leua dare tanti danari, ouer pizzoli della lira, & tante lire, come che la peſaua ancho<lb></lb>ra tanti altri danarigli uoleua dar pur della lira, & lui ſi contento, & io glidiedi ſol<lb></lb>di.7.domando quanto peſaua la detta trutta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002198">A<emph type="italics"></emph>nchorauno me impreſtalire.60.de danari à ragion de.5.per cento de utile à l'an<lb></lb>no. </s> <s id="s.002199">Et io gli laſſo poſſedere una caſa qual paga de fitto lire.23.à l'anno. </s> <s id="s.002200">Domando in <lb></lb>che tempo ſara pagato.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002201">A<emph type="italics"></emph>nchora ſono trei, che hanno comprato lire. </s> <s id="s.002202">20.di carne, & tante lire ne ha com <lb></lb>prato uno di loro, che moltiplicato tal numero de lire in ſe medeſimo tal produtto è <lb></lb>eguale alla moltiplicatione delle lire, che hanno comprate glialtri dui, cioe quelle del<lb></lb>l'uno fia quelle dell altro, & moltiplicati li due menor quantita de lire l'una fia l'altra <lb></lb>fanno preciſamente.8.Se adimanda la quantita delle libre di carne, che compro cadau<lb></lb>no per ſe.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>hi uiha dato queſti queſiti.<emph.end type="italics"></emph.end> M.D. E<emph type="italics"></emph>l me liha dati uno Speciaro qual <lb></lb>uien da Breſſa, il qual dice eſſerli ſtati dati da uno li in Breſſa, il qual l'ha pregato, che <lb></lb>ue li dia far hauer à uoi ſotto mane, & ueder da intendere la uoſtra riſpoſta.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>e<lb></lb>nendo da Breſſa, li ſono d'un maeſtro zuan da Coi, qual quando ſtantiaua anchora à Ve <lb></lb>rona l'Anno. 1530. me ne mandete dui altri, & quaſi che queſta mi raſſomiglia la ſua <lb></lb>lettera.<emph.end type="italics"></emph.end> M.D. P<emph type="italics"></emph>otria eſſer chi fuſſe quello.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>redo che il ſe ſia emendato del ſuo <lb></lb>coſtume antico, qual era de proponere alcuni caſi fantaſtichi, che lui medeſimo non ſa<lb></lb>peuariſoluere. </s> <s id="s.002203">Perche uedo che il primo de queſti, è coſa ſolubile, & non uol dir altro <lb></lb>in ſoſtantia, ſaluo che tante lire, come peſaua la trutta, tanti ſoldi, & tanti danari, ouer <lb></lb>pizzoli, la uoleua pagar la lira. </s> <s id="s.002204">Onde per aſſoluere tal queſito.Io ponero che tal trut<lb></lb>ta peſaſſe.1.coſa de lira, adunque la pagai à.1.coſa de ſoldo piu.1.coſa de danaro la lira. <lb></lb></s> <s id="s.002205">Onde moltiplicando.1.coſa de ſoldo piu.1.coſa de danaro fia.1.coſa de lira fara.1.cenſo <lb></lb>de ſoldo piu.1.cenſo de danaro. </s> <s id="s.002206">Et questo ſara egual à ſoldi.7. Hor reducendo ogni co<lb></lb>ſa in danari, ouer, pizzoli, à danari.12.al ſoldo, uenir anno in tutto.13.cenſi de danaris <lb></lb>& queſti ſaranno eguali à. </s> <s id="s.002207">84.danari, onde partendo il numero per li cenſi, ne uien.6. <lb></lb>6/13.& la Radice de.6.6/11.ualſe la coſa, & tante lire peſo la detta trutta, cioe lire<emph.end type="italics"></emph.end> <22>. <lb></lb></s> <s id="s.002208">6.6/13.<emph type="italics"></emph>che à ſoldi<emph.end type="italics"></emph.end> <22>.6.6/13.<emph type="italics"></emph>piu danari<emph.end type="italics"></emph.end> <22>.6.6/13.<emph type="italics"></emph>la lira montara preciſamente ſoldi.7. <lb></lb>che è il propoſito.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="104" xlink:href="042/01/208.jpg"></pb> <p type="main"> <s id="s.002209">L<emph type="italics"></emph>o ſecondo anchora che è coſa ſolubile, perche meritando le dette lire.60.(rece<lb></lb>pute impresto) per uno anno à.5.per cento à l'anno tornar anno tra cauedal è merito <lb></lb>lire.63.& di queſte biſogna cauarne el fitto della caſa di quell'anno (che ſono lire.23.) <lb></lb>reſtara anchor debitor de lire.40.in capo del primo anno, hor per il ſecondo anno bi <lb></lb>ſogna pur meritar le dette lire.40.à.5.per cento à l'anno, & tornaranno tra merito, <lb></lb>& capitale lire.42.& di queſte lire.42.biſogna cauarne el fitto della caſa di quell'an <lb></lb>no (che ſono lire.23.) reſta lire. </s> <s id="s.002210">19.& lire.19.uerria à eſſer debitore in capo de detti <lb></lb>dui anni, hor qui è la difficolta à ſaper determinare que parte del terzo anno die poſſe <lb></lb>dere la caſa colui à douer reſtare preciſamente ſatisfatto, perche eglie coſa chiara, che <lb></lb>douendo hauer ſolamente lire.19.dal patron della caſa non die poſſedere la detta caſa <lb></lb>tutto l'anno, ma ſolamente una parte, & per ritrouar quella parte.Io pono che la deb<lb></lb>bia poſſedere.1.coſa de giorni, & per tanto tempo merito lire.19.à ragion de.5.per <lb></lb>cento à l'anno à.365.giorni à l'anno, & per piu breuita moltiplico lire.100.per gior <lb></lb>ni.365.fanno.36500.fra giorni, & lire di cauedale, & dapoi moltiplico anchora lire. <lb></lb></s> <s id="s.002211">105.fra utile, & cauedale pur per giorni.365.fanno.38325.fra giorni, & lire de caue <lb></lb>dal è guadagno, poi moltiplico.1.coſa fia lire.19.fara.19.coſe, dapoi procedo per lare <lb></lb>gola (uolgarmente detta del tre) digando, ſe.36500.mi torna.38325.che me ritorna<lb></lb>ranno.19.coſe (cioe quelle lire.19.moltiplicate fia.1.coſa de giorni) operando me ne <lb></lb>uien.728175/36500.coſe, & questo è fra tempo è danari, & queſto biſogna partire per <lb></lb>lo tempo (qual è.1.coſa de giorni) ne uenira lire.728175/36500.& queſto ſaluo da banda, <lb></lb>dapoi biſogna meritar.1.coſa de giorni à lire.23.à l'anno, digando ſe giorni.365.uol <lb></lb>lire.23.che uorra.1.co.operando ſecondo la regola uorra.23/365.coſe, & queſto ſara <lb></lb>egual à.<emph.end type="italics"></emph.end>728175/36500.S<emph type="italics"></emph>eguitando il capitolo ſe trouara la coſa ualer.316.55/92.& tanti <lb></lb>giorni douera star nella detta caſa à douer eſſer integralmente ſatisfatto, oltragli an<lb></lb>ni integri, detti di ſopra, che è il propoſito.<emph.end type="italics"></emph.end> M.D. C<emph type="italics"></emph>ertamente li ſono aſſai belli que <lb></lb>ſiti.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>or uedemo un poco queſto terzo qual per quanto uedo, non uol dir altro in <lb></lb>ſoſtantia che fare de.20.tre parti continue proportionale in talſpecie di proportio<lb></lb>ne, che moltiplicando le due menore l'una fia l'altra faccia.8.etiam per quanto poſſo <lb></lb>coſi all'improuiſo conſiderare, dubito che in queſta faccia delle ſue, & che il non ſeſta <lb></lb>in tutto emendato, del ſuo diffetto pur la uoglio un poco meglio conſiderarla.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002212">QVESITO. XXI. FATTO DA VNO MER<lb></lb><emph type="italics"></emph>cante, qual gli era stato dato à lui da darmi l'anno.1535. <lb></lb>Adi.16.Ottobrio, in Venetia, & non uolſe <lb></lb>dir da chi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002213">MERCANTE. D<emph type="italics"></emph>ui fanno compagnia, il primo miſſe ducati.240.& ſtette <lb></lb>meſi.9.l'altro miſſe una gioia, & ſtette meſi.6.& guadagnorno ducati.100. <lb></lb>à quello della gioia gli tocco fra cauedal eguadagno ducati. </s> <s id="s.002214">150. Domando quan<lb></lb>to ualſe la gioia.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er ſoluere tal queſito. </s> <s id="s.002215">Io pongo, che la gioia uaglia.1.coſa, & <lb></lb>quella moltiplico fia limeſi.6.che ſta in la compagnia fa.6.coſe, poi moltiplico, li <lb></lb>ducati.240.fia.9.meſi fanno.2160.& queſto ſummo con. </s> <s id="s.002216">6. coſe fanno. </s> <s id="s.002217">2160. <pb xlink:href="042/01/209.jpg"></pb>piu.6.coſe.Poi dico per regola detta del tre, ſe.2160.piu.6.co.me guadagna duc.100. <lb></lb>la che mi guadagnaran.6.coſe <expan abbr="operãdo">operando</expan> trouo che guadagnariano.600.co. </s> <s id="s.002218">eſimi de. <lb></lb></s> <s id="s.002219">2160.piu.6.co. </s> <s id="s.002220">& queſto ſara eguale à duc.150.men.1.co. (cioe à quello, che tocco al <lb></lb>ſecondo, de puro guadagno, cioe trattone.1.coſa, che fu il ſuo puro capitale) leuando li <lb></lb>rotti, & ſeguitando il capitolo trouo la coſa ualer<emph.end type="italics"></emph.end> <22>.78025.<emph type="italics"></emph>men.155.& tanto ual<lb></lb>ſe la gioia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002221">QVESITO. XXII. FATTO DA VNO VICENTI <lb></lb><emph type="italics"></emph>di Gaffari Adi.13. Agoſto. 1536. In Venetia, in la Chieſa di San <lb></lb>Giouanepolo, in la capella de San Nicolo, iſponendo io la <lb></lb>13.propoſitione del terzodecimo di Euclide publica<lb></lb>mente, credendoſi lui con tal ſuo queſito di far<lb></lb>mi totalmente reſtar confuſo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002222">VICENTI. C<emph type="italics"></emph>ertamente uoi haueti iſpoſta queſta uoſtra lettione, ouer pro<lb></lb>poſitione tanto degnamente, quanto dir ſi poſſa. </s> <s id="s.002223">Ma uorria, che uoime riſol<lb></lb>ueſti anchora queſto queſito.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002224">S<emph type="italics"></emph>aggi diece di orc che tenia <lb></lb>De argento in ſe la ſua cuba Radice <lb></lb>Coſto ducati diece, hor stati al quia <lb></lb>Che alla raſon medeſima ſe dice.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002225">D<emph type="italics"></emph>iece altri ſaggi che tenia inſerto <lb></lb>De argento in ſe la ſua quadra Radice <lb></lb>Coſta ducati nuoue intendi il merto<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002226">P<emph type="italics"></emph>roportionatamente, qual dimanda <lb></lb>Che ualſe il ſaggio di ciaſcun incerto<emph.end type="italics"></emph.end><lb></lb>A <emph type="italics"></emph>uoi ſpirto gentil questa ſi manda <lb></lb>Et perche hormai ſi ſpanda <lb></lb>La fama di colui che l'ha compoſta <lb></lb>Di Gaffari Vicenti, è la propoſta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002227">NIC. Q<emph type="italics"></emph>uando che uno uol arguire contra ad alcuno, che legga publicamente in qual <lb></lb>che ſcientia, lui de ſempre arguire ſopra alle coſe da lui lette, & dichiarate, nella ſua <lb></lb>lettione, ouer iſpoſitione, & non in altre particolarita fuora di tal propoſito, & ſe pur <lb></lb>alcuno temerario (per moſtrar anchora lui di ſapere) ui proponeſſe, ouer parlaſſe di <lb></lb>qualche altra particolarita fuora di tal propoſito (come che haueti fatto uoi) il letto<lb></lb>re puo con ſuo honore, recuſare di darui riſpoſta, come coſa fuora di propoſito, nondi<lb></lb>meno allegramente, eccetto queſto uoſtro queſito, con queſto patto però, che anchora <lb></lb>uoi ne acettati un'altro da me.<emph.end type="italics"></emph.end> V. M<emph type="italics"></emph>ade uolontiera.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>auendo uoi tanto lauda <lb></lb>ta la miaiſpoſitione, eglie da credere, che uoi l'habbiati rettamente inteſa, & perche <lb></lb>non me ritrouo coſi all'improuiſo alcuno piu famigliar queſito, che la preſente propo<lb></lb>ſitione da me iſposta, ue impongo, che uoi di nuouo qui publicamente la iſponeti, & in <lb></lb>queſto meggio, mandaro à tuor penna, & inchioſtro, & uiriſoluero il uostro queſito.<emph.end type="italics"></emph.end><pb pagenum="105" xlink:href="042/01/210.jpg"></pb><emph type="italics"></emph>ſeſapero.<emph.end type="italics"></emph.end> VICENTI. I<emph type="italics"></emph>o ue diro io non intendo Geometria, ma el mio queſito è <lb></lb>in numeri, ouer in Algebra ſi che preponetime un queſito in numeri, ouer in Alge<lb></lb>bra, che io lo accettaro & ue lo riſoluero ſubito.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>on contento ſe uenereti à lal<lb></lb>tra mia lettione ue lo portero.<emph.end type="italics"></emph.end> VICENTI. V<emph type="italics"></emph>eniro ſenza fallo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002228">QVESITO XXIII. FATTO DAPOI LAL<lb></lb><emph type="italics"></emph>tralettione al detto Vicenti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002229">NICOLO. I<emph type="italics"></emph>n fin de l'altra mialettione, meſſer Vicenti. </s> <s id="s.002230">Voi me preponeſti <lb></lb>quel uoſtro queſito che ſappeti, & io lo accettai con queſta conditione che <lb></lb>uoi ne doueſti anchora uoi accettarne un'altro da me et uoi ue contentaſti di accettar<lb></lb>lo domente che talmio queſito, fuſſe in numeri, ouer per Algebra. </s> <s id="s.002231">Et coſi ue l'ho por <lb></lb>tato elqual è queſto, trouatime uno numero, che multiplicato fia la ſua Radice piu. <lb></lb></s> <s id="s.002232">6.faccia à ponto.<emph.end type="italics"></emph.end>100. VICENTI. B<emph type="italics"></emph>enlo riſoluero. </s> <s id="s.002233">Ma ditime haueti riſolto il <lb></lb>mio che io ui dedi.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>eſſer ſi che io l'ho reſolto, & tal uostro queſito è molto <lb></lb>bello, & ingenioſo, ma <expan abbr="nõ">non</expan> è uoſtra farina. </s> <s id="s.002234">Perche uoi confeſſaſti, quando mel deſti che <lb></lb>uoi non haueui, ouer intendeui geometria, & tal uoſtro queſito (anchor che ſia pro<lb></lb>poſto ſotto ombra de numeri) è coſa geometrica, ma uoi el doueti hauer ritrouato, <lb></lb>ſcritto ſopra qualche libro, da qualche perſona dotta, & con tal particolarita, ue re<lb></lb>putati eſſere un gran huomo in tal faculta, ma colui che coſi poſitiuamente ſe ucste di <lb></lb>panni d'altri preſto ſe ne ſpoglia. </s> <s id="s.002235">Hor per uenire alla concluſione, dico che'l ſaggio <lb></lb>del uoſtro ero ualſe ducati.1.1/90.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.1/72900.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba quadra.1/53144100000. <lb></lb>piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba quadra.1/5314410.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.1/7290.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>quadra<emph.end type="italics"></emph.end>1/810 <lb></lb>E<emph type="italics"></emph>t el ſaggio de l'argento ualſe ducati.9/10.men<emph.end type="italics"></emph.end> <22>.1/10.<emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba.1/100.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba <lb></lb>quadra<emph.end type="italics"></emph.end> 1/100000. H<emph type="italics"></emph>or guardati ſel ui pare che tal uostro queſito ſia ben reſolto.<emph.end type="italics"></emph.end><lb></lb>VICENTI. S<emph type="italics"></emph>el ſe incontra, con queſto che adeſſo, adeſſo ui moſtraro ſun queſto <lb></lb>mio libro lui ſara ben reſolto, & eſſendo altramente, lui ſara falſo.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>t io di<lb></lb>co che ſe la concluſione di quello che haueti ſul detto uoſtro libro ſe incontrara con la <lb></lb>mia, la uostra ſara bona, & eſſendo altramente, la ſara falſa.<emph.end type="italics"></emph.end> VICENTI. H<emph type="italics"></emph>or in <lb></lb>contramole un puoco, la ſe incontra benißimo.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>dunque confirmati, che la ſta <lb></lb>bene.<emph.end type="italics"></emph.end> VICENTI. L<emph type="italics"></emph>a ſta ben per certo.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>or ſu à laltra lettione ui aſpetto <lb></lb>con la reſolution del mio.<emph.end type="italics"></emph.end> VICENTI. V<emph type="italics"></emph>eniro.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002236">QVESITO XXIIII. FATTO DAL NOSTRO <lb></lb><emph type="italics"></emph>amicißimo miſſer Hieronimo Triuiſano, dapoi <lb></lb>laltra lettione.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002237">MISSER HIERONIMO. M<emph type="italics"></emph>olto mi allegro<emph.end type="italics"></emph.end> M. N. <emph type="italics"></emph>carißimo chel <lb></lb>Vicenti non habbia ſaputo riſoluere il uoſtro queſito, & eſſer reſtato total<lb></lb>mente confuſo, come meritaua la ſua audacia, qual ſe perſuadeua con tal ſua queſtione <lb></lb>di farue restare publicamente confuſo, & fu uolta ch'io dubitai che uoi non la ſapeſti <lb></lb>reſoluere perche lui ha giurato non hguer mai ritrouato huomo, che ge l'habbia ſapu-<emph.end type="italics"></emph.end><pb xlink:href="042/01/211.jpg"></pb><emph type="italics"></emph>ta riſoluere. </s> <s id="s.002238">Et per che in effetto tal ragione mi piace uoria che per uoſtra gentilez<lb></lb>za mi mostraſti il modo da riſoluerla.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>olio uolentera ſappiati che per riſolue <lb></lb>re tal ragione, ouer queſito biſogna conſiderar queſto. </s> <s id="s.002239">Che quello ducato che monta <lb></lb>de piu li primi ſaggi.10.é per eſſer in quello piu oro che non è nelli altri ſecondi ſaggi. <lb></lb></s> <s id="s.002240">10.& manco argento, & quel oro è tanto quanto che è la differentia ch'è fra la Radi<lb></lb>ce cuba di.10.& la Radice quadra de.10.laqual differentia, è<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.10.& <lb></lb>queſto reſiduo de oro ual uno ducato de più, che ſel fuſſe argento, cioe un tal reſiduo <lb></lb>a'oro ualeria de piu de un tal reſiduo di argento, uno docato à ponto. </s> <s id="s.002241">Adunque biſo<lb></lb>gna uedere che ualeria alla ratta<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba.10.de oro puro, digando ſe<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu<lb></lb>ba.10 dioro ual ducati.1.che ualeria<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>q.10.di oro operando haueremo<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.10.da <lb></lb>partir per<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.10.& per trouar el partitore rationale, multiplicare<lb></lb>mo el detto<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.10.per.10.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba quadra.100000. piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.100. <lb></lb>ne uenira<emph.end type="italics"></emph.end> <22>.1000.<emph type="italics"></emph>men.10.& questo reſiduo, lo remultiplicaremo per elſuo binomio, <lb></lb>cioe per<emph.end type="italics"></emph.end> <22>.1000.<emph type="italics"></emph>piu.10.produra.900.à ponto (che numero rationale) & questo ſer <lb></lb>uaremo per noſtro partitore. </s> <s id="s.002242">Dapoi multiplicaremo la coſa da partire, (cioe<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu. <lb></lb></s> <s id="s.002243">10.per la detta quantita trinomiale, et dapoi per quella binomiale, cioe prima per.10. <lb></lb>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba quadra 100000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.100 fara<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.10000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba quadra. <lb></lb></s> <s id="s.002244">10000000.piu.10. Dapoi biſogna anchora multiplicar queſto produtto per el bino<lb></lb>mio, cioe per.<emph.end type="italics"></emph.end> <22>.1000.<emph type="italics"></emph>piu.10.fara.100.piu.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.10000000. piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.quadra. <lb></lb></s> <s id="s.002245">10000000000000.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu.qua.100000000000000000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.100000000000 <lb></lb>00000.piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002246">100000. E<emph type="italics"></emph>t queſta quantita de ſei nomi, biſogna partirla per el no<lb></lb>ſtro partitor ſaluato, cioe per.900. & ne uenira.1/1.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10/729.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.002247">qua. <lb></lb></s> <s id="s.002248">10/531441.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.100000/531441.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.10000/531441.piu<emph.end type="italics"></emph.end> <22>.0/81.E<emph type="italics"></emph>t tan <lb></lb>to ualſe<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10.de oro piu de altro tanto argento. </s> <s id="s.002249">Onde <expan abbr="aggiungẽdo">aggiungendo</expan><emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10.in luo <lb></lb>co de lo argento alla prima uirga cioe à ſaggi.10.men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10.faranno ſaggi.10.de <lb></lb>oro puro elqual oro puro montaria piu di primi ducati.10.la ſopra ſcritta quantita <lb></lb>de ſei nomi compoſta, cioe ualeriano ducati.10.1/9.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.11/729.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.qua. <lb></lb></s> <s id="s.002250">10/531441.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.100000/531441.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.10000/531441.piu<emph.end type="italics"></emph.end> <22>.10/81.D<emph type="italics"></emph>a<lb></lb>poi uolendo ſaper che ualſe il ſaggio, biſogna partire li ſopra ſcritti. </s> <s id="s.002251">6.nomi per li.10 <lb></lb>ſaggine uenira ducati. </s> <s id="s.002252">1.1/90.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10/729000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.10/531441000000. <lb></lb>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua. </s> <s id="s.002253">10000/531441000000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.10000/531441000000. <lb></lb>piu<emph.end type="italics"></emph.end> <22>.10/8100.<emph type="italics"></emph>& tanto ualſe el ſaggio del detto oro puro ch'é il primo propoſi<lb></lb>to. </s> <s id="s.002254">Ma biſogna notare che li detti rotti ſe poſſono la maggior parte ſchiſſare & ſchi<lb></lb>ſandoli ſecondo il biſogno ſe trouarano ducati.1.1/90.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba.1/72900.piu.<emph.end type="italics"></emph.end> <22>. <lb></lb><emph type="italics"></emph>cu qua.1/53144100000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qu.1/5314410.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.1/53144100. <lb></lb>piu<emph.end type="italics"></emph.end> <22>.1/810.<emph type="italics"></emph>& tanto ualſe il detto ſaggio del detto oro puro. </s> <s id="s.002255">Anchor biſogna <lb></lb>notare, che quel penultimo nome, cioe<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.1/53144100. é numero quadra <lb></lb>to, onde cauandone la radice ſe trasferiria in<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.1/7290.& ſaria piu breue & ele<lb></lb>gante riſpoſta à dire che il ſaggio del detto oro puro ualſe du.1 1/90. piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.1/72900. <lb></lb>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.1/53144100000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu. </s> <s id="s.002256">qua.1/5314410.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cuba <lb></lb>1/7290.piu.<emph.end type="italics"></emph.end> <22>.1/810. H<emph type="italics"></emph>or per ſapere quanto ualſe il ſaggio del argento, biſogna ari <lb></lb>cordarſi di quello che di ſopra fu <expan abbr="cõcluſo">concluſo</expan>, cioe che.<emph.end type="italics"></emph.end> <22>.10 <emph type="italics"></emph>men.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu. </s> <s id="s.002257">10.dioro ual duc.<emph.end type="italics"></emph.end><pb pagenum="106" xlink:href="042/01/212.jpg"></pb>1.<emph type="italics"></emph>di piu di altro tanto argento, adunque altro tanto argento, cioe<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph><expan abbr="mẽ">men</expan>.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu. </s> <s id="s.002258">10 <lb></lb>d'argento ual un duc. </s> <s id="s.002259">manco di altro tanto oro & per tanto diremo ſe<emph.end type="italics"></emph.end> <22>.10. <emph type="italics"></emph>men.<emph.end type="italics"></emph.end><lb></lb><22>.<emph type="italics"></emph>cuba. </s> <s id="s.002260">10. di argento, ual duc.1.manco di altro tanto oro che ualera ſaggi.10.men.<emph.end type="italics"></emph.end><lb></lb><22>.10.<emph type="italics"></emph>di argento, operando come prima, cioe multiplicando duc.1.fia ſaggi.10.men.<emph.end type="italics"></emph.end><lb></lb><22>.10.<emph type="italics"></emph>fara pur ſaggi.10.men.<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>qual biſogna pur partir per<emph.end type="italics"></emph.end> <22>.10. <emph type="italics"></emph>men.<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu.10 <lb></lb>trouando per prima un partitor rationale come di ſopra fu fatto, cioe multiplicando <lb></lb>el detto partitor de<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>men.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10.per.10.piu.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.100000.piu.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.100 <lb></lb>fara<emph.end type="italics"></emph.end> <22>.1000.<emph type="italics"></emph>men.10.& queſto medeſimo multiplicandolo per el ſuo binomio fara. <lb></lb></s> <s id="s.002261">900. come prima qual biſogna ſeruar da banda per nostro partitore. </s> <s id="s.002262">Dapoi biſogna <lb></lb>multiplicare la nostra coſa da partire, cioe ſaggi.10.me<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>per lo medeſimo trino <lb></lb>mio & binomio, ma comenzar prima per el binomio, cioe per.<emph.end type="italics"></emph.end> <22>.1000.<emph type="italics"></emph>piu.10. (per<lb></lb>che comenzando dal trinomio ſe ueniria in gran confuſion de nomi) adunque multi<lb></lb>plicandolo prima per<emph.end type="italics"></emph.end> <22>.1000.<emph type="italics"></emph>piu.10 far.<emph.end type="italics"></emph.end> <22>.100000.<emph type="italics"></emph>men.<emph.end type="italics"></emph.end> <22>.1000. <emph type="italics"></emph>qual multiplican <lb></lb>dolo anchora per el trinomio, cioe per.10.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu qua.100000.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.100. fara.<emph.end type="italics"></emph.end><lb></lb><22>.10000000.<emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.100000000000000000000.piu.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qu.<emph.end type="italics"></emph.end>10000000000-<lb></lb>000000000.<emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>.100000.<emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.100000000000000.mẽ<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.<emph.end type="italics"></emph.end>10000-<lb></lb>000000000.<emph type="italics"></emph>& queſto tal produtto biſogna partirlo per el noſtro partitore, cioe per. <lb></lb></s> <s id="s.002263">900.ma per abreuiar li detti ſei nomi biſogna uedere s'eglie alcune de detta quantita, <lb></lb>che ſiano communicante, & quelle ſumarle, ouer ſotrarle ſecondo il biſogno il che fa <lb></lb>cendo ſe trasferira quelli tanti nomi in<emph.end type="italics"></emph.end> <22>.8100000.<emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.<emph.end type="italics"></emph.end>53144100000000-<lb></lb>000000.<emph type="italics"></emph>piu<emph.end type="italics"></emph.end> R.<emph type="italics"></emph>cu.qua.5314410000000000000.& queſto tal trinomio biſogna par<lb></lb>tirlo per el ſopradetto.900.recando ſempre el partitore alla natura della dignita che <lb></lb>ſi uol partire il che <expan abbr="facẽdo">facendo</expan> ne uenira<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.10. & <expan abbr="tãti">tanti</expan> duc. <lb></lb></s> <s id="s.002264">manco ual ſaggi.10.men.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002265">10. <emph type="italics"></emph>de argento puro de altro tante oro, onde cauandolo <lb></lb>de duc.9.lo rimanente ſara el ualor de ſaggi.10.di argento puro, el qual rimanente <lb></lb>ſara duc.9.men questo trinomio, cioe<emph.end type="italics"></emph.end> <22>.10.<emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.10.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.002266">qua.10.& tanto <lb></lb>ualſe ſaggi.10.di argento puro, lo qual ualor partendolo per.10.ne uenira duc.9/10. <lb></lb>men queſto trinomio<emph.end type="italics"></emph.end> <22>.1/10.<emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.1/100.piu<emph.end type="italics"></emph.end> R.<emph type="italics"></emph>cu.qua.1/100000.et tanto ual <lb></lb>ſe elſaggio del <expan abbr="argẽto">argento</expan> puro, & accio che meglio lo poßiati <expan abbr="cõſiderare">conſiderare</expan> qua de ſotto ue <lb></lb>lo uoglio distintamente notare. </s> <s id="s.002267">El ſaggio de l'oro ualſe ducati.1.1/90.piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.1/12900. <lb></lb>piu<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.1/53144100000.piu<emph.end type="italics"></emph.end> R.<emph type="italics"></emph>cu.qua.1/5314410.piu<emph.end type="italics"></emph.end> R.<emph type="italics"></emph>cuba. <lb></lb></s> <s id="s.002268">1/7290.piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002269">11/810. E<emph type="italics"></emph>l ſaggio de l'argento ualſe ducati.9/10.men<emph.end type="italics"></emph.end> R.1/10.<emph type="italics"></emph>piu<emph.end type="italics"></emph.end> R.<emph type="italics"></emph>cu. <lb></lb></s> <s id="s.002270">1/100.piu.<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>cu.qua.<emph.end type="italics"></emph.end>1/100000. M. H. Q<emph type="italics"></emph>uesta é una delle piu forte ragioni che <lb></lb>mai uedeſſe in mia uita, et ui è molte coſe nella uostra operatione lequale <expan abbr="nõ">non</expan> le ho trop <lb></lb>po ben inteſe, ma per al preſente non ui uoglio dar altro faſtidio perche mi pare che <lb></lb>habbiati fatto aſſai, ma la ſtudiaro un puoco da mia poſta, ſe <gap></gap>i<gap></gap>rouaro coſa ch'io non <lb></lb>intenda ritornaro da uoi.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>on ſempre parato à farue à piacere.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002271">QVESITO XXV. FATTO DA M. ZVANNE DI TONI<lb></lb><emph type="italics"></emph>ni da Coi perſonalmente l'anno. </s> <s id="s.002272">1536. adi. </s> <s id="s.002273">10. Decembre in Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002274">MISSER ZV ANNE. H<emph type="italics"></emph>o inteſo che za molti giorni uoi uenesti in di<lb></lb>ſputa con Maeſero Antoniomaria fior. </s> <s id="s.002275">Et che finalmente ue conneniſti<emph.end type="italics"></emph.end><pb xlink:href="042/01/213.jpg"></pb><emph type="italics"></emph>in queſto che lui ui doueſſe proponere.30.queſiti in ſcritto ſotto bolla realmente diuer <lb></lb>ſi in mane de<emph.end type="italics"></emph.end> M. <emph type="italics"></emph>pre Iacomo di zambelli notaro, & che ſimelmente uoi ne propone<lb></lb>reſti altri.30. à lui realmente diuerſi & coſi faceſti, & aßignaſti.40.ouer.50.giorni <lb></lb>di termine à cadauno di uoi per ſoluere li detti queſiti, & determinaſti che quello di <lb></lb>uoi, che al detto termine ſi trouaſſe hauer aſſolto piu numero di detti.30.receputi que <lb></lb>ſiti reſtaſſe con l'honore oltra noſoche puoco di ſcotto che limitaſti per ogni queſito. <lb></lb></s> <s id="s.002276">Et me ſtato referto, & accertado per fina à Breſſa che uoi reſolueſti tutti li ſuoi.30.in <lb></lb>termine di due, hore laqualcoſa mi par dura da credere.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie il uero quanto ue <lb></lb>ſtato detto, ouer referto. </s> <s id="s.002277">Et la cauſa che io reſolſe li ſuoi.30.con tanta breuita è queſta <lb></lb>che lui propoſe tutti li detti ſuoi.30.queſiti, che conduceuano l'operante per Algebra <lb></lb>in coſa, é cubo equal à numero, credendoſi che de quelli non ne doueſſe riſoluere alcu<lb></lb>no, perche frate Luca nella ſua opera afferma eſſer impoßibile à riſoluere tal capito<lb></lb>lo con Regola generale, & io che permia bona ſorte, ſolamente.8.giorni auanti al ter <lb></lb>mine di portar li.30.&.30.queſiti ſotto bolla dal notaro. </s> <s id="s.002278">Io haueua ritrouata la re<lb></lb>gola general a tal capitolo. </s> <s id="s.002279">Onde per eſſer tal inuentione coſi di freſco, mella trouai <lb></lb>molto prompta, & famigliar, & per queſto io lireſolſe tutti.30. contanta celerita, <lb></lb>ouer preſtezza.<emph.end type="italics"></emph.end> M. ZV ANNE. C<emph type="italics"></emph>he ue induſſe coſi à recercare à quel tempo <lb></lb>la regola di tal capitulo.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>ui medeſimo, perche lui ſi andaua uantando per far<lb></lb>me paura hauer trouata tal, regola, uero è che in principio non gli credena questa co <lb></lb>ſa, perche lui non haueua ſcientia, ma ſolamente gran pratica, & per la pura pratica, <lb></lb>io comprendeua chel non era atto neſofficiente à poter hauer ritrouata tal regolaper <lb></lb>ſe medeſmo. </s> <s id="s.002280">Ma lui per farme credere che haueſſe tal paſſo, & che doueſſe temere di <lb></lb>lui, anchor che non haueſſe theorica, ſe auantaua che gia trenta anni tal ſecreto gli era <lb></lb>ſtato moſtrato da un gran mathematico, il che mifece dubitar, che'l fuſſe il uero, e per <lb></lb>queſto io poſi ogni mio ſtudio, cura & arte per ritrouar regola à tal capitolo, & coſi <lb></lb>per mia bona ſorte (come di ſopra è detto) la ritrouai.8.giorni auanti al termine de <lb></lb>dar li detti.30.queſiti ſotto bolla al notaro, & queſto fu l'anno paſſato, cioe del.1535. <lb></lb>adi.12.di.Febraro (uero è che in Venetia ueneua à eſſer del.1534.) et per alcuni aui<gap></gap><lb></lb>& accidenti di tal inuentione il giorno ſeguente ritrouai anchora regola generale al <lb></lb>capitolo de coſe, & numero equal à cubo.<emph.end type="italics"></emph.end> M. Z. V<emph type="italics"></emph>oi haueſti una gran ſorte à ri<lb></lb>trouar tal paſſo coſi al improuiſo, perche ſe uoi non lo haueſti ritrouato uoi reſtaui ui <lb></lb>tuperato appreſſo al uolgo de gli ignoranti, non gia appreſſo delli intelligenti, perche <lb></lb>uno particolar ſecreto, non da la ſcientia à l'huomo, perche la ſcientia uerſa ſopra <lb></lb>le coſe generale, & non ſopra le particolare perche li partico'ari ſono infiniti, & pe <lb></lb>ro non è poßibile hauer cognitione de ogni particolare. </s> <s id="s.002281">Ma ditime un puoco in che <lb></lb>materia preponeſti li uoſtri.30.queſiti à lui.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ge li propoſi tutti realmente di<lb></lb>uerſi, & queſto feci per moſtrarli che io era uniuerſale, & chel mio fondamento, non <lb></lb>era in una, ne in due, ne in tre mie particolar inuentioni, ouer ſecreti, anchor che à <lb></lb>preſſo di me li haueſſe hauuti per ſicurißimi, & che ſopra di quelli ui haueſſe potuto <lb></lb>formar. </s> <s id="s.002282">10000. caſi non che. </s> <s id="s.002283">30. anci li uolſi proponere (come detto) tutti <lb></lb>realmenle diuerſi, per moſtrarli che io non lo ſtimaua ne temeua in conto alcuno.<emph.end type="italics"></emph.end> M. <lb></lb>ZV ANNE. E<emph type="italics"></emph>t quanti ne reſolſelo lui di uoſtri.<emph.end type="italics"></emph.end> NICOLO. D<emph type="italics"></emph>e niun mai poteti<emph.end type="italics"></emph.end><pb pagenum="107" xlink:href="042/01/214.jpg"></pb><emph type="italics"></emph>hauerne riſpoſta, uero é, che lui ſe andaua auantando, che gli baucua riſolti, ma el <lb></lb>non me li uolſe mai laſſar uedere tai ſue reſolutioni, ma per couerzer la coſa, lui uole<lb></lb>ua, che ſe eleggeſſe alcuni ſuoi amici, che giudicaſſeno ſe lui gli haueua ben riſolti, ouer <lb></lb>non, la qual coſa uedendo, che da ogniun era giudicato per perdente, io gli feci publi<lb></lb>camente un preſente del precio giocato.<emph.end type="italics"></emph.end> M.Z. D<emph type="italics"></emph>i gratia datemi in ſcritto li detti. <lb></lb></s> <s id="s.002284">30.queſiti, che lui ui propoſe, con le ſue ſolutioni, & ſimilmente li uoſtri. </s> <s id="s.002285">30.che pro <lb></lb>poneſti à lui.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uando che haueſſe tempo da coppiarli, io ue daria ben li detti que <lb></lb>ſiti, ma non le mie reſolutioni, perche ogni uolta, che uoi uedeſti lemie reſolutioni, imme <lb></lb>diate intender esti la regola, ma ſe pur uoleti li detti ſimplici queſiti, andati dal notaro, <lb></lb>& donategli una gentilezza, che ue ne dara la coppia immediate. </s> <s id="s.002286">Auiſandoui anchora <lb></lb>che de li mei.30. che gli propoſe à lui, io non ho coppia alcuna, perche, ſi come gli heb <lb></lb>bi notati, io li portai di ſubito ſotto bolla al notaro, & non ne tenni altramente coppia, <lb></lb>talmente che non ue li ſapria dire la mita de quelli, ſe io non andaſſe dal notaro à far<lb></lb>mene dar coppia.<emph.end type="italics"></emph.end> M.Z. D<emph type="italics"></emph>itemene un poco tre, ouer quattro de quelli, che uoi gli <lb></lb>proponesti à lui.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>l primo queſito delli miei.30.che io gli propoſi à lui, ſe ben <lb></lb>me aricordo, diceua in queſta forma. <lb></lb> Trouatemi una quantita che ſia irrationale, che moltiplicata ſia la ſua radice piu. <lb></lb></s> <s id="s.002287">40. faccia numero rationale, & diſereto. La ſeconda. <lb></lb> Trouatemi una quantita, che ſla irratienale, la qual moltiplicata fia.30.men la ra <lb></lb>dice di detta quantita, faccia numero rational, & diſcreto. La terza. <lb></lb> Trouatemi una quantita, qual gionta con il quadruplo della ſua radice cuba <lb></lb>faccia.13. La quarta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002288">T<emph type="italics"></emph>rouatemi una quantita, che ſottratone.5.delle ſue radice cube reſti.<emph.end type="italics"></emph.end>10. </s> </p> <p type="main"> <s id="s.002289">E<emph type="italics"></emph>t quantunque queſte quattro uarieta de equationi, ouer capitoli, da me ritrouati. <lb></lb></s> <s id="s.002290">Io gli haueſſe per fortißimi paßi, nondimeno non ui uolſe proponere, ſaluo che un ſol <lb></lb>queſito per cadauno capitolo, per moſtrarli, come di ſopra dißi, che lo non mi ſonda<lb></lb>ua, ne ſperaua di conuencerlo con una, ne due, ne tre, ne quattro particolar inuentioni, <lb></lb>ouer ſegreti, anci tutti li miei.30.queſiti eranotutti uarij, ſi in Geometria, come in el <lb></lb>operar de Algebra, che longo ſaria à uolerueli narrare à uno per uno.<emph.end type="italics"></emph.end> M.Z. P<emph type="italics"></emph>er <lb></lb>quanto uedo il primo uoſtro queſito conduce l'operante in cubo, e cenſi egual à qualub <lb></lb>que numero ſi uoglia, pur che dia la coſa irrationale, & lo ſecondo conduce in cubo, <lb></lb>& numero egual à cenſi. </s> <s id="s.002291">Il terzo poi in cubo é coſa egual à numero, & lo quarto in co <lb></lb>ſe è numero egual à cubo. </s> <s id="s.002292">Adunque uoi haueti ritrouato anchora regola al capitolo <lb></lb>de cubo é cenſo egual à numero, & à quello de cubo, e numero egual à cenſi.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ue <lb></lb>ſto trouai per fin dell'anno. </s> <s id="s.002293">1530. quando ſtantiaua à Verona, & quella uoſtra ra<lb></lb>gione, che mi mandaſti per meſſer pre Antonio da Cellatica, fu cauſa di farme ritro<lb></lb>uar regola à tai capitoli.<emph.end type="italics"></emph.end> M.Z. E<emph type="italics"></emph>t che ragion fu gia quella.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>e furno due, ma <lb></lb>in una. </s> <s id="s.002294">Voi me adimandaui, che ui trouaſſe un numero, che moltiplicato per la ſua ra<lb></lb>dice piu.3.faceſſe.5.qual queſito conduce l'operante, come ſapeti in.1.cubo piu.3.cen<lb></lb>ſi egual à.5.& io ue reſcrißi, che uoi non ſapreſti riſoluere tai dui queſiti à me man<lb></lb>dati, cioe quello inſieme con quell'altro, che me mandasti inſieme con quello, & che cir <lb></lb>ca cio. </s> <s id="s.002295">Io me offeriua di giocare duc.10.contra.<emph.end type="italics"></emph.end>5. M.Z. E<emph type="italics"></emph>me ne aricordo.<emph.end type="italics"></emph.end> N. R<emph type="italics"></emph>e-<pb xlink:href="042/01/215.jpg"></pb>plico <expan abbr="adũque">adunque</expan>, che tal uoſtro queſito fu cauſa di farme ritrouar la regola di tal capitolo <lb></lb>de cubo è cenſo egual à numero, & ritrouato quello il giorno ſeguente ritrouai regola <lb></lb>all'altro, cioe à quello de cubo è numero egual à cenſi, perche l'uno tira l'altro. </s> <s id="s.002296">Et coſi <lb></lb>maeſtro Antoniomaria Fiore per auantarſe di hauer quello di coſa è cubo egual à nu<lb></lb>mero (o fuſſe il uero, o no) non ſolamente mi fece à quel tempo ritrouare tal capitolo, <lb></lb>ma anchora immediate quello di coſe à numero egual à cubo, con le quale inuentioni, da <lb></lb>poi alquanti giorni, ritrouai molte altre regoli, & capitoli, & uolendoli ſtudiar ſopra <lb></lb>à tal materia ſe ne potria trouar infiniti, perche una regola apre gliocchi in molte al<lb></lb>tre, come poteti conſiderare, ma per eſſer hora tarda, non uoglio, che parlamo piu di <lb></lb>queste materie, anci uoglio andare à cena, & uoglio, che restati à cena con meco.<emph.end type="italics"></emph.end><lb></lb>M.Z. I<emph type="italics"></emph>o ſono aſpettato da uno mio cugino, che ſtantia qua in Venetia.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>ſpetti <lb></lb>quanto uoglia, che uoglio, che reſtati.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002297">QVESITO. XXVI. FATTO DAL MEDE<lb></lb><emph type="italics"></emph>ſimo Meſſer zuane de Tonini da Coi, l'Anno.<emph.end type="italics"></emph.end>1536. A<emph type="italics"></emph>di.15.Decembrio.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002298">I<emph type="italics"></emph>n Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002299">MAESTRO ZVANE. M<emph type="italics"></emph>eſſer Nicolo, mi uoglio partire per ritornarme<lb></lb>ne à Breſſa, uero è, che fra pochi giorni ritornaro, ma nanti, che mi parta ue uor <lb></lb>ria pregare, che uoi me deſti uno di quelli uostri quattro queſiti riſolto.<emph.end type="italics"></emph.end> N. V<emph type="italics"></emph>oi do<lb></lb>ueti ſapere Meſſer zuane, che le inuentioni ſono difficili, & lo aggiongergli è facile. <lb></lb></s> <s id="s.002300">Et per tanto eſſendomi molto affaticato per ritrouare tai particolarita, il non mi pare <lb></lb>licito, che io li debbia coſi facilmente publicare, & maßime doue non me ne reufiſca al<lb></lb>cuno honore, ne utilita, eglie ben uero, che il non è nanche licito à uoler tenere tai in<lb></lb>uentioni totalmente ſepolte, ma ſappiati, che la mia intentione non è di uolerle tener <lb></lb>oppreſſe, ma de publicar le à ogni huomo, & come che habbia ſpedito alcune mie altre <lb></lb>gia principiate fatiche, ſpero de eſſequir tal mia buona intentione, & accio che uoi <lb></lb>non penſaſti che tai inuentioni ſiano da me piu iſtimate del douere, io mi ue offeriſco, <lb></lb>ogni uolta che uoi me ſapereti formar uno, ouer piu queſiti, che io non ue li ſappia riſol <lb></lb>uere, di barattar con uoi à capo per capo, cioe à uno per uno, ilche non è poco à offe<lb></lb>rirue una coſa generale (ſopra della quale non ſolamente ſe puo formare infiniti caſi, <lb></lb>ma ſe puo con facilita ritrouare regola à molti altri capitoli) per un particolare.<emph.end type="italics"></emph.end><lb></lb>M.<gap></gap>. </s> <s id="s.002301">Q<emph type="italics"></emph>ueſta uoſtra mi par una honeſta oblatione. </s> <s id="s.002302">Et per tanto ue uoglio propone<lb></lb>re dui belli queſiti, li quali non ſapendoli riſoluere, io ue li inſignaro, & uoi me inſi<lb></lb>gnareti la regola di detti uoſtri capitoli, & maßime quella di coſa è cubo egual à nu<lb></lb>mero, il primo di quai queſiti è queſto.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002303">E<emph type="italics"></emph>glie il triangolo rettangolo, poniamo lo.a.b.c.del qual l'angolo.c.è retto, & nel <lb></lb>detto triangolo ui è iſcritto il cerchio.e.f.d.il cui diametro è. </s> <s id="s.002304">2. & trouo che la linea. <lb></lb></s> <s id="s.002305">a.c.gionta con la.c.b.tal ſumma ſara ſempre eguale alla linea.a.b. </s> <s id="s.002306">gionta con il dia<lb></lb>metro de cerchio (qual come detto è.<emph.end type="italics"></emph.end>2.) H<emph type="italics"></emph>or ue adimando la cauſa di queſto.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="108" xlink:href="042/01/216.jpg"></pb> <figure id="id.042.01.216.1.jpg" xlink:href="042/01/216/1.jpg"></figure> <p type="main"> <s id="s.002307">S<emph type="italics"></emph>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></lb>ſua 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 ſega dalla li<lb></lb>uea.a.d.la.f.d.la qual è.3.ſe adimanda la quantita delle due parti.a.e.&.e.c.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.216.2.jpg" xlink:href="042/01/216/2.jpg"></figure> <p type="main"> <s id="s.002311">H<emph type="italics"></emph>or guardati ſel ui pare di moſtrarmi quella uostra regola de cenſo é cubo egual à nu<lb></lb>mero, io ui moſtraro il modo di riſoluere queſti dui queſiti, quali in uero ſono belli, & <lb></lb>forti.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>ueſti egli ho per coſe facile, perche ſe mi dati tempo un'hora, io ue li da<lb></lb>ro riſolti. </s> <s id="s.002312">Ma fati una coſa ch'io ui diro, l'anno paſſato mi furono portatitre uoſtri <lb></lb>queſiti, quali me porto Maestro Dominico da Vderzo, fra li quali uno ue ne era, qual <lb></lb>diceua in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002313">S<emph type="italics"></emph>ono trei, che hanno comprato lire.20.di carne, & tante lire ne ha comprate uno <lb></lb>di loro, che moltiplicato tal numero de lire in ſe medeſimo, tal produtto è eguale alla <lb></lb>moltiplicatione delle lire, che hanno comprato glialtri dui, cioe quelle dell'uno fia quel <lb></lb>le dell'altro, & moltiplicate anchor le due menor quantita de lire, l'una ſia l'altra <lb></lb>fanno preciſamente.8. ſe adimanda la quantita delle lire della carne, che compro cadau <lb></lb>no per ſe, il qual queſito non uol dire altro in ſoſtantia, che far de.20.tre parti conti<lb></lb>nue proportionale, in tal ſpecie di proportione, che moltiplicando le due menore, l'u<lb></lb>na fia l'altra facciano.8.hor moſtratemi à ſoluere questo tal queſito con regola ge<lb></lb>nerale, che io me offeriſco à moſtrarui il modo, & regola generale da riſoluere, quala <lb></lb>equatione ui pare di ſopradetti quattro capitoli.<emph.end type="italics"></emph.end> A <emph type="italics"></emph>benche ſo, che uoi non accettareti <lb></lb>queſto partito, perche uoi medeſimo non ſapeti riſoluere tal queſito. </s> <s id="s.002314">Et è gran coſa, <lb></lb>che non ui poßiati in tutto rimouere del voſtro uſo antico.<emph.end type="italics"></emph.end> M.Z. </s> <s id="s.002315">E <emph type="italics"></emph>ue diro il non é <lb></lb>manco bello il ſapere dimoſtrare la impoßibilita d'un caſo irreſolubile, quanto che è <lb></lb>à riſoluezne uno ſolubile.<emph.end type="italics"></emph.end> NIC. Q<emph type="italics"></emph>ueſta uoſtra ſcuſa non è buona, perche uoi <pb xlink:href="042/01/217.jpg"></pb>non me lo haueti propoſto per impoßibile, anci me lo haueti propoſto, come co a, che <lb></lb>uoi non intendeti, ne ſapreti riſoluere, ne manco me ſapreti dimoſtrar che il ſia impoſ<lb></lb>ſibile, perche à me mi baſtaria l'animo di formar.1000.che uoi ne altri li ſapra riſol<lb></lb>uere, ne manco, ne uoi, ne altri mi potra con ragione dimostrare che il ſia impoßibile <lb></lb>à darli riſolutione. </s> <s id="s.002316">Anci è uoglio dire, che tal uoſtro queſito non ſolamente è l'ho per <lb></lb>poßibile, ma iſpedito alcune mie facende ſpero trouarui regola generale, come feci an<lb></lb>chora à quello, che me mandaſti à Verona.<emph.end type="italics"></emph.end> M.Z. F<emph type="italics"></emph>areti aſſai ſe la ritrouareti. </s> <s id="s.002317">Hor <lb></lb>perche il ſe appreſſa l'hora da douermi partire, ui prego che per uoſtra gentilezza <lb></lb>uogliati darme almen uno di quelli uoſtri quatro queſiti aſſolto che ui prometto come <lb></lb>ſon gionto à breſſa di ſcriuerui & di mandarue qualche bello queſito qual ſel non ſape <lb></lb>reti riſoluere mi offero à mandarue anchora la reſolutione, & ſe haueti anchora qual<lb></lb>che altra comuna queſtione fuora di queſti uoſtri capitolinoui ui prego me le uoglia<lb></lb>ti dar, che ſapendola riſoluere ui mandaro anchora la ſua reſolutione in ſcritto.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>e <lb></lb>uoſtre parole mi hann aſtretto à compiacerui alquanto et per tanto ui uoglio dar aſſol <lb></lb>to el primo, cioe quello che dice trouatime una quantita che ſia irrationale, che molti<lb></lb>ta fia la ſua radice piu.40.faccia numero rational & diſcreto, anchor che ſon certo <lb></lb>che ui trouareti regola generale, o uer particolare alla reſolutione di ſimili queſiti.<emph.end type="italics"></emph.end><lb></lb>E <emph type="italics"></emph>per tanto dicoche la detta quantita ſe puo conchiudere in infiniti modi per eſſer l'o<lb></lb>perante in liberta de eguagliarſe à che numero li piace, nondimeno io mi uoglio egua<lb></lb>gliar à.2888.perche la coſa miuerra un reſiduo ſimplice, onde la detta quantita ue<lb></lb>nira à eſſer.78.men<emph.end type="italics"></emph.end> <22>.308.<emph type="italics"></emph>la radice della quale uien à eſſer<emph.end type="italics"></emph.end> <22>.77.<emph type="italics"></emph>men.1.aggiongen<lb></lb>doli.40.fara.39.piu<emph.end type="italics"></emph.end> <22>.77.<emph type="italics"></emph>qual moltiplicata fia la detta quantita, cioe fia.78.men<emph.end type="italics"></emph.end><lb></lb><22>.308.<emph type="italics"></emph>fara preciſe.2888.che il propoſito.<emph.end type="italics"></emph.end> M.Z. </s> <s id="s.002318">A <emph type="italics"></emph>che fin gli proponeſti la coſa <lb></lb>tanto larga di poterſi eguagliar à che numero li pareſſe, pur che deſſe la coſa irra<lb></lb>tionale.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o il fece per due cauſe. </s> <s id="s.002319">La prima fu, che ſe per caſo lui haueſſe hauuto <lb></lb>opinione, che io non haueſſe ſaputo riſoluere tal capitolo, eſſendo tal queſito ſotto coſi <lb></lb>larga forma, ſempre mi poſſo eguagliar à tal numero, che il ualor della coſa me ueni<lb></lb>ra un ſimplice reſiduo, come di ſopra haueti uiſto, che la coſa ualſe<emph.end type="italics"></emph.end> <22>.77.<emph type="italics"></emph>men.1.il qual <lb></lb>reſiduo è una quantita facile da maneggiar, per poterne far la proua alla improuiſa, il <lb></lb>che non accade coſi facile in altre ſue equationi. </s> <s id="s.002320">La ſeconda fu, che per tal riſolutione, <lb></lb>non ſi puo coſi facilmente apprendere la regola generale da riſoluere ſimili capitoli, <lb></lb>come ſe apprendaria, quando che tal riſolutione ueniſſe da.4.ouer.5.nomi.<emph.end type="italics"></emph.end> M.Z. </s> <s id="s.002321">E <lb></lb><emph type="italics"></emph>ue ho inteſo. </s> <s id="s.002322">Hor ſe hauesti qualche altra bella ragione da darmi, mi fareti à piacere.<emph.end type="italics"></emph.end><lb></lb>N. I<emph type="italics"></emph>o ue ne uoglio dar una quala mi fu propoſta gia fa.4.meſi, in San zuanepolo, <lb></lb>iſponendo io la.13.propoſitione del.13.di Euclide, qual dice in queſta forma. </s> <s id="s.002323">Eglie una <lb></lb>uerga, che peſa ſaggi.10.di oro, qual tien di argento la Radice cuba de.10.& ual duc. <lb></lb></s> <s id="s.002324">10.Et eglie anchora un'altra uerga, qual peſa altri ſaggi.10.pur di oro, qual tien di ar <lb></lb>gento la Radice quadra de.10.& alla proportione del primo queſto ual ſolamente du <lb></lb>cati. </s> <s id="s.002325">9.ſe adimanda che ualſe il ſaggio del oro puro, & ſimilmente quello dell'argento <lb></lb>puro.<emph.end type="italics"></emph.end> M.Z. Q<emph type="italics"></emph>ueſta mi pare aſſai bella queſtione. </s> <s id="s.002326">Hora ue uoglio laſſare, come ſia <lb></lb>gionto à Breſſa ue ſcriuero, me arricomando.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>ndati in buon'hora, arricoman<lb></lb>datemi à Meſſer Pre Antonio da Cellatica.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="109" xlink:href="042/01/218.jpg"></pb> <p type="head"> <s id="s.002327">QVESITO XXVII. FATTO DA M. HIERONI<lb></lb><emph type="italics"></emph>mo Treuiſano.1536.adi.16. Decembrio in Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002328">MESSER HIERONIMO. E<emph type="italics"></emph>ue ho da dir de nouo.<emph.end type="italics"></emph.end> N. C<emph type="italics"></emph>he coſa ui é <lb></lb>accaduto meſſer Hieronimo.<emph.end type="italics"></emph.end> M. H. H<emph type="italics"></emph>ieri el mi fu à ritrouar un certo <expan abbr="grã">gram</expan> <lb></lb>don, qual dice eſſer anchora lui Breſſano, el qual ſi fa molto piu grande nelle mathema <lb></lb>tice di quello ch'è la grandezza della ſua perſona, et fra le altre coſe gli ho uoluto dir <lb></lb>di uoi, & come che haueti letto publicamente il terzodecimo di Euclide in ſan Zuanne <lb></lb>polo. </s> <s id="s.002329">Lui me ha riſpoſto che uoi haueti letto el detto.13.libro & che non intendeti <lb></lb>il decimo. </s> <s id="s.002330">Et chel non conoſce huomo, che ben intenda el detto decimo di Euclide ac<lb></lb>cetto che lui.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>glie ben stato qua da me due uolte & è andato uia per fin da hie <lb></lb>ri alla uolta de Breſſa, ma el mi dole che uoi non mi habbiati rifferto queſta ſua bra<lb></lb>uata auanti che lui ſe fuſſe partito perche gli hauria dato quella debbita riſpoſta che <lb></lb>à tal ſua arrogantia ſi conuenia. </s> <s id="s.002331">Et al preſente mi auedo che lui era uenuto qua per <lb></lb>uenire con meco alle conteſe, ma lui per quanto poſſo conſiderare) ſe ha meſſo paura di <lb></lb>quella mia inuentioni de capitoli Algebratici quali mi ricer caua con tanta iſtantia.<emph.end type="italics"></emph.end> M. <lb></lb>H. A<emph type="italics"></emph>dunque le ſtato qua da uoi à ricercarue de quelli uoſtri noui capitoli trouati.<emph.end type="italics"></emph.end> N. <lb></lb>E<emph type="italics"></emph>l cie stato due uolte.<emph.end type="italics"></emph.end> M. H. E<emph type="italics"></emph>t che glihaueti riſposto.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o gli ho riſpoſto che <lb></lb>ogni uolta che lui proponerauno, ouer piu caſi che io non li ſappia riſoluere mi offe<lb></lb>riſco à baratar con lui. </s> <s id="s.002332">Et coſi lui me ne proponete dui, ma io gli dißi, che tai ſuoi ca<lb></lb>ſt io li haueua per coſa facile & che ſe lui mi daſeua termine una hora che io me gli of<lb></lb>ferriua à dargeli ambidui raſolti.<emph.end type="italics"></emph.end> M. H. E<emph type="italics"></emph>t come dicano quelli caſi.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>l pri<lb></lb>mo dice in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002333"><gap></gap>E<emph type="italics"></emph>glie il triangolo rettangolo.a.b.c.del quale langolo.e.é retto & nel detto triango <lb></lb>lo ui è in ſcritto il cerchio.e.f.d. </s> <s id="s.002334">il cui diametro è.2. & trouo che la linea.a.c.gionta <lb></lb>con la.c.b.tal ſumma ſara ſempre equal alla lmea.a.b. </s> <s id="s.002335">gionta con el diametro del cer<lb></lb><gap></gap>hio, qual (come detto) è.2.ſe adimanda la cauſa di queſto.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.218.1.jpg" xlink:href="042/01/218/1.jpg"></figure> <p type="main"> <s id="s.002336">M. H. L<emph type="italics"></emph>a me par difficile.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci la è facilißima & il tutto ſi conclude & di<lb></lb>moſtra per la penultima del terzo di Euelide per la qual ſe uerifica le due linee.a.e. <lb></lb></s> <s id="s.002337">&.a.d.eſſer fra loro equale, & ſimelmente le due.b.d.&.b.f.eſſer pur fra loro equa<lb></lb>le & ſimelmente le due.c.e.&.c.f.& queſte due ultime, cioe.c.e.et.c.f.non <expan abbr="ſolamẽte">ſolamente</expan> <lb></lb>ſono ſra loro equale, ma per eſſer l'angolo.c. </s> <s id="s.002338">retto cadauna de loro uien a eſſer equale<emph.end type="italics"></emph.end><pb xlink:href="042/01/219.jpg"></pb><emph type="italics"></emph>alla mita del diametro del detto cerchio tal che ambedue inſieme uerano à eſſere equa <lb></lb>le à tutto il diametro del detto cerchio, onde per concludere tal queſito arguiremo in <lb></lb>queſto modo, per eſſer la partial linea.a.e.equale alla partial.a.d.& ſimelmente la <lb></lb>partial.b.f.eſſer equale alla partial.b.d.ſeguita che le due partiale linee.a.e.&.b.f. <lb></lb></s> <s id="s.002339">eſſer equale à tutta la linea.a.b.onde aggiongendo da luna è laltra banda equalmente <lb></lb>el diametro del detto cerchio (per comunaſententia) le dette due ſumme ſaranno an<lb></lb>chora equale, & perche le due linee.c.e.&.c.f.(come di ſopra fu detto) ſono equale <lb></lb>à tutto il diametro del detto cerchio, ſeguita adunque che le due linee.a.c.&.c.b.ſia<lb></lb>no equale alla linea.a.b.gionta con el diametro del detto cerchio ch'è il propoſito.<emph.end type="italics"></emph.end> M. <lb></lb>H. S<emph type="italics"></emph>ta bene. </s> <s id="s.002340">Hor ditime un puoco l'altra.<emph.end type="italics"></emph.end> N. L'<emph type="italics"></emph>altra dice in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002341">E<emph type="italics"></emph>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 ſua <lb></lb>perpendicolare è la.a.d. </s> <s id="s.002345">& da l'angolo.b.tiro la linea.b.f.e.la qual ſegha dalla linea. <lb></lb></s> <s id="s.002346">a.d.la.f.d.la qual è. </s> <s id="s.002347">3. ſe adimanda la quantita delle due parti.a.e.&.e.c.<emph.end type="italics"></emph.end></s> </p> <figure id="id.042.01.219.1.jpg" xlink:href="042/01/219/1.jpg"></figure> <p type="main"> <s id="s.002348">M. H. Q<emph type="italics"></emph>ueſto mipar piu difficile, di l'altro.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci ch'eglie aſſai piu facile, per <lb></lb>che ſe dal ponto.c.ſia tirata la.c.h.equidiſtante alla perpendicolar.a.d.& che ſia slon <lb></lb>gata la linea.b.e.per fina à tanto che quella ſeghila.c.h.in ponto.g. </s> <s id="s.002349">Et perche (per la. <lb></lb></s> <s id="s.002350">13. del ſecondo di Euclide) la perpendicolare.a.d.uien à eſſer. </s> <s id="s.002351">12. & la linea.b.d.uien <lb></lb>à eſſer. </s> <s id="s.002352">5. Et perche (per laſeconda del ſeſto di Euclide) la proportione della.g.c.à tut <lb></lb>ta la.b.c. (quala è. </s> <s id="s.002353">14. ) è ſi 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></lb>onde la.c.g.ueneria ad eſſer.<emph.end type="italics"></emph.end> 8. 2/5. E<emph type="italics"></emph>t perche il triangolo.f.a.e.éſimile al triangolo.g. <lb></lb></s> <s id="s.002356">e.c. (per eſſer fra linee <expan abbr="equidiſtãte">equidiſtante</expan>) la proportione del lato.a.f. (qual è. </s> <s id="s.002357">9. al lato.g.c <lb></lb>(qual è. </s> <s id="s.002358">8. 2/5. ſara ſi come quella dalla.a.e.alla.e.c.& (per la. </s> <s id="s.002359">18. del quinto di Euclide) <lb></lb>la proportione del conglonto della.a.f.&.g.c. (qual congionto ſaria. </s> <s id="s.002360">17. 2/5. )alla.g.c. <lb></lb>(qual é. </s> <s id="s.002361">8. 2/5. )ſara ſi come la proportione del congionto della.a.e.et.e.c. (qual è.<emph.end type="italics"></emph.end> 15.) <emph type="italics"></emph>alla.e.c. </s> <s id="s.002362">Onde procedendo per laregola ſe trouara la.c.c.eſſer. </s> <s id="s.002363">7. 7/29. & la.a.e.il re<lb></lb>ſtante per fin in. </s> <s id="s.002364">15. che ſaria. </s> <s id="s.002365">7. 22/29. ch'é il propoſito.<emph.end type="italics"></emph.end> M. H. L<emph type="italics"></emph>a non è ſtata tanto <lb></lb>difficile, come che mi penſaua. </s> <s id="s.002366">Ma diteme non gliuoleti mandar queſte uoſtre due re <lb></lb>ſolutioni acc io ch'el non ſi creda che uoi non li habbiate ſaputeriſſoluere.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci <lb></lb>non uoglio mandaruene alcuna. </s> <s id="s.002367">Perche comprendo che lui ha animo di uoler ueniro <lb></lb>ud habitar qua, & me ha promeſſo de ritornar fra pochi giornie pero non lo uoglio<emph.end type="italics"></emph.end><pb pagenum="110" xlink:href="042/01/220.jpg"></pb><emph type="italics"></emph>deſinanimare, perche non dandoui riſpoſta lui ſi penſara che io <expan abbr="nõ">non</expan> li ſappia reſſoluere, <lb></lb>& non ſe deffidara del uenire & uenendoui ui uoglio lauar il capo d'altro che di ſapo<lb></lb>ne, uſando pero termini, ouer parole non con conueniente, come che ſo che lui haue<lb></lb>ria fatto quando che lui non ſi fuſſe ſpaurito per quelle mie inaentioni de capitoli, anci <lb></lb>ſon certo che lui me ſcriuera, & me mandara qualche altro queſlto per meglio taſtar <lb></lb>me, ma de niuno non li uoglio dar riſpoſta.<emph.end type="italics"></emph.end> M. H. E<emph type="italics"></emph>ue ho inteſo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002368">QVESITO. XXVIII. FATTO DA M. ZV ANNE <lb></lb><emph type="italics"></emph>di Tonini da Coi con una ſua lettera quale me portò Bene<lb></lb>detto caualaro l'anno. </s> <s id="s.002369">1537. adi. </s> <s id="s.002370">8. Genaro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002371">MAESTRO ZV ANNE. Q<emph type="italics"></emph>uando da uoi mi ſcomiai Meſſer Nicolo ca<lb></lb>rißimo, uoi ſapete ch'io ui dißi che ſcritto ue harrei, & hora per pagar el de<lb></lb>bito che in cio teneua con uoihouui la preſente ſcritta. </s> <s id="s.002372">Nellaqual primieramente ui <lb></lb>ſcriuo la reſolution (ſe io non ſono errato) di quella domanda, che dice eglie una uer<lb></lb>zella di oro qual peſa ſaggi. </s> <s id="s.002373">10. & tien di argento la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba di. </s> <s id="s.002374">10. & ual duc. </s> <s id="s.002375">10. & <lb></lb>eglie anchora un'altra uerga pur di oro che peſa pur ſaggi. </s> <s id="s.002376">10. & tien di argento la <lb></lb>Radice quadra de. </s> <s id="s.002377">10. & alla proportion del primo ual ſolamente duc. </s> <s id="s.002378">9. ſe adiman<lb></lb>da che ualſe el ſaggio del oro puro & ſimelmente quello del argento puro. </s> <s id="s.002379">Io ue dico <lb></lb>cheloro della primaual<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua. </s> <s id="s.002380">1000. piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.002381">72. 9/10. <expan abbr="mẽ">men</expan><emph.end type="italics"></emph.end> <22> <emph type="italics"></emph>cu. </s> <s id="s.002382">7290. <expan abbr="mẽ">men</expan><emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu.qua. <lb></lb></s> <s id="s.002383">100000. Et <expan abbr="l'argẽto">l'argento</expan> ual la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua. </s> <s id="s.002384">100000. men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu 7. 2. 9/10. <expan abbr="mẽ">men</expan><emph.end type="italics"></emph.end> <22> <emph type="italics"></emph>cuba. </s> <s id="s.002385">10 <lb></lb>Et quella che tìen di argento la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua.di. </s> <s id="s.002386">10. l'oro ual<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua. </s> <s id="s.002387">1000. men. </s> <s id="s.002388">10. men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. <lb></lb></s> <s id="s.002389">7290. piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua.de<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu.<emph.end type="italics"></emph.end> 53144100000/7000000. E<emph type="italics"></emph>t l'argento ual. </s> <s id="s.002390">10. men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua. </s> <s id="s.002391">de<emph.end type="italics"></emph.end><lb></lb><22>. <emph type="italics"></emph>cu'a. </s> <s id="s.002392">53144100000/1000000. men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua. </s> <s id="s.002393">10. La proua di queſta ragione è aſſai bella <lb></lb>& la coſa ual<emph.end type="italics"></emph.end> <22> 10. <emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.002394">7. 29/100. men.<emph.end type="italics"></emph.end> 1. (N. P<emph type="italics"></emph>er mia fe che costui riſponde <lb></lb>aſſaiben à propoſito.)<emph.end type="italics"></emph.end> M. Z. L'<emph type="italics"></emph>altra uoſtraragione che dice trouatime un numero <lb></lb>che ſtairrationale che multiplicato uia la ſua Radice piu. </s> <s id="s.002395">40. faccia numero rationa <lb></lb>le a trouarlo ſi dupla il. </s> <s id="s.002396">40. & del duplato ſi tra due & reſta. </s> <s id="s.002397">78. & di queſto ne ca<lb></lb>namo uno resta. </s> <s id="s.002398">77. & queſto per. </s> <s id="s.002399">4. ſe multiplica & del prodotto ſi prende la Radi<lb></lb>ce che ſara<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>qua. </s> <s id="s.002400">308. & coſi aduiene in tutti. </s> <s id="s.002401">Et perche coſi dobbiamo fare ho tro<lb></lb>uata la cagione. </s> <s id="s.002402">Et ſi diremo trouame uno numero che multiplicato per la ſua Radice <lb></lb>piu. </s> <s id="s.002403">8. faccia numero rationale. </s> <s id="s.002404">Questo ſara. </s> <s id="s.002405">14. men.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002406">52. <emph type="italics"></emph>& la ſua<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>è.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002407">13. <emph type="italics"></emph>men <lb></lb>1. Et giongendoli. </s> <s id="s.002408">8. reſtara<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002409">13. <emph type="italics"></emph>piu. </s> <s id="s.002410">7. & queſto binomio multiplicato <expan abbr="cõ">com</expan> queſto re <lb></lb>ciſo. </s> <s id="s.002411">14. men.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002412">52. <emph type="italics"></emph>fara. </s> <s id="s.002413">72. Etſe not diremo, multiplicato per la ſua Radice men. </s> <s id="s.002414">8. <lb></lb>faremo dir il. </s> <s id="s.002415">52. piu.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002416">H<emph type="italics"></emph>ora ſe a uoipare di mandarme la ſolutione delle noſtre due oueramente di quelle che <lb></lb>ni trouarete hauer fatte uoi mi farete in cio tanto appiacer <expan abbr="quãto">quanto</expan> che io mi credo che <lb></lb>riceuer poteſſe giamai, maio uorrei che inſleme <expan abbr="cõloro">colloro</expan> mi mandaste queſte due etian <lb></lb>dio ſciolte delle quale la prima. </s> <s id="s.002417">Et che mi trouate tre quantita continue proportio<lb></lb>nale, che la maggiore ſia. </s> <s id="s.002418">700. & il prodotto delle due menore luna in l'altra multi<lb></lb>plicato in ſe produca<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.002419">10000. La ſeconda queſtione che io uorrei che uci fo <lb></lb>ste contento ditrouar una quantita che multiplicata in ſe & il produtto multiplicato<emph.end type="italics"></emph.end><pb xlink:href="042/01/221.jpg"></pb><emph type="italics"></emph>anchora per la detta quantita, & al prodotto giontoui la inuenta quantita faccia. </s> <s id="s.002420">8. <lb></lb>in queſta domanda <expan abbr="uolẽdo">uolendo</expan> noi adoperar lalgebra per trouarla, poneremo questa quan <lb></lb>tita eſſer una coſa, laqual multiplicata in ſe fara uno cenſo & queſto cenſo multiplica <lb></lb>to per una coſa fara uno cubo, & à queſto cubo aggiungerli la coſa che prima noi po<lb></lb>neßimo haueremo un cubo & una coſa equal al numero. </s> <s id="s.002421">8. Quando io ui domandai <lb></lb>meſſer Nicolo che una domanda di queſta manier a mi deſti fatta. </s> <s id="s.002422">Parmiche poco ſa<lb></lb>uiamente faceſti quando uoi del tutto à me la negaſti <expan abbr="hauẽdomi">hauendomi</expan> (<expan abbr="quãdo">quando</expan> à trouar la pri <lb></lb>ma uolta ui uenni) moſtrata tanta beniuolenza. </s> <s id="s.002423">Et uſandomi quella amicheuole cor<lb></lb>teſia, che uoi miuſaſte à farmi quella ſera quaſi per uiua forza uenir à cena con uoi. <lb></lb></s> <s id="s.002424">Ma dapoiche mi haueſti uſata quell'altra corteſia nouamente in darmi quella aſſo<gap></gap><lb></lb>che ſapeti (de cenſo è cubo equal à numero) mi parue che'l error, che fatto haueuate <lb></lb>in non uolermi quell'altra, che ui adimandai ſoluere, quaſi in tutto emendato haueste, <lb></lb>& perche di legiero uoipotreſti dire, per qual cagione, uoiſauiamente non ragionaſt<lb></lb>all'hora che mi negaſte di non uoler quella domanda ſoluere piacemi in queſta charta <lb></lb>al preſente dinarraruela in bona parte, uoiſapete meſſer Nicolo che <expan abbr="incontanẽte">incontanente</expan> che <lb></lb><gap></gap>o ui domandai quel caſo uoi me diceſti, che le inuentioni ſono difficile, & lo aggiun<lb></lb>gergliè coſa facile, & che per eſſerui molto affaticato per ritrouare tale, & tai capi<lb></lb>toli, chel non ui pareua coſa molto licita à douerli coſt facilmente publicare à ognipar <lb></lb>ticolar perſona, & maßime doue non ue ne reuſiſca alcunbonore, ne utilita, & per <lb></lb>tanto dico che il tener caro quello che in uoi ſolo non è ne pur di uoſtri amici, <expan abbr="manife-ſtamẽte">manife<lb></lb>ſtamente</expan> à ogn'uno ui paleſate di hauerne grandißima caraſtia, laqualcoſa eſſendo io <lb></lb>della <expan abbr="pfeßiõe">pfeßione</expan> uoſtra auoi laſſo il giudicio qual è piu, ò il biaſmo ò l'honor che ne porta <lb></lb>te, & ſe premio di cio cercate & <expan abbr="nõ">non</expan> honore parmi che quello debba eſſer pochißimo, et <lb></lb>miſerißimo, eſſendo uero quello che me fureferto, (come <expan abbr="ueramẽte">ueramente</expan> <expan abbr="tẽgo">tengo</expan> che ſia) che <lb></lb>30. caſi, ouer queſiti di queſta ſorte in due hore dauoierano ſtati aſſolti à maeſtro Gio <lb></lb>uanantonio Maria fior uoſtro riuallo, parmi che farebbestato il premio aſſai graſſo <lb></lb>bauendoui dato ſoldi. </s> <s id="s.002425">5. per ciaſcun deßi, ma ſe forſe uoleſti dire che non tanto é il pre <lb></lb>mio che domandate della fatica quanto è quello della inuentione, et del modo da ſoluer <lb></lb>gliſecreto, il che non ſi puo con uerita dire che il modo ſia ſecreto, ne etiandio che la ſia <lb></lb>propria inuentione ſapendolo nanti il uoſtro aduerſario. </s> <s id="s.002426">Hor ſe uogliamo dir della <lb></lb>muentione, non ſapeti uoi che ſolamente le prime inuentioni ſono lodate & premiate <lb></lb>da color che ſanno, & che premio & che loda uoreſti uoi che meritaſſe un huomo che <lb></lb>mai non haueſſe da niuno apparata Geometria, ne mai haueſſe ueduto Euclide, & che <lb></lb>daſe ſteſſo ne componeſſe uno, nel qual tutte quelle coſe diceſſe, chel detto autor ha<lb></lb>dette nel ſuo. </s> <s id="s.002427">Io non ſo gia con tutto queſto che loda potreſti dar à coſtui, ne che pre<lb></lb>mio, ma uolendolo incio biaſimare à uoi ſarebbe ageuolißimo, conſiderando che egli <lb></lb>haueſſe gettato uia tutto il tempo della ſuauita in coſe che de niente non foſſero, ne ſa<lb></lb>rebbe mai gioueueuole à niun <expan abbr="uiuẽte">uiuente</expan>, et ſe à uoi era di meſtiero per eſſeruimeſſo à con <lb></lb>tendere <expan abbr="cõ">com</expan> quel maeſtro che <21> inſegna tenea le corone, o da ſoluer li oda reſtar in <expan abbr="grã">gram</expan> <lb></lb>parte ſuergognato appreſſo aluolgo, <expan abbr="nõ">non</expan> gia appreſſo à gli huomini, dotti et <expan abbr="intelligẽti">intelligenti</expan> <lb></lb>di queſte ſcientie, baſtaui adunque per premio della fatica che uoi hauete fatta in tro<lb></lb>uar la <expan abbr="inuẽtione">inuentione</expan> da ſoluerei detti. </s> <s id="s.002428">30. caſi, l'honor & fauor, che per lei haueti hauuto<emph.end type="italics"></emph.end><pb pagenum="111" xlink:href="042/01/222.jpg"></pb><emph type="italics"></emph>in far quelmaeſtro reſtar uinto, & ſuperato da uoi. </s> <s id="s.002429">Et che il fuſſe ben fatto per trarne <lb></lb>premio, ouer honore à far queſte coſe stampare, come uoi me diceſti, non eſſendo coſe <lb></lb>quaſi in parte alcuna gioueuoli al mondo, io tengo fermamente, che niuno che diritta<lb></lb>mente giudichi non lo eſtimera giamai. </s> <s id="s.002430">Et che ſtara in penſiero, che di quegli non ſi tro<lb></lb>uino, che diranno, che per la uilta, & maluagita dell'animo uostro, non ui cur ate di pia <lb></lb>cere à glihuomini, ne in gentilezza, ne in beniuolenza, ne in corteſia alcuna, queſta uil <lb></lb>ta non credo, ne credero di leggeri, che in uoi alberghi, ne albergar poſſa giamai per <lb></lb>hauerui conoſciuto pieno d'amoreuolezza, pieno di gentilezza, pieno di lealta, pieno <lb></lb>di corteſia, & in fine pieno d'ogni honeſta, & gentil conuerſatione, per ilche io non ſto <lb></lb>in dubbio, che uoi diciate, che io me affatichi à trouare il modo da ſoluerle, ſi come uoi <lb></lb>anchor a haueti fatto, & quando pur diceſti queſto, queſta fatica non uoglio, ne debbo <lb></lb>farla per fuggir quel biaſmo, che ſi darebbe à colui, che una opera ſimile à quella di Eu <lb></lb>clide, componeſſe nuouamente, & ſe pur miueniſſe talento di far qualche fatica d'in<lb></lb>torno à una ſimil coſa, io la farei in biaſmare, & uituperare la mente uile, & maluag<lb></lb>gia di colui, che una tanta aſinaria uſaſſe, perche ſei dotti huomini per adictro ſtai, que <lb></lb>ſto haueſſero oſſeruato, ne Euclide, ne tanti altri dignißimi autori hoggi da niun uiuen <lb></lb>te non ſarebbono conoſciuti. </s> <s id="s.002431">Hora non ſo gia à che altro ui uogliate ne poßiate tenere <lb></lb>di non eſſer in cio altro, che liberale, ſe forſe non uoleſte dire, che ſe à uoi fuſſe di me<lb></lb>ſtieri di contendere con un'altro maeſtro di cio uiſeruireſti, ilche appena mi ſt laſſacre <lb></lb>dere, che uoi pur il penſate, perche ſe uoi conſiderate, che queſto modo per il quale ſi <lb></lb>ſoluono queſta maniera de domande non è ſaputo da uoi ſolamente, maetiandio è ſtato <lb></lb>inanzi da uoi ſaputo da colui, che malui uole, & non credete uoi, che ſe egliſapeſſe, che <lb></lb>uoi contendeſti, ch'egli ſi ingegnarebbe di dare ogni aiuto à uoſtri auerſarij, che per lui <lb></lb>ſi poteſſe il maggiore, & non che premio di cio à lor domandaſſe, magli pregarebbe <lb></lb>che ne di lui ne delſuo hauere in cio ponto non lo ſparmiaſſe per tentare di uendicarſe <lb></lb>della uergogna, & dishonore, che uoi gli haueti fatto, & ſi cio maeſtro Nicolo non cre <lb></lb>dete mal credete, & che uolete che altro d'intorno à queſta materia ui ſcriua, di cio che <lb></lb>maeſtro Antoniomaria Fior mi offerſi (ſi come ſaggio) di darmi una di quelle. </s> <s id="s.002432">30. do<lb></lb>mande che à lui ſoluesti, ma per che tanto piu mi piace la uoſtra amicitia della ſue quan <lb></lb>to che è la uostra uirtu della ſua maggiore. </s> <s id="s.002433">Et anche per eſſer della patria, io mi uenni <lb></lb>prima à trouarui uoi, & con quella instantia ue gli domandai che uoi iſteſſo ſapete, & <lb></lb>perche uoi mi deſti quello uoſtro caſo aſſolto che ſapeti, io non uolſi ritornar piu da lui <lb></lb>à richiederglilo per non obligarmegli altrimente, & perche anchora mi diceſti all'ho<lb></lb>ra cheſe io ue ne daua à uoi alcuni che non ſapeſti riſoluere, che altritanti ne daresti à <lb></lb>me, quanto all'hora il uostro parlar mi piacque, io non uel potrei dire di qui à un'anno <lb></lb>compiutamente, matanto in cio ſolamente ui dico, che adueniſſe (ch'io non m'il credo) <lb></lb>che uoi non haueſte tanti caſi coſi accommodati da mandarmi, quanti nell'animo ne ha<lb></lb>ueſti di domandarmene. </s> <s id="s.002434">Non uoglio percio che in parte alcuna ui retignate di non chie <lb></lb>dere tutti quelli, che nel uoſtro animo ui ſcorgeſſe di chiedermi. </s> <s id="s.002435">Et non ſolamente caſt, <lb></lb>maogn'altra coſa che ui piaccia, che in balia ſta dime, io coſiuolontieri, per uoi meſſer <lb></lb>Nicolo quanto che per ciaſcuno buomo che uiua lo faro certamente. </s> <s id="s.002436">Horauenendo al <lb></lb>fine di queſta ſcrittura, la qual per la maggior parte d'altro non ragiona (come uoi uc-<pb xlink:href="042/01/223.jpg"></pb>der poteti) che di quel capitolo di coſa, & cubo, egual à numero, moſtrando che à me <lb></lb>nou fia diſdiceuole il chiederuelo, ne il concederlo mi à uoi, altreſi, & ſe in lei trouare<lb></lb>te aggionta alcuna uoce, & de altre in tutto caſſe, & altre in tutto mutate, questiſono <lb></lb>gli inditij, che lei dimoſtrino eſſer ſtata ſcritta diſcontiamente, & benche io acconcio, <lb></lb>& adaggiato ſia non ſcriua bene, non dico giai caratteri, che cura alcuna in eßi non <lb></lb>ho poſta, come uoi ſteſſo ueder potete, ma dico nel ſtile, & per cio ſe in lei trouaſte uo<lb></lb>ce, che ui ſpiaceſſero, uaglia il perdonare, che ſe mailettra fu diſconciamente ſcritta, <lb></lb>credo che queſta ſia una d'eſſe, dico diſconciamente per hauerla ſcritta in cinque gior<lb></lb>ni, hora in un luoco, hora in un'altro, & di cio ne potrebbe eſſer buon teſtimonio mae <lb></lb>ſtro Battista, che ſtaua in caſa del Conte Nicolo de Lodron, il quale. </s> <s id="s.002437">& io altreſi à uoi <lb></lb>molto ſe aricomandiamo, & uorrei che al Frate, che ſta in Fricciaria me aricomanda<lb></lb>ſti, ma primieramente uorrei, che letta che harete la lettra, che incontanente notaſti i <lb></lb>caſi, che all hora all'hora piu ageuolmente uoi potrete, ma per mio contento piacciaui <lb></lb>di notar per il primo quello di coſa, è cubo, egual à numero, & all'hora all hora man<lb></lb>darmeli ſel fuſſe poßibile uia piu che digaloppo, & c. à. </s> <s id="s.002438">5. di Genaro.<emph.end type="italics"></emph.end> 1537. </s> </p> <p type="main"> <s id="s.002439">G<emph type="italics"></emph>iouanni di Tonini uostro à guiſa di buon fratello.<emph.end type="italics"></emph.end><lb></lb>NICOLO. Q<emph type="italics"></emph>ueſta ſua gran retorica non uoglio che habbia riſpoſta da me. </s> <s id="s.002440">Ma pur <lb></lb>uoglio conſiderar queſto ſuo queſito, nel qual lui uole, che io gli troui tre quantita con <lb></lb>tinue proportionale, che la maggior ſia. </s> <s id="s.002441">700. & che il produtto delle due menore, l'u <lb></lb>na fia l'altra, moltiplicato poi in ſe medeſimo produca la Radice cuba de. </s> <s id="s.002442">10000. <lb></lb>Qual credo, che ſia facile, uero è, che per riſoluerlo biſogna notar, che moltiplicando <lb></lb>la prima ditre quantita continue proportionale fia la ſ<17>conda, & quel produtto fia la <lb></lb>terza, quell'ultimo produtto ſempre ſara eguale al cubo della ſeconda, e per tunto ſe il <lb></lb>quadrato delle due menore l una fia l'altra fanno<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.002443">10000. adunque il puro pro <lb></lb>dutto fu la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>quadra della<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de. </s> <s id="s.002444">10000. cioe il fu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.002445">100. & queſto molti<lb></lb>plicandolo fia la terza, che ſu.<emph.end type="italics"></emph.end> 700. (<emph type="italics"></emph>cubando prima.<emph.end type="italics"></emph.end> 700.) <emph type="italics"></emph>fara<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.002446">34300000000. <lb></lb>& la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba di questo produtto ſara lo ſecondo termine, cioe<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. <lb></lb></s> <s id="s.002447">34300000000. Hor per trouar il primo termine quadro il ſecondo, cioe<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de<emph.end type="italics"></emph.end> <22>. <lb></lb><emph type="italics"></emph>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></lb>cando. </s> <s id="s.002450">700. à cubo de cubo) ne uenira<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.002451">117049/4035360700. & que<lb></lb>ſto ſara il primo termme, che è il propoſito.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002452">QVESITO. XXIX. FATTO DAL MEDESIMO <lb></lb>M<emph type="italics"></emph>eſſer Zuane de Tonini da Coi, con una ſua lettera alli. </s> <s id="s.002453">17. <lb></lb>di Febraro. </s> <s id="s.002454">1537. In Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002455">MESSER ZVANE. M<emph type="italics"></emph>eſſer Nicolo il me ha detto Benedetto cauallaro, <lb></lb>che uoi haueti hauuta la noſtra lettera, & che gli hauete detto, che uoi me ha<lb></lb>ueti à cio riſpoſto, ilche à me pare molto duro à douerlo credere, conſiderando ch'egli <lb></lb>è meſſo molto da fidarſe, & che all'uno, & a l'altro di noi ſerue uolontieri. </s> <s id="s.002456">Et che non <lb></lb>mi hauete uoluto per lui mandar mi lettra niuna la, onde non ſto gia in penſiero, che <lb></lb>uoi reſtar non doueuate, perche ui mancaſſe la carta, o per non ſaper ſcriuere, o per<emph.end type="italics"></emph.end><pb pagenum="112" xlink:href="042/01/224.jpg"></pb><emph type="italics"></emph>fuggir la fatica (che cio uoſtro coſtume non é) o per non ſapere con belli carattere <lb></lb>ſcriuermi, perche io coſi habbia ſcritto à uoi, che cio non è ſtato uſato da me in parte <lb></lb>ueruna à uoi. </s> <s id="s.002457">Ma ſolamente ſto in penſiero che uoi reſtate, o per il ſcriuermi Toſcana<lb></lb>mente, o per non uolermi mandar quel caſo ſciolto de coſa, & cubo egual à numero, <lb></lb>qual con tanta inſtanza ui ho adimandato. </s> <s id="s.002458">Io non aſpetto, che Toſcanamente mi ſcri<lb></lb>uiate, ne etiandio che mi mandate quel caſo ſe à uoi non ui piace. </s> <s id="s.002459">Ma ben di cio ui pre<lb></lb>go che ui uogliati degnar di ſcriuermi o poco, o aſſai, che ui piaccia, & ſe cio meſſer <lb></lb>Nicolo non fate io tenero per fermo, che uoi poca ſtima fareti di me, & della mia <lb></lb>amicitia, alli. </s> <s id="s.002460">14. Febraro.<emph.end type="italics"></emph.end> 1537. </s> </p> <p type="main"> <s id="s.002461">G<emph type="italics"></emph>iouanni di Tonini uoſtro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002462">NICOLO. M<emph type="italics"></emph>eſſer Zuane ho riceuuto due uoſtre, & hoggi un'altra, che ſono tre <lb></lb>delle quale le due ultime ſono ſolamente ammonitorie, che ui debbia dar riſposta alla <lb></lb>prima uoſtra, uer amente haueua deliberato, che ſolamente il mio tacere ui fuſſe riſpo<lb></lb>sta per molte ragioni, la prima è, che uolendo dar particolar riſpoſta à ogni uoſtra ri<lb></lb>chieſta, & ragioni da uoi allegate, biſognaria ſcriuere un quinterno di carta, ilche le <lb></lb>occupationi diurne, & notturne, non mel conciedono. </s> <s id="s.002463">La ſeconda è, che dapoi la parti<lb></lb>ta uoſtra da Venetia meſſer Hieronimo Triuiſano, & anchora quel maeſtro Dominico <lb></lb>da Vderzo (che mi portò quelle uoſtre.3.dimande) me hanno riferto tante uoſtre bra <lb></lb>uate, che longo ſaria à narrarle, ma molto mi dolſe con cadauno de loro, perche non mi <lb></lb>feceno intendere tal coſe auanti la partita uoſtra. </s> <s id="s.002464">Che haueria fatto qualche ſperien<lb></lb>tia diuoi, & uoi di me, & comprendo che uoi eriuenuto à poſta per tal effetto, ma ue <lb></lb>temeſti per quelli capitoli da me trouati, li quali me ricercati con tanta inſtantia, alla <lb></lb>qual richieſta breuiter riſpondo, che hauendoui dato aſſolto quello de cenſo, e cubo <lb></lb>egual à numero (per mia gentilezza) ue douereſti alquanto arroßire à richiedermi <lb></lb>anchora quell'altro, eſſendo quell'buomo, che ue teneti, & maßime hauendoui fatto <lb></lb>quella oblatione, che ogni uolta che me proponereti un caſo, & che il non ſappia ri<lb></lb>ſoluere di barattar conuoi, la qual offerta non è poco à offerire una coſa generale per <lb></lb>una particolare, ilche mi fa credere uoi non eſſere quello, che mi credeua, non baſtan<lb></lb>doui l'animo di componere un caſo, ouer queſito, che io non lo ſappia riſoluere, ma per <lb></lb>che non uoglio, che fati piu ſperientia di me, ne che piu me tediate con uoſtre dimande, <lb></lb>ouer queſiti, uoglio annullar tal oblatione, perche mi biſogna attendere ad altro, che <lb></lb>ſtar tutto il giorno aſſoluere uoſtri queſiti ſenza alcun frutto, ne honore, ne ancho<lb></lb>ra ue uoglio dar tal caſo aſſolto, per gentilezza, eſſendo di poco ualore appreſſo di <lb></lb>uoi, perche poca ſaria la mia gentilezza, eſſendo ſtimato da uoi ſoldi cinque per caſo, <lb></lb>che in uero piu non ualeria, premiandomi, come ſe fanno gli facchini, ouer manuali, <lb></lb>che lauorano à tanto al giorno, la qual propoſta è molto ridicoloſa appreſſo de ogni <lb></lb>intelligente. </s> <s id="s.002465">Et perche diceti (per calonniar tal mia inuentione) che ſolamente le pri<lb></lb>me inuentioni ſono laudate appreſſo di color, che ſanno, & che tal mia inuentione non <lb></lb>è propria inuentione, ſapendola il mio auerſario auanti di me. </s> <s id="s.002466">Et che poca laude meri<lb></lb>taria un'huomo, che mai haueſſe imparato Geometria, ne mai haueſſe ueduto Eucli<lb></lb>de, & che da ſeiſieſſo componeſſe un'altra opera ſimile à quella di Euclide, ma uo<lb></lb>lendolo in cio biaſimare ſarebbe ageuolißimo, conſiderando che egli haueſſe gettato <pb xlink:href="042/01/225.jpg"></pb>uia tutto il tempo della ſua uita in coſe, che de niente fuſſero, ne ſarebben mai gioueuo <lb></lb>le à niun uiuente, circa alla prima parte riſpondo, & dico, che uoi non hauetì altra cer <lb></lb>tezza, ouer indicio, che il mio auerſario haueſſe tal ſecreto, ſaluo per hauermi coſi pro <lb></lb>posti tutti li ſuoi. </s> <s id="s.002467">30. caſi, che mi conduceuano à tal difficultoſo paſſo, la qual coſa non <lb></lb>ui fa certo, che lui haueſſe, ouer ſapeſſe tal ſecreto, perche molti ſogliono ſpeſſeuolte, <lb></lb>per confutar il ſuo auerſario proponere delle queſtioni, che loro medeſiminon le inten <lb></lb>dono, ne le ſapriano riſoluere, ſi come feſti uoi à me, quando che io ſtantiaua à Verona <lb></lb>con quelle due dimande, che mi mandaſti per Meſſer Pre Antonio. </s> <s id="s.002468">Ma ſupponendo an<lb></lb>chor che il detto mio auerſario gliſapeſſe riſoluere auanti di me, & hauendola io ritro <lb></lb>uata da me ſenza aiuto di alcun autore, la ſe puo chiamare mia propria inuentione, per <lb></lb>che circa à quell'altra parte che uoi diceti, che poca laude meritaria uno, che compo<lb></lb>neſſe daſe un'altra opera ſimile à quella di Euclide, anchor che non haueſſe mai uiſto <lb></lb>Euclide, ne imparato Geometria. </s> <s id="s.002469">Et io dico, che quando il ſi ſapeſſe di certo, lui non ha <lb></lb>uer uiſto l opera di Euclide, ne cauato da quello, ne d'altri, che meritaria mille uolte <lb></lb>piu laude di Euclide, perche non hauemo certezza, che Euclide non habbia cauato d'al <lb></lb>tri anciani di lui. </s> <s id="s.002470">Et accio che non crediati, come diceti, che ui nega tai mie inuentioni, <lb></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></lb>ſa (accadendo) me ne potria ſeruire, nientedimeno accio non penſati, che ogni mio fon<lb></lb>damento ſia in tai mie particolarita. </s> <s id="s.002472">Quando che alcuno diſideraſſe di uenire al cimen <lb></lb>to con meco, & che non haueſſe altra temenza di me, ſaluo che delli detti capitoli di co <lb></lb>ſa, e cubo egual à numero, & di cenſo è cubo egual à numero, & delli ſuoi ederenti uo<lb></lb>lendo giocare un precio condecente per un meggio ſcudo me obligaro à non propo<lb></lb>nerui caſo alcuno, che conduca l'operante in alcuno de detti capitoli, & ſuoi ederenti, <lb></lb>& lo faro ſicuro di queſto. </s> <s id="s.002473">Oltra di queſto uoi me ammonite con grande iſtantia, che <lb></lb>ui uoglia mandare quelli caſi, che mi trouo hauer riſolti de quelli, che uoi mi laſciaſti in <lb></lb>ſcritto, & di quelli che me haueti rimandati, & ſimilmente quel maeſtro Dominico, <lb></lb>che mi portò quelli altri tre uoſtri me ha riferto qualmente uoi gli feſtiuna grandißi<lb></lb>maſtantia, che doueſſe uenir à domandarme, quelli, & perche lui ui diſſe (come il ue<lb></lb>ro) che io ne haueua aſſolti dui ſubito ch'io gli hebbi riceuuti alla ſua preſentia, dice <lb></lb>che uoiue ne ridesti, come che il non ſuſſe il uero. </s> <s id="s.002474">Et perche conoſco, che queſto uoſtro <lb></lb><expan abbr="tõto">tonto</expan> proponere non è altro, che un uoler taſtarme doue ſia diſarmato, ouer mco forte, <lb></lb>per ilche ho deliberato di non uoler riſpondere ad alcuna uostra propoſta fina a tanto <lb></lb>che uoi uenereti à Venetia perſonalmente, come me prometteſti al partir uoſtro diuo <lb></lb>ler ritornare à quell'hora, poi ui daro la <expan abbr="reſolutiõe">reſolutione</expan> di quelle, che hauero ſaputo ſoluere <lb></lb>& quelle che non hauero ſaputo ſoluere me le inſignareti, pagandoue però, non altro. <lb></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"></emph.end> 1537. </s> </p> <p type="main"> <s id="s.002478">N<emph type="italics"></emph>icolo Tartaglia Briſciano.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002479">QVESITO. XXX. FATTO DA MESSER <lb></lb>H<emph type="italics"></emph>ieronimo Triuiſano, qual gliera sta fatto a lui <lb></lb>l'Anno. 1537. Adi. 25. Agoſto.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002480">I<emph type="italics"></emph>n Venetia.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="113" xlink:href="042/01/226.jpg"></pb> <p type="main"> <s id="s.002481">MESSER HIERONIMO. V<emph type="italics"></emph>orria meſſer Nicolo caro che me mostra<lb></lb>ſti à riſoluere uno queſito che mi fu datto hieri da uno mercante qual dice in <lb></lb>queſta forma. </s> <s id="s.002482">Doi fanno compagnia, el primo meſſe duc. </s> <s id="s.002483">240. e ſtette meſi. </s> <s id="s.002484">9. l'altro <lb></lb>miſſe una gioia & ſtette meſi. </s> <s id="s.002485">6. & guadagnorono duc. </s> <s id="s.002486">100. a quello della gioia gli toc <lb></lb>co fra cauedal é guadagno duc. </s> <s id="s.002487">150. domanda quanto ualſe la gioia, cioe quanto la ſu <lb></lb>apprecciata nella compagnia.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>er riſoluere questa domanda biſogna poner che <lb></lb>la gioia uaglia una coſa, & multicarla fia li meſi. </s> <s id="s.002488">6. (che ste nella compagnia el ſecon <lb></lb>do) fara. </s> <s id="s.002489">6 co. </s> <s id="s.002490">poi el ſi die multiplicar li duc. </s> <s id="s.002491">240. fia li. </s> <s id="s.002492">9. meſi (che ſtete nella compa <lb></lb>gnia el primo) fara. </s> <s id="s.002493">2160. & queſte due multiplicationi. </s> <s id="s.002494">biſogna ſumarle inſieme & <lb></lb>faranno in ſomma. </s> <s id="s.002495">6. coſe piu. </s> <s id="s.002496">2160. Dapoi biſogna procedere per la regola del tre <lb></lb>digando ſe. </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. coſe ope <lb></lb>rando ſecondo che uol la detta regola ſe trouara che guadagnariano. </s> <s id="s.002501">600. coſe eſlmi <lb></lb>de. </s> <s id="s.002502">2160. piu. </s> <s id="s.002503">6. coſe & queſto rotto ſara equal à ducati. </s> <s id="s.002504">150. men. </s> <s id="s.002505">1. coſa (cioe à quello <lb></lb>che tocco al <expan abbr="ſecõdo">ſecondo</expan> d<gap></gap> puro guadagno, cioe trattone. </s> <s id="s.002506">1. coſa che fu el ſuo capitale) onde <lb></lb>de leuando el rotto, & ſeguitando el capitolo ſe trouara la coſa ualer<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002507">78025. <emph type="italics"></emph>men. <lb></lb></s> <s id="s.002508">155. & tanto ualſe la gioia.<emph.end type="italics"></emph.end> M. H. V<emph type="italics"></emph>e ringratio.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002509">QVESITO XXXI. FATTO DA M. ZVANAN<lb></lb><emph type="italics"></emph>tonio libraro, per nome d'un meſſer Hieronimo Cardano, Medico <lb></lb>& delle Mathematice lettor publico in Milano, <lb></lb>adi. </s> <s id="s.002510">2. Genaro.<emph.end type="italics"></emph.end> 1539.</s> </p> <p type="main"> <s id="s.002511">ZVANANTONIO. M<emph type="italics"></emph>eſſer Nicolo el me ha drizzato da uoi un huomo da <lb></lb>bene Medico da Millano chiamato miſſer Hieronimo Cardano elquale é un gran <lb></lb>dißimo Mathematico, & legge publicamente Euclide li in Millano, & al preſente fa <lb></lb><gap></gap><expan abbr="tãpare">tampare</expan> una ſua oper a in la pratica di Arithmetica & Geometria & in Algebra che <lb></lb>ſara una bella coſa. </s> <s id="s.002512">Et per che egli ha inteſo uoi eſſer ſtato in una diſputa con maestro <lb></lb>Antoniomaria fiore, & che uoi romaneſti daccordo di proponere. </s> <s id="s.002513">30. caſi, ouer que <lb></lb>ſtioni, per uno, & che coſi faceſti, & ſua eccellentia ha inteſo che il detto maestro An<lb></lb>toniomaria, ui propoſe tutti li ſuoi. </s> <s id="s.002514">30. che ui conduceuano in Algebra in un capito<lb></lb>lo di coſa è cubo equal à numero. </s> <s id="s.002515">Et che uoi trouaſti regola generale à tal capitolo, <lb></lb>& per uigore di tal uoſtra inuentione uoi riſolueſti tutti li detti. </s> <s id="s.002516">30. caſi à uoi propo<lb></lb>ſti in termine de due hore. </s> <s id="s.002517">Et per tanto ſua eccellentia ui prega che uoi gli uogliati <lb></lb>mandare di gratia tal regola da uoi trouata, & s'el ui pare lui la dara fora in la pre<lb></lb>ſente ſua opera ſotto uostro nome, & ſe anchor el non ui pare, che lui la dia fora, la te<lb></lb>neraſecreta.<emph.end type="italics"></emph.end> N. D<emph type="italics"></emph>iceti à ſua eccellentia, che quella mi perdona, che quando uoro pu <lb></lb>blicar tal mia inuentione la uoro publicar in opere mie, & non in opere de altri, ſi che <lb></lb>ſua eccellentia mi habbia per iſcuſo.<emph.end type="italics"></emph.end> Z. N<emph type="italics"></emph>on uolendoli dar tal uoſtra inuentione ſua <lb></lb>eccellentia mi ha or dinato che uiprega che gli uogliati almen dar li detti. </s> <s id="s.002518">30. caſi che <lb></lb>lui ui propoſe, con la uoſtra reſolutione, & ſime <expan abbr="lmẽte">lmente</expan> li uoſtri. </s> <s id="s.002519">30. che gli proponefti <lb></lb>a lui.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>anco questo ſarin perche ogni uolta che lui haueſſe uno de detti caſt con <lb></lb>la ſua ſolutione ſubito ſua eccellentia intendaria la regola da me rnrouata con laquale<emph.end type="italics"></emph.end><pb xlink:href="042/01/227.jpg"></pb><emph type="italics"></emph>molte altre regole ſe potria ritrouare, ſopra à tal materie.<emph.end type="italics"></emph.end> Z. S<emph type="italics"></emph>ua eccellentia mi ha <lb></lb>dato. </s> <s id="s.002520">8. queſtioni, ouer queſiti da darue pregandoui che ge li uogliati riſoluere liquai <lb></lb>queſiti ſono queſti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002521">P<emph type="italics"></emph>artime diece in quatro parti continue proportionale che la prima, ſia.<emph.end type="italics"></emph.end> 2. </s> </p> <p type="main"> <s id="s.002522">P<emph type="italics"></emph>artime diece in. </s> <s id="s.002523">4. parti continue proportionale che la ſeconda parte ſla.<emph.end type="italics"></emph.end> 2. </s> </p> <p type="main"> <s id="s.002524">T<emph type="italics"></emph>rouatime. </s> <s id="s.002525">4. numeri continui proportionali che il primo ſia. </s> <s id="s.002526">2. & el ſecondo é. </s> <s id="s.002527">4. <lb></lb>gionti inſieme faciano.<emph.end type="italics"></emph.end> 10. </s> </p> <p type="main"> <s id="s.002528">T<emph type="italics"></emph>rouatime. </s> <s id="s.002529">4. numeri continui proportionali ch'el primo ſia. </s> <s id="s.002530">2. & il terzo è quarto <lb></lb>gionti inſiema facciano.<emph.end type="italics"></emph.end> 10. </s> </p> <p type="main"> <s id="s.002531">T<emph type="italics"></emph>rouatime. </s> <s id="s.002532">4. quantita continue proportionale che la ſeconda ſia. </s> <s id="s.002533">2. & la prima & <lb></lb>quarta gionte inſieme facciano.<emph.end type="italics"></emph.end> 10. </s> </p> <p type="main"> <s id="s.002534">F<emph type="italics"></emph>atime de. </s> <s id="s.002535">10. tre parti continue proportionale che multiplicata la prima nella ſecon <lb></lb>da facia.<emph.end type="italics"></emph.end> 8. </s> </p> <p type="main"> <s id="s.002536">T<emph type="italics"></emph>rouatime uno numero che multiplicato nella ſua radice piu. </s> <s id="s.002537">3. facia.<emph.end type="italics"></emph.end> 21. </s> </p> <p type="main"> <s id="s.002538">NICOLO. Q<emph type="italics"></emph>ueſti queſiti ſono de meſſer Zuanne da Coi. </s> <s id="s.002539">Et <expan abbr="nõ">non</expan> d'altri, perche li co<lb></lb>noſco à queſte due ultime perche una ſimile à queſta ſesta mi mando gia fa dui anni et <lb></lb>tal ragione gli feci confeſſare che lui medeſimo non la intendeua ne la ſapeua riſolue<lb></lb>re & una ſimile à queſta ultima (quale induce l'oper ante in cenſo è cubo equal à nume <lb></lb>ro) glidei per gentilezza aſſolta non è anchora un'annno, & pertal ſolutione trouo <lb></lb>una regola particolare ſopra ſimili queſiti. </s> <s id="s.002540">z. </s> <s id="s.002541">Io ſo ben mi che queſti queſiti el me li <lb></lb>ba dati la detta eccellentia de meſſer Hieronimo Cardano & non altro.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>dun<lb></lb>que il detto meſſer zuanne da Coi debbe eſſer uenuto à Millano & ge li ha propoſti à <lb></lb>ſua eccellentia & quella per non ſaperli riſoluere melli ha mandati da riſoluere à me <lb></lb>& <27>ſto tengo per certo <21>che il detto meſſer <expan abbr="zuãne">zuanne</expan> me promiſſe gia fa un'anno da uo<lb></lb>ler uenire à ſtar qua à Venetia, & tamen il non ui é mai uenuto, e pero credo chel ſi ſia <lb></lb><expan abbr="pẽtito">pentito</expan> da uenir à Venetia, & ch'el ſe ſia uoltato alla uolta de Millano.<emph.end type="italics"></emph.end> z. </s> <s id="s.002542">N<emph type="italics"></emph><expan abbr="õ">om</expan> <expan abbr="pẽſati">penſati</expan> <lb></lb>che ſua <expan abbr="eccellẽtia">eccellentia</expan> ui mandaſſe queſte queſtioni ſe la non li <expan abbr="intẽdeſſe">intendeſſe</expan>, et ſapeſſe riſoluere <lb></lb>ouer che fuſſero de altra perſona, perche ſua eccellentia é di primi di Millano di dot<lb></lb>trina, & il Marcheſe dal Vaſto gliha dato una gran prouiſione per la ſua ſufficien<lb></lb>tia.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on nego che ſua eccellentia non ſia perſona dottißima, & ſufficientißima. <lb></lb></s> <s id="s.002543">Ma ben dico che quella non ſapera riſoluere queſti. </s> <s id="s.002544">7. queſiti ch'ella mi ha mandato à <lb></lb>me dariſoluere con regole generale. </s> <s id="s.002545">Perche ſe ſua eccellentia non ſa riſoluere quel<lb></lb>lo di coſa, é cubo equal à numero (che me haueti ricercato con tante preghere) come <lb></lb>ſaprala riſoluere la maggior parte di queſtiliquali conducano l'operante in molto piu <lb></lb>ſtranie ſorte de capitoli di quello di coſa, e cubo equal à numero, e pero ſe quella ſapeſ<lb></lb>ſe riſoluere tutti queſti, molto piu facilmente ſaperia anchora riſoluere quello di coſa <lb></lb>è cubo equal à numero, & ſapendolo riſoluere ſon certo che la non lo and aria <expan abbr="mẽdican">mendican</expan> <lb></lb>dolo ne <expan abbr="cercãdolo">cercandolo</expan>. </s> <s id="s.002546">z. </s> <s id="s.002547">Io <expan abbr="nõ">non</expan> ſo che <expan abbr="riſpõderui">riſponderui</expan> perche <expan abbr="nõ">non</expan> me <expan abbr="intẽdo">intendo</expan> di queſte coſe, ma <lb></lb><expan abbr="quãdo">quando</expan> che parlaſti <expan abbr="cõ">com</expan> lui credo che ui ſapria <expan abbr="riſpõdere">riſpondere</expan>, ma laſſamo andar tutte queſte <lb></lb>coſe, accioche <expan abbr="nõ">non</expan> ſia uenuto in darno datime <expan abbr="almẽ">almen</expan> la coppia delliſimplici. </s> <s id="s.002548">30. caſi che <lb></lb>il detto maeſtro Antonio Maria fior ui propoſſe à uoi et ſe poteſti anchora darmi la <lb></lb>coppia di uostri. </s> <s id="s.002549">30. che uoi preponeſti à lui me fareſti ſummo appiacer.<emph.end type="italics"></emph.end>N. D<emph type="italics"></emph>elli ſuoi<emph.end type="italics"></emph.end><pb pagenum="114" xlink:href="042/01/228.jpg"></pb><emph type="italics"></emph>anchor che habbia careſtia del tempo) ue ne daro coppia, ma delli mei, non ue la poſſo <lb></lb>dar perche io non ho coppia alcuna appreſſo di me ne <expan abbr="mãco">manco</expan> me li aricordo coſi preci<lb></lb>ſe tutti perche erano tutti uarii, ma ſe andati dal notaro lui ue ne potra dar coppia.<emph.end type="italics"></emph.end><lb></lb>Z. M<emph type="italics"></emph>orſu datime li ſuoi.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>ono questi preciſe come che luile ſcriſſe.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002550">L<emph type="italics"></emph>aus deo. </s> <s id="s.002551">1534. adi. </s> <s id="s.002552">22. Febraro in Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002553">Q<emph type="italics"></emph>ueſte ſono le. </s> <s id="s.002554">30. raſone propoſte per mi Antoniomaria <lb></lb>fior à uoi Maeſtro Nicolo Tartaglia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002555">1 T<emph type="italics"></emph>rouame uno numero che azontoli la ſua radice cuba uenghi ſie, cioe.<emph.end type="italics"></emph.end> 6. </s> </p> <p type="main"> <s id="s.002556">2 T<emph type="italics"></emph>rouame. </s> <s id="s.002557">2. numeri in dupla proportione che il quadrato del mazor numero mul <lb></lb>tiplicato, per el menore, & à quella multiplicatione zontoli li. </s> <s id="s.002558">2. primi numeri <lb></lb>uenga quaranta, cioe.<emph.end type="italics"></emph.end> 40. </s> </p> <p type="main"> <s id="s.002559">3 T<emph type="italics"></emph>rouame uno numero che cubiccato, & ſopra quella cubicatione azontoli el det<lb></lb>to numero uenghi cinque.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002560">4 T<emph type="italics"></emph>rouatime. </s> <s id="s.002561">3. numeri in tripla proportione chel quadrato del menore multiplica <lb></lb>to per el numero mazore & a quella multiplicatione azontoli el numero mezza<lb></lb>no uenghi ſette.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002562">5 D<emph type="italics"></emph>oi huomini fanno compagnia, & die mettere de cauedal tra tutti duoi ducati no<lb></lb>uecento con queſta conditione che uno metta la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del altro domandando che <lb></lb>die mettere cadauno in detta compagnia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002563">6 D<emph type="italics"></emph>oi huomini hanno guadagnato ducati cento, & die partire ditto uadagno in que<lb></lb>ſta forma, che luno dieba hauere la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del altro, domando che tocca per uno de <lb></lb>ditto guadagno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002564">7 T<emph type="italics"></emph>rouame un numero che azontolile due ſue<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cube uenghi tredeſe.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002565">8 T<emph type="italics"></emph>rouame un numero che azontolile tre ſue<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cube uenghi quindeſe.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002566">9 T<emph type="italics"></emph>rouame un numero che azontoli le ſue quatro<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cube uenga diſette.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002567">10 F<emph type="italics"></emph>ame de. </s> <s id="s.002568">14. doi parti che luna parte fia la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de l'altra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002569">11 F<emph type="italics"></emph>ame de. </s> <s id="s.002570">20. doital parte che una parte ſia la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de laltra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002571">12 V<emph type="italics"></emph>no zoielero uende due zoie per duc.mille & nouecento zoe uno diamante, et uno <lb></lb>rebino, et lo robino, fu <expan abbr="uẽduto">uenduto</expan> la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.002572">del diamente, <expan abbr="domãdo">domando</expan> che ualſe el robino.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002573">13 V<emph type="italics"></emph>no zudio impresta à uno dinari non ſo quanti con queſta conditione che in capo <lb></lb>de uno anno li debba dar de uſura la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del ſuo capitale in capo de l'anno haue <lb></lb>il zudio fra capital è guadagno ducati ottocento domando quanto fuel capital del <lb></lb>zudio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002574">14 F<emph type="italics"></emph>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></lb>ra el quadrato della menore multiplicato in ſe medeſimo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002576">15 V<emph type="italics"></emph>no uende uno Safil per ducati. </s> <s id="s.002577">500. & ha guadagnato la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del ſuo capitale <lb></lb>domando quanto fu el guadagno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002578">16 E<emph type="italics"></emph>glie uno riangolo orthogonio.a.b.c.la linea.a.b.& la linea.b.c.zonte inſieme <lb></lb>ſono brazzaſeite & la linea.a.b.é<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de.b.c.domando la linea.a.c.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/229.jpg"></pb> <figure id="id.042.01.229.1.jpg" xlink:href="042/01/229/1.jpg"></figure> <p type="main"> <s id="s.002579">17 E<emph type="italics"></emph>glie uno arboro alto ſopra terra brazza. </s> <s id="s.002580">12. il quale le rompete in dui pezzi iu <lb></lb>tal luogo che quello che rimaſe in pie fu la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba di quello fu ſegato uia, doman<lb></lb>do quanto fu quello pezzo, che rimaſe in pie.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002581">18 E<emph type="italics"></emph>glie una linea longa brazza. </s> <s id="s.002582">9 la qual uoglio diuidere in due parti ineguale in tal <lb></lb>luoco, che la linea menore fia la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba della maggiore, domando la quantita del<lb></lb>le parte menore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002583">19 S<emph type="italics"></emph>ono dui triangoli equilateri, che le loro ſuper ficie gionte inſieme ſono brazza. </s> <s id="s.002584">25. <lb></lb>& la menore è la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba della maggiore, domando la ſuperficie del menore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002585">20 S<emph type="italics"></emph>ono dui quadrati che le lor ſuperficie gionte inſteme ſono. </s> <s id="s.002586">26. e la menore ſuper<lb></lb>ficie è<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba della maggiore, domando la ſuperficie del maggiore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002587">21 S<emph type="italics"></emph>ono dui penthagoni equilateri, che le loro ſuperficie gionte inſieme ſono brazza. <lb></lb></s> <s id="s.002588">28. la menore è la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba della maggiore, domando la ſuperficie menore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002589">22 S<emph type="italics"></emph>ono dui eſſagoni equilateri che le loro ſuperficie gionte inſieme ſono brazza. </s> <s id="s.002590">27. <lb></lb>& lo eſſagono menore è la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del maggiore, <expan abbr="domãdo">domando</expan> la ſuperficie del menore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002591">23 S<emph type="italics"></emph>ono dui ottagoni equilateri che le lor ſuperficie gionte inſieme ſono brazza. </s> <s id="s.002592">29. <lb></lb>la menor è la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba della maggior, domando quanto è laſuperfioie maggior.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002593">24 S<emph type="italics"></emph>ono dui triangoli equilateri, che li loro cateti gionti inſieme ſono brazza. </s> <s id="s.002594">34. il <lb></lb>cateto menore é la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del maggiore, domando il cateto menore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002595">25 S<emph type="italics"></emph>ono dui triangoli equilateri, che le loro fazze gionte inſieme ſono brazza. </s> <s id="s.002596">12. la <lb></lb>fazza menore è la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba della maggior, <expan abbr="domãdo">domando</expan> la fazza del triangolo maggiore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002597">26 S<emph type="italics"></emph>ono dui corpi cubi che la loro Aree ſono in tutto brazza cento, & la area cor<lb></lb>poral del menor è<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del maggior, domando l'area menor.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002598">27 S<emph type="italics"></emph>ono dui corpi de quattro baſe triangolari che le loro aree corporale ſono braz<lb></lb>za. </s> <s id="s.002599">140. l'area corporal del menor è<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del maggior, domando l'area del <lb></lb>maggior.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002600">28 S<emph type="italics"></emph>ono dui corpi de otto baſe triangolari equilateri che le loro aree corporale ſono <lb></lb>brazza. </s> <s id="s.002601">300. & l'area corporal del menore è<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del maggior, domando l'a<lb></lb>rea menor.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002602">29 S<emph type="italics"></emph>ono dui corpi de. </s> <s id="s.002603">12. baſe penthagonale che le loro aree corporale gionte inſieme <lb></lb>ſono brazza. </s> <s id="s.002604">810. l'area corporal del menore è<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del maggior, domando l'a<lb></lb>rea maggior.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002605">30 S<emph type="italics"></emph>ono dui corpi de. </s> <s id="s.002606">20. baſe triangolare che le loro aree corporal gionte inſieme ſo <lb></lb>no brazza. </s> <s id="s.002607">700. & l'area del menor è<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del maggior, <expan abbr="domãdo">domando</expan> l'area menor. <lb></lb></s> <s id="s.002608">Io Antoniomaria Fior del.q.maestro Pelegrino ſcriſſe.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="115" xlink:href="042/01/230.jpg"></pb> <p type="main"> <s id="s.002609">H<emph type="italics"></emph>or queſti ſono li delti. </s> <s id="s.002610">30. caſi che mi propoſe el detto maeſtro Antoniomaria fior. </s> <s id="s.002611">li <lb></lb>quali tutti conducono l'operante in el capitolo de coſa é cubo el qual capitolo per ha <lb></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></lb>ſolſi tutti. </s> <s id="s.002614">30. in cermine de hore due ſi che toleti queſta coppia.<emph.end type="italics"></emph.end> Z. V<emph type="italics"></emph>e ringratio <gap></gap><lb></lb>recomando.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>ndati in bon'hora.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002615">QVESITO XXXII. FATTO CON VNA LET<lb></lb><emph type="italics"></emph>tera dalla eccellentia de meſſer Hieronimo Cardano l'anno <lb></lb>1539. adi. </s> <s id="s.002616">12. Febraro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002617">MISSER HIERONIMO. M<emph type="italics"></emph>imar auiglio molto Meſſer Nicolo caro de ſi <lb></lb>diſconueneuole riſpoſta haueti data à uno Zuanantonio da Baſſano libraro el qua <lb></lb>le da mia parte ui ha pregato li uoleſti dare la riſpoſta di ſette, ouer otto <27>ſtioni le qua<lb></lb>le ui mandai, & la coppia delle propoſte fatte trauoi & maeſtro Antoniomaria fior <lb></lb>con le ſue ſolutioni alle quale non ui è baſtato di non mandarmene niunaſaluo che quelle <lb></lb>de maeſtro Antoniomaria lequale ſono. </s> <s id="s.002618">30. propoſte ma reuera quaſt una ſola ſostan<lb></lb>tia, cioe cubo è coſa equal à numero, pero mi doglio tra l'altre diſgratie di queſta arte <lb></lb>che quelli li danno operaſono tanto diſcorteſi è tanto preſumeno di ſe ſteſſo, che non <lb></lb>ſenza cagion ſono iudicati dal uulgo apreſſo che pazzi à cio ui caui for a de queſta <lb></lb>fantaſta della quale cauai nouamente meſſer zuanne da Coi, cioe d'eſſere il primo ho<lb></lb>mo del mondo donde ſe partito da Millano per diſperato, ue uoglio ſcriuere amo<lb></lb>reuolmente & trarui fori di fantaſia che uoi ui crediati eſſere ſi grande ui faro co<lb></lb>noſcere con amoreuole admonitioni per le uoſtre parole medeſime che ſeti piu apreſſo <lb></lb>a la ualle che alla ſumita del monte, potria ben eſſere che in altra coſa foſti piu eſer<lb></lb>citato, & ualente che non dimoſtrati per la riſpoſta & prima ui auiſo pero che io ue <lb></lb>ho hauuto in bon conto & ſubito ariuo li uoſtri libri ſoprale artegliarie ne <expan abbr="cõprai">comprai</expan> dui <lb></lb>che ſolo porto zuanantonio delli quali uno ne dette al Signor Marcheſe, & l'altro ten <lb></lb>ne per mi, & oltra cio ui laudai molto al Signor Marcheſe penſando fosti piu gen<lb></lb>til reconoſcitore, & piu humano, & piu corteſe, & piu ſufficiente de Meſſer zuan<lb></lb>ne qual uoi allegati, ma mi pare poca differentia da luno à laltro ſe altro non mo<lb></lb>strati hora peruenire a fatti ue accuſo in quatro coſe de momento. </s> <s id="s.002619">La prima è <lb></lb>che uoi diceti che le mie interrogatione non eſſer mie ma de meſſer zuanne Colle qua<lb></lb>ſi uolendo dire che <expan abbr="nõ">non</expan> ſia huomo in Millano che ſapeſſe fare tale interrogatione, meſſer <lb></lb>mio li ualentomini <expan abbr="nõ">non</expan> ſi conoſcono a le propoſte come uoi penſati, ma alle riſpoſte pero <lb></lb>peecati di proſumptione grauißima, ce ſono in Millano molti che le ſanno, et io le ſape <lb></lb>ua auanti che meſſer <expan abbr="zuãne">zuanne</expan> ſapeſſe numerare ſin à. </s> <s id="s.002620">10. ſe lui è coſi giouine come ſi fa. <lb></lb></s> <s id="s.002621">La <expan abbr="ſecõda">ſeconda</expan> è che uoi haueti detto al libraro che ſolta una delle queſtioni de maestro An <lb></lb>toniomaria ſariano ſolte tutte le mie, ui domando di gratia <expan abbr="cõ">com</expan> che credetì parlare con <lb></lb>li uoſtri ſcolari, ouer con huomini, doue trouaſti uoimai che la inuentione de la radi<lb></lb>ce pronicamedia, la qual è il fondamento de la ſolutione de tutte le. </s> <s id="s.002622">30. queſtioni de <lb></lb>maeſtro Antoniomaria, laqual è fondata ſopra l'ottaua del ſeſto di Euclide poßi eſſere <lb></lb>la reſulutione duna queſtione di cubo è numero equal à <expan abbr="cẽſo">cenſo</expan> fopra elqual capitolo ſi fon <pb xlink:href="042/01/231.jpg"></pb>da la propoſta, che dice. </s> <s id="s.002623">Trouami quattro quantita continue proportionale, che la ſeo <lb></lb>conda ſia. </s> <s id="s.002624">2. & che la prima, e quarta gionte inſieme ſacciano. </s> <s id="s.002625">10. coſi dico delle al<lb></lb>tre, ſi che mentreſeti uoluto dimoſtr arui mir acoloſo nell'arte uoſtra con un libraro, ui <lb></lb>ſeti dimostrato un grande ignorante appreſſo à quelli, che intendono, ne pero per que <lb></lb>ſto ui eſistimo ignorante, ma troppo proſontuoſo, come ch'era meſſer Zuane da Coi, <lb></lb>qual penſando di far credere che il ſapeſſe quello, che il non ſapeua, fece credere, che il <lb></lb>non ſapeſſe quello, che il ſapeua.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002626">L<emph type="italics"></emph>a terza è, che uoi haueti detto al libraro, che ſolta una delle mie queſtioni ſono <lb></lb>ſolte tutte, la qual coſa è falſißima, & è una ingiuria coperta de dire, che penſando man <lb></lb>darui. </s> <s id="s.002627">7. questioni ue ne habbia mandato una, ilche arguirebbe in me un gran traſcor<lb></lb>ſo di mente, e certo s'io fuſſe dell'arte io uorrei deponere. </s> <s id="s.002628">100. ſcudi ſopra queſto paſ<lb></lb>ſo, cioe che non ſi ponno redurre, ne in una, ne in due, ne in tre queſtioni, & pur quando <lb></lb>li uoleſti mettere, to non li rifiutaria, et ueniro à Venetia à posta, e daro ſicurta de ban <lb></lb>co qua de accettare, ſe uoi uoleti uenir qua, ouer datila uoi la in Venetia ch'io ueniro, <lb></lb>ne per queſto fo la profeßione, penſati che fareti con quelli, che la fanno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002629">L<emph type="italics"></emph>a quarta è uno errore troppo manifeſto nel uoſtro libro, detto ſcientia nuoua de <lb></lb>artegliarie, nel qual uoleti alla quinta propoſitione del primo, che niuno corpo egual<lb></lb>mente graue poßi and are per alcuno ſpacio di tempo, ouer di luoco di moto naturale, <lb></lb>& uiolente inſieme miſto, la quale è falſißima, & contra ogni ragione, & iſperientia <lb></lb>naturale. </s> <s id="s.002630">Il uoſtro fondamento con che lo prouati è piu ſtorno aſſai, che non è la riſpo <lb></lb>sta, che haueti data al libraro, non ſapeti uoi che il non è inconueniente nel diſcendere <lb></lb>una coſa ſi moua piu uelocemente, & nel procedere uadi piu tardo, ſi come uedemo nel <lb></lb>la iſpertentia nel trare d'una pietra, la quale, come piu deſcende, piu uiene ueloce à ter <lb></lb>ra, e pur procedendo ua piu tardo, dalla qual concluſione faceti naſcere altre ragioni, <lb></lb>molto strane in detto libro, ſi che penſati bene, che gli huomini da bene non ſono al ri<lb></lb>prendere ſi facili. </s> <s id="s.002631">Ch'io ue ho hauuto per iſcuſato in uolerui riprendere, perche trat<lb></lb>tando de artegliaria, ch'era poco uoſtro meſtiero, ue ſiti pero ingegnato di dire qual<lb></lb>che bella coſa, ma accio non penſati, che ſia ſimile à uoi, & à meſſer Zuan Colle ui man <lb></lb>do due queſtioni con le ſue ſolutioni, ma le ſolutioni ſaranno ſeparate dalle queſtioni, & <lb></lb>il meſſo le portara ſeco, & ſe uoi non le ſapreti ſoluere lui ue dara ſubito hauendola, <lb></lb>pero ſieco à una, à una, accio non crediate l'habbia mandate per impararle, & non <lb></lb>per donaruele, ma ritorra prima le uoſtre in drieto, accio non gli daſeſti intendere ha<lb></lb>uerle ſolte, & non le haueſti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002632">O<emph type="italics"></emph>ltra di cio dignareteui di mandarme le propoſte fatte per uoi à maeſtro Antonio <lb></lb>maria Fior, & ſe non uoleti mandar le ſolutioni, tenetile per uoi, poi che ne ſeti coſi ca <lb></lb>restioſo, & ſe il ui piace riceuendo le ſolutioni delle dette mie questioni, ſenza che uoi <lb></lb>le ſappiati ſoluere, dapoi che ſeti chiaro le mie ſette queſtioni eſſer diuerſe, mandar<lb></lb>mene la ſolutione di qualche una di loro mi fareti ſingolarißimo appiacer, piu per la <lb></lb>amicitia, & per conoſcere il uostro grande ingegno, che per altro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002633">L<emph type="italics"></emph>a prima questione feme de. </s> <s id="s.002634">10. quattro quantita continue proportionale, che li <lb></lb>loro quadrati gionti inſieme facciano. </s> <s id="s.002635">60. una ſimile pone Frate Luca, ma non <lb></lb>la ſolue.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="116" xlink:href="042/01/232.jpg"></pb> <p type="main"> <s id="s.002636">L<emph type="italics"></emph>a ſeconda, duifeceno compagnia, & poſſeno non ſo quanti ducati, & guadagnor<lb></lb>no il cubo dellà decima parte del ſuo capitale, & ſe haueſſero guadagnato. </s> <s id="s.002637">3. meno di <lb></lb>quello che guadagnorno haueriano guadagnato tanto quanto fuil ſuo capitale aponto <lb></lb>ſe domanda il ſuo capital è guadagno, non altro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002638">H<emph type="italics"></emph>ieronimo Cardano Medico.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002639">NICOLO. E<emph type="italics"></emph>ccellentißimo meſſer Hieronimo ho riceuuto una uoſtra, nella quale <lb></lb>dite che molto ue mar auigliati de ſi diſconueneuole riſpoſta per me data à une Zuanan <lb></lb>tonio da Baſſano Libraro, per hauergli negato di dare la maggior parte di quello mi <lb></lb>richiedeua da parte di uoſtra Eccellentia, per ilche quella uſa de molte braue, arro<lb></lb>gante, & ingiurioſe parole, che à uolerle replicare, & riſpondere à una per una, <lb></lb>ui andaria da ſcriuere aſſai, fra le quale uoi dite, che me accuſate in quattro coſe <lb></lb>di momento.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002640">L<emph type="italics"></emph>a prima è, che uoi diceti, che io ho detto al libraro, che quelle ſette interrogatio<lb></lb>ni à me mandate non eſſer uoſtre, ma d'un meſſer Zuane da Coi, quaſi uolendo dire, che <lb></lb>il non ſia huomo in Millano, che ſapeſſe ſoluere tale interrogationi, con cio che ſugue. <lb></lb></s> <s id="s.002641">Circa à queſta uoſtra prima accuſa ui riſpondo, & dico, che eglie il uero, che io ho det <lb></lb>to, che tale queſtioni erano di meſſer Zuane da Coi, perche gia fa un'anno è meggio à <lb></lb>me, me ne propoſe una ſimile alla penultima di quella (ma ſotto altre parole) la quale à <lb></lb>lui medeſimo gli feciconfeſſare qua in Venetia, che non la intendeua, & non la ſapeua <lb></lb>riſoluere, ſi che per tal ragione, & altri inditij giudicai tale questioni eſſer ſue, et che <lb></lb>lui proprio me le mandaſſe ſotto nome uoſtro, ma quando che il libraro me acerto ha<lb></lb>uerle hauute da uoſtra Eccellentia, giudicai che il detto meſſer Zuane da Coi fuſſe ue<lb></lb>nuto à Millano, & che gli haueſſe proposte à quella (come che anchor giudico, & ten <lb></lb>go per fermo) & che quella per non ſaperle riſoluere me le habbia mandate dariſol<lb></lb>uere à me per le ragioni, che di ſotto ſe dira.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002642">S<emph type="italics"></emph>econdariamente quella dice, che mi accuſa, che ho detto al detto libraro, che ſolta <lb></lb>una delle queſtioni di<emph.end type="italics"></emph.end> M. A<emph type="italics"></emph>ntoniomaria ſariano ſolte tutte le uoſtre. </s> <s id="s.002643">7. à me mandate.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002644">T<emph type="italics"></emph>ertio quella dice, che mi accuſa anchora, che io ho detto al ſopradetto libraro, che <lb></lb>aſſolta una delle uoſtre. </s> <s id="s.002645">7. queſtioni à me mandate, ſariano riſolte tutte, & ſeguitando <lb></lb>dite, che queſta è una coſa falſißima, & che ſopra à queſto paſſo uoleti deponere. </s> <s id="s.002646">100. <lb></lb>ſcudi, cioe che tale. </s> <s id="s.002647">7. queſtioni non ſi ponno ridurre ne in una, ne in due, ne in tre que<lb></lb>ſtioni, & quando che mi pareſſe di uoler deponere gli detti. </s> <s id="s.002648">100. ſcudi ſopra à queſto <lb></lb>paſſo, che quella uenira à Venetia à posta, & chi quella dara ſicurta de banco la in Mil <lb></lb>lano uolendo io uenia la à Millano di accettare, oueramente che io debbia dare la detta <lb></lb>ſicurta qua in Venetia, che quella uenira qua à Venetia, &c.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002649">E<emph type="italics"></emph>t per tanto circa à queſta uoſtra ſeconda, & terza accuſa ue riſpondo, & dico, <lb></lb>che credo che uoi ue habbiati inſoniato queſte uostre zance. </s> <s id="s.002650">Eglie ben uero, che io ho <lb></lb>detto al detto libraro, che uoſtra Eccellentia non ſaperia riſoluere le dette. </s> <s id="s.002651">7. que<lb></lb>stioni à me mandate con regole generale, & accio che il non pareſſe, che io diceſſe tal <lb></lb>coſa ſenza qualche ragione, gli diſſe, che ſe quella non ſa riſoluere il capitolo de coſa è <lb></lb>cubo egual à numero (qual me ricercati con tanta iſtantia) manco ſapereti riſoluere <lb></lb>quelle uoſtre. </s> <s id="s.002652">7. à me mandate, le quale conducano l'operante in piu ſtranie equationi, <pb xlink:href="042/01/233.jpg"></pb>ouer capitoli di quello di coſa, e cubo egual à numero. </s> <s id="s.002653">Et che ſe pur quella li ſapeſſe ri<lb></lb>ſoluere, che molto piu facilmente ſoluereſti il capitolo di coſa è cubo egual à numero, <lb></lb>& queſto è quanto che ho detto al libraro. </s> <s id="s.002654">Ma per quanto poſſo conſiderare uoſtra Ec <lb></lb>cellentia molto deſidera di far conoſcere con meco la ſua ſofficientia, ilche eſſendo, ſe io <lb></lb>fuſſe ben certo di reſtar perdente, non uoglio rifiutare tal inuito, cioe di deponere cir<lb></lb>ca cio li detti ducati. </s> <s id="s.002655">100. & ueniro perſonalmente per fina à Millano, ſe quella non <lb></lb>uorra uenire à Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002656">Q<emph type="italics"></emph>uarto quella dice, che mi accuſa d'uno errore fra glialtritroppo manifesto, nel <lb></lb>mio libro, detto nuoua ſcientia, nella quinta propoſitione del primo libro, perche in <lb></lb>quella conchiudo, che niun corpo egualmente graue, poßi andare per alcuno ſpacio di <lb></lb>tempo, ouer di luoco, di moto naturale, & uiolente inſieme miſto, & dite che tal pro<lb></lb>poſitione è falſißima, & contra ogni ragione, & iſperientia naturale, & che il mio <lb></lb>fondamento con il quale approuo la detta propoſitione, uoi dite, ch'eglie piu ſtorno <lb></lb>aſſai, che non fu la riſpoſta, che io deti al libraro, circa à cio quella adduce molte ſue <lb></lb>ragioni contra à tal mia propoſitione.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002657">E<emph type="italics"></emph>t per tanto circa à queſta uoſtra quarta accuſa ue riſpondo, & dico, che le uoſtre <lb></lb>ragioni, & argomenti per uoi adutti à deſtruttione di tal mia quinta propoſltione ſono <lb></lb>tanto deboli, & mal conditionati, che una femina inferma ſaria ſofficiente à sbatterli <lb></lb>per terra, perche ſe la concluſione della detta mia quinta propoſitione è falſa, eglie ne<lb></lb>ceſſario, che li ſuoi primi principij ſtano falſi, ouer amente che alcuna delle ſue premeſ<lb></lb>ſe propoſitioni, con le quale ſe dimoſtra la detta quinta ſia falſa, la qual coſa eſſendo uoi <lb></lb>doueti pur ſapere, che l'officio del perito medico ſi è de inueſtigare con ſomma diligen<lb></lb>tia la cauſa principale de ogni infirmita, che gli occorra alle mani, & ritrouata quella, <lb></lb>anchora con ſomma diligentia di cercare piu di opponere, ouer di curare la detta cauſa <lb></lb>principale, che di opponere, ouer di cur are li ſuoi tristi effetti, perche rimoſſa che ſia <lb></lb>la cauſa de neceßita, ſaranno rimoßi anchora tutti li ſuoi triſti effetti.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>pero uo<lb></lb>lendo uoſtra Eccellentia opponere, ouer arguìre contra à tal mia quinta propoſitione <lb></lb>quella doueua primamente opponere, ouer arguire ſopra alli ſuoi primi principij, oue<lb></lb>ramente ſopra ad alcuna di quelle promeſſe propoſitioni, con le quale io conchiudo la <lb></lb>detta quinta propoſitione (come fondamento, & cauſa principale di tal effetto) per<lb></lb>che ſe uoi haueſti potuto diſtruggere il fondamento con qualche ſofiſtice ragioni tutta <lb></lb>la fabrica ſaria andata per terra, mauoi credendoui di dimostrarue à me miracoloſo <lb></lb>con tale uoſtre ridicoloſe oppoſitioni, ue ſeti dimoſtrato, non uoglio dire, un grande <lb></lb>ignorante, come haueti detto à me, ma un'huomo di poco giudicio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002658">E<emph type="italics"></emph>t perche<emph.end type="italics"></emph.end> V. E<emph type="italics"></emph><expan abbr="ccellẽtia">ccellentia</expan> dice, che me ha per iſcuſo, trattando de artegliarie, che è po <lb></lb>co mio meſtiero, anchor che me ſia ingegnato di dire circa a tal arte qualche bella coſa.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002659">C<emph type="italics"></emph>irca à queſta particolarita ue riſpondo, & dico, che me diletto de nuoue inuentio<lb></lb>ni, & di trattare, & parlare de coſe, che altri non habbia trattato, ne parlato, & non <lb></lb>me diletto di far, come fanno alcuni, che empiono li ſuoi uolumi di coſe robate da que<lb></lb>sto, & da quell'altro autore. </s> <s id="s.002660">Et quantunque à parlare delle artegliarie, et lor tiri non <lb></lb>ſia coſa molto honoreuole in ſe, pur per eſſer una materia nuoua, & di non poca ſpecu <lb></lb>latione, me apparſo di parlarne alquanto, & circa cio al preſente dago fuora due ſor-<emph.end type="italics"></emph.end><pb pagenum="117" xlink:href="042/01/234.jpg"></pb><emph type="italics"></emph>te de inſtrumenti circa à tal arte, cioe una ſquadra per regolar li tiri delle dette arte<lb></lb>gliarie, & anchora per liuellare, & inueſtigare ogni altezza. </s> <s id="s.002661">Et uno altro inſtru<lb></lb>mento, per inueſtigare ogni diſtantia in piano, con l'aſpetto, liquali inſtrumenti anda <lb></lb>rano con el detto mio libro de artegliaria. </s> <s id="s.002662">Et perche me haueti ſcritto che uoi com<lb></lb>peraſti dui de detti mei libri, delli quali uno ne deſti alla eccellentia del Signor Mar<lb></lb>cheſe, & laltro teneſti per uoi, me apparſo anchora dimandarue, quatro delli detti in <lb></lb><expan abbr="ſtrumẽti">ſtrumenti</expan> & li ho dati alla Signoria de meſſer Ottauian Scotto che ueda da farueli por <lb></lb>tar per qualche meſſo che uegna à quelle bande, delli quali quatro instrumenti, dui ne <lb></lb>donareti alla eccellentia del Signor, Marcheſe, & li altri dui tenereti per uoi, uoſtra <lb></lb>eccellentia anchora me ſcriue, che accio che io non penſa che quella ſia ſimile à me & <lb></lb>à meſſer Zuan Colle che quella me manda due queſtioni con le ſue ſolutioni, ma che il <lb></lb>meſſo tenera le dette ſolutioni ſeparate dalle dette questioni, & che ſe io non le ſapro <lb></lb>riſoluere che il detto meſſo me le dara ſubito <expan abbr="hauẽdole">hauendole</expan>, pero ſeco à una <21> una accio che <lb></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></lb>il detto meſſo retora prima le mie ſolutioni in drío <expan abbr="nãti">nanti</expan> che me dia le uoſtre accioche io <lb></lb>non li deſſe ad intendere di hauer le aſſolte, & chel non fuſſe il uero. </s> <s id="s.002663">della qualcoſa me <lb></lb>ne ho rideſto aſſai & la cauſa de tal mio ridere ſe narrara ſopra alla ſolutione della uo <lb></lb>ſtra ſeconda questione.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002664">H<emph type="italics"></emph>or per riſpondere alla uoſtra prima <expan abbr="queſtiõe">queſtione</expan> quale dice, che ui debbia far de. </s> <s id="s.002665">10. <lb></lb>quattro quantita continue proportionale, che li loro quadr ati gionti inſieme facciano. <lb></lb></s> <s id="s.002666">60. io ue riſpondo che le dette parti ſono le ſotto ſcritte cioe.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002667">L<emph type="italics"></emph>a prima ſara. </s> <s id="s.002668">6. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002669">7. 1/4. <emph type="italics"></emph>meno la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002670">49. 1/2. <expan abbr="mẽ">men</expan><emph.end type="italics"></emph.end> <22>. </s> <s id="s.002671">1225. 1/4. <emph type="italics"></emph>men <lb></lb>queſto eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002672">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002673">9396. <emph type="italics"></emph>men. </s> <s id="s.002674">288. eſimo de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002675">116. <emph type="italics"></emph>piu. </s> <s id="s.002676">4. cioe <lb></lb>da partire per el detto<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002677">116. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.002678">L<emph type="italics"></emph>a ſeconda ſara<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002679">7. 1/4. <emph type="italics"></emph>men. </s> <s id="s.002680">1. 1/2. men la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002681">9. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002682">65. 1/4 <emph type="italics"></emph>men que<lb></lb>ſto eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002683">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002684">9396. <emph type="italics"></emph>men. </s> <s id="s.002685">288. eſimo, cioe da partire per<emph.end type="italics"></emph.end> <22>. <lb></lb></s> <s id="s.002686">116. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.002687">L<emph type="italics"></emph>a terza ſara<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002688">7. 1/4. <emph type="italics"></emph>men. </s> <s id="s.002689">1. 1/2. piu la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002690">9. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002691">65. 1/4. <emph type="italics"></emph>men queſto <lb></lb>eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002692">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002693">9396. <emph type="italics"></emph>men. </s> <s id="s.002694">288. da partire per<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002695">116. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.002696">L<emph type="italics"></emph>a quarta ſara. </s> <s id="s.002697">6. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002698">7. 1/2. <emph type="italics"></emph>piu la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002699">49. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002700">1225. 1/4. <emph type="italics"></emph>men <lb></lb>questo eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002701">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002702">9396 <emph type="italics"></emph>men. </s> <s id="s.002703">288. da partire per<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002704">116. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.002705">E<emph type="italics"></emph>t queſte tai parti le ritrouo in queſto modo. </s> <s id="s.002706">Prima <expan abbr="tõſidero">tonſidero</expan> che ſe ſar anno. </s> <s id="s.002707">4. quan <lb></lb>tita continue proportionale delle quale la ſeconda & terza inſieme ne ſian note, et che <lb></lb>la prima & quarta inſieme ne ſian note eglie poßibile à potere ritrouare quanto ſia <lb></lb>cadauna delle dette quantita feparatamente, perche chi partira el cubo della ſumma <lb></lb>della <expan abbr="ſecõda">ſeconda</expan> & terza, per el <expan abbr="cõpoſto">compoſto</expan> di tutte quattro & del doppio della ſumma della <lb></lb>ſeconda & terza l'aduenimento ſara equale alla multiplicatione della ſeconda nella ter <lb></lb>za, ouer della prima nella quarta (ch'è il medeſimo) per ílche <expan abbr="facẽdo">facendo</expan> due tal parti della <lb></lb>ſumma della ſeconda, & terza, ouer della prima & quarta, che multiplicata luna fia <lb></lb>l'altra faccia lo detto aduemmento ſeguir a il propoſito. </s> <s id="s.002708">Hor con tal euidentia io po <lb></lb>so che la ſeconda & terza ínfleme ſiano. </s> <s id="s.002709">1. coſa adunque, la prima, & quarta inſieme <lb></lb>por ſorzaſarano. </s> <s id="s.002710">10. men.i.coſa, cubo la coſa fa. </s> <s id="s.002711">1. cubo el qual parto per. </s> <s id="s.002712">10. piu el<emph.end type="italics"></emph.end><pb xlink:href="042/01/235.jpg"></pb><emph type="italics"></emph>doppio della ſeconda & terza, cioe per. </s> <s id="s.002713">10. piu. </s> <s id="s.002714">2. coſe ne uien. </s> <s id="s.002715">1. cu.eſimo de. </s> <s id="s.002716">10. piu <lb></lb>2. coſe, et <27>sto ſara il pdutto della ſeconda nella terza, ouer della prima nella. </s> <s id="s.002717">4. Adun <lb></lb>que per trouar cadauna ſeparatamente faccio di. </s> <s id="s.002718">1. co. </s> <s id="s.002719">due tal parti che multiplicata <lb></lb>luna fia l'altra faccia. </s> <s id="s.002720">1. cu. </s> <s id="s.002721">eſimo de. </s> <s id="s.002722">10. piu. </s> <s id="s.002723">2. coſe, <expan abbr="operãdo">operando</expan> come biſogna trouo che <lb></lb>la menore è. </s> <s id="s.002724">1/2. co.men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 1/4. ce.mẽ. </s> <s id="s.002725">1. cubo.eſimo de. </s> <s id="s.002726">10. piu. </s> <s id="s.002727">2. coſe et la maggiore <lb></lb>ſara. </s> <s id="s.002728">1/2. co.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 1/4. ce.mẽ. </s> <s id="s.002729">1. cubo eſimo de. </s> <s id="s.002730">10. piu. </s> <s id="s.002731">2. coſe, & coſi <expan abbr="ſordamẽte">ſordamente</expan> haro <lb></lb>trouata la ſeconda & terza <expan abbr="ſeparatamẽte">ſeparatamente</expan>. </s> <s id="s.002732">Simelmente trouaro la prima & quarta fa <lb></lb><expan abbr="cẽdo">cendo</expan> de. </s> <s id="s.002733">10. <expan abbr="mẽ">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.eſimo de. <lb></lb></s> <s id="s.002736">10. piu, 2. coſe, <expan abbr="operãdo">operando</expan> come biſogna trouo che la prima ſara. </s> <s id="s.002737">5. <expan abbr="mẽ">men</expan>. </s> <s id="s.002738">1/2. co.mẽ<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 25. <lb></lb><expan abbr="mẽ">men</expan>. </s> <s id="s.002739">5. co piu. </s> <s id="s.002740">14. ce <expan abbr="mẽ">men</expan>. </s> <s id="s.002741">1. cubo eſimo de. </s> <s id="s.002742">10. piu: 2. coſe (cioe la menor) la quarta cioe la <lb></lb>maggiore ſara. </s> <s id="s.002743">5. men. </s> <s id="s.002744">1/2. co.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 25. men. </s> <s id="s.002745">5. co.piu. </s> <s id="s.002746">1/4. ce.mẽ. </s> <s id="s.002747">1 cubo.eſimo de. </s> <s id="s.002748">10. <lb></lb>piu. </s> <s id="s.002749">2. coſe, & coſi li haueremo tutte quatro ſeparate come di ſotto appare.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002750">P<emph type="italics"></emph>rima ſara. </s> <s id="s.002751">5. men. </s> <s id="s.002752">1/2. co.men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 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 eſimo de. </s> <s id="s.002756">10. <lb></lb>piu. </s> <s id="s.002757">2. co. </s> <s id="s.002758">El quadrato della qual quantita ſara. </s> <s id="s.002759">50. men. </s> <s id="s.002760">10. co.piu. </s> <s id="s.002761">1/2. cenſo men. <lb></lb></s> <s id="s.002762">1. cubo. </s> <s id="s.002763">eſimo 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></lb>te in laltra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002766">L<emph type="italics"></emph>a ſeconda ſara. </s> <s id="s.002767">1/2. co.men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 1/4. ce.men. </s> <s id="s.002768">1. cubo eſimo de. </s> <s id="s.002769">10. piu. </s> <s id="s.002770">2. coſe. </s> <s id="s.002771">Et el ſuo <lb></lb>quadrato ſara. </s> <s id="s.002772">1/2. ce.men. </s> <s id="s.002773">1. cu.eſimo de. </s> <s id="s.002774">10 piu. </s> <s id="s.002775">2. co.men, anchora el doppio de lu <lb></lb>na parte in l'altra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002776">L<emph type="italics"></emph>aterza ſara. </s> <s id="s.002777">1/2. co.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 1/4. ce.men.u.cu.eſimo 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></lb>tal quantita ſara. </s> <s id="s.002781">1/2. ce.men. </s> <s id="s.002782">1. cu.eſimo de. </s> <s id="s.002783">10. piu. </s> <s id="s.002784">2. co.piu, anchora il doppio de <lb></lb>luna parte in l'altra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002785">L<emph type="italics"></emph>a quartaſara. </s> <s id="s.002786">5. men. </s> <s id="s.002787">1/2. co.piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. 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.eſimo de. </s> <s id="s.002791">10. <lb></lb>piu. </s> <s id="s.002792">2. co. </s> <s id="s.002793">Et il quadrato de questa quantita ſara. </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></lb>cu.eſimo 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"></emph.end></s> </p> <p type="main"> <s id="s.002800">E<emph type="italics"></emph>t dapoi ſummo li detti quatro quadr ati et fanno in ſumma. </s> <s id="s.002801">100. men. </s> <s id="s.002802">20. co.piu. </s> <s id="s.002803">2. ce. <lb></lb></s> <s id="s.002804">men. </s> <s id="s.002805">4. cubi eſimi de. </s> <s id="s.002806">10. piu. </s> <s id="s.002807">2. co.& questa ſumma ſara equale à. </s> <s id="s.002808">60. egualio le par <lb></lb>ti & riſtoro 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></lb>gual à. </s> <s id="s.002812">20. ſeguito el capitolo & trouo la coſa ualer<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002813">29. <emph type="italics"></emph>men. </s> <s id="s.002814">3. & tanto dico che <lb></lb>fu la ſumma della ſeconda, & terza quantita. </s> <s id="s.002815">Onde che la ſumma della príma et quan <lb></lb>ta de neceßita ſara. </s> <s id="s.002816">13. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002817">29. <emph type="italics"></emph>cioe el <expan abbr="restãte">restante</expan> per fina in. </s> <s id="s.002818">10. Hor per trouar le par <lb></lb>te ſeparate biſogna procedere come fuproceſſo ſordamente, cioe trouando el produt<lb></lb>to della ſeconda in la terza, ouer della prima nella quarta, el qual <expan abbr="uolẽdolo">uolendolo</expan> trouar cu<lb></lb>bo<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002819">29. <emph type="italics"></emph>men. </s> <s id="s.002820">3. fa.in ſumma<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002821">41876. <emph type="italics"></emph>men. </s> <s id="s.002822">288. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002823">9396. <emph type="italics"></emph>et queſto parto per. <lb></lb></s> <s id="s.002824">10. piu el doppio de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002825">29. <emph type="italics"></emph>men. </s> <s id="s.002826">3. cioe per<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002827">116. <emph type="italics"></emph>piu. </s> <s id="s.002828">4. mene uiene<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002829">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end><lb></lb><22>. </s> <s id="s.002830">9396. <emph type="italics"></emph><expan abbr="mẽ">men</expan>. </s> <s id="s.002831">288. eſimo de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002832">116. <emph type="italics"></emph>piu. </s> <s id="s.002833">4. & questo ſara equale al produtto della ſe <lb></lb><expan abbr="cõda">conda</expan> nella terza, ouer della prima nella quarta. </s> <s id="s.002834">Hor per trouare cadauno <expan abbr="ſeparatamẽ-te">ſeparatamen<lb></lb>te</expan> procedendo <expan abbr="ſecõdo">ſecondo</expan> il ſolito trouo che la ſeconda è<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002835">7. 1/4. <emph type="italics"></emph><expan abbr="mẽ">men</expan>. </s> <s id="s.002836">1. 1/2. <expan abbr="mẽ">men</expan> la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u.de. 9. <lb></lb>1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002837">65. 1/2. <emph type="italics"></emph><expan abbr="mẽ">men</expan> anchora<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002838">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002839">9396. <emph type="italics"></emph><expan abbr="mẽ">men</expan>. </s> <s id="s.002840">288. eſimo.de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002841">116. <emph type="italics"></emph><expan abbr="mẽ">men</expan>. </s> <s id="s.002842">4. <lb></lb>La terza uera à eſſere la medeſima<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002843">7. 1/4. <emph type="italics"></emph>me.<emph.end type="italics"></emph.end> 1/2. M<emph type="italics"></emph>a piu la ſopraſcritta<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuer <lb></lb>ſale de. </s> <s id="s.002844">9. 1/2. men.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002845">65. 1/4. <emph type="italics"></emph>men, anchora la<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002846">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002847">9396, <emph type="italics"></emph>men. </s> <s id="s.002848">288. eſimo <lb></lb>de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002849">116. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <pb pagenum="118" xlink:href="042/01/236.jpg"></pb> <p type="main"> <s id="s.002850">H<emph type="italics"></emph>or per ritrouar la prima & quarta ſeparatamente procedero, come di ſopra fa <lb></lb><expan abbr="cẽdo">cendo</expan> de. </s> <s id="s.002851">13. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002852">29. <emph type="italics"></emph>due tal parti che multiplicata luna in l'altra facia pur il ſopra <lb></lb>ſcritto eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002853">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002854">9396. <emph type="italics"></emph>men. </s> <s id="s.002855">288. eſimo de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002856">116. P<emph type="italics"></emph>iu. </s> <s id="s.002857">4. onde <lb></lb>operando <expan abbr="ſecõdo">ſecondo</expan> il ſolito trouo che la prima (cioe la menore) ſara preciſamente. </s> <s id="s.002858">6. <lb></lb>1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002859">7. 1/4. <emph type="italics"></emph>men la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002860">49. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002861">1225. 1/4. <emph type="italics"></emph><expan abbr="mẽ">men</expan> queſto eſimo, cioe<emph.end type="italics"></emph.end><lb></lb><22>. </s> <s id="s.002862">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002863">9396. <emph type="italics"></emph><expan abbr="mẽ">men</expan>. </s> <s id="s.002864">288. eſimo de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002865">116. <emph type="italics"></emph>piu. </s> <s id="s.002866">4. et la maggiore cioe la quar <lb></lb>taſara. </s> <s id="s.002867">6. 1/2. <expan abbr="mẽ">men</expan><emph.end type="italics"></emph.end> <22>. </s> <s id="s.002868">7 1/4. <emph type="italics"></emph>piu la ſopra ſcritta<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale. </s> <s id="s.002869">Onde le dette quatro parti <lb></lb>del detto. </s> <s id="s.002870">10. adimandate dauoſtra eccellentia ſarano come diſotto appare.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002871">L<emph type="italics"></emph>a prima ſara. </s> <s id="s.002872">6. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002873">7. 1/4. <emph type="italics"></emph>men la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002874">49. 1/2. men.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002875">1225. 1/4. <lb></lb><emph type="italics"></emph>men queſto eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002876">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002877">9396. <emph type="italics"></emph>men. </s> <s id="s.002878">288. eſimo de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002879">116. <emph type="italics"></emph>piu. </s> <s id="s.002880">4. <lb></lb>cioe da partire per<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002881">116. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.002882">L<emph type="italics"></emph>a ſeconda ſara<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002883">7. 1/4. <emph type="italics"></emph>men. </s> <s id="s.002884">1. 1/2. men la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002885">9. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002886">65. 1/4. <emph type="italics"></emph>men <lb></lb>queſto eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002887">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002888">9396. <emph type="italics"></emph>men. </s> <s id="s.002889">288. da partire per.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002890">116 <lb></lb><emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.002891">L<emph type="italics"></emph>a terza ſara<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002892">7. 1. 1/4. <emph type="italics"></emph>men. </s> <s id="s.002893">1. 1/2. piu.la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002894">9. 1/2. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002895">65. 1/4. <emph type="italics"></emph>men que <lb></lb>ſto eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002896">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002897">9396. <emph type="italics"></emph>men. </s> <s id="s.002898">288. da partire per<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002899">116. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 4. </s> </p> <p type="main"> <s id="s.002900">L<emph type="italics"></emph>a quarta ſara. </s> <s id="s.002901">6. 1/2. <expan abbr="mẽ">men</expan><emph.end type="italics"></emph.end> <22>. </s> <s id="s.002902">7. 1/4. <emph type="italics"></emph>piu la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale de. </s> <s id="s.002903">49. 1/2. men.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002904">1225. 1/4. <emph type="italics"></emph>men <lb></lb>queſto eſimo, cioe<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002905">41876. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002906">9396. <emph type="italics"></emph>men. </s> <s id="s.002907">288. eſimo de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002908">116. <emph type="italics"></emph>piu. </s> <s id="s.002909">4. come <lb></lb>che nel principio fu concluſo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002910">C<emph type="italics"></emph>irca à l'altra uostra ſeconda questione, quala dice che ſono doi che feceno compagnia <lb></lb>& poſeno non ſo quanti ducati & guadagnorno el cubo della decima parte del ſuo ca <lb></lb>pitale & che ſe haueſſero guadagnato. </s> <s id="s.002911">3. meno de quello che guadagnorono, haueria<lb></lb>no guadagnato tanto quanto fu il ſuo capitale aponto, ſe adimanda il ſuo capitale & <lb></lb>guadagno. </s> <s id="s.002912">Certamente di queſta come di ſopra dißi me ne ſon rideſto aſſai, perche ue<lb></lb>do che uostra eccellentia cerca di uoler giocare con meco à trapola, oueramente al gio <lb></lb>co della corrigiola, come coſtumano li cingheni & ſi crede di uolermi agabare con di<lb></lb>re di hauermi mandato la ſalutione di queſta ragione ſe io non la ſapero riſoluere. </s> <s id="s.002913">La <lb></lb>qual ragione procedendo per Algebra (come credo che ſapeti) conduſſe l'operante in <lb></lb>el capitolo de coſe, et numero equal à cubo Et la regola da riſoluere tal capitolo, affer <lb></lb>mo eſſer totalmente ignorata da uoi, & per moſtrarue che di queſto ne ſon certißi<lb></lb>mo me offeriſco à deponere circa cio ducati diece contra uno, & accio non crediate <lb></lb>ch'io parli auentura dico che dapoi che io hebbe ritrouato la regola del capitolo de co <lb></lb>ſa è cubo equal à numero, per alcuni auiſi di tal inuentione il giorno ſeguente ritrouai <lb></lb>regola general anchora à queſto di coſe et numero equal à cubo, la cur regola gia mai <lb></lb>haueria potuta inueſtigare ſenza la prima, cioe ſenza quella di coſa è cubo equal à nu<lb></lb>mero, & perche tal regola è da uoi ignorata, tanto piu ui è occulta queſta di coſe, & <lb></lb>numero equale, a cubo, la quale con cautela ue credeui di cauarmela da le mani con di<lb></lb>re che haueui data la ſua ſolutione al meſſo, la qual bogia mi fa dubitare che uoi non <lb></lb>ſappiati riſoluere nanche la uoſtra prima qual ui mando reſolta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002914">O<emph type="italics"></emph>ltra di queſto mi pregati ch'io ui <expan abbr="mãda">manda</expan> le propoſte per me fatte à maeſtro Anto <lb></lb>niomaria fiore et che ſe non ui uoglio mandar le ſue ſolutioni che le debbia ritener per <lb></lb>me.<emph.end type="italics"></emph.end> E <emph type="italics"></emph>per <expan abbr="tãto">tanto</expan> ue faccio <expan abbr="intẽdere">intendere</expan> che le dette m<gap></gap>. 30. queſtioni ſono digran ſcrittura<emph.end type="italics"></emph.end><pb xlink:href="042/01/237.jpg"></pb><emph type="italics"></emph>& à douerucle regiſtrare tutte ue andaria da ſcriuere aſſai & ſi mal me ritrouaioe<lb></lb>cupato me ritrouo al preſente & la cauſa é che ho posto fuora alcuni cartelli publici <lb></lb>qualmente dominica proßima uoglio principiare à iſponere publicamente in ſan zuan <lb></lb>nepolo, la ſcientia di peſi & mostr are alcune coſe operatiui ſopra la pratica delle co<lb></lb>ſe per me ritrouate ſopra li tiri delle artegliarie con altre uarie particolarita. </s> <s id="s.002915">Et ac<lb></lb>cio che uoſtra eccellentia non ſi creda che queſta ſia una finta per non uolerui ſeruire à <lb></lb>mandarue le dette mie. </s> <s id="s.002916">30. queſtioni ui mando la coppia del cartello che ho poſto fuo<lb></lb>ra gia fa dui giorni, & per moſtrarui che ho uolonta de ſeruirui (anchor che ſia occu <lb></lb>pato) ue ne mando, per al preſente noue che mi ſono reſtati in memoria delle dette mie <lb></lb>questioni (perche in uero) io non ne fece de quelli nota ne memorria alcuna da tener ap <lb></lb>preſſo di me, ma ceſſato che me ſia queſte mie occupationi di leggere publico, ne anda<lb></lb>ro à cauar la coppia dal notaro, & ue la mandaro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002917">E<emph type="italics"></emph>l primo de detti queſiti ſe ben me aricordo fu ſopra il capitolo de cenſo è cubo e<lb></lb>qual à numero, & ue lo propoſi largamente da poterſi egualiar à che numero liparea <lb></lb>pur che deſſela coſa irrationale. </s> <s id="s.002918">Qual diceua in queſto modo trouatime una quantita <lb></lb>che ſia irrationale che multiplicata fia la ſua radice piu. </s> <s id="s.002919">40. faccia numero rationale <lb></lb>è diſcreto, & ue la propoſi coſi larga di poterſi egualiar à che numero gli parea per un <lb></lb>certo mio riſpetto, et non ue ne detti altro ſopra à tal capitolo, uero è che meſſer zuan <lb></lb>ne da Coi mi prego che ui deſſe queſto caſo aſſolto & io ge lo dedi riſolto in uno ſimpli <lb></lb>ce reciſo qual ſuſe <expan abbr="bẽ">bem</expan> me aricordo. </s> <s id="s.002920">78. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.002921">308. <emph type="italics"></emph>et per tal ſolutione lui ui trouo una <lb></lb>certa regola da ſoluere tutti ſimili, e pero piu non mi fidaria à proporli ſotto tal for<lb></lb>ma, ma tal, ſua regola non ſerue ſaluo in quelli numeri, ouer ſolutioni, che ſe riſolueno <lb></lb>in un reſiduo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002922">E<emph type="italics"></emph>l ſecondo queſito fu ſopra il capitolo de cenſo é numero equal à cubo & non ue ne <lb></lb>detti ſimelmente altro che uno ſopra tal capitolo. </s> <s id="s.002923">Ma ſopra al capitolo de cubo, e nu<lb></lb>mero equal à cenſi non ue ne dette elcuno perche coſi al improuiſo non potei trouar re <lb></lb>gola à tal capitolo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002924">E<emph type="italics"></emph>l terzo poi fu ſopra il capitolo de coſa è cubo equal à numero & ge lo detti pur <lb></lb><expan abbr="largamẽte">largamente</expan> da poterſi egualiare à che numero gli parea pur che deſſe la coſa irrationa <lb></lb>le, et <expan abbr="nõ">non</expan> ue ne ppoſi altro ſopra à tal capitolo, ma <expan abbr="nõ">non</expan> me aricordo come diceua preciſe.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002925">E<emph type="italics"></emph>l quarto fu ſopra el capitolo de coſe, e numero equal à cubo ne piu ue ne uolſi pro <lb></lb>ponere ſopro à tal capitolo, et ſopra al capitolo de cubo, é numero equal à coſe <expan abbr="nõ">non</expan> ue ne <lb></lb>propoſi alcuno perche coſi al improuiſa <expan abbr="nõ">non</expan> potetitrouare la regola de tal capitolo. <lb></lb></s> <s id="s.002926">Del quinto <expan abbr="nõ">non</expan> me aricordo, come diceſſe ne manco de li altri <expan abbr="ordinariamẽte">ordinariamente</expan>, ma ſo ben <lb></lb>che io gli propoſe fra le altre coſe che mi doueſſe ritrouar una quantita, qual multipli <lb></lb>cata per<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.002927">24. piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.002928">6. piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.002929">1. 1/2. faceſſe numero rationale, et diſcreto.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002930">A<emph type="italics"></emph>nchora io gli propoſi una linea retta et gli adimandai che me la ſegaſſe geometri <lb></lb>camente in. </s> <s id="s.002931">3. tal parti che facendo di quelle parti un triangolo quel fuſſe retangolo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002932">A<emph type="italics"></emph>nchora io gli propoſiuna piramide troncata & gli adimandai che geometrica<lb></lb>mente, me la ſegaſſe in. </s> <s id="s.002933">3. parti equali per trauerſo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002934">A<emph type="italics"></emph>nchora gli propoſi uno <expan abbr="triãgolo">triangolo</expan> de tre lati inequale et gli adimandai che in quel<lb></lb>lo geometricamente me gli inſcriueſſe un quadrato.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="119" xlink:href="042/01/238.jpg"></pb> <p type="main"> <s id="s.002935">A<emph type="italics"></emph>nchora io gli propoſi la ſottoſcritta questione per eſſermene ſtata propoſta quaſi <lb></lb>una ſimile ſotto mane da lui qual tenea <21> ragion fortißima, ma <expan abbr="l'agunẽtai">l'agunentai</expan> in difficult<gap></gap><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002936">H<emph type="italics"></emph>aggio una botta piena de uino puro, della quale ne cauo dui ſecchi, & la riempio <lb></lb>di acqua, & dapoi queſto ne recauò fuora dui altriſecchi, & la reimpio di acqua, & da <lb></lb>poi queſto ne recauo pur fuora dui ſecchi, & la riempio di acqua, & coſiuado faccian <lb></lb>do per fin al numero de. </s> <s id="s.002937">6. uolte & fatto queſto in ultimo ritrouo, che in la detta bot<lb></lb>ta era la mita uino, & la mita acqua, & gli adimandaua la tenuta della botta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002938">Q<emph type="italics"></emph>uattro altri queſiti gli propoſi anchora in Algebra communa, quali non me ari<lb></lb>cordo, come preciſamente diceuano. </s> <s id="s.002939">Molti ue ne propoſe de aſſoluere geometrice, per <lb></lb>che lui non haueua alcuna ſcientia in tal operare, maſolamente pratica nelli numeri, li <lb></lb>quali non gli ho allamente, ma un'altra uolta con piu commodita, come detto, ue li man <lb></lb>daro, perche li andaro à tuor dal notaro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002940">A<emph type="italics"></emph>nchora uoſtra Eccellentia mi prega, che ui uoglia mandar la ſolutione di qualche <lb></lb>una delle uostre prime. </s> <s id="s.002941">7. queſtioni, che mi portò il libraro. </s> <s id="s.002942">Certamente molto mi ma<lb></lb>rauiglio, & ſtupiſco, hauendo quella hauuto tanto per male, per hauer io detto al li<lb></lb>braro, che uoſtra Eccellentia non ſaperia riſoluere tai propoſitioni, & hauendoſi poi <lb></lb>quella con tanta arrogantia auantato, che lei li ſapeua riſoluere auanti, che maeſtro <lb></lb>Zuane ſapeſſe numerar fina à. </s> <s id="s.002943">10. & che anchora me richiedeti, che ue le debbia riſol<lb></lb>uere, ma tengo, che uoi non ue aricordati di quello, che hauueti detto nel principio del <lb></lb>la uoſtra lettera, non altro. </s> <s id="s.002944">In Venetia alli. </s> <s id="s.002945">18. Febraro.<emph.end type="italics"></emph.end> 1539. </s> </p> <p type="main"> <s id="s.002946">N<emph type="italics"></emph>icolo Tartaglia<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002947">QVESITO. XXXIII. FATTO CON VNA <lb></lb><emph type="italics"></emph>lettera dalla eccellentia de meſſer Hieronimo Cardano <lb></lb>l'Anno. 1539. Adi. 19. Marzo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002948">MESSER HIER ONIMO. M<emph type="italics"></emph>eſſer Nicolo mio carißimo ho riceuuto <lb></lb>una uoſtra lettera aſſai longa, la quale quanto piu è ſtata longa, tanto piu me <lb></lb>piacciuta, & uorria fuſſe ſtata doppia, tanto ne ui penſate, che le mie mordente paro<lb></lb>le ſiano procedute, ne da odio non eſſendogli cauſa, ne da maligna natura facendo io be <lb></lb>ne doue poſſo, piu preſto, che male, eſſendo aſſueto nell eſſercitio mio del medicare, <lb></lb>che porta queſto, ne manco ſon moſſo da inuidia, perche ſe uoiſeti, o eguale, o menore, <lb></lb>non ne ho cauſa ſe ſeti maggiore in queſt'arte debbo cercare di agguagliarue, & non <lb></lb>de dirne male, oltra di cio l'inuidioſo maledice in abſentia, & non in preſentia, ma io <lb></lb>ſcriſſe queſto per eſcitarui à reſcriuere, giudicandoui di pelegrino ingegno, come ſeti <lb></lb>per relatione de meſſer zuan Colle, il quale è ſtato qua, & hauendolo io molto fauori<lb></lb>giato, & fattogli appiacere, ſecondo il mio potere, donde che lui ui faceua aſſai bene, <lb></lb>& haueua anchora in diſſegno di laſſarui una mia lettura, ma lui ſi portò ingratamen<lb></lb>te, dicendo male priuatamente, & publicamente, & inuitandomi fuora di propoſito, <lb></lb>con cartelli, & ſcritture, la qual coſa non riuſcendoli à ſuo modo, che di una petitione <lb></lb>hebbe. </s> <s id="s.002949">3. ſolutioni, una di Euclide, l'altra di Ptolomeo, l'altra di zebber, ſi confuſe tal<lb></lb>mente, che ſi parti per diſperato, & laſſo una ſcuola de forſi. </s> <s id="s.002950">60. ſcolari, dilche me ne <pb xlink:href="042/01/239.jpg"></pb>dolſe aſſai, ſi che ſe ue ho ſcritto aſper amente l'ho fatto uolontieri, penſando di far ſe<lb></lb>guire quello, che ne ſeguito, cioe di hauere la riſpoſta uoſtra con l'amicitia di coſi ſin<lb></lb>golar huomo in queſt'arte à quel giudico per le coſe ſcritte nella uoſtra lettera, ſi che <lb></lb>ho fatto un peccato di che non me ne uoglio pentire.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002951">H<emph type="italics"></emph>ora doueti ſapere, che oltra la lettera uoſtra, ho riceuuto uno cartello delle coſe, <lb></lb>che al preſente ſeti per leggere publicamente in San Zuanepolo, il qual cartello mi è <lb></lb>ſommamente piacciuto, & oltra di cio mi prometteti duiiſtromenti per dare al<emph.end type="italics"></emph.end> S.M<emph type="italics"></emph>ar <lb></lb>cheſe, & dui per me, et il<emph.end type="italics"></emph.end> S. O<emph type="italics"></emph>ttauiano ſcriue ne manda quattro pur ſin al preſente non <lb></lb>ho hauuto ne dui, ne quattro, ma dice, ch'io li hauero con certi libri, che mi manda uo<lb></lb>lontieri, gli hauerei hauuti da dare al<emph.end type="italics"></emph.end> S.M<emph type="italics"></emph>archeſe, come gli hauero ue li daro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002952">Q<emph type="italics"></emph>uanto alla riſpoſta delle quattro mie accuſe mi accaſca ſolo riſponderui à due, l'u<lb></lb>na ſi è della accuſatione della uostra quinta propoſitione dell'arte nuoua l'altra è dal ue <lb></lb>nire al cimento con uoi, che ſia piu ualente huomo in queſt'arte.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002953">Q<emph type="italics"></emph>uanto à queſta ſeconda uoglio piu preſto uiuere un poco poltrone, che morire ua <lb></lb>lent'huomo, dapoi che gia ui rendeti, dicendo che Zuanantonio ha mal inteſo, ſi che fac <lb></lb>cio fine à queſto combattimento, ſpero uerreti à Millano, & uoi me conoſcereti ſenza <lb></lb>il depoſito di. </s> <s id="s.002954">100. ducati, perche reuera io ue conoſco per ualent'huomo, & coſi co<lb></lb>noſcendoſi tutti dui poi potremo deliberare.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002955">C<emph type="italics"></emph>irca alla diſputatione della uostra quinta propoſitione certo uoi fati bene à uſar <lb></lb>parole braue, & difendere la uoſtra coſa gia diuulgata Et certo uenendo (come ſpero <lb></lb>piacendo à Dio) uoi à Millano ne parlaremo piu adaggio, et tanto piu ch'io hebbe le uo <lb></lb>ſtre lettere hierſera, & hoggi me biſognato reſcriuerui per commandamento del Sig. <lb></lb>Marcheſe, ſi che non ho potuto hauer conſideratione delle altre uostre propoſitioni, <lb></lb>pregoui mandati, ouer portati quel reſto delle uoſtre. </s> <s id="s.002956">30. concluſioni, che deſti à mae<lb></lb>ſtro Antoniomaria ad ogni modo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002957">S<emph type="italics"></emph>e mi mandaſti qualche ſolutione delle uoſtre, cioe regole, ouer mi dareti, uenendo <lb></lb>l'hauero ſommo appiacere, perche doueti ſapere, ch'io me diletto de ogni gentilezza, <lb></lb>& ch'io ho dato fuora una opera pur di pratica di Geometria, & di Arithmetica, & <lb></lb>di Algebra, della quale ſin à queſt'hora è ſtampato piu della mita, & ſe uoleti, dando<lb></lb>mene ch'io la daga fuora ſotto uoſtro nome, io le daro fuora in fin dell'opera, come ho <lb></lb>fatto de tutti glialtri me hanno dato qualche coſa di bello, & ui ponero uoi per l'inuen <lb></lb>tore, & ſé uoleti ch'io le tenghi occulte, faro come uorreti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002958">I<emph type="italics"></emph>o auiſai la eccellentia del<emph.end type="italics"></emph.end> S.M<emph type="italics"></emph>archeſe de gli iſtromenti quali gli mandati (anchor <lb></lb>che non ſiano per fina hora gionti) et gli dißi del cartello, et ſua eccellentia mi <expan abbr="cõmando">commando</expan> <lb></lb>lo leggeſſe, et tutte queste uoſtre coſe, piacque grandemente à ſua eccellentia. </s> <s id="s.002959">Et mi <expan abbr="cõ-mando">con<lb></lb>mando</expan> di ſubito ui ſcriueſſe la preſente con grande iſtantia in nome ſuo, auiſandoui che <lb></lb>uiſta la preſente doueſti uenir à Millano ſenza fallo, che uorria parlar con uoi. </s> <s id="s.002960">Et coſi <lb></lb>ue eſſorto à douer uenire ſubito, et non penſarui ſu, perche il detto<emph.end type="italics"></emph.end> S.M<emph type="italics"></emph>archeſe è ſi gen <lb></lb>til remuneratore delli uirtuoſi, ſi liberale, et ſi magnamimo che niuna perſona chiſerue <lb></lb>ſua eccellentia, mentre ſia da qualche coſa, reſta <expan abbr="diſcontẽta">diſcontenta</expan>. </s> <s id="s.002961">Si che non reſtati de uenire, <lb></lb>et uenireti à logiare in caſa mia, <expan abbr="nõ">non</expan> altro. </s> <s id="s.002962">Chriſto da mal ui guardi alli. </s> <s id="s.002963">13. marzo.<emph.end type="italics"></emph.end> 1539. </s> </p> <p type="main"> <s id="s.002964">H<emph type="italics"></emph>ieronimo Cardano medico.<emph.end type="italics"></emph.end><pb pagenum="120" xlink:href="042/01/240.jpg"></pb>NICOLO. P<emph type="italics"></emph>er coſtui ſon ridutto à un ſtranio paſſo, perche ſenon uado à Millano <lb></lb>il<emph.end type="italics"></emph.end> S.M<emph type="italics"></emph>archeſe il potria hauer per male, & qualche male me potria riuſcire, & mal u<gap></gap><lb></lb>lontiera ui uado, pur ui uoglio andare.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002965">QVESITO. XXXIIII. FATTO PERSONAL<lb></lb><emph type="italics"></emph>mente dalla eccellentia del medeſimo meſſer Hieronimo Car <lb></lb>dano in Millano in caſa ſua Adi. 25. Marzo.<emph.end type="italics"></emph.end> 1539.</s> </p> <p type="main"> <s id="s.002966">MESSER HIERONIMO. H<emph type="italics"></emph>o molto accaro che uoiſiati uenuto in que <lb></lb>ſta, che la eccellentia del<emph.end type="italics"></emph.end> S.M<emph type="italics"></emph>archeſe è caualcato per fina à Vegeuene, perche <lb></lb>haueremo commodita di poterſe galdere, et ragionare inſieme delle coſe noſtre per fin <lb></lb>che torni. </s> <s id="s.002967">Certamente uoi ſeti ſtato pur troppo diſcorteſe à non hauermi uoluto da<lb></lb>re quella regola da uoi ritrouata ſopra il capitolo di coſa, e cubo egual à numero, et maſ <lb></lb>ſime hauendouene tanto pregato.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ue diro, io non fazzo tanto il careſtioſo, per <lb></lb>il ſimplice capitolo, ne per le coſe ritrouate per lui, ma per quelle, che per notitia di <lb></lb>quello ſi poſſono ritrouare, perche eglie una chiaue, che ne apre la uia à potere inueſti<lb></lb>gare infiniti altri capitoli, & ſe il non fuſſe che al preſente io ſon occupato nella tradut <lb></lb>tione di Euclide, in uolgare (& per fin à queſt'hora l'ho tradutto per fin al ſuo. </s> <s id="s.002968">13. li<lb></lb>bro) à molti altri capitoli haueria gia trouato regola generale, ma ſpedito che habbia <lb></lb>queſta mia fatica di Euclide gia principiata, ho deſignato di <expan abbr="cõponere">componere</expan> un'opera di pra<lb></lb>tica, & inſieme con quella, una nuoua Algebra, nella quale non ſolamente ho deliberato <lb></lb>di publicare ad ogni huomo tutte le dette mie inuentioni de capitoli nuoui, ma molti al <lb></lb>tri, che ſpero di ritrouare, & anchora uoglio moſtrare la regola di poterne inueſtigar <lb></lb>ne infiniti altri qualſpero, che la ſara una coſa utile, & bella, & queſta é la cauſa, che <lb></lb>me glifa negar ad ogniuno, per che io al preſente non ui pongo alcuna cura ſopra di <lb></lb>loro (per eſſer, come detto, occupato ſopra Euclide) & inſignandoli ad alcuno ſpecu<lb></lb>latiuo (come che è uoſtra eccellentia) facilmente potria con tal euidentia trouar altri <lb></lb>capitoli (per eſſer facile lo aggiongere alle coſe trouate) & publicarli, come inuento<lb></lb>re, ilche facendo mi guaſtaria ogni mio diſſegno. </s> <s id="s.002969">Si che questa è la principal cauſa, che <lb></lb>mi ha fatto eſſer tanto diſcorteſe con uoſtra Eccellentia, & tanto piu facendo al preſen <lb></lb>te imprimere quella ſua opera in ſimil materia, & hauendomi anchor ſcritto di uoler <lb></lb>dar fuora tai mie inuentioni ſotto mio nome, & farmene inuentore La qual coſa in ef<lb></lb>fetto non mi piace in conto alcuno, perche tale mie <expan abbr="inuẽtioni">inuentioni</expan> le uoglio publicare in ope <lb></lb>re mie, et non in opere de altra perſona.<emph.end type="italics"></emph.end> M.H. E<emph type="italics"></emph>ue ho pur ſcritto anchora che ſe uoi <lb></lb>non ui contentati, che io ue le dia fuora, che io le reteniro ſecrete.<emph.end type="italics"></emph.end> N. B<emph type="italics"></emph>aſta che in que <lb></lb>ſta parte non ui ho uolesto credere.<emph.end type="italics"></emph.end> M.H. I<emph type="italics"></emph>o ui giuro, adſacra Dei euangelia, & da <lb></lb>real gentil'huomo, non ſolamente da non publicar giamai tale uoſtre inuentioni, ſe me <lb></lb>le inſignate. </s> <s id="s.002970">Ma anchora ui prometto, et impegno la fede mia da real Christiano, da no <lb></lb>tarmele in zifera, accio che dapoi la mia morte alcuno non le poſſa intendere, ſe me il <lb></lb>uoleti mo credere credetilo, ſe non laſſatilo ſtare.<emph.end type="italics"></emph.end> N. N<emph type="italics"></emph>on uolendo io preſtar fede à <lb></lb>tanti uoſtri giur amenti io meritaria certamente da eſſer giudicato huomo ſenza fede, <lb></lb>ma perche ho deliberato caualcare per fina à Vegeuene à ritrouar la eccellentia del<emph.end type="italics"></emph.end> S. <lb></lb>M<emph type="italics"></emph>archeſe, perche eglie hormai tre giorni ch'io ſon qua, & me rincreſſe lo aſpettare <pb xlink:href="042/01/241.jpg"></pb>tanto, ritornato che ſia ui prometto di moſtrarui il tutto.<emph.end type="italics"></emph.end> M.H. D<emph type="italics"></emph>apoi che haueti <lb></lb>deliberato da uolere adogni modo caualcare per fina à Vegeuene dal<emph.end type="italics"></emph.end> S. M<emph type="italics"></emph>archeſe, ni <lb></lb>uoglio dar una lettera da dar à ſua Eccellentia, accio che quella ſappia, che uoi ſeti, ma <lb></lb>nanti che ue parteti, uoglio che mi moſtrati la regola di queſti uostri capitoli, come che <lb></lb>me haueti promeſſo.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>o ſon contento, ma uoglio che ſappiati, che per potermi ari <lb></lb>cordare in ogni mia improuiſa occorrentia tal modo operatiuo, io l'ho redutto in uno <lb></lb>capitolo in rima, perche ſe io non haueſſe uſato questa cautella ſpeſſo me ſaria uſcito di <lb></lb>mente, & quantunque tal mio dire in rima non ſia molto terſo non mi ho curato, per<lb></lb>che mi basta che miſerua à ridurme in memoria tal regola ogni uolta, che io il dica, il <lb></lb>qual capitolo ue lo uoglio ſcriuere de mia mano, accio che ſiati ſicuro, che ui dia tal <lb></lb>inuentione giuſta, & buona.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002971">Q<emph type="italics"></emph>uando chel cubo con le coſe appreſſo <lb></lb>Se agguaglia à qualche numero diſcreto <lb></lb>Trouan dui altri differenti in eſſo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002972">D<emph type="italics"></emph>apoi terrai queſto per conſueto <lb></lb>Che'llor produtto ſempre ſia eguale <lb></lb>Alterzo cubo delle coſe neto,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002973">E<emph type="italics"></emph>l reſiduo poi ſuo generale <lb></lb>Delli lor lati cubi ben ſottratti <lb></lb>Varra la tua coſa principale.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002974">I<emph type="italics"></emph>n el ſecondo de coteſtiatti <lb></lb>Quando che'l cubo reſtaſſe lui ſolo <lb></lb>Tu oſſeruarai queſt'altri contratti,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002975">D<emph type="italics"></emph>el numer farai due tal part'à uolo <lb></lb>Che l'una in l'altra ſi produca ſchietto <lb></lb>El terzo cubo delle coſe in ſtolo<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002976">D<emph type="italics"></emph>elle qual poi, per communprecetto <lb></lb>Torrai li lati cubi inſieme gionti <lb></lb>Et cotal ſomma ſara il tuo concetto.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002977">E<emph type="italics"></emph>l terzo poi de queſti noſtri conti <lb></lb>Se ſolue col ſecondo ſe ben guardi <lb></lb>Che per natura ſon quaſi congionti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002978">Q<emph type="italics"></emph>ueſti trouai, & non con paßi tardi <lb></lb>Nel mille cinquecentè, quatroe trenta <lb></lb>Con fondamenti ben ſald'è gagliardi<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002979">N<emph type="italics"></emph>ella citta dal mar'intorno centa.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002980">I<emph type="italics"></emph>l qual capitolo parla tanto chiaro, che ſenz'altro eſſempio credo che uoſtra Eccel <lb></lb>lentia intendera il tutto.<emph.end type="italics"></emph.end> M.H. C<emph type="italics"></emph>ome ſe lo intendero, e l'ho quaſi inteſo per fina el<lb></lb>preſente, andati pur, che, come ſareti ritornato, ue faro poi uedere ſe l hauero inteſo.<emph.end type="italics"></emph.end><lb></lb>N. H<emph type="italics"></emph>or uoſtra Eccellentia ſe aricordi mo à non mancar della promeſſa fede, perche <lb></lb>ſe per mala ſorte quella me mancaſſe, <gap></gap> che me deſſe fuora queſti capitoli, o ſia in<emph.end type="italics"></emph.end><pb pagenum="121" xlink:href="042/01/242.jpg"></pb><emph type="italics"></emph>queſta opera che fatti imprimere al preſente, ouer in altra anch or che quella li deſſe <lb></lb>fora ſatto mio nome, & che mi faceſſe il proprio inuentore, ui prometto, & giuro di <lb></lb>ſarne ſtampare immediate drio un'altra, laqual non ui ſara molto agrata.<emph.end type="italics"></emph.end> M. H. <lb></lb>N<emph type="italics"></emph>on ue dubitati che quello che ui ho promeſſo ue lo attendaro, andati è ſtati ſicuro to<lb></lb>le, dareti queſta mia lettera al Signor Marcheſe da mia parte.<emph.end type="italics"></emph.end> N. H<emph type="italics"></emph>or ſume arrico <lb></lb>mando.<emph.end type="italics"></emph.end> M. H. A<emph type="italics"></emph>ndati in bon'hora.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002981">N. P<emph type="italics"></emph>er la fede mia che non uoglio andare altramente à Vigeuene, ancime uoglio <lb></lb>uoltare alla uolta di Venetia, uada la coſa come ſi uoglia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.002982">QVESITO XXXV. FATTO DALLA ECCELLEN<lb></lb><emph type="italics"></emph>tia del medeſimo<emph.end type="italics"></emph.end> M. H<emph type="italics"></emph>ieronimo Cardano, con una lettera fatta <lb></lb>alli. </s> <s id="s.002983">9. Aprile. </s> <s id="s.002984">1539. mandatame in Venetia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002985">MESSER HIERONIMO. M<emph type="italics"></emph>eſſer Nicolo mio carißimo mi ſono molto <lb></lb>mar auigliato della uoſtra partita coſi al improuiſta ſenza parlare al Signor <lb></lb>Marcheſe qual <expan abbr="uẽne">uenne</expan> el ſabbato Santo, & non pote hauer li uoſtri inſtromenti per fin <lb></lb>al marti dapo Paſqua & con grandißima difficulta, pur gli hebbi & li conzai & ge <lb></lb>li appreſentai il medemo martidi de ſera, certo io penſo che falaſti à non farui conoſce <lb></lb>re da ſua eccellentia, perche eglie Principe liber alißimo & grande amatore de uirtu, <lb></lb>& fautore, & hebbe molto à caro li uostri instromenti, & li uolſe intendere, & io li <lb></lb>moſtrai ſucitamente la ſua ualuta, hor queſto baſta potria anchor uenir tempo che ui <lb></lb>giouaria l'eſſere conoſciuto dal<emph.end type="italics"></emph.end> S. M<emph type="italics"></emph>archeſe, anchor ch'io ſo perche cauſa ue ſiti par <lb></lb>tito perche coloro che ui conſigliorono me lo diſſero.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002986">Q<emph type="italics"></emph>uanto à l'opera mia penſo ſera fornita la ſettimana che uiene che non li manta <lb></lb>ſaluo che tre fogli à fornirla. </s> <s id="s.002987">Quanto alla queſtione del uoſtro capitolo di coſa é cubo <lb></lb>equal à numero ui ringratio aſſai che mi daſeſti tal capitolo, & ui faro conoſcere ch'io <lb></lb>non uiſaro ingrato. </s> <s id="s.002988">Ma pero io confeſſo il mio errore di non hauer hauuto tanto inge <lb></lb>gno che io lo habbia potuto anchora intendere, e pero ui ſupplico per l'amor che mi <lb></lb>portati, & per l'amicitia ch'è tra noi che ſpero durara fin che uiueremo che mi man<lb></lb>dati ſciolta queſta queſtione. </s> <s id="s.002989">1. cubo piu. </s> <s id="s.002990">3. coſe, equal à. </s> <s id="s.002991">10. & ſpero che mandandome <lb></lb>la ue ne trouareti ſi contento quanto io di hauerla riceuuta non altro Chriſto da mal <lb></lb>ui guardi in Millano alli. </s> <s id="s.002992">9. Aprile.<emph.end type="italics"></emph.end> 1539. </s> </p> <p type="main"> <s id="s.002993">H<emph type="italics"></emph>ieronimo Cardano medico tutto uoſtro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002994">NICOLO. H<emph type="italics"></emph>onorando meſſer Hieronimo ho riceputa una uoſtra di. </s> <s id="s.002995">9. Aprile <lb></lb>& ho inteſo il tenor di quella, la cauſa della mia coſi improuiſa et tacita partita da Mi <lb></lb>lano ſenza parlare alla eccellentia del Signor Marcheſe è queſta che quando me par<lb></lb><gap></gap>eti da Venetia per uenir à Milano io promißi alli mei amici di eſſer qua infalante à <lb></lb>Paſqua & conſider ando che ſe io ſtaſeua niente piu di quello ch'io ſteti à partirme da <lb></lb>Millano egliera forza à reſtar mendace, perche uenendo uia à ſtaffetta hebbi fatica ad <lb></lb>eſſer qua el ſebbo Santo ſi che non incolpati alcun che mi habbia conſigliato.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002996">C<emph type="italics"></emph>irca alla uoſtra opera molto deſidero che laſe forniſca presto, & di uederla, per<lb></lb>che per fin che <expan abbr="nõ">non</expan> la uedo ſto ſuſpettoſo che quella non mi manchi di ſede, cioe che quel-<emph.end type="italics"></emph.end><pb xlink:href="042/01/243.jpg"></pb><emph type="italics"></emph>la non ue interponga, li mei capitoli.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002997">C<emph type="italics"></emph>irca al detto mio capitolo de coſa è cubo equal à numero molto mi marauiglio che <lb></lb>uoſtra <expan abbr="eccellẽtia">eccellentia</expan> <expan abbr="nõ">non</expan> habbia inteſo maßime che io parlo chiaro nel detto mio capitolo, <lb></lb>ma ho penſato che uoi ui ſiati ingannato in quel ditto, che dice al terzo cubo delle coſe <lb></lb>netto, cioe penſo che uoi habbiati tolto il terzo del cubo delle coſe, et biſogna tor il cu <lb></lb>bo del terzo delle coſe eſſempi gratia à uoler riſoluere quella equatione de. </s> <s id="s.002998">1. cubo piu. <lb></lb></s> <s id="s.002999">3. coſe equal à. </s> <s id="s.003000">10. che uoſtra <expan abbr="eccellẽtia">eccellentia</expan> mi ha mandata dico che biſogna trouar dui nu<lb></lb>meri (ouer quantita) che la differentia de luno à laltro ſia. </s> <s id="s.003001">10. (cioe tanto quanto è <lb></lb>il noſtro numero) & che il produtto de queſte due quantita multiplicate luna fia l'al<lb></lb>tra facciamo à ponto. </s> <s id="s.003002">1. cioe el cubo della terza parte delle coſe, liquali dui numeri, <lb></lb>ouer quantita, operando per Algebra, ouer per qual altra uia para piu commoda ſe <lb></lb>trouara luna de loro, cioe la menore eſſer<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003003">26. <emph type="italics"></emph>men. </s> <s id="s.003004">5. & laltra, cioe la maggiore<emph.end type="italics"></emph.end> <22><lb></lb>26. <emph type="italics"></emph>piu. </s> <s id="s.003005">5. Hor de cadauna di queſte due quantita biſogna trouar il ſuo lato cubo, cioe <lb></lb>la ſua<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba, & quella della menor ſara<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerrſale cuba de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003006">26. <emph type="italics"></emph>men. </s> <s id="s.003007">5. & quel<lb></lb>la della maggiore ſara<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale cuba de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003008">26. <emph type="italics"></emph>piu. </s> <s id="s.003009">5. Hor biſogna ſottrare il lato <lb></lb>menore del maggiore, et il reſtante ſara el ualore della noſtra coſa principale, el qual <lb></lb><expan abbr="restãte">restante</expan> uenira à eſſer el reſiduo di quelle due<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>uniuerſale cu.cioe ſara<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u.cu.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003010">26. <lb></lb><emph type="italics"></emph>piu. </s> <s id="s.003011">5. men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>u.cuba<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003012">26. <emph type="italics"></emph>me. </s> <s id="s.003013">5. & tanto ualſe la noſtra coſa principale, la qual con<lb></lb>cluſione, oltra che la iſperienza ne renda bona testimonianza, cioe cubando la detta <lb></lb>quantita, ouer coſa, & à tal cubo giongendoui il triplo di detta quantita tal ſumma fa <lb></lb>ra preciſamente. </s> <s id="s.003014">10. come ſe propone, ma anchora <expan abbr="Geometricamẽte">Geometricamente</expan> facilmente ſe di <lb></lb>moſtra la bonta et cauſa di tal operare, & <expan abbr="quãdo">quando</expan> chel fuſſe. </s> <s id="s.003015">1. cubo piu. </s> <s id="s.003016">1. coſa equal <lb></lb>à. </s> <s id="s.003017">11. biſognaria pur trouar dui numeri, ouer quantita, che luna fuſſe. </s> <s id="s.003018">11. piu de laltra, <lb></lb>& che il produtto de luna in laltra faccia. </s> <s id="s.003019">1/27. cioe il cubo del terzo delle coſe, onde <lb></lb><expan abbr="operãdo">operando</expan> come diſopra fu fatto ſe trouara la noſtra coſa ualer<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u.cuba<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003020">30.31/108. <lb></lb><emph type="italics"></emph>piu. </s> <s id="s.003021">5. 1/2. men<emph.end type="italics"></emph.end> <22>.<emph type="italics"></emph>u.cuba<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003022">30.31/108. <emph type="italics"></emph>men, 5. 1/2. non altro Iddio da mal ui guardi in Ve <lb></lb>netia alli. </s> <s id="s.003023">23. di Aprile. </s> <s id="s.003024">1539. aricordatiue della promeſſa.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003025">N<emph type="italics"></emph>icolo Tartaglia<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003026">QVESITO. XXXVI FATTO DALLA ECCEL<lb></lb><emph type="italics"></emph>lentia de meſſer Hieronimo Cardano con una ſua lettera <lb></lb>fatta all. </s> <s id="s.003027">12. di Mazzo.<emph.end type="italics"></emph.end> 1539.</s> </p> <p type="main"> <s id="s.003028">MESSER HIER ONIMO. I<emph type="italics"></emph>n riſpoſta de una uoſtra delli. </s> <s id="s.003029">23. d'Aprile, <lb></lb>hauuta non hieri l'altro, meſſer Nicolo carißimo, ui riſpondero ſucintamente à <lb></lb>partita per partita, & prima, quanto alla eſcuſatione del eſſer partito, ſenza andar à <lb></lb>Vigeueno. </s> <s id="s.003030">Io non uoglio ſaluo quello che uoleti uoi, me rincreſſe l'habbiati pigliato <lb></lb>queſta fatica per cauſa della mia amicitia ſenza frutto alcuno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003031">Q<emph type="italics"></emph>anto à l'opera che ſia fornita per cauarui di ſoſpetto ue ne mando una e ue la <lb></lb>mando disligata che non ho uoluto farla battere per eſſer troppo freſca,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003032">Q<emph type="italics"></emph>uanto al capitolo uostro & al mio caſo per uoi aſſolto ue ne ringratio <expan abbr="ſingola-rißimamẽte">ſingola<lb></lb>rißimamente</expan>, & laudo il uoſtro ingegno ſopra tutti quelli che ho conoſciuti, & me ſta-<emph.end type="italics"></emph.end><pb pagenum="122" xlink:href="042/01/244.jpg"></pb><emph type="italics"></emph>to accaro piu che ſe mi hauesti donato duc. </s> <s id="s.003033">100. & ui conoſco per mìo amicißimo & <lb></lb>ne ho fatto proua & l'ho trouato generalißimo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003034">Q<emph type="italics"></emph>uanto al dubbio che uoi haueti che non ui faccia ſtampare tai uostre inuentioni, <lb></lb>la mia fede che ui ho data con giuramento, ui doueua baſtare, perche la ſpeditione del <lb></lb>mio libro non faceua niente à queſto, perche ſempre che mi pare gli poſſo ſempre ag<lb></lb>giongere, ma ue ho per eſcuſo che la dignita della coſa, non ui laſſa fondare ſopra quel <lb></lb>lo che ui doueti fondare, cioe ſopra la fede d'un gentilhuomo & ui fondati ſopra una <lb></lb>coſa che non ual niente, cioe ſopra il finir d'un libro al quale ſi potria ſempre agion<lb></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></lb>qua chel non è mazor tradimento che à eſſer mancator di fede, & far diſpiacere à chi <lb></lb>ha fatto appiacere, & ſe me eſperimentareti trouareti ſe io ui ſaro amico, ouer nò, <lb></lb>& ſe hauero grato l'amicitia uoſtra, & li piaceri che me haueti fatti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003037">V<emph type="italics"></emph>e auiſo anchora, et caramente ui prego che di queſte mie opere ſtampate per amo <lb></lb>re di quello che li ha <expan abbr="ſtãpate">ſtampate</expan> qual ne <expan abbr="mãdara">mandara</expan> iui da uendere, che ge ne facciati ſpazzar <lb></lb>piu che poßibel ſia per mio amore che, ſe fuſſero ſtampate à mie ſpeſe <expan abbr="nõ">non</expan> ue ne diria pa <lb></lb>rola perche ſon piu caldo del ben di mei amici che del mio, <expan abbr="nõ">non</expan> altro Dio da mal ui guar <lb></lb>di in Milano alli. </s> <s id="s.003038">12. di Marzo.<emph.end type="italics"></emph.end> 1539. </s> </p> <p type="main"> <s id="s.003039">H<emph type="italics"></emph>ieronimus Cardanus Medicus totus ueſter.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003040">NICOLO. H<emph type="italics"></emph>onorandißimo meſſer Hieronimo ho riceputo una uoſtra inſieme <lb></lb>con una delle uoſtre, opere della quale ue ne ringratio, & quantunque al preſente non <lb></lb>habbia tempo di poterla uedere ordinnariamente come ſi de, ſi per eſſer molto occupa <lb></lb>to nella iſpeditione di Euclide ſi per eſſer anchora mezzo amalato, nondimeno ui ho <lb></lb>dato una occchiata coſi disligata, & ho guardato quel uoſtro modo di formar el rotto <lb></lb>di quello reſiduo che rimane nella eſtratione della radice cuba al. 23 capi.alla carta ſi<lb></lb>gnata<emph.end type="italics"></emph.end> D.<emph type="italics"></emph>iiij.doue che uostra eccellentia uole che ſi metta quel detto reſiduo che auan <lb></lb>za nella eſtratione delle radice cube, ſopra una uirgula per numeratore, & di ſotto di <lb></lb>tal uirgulaquella uole che ſi ue metta el treppio del quadrato della radice per denomin<lb></lb>tore nella qual coſa uoſtra eccellentia err a tanto de groſſo che me ne ſtupiſco, perche <lb></lb>cadauno che haueſſe ſolamente mezzo un'occhio lo potria uedere, & ſel non fuſſe che <lb></lb>quella con eſſempij la ua replicando io haueria giudicato che fuſſe errore di ſtampa, <lb></lb>& che el ſia eluero che tal uoſtra regola ſia falſißima ſe puo conoſcere uolendo cauar <lb></lb>la Radice cuba propinqua de. </s> <s id="s.003041">24. la quale primamente ſaria. </s> <s id="s.003042">2. & auanzaria. </s> <s id="s.003043">16. el<lb></lb>qual. </s> <s id="s.003044">16. <expan abbr="partẽdolo">partendolo</expan> per el treppio del quedrato del.<emph.end type="italics"></emph.end> 2. (<emph type="italics"></emph>qualſaria.<emph.end type="italics"></emph.end> 12.) <emph type="italics"></emph>ne uenira. </s> <s id="s.003045">1. 1/3. <lb></lb>qual gionto con la prima radice, cioe con. </s> <s id="s.003046">2. fara. </s> <s id="s.003047">3. 1/3. & coſi ſecondo tal uoſtra rego <lb></lb>la la radice cu. </s> <s id="s.003048">propinqua de. </s> <s id="s.003049">24. ſaria. </s> <s id="s.003050">3. 1/3. coſa molto rediculoſa, perche il cubo de. <lb></lb></s> <s id="s.003051">3. 1/3. ſaria. </s> <s id="s.003052">37. 1/72. coſa molto <expan abbr="lõtana">lontana</expan> dalla uerita, della qualcoſa molto me ne rincreſce <lb></lb>per honor uoſtro <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"></emph.end> 1539. </s> </p> <p type="main"> <s id="s.003054">N<emph type="italics"></emph>icolo Tartaglia tutto uoſtro.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003055">QVESITO XXXVII. FATTO DA MAESTRO <lb></lb>M<emph type="italics"></emph>aphio Poueiani gia noſtro diſcipulo qual stantiaua à Ber <lb></lb>gamo, con una lettera de di. </s> <s id="s.003056">10. Luio.<emph.end type="italics"></emph.end> 1539.</s> </p> <pb xlink:href="042/01/245.jpg"></pb> <p type="main"> <s id="s.003057">MAESTRO MAPHIO. H<emph type="italics"></emph>onorando meſſer maeſtro ſaluti &c. </s> <s id="s.003058">Pre<lb></lb>go uoſtra eccellentia mi uoglia chiarire questa <expan abbr="ragiõcella">ragioncella</expan>, la quale io non la ſo <lb></lb>ne per poſitione ne per altra regola riſoluere. </s> <s id="s.003059">Hor guardati ſe io ſon un cauallo, qual <lb></lb>ragione dice à queſto modo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003060">E<emph type="italics"></emph>glie uno che uorebbe comprar un peſſe, & <expan abbr="domāda">domanda</expan> quanto ne uoi tu della lira groſ <lb></lb>ſa da once. </s> <s id="s.003061">30. come qui in Bergamo ſiuſa, & colui riſponde & dice, ne uoglio tanti de <lb></lb>nari della lira con quante once peſa tutto il peſſe, et coſi à quel mercato fu peſato il det <lb></lb>to peſce qual monto ſoldi. </s> <s id="s.003062">8. ſe adimanda quante lire peſaua tutto il peſce. </s> <s id="s.003063">Et ue de<lb></lb>gnareti di darmene auiſo & perdonatime ſe ogni tratto ue dago diſturbo con qualche <lb></lb>chimera di poco ſugo certo ui poteti accorgere che io dago poca opera al ſtudio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003064">A<emph type="italics"></emph>nchora ui ho da auiſarue queſto de nouo, che uno mio amico da Milano m'ha ſcrit <lb></lb>to come che il Medico Cardano compone un'altra opera, in Algebra, ſopra certi ca<lb></lb>pitoli nouamente trouati, onde penſo che le ſiano le coſe che gia me diceſti hauerli in<lb></lb>ſegnate ſi che mi dubito che ui uoglia gabbare non altro à uoimol to mi aricomando, <lb></lb>& offero in Bergamo alli. </s> <s id="s.003065">10. di Luio.<emph.end type="italics"></emph.end> 1339. </s> </p> <p type="main"> <s id="s.003066">M<emph type="italics"></emph>aphio Poueiani uoſtro diſcepolo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003067">NICOLO. M<emph type="italics"></emph>aeſtro Maphio carißimo ho riceuuto la uoſtra alla qual breuemen <lb></lb>te riſpondo, & dico che il detto peſſe peſaua once<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003068">2880. <emph type="italics"></emph>lequal once le ritrouo in <lb></lb>questo modo. </s> <s id="s.003069">Io pongo chel peſſe peſaſſe. </s> <s id="s.003070">1. coſa di once, adunque fu poſto la lira una <lb></lb>coſa de danari diro adunque ſe onci. </s> <s id="s.003071">30. ual una co.de danari, che ualera. </s> <s id="s.003072">1. coſa de on<lb></lb>ce multiplico. </s> <s id="s.003073">1. coſa.de once fia. </s> <s id="s.003074">1. coſa de danari fara. </s> <s id="s.003075">1. cenſo de danari da partir <lb></lb>per. </s> <s id="s.003076">30. qual partendolo me ne uien. </s> <s id="s.003077">1. cenſo, eſimo de. </s> <s id="s.003078">30. & queſto tal rotto ſara equa <lb></lb>le à danari. </s> <s id="s.003079">96. cioe à ſoldi. </s> <s id="s.003080">8. fatto in danari, leuo li rotti et feguito el capitolo trouo la <lb></lb>coſa ualer<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003081">2880. <emph type="italics"></emph>& tante once peſaua el detto peſſe, come di ſopra dißi, & ancho <lb></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></lb>ciſamonte danari. </s> <s id="s.003083">96. cioe ſoldi. </s> <s id="s.003084">8. ch'è il propoſito.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003085">C<emph type="italics"></emph>irca alla noua che me ſcriueti hauer inteſo del Medico Cardano da Mila no, cer <lb></lb>tamente ne ho riceuuto faſtidio aſſai, perche s'eglie il uero che lui dice di uo ler darfo <lb></lb>ra capitoli nouamente ritrouati, el non puo eſſer altramente di quello che haueti det<lb></lb>to, e pero il prouerbio <expan abbr="nõ">non</expan> <expan abbr="mẽtiſſe">mentiſſe</expan>, qual dice. </s> <s id="s.003086">Quello che tu non uoi che ſi ſappia nol dir <lb></lb>ad alcuno, stati attento ſe intendereti altro ſopra di queſto datimene auiſo non altro <lb></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"></emph.end> 1539. </s> </p> <p type="head"> <s id="s.003089">QVESITO. XXXVIII. FATTO CON VNA <lb></lb><emph type="italics"></emph>lettera dalla eccellentia de meſſer Hieronimo Cardano <lb></lb>riceputa alli. </s> <s id="s.003090">4. di Agoſto.<emph.end type="italics"></emph.end> 1539.</s> </p> <p type="main"> <s id="s.003091">MESSER HIERONIMO. P<emph type="italics"></emph>er auiſo del noſtro ben ſtare, & de molte <lb></lb>altre lettere quale ue ho ſcritte anchor non ue ſiati dignato di reſcriuermi, & <lb></lb>tanto piu io ue ho mandato adomandare la reſolutione de diuerſi queſiti alli quali non <lb></lb>mi haueti riſpoſto, & tra li altri quello di cubo equale à coſe, e numero, eglie ben <lb></lb>uero che ho inteſo tal regola, ma quando che il cubo della terza parte delle coſe ec-<emph.end type="italics"></emph.end><pb pagenum="123" xlink:href="042/01/246.jpg"></pb><emph type="italics"></emph>cede il qu adrato della mita del numero, all'hora non poſſo farli ſeguir la equatione, <lb></lb>come appare, pero haueria appiacere me ſolueſti queſta. </s> <s id="s.003092">1. cubo egual à. </s> <s id="s.003093">9. eoſe piu. <lb></lb></s> <s id="s.003094">10. & di queſto mi fareti ſommo appiacere.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003095">V<emph type="italics"></emph>i prego anchora che mi uogliati mandarme quel uostro modo da deſcriuere Geo<lb></lb>metrice uno quadrato in un triangolo de lati diuerſi, pero che circa à tal coſa me gliſo <lb></lb>no affaticato aſſai, & mai ho potuto ritrouar modo da ſaperlo fare, offerendomi an<lb></lb>chora mi per uoi, ſe poſſo, e uaglio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003096">V<emph type="italics"></emph>e auiſo anchora qualmente io indrizzai da uoi il signor Don Diego de Mendo<lb></lb>cia Ambaſciatore della maesta dell'Imper atore, qual ſe diletta di queste ſcientie, qual <lb></lb>penſo non ui ſara inutile, & gli dißi dell'altezza delle uirtu uoſtre, come meritati.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003097">Q<emph type="italics"></emph>uanto alla proßimatione della Radice, & della formatione del ſuo rotto, nelli re<lb></lb>ſidui delli numeri, che non ſono cubi. </s> <s id="s.003098">Dico che ne ſono due altre regole buone poſte nelle <lb></lb>detta opera, & in quella non ui caſca errore, ſaluo che nel detto eſſempio de<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. <lb></lb></s> <s id="s.003099">24. perche la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba del detto. </s> <s id="s.003100">24. reuera ſarebbe circa. </s> <s id="s.003101">2. 1/4. ouer parlando piu <lb></lb>preciſamente ſaria. </s> <s id="s.003102">2. 20/81. non altro. </s> <s id="s.003103">Chriſto da mal ui guardi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003104">H<emph type="italics"></emph>ieronymus Cardanus medicus totus ueſter.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003105">NICOLO. S<emph type="italics"></emph>to in fantaſia di non dar riſpoſta à questa, ſi come che ho fatto ancho <lb></lb>ra alle altre due, pur ui uoglio riſpondere, & farli intendere quello, che ho inteſo di <lb></lb>lui. </s> <s id="s.003106">Et dapoi che uedo, che ua ſoſpettando ſopra la retta uia della regola del capitolo di <lb></lb>coſe, e numero, egual à cubo, uoglio tentareſe gli poteſſe cambiare li dati che ha in ma <lb></lb>ne, cioe remouerlo di tal uia retta, & farlo entrare in qualche altra, à benche credo <lb></lb>non ui ſara meggio, nondimeno il tentar non nuoce.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003107">M<emph type="italics"></emph>eſſer Hieronimo ho riceuuta una uoſtra, nella quale me ſcriueti qualmente haue<lb></lb>ti inteſo il capitolo de cubo, eguale à coſe, & numero, ma che quando il cubo della ter<lb></lb>za parte delle coſe, eccede il quadrato della mita del numero, che all'hora non poteti <lb></lb>fargli ſeguir la equatione, & che per tanto me pregati, che ue dia riſolto queſto capi<lb></lb>tolo de. </s> <s id="s.003108">1. cubo, eguale à. </s> <s id="s.003109">9. coſe piu.<emph.end type="italics"></emph.end> 10. </s> </p> <p type="main"> <s id="s.003110">E<emph type="italics"></emph>per tanto ue riſpondo, & dico, che uoi non haueti appreſa la buona uia per riſol<lb></lb>uere tal capitolo, anci dico, che tal uoſtro procedere è in tutto falſo, circa al darui que<lb></lb>ſto capitolo, che me haueti mandato riſolto, ue dico, che molto me rincreſce di quello, <lb></lb>che per fina à quest'hora ui ho dato, attento che ho inteſo da perſone degne di fede, <lb></lb>che uoi ſeti per dar fuora un'altra opera in Algebra, & che ue andati auantando per <lb></lb>Millano hauer trouato nuoui capitoli in Algebra, ma auertite, che ſe uoi mancareti di <lb></lb>fede à me, che certamente io non ui mancaro à uoi (per non eſſer mio coſtume) anci ui <lb></lb>prometto di attenderui piu di quello, che ui ho promeſſo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003111">A<emph type="italics"></emph>nchora me pregati, che ui uoglia mandare il modo da deſcriuere in uno triangolo <lb></lb>de lati diuerſi Geometricamente uno quadrato. </s> <s id="s.003112">Per moſtr arui che ho fatto qua in Ve<lb></lb>netia qualche buon diſcipulo, ue auiſo qualmente ho proposto queſto caſo à dui miei di <lb></lb>ſcepoli, delli quali l'uno ha nome meſſer Ricardo Ventuorthe gentil'huomo Ingleſe, & <lb></lb>l'altro è un meſſer Zuanantonio di Ruſconi qua di Venetia, & cadauno di loro à con<lb></lb>correntia dell'altro, la mattina ſeguente à buon'hora mi porto tal caſo aſſolto. </s> <s id="s.003113">& lauia <lb></lb>del procedere dell'uno è molto differente di quella dell'altro, & anchor della mia, & <pb xlink:href="042/01/247.jpg"></pb>accio che quella ſia certa di queſto, ho uoleſto che cadauno di loro ui manda tal ſolutlo<lb></lb>ne ſcritta de ſua mano, le quale ſono le inchiuſe in queſta, & ſe nella riſolutione di meſ<lb></lb>ſer Ricardo, ui trouareti qualche uocabolo, ouer parola mal proferta per non hauer <lb></lb>la retta pronontia della lingua Italiana uoi l'hauereti per iſcuſo, tamen ſo che per di<lb></lb>ſcrettione quella intendera il tutto.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003114">C<emph type="italics"></emph>irca all'errore per quella commeſſo, ouer fatto doue che inſegna à formar il rot<lb></lb>to delli reſidui, che auanzano nella eſtratione della radice cuba, nelli numeri non cubi, e <lb></lb>quella ſe ſcuſa, et dice primamente che in la detta opera ue ne ſono due altre regole buo <lb></lb>ne, ma non dice in che capitolo, ouer à quante carte ſiano.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003115">C<emph type="italics"></emph>irca questa particolarita riſpondo ch'io non ho guardata da quella uolta in qua al <lb></lb>tramente la detta uoſtra opera, ne manco l'ho fatta, anchora ligare ne manco ho tem<lb></lb>po di uederla al preſente per eſſer (come piu uolte ho detto, e ſcritto) occupato, circa <lb></lb>la traduttione di Euclide, e pero non ſo che riſpondere, de quelle altre due uostre re<lb></lb>gole, quale dite che ſono buoue. </s> <s id="s.003116">Ma ben ui dico (eſſendo come haueti detto) che il mi pa<lb></lb>re il uoſtro procedere molto diſordinato, & diſregolato, & non ſo doue che quella <lb></lb>habbia tolto tal ordine, à dar regola à una medeſima particolarita in tre diuerſi luo<lb></lb>chi in una medeſima opera.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003117">M<emph type="italics"></emph>a me ho poi penſato che forſi quella non ha datta fuora tal opera, come coſe com<lb></lb>poste da ſua teſta, ma come coſe elette raccolte, & copiate de diuerſi libri à penna, & <lb></lb>in diuerſi tempi, ſi come che gliſono uenuti alle mani. </s> <s id="s.003118">Perche ſe quelle fuſſeno coſe com <lb></lb>poſte, & ordinate di ſua teſta. </s> <s id="s.003119">Certamente io giudicaria in quella piu preſto ignoran<lb></lb>tia, che intelligentia perche la ſofficientia dell'huomo nella compoſitione d'un'opera ſi <lb></lb>conoſce nell'ordine ſuo, & non nella altezza della materia di che tratta. </s> <s id="s.003120">Et che il ſia il <lb></lb>uero, il ſi uede che l'altezza delle coſe di che ha trattato Euclide, non ſono quelle, che <lb></lb>ui habbiano dato ſi gran nome, perche la maggior parte di quelle erano note à cadau<lb></lb>no Philoſofo, perche molti altri anciani haueuano di tal materie abbondantemente <lb></lb>trattato. </s> <s id="s.003121">Auanti di Euclide, ma ſolamente per hauerle coſi con tanto mirabil ordine <lb></lb>raccolte, aſſettate, & ordinate.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003122">S<emph type="italics"></emph>econdariamente quella ſottogionge, & dice, che in quella tal ſua regola da me tan<lb></lb>ſata, non ui caſca errore, ſaluo che nel detto eſſempio de Radice cuba. </s> <s id="s.003123">24. Et io dico, <lb></lb>che in cadauno rotto formato con tal uoſtro ordine ſempre ui caſcara errore, & non <lb></lb>poco, ma io ui diedi lo eſſempio coſi ſopra la Radice cuba de. </s> <s id="s.003124">24. per farui piu eui<lb></lb>dente tal errore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003125">T<emph type="italics"></emph>ertio quella concede che nel detto eſſempio de Radice cuba de. </s> <s id="s.003126">24. cauato ſecon<lb></lb>do la regola per lei poſta, eſſer falſo, & credendoſi di hauerlo conoſciuto, & emen<lb></lb>dato dice, che reuera non ſarebbe, ſaluo circa. </s> <s id="s.003127">2. 1/4. ouer parlando piu preciſamente, <lb></lb>che quella ſaria. </s> <s id="s.003128">2. 20/81. della qual concluſione me ne ho rideſto aſſai, perche quella cre<lb></lb>dendoſi di emendare il ſuo primo errore, ne ha commeſſo dui altri maggiori, dicendo <lb></lb>che reuera, la Radice cuba propinqua del detto. </s> <s id="s.003129">24. ſaria circa. </s> <s id="s.003130">2. 1/4. & che parlan<lb></lb>do piu preciſamente, che quella ſaria.<emph.end type="italics"></emph.end> 2. 20/81. P<emph type="italics"></emph>erche il cubo de. </s> <s id="s.003131">2. 1/4. ſaria ſolamente.<emph.end type="italics"></emph.end><lb></lb>11.25/<gap></gap>4. <emph type="italics"></emph>il qual cubo il ſi uede quanto ch'eglie menore, ouer lontano dal noſtro. </s> <s id="s.003132">24. & <lb></lb>perche. </s> <s id="s.003133">2. 20/81. è alquanto menore de. </s> <s id="s.003134">2. 1/4. ſenz'altra proua, ouer iſperientia, eglie co-<emph.end type="italics"></emph.end><pb pagenum="124" xlink:href="042/01/248.jpg"></pb><emph type="italics"></emph>ſa chiara, che il ſuo cubo ſara 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></lb>e pero ſara anchora piu lontano del noſtro. </s> <s id="s.003137">24. & quella uole che ſta piu preciſe, coſa <lb></lb>come che ho detto, molto ridicoloſa. </s> <s id="s.003138">Eglie ben uero, che il non è da marauigliarſi mol<lb></lb>to quando che un'huomo erra in qualche particolarita (per eſſer lo errare coſa huma <lb></lb>na) ma ben eglie da marauigliarſi, & da ſtupirſi, quando che lui è stato auertito del ſuo <lb></lb>errore, & che quello non ſolamente nonſe ſia ſaputo emendare, ma che quello ſia incor <lb></lb>ſo in un'altro maggiore, come che quella ha fatto. </s> <s id="s.003139">Et me aricordo quando ch'era à M<gap></gap><lb></lb>lano in caſa uoſtra, che quella me diſſe, che la non haueua mai tentato de ritrouare il ca <lb></lb>pitolo di coſa, e cubo egual à numero da me trouato, perche Frate Luca haueua detto, <lb></lb>ch'egliera impoßibile, quaſi uolendo dire, che ſe uoi ui fuſti meſſo à ricercarlo, che l'ha <lb></lb>uereſti ritrouato, della qual coſa al preſente me ne rido, perche uedo ch'eglie horamai <lb></lb>dui meſi, che ui ho auiſato del uoſtro error commeſſo nella eſtratione della Radice cu<lb></lb>ba, il qual atto è quaſi uno di primi principij che ſe inſegna à un ſcolaro, che uoglia dar <lb></lb>principio à l'Algebra, & ſe in tanto tempo non haueti ſaputo ritrouar medicina da <lb></lb>medicare il detto uoſtro errore (che è una coſa minima) hor penſati mo ſe uoi eri ſoffi <lb></lb>ciente à ritrouare il detto capitolo. </s> <s id="s.003140">Et certamente il fu gia, che ui haueua in buon con<lb></lb>to, ma al preſente uedo, che me ingannaua de groſſo, non altro. </s> <s id="s.003141">Iddio ui conſerui, in <lb></lb>Venetia alli. </s> <s id="s.003142">7. Agoſto.<emph.end type="italics"></emph.end> 1539. </s> </p> <p type="main"> <s id="s.003143">N<emph type="italics"></emph>icolo Tartaglia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003144">QVESITO. XXXIX. FATTO DALLA ECCEL<lb></lb><emph type="italics"></emph>lentia del medeſimo meſſer Hieronimo Cardano, con una <lb></lb>lettera de di. </s> <s id="s.003145">18. Ottobrio.<emph.end type="italics"></emph.end> 1539.</s> </p> <p type="main"> <s id="s.003146">MESSER HIERONIMO. H<emph type="italics"></emph>o riceuuto una uoſtra, meſſer Nicolo oſſer<lb></lb>uandißimo, nella quale me pare ſiati uſcito di uoi à dire, che io non ho inteſo la <lb></lb>regola del capitolo de cubo, egual à coſe è nuuiero, & che tal mia uia è in tutto falſa, <lb></lb>onde credo, che uoi zauariati, & che ſiati uſcito di ceruello forſi per il troppo uostro <lb></lb>ſtudiare, ouer leggere, onde ui eſſorto à torne un poco meno con menor utilita, perche <lb></lb>certo uoi uſcireti del ſenno, o della uita, & per queſto non mi marauiglio de gli impro<lb></lb>perij fuora di propoſito, che me ſcriueti, che io ui ſon uoſtro grande amico, & ui ho <lb></lb>laudato fina al Cielo ſenza inuidia di alcuno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003147">A <emph type="italics"></emph>quel che me ſcriueti della uia del ſcioluere il capitolo de cubo egual à coſe è nume <lb></lb>ro. </s> <s id="s.003148">Dico che ſta benißimo, & ſe uoletimettere. </s> <s id="s.003149">25. ſcudi, ne ponero. </s> <s id="s.003150">100. all'incontro, <lb></lb>& ui mando la ſolutione de. </s> <s id="s.003151">1. cubo eguale à. </s> <s id="s.003152">12. coſe piu. </s> <s id="s.003153">20. Dico che la coſa ualſe<emph.end type="italics"></emph.end> <22>. <lb></lb><emph type="italics"></emph>cuba. </s> <s id="s.003154">16. piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.003155">4. & il cubo ualſe<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba. </s> <s id="s.003156">27648. piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.003157">6912. piu. </s> <s id="s.003158">20. la <lb></lb>qual coſa prouandola la trouareti buona. </s> <s id="s.003159">Se uoleti mo dire, che ue ſia altro modo piu <lb></lb>generale di questo non contendo con uoi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003160">A<emph type="italics"></emph>nchora circa all'altra parte dico, che zauariati à dire, che haueti inteſo, che uo<lb></lb>glio dar fuora l'atre magna, & che uoglio dar fuora li uoſtri capitoli. </s> <s id="s.003161">Ma penſo ue ra <lb></lb>degati de meſſer Ottauiano Scotto, quanto all'opera de Myſterijs æternitatis, che ui <lb></lb>penſati ſia l'arte magna, che io uoglia dar fuora.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="042/01/249.jpg"></pb> <p type="main"> <s id="s.003162">Q<emph type="italics"></emph>uanto al pentirue hauermi dato quel uostro capitolo per questo non mi mouo, <lb></lb>per uostre parole à niuna coſa contra la fede ui promiſes.,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003163">D<emph type="italics"></emph>apoi doueti ſapere, che nella mia opera ho ritrouati molti errori di ſcarſo, e non <lb></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></lb>guardi in Millano alli. </s> <s id="s.003165">18. Ottobrio.<emph.end type="italics"></emph.end> 1539. </s> </p> <p type="main"> <s id="s.003166">H<emph type="italics"></emph>ieronymus Cardanus medicus.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003167">NIC. D<emph type="italics"></emph>apoi che il <expan abbr="nõ">non</expan> miha giouato lamia cautella, io <expan abbr="nõ">non</expan> ui uoglio dar altra riſpoſta.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003168">QVESITO. XL. FATTO DALLA ECCELL EN<lb></lb><emph type="italics"></emph>tia del medeſimo meſſer Hieronimo Cardano, con una <lb></lb>lettera de di. </s> <s id="s.003169">5. Genaro.<emph.end type="italics"></emph.end> 1540.</s> </p> <p type="main"> <s id="s.003170">MESSER HIER ONIMO. M<emph type="italics"></emph>eſſer Nicolo quanto fratello, auiſoui qual <lb></lb>mente eglie ritornato qui quel diauolo de meſſer Zuane Colle, il qual è uenuto <lb></lb>per hauere inteſo, che io era contento renontiarli una delle mie letture, cioe quella di <lb></lb>Arithmetica, trouando che lui fuſſe ualent'huomo, & in queſto lo prouato, & non tro <lb></lb>uo, che lui ſia quello, che il ſi penſa ne ſi dimostra, auiſoui che lui ha il uoſtro capitolo <lb></lb>de coſa, e cubo egual à numero, & quello de coſa è numero egual à cubo, lo <gap></gap>dato <lb></lb>come haueua hauuti detti capitoli, me riſpoſe, che eſſendo lui à Venetia, operò talmente <lb></lb>che ui poſe un'altra uolta alle mani con maeſtro Antoniomaria & che per tal uia gli <lb></lb>auenne cio, che cercaua, perche contraſtando inteſe la natura della equatione, & tan<lb></lb>dem per diuerſe conietture trouò detti capitoli inſieme con un ſuo compagno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003171">D<emph type="italics"></emph>apoi ſappiati 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></lb>per regola generale in tutti quelli bin omi, che hanno detta Radice cuba, & coſi dice, <lb></lb>come è il uero, che la è <22>. </s> <s id="s.003174">3. piu. </s> <s id="s.003175">1. & coſi dice, che la Radice cuba de <22>. </s> <s id="s.003176">108. men. </s> <s id="s.003177">10. é <lb></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></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. ſo che le il uero queſto, ma non ho hauuto tempo <lb></lb>di trouar tal regola, e per tanto ui prego uogliati ueder di trouarla, & contentarui <lb></lb>dell'honore, anchora mi non reſtaro di cercarla, & ſe io la trouaro auanti di uoi ue <lb></lb>la mandaro anchora mi à uoi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003191">A<emph type="italics"></emph>uiſoui anchora che lui ha certo la ſolutione di tal queſtione fame di. </s> <s id="s.003192">10. tre parti <lb></lb>continue proportionale, che la prima moltiplicata nella <expan abbr="ſecõda">ſeconda</expan> facia. </s> <s id="s.003193">8. perche il me la <lb></lb>uoleſta inſignar ſe io gli uoleua renontiar la lettura, e pero uorria che uoi uedesti di tro <lb></lb>uarla, et coſi faro anchora io, et chi piu preſto la troua la <expan abbr="cõmunichi">communichi</expan> al <expan abbr="cõpagno">compagno</expan>. </s> <s id="s.003194">An<lb></lb>chora uorria che uoi uedeſti da trouar queſta, la quale lui <expan abbr="cõfeſſa">confeſſa</expan> à non ſaperla ſoluere.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003195">T<emph type="italics"></emph>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></lb>& la prima nella ſeconda moltiplicata facia. </s> <s id="s.003198">7. ma lui non l'ha, ſi che <expan abbr="ſapẽdo">ſapendo</expan> che ſi puo <lb></lb>ſoluere certo, & lui non è piu de huomo, cercatela ui prego, & coſi faro anchora io, et <lb></lb>chi la troua la <expan abbr="cõmunichi">communichi</expan> al compagno, cioe tra noi, perche ello confeſſa, che ſi troua <21><lb></lb>un certo andare. </s> <s id="s.003199">Dice anchora hauer la dimoſtr atione qualmente il cerchio è di mag<lb></lb>gior contenuta d'ogn'altra figura, et che detta dimoſtr atione è in Greco à ſtampa forſi <lb></lb>è in proclo, ouero in theone, & che un meſſer Phileno da Bologna gli l'ha inſignata, et <lb></lb>dice, che gli la dette per coſa grande. </s> <s id="s.003200">L'altra domanda che lui ha è queſta.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="125" xlink:href="042/01/250.jpg"></pb> <p type="main"> <s id="s.003201">E<emph type="italics"></emph>glie uno paralellogramo.a.c.che.a.b.e. </s> <s id="s.003202">2. &.b.c.è 3. et ſi ſegna dentro el centro <lb></lb>d. </s> <s id="s.003203">et ſi trazeno due linee.d.f.&.d.e.equale ita ch'el ponto.e.&.f.con el ponto.g.ſono <lb></lb>in linea una, cioe.e.g.f.ſe adimanda quanta è la linea.d.e. </s> <s id="s.003204">Vedeti ui prego di mandar<lb></lb>ne qualcuna di queste aſciolte, non altro ricomandatime al Signor Ambaſciatore et ba <lb></lb>ſciateli la mano in Milano alli. </s> <s id="s.003205">5. Zenaro.<emph.end type="italics"></emph.end> 1540. </s> </p> <figure id="id.042.01.250.1.jpg" xlink:href="042/01/250/1.jpg"></figure> <p type="main"> <s id="s.003206">NICOLO. I<emph type="italics"></emph>n piu coſe conoſco costui eſſer molto piu tondo di quello che io iſti <lb></lb>maua, et prima lo dimoſtra nel parlare, nel quale dice alcune coſe che <expan abbr="nõ">non</expan> <expan abbr="hãno">hanno</expan> alcuna <lb></lb>coſonantia, cioe dice prima ch'eglie ritornato quel diauolo de<emph.end type="italics"></emph.end> M. Z<emph type="italics"></emph><expan abbr="uãne">uanne</expan> Colle per ha <lb></lb>uer inteſo che lui li uol renonciar la lettura de Arithmetica trouando che lui fuſſe ua <lb></lb>lent'huomo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003207">A<emph type="italics"></emph>nci credo che gli ſia ritornato per torge la detta lettura contra il ſuo uolere. </s> <s id="s.003208">Poi <lb></lb>dice ch'el l'ha prouato & che non lo ritroua che lui ſia quello ch'el ſi penſa. </s> <s id="s.003209">Et per <lb></lb><expan abbr="quãto">quanto</expan> uedo lui trema di paura di lui. </s> <s id="s.003210">Dapoi uedo che lui ſi laſſa dar ad intender al detto<emph.end type="italics"></emph.end><lb></lb>M. Z<emph type="italics"></emph>uanne che ha li mei capitoli di coſa è cubo equal à numero, & de coſe, e nume <lb></lb>ro equal à cubo la qual coſa non è uera maſi laſſa infenocchiare da lui. </s> <s id="s.003211">Dapoi dice chel <lb></lb>detto<emph.end type="italics"></emph.end> M.Z.<emph type="italics"></emph>ha ritrouato la regola generale de cauar la radice cu.de<emph.end type="italics"></emph.end> <22> 108. <emph type="italics"></emph>piu. </s> <s id="s.003212">10. & <lb></lb>coſi in tutti li altri binomi che hanno la detta<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu.& li pare che questo ſia una gran <lb></lb>coſa maßime nelli binomi cubi, perche tal ſua radice ſe puo trouar, ouer cauare ſola<lb></lb>mente de luno di ſuoi nomi qual ſi uoglia, cioe uolendola cauar del ſopradetto<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003213">108. <lb></lb><emph type="italics"></emph>piu. </s> <s id="s.003214">10. per maggior mia commodita la trouaria ſopra el. </s> <s id="s.003215">10. (per eſſer piu facile da <lb></lb>maneggiare nel ſlmplice numero che nelle radice) e per cauarla queſta é la ſua pro<lb></lb>priaregola, biſogna far del detto. </s> <s id="s.003216">10. due tal parti, che luna di quelle ſia numero cubo, <lb></lb>& che l'altra ſia diuiſibile in tre parti equali ſenza rotto, & per trouarli ſottro del <lb></lb>detto. </s> <s id="s.003217">10. luno de quelli numeri cubi contenuti dal detto. </s> <s id="s.003218">10. liquali ſono. </s> <s id="s.003219">1. &. </s> <s id="s.003220">8. & ue <lb></lb>do qual di loro mi da il rimanente diuiſibile (come detto) in tre parti equali & troua<lb></lb>remo che ſara. </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"></emph.end> <22>. <emph type="italics"></emph>cu. </s> <s id="s.003223">de. </s> <s id="s.003224">1. qual è pur. </s> <s id="s.003225">1. ſara el menor nome <lb></lb>della detta radice binomiale, et laltro ſara la radice quadra del <expan abbr="aduenimẽto">aduenimento</expan> che perue <lb></lb>nira a partire la terza parte del ſopradetto <expan abbr="rimanẽte">rimanente</expan> partita <21> el detto nostro menor <lb></lb>nome, cioeſottrato 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 ſua <lb></lb>terza parte qual è. </s> <s id="s.003230">3. et quella partiremo per la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu.del nostro numero cubo. </s> <s id="s.003231">1. qual <lb></lb>ſara 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. ſara el mag <lb></lb>gior nome del noſtro radical binomio, cioe che la radice cuba. </s> <s id="s.003235">de de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003236">108. <emph type="italics"></emph>piu. </s> <s id="s.003237">10. <lb></lb>ſara<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003238">3. <emph type="italics"></emph>piu. </s> <s id="s.003239">1. ch'è il propoſito, & de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003240">108. <emph type="italics"></emph>men. </s> <s id="s.003241">10. la ſaria<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003242">3. <emph type="italics"></emph>men. </s> <s id="s.003243">1. Et queſta<emph.end type="italics"></emph.end><pb xlink:href="042/01/251.jpg"></pb><emph type="italics"></emph>medema radice ſe puo anchora trouar ſopra el maggior nome, cioe ſopra<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003244">108. <emph type="italics"></emph>per <lb></lb>el medeſimo modo, ma la radice cu. </s> <s id="s.003245">del noſtro numero cubo ſara el maggior nome del<lb></lb>la noſtra binomial radice, ouer reſiduale eſſendo reſiduo eſſempi gratia, faremo, pur <lb></lb>de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003246">108 <emph type="italics"></emph>ſimplicemente due tal parti, che luna ſia<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>de un numero cubo & che l'al<lb></lb>tra ſia diuiſibile 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="inueſtigãdo">inueſtigando</expan> <lb></lb>come di ſopra fu fatto ſopra li numeri cubi ſe ritrouara che tal<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>de numero cubo ſa <lb></lb>ra la<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003250">27. <emph type="italics"></emph>hor dico che la radice cu.de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003251">27. (<emph type="italics"></emph>qual è<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003252">3.) <emph type="italics"></emph>ſara el maggior nomè <lb></lb>del noſtro Radical binomio, (ouer reſiduo) ſe fuſſe reſiduo & queſta parte de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003253">27. <lb></lb><emph type="italics"></emph><expan abbr="ſottrahẽdo">ſottrahendo</expan> la del tutto, cioe de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003254">108. <emph type="italics"></emph>reſtara pur<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003255">27. <emph type="italics"></emph>della quale <expan abbr="pigliãdone">pigliandone</expan> la ſua <lb></lb>terza parte, come radice, (che ſara la nona) ne uenira<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003256">3. <emph type="italics"></emph>& queſta <expan abbr="partẽdola">partendola</expan> per el <lb></lb>noſtro primo nome, (cioe <21> la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cu.della noſtra<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003257">27. <emph type="italics"></emph>qual è pur<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003258">3.) <emph type="italics"></emph>de tal parti <lb></lb><expan abbr="mẽto">mento</expan> ne uenira. </s> <s id="s.003259">1. et la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>de. </s> <s id="s.003260">1. qual è pur. </s> <s id="s.003261">1. ſara el menor nome del noſtro radical bi<lb></lb>nomio ouer reſiduo, cioe che la radice cu.de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003262">108. <emph type="italics"></emph>piu. </s> <s id="s.003263">10. ſaria<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003264">3. <emph type="italics"></emph>piu. </s> <s id="s.003265">1. e de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003266">108 <lb></lb><emph type="italics"></emph>men. </s> <s id="s.003267">10 la ſaria<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003268">3. <emph type="italics"></emph>men. </s> <s id="s.003269">1. ſi come fu anchor a determinato, ouer trouato ſopra el. </s> <s id="s.003270">10. <lb></lb>& per tal uia ſi puo anchora conoſcere ſe uno binomio, ouer reſiduo propoſto è cubo, <lb></lb>ouer non cubo, perche s'eglie cubo biſogna che il nostro operare ſe incontri in luno et <lb></lb>laltro nome et non potendoli far incontrare, tal binomio, ouer reſiduo non ſaria cubo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003271">D<emph type="italics"></emph>apoi uedo anchora che lui ſe laſſa dar ad intendere dal detto<emph.end type="italics"></emph.end> M. Z<emph type="italics"></emph>uane, che lui <lb></lb>habbia ritrouato il modo, ouer regola di ſoluere quella queſtione, che dice, fame di. </s> <s id="s.003272">10. <lb></lb>tre parti continue proportionale, che la prima moltiplicata nella ſeconda faccia. </s> <s id="s.003273">8. Et <lb></lb>gli crede fermamente per hauerli fatto offerta de inſignarglila ſe gli renoncia la lettu<lb></lb>ra, et non ſi auede il poueretto, che il non gli fa tal oblatione ſe non per fargli credere, <lb></lb>che habbia detta regola, accio che habbia tema di lui, perche luiſa bene, che non ui re<lb></lb>nontiaria la lettura per inſignargli la regola di riſoluere tal ragione, non tanto per la <lb></lb>lettura, ma per la uergogna, che gli ne ſeguiria, e pero uedo che eglie di poco ingegno.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003274">D<emph type="italics"></emph>apoi dice, che il detto<emph.end type="italics"></emph.end> M.Z<emph type="italics"></emph>uane confeſſa non ſaper ſoluere quell'altra ſua propo<lb></lb>ſta ragione, et che la è ſolubile, perche il detto<emph.end type="italics"></emph.end> M.Z<emph type="italics"></emph>uane gli ha detto, che la ſe riſolue <lb></lb>per un certo andare, et non ſe auede, che lui dice due coſe contrarie, cioe che il non la ſa <lb></lb>riſoluere, et che la ſe riſolue per un certo andar, perche ſe il non la ſa riſoluere manco <lb></lb>el puo ſapere perche uia, ouer perche andar laſe riſolue. </s> <s id="s.003275">Dapoi dice che lui ha la de<lb></lb>moſtratione <expan abbr="qualmẽte">qualmente</expan> il cerchio é di maggior contenuta de ogni altra figura, & li pa <lb></lb>re a lui che queſto ſia troppo gran coſa, la quale quantunque alcun autor non haueſſe <lb></lb>mai parlato, ſe potria trouar di dimostrarla in piu modi, cioe ch'eglie piu capace de <lb></lb>ogni figura iſoperimetra per le coſe dimostrate da Archimede, & anchora dal Cardi <lb></lb>nal de Cuſa. </s> <s id="s.003276">In quello de traſmutatiouibus Geometricis, e per queſto conoſco che con<lb></lb>tien poco ſugo. </s> <s id="s.003277">Dapoi uedendo anchora che lui non ſa riſoluere quella ultima queſtio <lb></lb>ne geometrica ch'é una coſa facile, (perche la maggior difficulta che occorra nella ri <lb></lb>ſolution di quella é à ſaper ritrouar le due partiale linee.c.e.et.a.f.le quale ſon medie <lb></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></lb>& laltro. </s> <s id="s.003280">3. dal preſuppoſito & trouate quelle con facilita ſe ritrouara la quanti<lb></lb>ta de la linea.d.e.ouer.d.f.) lo giudico di poco diſcorſo. </s> <s id="s.003281">Et per queſto non li uo<lb></lb>glio dar altrariſpoſta, perche è non ui ho piu affetione à lui che à meſſer Zuanne, e<emph.end type="italics"></emph.end><pb pagenum="126" xlink:href="042/01/252.jpg"></pb><emph type="italics"></emph>pero li uoglio laſſar ar tra loro, ma me la uedo che lui é perſo de animo, non ſo mo <lb></lb>come la andara.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003282">QVESITO XLI. FATTO DA MAESTRO MA<lb></lb><emph type="italics"></emph>phio Poueiani, con una lettera de di. </s> <s id="s.003283">15. Aprile.<emph.end type="italics"></emph.end> 1540.</s> </p> <p type="main"> <s id="s.003284">MAESTRO MAPHIO. E<emph type="italics"></emph>ccellente meſſer Maeſtro ſaluti infiniti &c. <lb></lb></s> <s id="s.003285">Sono molti giorni che ho hauuto deſiderio di domandarui uno apiacere, ma <lb></lb>conſiderando le uoſtre occupationi non mi è mai dato il core, temendo di non efferui <lb></lb>moleſto, pur caſſando ogni riſpetto me è apparſo de ſcriuerloui ogni modo fareti poi <lb></lb>il parer uostro &c. </s> <s id="s.003286">La coſa che ue uoria domandar ſi é queſta, che haueria ſingolar <lb></lb>appiacer che me mandaſte una nota di quel miſurar di terre alla Venetiana, ouer ſecon <lb></lb>do il coſtume di là, cioe ſel ſi ua à campi, ouer à tornidure, & quante tauole fa un cam <lb></lb>po, & ſe ue dago faſtidio perdonatime, ui haueria de auiſare de molti maeſtri che mi ſo <lb></lb>no capitati inanti mentre ſtaua in Bergamo, come é el figliuolo del Tagliente, & tra li <lb></lb>altri maeſtro zuanne da Coi doue tra noi fu alquante parole in fin fatti amici gli par<lb></lb>ſe per ſua gratia di laudarmi, & diſſe che uifaceua honore, al fin el ſe parti da Berga <lb></lb>mo quantunque el fuſſe partito da Breſſa per uenir à ſtantiar in Bergamo, & an à <lb></lb>Millano con tanta importunita che non uoleua laſſar far bene quelli maeſtri, tenu<lb></lb>to ſchola che ghe hebbe alquanti meſi ſe ne partete con ſua grandißima ignominia, <lb></lb>ma ritrouandomi queſti giorni paſſati in Milano, trouai chel ghe era ritornato, & <lb></lb>non ſo per qual cauſa gli habbiano tolto la lettura al Cardano (gia amico uoſtro) <lb></lb>& data à lui, cioe al detto maestro zuanne, a benche forſi el poteti hauer inteſo pri<lb></lb>mache adeſſo, pur me apparſo di daruene auiſo caſo che nol ſapeſti, non altro ſe <lb></lb>non che con tutto il core humilmente me aricomando et offero, a quo benignum et gra<lb></lb>tioſum expecto riſponſum. </s> <s id="s.003287">Di Trento adi. </s> <s id="s.003288">15. Aprile.<emph.end type="italics"></emph.end> 1540. </s> </p> <p type="main"> <s id="s.003289">D<emph type="italics"></emph>iuostra eccellentia ſeruitor & diſcipulo Maphio Poueiani.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003290">NICOLO. M<emph type="italics"></emph>aeſtro Maphio carißimo ho riceputo una uoſtra & inteſo quan <lb></lb>to me ſcriueti, & per tanto ue auiſo qualmente ſul Treuiſano li terreni ſe uendeno et <lb></lb>comprano à campi & un campo é de tauole. </s> <s id="s.003291">1250. & una tauola (per quanto ho in<lb></lb>teſo) è un quadretto di terra de una pertega de miſura per fazza, el campo poi Pado <lb></lb>uano è <expan abbr="ſolamẽte">ſolamente</expan> de tauole. </s> <s id="s.003292">840. Et coſi el Viſentino, uero é che la pertega Padouano <lb></lb>credo che laſla alquanto piu <expan abbr="lõga">longa</expan> della Triuiſana, el <expan abbr="cãpo">campo</expan> Veroneſe e de tauole. </s> <s id="s.003293">720. <lb></lb>in Mantoana el terreno ſe uende à biolchi et il biolco è de tauole. </s> <s id="s.003294">100. ma la tauola é <lb></lb>uno quadretto di terra de dui cauezzi per fazza elqual cauezzo è una miſura lon<lb></lb>ga. </s> <s id="s.003295">6. brazza tal che la tauola ueneria à eſſer uno quadretto di terra de brazza. </s> <s id="s.003296">12. <lb></lb>per fazza, a Breſſa poi el detto terreno ſe uende à pio, el qual pio é pur de tauole. </s> <s id="s.003297">100 <lb></lb>ſi come il Mantouano, & ſimelmente la ſua tauola è pur uno quadretto di terra de dui <lb></lb>cauezzi per fazza, liquali cauezzi ſono pur longhi brazza. </s> <s id="s.003298">6. luno ſi come el Man<lb></lb>touan. </s> <s id="s.003299">Sul Bergamaſco el detto terreno ſe uende à perteghe & una pertegha de terra <lb></lb>ſi è di tauole. </s> <s id="s.003300">24. Et la tauola è ſi come la tauola Breſſana, cioe de dui cauezzi, ouer <lb></lb>de. </s> <s id="s.003301">12. brazza per fazza. </s> <s id="s.003302">Sul Millaneſe, <expan abbr="ſimilmẽte">ſimilmente</expan> ſe <expan abbr="uẽde">uende</expan> el terreno à perteghe ſi co <lb></lb>me ſul Bergamaſco 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"></emph.end><pb xlink:href="042/01/253.jpg"></pb><emph type="italics"></emph>quadretto de due miſure longhe. </s> <s id="s.003304">6. brazza luna per fazza, cioe brazza. </s> <s id="s.003305">12. in tutto <lb></lb>per fazza.<emph.end type="italics"></emph.end> A <emph type="italics"></emph><expan abbr="bẽche">benche</expan> ſo che quelle pratiche di Bergamo et da Milano ui debbiano eſſer <lb></lb>note nondimeno ui mando la coppia de una nota che me ritrouo apreſſo di me circa al <lb></lb>auiſo del medico Cardano da Milano, a me é coſa noua, che gliſia ſtata tolta la lettura, <lb></lb>& data a<emph.end type="italics"></emph.end> M. z<emph type="italics"></emph>uanne, eglie <expan abbr="bẽ">bem</expan> uero, che per lettere del Cardano mi haueua antiueduto <lb></lb>tal coſa non altro Iddio ui conſerui di Venetia alli. </s> <s id="s.003306">24. Aprile.<emph.end type="italics"></emph.end> 1540. </s> </p> <p type="head"> <s id="s.003307">QVESITO. XLII. FATTO DAL MIO HONORANDO <lb></lb><emph type="italics"></emph>compare<emph.end type="italics"></emph.end> M. R<emph type="italics"></emph>icardo Ventuorthe gentil'huomo Ingleſe l'anno.<emph.end type="italics"></emph.end> 1541.</s> </p> <p type="main"> <s id="s.003308">MESSER RICAR. C<emph type="italics"></emph>ompar carißimo io ſon al preſente per partirme da <lb></lb>uoi, & ritornarmene in Inghilterra. </s> <s id="s.003309">& hauendome moſtrata la regola del ca <lb></lb>pitolo de coſa, et cubo equal à numero, & delli altri dui ſoi <expan abbr="cõpagni">compagni</expan> uoria piacendoui, <lb></lb>che feſti la coſa <expan abbr="cõpita">compita</expan>, cioe che mi moſtraſti anchora la Regola del capitolo de cenſo, <lb></lb>e cubo equal à numero, & ſimelmente delli altri dui ſuoi <expan abbr="cõpagni">compagni</expan>.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>eſſer compa <lb></lb>re <expan abbr="certamẽte">certamente</expan> è non me ritrouo coſa, qual eſſendoui agrata giamai ui poteſſe ne doueſſe <lb></lb>negare, per le molte obligationi, che ho con uoi. </s> <s id="s.003310">Ma perche ho deliberato, ſubito cho <lb></lb>habbia iſpedito di tradur Euclide, & di correggere le figure, & altrierrori fatti da <lb></lb>ſcrittori & traduttori ſopra Archimede Sir acuſano, di <expan abbr="cõponere">componere</expan> una opera in la pra <lb></lb>tica di Arithmetica, et Geometria, et inſieme con quella una noua Algebra, nella quale <lb></lb>non <expan abbr="ſolamẽte">ſolamente</expan> uoglio ponere tutte le regole per me ritrouate ſopra li detti capitoli con <lb></lb>tutte le ſue ragioni, & fondamenti, ma molte altre, che ſpero per loro euidentie de ri<lb></lb>trouare & quella dadicaruela à uoi, per due cauſe luna per ſatisfare imparte alli detti <lb></lb>molti oblighi ho <expan abbr="cõ">com</expan> uoi, laltra come à perſona piu atta cauar di lei coſtrutto di qualun <lb></lb>que altra, per ſuo mirabile & profondo ingegno. </s> <s id="s.003311">Et per tanto <expan abbr="moſtrãdoui">moſtrandoui</expan> al preſente, <lb></lb>quello che nella detta opera offerirue intendo, ſaria un degradare la reputatione della <lb></lb>detta opera appreſſo di uoi, e per questa cauſa uoglio che per al preſente me habbiate <lb></lb>per iſcuſo, & che non ue ſia graue lo aſpettare perche hauereti poi la coſa meglio dige <lb></lb>ſta.<emph.end type="italics"></emph.end> M. R. D<emph type="italics"></emph>apoi che uoleti che aſpetti aſpettaro, ma uoglio che me dati almen dui, <lb></lb>ouer treicaſi aſſolti ſopra à tal materia de capitoli, per che in queſto mezzo me uoglio <lb></lb>eſſercitare, & tentare ſe per mezzo de tai ſolutioni ſapeſſe trouar per me le dette re<lb></lb>gole, ouer parti de quelle. </s> <s id="s.003312">Et fra li altriuoglio che mi dati aſſolto quel caſo, ouer que<lb></lb>ſtione che preponeſti al uicenti in ſan zuannepolo, perche me li ſono affaticato aſſai <lb></lb>per riſoluerla, & mai ho potuto.<emph.end type="italics"></emph.end> N. E<emph type="italics"></emph>t come diceua tal queſtione.<emph.end type="italics"></emph.end> M. R. L<emph type="italics"></emph>a di <lb></lb>ceua in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003313">T<emph type="italics"></emph>rouatime una quantita che multiplicata fiala ſua Radice piu. </s> <s id="s.003314">6. faccia aponto. <lb></lb></s> <s id="s.003315">100 Onde ponendo che tal quantita ſia un cenſo, la ſua Radice ſaria una coſa alla qua <lb></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. cenſo faria. </s> <s id="s.003320">1. cubo piu. </s> <s id="s.003321">6. <lb></lb>cenſi et queſto ſaria equal à.<emph.end type="italics"></emph.end> 100. N. I<emph type="italics"></emph>n queſto caſo la coſa ualeua<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u.cu. 42. piu<emph.end type="italics"></emph.end> <22>. <lb></lb></s> <s id="s.003322">17000. <emph type="italics"></emph>piu<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u.cu. 42. <expan abbr="mẽ">men</expan><emph.end type="italics"></emph.end> <22>. </s> <s id="s.003323">17000. <emph type="italics"></emph><expan abbr="mẽ">men</expan> el terzo di cenſi cioe men.<emph.end type="italics"></emph.end> 2. M.R.A <emph type="italics"></emph>uoler <lb></lb>far la proua di queſta uoſtra concluſione, la ſaraue molto, faticoſa & diſſicile.<emph.end type="italics"></emph.end> N. I<emph type="italics"></emph>n <lb></lb>effetto la non è molto facile.<emph.end type="italics"></emph.end> M R. N<emph type="italics"></emph>on me ne potreſti dar un'altro ſimile riſolto,<emph.end type="italics"></emph.end><pb pagenum="127" xlink:href="042/01/254.jpg"></pb><emph type="italics"></emph>che mi deſſe il ualor della coſa di un'altra quantita piu facile da maneggiare.<emph.end type="italics"></emph.end> N. S<emph type="italics"></emph>t <lb></lb>bene, perche mi poſſo ſempre eguagliare à tal numero che mi dara el ualor della coſa <lb></lb>in un ſimplice reſiduo. </s> <s id="s.003324">Eſſempi gratia ſe io baueſſe detto trouatime una quantita che <lb></lb>multiplicata fia la ſua<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>piu. </s> <s id="s.003325">9. faccia à ponto. </s> <s id="s.003326">100. apponendoſi come di ſopra uoi fe <lb></lb>ſti ſe perueneria in 1. cubo piu. </s> <s id="s.003327">9. cenſi equal à. </s> <s id="s.003328">100. & in queſto caſo la coſa ualeria<emph.end type="italics"></emph.end><lb></lb><22>. </s> <s id="s.003329">24 <emph type="italics"></emph>men. </s> <s id="s.003330">2. & la adimondata quantita ſaria el quadrato de<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003331">24. <emph type="italics"></emph>men. </s> <s id="s.003332">2. elqual <lb></lb>quadrato ſaria. </s> <s id="s.003333">26. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003334">384 M. R. Q<emph type="italics"></emph>uesta reſolutione mi piace molto piu de <lb></lb>l'altra, perche piu facilmente ne poſſo far la proua. </s> <s id="s.003335">perche ſe alla coſa, cioe à<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003336">24. <lb></lb><emph type="italics"></emph>men. </s> <s id="s.003337">2. gli aggiongo. </s> <s id="s.003338">9. fara<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003339">24. <emph type="italics"></emph>piu. </s> <s id="s.003340">7. qual ſumma multiplicata fia. </s> <s id="s.003341">26. men<emph.end type="italics"></emph.end> <22>. <lb></lb></s> <s id="s.003342">384. <emph type="italics"></emph>fa preciſamente. </s> <s id="s.003343">100. come ſe <expan abbr="adimãda">adimanda</expan> hor uoria che me ne deſti dui altri ſimili.<emph.end type="italics"></emph.end><lb></lb>NICO. Q<emph type="italics"></emph>uando che. </s> <s id="s.003344">1. cubo piu. </s> <s id="s.003345">3. cenſi fuſſe equal à. </s> <s id="s.003346">2. la coſa ualeria<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003347">3. <emph type="italics"></emph>men. <lb></lb></s> <s id="s.003348">1. Et coſi quando che. </s> <s id="s.003349">1. cubo piu. </s> <s id="s.003350">7. cenſi fuſſe equale à. </s> <s id="s.003351">50. la coſa ualeria.<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003352">11. <emph type="italics"></emph><expan abbr="mẽ">men</expan>.<emph.end type="italics"></emph.end> 1. <lb></lb>M.R. B<emph type="italics"></emph>aſta circa à queſto capitolo, hor datemene anchora dui altri ſolti ſopra il ca<lb></lb>pitolo de cubo, e numero egual à cenſi, & ſe poßibile é proponeteli, che diano il ualor <lb></lb>della coſa in quantita facile da maneggiare, accio che io ne poſſa far la proua.<emph.end type="italics"></emph.end> N. <lb></lb>Q<emph type="italics"></emph>uando che il fuſſe. </s> <s id="s.003353">1. cubo piu. </s> <s id="s.003354">4. egual à. </s> <s id="s.003355">5. cenſi la coſa ualcria<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003356">8. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 2. M.R. <lb></lb>A<emph type="italics"></emph>nchora queſta riſolutione me piace, perche la poſſo prouare facilmente, perche ſe la <lb></lb>coſa ual<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003357">8. <emph type="italics"></emph>piu. </s> <s id="s.003358">2. il cenſo ualera. </s> <s id="s.003359">12. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003360">128. <emph type="italics"></emph>& il cubo ualera. </s> <s id="s.003361">56. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003362">3200. <lb></lb><emph type="italics"></emph>al qual cubo giontoli. </s> <s id="s.003363">4. fara. </s> <s id="s.003364">60. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003365">3200. <emph type="italics"></emph>& queſto è preciſamente eguale à. </s> <s id="s.003366">5. <lb></lb>cenſi, cioe à. </s> <s id="s.003367">5. fia. </s> <s id="s.003368">12. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003369">128. <emph type="italics"></emph>qual fa medeſimamente. </s> <s id="s.003370">60. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003371">3200. <emph type="italics"></emph>che é il <lb></lb>propoſito hor datemene anchora un'altro.<emph.end type="italics"></emph.end> N. Q<emph type="italics"></emph>uando che. </s> <s id="s.003372">1. cubo piu. </s> <s id="s.003373">6. fuſſe egua <lb></lb>le à. </s> <s id="s.003374">7. cenſi la coſa ualeria<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003375">15. <emph type="italics"></emph>piu.<emph.end type="italics"></emph.end> 3. M.R. L<emph type="italics"></emph>auoglio prouare. </s> <s id="s.003376">Se la coſa ual<emph.end type="italics"></emph.end> <22>. <lb></lb></s> <s id="s.003377">15. <emph type="italics"></emph>piu. </s> <s id="s.003378">3. il cenſo ualera. </s> <s id="s.003379">24. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003380">540. <emph type="italics"></emph>& il cubo. </s> <s id="s.003381">162. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003382">26460. <emph type="italics"></emph>al qual cubo <lb></lb>giontoli. </s> <s id="s.003383">6. fara. </s> <s id="s.003384">168. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003385">26460 <emph type="italics"></emph>horſe. </s> <s id="s.003386">7. fia. </s> <s id="s.003387">24. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003388">540. <emph type="italics"></emph>fara quel medeſi<lb></lb>mo la ſtara benißimo, in effetto trouo che la fa quel medeſimo, ſi che ſta benißimo, hor<lb></lb>ſu credo che queſti me baſtara.<emph.end type="italics"></emph.end> N. M<emph type="italics"></emph>eſſer Compare anchor che per uoſtra ſatisfat<lb></lb>tione ue habbia dati li ſopraſcritti capitoli riſolti, ue eſſorto à non ſtare à perder tem<lb></lb>po, ne à romperue la teſta in uolere con iſperientie de numeri (per meggio delle dette <lb></lb>mie riſolutioni) ritrouar la regola generale ad alcuno de detti capitoli, perche credo, <lb></lb>che uoi ue affaticareti in darno, la cauſa è, che tutti tai capitoli riceueno due diuerſe ri<lb></lb>ſpoſte, & forſi piu, onde ſeguita, che habbiano, ouer riceuano due diuerſe regole, e for <lb></lb>ſi piu, & l'una piu difficultoſa dell'altra, la qual coſa fondandoui ſopra la ſperientia <lb></lb>de numeri ue fara zauariar aſſai, et in ultimo credo, che non trouareti niente che uaia, <lb></lb>perche questi tai capitoli uogliono eſſer ricercati ſpeculatiuamente, & non con iſpe<lb></lb>rientie de numeri, e per tanto ui eſſorto ad hauer patientia per fin che ue manda le det <lb></lb>te regole con li ſuoi fondamenti dimostrartiui, & prima di quelli de coſa, e cubo egual <lb></lb>à numero con glialtri dui ſuoi compagni, dalle quale regole ſe caua le regole dimoſtra <lb></lb>tiue de tutti glialtri perche tutte ſono inſieme concatenate, dico quelle de cenſo, e cubo <lb></lb>egual à numero, & ſuoi compagni, à quelle de coſa, e cubo egual à numero, et ſuoi com <lb></lb>pagni, come à luoco é tempo ui faro uedere.<emph.end type="italics"></emph.end> M.R. I<emph type="italics"></emph>l me pare diſtranio di quello, che <lb></lb>haue ti detto, cioe che tutti tai capitoli riceuano due diuerſe riſpoſte, & forſi piu, et che <lb></lb>per tal cauſa riceueno due diuerſe regole, & forſi piu, la qual coſa mi pare dura da <pb xlink:href="042/01/255.jpg"></pb>credere.<emph.end type="italics"></emph.end> N. L<emph type="italics"></emph>a è certo coſa dura da credere, & certamente ſe la ſperientia non me <lb></lb>ne faceſſe testimonianza, quaſi che non il crederei, perche ſe io diceſſe trouatemi un <lb></lb>numero, ouer quantita, che gionta con tre delle ſue radice cube faccia. </s> <s id="s.003389">14. Eglie coſa <lb></lb>chiara, che il numero. </s> <s id="s.003390">8. fara questo, che ſe adimanda, perche la ſua radice cuba è. </s> <s id="s.003391">2. <lb></lb>& tre ſue radice cube ſaranno. </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 ſe ri<lb></lb>cerca, hor dico, che chi riſoluera tal capitolo de. </s> <s id="s.003395">1. cu.piu. </s> <s id="s.003396">3. coſe egual à. </s> <s id="s.003397">14. ſecondo <lb></lb>la regola da me ritrouata, ſe ritrouara la coſa ualer<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u.cuba. 7. piu<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003398">41. <emph type="italics"></emph>men<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>u. <lb></lb>cuba. </s> <s id="s.003399">7. men<emph.end type="italics"></emph.end> <22>. </s> <s id="s.003400">41. <emph type="italics"></emph>la qual coſa treplicandola, & tal treplicatione aggiongerla al ſuo <lb></lb>cubo fara medeſimamente. </s> <s id="s.003401">14. ſi come fa anchora ualendo la coſa ſimplicemente.<emph.end type="italics"></emph.end> 2. <lb></lb>E <emph type="italics"></emph>pero eglie coſa manifeſta, che il capitolo de coſa, e cubo egual à numero riceue due <lb></lb>regole, cioe l'una (che nel ſopr adetto capitolo) me doueria dar il ualor della coſa ra<lb></lb>tionale, cioe. </s> <s id="s.003402">2. & l'altra è la noſtra qual me da la coſa irrationale, come diſopra ſi è <lb></lb>uisto. </s> <s id="s.003403">Et da qui è naſciuto, che coloro che per auanti di me hanno ricercato regola à tal <lb></lb>capitolo, credendoſi che tal capitolo non riceueſſe altro, che una ſol regola, cioe una <lb></lb>che ſerueſſe ſi nelle concluſioni rationale, come nelle irrationale loro la ricercauano <lb></lb>ſolamente con la iſperientia de numeri rationali apoſtati, come diſopra per noi fu fat<lb></lb>to de. </s> <s id="s.003404">1. cubo piu. </s> <s id="s.003405">3. coſe egual à. </s> <s id="s.003406">14. del qual capitolo gia ſapemo che la coſa ual. </s> <s id="s.003407">2. & <lb></lb>la regola de ritrouar, che la coſa uaglia. </s> <s id="s.003408">2. eglie da penſare che la ue ſia, anchor che da <lb></lb>gli noſtri anciani la non ſia stata ritrouata.<emph.end type="italics"></emph.end> L'<emph type="italics"></emph>alira regola da me ritrouata con dimo<lb></lb>ſtrationi Geometrice ſe conoſce la ſua bontà, & ſi conoſce anchora che da me la non fu <lb></lb>ricercata con numeri apoſtati (come forſihanno fatto coloro, che ui ſe ſono affaticati <lb></lb>auanti di me) ma con la pura ſpeculatione, & queſte due uarie riſpoſte ſe ritrouara non <lb></lb>ſolamente in tutte le ſorte de equationi de coſe é cubi eguali à numero, doue accaſchi la <lb></lb>coſa eſſer rationale (come fu nel ſopra datto eſſempio del.<emph.end type="italics"></emph.end> 14.) <emph type="italics"></emph>ma anchora il medeſi<lb></lb>mo ſeguira nel capitolo de coſa è numero egual à cubo, & in quello de cubo, e numero <lb></lb>egual à coſe, & in quello de cenſo è cubo egual à numero, & in quello de cubo egual à <lb></lb>cenſo è numero, & finalmente in quello de cubo, è numero egual à cenſi, e pero eglie da <lb></lb>credere che riceuono anchora due uarie regole, & in alcuni de loro per certe ſue ua<lb></lb>riationi, & accidenti mi fanno quaſi certo riceuere piu di due regole, come che in bre<lb></lb>ue, piacendo à Iddio, ſe dimoſtrara. </s> <s id="s.003409">& pero meſſer Compare non ſtati à durar fatica <lb></lb>in ricercar tale regole con iſperientie, che in breue le hauereti con le ſue ragioni, & <lb></lb>fondamenti chiare, & nette.<emph.end type="italics"></emph.end> M.R. E<emph type="italics"></emph>uoglio far quello, che me conſigliati, & maßi<lb></lb>me che uedo in alcune equationi ſeguitar riſolutione de certe quantita de molto ſtrania <lb></lb>irrationalita, & molto difficile, & faſtidioſe da maneggiare in pratica, & ſe in queste <lb></lb>ſorte de capitoli de coſe, cubi, cenſi, enumero ui caſca coſi ſtranie concluſioni, che ſe<lb></lb>guiria poi nelle altre dignita, cioe doue interueniſſe il primo relato, oueramente cenſo <lb></lb>de cubo, ouer amente il ſecondo relato, e per tanto credo, che in tal pratica di Algebra, <lb></lb>uoi ſiati peruenuto per fin doue ſia poßibile à peruenire, perche il ſe entraria in un <lb></lb>Chaos à uoler tentar piu oltra de tai capitoli per uoi trouati.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>nci ui uoglio di<lb></lb>re, che nelle equationi di alcune altre piu alte dignita, non ſeguiria forſi nella ſua con<lb></lb>cluſione quantita de coſi ſtrania irrationalita, quanto che ſeguita nelli predetti capito<lb></lb>li, & queſto procede per la ſua diſproportionalita, ch'è ſtrania Anci me aricordo che<emph.end type="italics"></emph.end><pb pagenum="128" xlink:href="042/01/256.jpg"></pb><emph type="italics"></emph>l'anno. </s> <s id="s.003410">1536. la notte de ſan Martin, laqual feſta fu in ſabbo, fantaſticando in letto quan <lb></lb>do che non potea dormire trouai la regola generale allo capitolo de cenſo de cubo; & <lb></lb>cubi, equal à numero & ſimelmente alli altri dui ſuoi compagni, nella medeſima notte, <lb></lb>il che non me fu difficile anchor che fuſſeno compoſti di piu alte dignita di coſa è cubo <lb></lb>equal à numero, per eſſer di megliore proportionalita & la ſua regola è piu facile, & <lb></lb>di piu amena concluſione & piu uniuerſale, perche quella ne ſerue ſi nelle <expan abbr="cõcluſioni">concluſioni</expan> ra<lb></lb>tionale come nelle irrationale.<emph.end type="italics"></emph.end> M.R. H<emph type="italics"></emph>or queste hauero molto accaro de intende<lb></lb>re nanti che me parta da uoi et forſi piu di quelle di <expan abbr="cẽſi">cenſi</expan> è cubo equal à numero, et delli <lb></lb>altri dui ſuoi compagni, per eſſer, come haueti detto, di piu amena concluſione, e pe <lb></lb>ro datemene una nota.<emph.end type="italics"></emph.end> N. P<emph type="italics"></emph>igliati la penna, & ſcriueti in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003411">Q<emph type="italics"></emph>uando li cenſi de cubi inſieme con li cubi ſe eguagliarano al numero reccareti la <lb></lb>equatione à un cenſo de cubo. </s> <s id="s.003412">Dapoi smezzareti li cubi, & tal mita multiplicareti in <lb></lb>ſe medeſima & à tal quadrato aggiongereti el numero & di quella ſumma cauaretine <lb></lb>la Radice quadrata & di tal radice quadrata cauaritene la mita di cubi & la radice cu <lb></lb>ba del rimanente ualera la coſa. </s> <s id="s.003413">Eſſempio in numeri diſcreti per uoſtra maggior intel <lb></lb>ligentia, (elqual eſſempio non ſe potria dar in el capitolo de coſa è cubo equal à nume <lb></lb>ro, & altri ſuoi ederenti, ne in quello de cenſo, e cubo equal à numero, & ſuoi edderen <lb></lb>ti<emph.end type="italics"></emph.end>). 1. <emph type="italics"></emph>cubo de cenſo piu. </s> <s id="s.003414">4. cubi equal à. </s> <s id="s.003415">96. ſmezzo li cubi mene uien. </s> <s id="s.003416">2. lo quadro fa. <lb></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 queſto. </s> <s id="s.003420">10. <lb></lb>ne cauo, la mita del numero di cubi qual è. </s> <s id="s.003421">2. reſta. </s> <s id="s.003422">8. & la radice cuba de. </s> <s id="s.003423">8. qual e. 2. <lb></lb>ual la noſtra coſa el ſimile oſſeruareti quando che fuſſeno quantita irrationale. </s> <s id="s.003424">Hor <lb></lb>per el ſecondo ſcriueti in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003425">Q<emph type="italics"></emph>uando li cenſi de cubi, ſe eguagliano alli cubi, & al numero, fareti come di ſopra, <lb></lb>cioe reccareti tutta la equatione à un cenſo de cubo, dapoi ſmezzati li cubi & tal mita <lb></lb>multiplicati in ſe & à tal multiplicatione, ouer quadrato aggiongereti el numero, & <lb></lb>di tal ſumma cauaretine la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>quadra alla qual<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>quadra aggiongereti la mita di cubi <lb></lb>& la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba di tal ſumma ualera la coſa. </s> <s id="s.003426">Eſſempio in numeri diſcreti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003427">S<emph type="italics"></emph>ia. </s> <s id="s.003428">1. cubo de cenſo egual à. </s> <s id="s.003429">4. cubi piu. </s> <s id="s.003430">32. ſmezzo li. </s> <s id="s.003431">4. cubi ne uien. </s> <s id="s.003432">2. lo quadro <lb></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"></emph.end> <22>. <emph type="italics"></emph>quadra qual è. </s> <s id="s.003436">6. alla qual <lb></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"></emph.end> <22>. <emph type="italics"></emph>cuba de. </s> <s id="s.003439">8. qual è. </s> <s id="s.003440">2. ualera la coſa, <lb></lb>& per ſimil modo ſe doueria procedere quando che ne riſultaſſe quantita irrationale. <lb></lb></s> <s id="s.003441">Hor per el terzo ſcriueti in queſta forma.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003442">Q<emph type="italics"></emph>uando li cenſi de cubi piu numero, ſe eguagliano alli cubi, reccareti la equatione <lb></lb>tutta à un cenſo di cubo. </s> <s id="s.003443">Dapoi ſmezzareti li cubi & tal mita multiplicareti in ſe, & <lb></lb>di quel produtto, ouer quadrato ne cauareti el numero, & del rimanente ne trouareti <lb></lb>la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>quadra, & à tal radice quadra gli aggiongereti, ouer cauareti la mita di cubi, & <lb></lb>la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba di tal ſumma, ouer reſto ualera la coſa. </s> <s id="s.003444">Eſſempio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003445">S<emph type="italics"></emph>ia. </s> <s id="s.003446">1. cubo de cenſo piu. </s> <s id="s.003447">48. egual à. </s> <s id="s.003448">14. cubi, ſmezzo li cubi. </s> <s id="s.003449">14. ne uien. </s> <s id="s.003450">7. quadro <lb></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.) reſta. </s> <s id="s.003455">1. & di queſto <lb></lb>ne cauo la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>quadra qual è pur. </s> <s id="s.003456">1. al qual gli aggiongo, ouer cauo la mita di cubi che è. <lb></lb></s> <s id="s.003457">7. & perche in queſto caſo il detto. </s> <s id="s.003458">7. è maggior de. </s> <s id="s.003459">1. Io non lo poſſo ſe non aggionge<lb></lb>re, & fara. </s> <s id="s.003460">8. & la<emph.end type="italics"></emph.end> <22>. <emph type="italics"></emph>cuba de. </s> <s id="s.003461">8. ualera la coſa, cioe. </s> <s id="s.003462">2. & biſogna notar, che queſto <pb xlink:href="042/01/257.jpg"></pb>capitolo alcuna fiata dara riſpoſta in dui modi, alcun'altra ſolamente in un modo ſolo, <lb></lb>come accaduto in queſto ſopraſcritto, cioe che la mita di cubi nonſe puo ſe non aggion<lb></lb>gere alla radice di quel rimanente, che fu. </s> <s id="s.003463">1. ma quando ſe fuſſe potuto aggiongere, & <lb></lb>cauare forſi, che l'uno, e l'altro haueriano dato perfetta riſpoſta, ma per una riſpoſta <lb></lb>ſempre la dara, o in el aggiongere, ouer nel cauare, et mai falla, ma alcuna uolta riſpon<lb></lb>dera all'uno, e l'altro medo.<emph.end type="italics"></emph.end> M.R. Q<emph type="italics"></emph>ueſti tre capitoli certamente non gli ho manco <lb></lb>accari di quello hauero quelli de cenſo è cubo egual à numero con glialtri dui ſuoi com<lb></lb>pagni, quando che me li mandareti, horſu ui uoglio laſſare Compare, gionto che ſia in <lb></lb>Inghilterra ue ſcriuero.<emph.end type="italics"></emph.end> N. A<emph type="italics"></emph>ndati meſſer Compare, che Iddio ue dia il buon uiag<lb></lb>gio, & ui prego che me ſcriueti ſubito, che ui ſeti aggionto, come haueti detto.<emph.end type="italics"></emph.end> M.R. <lb></lb>F<emph type="italics"></emph>aro ſenza fallo.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003464">F<emph type="italics"></emph>ine delli Queſiti, & Inuentioni diuerſe de Nicolo Tartaglia.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003465">REGISTRO.</s> </p> <p type="head"> <s id="s.003466">ABCDEFGHIKLMNOPQRSTVXYZ <lb></lb>AA BB CC DD EE FF GG HH II.</s> </p> <p type="head"> <s id="s.003467">T<emph type="italics"></emph>utti ſono Duerni.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003468">I<emph type="italics"></emph>n Venetia per Nicolo de Baſcarini, ad inſtantia & requiſitione, <lb></lb>& à proprie ſpeſe de Nicolo Tartaglia Autore.<emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="s.003469">N<emph type="italics"></emph>ell'anno di noſtra ſalute.<emph.end type="italics"></emph.end> M D LIIII.</s> </p> </subchap1> </chap> </body> <back></back> </text> </archimedes>