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DESpecs 2.0 Autumn 2009
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Thu, 02 May 2013 11:14:40 +0200 |
| parents | 22d6a63640c6 |
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<?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC"> <metadata> <dcterms:identifier>ECHO:ZBAS6ZM1.xml</dcterms:identifier> <dcterms:creator identifier="GND:129226815">Cataneo, Girolamo</dcterms:creator> <dcterms:title xml:lang="it">Opera del misurare di M. Girolamo Cataneo Novarese libri II : nel primo s'insegna a misurar, e partir' i campi ; nel secondo a misurar le muraglie, imbottar grani, vini, fieni, e strami ; col liuellar l' acque, & altre cose 'necessarie a gli agrimensori </dcterms:title> <dcterms:date xsi:type="dcterms:W3CDTF">1572</dcterms:date> <dcterms:language xsi:type="dcterms:ISO639-3">ita</dcterms:language> <dcterms:rights>CC-BY-SA</dcterms:rights> <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license> <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder> <parameters>despecs=1.1.2</parameters> <log>moved &lt;hd&gt; tag in approx. line 3404 to end of the line</log> </metadata> <text xml:lang="it" type="free"> <div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="001" n="1"/> <pb file="002" n="2"/> <pb file="003" n="3"/> <pb file="004" n="4"/> <pb file="005" n="5"/> </div> <div xml:id="echoid-div2" type="section" level="1" n="2"> <head xml:id="echoid-head1" xml:space="preserve">OPERA</head> <head xml:id="echoid-head2" xml:space="preserve">DEL MISVRARE,</head> <head xml:id="echoid-head3" xml:space="preserve">DI M. GIROLAMO</head> <head xml:id="echoid-head4" xml:space="preserve">CATANEO NOVARESE</head> <head xml:id="echoid-head5" xml:space="preserve">LIBRI II.</head> <head xml:id="echoid-head6" xml:space="preserve">NEL PRIMO S’INSEGNA A'</head> <head xml:id="echoid-head7" xml:space="preserve">Miſurar, & partir’ i Campi,</head> <head xml:id="echoid-head8" xml:space="preserve">NEL SECONDO A MISVRAR LE MVRAGLIE,</head> <head xml:id="echoid-head9" xml:space="preserve">imbottar Grani, Vini, Fieni, & Strami; col liuellar <lb/>l’Acque, & altre coſe neceſſarie a gli <lb/>Agrimenſori.</head> <head xml:id="echoid-head10" xml:space="preserve">LIBRO PRIMO.</head> <figure> <image file="005-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/005-01"/> </figure> </div> <div xml:id="echoid-div3" type="section" level="1" n="3"> <head xml:id="echoid-head11" xml:space="preserve">IN BRESCIA</head> <head xml:id="echoid-head12" xml:space="preserve">APPRESSO FRANCESCO, ET PIE: MARIA</head> <head xml:id="echoid-head13" xml:space="preserve">DI MARCHETTI FRATELLI.</head> <pb file="006" n="6"/> <handwritten/> <handwritten/> <handwritten/> <pb file="007" n="7"/> <figure> <image file="007-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/007-01"/> </figure> </div> <div xml:id="echoid-div4" type="section" level="1" n="4"> <head xml:id="echoid-head14" xml:space="preserve">AL MAGNIFICO SIG. GIO. <lb/>FRANCESCO NICOLINI, <lb/>DA SOVERE. <lb/>SIG. MIO HONORANDISS.</head> <figure> <image file="007-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/007-02"/> </figure> <p style="it"> <s xml:id="echoid-s1" xml:space="preserve">L’A MOREVOLE & </s> <s xml:id="echoid-s2" xml:space="preserve">Si-<lb/>gnorile conuerſatione, & </s> <s xml:id="echoid-s3" xml:space="preserve">i prudenti <lb/>& </s> <s xml:id="echoid-s4" xml:space="preserve">accorti diſcor ſi uoſtri, Magni-<lb/>fico Signor Gio: </s> <s xml:id="echoid-s5" xml:space="preserve">Franceſco, hauuti <lb/>con meco in quel tempo, che mi trat-<lb/>tenni nella terra uoſtra di Souere, <lb/>mi ui reſero oltre modo obligato & </s> <s xml:id="echoid-s6" xml:space="preserve">affettionato. </s> <s xml:id="echoid-s7" xml:space="preserve">Co-<lb/>nobbi in uoi una lealtà, una fede, & </s> <s xml:id="echoid-s8" xml:space="preserve">una carità ne’ co- <pb file="008" n="8"/> stumi, che in pochi della noſtra età, che trattino merce, <lb/>ſiuede tale & </s> <s xml:id="echoid-s9" xml:space="preserve">tanta. </s> <s xml:id="echoid-s10" xml:space="preserve">Echi fù mai più uago delſ hoſpi-<lb/>talità, & </s> <s xml:id="echoid-s11" xml:space="preserve">della corteſia, di uoi, & </s> <s xml:id="echoid-s12" xml:space="preserve">de’ uostri fratelli, <lb/>liquali come con mar auiglioſo conſenſo ſono uniti con uoi <lb/>ne’ traffichi giusti delle facende, che pratticate: </s> <s xml:id="echoid-s13" xml:space="preserve">coſi in <lb/>honorar’ ogni uirtuoſo, & </s> <s xml:id="echoid-s14" xml:space="preserve">fauorirlo & </s> <s xml:id="echoid-s15" xml:space="preserve">ſoccorrerlo ſi <lb/>moſtrano pronti? </s> <s xml:id="echoid-s16" xml:space="preserve">Ben chiaro testimonio ne poſſo ren-<lb/>der’ io, che ſe non uirtuoſo, almen amico di uirtù eſſendo, <lb/>hô riceuuto tanti honorati ſegni di gentilezza, che niun <lb/>tempo, quantunque lungo, me li potrebbe ſcancellar dalla <lb/>mente. </s> <s xml:id="echoid-s17" xml:space="preserve">Et poiche l’eſſercitio della mercatura non ſcema <lb/>nella famiglia uostra la nobiltâ del ſangue: </s> <s xml:id="echoid-s18" xml:space="preserve">anzi l’accre-<lb/>ſce col ſommini ſtrarle di continuo occaſioni di giouar al <lb/>mondo, & </s> <s xml:id="echoid-s19" xml:space="preserve">di ſcoprir i theſori delle qualità ſue, a uoi ſi <lb/>conuengono piûle fatiche & </s> <s xml:id="echoid-s20" xml:space="preserve">i ſudori de’ uirtuoſi & </s> <s xml:id="echoid-s21" xml:space="preserve">eſſer-<lb/>citati huomini, che ài Signori d’hoggidi, li quali gonfi d’i <lb/>titoli de’ maggiori ſedendo nell’otio hanno in diſprezzo le <lb/>carte uergate da begli ingegni. </s> <s xml:id="echoid-s22" xml:space="preserve">Però ho diſpoſto, qual’ io <lb/>mi ſia, di più prezzar’ i mezani & </s> <s xml:id="echoid-s23" xml:space="preserve">communi huomini, che <lb/>di tanto faſto non uanno carichi, che inchinar la dipinta <lb/>magnanimità di quelli, che piû d’oro, che di bontà ſono <lb/>ingordi. </s> <s xml:id="echoid-s24" xml:space="preserve">Et ricordandomi, che fra tanti amici & </s> <s xml:id="echoid-s25" xml:space="preserve">Si-<lb/>gnori miei hò conoſciuto à miei di, che uoi nel cuor mio te-<lb/>nete per debito il primo luogo, mi è paruto non dirò d’ho-<lb/>norarui di questa preſente fatica: </s> <s xml:id="echoid-s26" xml:space="preserve">ma di ſodisfar a me <lb/>steſſo, & </s> <s xml:id="echoid-s27" xml:space="preserve">moſtrarui inſieme di quanto pregio tenga la <pb file="009" n="9"/> nobilißima caſa uostra, nella quale hebbi tante uolte ri-<lb/>cetto caro & </s> <s xml:id="echoid-s28" xml:space="preserve">pieno d’infinita amoreuolezza. </s> <s xml:id="echoid-s29" xml:space="preserve">Et in ciò <lb/>non ſarò io già di poco giudicio dannato, poſcia che di <lb/>materia hc<unsure/> trattato non lontana dalla facultà del Mer-<lb/>catante, la quale ancora che drizzi l’ingegno humano al <lb/>guadagno, nondimeno portando ſeco & </s> <s xml:id="echoid-s30" xml:space="preserve">prudentia & </s> <s xml:id="echoid-s31" xml:space="preserve">ma <lb/>teria diſolleuar’ iproßimi & </s> <s xml:id="echoid-s32" xml:space="preserve">lontani ſenzaingiuſtitia, ri-<lb/>ceue tanto d’illuſtrezza nelle mani uoſtre, quanto nelle <lb/>mani de gli otioſi & </s> <s xml:id="echoid-s33" xml:space="preserve">ignoranti ricchi ſi oſcura il lume de <lb/>gli auoli loro. </s> <s xml:id="echoid-s34" xml:space="preserve">Con la uſata ſinceritâ dell’animo uoſtro ui <lb/>prego ad accettar il dono di queſto prattico libro, del più <lb/>calamitoſo amico & </s> <s xml:id="echoid-s35" xml:space="preserve">ſeruitore forſe, che hauete, la cui <lb/>picciolezza, ſe nonſuppliſce la grandezza de’meriti uoſtri, <lb/>perdoniſi al mio più non potere nelle anguſtie della miſe-<lb/>riamia, giungendo il deſiderio mio tant’ alto, quanto a <lb/>uoi nella magnificenza ſua ſi conuiene, & </s> <s xml:id="echoid-s36" xml:space="preserve">à me nella te-<lb/>nuità mia non ſi diſdice. </s> <s xml:id="echoid-s37" xml:space="preserve">Et qui col baſciar la mano a <lb/>V. </s> <s xml:id="echoid-s38" xml:space="preserve">S. </s> <s xml:id="echoid-s39" xml:space="preserve">& </s> <s xml:id="echoid-s40" xml:space="preserve">ai Signori ſuoi fratelli mi raccomando hu-<lb/>milmente.</s> <s xml:id="echoid-s41" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s42" xml:space="preserve">Di Breſcia alli 25. </s> <s xml:id="echoid-s43" xml:space="preserve">Gennaro. </s> <s xml:id="echoid-s44" xml:space="preserve">M. </s> <s xml:id="echoid-s45" xml:space="preserve">D. </s> <s xml:id="echoid-s46" xml:space="preserve">LXXII.</s> <s xml:id="echoid-s47" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s48" xml:space="preserve">DiVostra Signoria, <lb/>Seru. </s> <s xml:id="echoid-s49" xml:space="preserve">Girolamo Cataneo <lb/>Nouareſe.</s> <s xml:id="echoid-s50" xml:space="preserve"/> </p> <pb file="010" n="10"/> <pb file="011" n="11"/> </div> <div xml:id="echoid-div5" type="section" level="1" n="5"> <head xml:id="echoid-head15" xml:space="preserve">TAVOLA DELLA PRESENTE OPERA.</head> <note position="right" xml:space="preserve"> <lb/>PROEMIO # a carte # 2 <lb/>Prima diffinitione # a carte # 5 <lb/>Seconda diffinitione # 5 <lb/>Terza diffinitione # 5 <lb/>Quarta diffinitione # 6 <lb/>Quinta diffinitione # 7 <lb/>Seſta diffinitione del corpo # 8 <lb/>Delle rappreſentationi de numeri del miſurar le terre. # 10 <lb/>Perche cauezzi fia cauezzi fanno quarti ditauole. # 11 <lb/>Perche cauezzi fia braccia, fanno mezipiedi. # 11 <lb/>Perche cauezzi fia oncie fanno meze oncie # 11 <lb/>Perche cauezzo fia punto, fanno mezo punto # 12 <lb/>Perche braccia fia braccia fanno oncie # 12 <lb/>Perche braccia fia oncie fanno punti # 13 <lb/>Perche braccia fia punti fanno atomi # 13 <lb/>Perche oncie fia oncie fanno atomi # 13 <lb/>Perche oncie fia punti fanno minuti # 14 <lb/>Perche punti fia punti fanno momenti. # 14 <lb/>Primo eſſempio del moltiplicar la larghezza con la lunghezza del quadran-<lb/># golo rettangolo, per hauere la ſua ſuperficie d’una pezza di terra. # 15 <lb/>Prima ragione della prima figura # 15 <lb/>Seconda ragione della ſeconda figura # 18 <lb/>Terza ragione della prima figura # 21 <lb/>Quarta ragione della ſeconda figura # 22 <lb/>Quinta ragione della terza figura # 24 <lb/>Seſta ragione della quarta figura # 26 <lb/>Settima ragione della quinta figura # 27 <lb/>Ottaua ragione della nona figura # 29 <lb/>Nona ragione della nona figura # 30 <lb/>Decima ragione # 36 <lb/>Vndecima ragione. # 36 <lb/>Del ſquadrare, diuidere, & aggiontare una pezza di terra # 37 <lb/>Primo eſſempio # 42 <lb/>Duodecima ragione. # 43 <lb/>Secondo eſſempio # 44 <lb/>Terzo eſſempio # 45 <lb/>Quarto eſſempio # 46 <lb/>Quinto eſſempio # 47 <lb/>Seſto eſſempio # 47 <lb/>Settimo eſſempio # 48 <lb/>Ottauo eſſempio # 48 <lb/>Nono eſſempio # 49 <lb/>Decimo eſſempio # 49 <lb/>Regola di ſap er proportionare la miſura & la differenza, ch’e il miſurare una <lb/># ſuperficie di terra trail Breſciano, & Bergamaſco. # 55 <lb/></note> <pb file="012" n="12"/> <pb o="1" file="013" n="13"/> </div> <div xml:id="echoid-div6" type="section" level="1" n="6"> <head xml:id="echoid-head16" xml:space="preserve">A LETTORI, <lb/>GIROLAMO CATANEO.</head> <p> <s xml:id="echoid-s51" xml:space="preserve"><emph style="sc">BEnche</emph>, vertuoſiſsimi Lettori, mandando <lb/>in luce il preſente trattato di Geometria prat <lb/>tica, del miſurare ſuperficij, & </s> <s xml:id="echoid-s52" xml:space="preserve">corpi, io fuſsi <lb/>reſtato di indrizzarui ſenza intacco di ripren <lb/>ſione, lettera veruna; </s> <s xml:id="echoid-s53" xml:space="preserve">pur ne queſto, ne gli al-<lb/>tri libri, ch’io ho dati alla ſtampa per lo paſſa-<lb/>to, non m’è parſo mai conueneuole laſſarli vſcir fuori, ſen-<lb/>za il voſtro ricorſo; </s> <s xml:id="echoid-s54" xml:space="preserve">conſiderando io, di che importanza è, <lb/>l’hauere benigni & </s> <s xml:id="echoid-s55" xml:space="preserve">fauoreuoli i lettori; </s> <s xml:id="echoid-s56" xml:space="preserve">nelle coſe maſsime <lb/>di momento; </s> <s xml:id="echoid-s57" xml:space="preserve">à fine che occorrendo che inuidioſo, ò ma-<lb/>ligno, à ſua voglia morder mi voleſſe, voi lettori cariſsimi <lb/>vi ritrouaſte pronti nelle mie difeſe.</s> <s xml:id="echoid-s58" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s59" xml:space="preserve">Voglio dunq; </s> <s xml:id="echoid-s60" xml:space="preserve">in gratia dimandarui queſto fauore, che in <lb/>ogni occaſione, che men che honoratamente di queſta opra <lb/>venga sparlato, vi degnate eſſer noſtri fautori & </s> <s xml:id="echoid-s61" xml:space="preserve">protetto-<lb/>ri, che quale ella ſia, è parto mio, inſieme con le altre, che’l <lb/>rozo & </s> <s xml:id="echoid-s62" xml:space="preserve">debil ingegno ha conceputo. </s> <s xml:id="echoid-s63" xml:space="preserve">La qual mia fatica <lb/>s’io vedrò apportar frutto, & </s> <s xml:id="echoid-s64" xml:space="preserve">eſſer cara à gl’huomini, & </s> <s xml:id="echoid-s65" xml:space="preserve">ac-<lb/>cetta, lodi infinite ne renderò al ſommo Autor del tutto; </s> <s xml:id="echoid-s66" xml:space="preserve">& </s> <s xml:id="echoid-s67" xml:space="preserve"><lb/>obligo perpetuo n’hauerò à colui che mi confortò à com-<lb/>porla, il mio Reuerendo Padre Don Gio: </s> <s xml:id="echoid-s68" xml:space="preserve">Battiſta Stella <lb/>Breſciano, Monaco di S. </s> <s xml:id="echoid-s69" xml:space="preserve">Benedetto, Reuerendo (benche <lb/>di freſca etade) per la religione, & </s> <s xml:id="echoid-s70" xml:space="preserve">nelle lettere riguardeuo <pb file="014" n="14"/> le, le cui belle doti baſteriano à ſtancare ogni facondo in-<lb/>telletto; </s> <s xml:id="echoid-s71" xml:space="preserve">al quale, mentre con ſeco vn giorno ragionando di <lb/>varie materie, li ſcoperſi il penſier mio; </s> <s xml:id="echoid-s72" xml:space="preserve">egli col ſuo veloce <lb/>diſcorſo antiuedendo quanto giouamento ella era per ap-<lb/>portare, mi eſſortò à ſpedirmi tantoſto & </s> <s xml:id="echoid-s73" xml:space="preserve">darle principio, & </s> <s xml:id="echoid-s74" xml:space="preserve"><lb/>fine; </s> <s xml:id="echoid-s75" xml:space="preserve">il cui buono conſiglio non ſprezzai, ma ben abbracciai <lb/>volontieri; </s> <s xml:id="echoid-s76" xml:space="preserve">perſuadendomi egli di più ancora di rendermi <lb/>grati con eſſa molti gentilhuomini, & </s> <s xml:id="echoid-s77" xml:space="preserve">mercanti miei bene-<lb/>fattori della terra di Souere contado di Bergamo, tra il nu-<lb/>mero de quali, accio che ſi vegga, che non nelle Città ſola-<lb/>mente; </s> <s xml:id="echoid-s78" xml:space="preserve">ma nelle ville ancora, ritrouanſi huomini d’alto va-<lb/>lore, gentili, corteſi, & </s> <s xml:id="echoid-s79" xml:space="preserve">cariteuoli, ricorderò breuemente <lb/>alcuni miei ſingolariſsimi Signori; </s> <s xml:id="echoid-s80" xml:space="preserve">Il Sig. </s> <s xml:id="echoid-s81" xml:space="preserve">Gio: </s> <s xml:id="echoid-s82" xml:space="preserve">Franceſco, <lb/>il Signor Nicolino, il Signor Gio: </s> <s xml:id="echoid-s83" xml:space="preserve">Antonio, & </s> <s xml:id="echoid-s84" xml:space="preserve">il Signor <lb/>Gio: </s> <s xml:id="echoid-s85" xml:space="preserve">Maria Fratelli di Nicolini Mercanti leali, & </s> <s xml:id="echoid-s86" xml:space="preserve">Gen-<lb/>tilhuomini degni d’ogni commendatione, in corteſia, & </s> <s xml:id="echoid-s87" xml:space="preserve">in <lb/>carità verſo i poueri; </s> <s xml:id="echoid-s88" xml:space="preserve">Il Magnifico ancora Signor Gio: </s> <s xml:id="echoid-s89" xml:space="preserve">Pie-<lb/>tro Pacieno, gentilhuomo ricchiſsimo, & </s> <s xml:id="echoid-s90" xml:space="preserve">perle qualità ſue <lb/>honoratiſsimo, il qual non ſolo non ſi contenta gia mai, ne <lb/>ſatio ſi vede dell’vſar di continuo corteſie, che anco diſtri-<lb/>buire è ſolito ſempre gran parte delle ſue facoltà, in ſoue-<lb/>nire i poueri biſognoſi; </s> <s xml:id="echoid-s91" xml:space="preserve">ne voglio tacer anco i miei patroni <lb/>amoreuoli, Il Signor Lodouico Maffetto, & </s> <s xml:id="echoid-s92" xml:space="preserve">il Signor Gio: <lb/></s> <s xml:id="echoid-s93" xml:space="preserve">Antonio Foreſti ambidue chiari ſpecchi di gentilezza, & </s> <s xml:id="echoid-s94" xml:space="preserve"><lb/>liberalità onde conchiudo, che Souere eſſendo, come è, <lb/>madre di tanti magnanimi, & </s> <s xml:id="echoid-s95" xml:space="preserve">ſplendidi Signori, non ſolo à <lb/>terrieri; </s> <s xml:id="echoid-s96" xml:space="preserve">ma à foreſtieri, & </s> <s xml:id="echoid-s97" xml:space="preserve">peregrini, larghi donatori, è de-<lb/>gna, & </s> <s xml:id="echoid-s98" xml:space="preserve">meriteuole di eſſer celebrata, per terra famoſa, & </s> <s xml:id="echoid-s99" xml:space="preserve">fe-<lb/>lice; </s> <s xml:id="echoid-s100" xml:space="preserve">Qui humaniſsimi lettori facendo fine, mi reſta pre-<lb/>garui caldamente, che queſto mio libro raccomãdato vi ſia, <lb/>promettendoui di darui à leggere delle altre coſe noue, & </s> <s xml:id="echoid-s101" xml:space="preserve"><lb/>di giouamento, ſecondo che di mano in mano mi verra cõ-<lb/>modità, & </s> <s xml:id="echoid-s102" xml:space="preserve">occaſione eſſer data: </s> <s xml:id="echoid-s103" xml:space="preserve">ſtate allegri.</s> <s xml:id="echoid-s104" xml:space="preserve"/> </p> <pb o="2" file="015" n="15"/> </div> <div xml:id="echoid-div7" type="section" level="1" n="7"> <head xml:id="echoid-head17" xml:space="preserve">PROEMIO DELLA PRE-<lb/>SENTE OPERA.</head> <p> <s xml:id="echoid-s105" xml:space="preserve">IN <emph style="sc">TVTTE</emph> le ſcienze, & </s> <s xml:id="echoid-s106" xml:space="preserve">arti liberali, <lb/>le quali s’inſegnano con dritto ordi-<lb/>ne, inanzi che ſi vẽghi a trattare le co <lb/>ſele quali pertẽgono al ſuggetto lo-<lb/>ro, è ben fatto che prima s’inſegnino <lb/>i principi d’eſſe. </s> <s xml:id="echoid-s107" xml:space="preserve">Concioſia che da <lb/>quelle dipendono tutte l’altre coſe; </s> <s xml:id="echoid-s108" xml:space="preserve">& </s> <s xml:id="echoid-s109" xml:space="preserve"><lb/>ſopra queſti, come ne’ fondamenti ſi <lb/>drizza tutto il rimanente; </s> <s xml:id="echoid-s110" xml:space="preserve">E conte-<lb/>nendoſi i principij in ſe medeſimi, & </s> <s xml:id="echoid-s111" xml:space="preserve">la forza di tutte l’altre <lb/>coſe, lequali s’inſegnano doppo loro, è neceſſario che nel <lb/>porre & </s> <s xml:id="echoid-s112" xml:space="preserve">ſtabilire i principij, ſi ponga diligente fatica, accio-<lb/>che ſtabiliti, & </s> <s xml:id="echoid-s113" xml:space="preserve">ben collocati piu facilmente l’altre coſe s’in-<lb/>tendino. </s> <s xml:id="echoid-s114" xml:space="preserve">Hora volendo io trattare della Geometria prat-<lb/>tica, inanzi che à particolari diſcenda, è di biſogno, che ſi <lb/>pongan o quei principij, e termini, i quali fanno meſtieri al-<lb/>la intelligenza di queſt’arte.</s> <s xml:id="echoid-s115" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s116" xml:space="preserve">Et trattando io di quella parte, la quale ha più del pratti-<lb/>co, che dell’aſtratto: </s> <s xml:id="echoid-s117" xml:space="preserve">non conuiene che qui ſi pongano tutti <lb/>quei principij, & </s> <s xml:id="echoid-s118" xml:space="preserve">termini i quali ſi ricercano nella Geome-<lb/>tria aſtratta. </s> <s xml:id="echoid-s119" xml:space="preserve">Anzi ſupponendo io per veri, & </s> <s xml:id="echoid-s120" xml:space="preserve">noti i princi <lb/>pi dati da Euclide; </s> <s xml:id="echoid-s121" xml:space="preserve">di quelli ſon io per ſeruirmi, nel progreſ-<lb/>ſo di queſta opera. </s> <s xml:id="echoid-s122" xml:space="preserve">Togliendo ſolo alcune diffinitioni, ſen <lb/>za lequali imperfetto ſarebbe queſto trattato, & </s> <s xml:id="echoid-s123" xml:space="preserve">quelle ver- <pb file="016" n="16" rhead="PROEMIO."/> rò dichiarando che ben’inteſe queſte, l’altre coſe poi ſi ren-<lb/>deranno più facili. </s> <s xml:id="echoid-s124" xml:space="preserve">Etaccioche meglio ſi poſſa intendere, <lb/>quanto ſi dirà intorno à queſte diſſinitioni & </s> <s xml:id="echoid-s125" xml:space="preserve">principij, giu-<lb/>dico eſſere non ſolo pertinente al noſtro propoſito; </s> <s xml:id="echoid-s126" xml:space="preserve">ma <lb/>etiandio neceſſario primatrattare qual ſia il ſuggetto, & </s> <s xml:id="echoid-s127" xml:space="preserve">la <lb/>matteria, cerca la quale verſa il Geometra, concioſia che <lb/>dalla intelligenza di queſto ſi apporterà gran luce alle coſe, <lb/>le quali ſi diranno nel progreſſo di tutta l’opra. </s> <s xml:id="echoid-s128" xml:space="preserve">Verſano tut <lb/>te le arti matematiche intorno alla quantità, ma tra ſe ſono <lb/>diſſerenti; </s> <s xml:id="echoid-s129" xml:space="preserve">altre per le diuerſe nature della quantità conſi-<lb/>derata; </s> <s xml:id="echoid-s130" xml:space="preserve">& </s> <s xml:id="echoid-s131" xml:space="preserve">altre per il modo del conſiderarle. </s> <s xml:id="echoid-s132" xml:space="preserve">La quantità, <lb/>come è noto à ciaſcheduno, altra è continua, altra è diſcre-<lb/>ta; </s> <s xml:id="echoid-s133" xml:space="preserve">Continua quantità è quella, le cui partitra ſe ſono vnite <lb/>& </s> <s xml:id="echoid-s134" xml:space="preserve">congiunte per vn termine commune ad eſſe parti, la qual <lb/>diffinitione per mezo delli eſſempi ſirenderà chiara; </s> <s xml:id="echoid-s135" xml:space="preserve">conti-<lb/>nua quantità, ſono, linea, ſuperſicie, & </s> <s xml:id="echoid-s136" xml:space="preserve">corpo (laſciando ho <lb/>ra da parte il tempo, & </s> <s xml:id="echoid-s137" xml:space="preserve">il moto, come quelli, che al noſtro <lb/>propoſito non fanno) ma il punto non è quantità, ne parte <lb/>di quantità, ma ſolo principio, ò termine d’alcuna quanti-<lb/>tà continua, come poco dapoi ſi dirà: </s> <s xml:id="echoid-s138" xml:space="preserve">& </s> <s xml:id="echoid-s139" xml:space="preserve">per queſta cagione <lb/>il punto è compreſo ſotto la quantità continua; </s> <s xml:id="echoid-s140" xml:space="preserve">perche ſi <lb/>comprende nella diffinitione d’alcuna ſorte di quãtità con-<lb/>tinua, nead altro genere ſi può accommodare; </s> <s xml:id="echoid-s141" xml:space="preserve">Eſſendo adũ <lb/>que la linea, la ſuperficie, & </s> <s xml:id="echoid-s142" xml:space="preserve">il corpo, quantità continua da-<lb/>ta di ſopra. </s> <s xml:id="echoid-s143" xml:space="preserve">Et prima nella linea, io dico che la linea <lb/><emph style="sc">A</emph>------------------<emph style="sc">B</emph>. </s> <s xml:id="echoid-s144" xml:space="preserve">è quantità continua, perche piglian-<lb/>do con la imaginatione due parti d’eſſa, & </s> <s xml:id="echoid-s145" xml:space="preserve">diuidendola nel <lb/>punto c, come ſi vede la linea <emph style="sc">A</emph> -----------<emph style="sc">C</emph>----------<emph style="sc">B</emph> <lb/>la parte <emph style="sc">A C</emph>, ſi vniſce & </s> <s xml:id="echoid-s146" xml:space="preserve">ſi congiunge con l’altra parte <emph style="sc">C B</emph>, <lb/>nel punto <emph style="sc">C</emph>, il quale è commune termine della parte <emph style="sc">A C</emph>, <lb/>& </s> <s xml:id="echoid-s147" xml:space="preserve">dell’altra parte <emph style="sc">C B</emph>, talmente che’l punto c, e fine della <lb/>parte <emph style="sc">A C</emph>, & </s> <s xml:id="echoid-s148" xml:space="preserve">principio dell’altra <emph style="sc">C B</emph>, per tanto diremo, che <lb/>ogni linea è quantità continua; </s> <s xml:id="echoid-s149" xml:space="preserve">percioche prendendo con <lb/>la imaginatione qual ſi voglia parte dieſſa linea, queſta par <pb o="3" file="017" n="17" rhead="PROEMIO."/> te è vnita con l’altra qualunq; </s> <s xml:id="echoid-s150" xml:space="preserve">parte, con vn termine commu <lb/>ne, il quale nella linea è il punto. </s> <s xml:id="echoid-s151" xml:space="preserve">Et da qui ſegue, che il <lb/>punto è termine commune di qualunq; </s> <s xml:id="echoid-s152" xml:space="preserve">parte, la quale s’ima <lb/>giniamo che ſia qual ſi voglia linea; </s> <s xml:id="echoid-s153" xml:space="preserve">Similmente ancora la <lb/>ſuperfice è quantità continua, percioche ſe imaginandoſi <lb/>noi ſuperſicie, la quale per eſſempio ſia <emph style="sc">A B C D</emph>, <lb/> <anchor type="figure" xlink:label="fig-017-01a" xlink:href="fig-017-01"/> & </s> <s xml:id="echoid-s154" xml:space="preserve">di queſt a intendiamo di pigliar vna parte, ouer più, ve-<lb/>dremo che ciaſcuna d’eſse parti ſarà congionta, & </s> <s xml:id="echoid-s155" xml:space="preserve">vnita all’ <lb/>altra ſua, per vn termine commune. </s> <s xml:id="echoid-s156" xml:space="preserve">Diuidaſi adunq; </s> <s xml:id="echoid-s157" xml:space="preserve">la ſu-<lb/>perſicie <emph style="sc">A B C D</emph>, <lb/> <anchor type="figure" xlink:label="fig-017-02a" xlink:href="fig-017-02"/> in due parti con la linea <emph style="sc">E F</emph>; </s> <s xml:id="echoid-s158" xml:space="preserve">la parte <emph style="sc">A C E F</emph>, è congionta cõ <lb/>la parte <emph style="sc">E F B D</emph>, per la linea <emph style="sc">E F</emph>, commune termine della ſu-<lb/>perſicie <emph style="sc">A C E F</emph>, & </s> <s xml:id="echoid-s159" xml:space="preserve">della ſuperſicie <emph style="sc">E F B D</emph>; </s> <s xml:id="echoid-s160" xml:space="preserve">talmente che la li-<lb/>nea <emph style="sc">E F</emph>, è fine dell’vna, & </s> <s xml:id="echoid-s161" xml:space="preserve">principio dell’altra. </s> <s xml:id="echoid-s162" xml:space="preserve">Et da queſto <lb/>ſegue, che il termine, il qual’vniſce & </s> <s xml:id="echoid-s163" xml:space="preserve">congiunge le parti <lb/>della ſuperſicie, è la linea. </s> <s xml:id="echoid-s164" xml:space="preserve">Non altrimente diciamo, che <lb/>il corpo è quantità continua, ſe non, perche le ſue parti; </s> <s xml:id="echoid-s165" xml:space="preserve">del <lb/>le quali con l’imaginatione ſupponiamo, che il corpo ſia <lb/>compoſto, ſivniſcono tra ſe, per la ſuperſicie commune, ter <lb/>mine delle parti di quello; </s> <s xml:id="echoid-s166" xml:space="preserve">& </s> <s xml:id="echoid-s167" xml:space="preserve">ſia (per maggior dechiaratio-<lb/>ne) vn corpo ſolido <emph style="sc">A, B, E, F, D, G, C.</emph></s> </p> <div xml:id="echoid-div7" type="float" level="2" n="1"> <figure xlink:label="fig-017-01" xlink:href="fig-017-01a"> <image file="017-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/017-01"/> </figure> <figure xlink:label="fig-017-02" xlink:href="fig-017-02a"> <image file="017-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/017-02"/> </figure> </div> <pb file="018" n="18" rhead="PROEMIO."/> <figure> <image file="018-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/018-01"/> </figure> <p> <s xml:id="echoid-s168" xml:space="preserve">Hor imaginiamoſi, che queſto corpo ſia diuiſo in due par <lb/>ti dalla ſuperficie <emph style="sc">H I K</emph>, noi diremo che vna d’eſſe parti è <lb/>congionta all’altra per vn termine commune ad ambedue <lb/>eſſe parti, il qual termine commune è la ſuperficie <emph style="sc">H I K</emph>, cioè <lb/>diremo, che la parte, <emph style="sc">H I K D G C</emph>, ſi congiunge con l’altra par <lb/>te <emph style="sc">H I K E F A B</emph>, per la ſuperfice, <emph style="sc">H I K</emph>, & </s> <s xml:id="echoid-s169" xml:space="preserve">queſta ſuperſicie è ter <lb/> <anchor type="figure" xlink:label="fig-018-02a" xlink:href="fig-018-02"/> mine d’ambedue le parti del corpo. </s> <s xml:id="echoid-s170" xml:space="preserve">Onde è da conchiude-<lb/>re che ſi come il punto nella linea è termine commune del-<lb/>le parti della linea; </s> <s xml:id="echoid-s171" xml:space="preserve">coſi che diuidendoſi la linea, la diuiſione <lb/>ſi fà in punto. </s> <s xml:id="echoid-s172" xml:space="preserve">Similmente ancora deuendoſi diuidere la <lb/>ſuperficie la diuiſione ſi fà per vna linea; </s> <s xml:id="echoid-s173" xml:space="preserve">Non altrimente <lb/>hauendoſi da partire alcun corpo, è neceſſario che la diuiſio <lb/>ne ſi faccia per ſuperficie.</s> <s xml:id="echoid-s174" xml:space="preserve"/> </p> <div xml:id="echoid-div8" type="float" level="2" n="2"> <figure xlink:label="fig-018-02" xlink:href="fig-018-02a"> <image file="018-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/018-02"/> </figure> </div> <pb o="4" file="019" n="19" rhead="PROEMIO."/> <p> <s xml:id="echoid-s175" xml:space="preserve">Fin qui ſia detto a ſufficienza della diffinitione della quã <lb/>tità continua, la qual con eſſempi hauemo dechiarato, quan <lb/>to al preſente loco è conueniente. </s> <s xml:id="echoid-s176" xml:space="preserve">Quantità diſcreta di-<lb/>ciamo, quella, le cui partinon ſi congiungano da termine <lb/>commune.</s> <s xml:id="echoid-s177" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s178" xml:space="preserve">Fra le ſpecie di queſta quãtità è il numero, concioſia che <lb/>diuidendoſi qualunq; </s> <s xml:id="echoid-s179" xml:space="preserve">numero, la diuiſione ſi fà in parti, le <lb/>quali non hanno numero alcuno, che ſia fine d’vna, & </s> <s xml:id="echoid-s180" xml:space="preserve">prin-<lb/>cipio dell’altra. </s> <s xml:id="echoid-s181" xml:space="preserve">Partiſi il ſei in due termini, ciaſcuno d’eſsi <lb/>è ſeparato, & </s> <s xml:id="echoid-s182" xml:space="preserve">diuiſo dall’altro, ſenza legame alcuno, per-<lb/>cioche il tre è fine del primo ternario; </s> <s xml:id="echoid-s183" xml:space="preserve">ma non è principio <lb/>del ſecondo, ſimilmente il quattro è principio del ſecondo <lb/>termario; </s> <s xml:id="echoid-s184" xml:space="preserve">ma non è fine del primo; </s> <s xml:id="echoid-s185" xml:space="preserve">& </s> <s xml:id="echoid-s186" xml:space="preserve">per queſto il numero è <lb/>quantità diſcreta.</s> <s xml:id="echoid-s187" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s188" xml:space="preserve">Diuiſa la quantità nel modo poſto di ſopra, tornando al <lb/>noſtro propoſito, dico, che la Geometria verſa attorno alla <lb/>quantità continua; </s> <s xml:id="echoid-s189" xml:space="preserve">ma non tutta, percioche il tẽpo, & </s> <s xml:id="echoid-s190" xml:space="preserve">il mo-<lb/>to ſono d’altra cõſideratione, che del Geometra; </s> <s xml:id="echoid-s191" xml:space="preserve">percioche <lb/>egli conſidera ſolamente la linea, la ſuperſicie, & </s> <s xml:id="echoid-s192" xml:space="preserve">il corpo; </s> <s xml:id="echoid-s193" xml:space="preserve">ò <lb/>per dir meglio gli accidenti, & </s> <s xml:id="echoid-s194" xml:space="preserve">le paſsioni loro, come ſono <lb/>figure, grandezze, e qualità, inequalitâ, & </s> <s xml:id="echoid-s195" xml:space="preserve">ſimili al-<lb/>tri accidenti; </s> <s xml:id="echoid-s196" xml:space="preserve">Ma conſidera molto diuerſamente di quel-<lb/>lo che fà l’Aſtronomo, il perſpettiuo, & </s> <s xml:id="echoid-s197" xml:space="preserve">il Filoſofo natu-<lb/>rale; </s> <s xml:id="echoid-s198" xml:space="preserve">concioſia che l’Aſtronomo conſidera i corpi celeſti, <lb/>la terra, & </s> <s xml:id="echoid-s199" xml:space="preserve">la lor grandezza, & </s> <s xml:id="echoid-s200" xml:space="preserve">illor moto, ne in tutto ſepa-<lb/>ra gli accidenti dalla materia; </s> <s xml:id="echoid-s201" xml:space="preserve">percioche tratta egli di eſsi <lb/>in quanto ſono, nel Sole, nella Luna, & </s> <s xml:id="echoid-s202" xml:space="preserve">ne gl’altri corpi ce-<lb/>leſti, ma non con quelli mezi che fà il Filoſofo natura-<lb/>le, ne in quanto in eſsi è natura tale; </s> <s xml:id="echoid-s203" xml:space="preserve">il perſpettiuo tratta <lb/>di linee, di ſuperficie, & </s> <s xml:id="echoid-s204" xml:space="preserve">di corpi, & </s> <s xml:id="echoid-s205" xml:space="preserve">de i loro accidenti, in <lb/>quanto caſcano ſotto il ſenſo del vedere; </s> <s xml:id="echoid-s206" xml:space="preserve">ma con proue ma <lb/>tematiche. </s> <s xml:id="echoid-s207" xml:space="preserve">Ilnaturale Filoſofo, conſidera tutte le coſe in <lb/>quel modo che hãno l’eſſere, nella ſua propria materia ſen-<lb/>ſibile; </s> <s xml:id="echoid-s208" xml:space="preserve">Mail Geometra queſto fa differentemẽte da ciaſcun <pb file="020" n="20" rhead="PROEMIO."/> de i ſopra detti; </s> <s xml:id="echoid-s209" xml:space="preserve">Concioſia che con l’intelletto ſepara leco <lb/>ſe, ch’egli conſiderà, dalla materia ſenſibile dal moto, e da <lb/>qualunq; </s> <s xml:id="echoid-s210" xml:space="preserve">alteratione; </s> <s xml:id="echoid-s211" xml:space="preserve">che ſe bene l’eſſere della quantità è <lb/>ne corpi naturali, nondimeno con l’intelletto le conſiderà <lb/>ſenza materia, è ſenza gli accidenti ſenſibili. </s> <s xml:id="echoid-s212" xml:space="preserve">Ilperche nel <lb/>le diffinitioni delle quantità, & </s> <s xml:id="echoid-s213" xml:space="preserve">de gl’accidenti, i quali ſono <lb/>conſiderati dal Geometra, non ſi piglia nome alcuno, il qua <lb/>le non ſi poſſa imaginare ſenza concetto ſenſibile, onde <lb/>non ſi fà mentione di moto, di tempo, di leggierezza, di <lb/>grandezza, di caldo, di bianchezza, ò d’altri ſimili acci-<lb/>denti.</s> <s xml:id="echoid-s214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s215" xml:space="preserve">Et quantunq; </s> <s xml:id="echoid-s216" xml:space="preserve">le diffinitioni, & </s> <s xml:id="echoid-s217" xml:space="preserve">i principij della Geome-<lb/>tria ſiano intelligibili, & </s> <s xml:id="echoid-s218" xml:space="preserve">aſtratti da i ſenſi; </s> <s xml:id="echoid-s219" xml:space="preserve">nondimeno ſi ac-<lb/>commodano ancora nella Aſtronomia, nella perſpettiua, <lb/>nella mecanica, & </s> <s xml:id="echoid-s220" xml:space="preserve">nella filoſofia naturale; </s> <s xml:id="echoid-s221" xml:space="preserve">& </s> <s xml:id="echoid-s222" xml:space="preserve">per il mezo lo-<lb/>ro ſi prouano le propoſitioni in ciaſcheduna di queſte ſcien-<lb/>ze, doue ſitratta delle grandezze, & </s> <s xml:id="echoid-s223" xml:space="preserve">delle figure, delle linee, <lb/>delle ſuperficij, e de’ corpi ſoggetti al moto, & </s> <s xml:id="echoid-s224" xml:space="preserve">alla materia <lb/>ſenſibile, ſicome chiaramente ſi vede, non ſolo in infiniti <lb/>luoghi appre ſſo di Ariſtotile; </s> <s xml:id="echoid-s225" xml:space="preserve">ma ancora d’altri Filoſofi.</s> <s xml:id="echoid-s226" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s227" xml:space="preserve">Hora ſe altre ſcienze ſi ſeruono de i principij della Geo-<lb/>metria contemplatiua; </s> <s xml:id="echoid-s228" xml:space="preserve">quanto più a me ſarà lecito di vſarli <lb/>in queſta opra di Geometria prattica? </s> <s xml:id="echoid-s229" xml:space="preserve">Et come da la pratti-<lb/>ca è nata la Geometria ſemplice, & </s> <s xml:id="echoid-s230" xml:space="preserve">aſtratta, & </s> <s xml:id="echoid-s231" xml:space="preserve">dalle coſe oſ-<lb/>ſeruate nel cotidiano vſo del miſurare ha ella hauuto il ſuo <lb/>principio, coſi è coſa ragioneuole che eſſa accommodi ſe <lb/>medeſima alla prattica, come a quella, a cui è obligata. <lb/></s> <s xml:id="echoid-s232" xml:space="preserve">Nacque la Geometria appreſſo gli Egittij per coſi fatta oc-<lb/>caſione, il Nillo ciaſcun’anno l’eſtate creſciendo l’acqua <lb/>inondaua le campagne dell’Egitto, & </s> <s xml:id="echoid-s233" xml:space="preserve">confondeua i confini <lb/>& </s> <s xml:id="echoid-s234" xml:space="preserve">termini loro; </s> <s xml:id="echoid-s235" xml:space="preserve">per ilche erano conſtretti ogn’anno di nuo <lb/>uo miſurare i termini, per poter ſapere qual fuſſe la parte <lb/>ſua, talmente dal frequente vſo del miſurare l’ingegno di <lb/>quegli huomini a poco a poco riduſſe l’arte in quella perfet <pb o="5" file="021" n="21" rhead="PROEMIO."/> tione, la quale quegli antichi tempi comportauano, & </s> <s xml:id="echoid-s236" xml:space="preserve">da <lb/>gli Egittij fù poi communicata a Greci; </s> <s xml:id="echoid-s237" xml:space="preserve">ſi come ancora la <lb/>Aritmetica da Fenici ha la propria origine hauuto, per le <lb/>molte mercantie da loro eſſercitate, nelle quali eſſendo ne-<lb/>ceſſaria l’arte del ſupputare, finalmente fù appreſſo loro l’A-<lb/>ritmetica primieramente ritrouata, & </s> <s xml:id="echoid-s238" xml:space="preserve">poſta in luce; </s> <s xml:id="echoid-s239" xml:space="preserve">Adun-<lb/>que, accioche meglio s’intendono le coſe della Geometria <lb/>prattica, laquale inſegna l’arte, & </s> <s xml:id="echoid-s240" xml:space="preserve">il modo di miſurare, pia-<lb/>ni, altezze, profondità ò baſſezze, che dir vogliamo, capa-<lb/>cità & </s> <s xml:id="echoid-s241" xml:space="preserve">ampiezze de corpi, caui, ò ſolidi; </s> <s xml:id="echoid-s242" xml:space="preserve">qui porremo le dif-<lb/>finitioni, e i principij poſti da Euclide nel primo libro, cioè <lb/>del punto, della linea, della ſuperſicie, e del corpo; </s> <s xml:id="echoid-s243" xml:space="preserve">& </s> <s xml:id="echoid-s244" xml:space="preserve">quelli <lb/>dichiararemo.</s> <s xml:id="echoid-s245" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div10" type="section" level="1" n="8"> <head xml:id="echoid-head18" xml:space="preserve">PRIMA DIFFINITIONE.</head> <p style="it"> <s xml:id="echoid-s246" xml:space="preserve">Il punto è quello, che non ba parte.</s> <s xml:id="echoid-s247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s248" xml:space="preserve"><emph style="sc">In qvesta</emph> prima difſinitioneſi diffiniſceil principio della <lb/>quantità continua (che è il punto) & </s> <s xml:id="echoid-s249" xml:space="preserve">dico che il pũto è quel <lb/>lo, che non ha parte alcuna, ne è parte d’alcuna quantità; <lb/></s> <s xml:id="echoid-s250" xml:space="preserve">onde ſegue ch’egli è indiuiſibile ſecondo qual ſi voglia di-<lb/>menſione, manca adunque di lunghezza, di larghezza, & </s> <s xml:id="echoid-s251" xml:space="preserve"><lb/>di profundità; </s> <s xml:id="echoid-s252" xml:space="preserve">l’vnità, è anch’eſſa indiuiſibile in quanto vni-<lb/>ta, nondimeno non ſolo è principio di numeri; </s> <s xml:id="echoid-s253" xml:space="preserve">ma ancora <lb/>compone quelli: </s> <s xml:id="echoid-s254" xml:space="preserve">Concioſia che numero altro non è, che <lb/>moltitudine compoſta di vnità, Non coſi è il punto, percio-<lb/>che ſe bene è termine, & </s> <s xml:id="echoid-s255" xml:space="preserve">principio della linea, nondimeno <lb/>i punti non poſſono conſtituire linea, ancor che infiniti ſi <lb/>prendano: </s> <s xml:id="echoid-s256" xml:space="preserve">Ne la linea ſi può riſoluere in punti. </s> <s xml:id="echoid-s257" xml:space="preserve">Eſſendo <lb/>adunq; </s> <s xml:id="echoid-s258" xml:space="preserve">coſi, non può il punto hauer l’eſſer ſuo, ſe non nella <lb/>imaginatione: </s> <s xml:id="echoid-s259" xml:space="preserve">concioſiache tutte le coſe, le quali hanno <lb/>l’eſſer nella materia, patiſcano diuiſione almeno per mezo <lb/>della ſeguita materia. </s> <s xml:id="echoid-s260" xml:space="preserve">Ne appreſſo il Filoſofo naturale ſi <lb/>concede, che il contatto ſi faccia in punto, ſi come vole il <pb file="022" n="22" rhead="PROEMIO."/> matematico, & </s> <s xml:id="echoid-s261" xml:space="preserve">lo dimoſtra quando s’imagina che il cerco-<lb/>lo tocchi vna linea retta.</s> <s xml:id="echoid-s262" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div11" type="section" level="1" n="9"> <head xml:id="echoid-head19" xml:space="preserve">SECONDA DIFFINITIONE.</head> <p style="it"> <s xml:id="echoid-s263" xml:space="preserve">La linea è una lungbezza ſenza largbezza: </s> <s xml:id="echoid-s264" xml:space="preserve">li termini della quale ſe <lb/>no due punti.</s> <s xml:id="echoid-s265" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s266" xml:space="preserve"><emph style="sc">In qvesta</emph> diffinitione ſi diffiniſce la prima ſpecie della <lb/>quantità continua (che è la linea.) </s> <s xml:id="echoid-s267" xml:space="preserve">Et dico che la linea è vna <lb/>lunghezza, ſenza larghezza alcuna, e conſeguentemente <lb/>ſenza profondità; </s> <s xml:id="echoid-s268" xml:space="preserve">i cui termini ſono due punti, pur che s’in-<lb/>tenda terminata & </s> <s xml:id="echoid-s269" xml:space="preserve">finita, percioche il Matematico non ſem <lb/>pre s’imagina la linea finita; </s> <s xml:id="echoid-s270" xml:space="preserve">ma prolungandola indifinita, <lb/>& </s> <s xml:id="echoid-s271" xml:space="preserve">indeterminata non và con l’imaginatione ricercando il <lb/>fine.</s> <s xml:id="echoid-s272" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s273" xml:space="preserve">Et appreſſo il Matematico non è coſa impoſsibile, che la <lb/>quantità & </s> <s xml:id="echoid-s274" xml:space="preserve">grandezza accreſca in inſinito; </s> <s xml:id="echoid-s275" xml:space="preserve">laqual coſa è cõ-<lb/>tro al parer del Filoſofo naturale, il qual vuole che tutte le <lb/>coſe habbiano determinata grandezza, & </s> <s xml:id="echoid-s276" xml:space="preserve">determinata pic-<lb/>ciolezza. </s> <s xml:id="echoid-s277" xml:space="preserve">Oltre a ciò non è neceſſario che ogni linea fini-<lb/>ta habbia i punti, i quali effetualmẽte la terminino; </s> <s xml:id="echoid-s278" xml:space="preserve">concio <lb/>fiacoſa che il circolo non ha principio, ò fine alcuno, eſſen-<lb/>do fatto d’vna linea ſola, il cui fine è vnito al principio, e <lb/>quello iſteſſo punto che ſia ſuppoſto eſſer fine, quello ſteſſo <lb/>ſarà ancora principio. </s> <s xml:id="echoid-s279" xml:space="preserve">Onde il circolo è chiamato figura <lb/>inſinita: </s> <s xml:id="echoid-s280" xml:space="preserve">coſi ancora è da dire di qualunq; </s> <s xml:id="echoid-s281" xml:space="preserve">altra linea, la qua <lb/>le ſi rauuolga in ſe ſteſſa, come la figura ouale, & </s> <s xml:id="echoid-s282" xml:space="preserve">ſimili.</s> <s xml:id="echoid-s283" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div12" type="section" level="1" n="10"> <head xml:id="echoid-head20" xml:space="preserve">TERZA DIFFINITIONE.</head> <p style="it"> <s xml:id="echoid-s284" xml:space="preserve">La linea retta è la breui{Ss}ima eſtenſione da un punto ad un’altro, cbe <lb/>riceue l’uno e l’altro di quelli nelle ſue eſtremità.</s> <s xml:id="echoid-s285" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s286" xml:space="preserve"><emph style="sc">Esposta</emph> la diffinitione della linea vniuerſalmente inteſa, <lb/>ſegue che ſi diffiniſcano le ſue differenze, le quali ſono que <pb o="6" file="023" n="23" rhead="PROEMIO."/> ſte; </s> <s xml:id="echoid-s287" xml:space="preserve">che della linea alcune ſono rette, alcune curue, ò torte; <lb/></s> <s xml:id="echoid-s288" xml:space="preserve">linea retta è quella, la quale da vn punto all’altro ſi ſtende <lb/>con breuiſsimo interuallo. </s> <s xml:id="echoid-s289" xml:space="preserve">Siano per eſſempio due punti <emph style="sc">A</emph>, <lb/>& </s> <s xml:id="echoid-s290" xml:space="preserve"><emph style="sc">B</emph>, io dico, che quella linea, la qual è tirata dal punto <emph style="sc">A</emph>, <lb/>al punto <emph style="sc">B</emph>, è più breue, & </s> <s xml:id="echoid-s291" xml:space="preserve">quella è retta; </s> <s xml:id="echoid-s292" xml:space="preserve">da qui viene che <lb/>linea curua, ò torta, è quella, la quale ſarà meno breue, tra <lb/>quegli ſteſsi punti. </s> <s xml:id="echoid-s293" xml:space="preserve">In qualunq; </s> <s xml:id="echoid-s294" xml:space="preserve">modo adunq; </s> <s xml:id="echoid-s295" xml:space="preserve">ſiano collo-<lb/>cati due punti, & </s> <s xml:id="echoid-s296" xml:space="preserve">dall’vno d’eſsi la linea, non piegandoſi in <lb/>alcun lato, ſia tirata all’altro punto, quella linea chiamare-<lb/>monoi diretta, non riguardando, che in sù, ò in giù, ò al-<lb/>trimente guardi, & </s> <s xml:id="echoid-s297" xml:space="preserve">quella linea, laquale più ſi allontanerà <lb/>della linea retta, quella ſarà più curua, è conſeguentemen-<lb/>te più lunga, come ſi può vedere qui ſotto per maggior <lb/>dichiaratione.</s> <s xml:id="echoid-s298" xml:space="preserve"/> </p> <figure> <image file="023-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/023-01"/> </figure> <p> <s xml:id="echoid-s299" xml:space="preserve">La linea <emph style="sc">A C B</emph>, è più curta della linea <emph style="sc">A D B</emph>, & </s> <s xml:id="echoid-s300" xml:space="preserve"><emph style="sc">A E B</emph>, & </s> <s xml:id="echoid-s301" xml:space="preserve"><lb/><emph style="sc">A F B</emph>, adunq; </s> <s xml:id="echoid-s302" xml:space="preserve">la linea <emph style="sc">A C B</emph>, è la linea retta, ne potendoſi ti-<lb/>rare altra linea dal punto <emph style="sc">A</emph>, al punto <emph style="sc">B</emph>, più curta che la li-<lb/>nea, <emph style="sc">A C B</emph>, dunq; </s> <s xml:id="echoid-s303" xml:space="preserve">tutte l’altre linee ſaranno curue, & </s> <s xml:id="echoid-s304" xml:space="preserve">eſſen-<lb/>do la linea <emph style="sc">A F B</emph>, più lontana dalla linea retta <emph style="sc">A C B</emph>, che qual <lb/>ſi voglia delle altre due, adunq; </s> <s xml:id="echoid-s305" xml:space="preserve">la linea <emph style="sc">A F B</emph>, è più curua <lb/>dell’altre due.</s> <s xml:id="echoid-s306" xml:space="preserve"/> </p> <pb file="024" n="24" rhead="PROEMIO."/> </div> <div xml:id="echoid-div13" type="section" level="1" n="11"> <head xml:id="echoid-head21" xml:space="preserve">QVARTA DIFFINITIONE.</head> <p style="it"> <s xml:id="echoid-s307" xml:space="preserve">La ſuperficie è quella che ba ſolamente lungbezza & </s> <s xml:id="echoid-s308" xml:space="preserve">largbezza: </s> <s xml:id="echoid-s309" xml:space="preserve">liter <lb/>mini della quale ſono linee.</s> <s xml:id="echoid-s310" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s311" xml:space="preserve"><emph style="sc">In qvesta</emph> quarta diffinitione ſi diffiniſce la ſeconda ſpe-<lb/>cie della quantità continua (che è la ſuperſicie) & </s> <s xml:id="echoid-s312" xml:space="preserve">la ſuper-<lb/>ficie è quella che ha ſolamente lunghezza e larghezza, cioè <lb/>che gli manca la profondità, ouer groſſezza: </s> <s xml:id="echoid-s313" xml:space="preserve">i termini del-<lb/>la quale ſono linee, ò almeno vna ſola linea.</s> <s xml:id="echoid-s314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s315" xml:space="preserve">La ſuperficie dunq; </s> <s xml:id="echoid-s316" xml:space="preserve">aggiunge larghezza alla lunghezza, <lb/>& </s> <s xml:id="echoid-s317" xml:space="preserve">per la larghezza è differente dalla linea.</s> <s xml:id="echoid-s318" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s319" xml:space="preserve">Di più, ſi come i termini della linea ſono i punti, coſi i ter <lb/>mini della ſuperficie ſono linee; </s> <s xml:id="echoid-s320" xml:space="preserve">quando la ſuperficie non <lb/>ſia di ſigura circolare, ouale, o ſimigliante a queſte; </s> <s xml:id="echoid-s321" xml:space="preserve">concio-<lb/>ſia che a terminare vna ſuperficie, & </s> <s xml:id="echoid-s322" xml:space="preserve">a conchiudere alcuna <lb/>figura baſta alle fiate vna linea ſola, la quale ripiegandoſi <lb/>in ſe ſteſſa vniſce il fine al ſuo principio, come di ſopra è ſta-<lb/>to detto nella diffinitione della linea.</s> <s xml:id="echoid-s323" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s324" xml:space="preserve">Et nella ſuperficie, la lunghezza vniuerſalmente ſi diſſe-<lb/>gna ſecondo quella parte, la quale è di maggior ſpatio, la <lb/>larghezza ſecondo il minore ſpatio, come in queſta ſuper-<lb/>ficie quadrilatera <emph style="sc">A B C D</emph>, <lb/> <anchor type="figure" xlink:label="fig-024-01a" xlink:href="fig-024-01"/> la lunghezza diremo noi ſtenderſi dal lato <emph style="sc">A C</emph>, in fino al la-<lb/>to <emph style="sc">B D</emph>; </s> <s xml:id="echoid-s325" xml:space="preserve">& </s> <s xml:id="echoid-s326" xml:space="preserve">la larghezza eſſere dal lato <emph style="sc">C D</emph>, al lato <emph style="sc">A B</emph>, Nelle ſu-<lb/>perſicij quadrati, ò cercolari, ſiprende la lunghezza ſecon-<lb/>do qual ſi voglia lato; </s> <s xml:id="echoid-s327" xml:space="preserve">& </s> <s xml:id="echoid-s328" xml:space="preserve">eſſendo aſſegnata la lunghezza, <lb/>ſecondo vn ſito; </s> <s xml:id="echoid-s329" xml:space="preserve">la larghezza s’intenderà per laltro ſito, co-<lb/>me nella ſuperficie <emph style="sc">EFGH</emph>, <pb o="7" file="025" n="25" rhead="PROEMIO."/> <anchor type="figure" xlink:label="fig-025-01a" xlink:href="fig-025-01"/> Nella quale poſsiamo intendere la lunghezza, da qual ſi vo <lb/>glia lato, all’altro oppoſito lato; </s> <s xml:id="echoid-s330" xml:space="preserve">Et ſe ſupponiamo che la <lb/>lunghezza ſia dal lato <emph style="sc">E G</emph>, al lato <emph style="sc">F H</emph>, diremo che la lar-<lb/>ghezza ſarà dal lato <emph style="sc">E F</emph>, allato <emph style="sc">G H</emph>, ſimilmẽte nel circolo <emph style="sc">A</emph>, <lb/> <anchor type="figure" xlink:label="fig-025-02a" xlink:href="fig-025-02"/> Poſsiamo ſecondo qualunq; </s> <s xml:id="echoid-s331" xml:space="preserve">diametro aſſegnarla lunghez-<lb/>za, & </s> <s xml:id="echoid-s332" xml:space="preserve">la larghezza; </s> <s xml:id="echoid-s333" xml:space="preserve">Nondimeno ſe diceſsimo, che la lun-<lb/>ghezza ſia ſecondo il diametro, <emph style="sc">B A C</emph>, ragioneuolmente di- <pb file="026" n="26" rhead="PROEMIO."/> remo la larghezza douerſi intendere in tutto il circolo, <lb/>ſecondo il diametro <emph style="sc">D A E</emph>, Et per conchiudere brieue-<lb/>mente la diffinitione della ſuperſicie poſsiamo dire, che <lb/>ſuperſicie, altro non è, che lunghezza, & </s> <s xml:id="echoid-s334" xml:space="preserve">larghezza in-<lb/>ſieme, talmente che mentre con l’imaginatione intendia-<lb/>mo lunghezza, a quella inſieme cógiungiamo la larghezza.</s> <s xml:id="echoid-s335" xml:space="preserve"/> </p> <div xml:id="echoid-div13" type="float" level="2" n="1"> <figure xlink:label="fig-024-01" xlink:href="fig-024-01a"> <image file="024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/024-01"/> </figure> <figure xlink:label="fig-025-01" xlink:href="fig-025-01a"> <image file="025-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/025-01"/> </figure> <figure xlink:label="fig-025-02" xlink:href="fig-025-02a"> <image file="025-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/025-02"/> </figure> </div> <p> <s xml:id="echoid-s336" xml:space="preserve">Et quanta ſupponiamo che ſia alcuna ſuperſicie, tanta <lb/>dobbiamo noi imaginare, che la lunghezza ſi dilati, e che <lb/>la larghezza ſiprolunghi.</s> <s xml:id="echoid-s337" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div15" type="section" level="1" n="12"> <head xml:id="echoid-head22" xml:space="preserve">QVINTA DIFFINITIONE.</head> <p style="it"> <s xml:id="echoid-s338" xml:space="preserve">La ſuperficie piana è la breuiſſima eſtenſione da una linea a un’altra, <lb/>che riceua nelle ſue eſtremità l’una e l’altra di quelle.</s> <s xml:id="echoid-s339" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s340" xml:space="preserve"><emph style="sc">Havendo</emph> di ſopra diffinito che coſaſia ſuperficie, in ge-<lb/>nere (eperche ſono due ſpecie principali de ſuperficie, cioè <lb/>piana, e globoſa, ouer conuerſa, ouer sferica, ouer mon-<lb/>tuoſa) però in queſta diffinitione ſi fà poi chiaro che coſa <lb/>ſia ſuperficie nõ piana, ſi come ancora dalla diffinitione del <lb/>la linearetta, ſiconoſcela linea torta. </s> <s xml:id="echoid-s341" xml:space="preserve">Quando adunq; </s> <s xml:id="echoid-s342" xml:space="preserve">ſia <lb/>no determinate più linee, ouer vna, le quali diſſegnino al-<lb/>cuna ſuperficie, noi diremo che quella ſuperficie, la quale, <lb/>& </s> <s xml:id="echoid-s343" xml:space="preserve">ſecondo la lunghezza, & </s> <s xml:id="echoid-s344" xml:space="preserve">larghezza è breuiſsima, epiana, <lb/>& </s> <s xml:id="echoid-s345" xml:space="preserve">non baſta aſſegnare due oppoſte lineerette, accioche ſi <lb/>determini ſuperficie, concioſiache nõ ne riſulta ſuperficie <lb/>alcuna; </s> <s xml:id="echoid-s346" xml:space="preserve">ma biſogna che inſieme conchiudano determinato <lb/>ſpatio, ſia per eſſempio la ſuperficie <emph style="sc">A B C D</emph>, <lb/> <anchor type="figure" xlink:label="fig-026-01a" xlink:href="fig-026-01"/> itermini della quale ſecondo lalunghezza ſiano il lato <emph style="sc">A B</emph>, <pb o="8" file="027" n="27" rhead="PROEMIO."/> & </s> <s xml:id="echoid-s347" xml:space="preserve">il lato <emph style="sc">C D</emph>, & </s> <s xml:id="echoid-s348" xml:space="preserve">ſecondo la larghezza il lato <emph style="sc">A C</emph>, & </s> <s xml:id="echoid-s349" xml:space="preserve">illato <emph style="sc">B D</emph>, <lb/>io dico, che quella fuperficie, la quale è tra tutti queſti lati <lb/>è curtiſsima & </s> <s xml:id="echoid-s350" xml:space="preserve">piana: </s> <s xml:id="echoid-s351" xml:space="preserve">quale dũq; </s> <s xml:id="echoid-s352" xml:space="preserve">ſarà meno curta tra gli ſteſ <lb/>ſitermini, quella non ſarà piana; </s> <s xml:id="echoid-s353" xml:space="preserve">ma concaua ripiegandoſi <lb/>all’ in giù, oueramente ripiegandoſi allo in sù; </s> <s xml:id="echoid-s354" xml:space="preserve">ſimilméte ſe <lb/>noi s’imaginiamo vna linea circolare come moſtra la <emph style="sc">A B C D</emph>, <lb/> <anchor type="figure" xlink:label="fig-027-01a" xlink:href="fig-027-01"/> io dico, che quella ſuperficie, la quale compreſa da queſta <lb/>linea è breuiſsima, che queſta è piana, & </s> <s xml:id="echoid-s355" xml:space="preserve">tutte l’altre farãno <lb/>cupe, ò leuate, e per cenſeguenza non ſaranno piane; </s> <s xml:id="echoid-s356" xml:space="preserve">Etin <lb/>queſto luogo è diligentemente d’auertire, che non penſia-<lb/>mo che quella ſuperficie non ſia piana, la quale è compreſa <lb/>da lati curui, come queſta ſuperficie <emph style="sc">A B C D</emph>, <lb/> <anchor type="figure" xlink:label="fig-027-02a" xlink:href="fig-027-02"/> <pb file="028" n="28" rhead="PROEMIO."/> il cui lato <emph style="sc">A G M</emph>, & </s> <s xml:id="echoid-s357" xml:space="preserve">il lato <emph style="sc">C H D</emph>, ſono curui, percioche eſſen-<lb/>do ſteſa in piano, è di neceſsità piana, non ripiegandoſine al <lb/>baſſo, ne all’ alto, & </s> <s xml:id="echoid-s358" xml:space="preserve">fra queſti lati <emph style="sc">A B</emph>, & </s> <s xml:id="echoid-s359" xml:space="preserve"><emph style="sc">C D</emph>, non ſi potrà pi-<lb/>gliare ſuperficie minore; </s> <s xml:id="echoid-s360" xml:space="preserve">che ſe alcuno diceſſe la ſuperficie <lb/><emph style="sc">A E B C F D</emph>, de’ lati retta eſſer minore, che la ſuperficie <emph style="sc">A G B</emph>, <lb/>& </s> <s xml:id="echoid-s361" xml:space="preserve"><emph style="sc">C H D</emph>, de lati torti, e conſeguentemente quella ancora eſ-<lb/>ſer piana, coſtui s’ingannarebbe; </s> <s xml:id="echoid-s362" xml:space="preserve">concioſiache non reſtano <lb/>quelli ſteſsi termini di prima, che da quelli è compreſala ſu-<lb/>perficie <emph style="sc">A B C D</emph>; </s> <s xml:id="echoid-s363" xml:space="preserve">Debbiamo dunq; </s> <s xml:id="echoid-s364" xml:space="preserve">riguardare qual ſuperfi-<lb/>cieſia più curta fra i medeſimi lati, & </s> <s xml:id="echoid-s365" xml:space="preserve">queſta diremo eſſer <lb/>piana, e l’altre eſſer cupe, ò eleuate, e per conſeguenza mag <lb/>giori. </s> <s xml:id="echoid-s366" xml:space="preserve">Ma retta, ouer obliqua chiamaremo noi quella, la <lb/>quale hà i ſuoi lati retti, oueramente obliqui, ancorche ſia <lb/>poſta in piano, qual ſarebbe queſta ſuperficie <emph style="sc">A B C D E F</emph>, <lb/> <anchor type="figure" xlink:label="fig-028-01a" xlink:href="fig-028-01"/> i cui lati <emph style="sc">A B C, D E F</emph>, ſono obliqui, perche ſupponiamo, ch’eſ <lb/>ſa ſia ſtata in piano, non in concauità, ne in conueſſo ele-<lb/>uata.</s> <s xml:id="echoid-s367" xml:space="preserve"/> </p> <div xml:id="echoid-div15" type="float" level="2" n="1"> <figure xlink:label="fig-026-01" xlink:href="fig-026-01a"> <image file="026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/026-01"/> </figure> <figure xlink:label="fig-027-01" xlink:href="fig-027-01a"> <image file="027-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/027-01"/> </figure> <figure xlink:label="fig-027-02" xlink:href="fig-027-02a"> <image file="027-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/027-02"/> </figure> <figure xlink:label="fig-028-01" xlink:href="fig-028-01a"> <image file="028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/028-01"/> </figure> </div> </div> <div xml:id="echoid-div17" type="section" level="1" n="13"> <head xml:id="echoid-head23" xml:space="preserve">SESTA DIFFINITIONE <lb/>del corpo.</head> <p style="it"> <s xml:id="echoid-s368" xml:space="preserve">Corpo è quello, il quale ha lunghezza, larghezza, & </s> <s xml:id="echoid-s369" xml:space="preserve">profondità, ò groſ <lb/>ſezza, che uogliamo dire, i cui termini, ouero estremi ſono ſuperficij, più, <lb/>ò una.</s> <s xml:id="echoid-s370" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s371" xml:space="preserve"><emph style="sc">Il corpo</emph> adunq; </s> <s xml:id="echoid-s372" xml:space="preserve">altro di più non contiene della ſuperficie <lb/>che la profondità, ò groſſezza. </s> <s xml:id="echoid-s373" xml:space="preserve">Inteſo adunq; </s> <s xml:id="echoid-s374" xml:space="preserve">che coſa ſia <lb/>ſuperficie, facilmente poſſiamo intendere, che coſa è corpo. <lb/></s> <s xml:id="echoid-s375" xml:space="preserve">Ogni volta dunq; </s> <s xml:id="echoid-s376" xml:space="preserve">che ſia alcuna lunghezza, & </s> <s xml:id="echoid-s377" xml:space="preserve">larghezza, la <pb o="9" file="029" n="29" rhead="PROEMIO."/> qual contenga in groſſezza, queſto diremo noi eſſer cor-<lb/>po, ſi come adunq; </s> <s xml:id="echoid-s378" xml:space="preserve">la linea è diuiſibile ſecondo la lun-<lb/>ghezza, la ſuperficie ſecondo la lunghezza, & </s> <s xml:id="echoid-s379" xml:space="preserve">larghez-<lb/>za: </s> <s xml:id="echoid-s380" xml:space="preserve">coſi il corpo ſi può diuidere ancora ſecondo la pro-<lb/>fondità, imaginandoſi noi, che vn piano, ò qual ſi vo-<lb/>glia ſuperficie diuidendo le ſuperficij che contengono, <lb/>& </s> <s xml:id="echoid-s381" xml:space="preserve">terminano il corpo per il lungo, & </s> <s xml:id="echoid-s382" xml:space="preserve">per il largo, di-<lb/>uida ancora il profondo d’eſſo corpo, come per inanzi <lb/>habbiamo detto. </s> <s xml:id="echoid-s383" xml:space="preserve">I termini del corpo ſono ſuperficij più, <lb/>ò vna; </s> <s xml:id="echoid-s384" xml:space="preserve">più, quando il corpo non ſia vn corpo ſolido sfe-<lb/>rico, oueramente ouale; </s> <s xml:id="echoid-s385" xml:space="preserve">percioche queſti hanno vna ſo-<lb/>la ſuperficie, la quale vniti i ſuoi fini à ſe ſteſſa, non hà <lb/>in parte alcuna principio, ò fine, i quali effetualmen-<lb/>te ſi poſſano aſſegnare. </s> <s xml:id="echoid-s386" xml:space="preserve">Può eſſere alcuno corpo, il <lb/>quale habbia due ſuperficij ſole, come ſono i cieli, i qua-<lb/>li hanno vna ſuperficie interiore concaua, l’altra eſte-<lb/>riore conueſſa: </s> <s xml:id="echoid-s387" xml:space="preserve">tra le quali ſi comprende la profondità ò <lb/>groſſezza d’eſſo corpo. </s> <s xml:id="echoid-s388" xml:space="preserve">Doue alcun corpo habbia le ſu-<lb/>perficij, le quali occorrendo inſieme fanno angoli, è ne-<lb/>ceſſario, che il corpo ſia terminato da più ſuperficij, co-<lb/>me ſono le figure colonnali, piramidali, quadrangolari, <lb/>& </s> <s xml:id="echoid-s389" xml:space="preserve">tutte l’altre.</s> <s xml:id="echoid-s390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s391" xml:space="preserve">Quello che habbiamo detto della lunghezza, & </s> <s xml:id="echoid-s392" xml:space="preserve">lar-<lb/>ghezza nella diffinitione delle ſuperficij, è ancora da <lb/>intendere nel corpo: </s> <s xml:id="echoid-s393" xml:space="preserve">concioſiache nel corpo intendia-<lb/>mo la lunghezza, & </s> <s xml:id="echoid-s394" xml:space="preserve">larghezza per hauere egli in ſe la ſu-<lb/>perficie. </s> <s xml:id="echoid-s395" xml:space="preserve">Adunq;</s> <s xml:id="echoid-s396" xml:space="preserve">, benche nella sfera, nella palla, ò nella <lb/>figura ouale non ſia principio di lunghezza, ò di larghez <lb/>za: </s> <s xml:id="echoid-s397" xml:space="preserve">nondimeno imaginandoſi noi la lunghezza ſecon-<lb/>do alcun lato, diremo che la larghezza ſia ſecondo l’al-<lb/>tro.</s> <s xml:id="echoid-s398" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s399" xml:space="preserve">Vltimamente la profondità ſempre è cont enuta <lb/>trà le ſuperficij più, ouer vna, le quali termina no il <lb/>corpo.</s> <s xml:id="echoid-s400" xml:space="preserve"/> </p> <pb file="030" n="30" rhead="PROEMIO."/> </div> <div xml:id="echoid-div18" type="section" level="1" n="14"> <head xml:id="echoid-head24" xml:space="preserve">Hauendo fin qui eſpoſto quelle diffinitioni, ſarà a ba-<lb/>ſtanza, per l’altre in quel modo, che ſono poſte da Eucli-<lb/>de ſenza aggiungerui alcuna dichiaratione, con-<lb/>cioſiache talmente da ſe ſono chiare, & fa-<lb/>cili, che non hanno biſogno <lb/>d’eſſere eſpo-<lb/>ſte;</head> <head xml:id="echoid-head25" xml:space="preserve">Seguiròa ragionare di quelle coſe che alſcopo, & <lb/>particolar noſtro s’appartengono.</head> <pb o="10" file="031" n="31"/> </div> <div xml:id="echoid-div19" type="section" level="1" n="15"> <head xml:id="echoid-head26" xml:space="preserve">DELLE RAPPRESENTATIONI</head> <head xml:id="echoid-head27" style="it" xml:space="preserve">DE NVMERI DEL MISVRAR</head> <head xml:id="echoid-head28" xml:space="preserve"><emph style="sc">LE TERRE.</emph></head> <figure> <image file="031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/031-01"/> </figure> </div> <div xml:id="echoid-div20" type="section" level="1" n="16"> <head xml:id="echoid-head29" xml:space="preserve">LIBRO PRIMO.</head> <p> <s xml:id="echoid-s401" xml:space="preserve"><emph style="sc">HOra</emph>è tempo, che diſcendendo al particola-<lb/>re, diamo principio alla materia noſtra; </s> <s xml:id="echoid-s402" xml:space="preserve">co-<lb/>minciando dalle rappreſentationi de’ nume-<lb/>ri, del miſurar le terre, coſi Ariſimeticamen-<lb/>te, come Geometricamente; </s> <s xml:id="echoid-s403" xml:space="preserve">& </s> <s xml:id="echoid-s404" xml:space="preserve">prima Ariſ-<lb/>meticamente.</s> <s xml:id="echoid-s405" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s406" xml:space="preserve">Cauezzi fia cauezzi, fanno quarti di tauole, ouero piedi 3, <lb/>ſuperficiali.</s> <s xml:id="echoid-s407" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s408" xml:space="preserve">Cauezzi fia braccie, fanno mezi piedi ſuperficiali.</s> <s xml:id="echoid-s409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s410" xml:space="preserve">Cauezzi fia oncie, fanno meze oncie ſuperficiali.</s> <s xml:id="echoid-s411" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s412" xml:space="preserve">Cauezzi fia punti, fanno mezi punti ſuperficiali.</s> <s xml:id="echoid-s413" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s414" xml:space="preserve">Braccia fia braccia, fanno oncie ſuperficiali.</s> <s xml:id="echoid-s415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s416" xml:space="preserve">Braccia fia oncie, fanno punti ſuperficiali.</s> <s xml:id="echoid-s417" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s418" xml:space="preserve">Braccia fia punti, fanno atomi ſuperficiali.</s> <s xml:id="echoid-s419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s420" xml:space="preserve">Oncie fia oncie, fanno atomi ſuperficiali.</s> <s xml:id="echoid-s421" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s422" xml:space="preserve">Oncie fia punti, fanno minuti ſuperficiali.</s> <s xml:id="echoid-s423" xml:space="preserve"/> </p> <pb file="032" n="32" rhead="LIBRO"/> <p> <s xml:id="echoid-s424" xml:space="preserve">Punti fia punti, fanno momenti ſuperficiali.</s> <s xml:id="echoid-s425" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s426" xml:space="preserve">12, momenti, fanno vn minuto.</s> <s xml:id="echoid-s427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s428" xml:space="preserve">12, minuti, fanno vn atomo.</s> <s xml:id="echoid-s429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s430" xml:space="preserve">12, atomi, fanno vn punto.</s> <s xml:id="echoid-s431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s432" xml:space="preserve">12, punti, fanno vn’oncia.</s> <s xml:id="echoid-s433" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s434" xml:space="preserve">12, oncie, fanno vn piede, in ſuperficie, & </s> <s xml:id="echoid-s435" xml:space="preserve">vn braccio in li-<lb/>nea; </s> <s xml:id="echoid-s436" xml:space="preserve">perche vorrei intendere in ſuperficie piedi, & </s> <s xml:id="echoid-s437" xml:space="preserve">in li-<lb/>nea braccia.</s> <s xml:id="echoid-s438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s439" xml:space="preserve">12, piedi fanno vna tauola.</s> <s xml:id="echoid-s440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s441" xml:space="preserve">25, Tauole alla Breſciana, & </s> <s xml:id="echoid-s442" xml:space="preserve">24, alla Bergamaſca fanno <lb/>vna pertica.</s> <s xml:id="echoid-s443" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s444" xml:space="preserve">Aduertendo che il cauezzo è diuiſo in braccia 6, & </s> <s xml:id="echoid-s445" xml:space="preserve">il brac-<lb/>cio, in oncie 12, & </s> <s xml:id="echoid-s446" xml:space="preserve">altra diuiſione non ſi fà ſopra il ca-<lb/>uezzo.</s> <s xml:id="echoid-s447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s448" xml:space="preserve">Aduertendoui ancora, che il cauezzo Breſciano è oncie 6, <lb/>di più del cauezzo Bergamaſco, della ſua miſura, cioè di <lb/>quella Bergamaſca.</s> <s xml:id="echoid-s449" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s450" xml:space="preserve">Etil cauezzo Bergamaſco è braccia 5, oncie 6, & </s> <s xml:id="echoid-s451" xml:space="preserve">13, <lb/> <anchor type="handwritten" xlink:label="hd-032-01a" xlink:href="hd-032-01"/> <anchor type="handwritten" xlink:label="hd-032-01a" xlink:href="hd-032-01"/> del Breſciano. </s> <s xml:id="echoid-s452" xml:space="preserve">Qui ſotto ſi vedrà la lunghezza, della <lb/>quarta partẽ d’vn braccio Breſciano, & </s> <s xml:id="echoid-s453" xml:space="preserve">Bergamaſco; </s> <s xml:id="echoid-s454" xml:space="preserve">diui <lb/>ſa in oncie 3.</s> <s xml:id="echoid-s455" xml:space="preserve"/> </p> <div xml:id="echoid-div20" type="float" level="2" n="1"> <handwritten xlink:label="hd-032-01" xlink:href="hd-032-01a"/> <handwritten xlink:label="hd-032-01" xlink:href="hd-032-01a"/> </div> <figure> <image file="032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/032-01"/> <caption xml:id="echoid-caption1" xml:space="preserve">Quarta parte d’vn braccio Breſciano.</caption> </figure> <figure> <image file="032-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/032-02"/> <caption xml:id="echoid-caption2" xml:space="preserve">Quarta parte d’vn braccio Bergamaſco.</caption> </figure> <p> <s xml:id="echoid-s456" xml:space="preserve">Detto hauendo della rappreſentatione Ariſmeticamente, <lb/>qui conſeguentemente ſi dirà delle rappreſentationi <lb/>Geometriche.</s> <s xml:id="echoid-s457" xml:space="preserve"/> </p> <pb o="11" file="033" n="33" rhead="PRIMO."/> </div> <div xml:id="echoid-div22" type="section" level="1" n="17"> <head xml:id="echoid-head30" xml:space="preserve">RAPPRESENTATIONE GEOMETRICA,</head> <head xml:id="echoid-head31" xml:space="preserve">perche cauezzi, fia cauezzi fanno quarti <lb/>di Tauole.</head> <p> <s xml:id="echoid-s458" xml:space="preserve"><emph style="sc">Iprattichi</emph> miſuratori hanno ritrouato Geome-<lb/>tricamente, che vna figura quadra rett’angola lun ga due ca <lb/>uezzi, & </s> <s xml:id="echoid-s459" xml:space="preserve">larga altri due, fanno vna Tauola di terreno, ſul <lb/>Breſciano, & </s> <s xml:id="echoid-s460" xml:space="preserve">ſul Bergamaſco, & </s> <s xml:id="echoid-s461" xml:space="preserve">in altri particolari luoghi: <lb/></s> <s xml:id="echoid-s462" xml:space="preserve">adunq; </s> <s xml:id="echoid-s463" xml:space="preserve">vn cauezzo lungo, & </s> <s xml:id="echoid-s464" xml:space="preserve">vn largo faranno vn quarto di <lb/>Tauola, come moſtra la Figura quadra rettangola <emph style="sc">A B C D</emph>; </s> <s xml:id="echoid-s465" xml:space="preserve"><lb/>che moltiplicando cauezzi 2, lungo, con 2, largo fanno 4, <lb/>quarti di tauola, che ſono vna tauola.</s> <s xml:id="echoid-s466" xml:space="preserve"/> </p> <figure> <image file="033-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/033-01"/> </figure> </div> <div xml:id="echoid-div23" type="section" level="1" n="18"> <head xml:id="echoid-head32" xml:space="preserve">RAPPRESENTATIONE, PERCHE CA-</head> <head xml:id="echoid-head33" xml:space="preserve">uezzi fia braccia, fanno mezi piedi.</head> <p> <s xml:id="echoid-s467" xml:space="preserve"><emph style="sc">Si fara'</emph> vna figura quadra rett’angola, come moſtra <lb/>la figura <emph style="sc">A B C D</emph>, lungavn cauezzo, & </s> <s xml:id="echoid-s468" xml:space="preserve">larga vn’altro cauezzo;</s> <s xml:id="echoid-s469" xml:space="preserve"> <pb file="034" n="34" rhead="LIBRO"/> & </s> <s xml:id="echoid-s470" xml:space="preserve">il cauezzo di larghezza ſi è diuiſo in braccia 6; </s> <s xml:id="echoid-s471" xml:space="preserve">hor multi-<lb/>plicando vn cauezzo, con braccia 6 ſ<unsure/>anno 6, mezi piedi, <lb/>come moſtra la figura <emph style="sc">A B C D</emph>, che è<unsure/> vn quarto di ta-<lb/>uola.</s> <s xml:id="echoid-s472" xml:space="preserve"/> </p> <figure> <image file="034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/034-01"/> </figure> </div> <div xml:id="echoid-div24" type="section" level="1" n="19"> <head xml:id="echoid-head34" xml:space="preserve">RAPPRESENTATIONE, PERCHE</head> <head xml:id="echoid-head35" xml:space="preserve">cauezzifia oncie fanno meze oncie.</head> <p> <s xml:id="echoid-s473" xml:space="preserve"><emph style="sc">Hor</emph> ſupponiamo di formare vn quadrangolo rett’an-<lb/>golo, che ſia lungo vn cauezzo, & </s> <s xml:id="echoid-s474" xml:space="preserve">largo vn braccio, & </s> <s xml:id="echoid-s475" xml:space="preserve">il brac <lb/>cio di larghezza ſia diuiſo in dodeci oncie, come moſtra la <lb/>figura <emph style="sc">A B C D</emph>, che rappreſentano 12, meze oncie che fanno <lb/>oncie 6, tanto come è vn mezo piede; </s> <s xml:id="echoid-s476" xml:space="preserve">come diſopra ſi è det <lb/>to che cauezzi fia braccia fanno mezi piedi.</s> <s xml:id="echoid-s477" xml:space="preserve"/> </p> <pb o="12" file="035" n="35" rhead="PRIMO."/> <figure> <image file="035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/035-01"/> </figure> </div> <div xml:id="echoid-div25" type="section" level="1" n="20"> <head xml:id="echoid-head36" xml:space="preserve">RAPPRESENTATIONE, PERCHE CA-</head> <head xml:id="echoid-head37" xml:space="preserve">uezzo fia punto, fanno mezo punto.</head> <p> <s xml:id="echoid-s478" xml:space="preserve"><emph style="sc">Svpponeremo</emph> vn quadrangolo rett’angolo, lungo <lb/>vn cauezzo, & </s> <s xml:id="echoid-s479" xml:space="preserve">largo vn’oncia, la larghezza dell’oncia ſi di-<lb/>uiderà in 12, parti eguali, che ogni parte ſarà vn punto, co-<lb/>me ſi vede nella figura <emph style="sc">A B C D</emph>, che moltiplicando vn cauez-<lb/>zo con 12, punti fanno 12, mezi punti, che ſono meza on-<lb/>cia, come di ſopra s’è detto.</s> <s xml:id="echoid-s480" xml:space="preserve"/> </p> <pb file="036" n="36" rhead="LIBRO"/> <figure> <image file="036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/036-01"/> </figure> </div> <div xml:id="echoid-div26" type="section" level="1" n="21"> <head xml:id="echoid-head38" xml:space="preserve">RAPPRESENTATIONE, PERCHE <lb/>braccia fia braccia, fanno oncie.</head> <p> <s xml:id="echoid-s481" xml:space="preserve"><emph style="sc">Si svpponera</emph>’ di fare vn quadrato rett’angolo, che <lb/>ſia lungo, & </s> <s xml:id="echoid-s482" xml:space="preserve">largo, vn cauezzo; </s> <s xml:id="echoid-s483" xml:space="preserve">& </s> <s xml:id="echoid-s484" xml:space="preserve">per ogni lato ſi diuiderà <lb/>in parti 6, che ſaranno braccia 6, che tutta la ſuperficie di tal <lb/>quadrato, ſaranno quadretti 36, che ſono pur oncie 36, co-<lb/>me moſtra la figura <emph style="sc">A B C D</emph>, & </s> <s xml:id="echoid-s485" xml:space="preserve">ancor di ſopra ſi è detto che <lb/>braccia fia bracci fà oncie.</s> <s xml:id="echoid-s486" xml:space="preserve"/> </p> <pb o="13" file="037" n="37" rhead="PRIMO."/> <figure> <image file="037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/037-01"/> </figure> </div> <div xml:id="echoid-div27" type="section" level="1" n="22"> <head xml:id="echoid-head39" xml:space="preserve">RAPPRESENTATIONE, PERCHE <lb/>braccia fia oncie fanno punti.</head> <p> <s xml:id="echoid-s487" xml:space="preserve"><emph style="sc">Svpponeremo</emph> difare vn quadrato rett’angolo, che <lb/>per ogni lato ſarà vn braccio, & </s> <s xml:id="echoid-s488" xml:space="preserve">ſi diuiderà la larghezza in <lb/>12, parti eguali, che ogni parte ſarà vn’oncia; </s> <s xml:id="echoid-s489" xml:space="preserve">& </s> <s xml:id="echoid-s490" xml:space="preserve">nella figura <lb/>ſaranno 12, quadrangoli rett’angoli, ch’ogn’vn di loro ſarà <lb/>vn punto di ſuperficie, come ſi vede nella figura <emph style="sc">A B C D.</emph></s> </p> <figure> <image file="037-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/037-02"/> </figure> <pb file="038" n="38" rhead="LIBRO"/> </div> <div xml:id="echoid-div28" type="section" level="1" n="23"> <head xml:id="echoid-head40" xml:space="preserve">RAPPRESENTATIONE, PERCHE <lb/>braccia fia punti, fanno atomi.</head> <p> <s xml:id="echoid-s491" xml:space="preserve"><emph style="sc">Svpponemo</emph> difare vn quadrangolo rett’angolo, che <lb/>ſia lungo vn braccio, & </s> <s xml:id="echoid-s492" xml:space="preserve">largo vn’oncia, & </s> <s xml:id="echoid-s493" xml:space="preserve">la larghezza ſia <lb/>diuiſa in 12, parti eguali, che ſarà diuiſo il quadrangolo in <lb/>12, quadrangoli rett’angoli, ch’ogn’vn di loro ſarà vn ato-<lb/>mo di ſuperficie, come ſi vede nella figura <emph style="sc">A B C D.</emph></s> </p> <figure> <image file="038-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/038-01"/> </figure> </div> <div xml:id="echoid-div29" type="section" level="1" n="24"> <head xml:id="echoid-head41" xml:space="preserve">RAPPRESENTATIONE, PERCHE <lb/>oncie fia oncie, fanno atomi.</head> <p> <s xml:id="echoid-s494" xml:space="preserve"><emph style="sc">Hor</emph> ſi farà vn quadro rett’angolo, che per lũgo, & </s> <s xml:id="echoid-s495" xml:space="preserve">per lar <lb/>go ſarà vn braccio, & </s> <s xml:id="echoid-s496" xml:space="preserve">ſi diuiderà il lũgo, & </s> <s xml:id="echoid-s497" xml:space="preserve">illargo in dodici <pb o="14" file="039" n="39" rhead="PRIMO."/> parti eguali, che ſarãno quadretti 144, ſupficiali, ch’ogn’un <lb/>di loro ſarà vn atomo; </s> <s xml:id="echoid-s498" xml:space="preserve">come ſi vede nella figura <emph style="sc">A B C D,</emph></s> </p> <figure> <image file="039-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/039-01"/> </figure> </div> <div xml:id="echoid-div30" type="section" level="1" n="25"> <head xml:id="echoid-head42" xml:space="preserve">RAPPRESENTATIONE, PERCHE <lb/>oncie fia punti fanno minuti.</head> <p> <s xml:id="echoid-s499" xml:space="preserve"><emph style="sc">Et volen do</emph> vedere, perche oncia fia punto fanno mi <lb/>nuti, ſi farà vn quadrangolo rett’angolo, che ſarà per ogni la <lb/>to vn’oncia, & </s> <s xml:id="echoid-s500" xml:space="preserve">ſi diuiderà il largo in dodici parti eguali, & </s> <s xml:id="echoid-s501" xml:space="preserve">ſa <lb/>ranno 12, quadrangoli rett’angoli, ch’ogn’un diloro ſarà di <lb/>ſuperficie vn minuto, come ſi vede nella figura <emph style="sc">A B C D,</emph></s> </p> <figure> <image file="039-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/039-02"/> </figure> <pb file="040" n="40" rhead="LIBRO"/> </div> <div xml:id="echoid-div31" type="section" level="1" n="26"> <head xml:id="echoid-head43" xml:space="preserve">RAPPRESENTATIONE, PERCHE <lb/>punti fia punti fanno momenti.</head> <p> <s xml:id="echoid-s502" xml:space="preserve"><emph style="sc">Volendo</emph> venire alla cognitione perche punto fia pun-<lb/>to faccia momenti, ſi farà vn quadro rett’angolo, che ſia per <lb/>lungo, & </s> <s xml:id="echoid-s503" xml:space="preserve">per largo vn’oncia, poi ſi diuiderà il lungo, & </s> <s xml:id="echoid-s504" xml:space="preserve">il lar <lb/>go in parti 12, eguali, che faranno quadretti 144, ſuperficia <lb/>li, ch’ogn’vno di loro ſarà vn momento, come ſi vede nella <lb/>figura ſeguente <emph style="sc">A B C D.</emph></s> </p> <figure> <image file="040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/040-01"/> </figure> <p> <s xml:id="echoid-s505" xml:space="preserve">Aduertendo chele figure ſopraſcritte, non ſono diſe-<lb/>gnate ſecondo il debito della ſua proportione; </s> <s xml:id="echoid-s506" xml:space="preserve">maperò do <lb/>uemo con l’imaginatione dell’intelletto, imaginarſi che ſia <lb/>no proportionate. </s> <s xml:id="echoid-s507" xml:space="preserve">Detto aſſai della rappreſentatione, che <lb/>fa vn numero moltiplicãdolo con un’altro, non tanto Arit-<lb/>meticamente, quanto ancor Geometricamente. </s> <s xml:id="echoid-s508" xml:space="preserve">Qui ſe-<lb/>guentemente ſi darà intendere le ſuperficij de’quadrango-<lb/>li, rett’angoli, triangoli, capitagliati, & </s> <s xml:id="echoid-s509" xml:space="preserve">doppicapitagliati:</s> <s xml:id="echoid-s510" xml:space="preserve">co <lb/>minciando prima al quadrangolo rett’angolo, che moltipli <lb/>cando la larghezza, con la lunghezza ſi hauerà la ſua ſuper-<lb/>ficie, cioè tante Tauole, piedi, oncie, & </s> <s xml:id="echoid-s511" xml:space="preserve">altre minutie; </s> <s xml:id="echoid-s512" xml:space="preserve">come <lb/>qui ſotto ſi vedrà.</s> <s xml:id="echoid-s513" xml:space="preserve"/> </p> <pb o="15" file="041" n="41" rhead="PRIMO."/> </div> <div xml:id="echoid-div32" type="section" level="1" n="27"> <head xml:id="echoid-head44" xml:space="preserve">PRIMO ESSEMPIO, DEL MOLTIPLICA-<lb/>re la larghezza, con la lunghezza del quadrangolo <lb/>rett’angolo: per hauere la ſua ſuperſicie <lb/>d’vna pezza diterra.</head> <p> <s xml:id="echoid-s514" xml:space="preserve"><emph style="sc">Hor</emph> pongo, che s’habbia vna figura d’vn quadragolo <lb/>rett’angolo d’vna pezza di terra, che ſia di larghezza cauez-<lb/>zi 12, braccia 5, oncie 7, & </s> <s xml:id="echoid-s515" xml:space="preserve">di lunghezza cauezzi 15, braccia <lb/>4, oncie 6, come moſtra la figura <emph style="sc">A B C D</emph>, & </s> <s xml:id="echoid-s516" xml:space="preserve">per hauer la ſua <lb/>ſuperſicie, ſi commodarà la larghezza ſotto la lunghezza, <lb/>come qui ſotto ſi vede.</s> <s xml:id="echoid-s517" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s518" xml:space="preserve">Auertendo che i circoletti ne gl’angoli delle ſigure, ſi-<lb/>gniſicano angoli retti.</s> <s xml:id="echoid-s519" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Lunghezza cau. # 15, # bra. # 4, # on. # 6. <lb/>Lunghezza cau. # 12, # bra. # 5, # on. # 7. <lb/></note> </div> <div xml:id="echoid-div33" type="section" level="1" n="28"> <head xml:id="echoid-head45" xml:space="preserve">Prima Figura.</head> <figure> <image file="041-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/041-01"/> </figure> <pb file="042" n="42" rhead="LIBRO"/> <p> <s xml:id="echoid-s520" xml:space="preserve">Fatto queſto ſi moltiplicaranno i cauezzi della larghez-<lb/>za, con i cauezzi, braccia, & </s> <s xml:id="echoid-s521" xml:space="preserve">oncie della lunghezza, & </s> <s xml:id="echoid-s522" xml:space="preserve">quel-<lb/>lo che ne venirà, ſi faranno in tauole, piedi, oncie, & </s> <s xml:id="echoid-s523" xml:space="preserve">punti, <lb/>& </s> <s xml:id="echoid-s524" xml:space="preserve">ſi accommoderanno ſotto alla lunghezza, & </s> <s xml:id="echoid-s525" xml:space="preserve">larghezza.</s> <s xml:id="echoid-s526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s527" xml:space="preserve">Appreſſo ſi moltiplicarà le braccia della larghezza, coni <lb/>cauezzi, brac. </s> <s xml:id="echoid-s528" xml:space="preserve">& </s> <s xml:id="echoid-s529" xml:space="preserve">on. </s> <s xml:id="echoid-s530" xml:space="preserve">della lungezza, reducendo a tauole, pie <lb/>di, on. </s> <s xml:id="echoid-s531" xml:space="preserve">& </s> <s xml:id="echoid-s532" xml:space="preserve">punti, & </s> <s xml:id="echoid-s533" xml:space="preserve">ſeguire come di ſopra.</s> <s xml:id="echoid-s534" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s535" xml:space="preserve">Oltra di queſto ſi moltiplicarà le on. </s> <s xml:id="echoid-s536" xml:space="preserve">della larghezza, coi <lb/>cauezzi, piedi, & </s> <s xml:id="echoid-s537" xml:space="preserve">oncie della lunghezza, & </s> <s xml:id="echoid-s538" xml:space="preserve">ſi ſeguirà il <lb/>modo di ſopra; </s> <s xml:id="echoid-s539" xml:space="preserve">come qui ſeguendo il tutto ſi potrà vedere.</s> <s xml:id="echoid-s540" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div34" type="section" level="1" n="29"> <head xml:id="echoid-head46" xml:space="preserve">PRIMA RAGIONE, DELLA <lb/>prima figura.</head> <note position="right" xml:space="preserve"> <lb/><emph style="sc">Lvnga</emph> cau. # 15, # bra. # 4, # on. # 6. <lb/>Larga cau. # 12, # bra. # 5, # on. # 7. <lb/>Tauole # 45, <lb/>Tauole # 2, <lb/>Tauole # 0, # piè # 3, <lb/>Tauole # 3, # piè # 1, # on. # 6, <lb/>Tauole # 0, # piè # 1, # on. # 8, <lb/>Tauole # 0, # piè # 0, # on. # 2, # pun. # 6, <lb/>Tauole # 0, # piè # 4, # on. # 4, # pun. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 2, # pun. # 4, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 3, # atomi # 6, <lb/>Tauole # 50, # piè # 10, # on. # 11, # pun. # 7, # at. # 6, <lb/></note> <pb o="16" file="043" n="43" rhead="PRIMO."/> <p> <s xml:id="echoid-s541" xml:space="preserve"><emph style="sc">Prima</emph> moltiplicatione, del <lb/>moltiplicare i cauezzi del-<lb/>la larghezza con tutta la <lb/>lunghezza.</s> <s xml:id="echoid-s542" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># cauezzi # 15 <lb/># cauezzi # 12 <lb/># # 30 <lb/># # 15 <lb/>Quarti di Tauole # 180 <lb/># partire per # 4 <lb/># tauole # 45 <lb/># cauezzi # 12 <lb/># braccia # 4 <lb/>Mezi piedi # # 48 <lb/># partire per # 2 <lb/># piedi # 24 <lb/># partire per # 12 <lb/># tauole # 2 <lb/># cauezzi # 12 <lb/># oncie # 6 <lb/>Mezeoncie # 72 <lb/># partire per # 2 <lb/># oncie # 36 <lb/># partire per # 12 <lb/># piedi # 3 <lb/></note> <p> <s xml:id="echoid-s543" xml:space="preserve"><emph style="sc">Seconda</emph> moltiplicatio-<lb/>ne del moltiplicare le <lb/>braccia della larghezza, <lb/>con tutta la lunghez-<lb/>za.</s> <s xml:id="echoid-s544" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># cauezzi # 15 <lb/># braccia # 5 <lb/>Mezi piè # # 75 <lb/># partir per # 2 <lb/># piè 37, on. # 6 <lb/># partire per 12 <lb/># tauole 3, piè 1, onc. # 6 <lb/># braccia # 5 <lb/># braccia # 4 <lb/># oncie # 20 <lb/># partir per # 12 <lb/># piè 1, on. # 8 <lb/># oncie # 6 <lb/># braccia # 5 <lb/># punti # 30 <lb/># partir per # 12 <lb/># oncie 2, punti # 6 <lb/></note> <pb file="044" n="44" rhead="LIBRO"/> <p> <s xml:id="echoid-s545" xml:space="preserve"><emph style="sc">Terza</emph> moltiplicatione, del <lb/>moltiplicare le oncie del-<lb/>la larghezza, con tutta la <lb/>lunghezza.</s> <s xml:id="echoid-s546" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># cauezzi # 15 <lb/># oncie # 7 <lb/>Meze oncie # # 105 <lb/># partir per # 2 <lb/># oncie 52, punti # 6 <lb/># partir per 12 <lb/># piè 4, on. 4, punti # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># oncie # 7 <lb/># braccia # 4 <lb/># punti # 28 <lb/># partir per # 12 <lb/># oncie 2, punti # 4 <lb/># oncie # 7 <lb/># oncie # 6 <lb/># atomi # 42 <lb/># partir per # 12 <lb/># punti 3, ato. # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua della prima ragione. # on. # 0 # 0 # atomi. <lb/># on. # 0 # 0 # atomi. <lb/></note> <p> <s xml:id="echoid-s547" xml:space="preserve">Coſi moltiplicando cauezzi 12, braccia 5, oncie 7, della <lb/>larghezza, con cauezzi 15, braccia 4, oncie 6, della lunghez <lb/>za, faranno tauole 50, piedi 10, oncie 11, punti 7, atomi 6, <lb/>& </s> <s xml:id="echoid-s548" xml:space="preserve">di queſto ſe moſtra la ſua proua per il 7.</s> <s xml:id="echoid-s549" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s550" xml:space="preserve">Et per far queſto, prima ſi farà vna croce, come ſi vede <lb/> <anchor type="figure" xlink:label="fig-044-01a" xlink:href="fig-044-01"/> poi ſi torrà la proua della lunghezza, cominciando dai ca-<lb/>uezzi 15, che la ſua proua ſarà 1, oltra di queſto, ſi farà vn ca <lb/>uezzo in braccia, che ſaranno braccia 6, & </s> <s xml:id="echoid-s551" xml:space="preserve">braccia 6, ſi mol <lb/>tiplicaranno con 1, proua del 15, farannno braccia 6, & </s> <s xml:id="echoid-s552" xml:space="preserve"><lb/>braccia 6, ſi a ggiungeranno con braccia 4, che faranno brac <lb/>cia 10, & </s> <s xml:id="echoid-s553" xml:space="preserve">di braccia 10, ſi torrà la ſua proua, che ſarà 3, poi <pb o="17" file="045" n="45" rhead="PRIMO."/> ſi farà vn braccio in oncie che ſono oncie 12, & </s> <s xml:id="echoid-s554" xml:space="preserve">la proua di <lb/>12, è 5, & </s> <s xml:id="echoid-s555" xml:space="preserve">5, ſi moltiplicherà cõ 3, proua di 10, braccia, farãno <lb/>oncie 15, la proua di 15, ſarà oncia 1, & </s> <s xml:id="echoid-s556" xml:space="preserve">oncia 1, ſi aggiũgerà <lb/>con oncie 6, faranno oncie 7, & </s> <s xml:id="echoid-s557" xml:space="preserve">la proua di oncie 7, ſarà o, & </s> <s xml:id="echoid-s558" xml:space="preserve"><lb/>o, ſi ponerà ſopra alla croce da parte ſiniſtra, come ſi vede</s> </p> <div xml:id="echoid-div34" type="float" level="2" n="1"> <figure xlink:label="fig-044-01" xlink:href="fig-044-01a"> <image file="044-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/044-01"/> </figure> </div> <note position="right" xml:space="preserve"> <lb/>onc. # 0 <lb/></note> <p> <s xml:id="echoid-s559" xml:space="preserve">Fatto queſto per il medeſimo modo ſi torrà la proua di ca-<lb/>uezzi 12, brac. </s> <s xml:id="echoid-s560" xml:space="preserve">5, oncie 7, della larghezza, ne venirà pur o, <lb/>& </s> <s xml:id="echoid-s561" xml:space="preserve">o, ſi metterà ſotto alla croce da mano ſiniſtra come ſi vede</s> </p> <note position="right" xml:space="preserve"> <lb/>onc. # 0 <lb/>onc. # 0 <lb/></note> <p> <s xml:id="echoid-s562" xml:space="preserve">Poi ſi moltiplicherà le due proue della lũghezza, & </s> <s xml:id="echoid-s563" xml:space="preserve">larghez <lb/>za, l’vna nell’altra faranno pur o, & </s> <s xml:id="echoid-s564" xml:space="preserve">la proua del o, è pur o, <lb/>cioè o, atomo, perche moltiplicando oncie fia oncie fanno <lb/>atomi, & </s> <s xml:id="echoid-s565" xml:space="preserve">o, atomo, ſi metterà di ſopra alla croce da mano de <lb/>ſtra, come ſi vede</s> </p> <note position="right" xml:space="preserve"> <lb/>onc. # 0 # 0 # ato. <lb/>onc. # 0 <lb/></note> <p> <s xml:id="echoid-s566" xml:space="preserve">Et to gliẽdo la proua di tauole 50, piè 10, oncie 11, punti 7, <lb/>atomi 6, è neceſſario che faccia pur atomi o, da ponere ſotto <lb/>alla croce da mano deſtra; </s> <s xml:id="echoid-s567" xml:space="preserve">& </s> <s xml:id="echoid-s568" xml:space="preserve">per voler torre la proua di ta-<lb/>uole 50, piè 10, oncie 11, punti 7, atomi 6, ſi comincierà a <lb/>torre la proua di tauole 50, ch’è 1, poi ſi farà vna tauola in <lb/>piedi che ſaranno piedi 12, che la proua di 12, ſi è 5, & </s> <s xml:id="echoid-s569" xml:space="preserve">5, ſi <pb file="046" n="46" rhead="LIBRO"/> moltiplicherà con 1, proua delle tauole 50, farà pur 5, che <lb/>ſono piè 5; </s> <s xml:id="echoid-s570" xml:space="preserve">& </s> <s xml:id="echoid-s571" xml:space="preserve">piè 5, ſi aggiungeranno con piedi 10, che fa-<lb/>ranno piedi 15, la proua di 15, ſi è 1; </s> <s xml:id="echoid-s572" xml:space="preserve">poi ſi farà d’vn piede in <lb/>oncie, che ſaranno oncie 12, la proua di 12, ſi è 5, poi ſi mol <lb/>tiplicherà la proua di braccia 15, ch’è 1, con oncie 5, faran-<lb/>no oncie 5, & </s> <s xml:id="echoid-s573" xml:space="preserve">oncie 5, ſi aggiungeranno con oncie 11, fa-<lb/>ranno oncie 16, & </s> <s xml:id="echoid-s574" xml:space="preserve">la proua del 16, ſi è oncie 2; </s> <s xml:id="echoid-s575" xml:space="preserve">poi ſi farà <lb/>vn’oncia in punti, faranno punti 12, la proua del 12, ſi è pun <lb/>ti 5, poi ſi moltiplicherà le oncie 2, proua del 16, con punti <lb/>5, faranno punti 10, la proua del 10, ſi è punti 3, poi ſi farà vn <lb/>punto in atomi, che ſono atomi 12, la proua di atomi 12, ſo <lb/>no atomi 5, hor ſi moltiplicherà punti 3, proua di punti 10, <lb/>con atomi 5, faranno atomi 15, & </s> <s xml:id="echoid-s576" xml:space="preserve">à atomi 15, ſi aggiunge-<lb/>rà atomi 6, faranno atomi 21, la proua del 21, ſi è o, & </s> <s xml:id="echoid-s577" xml:space="preserve">o, ſi <lb/>metterà ſotto alla croce da mano deſtra, come ſi vede <lb/> <anchor type="note" xlink:label="note-046-01a" xlink:href="note-046-01"/> Coſila noſtra ragione ſtarà bene; </s> <s xml:id="echoid-s578" xml:space="preserve">trouandoſi li due numeri <lb/>di ſopra, & </s> <s xml:id="echoid-s579" xml:space="preserve">di ſotto della croce da mano deſtra, vn medeſi-<lb/>mo; </s> <s xml:id="echoid-s580" xml:space="preserve">cioè tutte due o, ouero altro numero, pur che ſieno <lb/>eguali; </s> <s xml:id="echoid-s581" xml:space="preserve">& </s> <s xml:id="echoid-s582" xml:space="preserve">ancora d’vn medeſimo vocabolo. </s> <s xml:id="echoid-s583" xml:space="preserve">Et per miglior <lb/>dechiaratione delle coſe ſopradette, qui ſotto ſi darà <lb/>vn’altra moltiplicatione d’vn quadrangolo rett’angolo <lb/>che hauerà nella lunghezza, & </s> <s xml:id="echoid-s584" xml:space="preserve">larghezza ſegnato fino <lb/>a punti.</s> <s xml:id="echoid-s585" xml:space="preserve"/> </p> <div xml:id="echoid-div35" type="float" level="2" n="2"> <note position="right" xlink:label="note-046-01" xlink:href="note-046-01a" xml:space="preserve"> <lb/>onc. # o # o # ato. <lb/>onc. # o. # o # ato. <lb/></note> </div> <p> <s xml:id="echoid-s586" xml:space="preserve">Horſia vn quadrangolo rett’angolo come moſtra la fi-<lb/>gura <emph style="sc">A B C D</emph>, a modo d’vna pezza di terra; </s> <s xml:id="echoid-s587" xml:space="preserve">che ſia lunga ca-<lb/>uezzi 15, braccia 4, oncie 6, punti 6, & </s> <s xml:id="echoid-s588" xml:space="preserve">larga cauezzi 12, <lb/>braccia 5, oncie 7, punti 6.</s> <s xml:id="echoid-s589" xml:space="preserve"/> </p> <pb o="18" file="047" n="47" rhead="PRIMO."/> </div> <div xml:id="echoid-div37" type="section" level="1" n="30"> <head xml:id="echoid-head47" xml:space="preserve">Seconda Figura.</head> <figure> <image file="047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/047-01"/> </figure> <p> <s xml:id="echoid-s590" xml:space="preserve">Volendo ſapere quanto è di ſuperficie, cioè quante ta-<lb/>uole, piedi, oncie, & </s> <s xml:id="echoid-s591" xml:space="preserve">punti di terreno: </s> <s xml:id="echoid-s592" xml:space="preserve">ſi concierà la larghez <lb/>za ſotto la lunghezza; </s> <s xml:id="echoid-s593" xml:space="preserve">come qui ſeguente ſi vede; </s> <s xml:id="echoid-s594" xml:space="preserve">& </s> <s xml:id="echoid-s595" xml:space="preserve">& </s> <s xml:id="echoid-s596" xml:space="preserve">ſi mol-<lb/>tiplicherà l’vno con l’altro, come diſopra.</s> <s xml:id="echoid-s597" xml:space="preserve"/> </p> <pb file="048" n="48" rhead="LIBRO"/> </div> <div xml:id="echoid-div38" type="section" level="1" n="31"> <head xml:id="echoid-head48" xml:space="preserve">SECONDA RAGIONE, DELLA</head> <head xml:id="echoid-head49" xml:space="preserve">ſeconda figura.</head> <note position="right" xml:space="preserve"> <lb/><emph style="sc">Lvnga</emph> cau. # 15, # bra. # 4, # on. # 6. # punti # 6. <lb/>Larga cau. # 12, # bra. # 5, # on. # 7. # punti # 6. <lb/>Tauole # 45, <lb/>Tauole # 2, <lb/>Tauole # 0, # piè # 3, <lb/>Tauole # 0, # piè # 0, # on. # 3, <lb/>Tauole # 3, # piè # 1, # on. # 6, <lb/>Tauole # 0, # piè # 1, # on. # 8, <lb/>Tauole # 0, # piè # 0, # on. # 2, # pun. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 2, # at. # 6, <lb/>Tauole # 0, # piè # 4, # on. # 4, # pun. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 2, # pun. # 4, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 3, # at. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0, # at. # 3, # mi. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 3, # pun. # 9, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 2, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0, # at. # 3, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0, # at. # 0, # mi. # 3, <lb/>Tauole # 50, # piè # 11, # on. # 6, # pun. # 9, # at. # 6, # mi. # 9, <lb/></note> </div> <div xml:id="echoid-div39" type="section" level="1" n="32"> <head xml:id="echoid-head50" xml:space="preserve"><emph style="sc">Prima</emph> moltiplicatione del moltiplicare li cauezzi <lb/>della larghezza, con tutta la <lb/>lunghezza.</head> <pb o="19" file="049" n="49" rhead="PRIMO."/> <note position="right" xml:space="preserve"> <lb/># cauezzi # 15 <lb/># cauezzi # 12 <lb/># # 30 <lb/># # 15 <lb/>Quarti di Tauole # # 180 <lb/># partire per # 4 <lb/># tauole # 45 <lb/># cauezzi # 12 <lb/># braccia # 4 <lb/>Mezi piedi # # 48 <lb/># partir per # 2 <lb/># piedi # 24 <lb/># partire per # 12 <lb/># tauole # 2 <lb/># cauezzi # 12 <lb/># oncie # 6 <lb/>Mezi oncie # # 72 <lb/># partire per # 2 <lb/># oncie # 36 <lb/># partir per # 12 <lb/># piedi # 3 <lb/># cauezzi # 12 <lb/># punti # 6 <lb/>Mezi punti # # 72 <lb/># partir per # 2 <lb/># punti # 36 <lb/># partir per # 12 <lb/># oncie # 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # <emph style="sc">Seconda</emph> moltiplicatione, \\ di braccia della larghez- \\ za, con tutta la lunghez- \\ za. <lb/># cauezzi # 15 <lb/># braccia # 5 <lb/>Mezi piè # # 75 <lb/># partir per # 2 <lb/># piè 37, on. # 6 <lb/># partir per # 12 <lb/># tauole 3, piè 1, on. # 6 <lb/># braccia # 5 <lb/># braccia # 4 <lb/># oncie # 20 <lb/># parti per # 12 <lb/># piè 1, on. # 8 <lb/># oncie # 6 <lb/># braccia # 5 <lb/># punti # 30 <lb/># partir per # 12 <lb/># oncie 2, punti # 6 <lb/># punti # 6 <lb/># braccia # 5 <lb/># atomi # 30 <lb/># partir per # 12 <lb/># punti 2, ato. # 6 <lb/></note> <pb file="050" n="50" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># # Terza moltiplicatione, le \\ oncie della larghezza, \\ con tutta la lunghezza. <lb/># cauezzi # 15 <lb/># oncie # 7 <lb/>Meze oncie # # 105 <lb/># partir per # 2 <lb/># on. 52, pun. # 6 <lb/># partir per # 12 <lb/># piè 4, on. 4, pun. # 6 <lb/># oncie # 7 <lb/># braccia # 4 <lb/># punti # 28 <lb/># partir per # 12 <lb/># oncie 2, punti # 4 <lb/># oncie # 7 <lb/># oncie # 6 <lb/># atomi # 42 <lb/># partir per # 12 <lb/># punti 3, atomi # 6 <lb/># oncie # 7 <lb/># punti # 6 <lb/># minuti # 42 <lb/># partir per # 1 <lb/># atomi 3, minuti # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Quarta moltiplicatione, di \\ punti della larghezza, con \\ tutta la lunghezza. <lb/># cauezzi # 15 <lb/># punti # 6 <lb/>Mezi punti # # 90 <lb/># partir per # 2 <lb/># punti # 45 <lb/># partir per # 12 <lb/># onzi 3, pun. # 9 <lb/># punti # 6 <lb/># braccia # 4 <lb/># attimi # 24 <lb/># parti per # 12 <lb/># punti # 2 <lb/># oncie # 6 <lb/># punti # 6 <lb/># minuti # 36 <lb/># partir per # 12 <lb/># atomi # 3 <lb/># punti # 6 <lb/># punti # 6 <lb/># momenti # 36 <lb/># partire per # 12 <lb/># minuti # 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua della ſeconda ragione # punti # 6 # 1 # momẽti <lb/># punti # 6 # 1 # momẽti <lb/></note> <pb o="20" file="051" n="51" rhead="PRIMO."/> <p> <s xml:id="echoid-s598" xml:space="preserve">Coſi ſi vede, che moltiplicando cauezzi 12, braccia 5, <lb/>oncie 7, punti 6, di larghezza; </s> <s xml:id="echoid-s599" xml:space="preserve">con cauezzi 15, braccia 4, <lb/>oncie 6, punti 6, di lunghezza, d’vna pezza di terra, in for-<lb/>ma quadrangolare rettt’angola, come moſtra la figura di <lb/>ſopra <emph style="sc">A B C D</emph>; </s> <s xml:id="echoid-s600" xml:space="preserve">fanno tauole 50, piè 11, oncie 6, pũti 9, atomi <lb/>6, minuti 9; </s> <s xml:id="echoid-s601" xml:space="preserve">Et di queſto ſi farà la ſua proua.</s> <s xml:id="echoid-s602" xml:space="preserve">Lunga cau. 15, 4, 6, 6, \\ Larga cau. 12, 5, 7, 6, } Tau. 50, piè 11, on. 6, p. 9, at. 6 mi. 9</s> </p> <p> <s xml:id="echoid-s603" xml:space="preserve">Volendo far la proua, ſi comincierà dalla lunghezza; </s> <s xml:id="echoid-s604" xml:space="preserve">co-<lb/>me di ſopra, facendo però prima la croce come ſivede, <lb/> <anchor type="figure" xlink:label="fig-051-01a" xlink:href="fig-051-01"/> la proua dei cauezzi 15, ſiè 1, ſi farà vn cauezzo in braccia <lb/>che ſono braccia 6, & </s> <s xml:id="echoid-s605" xml:space="preserve">braccia 6, ſi moltiplicherà con la <lb/>proua del 15, ch’è 1, farà bra. </s> <s xml:id="echoid-s606" xml:space="preserve">6, & </s> <s xml:id="echoid-s607" xml:space="preserve">brac. </s> <s xml:id="echoid-s608" xml:space="preserve">6, ſi aggiungerãno cõ <lb/>braccia 4, faranno braccia 10, & </s> <s xml:id="echoid-s609" xml:space="preserve">di braccia 10, ſitorrà la ſua <lb/>proua, che ſarà 3, poi ſi farà d’vn braccio in oncie che ſono <lb/>oncie 12, & </s> <s xml:id="echoid-s610" xml:space="preserve">di 12, la proua ſi è 5, hor ſi moltiplicherà la pro-<lb/>ua di braccia 10, ch’è 3, con la proua di oncie 12, ch’è 5, fa-<lb/>ranno oncie 15, a oncie 15, ſi aggiungerà oncie 6, faranno <lb/>oncie 21, ſi torrà la proua di oncie 21, che’ o; </s> <s xml:id="echoid-s611" xml:space="preserve">poi ſi farà vn’ <lb/>oncia in punti che faranno punti 12, & </s> <s xml:id="echoid-s612" xml:space="preserve">di punti 12, ſi torrà <lb/>la proua, che ſarà punti 5, & </s> <s xml:id="echoid-s613" xml:space="preserve">punti 5, ſi moltiplicheranno, <lb/>con la proua di oncie 21, ch’è o, faranno pur o, punti, & </s> <s xml:id="echoid-s614" xml:space="preserve">o, ſi <lb/>aggiungerà con punti 6, faranno pur punti 6, & </s> <s xml:id="echoid-s615" xml:space="preserve">punti 6, ſi <lb/>metterãno ſopra della croce, da mano ſiniſtra; </s> <s xml:id="echoid-s616" xml:space="preserve">come ſi vede <lb/> <anchor type="note" xlink:label="note-051-01a" xlink:href="note-051-01"/> poi ſi torrà la proua della larghezza, come s’è fatto della lun <lb/>ghezza, ne venirà pur punti 6, per proua, & </s> <s xml:id="echoid-s617" xml:space="preserve">punti 6, ſi mette-<lb/>ranno ſotto alla croce, da mano ſiniſtra come ſi vede <pb file="052" n="52" rhead="LIBRO"/> <anchor type="note" xlink:label="note-052-01a" xlink:href="note-052-01"/> Oltra di queſto ſi moltiplicherà vna proua, con l’altra faran <lb/>no momenti 36, perche a moltiplicare punti con punti fan-<lb/>no momenti, & </s> <s xml:id="echoid-s618" xml:space="preserve">la proua di momenti 36, ſi è 1, & </s> <s xml:id="echoid-s619" xml:space="preserve">1, ſi mete-<lb/>rà ſopra alla croce da mano deſtra; </s> <s xml:id="echoid-s620" xml:space="preserve">come ſi vede <lb/> <anchor type="note" xlink:label="note-052-02a" xlink:href="note-052-02"/> Fatto le coſe ſopra dette, ſi torrà poi la proua delle tauole <lb/>50, piè 11, oncie 6, punti 9, atomi 6, minuti 9, cominciando <lb/>dalle tauole 50, che la ſua proua ſi è 1, poi ſi farà vna tauola <lb/>in piedi, che ſono piedi 12, & </s> <s xml:id="echoid-s621" xml:space="preserve">di piedi 12, ſi torrà ſa ſua pro-<lb/>ua, che ſono piedi 5, & </s> <s xml:id="echoid-s622" xml:space="preserve">piedi 5, ſi moltiplicherà con 1, pro-<lb/>ua di tauole 50, faranno piedi 5, & </s> <s xml:id="echoid-s623" xml:space="preserve">piedi 5, ſi aggiungeran-<lb/>no con piedi 11, faranno piedi 16, & </s> <s xml:id="echoid-s624" xml:space="preserve">la proua del 16, ſi è 2; <lb/></s> <s xml:id="echoid-s625" xml:space="preserve">poi ſi farà vn piede in oncie, che ſono oncie 12, & </s> <s xml:id="echoid-s626" xml:space="preserve">la proua <lb/>del 12, ſiè 5, & </s> <s xml:id="echoid-s627" xml:space="preserve">5, ſi moltiplicherà con la proua di piedi 16, <lb/>ch’è 2, faranno oncie 10, & </s> <s xml:id="echoid-s628" xml:space="preserve">oncie 10, ſi aggiungeranno con <lb/>oncie 6, faranno oncie 16, & </s> <s xml:id="echoid-s629" xml:space="preserve">la proua di oncie 16, ſarà oncie <lb/>2; </s> <s xml:id="echoid-s630" xml:space="preserve">poi ſi farà vn’oncia in punti, che ſaranno punti 12, la pro-<lb/>ua di punti 12, ſi è punti 5, & </s> <s xml:id="echoid-s631" xml:space="preserve">punti 5, ſi moltiplicherà con <lb/>la proua di oncie 16, ch’è 2, faranno punti 10, & </s> <s xml:id="echoid-s632" xml:space="preserve">a punti 10, <lb/>ſi aggiungerà punti 9, faranno punti 19, la proua di punti <lb/>19, ſi è 5; </s> <s xml:id="echoid-s633" xml:space="preserve">poi ſi farà vn punto in atomi, che ſono atomi 12, la <lb/>proua del 12, ſi è 5, poi ſi moltiplicherà la proua de punti <lb/>19, ch’e 5, con atomi 5, faranno atomi 25, & </s> <s xml:id="echoid-s634" xml:space="preserve">a atomi 25, ſi <lb/>aggiungerà atomi 6, faranno atomi 31, & </s> <s xml:id="echoid-s635" xml:space="preserve">la proua del 31, <lb/>ſi è atomi 3, poi ſi farà vn atomo in minuti faranno minuti <lb/>12, & </s> <s xml:id="echoid-s636" xml:space="preserve">la proua del 12, ſi è minuti 5, & </s> <s xml:id="echoid-s637" xml:space="preserve">5, ſi moltiplicherà con <lb/>atomi 3, proua di atomi 31, faranno minuti 15, & </s> <s xml:id="echoid-s638" xml:space="preserve">a minuti <lb/>15, ſi aggiungerà minuti 9, faranno minuti 24, & </s> <s xml:id="echoid-s639" xml:space="preserve">la proua di <pb o="21" file="053" n="53" rhead="PRIMO."/> minuti 24, ſono minuti 3, & </s> <s xml:id="echoid-s640" xml:space="preserve">perche di ſopra hauemo vn mo <lb/>mento per proua, poſto di ſopra alla croce da mano deſtra; <lb/></s> <s xml:id="echoid-s641" xml:space="preserve">ancor ſotto alla croce da mano deſtra, è neceſſario ponere <lb/>vn momento, s’eſſa ragione deue ſtar bene, adunque fare-<lb/>mo vn minuto in momenti 12, & </s> <s xml:id="echoid-s642" xml:space="preserve">la proua di momenti 12, <lb/>ſi è 5, & </s> <s xml:id="echoid-s643" xml:space="preserve">5, ſi moltiplicherà per 3, proua di minuti 24, faran-<lb/>no momenti 15; </s> <s xml:id="echoid-s644" xml:space="preserve">& </s> <s xml:id="echoid-s645" xml:space="preserve">la proua di momenti 15, ſi è vn momen-<lb/>to, da ponere ſotto alla croce da mano deſtra, come ſi vede; </s> <s xml:id="echoid-s646" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-053-01a" xlink:href="note-053-01"/> & </s> <s xml:id="echoid-s647" xml:space="preserve">per queſto la noſtra ragione ſtarà bene; </s> <s xml:id="echoid-s648" xml:space="preserve">il medeſimo fa-<lb/>rà ogn’altra ragione, con la ſua proua.</s> <s xml:id="echoid-s649" xml:space="preserve"/> </p> <div xml:id="echoid-div39" type="float" level="2" n="1"> <figure xlink:label="fig-051-01" xlink:href="fig-051-01a"> <image file="051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/051-01"/> </figure> <note position="right" xlink:label="note-051-01" xlink:href="note-051-01a" xml:space="preserve"> <lb/>6 <lb/></note> <note position="right" xlink:label="note-052-01" xlink:href="note-052-01a" xml:space="preserve"> <lb/>6 <lb/>6 <lb/></note> <note position="right" xlink:label="note-052-02" xlink:href="note-052-02a" xml:space="preserve"> <lb/>6 # 1 <lb/>6 <lb/></note> <note position="right" xlink:label="note-053-01" xlink:href="note-053-01a" xml:space="preserve"> <lb/>punti # 6 # 1 # momenti <lb/>punti # 6 # 1 # momenti <lb/></note> </div> <p> <s xml:id="echoid-s650" xml:space="preserve">Et volendo far la ragione con maggior preſtezza, cioè à <lb/>doppicauezzi; </s> <s xml:id="echoid-s651" xml:space="preserve">prima ſi metteran no le ſue rappreſentationi, <lb/>come qui ſotto ſi potrà comprendere. </s> <s xml:id="echoid-s652" xml:space="preserve">Vn doppiocauezzo, <lb/>ſi ha da intendere lungo braccia 12.</s> <s xml:id="echoid-s653" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s654" xml:space="preserve">Doppicauezzi fia doppicauezzi, fanno tauole.</s> <s xml:id="echoid-s655" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s656" xml:space="preserve">Doppicauezzi fia braccia, fanno piedi</s> </p> <p> <s xml:id="echoid-s657" xml:space="preserve">Doppicauezzi fia oncie, fanno oncie.</s> <s xml:id="echoid-s658" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s659" xml:space="preserve">Doppicauezzi fia punti, fanno punti.</s> <s xml:id="echoid-s660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s661" xml:space="preserve">Io replicherò le due miſurationi di ſopra in douere haue-<lb/>re la ſua ſuperficie a doppicauezzi.</s> <s xml:id="echoid-s662" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div41" type="section" level="1" n="33"> <head xml:id="echoid-head51" xml:space="preserve">TERZA RAGIONE, DELLA <lb/>prima figura.</head> <note position="right" xml:space="preserve"> <lb/><emph style="sc">Lvnga</emph> cau. # 15, # bra. # 4, # on. # 6. <lb/>Larga cau. # 12, # bra. # 5, # on. # 7. <lb/>Doppicauezzi # 7, # bra. # 10, # on. # 6. <lb/>Doppicauezzi # 6, # bra. # 5, # on. # 7, <lb/></note> <pb file="054" n="54" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/>Tauole # 42, <lb/>Tauole # 5, <lb/>Tauole # 0, # piè # 3, <lb/>Tauole # 2, # piè # 11 <lb/>Tauole # 0, # piè # 4, # on. # 2, <lb/>Tauole # 0, # piè # 0, # on. # 2, # pun. # 6, <lb/>Tauole # 0, # piè # 4, # on. # 1, <lb/>Tauole # 0, # piè # 0, # on. # 5, # pun. # 10, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 3, # at. # 6, <lb/>Tauole # 50, # piè # 10, # on. # 11, # pun. # 7, # at. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/># # <emph style="sc">Prima</emph> moltiplicatione, i \\ doppicauezzi della lar- \\ ghezza, con tutta la lun- \\ ghezza. <lb/># Dopp. # 7 <lb/># Dopp. # 6 <lb/># tauole # 42 <lb/># Dopp. # 6 <lb/># braccia # 10 <lb/>piedi # # 60 <lb/># partir per # 12 <lb/># tauole # 5 <lb/># Dopp. # 6 <lb/># oncie # 6 <lb/>oncie # # 36 <lb/># partir per # 12 <lb/># piedi # 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Secóda moltipli. delle brac. \\ della larghezza, moltipli- \\ cati, có tutta la lũghezza. <lb/># Dopp. # 7 <lb/># brac. # 5 <lb/>piedi # # 35 <lb/># partire per # 12 <lb/># tauole 2, # piè 11 <lb/># braccia # 10 <lb/># braccia # 5 <lb/>oncie # # 50 <lb/># partir per # 12 <lb/># piedi 4, # oncie 2, <lb/># braccia # 5 <lb/># oncie # 6 <lb/>punti # # 30 <lb/># partir per # 12 <lb/># oncie 2, # pun. 6. <lb/></note> <pb o="22" file="055" n="55" rhead="PRIMO."/> <note position="right" xml:space="preserve"> <lb/># # Terza moltiplicatione, del- \\ le oncie della larghezza, \\ con tutta la lunghezza. <lb/># Dopp. # 7 <lb/># oncie # 7 <lb/>oncie # # 49 <lb/># partir per # 12 <lb/># piedi 4, # on. 1 <lb/></note> <note position="right" xml:space="preserve"> <lb/># braccia # 10 <lb/># oncie # 7 <lb/>punti # # 70 <lb/># partir per # 12 <lb/># oncie 5 # pun. 10 <lb/># oncie # 7 <lb/># oncie # 6 <lb/>atomi # # 42 <lb/># partir per # 12 <lb/># punti 3 # atti. 6 <lb/></note> <p> <s xml:id="echoid-s663" xml:space="preserve">La proua ſi farà come di ſopra nella prima ragione, ec-<lb/>cetto tolto la proua de i doppicauezzi, in cambio di fare <lb/>il cauezzo in braccia 6, ne i doppicauezzi, ſi farà in brac-<lb/>cia 12, & </s> <s xml:id="echoid-s664" xml:space="preserve">ſeguire l’ordine di ſopra, come qui ſotto.</s> <s xml:id="echoid-s665" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Proua della terza ragione. # oncie # 0 # 0 # attimi <lb/># oncie # 0 # 0 # atomi <lb/></note> <pb file="056" n="56" rhead="LIBRO"/> </div> <div xml:id="echoid-div42" type="section" level="1" n="34"> <head xml:id="echoid-head52" xml:space="preserve">QVARTA RAGIONE, DELLA <lb/>ſeconda Figura.</head> <note position="right" xml:space="preserve"> <lb/>Lunga cau. # 15, # bra. # 4, # on. # 6, # pun. # 6. <lb/>Larga cau. # 12, # bra. # 5, # on. # 7, # pun. # 6. <lb/>Doppicauezzi # 7, # bra. # 10, # on. # 6, # pun. # 6. <lb/>Doppicauezzi # 6, # bra. # 5, # on. # 7, # pun. # 6. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua della quarta ragione. # punti # 6 # 1 # momẽti <lb/># punti # 6 # 1 # momẽti <lb/></note> <note position="right" xml:space="preserve"> <lb/>Tauole # 42, <lb/>Tauole # 5, <lb/>Tauole # 0, # piè # 3, <lb/>Tauole # 0, # piè # 0, # on. # 3, <lb/>Tauole # 2, # piè # 11, # on. # 0, <lb/>Tauole # 0, # piè # 4, # on. # 2, <lb/>Tauole # 0, # piè # 0, # on. # 2, # pun. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 2, # at. # 6, <lb/>Tauole # 0, # piè # 4, # on. # 1, <lb/>Tauole # 0, # piè # 0, # on. # 5, # pun. # 10, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 3, # at. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0, # at. # 3, # m. # 6. <lb/>Tauole # 0, # piè # 0, # on. # 3, # pun. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 5, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0. # at. # 3, <lb/>Tauole # 0, # pie # 0, # on. # 0, # pun. # 0, # at. # 0, # m. # 3, <lb/>Tauole # 50, # piè # 11, # on. # 6, # pun. # 9, # at. # 6, # m. # 9. <lb/></note> <pb o="23" file="057" n="57" rhead="PRIMO."/> <note position="right" xml:space="preserve"> <lb/># # <emph style="sc">Prima</emph> moltiplicatione, i \\ doppicauezzi della lar- \\ ghezza, con tutta la lun- \\ ghezza. <lb/># Dopp. # 7 <lb/># Dopp. # 6 <lb/># tauole # 42 <lb/># Dopp. # 6 <lb/># braccia # 10 <lb/>piedi # # 60 <lb/># partir per # 12 <lb/># tauole # 5 <lb/># Dopp. # 6 <lb/># oncie # 6 <lb/>oncie # # 36 <lb/># partir per # 12 <lb/># piedi # 3 <lb/># Dopp. # 6 <lb/># punti # 6 <lb/>punti # # 36 <lb/># partir per # 12 <lb/># oncie # 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Seconda moltiplicatione de \\ i Doppicauezzi, della lar- \\ ghezza, con tutta la lun- \\ ghezza. <lb/># Dopp. # 4<unsure/> <lb/># brac. # 5 <lb/>piedi # # 35 <lb/># partir per # 12 <lb/># tauole 2, # piè 11 <lb/># braccia # 10 <lb/># braccia # 5 <lb/>oncie # # 50 <lb/># partir per # 12 <lb/># piedi 4, # oncie 2, <lb/># braccia # 5 <lb/># oncie # 6 <lb/>punti # # 30 <lb/># partir per # 12 <lb/># oncie 2, # pun. 6. <lb/># braccia # 5 <lb/># punti # 6 <lb/>atomi # # 30 <lb/># partir per # 12 <lb/># punti 2 # ato. 6 <lb/></note> <pb file="058" n="58" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># # Terza moltiplicatione, le \\ oncie della larghezza, \\ con tutta la lunghezza. <lb/># Dopp. # 7 <lb/># oncie # 7 <lb/>oncie # # 49 <lb/># partir per # 12 <lb/># piedi 4, # oncie 1 <lb/># braccia # 10 <lb/># oncie # 7 <lb/>punti # # 70 <lb/># partir per # 12 <lb/># oncie 5, # pun. 10 <lb/># oncie # 7 <lb/># oncie # 6 <lb/>atomi # # 42 <lb/># partir per # 12 <lb/># punti 3, # atomi 6 <lb/># oncie # 7 <lb/># punti # 6 <lb/>minuti # # 42 <lb/># partir per # 12 <lb/># atomi 3, # minuti 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Quarta moltiplicatione, di \\ punti della larghezza, con \\ tutta la lunghezza. <lb/># Dopp. # 7 <lb/># punti # 6 <lb/>punti # # 42 <lb/># partir per # 12 <lb/># oncie 3, # pun.6 <lb/># braccia # 10 <lb/># punti # 6 <lb/>atomi # # 60 <lb/># partir per # 12 <lb/># punti # 5 <lb/># oncie # 6 <lb/># punti # 6 <lb/>minuti # # 36 <lb/># partir per # 12 <lb/># atomi # 3 <lb/># punti # 6 <lb/># punti # 6 <lb/>momenti # # 36 <lb/># partir per # 12 <lb/># minuti # 3 <lb/></note> <p> <s xml:id="echoid-s666" xml:space="preserve">La proua di queſta quarta ragione ſi farà come s’è fatta <lb/>quella della ſeconda ragione, eccetto che in quella ſi tolſe <lb/>la proua ne i cauczzi, & </s> <s xml:id="echoid-s667" xml:space="preserve">ſiè fatto vn cauezzo in braccie 6, <lb/>& </s> <s xml:id="echoid-s668" xml:space="preserve">in queſta i doppicauezzi ſi faranno in braccie 12, & </s> <s xml:id="echoid-s669" xml:space="preserve">poi ſi <lb/>ſeguirà l’ ordine della ſeconda ragione, in voler la proua.</s> <s xml:id="echoid-s670" xml:space="preserve"/> </p> <pb o="24" file="059" n="59" rhead="PRIMO."/> <p> <s xml:id="echoid-s671" xml:space="preserve">Auuertendo chei quadrangoli rett’ angoli, hanno tutti i <lb/>quattr’angoli retti, & </s> <s xml:id="echoid-s672" xml:space="preserve">de’ lati oppoſiti eguali, cõ vna ſollun-<lb/>ghezza, & </s> <s xml:id="echoid-s673" xml:space="preserve">larghezza.</s> <s xml:id="echoid-s674" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s675" xml:space="preserve">Il capo tagliato, hai lati oppoſiti ineguali, & </s> <s xml:id="echoid-s676" xml:space="preserve">due di quel-<lb/>li lati oppoſiti ſono equi diſtanti, ouero paralelli, con due an <lb/>goli retti d’una medeſima parte.</s> <s xml:id="echoid-s677" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s678" xml:space="preserve">Il doppiocapotagliato puo hauere i lati oppoſiti eguali, <lb/>& </s> <s xml:id="echoid-s679" xml:space="preserve">ineguali, & </s> <s xml:id="echoid-s680" xml:space="preserve">hà due lati equidiſtanti, ouero paralelli. </s> <s xml:id="echoid-s681" xml:space="preserve">anco <lb/>ra ha vna linea retta, che cade ſopra le due linee equidiſtãti <lb/>ad angoli retti. </s> <s xml:id="echoid-s682" xml:space="preserve">Et di queſti capitagliati, e doppi capitag liati, <lb/>& </s> <s xml:id="echoid-s683" xml:space="preserve">ancor de i triangoli ſi moſtrerà il modo di redurli in qua-<lb/>drangoli, per hauer le ſue ſuperficij, ouero quantità del ter-<lb/>reno; </s> <s xml:id="echoid-s684" xml:space="preserve">cominciando dal capotagliato.</s> <s xml:id="echoid-s685" xml:space="preserve"/> </p> <figure> <image file="059-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/059-01"/> <caption xml:id="echoid-caption3" xml:space="preserve">Terza Figura.</caption> </figure> <pb file="060" n="60" rhead="LIBRO"/> <p> <s xml:id="echoid-s686" xml:space="preserve">Hor ſia dunque il capotagliato <emph style="sc">A B C D,</emph> de lati oppoſiti <lb/>ineguali, & </s> <s xml:id="echoid-s687" xml:space="preserve">i due angoli A, & </s> <s xml:id="echoid-s688" xml:space="preserve">B, retti; </s> <s xml:id="echoid-s689" xml:space="preserve">ouero fatti à squadra, <lb/>ne’ due punti A, & </s> <s xml:id="echoid-s690" xml:space="preserve">B, le due teſte <emph style="sc">A, C,</emph> & </s> <s xml:id="echoid-s691" xml:space="preserve"><emph style="sc">B, D,</emph> ſono equidiſtan <lb/>ti, ouero paralelli; </s> <s xml:id="echoid-s692" xml:space="preserve">la teſta A, C, è cau. </s> <s xml:id="echoid-s693" xml:space="preserve">15, brac. </s> <s xml:id="echoid-s694" xml:space="preserve">2, onc. </s> <s xml:id="echoid-s695" xml:space="preserve">5, & </s> <s xml:id="echoid-s696" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s697" xml:space="preserve">la teſta <emph style="sc">B, D</emph>, è cau. </s> <s xml:id="echoid-s698" xml:space="preserve">7, brac. </s> <s xml:id="echoid-s699" xml:space="preserve">3, oncie 6; </s> <s xml:id="echoid-s700" xml:space="preserve">& </s> <s xml:id="echoid-s701" xml:space="preserve">è lungo cauezzi <lb/>13, brac. </s> <s xml:id="echoid-s702" xml:space="preserve">4, oncie 7, cioè la linea <emph style="sc">A, B</emph>; </s> <s xml:id="echoid-s703" xml:space="preserve">Et volendo la ſua ſu-<lb/>perficie, ouero quantità del terreno d’eſſo capotagliato, ſi <lb/>ſommerà inſieme le due teſte, che ſaranno cauezzi 22, brac. <lb/></s> <s xml:id="echoid-s704" xml:space="preserve">5, oncie 11, & </s> <s xml:id="echoid-s705" xml:space="preserve">de cauezzi 22, brac. </s> <s xml:id="echoid-s706" xml:space="preserve">5, oncie 11, ſi pi glierà la <lb/>metà, che ſarà cau. </s> <s xml:id="echoid-s707" xml:space="preserve">11, brac. </s> <s xml:id="echoid-s708" xml:space="preserve">2, oncie 11, punti 6; </s> <s xml:id="echoid-s709" xml:space="preserve">& </s> <s xml:id="echoid-s710" xml:space="preserve">queſta <lb/>metà ſi moltiplicarà con la lunghezza de cau. </s> <s xml:id="echoid-s711" xml:space="preserve">13, braccia 4, <lb/>oncie 7; </s> <s xml:id="echoid-s712" xml:space="preserve">come qui ſotto ſi vede, & </s> <s xml:id="echoid-s713" xml:space="preserve">come ha moſtrato la pri-<lb/>ma, & </s> <s xml:id="echoid-s714" xml:space="preserve">quarta ragione, venerà tauole 39, piè 6, oncie 6, pun <lb/>ti 9, atomi 8, minuti 6, & </s> <s xml:id="echoid-s715" xml:space="preserve">tanta ſarà la ſuperficie, ouero quã <lb/>tità del terreno, à modo del capotagliato,<emph style="sc">A, B, C, D,</emph> ſopra-<lb/>detto.</s> <s xml:id="echoid-s716" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div43" type="section" level="1" n="35"> <head xml:id="echoid-head53" xml:space="preserve">QVINTA RAGIONE, DELLA <lb/>terza Figura.</head> <note position="right" xml:space="preserve"> <lb/><emph style="sc">Lvnga</emph> # cau. # 13, # brac. # 4, # oncie # 7. <lb/>Larga # cau. # 11, # brac. # 2, # oncie # 11, # punti # 6. <lb/>Doppicauezzi # 6, # brac. # 10, # oncie # 7. <lb/>Doppicauezzi # 5, # brac. # 8, # oncie # 11, # punti # 6. <lb/>Tauole # 30, <lb/>Tauole # 4, # piè # 2, <lb/>Tauole # 0, # piè # 2, # on. # 11, <lb/>Tauole # 4, # piè # 6, # on. # 8, <lb/>Tauole # 0, # piè # 0, # on. # 4, # pun. # 8, <lb/>Tauole # 0, # piè # 5, # on. # 6, # pun. # 2, <lb/>Tauole # 0, # piè # 0, # on. # 9, <lb/>Tauole # 0, # piè # 0, # on. # 3, # pun. # 6, # at. # 5, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 5, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0, # at. # 3, # mi. # 6 <lb/>Tauole # 39 # pie # 6, # on. # 6, # pun. # 9, # at. # 8, # mi. # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # onc. # 4 # 2 # min. <lb/># pun. # 4 # 2 # min. <lb/></note> <pb o="25" file="061" n="61" rhead="PRIMO."/> <p> <s xml:id="echoid-s717" xml:space="preserve">Moſtrato il modo che ſi tiene, di hauere la quadratura, <lb/>ouero quantità del terreno con la ſua proua Aritmetica-<lb/>mente, del ſopradetto capotagliato <emph style="sc">A B C D</emph>, qui di ſotto ſi <lb/>moſtrerà Geometricamente. </s> <s xml:id="echoid-s718" xml:space="preserve">Et per far queſto ſi taglierà <lb/>della linea <emph style="sc">A C</emph>, vna eguale alla linea <emph style="sc">B D</emph>, la qual ſarà la linea <lb/><emph style="sc">A G</emph>; </s> <s xml:id="echoid-s719" xml:space="preserve">& </s> <s xml:id="echoid-s720" xml:space="preserve">la linea <emph style="sc">G C</emph>, ſitaglierà in due parti eguali in punto <emph style="sc">F</emph>, <lb/>& </s> <s xml:id="echoid-s721" xml:space="preserve">dal punto <emph style="sc">G</emph>, al punto <emph style="sc">D</emph>, ſi tirerà vna linea retta, che ſarà <lb/>la linea <emph style="sc">G D</emph>, & </s> <s xml:id="echoid-s722" xml:space="preserve">dal punto <emph style="sc">F</emph>, ſi tirerà vna linea equidiſtante al <lb/>la linea <emph style="sc">G D</emph>, che ſarà la linea <emph style="sc">F E</emph>, & </s> <s xml:id="echoid-s723" xml:space="preserve">la linea <emph style="sc">B D</emph>, ſi allungherà <lb/>fina al punto <emph style="sc">E</emph>; </s> <s xml:id="echoid-s724" xml:space="preserve">coſi i due triágoli <emph style="sc">D H E</emph>, & </s> <s xml:id="echoid-s725" xml:space="preserve"><emph style="sc">F H C</emph>, ſono eguali <lb/>di ſuperficie, trouandoſi l’un l’altro di lati eguali; </s> <s xml:id="echoid-s726" xml:space="preserve">leuando <lb/>adunque con l’imaginatione iltriangolo <emph style="sc">F H C</emph>, & </s> <s xml:id="echoid-s727" xml:space="preserve">ponendo <lb/>eguale à eſſo il triãgolo <emph style="sc">D H E</emph>, venirà a formare vn quadran-<lb/>golo rett’angolo, che ſarà <emph style="sc">A B F E</emph>, che ſarà per lunghezza ca <lb/>uezzi 13, brac. </s> <s xml:id="echoid-s728" xml:space="preserve">4, on, 7, & </s> <s xml:id="echoid-s729" xml:space="preserve">per larghezza la metà della ſom-<lb/>ma delle due teſte, che viene à eſſere cau. </s> <s xml:id="echoid-s730" xml:space="preserve">11, brac. </s> <s xml:id="echoid-s731" xml:space="preserve">2. </s> <s xml:id="echoid-s732" xml:space="preserve">on. </s> <s xml:id="echoid-s733" xml:space="preserve">11, <lb/>pun. </s> <s xml:id="echoid-s734" xml:space="preserve">6; </s> <s xml:id="echoid-s735" xml:space="preserve">& </s> <s xml:id="echoid-s736" xml:space="preserve">che queſto ſia il vero ſi cauerà la linea <emph style="sc">B D</emph>, cau. </s> <s xml:id="echoid-s737" xml:space="preserve">7, <lb/>brac. </s> <s xml:id="echoid-s738" xml:space="preserve">3, on. </s> <s xml:id="echoid-s739" xml:space="preserve">6, dalla linea <emph style="sc">A C</emph>, cau. </s> <s xml:id="echoid-s740" xml:space="preserve">15, brac. </s> <s xml:id="echoid-s741" xml:space="preserve">2, on. </s> <s xml:id="echoid-s742" xml:space="preserve">5, reſterà <lb/>la linea <emph style="sc">G C</emph>, cauez. </s> <s xml:id="echoid-s743" xml:space="preserve">7, brac. </s> <s xml:id="echoid-s744" xml:space="preserve">4, on. </s> <s xml:id="echoid-s745" xml:space="preserve">11, & </s> <s xml:id="echoid-s746" xml:space="preserve">cauezzi 7, brac. </s> <s xml:id="echoid-s747" xml:space="preserve">4, <lb/>on. </s> <s xml:id="echoid-s748" xml:space="preserve">11, ch’è la linea <emph style="sc">G C</emph>, ſi partirà in due parti eguali in punto <lb/><emph style="sc">F</emph>, ch’è la linea <emph style="sc">F C</emph>, & </s> <s xml:id="echoid-s749" xml:space="preserve"><emph style="sc">G F</emph>, ſaranno cauez. </s> <s xml:id="echoid-s750" xml:space="preserve">3, brac. </s> <s xml:id="echoid-s751" xml:space="preserve">5, on. </s> <s xml:id="echoid-s752" xml:space="preserve">5, pun <lb/>ti 6, & </s> <s xml:id="echoid-s753" xml:space="preserve">tanto ancora ſarà la linea <emph style="sc">D E</emph>, cau. </s> <s xml:id="echoid-s754" xml:space="preserve">3, brac. </s> <s xml:id="echoid-s755" xml:space="preserve">5, on. </s> <s xml:id="echoid-s756" xml:space="preserve">5, <lb/>punti 6; </s> <s xml:id="echoid-s757" xml:space="preserve">& </s> <s xml:id="echoid-s758" xml:space="preserve">ſarà compito il quadrangolo rett’angolo <emph style="sc">A B F E</emph>, <lb/>che ſarà lungo cau. </s> <s xml:id="echoid-s759" xml:space="preserve">13, brac. </s> <s xml:id="echoid-s760" xml:space="preserve">4, on. </s> <s xml:id="echoid-s761" xml:space="preserve">7, largo cauez. </s> <s xml:id="echoid-s762" xml:space="preserve">11, bra. </s> <s xml:id="echoid-s763" xml:space="preserve">2, <lb/>on. </s> <s xml:id="echoid-s764" xml:space="preserve">11, punti 6; </s> <s xml:id="echoid-s765" xml:space="preserve">come ancor è il medeſimo à ſommare le due <lb/>teſte inſieme, & </s> <s xml:id="echoid-s766" xml:space="preserve">di quella ſomma pigliar la metà; </s> <s xml:id="echoid-s767" xml:space="preserve">come di <lb/>ſopra s’è fatto in volere la ſuperficie, ouero quantità del ter <lb/>reno del capotagliato <emph style="sc">A B C D</emph>; </s> <s xml:id="echoid-s768" xml:space="preserve">Io non ho voluto dire, doue <lb/>Euclide li dimoſtrinel ſuo libro di Geometria, perche l’in <lb/>tention mia è ſolo di trattar delle prattiche Geometriche. <lb/></s> <s xml:id="echoid-s769" xml:space="preserve">Detto aſſai del capotagliato, appreſſo ſi dirà della ſuperfi-<lb/>cie, ouero quantità del terreno d’un doppiocapotagliato.</s> <s xml:id="echoid-s770" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s771" xml:space="preserve">Hor ſia i due doppicapitagliati <emph style="sc">A B C D</emph>, & </s> <s xml:id="echoid-s772" xml:space="preserve"><emph style="sc">E F G H</emph>, diuerſi, <lb/>come ſi vede nelle ſeguenti figure.</s> <s xml:id="echoid-s773" xml:space="preserve"/> </p> <pb file="062" n="62" rhead="LIBRO"/> <figure> <image file="062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/062-01"/> <caption xml:id="echoid-caption4" xml:space="preserve">Quarta Figura.</caption> </figure> <figure> <image file="062-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/062-02"/> <caption xml:id="echoid-caption5" xml:space="preserve">Quinta Figura.</caption> </figure> <pb o="26" file="063" n="63" rhead="PRIMO."/> <p> <s xml:id="echoid-s774" xml:space="preserve">Auuertendo che li doppic apitagliati, non hanno alcun <lb/>angolo retto; </s> <s xml:id="echoid-s775" xml:space="preserve">com’ha il capotagliato della terza figura; </s> <s xml:id="echoid-s776" xml:space="preserve">& </s> <s xml:id="echoid-s777" xml:space="preserve"><lb/>ch’eſſo ha due angoli retti, & </s> <s xml:id="echoid-s778" xml:space="preserve">due linee paralelle, cioè le due <lb/><emph style="sc">A C</emph>, & </s> <s xml:id="echoid-s779" xml:space="preserve"><emph style="sc">B D</emph>; </s> <s xml:id="echoid-s780" xml:space="preserve">I doppicapitagliati hãno ancor eſsi due linee equi <lb/>diſtanti, come il doppiocapotagliato <emph style="sc">A B C D</emph>, che ha le due li <lb/>nee <emph style="sc">A C</emph>, & </s> <s xml:id="echoid-s781" xml:space="preserve"><emph style="sc">B D</emph>, équidiſtãti; </s> <s xml:id="echoid-s782" xml:space="preserve">& </s> <s xml:id="echoid-s783" xml:space="preserve">ancora il doppiocapotagliato <lb/><emph style="sc">E F G H</emph>, che ha le due equidiſtãti <emph style="sc">E G</emph>, & </s> <s xml:id="echoid-s784" xml:space="preserve"><emph style="sc">F H</emph>; </s> <s xml:id="echoid-s785" xml:space="preserve">Et p volere la ſua <lb/>ſuperficie, ouero quãtità del terreno dei doppicapitagliati, <lb/>ſolo s’ha datirare có lo ſquadro vna linea che cadi ſopra alle <lb/>due linee equidiſtanti, ad angolo retto, come moſtrale due <lb/>linee <emph style="sc">I, L,</emph> & </s> <s xml:id="echoid-s786" xml:space="preserve">la <emph style="sc">K M</emph>, dei due doppicapitagliati <emph style="sc">A B C D</emph>, & </s> <s xml:id="echoid-s787" xml:space="preserve"><emph style="sc">E F G H</emph>, <lb/>& </s> <s xml:id="echoid-s788" xml:space="preserve">miſurar le due linee equidiſtanti, & </s> <s xml:id="echoid-s789" xml:space="preserve">la linea che cade ſo-<lb/>pra à eſsi ad angolo retto, come di ſopra ſivede nei due dop <lb/>picapitagliati, & </s> <s xml:id="echoid-s790" xml:space="preserve">quelle due linee equidiſtanti ſi poſſono di <lb/>mandar Teſte, come quelle due equidiſtanti del capotaglia <lb/>to; </s> <s xml:id="echoid-s791" xml:space="preserve">& </s> <s xml:id="echoid-s792" xml:space="preserve">comela linea che cade ſopra alla due linee equidiſtan <lb/>ti ad angolo retto, ſi piglierà per lunghezza; </s> <s xml:id="echoid-s793" xml:space="preserve">horſia adunq; <lb/></s> <s xml:id="echoid-s794" xml:space="preserve">la linea ouer teſta <emph style="sc">A C</emph>, lunga cauezzi 14, brac. </s> <s xml:id="echoid-s795" xml:space="preserve">3, on. </s> <s xml:id="echoid-s796" xml:space="preserve">3, late-<lb/>ſta, ouero linea <emph style="sc">B D</emph>, cau 21, brac. </s> <s xml:id="echoid-s797" xml:space="preserve">4, on. </s> <s xml:id="echoid-s798" xml:space="preserve">6, la linea, ouer lun-<lb/>ghezza <emph style="sc">I, L,</emph> cauezzi 18, brac. </s> <s xml:id="echoid-s799" xml:space="preserve">2, on. </s> <s xml:id="echoid-s800" xml:space="preserve">4, del doppiocapota-<lb/>gliato <emph style="sc">A B C D</emph>.</s> <s xml:id="echoid-s801" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s802" xml:space="preserve">Et la linea, ouer teſta <emph style="sc">E G</emph>, cauezzi 17, brac. </s> <s xml:id="echoid-s803" xml:space="preserve">2, on. </s> <s xml:id="echoid-s804" xml:space="preserve">57, la li-<lb/>nea, ouer teſta <emph style="sc">F H</emph>, cau. </s> <s xml:id="echoid-s805" xml:space="preserve">19, brac. </s> <s xml:id="echoid-s806" xml:space="preserve">5, on. </s> <s xml:id="echoid-s807" xml:space="preserve">8; </s> <s xml:id="echoid-s808" xml:space="preserve">la linea, ouer lun <lb/>ghezza <emph style="sc">K M</emph>, cau. </s> <s xml:id="echoid-s809" xml:space="preserve">22, brac. </s> <s xml:id="echoid-s810" xml:space="preserve">4, on. </s> <s xml:id="echoid-s811" xml:space="preserve">9, & </s> <s xml:id="echoid-s812" xml:space="preserve">volendo la ſuperficie, <lb/>ouer quantità del terreno, de idoppicapitagliati; </s> <s xml:id="echoid-s813" xml:space="preserve">ſi proce-<lb/>derà con quel medeſimo ordine, che s’è fatto nel capota-<lb/>gliato, ſommando le due teſte inſieme, & </s> <s xml:id="echoid-s814" xml:space="preserve">di quella ſomma <lb/>pigliarne la metà, & </s> <s xml:id="echoid-s815" xml:space="preserve">quella metà ſarà la larghezza del qua-<lb/>drangolo, da moltiplicare con la lunghezza, & </s> <s xml:id="echoid-s816" xml:space="preserve">ſi hauerà la <lb/>ſua ſuperficie, ouero quantità del terreno, in forma de dop-<lb/>piocapotagliato; </s> <s xml:id="echoid-s817" xml:space="preserve">come qui ſotto ſi vedrà.</s> <s xml:id="echoid-s818" xml:space="preserve"/> </p> <pb file="064" n="64" rhead="LIBRO"/> </div> <div xml:id="echoid-div44" type="section" level="1" n="36"> <head xml:id="echoid-head54" xml:space="preserve">SESTA RAGIONE, DELLA <lb/>quarta Figura.</head> <note position="right" xml:space="preserve"> <lb/>Teſta cau. # 14, # bra. # 3, # on. # 3. <lb/>Teſta cau. # 21, # bra. # 4, # on. # 6. <lb/>Somma cau. # 36, # bra. # 1, # on. # 9. <lb/>Larghezza cau. # 18, # bra. # 0, # on. # 10, # pun. # 6. <lb/>Lunghezza cau. # 18, # bra. # 2, # on. # 4. <lb/>Doppicauezzi # 9, # bra. # 0, # on. # 10, # pun. # 6. <lb/>Doppicauezzi # 9, # bra. # 2, # on. # 4, <lb/>Tauole # 81, <lb/>Tauole # 0, # piè # 7, # on. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 4, # pun. # 6, <lb/>Tauole # 1, # piè # 6, <lb/>Tauole # 0, # piè # 0, # on. # 1, # pun. # 8, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 1, <lb/>Tauole # 0, # piè # 3, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 3, # at. # 4, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0. # at. # 2, <lb/>Tauole # 83, # pie # 5, # on. # 0, # pun. # 6, # at. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # punti # 5 # 5 # minuti <lb/># onc. # 1 # 5 # minuti <lb/></note> <p> <s xml:id="echoid-s819" xml:space="preserve">Coſi ſivede chel doppiocapotagliato <emph style="sc">A B C D</emph>, della quar-<lb/>ta figura ſi è di ſuperficie, ouero quantità di terreno Tauole <lb/>83, piedi 5, on. </s> <s xml:id="echoid-s820" xml:space="preserve">o pun. </s> <s xml:id="echoid-s821" xml:space="preserve">6, atomi 6; </s> <s xml:id="echoid-s822" xml:space="preserve">Il medeſimo ordine ſite-<lb/>nerà, in volere la ſuperficie, ouero quantità di terreno del <lb/>doppiocapotagliato <emph style="sc">E F G H</emph>, come qui ſotto ancorſi vedrà.</s> <s xml:id="echoid-s823" xml:space="preserve"/> </p> <pb o="27" file="065" n="65" rhead="PRIMO."/> </div> <div xml:id="echoid-div45" type="section" level="1" n="37"> <head xml:id="echoid-head55" xml:space="preserve">SETTIMA RAGIONE, DELLA <lb/>quinta Figura.</head> <note position="right" xml:space="preserve"> <lb/>Teſta cau. # 17, # bra. # 2, # on. # 57, <lb/>Teſta cau. # 19, # bra. # 5, # on. # 8, <lb/>Somma cau. # 37, # bra. # 2, # on. # 5, <lb/>Larghez. cau. # 18, # bra. # 4, # on. # 2, # pun. # 6. <lb/>Lunghez. cau. # 22, # bra. # 4, # on. # 9, <lb/>Doppicauezzi # 9, # bra. # 4, # on. # 2, # pun. # 6. <lb/>Doppicauezzi # 11, # bra. # 4, # on. # 9, <lb/>Tauole # 99, <lb/>Tauole # 3, # piè # 8, <lb/>Tauole # 0, # piè # 1, # on. # 10, <lb/>Tauole # 0, # piè # 0, # on. # 5, # pun. # 6, <lb/>Tauole # 3, # piè # 0, <lb/>Tauole # 0, # piè # 1, # on. # 4, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 8, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 2, <lb/>Tauole # 0, # piè # 6, # on. # 9, <lb/>Tauole # 0, # piè # 0, # on. # 3, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 1, # at. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 0, # at. # 4, # m. # 6. <lb/>Tauole # 106, # piè # 6, # on. # 8, # pun. # 5, # at. # 10, # m. # 6. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # pun. # 2 # 6 # min. <lb/># onc. # 3 # 6 # min. <lb/></note> <pb file="066" n="66" rhead="LIBRO"/> <p> <s xml:id="echoid-s824" xml:space="preserve">Ancor ſi vede che’l doppiocapotagliato <emph style="sc">E F G H</emph>, della <lb/>quinta figura, ſiè di ſuperficie, ouero quantità di terreno, ta <lb/>uole 106, piè 6, on. </s> <s xml:id="echoid-s825" xml:space="preserve">8, pun. </s> <s xml:id="echoid-s826" xml:space="preserve">5. </s> <s xml:id="echoid-s827" xml:space="preserve">atomi 10, minuti 6; </s> <s xml:id="echoid-s828" xml:space="preserve">Il mede-<lb/>ſimo ordine ſi tenerà, in volere la ſuperficie, ouero quantità <lb/>del terreno, d’ogn’altro doppiocapotagliato. </s> <s xml:id="echoid-s829" xml:space="preserve">Et hauendo <lb/>moſtrato à fare i conti di hauere la ſuperficie, ouero la quan <lb/>tità del terreno con le ſue proue Aritmeticamente d’ogni <lb/>doppiocapotagliato; </s> <s xml:id="echoid-s830" xml:space="preserve">Qui ſeguendo con breuità ſi moſtre-<lb/>ra il modo di ſaper quadrarli Geometricamente.</s> <s xml:id="echoid-s831" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s832" xml:space="preserve">Et ſia adunque li due doppicapitagliati <emph style="sc">A B C D</emph>, & </s> <s xml:id="echoid-s833" xml:space="preserve"><emph style="sc">E F G H</emph>, <lb/>della ſeſta, & </s> <s xml:id="echoid-s834" xml:space="preserve">ſettima figura, ſimili alli due della quarta, & </s> <s xml:id="echoid-s835" xml:space="preserve"><lb/>quinta figura; </s> <s xml:id="echoid-s836" xml:space="preserve">hor ſi vede che la linearetta, che caſca ad an <lb/>golo retto, ſopra le due linee equidiſtanti, de i doppicapita <lb/>gliati; </s> <s xml:id="echoid-s837" xml:space="preserve">diuide i doppicapitagliati, in due capitagliati, come <lb/>moſtra le due linee <emph style="sc">I L</emph>, & </s> <s xml:id="echoid-s838" xml:space="preserve"><emph style="sc">K M</emph>; </s> <s xml:id="echoid-s839" xml:space="preserve">& </s> <s xml:id="echoid-s840" xml:space="preserve">coſi per la dimoſtratione <lb/>del capotagliato della figura terza; </s> <s xml:id="echoid-s841" xml:space="preserve">facilmente ſi potrà in-<lb/>tendere lo ſquadrare delli doppicapitagliati; </s> <s xml:id="echoid-s842" xml:space="preserve">& </s> <s xml:id="echoid-s843" xml:space="preserve">per eſſere <lb/>manifeſto al ſenſo, più oltra non mi ſtenderò in tal dimo-<lb/>ſtratione.</s> <s xml:id="echoid-s844" xml:space="preserve"/> </p> <figure> <image file="066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/066-01"/> <caption xml:id="echoid-caption6" xml:space="preserve">Seſta Figura.</caption> </figure> <pb o="28" file="067" n="67" rhead="PRIMO."/> <figure> <image file="067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/067-01"/> <caption xml:id="echoid-caption7" xml:space="preserve">Settima Figura.</caption> </figure> <p> <s xml:id="echoid-s845" xml:space="preserve">Detto aſſai delle ſuperficij di quadrangoli, capitagliati, <lb/>& </s> <s xml:id="echoid-s846" xml:space="preserve">doppicapitagliati, appreſſo ſi dirà delle ſuperficij, ouero <lb/>quantità del terreno, d’un triangolo, col modo di ridurlo <lb/>in vn quadrangolo.</s> <s xml:id="echoid-s847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s848" xml:space="preserve">Sia adunque il triangolo <emph style="sc">A B C</emph>, dell’ottaua ſigura, in mo-<lb/>do d’una pezza di terra, che debbia hauere la ſua ſuperficie, <lb/>ouero quantità del terreno, la prima coſa che ſi douerà fare <lb/>ſi giuſteranno i lati del triangolo; </s> <s xml:id="echoid-s849" xml:space="preserve">fatto queſto ſi pianterà lo <lb/>ſquadro ſopra del lato maggior del triangolo, potendolo fa <lb/>re; </s> <s xml:id="echoid-s850" xml:space="preserve">& </s> <s xml:id="echoid-s851" xml:space="preserve">pongo che ſia il lato <emph style="sc">B C</emph>, s’anderà tanto portando lo <lb/>ſquadro ſopra il lato, ouero Baſe del triangolo <emph style="sc">A B C</emph>, che ve <lb/>da il punto <emph style="sc">A</emph>, & </s> <s xml:id="echoid-s852" xml:space="preserve"><emph style="sc">B</emph>; </s> <s xml:id="echoid-s853" xml:space="preserve">ouero <emph style="sc">A</emph> & </s> <s xml:id="echoid-s854" xml:space="preserve"><emph style="sc">C</emph>, & </s> <s xml:id="echoid-s855" xml:space="preserve">viſto che ſi hauerà due di <lb/>quei ponti, iui ſi fermerà con lo ſquadro, & </s> <s xml:id="echoid-s856" xml:space="preserve">pongo in punto <lb/><emph style="sc">D</emph>, che ſarà la linea <emph style="sc">D A</emph>; </s> <s xml:id="echoid-s857" xml:space="preserve">& </s> <s xml:id="echoid-s858" xml:space="preserve">la linea <emph style="sc">D A</emph>, ſi dimanderà perpen-<lb/>dicolare ouero catetto che caſca ſopra la Baſe <emph style="sc">B C</emph>; </s> <s xml:id="echoid-s859" xml:space="preserve">dal pun-<lb/>to <emph style="sc">A</emph>, angolo; </s> <s xml:id="echoid-s860" xml:space="preserve">come moſtra il triangolo <emph style="sc">A B C</emph>, dell’ottaua fi-<lb/>gura.</s> <s xml:id="echoid-s861" xml:space="preserve"/> </p> <pb file="068" n="68" rhead="LIBRO"/> <figure> <image file="068-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/068-01"/> <caption xml:id="echoid-caption8" xml:space="preserve">Ottaua Figura.</caption> </figure> <p> <s xml:id="echoid-s862" xml:space="preserve">Et per hauere la quadratura del triangolo <emph style="sc">A B C</emph>, ſi miſurerà <lb/>la linea <emph style="sc">A D</emph>, perpendicolare, & </s> <s xml:id="echoid-s863" xml:space="preserve">la linea <emph style="sc">B C</emph>, baſe; </s> <s xml:id="echoid-s864" xml:space="preserve">come ſi ve-<lb/>drà nel triangolo <emph style="sc">E F G</emph>; </s> <s xml:id="echoid-s865" xml:space="preserve">nona figura; </s> <s xml:id="echoid-s866" xml:space="preserve">& </s> <s xml:id="echoid-s867" xml:space="preserve">la baſe <emph style="sc">F G</emph>, ſia cauez-<lb/>zi 15, bra. </s> <s xml:id="echoid-s868" xml:space="preserve">3, on. </s> <s xml:id="echoid-s869" xml:space="preserve">4, & </s> <s xml:id="echoid-s870" xml:space="preserve">la perpẽdicolare cau. </s> <s xml:id="echoid-s871" xml:space="preserve">12. </s> <s xml:id="echoid-s872" xml:space="preserve">bra. </s> <s xml:id="echoid-s873" xml:space="preserve">5. </s> <s xml:id="echoid-s874" xml:space="preserve">on. </s> <s xml:id="echoid-s875" xml:space="preserve">8. <lb/></s> <s xml:id="echoid-s876" xml:space="preserve">Volendo ſapere la ſuperficie, ouer quantità del terreno, ſi <lb/>piglierà la metà della perpendicolare, & </s> <s xml:id="echoid-s877" xml:space="preserve">ſi multiplicerà con <lb/>tutta la Baſe, ouero ſi torrà la metà della Baſe, & </s> <s xml:id="echoid-s878" xml:space="preserve">ſi moltipli <lb/>cherà con tutta la perpendicolare, come dimoſtra la Nona <lb/>figura ſeguente.</s> <s xml:id="echoid-s879" xml:space="preserve"/> </p> <pb o="29" file="069" n="69" rhead="PRIMO."/> <figure> <image file="069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/069-01"/> <caption xml:id="echoid-caption9" xml:space="preserve">Nona Figura.</caption> </figure> </div> <div xml:id="echoid-div46" type="section" level="1" n="38"> <head xml:id="echoid-head56" xml:space="preserve">OTTAVA RAGIONE DELLA <lb/>Nona Figura.</head> <p> <s xml:id="echoid-s880" xml:space="preserve">Hor ſia per eſſempio la metà della perpendicolare cau. </s> <s xml:id="echoid-s881" xml:space="preserve">6. <lb/></s> <s xml:id="echoid-s882" xml:space="preserve">brac. </s> <s xml:id="echoid-s883" xml:space="preserve">2, on. </s> <s xml:id="echoid-s884" xml:space="preserve">10; </s> <s xml:id="echoid-s885" xml:space="preserve">& </s> <s xml:id="echoid-s886" xml:space="preserve">cau. </s> <s xml:id="echoid-s887" xml:space="preserve">6, bra. </s> <s xml:id="echoid-s888" xml:space="preserve">2, on. </s> <s xml:id="echoid-s889" xml:space="preserve">10. </s> <s xml:id="echoid-s890" xml:space="preserve">ſi moltiplicherà con <lb/>cau. </s> <s xml:id="echoid-s891" xml:space="preserve">15, brac. </s> <s xml:id="echoid-s892" xml:space="preserve">3, on. </s> <s xml:id="echoid-s893" xml:space="preserve">4; </s> <s xml:id="echoid-s894" xml:space="preserve">come qui ſeguente ſi vede, reducen-<lb/>do à doppicauezzi.</s> <s xml:id="echoid-s895" xml:space="preserve"/> </p> <pb file="070" n="70" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/>Doppicauezzi # 7, # bra. # 9, # on. # 4, <lb/>Doppicauezzi # 3, # bra. # 2, # on. # 10, <lb/>Tauole # 21, <lb/>Tauole # 2, # piè # 3, <lb/>Tauole # 0, # piè # 1, <lb/>Tauole # 1, # piè # 2, <lb/>Tauole # 0, # piè # 1, # on. # 6, <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 8, <lb/>Tauole # 0, # piè # 5, # on. # 10, <lb/>Tauole # 0, # piè # 0, # on. # 7, # pun. # 6. <lb/>Tauole # 0, # piè # 0, # on. # 0, # pun. # 3, # at. # 4. <lb/>Tauole # 25 # pie # 2, # on. # 0, # pun. # 5, # at. # 4. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # on. # 0 # 0 # at. <lb/># on. # 4 # 0 # at. <lb/></note> <p> <s xml:id="echoid-s896" xml:space="preserve">Et coſi ſi vede, che tolendo la metà della perpendicola-<lb/>re, & </s> <s xml:id="echoid-s897" xml:space="preserve">quella moltiplicarla con tutta la Baſe, farà di ſuper-<lb/>ficie ouero quantità di terreno Tauole 25, piè 2, oncie 0, <lb/>punti 5, atomi 4; </s> <s xml:id="echoid-s898" xml:space="preserve">& </s> <s xml:id="echoid-s899" xml:space="preserve">tanto douerebbe fare tolendo la metà <lb/>della Baſe, & </s> <s xml:id="echoid-s900" xml:space="preserve">quella moltiplicarla con tutta la perpendico-<lb/>lare; </s> <s xml:id="echoid-s901" xml:space="preserve">& </s> <s xml:id="echoid-s902" xml:space="preserve">queſto qui ſotto ſi vedrà la metà della Baſe ſia ca-<lb/>uez. </s> <s xml:id="echoid-s903" xml:space="preserve">7, brac. </s> <s xml:id="echoid-s904" xml:space="preserve">4, on. </s> <s xml:id="echoid-s905" xml:space="preserve">8, & </s> <s xml:id="echoid-s906" xml:space="preserve">tanto ſi moltiplicherà con tutta la <lb/>perpendicolare, ch’è cau, 12, bra. </s> <s xml:id="echoid-s907" xml:space="preserve">5, on. </s> <s xml:id="echoid-s908" xml:space="preserve">8; </s> <s xml:id="echoid-s909" xml:space="preserve">& </s> <s xml:id="echoid-s910" xml:space="preserve">queſta molti-<lb/>plicatione ſi farà per doppicauezzi; </s> <s xml:id="echoid-s911" xml:space="preserve">intendendo però, le ſu-<lb/>perficij delle terre, di far tutte à doppicauezzi, per eſſer lo-<lb/>ro piu facile.</s> <s xml:id="echoid-s912" xml:space="preserve"/> </p> <pb o="30" file="071" n="71" rhead="PRIMO."/> </div> <div xml:id="echoid-div47" type="section" level="1" n="39"> <head xml:id="echoid-head57" xml:space="preserve">NONA RAGIONE DELLA <lb/>Nona Figura.</head> <note position="right" xml:space="preserve"> <lb/>Doppicauezzi # 6, # brac. 5, # oncie # 8. <lb/>Doppicauezzi # 3, # brac. 10, # oncie # 8, <lb/>Tauole # 18, <lb/>Tauole # 1, # piè, # 3, <lb/>Tauole # 0, # piè, # 2, <lb/>Tauole # 5, <lb/>Tauole # 0, # piè, # 4, # on. # 2, <lb/>Tauole # 0, # piè, # 0, # on. # 6, # pun. # 8, <lb/>Tauole # 0, # piè, # 4, <lb/>Tauole # 0, # piè, # 0, # on. # 3, # pun. # 4, <lb/>Tauole # 0, # piè, # 0, # on. # 0, # pun. # 5 # at. # 4. <lb/>Tauole # 25, # pie, # 2, # on. # 0, # pun. # 5, # at. # 4, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # on. # 1 # 0 # at. <lb/># on. # 0 # 0 # at. <lb/></note> <p> <s xml:id="echoid-s913" xml:space="preserve">Hor coſi ſi vede, che tanto fà di ſuperficie, ouero di ter-<lb/>reno, à moltiplicare la metà della perpendicolare con tut <lb/>ta la Baſe; </s> <s xml:id="echoid-s914" xml:space="preserve">come è à moltiplicare la metà della Baſe, con tut <lb/>ta la perpendicolare.</s> <s xml:id="echoid-s915" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s916" xml:space="preserve">Moſtrato di ſopra, il modo di hauere la ſuperficie, ouer <lb/>quantità del terreno, d’un triangolo, qui di ſotto ſi moſtre <lb/>rà geometricamente la cauſa perche il detto modo debba <lb/>fare vna ſuperficie quadrangolare rettangola, tolendo la <lb/>metà della perpendicolare con tutta la Baſe, & </s> <s xml:id="echoid-s917" xml:space="preserve">che queſta <lb/>ſia equale à quella che ſi pigliarà della metà della Baſe con <lb/>tutta la perpendicolare.</s> <s xml:id="echoid-s918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s919" xml:space="preserve">Sia adunque il. </s> <s xml:id="echoid-s920" xml:space="preserve">Triangolo <emph style="sc">E F G</emph>, ſopradetto, dico che <lb/>tanto farà di ſuperficie, tolendo la metà della perpendi- <pb file="072" n="72" rhead="LIBRO"/> Colare con tutta la Baſe; </s> <s xml:id="echoid-s921" xml:space="preserve">come tolendo la metà della Baſe <lb/>con tutta la perpendicolare; </s> <s xml:id="echoid-s922" xml:space="preserve">Et queſto ſi moſtrerà.</s> <s xml:id="echoid-s923" xml:space="preserve"/> </p> <figure> <image file="072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/072-01"/> <caption xml:id="echoid-caption10" xml:space="preserve">Decima Figura.</caption> </figure> <p> <s xml:id="echoid-s924" xml:space="preserve">Prima ſi farà la perpendicolare <emph style="sc">E H</emph>, in due parti eguali in <lb/>punto <emph style="sc">I</emph>, & </s> <s xml:id="echoid-s925" xml:space="preserve">dal punto <emph style="sc">I</emph>, ſi tiri vna linea retta equidiſtante <lb/>alla Baſe <emph style="sc">F G</emph>, che ſarà la linea <emph style="sc">K L</emph>, & </s> <s xml:id="echoid-s926" xml:space="preserve">la <emph style="sc">K L</emph>, è eguale alla <emph style="sc">F G</emph>, <lb/>Baſe del triangolo <emph style="sc">E F G</emph>; </s> <s xml:id="echoid-s927" xml:space="preserve">& </s> <s xml:id="echoid-s928" xml:space="preserve">dal punto <emph style="sc">K</emph>, al punto <emph style="sc">F</emph>, tiriſi <lb/>vua linea retta, che ſarà la linea <emph style="sc">K F</emph>; </s> <s xml:id="echoid-s929" xml:space="preserve">ancor dal punto <emph style="sc">L</emph>, al <lb/>punto <emph style="sc">G</emph>, ſe ne tiri vn’altra linea retta, che ſarà la linea <emph style="sc">L G</emph>; <lb/></s> <s xml:id="echoid-s930" xml:space="preserve">& </s> <s xml:id="echoid-s931" xml:space="preserve">coſi ſarà compito il qua drangolo rettangolo <emph style="sc">K F L G</emph>, il <lb/>quale ſarà eguale al triangolo <emph style="sc">E F G</emph>, come diſopra s’è mo-<lb/>ſtrato nel capotagliato, & </s> <s xml:id="echoid-s932" xml:space="preserve">doppiocapotagliato; </s> <s xml:id="echoid-s933" xml:space="preserve">perche li <lb/>due triangoli <emph style="sc">E I M</emph>, & </s> <s xml:id="echoid-s934" xml:space="preserve"><emph style="sc">F M K</emph>, de lati eguali, ancor fra loro ſo <lb/>no eguali; </s> <s xml:id="echoid-s935" xml:space="preserve">il medeſimo è dei due triangoli <emph style="sc">E I N</emph>, & </s> <s xml:id="echoid-s936" xml:space="preserve"><emph style="sc">G N L</emph>, <lb/>che ancor fra lor due ſaranno eguali.</s> <s xml:id="echoid-s937" xml:space="preserve"/> </p> <pb o="31" file="073" n="73" rhead="PRIMO"/> <figure> <image file="073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/073-01"/> <caption xml:id="echoid-caption11" xml:space="preserve">Vndecima Figura.</caption> </figure> <p> <s xml:id="echoid-s938" xml:space="preserve">Moſtrato di ſopra che il quadrangolo rettangolo <emph style="sc">K F L G</emph>, <lb/>è eguale al triangolo <emph style="sc">E F G</emph>; </s> <s xml:id="echoid-s939" xml:space="preserve">& </s> <s xml:id="echoid-s940" xml:space="preserve">queſto fatto vedere, tolendo <lb/>la metà della perpendicolare, in tutta la Baſe appreſſo ſi <lb/>moſtrerà, che tolendo la metà della Baſe con tutta la per-<lb/>pendicolare, farà vn rettangolo eguale al rettangolo to <lb/>lendo la metà della perpendicolare, con tutta la Baſe.</s> <s xml:id="echoid-s941" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s942" xml:space="preserve">Hor ſia dunq; </s> <s xml:id="echoid-s943" xml:space="preserve">il triangolo <emph style="sc">E F G</emph>, di ſopra detto, dico che <lb/>ancora tolendo la metà della baſe con tutta la perpendico-<lb/>lare, ſarà eguale al rettangolo, tolendo la metà della per-<lb/>pendicolare, con tutta la baſe. </s> <s xml:id="echoid-s944" xml:space="preserve">prima diuiderò le due linee <lb/><emph style="sc">F H</emph>, & </s> <s xml:id="echoid-s945" xml:space="preserve"><emph style="sc">H G</emph>, baſe del triangolo in due parti eguali in punto <emph style="sc">L</emph>, <lb/>& </s> <s xml:id="echoid-s946" xml:space="preserve"><emph style="sc">M</emph>, & </s> <s xml:id="echoid-s947" xml:space="preserve">delli due punti <emph style="sc">L</emph>, & </s> <s xml:id="echoid-s948" xml:space="preserve"><emph style="sc">M</emph>, ſi tirerà due perpendicolari <lb/>all’angolo retto, che ſaranno <emph style="sc">L I</emph>, & </s> <s xml:id="echoid-s949" xml:space="preserve"><emph style="sc">M K</emph>, & </s> <s xml:id="echoid-s950" xml:space="preserve">dal punto <emph style="sc">E</emph>, an-<lb/>golo del triangolo, <emph style="sc">E F G</emph>, ſitirerà vna linea retta equidiſtan- <pb file="074" n="74" rhead="LIBRO"/> te alla linea <emph style="sc">F G</emph>, baſe del triangolo <emph style="sc">E F G</emph>, che taglierà in pun-<lb/>to <emph style="sc">I</emph>, & </s> <s xml:id="echoid-s951" xml:space="preserve"><emph style="sc">K</emph>, coſi ſarà formato il quadrangolo rettangolo <emph style="sc">I K L</emph> <lb/><emph style="sc">M</emph>, eguale al triangolo <emph style="sc">E F G</emph>; </s> <s xml:id="echoid-s952" xml:space="preserve">perche li due triangoli <emph style="sc">E N I</emph>, & </s> <s xml:id="echoid-s953" xml:space="preserve"><lb/><emph style="sc">L N F</emph>, ſono de lati eguali, & </s> <s xml:id="echoid-s954" xml:space="preserve">ſaranno a dunque ancora fra lo-<lb/>ro eguali; </s> <s xml:id="echoid-s955" xml:space="preserve">Il medeſimo ſarà de i due triangoli <emph style="sc">E O K</emph>, & </s> <s xml:id="echoid-s956" xml:space="preserve"><emph style="sc">M O G</emph>, <lb/>fra loro due eguali; </s> <s xml:id="echoid-s957" xml:space="preserve">& </s> <s xml:id="echoid-s958" xml:space="preserve">eſſendo il quadrangolo rett’angolo <lb/><emph style="sc">I K L M</emph>, eguale al triangolo <emph style="sc">E F G</emph>; </s> <s xml:id="echoid-s959" xml:space="preserve">il medeſimo è che il qua-<lb/>drangolo rett’angolo <emph style="sc">K L F G</emph>, ancor eſſo è eguale al medeſi-<lb/>mo triangolo <emph style="sc">E F G</emph>; </s> <s xml:id="echoid-s960" xml:space="preserve">adunque per la prima commune ſen-<lb/>tenza del primo libro di Euclide; </s> <s xml:id="echoid-s961" xml:space="preserve">li due quadrangoli rett’ <lb/>angoli ſaranno fra loro eguali; </s> <s xml:id="echoid-s962" xml:space="preserve">ilche è quello, che douea <lb/>moſtrare.</s> <s xml:id="echoid-s963" xml:space="preserve"/> </p> <figure> <image file="074-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/074-01"/> <caption xml:id="echoid-caption12" xml:space="preserve">Duodecima Figura.</caption> </figure> <p> <s xml:id="echoid-s964" xml:space="preserve">Moſtrato di ſopra Aritmeticamente, & </s> <s xml:id="echoid-s965" xml:space="preserve">Geometrica-<lb/>mente, che tanto è torre la metà della perpendicolare, con <lb/>tutta la Baſe; </s> <s xml:id="echoid-s966" xml:space="preserve">quanto ancor’è torre la metà della Baſe con <lb/>tutta la perpendicolare, per douer hauere la ſuperficie, oue- <pb o="32" file="075" n="75" rhead="PRIMO"/> ro la quantità del terreno in forma triangolare; </s> <s xml:id="echoid-s967" xml:space="preserve">& </s> <s xml:id="echoid-s968" xml:space="preserve">queſta <lb/>regola è generale à tutti i triangoli; </s> <s xml:id="echoid-s969" xml:space="preserve">perche de’triangoli <lb/>ſe ne ritroua de quattro ſorti; </s> <s xml:id="echoid-s970" xml:space="preserve">come qui di ſotto in figura <lb/>ſi vede.</s> <s xml:id="echoid-s971" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s972" xml:space="preserve">Triangolo equilatero, ouer Iſopleuro, & </s> <s xml:id="echoid-s973" xml:space="preserve">ancora oſigonio, <lb/>perche hà tutti li ſuoi triangoli acuti.</s> <s xml:id="echoid-s974" xml:space="preserve"/> </p> <figure> <image file="075-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/075-01"/> </figure> <p> <s xml:id="echoid-s975" xml:space="preserve">Triangolo iſocelo, ouer equicurio, perche ha li due lati <lb/>eguali, & </s> <s xml:id="echoid-s976" xml:space="preserve">l’altro inequale; </s> <s xml:id="echoid-s977" xml:space="preserve">ouero triangolo oſi-<lb/>gonio perche ha tutti tre li ſuoi <lb/>angoli acuti.</s> <s xml:id="echoid-s978" xml:space="preserve"/> </p> <figure> <image file="075-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/075-02"/> </figure> <pb file="076" n="76" rhead="LIBRO"/> <p> <s xml:id="echoid-s979" xml:space="preserve">Triangolo ſcaleno, è quello che ha i tre lati ineguali, & </s> <s xml:id="echoid-s980" xml:space="preserve">an <lb/>cor può eſſere triangolo ampligonio, c’ha <lb/>vn’ angolo ottuſo.</s> <s xml:id="echoid-s981" xml:space="preserve"/> </p> <figure> <image file="076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/076-01"/> </figure> <p> <s xml:id="echoid-s982" xml:space="preserve">Triangolo ortogonio può hauere, & </s> <s xml:id="echoid-s983" xml:space="preserve">non può i due lati egua <lb/>li, & </s> <s xml:id="echoid-s984" xml:space="preserve">l’altro ineguale, maperò ha <lb/>vn’angolo retto.</s> <s xml:id="echoid-s985" xml:space="preserve"/> </p> <figure> <image file="076-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/076-02"/> </figure> <pb o="33" file="077" n="77" rhead="PRIMO."/> <p> <s xml:id="echoid-s986" xml:space="preserve">Auuertendo che nelli due triangoli, cioè equilatero, & </s> <s xml:id="echoid-s987" xml:space="preserve"><lb/>equicurio, piantando lo ſquadro in qual lato ſi voglia, ſem-<lb/>pre la perpen dicolare caderà di dentro del triangolo; </s> <s xml:id="echoid-s988" xml:space="preserve">& </s> <s xml:id="echoid-s989" xml:space="preserve">al <lb/>triangolo ortogonio, piantando lo ſquadro nel lato mag-<lb/>giore, la perpendicolare caderà di dentro del triangolo, & </s> <s xml:id="echoid-s990" xml:space="preserve"><lb/>piantandolo in vn de i due altri lati, la perpendicolare ca-<lb/>ſcherà nell’a ltro lato.</s> <s xml:id="echoid-s991" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s992" xml:space="preserve">Et ſel ſarà vn triangolo ampligonio, che habbia vn an-<lb/>golo ottuſo ſelo ſquadro ſarà piantato nel lato maggiore <lb/>la perpendicolare caſcherà di dentro del triangolo, & </s> <s xml:id="echoid-s993" xml:space="preserve">in <lb/>vno dei due altri lati, la perpendicolare caſcherà di fuori <lb/>del triangolo; </s> <s xml:id="echoid-s994" xml:space="preserve">come qui ſotto il tutto ſivedrà.</s> <s xml:id="echoid-s995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s996" xml:space="preserve">Auuertendoui Lettori, che in tutti i ſeguenti triangoli <lb/>quantun que non ſarà ſegnato come è in queſto la perpendi <lb/>colare, i lati, & </s> <s xml:id="echoid-s997" xml:space="preserve">la Baſe, potrete però da voi ſteſsi conoſcer <lb/>dette parti, poi che tutte le linee che caderãno nel cerchio <lb/>in punto <emph style="sc">D,</emph> ſaranno le perpen dicolari, quella che interſeca <lb/>detto cerchio per trauerſo s’intende ſempre la Baſe, leal-<lb/>tre linee poi ſonoi lati.</s> <s xml:id="echoid-s998" xml:space="preserve"/> </p> <figure> <image file="077-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/077-01"/> <caption xml:id="echoid-caption13" xml:space="preserve">Triangolo equilatero <emph style="sc">A B C.</emph></caption> </figure> <pb file="078" n="78" rhead="LIBRO"/> <figure> <image file="078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/078-01"/> <caption xml:id="echoid-caption14" xml:space="preserve">Triangolo equicurio. <emph style="sc">E F G.</emph></caption> </figure> <figure> <image file="078-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/078-02"/> <caption xml:id="echoid-caption15" xml:space="preserve">Triangolo equicurio. <emph style="sc">E F G.</emph></caption> </figure> <pb o="34" file="079" n="79" rhead="PRIMO."/> <figure> <image file="079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/079-01"/> <caption xml:id="echoid-caption16" xml:space="preserve">Triangolo equicurio, <emph style="sc">E F G.</emph></caption> </figure> <p> <s xml:id="echoid-s999" xml:space="preserve">Triangolo ampligonio <emph style="sc">H I K,</emph> che ha vn’ <lb/>angolo ottuſo.</s> <s xml:id="echoid-s1000" xml:space="preserve"/> </p> <figure> <image file="079-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/079-02"/> </figure> <pb file="080" n="80" rhead="LIBRO"/> <p> <s xml:id="echoid-s1001" xml:space="preserve">Triangolo ampligonio <emph style="sc">H I K,</emph> che ha vn’ <lb/>angolo ottuſo,</s> </p> <figure> <image file="080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/080-01"/> </figure> <p> <s xml:id="echoid-s1002" xml:space="preserve">Triangolo ampligonio <emph style="sc">H I K,</emph> che ha vn’ <lb/>angolo ottuſo.</s> <s xml:id="echoid-s1003" xml:space="preserve"/> </p> <figure> <image file="080-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/080-02"/> </figure> <pb o="35" file="081" n="81" rhead="PRIMO"/> <p> <s xml:id="echoid-s1004" xml:space="preserve">Triangolo ortogonio <emph style="sc">L M N</emph>, che ha vn<unsure/> <lb/>angolo retto.</s> <s xml:id="echoid-s1005" xml:space="preserve"/> </p> <figure> <image file="081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/081-01"/> </figure> <p> <s xml:id="echoid-s1006" xml:space="preserve">Hauendo detto aſſai de i triangoli, mi reſta dir ſolo del-<lb/>la ſuperficie, ouer quantità del terreno, del triangolo am-<lb/>pligonio, che ha vn’angolo ottuſo, quando la perpendico-<lb/>lare caſca di fuori del triangolo.</s> <s xml:id="echoid-s1007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1008" xml:space="preserve">Hor ſia il triangolo <emph style="sc">K I H</emph>, & </s> <s xml:id="echoid-s1009" xml:space="preserve">la ſua Baſe ſia cauezzi 15, <lb/>bra. </s> <s xml:id="echoid-s1010" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1011" xml:space="preserve">4, la perpendicolare caſcarà in punto <emph style="sc">D</emph>, di fuori <lb/>del triangolo, & </s> <s xml:id="echoid-s1012" xml:space="preserve">è lunga cauez. </s> <s xml:id="echoid-s1013" xml:space="preserve">12, bra. </s> <s xml:id="echoid-s1014" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1015" xml:space="preserve">6; </s> <s xml:id="echoid-s1016" xml:space="preserve">in queſto <lb/>triangolo s’ha da conſiderare due triangoli ortogoni, l’uno <lb/>ſi è il triangolo <emph style="sc">K D I</emph>, l’altro il triangolo <emph style="sc">K D H</emph>.</s> <s xml:id="echoid-s1017" xml:space="preserve"/> </p> <pb file="082" n="82" rhead="LIBRO"/> <figure> <image file="082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/082-01"/> </figure> <p> <s xml:id="echoid-s1018" xml:space="preserve">Et per hauere la ſuperficie, ouero quantità del terreno <lb/>del triangolo <emph style="sc">K H I</emph>; </s> <s xml:id="echoid-s1019" xml:space="preserve">ſi cauerà prima la quantità del terreno <lb/>delli due triangoli k <emph style="sc">D I</emph>, & </s> <s xml:id="echoid-s1020" xml:space="preserve">k <emph style="sc">H D</emph>; </s> <s xml:id="echoid-s1021" xml:space="preserve">poi della ſuperficie, ouer <lb/>quantità del terreno, del triangolo k <emph style="sc">D I</emph>; </s> <s xml:id="echoid-s1022" xml:space="preserve">ſi cauerà la ſuper-<lb/>ficie, ouero quantità del terreno, del triangolo k <emph style="sc">H D</emph>; </s> <s xml:id="echoid-s1023" xml:space="preserve">& </s> <s xml:id="echoid-s1024" xml:space="preserve"><lb/>quello che reſterà ſarà la ſuperficie, ouero quantità del ter <lb/>reno del triangolo k <emph style="sc">H I</emph>, come qui ſotto per eſſempio ſi <lb/>vedrà.</s> <s xml:id="echoid-s1025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1026" xml:space="preserve">La metà<unsure/> della perpendicolare k <emph style="sc">D</emph>, ſia cauez. </s> <s xml:id="echoid-s1027" xml:space="preserve">6, bra. </s> <s xml:id="echoid-s1028" xml:space="preserve">2, <lb/>on. </s> <s xml:id="echoid-s1029" xml:space="preserve">9. </s> <s xml:id="echoid-s1030" xml:space="preserve">la Baſe <emph style="sc">I D</emph>, del triangolo k <emph style="sc">D I</emph>, ſia cauezzi 15, bra. </s> <s xml:id="echoid-s1031" xml:space="preserve">2.</s> <s xml:id="echoid-s1032" xml:space="preserve"/> </p> <pb o="36" file="083" n="83" rhead="TRIMO"/> </div> <div xml:id="echoid-div48" type="section" level="1" n="40"> <head xml:id="echoid-head58" xml:space="preserve">DECIMA RAGIONE.</head> <note position="right" xml:space="preserve"> <lb/>Cauezzi # 15, # bra. # 2, # on. # 4, <lb/>Cauezzi # 6, # bra. # 2, # on. # 9, <lb/>Doppicauez. # 7, # bra. # 8, # on. # 4, <lb/>Doppicauez. # 3, # bra. # 2, # on. # 9, <lb/>Tauole # 21, <lb/>Tauole # 2, <lb/>Tauole # 0, # piè, # 1, <lb/>Tauole # 1, # piè, # 2, <lb/>Tauole # 0, # piè, # 1, # on. # 4, <lb/>Tauole # 0, # piè, # 0, # on. # 0, # pun. # 8, <lb/>Tauole # 0, # piè, # 5, # on. # 4<unsure/>, <lb/>Tauole # 0, # piè, # 0, # on. # 6, <lb/>Tauole # 0, # piè, # 0, # on. # 0, # pun. # 3, <lb/>Tauole # 24, # pie, # 10, # on. # 1, # pun. # 11, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # on. # 2 # 6 # at. <lb/># on. # 3 # 6 # at. <lb/></note> <pb file="084" n="84" rhead="LIERO"/> </div> <div xml:id="echoid-div49" type="section" level="1" n="41"> <head xml:id="echoid-head59" xml:space="preserve">VNDECIMA RAGIONE.</head> <note position="right" xml:space="preserve"> <lb/>Cau. # 2, # bra. # 3, # on. # 4, # pun. # 8, # la linea <emph style="sc">H D</emph>, <lb/>Cau. # 12, # bra. # 5, # on. # 6, # # # perpendicolare. <lb/>Cau. # 6, # bra. # 2, # on. # 9, # # # metà della perpẽdico. <lb/>Cau. # 2, # bra. # 3, # on. # 4, # pun. # 8. # linea <emph style="sc">H D</emph>, <lb/>Doppicau. # 3, # bra. # 2, # on. # 9, <lb/>Doppicau. # 1, # bra. # 3, # on. # 4, # pun. # 8, <lb/>Tauole # 3, # piè, # 2, # on. # 9, <lb/>Tauole # 0, # piè, # 9, # on. # 6, <lb/>Tauole # 0, # piè, # 0, # on. # 2, # pun. # 3. <lb/>Tauole # 0, # piè, # 1, # on. # 0, # pun. # 8, <lb/>Tauole # 0, # piè, # 0, # on. # 0, # pun. # 3, <lb/>Tauole # 0, # piè, # 0, # on. # 2, # pun. # 1, # at. # 4. <lb/>Tauole # 0, # piè, # 0, # on. # 0, # pun. # 0, # at. # 6. <lb/>Tauole # 4, # pie, # 1, # on. # 8, # pun. # 3, # at. # 10. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # on. # 3 # 5 # min. <lb/># pun. # 4 # 5 # min. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Tauole # 24, # piè, # 10, # on. # 1, # pun. # 11, <lb/>Tauole # 4, # piè, # 1, # on, # 8, # pun. # 3, # at. # 10, <lb/>Tauole # 20, # piè, # 8, # on. # 5, # pun. # 7. # at. # 2, <lb/></note> <p> <s xml:id="echoid-s1033" xml:space="preserve">Et per le ragioni fatte di ſopra, ſi trouerà che la ſuperfi-<lb/>cie, ouero quantità del terreno, del triangolo <emph style="sc">K H I</emph>, ſarà <lb/>Tauole 20, piè 8, on. </s> <s xml:id="echoid-s1034" xml:space="preserve">5, pun. </s> <s xml:id="echoid-s1035" xml:space="preserve">7, atomi 2. </s> <s xml:id="echoid-s1036" xml:space="preserve">Il medeſimo ſi fa-<unsure/> <lb/>rà in ogni triangolo, cadendo la ſua perpendicolare di fuo <lb/>ri d’eſſo triangolo.</s> <s xml:id="echoid-s1037" xml:space="preserve"/> </p> <pb o="37" file="085" n="85" rhead="PRIMO."/> </div> <div xml:id="echoid-div50" type="section" level="1" n="42"> <head xml:id="echoid-head60" xml:space="preserve">DEL SQVADRARE, DIVIDERE, <lb/>& aggiontare vna pezza di terra.</head> <p> <s xml:id="echoid-s1038" xml:space="preserve"><emph style="sc">Havendo</emph> detto aſſai della quantità del terreno, che <lb/>contiene le figure Geometriche, cioè quadrangoli ret-<lb/>t’angoli, capitagliati, doppicapitagliati, & </s> <s xml:id="echoid-s1039" xml:space="preserve">di tutte le quali-<lb/>tà di triangoli; </s> <s xml:id="echoid-s1040" xml:space="preserve">co’l modo che ſi deueno ſquadrare Geome-<lb/>tricamente, come moſtra la Figura quinta, ſeſta, ſettima, vn-<lb/>decima, & </s> <s xml:id="echoid-s1041" xml:space="preserve">duodecima. </s> <s xml:id="echoid-s1042" xml:space="preserve">Hora parmi di dare l’ordine che ſi <lb/>deue tenere nel ſquadrare vna Pezza di terra.</s> <s xml:id="echoid-s1043" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1044" xml:space="preserve">Quando ſi hauerà da ſquadrare vna Pezza di terra, la <lb/>qual ſia picciola, che ſi poſſa vedere da un capo all’altro coſi <lb/>per la lunghezza, come per la larghezza; </s> <s xml:id="echoid-s1045" xml:space="preserve">la prima coſa che <lb/>ſi deue fare, ſi circonderà eſſa Pezza di terra, & </s> <s xml:id="echoid-s1046" xml:space="preserve">ſi vedrà mi-<lb/>nutamente li ſuoi confini; </s> <s xml:id="echoid-s1047" xml:space="preserve">fatto queſto ſi piãtarà lo ſquadro <lb/>appreſſo vn’angolo di detta poſſeſsione & </s> <s xml:id="echoid-s1048" xml:space="preserve">ſi formerà vn’an-<lb/>golo retto, che vn lato d’eſſo angolo ſi deſtenda per la lun-<lb/>ghezza, & </s> <s xml:id="echoid-s1049" xml:space="preserve">l’altro lato, per la larghezza, cioè il lato <emph style="sc">D C</emph>, per <lb/>la larghezza, & </s> <s xml:id="echoid-s1050" xml:space="preserve">il lato <emph style="sc">C E</emph>, per la lunghezza, & </s> <s xml:id="echoid-s1051" xml:space="preserve">il ſquadro <lb/>nell’angolo in punto c, come moſtra la Figura A; </s> <s xml:id="echoid-s1052" xml:space="preserve">Et queſti <lb/>tali lati ſi poſſono allungare per la lunghezza, & </s> <s xml:id="echoid-s1053" xml:space="preserve">per la lar-<lb/>ghezza, fino in capo della poſſeſsione; </s> <s xml:id="echoid-s1054" xml:space="preserve">Oltra di queſto ſi an <lb/>derà ſquadrando, & </s> <s xml:id="echoid-s1055" xml:space="preserve">miſurando à parte, per parte, à torno la <lb/>poſſeſsione, facendo triangoli, & </s> <s xml:id="echoid-s1056" xml:space="preserve">capitagliati; </s> <s xml:id="echoid-s1057" xml:space="preserve">come ſi vede <lb/>in eſſa figura A, & </s> <s xml:id="echoid-s1058" xml:space="preserve">nel mezo gli reſtarà vna figura quadrila-<lb/>tera, che molti torrebbono la metà delle due larghezze, & </s> <s xml:id="echoid-s1059" xml:space="preserve"><lb/>le metà delle due lunghezze; </s> <s xml:id="echoid-s1060" xml:space="preserve">ilche ſarebbe errore; </s> <s xml:id="echoid-s1061" xml:space="preserve">ouero <lb/>lo torrebbero per vn capotagliato, ilche ancora ſarebbe er-<lb/>rore, perche li due angoli che ſi formano in vno de lati del-<lb/>la figura quadrangolare, per formare il capotagliato, non <lb/>poſſono riuſcire angoli retti, per formare vn capotagliato <lb/>di quella grandezza; </s> <s xml:id="echoid-s1062" xml:space="preserve">& </s> <s xml:id="echoid-s1063" xml:space="preserve">queſto viene; </s> <s xml:id="echoid-s1064" xml:space="preserve">perche non ſiritroua <lb/>ſquadro, che ſia perfetto. </s> <s xml:id="echoid-s1065" xml:space="preserve">Et il meglior modo di ſquad@@-<lb/>re queſta figura quadrilatera è farla in due triangoli, com@ <lb/>ſi vede nella detta figura A.</s> <s xml:id="echoid-s1066" xml:space="preserve"/> </p> <pb file="086" n="86" rhead="LIBRO"/> <p> <s xml:id="echoid-s1067" xml:space="preserve">Et volendo ſquadrare, & </s> <s xml:id="echoid-s1068" xml:space="preserve">miſurare vna Pezza di terra, <lb/>che fuſſe grande, ch@ non ſipoteſſe vedere da vn capo all’al-<lb/>tro; </s> <s xml:id="echoid-s1069" xml:space="preserve">coſi per la larghezza, come per la lunghezza; </s> <s xml:id="echoid-s1070" xml:space="preserve">ſi pianta-<lb/>rà il ſquadro appreſſo di vno delli ſuoi angoli ouero can-<lb/>ton della poſſeſsione, ma però ranto lontano, che i lati del <lb/>l’angolo retto, che fa eſſo ſquadro, ſi poſſano allungare tan <lb/>to che concorrano dall’un capo all’altro, coſi per la lunghez <lb/>za come per la larghezza, poi ſi anderà attorno miſurando <lb/>facendo capitagliati, & </s> <s xml:id="echoid-s1071" xml:space="preserve">triangoli, oſſeruando l’ordine del-<lb/>la Figura A, col vedere tutti i confini attorno, attorno di eſ-<lb/>ſa Pezza di terra; </s> <s xml:id="echoid-s1072" xml:space="preserve">& </s> <s xml:id="echoid-s1073" xml:space="preserve">della Figura quadrilatera, che nel mez-<lb/>zo reſta in volerla miſurare; </s> <s xml:id="echoid-s1074" xml:space="preserve">ſi andrà miſurando à parte, per <lb/>parte con capitagliati; </s> <s xml:id="echoid-s1075" xml:space="preserve">come ſi vede nella Figura C;</s> <s xml:id="echoid-s1076" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1077" xml:space="preserve">Et vn’altro modo ſi deue tenere per ſquadrare vna pez <lb/>za di terra piccola; </s> <s xml:id="echoid-s1078" xml:space="preserve">piantando il ſuo ſquadro ne ll’@un di <lb/>capi, nel mezo d’eſſa pezza di terra, come ſi vede nel punto <lb/><emph style="sc">A</emph>, ouer nel punto <emph style="sc">B</emph>, tirando la linearetta nel capo, & </s> <s xml:id="echoid-s1079" xml:space="preserve">vna <lb/>ſopra à eſſa nel mezzo ad angolo retto, che camina per mez <lb/>zo d’eſſa pezza di terra, facendo i capitagliati, & </s> <s xml:id="echoid-s1080" xml:space="preserve">triangoli <lb/>d’una parte, & </s> <s xml:id="echoid-s1081" xml:space="preserve">l’altra, come per il noſtro ritratto B, ſi moſtra.</s> <s xml:id="echoid-s1082" xml:space="preserve"/> </p> <pb o="38" file="087" n="87" rhead="PRIMO."/> </div> <div xml:id="echoid-div51" type="section" level="1" n="43"> <head xml:id="echoid-head61" xml:space="preserve">AVERTIMENTO.</head> <p> <s xml:id="echoid-s1083" xml:space="preserve">Nelle tre Figure precedenti A C B, ſe ben moſtra eſſer <lb/>più la larghezza, che la lunghezza, però ſi ha da imaginare <lb/>più aſſai la lunghezza, che la larghezza, che queſto ſi è <lb/>fatto ſolo per meglio accomodarle nel libro. </s> <s xml:id="echoid-s1084" xml:space="preserve">Però à carte <lb/>37, à righe 18, doue dice larghezza, vuol dire lunghezza.</s> <s xml:id="echoid-s1085" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1086" xml:space="preserve">Appreſſo, i circoletti ſignificano il luogo doue ſi ferma <lb/>lo ſquadro per formare le linee delle teſte, perpendico-<lb/>lari, lunghezze & </s> <s xml:id="echoid-s1087" xml:space="preserve">larghezze de i capitagliati, doppica-<lb/>pitagliati, & </s> <s xml:id="echoid-s1088" xml:space="preserve">triangoli, come ſi vede in dette tre Figu-<lb/>re ſequenti.</s> <s xml:id="echoid-s1089" xml:space="preserve"/> </p> <pb o="39" file="088" n="88" rhead="LIBRO PRIMO."/> <figure> <image file="088-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/088-01"/> <caption xml:id="echoid-caption17" xml:space="preserve">Figura Prima.</caption> </figure> <pb file="089" n="89"/> <pb o="40" file="090" n="90" rhead="LIBRO PRIMO."/> <figure> <image file="090-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/090-01"/> <caption xml:id="echoid-caption18" xml:space="preserve">Figura Seconda.</caption> </figure> <pb o="41" file="091" n="91" rhead="LIBRO PRIMO."/> <figure> <image file="091-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/091-01"/> <caption xml:id="echoid-caption19" xml:space="preserve">Figura Terza.</caption> </figure> </div> <div xml:id="echoid-div52" type="section" level="1" n="44"> <head xml:id="echoid-head62" xml:space="preserve">ERRORE.</head> <head xml:id="echoid-head63" xml:space="preserve">Auertiſci Lettore, che a carte 42. linea 6. doue dice della figura B, vuol dire della figura C.</head> <pb file="092" n="92"/> <pb o="42" file="093" n="93" rhead="PRIMO"/> <p> <s xml:id="echoid-s1090" xml:space="preserve">Auuertendo quando non ſi poteſſe far angolo retto; </s> <s xml:id="echoid-s1091" xml:space="preserve">cioè <lb/>che allun gando li ſuoi lati non poteſſero aggiungere dal-<lb/>l’uno, all’ altro capo della poſſe ſsione; </s> <s xml:id="echoid-s1092" xml:space="preserve">come l’angolo retto <lb/><emph style="sc">D C E</emph>, della Figura A, & </s> <s xml:id="echoid-s1093" xml:space="preserve">l’angolo retto <emph style="sc">F G H</emph>, della ſigura <lb/>C; </s> <s xml:id="echoid-s1094" xml:space="preserve">che l’uno, & </s> <s xml:id="echoid-s1095" xml:space="preserve">l’altro ſon fatti nel principio, per voler mi <lb/>ſurare la pezaa di terra; </s> <s xml:id="echoid-s1096" xml:space="preserve">in tal caſo la poſſeſsione ſi deurà mi <lb/>ſurare in due parti.</s> <s xml:id="echoid-s1097" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1098" xml:space="preserve">Hor hauendo detto aſſai dello ſquadrare, & </s> <s xml:id="echoid-s1099" xml:space="preserve">miſurare de <lb/>i quadrangoli, capitagliati, doppicapitagliati, & </s> <s xml:id="echoid-s1100" xml:space="preserve">triangoli; <lb/></s> <s xml:id="echoid-s1101" xml:space="preserve">qui conſeguentemente ſi dirà del cauare, ouero aggiunge-<lb/>re quel tanto che biſognerà à vna pezza di terra; </s> <s xml:id="echoid-s1102" xml:space="preserve">& </s> <s xml:id="echoid-s1103" xml:space="preserve">ancora <lb/>s’inſegnerà à diuidere vna pezza di terra, oue ovna poſſeſ-<lb/>ſione, in quante parti ſi vorrà; </s> <s xml:id="echoid-s1104" xml:space="preserve">oltra di queſto, @econdo l’oc <lb/>caſione, s’inſegnerà che tutti ſi ſeruiranno d’un medeſimo <lb/>punto; </s> <s xml:id="echoid-s1105" xml:space="preserve">come vn caſamento, ouero vna ciſterna, ò altra co-<lb/>ſa, ſenza andare ſopra quello del compagno; </s> <s xml:id="echoid-s1106" xml:space="preserve">come qui ſot-<lb/>to ſi moſtrerà; </s> <s xml:id="echoid-s1107" xml:space="preserve">cominciando di ritrouare per numeri, nõ tan-<lb/>to la larghezza, com’ancora la lunghezza d’una pezza di ter <lb/>ra; </s> <s xml:id="echoid-s1108" xml:space="preserve">della qual pezza di terra, s’haurà da pigliare qualche par <lb/>te, ouero aggiungere; </s> <s xml:id="echoid-s1109" xml:space="preserve">Et di queſta tal regola ſi comincie-<lb/>rà à darne eſſempio.</s> <s xml:id="echoid-s1110" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div53" type="section" level="1" n="45"> <head xml:id="echoid-head64" xml:space="preserve">PRIMO ESSEMPIO.</head> <p> <s xml:id="echoid-s1111" xml:space="preserve"><emph style="sc">Hora</emph> ſi ponga, che s’habbia da pigliare d’una pezza di <lb/>terra, vna parte, qual ſi voglia; </s> <s xml:id="echoid-s1112" xml:space="preserve">& </s> <s xml:id="echoid-s1113" xml:space="preserve">ſi ponga di pigliarne vna <lb/>parte, che ſia di ſuperficie Tauole 35, piedi 5, on. </s> <s xml:id="echoid-s1114" xml:space="preserve">6; </s> <s xml:id="echoid-s1115" xml:space="preserve">ouero <lb/>altra parte, che queſto non fa caſo; </s> <s xml:id="echoid-s1116" xml:space="preserve">& </s> <s xml:id="echoid-s1117" xml:space="preserve">ponendo ancora eſſa <lb/>pezza di terra eſſer lunga caue. </s> <s xml:id="echoid-s1118" xml:space="preserve">25, brac. </s> <s xml:id="echoid-s1119" xml:space="preserve">2, oncie 4, lineali.</s> <s xml:id="echoid-s1120" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1121" xml:space="preserve">Et volendo ſapere quanto ſe ne deue pigliare, per la linea <lb/>della larghezza, che moltiplicando eſſa larghezza, con la <lb/>lunghezza, faccia di ſuperficie Tauole 35, piedi 5, on. </s> <s xml:id="echoid-s1122" xml:space="preserve">6.</s> <s xml:id="echoid-s1123" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1124" xml:space="preserve">Et per voler venire all’ operatione, ſi tirerà coſi la ſuper-<lb/>fici@ delle tauole 35, piedi 5, on. </s> <s xml:id="echoid-s1125" xml:space="preserve">6, tutt’a oncie, come an- <pb file="094" n="94" rhead="LIBRO"/> cora ca uezzi 25, brac. </s> <s xml:id="echoid-s1126" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1127" xml:space="preserve">4, linea della lunghezza; </s> <s xml:id="echoid-s1128" xml:space="preserve">fatto <lb/>queſto ſi partiranno le on. </s> <s xml:id="echoid-s1129" xml:space="preserve">della ſuperficie, con le oncie del <lb/>la lunghezza, & </s> <s xml:id="echoid-s1130" xml:space="preserve">quello che ne venirà ſarà per la linea della <lb/>larghezza; </s> <s xml:id="echoid-s1131" xml:space="preserve">& </s> <s xml:id="echoid-s1132" xml:space="preserve">volẽdo tirare tutt’à oncie, l’una, & </s> <s xml:id="echoid-s1133" xml:space="preserve">l’altra, cioè <lb/>la ſuperficie delle tauole 35, piedi 5, on. </s> <s xml:id="echoid-s1134" xml:space="preserve">6; </s> <s xml:id="echoid-s1135" xml:space="preserve">& </s> <s xml:id="echoid-s1136" xml:space="preserve">la linea della <lb/>lunghezza, ch’è cau. </s> <s xml:id="echoid-s1137" xml:space="preserve">25, brac. </s> <s xml:id="echoid-s1138" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1139" xml:space="preserve">4; </s> <s xml:id="echoid-s1140" xml:space="preserve">ſi comincierà dalle <lb/>tauole 35, facendogli in quarti di tauole, faranno quarti di <lb/>tauole 140; </s> <s xml:id="echoid-s1141" xml:space="preserve">moltiplicando 35, per 4, quarti di tauo -<lb/>le; </s> <s xml:id="echoid-s1142" xml:space="preserve">& </s> <s xml:id="echoid-s1143" xml:space="preserve">à quarti ſi aggiungerà vn quarto di tauola; </s> <s xml:id="echoid-s1144" xml:space="preserve">che ſi ri -<lb/>troua in piedi 5, faranno quarti di tauole 141; </s> <s xml:id="echoid-s1145" xml:space="preserve">& </s> <s xml:id="echoid-s1146" xml:space="preserve">in pie-<lb/>di 5, ſuperficiali, rimanendo ancora piedi 2, ſuperficiali: <lb/></s> <s xml:id="echoid-s1147" xml:space="preserve">& </s> <s xml:id="echoid-s1148" xml:space="preserve">eſſendo piedi 3, vn quarto di tauola, ſecondo il coſtume <lb/>Breſciano, & </s> <s xml:id="echoid-s1149" xml:space="preserve">altri particolari luoghi; </s> <s xml:id="echoid-s1150" xml:space="preserve">come nel principio <lb/>delle rappreſentationi, coſi Aritmeticamente, come Geo-<lb/>metricamente, s’è moſtrato; </s> <s xml:id="echoid-s1151" xml:space="preserve">adunque vn quarto di tauola <lb/>ſuperficiale, ſarà in linea brac. </s> <s xml:id="echoid-s1152" xml:space="preserve">6, hor volendo ridurre quar <lb/>ti di tauole 141, in brac ſi moltiplicherà per brac. </s> <s xml:id="echoid-s1153" xml:space="preserve">6, che fa <lb/>ranno brac. </s> <s xml:id="echoid-s1154" xml:space="preserve">846, & </s> <s xml:id="echoid-s1155" xml:space="preserve">à brac. </s> <s xml:id="echoid-s1156" xml:space="preserve">846, ſiaggiungerà il doppio de’ <lb/>piedi 2, che faranno brac. </s> <s xml:id="echoid-s1157" xml:space="preserve">850; </s> <s xml:id="echoid-s1158" xml:space="preserve">& </s> <s xml:id="echoid-s1159" xml:space="preserve">brac. </s> <s xml:id="echoid-s1160" xml:space="preserve">850, ſi faranno in <lb/>oncie, moltiplican do brac. </s> <s xml:id="echoid-s1161" xml:space="preserve">850, per oncie 12, faranno on. </s> <s xml:id="echoid-s1162" xml:space="preserve"><lb/>10200; </s> <s xml:id="echoid-s1163" xml:space="preserve">& </s> <s xml:id="echoid-s1164" xml:space="preserve">à on. </s> <s xml:id="echoid-s1165" xml:space="preserve">10200, ſiaggiungerà il doppio di oncie 6, <lb/>farannoon. </s> <s xml:id="echoid-s1166" xml:space="preserve">10212, ſuperficiali, & </s> <s xml:id="echoid-s1167" xml:space="preserve">on. </s> <s xml:id="echoid-s1168" xml:space="preserve">10212, ſuperficiali, <lb/>ſonoleon. </s> <s xml:id="echoid-s1169" xml:space="preserve">di tauole 35, piè 5, on. </s> <s xml:id="echoid-s1170" xml:space="preserve">6, hor hauendo ridutto <lb/>le tauole 35, piè, 5, on. </s> <s xml:id="echoid-s1171" xml:space="preserve">6, tutte à oncie; </s> <s xml:id="echoid-s1172" xml:space="preserve">ſi deue ancora li <lb/>cau. </s> <s xml:id="echoid-s1173" xml:space="preserve">25, bra. </s> <s xml:id="echoid-s1174" xml:space="preserve">2, on 4; </s> <s xml:id="echoid-s1175" xml:space="preserve">ridurre tutto a oncie, che faranno on-<lb/>cie 1828 lineali; </s> <s xml:id="echoid-s1176" xml:space="preserve">poi ſi partiran no on. </s> <s xml:id="echoid-s1177" xml:space="preserve">10212, ſuperficiali <lb/>per on. </s> <s xml:id="echoid-s1178" xml:space="preserve">1828, lineali, & </s> <s xml:id="echoid-s1179" xml:space="preserve">ne venirà cau. </s> <s xml:id="echoid-s1180" xml:space="preserve">5, & </s> <s xml:id="echoid-s1181" xml:space="preserve">auanza cauez-<lb/>zi 1072; </s> <s xml:id="echoid-s1182" xml:space="preserve">& </s> <s xml:id="echoid-s1183" xml:space="preserve">cau. </s> <s xml:id="echoid-s1184" xml:space="preserve">1072, moltiplicandoſi per brac. </s> <s xml:id="echoid-s1185" xml:space="preserve">6, faranno <lb/>brac. </s> <s xml:id="echoid-s1186" xml:space="preserve">6432; </s> <s xml:id="echoid-s1187" xml:space="preserve">& </s> <s xml:id="echoid-s1188" xml:space="preserve">brac. </s> <s xml:id="echoid-s1189" xml:space="preserve">6432, ſi partiranno per 1828, & </s> <s xml:id="echoid-s1190" xml:space="preserve">ne ve-<lb/>niranno brac. </s> <s xml:id="echoid-s1191" xml:space="preserve">3, & </s> <s xml:id="echoid-s1192" xml:space="preserve">auanza brac. </s> <s xml:id="echoid-s1193" xml:space="preserve">948, ſuperficiali, & </s> <s xml:id="echoid-s1194" xml:space="preserve">brac. </s> <s xml:id="echoid-s1195" xml:space="preserve"><lb/>948, ſi faranno in oncie, moltiplicando 948, per 12, ne ve-<lb/>nirà on. </s> <s xml:id="echoid-s1196" xml:space="preserve">11376, ſuperficiali, & </s> <s xml:id="echoid-s1197" xml:space="preserve">on. </s> <s xml:id="echoid-s1198" xml:space="preserve">11376, partirannoſi per <lb/>on. </s> <s xml:id="echoid-s1199" xml:space="preserve">1828, & </s> <s xml:id="echoid-s1200" xml:space="preserve">ne venirà on. </s> <s xml:id="echoid-s1201" xml:space="preserve">6, lineali, auanzando on. </s> <s xml:id="echoid-s1202" xml:space="preserve">408, ſu <lb/>perficiali, & </s> <s xml:id="echoid-s1203" xml:space="preserve">on. </s> <s xml:id="echoid-s1204" xml:space="preserve">408, ſi faranno in punti, multiplicando <pb o="43" file="095" n="95" rhead="PRIMO."/> 408, per 12, faranno punti 4896, ſuperficiali, & </s> <s xml:id="echoid-s1205" xml:space="preserve">4896, par-<lb/>tiraſsi per 1828, ne venirà punti 2, & </s> <s xml:id="echoid-s1206" xml:space="preserve">auanza punti 1240, <lb/>ſuperficiali; </s> <s xml:id="echoid-s1207" xml:space="preserve">& </s> <s xml:id="echoid-s1208" xml:space="preserve">perche 1240, ſono più della metà dei 1828, <lb/>ſi ponerà 1240, per vn punto faranno punti 3; </s> <s xml:id="echoid-s1209" xml:space="preserve">coſi la lar-i <lb/>ghezza venirà cau. </s> <s xml:id="echoid-s1210" xml:space="preserve">5, brac. </s> <s xml:id="echoid-s1211" xml:space="preserve">3, on. </s> <s xml:id="echoid-s1212" xml:space="preserve">6, & </s> <s xml:id="echoid-s1213" xml:space="preserve">punti 3; </s> <s xml:id="echoid-s1214" xml:space="preserve">hor multi-<lb/>plicando cau. </s> <s xml:id="echoid-s1215" xml:space="preserve">25, bra. </s> <s xml:id="echoid-s1216" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1217" xml:space="preserve">4, lunghezza, con cau. </s> <s xml:id="echoid-s1218" xml:space="preserve">5, bra. </s> <s xml:id="echoid-s1219" xml:space="preserve">3, <lb/>on. </s> <s xml:id="echoid-s1220" xml:space="preserve">6. </s> <s xml:id="echoid-s1221" xml:space="preserve">punti 3, larghezza, faranno Tauole 35, piè 5, on. </s> <s xml:id="echoid-s1222" xml:space="preserve">6, <lb/>pun. </s> <s xml:id="echoid-s1223" xml:space="preserve">4, atomi 1; </s> <s xml:id="echoid-s1224" xml:space="preserve">come qui ſotto ſi vede.</s> <s xml:id="echoid-s1225" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div54" type="section" level="1" n="46"> <head xml:id="echoid-head65" xml:space="preserve">DVODECIMA RAGIONE.</head> <note position="right" xml:space="preserve"> <lb/>Lunga cau. # 25, # bra. # 2, # on. # 4, <lb/>Larga cau. # 5, # bra. # 3, # on. # 6, # pun. # 3, <lb/>Doppicauez. # 12, # bra. # 8, # on. # 4, <lb/>Doppicauez. # 2, # bra. # 9, # on. # 6, # pun. # 3, <lb/>Tauole # 24, <lb/>Tauole # 1, # piè, # 4, # on. # 8, <lb/>Tauole # 9, # piè, # 6, # on. # 3, <lb/>Tauole # 0, # piè, # 6, # on. # 4, # pun. # 2, <lb/>Tauole # 0, # piè, # 0, # on. # 3, # pun. # 2, # at. # 1, <lb/>Tauole # 35, # pie, # 5, # on. # 6, # pun. # 4, # at. # 1. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # onc. # 1 # 4 # mi. <lb/># pun. # 4 # 4 # mi. <lb/></note> <p> <s xml:id="echoid-s1226" xml:space="preserve">Coſi ſi vede, che moltiplicando la lunghezza, con la lar-<lb/>ghezza fanno tauole 35, piedi 5, oncie 6, punti. </s> <s xml:id="echoid-s1227" xml:space="preserve">4, at. </s> <s xml:id="echoid-s1228" xml:space="preserve">1, <lb/>& </s> <s xml:id="echoid-s1229" xml:space="preserve">pun. </s> <s xml:id="echoid-s1230" xml:space="preserve">4, at. </s> <s xml:id="echoid-s1231" xml:space="preserve">1, di piu, ſono per quella parte di piu, che ſi è <lb/>meſſa di più.</s> <s xml:id="echoid-s1232" xml:space="preserve"/> </p> <pb file="096" n="96" rhead="LIBRO"/> <p> <s xml:id="echoid-s1233" xml:space="preserve">Horſivede che per la notitia della linea della lunghez-<lb/>za, ſiviene hauere, la notitia della linea della lar<unsure/>ghezza.</s> <s xml:id="echoid-s1234" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1235" xml:space="preserve">Et medeſimamente hauendo la linea della larghezza, ſi <lb/>hauerà la notitia della linea della lunghezza; </s> <s xml:id="echoid-s1236" xml:space="preserve">Et queſto ſa-<lb/>rà d’una parte di pezza di terra, che ſi voleſſe cauare, ouero <lb/>aggiungere, ad vn’altra pezza di terra: </s> <s xml:id="echoid-s1237" xml:space="preserve">& </s> <s xml:id="echoid-s1238" xml:space="preserve">qui conſeguente-<lb/>mente ſi moſtrarà per vn’altro modo, quello che di ſopra <lb/>ſiè moſtrato.</s> <s xml:id="echoid-s1239" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1240" xml:space="preserve">Verbi gratia mi ritrouo da cauare le medeſime tauole 35, <lb/>piè 5, on. </s> <s xml:id="echoid-s1241" xml:space="preserve">6, d’una pezza di terra; </s> <s xml:id="echoid-s1242" xml:space="preserve">ch’è pur lunga cauez. </s> <s xml:id="echoid-s1243" xml:space="preserve">25, <lb/>bra. </s> <s xml:id="echoid-s1244" xml:space="preserve">2, on 4, come ancor s’è poſto di ſopra; </s> <s xml:id="echoid-s1245" xml:space="preserve">vorrei ancor ſa-<lb/>pere la linea della larghezza; </s> <s xml:id="echoid-s1246" xml:space="preserve">hor volẽdo far queſto, ſi piglie <lb/>rà vn cauez. </s> <s xml:id="echoid-s1247" xml:space="preserve">per la linea della larghezza il quale ſi moltipli-<lb/>carà cõ la linea della lunghezza, cioè cõ cau. </s> <s xml:id="echoid-s1248" xml:space="preserve">25, bra. </s> <s xml:id="echoid-s1249" xml:space="preserve">2, on 4 <lb/>faranno tauole 6, piè, 4, on. </s> <s xml:id="echoid-s1250" xml:space="preserve">2; </s> <s xml:id="echoid-s1251" xml:space="preserve">poiſitorrà tanti cau. </s> <s xml:id="echoid-s1252" xml:space="preserve">in lar-<lb/>ghezza, che moltiplicando con tauole 6, pie. </s> <s xml:id="echoid-s1253" xml:space="preserve">4, on. </s> <s xml:id="echoid-s1254" xml:space="preserve">2, fac-<lb/>ciano tauole 35, piè, 5, on. </s> <s xml:id="echoid-s1255" xml:space="preserve">6, ouero piu proſsimo che ſia <lb/>poſsibile, & </s> <s xml:id="echoid-s1256" xml:space="preserve">ſi torrà cau. </s> <s xml:id="echoid-s1257" xml:space="preserve">5: </s> <s xml:id="echoid-s1258" xml:space="preserve">hor moltiplicando cau. </s> <s xml:id="echoid-s1259" xml:space="preserve">5, con <lb/>tauole 6, pie. </s> <s xml:id="echoid-s1260" xml:space="preserve">4, on. </s> <s xml:id="echoid-s1261" xml:space="preserve">2, faranno tauole 31, pie, 8, oncie 10. <lb/></s> <s xml:id="echoid-s1262" xml:space="preserve">Et da tauole 31, pie. </s> <s xml:id="echoid-s1263" xml:space="preserve">8, on. </s> <s xml:id="echoid-s1264" xml:space="preserve">10, ſin à tauole 35, pie 5, on. </s> <s xml:id="echoid-s1265" xml:space="preserve">6, <lb/>gli manca tauole 3, pie, 8, on. </s> <s xml:id="echoid-s1266" xml:space="preserve">8 è neceſſario dunque pigliar <lb/>tanto per la larghezza, che è moltiplicata con la lunghezza, <lb/>che faccia tauole 3, pie 8, on. </s> <s xml:id="echoid-s1267" xml:space="preserve">8, pigliando vn cauez. </s> <s xml:id="echoid-s1268" xml:space="preserve">in lar <lb/>ghezza farà tauole 6, pie, 4, on. </s> <s xml:id="echoid-s1269" xml:space="preserve">2; </s> <s xml:id="echoid-s1270" xml:space="preserve">& </s> <s xml:id="echoid-s1271" xml:space="preserve">tauole 6, pie 4, on. </s> <s xml:id="echoid-s1272" xml:space="preserve">2, <lb/>ſon piu di tauole 3, pie 8, on. </s> <s xml:id="echoid-s1273" xml:space="preserve">8, tauole 2, pie 7, on. </s> <s xml:id="echoid-s1274" xml:space="preserve">6; </s> <s xml:id="echoid-s1275" xml:space="preserve">& </s> <s xml:id="echoid-s1276" xml:space="preserve">per <lb/>queſto ſitorrà vn brac. </s> <s xml:id="echoid-s1277" xml:space="preserve">in larghezza, ilqual brac. </s> <s xml:id="echoid-s1278" xml:space="preserve">ſi molti-<lb/>plicherà con cau. </s> <s xml:id="echoid-s1279" xml:space="preserve">25, bra. </s> <s xml:id="echoid-s1280" xml:space="preserve">4, on. </s> <s xml:id="echoid-s1281" xml:space="preserve">4, faranno tauole 1, pie, 0, <lb/>on. </s> <s xml:id="echoid-s1282" xml:space="preserve">8, pun. </s> <s xml:id="echoid-s1283" xml:space="preserve">4: </s> <s xml:id="echoid-s1284" xml:space="preserve">& </s> <s xml:id="echoid-s1285" xml:space="preserve">tauole 1, pie 0, on. </s> <s xml:id="echoid-s1286" xml:space="preserve">8, pun. </s> <s xml:id="echoid-s1287" xml:space="preserve">4, ſi moltipli-<lb/>cheranno con tante brac. </s> <s xml:id="echoid-s1288" xml:space="preserve">che facciano tauole 3, piè 8, on. </s> <s xml:id="echoid-s1289" xml:space="preserve">8, <lb/>ouero piu proſsimo che ſia poſsibile, & </s> <s xml:id="echoid-s1290" xml:space="preserve">ſi torrà brac. </s> <s xml:id="echoid-s1291" xml:space="preserve">3; </s> <s xml:id="echoid-s1292" xml:space="preserve">hora <lb/>multiplicando brac. </s> <s xml:id="echoid-s1293" xml:space="preserve">3, con tauole 1, piè 0, on. </s> <s xml:id="echoid-s1294" xml:space="preserve">8, pun. </s> <s xml:id="echoid-s1295" xml:space="preserve">4, <lb/>fanno tauole 3, piè 2, on. </s> <s xml:id="echoid-s1296" xml:space="preserve">1, & </s> <s xml:id="echoid-s1297" xml:space="preserve">tauole 3, piè 2, on. </s> <s xml:id="echoid-s1298" xml:space="preserve">1, douen <lb/>do arriuare à tauole 3, piè 8, on. </s> <s xml:id="echoid-s1299" xml:space="preserve">8, gli mancan piè 6, on. </s> <s xml:id="echoid-s1300" xml:space="preserve">7, <lb/>po ſi torrà vn’oncia in larghezza, che moltiplicando cõ cau- <pb o="44" file="097" n="97" rhead="PRIMO."/> 25, bra. </s> <s xml:id="echoid-s1301" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1302" xml:space="preserve">4, lunghezza farãno piedir, on. </s> <s xml:id="echoid-s1303" xml:space="preserve">0, pun. </s> <s xml:id="echoid-s1304" xml:space="preserve">8, at. </s> <s xml:id="echoid-s1305" xml:space="preserve">4; <lb/></s> <s xml:id="echoid-s1306" xml:space="preserve">moltiplicando piedi 1, on. </s> <s xml:id="echoid-s1307" xml:space="preserve">0, pun.</s> <s xml:id="echoid-s1308" xml:space="preserve">8, at. </s> <s xml:id="echoid-s1309" xml:space="preserve">4, con tante oncie, <lb/>che facciano piedi 6, on 7, ouero più proſsimo che ſi può, <lb/>che ſaranno oncie 6, faranno piè 6, on. </s> <s xml:id="echoid-s1310" xml:space="preserve">4, pun. </s> <s xml:id="echoid-s1311" xml:space="preserve">2; </s> <s xml:id="echoid-s1312" xml:space="preserve">& </s> <s xml:id="echoid-s1313" xml:space="preserve">piè 6, <lb/>on. </s> <s xml:id="echoid-s1314" xml:space="preserve">4, pun. </s> <s xml:id="echoid-s1315" xml:space="preserve">2, ſono meno di piè 6, on. </s> <s xml:id="echoid-s1316" xml:space="preserve">7, oncie 2, pun. </s> <s xml:id="echoid-s1317" xml:space="preserve">10, <lb/>ancor ſitorrà tanto in larghezza, che moltiplicato con ca-<lb/>uez. </s> <s xml:id="echoid-s1318" xml:space="preserve">25, bra. </s> <s xml:id="echoid-s1319" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1320" xml:space="preserve">4, lunghezza, faccia on. </s> <s xml:id="echoid-s1321" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s1322" xml:space="preserve">10, & </s> <s xml:id="echoid-s1323" xml:space="preserve">ſi <lb/>torrà vn punto, che moltiplicando con cau. </s> <s xml:id="echoid-s1324" xml:space="preserve">25, bra. </s> <s xml:id="echoid-s1325" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1326" xml:space="preserve">4 <lb/>fanno on. </s> <s xml:id="echoid-s1327" xml:space="preserve">1, pun.</s> <s xml:id="echoid-s1328" xml:space="preserve">0, at.</s> <s xml:id="echoid-s1329" xml:space="preserve">8, mi.</s> <s xml:id="echoid-s1330" xml:space="preserve">4; </s> <s xml:id="echoid-s1331" xml:space="preserve">& </s> <s xml:id="echoid-s1332" xml:space="preserve">on.</s> <s xml:id="echoid-s1333" xml:space="preserve">1, pun.</s> <s xml:id="echoid-s1334" xml:space="preserve">0, at.</s> <s xml:id="echoid-s1335" xml:space="preserve">8, mi.</s> <s xml:id="echoid-s1336" xml:space="preserve">4, nõ <lb/>giungono à on. </s> <s xml:id="echoid-s1337" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s1338" xml:space="preserve">10; </s> <s xml:id="echoid-s1339" xml:space="preserve">hor ſi moltiplicherà on. </s> <s xml:id="echoid-s1340" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s1341" xml:space="preserve">0, <lb/>at.</s> <s xml:id="echoid-s1342" xml:space="preserve">8, mi.</s> <s xml:id="echoid-s1343" xml:space="preserve">4, con pun. </s> <s xml:id="echoid-s1344" xml:space="preserve">3, farãno on.</s> <s xml:id="echoid-s1345" xml:space="preserve">3, pun.</s> <s xml:id="echoid-s1346" xml:space="preserve">2, at.</s> <s xml:id="echoid-s1347" xml:space="preserve">1,& </s> <s xml:id="echoid-s1348" xml:space="preserve">on.</s> <s xml:id="echoid-s1349" xml:space="preserve">3, pun. </s> <s xml:id="echoid-s1350" xml:space="preserve"><lb/>2, at. </s> <s xml:id="echoid-s1351" xml:space="preserve">1, ſono di piu di on. </s> <s xml:id="echoid-s1352" xml:space="preserve">2, pun.</s> <s xml:id="echoid-s1353" xml:space="preserve">10, pun.</s> <s xml:id="echoid-s1354" xml:space="preserve">4, at.</s> <s xml:id="echoid-s1355" xml:space="preserve">1; </s> <s xml:id="echoid-s1356" xml:space="preserve">& </s> <s xml:id="echoid-s1357" xml:space="preserve">queſto pro <lb/>cede, come hauemo detto nella prima operatione che pun. </s> <s xml:id="echoid-s1358" xml:space="preserve"><lb/>3, in larghezza ſono di piu del douere, coſian cora in queſta <lb/>ſeconda operatione, viene di larghezza cau. </s> <s xml:id="echoid-s1359" xml:space="preserve">5, bra. </s> <s xml:id="echoid-s1360" xml:space="preserve">3, on.</s> <s xml:id="echoid-s1361" xml:space="preserve">6, <lb/>pun. </s> <s xml:id="echoid-s1362" xml:space="preserve">3, come nella prima operatione; </s> <s xml:id="echoid-s1363" xml:space="preserve">& </s> <s xml:id="echoid-s1364" xml:space="preserve">ancor volendone <lb/>far la proua; </s> <s xml:id="echoid-s1365" xml:space="preserve">cioè moltiplicando cau. </s> <s xml:id="echoid-s1366" xml:space="preserve">5, bra. </s> <s xml:id="echoid-s1367" xml:space="preserve">3, on. </s> <s xml:id="echoid-s1368" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1369" xml:space="preserve">3, <lb/>larghezza, con cau. </s> <s xml:id="echoid-s1370" xml:space="preserve">25, bra. </s> <s xml:id="echoid-s1371" xml:space="preserve">2, on. </s> <s xml:id="echoid-s1372" xml:space="preserve">4, lunghezza, faranno ta <lb/>uole 35, pie 5, on. </s> <s xml:id="echoid-s1373" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1374" xml:space="preserve">4, ato. </s> <s xml:id="echoid-s1375" xml:space="preserve">1, come di ſopra; </s> <s xml:id="echoid-s1376" xml:space="preserve">non tan <lb/>to in queſta operatione, come nella prima ſi può trouare la <lb/>lunghezza, come la larghezza.</s> <s xml:id="echoid-s1377" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1378" xml:space="preserve">Hauendo fin qui moſtrato il modo di fare i conti Aritme <lb/>ticamente, per cauare, ouero aggiungere quelche parte à <lb/>vna pezza di terra; </s> <s xml:id="echoid-s1379" xml:space="preserve">conſeguentemente ſi moſtrerà il modo <lb/>di cauarla, ouero aggiungerla, con ragioni Geometriche.</s> <s xml:id="echoid-s1380" xml:space="preserve"/> </p> <pb file="098" n="98" rhead="LI RO"/> </div> <div xml:id="echoid-div55" type="section" level="1" n="47"> <head xml:id="echoid-head66" xml:space="preserve">SECONDO ESSEMPIO.</head> <figure> <image file="098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/098-01"/> <caption xml:id="echoid-caption20" xml:space="preserve">Prima Figura.</caption> </figure> <p> <s xml:id="echoid-s1381" xml:space="preserve">Hor pongo, che s’habbia vna pezza diterra lunga cauez <lb/>32, & </s> <s xml:id="echoid-s1382" xml:space="preserve">ſia di ſuperficie tauole 150, come moſtra la figura pri <lb/>ma, ſupponendo, che ſia d’angoliretti; </s> <s xml:id="echoid-s1383" xml:space="preserve">dimando quanto ſa <lb/>rà la larghezza, ouer le due teſte. </s> <s xml:id="echoid-s1384" xml:space="preserve">Et volendo trouare la lar <lb/>ghezza, ſi farà le tauole 150, in quarti di tauole, moltipli-<lb/>cando tauole 150, con 4, quarti di tauola, faranno quarti di <lb/>tauole 600, & </s> <s xml:id="echoid-s1385" xml:space="preserve">quarti 600, ſi partiranno per cauezzi 32, ne <lb/>venirà cauezzi 18, & </s> <s xml:id="echoid-s1386" xml:space="preserve">auanza cauezzi 24, & </s> <s xml:id="echoid-s1387" xml:space="preserve">cauezzi 24, ſi fa <lb/>ranno in brac. </s> <s xml:id="echoid-s1388" xml:space="preserve">moltiplicando cau. </s> <s xml:id="echoid-s1389" xml:space="preserve">24, per brac. </s> <s xml:id="echoid-s1390" xml:space="preserve">6, faranno <lb/>brac. </s> <s xml:id="echoid-s1391" xml:space="preserve">144, & </s> <s xml:id="echoid-s1392" xml:space="preserve">brac. </s> <s xml:id="echoid-s1393" xml:space="preserve">144, ſi partiranno per cau. </s> <s xml:id="echoid-s1394" xml:space="preserve">32, & </s> <s xml:id="echoid-s1395" xml:space="preserve">ne ve-<lb/>niran brac. </s> <s xml:id="echoid-s1396" xml:space="preserve">4, auanzando brac. </s> <s xml:id="echoid-s1397" xml:space="preserve">16, & </s> <s xml:id="echoid-s1398" xml:space="preserve">brac. </s> <s xml:id="echoid-s1399" xml:space="preserve">16, ſi faranno in <lb/>oncie, moltiplicando brac. </s> <s xml:id="echoid-s1400" xml:space="preserve">16, per oncie 12, ne venirà on. <lb/></s> <s xml:id="echoid-s1401" xml:space="preserve">192, & </s> <s xml:id="echoid-s1402" xml:space="preserve">oncie 192, ſi partiranno per cauez. </s> <s xml:id="echoid-s1403" xml:space="preserve">32, venendone <lb/>on. </s> <s xml:id="echoid-s1404" xml:space="preserve">6; </s> <s xml:id="echoid-s1405" xml:space="preserve">coſile due larghezze, ouer teſte ſaranno cauezzi 18, <pb o="45" file="099" n="99" rhead="PRIMO"/> brac. </s> <s xml:id="echoid-s1406" xml:space="preserve">4, oncie 6; </s> <s xml:id="echoid-s1407" xml:space="preserve">come ſi vede in queſta ſeguente ſeconda fi-<lb/>gura.</s> <s xml:id="echoid-s1408" xml:space="preserve"/> </p> <figure> <image file="099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/099-01"/> <caption xml:id="echoid-caption21" xml:space="preserve">Seconda Figura.</caption> </figure> <p> <s xml:id="echoid-s1409" xml:space="preserve">Il medeſimo ſi farebbe hauendo nota la larghezza, & </s> <s xml:id="echoid-s1410" xml:space="preserve">che <lb/>ſi voleſſe la lunghezza. </s> <s xml:id="echoid-s1411" xml:space="preserve">Et per veder queſto, ſi ſupponerà <lb/>queſta ſeconda figura ditauole, pur 150, che ſia per teſta, <lb/>ouer larghezza cauez. </s> <s xml:id="echoid-s1412" xml:space="preserve">18, bra. </s> <s xml:id="echoid-s1413" xml:space="preserve">4, on. </s> <s xml:id="echoid-s1414" xml:space="preserve">6; </s> <s xml:id="echoid-s1415" xml:space="preserve">Prima ſi faranno le <lb/>tauole 150, in quarti di tauola, che faranno quarti 600, co <lb/>me di ſopra; </s> <s xml:id="echoid-s1416" xml:space="preserve">& </s> <s xml:id="echoid-s1417" xml:space="preserve">queſti quarti 600, ſi faranno in brac. </s> <s xml:id="echoid-s1418" xml:space="preserve">molti-<lb/>plicando i quarti 600, per brac. </s> <s xml:id="echoid-s1419" xml:space="preserve">6, faranno brac. </s> <s xml:id="echoid-s1420" xml:space="preserve">3600, le-<lb/>quali ſi faranno in on. </s> <s xml:id="echoid-s1421" xml:space="preserve">moltiplicãdo brac. </s> <s xml:id="echoid-s1422" xml:space="preserve">3600, per on. </s> <s xml:id="echoid-s1423" xml:space="preserve">12, <lb/>& </s> <s xml:id="echoid-s1424" xml:space="preserve">faranno on. </s> <s xml:id="echoid-s1425" xml:space="preserve">43200, & </s> <s xml:id="echoid-s1426" xml:space="preserve">on. </s> <s xml:id="echoid-s1427" xml:space="preserve">43200, ſi partiranno pe<unsure/>r cauez <lb/>zi 18, brac. </s> <s xml:id="echoid-s1428" xml:space="preserve">4, on. </s> <s xml:id="echoid-s1429" xml:space="preserve">6, ma prima cauez. </s> <s xml:id="echoid-s1430" xml:space="preserve">18, brac. </s> <s xml:id="echoid-s1431" xml:space="preserve">4, on. </s> <s xml:id="echoid-s1432" xml:space="preserve">6, ſi ri-<lb/>durranno tutt’à oncie, & </s> <s xml:id="echoid-s1433" xml:space="preserve">faranno on. </s> <s xml:id="echoid-s1434" xml:space="preserve">1350, le quali parti-<lb/>ranno oncie 43200, ne venirà cau. </s> <s xml:id="echoid-s1435" xml:space="preserve">32, per la lunghezza, <lb/>come ſivede nella figura ſeconda.</s> <s xml:id="echoid-s1436" xml:space="preserve"/> </p> <pb file="100" n="100" rhead="LIBRO"/> </div> <div xml:id="echoid-div56" type="section" level="1" n="48"> <head xml:id="echoid-head67" xml:space="preserve">TERZO ESSEMPIO.</head> <figure> <image file="100-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/100-01"/> <caption xml:id="echoid-caption22" xml:space="preserve">Terza figura.</caption> </figure> <p> <s xml:id="echoid-s1437" xml:space="preserve">Io mi ritrouo vna pezza di terra, come la Figura terza, <lb/>di tauole 400, & </s> <s xml:id="echoid-s1438" xml:space="preserve">lunga cau. </s> <s xml:id="echoid-s1439" xml:space="preserve">24, ne vorrei cauare tauole 60, <lb/>& </s> <s xml:id="echoid-s1440" xml:space="preserve">queſte le vorrei per lunghezza della detta pezza di terra, <lb/>ſopponendola di due angoli retti; </s> <s xml:id="echoid-s1441" xml:space="preserve">come ſignificano i circo-<lb/>letti; </s> <s xml:id="echoid-s1442" xml:space="preserve">per voler far queſto, prima ſi faranno le tauole 60, in <lb/>quarti di tauole, moltiplicando 60, per 4, faranno quarti di <lb/>tauole 240; </s> <s xml:id="echoid-s1443" xml:space="preserve">i quali 240, ſi partirãno per cau. </s> <s xml:id="echoid-s1444" xml:space="preserve">24, lunghezza, <lb/>& </s> <s xml:id="echoid-s1445" xml:space="preserve">ne venirà cau. </s> <s xml:id="echoid-s1446" xml:space="preserve">10, & </s> <s xml:id="echoid-s1447" xml:space="preserve">cau. </s> <s xml:id="echoid-s1448" xml:space="preserve">10, ſi pigliaranno per larghez-<lb/>za, cominciando da gl’angoli retti; </s> <s xml:id="echoid-s1449" xml:space="preserve">come ſi vede nella ſe-<lb/>guente figura Quarta.</s> <s xml:id="echoid-s1450" xml:space="preserve"/> </p> <pb o="46" file="101" n="101" rhead="PRIMO"/> </div> <div xml:id="echoid-div57" type="section" level="1" n="49"> <head xml:id="echoid-head68" xml:space="preserve">QVARTO ESSEMPIO.</head> <figure> <image file="101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/101-01"/> <caption xml:id="echoid-caption23" xml:space="preserve">Quarta Figura.</caption> </figure> <p> <s xml:id="echoid-s1451" xml:space="preserve">Io mi ritrouo vna pezza diterra, come moſtra la Figura <lb/>Quinta di tauole 500, & </s> <s xml:id="echoid-s1452" xml:space="preserve">lunga cauezzi 25; </s> <s xml:id="echoid-s1453" xml:space="preserve">dimando vo-<lb/>lendone aggiunger tauole 100, in lunghezza, quanta mi-<lb/>ſura in larghezza ſi gli deue aggiungere; </s> <s xml:id="echoid-s1454" xml:space="preserve">ſi faccia come di <lb/>ſopra, riducendo prima tauole 100, tutte à quarti di tauola, <lb/>moltiplicando tauole 100, per 4, faranno quarti di tauola <lb/>400; </s> <s xml:id="echoid-s1455" xml:space="preserve">poiſipartirà 400, per 25, lunghezza & </s> <s xml:id="echoid-s1456" xml:space="preserve">ne veniran ca-<lb/>uezzi 16, iquai cauezzi 16, ſi aggiungerà in larghezza, co-<lb/>me ſivede nella Quinta Figura.</s> <s xml:id="echoid-s1457" xml:space="preserve"/> </p> <pb file="102" n="102" rhead="LIBRO"/> <figure> <image file="102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/102-01"/> <caption xml:id="echoid-caption24" xml:space="preserve">Quinta Figura.</caption> </figure> <p> <s xml:id="echoid-s1458" xml:space="preserve">Il medeſimo ſi farebbe, quando ſi voleſſe aggiungere, <lb/>ouer cauare, qualche parte a vna pezza di terra, hauen do <lb/>nota la larghezza, per ſapere quanto ſene douerà pigliare <lb/>in lunghezza; </s> <s xml:id="echoid-s1459" xml:space="preserve">& </s> <s xml:id="echoid-s1460" xml:space="preserve">queſto ſi può fare come di ſopra s’è mo-<lb/>ſtrato.</s> <s xml:id="echoid-s1461" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1462" xml:space="preserve">Auuertendo anchora volendo torre, ouer dar qualche <lb/>parte, à vna pezza diterra; </s> <s xml:id="echoid-s1463" xml:space="preserve">ſecondo l’operatione data diſo <lb/>pra, & </s> <s xml:id="echoid-s1464" xml:space="preserve">queſto ſipotrà fare, ſenza ſapere la ſuperficie d’eſſa <lb/>pezza di terra, che ſol baſta hauer noto la lunghezza, ouer <lb/>larghezza; </s> <s xml:id="echoid-s1465" xml:space="preserve">& </s> <s xml:id="echoid-s1466" xml:space="preserve">operare ſecondo l’ordine dato di ſopra.</s> <s xml:id="echoid-s1467" xml:space="preserve"/> </p> <pb o="47" file="103" n="103" rhead="TRIMO."/> </div> <div xml:id="echoid-div58" type="section" level="1" n="50"> <head xml:id="echoid-head69" xml:space="preserve">QVINTO ESSEMPIO.</head> <figure> <image file="103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/103-01"/> <caption xml:id="echoid-caption25" xml:space="preserve">Seſta Figura.</caption> </figure> <p> <s xml:id="echoid-s1468" xml:space="preserve">Io mi ritrouo vna pezza diterra di tauole 600, & </s> <s xml:id="echoid-s1469" xml:space="preserve">lunga <lb/>cau. </s> <s xml:id="echoid-s1470" xml:space="preserve">35, come è la Figura Seſta; </s> <s xml:id="echoid-s1471" xml:space="preserve">dimando il modo per do-<lb/>uerla diuidere in due parti eguali; </s> <s xml:id="echoid-s1472" xml:space="preserve">volendo far queſto ſitor <lb/>rà la metà delle tauole 600, che ſono tauole 300, & </s> <s xml:id="echoid-s1473" xml:space="preserve">ſi fa-<lb/>ranno in quarti di tauole, che farãno quarti di tauole 1200, <lb/>& </s> <s xml:id="echoid-s1474" xml:space="preserve">quarti 1200, ſi partiranno per cau. </s> <s xml:id="echoid-s1475" xml:space="preserve">35, lunghezza, & </s> <s xml:id="echoid-s1476" xml:space="preserve">ne <lb/>veniranno cauezzi 34, bra. </s> <s xml:id="echoid-s1477" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1478" xml:space="preserve">8, & </s> <s xml:id="echoid-s1479" xml:space="preserve">quaſi punti 7, & </s> <s xml:id="echoid-s1480" xml:space="preserve">tan <lb/>to ſi torrà per l’una, & </s> <s xml:id="echoid-s1481" xml:space="preserve">l’altra larghezza, come di ſopra ſive <lb/>de nella Seſta Figura. </s> <s xml:id="echoid-s1482" xml:space="preserve">Il medeſimo ſi farebbe volendola <lb/>diuidere per il largo, in due parti eguali.</s> <s xml:id="echoid-s1483" xml:space="preserve"/> </p> <pb file="104" n="104" rhead="LIBRO"/> </div> <div xml:id="echoid-div59" type="section" level="1" n="51"> <head xml:id="echoid-head70" xml:space="preserve">SESTO ESSEMPIO.</head> <figure> <image file="104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/104-01"/> <caption xml:id="echoid-caption26" xml:space="preserve">Settima Figura.</caption> </figure> <p> <s xml:id="echoid-s1484" xml:space="preserve">Io mi ritrouo vna pezza di terra, come moſtra la Figura <lb/>ſettima, da diuidere in tre parti eguali, & </s> <s xml:id="echoid-s1485" xml:space="preserve">è di ſuperficie ta-<lb/>uole 600, & </s> <s xml:id="echoid-s1486" xml:space="preserve">lunga cau. </s> <s xml:id="echoid-s1487" xml:space="preserve">45, dimando quanto ſe ne darà per <lb/>larghezza à ciaſcuna parte; </s> <s xml:id="echoid-s1488" xml:space="preserve">prima ſi torrà di tauole 600, la <lb/>terza parte, che ſono tauole 200, & </s> <s xml:id="echoid-s1489" xml:space="preserve">le tauole 200, ſi faran-<lb/>no in quarti di tauole, che ſono quarti 800, & </s> <s xml:id="echoid-s1490" xml:space="preserve">li 800, ſi par-<lb/>tiran per cauezzi 45, lunghezza, & </s> <s xml:id="echoid-s1491" xml:space="preserve">ne venirà cau. </s> <s xml:id="echoid-s1492" xml:space="preserve">17, bra. </s> <s xml:id="echoid-s1493" xml:space="preserve">4, <lb/>on. </s> <s xml:id="echoid-s1494" xml:space="preserve">8; </s> <s xml:id="echoid-s1495" xml:space="preserve">& </s> <s xml:id="echoid-s1496" xml:space="preserve">tanto ſarà per larghezza, per ciaſcuna parte; </s> <s xml:id="echoid-s1497" xml:space="preserve">come <lb/>di ſopra ſi vede nella Settima figura. </s> <s xml:id="echoid-s1498" xml:space="preserve">Il ſimile ſi farebbe <lb/>volendola diuider per largo; </s> <s xml:id="echoid-s1499" xml:space="preserve">facendo però le due linee del-<lb/>la lunghezza paralelli, ouer equidiſtanti, come di ſopra s è <lb/>fatto di quelli della larghezza; </s> <s xml:id="echoid-s1500" xml:space="preserve">& </s> <s xml:id="echoid-s1501" xml:space="preserve">con queſta regola ſi diui-<lb/>derà vna pezza di terra in quante parti ſivorrà.</s> <s xml:id="echoid-s1502" xml:space="preserve"/> </p> <pb o="48" file="105" n="105" rhead="PRIMO."/> </div> <div xml:id="echoid-div60" type="section" level="1" n="52"> <head xml:id="echoid-head71" xml:space="preserve">SETTIMO ESSEMPIO.</head> <figure> <image file="105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/105-01"/> <caption xml:id="echoid-caption27" xml:space="preserve">Otraua Figura.</caption> </figure> <p> <s xml:id="echoid-s1503" xml:space="preserve">Io mi ritrouo vna pezza di terra da douerne pigliare ta-<lb/>uole 85, per lunghezza, & </s> <s xml:id="echoid-s1504" xml:space="preserve">è lunga cauezzi 32; </s> <s xml:id="echoid-s1505" xml:space="preserve">ma però da <lb/>vna parte della larghezza non paſsa la miſura di cauezzi 8; <lb/></s> <s xml:id="echoid-s1506" xml:space="preserve">vorrei ſapere quanta miſura ſitorrà per l’altra larghezza; </s> <s xml:id="echoid-s1507" xml:space="preserve">vo <lb/>lendo far queſto, prima ſi farà delle tauole 85, quarti di ta-<lb/>uole, che ſaranno quarti 340, iquali 340, ſi partiran per ca-<lb/>uezzi 32, & </s> <s xml:id="echoid-s1508" xml:space="preserve">ne venirà cau. </s> <s xml:id="echoid-s1509" xml:space="preserve">10, brac. </s> <s xml:id="echoid-s1510" xml:space="preserve">3, on. </s> <s xml:id="echoid-s1511" xml:space="preserve">9,& </s> <s xml:id="echoid-s1512" xml:space="preserve">tanto ſirad-<lb/>doppiarà che faranno cau 21, bracia 1, on. </s> <s xml:id="echoid-s1513" xml:space="preserve">6. </s> <s xml:id="echoid-s1514" xml:space="preserve">& </s> <s xml:id="echoid-s1515" xml:space="preserve">dicau. </s> <s xml:id="echoid-s1516" xml:space="preserve">21, <lb/>bra. </s> <s xml:id="echoid-s1517" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1518" xml:space="preserve">6, ſi cauerà cauezzi 8, & </s> <s xml:id="echoid-s1519" xml:space="preserve">reſterà cau. </s> <s xml:id="echoid-s1520" xml:space="preserve">13, brac. </s> <s xml:id="echoid-s1521" xml:space="preserve">1, <lb/>on. </s> <s xml:id="echoid-s1522" xml:space="preserve">6, per l’altra larghezza; </s> <s xml:id="echoid-s1523" xml:space="preserve">come ſi vede nell’ottaua figura.</s> <s xml:id="echoid-s1524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1525" xml:space="preserve">Ancora per vn’altro bel modo ſi potrà ritrouare l’altra lar <pb file="106" n="106" rhead="LIBKO"/> ghezza, cioè cauare cau. </s> <s xml:id="echoid-s1526" xml:space="preserve">8, da cau. </s> <s xml:id="echoid-s1527" xml:space="preserve">10, brac. </s> <s xml:id="echoid-s1528" xml:space="preserve">3, on. </s> <s xml:id="echoid-s1529" xml:space="preserve">9, che re <lb/>ſterà cau. </s> <s xml:id="echoid-s1530" xml:space="preserve">2, brac. </s> <s xml:id="echoid-s1531" xml:space="preserve">3, oncie 9, & </s> <s xml:id="echoid-s1532" xml:space="preserve">cauezzi. </s> <s xml:id="echoid-s1533" xml:space="preserve">2, bra. </s> <s xml:id="echoid-s1534" xml:space="preserve">3, on. </s> <s xml:id="echoid-s1535" xml:space="preserve">9, ſi ag-<lb/>giungeranno con cau. </s> <s xml:id="echoid-s1536" xml:space="preserve">10, bra. </s> <s xml:id="echoid-s1537" xml:space="preserve">3, on 9, che faranno cau. </s> <s xml:id="echoid-s1538" xml:space="preserve">13, <lb/>brac. </s> <s xml:id="echoid-s1539" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1540" xml:space="preserve">6, ch’èil medeſimo dell’altra larghezza, come <lb/>diſopra.</s> <s xml:id="echoid-s1541" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div61" type="section" level="1" n="53"> <head xml:id="echoid-head72" xml:space="preserve">OTTAVO ESSEMPIO.</head> <figure> <image file="106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/106-01"/> <caption xml:id="echoid-caption28" xml:space="preserve">Nona Figura.</caption> </figure> <p> <s xml:id="echoid-s1542" xml:space="preserve">Io mi ritrouo da cauare tauole 100, per lunghezza d’una <lb/>pezza di terra, & </s> <s xml:id="echoid-s1543" xml:space="preserve">è lunga cau 32; </s> <s xml:id="echoid-s1544" xml:space="preserve">ma d’una larghezza io vor <lb/>rei che fuſſe cauezzi 16, brac. </s> <s xml:id="echoid-s1545" xml:space="preserve">3, dimando quanto ſarà l’al-<lb/>tra larghezza; </s> <s xml:id="echoid-s1546" xml:space="preserve">Per far queſto, ſi farà tauole 100, in quarti <lb/>di tauole, che ſaranno quarti 400, iquali quarti 400, ſi parti <lb/>rãno per cau. </s> <s xml:id="echoid-s1547" xml:space="preserve">32, & </s> <s xml:id="echoid-s1548" xml:space="preserve">ne venirà cau. </s> <s xml:id="echoid-s1549" xml:space="preserve">12. </s> <s xml:id="echoid-s1550" xml:space="preserve">bra. </s> <s xml:id="echoid-s1551" xml:space="preserve">3, & </s> <s xml:id="echoid-s1552" xml:space="preserve">cau. </s> <s xml:id="echoid-s1553" xml:space="preserve">12, bra. </s> <s xml:id="echoid-s1554" xml:space="preserve">3 <pb o="49" file="107" n="107" rhead="PRIMO"/> ſi radoppieranno, facendone cau. </s> <s xml:id="echoid-s1555" xml:space="preserve">25, & </s> <s xml:id="echoid-s1556" xml:space="preserve">di cau. </s> <s xml:id="echoid-s1557" xml:space="preserve">25, ſene ca-<lb/>ueran cauezzi 16, bra. </s> <s xml:id="echoid-s1558" xml:space="preserve">3, & </s> <s xml:id="echoid-s1559" xml:space="preserve">reſteran cau. </s> <s xml:id="echoid-s1560" xml:space="preserve">8, bra. </s> <s xml:id="echoid-s1561" xml:space="preserve">3, & </s> <s xml:id="echoid-s1562" xml:space="preserve">cau. </s> <s xml:id="echoid-s1563" xml:space="preserve">8, <lb/>bra. </s> <s xml:id="echoid-s1564" xml:space="preserve">3, ſaranno per l’altra larghezza, come ſi vede di ſopra <lb/>nella nona ſigura.</s> <s xml:id="echoid-s1565" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div62" type="section" level="1" n="54"> <head xml:id="echoid-head73" xml:space="preserve">NONO ESSEMPIO.</head> <figure> <image file="107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/107-01"/> <caption xml:id="echoid-caption29" xml:space="preserve">Decima Figura</caption> </figure> <p> <s xml:id="echoid-s1566" xml:space="preserve">Io mi ritrouo vna pezza di terra da diuidere in due parti <lb/>eguali, & </s> <s xml:id="echoid-s1567" xml:space="preserve">è di tauole 400, & </s> <s xml:id="echoid-s1568" xml:space="preserve">lunga cau. </s> <s xml:id="echoid-s1569" xml:space="preserve">25, & </s> <s xml:id="echoid-s1570" xml:space="preserve">in vn delli <lb/>ſuoi lati della larghezza, ſiritroua vna fonte, ouer vn caſa <lb/>mento, ò altra coſa, ſi vuole diuidere la detta poſſeſsione co <lb/>ſi conditionatamente in due parti eguali, ch’ogn’uno vada <lb/>alla fonte, ouer caſamento ſenza andare ſopra quel del com <pb file="108" n="108" rhead="LIBRO"/> pagno, & </s> <s xml:id="echoid-s1571" xml:space="preserve">in quellato della larghezza doue è la fonte, ouer <lb/>caſamento, ſono cau. </s> <s xml:id="echoid-s1572" xml:space="preserve">10, come ſive de di ſopra nella Deci-<lb/>ma figura; </s> <s xml:id="echoid-s1573" xml:space="preserve">dimando quanto ſe ne darà di miſura per l’altro <lb/>lato di larghezza: </s> <s xml:id="echoid-s1574" xml:space="preserve">Volendo far queſto, ſi piglierà la metà <lb/>delle tauole 400, che ſono tauole 200, & </s> <s xml:id="echoid-s1575" xml:space="preserve">le 200, ſi faranno <lb/>in quarti di tauole, che ſaranno quarti 800, & </s> <s xml:id="echoid-s1576" xml:space="preserve">queſti 800, ſi <lb/>partiranno per cauezzi 25. </s> <s xml:id="echoid-s1577" xml:space="preserve">lunghezza, & </s> <s xml:id="echoid-s1578" xml:space="preserve">ne veniranno ca-<lb/>uezzi 32, & </s> <s xml:id="echoid-s1579" xml:space="preserve">i 32, ſiradoppieranno, & </s> <s xml:id="echoid-s1580" xml:space="preserve">faranno cauezzi 64, <lb/>& </s> <s xml:id="echoid-s1581" xml:space="preserve">de cau. </s> <s xml:id="echoid-s1582" xml:space="preserve">64, ſi cauerà cau. </s> <s xml:id="echoid-s1583" xml:space="preserve">10, reſterà cau. </s> <s xml:id="echoid-s1584" xml:space="preserve">54, & </s> <s xml:id="echoid-s1585" xml:space="preserve">cauezzi <lb/>54, ſarà per l’altro lato della larghezza; </s> <s xml:id="echoid-s1586" xml:space="preserve">come ſi vede nel-<lb/>la Decima figura.</s> <s xml:id="echoid-s1587" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div63" type="section" level="1" n="55"> <head xml:id="echoid-head74" xml:space="preserve">DECIMO ESSEMPIO.</head> <figure> <image file="108-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/108-01"/> <caption xml:id="echoid-caption30" xml:space="preserve">Vndecima Figura.</caption> </figure> <handwritten/> <pb o="50" file="109" n="109" rhead="PRIMO"/> <p> <s xml:id="echoid-s1588" xml:space="preserve">Io mi ritrouo vna pezza di terra lunga cauezzi 42, & </s> <s xml:id="echoid-s1589" xml:space="preserve">di <lb/>ſuperficie tauole 600; </s> <s xml:id="echoid-s1590" xml:space="preserve">la vorrei diuiderla in tre parti eguali, <lb/>con le medeſime conditioni che s’è detto nello nono eſſem <lb/>pio; </s> <s xml:id="echoid-s1591" xml:space="preserve">cioè che tutte tre ſi veniſſero à ſeruire della fonte, ò ca-<lb/>ſamento, ouer altra coſa, ſenza andare ſopra quel del com-<lb/>pagno; </s> <s xml:id="echoid-s1592" xml:space="preserve">& </s> <s xml:id="echoid-s1593" xml:space="preserve">dall’angolo retto infino alla fonte ſono cauezzi <lb/>12; </s> <s xml:id="echoid-s1594" xml:space="preserve">dimando quanto ſarà per gli altritre lati, oppoſiti, & </s> <s xml:id="echoid-s1595" xml:space="preserve">an <lb/>cor il lato ſeguente alli cauezzi 12, ouer alla fonte.</s> <s xml:id="echoid-s1596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1597" xml:space="preserve">Volendo far queſto, ſi farà in queſto modo, prima ſi torrà <lb/>la terza parte delle tauole 600, che ſono tauole 200, le <lb/>quali 200, ſi farãno in quarti di tauole, che ſono quarti 800, <lb/>& </s> <s xml:id="echoid-s1598" xml:space="preserve">800, ſi partiranno per cau. </s> <s xml:id="echoid-s1599" xml:space="preserve">42, lunghezza, & </s> <s xml:id="echoid-s1600" xml:space="preserve">ne veniran <lb/>cau. </s> <s xml:id="echoid-s1601" xml:space="preserve">19, bra. </s> <s xml:id="echoid-s1602" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1603" xml:space="preserve">{3/6}, pun. </s> <s xml:id="echoid-s1604" xml:space="preserve">{5/10}, & </s> <s xml:id="echoid-s1605" xml:space="preserve">tanto ſiradoppierà, che fa-<lb/>rãno cau. </s> <s xml:id="echoid-s1606" xml:space="preserve">38, bra. </s> <s xml:id="echoid-s1607" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1608" xml:space="preserve">6, pũ. </s> <s xml:id="echoid-s1609" xml:space="preserve">10, & </s> <s xml:id="echoid-s1610" xml:space="preserve">de i cau. </s> <s xml:id="echoid-s1611" xml:space="preserve">38 bra. </s> <s xml:id="echoid-s1612" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1613" xml:space="preserve">6, <lb/>pun. </s> <s xml:id="echoid-s1614" xml:space="preserve">10, ſi cauerà cau. </s> <s xml:id="echoid-s1615" xml:space="preserve">12, che ſono dall’angolo retto fina al <lb/>caſamẽto, reſterãno ca. </s> <s xml:id="echoid-s1616" xml:space="preserve">26, bra. </s> <s xml:id="echoid-s1617" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1618" xml:space="preserve">6, pũ. </s> <s xml:id="echoid-s1619" xml:space="preserve">10, per lo lato op <lb/>poſito della prima parte; </s> <s xml:id="echoid-s1620" xml:space="preserve">Etvolẽdo il lato oppoſito della ſe <lb/>conda parte, ſi piglierà li due terzi delle tauole 600, che ſo <lb/>no tauole 400, & </s> <s xml:id="echoid-s1621" xml:space="preserve">400, ſi faranno in quarti di tauole che ſa-<lb/>ranno quarti di tauole 1600, i quali quarti 1600, ſi partiran <lb/>no per cauezzi 42, lunghezza, & </s> <s xml:id="echoid-s1622" xml:space="preserve">ne veniran cauezzi 38, <lb/>brac. </s> <s xml:id="echoid-s1623" xml:space="preserve">o, onc. </s> <s xml:id="echoid-s1624" xml:space="preserve">6, punti 10, & </s> <s xml:id="echoid-s1625" xml:space="preserve">tanto ſi raddoppiarà, che fa-<lb/>ranno cauezzi 76, brac. </s> <s xml:id="echoid-s1626" xml:space="preserve">1, onc. </s> <s xml:id="echoid-s1627" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s1628" xml:space="preserve">8, & </s> <s xml:id="echoid-s1629" xml:space="preserve">dei cau 76, <lb/>brac. </s> <s xml:id="echoid-s1630" xml:space="preserve">1, onc. </s> <s xml:id="echoid-s1631" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s1632" xml:space="preserve">8, ſi caueranno cauezzi 12, che ſono <lb/>dall’angoloretto, fina al caſamento reſtaran cau. </s> <s xml:id="echoid-s1633" xml:space="preserve">64, bra. </s> <s xml:id="echoid-s1634" xml:space="preserve">1, <lb/>on. </s> <s xml:id="echoid-s1635" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s1636" xml:space="preserve">8, per il lato oppoſito per la prima, & </s> <s xml:id="echoid-s1637" xml:space="preserve">ſeconda par <lb/>te, & </s> <s xml:id="echoid-s1638" xml:space="preserve">per hauer il lato oppoſito della ſeconda parte, ſi caue-<lb/>rà cau. </s> <s xml:id="echoid-s1639" xml:space="preserve">26, bra, o, on. </s> <s xml:id="echoid-s1640" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1641" xml:space="preserve">10, che ſono per il lato oppoſi-<lb/>to della prima parte, da cau 64, brac. </s> <s xml:id="echoid-s1642" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1643" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s1644" xml:space="preserve">8, reſterà <lb/>cau. </s> <s xml:id="echoid-s1645" xml:space="preserve">38, bra. </s> <s xml:id="echoid-s1646" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1647" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1648" xml:space="preserve">10, per il lato oppoſito della ſe-<lb/>conda parte; </s> <s xml:id="echoid-s1649" xml:space="preserve">come ſi vede nella Vndecima Figura.</s> <s xml:id="echoid-s1650" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1651" xml:space="preserve">Et ſe per caſo ſi voleſſe hauere li due lati oppoſiti, ouer <lb/>vno della terza parte; </s> <s xml:id="echoid-s1652" xml:space="preserve">perche queſto in due modi può occor <lb/>rere; </s> <s xml:id="echoid-s1653" xml:space="preserve">il primo che dal punto della fonte, ouer caſamento, <pb file="110" n="110" rhead="LIBRO"/> non ſi poteſſe paſſare per linea retta, che delli cau. </s> <s xml:id="echoid-s1654" xml:space="preserve">12, più <lb/>ò meno ſecondo la miſura, che s’è fatta fino al punto aſſe-<lb/>gnato, ouero ſi poteſſe paſſare con miſura, più oltra del pun <lb/>to aſſegnato per linea retta, come moſtra la figura Vndeci-<lb/>ma, che ſi pò paſſare per linea retta, con miſura di cau. </s> <s xml:id="echoid-s1655" xml:space="preserve">36; </s> <s xml:id="echoid-s1656" xml:space="preserve">in <lb/>queſto caſo volendo il lato oppoſito à ca. </s> <s xml:id="echoid-s1657" xml:space="preserve">36, ſi farà di tauo-<lb/>le 200, che ſono la terza parte di tauole 600, in quarti di <lb/>tauole, che ſaranno quarti di tauole 800, & </s> <s xml:id="echoid-s1658" xml:space="preserve">quarti di tauo-<lb/>le 800, ſi partiranno per cau. </s> <s xml:id="echoid-s1659" xml:space="preserve">42, lunghezza, & </s> <s xml:id="echoid-s1660" xml:space="preserve">ne venirà ca <lb/>uezzi 19, bra. </s> <s xml:id="echoid-s1661" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1662" xml:space="preserve">3, pun. </s> <s xml:id="echoid-s1663" xml:space="preserve">5. </s> <s xml:id="echoid-s1664" xml:space="preserve">& </s> <s xml:id="echoid-s1665" xml:space="preserve">cau. </s> <s xml:id="echoid-s1666" xml:space="preserve">19, bra. </s> <s xml:id="echoid-s1667" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1668" xml:space="preserve">3, pun. </s> <s xml:id="echoid-s1669" xml:space="preserve">5 <lb/>ſi raddoppieranno facendo cau. </s> <s xml:id="echoid-s1670" xml:space="preserve">38, bra. </s> <s xml:id="echoid-s1671" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1672" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1673" xml:space="preserve">10, & </s> <s xml:id="echoid-s1674" xml:space="preserve"><lb/>de’cau. </s> <s xml:id="echoid-s1675" xml:space="preserve">38. </s> <s xml:id="echoid-s1676" xml:space="preserve">bra. </s> <s xml:id="echoid-s1677" xml:space="preserve">o, on 6, pun. </s> <s xml:id="echoid-s1678" xml:space="preserve">10, ſicaueran cauezzi 36, & </s> <s xml:id="echoid-s1679" xml:space="preserve">re <lb/>ſteran cau. </s> <s xml:id="echoid-s1680" xml:space="preserve">2, bra. </s> <s xml:id="echoid-s1681" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1682" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1683" xml:space="preserve">10, & </s> <s xml:id="echoid-s1684" xml:space="preserve">tanto ſarà il lato oppo <lb/>ſito di cau. </s> <s xml:id="echoid-s1685" xml:space="preserve">36, come moſtra la figura Vndecima.</s> <s xml:id="echoid-s1686" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1687" xml:space="preserve">Et quan do non ſi poteſſe paſſare al punto aſſegnato; </s> <s xml:id="echoid-s1688" xml:space="preserve">ſi fa <lb/>rà in queſto modo; </s> <s xml:id="echoid-s1689" xml:space="preserve">ſi ridurranno le tauole 600, tutte à quar <lb/>ti di lauole, & </s> <s xml:id="echoid-s1690" xml:space="preserve">faranno quarti di tauole 2400, & </s> <s xml:id="echoid-s1691" xml:space="preserve">i quarti <lb/>2400, ſi partiranno per cauez. </s> <s xml:id="echoid-s1692" xml:space="preserve">42, lunghezza, & </s> <s xml:id="echoid-s1693" xml:space="preserve">ne venirà <lb/>cau. </s> <s xml:id="echoid-s1694" xml:space="preserve">57, brac. </s> <s xml:id="echoid-s1695" xml:space="preserve">0, on. </s> <s xml:id="echoid-s1696" xml:space="preserve">10, pun. </s> <s xml:id="echoid-s1697" xml:space="preserve">3, & </s> <s xml:id="echoid-s1698" xml:space="preserve">cau. </s> <s xml:id="echoid-s1699" xml:space="preserve">57, brac. </s> <s xml:id="echoid-s1700" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1701" xml:space="preserve">10, <lb/>pun. </s> <s xml:id="echoid-s1702" xml:space="preserve">3, ſi raddoppiaranno facendone cau. </s> <s xml:id="echoid-s1703" xml:space="preserve">114, bra. </s> <s xml:id="echoid-s1704" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1705" xml:space="preserve">8, <lb/>pun. </s> <s xml:id="echoid-s1706" xml:space="preserve">6; </s> <s xml:id="echoid-s1707" xml:space="preserve">& </s> <s xml:id="echoid-s1708" xml:space="preserve">de’ cau. </s> <s xml:id="echoid-s1709" xml:space="preserve">114, bra. </s> <s xml:id="echoid-s1710" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1711" xml:space="preserve">8, pun. </s> <s xml:id="echoid-s1712" xml:space="preserve">6, ſi caueran cauez. <lb/></s> <s xml:id="echoid-s1713" xml:space="preserve">12, che ſono li cau. </s> <s xml:id="echoid-s1714" xml:space="preserve">ſegnati dall’angolo retto, fina al punto <lb/>aſſegnato, reſteran cau. </s> <s xml:id="echoid-s1715" xml:space="preserve">102, bra. </s> <s xml:id="echoid-s1716" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1717" xml:space="preserve">8, pun. </s> <s xml:id="echoid-s1718" xml:space="preserve">6, & </s> <s xml:id="echoid-s1719" xml:space="preserve">de’ cau. </s> <s xml:id="echoid-s1720" xml:space="preserve"><lb/>102, bra. </s> <s xml:id="echoid-s1721" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1722" xml:space="preserve">8, pũ. </s> <s xml:id="echoid-s1723" xml:space="preserve">6, ſi cauerã ca. </s> <s xml:id="echoid-s1724" xml:space="preserve">64, bra. </s> <s xml:id="echoid-s1725" xml:space="preserve">1, on. </s> <s xml:id="echoid-s1726" xml:space="preserve">1, pũ. </s> <s xml:id="echoid-s1727" xml:space="preserve">8, che <lb/>ſono cau. </s> <s xml:id="echoid-s1728" xml:space="preserve">26, bra. </s> <s xml:id="echoid-s1729" xml:space="preserve">0, on. </s> <s xml:id="echoid-s1730" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1731" xml:space="preserve">10, & </s> <s xml:id="echoid-s1732" xml:space="preserve">cau. </s> <s xml:id="echoid-s1733" xml:space="preserve">38, brac. </s> <s xml:id="echoid-s1734" xml:space="preserve">0, on. </s> <s xml:id="echoid-s1735" xml:space="preserve">6, <lb/>pun. </s> <s xml:id="echoid-s1736" xml:space="preserve">10, reſteran cau. </s> <s xml:id="echoid-s1737" xml:space="preserve">38, bra. </s> <s xml:id="echoid-s1738" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1739" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1740" xml:space="preserve">10. </s> <s xml:id="echoid-s1741" xml:space="preserve">Ma queſto <lb/>ſi può anco fare con magior preſtezza in queſto modo, pi-<lb/>gliando la terza parte di tauole 600, che ſono tauole 200, <lb/>& </s> <s xml:id="echoid-s1742" xml:space="preserve">le tauole 200, farle in quarti di tauole, che faranno quar-<lb/>ti di tauole 800, & </s> <s xml:id="echoid-s1743" xml:space="preserve">quarti di tauole 800, ſi partiran ꝑ cau. </s> <s xml:id="echoid-s1744" xml:space="preserve">42 <lb/>lunghezza, & </s> <s xml:id="echoid-s1745" xml:space="preserve">ne ueniran cau. </s> <s xml:id="echoid-s1746" xml:space="preserve">19, bra. </s> <s xml:id="echoid-s1747" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1748" xml:space="preserve">3, pun. </s> <s xml:id="echoid-s1749" xml:space="preserve">5, & </s> <s xml:id="echoid-s1750" xml:space="preserve">ca-<lb/>uezzi 19, bra. </s> <s xml:id="echoid-s1751" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1752" xml:space="preserve">3, pun. </s> <s xml:id="echoid-s1753" xml:space="preserve">5, ſi raddoppieranno facendo ca <lb/>uezzi 38, bra. </s> <s xml:id="echoid-s1754" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1755" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1756" xml:space="preserve">10, & </s> <s xml:id="echoid-s1757" xml:space="preserve">de’ cau. </s> <s xml:id="echoid-s1758" xml:space="preserve">38, brac. </s> <s xml:id="echoid-s1759" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1760" xml:space="preserve">6, <lb/>pun. </s> <s xml:id="echoid-s1761" xml:space="preserve">10, non gli eſſendo coſa alcuna da cauare, ſaran pur <pb o="51" file="111" n="111" rhead="PRIMO"/> cau. </s> <s xml:id="echoid-s1762" xml:space="preserve">38, bra. </s> <s xml:id="echoid-s1763" xml:space="preserve">o, on. </s> <s xml:id="echoid-s1764" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1765" xml:space="preserve">10, come di ſopra, & </s> <s xml:id="echoid-s1766" xml:space="preserve">come ancora <lb/>qui ſeguente ſi vede nella duodecima Figura.</s> <s xml:id="echoid-s1767" xml:space="preserve"/> </p> <figure> <image file="111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/111-01"/> <caption xml:id="echoid-caption31" xml:space="preserve">Duodecima Figura.</caption> </figure> <p> <s xml:id="echoid-s1768" xml:space="preserve">Auuertendo, che volendo far le ſopradette diuiſioni; </s> <s xml:id="echoid-s1769" xml:space="preserve">ſi <lb/>farà prima li due angoliretti, con le due linee equidiſtanti, <lb/>ouer paralelli, & </s> <s xml:id="echoid-s1770" xml:space="preserve">facendo tal operatione, s’anderà cauando <lb/>la ſuperficie del terreno che fa panza contingentealle par-<lb/>ti, da eſſe parti; </s> <s xml:id="echoid-s1771" xml:space="preserve">& </s> <s xml:id="echoid-s1772" xml:space="preserve">poiſi ſeguirà l’ordine dato di ſopra.</s> <s xml:id="echoid-s1773" xml:space="preserve"/> </p> <pb file="112" n="112" rhead="LIBRO"/> <figure> <image file="112-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/112-01"/> <caption xml:id="echoid-caption32" xml:space="preserve">Decimaterza Figura.</caption> </figure> <p> <s xml:id="echoid-s1774" xml:space="preserve">Siano due confinanti, iquali hãno terreni che confinano <lb/>inſieme, come ſi vede nella Figura <emph style="sc">ABCDEF</emph>, & </s> <s xml:id="echoid-s1775" xml:space="preserve">che la linea <lb/>del termine <emph style="sc">BC</emph>, della figura, ſia cauezzi 12, quella del <emph style="sc">D E</emph>, <lb/>cau. </s> <s xml:id="echoid-s1776" xml:space="preserve">8, & </s> <s xml:id="echoid-s1777" xml:space="preserve">quella del <emph style="sc">D C</emph>, ſia cau. </s> <s xml:id="echoid-s1778" xml:space="preserve">6, vorrebbon tirare vna li<unsure/> <lb/>nea che tagliaſſe la linea <emph style="sc">D C</emph>, talmẽte proportionabile, che <lb/>ſia equidiſtante alle due linee <emph style="sc">B C</emph>, & </s> <s xml:id="echoid-s1779" xml:space="preserve"><emph style="sc">D E</emph>; </s> <s xml:id="echoid-s1780" xml:space="preserve">& </s> <s xml:id="echoid-s1781" xml:space="preserve">queſta tallinea <lb/>ſia termine dell’uno, & </s> <s xml:id="echoid-s1782" xml:space="preserve">dell’altro; </s> <s xml:id="echoid-s1783" xml:space="preserve">come ſi vede nella figura <lb/><emph style="sc">G H I K L M</emph>;</s> <s xml:id="echoid-s1784" xml:space="preserve"/> </p> <figure> <image file="112-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/112-02"/> <caption xml:id="echoid-caption33" xml:space="preserve">Decimaquarta Figura.</caption> </figure> <p> <s xml:id="echoid-s1785" xml:space="preserve">La linea equidiſtante alle due linee <emph style="sc">H I</emph>, & </s> <s xml:id="echoid-s1786" xml:space="preserve"><emph style="sc">K L</emph>, ta-<lb/>glia la linea proportionale <emph style="sc">K I</emph>, che viene ancora la ſuperfi-<lb/>cie <emph style="sc">H N I O</emph>, è vguale alla ſuperſicie <emph style="sc">O K P L</emph>; </s> <s xml:id="echoid-s1787" xml:space="preserve">coſila ſuperficie <lb/>del terreno <emph style="sc">H N I O</emph>, viene à ſoprabondare la ſuperficie <emph style="sc">O K</emph> <lb/><emph style="sc">P L</emph>, del terreno dell’altro, perche le due ſuperficij ſono vgua <lb/>li, come qui ſotto ſi moſtrerà; </s> <s xml:id="echoid-s1788" xml:space="preserve">ſi farà dunque l’angolo <emph style="sc">H I K L</emph>, <pb o="52" file="113" n="113" rhead="PRIMO."/> retto conlo ſquadro & </s> <s xml:id="echoid-s1789" xml:space="preserve">le tre linee <emph style="sc">H G</emph>, & </s> <s xml:id="echoid-s1790" xml:space="preserve"><emph style="sc">I K</emph>, & </s> <s xml:id="echoid-s1791" xml:space="preserve">la <emph style="sc">M L</emph>, ſi fa <lb/>ranno vguali; </s> <s xml:id="echoid-s1792" xml:space="preserve">poi dal punto <emph style="sc">M</emph>, al punto <emph style="sc">G</emph>, ſi tirerà vna li-<lb/>nea retta, & </s> <s xml:id="echoid-s1793" xml:space="preserve">compirà la figura, & </s> <s xml:id="echoid-s1794" xml:space="preserve">dal punto <emph style="sc">O</emph>, ſi tirerà vna <lb/>equidiſtante alla linea <emph style="sc">H I</emph>, & </s> <s xml:id="echoid-s1795" xml:space="preserve">s’ella ſarà equidiſtante alla <lb/><emph style="sc">H I</emph>, ancor ſarà equidiſtante alla <emph style="sc">K L</emph>; </s> <s xml:id="echoid-s1796" xml:space="preserve">& </s> <s xml:id="echoid-s1797" xml:space="preserve">ſarà la Figura <emph style="sc">H G M L</emph>, <lb/> <anchor type="figure" xlink:label="fig-113-01a" xlink:href="fig-113-01"/> perchei due ſupplimenti vengono ad eſſere vguali, cioè la ſuperficie <emph style="sc">H N C O</emph>, & </s> <s xml:id="echoid-s1798" xml:space="preserve"><emph style="sc">O D E L</emph>; </s> <s xml:id="echoid-s1799" xml:space="preserve">come moſtra Euclide nella qua ranteſima propoſitione del ſuo primo libro, & </s> <s xml:id="echoid-s1800" xml:space="preserve">volendo di- uidere la linea <emph style="sc">D C</emph>, ch’è cauezzi 6, in due parti proportio- nali, che moltiplicato vna parte con la lunghezza della li- nea <emph style="sc">B C</emph>, ch’è cauezzi 12, & </s> <s xml:id="echoid-s1801" xml:space="preserve">l’altra parte moltiplicata conla linea <emph style="sc">D E</emph>, ch’è cauezzi 8, faccia tanto vna ſuperficie quanto l’altra; </s> <s xml:id="echoid-s1802" xml:space="preserve">in due modi ſi potrà fare; </s> <s xml:id="echoid-s1803" xml:space="preserve">l’uno per la regola della co ſa, & </s> <s xml:id="echoid-s1804" xml:space="preserve">l’altra perle poſitioni falſe: </s> <s xml:id="echoid-s1805" xml:space="preserve">come qui ſotto ſi potrà ve dere.</s> <s xml:id="echoid-s1806" xml:space="preserve"/> </p> <div xml:id="echoid-div63" type="float" level="2" n="1"> <figure xlink:label="fig-113-01" xlink:href="fig-113-01a"> <image file="113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/113-01"/> <caption xml:id="echoid-caption34" xml:space="preserve">Decimaquinta Figura.</caption> </figure> </div> <pb file="114" n="114" rhead="LIBRO"/> <p> <s xml:id="echoid-s1807" xml:space="preserve">Horvolendo diuidere cauezzi 6, in due parti proportio-<lb/>nali, che tanto faccia vna parte à moltiplicarla con cauezzi <lb/>12, come l’altra à moltiplicarla per 8; </s> <s xml:id="echoid-s1808" xml:space="preserve">prima ſi ſoluerà per la <lb/>regola della coſa in queſto modo; </s> <s xml:id="echoid-s1809" xml:space="preserve">ponendo che vna parte ſia <lb/>vna coſa l’altra ſarà 6, men 1, coſa; </s> <s xml:id="echoid-s1810" xml:space="preserve">poi ſimoltiplicarà 1, coſa <lb/>con 12, farà 12, coſe, & </s> <s xml:id="echoid-s1811" xml:space="preserve">moltiplicando 6, men 1, coſa, con <lb/>8, faranno 48, men 8, coſe; </s> <s xml:id="echoid-s1812" xml:space="preserve">ſi ſommerà le coſe inſieme fa-<lb/>ranno 20, coſe; </s> <s xml:id="echoid-s1813" xml:space="preserve">& </s> <s xml:id="echoid-s1814" xml:space="preserve">48, ſipartirà per 20, coſe, & </s> <s xml:id="echoid-s1815" xml:space="preserve">ne venirà 2, e <lb/>doi quinti, & </s> <s xml:id="echoid-s1816" xml:space="preserve">2, e doi quinti, ſarà vna parte; </s> <s xml:id="echoid-s1817" xml:space="preserve">& </s> <s xml:id="echoid-s1818" xml:space="preserve">l’altra, ſarà 3, <lb/>e tre quinti, che moltiplicando 2, e doi quinti, con 12, farà <lb/>28, e quattro quinti; </s> <s xml:id="echoid-s1819" xml:space="preserve">anchor moltiplicando 3, e tre quinti <lb/>con 8, farà più 28, e quattro quinti, che ſarà l’un come l’al-<lb/>tro.</s> <s xml:id="echoid-s1820" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1821" xml:space="preserve">Et volendo diuidere 6, in due parti proportionali, come <lb/>diſopra, per la regola delle poſitio-<lb/> <anchor type="figure" xlink:label="fig-114-01a" xlink:href="fig-114-01"/> ni falſe; </s> <s xml:id="echoid-s1822" xml:space="preserve">ſi ponerà come qui ſi ve-<lb/>de, che per la prima poſitione, ne <lb/>viene meno 8, & </s> <s xml:id="echoid-s1823" xml:space="preserve">per la ſecondane <lb/>viene più 12; </s> <s xml:id="echoid-s1824" xml:space="preserve">che ſommati inſieme <lb/>fanno 20, & </s> <s xml:id="echoid-s1825" xml:space="preserve">20, ſarà partitore; </s> <s xml:id="echoid-s1826" xml:space="preserve">poi ſi moltiplicarà 2, con <lb/>12, farà 24, & </s> <s xml:id="echoid-s1827" xml:space="preserve">3, con 8, farà pur 24, che ſommati inſieme <lb/>fanno 48, & </s> <s xml:id="echoid-s1828" xml:space="preserve">48, ſi partirà per 20, & </s> <s xml:id="echoid-s1829" xml:space="preserve">ne venirà 2, e doi quinti <lb/>per vna parte; </s> <s xml:id="echoid-s1830" xml:space="preserve">& </s> <s xml:id="echoid-s1831" xml:space="preserve">l’altra, ſarà 3, e tre quinti, come di ſopra.</s> <s xml:id="echoid-s1832" xml:space="preserve"/> </p> <div xml:id="echoid-div64" type="float" level="2" n="2"> <figure xlink:label="fig-114-01" xlink:href="fig-114-01a"> <image file="114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/114-01"/> </figure> </div> <p> <s xml:id="echoid-s1833" xml:space="preserve">Detto eſſendoſi del diuider le figure quadrilatere; </s> <s xml:id="echoid-s1834" xml:space="preserve">ſi dirà <lb/>hora del diuidere li triangoli, coſi peril trauerſo; </s> <s xml:id="echoid-s1835" xml:space="preserve">come per <lb/>l’altezza.</s> <s xml:id="echoid-s1836" xml:space="preserve"/> </p> <pb o="53" file="115" n="115" rhead="PRIMO"/> <figure> <image file="115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/115-01"/> <caption xml:id="echoid-caption35" xml:space="preserve">Decimaſeſta Figura.</caption> </figure> <p> <s xml:id="echoid-s1837" xml:space="preserve">Sia adunque il triangolo della Figura decimaſeſta da <lb/>diuider perl’alto, cioè dal vertice <emph style="sc">B</emph>, alla Baſe <emph style="sc">A C</emph>, in tre par <lb/>ti vguali, & </s> <s xml:id="echoid-s1838" xml:space="preserve">pongo che la Baſe <emph style="sc">A C</emph>, ſia cauezzi 14, & </s> <s xml:id="echoid-s1839" xml:space="preserve">illa-<lb/>to <emph style="sc">A B</emph>, cauezzi 15, & </s> <s xml:id="echoid-s1840" xml:space="preserve">illato <emph style="sc">B C</emph>, cauezzi 13; </s> <s xml:id="echoid-s1841" xml:space="preserve">& </s> <s xml:id="echoid-s1842" xml:space="preserve">volendo-<lb/>lo diuidere dall’alto al baſſo, in tre partivguali, altro n on <lb/>ſi deue fare, che diuidere la Baſe <emph style="sc">A C</emph>, ehe è cauezzi 14, in <lb/>tre parti vguali, che ſarà per ogni parte cauezzi 4, e doi ter-<lb/>zi; </s> <s xml:id="echoid-s1843" xml:space="preserve">& </s> <s xml:id="echoid-s1844" xml:space="preserve">ſarà diuiſo il triangolo <emph style="sc">A B C</emph>, in tre parti vguali; </s> <s xml:id="echoid-s1845" xml:space="preserve">co-<lb/>me moſtra la prima propoſitione del ſeſto di Euclide, & </s> <s xml:id="echoid-s1846" xml:space="preserve">co <lb/>me ſi vede il triangolo <emph style="sc">D E F</emph>, diuiſo nella Baſe <emph style="sc">E F</emph>, in pun-<lb/>to <emph style="sc">G</emph>, & </s> <s xml:id="echoid-s1847" xml:space="preserve"><emph style="sc">H</emph>,</s> </p> <pb file="116" n="116" rhead="LIBRO"/> <figure> <image file="116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/116-01"/> <caption xml:id="echoid-caption36" xml:space="preserve">Decimaſettima Figura.</caption> </figure> <p> <s xml:id="echoid-s1848" xml:space="preserve">Et volendo diuidere il ſopradetto triangolo per il tra-<lb/>uerſo della Decimaſettima Figura, ponendo come di ſo-<lb/>pra di volerlo diuidere in tre parti vguali: </s> <s xml:id="echoid-s1849" xml:space="preserve">tale operation <lb/>in tre modi ſi potrà fare.</s> <s xml:id="echoid-s1850" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1851" xml:space="preserve">Il primo modo è, ſi pigliarà la terza parte d’un lato, & </s> <s xml:id="echoid-s1852" xml:space="preserve">pon <lb/>go di pigliare la terza parte del lato <emph style="sc">D E</emph>, che ſarà 5, & </s> <s xml:id="echoid-s1853" xml:space="preserve">5, <lb/>moltiplicarlo collato, cioè con 15, farà 75, & </s> <s xml:id="echoid-s1854" xml:space="preserve">la radice di <lb/>75, ſarà il lato del triangolo, che ſarà la terza parte del trian <lb/>golo <emph style="sc">D E F</emph>, che pigliando vna linea, che ſia la radice de 75, <lb/>dallato <emph style="sc">D E</emph>, cominciando dal punto <emph style="sc">E</emph>, vertice del triango-<lb/>lo <emph style="sc">D E F</emph>, & </s> <s xml:id="echoid-s1855" xml:space="preserve">doue finiſce tirare vna equidiſtāte alla Baſe <emph style="sc">D F</emph>, <pb o="54" file="117" n="117" rhead="PRIMO"/> & </s> <s xml:id="echoid-s1856" xml:space="preserve">quella linea debba tagliare la terza parte del triangolo <lb/><emph style="sc">D E F</emph>, verſo il vertice, come moſtra il triangolo <emph style="sc">D E F</emph>, ta-<lb/>gliato dalla linea <emph style="sc">G H</emph>, & </s> <s xml:id="echoid-s1857" xml:space="preserve">il triangolo <emph style="sc">G E H</emph>, ſarà la terza par-<lb/>te del triangolo <emph style="sc">D E F</emph>,</s> </p> <figure> <image file="117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/117-01"/> <caption xml:id="echoid-caption37" xml:space="preserve">Decima ottaua Figura.</caption> </figure> <p> <s xml:id="echoid-s1858" xml:space="preserve">Il ſecondo modo è, che ſi potrà moltiplicare il lato <emph style="sc">D E</emph>, <lb/>ch’è 15, in ſe farà 225, & </s> <s xml:id="echoid-s1859" xml:space="preserve">di 225, ſi piglierà la terza parte, <lb/>che ſarà la radice 75, che ſarà come di ſopra.</s> <s xml:id="echoid-s1860" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1861" xml:space="preserve">Il terzo modo è queſto, & </s> <s xml:id="echoid-s1862" xml:space="preserve">ſi potrà fare Geometricamen <lb/>te, cioè, trouando due linee, l’una ſia tre volte tanto, come <lb/>l’altra, che la maggiore ſia la prima, la minore la ſeconda, & </s> <s xml:id="echoid-s1863" xml:space="preserve"><lb/>vn de’lati la terza, & </s> <s xml:id="echoid-s1864" xml:space="preserve">trouare la quarta proportionale, co-<lb/>me inſegna l’undecima propoſitione del ſeſto di Euclide; <lb/></s> <s xml:id="echoid-s1865" xml:space="preserve">& </s> <s xml:id="echoid-s1866" xml:space="preserve">come qui ſotto ſi vede, nella figura, ouero triangolo <emph style="sc">B A C</emph>, <pb file="118" n="118" rhead="LIBRO"/> <anchor type="figure" xlink:label="fig-118-01a" xlink:href="fig-118-01"/> che la linea maggiore ſia <emph style="sc">A D</emph>, & </s> <s xml:id="echoid-s1867" xml:space="preserve">la minore <emph style="sc">D E</emph>, il lato del triangolo <emph style="sc">A F</emph>, la quarta proportionale è la linea <emph style="sc">F G</emph>; </s> <s xml:id="echoid-s1868" xml:space="preserve">& </s> <s xml:id="echoid-s1869" xml:space="preserve">fra le due linee <emph style="sc">A F</emph>, & </s> <s xml:id="echoid-s1870" xml:space="preserve"><emph style="sc">F G</emph>, ſi trouarà vna media proportionale, come inſegna la nona propoſitione del ſeſto di Eu clide; </s> <s xml:id="echoid-s1871" xml:space="preserve">&</s> <s xml:id="echoid-s1872" xml:space="preserve"> quella media proportionale ſarà il lato del triangolo, della terza parte del triangolo <emph style="sc">D E F</emph>, come di ſopra; </s> <s xml:id="echoid-s1873" xml:space="preserve">& </s> <s xml:id="echoid-s1874" xml:space="preserve">queſta tal operatione ſeruirà à creſcere, ouer ſminuire, qualunque al tra ſuperficie; </s> <s xml:id="echoid-s1875" xml:space="preserve">come nel mio libro delle fortezze ſi è mo- ſtrato.</s> <s xml:id="echoid-s1876" xml:space="preserve"/> </p> <div xml:id="echoid-div65" type="float" level="2" n="3"> <figure xlink:label="fig-118-01" xlink:href="fig-118-01a"> <image file="118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/118-01"/> <caption xml:id="echoid-caption38" xml:space="preserve">Decimanona Figura.</caption> </figure> </div> <pb o="55" file="119" n="119" rhead="PRIMO."/> </div> <div xml:id="echoid-div67" type="section" level="1" n="56"> <head xml:id="echoid-head75" xml:space="preserve">REGOLA DI SAPER PROPORTIONARE <lb/>la miſura, & la differenza, ch’è il miſurare vna ſu-<lb/>perficie di terra tra il Breſciano, <lb/>& Bergamaſco.</head> <p> <s xml:id="echoid-s1877" xml:space="preserve"><emph style="sc">La</emph> differenza della ſuperficie, che fà co’l miſurare del <lb/>cauezzo Breſciano al Bergamaſco le terre, eſſendo il ca-<lb/>uezzo Breſciano braccie 6 e mezzo, del Bergamaſco, ouero <lb/>il cauezzo Bergamaſco, ſiè brac. </s> <s xml:id="echoid-s1878" xml:space="preserve">5, oncie 6, & </s> <s xml:id="echoid-s1879" xml:space="preserve">delle tredeci <lb/>parti le ſei d’vn’oncia del Breſciano, come à carte 10, nel-<lb/>la ſeconda faccia s’è detto; </s> <s xml:id="echoid-s1880" xml:space="preserve">& </s> <s xml:id="echoid-s1881" xml:space="preserve">volendo vedere la differenza <lb/>della ſuperficie, che fà vn cauezzo longo, & </s> <s xml:id="echoid-s1882" xml:space="preserve">largo del Bre-<lb/>ſciano, & </s> <s xml:id="echoid-s1883" xml:space="preserve">Bergamaſco, ſi moltiplicarà in ſebrac. </s> <s xml:id="echoid-s1884" xml:space="preserve">5, on. </s> <s xml:id="echoid-s1885" xml:space="preserve">6, & </s> <s xml:id="echoid-s1886" xml:space="preserve"><lb/>delle tredeci parti d’un’oncia le ſei, che la lunghezza del ca <lb/>uezzo Bergamaſco, alla miſura del cau. </s> <s xml:id="echoid-s1887" xml:space="preserve">Breſciano, faranno <lb/>piedi 2, on. </s> <s xml:id="echoid-s1888" xml:space="preserve">6, punti 7, & </s> <s xml:id="echoid-s1889" xml:space="preserve">atomi 8, ſuperficiali; </s> <s xml:id="echoid-s1890" xml:space="preserve">& </s> <s xml:id="echoid-s1891" xml:space="preserve">tanto ſarà <lb/>vn quarto ditauola Bergamaſco & </s> <s xml:id="echoid-s1892" xml:space="preserve">vn cauezzo longo, & </s> <s xml:id="echoid-s1893" xml:space="preserve">vn <lb/>largo Breſciano fà di ſuperficie piedi 3, che ſono vn quarto <lb/>ditauola Breſciano; </s> <s xml:id="echoid-s1894" xml:space="preserve">& </s> <s xml:id="echoid-s1895" xml:space="preserve">volendo vedere la differenza ch’è il <lb/>quarto di tauola Breſciano al Bergamaſco; </s> <s xml:id="echoid-s1896" xml:space="preserve">ſi cauerà piedi <lb/>2, on. </s> <s xml:id="echoid-s1897" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s1898" xml:space="preserve">7, ato. </s> <s xml:id="echoid-s1899" xml:space="preserve">8, da piedi 3, reſtarà on. </s> <s xml:id="echoid-s1900" xml:space="preserve">5, pun. </s> <s xml:id="echoid-s1901" xml:space="preserve">4, & </s> <s xml:id="echoid-s1902" xml:space="preserve">ato. <lb/></s> <s xml:id="echoid-s1903" xml:space="preserve">4; </s> <s xml:id="echoid-s1904" xml:space="preserve">& </s> <s xml:id="echoid-s1905" xml:space="preserve">tanto ſarà la differenza ch’è dal quarto di tauola Berga <lb/>maſco al Breſciano, cioè il quarto di tauola Breſciano è mag <lb/>giore del quarto di tauola Bergamaſco, on. </s> <s xml:id="echoid-s1906" xml:space="preserve">5, pun. </s> <s xml:id="echoid-s1907" xml:space="preserve">4, at. </s> <s xml:id="echoid-s1908" xml:space="preserve">4; </s> <s xml:id="echoid-s1909" xml:space="preserve">& </s> <s xml:id="echoid-s1910" xml:space="preserve"><lb/>ſe ſi vorrà ſapere la differẽza della tauola Breſciana, à quel-<lb/>la Bergamaſca, ſi moltiplicarà on. </s> <s xml:id="echoid-s1911" xml:space="preserve">5, punti 4, & </s> <s xml:id="echoid-s1912" xml:space="preserve">atomi 4, per <lb/>quattro quarti di tauola, faranno piedi 1, on. </s> <s xml:id="echoid-s1913" xml:space="preserve">9, pun. </s> <s xml:id="echoid-s1914" xml:space="preserve">5, at. </s> <s xml:id="echoid-s1915" xml:space="preserve">4, <lb/>& </s> <s xml:id="echoid-s1916" xml:space="preserve">tanto ſarà di più, vna tauola Breſciana à vna Bergamaſca; </s> <s xml:id="echoid-s1917" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s1918" xml:space="preserve">ſe ſi vorrà ſapere quanto è di più vna pertica Breſciana, <lb/>à quella Bergamaſca, ſi moltiplicarà piedi 1, on. </s> <s xml:id="echoid-s1919" xml:space="preserve">9, punti 5, <lb/>atomi 4, per 24, tauole, ch’è vna pertica Bergamaſca, faran-<lb/>no tauole 3, piedi 6, on. </s> <s xml:id="echoid-s1920" xml:space="preserve">10, punti 8, & </s> <s xml:id="echoid-s1921" xml:space="preserve">tanto ſarà la differen <lb/>za de tauole 24, Breſciane, à tauole 24, Bergamaſche; </s> <s xml:id="echoid-s1922" xml:space="preserve">& </s> <s xml:id="echoid-s1923" xml:space="preserve">per <lb/>che la pertica Breſciana ſiè tauole 25, ſi aggiongerà vna ta- <pb file="120" n="120" rhead="LIBRO"/> uola à tauole 3, piedi 6, on. </s> <s xml:id="echoid-s1924" xml:space="preserve">10, punti 8, faranno tauole 4, <lb/>piedi 6, on. </s> <s xml:id="echoid-s1925" xml:space="preserve">10, punti 8; </s> <s xml:id="echoid-s1926" xml:space="preserve">& </s> <s xml:id="echoid-s1927" xml:space="preserve">tanto ſarà la differenza d’una per <lb/>tica Breſciana, à quella Bergamaſca. </s> <s xml:id="echoid-s1928" xml:space="preserve">Et con queſta regola ſi <lb/>potrà proportionare ogni miſura, & </s> <s xml:id="echoid-s1929" xml:space="preserve">ſuperficie di terreno <lb/>d’ogn’altro paeſe.</s> <s xml:id="echoid-s1930" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div68" type="section" level="1" n="57"> <head xml:id="echoid-head76" xml:space="preserve">IL FINE.</head> <head xml:id="echoid-head77" xml:space="preserve">ERRORI OCCORSI.</head> <note position="right" xml:space="preserve"> <lb/>A carte 3. # faccia 2. # righe 5. # H I K D G E. # dica # H I K D G C <lb/>A car. 8. # faccia 2. # righe 1. # A G H # dica # A G B <lb/>A car. 10. # fac. 2. # righe 18. # 13 ſeſti, # dica # de 13 parti, 6. <lb/>A carte 11. # faccia 2. # righe 2. # anno # dica # fanno <lb/>A carte 15. # faccia 1. # righe 12. # d’angolo retto # dica # angolo retto <lb/>A carte 25. # # Figura quinta. # oncie 7 # dica # oncie 9. <lb/>A carte 26. # faccia 1. # righe 6. # A B # dica # B D <lb/>A carte 26. # faccia 1. # righe 16. # alla # dica # alle <lb/>A carte 26. # faccia 1. # righe 22. # oncie 7, # dica # oncie 9, <lb/>A carte 27. # faccia 1. # righe 3. # oncie 7, # dica # oncie 9, <lb/>A carte 27. # faccia 1. # righe 5. # oncie 3, # dica # oncie 5, <lb/>A carte 27. # faccia 2. # righe 12. # alla # dica # ad <lb/>A carte 28. # faccia 1. # righe 7. # che # dica # che ſi <lb/>A carte 31. # faccia 1. # righe 14. # all’angolo # dica # ad angolo <lb/>A carte 32. # faccia 2. # # # # # primo triangolo s’ha da immaginare c’habbi un \\ angolo ottuſo, & al ſecondo c’habbi un’angolo retto. <lb/>A carte 36. # faccia 1. # righe 12. # pie 5, on 4, # dica # pie 5, on. 3. <lb/>A carte 43. # faccia 1. # righe 2. # punti 12, # dica # punti 2, <lb/>A carte 45. # faccia 1. # righe 3. # # # ſi partiranno con on.<unsure/> 43200, # dica partiran- \\ no on. 43200. <lb/>A carte 52. # faccia 2 # righe 12. # piu # dica # pur <lb/></note> <pb file="121" n="121"/> <figure> <image file="121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/121-01"/> </figure> </div> <div xml:id="echoid-div69" type="section" level="1" n="58"> <head xml:id="echoid-head78" xml:space="preserve">IN BRESCIA, <lb/>APPRESSO FRANCESCO, ET PIE: MARIA <lb/>DI MARCHETTI FRATELLI. <lb/>M. D. LXXII.</head> <figure> <image file="121-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/121-02"/> </figure> <pb file="122" n="122"/> <pb file="123" n="123"/> </div> <div xml:id="echoid-div70" type="section" level="1" n="59"> <head xml:id="echoid-head79" xml:space="preserve">DEL MISVRARE <lb/>LE MVRAGLIE, <lb/>IMBOTTARE GRANI, VINI, FIENI, ET STRAMI, <lb/>COL LIVELLARE DELL’ACQVE, <lb/>& altre coſe neceſſarie à gli <lb/>Agrimenſori, <lb/>DI M. CIROLAMO CATANEO NOVARESE. <lb/>LIBRO SECONDO.</head> <figure> <image file="123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/123-01"/> </figure> </div> <div xml:id="echoid-div71" type="section" level="1" n="60"> <head xml:id="echoid-head80" xml:space="preserve">IN BRESCIA, <lb/>APPRESSO FRANCESCO, ET PIE: MARIA <lb/>DI MARCHETTI FRATELLI. <lb/>M. D. LXXII.</head> <pb file="124" n="124"/> <pb file="125" n="125"/> <figure> <image file="125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/125-01"/> </figure> </div> <div xml:id="echoid-div72" type="section" level="1" n="61"> <head xml:id="echoid-head81" xml:space="preserve">AL MAGNIFICO SIG. NICOLO’ <lb/>BARBOLLII, ALGISI, <lb/>ET GAIONCELLI. <lb/>SIG. MIO HONORANDISS.</head> <figure> <image file="125-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/125-02"/> </figure> <p style="it"> <s xml:id="echoid-s1931" xml:space="preserve">HAVENDO io ridotte ins <lb/>ſieme le regole del miſurare muri, <lb/>biade, uini, liuellar acque, & </s> <s xml:id="echoid-s1932" xml:space="preserve">al-<lb/>tre coſe ſimili, non prima ho deli-<lb/>berato di darle fuori, che di ſa-<lb/>crarle all’honorato nome di V. </s> <s xml:id="echoid-s1933" xml:space="preserve">S. <lb/></s> <s xml:id="echoid-s1934" xml:space="preserve">percioche quanto da l’un canto il deſiderio di giouare <lb/>a i profeſſori di questa arte mi moueua a darle alla <pb file="126" n="126"/> ſtampa: </s> <s xml:id="echoid-s1935" xml:space="preserve">tanto dall’altro per non dir più, le ſingolari <lb/>ſue qualità mi ſpronauano à farle uſcire ſotto la ſua <lb/>protettione, & </s> <s xml:id="echoid-s1936" xml:space="preserve">per laſciar da parte Pantico ſplendo= <lb/>re della famiglia ſua illustrata poſcia molto più dal= <lb/>Peſſercitio delle uirtù, maßimamente dell’arte milita-<lb/>re, nellaquale porta in ogni luoco titolo grande, maſ= <lb/>ſimamente preſſo queſti Illustriß<unsure/> noſtri Signori: </s> <s xml:id="echoid-s1937" xml:space="preserve">co= <lb/>me nella perſona del ualoroſi<unsure/>ßi<unsure/>mo Signor Capitano <lb/>il Signor Giacomo ſuo fratello può ogniuno chiara= <lb/>mente uedere, parmi in uerità, che P<unsure/>hauer V. </s> <s xml:id="echoid-s1938" xml:space="preserve">S: <lb/></s> <s xml:id="echoid-s1939" xml:space="preserve">con la profeßione dell’arme accompagnata oltra la <lb/>gentilißima creanza, il gusto di tutte le uirtù, & </s> <s xml:id="echoid-s1940" xml:space="preserve">la <lb/>diffeſa ch’ella inſieme con tutti gli altri Sig. </s> <s xml:id="echoid-s1941" xml:space="preserve">ſuoi fra= <lb/>telli tiene de’ uertuoſi, diano animo ad ogni uno di <lb/>raccomandarle le fatiche de gli honeſti ſuoi ſtudi. </s> <s xml:id="echoid-s1942" xml:space="preserve"><lb/>Da queſto dunque affidato anch’io le offeriſco que= <lb/>sta mia opera qual ella ſi ſia: </s> <s xml:id="echoid-s1943" xml:space="preserve">con animo ſicuro, che <lb/>ſe bene il ſuo penſiero non meno è<unsure/> ricetto di impreſe <lb/>grandi, che la caſa ſua de’ perſonaggi & </s> <s xml:id="echoid-s1944" xml:space="preserve">de’ Pren= <lb/>cipi: </s> <s xml:id="echoid-s1945" xml:space="preserve">non però ſi sdegnarà di dare & </s> <s xml:id="echoid-s1946" xml:space="preserve">all’opera, & </s> <s xml:id="echoid-s1947" xml:space="preserve"><lb/>all’authore, che ſempre uiuerà ſuo, un picciol luoco <lb/>della ſua gratia.</s> <s xml:id="echoid-s1948" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div73" type="section" level="1" n="62"> <head xml:id="echoid-head82" style="it" xml:space="preserve">Di Breſcia alli XV.<unsure/> Gennaro. M. D. LXXII. <lb/>Di Voſtra Sig.</head> <p style="it"> <s xml:id="echoid-s1949" xml:space="preserve">Ser. </s> <s xml:id="echoid-s1950" xml:space="preserve">Girolamo Cataneo</s> </p> <p style="it"> <s xml:id="echoid-s1951" xml:space="preserve">Nouareſe.</s> <s xml:id="echoid-s1952" xml:space="preserve"/> </p> <pb file="127" n="127"/> <figure> <image file="127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/127-01"/> </figure> </div> <div xml:id="echoid-div74" type="section" level="1" n="63"> <head xml:id="echoid-head83" xml:space="preserve">AILETTORI.</head> <p> <s xml:id="echoid-s1953" xml:space="preserve">GIA` molti meſi humaniſsimi Lettori, hauen-<lb/>do io poſto fine à queſta ſeconda parte della <lb/>Geometria prattica, del miſurar muragl e, <lb/>imbottar Biade, Vini, Fieni, & </s> <s xml:id="echoid-s1954" xml:space="preserve">altri ſtrami, <lb/>col liuellar le Acque, & </s> <s xml:id="echoid-s1955" xml:space="preserve">altre coſe neceſſa-<lb/>rie à gl’Agrimenſori; </s> <s xml:id="echoid-s1956" xml:space="preserve">& </s> <s xml:id="echoid-s1957" xml:space="preserve">eſſendo inſtato per <lb/>beneficio vniuerſale à farla imprimere, dubitaua facen-<lb/>do ciò ſenza gratificarne qualche perſona honorata & </s> <s xml:id="echoid-s1958" xml:space="preserve"><lb/>degna, di riportarne non poco di riprenſione. </s> <s xml:id="echoid-s1959" xml:space="preserve">Maecco <lb/>che mentre un giorno di queſto diſcorreſsi col mio giu-<lb/>dicioſo & </s> <s xml:id="echoid-s1960" xml:space="preserve">prudente M. </s> <s xml:id="echoid-s1961" xml:space="preserve">Giulio Todeſchini Architetto Bre-<lb/>ſciano intendentiſsimo, & </s> <s xml:id="echoid-s1962" xml:space="preserve">de tempi noſtri altro nouo Vi-<lb/>truuio, egli mi ricordò il gentiliſsimo, & </s> <s xml:id="echoid-s1963" xml:space="preserve">generoſo Signor <lb/>Nicolò Barboglio, Algiſi, & </s> <s xml:id="echoid-s1964" xml:space="preserve">Gaioncelli gentilhuomo di <lb/>Louere Magnifico & </s> <s xml:id="echoid-s1965" xml:space="preserve">magnanimo, inſieme co’l valoroſiſsi-<lb/>mo Capitano & </s> <s xml:id="echoid-s1966" xml:space="preserve">gli altri Signori ſuoi fratelli, veramente <lb/>ſpecchi di ogni maniera di vertù & </s> <s xml:id="echoid-s1967" xml:space="preserve">corteſia, à quali mi eſ-<lb/>ſortò & </s> <s xml:id="echoid-s1968" xml:space="preserve">perſuaſe à dedicarla & </s> <s xml:id="echoid-s1969" xml:space="preserve">farne dono; </s> <s xml:id="echoid-s1970" xml:space="preserve">Il che con mia <lb/>ſodisfattione & </s> <s xml:id="echoid-s1971" xml:space="preserve">ſomma contentezza ho eſſequito & </s> <s xml:id="echoid-s1972" xml:space="preserve">fatto. <lb/></s> <s xml:id="echoid-s1973" xml:space="preserve">La on de voi benigni lettori, accettarete queſte mie fatiche <lb/>con lieto animo, poi che ſolo holle fatte per giouare al mõ-<lb/>do, & </s> <s xml:id="echoid-s1974" xml:space="preserve">non per applauſo o<unsure/> gloria; </s> <s xml:id="echoid-s1975" xml:space="preserve">Valete.</s> <s xml:id="echoid-s1976" xml:space="preserve"/> </p> <pb o="1" file="128" n="128"/> </div> <div xml:id="echoid-div75" type="section" level="1" n="64"> <head xml:id="echoid-head84" xml:space="preserve">DEL MISVRARE <lb/>OGNI SORTE DI <lb/>MVRAGLIA.</head> <head xml:id="echoid-head85" xml:space="preserve">LIBRO SECONDO.</head> <p> <s xml:id="echoid-s1977" xml:space="preserve">L’<emph style="sc">Ordine</emph> che ſi deue tenere nel miſurarle <lb/>muraglie; </s> <s xml:id="echoid-s1978" xml:space="preserve">cominciando però dalle ſue rap-<lb/>preſentationi, quello ch’eſſe ſignificano.</s> <s xml:id="echoid-s1979" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1980" xml:space="preserve">Braccia fia Braccia fanno Braccia, nella prima <lb/>moltiplicatione, & </s> <s xml:id="echoid-s1981" xml:space="preserve">nella ſeconda quadretti.</s> <s xml:id="echoid-s1982" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1983" xml:space="preserve">Braccia fia oncie, fanno oncie.</s> <s xml:id="echoid-s1984" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1985" xml:space="preserve">Braccie fia punti, fanno punti.</s> <s xml:id="echoid-s1986" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1987" xml:space="preserve">Oncie fia oncie, fanno punti.</s> <s xml:id="echoid-s1988" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1989" xml:space="preserve">Oncie fia punti, fanno atomi.</s> <s xml:id="echoid-s1990" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1991" xml:space="preserve">Punti fia punti, fanno minuti.</s> <s xml:id="echoid-s1992" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>12, # Minuti fanno vn atomo. <lb/>12, # Atomi fanno vn punto. <lb/>12, # Punti fanno vn’oncia. <lb/>12, # Oncie fanno vn Braccio, ouer vn Quadretto. <lb/>36, # Quadretti fanno vna pertica di muro. <lb/>25, # Quadreti à miſura Venitiana, fanno vn paſſo. <lb/>30, # Quadrelli di preda cotta, cioè matoni, fanno vn qua- \\ dretto di muro, cioè vn braccio lungo, largo, & vn’alto. <lb/></note> <p> <s xml:id="echoid-s1993" xml:space="preserve">Hor volendo miſurare vn muro quadrangolare; </s> <s xml:id="echoid-s1994" xml:space="preserve">prima ſi <lb/>miſurerà la lunghezza, l’altezza, & </s> <s xml:id="echoid-s1995" xml:space="preserve">groſſezza; </s> <s xml:id="echoid-s1996" xml:space="preserve">Verbigratia, <lb/>egliè vn muro lungo brac. </s> <s xml:id="echoid-s1997" xml:space="preserve">37, on. </s> <s xml:id="echoid-s1998" xml:space="preserve">8, alto brac. </s> <s xml:id="echoid-s1999" xml:space="preserve">25, on. </s> <s xml:id="echoid-s2000" xml:space="preserve">6, & </s> <s xml:id="echoid-s2001" xml:space="preserve"><lb/>è groſſo braccia 1, on. </s> <s xml:id="echoid-s2002" xml:space="preserve">2; </s> <s xml:id="echoid-s2003" xml:space="preserve">dimando quante pertiche di mu-<lb/>ro ſono.</s> <s xml:id="echoid-s2004" xml:space="preserve"/> </p> <pb o="2" file="129" n="129" rhead="SECONDO."/> <p> <s xml:id="echoid-s2005" xml:space="preserve">Et per fare il ſopradetto conto, ſi concierà l’altezza, ſot-<lb/>to la lunghezza, ouer la lunghezza ſotto all’altezza, cioè il <lb/>numero minore ſotto al maggiore, come qui ſotto ſi vedrà; <lb/></s> <s xml:id="echoid-s2006" xml:space="preserve">poi ſi moltiplicarà, come nella ragione delle terre s’è detto; </s> <s xml:id="echoid-s2007" xml:space="preserve"><lb/>cioè ogni numero di ſotto, ſi moltiplicarà con tutti inume <lb/>ri di ſopra: </s> <s xml:id="echoid-s2008" xml:space="preserve">Ma però prima ſi ritrouerà la ſuperficie del muro, <lb/>moltiplicando la lunghezza con l’altezza; </s> <s xml:id="echoid-s2009" xml:space="preserve">fatto queſto ſi ri-<lb/>trouerà il corpo, moltiplican do la ſuperficie con la groſſez-<lb/>za; </s> <s xml:id="echoid-s2010" xml:space="preserve">come quiſotto il tutto ſi potrà vedere.</s> <s xml:id="echoid-s2011" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div76" type="section" level="1" n="65"> <head xml:id="echoid-head86" xml:space="preserve">PRIMA RAGIONE <lb/>della ſuperficie.</head> <note position="right" xml:space="preserve"> <lb/>Lungo Brac. # 37, # on. # 8,} # groſſo brac. 1, on. 2. <lb/>Alto Brac. # 25, # on. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Brac. # 925, <lb/>Brac. # 16, # on. # 8, <lb/>Brac. # 18, # on. # 6, <lb/>Brac. # 0, # on. # 4, <lb/>Brac. # 960, # on. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # onc. # 4 # 6 # pun. <lb/># onc. # 5 # 6 # pun. <lb/></note> <pb file="130" n="130" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># braccia # # # 37 <lb/># braccia # # # 25 <lb/># # # # 185 <lb/># # # # 74 <lb/>braccia # # # # 925 <lb/># brac. # # # 25 <lb/># oncie # # # 8 <lb/>oncie # # # # 200 <lb/># # partir per # 12 <lb/># brac. # 16, # on. # 8 <lb/></note> <note position="right" xml:space="preserve"> <lb/># brac. # # # 37 <lb/># oncie # # # 6 <lb/>oncie # # # # 222 <lb/># partir per # 12 <lb/># brac. 18, # on. # 6 <lb/># oncie # # # 8 <lb/># oncie # # # 6 <lb/>punti # # # # 48 <lb/># partir per # 12 <lb/># on. # # # 4 <lb/></note> </div> <div xml:id="echoid-div77" type="section" level="1" n="66"> <head xml:id="echoid-head87" xml:space="preserve">SECONDA RAGIONE</head> <head xml:id="echoid-head88" xml:space="preserve">della quantità del corpo della <lb/>prima ragione.</head> <note position="right" xml:space="preserve"> <lb/>Brac. # 960, # on. # 6, <lb/>groſſo brac. # 1, # on. # 2, <lb/>Quad. # 960, <lb/>Quad. # 0, # on. # 6, <lb/>Quad. # 160, <lb/>Quad. # 0, # on. # 1, <lb/>Quad. # 1120, # on. # 7, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # on. # 4, # 0, # pun. <lb/># # 0, # 0, # pun. <lb/></note> <pb o="3" file="131" n="131" rhead="SECONDO."/> <note position="right" xml:space="preserve"> <lb/># Brac. # 960 <lb/># groſſo brac. # 1 <lb/>Quadretti # # 960 <lb/># oncie # 6 <lb/># groſſo brac. # 1 <lb/>oncie # # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># brac. # 960 <lb/># oncie # 2 <lb/>oncie # # 1920 <lb/># partir per # 12 <lb/># quad. # 160 <lb/># on. # 6 <lb/># on. # 2 <lb/>punti # # 12 <lb/># partir per # 12 <lb/># oncie # 1 <lb/></note> <p> <s xml:id="echoid-s2012" xml:space="preserve">Et detti quadretti 1120, ſi faranno in pertiche, partendo <lb/>quadretti 1120, per quadretti 36, ne venirà pertiche 31, <lb/>quadr. </s> <s xml:id="echoid-s2013" xml:space="preserve">4, on. </s> <s xml:id="echoid-s2014" xml:space="preserve">7; </s> <s xml:id="echoid-s2015" xml:space="preserve">& </s> <s xml:id="echoid-s2016" xml:space="preserve">tanto ſarà il ſopra detto muro.</s> <s xml:id="echoid-s2017" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2018" xml:space="preserve">Ancora ſi potran partire i quadretti 1120, due volte per <lb/>6, il primo auanzo ſaranno quadretti, il ſecondo ſeſti di per-<lb/>tica.</s> <s xml:id="echoid-s2019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2020" xml:space="preserve">Ancora ſi potran fare detti quadretti 1120, in paſsi, par-<lb/>tendo i qua dretti 1120, per quadretti 25, & </s> <s xml:id="echoid-s2021" xml:space="preserve">ne veniran <lb/>paſsi 44, quad. </s> <s xml:id="echoid-s2022" xml:space="preserve">20, & </s> <s xml:id="echoid-s2023" xml:space="preserve">ancor on. </s> <s xml:id="echoid-s2024" xml:space="preserve">7.</s> <s xml:id="echoid-s2025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2026" xml:space="preserve">Ancor ſi potrebbe far detti quadretti 1120, in paſsi, par <lb/>tendo quad. </s> <s xml:id="echoid-s2027" xml:space="preserve">1120, per due volte 5, & </s> <s xml:id="echoid-s2028" xml:space="preserve">nel primo partire quel <lb/>che auanza ſono quadretti, nel ſecondo ſono tanti quinti <lb/>di quadretti; </s> <s xml:id="echoid-s2029" xml:space="preserve">coſi parten do quadretti 1120, due volte per 5, <lb/>ne veniranno paf<unsure/>si 44, quad. </s> <s xml:id="echoid-s2030" xml:space="preserve">20, & </s> <s xml:id="echoid-s2031" xml:space="preserve">con le on. </s> <s xml:id="echoid-s2032" xml:space="preserve">7, fanno paſsi <lb/>44, quad. </s> <s xml:id="echoid-s2033" xml:space="preserve">20, on. </s> <s xml:id="echoid-s2034" xml:space="preserve">7, & </s> <s xml:id="echoid-s2035" xml:space="preserve">tanto ſarà il ſopradetto muro.</s> <s xml:id="echoid-s2036" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2037" xml:space="preserve">Et ſe per caſo ſi voleſſe ſapere quanti quadrelliſono in <lb/>quadretti 1120, ſi moltiplicarà quadretti 1120, per qua-<lb/>drelli 30, & </s> <s xml:id="echoid-s2038" xml:space="preserve">quello che venirà ſaranno tanti quadrelli, coſi <lb/>moltiplicando 30, con 1120, faranno quadrelli 33600.</s> <s xml:id="echoid-s2039" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2040" xml:space="preserve">Per vn’altro bel modo, ſecondo il coſtume de’ Paeſi ſi po <pb file="132" n="132" rhead="LIBRO"/> trà ſapere quanti quadrelli ſono in vn muro; </s> <s xml:id="echoid-s2041" xml:space="preserve">concioſia che <lb/>in vn quadretto di muro gli ſono teſte tre, & </s> <s xml:id="echoid-s2042" xml:space="preserve">in ogni teſta ſi <lb/>danno quadrelli diece, adunque ſe’l muro fuſſe groſſo vn <lb/>brac. </s> <s xml:id="echoid-s2043" xml:space="preserve">& </s> <s xml:id="echoid-s2044" xml:space="preserve">on. </s> <s xml:id="echoid-s2045" xml:space="preserve">2, ſarebbero teſte tre e mezza, che ſono qua-<lb/>drelli 35; </s> <s xml:id="echoid-s2046" xml:space="preserve">& </s> <s xml:id="echoid-s2047" xml:space="preserve">con quadrelli 35, ſi moltiplicherà la prima ſu-<lb/>perficie, & </s> <s xml:id="echoid-s2048" xml:space="preserve">pongo quella di ſopra, che ſia bracc. </s> <s xml:id="echoid-s2049" xml:space="preserve">960, on. </s> <s xml:id="echoid-s2050" xml:space="preserve">6, <lb/>& </s> <s xml:id="echoid-s2051" xml:space="preserve">coſi moltiplicando quadrelli 35, con brac. </s> <s xml:id="echoid-s2052" xml:space="preserve">960, faranno <lb/>quadrelli 33600, & </s> <s xml:id="echoid-s2053" xml:space="preserve">à quadrelli 33600, ſiaggiungerà la me-<lb/>tà de’ quadrelli 35, che ſono quadrelli 17 e mezzo, faran-<lb/>no quadrelli 33617 e mezzo, & </s> <s xml:id="echoid-s2054" xml:space="preserve">tanto ſarà di quadrelli nel <lb/>ſopradetto muro.</s> <s xml:id="echoid-s2055" xml:space="preserve"/> </p> <figure> <image file="132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/132-01"/> <caption xml:id="echoid-caption39" xml:space="preserve">Prima Figura.</caption> </figure> <p> <s xml:id="echoid-s2056" xml:space="preserve">Io mi ritrouo da miſurare vn muro à modo di triangolo <lb/><emph style="sc">A B C</emph>, come moſtra la Figura prima. </s> <s xml:id="echoid-s2057" xml:space="preserve">Et volendo ſapere, <lb/>quante pertiche, paſsi, ouer quadrelli ſaranno nel detto mu <pb o="4" file="133" n="133" rhead="SECONDO."/> ro a modo di triangolo; </s> <s xml:id="echoid-s2058" xml:space="preserve">ſi trouerà prima la ſupë<unsure/>rficie d’eſſo <lb/>triangolo, come nella ſuperficie de’ triangoli di terra s’è fat <lb/>to; </s> <s xml:id="echoid-s2059" xml:space="preserve">cioè ſapere la miſura della perpendicolare, & </s> <s xml:id="echoid-s2060" xml:space="preserve">della Baſe <lb/>d’eſſo triangolo; </s> <s xml:id="echoid-s2061" xml:space="preserve">& </s> <s xml:id="echoid-s2062" xml:space="preserve">per hauere eſſa perpendicolare, ſi torrà <lb/>vn riforcino, & </s> <s xml:id="echoid-s2063" xml:space="preserve">quello ſi laſcierà cadere a piombo dall’an-<lb/>golo ſuperiore, cioè dal punto <emph style="sc">B</emph>, doue ſega eſſa Baſe il re-<lb/>forzino, & </s> <s xml:id="echoid-s2064" xml:space="preserve">pono che ſega in punto <emph style="sc">D</emph>, come qui ſotto ſi ve-<lb/>de nel triangolo <emph style="sc">A B C</emph>, nella Figura ſeconda.</s> <s xml:id="echoid-s2065" xml:space="preserve"/> </p> <figure> <image file="133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/133-01"/> <caption xml:id="echoid-caption40" xml:space="preserve">Seconda Figura.</caption> </figure> <p> <s xml:id="echoid-s2066" xml:space="preserve">Et pongo che la perpendicolare che fa lo reforzino <emph style="sc">B D</emph>, ſia <lb/>brac. </s> <s xml:id="echoid-s2067" xml:space="preserve">21, on. </s> <s xml:id="echoid-s2068" xml:space="preserve">3, la Baſe <emph style="sc">A C</emph>, brac. </s> <s xml:id="echoid-s2069" xml:space="preserve">15, on. </s> <s xml:id="echoid-s2070" xml:space="preserve">7; </s> <s xml:id="echoid-s2071" xml:space="preserve">& </s> <s xml:id="echoid-s2072" xml:space="preserve">per hauere la <lb/>ſuperficie di eſſo triangolo, ſi torrà la metà della perpendi-<lb/>colare, ouero quella della Baſe; </s> <s xml:id="echoid-s2073" xml:space="preserve">& </s> <s xml:id="echoid-s2074" xml:space="preserve">ſi multiplicherà con la <lb/>Baſe, ouer con la perpendicolare; </s> <s xml:id="echoid-s2075" xml:space="preserve">come s’è detto della ſu- <pb file="134" n="134" rhead="LIBRO"/> perficie de’ triangoli delle terre, & </s> <s xml:id="echoid-s2076" xml:space="preserve">moſtrato nella nona fi-<lb/>gura del primo libro; </s> <s xml:id="echoid-s2077" xml:space="preserve">Hor pongo di pigliare la metà della <lb/>perpendicolare, ch’è brac. </s> <s xml:id="echoid-s2078" xml:space="preserve">10, onc. </s> <s xml:id="echoid-s2079" xml:space="preserve">7, pun. </s> <s xml:id="echoid-s2080" xml:space="preserve">6; </s> <s xml:id="echoid-s2081" xml:space="preserve">& </s> <s xml:id="echoid-s2082" xml:space="preserve">brac. </s> <s xml:id="echoid-s2083" xml:space="preserve">10, <lb/>on. </s> <s xml:id="echoid-s2084" xml:space="preserve">7, pun. </s> <s xml:id="echoid-s2085" xml:space="preserve">6, ſi multiplicheranno con brac. </s> <s xml:id="echoid-s2086" xml:space="preserve">15, on. </s> <s xml:id="echoid-s2087" xml:space="preserve">7, mi-<lb/>fura della Baſe; </s> <s xml:id="echoid-s2088" xml:space="preserve">come qui ſotto ſi vede.</s> <s xml:id="echoid-s2089" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div78" type="section" level="1" n="67"> <head xml:id="echoid-head89" xml:space="preserve">TERZA RAGIONE</head> <head xml:id="echoid-head90" xml:space="preserve">della ſuperficie.</head> <note position="right" xml:space="preserve"> <lb/>Brac. # 15, # on. # 7, <lb/>Brac. # 10, # on. # 7, # pun. # 6, <lb/>Brac. # 150, <lb/>Brac. # 5, # on. # 10, <lb/>Brac. # 8, # on. # 9, <lb/>Brac. # 0, # on. # 4, # pun. # 1, <lb/>Brac. # 0, # on. # 7, # pun. # 6, <lb/>Brac. # 0, # on, # 0, # pun. # 3, # at. # 6. <lb/>Brac. # 165, # on. # 6, # pun. # 10, # at. # 6. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # on. # 5, # 6, # ato. <lb/># pun. # 4, # 6, # ato. <lb/></note> <pb o="5" file="135" n="135" rhead="SECONDO."/> <note position="right" xml:space="preserve"> <lb/># braccia # 15 <lb/># braccia # 10 <lb/>braccia # # 150 <lb/># brac. # 10 <lb/># oncie # 7 <lb/>oncie # # 70 <lb/># partir per # 12 <lb/># brac. # 5, on. 10 <lb/># brac. # 15 <lb/># oncie # 7 <lb/>oncie # # 105 <lb/># partir per # 12 <lb/># brac. # 8, on. 9 <lb/></note> <note position="right" xml:space="preserve"> <lb/># oncie # 7 <lb/># oncie # 7 <lb/>punti # # 49 <lb/># partir per # 12 <lb/># on. # 4, pun. 1 <lb/># braccia # 15 <lb/># pun. # 6 <lb/>punti # # 90 <lb/># partir per # 12 <lb/># onc. # 7, pun. 6 <lb/># oncie # 7 <lb/># punti # 6 <lb/>atomi # # 42 <lb/># partir per # 12 <lb/># punti # 3, ato. 6 <lb/></note> <p> <s xml:id="echoid-s2090" xml:space="preserve">Coſi ſi vede che la ſuperſicie del triangolo ſono bra. </s> <s xml:id="echoid-s2091" xml:space="preserve">165, <lb/>onc. </s> <s xml:id="echoid-s2092" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s2093" xml:space="preserve">10, atomi 6; </s> <s xml:id="echoid-s2094" xml:space="preserve">& </s> <s xml:id="echoid-s2095" xml:space="preserve">tanto ſi moltiplicherà con la <lb/>groſſezza del muro, che pongo, che ſia vn braccio, & </s> <s xml:id="echoid-s2096" xml:space="preserve">on. </s> <s xml:id="echoid-s2097" xml:space="preserve">4, <lb/>come qui ſotto ſi vede.</s> <s xml:id="echoid-s2098" xml:space="preserve"/> </p> <pb file="136" n="136" rhead="LIBRO"/> </div> <div xml:id="echoid-div79" type="section" level="1" n="68"> <head xml:id="echoid-head91" xml:space="preserve">QVARTA RAGIONE <lb/>della quantità del corpo della <lb/>terza ragione.</head> <note position="right" xml:space="preserve"> <lb/>Brac. # 165, # on. # 6, # pun. # 10, # at. # 6, <lb/>Brac. # 1, # on. # 4, <lb/>Quadretti # 165, <lb/>Quadretti # 0, # on. # 6, <lb/>Quadretti # 0, # on. # 0, # pun. # 10, <lb/>Quadretti # 0, # on. # 0, # pun. # 0, # at. # 6, <lb/>Quadretti # 55, # on. # 0. <lb/>Quadretti # 0, # on. # 2, <lb/>Quadretti # 0, # on. # 0, # pun. # 3, # at. # 4, <lb/>Quadretti # 0, # on. # 0, # pun. # 0, # at. # 2, <lb/>Quadretti # 220, # on. # 9, # pun. # 2, # at. # 0, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # at. # 6, # 5, # min. <lb/># on. # 2, # 5, # min. <lb/></note> <pb o="6" file="137" n="137" rhead="SECONDO."/> <note position="right" xml:space="preserve"> <lb/># brac. # 165 <lb/># brac. # 1 <lb/>Quadretti # # 165 <lb/># oncie # 6 <lb/># brac. # 1 <lb/>oncie # # 6 <lb/># punti # 10 <lb/># bracc. # 1 <lb/>punti # # 10 <lb/># atomi # 6 <lb/># braccia # 1 <lb/>atomi # # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># brac. # 165 <lb/># oncie # 4 <lb/>oncie # # 660 <lb/># partir per # 12 <lb/># quadretti # 55 <lb/># oncie # 6 <lb/># oncie # 4 <lb/>punti # # 24 <lb/># partir per # 12 <lb/># oncie # 2 <lb/># punti # 10 <lb/># oncie # 4 <lb/>atomi # # 40 <lb/># partir per # 12 <lb/># pun. # 3, at. 4 <lb/># atomi # 6 <lb/># oncie # 4 <lb/>minuti # # 24 <lb/># partir per # 12 <lb/># atomi # 2 <lb/></note> <p> <s xml:id="echoid-s2099" xml:space="preserve">Coſi ſi vede che’l ſopra detto muro in triangolo è qua-<lb/>dretti 220, on. </s> <s xml:id="echoid-s2100" xml:space="preserve">9, pun. </s> <s xml:id="echoid-s2101" xml:space="preserve">2, ato. </s> <s xml:id="echoid-s2102" xml:space="preserve">o; </s> <s xml:id="echoid-s2103" xml:space="preserve">Et s’egli ſi vorrà vedere <lb/>quante pertiche, paſsi, & </s> <s xml:id="echoid-s2104" xml:space="preserve">quadrelli ſia, ſi farà come di ſopra.</s> <s xml:id="echoid-s2105" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2106" xml:space="preserve">Io mitrouo hauere da miſurar vna ſcarpa di cortina fino <lb/>al cordone d’una fortezza, come queſta ſeguente ſi vede.</s> <s xml:id="echoid-s2107" xml:space="preserve"/> </p> <pb file="138" n="138" rhead="LIBRO"/> <figure> <image file="138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/138-01"/> <caption xml:id="echoid-caption41" xml:space="preserve">Figura terza.</caption> </figure> <p> <s xml:id="echoid-s2108" xml:space="preserve">Lunga brac. </s> <s xml:id="echoid-s2109" xml:space="preserve">390, on. </s> <s xml:id="echoid-s2110" xml:space="preserve">4, nei capi ſia à modo di triangolo, <lb/>la Baſe del triangolo ſia brac. </s> <s xml:id="echoid-s2111" xml:space="preserve">6, onz, 6, & </s> <s xml:id="echoid-s2112" xml:space="preserve">venendoſi alzan-<lb/>do d’ognicinque piedi ne perde vno di ſcarpa; </s> <s xml:id="echoid-s2113" xml:space="preserve">dimando <lb/>quanto ſarà alta la detta ſcarpa, & </s> <s xml:id="echoid-s2114" xml:space="preserve">quante pertiche di mu-<lb/>ro ſarà. </s> <s xml:id="echoid-s2115" xml:space="preserve">Prima volendo dare d’ogni cinque piedi vno di <lb/>ſcarpa, lipiedi 6, di ſcarpane danno piedi 30, in altezza, le <lb/>ſei oncie di ſcarpane danno piedi doie mezzo in altezza, <lb/>che fanno piedi 32 e mezzo di altezza, & </s> <s xml:id="echoid-s2116" xml:space="preserve">tanto viene alta <lb/>la ſcarpa fina al cordone. </s> <s xml:id="echoid-s2117" xml:space="preserve">Etvolendo ſapere quante perti-<lb/>cheſaràla ſopradetta ſcarpa; </s> <s xml:id="echoid-s2118" xml:space="preserve">prima ſi hauerà la ſuperficie <lb/>del triangolo d’uno de icapi, & </s> <s xml:id="echoid-s2119" xml:space="preserve">queſto ſi hauerà per lere-<lb/>gole date di ſopra; </s> <s xml:id="echoid-s2120" xml:space="preserve">perchela ſua perpendicolare ſarà brac. <lb/></s> <s xml:id="echoid-s2121" xml:space="preserve">32, on. </s> <s xml:id="echoid-s2122" xml:space="preserve">6, & </s> <s xml:id="echoid-s2123" xml:space="preserve">la baſe ſarà bracc. </s> <s xml:id="echoid-s2124" xml:space="preserve">6, onc. </s> <s xml:id="echoid-s2125" xml:space="preserve">6; </s> <s xml:id="echoid-s2126" xml:space="preserve">la metà della qual <lb/>perpendicolare ſarà brac. </s> <s xml:id="echoid-s2127" xml:space="preserve">16; </s> <s xml:id="echoid-s2128" xml:space="preserve">onc. </s> <s xml:id="echoid-s2129" xml:space="preserve">3, hor ſi multiplicarà <lb/>brac. </s> <s xml:id="echoid-s2130" xml:space="preserve">6, on. </s> <s xml:id="echoid-s2131" xml:space="preserve">6, con brac. </s> <s xml:id="echoid-s2132" xml:space="preserve">16, onc. </s> <s xml:id="echoid-s2133" xml:space="preserve">3; </s> <s xml:id="echoid-s2134" xml:space="preserve">come qui ſotto ſi ve-<lb/>drà.</s> <s xml:id="echoid-s2135" xml:space="preserve"/> </p> <pb o="7" file="139" n="139" rhead="SECONDO."/> </div> <div xml:id="echoid-div80" type="section" level="1" n="69"> <head xml:id="echoid-head92" xml:space="preserve">QVINTA RAGIONE <lb/>della ſuperficie.</head> <note position="right" xml:space="preserve"> <lb/>Brac. # 16, # on. # 3, <lb/>Brac. # 6, # on. # 6, <lb/>Brac. # 96, <lb/>Brac. # 1, # on. # 6, <lb/>Brac. # 8, # on. # 0, <lb/>Brac. # 0, # on. # 1, # pun. # 6, <lb/>Brac. # 105, # on. # 7, # pun. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # onc. # 6 # 6 # pun. <lb/># onc. # 1 # 6 # pun. <lb/></note> <note position="right" xml:space="preserve"> <lb/># braccia # 16 <lb/># braccia # 6 <lb/>braccia # # 96 <lb/># brac. # 6 <lb/># oncie # 3 <lb/>oncie # # 18 <lb/># partir per # 12 <lb/># brac. # 1, on. 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># brac. # 16 <lb/># oncie # 6 <lb/>oncie # # 96 <lb/># partir per # 12 <lb/># brac. # 8, <lb/># oncie # 6 <lb/># oncie # 3 <lb/>punti # # 18 <lb/># partir per # 12 <lb/># on. # 1, pun. 6 <lb/></note> <pb file="140" n="140" rhead="LIBRO"/> <p> <s xml:id="echoid-s2136" xml:space="preserve">Coſiſi vede, che la ſuperficie del triangolo da vn de’ ca-<lb/>pi della ſcarpa è di ſuperficie brac. </s> <s xml:id="echoid-s2137" xml:space="preserve">105, on. </s> <s xml:id="echoid-s2138" xml:space="preserve">7, pun. </s> <s xml:id="echoid-s2139" xml:space="preserve">6, & </s> <s xml:id="echoid-s2140" xml:space="preserve">tan <lb/>to ſi moltiplicarà con la lunghezza della ſcarpa; </s> <s xml:id="echoid-s2141" xml:space="preserve">come que<unsure/> <lb/>ſotto ſi vedrà, & </s> <s xml:id="echoid-s2142" xml:space="preserve">ſi hauerà la quantità del muro di tutta la <lb/>ſcarpa.</s> <s xml:id="echoid-s2143" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div81" type="section" level="1" n="70"> <head xml:id="echoid-head93" xml:space="preserve">SESSTA RAGIONE <lb/>della quantità del corpo della <lb/>quinta Ragione.</head> <note position="right" xml:space="preserve"> <lb/>Lunga brac. # 390, # on. # 4, <lb/>Superficiebra. # 105, # on. # 7, # pun. # 6, <lb/>Qradretti # 40950, <lb/>Quadretti # 35, <lb/>Quadretti # 227, # on. # 6, <lb/>Quadretti # 0, # on. # 2, # pun. # 4, <lb/>Quadretti # 16, # on. # 3, <lb/>Quadretti # 0, # on. # 0, # pun. # 2, <lb/>Quadretti # 41228, # on. # 11, # pun. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # on. # 1, # 6, # ato. <lb/># pun. # 6, # 6, # ato. <lb/></note> <pb o="8" file="141" n="141" rhead="SECONDO."/> <note position="right" xml:space="preserve"> <lb/># # 390 <lb/># # 105 <lb/># # 1950 <lb/># # 000 <lb/># # 390 <lb/>Quad. # # 40950 <lb/># brac. # 105 <lb/># oncie # 4 <lb/>oncie # # 420 <lb/># partir per # 12 <lb/># quadretti # 35 <lb/># brac. # 390 <lb/># oncie # 7 <lb/>oncie # # 2730 <lb/># partir per # 12 <lb/># quad. # 227, on. 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># on. # 7 <lb/># on. # 4 <lb/>punti # # 28 <lb/># partir per # 12 <lb/># oncie # 2, pun. 4 <lb/># brac. # 390 <lb/># punti # 6 <lb/>punti # # 2340 <lb/># partir per # 12 <lb/>oncie # # 195 <lb/># partir per # 12 <lb/># quad. # 16, on. 3 <lb/># punti # 6 <lb/># oncie # 4 <lb/>atomi # # 24 <lb/># partir per # 12 <lb/># pun. # 2 <lb/></note> <p> <s xml:id="echoid-s2144" xml:space="preserve">Coſi ſi vede, che la ſopradetta ſcarpa ſi è Quadretti <lb/>41228, on. </s> <s xml:id="echoid-s2145" xml:space="preserve">11, pun. </s> <s xml:id="echoid-s2146" xml:space="preserve">6.</s> <s xml:id="echoid-s2147" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2148" xml:space="preserve">Per vn’altro modo ancora ſi potrà vedere quanti quadret <lb/>ti di muro, era la ſopradetta ſcarpa, imaginandoſi vna ſuper <lb/>ſicie quadrangolare dalla parte di dentro lunga brac. </s> <s xml:id="echoid-s2149" xml:space="preserve">390, <lb/>on. </s> <s xml:id="echoid-s2150" xml:space="preserve">4. </s> <s xml:id="echoid-s2151" xml:space="preserve">larga brac. </s> <s xml:id="echoid-s2152" xml:space="preserve">32, on. </s> <s xml:id="echoid-s2153" xml:space="preserve">6, & </s> <s xml:id="echoid-s2154" xml:space="preserve">moltiplicando l’una con l’al <lb/>tra, come di ſopra, taranno brac. </s> <s xml:id="echoid-s2155" xml:space="preserve">12685, on. </s> <s xml:id="echoid-s2156" xml:space="preserve">10, & </s> <s xml:id="echoid-s2157" xml:space="preserve">moltipli <lb/>cando con la metà di braccia 6, oncie 6, faranno quadretti <lb/>41228, on. </s> <s xml:id="echoid-s2158" xml:space="preserve">11, pun. </s> <s xml:id="echoid-s2159" xml:space="preserve">6; </s> <s xml:id="echoid-s2160" xml:space="preserve">come di ſopra, & </s> <s xml:id="echoid-s2161" xml:space="preserve">quadretti 41228, <lb/>on. </s> <s xml:id="echoid-s2162" xml:space="preserve">11, pun. </s> <s xml:id="echoid-s2163" xml:space="preserve">6, ſi potranno fare in pertiche, paſsi, & </s> <s xml:id="echoid-s2164" xml:space="preserve">qua-<lb/>drelli.</s> <s xml:id="echoid-s2165" xml:space="preserve"/> </p> <pb file="142" n="142" rhead="LIBRO"/> <p> <s xml:id="echoid-s2166" xml:space="preserve">Io mi ritrouo vn pezzo di cortina, lungo brac. </s> <s xml:id="echoid-s2167" xml:space="preserve">390, on. </s> <s xml:id="echoid-s2168" xml:space="preserve">4 <lb/>alto fina al cordone brac. </s> <s xml:id="echoid-s2169" xml:space="preserve">32 e mezzo, & </s> <s xml:id="echoid-s2170" xml:space="preserve">è di ſcarpa brac. </s> <s xml:id="echoid-s2171" xml:space="preserve">6, <lb/>on. </s> <s xml:id="echoid-s2172" xml:space="preserve">6; </s> <s xml:id="echoid-s2173" xml:space="preserve">Etha vn muro contingente alla ſcarpa,<unsure/> di dentrouia, <lb/>che và creſcendo fino di ſopra al cordone brac. </s> <s xml:id="echoid-s2174" xml:space="preserve">6; </s> <s xml:id="echoid-s2175" xml:space="preserve">& </s> <s xml:id="echoid-s2176" xml:space="preserve">nel fi-<lb/>nire viene di groſſezza brac. </s> <s xml:id="echoid-s2177" xml:space="preserve">3.</s> <s xml:id="echoid-s2178" xml:space="preserve"/> </p> <figure> <image file="142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/142-01"/> <caption xml:id="echoid-caption42" xml:space="preserve">Quarta Figura.</caption> </figure> <p> <s xml:id="echoid-s2179" xml:space="preserve">La prima coſa ſi conſiderano due triangoli, l’uno il trian-<lb/>golo <emph style="sc">B A C</emph>, fino al cordone, con l’angolo <emph style="sc">B</emph>, retto, come <lb/>nell’antecedente eſſempio s’è detto, & </s> <s xml:id="echoid-s2180" xml:space="preserve">l’altro il triangolo <lb/><emph style="sc">F A G</emph>, con l’angolo <emph style="sc">G</emph>, retto; </s> <s xml:id="echoid-s2181" xml:space="preserve">ci ſeruirà il modo dell’antece-<lb/>dente eſſempio, per ſapere quanti quadretti ſi è la figura del <lb/>la ſcarpa fino al cordone <emph style="sc">B A C E F D</emph>, & </s> <s xml:id="echoid-s2182" xml:space="preserve">ſi ritrouerà eſſere <lb/>quadretti 41228, on. </s> <s xml:id="echoid-s2183" xml:space="preserve">11, punti 6, come di ſopra ſi è moſtra <lb/>to; </s> <s xml:id="echoid-s2184" xml:space="preserve">& </s> <s xml:id="echoid-s2185" xml:space="preserve">per vedere quanti quadretti ſi è il muro di dentrouia, <lb/>ſi ſaprà prima la ſuperficie del triangolo <emph style="sc">F A G</emph>, che ſe la ſua <pb o="9" file="143" n="143" rhead="SECONDO."/> perpendicolare ſarà brac. </s> <s xml:id="echoid-s2186" xml:space="preserve">38, on. </s> <s xml:id="echoid-s2187" xml:space="preserve">6, la baſe brac. </s> <s xml:id="echoid-s2188" xml:space="preserve">3; </s> <s xml:id="echoid-s2189" xml:space="preserve">ſitorrà <lb/>la metà di brac. </s> <s xml:id="echoid-s2190" xml:space="preserve">38, on. </s> <s xml:id="echoid-s2191" xml:space="preserve">6, che ſono brac. </s> <s xml:id="echoid-s2192" xml:space="preserve">19, on. </s> <s xml:id="echoid-s2193" xml:space="preserve">3, & </s> <s xml:id="echoid-s2194" xml:space="preserve">tanto <lb/>ſi moltiplicarà con brac. </s> <s xml:id="echoid-s2195" xml:space="preserve">3, come di ſotto ſi vede, & </s> <s xml:id="echoid-s2196" xml:space="preserve">ſi haue-<lb/>rà di ſuperficie brac. </s> <s xml:id="echoid-s2197" xml:space="preserve">57, on. </s> <s xml:id="echoid-s2198" xml:space="preserve">8, & </s> <s xml:id="echoid-s2199" xml:space="preserve">tanto ſi multiplicarà con</s> </p> <note position="right" xml:space="preserve"> <lb/>Brac. # 19, # on. # 3, <lb/>Brac. # 3, <lb/>Brac. # 57, # on. # 9, <lb/>Brac. # 390, # on. # 4, <lb/>Brac. # 57, # on. # 9, <lb/># 2730, <lb/># 1950, <lb/># 195, <lb/># 97, # on. # 6. <lb/># 19, # on. # 3, <lb/>quadr@ # 22541, # on. # 9, <lb/></note> <p> <s xml:id="echoid-s2200" xml:space="preserve">Braccid. </s> <s xml:id="echoid-s2201" xml:space="preserve">390, on. </s> <s xml:id="echoid-s2202" xml:space="preserve">4, di lunghez <lb/>za faranno quadretti 22541, <lb/>on. </s> <s xml:id="echoid-s2203" xml:space="preserve">9, & </s> <s xml:id="echoid-s2204" xml:space="preserve">tanto ſarà il muro di <lb/>dentrouia, contingente alla <lb/>ſcarpa, & </s> <s xml:id="echoid-s2205" xml:space="preserve">nella baſe della ſcar <lb/>pa finiſce in nulla, & </s> <s xml:id="echoid-s2206" xml:space="preserve">di ſopra <lb/>della ſcarpa è alto brac. </s> <s xml:id="echoid-s2207" xml:space="preserve">6, & </s> <s xml:id="echoid-s2208" xml:space="preserve"><lb/>di groſſezza brac. </s> <s xml:id="echoid-s2209" xml:space="preserve">3, & </s> <s xml:id="echoid-s2210" xml:space="preserve">queſto <lb/>muro ſopra del cordone, ſerue <lb/>per camiſcia della fortezza; </s> <s xml:id="echoid-s2211" xml:space="preserve">co <lb/>ſi quadretti 22541, on. </s> <s xml:id="echoid-s2212" xml:space="preserve">9; </s> <s xml:id="echoid-s2213" xml:space="preserve">con <lb/>quadretti 41228, on. </s> <s xml:id="echoid-s2214" xml:space="preserve">11, pun.</s> <s xml:id="echoid-s2215" xml:space="preserve">6 <lb/>fanno quadretti 63770, on. </s> <s xml:id="echoid-s2216" xml:space="preserve">8, <lb/>pun, 6, & </s> <s xml:id="echoid-s2217" xml:space="preserve">de quadretti 63770, on. </s> <s xml:id="echoid-s2218" xml:space="preserve">8, pun. </s> <s xml:id="echoid-s2219" xml:space="preserve">6, ſe la fabrica è <lb/>di matoni ſi potranno fare in matoni, moltiplicando per <lb/>quadrelli 30; </s> <s xml:id="echoid-s2220" xml:space="preserve">& </s> <s xml:id="echoid-s2221" xml:space="preserve">ancora ſe i quadretti 63770, ſi vorranno <lb/>fare in pertiche, ſi partiranno due volte per 6; </s> <s xml:id="echoid-s2222" xml:space="preserve">ouero ſe ſi <lb/>vorranno fare in paſsi, ſi partiranno due volte per 5; </s> <s xml:id="echoid-s2223" xml:space="preserve">come <lb/>di ſopra s’è detto; </s> <s xml:id="echoid-s2224" xml:space="preserve">& </s> <s xml:id="echoid-s2225" xml:space="preserve">per quello che ſegue, è neceſſario qui <lb/>ſotto poner le tauole delle corde, & </s> <s xml:id="echoid-s2226" xml:space="preserve">archi; </s> <s xml:id="echoid-s2227" xml:space="preserve">per ritrouar gli <lb/>archi della portion minore, & </s> <s xml:id="echoid-s2228" xml:space="preserve">maggiore di cerchio.</s> <s xml:id="echoid-s2229" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Archi minori, \\ Brac. # Archi maggiori, \\ Brac. # Corde, \\ Brac. # on. <lb/>1 # 131 # 0 # 11 <lb/>2 # 130 # 1 # 11 <lb/>3 # 129 # 2 # 11 <lb/>4 # 128 # 3 # 11 <lb/>5 # 127 # 4 # 9 <lb/>6 # 126 # 5 # 11 <lb/></note> <pb file="144" n="144" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/>Archi minori, \\ Brac. # Archi maggiori, \\ Brac. # Corde, \\ Brac. # on. <lb/>7 # 125 # 6 # 11 <lb/>8 # 124 # 7 # 11 <lb/>9 # 123 # 8 # 10 <lb/>10 # 122 # 9 # 11 <lb/>11 # 121 # 10 # 11 <lb/>12 # 120 # 11 # 9 <lb/>13 # 119 # 12 # 9 <lb/>14 # 118 # 13 # 8 <lb/>15 # 117 # 14 # 8 <lb/>16 # 116 # 15 # 7 <lb/>17 # 115 # 16 # 7 <lb/>18 # 114 # 17 # 5 <lb/>19 # 113 # 18 # 0 <lb/>20 # 112 # 19 # 3 <lb/>21 # 111 # 20 # 1 <lb/>22 # 110 # 21 # 0 <lb/>23 # 109 # 21 # 10 <lb/>24 # 108 # 22 # 8 <lb/>25 # 107 # 23 # 6 <lb/>26 # 106 # 24 # 4 <lb/>27 # 105 # 25 # 2 <lb/>28 # 104 # 25 # 10 <lb/>29 # 103 # 26 # 8 <lb/>30 # 102 # 27 # 2 <lb/>31 # 101 # 28 # 11 <lb/>32 # 100 # 29 # 8 <lb/>33 # 99 # 30 # 4 <lb/>34 # 98 # 31 # 0 <lb/>35 # 97 # 31 # 8 <lb/>36 # 96 # 32 # 4 <lb/>37 # 95 # 33 # 0 <lb/>38 # 94 # 34 # 7 <lb/>39 # 93 # 35 # 2 <lb/>40 # 92 # 36 # 4 <lb/>41 # 91 # 36 # 10 <lb/></note> <pb o="10" file="145" n="145" rhead="SECONDO."/> <note position="right" xml:space="preserve"> <lb/>Archi minori, \\ Brac. # Archi maggiori, \\ Brac. # Corde, \\ Brac. # on. <lb/>42 # 90 # 37 # 4 <lb/>43 # 89 # 37 # 10 <lb/>44 # 88 # 38 # 5 <lb/>45 # 87 # 38 # 10 <lb/>46 # 86 # 39 # 4 <lb/>47 # 85 # 39 # 11 <lb/>48 # 84 # 40 # 5 <lb/>49 # 83 # 40 # 8 <lb/>50 # 82 # 41 # 0 <lb/>51 # 81 # 41 # 3 <lb/>52 # 80 # 41 # 6 <lb/>53 # 79 # 41 # 9 <lb/>54 # 78 # 41 # 0 <lb/>55 # 77 # 41 # 2 <lb/>76 # 76 # 41 # 4 <lb/>57 # 75 # 41 # 6 <lb/>58 # 74 # 41 # 9 <lb/>59 # 73 # 41 # 10 <lb/>60 # 72 # 41 # 11 <lb/>61 # 71 # 41 # 11 <lb/>62 # 70 # 42 # 0 <lb/>63 # 69 <lb/>64 # 68 <lb/>65 # 67 <lb/>66 # 66 <lb/></note> <pb file="146" n="146" rhead="LIBRO"/> <figure> <image file="146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/146-01"/> <caption xml:id="echoid-caption43" xml:space="preserve">Quinta Figura.</caption> </figure> <p> <s xml:id="echoid-s2230" xml:space="preserve">Volendo l’arco della portion minore, ouer maggiore, <lb/>d’un cerchio; </s> <s xml:id="echoid-s2231" xml:space="preserve">hor ſi ponerà di volere l’arco <emph style="sc">A B</emph>, della por-<lb/>tion <emph style="sc">A B</emph>, del cerchio <emph style="sc">A B C</emph>, la corda <emph style="sc">A B</emph>, ſia brac. </s> <s xml:id="echoid-s2232" xml:space="preserve">8, & </s> <s xml:id="echoid-s2233" xml:space="preserve">il <lb/>diametro del cerchio <emph style="sc">A B C</emph>, ſia brac. </s> <s xml:id="echoid-s2234" xml:space="preserve">10; </s> <s xml:id="echoid-s2235" xml:space="preserve">ſi farà in queſto mo <lb/>do: </s> <s xml:id="echoid-s2236" xml:space="preserve">ſe 10, di diametro mi dà di corda brac. </s> <s xml:id="echoid-s2237" xml:space="preserve">8, che mi darà <lb/>di corda il diametro delle tauole, ch’è brac. </s> <s xml:id="echoid-s2238" xml:space="preserve">42? </s> <s xml:id="echoid-s2239" xml:space="preserve">ſi multipli-<lb/>cherà brac. </s> <s xml:id="echoid-s2240" xml:space="preserve">8, con brac. </s> <s xml:id="echoid-s2241" xml:space="preserve">42, delle tauole, faranno braccia <lb/>336, & </s> <s xml:id="echoid-s2242" xml:space="preserve">tanto ſi partirà per brac. </s> <s xml:id="echoid-s2243" xml:space="preserve">10, di diametro del cer-<lb/>chio, che ſi ricerca l’arco, & </s> <s xml:id="echoid-s2244" xml:space="preserve">ne venirà brac. </s> <s xml:id="echoid-s2245" xml:space="preserve">33, oncie 7, & </s> <s xml:id="echoid-s2246" xml:space="preserve"><lb/>braccia 33. </s> <s xml:id="echoid-s2247" xml:space="preserve">on. </s> <s xml:id="echoid-s2248" xml:space="preserve">7, ſono la corda delle tauole; </s> <s xml:id="echoid-s2249" xml:space="preserve">cioè, che’l <lb/>cerchio <emph style="sc">D E F</emph>, ha di diametro braccia 42, & </s> <s xml:id="echoid-s2250" xml:space="preserve">ha la corda di <lb/>braccia 33, oncie 7, alla proportion del cerchio <emph style="sc">A B C</emph>, di <pb o="11" file="147" n="147" rhead="SECONDO."/> diametro brac. </s> <s xml:id="echoid-s2251" xml:space="preserve">10, alla ſua corda brac. </s> <s xml:id="echoid-s2252" xml:space="preserve">8, & </s> <s xml:id="echoid-s2253" xml:space="preserve">queſta corda <lb/>di brac. </s> <s xml:id="echoid-s2254" xml:space="preserve">33, on. </s> <s xml:id="echoid-s2255" xml:space="preserve">7, ſi pigliarà nelle tauole, più proſsima che <lb/>ſia poſsibile, & </s> <s xml:id="echoid-s2256" xml:space="preserve">ſi piglierà brac. </s> <s xml:id="echoid-s2257" xml:space="preserve">33, & </s> <s xml:id="echoid-s2258" xml:space="preserve">all’incontro di 33, da <lb/>mano ſiniſtra ſi piglierà il ſuo arco, nelli archi minori, che <lb/>ſignificano gl’archi della portiõ minore, del mezo cerchio, <lb/>& </s> <s xml:id="echoid-s2259" xml:space="preserve">iui ſi ritrouerà bra. </s> <s xml:id="echoid-s2260" xml:space="preserve">37, & </s> <s xml:id="echoid-s2261" xml:space="preserve">perle on. </s> <s xml:id="echoid-s2262" xml:space="preserve">7, che mãcano, ſi dirà, <lb/> <anchor type="figure" xlink:label="fig-147-01a" xlink:href="fig-147-01"/> ſe brac. </s> <s xml:id="echoid-s2263" xml:space="preserve">33, di corda, mi danno brac. </s> <s xml:id="echoid-s2264" xml:space="preserve">35, d’arco, che mi da- rà on. </s> <s xml:id="echoid-s2265" xml:space="preserve">7, pur di corda? </s> <s xml:id="echoid-s2266" xml:space="preserve">ſi trouerà, che ti darà cerca à on. </s> <s xml:id="echoid-s2267" xml:space="preserve">8, di arco, & </s> <s xml:id="echoid-s2268" xml:space="preserve">coſi l’arco del cerchio delle tauole ſono brac. </s> <s xml:id="echoid-s2269" xml:space="preserve">37, on. </s> <s xml:id="echoid-s2270" xml:space="preserve">8; </s> <s xml:id="echoid-s2271" xml:space="preserve">Et pervolere l’arco della portiõ minore del mezo cer chio, ſi farà in queſto modo, ſel diametro del cerchio delle tauole, brac. </s> <s xml:id="echoid-s2272" xml:space="preserve">42, mi danno di arco brac. </s> <s xml:id="echoid-s2273" xml:space="preserve">37, on. </s> <s xml:id="echoid-s2274" xml:space="preserve">8; </s> <s xml:id="echoid-s2275" xml:space="preserve">quanto <pb file="148" n="148" rhead="LIBRO"/> arco mi darà il cerchio di diametro brac. </s> <s xml:id="echoid-s2276" xml:space="preserve">10, ſi moltiplica- rà brac. </s> <s xml:id="echoid-s2277" xml:space="preserve">10, con brac. </s> <s xml:id="echoid-s2278" xml:space="preserve">37, on. </s> <s xml:id="echoid-s2279" xml:space="preserve">8, come qui ſotto ſivede & </s> <s xml:id="echoid-s2280" xml:space="preserve">fa ranno brac. </s> <s xml:id="echoid-s2281" xml:space="preserve">376, on. </s> <s xml:id="echoid-s2282" xml:space="preserve">8.</s> <s xml:id="echoid-s2283" xml:space="preserve"/> </p> <div xml:id="echoid-div81" type="float" level="2" n="1"> <figure xlink:label="fig-147-01" xlink:href="fig-147-01a"> <image file="147-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/147-01"/> <caption xml:id="echoid-caption44" xml:space="preserve">Figura Seſta.</caption> </figure> </div> <note position="right" xml:space="preserve"> <lb/>Brac. # 37, # on. # 8, <lb/>Brac, # 10, <lb/>Brac. # 370, <lb/>Brac. # 6, # on. # 8, <lb/>Brac. # 376, # on. # 8, <lb/></note> <note position="right" xml:space="preserve"> <lb/># 37 <lb/># 10 <lb/># 00 <lb/># 37 <lb/>brac. # 370 <lb/># 10 <lb/># 8 <lb/>on. # 80 <lb/>partir per # 12 <lb/>bra. # 6, # on. # 8 <lb/></note> <p> <s xml:id="echoid-s2284" xml:space="preserve">Et brac. </s> <s xml:id="echoid-s2285" xml:space="preserve">376, on. </s> <s xml:id="echoid-s2286" xml:space="preserve">8, ſi partiranno <lb/>per brac. </s> <s xml:id="echoid-s2287" xml:space="preserve">42, & </s> <s xml:id="echoid-s2288" xml:space="preserve">ne venirà brac. </s> <s xml:id="echoid-s2289" xml:space="preserve">8, <lb/>& </s> <s xml:id="echoid-s2290" xml:space="preserve">intorno à on. </s> <s xml:id="echoid-s2291" xml:space="preserve">11 e meza; </s> <s xml:id="echoid-s2292" xml:space="preserve">& </s> <s xml:id="echoid-s2293" xml:space="preserve">brac. </s> <s xml:id="echoid-s2294" xml:space="preserve">8, on. </s> <s xml:id="echoid-s2295" xml:space="preserve">11 e meza, ſarà <lb/>l’arco <emph style="sc">A B</emph>, della portion minore del mezo cerchio, <emph style="sc">A B C</emph>; <lb/></s> <s xml:id="echoid-s2296" xml:space="preserve">come di ſopra ſivede. </s> <s xml:id="echoid-s2297" xml:space="preserve">Et ſe ſi voleſſe l’arco della portion <lb/>maggiore del mezo cerchio, in cambio del 37, ſipigliareb-<lb/>be il 95; </s> <s xml:id="echoid-s2298" xml:space="preserve">ne gli archi maggiori, & </s> <s xml:id="echoid-s2299" xml:space="preserve">per le on. </s> <s xml:id="echoid-s2300" xml:space="preserve">8, di piu s’ha da <lb/>vedere quanto creſce da 37, à 38, & </s> <s xml:id="echoid-s2301" xml:space="preserve">ſi vede che creſce vno, <lb/>ancora s’ha da vedere quanto manca da 95, à 94, & </s> <s xml:id="echoid-s2302" xml:space="preserve">ſi troua <lb/>che manca un brac. </s> <s xml:id="echoid-s2303" xml:space="preserve">coſi ſi dirà; </s> <s xml:id="echoid-s2304" xml:space="preserve">ſe on. </s> <s xml:id="echoid-s2305" xml:space="preserve">12, mancano on. </s> <s xml:id="echoid-s2306" xml:space="preserve">12, <lb/>quanto mancarà oncie 8? </s> <s xml:id="echoid-s2307" xml:space="preserve">ſiritrouerà che mancarà on. </s> <s xml:id="echoid-s2308" xml:space="preserve">8, & </s> <s xml:id="echoid-s2309" xml:space="preserve"><lb/>on. </s> <s xml:id="echoid-s2310" xml:space="preserve">8, ſi caueranno da brac. </s> <s xml:id="echoid-s2311" xml:space="preserve">95, reſterà brac. </s> <s xml:id="echoid-s2312" xml:space="preserve">94, on. </s> <s xml:id="echoid-s2313" xml:space="preserve">4; </s> <s xml:id="echoid-s2314" xml:space="preserve">poi ſi <lb/>dirà, ſe brac. </s> <s xml:id="echoid-s2315" xml:space="preserve">42, mi danno d’arco brac. </s> <s xml:id="echoid-s2316" xml:space="preserve">94, oncie 4; </s> <s xml:id="echoid-s2317" xml:space="preserve">che mi <lb/>darà brac. </s> <s xml:id="echoid-s2318" xml:space="preserve">10, ſi ritrouerà che daranno bracc. </s> <s xml:id="echoid-s2319" xml:space="preserve">22, on. </s> <s xml:id="echoid-s2320" xml:space="preserve">5, in-<lb/>torno, & </s> <s xml:id="echoid-s2321" xml:space="preserve">brac. </s> <s xml:id="echoid-s2322" xml:space="preserve">22, on. </s> <s xml:id="echoid-s2323" xml:space="preserve">5, ſarà l’arco della portion maggio-<lb/>re del mezo cerchio, di diametro brac. </s> <s xml:id="echoid-s2324" xml:space="preserve">10, come di ſopra ſi <lb/>vede. </s> <s xml:id="echoid-s2325" xml:space="preserve">Per due altri modi ſi potrà ritrouare l’arco della <lb/>portion minore; </s> <s xml:id="echoid-s2326" xml:space="preserve">prima ſi ritrouerà la ſaetta della portion <lb/>minore, in queſto modo; </s> <s xml:id="echoid-s2327" xml:space="preserve">tolendo la metà della corda, & </s> <s xml:id="echoid-s2328" xml:space="preserve"><lb/>pongo come di ſopra braccia 8, la metà ſarà 4, moltipli-<lb/>cato in ſe farà 16, di poi ſi torrà la metà del diametro, di tal <pb o="12" file="149" n="149" rhead="SECONDO."/> cerchio ch’è bra. </s> <s xml:id="echoid-s2329" xml:space="preserve">10, la metà di 10, ſiè 5, multiplicato 5, in <lb/>ſe fa 25, & </s> <s xml:id="echoid-s2330" xml:space="preserve">di 25, ne cauo 16, di ſopra, reſta 9, & </s> <s xml:id="echoid-s2331" xml:space="preserve">di 9, ne pi-<lb/>glio la radice, ch’è 3, & </s> <s xml:id="echoid-s2332" xml:space="preserve">3, l’aggiungo à 5, fa 8, & </s> <s xml:id="echoid-s2333" xml:space="preserve">bra. </s> <s xml:id="echoid-s2334" xml:space="preserve">8, ſarà <lb/>la ſaetta della portion maggiore; </s> <s xml:id="echoid-s2335" xml:space="preserve">anchor cauo 3, pur da 5, <lb/>reſta 2, & </s> <s xml:id="echoid-s2336" xml:space="preserve">2, ſarà la ſaetta della portione minore, come qui <lb/>ſotto ſi vede, nel cerchio <emph style="sc">A B C D</emph>, la corda brac. </s> <s xml:id="echoid-s2337" xml:space="preserve">8, la ſaetta <lb/><emph style="sc">D E</emph>, brac. </s> <s xml:id="echoid-s2338" xml:space="preserve">8, la ſaetta <emph style="sc">E B</emph>, brac. </s> <s xml:id="echoid-s2339" xml:space="preserve">2, il diametro <emph style="sc">D B</emph>, brac. </s> <s xml:id="echoid-s2340" xml:space="preserve">10, <lb/> <anchor type="figure" xlink:label="fig-149-01a" xlink:href="fig-149-01"/> Il medeſimo ſi farà in ogn’altro; </s> <s xml:id="echoid-s2341" xml:space="preserve">hauuto la ſaetta <emph style="sc">E B</emph>, ch’è brac. </s> <s xml:id="echoid-s2342" xml:space="preserve">2, ſi multiplicherà 2, in ſe & </s> <s xml:id="echoid-s2343" xml:space="preserve">farà 4, & </s> <s xml:id="echoid-s2344" xml:space="preserve">di 4, ſe ne piglia rà li 11 decimiquarti, che ſarà tre e vn ſettimo, & </s> <s xml:id="echoid-s2345" xml:space="preserve">di tanto ſe ne pigliarà la radice, che intorno à vno e cinque ſeſti, &</s> <s xml:id="echoid-s2346" xml:space="preserve"> vno e cinque ſeſti, ſi aggiungerà alla multiplicatione, che farà la ſaetta, con la metà della corda, cioè 2, con 4, fa 8, hor ſommando 8, con vno e cinque ſeſti, fanno brac. </s> <s xml:id="echoid-s2347" xml:space="preserve">9, e <pb file="150" n="150" rhead="LIBRO"/> cinque ſeſti, larco della portion minore:</s> <s xml:id="echoid-s2348" xml:space="preserve">il qual arco è di più del primo quaſi cinque ſeſti, di brac. </s> <s xml:id="echoid-s2349" xml:space="preserve">l’altro modo è, per la piu parte de i muratori, aggiungono la ſaetta, cioè 2, con tutta la corda ch’è 8, & </s> <s xml:id="echoid-s2350" xml:space="preserve">fanno brac. </s> <s xml:id="echoid-s2351" xml:space="preserve">10, per l’a rco della por- tion minore, li quali brac. </s> <s xml:id="echoid-s2352" xml:space="preserve">10, ſono maggior di brac. </s> <s xml:id="echoid-s2353" xml:space="preserve">9 e cin que ſeſti per vn ſeſto, & </s> <s xml:id="echoid-s2354" xml:space="preserve">tanto più ſarà maggior della prima operatione; </s> <s xml:id="echoid-s2355" xml:space="preserve">& </s> <s xml:id="echoid-s2356" xml:space="preserve">per queſto la prima ſarà minore dell’altre due, come moſtra Tolomeo nel ſuo Almageſto. </s> <s xml:id="echoid-s2357" xml:space="preserve">Hor ritro uato gli archi, ſi moſtrerà à ritrouare le ſuperficij delle por- tioni minore, & </s> <s xml:id="echoid-s2358" xml:space="preserve">maggiore; </s> <s xml:id="echoid-s2359" xml:space="preserve">Sia il cerchio <emph style="sc">A B C D</emph>, il diametro <emph style="sc">A D</emph>, brac. </s> <s xml:id="echoid-s2360" xml:space="preserve">10, la corda <emph style="sc">B C</emph>, brac. </s> <s xml:id="echoid-s2361" xml:space="preserve">8, l’arco <emph style="sc">B C</emph>, brac. </s> <s xml:id="echoid-s2362" xml:space="preserve">9, & </s> <s xml:id="echoid-s2363" xml:space="preserve">per <anchor type="figure" xlink:label="fig-150-01a" xlink:href="fig-150-01"/> hauere la ſuperficie della portione minore <emph style="sc">B C</emph>, ſi moltipli- cherà la metà dell’arco ch’è brac. </s> <s xml:id="echoid-s2364" xml:space="preserve">4 e mezzo, con la metà del diametro <emph style="sc">A D</emph>, ch’è brac. </s> <s xml:id="echoid-s2365" xml:space="preserve">5, & </s> <s xml:id="echoid-s2366" xml:space="preserve">faranno brac. </s> <s xml:id="echoid-s2367" xml:space="preserve">22, e mezo, <pb o="13" file="151" n="151" rhead="SECONDO."/> & </s> <s xml:id="echoid-s2368" xml:space="preserve">de’brac. </s> <s xml:id="echoid-s2369" xml:space="preserve">22 e mezo, ſi cauerà la ſuperficie del triangolo <emph style="sc">B E C</emph>, ch’èbrac. </s> <s xml:id="echoid-s2370" xml:space="preserve">12, reſtarà brac. </s> <s xml:id="echoid-s2371" xml:space="preserve">10 e mezo, per la ſuperficie della portiõ minore del mezo cerchio; </s> <s xml:id="echoid-s2372" xml:space="preserve">Et per hauer la ſuper ficie della portion maggiore del mezo cerchio, ſi cauerà la ſuperſicie della portion minore, dalla ſuperficie di tutto il cerchio, & </s> <s xml:id="echoid-s2373" xml:space="preserve">quello che rimane ſara la ſuperficie della por- tion maggiore, del mezo cerchio; </s> <s xml:id="echoid-s2374" xml:space="preserve">& </s> <s xml:id="echoid-s2375" xml:space="preserve">volendo la ſuperficie di tutto il cerchio, più di ſotto la moſtrarò.</s> <s xml:id="echoid-s2376" xml:space="preserve"/> </p> <div xml:id="echoid-div82" type="float" level="2" n="2"> <figure xlink:label="fig-149-01" xlink:href="fig-149-01a"> <image file="149-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/149-01"/> <caption xml:id="echoid-caption45" xml:space="preserve">Settima Figura.</caption> </figure> <figure xlink:label="fig-150-01" xlink:href="fig-150-01a"> <image file="150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/150-01"/> <caption xml:id="echoid-caption46" xml:space="preserve">Figura ottaua.</caption> </figure> </div> <figure> <image file="151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/151-01"/> <caption xml:id="echoid-caption47" xml:space="preserve">Figura nona.</caption> </figure> <p> <s xml:id="echoid-s2377" xml:space="preserve">Sia adunque il cerchio <emph style="sc">A B C D</emph>, del quale il diametro <emph style="sc">A C</emph> <lb/>brac. </s> <s xml:id="echoid-s2378" xml:space="preserve">10, vorrei ſapere quant’è di ſuperficie eſſo cerchio. <lb/></s> <s xml:id="echoid-s2379" xml:space="preserve">Prima ſi ritrouerà la ſua circonferenza, multiplicando il <lb/>diametro <emph style="sc">A C</emph>, con 3 e vn ſettimo, cioè multiplicando 22 <lb/>fiate 10, fanno 220, & </s> <s xml:id="echoid-s2380" xml:space="preserve">220, ſipartirà per 7, ne venirà brac. </s> <s xml:id="echoid-s2381" xml:space="preserve"><lb/>31 e tre ſettimi di circonferenza, & </s> <s xml:id="echoid-s2382" xml:space="preserve">volendo la ſuperficie ſi <lb/>torrà la metà de’ 31 e tre ſettimi, che 15 e cinque ſettimi, <pb file="152" n="152" rhead="LIBRO"/> & </s> <s xml:id="echoid-s2383" xml:space="preserve">brac. </s> <s xml:id="echoid-s2384" xml:space="preserve">15 e cinque ſi moltiplicheranno con la metà <lb/> <anchor type="handwritten" xlink:label="hd-152-01a" xlink:href="hd-152-01"/> de brac. </s> <s xml:id="echoid-s2385" xml:space="preserve">10, diametro, ch’èbrac. </s> <s xml:id="echoid-s2386" xml:space="preserve">5, & </s> <s xml:id="echoid-s2387" xml:space="preserve">faranno braccia 78 e <lb/>quattro ſettimi di ſuperficie del cerchio; </s> <s xml:id="echoid-s2388" xml:space="preserve">ancora hauendo <lb/>la circonferenza del cerchio, & </s> <s xml:id="echoid-s2389" xml:space="preserve">volẽdo il diametro del cer <lb/>chio, ſi partirà la circonferenza per 3 e vn ſettimo, & </s> <s xml:id="echoid-s2390" xml:space="preserve">quello <lb/>che venirà ſarà il diametro del cerchio; </s> <s xml:id="echoid-s2391" xml:space="preserve">& </s> <s xml:id="echoid-s2392" xml:space="preserve">pono come di ſo <lb/>pra la circonferenza ſia bra. </s> <s xml:id="echoid-s2393" xml:space="preserve">31 e tre ſettimi, ſi moltiplicarà <lb/>7, con 31 e tre ſettimi, & </s> <s xml:id="echoid-s2394" xml:space="preserve">faranno brac. </s> <s xml:id="echoid-s2395" xml:space="preserve">220, & </s> <s xml:id="echoid-s2396" xml:space="preserve">220, ſi par <lb/>tiranno per 22, & </s> <s xml:id="echoid-s2397" xml:space="preserve">ne venirà brac. </s> <s xml:id="echoid-s2398" xml:space="preserve">10, & </s> <s xml:id="echoid-s2399" xml:space="preserve">brac. </s> <s xml:id="echoid-s2400" xml:space="preserve">10, ſarà il dia-<lb/>metro del cerchio: </s> <s xml:id="echoid-s2401" xml:space="preserve">il medeſimo ſifarà in ogn’altro cerchio.</s> <s xml:id="echoid-s2402" xml:space="preserve"/> </p> <div xml:id="echoid-div83" type="float" level="2" n="3"> <handwritten xlink:label="hd-152-01" xlink:href="hd-152-01a"/> </div> <p> <s xml:id="echoid-s2403" xml:space="preserve">Volendo anchora la ſuperficie del cerchio per vn’altro <lb/>modo, multiplicando il diametro in ſe; </s> <s xml:id="echoid-s2404" xml:space="preserve">cioè 10, fia 10, fa <lb/>100, & </s> <s xml:id="echoid-s2405" xml:space="preserve">di 100, pigliarne li vndeci decimiquarti, ſarà la ſu <lb/>perficie del triangolo, cioè multiplicando 11, fia 100, fan-<lb/>no 1100, & </s> <s xml:id="echoid-s2406" xml:space="preserve">1100, ſi partirà per 14, e ne viene brac. </s> <s xml:id="echoid-s2407" xml:space="preserve">78 e <lb/>quattro ſettimi di ſuperficie; </s> <s xml:id="echoid-s2408" xml:space="preserve">& </s> <s xml:id="echoid-s2409" xml:space="preserve">ſe’l cerchio fuſſe terreno, il <lb/>78, e quattro ſettimi, ſarebbono, on. </s> <s xml:id="echoid-s2410" xml:space="preserve">78, e quattro ſettimi; <lb/></s> <s xml:id="echoid-s2411" xml:space="preserve">Con le ſopra dette regole, ſi potrà miſurare qualunque co <lb/>ſa ſi vorrà, nelle fabriche di muri & </s> <s xml:id="echoid-s2412" xml:space="preserve">ogni cauamento.</s> <s xml:id="echoid-s2413" xml:space="preserve"/> </p> <pb o="14" file="153" n="153" rhead="SECONDO."/> </div> <div xml:id="echoid-div85" type="section" level="1" n="71"> <head xml:id="echoid-head94" xml:space="preserve">DEL MISVRARE DELLE</head> <head xml:id="echoid-head95" xml:space="preserve">BIADE.</head> <p> <s xml:id="echoid-s2414" xml:space="preserve"><emph style="sc">HAvendo</emph> detto diſopra aſſai, del miſurare <lb/>de muri, qui ſeguendo ſi dirà del miſurare <lb/>delle Biade; </s> <s xml:id="echoid-s2415" xml:space="preserve">dando però prima le ſue rap-<lb/>preſentationi, che fanno i numeri molti-<lb/>plicati l’uno con l’altro.</s> <s xml:id="echoid-s2416" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2417" xml:space="preserve">Braccia fia braccia fanno brac. </s> <s xml:id="echoid-s2418" xml:space="preserve">nella prima moltiplica-<lb/>tione; </s> <s xml:id="echoid-s2419" xml:space="preserve">nella ſeconda moltiplicatione fanno quadretti.</s> <s xml:id="echoid-s2420" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>### Brac. fia on. fanno on. <lb/>### Brac. fia punti fanno punti. <lb/>### Oncie fia on. fanno punti. <lb/>### Oncie fia punti, fanno atomi. <lb/>### Punti fia punti, fanno minuti. <lb/>12, # minuti, # fanno vn atomo. <lb/>12, # atomi, # fanno vn punto. <lb/>12, # punti, # fanno vn’ oncia. <lb/>12, # oncie, # fanno vn brac. ouer vn quadretto. <lb/></note> <p> <s xml:id="echoid-s2421" xml:space="preserve">Vn quadretto di biada ſi è cubo, lungo, largo, & </s> <s xml:id="echoid-s2422" xml:space="preserve">alto vn <lb/>braccio; </s> <s xml:id="echoid-s2423" xml:space="preserve">& </s> <s xml:id="echoid-s2424" xml:space="preserve">è la ſua capacità quarte 9. </s> <s xml:id="echoid-s2425" xml:space="preserve">di biada, & </s> <s xml:id="echoid-s2426" xml:space="preserve">ogni quar-<lb/>ta peſa vn peſo, & </s> <s xml:id="echoid-s2427" xml:space="preserve">libre quattro, in circa di biada; </s> <s xml:id="echoid-s2428" xml:space="preserve">come più <lb/>auanti s’è detto.</s> <s xml:id="echoid-s2429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2430" xml:space="preserve">Hor volendo miſurare vn monton di biada, à modo di <lb/>quadrangolo, prima ſi ſquadra tal monton di biada con di-<lb/>ligenza, com’è il quadrangolo <emph style="sc">A B C D</emph>, della decima figura, <lb/>qui ſeguente diſſegnata.</s> <s xml:id="echoid-s2431" xml:space="preserve"/> </p> <pb file="154" n="154" rhead="LIBRO"/> <figure> <image file="154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/154-01"/> <caption xml:id="echoid-caption48" xml:space="preserve">Decima Figura.</caption> </figure> <p> <s xml:id="echoid-s2432" xml:space="preserve">La lunghezza ſia brac. </s> <s xml:id="echoid-s2433" xml:space="preserve">8, on. </s> <s xml:id="echoid-s2434" xml:space="preserve">6, la larghezza ſia bracc. </s> <s xml:id="echoid-s2435" xml:space="preserve">5, <lb/>on. </s> <s xml:id="echoid-s2436" xml:space="preserve">3, & </s> <s xml:id="echoid-s2437" xml:space="preserve">è alto brac. </s> <s xml:id="echoid-s2438" xml:space="preserve">1. </s> <s xml:id="echoid-s2439" xml:space="preserve">on. </s> <s xml:id="echoid-s2440" xml:space="preserve">2, le miſure ſi piglino, nella lun-<lb/>ghezza, & </s> <s xml:id="echoid-s2441" xml:space="preserve">larghezza, nella metà della ſcarpa, che fa eſſa bia <lb/>da in montone; </s> <s xml:id="echoid-s2442" xml:space="preserve">Et nella altezza ſi piglino tre miſure, vna <lb/>per ogni capo, & </s> <s xml:id="echoid-s2443" xml:space="preserve">vna nel mezo, perche la biada può eſſer <lb/>più alta, in vn luogo, che in vn’altro; </s> <s xml:id="echoid-s2444" xml:space="preserve">ma però la miſura del-<lb/>l’altezza di mezo ſi raddoppia, & </s> <s xml:id="echoid-s2445" xml:space="preserve">quello raddoppiamento <lb/>s’aggiunge con l’altre due miſure delle teſte, & </s> <s xml:id="echoid-s2446" xml:space="preserve">di quella <lb/>ſomma ſe ne piglia la quarta parte, & </s> <s xml:id="echoid-s2447" xml:space="preserve">quella quarta parte <lb/>ſarà la vera altezza della biada. </s> <s xml:id="echoid-s2448" xml:space="preserve">Et volendo vedere quan-<lb/>ta biada ſarà il ſopradetto montone, ſi moltiplicherà come <lb/>di ſopra ſi è detto de i muri; </s> <s xml:id="echoid-s2449" xml:space="preserve">cioè la larghezza, con la lun-<lb/>ghezza; </s> <s xml:id="echoid-s2450" xml:space="preserve">& </s> <s xml:id="echoid-s2451" xml:space="preserve">queſta prima moltiplicatione s’ha da dire nelle <lb/>brac. </s> <s xml:id="echoid-s2452" xml:space="preserve">braccia; </s> <s xml:id="echoid-s2453" xml:space="preserve">fatto queſto ſi moltiplicherà l’altezza con <pb o="15" file="155" n="155" rhead="SECONDO."/> queſta prima m oltiplicatione, & </s> <s xml:id="echoid-s2454" xml:space="preserve">quello che venirà in que-<lb/>ſta ſeconda moltiplicatione, nelle bracc. </s> <s xml:id="echoid-s2455" xml:space="preserve">ſe dira quadretti; <lb/></s> <s xml:id="echoid-s2456" xml:space="preserve">come ancora di ſopra ſiè detto de’ muri.</s> <s xml:id="echoid-s2457" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2458" xml:space="preserve">Hor veniremo alle moltiplicationi, hauendo fatto le ſo-<lb/>pradette operationi, & </s> <s xml:id="echoid-s2459" xml:space="preserve">conſiderationi; </s> <s xml:id="echoid-s2460" xml:space="preserve">come qui di ſotto <lb/>il tutto ſi può vedere.</s> <s xml:id="echoid-s2461" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div86" type="section" level="1" n="72"> <head xml:id="echoid-head96" xml:space="preserve">PRIMA RAGIONE</head> <head xml:id="echoid-head97" xml:space="preserve">delle Biade.</head> <note position="right" xml:space="preserve"> <lb/>Lunga brac. # 8, # on. # 6,} # Alta brac. 1, on. 2, <lb/>Larga brac. # 5, # on. # 3, <lb/>Brac. # 40, <lb/>Brac. # 2, # on. # 6, <lb/>Brac. # 2, # on. # 0, <lb/>Brac. # 0, # on. # 1, # pun. # 6, <lb/>Brac. # 44, # on. # 7, # pun. # 6, <lb/></note> </div> <div xml:id="echoid-div87" type="section" level="1" n="73"> <head xml:id="echoid-head98" xml:space="preserve">Proua della prima moltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>onc. # 4 # 0 # pun. <lb/>onc. # 0 # 0 # pun. <lb/></note> <note position="right" xml:space="preserve"> <lb/># braccia # # # 8 <lb/># braccia # # # 5 <lb/>braccia # # # # 40 <lb/># oncie # # # 6 <lb/># brac. # # # 5 <lb/>oncie # # # # 30 <lb/># partir per # # 12 <lb/># brac. # 2, # on. # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># brac. # # # 8 <lb/># oncie # # # 3 <lb/>oncie # # # # 24 <lb/># partir per # # 12 <lb/># brac. # 2, # on. # 0, <lb/># oncie # # # 6 <lb/># oncie # # # 3 <lb/>punti # # # # 18 <lb/># partir per # # 12 <lb/># on. # 1, # pun. # 6 <lb/></note> <pb file="156" n="156" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/>Brac. # 44, # on. # 7, # pun. # 6, <lb/>Brac. # 1, # on. # 2, <lb/>Quadretti # 44, # on. # 7, # pun. # 6, <lb/>Quadretti # 7, # on. # 4, <lb/>Quadretti # 0, # on. # 1, # pun. # 2, <lb/>Quadretti # 0, # on. # 0, # pun. # 1, <lb/>Quadretti # 52, # on. # 0, # pun. # 9, <lb/></note> </div> <div xml:id="echoid-div88" type="section" level="1" n="74"> <head xml:id="echoid-head99" xml:space="preserve">Proua della ſeconda moltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>pun. # 1, # 0, # ato. <lb/># 0, # 0, # ato. <lb/></note> <note position="right" xml:space="preserve"> <lb/># brac. # # # 44 <lb/># oncie # # # 2 <lb/>oncie # # # # 88 <lb/># partir per # # 12 <lb/># quadretti # 7, # on. # 4 <lb/></note> <note position="right" xml:space="preserve"> <lb/># punti # # 6 <lb/># oncie # # 2 <lb/>atomi # # # 12 <lb/># partir per # 12 <lb/>punti # # 1 <lb/></note> <p> <s xml:id="echoid-s2462" xml:space="preserve">Coſi hauendo moltiplicato la larghezza, con la lunghez <lb/>za, & </s> <s xml:id="echoid-s2463" xml:space="preserve">poi con l’altezza, ne ſono riuſciti quadretti 52, on.</s> <s xml:id="echoid-s2464" xml:space="preserve">0, <lb/>punti 9; </s> <s xml:id="echoid-s2465" xml:space="preserve">queſta ragione di biada è ſimile à quella delle mu-<lb/>raglie; </s> <s xml:id="echoid-s2466" xml:space="preserve">ma però volendo fare le ragioni delle biade à que-<lb/>ſto modo, ogni quadret to darà di biada quarte 9, & </s> <s xml:id="echoid-s2467" xml:space="preserve">ogni <lb/>oncia darà coppi 3, & </s> <s xml:id="echoid-s2468" xml:space="preserve">ogni punto, da vno ſtopello; </s> <s xml:id="echoid-s2469" xml:space="preserve">coſi qua <lb/>dretti 52, moltiplican doli per quarte 9, veniranno ad eſſere <lb/>quarte 468, & </s> <s xml:id="echoid-s2470" xml:space="preserve">punti 9, che ſono ſtop. </s> <s xml:id="echoid-s2471" xml:space="preserve">9, che fanno coppi 2, & </s> <s xml:id="echoid-s2472" xml:space="preserve"><lb/>ſtopello vno, che faranno in tutto quarte 468, coppi 2, ſto- <pb o="16" file="157" n="157" rhead="SECONDO."/> pello vno, & </s> <s xml:id="echoid-s2473" xml:space="preserve">tanto ſarà quad. </s> <s xml:id="echoid-s2474" xml:space="preserve">52, on. </s> <s xml:id="echoid-s2475" xml:space="preserve">0, pun. </s> <s xml:id="echoid-s2476" xml:space="preserve">9; </s> <s xml:id="echoid-s2477" xml:space="preserve">& </s> <s xml:id="echoid-s2478" xml:space="preserve">di quar-<lb/>te 468, ſi faranno in ſome, ouer carghe, volendole far in ſo-<lb/>me, ſi partiran per quarte 12, & </s> <s xml:id="echoid-s2479" xml:space="preserve">in carghe per quarte 14.</s> <s xml:id="echoid-s2480" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2481" xml:space="preserve">Appreſſo di queſto ſi moſtrerà il conto più facile, in que-<lb/>ſto modo; </s> <s xml:id="echoid-s2482" xml:space="preserve">ogni braccio in lunghezza fa coppi 3, ouer ogni <lb/>oncia vno ſtopello; </s> <s xml:id="echoid-s2483" xml:space="preserve">adunque brac. </s> <s xml:id="echoid-s2484" xml:space="preserve">8, in lunghezza ſaranno <lb/>coppi 24, che ſono quarte 6; </s> <s xml:id="echoid-s2485" xml:space="preserve">& </s> <s xml:id="echoid-s2486" xml:space="preserve">oncie 6, ſaranno vn coppo, <lb/>& </s> <s xml:id="echoid-s2487" xml:space="preserve">ſtopelli 2; </s> <s xml:id="echoid-s2488" xml:space="preserve">& </s> <s xml:id="echoid-s2489" xml:space="preserve">ogni braccio in larghezza, fa tutta la miſura <lb/>della lunghezza; </s> <s xml:id="echoid-s2490" xml:space="preserve">adunque moltiplicando braccia 5, on. </s> <s xml:id="echoid-s2491" xml:space="preserve">3, <lb/>con quarte 6, coppo 1, ſtopelli 2, faranno la prima ſuperfi-<lb/>cie, tutta a quarte, coppi, & </s> <s xml:id="echoid-s2492" xml:space="preserve">ſtopelli; </s> <s xml:id="echoid-s2493" xml:space="preserve">come qui ſotto il tutto <lb/>ſi vedrà.</s> <s xml:id="echoid-s2494" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div89" type="section" level="1" n="75"> <head xml:id="echoid-head100" xml:space="preserve">SECONDA RAGIONE</head> <head xml:id="echoid-head101" xml:space="preserve">delle Biade.</head> <note position="right" xml:space="preserve"> <lb/>Quarte # 6, # cop. # 1, # ſtopelli # 2, <lb/>Brac. # 5, # on. # 3, <lb/>Quarte # 30, <lb/>Quarte # 1, # cop. # 1, <lb/>Quarte # 0, # cop. # 2, # ſtop. # 2, <lb/>Quarte # 1, # cop. # 2, # ſtop. # 0, <lb/>Quarte # 0, # cop. # 0, # ſtop. # 1, <lb/>Quarte # 0, # cop. # 0, # ſtop. # mezo. <lb/>Quarte # 33, # cop. # 1, # ſtop. # 3 e mezo. <lb/></note> </div> <div xml:id="echoid-div90" type="section" level="1" n="76"> <head xml:id="echoid-head102" xml:space="preserve">Proua della prima m oltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>mezi ſtop. # 1, # 0, # on. de mezi ſtop. <lb/>oncie # 0, # 0, # on. de mezi ſtop. <lb/></note> <pb file="158" n="158" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># quarte # 6 <lb/># brac. # 5 <lb/>quarte # # 30 <lb/># brac. # 5 <lb/># cop. # 1 <lb/>cop. # # 5 <lb/># partir per # 4 <lb/># quarte # 1, cop. 1 <lb/># brac. # 5 <lb/># ſtop. # 2 <lb/>ſtop. # # 10 <lb/># partir per # 4 <lb/># cop. # 2, ſtop. 2 <lb/></note> <note position="right" xml:space="preserve"> <lb/># quarte # 6 <lb/># oncie # 3 <lb/>on. di quarte # # 18 <lb/># partir per # 12 <lb/># quar. # 1, cop. 2 <lb/># on. # 3 <lb/># cop. # 1 <lb/>on. di cop. # # 3 <lb/># partir per # 12 <lb/># cop. # 0, ſtop. 1 <lb/># on. # 3 <lb/># ſtop. # 2 <lb/>on. di ſtop. # # 6 <lb/># partir per # 12 <lb/># ſtop. # mezo <lb/></note> <p> <s xml:id="echoid-s2495" xml:space="preserve">Coſi moltiplicando brac. </s> <s xml:id="echoid-s2496" xml:space="preserve">5, on. </s> <s xml:id="echoid-s2497" xml:space="preserve">3, con quarte 6, cop. </s> <s xml:id="echoid-s2498" xml:space="preserve">1, <lb/>ſtop. </s> <s xml:id="echoid-s2499" xml:space="preserve">2, faranno quarte 33, cop. </s> <s xml:id="echoid-s2500" xml:space="preserve">1, ſtop. </s> <s xml:id="echoid-s2501" xml:space="preserve">3 e mezo, & </s> <s xml:id="echoid-s2502" xml:space="preserve">ſarà la <lb/>prima moltiplicatione della ſuperficie, & </s> <s xml:id="echoid-s2503" xml:space="preserve">la ſeconda molti-<lb/>plicatione ſarà il moltiplicare le onc. </s> <s xml:id="echoid-s2504" xml:space="preserve">14, dell’altezza, con <lb/>quarte 33, cop. </s> <s xml:id="echoid-s2505" xml:space="preserve">1, ſtop. </s> <s xml:id="echoid-s2506" xml:space="preserve">3 e mezzo,, & </s> <s xml:id="echoid-s2507" xml:space="preserve">quello che venirà ſa-<lb/>rà la quantità della biada, in figura quadrangolare. </s> <s xml:id="echoid-s2508" xml:space="preserve">Auuer <lb/>tendo però che ogni oncia in altezza darà tutta la ſuperfi-<lb/>cie prima della biada, come qui ſeguente ſi potrà vedere.</s> <s xml:id="echoid-s2509" xml:space="preserve"/> </p> <pb o="17" file="159" n="159" rhead="SECONDO"/> <note position="right" xml:space="preserve"> <lb/>Quarte # 33, # cop. # 1, # ſtop. # 3 e mezo <lb/>Oncie # 14, <lb/>Quarte # 462, <lb/>Quarte # 3, # cop. # 2, <lb/>Quarte # 3, # cop, # 0, # ſtop. 1, <lb/>Quarte # 468, # cop. # 2, # ſtop. 1. <lb/></note> </div> <div xml:id="echoid-div91" type="section" level="1" n="77"> <head xml:id="echoid-head103" xml:space="preserve">Proua della ſeconda moltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>mezi ſtop. # 0, # 0, # mezi ſtop. <lb/>oncie # 0, # 0, # mezi ſtop. <lb/></note> <note position="right" xml:space="preserve"> <lb/># quarte # 33 <lb/># oncie # 14 <lb/># # 132 <lb/># # 33 <lb/>quar. # # 462 <lb/># oncie # 14 <lb/># cop. # 1 <lb/>cop. # # 14 <lb/># partir per # 4 <lb/># quar. # 3, cop. 2 <lb/></note> <note position="right" xml:space="preserve"> <lb/># oncie # 14 <lb/># ſtop. # 3, e me. <lb/># # 42 <lb/># # 7 <lb/>ſtop. # # 49 <lb/># partir per # 4 <lb/># cop. # 12, ſto. 1. <lb/># partir per # 4 <lb/># quarte # 3 <lb/></note> <p> <s xml:id="echoid-s2510" xml:space="preserve">Coſi queſta ſeconda operatione, darà quarte 468, cop. </s> <s xml:id="echoid-s2511" xml:space="preserve">2, <lb/>ſtopel. </s> <s xml:id="echoid-s2512" xml:space="preserve">1. </s> <s xml:id="echoid-s2513" xml:space="preserve">Auuertendo, che non ſolamente ſipuò torre <lb/>la miſura dell’altezza, ma anchora quella della lunghez-<lb/>za, & </s> <s xml:id="echoid-s2514" xml:space="preserve">larghezza, ſeguitando l’ordine di ſopra, & </s> <s xml:id="echoid-s2515" xml:space="preserve">venirà tan-<lb/>to l’una, come l’altra, come qui ſotto meglio ſi potrà com-<lb/>prendere.</s> <s xml:id="echoid-s2516" xml:space="preserve"/> </p> <pb file="160" n="160" rhead="LIBRO"/> <p> <s xml:id="echoid-s2517" xml:space="preserve">Nella ſeconda ragione ſi è moltiplicato la larghezza cõ <lb/>la lunghezza; </s> <s xml:id="echoid-s2518" xml:space="preserve">& </s> <s xml:id="echoid-s2519" xml:space="preserve">poi ſi è fatta l’altezza à oncie, & </s> <s xml:id="echoid-s2520" xml:space="preserve">le oncie <lb/>dell’altezza ſono moltiplicate, con la moltiplicatione che <lb/>ha fatto la larghezza, nella lunghezza; </s> <s xml:id="echoid-s2521" xml:space="preserve">Appreſſo ſi molti-<lb/>plicherà l’altezza, con la larghezza, & </s> <s xml:id="echoid-s2522" xml:space="preserve">poila lunghezza ſi fa <lb/>rà a oncie, & </s> <s xml:id="echoid-s2523" xml:space="preserve">le on. </s> <s xml:id="echoid-s2524" xml:space="preserve">della lunghezza ſi moltiplicaranno, con <lb/>la ſuperficie che ha fatto l’altezza nella larghezza.</s> <s xml:id="echoid-s2525" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2526" xml:space="preserve">Ancora ſe ſi moltiplicheranno le oncie della larghezza <lb/>con la ſuperficie che ha fatto l’altezza nella lunghezza, ſi fa <lb/>rà l’una eguale all’altra come di ſopra ſi è detto; </s> <s xml:id="echoid-s2527" xml:space="preserve">& </s> <s xml:id="echoid-s2528" xml:space="preserve">per piu <lb/>chiarezza delle due che mancano, ſe ne darà eſſempio nel-<lb/>la terza, & </s> <s xml:id="echoid-s2529" xml:space="preserve">quarta ragione qui ſotto.</s> <s xml:id="echoid-s2530" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div92" type="section" level="1" n="78"> <head xml:id="echoid-head104" xml:space="preserve">TERZA RAGIONE</head> <head xml:id="echoid-head105" xml:space="preserve">delle Biade.</head> <note position="right" xml:space="preserve"> <lb/>Brac. # 8, # on. # 6, # lunga # } # Alta brac. 1. on. 2 <lb/>Brac. # 5, # on. # 3, # lunga <lb/></note> <note position="right" xml:space="preserve"> <lb/>###### Hor torremo il largo, che ſono quarte 3,|cop. 3, ſtop. 3. <lb/>Quarte # 3, # cop. # 3, # ſtop. # 3, <lb/>Brac. # 1, # on. # 2, <lb/>Quar. # 3, # cop. # 3. # ſtop. # 3, <lb/>Quar. # 0, # cop. # 2, <lb/>Quar. # 0, # cop. # 0, # ſtop. # 2, <lb/>Quar. # 0, # cop. # 0, # ſtop. # mezo. <lb/>Quar. # 4, # cop. # 2, # ſtop. # 1, # e mezzo. <lb/></note> </div> <div xml:id="echoid-div93" type="section" level="1" n="79"> <head xml:id="echoid-head106" xml:space="preserve">Proua della prima ’<unsure/>moltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>ſtop. # 0, # 0, # on. di ſtop. <lb/>on. # 0, # 0, # on. di ſtop. <lb/></note> <pb o="18" file="161" n="161" rhead="SECONDO"/> <note position="right" xml:space="preserve"> <lb/># quarte # 3 <lb/># oncie # 2 <lb/>oncie de # # 6 quar. <lb/># cop. # 2 <lb/># cop. # 3 <lb/># oncie # 2 <lb/>oncie de # # 6 copi. <lb/># ſtop. # 2 <lb/></note> <note position="right" xml:space="preserve"> <lb/># ſtop. # 3 <lb/># oncie # 2 <lb/>oncie de # # 6 ſtop. <lb/># ſtop. # mezo. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Quarte # 4, # cop. # 2, # ſtop. # 1 # emezo. <lb/>Oncie # 102, # della lunghezza, <lb/>Some # 34, <lb/>Some # 4, # quar. # 3, <lb/>Some # 0, # quar. # 9, # cop. # 2, # ſtop. # 1 <lb/>Some # 39, # quar. # 0, # cop. # 2, # ſtop. # 1 <lb/></note> </div> <div xml:id="echoid-div94" type="section" level="1" n="80"> <head xml:id="echoid-head107" xml:space="preserve">Proua della ſeconda moltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>ſtop. # 0, # 0, # mezi ſtop. <lb/>onc. # 4, # 0, # mezi ſtop. <lb/></note> <pb file="162" n="162" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># oncie # 102 <lb/># quarte # 4 <lb/>quarte # # 408 <lb/># partir per # 12 <lb/># ſome # 34 <lb/># onc. # 102 <lb/># cop. # 2 <lb/>cop. # # 204 <lb/># partir pe # 4 <lb/># quarte # 51 <lb/># partir per # 12 <lb/># ſome # 4, quar, 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/># onc. # 102 <lb/># ſtop. # 1, eme. <lb/># ſtop. # 102 <lb/># ſtop. # 51 <lb/>ſtop. # # 153 <lb/># partir per # 4 <lb/># cop. # 38, ſtop. 1, <lb/># partir per # 4 <lb/># quar.9, # cop. 2, ſto. 1, <lb/></note> </div> <div xml:id="echoid-div95" type="section" level="1" n="81"> <head xml:id="echoid-head108" xml:space="preserve">QVARTA RAGIONE <lb/>delle Biade.</head> <p> <s xml:id="echoid-s2531" xml:space="preserve">Hor ſi torrà l’ altezza, che ſono ſto. </s> <s xml:id="echoid-s2532" xml:space="preserve">14, che fanno cop.</s> <s xml:id="echoid-s2533" xml:space="preserve">3, ſt. </s> <s xml:id="echoid-s2534" xml:space="preserve">2.</s> <s xml:id="echoid-s2535" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Altezza cop. # 3, # ſtop. # 2, <lb/>Lunghezza bra. # 8, # onc. # 6, <lb/>Quarte # 6, <lb/>Quarte # 1, <lb/>Quarte # 0, # cop. # 1, # ſtop. # 2, <lb/>Quarte # 0, # cop. # 0, # ſtop. # 1, <lb/>Quarte # 7, # cop. # 1, # ſtop. # 3, <lb/></note> </div> <div xml:id="echoid-div96" type="section" level="1" n="82"> <head xml:id="echoid-head109" xml:space="preserve">Proua della prima moltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>ſtop. # 0, # 0, # on. di ſtop. <lb/>on. # 0, # 0, # on. di ſtop. <lb/></note> <pb o="19" file="163" n="163" rhead="ECONDO."/> <note position="right" xml:space="preserve"> <lb/># brac. # 8 <lb/># cop. # 3 <lb/>cop. # # 24 <lb/># partir per # 4 <lb/># quarte # 6 <lb/># brac. # 8 <lb/># ſtop. # 2 <lb/>ſtop. # # 16 <lb/># partir per # 4 <lb/># cop. # 4 <lb/># partir per # 4 <lb/># quarte # 1 <lb/></note> <note position="right" xml:space="preserve"> <lb/># oncie # 6 <lb/># cop. # 3 <lb/># on. de # 18 cop. <lb/># partir per # 12 <lb/># cop. # 1, ſto. 2 <lb/># oncie # 6 <lb/># ſtop. # 2 <lb/># oncie di # 12 ſtop. <lb/># partir per # 12 <lb/># ſtop. # 1 <lb/></note> <note position="right" xml:space="preserve"> <lb/># Quarte # 7, # cop. # 1, # ſtop. # 3, <lb/>## Larghezza on. # 63, <lb/>Some # # 36, # quar. # 9, <lb/>Some # # 1, # quar. # 3, # cop. # 3, <lb/>Some # # 0, # quar. # 11, # cop. # 3, # ſtop. # 1 <lb/>Some # # 39, # quar. # 0, # cop. # 2, # ſtop. # 1 <lb/></note> </div> <div xml:id="echoid-div97" type="section" level="1" n="83"> <head xml:id="echoid-head110" xml:space="preserve">Proua della ſeconda moltiplicatione.</head> <note position="right" xml:space="preserve"> <lb/>ſtop. # 0, # 0, # on. di ſtop. <lb/>onc. # 0, # 0, # on. di ſtop. <lb/></note> <pb file="164" n="164" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># oncie # 63 <lb/># quarte # 7 <lb/>quarte # # 441 <lb/># partir per # 12 <lb/># ſome # 36, quar. 9 <lb/># onc. # 63 <lb/># cop. # 1 <lb/>cop. # # 63 <lb/># partir per # 4 <lb/># quarte # 15, co. 3 <lb/># partir per # 12 <lb/># ſome 1, quar. # 3, cop. 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/># onc. # 63 <lb/># ſtop. # 3 <lb/>ſtop. # # 189 <lb/># partir per # 4 <lb/># cop. # 47, ſtop. 1, <lb/># partir per # 4 <lb/># quar. # 11, cop. 3, ſto. 1 <lb/></note> <p> <s xml:id="echoid-s2536" xml:space="preserve">Coſi ſi vede che in tutti trei modi, viene l’uno come l’ al <lb/>tro; </s> <s xml:id="echoid-s2537" xml:space="preserve">Ancora con maggior facilità ſi può farei conti ſenza ti <lb/>rarli a onc. </s> <s xml:id="echoid-s2538" xml:space="preserve">ma laſſarli in ſuo grado di brac. </s> <s xml:id="echoid-s2539" xml:space="preserve">& </s> <s xml:id="echoid-s2540" xml:space="preserve">oncie, perche <lb/>à moltiplicare brac. </s> <s xml:id="echoid-s2541" xml:space="preserve">con ſome ogni bra. </s> <s xml:id="echoid-s2542" xml:space="preserve">da 12. </s> <s xml:id="echoid-s2543" xml:space="preserve">ſome, a mol <lb/>tiplicare brac. </s> <s xml:id="echoid-s2544" xml:space="preserve">con quarte, ogni brac. </s> <s xml:id="echoid-s2545" xml:space="preserve">da vna ſoma, à molti-<lb/>plicare brac. </s> <s xml:id="echoid-s2546" xml:space="preserve">con cop. </s> <s xml:id="echoid-s2547" xml:space="preserve">ogni brac. </s> <s xml:id="echoid-s2548" xml:space="preserve">da tre quarte, à moltipli-<lb/>care brac. </s> <s xml:id="echoid-s2549" xml:space="preserve">con ſtopelli, ogni brac. </s> <s xml:id="echoid-s2550" xml:space="preserve">dà tre cop. </s> <s xml:id="echoid-s2551" xml:space="preserve">come qui ſot-<lb/>to ſiv edrà.</s> <s xml:id="echoid-s2552" xml:space="preserve"/> </p> <pb o="20" file="165" n="165" rhead="SECONDO."/> </div> <div xml:id="echoid-div98" type="section" level="1" n="84"> <head xml:id="echoid-head111" xml:space="preserve">QVINTA RAGIONE <lb/>delle Biade.</head> <note position="right" xml:space="preserve"> <lb/>Some # 2, # quar. # 9, # cop. # 1, # ſtop. # 3, # e mezo. <lb/>Brac. # 1, # oncie # 2 <lb/>Some # 24, <lb/>Some # 9, <lb/>Some # 0, # quar. # 3, <lb/>Some # 0, # quar. # 2, # cop. # 2, # ſtop. # 2, <lb/>Some # 4, # quar. # 0, # cop. # 0, <lb/>Some # 1, # quar. # 6, # cop. # 0, <lb/>Some # 0, # quar. # 0, # cop. # 2, <lb/>Some # 0, # quar. # 0, # cop. # 1, # ſtop. # 3, <lb/>Some # 39, # quar. # 0, # cop. # 2, # ſtop. # 1, <lb/></note> </div> <div xml:id="echoid-div99" type="section" level="1" n="85"> <head xml:id="echoid-head112" xml:space="preserve">Proua.</head> <note position="right" xml:space="preserve"> <lb/>ſtop. # 0, # 0, # on. de mezi ſtop. <lb/>oncie # 0, # 0, # on. de mezi ſtop. <lb/></note> <note position="right" xml:space="preserve"> <lb/># ſome # 2 <lb/># brac. # 1 <lb/>Some # # 24 <lb/># quar. # 9 <lb/># brac. # 1 <lb/>ſome # # 9 <lb/></note> <note position="right" xml:space="preserve"> <lb/># cop. # 1 <lb/># brac. # 1 <lb/>quarte # # 3 <lb/># ſtop. # 3 e mez. <lb/># brac. # 1 <lb/>cop. # # 10, ſtop. 2 <lb/># partir per # 4 <lb/># quar. # 2, cop.2,ſt. 2 <lb/></note> <pb file="166" n="166" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># ſome # 2 <lb/># on. # 2 <lb/>ſome # # 4 <lb/># quarte # 9 <lb/># on. # 2 <lb/>quarte # # 18 <lb/># partir per # 12 <lb/># ſome # 1, quar. 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/># on. # 2 <lb/># cop. # 1 <lb/>cop. # # 2 <lb/># ſtop. # 3 e mezo <lb/># oncie # 2 <lb/>ſtop. # # 7 <lb/># partir per # 4 <lb/># cop. 1 # ſtop. 3 <lb/></note> <p> <s xml:id="echoid-s2553" xml:space="preserve">Coſi ſi vede, che à queſto modo ſi caueranno ſome 39, <lb/>quar. </s> <s xml:id="echoid-s2554" xml:space="preserve">0, cop. </s> <s xml:id="echoid-s2555" xml:space="preserve">2. </s> <s xml:id="echoid-s2556" xml:space="preserve">ſtop. </s> <s xml:id="echoid-s2557" xml:space="preserve">1, come ne gl’altritre modi moſtrati di <lb/>ſopra. </s> <s xml:id="echoid-s2558" xml:space="preserve">il medeſimo ſi farà f<unsure/>e ſi voleſſe fare gl’altri due modi, <lb/>oſſeruati di ſopra. </s> <s xml:id="echoid-s2559" xml:space="preserve">Detto aſſai del fare i conti delle biade,?</s> <s xml:id="echoid-s2560" xml:space="preserve">? <lb/> <anchor type="handwritten" xlink:label="hd-166-01a" xlink:href="hd-166-01"/> ſeguendo ſe ne daranno altri eſſempi; </s> <s xml:id="echoid-s2561" xml:space="preserve">come di miſurarle in <lb/> <anchor type="handwritten" xlink:label="hd-166-01a" xlink:href="hd-166-01"/> triangoli, & </s> <s xml:id="echoid-s2562" xml:space="preserve">in piramide rotonda.</s> <s xml:id="echoid-s2563" xml:space="preserve"/> </p> <div xml:id="echoid-div99" type="float" level="2" n="1"> <handwritten xlink:label="hd-166-01" xlink:href="hd-166-01a"/> <handwritten xlink:label="hd-166-01" xlink:href="hd-166-01a"/> </div> <p> <s xml:id="echoid-s2564" xml:space="preserve">Verbi gratia ſi ritroua vn montone di biada à modo di <lb/>triangolo in vn cantone, il quale è neceſſario miſurare; </s> <s xml:id="echoid-s2565" xml:space="preserve">pri-<lb/>mieramente ſi ſpianerà eſſa biada di ſoprauia, con vna pala <lb/>ouer altro ſtromento, & </s> <s xml:id="echoid-s2566" xml:space="preserve">ſpianato eſſo montone talmente, <lb/>che non habbia portion di piramide rotonda, perche altra-<lb/>mente ſarebbe difficile miſurarlo; </s> <s xml:id="echoid-s2567" xml:space="preserve">& </s> <s xml:id="echoid-s2568" xml:space="preserve">la cauſa di queſto è per <lb/>che ſarebbe difficile hauere la portion del cerchio, che eſſa <lb/>piramide ha formato; </s> <s xml:id="echoid-s2569" xml:space="preserve">Sia adunque il montone della biada <lb/>à modo deltriangolo <emph style="sc">A B C</emph>, & </s> <s xml:id="echoid-s2570" xml:space="preserve">l’angolo <emph style="sc">B</emph>, ſia ſoppoſto ret-<lb/>to, perche le due linee <emph style="sc">A B</emph>, & </s> <s xml:id="echoid-s2571" xml:space="preserve"><emph style="sc">B C</emph>, ſi ſuppone che ſiano i due <lb/>muri che contengano il montone di biada, & </s> <s xml:id="echoid-s2572" xml:space="preserve">perche gli an-<lb/>goli de’ muri ſono retti la maggior parte, percio il monton <lb/>ſi miſurerà appreſſo i muri, cioè le due linee <emph style="sc">A B</emph>, & </s> <s xml:id="echoid-s2573" xml:space="preserve"><emph style="sc">C B</emph>; </s> <s xml:id="echoid-s2574" xml:space="preserve">& </s> <s xml:id="echoid-s2575" xml:space="preserve"><lb/>poniamo che la linea <emph style="sc">A B</emph>, ſia braccia 7, oncie 4, & </s> <s xml:id="echoid-s2576" xml:space="preserve">la linea <lb/><emph style="sc">C B</emph>, bracc. </s> <s xml:id="echoid-s2577" xml:space="preserve">6, oncie 2.</s> <s xml:id="echoid-s2578" xml:space="preserve"/> </p> <pb o="21" file="167" n="167" rhead="SECONDO"/> <figure> <image file="167-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/167-01"/> </figure> <p> <s xml:id="echoid-s2579" xml:space="preserve">Et per quadrare detto triangolo ſi torrà la metà d’una del-<lb/>le dette miſure qual ſi vorrà, hor pigliaſi la metà della linea <lb/><emph style="sc">A B</emph>, brac. </s> <s xml:id="echoid-s2580" xml:space="preserve">7, on. </s> <s xml:id="echoid-s2581" xml:space="preserve">4, che la ſua metà ſarà brac. </s> <s xml:id="echoid-s2582" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s2583" xml:space="preserve">8, & </s> <s xml:id="echoid-s2584" xml:space="preserve">ſa-<lb/>rà quadrato il detto triangolo, come di ſopra ſi è moſtrato <lb/>ne i triangoli delle miſure di terra; </s> <s xml:id="echoid-s2585" xml:space="preserve">coſi f<unsure/>arà lunga brac. </s> <s xml:id="echoid-s2586" xml:space="preserve">6, <lb/>on. </s> <s xml:id="echoid-s2587" xml:space="preserve">2, larga brac. </s> <s xml:id="echoid-s2588" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s2589" xml:space="preserve">8; </s> <s xml:id="echoid-s2590" xml:space="preserve">& </s> <s xml:id="echoid-s2591" xml:space="preserve">ponendo che’l formento ſia <lb/>alto brac. </s> <s xml:id="echoid-s2592" xml:space="preserve">1, on. </s> <s xml:id="echoid-s2593" xml:space="preserve">3, ſi farà il conto come di ſopra, in qual mo <lb/>do ſi vorrà, & </s> <s xml:id="echoid-s2594" xml:space="preserve">ſi trouarà, che ſaranno quarte 254, coppo 1, <lb/>& </s> <s xml:id="echoid-s2595" xml:space="preserve">ſtop. </s> <s xml:id="echoid-s2596" xml:space="preserve">2, come qui ſeguente ſi vedrà.</s> <s xml:id="echoid-s2597" xml:space="preserve"/> </p> <pb file="168" n="168" rhead="LIBRO"/> </div> <div xml:id="echoid-div101" type="section" level="1" n="86"> <head xml:id="echoid-head113" xml:space="preserve">SESTA RAGIONE <lb/>delle Biade.</head> <note position="right" xml:space="preserve"> <lb/>Lungobrac. # 6, # on. # 2. # } # Alto brac. 1, on. 3. <lb/>Largo brac. # 3, # on. # 8. <lb/>Lunghezza quar. # 4, # cop. # 2, # ſtop. # 2. <lb/>Larghezza brac. # 3, # on. # 8, <lb/>Quar. # 12, <lb/>Quar. # 1, # cop. # 2, <lb/>Quar. # 0, # cop. # 1, # ſtop. # 2, <lb/>Quar. # 2, # cop. # 2, # ſtop. # 2, # e dueterzi. <lb/>Quar. # 0, # cop. # 1, # ſtop. # 1, # e vn terzo. <lb/>Quarte # 0, # cop. # 0, # ſtop. # 1, # e vn terzo. <lb/>Quarte # 16, # cop. # 3, # ſtop. # 3, # ’e vn terzo. <lb/></note> </div> <div xml:id="echoid-div102" type="section" level="1" n="87"> <head xml:id="echoid-head114" xml:space="preserve">Proua.</head> <note position="right" xml:space="preserve"> <lb/>ſtop. # 4, # 3, # on. de terzi di ſtop. <lb/>on. # 2, # 3, # on. de terzi di ſtop. <lb/></note> <note position="right" xml:space="preserve"> <lb/># quarte # 4 <lb/># brarc. # 3 <lb/>quar. # # 12 <lb/># brac. # 3 <lb/># cop. # 2 <lb/>cop. # # 6 <lb/># quar. # 1, cop. 2 <lb/></note> <note position="right" xml:space="preserve"> <lb/># brac. # 3 <lb/># ſtop. # 2 <lb/># ſtop. # 6 <lb/># cop. # 1, ſtop. 2 <lb/># onc. # 8 <lb/># quar. # 4 <lb/>onc. di # quar. # 32 <lb/># partir per # 12 <lb/>quar. 2, # cop. 2,ſt. # 2, e doi ter. <lb/></note> <pb o="22" file="169" n="169" rhead="SECONDO"/> <note position="right" xml:space="preserve"> <lb/># onc. # 8 <lb/># cop. # 2 <lb/>onc. di # cop. # 16 <lb/># partir per # 12 <lb/>cop. # 1, # ſto.1, e vn ter. <lb/></note> <note position="right" xml:space="preserve"> <lb/># oncie # 8 <lb/># ſtop. # 2 <lb/>onc. de # ſtop. # 16 <lb/># partir per # 12 <lb/># ſtop. # 1, e vn ter. <lb/></note> <p> <s xml:id="echoid-s2598" xml:space="preserve">Coſi moltiplicando le brac. </s> <s xml:id="echoid-s2599" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s2600" xml:space="preserve">8, della larghezza, <lb/>con le quarte 4. </s> <s xml:id="echoid-s2601" xml:space="preserve">coppi 2, ſtop. </s> <s xml:id="echoid-s2602" xml:space="preserve">2, della lunghezza, fanno <lb/>quarte 16, cop. </s> <s xml:id="echoid-s2603" xml:space="preserve">3, ſtop. </s> <s xml:id="echoid-s2604" xml:space="preserve">3 e vn terzo. </s> <s xml:id="echoid-s2605" xml:space="preserve">Poi ſi moltiplicarà <lb/>on. </s> <s xml:id="echoid-s2606" xml:space="preserve">15, dell’altezza, con quarte 16, cop. </s> <s xml:id="echoid-s2607" xml:space="preserve">3, ſtop. </s> <s xml:id="echoid-s2608" xml:space="preserve">3 e vn terzo; <lb/></s> <s xml:id="echoid-s2609" xml:space="preserve">come qui ſotto ſi vede.</s> <s xml:id="echoid-s2610" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div103" type="section" level="1" n="88"> <head xml:id="echoid-head115" xml:space="preserve">SETTIMA RAGIONE <lb/>delle Biade.</head> <note position="right" xml:space="preserve"> <lb/>Quarte # 16, # cop. # 3, # ſtop. # 3 e vn tezo. <lb/>Oncie # 15, <lb/>Quarte # 240, <lb/>Quarte # 11, # cop. # 1, <lb/>Quarte # 3, # cop. # 0, # ſtop. # 2, <lb/>Quarte # 254, # cop. # 2, # ſtop. # 2. <lb/></note> </div> <div xml:id="echoid-div104" type="section" level="1" n="89"> <head xml:id="echoid-head116" xml:space="preserve">Proua</head> <note position="right" xml:space="preserve"> <lb/>terzi de ſtop. # 2, # 2, # terzi de ſtop. <lb/>oncie # 1, # 2, # terzi de ſtop. <lb/></note> <pb file="170" n="170" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># quar. # 16 <lb/># oncie # 15 <lb/># # 80 <lb/># # 16 <lb/>quarte # # 240 <lb/># on. # 15 <lb/># cop. # 3 <lb/># cop. # 45 <lb/># partir per # 4 <lb/>quarte # # 11, cop. 1 <lb/></note> <note position="right" xml:space="preserve"> <lb/># onc. # 15 <lb/># ſtop. # 3 e vn ter. <lb/>ſtop. # # 45 <lb/># # 5 <lb/># ſtop. # 50 <lb/># partir per # 4 <lb/># cop. # 12, ſtop. 2 <lb/># partir per # 4 <lb/># quarte # 3, ſto. 2 <lb/></note> <p> <s xml:id="echoid-s2611" xml:space="preserve">Coſi il ſopradetto monton di biada à modo di triangolo <lb/>ſia quarte 254, cop. </s> <s xml:id="echoid-s2612" xml:space="preserve">1, ſtop. </s> <s xml:id="echoid-s2613" xml:space="preserve">2. </s> <s xml:id="echoid-s2614" xml:space="preserve">Il medeſimo ſi farà d’ogn’al-<lb/>tro monton di biada a modo di triangolo.</s> <s xml:id="echoid-s2615" xml:space="preserve"/> </p> <figure> <image file="170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/170-01"/> </figure> <pb o="23" file="171" n="171" rhead="SECONDO."/> <p> <s xml:id="echoid-s2616" xml:space="preserve">Et hauẽ do da miſurare vn monton di biada à modo d’vn <lb/>triangolo, che non haueſſe angolo retto, come il trian golo <lb/><emph style="sc">D E F</emph>; </s> <s xml:id="echoid-s2617" xml:space="preserve">pervolere miſurare tal monton di biada ſi piglierà la <lb/>perpendico lare più giuſta che ſia poſsibile, che venga à ca-<lb/>dere perpendicolarmente dall’angolo ſuperiore ſopra la <lb/>metà della ſcarpa che fa eſſa biada à modo di triangolo ſo-<lb/>pra la baſe; </s> <s xml:id="echoid-s2618" xml:space="preserve">& </s> <s xml:id="echoid-s2619" xml:space="preserve">pono che la miſura della perpendicolare, ſia <lb/>la linea <emph style="sc">E G</emph>, brac. </s> <s xml:id="echoid-s2620" xml:space="preserve">8, on. </s> <s xml:id="echoid-s2621" xml:space="preserve">3; </s> <s xml:id="echoid-s2622" xml:space="preserve">& </s> <s xml:id="echoid-s2623" xml:space="preserve">la baſe <emph style="sc">D F</emph>, brac. </s> <s xml:id="echoid-s2624" xml:space="preserve">7, on. </s> <s xml:id="echoid-s2625" xml:space="preserve">8, pri-<lb/>ma ſi piglierà la metà, come di ſopra s’è detto, ò dell<unsure/>a per-<lb/>pendicolare, ouer della baſe, & </s> <s xml:id="echoid-s2626" xml:space="preserve">pongo pigliar la metà del-<lb/>la perpendicolare, che ſarà brac. </s> <s xml:id="echoid-s2627" xml:space="preserve">4, on. </s> <s xml:id="echoid-s2628" xml:space="preserve">1, punti 6, queſta ſi <lb/>ponerà per larghezza; </s> <s xml:id="echoid-s2629" xml:space="preserve">& </s> <s xml:id="echoid-s2630" xml:space="preserve">per lunghezza ſi piglierà la baſe, <lb/>che ſon brac. </s> <s xml:id="echoid-s2631" xml:space="preserve">7, on. </s> <s xml:id="echoid-s2632" xml:space="preserve">8, & </s> <s xml:id="echoid-s2633" xml:space="preserve">à queſto modo il trriangolo ſarà <lb/>ſquadrato, come di ſopra ne’ triangoli del miſurare le terre; <lb/></s> <s xml:id="echoid-s2634" xml:space="preserve">& </s> <s xml:id="echoid-s2635" xml:space="preserve">l’altezza del montone, à modo di triangolo verrà ad eſ-<lb/>ſere on. </s> <s xml:id="echoid-s2636" xml:space="preserve">8, & </s> <s xml:id="echoid-s2637" xml:space="preserve">ſi faranno i conti, come di ſopra, & </s> <s xml:id="echoid-s2638" xml:space="preserve">qui di ſot-<lb/>to ſi trouerà la biada quarte 189, coppi 3, in miſura.</s> <s xml:id="echoid-s2639" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Lungo brac. # 7, # on. # 8, # # } # Alto on. 8, <lb/>Largo brac. # 4, # on. # 1, # pun. 6, <lb/></note> <p> <s xml:id="echoid-s2640" xml:space="preserve">La lunghezza ſono quarte 5, cop. </s> <s xml:id="echoid-s2641" xml:space="preserve">3, & </s> <s xml:id="echoid-s2642" xml:space="preserve">à tanto ſi pone-<lb/>ranno ſotto brac. </s> <s xml:id="echoid-s2643" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s2644" xml:space="preserve">1. </s> <s xml:id="echoid-s2645" xml:space="preserve">pun. </s> <s xml:id="echoid-s2646" xml:space="preserve">6; </s> <s xml:id="echoid-s2647" xml:space="preserve">& </s> <s xml:id="echoid-s2648" xml:space="preserve">ſi farannoi conti co-<lb/>me qui ſeguente.</s> <s xml:id="echoid-s2649" xml:space="preserve"/> </p> <pb file="172" n="172" rhead="LIBRO"/> </div> <div xml:id="echoid-div105" type="section" level="1" n="90"> <head xml:id="echoid-head117" xml:space="preserve">SETTIMA RAGIONE <lb/>delle biade.</head> <note position="right" xml:space="preserve"> <lb/>Quarte # 5, # cop. # 3, <lb/>Brac. # 4, # on. # 1, # pun. # 6, <lb/>Quarte # 20, <lb/>Quarte # 3, <lb/>Quarte # 0, # cop. # 1, # ſtop. # 2, # e doiterzi. <lb/>Quarte # 0, # cop. # 0, # ſtop. # 1, <lb/>Quarte # 0, # cop. # 0, # ſtop. # 3, # evn terzo. <lb/>Quarte # 0, # cop. # 0, # ſtop. # # mezo. <lb/>Quarte # 23, # cop. # 2, # ſtop. # 3, # e mezo. <lb/></note> </div> <div xml:id="echoid-div106" type="section" level="1" n="91"> <head xml:id="echoid-head118" xml:space="preserve">Proua.</head> <note position="right" xml:space="preserve"> <lb/>ſtop. # 1, # 5, # on. pun. de mezi ſtop. <lb/>mezi pun. # 5, # 5, # on. pun de mezi ſtop. <lb/></note> <note position="right" xml:space="preserve"> <lb/># quarte # 5 <lb/># brac. # 4 <lb/>quar. # # 20 <lb/># brac. # 4 <lb/># cop. # 3 <lb/>cop. # # 12 <lb/># partir per # 4 <lb/># quar. # 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/># quar. # 5 <lb/># onc. # 1 <lb/>onc. di quar. # # 5 <lb/># partir per # 12 <lb/>cop. # # 1, ſtop. 2, e doi ter. <lb/></note> <pb o="24" file="173" n="173" rhead="SECONDO."/> <note position="right" xml:space="preserve"> <lb/># cop. # 3 <lb/># oncie # 1 <lb/>onc. di cop. # # 3 <lb/># partir per # 12 <lb/># ſtop. # 1 <lb/># quarte # 5 <lb/># punti # 6 <lb/>punti # # 30 <lb/># partir per # 12 <lb/># on. de quar. # 2 e me. <lb/># # 4 <lb/>oncie de cop. # # 10 <lb/># # 4 <lb/>onc. de ſtop. # # 40 <lb/># partir per # 12 <lb/># ſtop. # 3, evn ter. <lb/></note> <note position="right" xml:space="preserve"> <lb/># puuti # 6 <lb/># cop. # 3 <lb/>punti # # 18 <lb/># partir per # 12 <lb/># on. de cop. # 1, e me. <lb/># # 4 <lb/>on. de ſtop. # # 6 <lb/># partir per # 12 <lb/># ſtop. # mezo. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Quarte # 37<unsure/>, # cop. # 2, # ſtop. # 3 e mezo. <lb/>Oncie # 8, <lb/>Quarte # 184, <lb/>Quarte # 4, <lb/>Quarte # 1, # cop, # 3, <lb/>Quarte # 189, # cop. # 3, <lb/></note> </div> <div xml:id="echoid-div107" type="section" level="1" n="92"> <head xml:id="echoid-head119" xml:space="preserve">Proua</head> <note position="right" xml:space="preserve"> <lb/>mezi ſtop. # 3, # 3, # mezi ſtop. <lb/>oncie # 1, # 3, # mezi ſtop. <lb/></note> <pb file="174" n="174" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># quar. # 23 <lb/># oncie # 8 <lb/>quarte # # 184 <lb/># on. # 8 <lb/># cop. # 2 <lb/>cop. # # 16 <lb/># partir per # 4 <lb/>quarte # # 4 <lb/></note> <note position="right" xml:space="preserve"> <lb/># onc. # 8 <lb/># ſtop. # 3 e mezo <lb/># # 24 <lb/># # 4 <lb/># ſtop. # 28 <lb/># partir per # 4 <lb/># cop. # 7 <lb/># partir per # 4 <lb/># quarte # 1, cop.3 <lb/></note> <p> <s xml:id="echoid-s2650" xml:space="preserve">Coſi ſi vede, che’l ſopradetto montone di biada, à modo <lb/>ditriangolo, ſiè quarte 189, cop. </s> <s xml:id="echoid-s2651" xml:space="preserve">3; </s> <s xml:id="echoid-s2652" xml:space="preserve">Il medeſimo ſi farà vo-<lb/>lendo miſurar’ ogn’altro montone di bia da ſimile à queſto.</s> <s xml:id="echoid-s2653" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2654" xml:space="preserve">Hauendo fin qui detto del miſurare le biade in quadran-<lb/>golo, & </s> <s xml:id="echoid-s2655" xml:space="preserve">in triangolo, conſeguentemente ſi dirà del miſu-<lb/>rarle à modo di piramide rotonda, doue ſi miſura ſolo <lb/>il diametro della baſe, & </s> <s xml:id="echoid-s2656" xml:space="preserve">la linea che cade dal vertice della <lb/> <anchor type="figure" xlink:label="fig-174-01a" xlink:href="fig-174-01"/> <pb o="25" file="175" n="175" rhead="SECONDO"/> piramide perpendicolare ſopra il centro d’eſſa baſe, come <lb/>moſtra la piramide <emph style="sc">A B C</emph>, diametro <emph style="sc">A C</emph>, vertice, <emph style="sc">B</emph>, la linea <lb/>perpendicolare <emph style="sc">B D</emph>, che cade perpendico larmente dal pun <lb/>to <emph style="sc">B</emph>, vertice al punto <emph style="sc">D</emph>, centro del cerchio della baſe, <emph style="sc">A B<unsure/> C</emph>;</s> <s xml:id="echoid-s2657" xml:space="preserve">f<unsure/> <lb/>hor ſi pone, che la perpendicolare <emph style="sc">B D</emph>, ſia brac. </s> <s xml:id="echoid-s2658" xml:space="preserve">3, on. </s> <s xml:id="echoid-s2659" xml:space="preserve">6, il <lb/>diametro <emph style="sc">A C</emph>, brac. </s> <s xml:id="echoid-s2660" xml:space="preserve">2, on. </s> <s xml:id="echoid-s2661" xml:space="preserve">8; </s> <s xml:id="echoid-s2662" xml:space="preserve">per vedere quanta biada ſarà <lb/>in eſſa piramide, in due modi ſi moſtrerà; </s> <s xml:id="echoid-s2663" xml:space="preserve">il primo è, che ſi <lb/>pigli la quadratura del cerchio della baſe in queſto modo ſi <lb/>moltiplicherà il diametro in ſe, & </s> <s xml:id="echoid-s2664" xml:space="preserve">di quella moltiplicatio-<lb/>ne ſitorrà gli vndeci quator decimi, & </s> <s xml:id="echoid-s2665" xml:space="preserve">quella ſarà la quadra <lb/>tura del cerchio; </s> <s xml:id="echoid-s2666" xml:space="preserve">come moltiplicando brac. </s> <s xml:id="echoid-s2667" xml:space="preserve">2, onc. </s> <s xml:id="echoid-s2668" xml:space="preserve">8, con <lb/>brac. </s> <s xml:id="echoid-s2669" xml:space="preserve">2, on. </s> <s xml:id="echoid-s2670" xml:space="preserve">8; </s> <s xml:id="echoid-s2671" xml:space="preserve">faranno brac. </s> <s xml:id="echoid-s2672" xml:space="preserve">7, onc. </s> <s xml:id="echoid-s2673" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s2674" xml:space="preserve">4, & </s> <s xml:id="echoid-s2675" xml:space="preserve">di brac. </s> <s xml:id="echoid-s2676" xml:space="preserve">7, <lb/>onc. </s> <s xml:id="echoid-s2677" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s2678" xml:space="preserve">4, pigliando li vndeci quatordecimi, in que-<lb/>ſto modo, moltiplicando 11, con brac. </s> <s xml:id="echoid-s2679" xml:space="preserve">7, on. </s> <s xml:id="echoid-s2680" xml:space="preserve">1, pun. </s> <s xml:id="echoid-s2681" xml:space="preserve">4, co-<lb/>me qui ſotto ſi vede.</s> <s xml:id="echoid-s2682" xml:space="preserve"/> </p> <div xml:id="echoid-div107" type="float" level="2" n="1"> <figure xlink:label="fig-174-01" xlink:href="fig-174-01a"> <image file="174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/174-01"/> </figure> </div> <note position="right" xml:space="preserve"> <lb/>Brac. # 7, # on. # 1, # pun. # 4. <lb/># 11, <lb/>Brac. # 77, # on. # 11, <lb/>Brac. # 0, # on. # 3, # pun. # 8. <lb/>Brac. # 78, # on. # 2, # pun. # 8. <lb/></note> </div> <div xml:id="echoid-div109" type="section" level="1" n="93"> <head xml:id="echoid-head120" xml:space="preserve">Proua.</head> <note position="right" xml:space="preserve"> <lb/>pun. # 2 # 1 # pun. <lb/>brac. # 4 # 1 # pun. <lb/></note> <p> <s xml:id="echoid-s2683" xml:space="preserve">Hor ſi partiranno brac. </s> <s xml:id="echoid-s2684" xml:space="preserve">78, on. </s> <s xml:id="echoid-s2685" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s2686" xml:space="preserve">8, per 14, ne veni <lb/>rà brac. </s> <s xml:id="echoid-s2687" xml:space="preserve">5, on. </s> <s xml:id="echoid-s2688" xml:space="preserve">7, & </s> <s xml:id="echoid-s2689" xml:space="preserve">quattro ſettimi d’un pun. </s> <s xml:id="echoid-s2690" xml:space="preserve">& </s> <s xml:id="echoid-s2691" xml:space="preserve">brac. </s> <s xml:id="echoid-s2692" xml:space="preserve">5, on. <lb/></s> <s xml:id="echoid-s2693" xml:space="preserve">7, e quattro ſettimi d’un pun. </s> <s xml:id="echoid-s2694" xml:space="preserve">ſarà la ſuperficie del cerchio <pb file="176" n="176" rhead="LIBRO"/> <emph style="sc">A E C F</emph>; </s> <s xml:id="echoid-s2695" xml:space="preserve">Hor brac. </s> <s xml:id="echoid-s2696" xml:space="preserve">5, onc. </s> <s xml:id="echoid-s2697" xml:space="preserve">7, & </s> <s xml:id="echoid-s2698" xml:space="preserve">quattro ſettimi d’un pun. </s> <s xml:id="echoid-s2699" xml:space="preserve">ſi <lb/>moltiplicheranno per la terza parte di brac. </s> <s xml:id="echoid-s2700" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s2701" xml:space="preserve">6, della <lb/>perpendicolare <emph style="sc">E D</emph>; </s> <s xml:id="echoid-s2702" xml:space="preserve">che la ſua terza parte ſarà bra. </s> <s xml:id="echoid-s2703" xml:space="preserve">1. </s> <s xml:id="echoid-s2704" xml:space="preserve">on. </s> <s xml:id="echoid-s2705" xml:space="preserve">2; <lb/></s> <s xml:id="echoid-s2706" xml:space="preserve">& </s> <s xml:id="echoid-s2707" xml:space="preserve">ſi moltiplicheranno brac. </s> <s xml:id="echoid-s2708" xml:space="preserve">1, onc. </s> <s xml:id="echoid-s2709" xml:space="preserve">2, con brac. </s> <s xml:id="echoid-s2710" xml:space="preserve">5, on. </s> <s xml:id="echoid-s2711" xml:space="preserve">7, & </s> <s xml:id="echoid-s2712" xml:space="preserve"><lb/>quattro ſettimi d’un pun. </s> <s xml:id="echoid-s2713" xml:space="preserve">come qui ſi vede, faranno quadret <lb/>ti 6, on. </s> <s xml:id="echoid-s2714" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s2715" xml:space="preserve">2, atomi 8.</s> <s xml:id="echoid-s2716" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Brac. # 5, # on. # 7, # pun. # 0, # at. # 6, # e ſei ſettimi. <lb/>Brac. # 1, # on. # 2, <lb/>Quadr. # 5, <lb/>Quadr. # 0, # on. # 7, <lb/>Quadr. # 0, # on. # 0, # pun. # 0, # at. # 6, # e ſei ſettimi. <lb/>Quadr. # 0, # on. # 10, # pun, # 0, <lb/>Quadr. # 0, # on. # 1, # pun. # 2, <lb/>Quadr. # 0, # on. # 0, # pun. # 0, # at. # 0, <lb/>Quadr. # 0, # on. # 0, # pun. # 0, # at. # 1, # mi. 1, # e 5 ſetti. <lb/>Quadr. # 6, # on. # 6, # pun. # 2, # at. # 8, # mi.0, <lb/></note> </div> <div xml:id="echoid-div110" type="section" level="1" n="94"> <head xml:id="echoid-head121" xml:space="preserve">Proua.</head> <note position="right" xml:space="preserve"> <lb/>ſettimi d’at. # 6, # 0, # ſettimi di min. <lb/>onc. # 0, # 0, # ſettimi di min. <lb/></note> <p> <s xml:id="echoid-s2717" xml:space="preserve">Coſi ſi vede che la piramide di biada detta di ſopra, ſarà <lb/>quadr. </s> <s xml:id="echoid-s2718" xml:space="preserve">6, on. </s> <s xml:id="echoid-s2719" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s2720" xml:space="preserve">2, at. </s> <s xml:id="echoid-s2721" xml:space="preserve">8: </s> <s xml:id="echoid-s2722" xml:space="preserve">hor di quadretti 6, on. </s> <s xml:id="echoid-s2723" xml:space="preserve">6, pun@2 <lb/>at. </s> <s xml:id="echoid-s2724" xml:space="preserve">8, ſi trouerà che ſarà quarte 58, cop. </s> <s xml:id="echoid-s2725" xml:space="preserve">2, ſtop. </s> <s xml:id="echoid-s2726" xml:space="preserve">2, e due terzi; <lb/></s> <s xml:id="echoid-s2727" xml:space="preserve">& </s> <s xml:id="echoid-s2728" xml:space="preserve">tanto ſarà la ſopradetta piramide di biada.</s> <s xml:id="echoid-s2729" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div111" type="section" level="1" n="95"> <head xml:id="echoid-head122" xml:space="preserve">ESSEMPIO DEL SECONDO MODO.</head> <p> <s xml:id="echoid-s2730" xml:space="preserve">Il ſecondo modo è aſſai piu facile del primo; </s> <s xml:id="echoid-s2731" xml:space="preserve">ſi ridurrà la <lb/>miſura del diametro della piramide tutta à on. </s> <s xml:id="echoid-s2732" xml:space="preserve">che ſaranno <pb o="26" file="177" n="177" rhead="SECONDO"/> on. </s> <s xml:id="echoid-s2733" xml:space="preserve">32; </s> <s xml:id="echoid-s2734" xml:space="preserve">& </s> <s xml:id="echoid-s2735" xml:space="preserve">on. </s> <s xml:id="echoid-s2736" xml:space="preserve">32, ſi moltiplicheranno in ſe, & </s> <s xml:id="echoid-s2737" xml:space="preserve">faranno pun. <lb/></s> <s xml:id="echoid-s2738" xml:space="preserve">1024, & </s> <s xml:id="echoid-s2739" xml:space="preserve">punti 1024, ſi partiranno per pun. </s> <s xml:id="echoid-s2740" xml:space="preserve">20; </s> <s xml:id="echoid-s2741" xml:space="preserve">& </s> <s xml:id="echoid-s2742" xml:space="preserve">ne venirà <lb/>quarte di biada 51, e vn quinto, & </s> <s xml:id="echoid-s2743" xml:space="preserve">51, e vn quinto, ſi molti-<lb/>plicheranno per brac. </s> <s xml:id="echoid-s2744" xml:space="preserve">1, on. </s> <s xml:id="echoid-s2745" xml:space="preserve">2, per la terza parte dell’altez-<lb/>za, ouer perpendicolare della piramide, & </s> <s xml:id="echoid-s2746" xml:space="preserve">ne veniranno <lb/>quarte 59, cop. </s> <s xml:id="echoid-s2747" xml:space="preserve">2, ſtop. </s> <s xml:id="echoid-s2748" xml:space="preserve">3, e vndeci quintidecimi.</s> <s xml:id="echoid-s2749" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div112" type="section" level="1" n="96"> <head xml:id="echoid-head123" xml:space="preserve">TERZO ESSEMPIO PIV FACILE.</head> <p> <s xml:id="echoid-s2750" xml:space="preserve">Volendo far queſto, ſi multiplicherà le decene di 32, in <lb/>ſe, che faranno 9, & </s> <s xml:id="echoid-s2751" xml:space="preserve">9, ſi moltiplicheranno per quarte 5, & </s> <s xml:id="echoid-s2752" xml:space="preserve"><lb/>faranno quarte 45, poi ſi moltiplicherà le decene co’l nu-<lb/>mero, cioè 3, fia 2, faranno quarte 6, con quarte 45, fanno <lb/>quarte 51, ancor ſi moltiplicherà numero, cõ numero, cioè <lb/>2, con 2, farà 4, & </s> <s xml:id="echoid-s2753" xml:space="preserve">4, è la quinta parte d’una quarta; </s> <s xml:id="echoid-s2754" xml:space="preserve">& </s> <s xml:id="echoid-s2755" xml:space="preserve">faran <lb/>no come diſopra quarte 51, evn quinto; </s> <s xml:id="echoid-s2756" xml:space="preserve">oltra di queſto 51, <lb/>e vn quinto, ſi moltiplicherà con bra. </s> <s xml:id="echoid-s2757" xml:space="preserve">1, on. </s> <s xml:id="echoid-s2758" xml:space="preserve">2, terza parte del <lb/>l’altezza della piramide, come diſopra, & </s> <s xml:id="echoid-s2759" xml:space="preserve">farãno quarte 59, <lb/>cop. </s> <s xml:id="echoid-s2760" xml:space="preserve">2, ſtop. </s> <s xml:id="echoid-s2761" xml:space="preserve">3, e vndeci quintidecimi.</s> <s xml:id="echoid-s2762" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2763" xml:space="preserve">Alcuno mi potria dire, che ui è differenza d’importanza <lb/>dal primo modo al ſecondo, quaſi quar. </s> <s xml:id="echoid-s2764" xml:space="preserve">3, e meza, io riſpon <lb/>do (in fauore de’prattichi miſuratori) che queſto ſarebbe <lb/>vero, ſe le piramidi delle biade ſteſſero in quel eſſere, che di <lb/>ſcriue Euclide, cioè, che and aſſero proportionatamente co <lb/>me vn pane di zuccaro; </s> <s xml:id="echoid-s2765" xml:space="preserve">ma quelle delle biade non fanno tal <lb/>effetto, anci più preſto fanno del maccato; </s> <s xml:id="echoid-s2766" xml:space="preserve">effetto contra-<lb/>rio à quello che diſcriue Euclide. </s> <s xml:id="echoid-s2767" xml:space="preserve">Et perciò per il mio pa-<lb/>rere ſaria meglio pigliar più della terza parte dell’altezza <lb/>della piramide della biada, al che ancora io ſempre ho ve-<lb/>duto che i prattici miſuratori ſi ſono accoſtati, come al do-<lb/>uere. </s> <s xml:id="echoid-s2768" xml:space="preserve">Etancor io ho ſcritto queſto per la iſperienza, che <lb/>già lungo tempo ho hauuto. </s> <s xml:id="echoid-s2769" xml:space="preserve">Moſtrato hauendo i tre modi <lb/>ſopradetti del miſurar le biade; </s> <s xml:id="echoid-s2770" xml:space="preserve">Seguirò in dimoſtrare il <lb/>modo di miſurar le biade in piramide, con le tauole, che in-<lb/>ſegnaranno à miſurare il Vino nelle botti, & </s> <s xml:id="echoid-s2771" xml:space="preserve">tinazzi.</s> <s xml:id="echoid-s2772" xml:space="preserve"/> </p> <pb file="178" n="178" rhead="LIBRO"/> </div> <div xml:id="echoid-div113" type="section" level="1" n="97"> <head xml:id="echoid-head124" xml:space="preserve">PER FAR LI CONTI DELLE BIADE</head> <head xml:id="echoid-head125" xml:space="preserve">in piramide, & quelli del vino <lb/>con breuità.</head> <p> <s xml:id="echoid-s2773" xml:space="preserve">ET volendo fare i conti delle biade in pira-<lb/>mide, & </s> <s xml:id="echoid-s2774" xml:space="preserve">quelli del vino, con breuità; </s> <s xml:id="echoid-s2775" xml:space="preserve">ſi faran <lb/>no con le tauole ſeguenti; </s> <s xml:id="echoid-s2776" xml:space="preserve">Et ſe per caſo ſo-<lb/>pra alle tauole non fuſſe quel numero, che <lb/>il diametro della piramide, ouer la metà del <lb/>la ſomma di due diametri, cioè del fondo & </s> <s xml:id="echoid-s2777" xml:space="preserve">del cocone <lb/>d’una botte, ouer tinazzo, come ſaria, ſe voleſſe alcuno <lb/>pigliare ſopra le tauole oncie 71, perche non ui è tal nume <lb/>ro ſopra, ſi piglierà la metà del detto numero 71, che ſarà <lb/>35, e mezo, & </s> <s xml:id="echoid-s2778" xml:space="preserve">35, e mezo ſi trouerà ſopra le tauole; </s> <s xml:id="echoid-s2779" xml:space="preserve">& </s> <s xml:id="echoid-s2780" xml:space="preserve">al-<lb/>l’incontro della terza parte dell’altezza del monton di bia <lb/>da in piramide, ouer lunghezza della botte, ſotto al nume-<lb/>ro 35 e mezzo, ſi pigliera il numero, & </s> <s xml:id="echoid-s2781" xml:space="preserve">quel tal numero ſi <lb/>moltiplicherà per 4, & </s> <s xml:id="echoid-s2782" xml:space="preserve">quel che ne venirà ſarà tanta biada, <lb/>ouer vino.</s> <s xml:id="echoid-s2783" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2784" xml:space="preserve">Ancora, ſe per caſo, che’l diametro della piramide della <lb/>biada, ouero la metà del fondo, & </s> <s xml:id="echoid-s2785" xml:space="preserve">del cocone della botte <lb/>fuſſero oncie 72, e meza, & </s> <s xml:id="echoid-s2786" xml:space="preserve">nelle tauole non ſi ritroui il <lb/>72, e mezo, non ſi piglierà la metà, perche la metà di 72, e <lb/>mezo ſaria 36, e vn quarto, & </s> <s xml:id="echoid-s2787" xml:space="preserve">36, e vn quarto, non ſi ritro-<lb/>ua ſopra le tauole, ma per il numero 72, e mezo, ſi piglierà <lb/>36; </s> <s xml:id="echoid-s2788" xml:space="preserve">& </s> <s xml:id="echoid-s2789" xml:space="preserve">36 e mezo, & </s> <s xml:id="echoid-s2790" xml:space="preserve">quel numero che ſi trouerà ſotto al 36, <lb/>& </s> <s xml:id="echoid-s2791" xml:space="preserve">al 36, e mezo, all’incontro della terza parte dell’altezza <lb/>della piramide, ouer della lunghezza della botte; </s> <s xml:id="echoid-s2792" xml:space="preserve">& </s> <s xml:id="echoid-s2793" xml:space="preserve">ancora <lb/>dell’altezza d’un tinazzo, ſi raddoppierà l’uno & </s> <s xml:id="echoid-s2794" xml:space="preserve">l’altro nu-<lb/>mero, & </s> <s xml:id="echoid-s2795" xml:space="preserve">ne venirà la quantità della biada, ouer tenuta del-<lb/>la botte, & </s> <s xml:id="echoid-s2796" xml:space="preserve">ancora quella del tinazzo; </s> <s xml:id="echoid-s2797" xml:space="preserve">come più chiaramen <lb/>te il tutto ſi moſtrarà.</s> <s xml:id="echoid-s2798" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2799" xml:space="preserve">Di ſopra ſi è ſuppoſto il diametro della piramide di onc. <lb/></s> <s xml:id="echoid-s2800" xml:space="preserve">32, & </s> <s xml:id="echoid-s2801" xml:space="preserve">la terza parte dell’altezza ſua brac. </s> <s xml:id="echoid-s2802" xml:space="preserve">1, on. </s> <s xml:id="echoid-s2803" xml:space="preserve">2, ſi entrerà <pb o="27" file="179" n="179" rhead="SECONDO."/> nelle tauole, pigliando il numero di onc. </s> <s xml:id="echoid-s2804" xml:space="preserve">32, di ſopra à eſſe <lb/>tauole poſte; </s> <s xml:id="echoid-s2805" xml:space="preserve">ilqual numero ſignifica le onc. </s> <s xml:id="echoid-s2806" xml:space="preserve">del diametro <lb/>della baſe della piramide, & </s> <s xml:id="echoid-s2807" xml:space="preserve">la metà delle on. </s> <s xml:id="echoid-s2808" xml:space="preserve">del fondo, & </s> <s xml:id="echoid-s2809" xml:space="preserve"><lb/>del cocone d’una botte, & </s> <s xml:id="echoid-s2810" xml:space="preserve">ancora la metà del diametro del <lb/>la bocca, & </s> <s xml:id="echoid-s2811" xml:space="preserve">quello del fondo d’un tinazzo; </s> <s xml:id="echoid-s2812" xml:space="preserve">& </s> <s xml:id="echoid-s2813" xml:space="preserve">da mano ſini-<lb/>ſtra nella prima colonna, ſi piglierà braccia 1, oncie 2; </s> <s xml:id="echoid-s2814" xml:space="preserve">& </s> <s xml:id="echoid-s2815" xml:space="preserve"><lb/>ſotto al 32, all’incõtro del braccio 1, ſi trouerà ſegnato 12, <lb/>et 3, e vn quinto, il 12, ſaranno quarte di biada 48, di vino <lb/>zerle 12; </s> <s xml:id="echoid-s2816" xml:space="preserve">e il 3, & </s> <s xml:id="echoid-s2817" xml:space="preserve">vn quinto ſaranno quarte 3, & </s> <s xml:id="echoid-s2818" xml:space="preserve">vn quinto, <lb/>di biada, & </s> <s xml:id="echoid-s2819" xml:space="preserve">di vino zerle 12, ſecchie 3, & </s> <s xml:id="echoid-s2820" xml:space="preserve">boccali 3, e mezo, <lb/>& </s> <s xml:id="echoid-s2821" xml:space="preserve">ancora all’incontro di on. </s> <s xml:id="echoid-s2822" xml:space="preserve">2, ſotto al 32, ſi trouerà ſegna <lb/>to 2, & </s> <s xml:id="echoid-s2823" xml:space="preserve">mezo; </s> <s xml:id="echoid-s2824" xml:space="preserve">il 2, ſono quarte 8, di biada, & </s> <s xml:id="echoid-s2825" xml:space="preserve">di vino zerle <lb/>due, & </s> <s xml:id="echoid-s2826" xml:space="preserve">il mezo ſarà meza quarta di biada, & </s> <s xml:id="echoid-s2827" xml:space="preserve">di vino meza <lb/>ſecchia, che ſommati inſieme, ſaranno quarte di biada 59, <lb/>& </s> <s xml:id="echoid-s2828" xml:space="preserve">circa coppi 3; </s> <s xml:id="echoid-s2829" xml:space="preserve">& </s> <s xml:id="echoid-s2830" xml:space="preserve">di vino zerle 14, & </s> <s xml:id="echoid-s2831" xml:space="preserve">ſecchie 3, & </s> <s xml:id="echoid-s2832" xml:space="preserve">boccali <lb/>4, e mezzo.</s> <s xml:id="echoid-s2833" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2834" xml:space="preserve">Auuertendo ancora, che le tauole qui ſeguenti, ſerueno <lb/>fino à onc. </s> <s xml:id="echoid-s2835" xml:space="preserve">72, e meza, di diametro, coſi della baſe della pi-<lb/>ramide; </s> <s xml:id="echoid-s2836" xml:space="preserve">come della metà di due diametri del fondo, & </s> <s xml:id="echoid-s2837" xml:space="preserve">del <lb/>cocone d’una botte; </s> <s xml:id="echoid-s2838" xml:space="preserve">come ancora della metà di due diame-<lb/>tri della bocca d’un tinazzo, & </s> <s xml:id="echoid-s2839" xml:space="preserve">del ſuo fondo.</s> <s xml:id="echoid-s2840" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2841" xml:space="preserve">Auuertendo ancora che vna quarta di biada ſul Breſcia-<lb/>no peſa intorno à vn peſo, & </s> <s xml:id="echoid-s2842" xml:space="preserve">quattro librette; </s> <s xml:id="echoid-s2843" xml:space="preserve">& </s> <s xml:id="echoid-s2844" xml:space="preserve">vna ſecchia <lb/>di vino circa vn peſo & </s> <s xml:id="echoid-s2845" xml:space="preserve">mezo; </s> <s xml:id="echoid-s2846" xml:space="preserve">ſul Breſciano ſi vendeil for <lb/>mento, & </s> <s xml:id="echoid-s2847" xml:space="preserve">altre biade à carga, & </s> <s xml:id="echoid-s2848" xml:space="preserve">à ſome; </s> <s xml:id="echoid-s2849" xml:space="preserve">la carga è quar. </s> <s xml:id="echoid-s2850" xml:space="preserve">14, <lb/>& </s> <s xml:id="echoid-s2851" xml:space="preserve">la ſoma quarte 12; </s> <s xml:id="echoid-s2852" xml:space="preserve">il vino ſi vende ſul Breſciano à carro <lb/>& </s> <s xml:id="echoid-s2853" xml:space="preserve">à zerla; </s> <s xml:id="echoid-s2854" xml:space="preserve">al carro vanno zerle 12, la zerla contien ſecchie <lb/>4, & </s> <s xml:id="echoid-s2855" xml:space="preserve">la ſecchia boccali 18.</s> <s xml:id="echoid-s2856" xml:space="preserve"/> </p> <pb file="180" n="180" rhead="LIBRO"/> </div> <div xml:id="echoid-div114" type="section" level="1" n="98"> <head xml:id="echoid-head126" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # ### 10 ### 10 {1/2} ### 11 ### 11 {1/2} ### 12 ### 12 {1/2} <lb/># # Z. # S. # B. # Z. # S. # B. # Z. # S. # B # Z. # S. # B # Z. # S. # B. # Z. # S. # B <lb/>On. # {1/2} # 0 # 0 # 3 {1/2} # 0 # 0 # 3 {1/2} # 0 # 0 # 3 {1/2} # 0 # 0 # 3 {1/2} # 0 # 0 # 6 # 0 # 0 # 6 <lb/>On. # 1 # 0 # 0 # 6 # 0 # {1/2} # 0 # 0 # {1/2} # 0 # 0 # {1/2} # 0 # 0 # 0 # 12 # 0 # 0 # 12 <lb/>On. # 2 # 0 # 0 # 12 # 0 # 0 # 12 # 0 # 1 # 0 # 0 # 1 # 0 # 0 # 1 # 6 # 0 # 1 # 6 <lb/>On. # 3 # 0 # 1 # 3 # 0 # 1 # 6 # 0 # 1 # 6 # 0 # 1 # 12 # 0 # 1 # 14 # 0 # 2 # 0 <lb/>On. # 4 # 0 # 1 # 12 # 0 # 1 # 12 # 0 # 2 # 0 # 0 # 2 # 3 # 0 # 2 {1/2} # 0 # 0 # 2 # 12 <lb/>On. # 5 # 0 # 2 # 0 # 0 # 2 # 3 {1/2} # 0 # 2 {1/2} # 0 # 0 # 2 # 13 {1/2} # 0 # 3 # 0 # 0 # 3 # 6 <lb/>On. # 6 # 0 # 2 {1/2} # 0 # 0 # 2 # 12 # 0 # 3 # 0 # 0 # 3 # 6 # 0 # 3 {1/2} # 0 # 1 # 0 # 0 <lb/>On. # 7 # 0 # 3 # 0 # 0 # 3 # 6 # 0 # 3 {1/2} # 0 # 0 # 3 # 15 # 1 # 0 # 3 # 1 # 0 # 6 <lb/>On. # 8 # 0 # 3 # 6 # 0 # 3 # 12 # 1 # 0 # 0 # 1 # 0 # 6 # 1 # 0 # 12 # 1 # 1 # 0 <lb/>On. # 9 # 0 # 3 # 13 {1/2} # 1 # 0 # 0 # 1 # {1/2} # 0 # 1 # 0 # 14 # 1 # 1 # 3 {1/2} # 1 # 1 # 14 <lb/>On. # 10 # 1 # 0 # 0 # 1 # {1/2} # 0 # 1 # 1 # 0 # 1 # 1 {1/2} # 0 # 1 # 2 # 0 # 1 # 2 {1/2} # 0 <lb/>On. # 11 # 1 # {1/2} # 0 # 1 # 1 # 0 # 1 # 1 {1/2} # 0 # 1 # 2 # 0 # 1 # 2 # 12 # 1 # 3 # 3 <lb/>Bra. # 1 # 1 # 1 # 0 # 1 # 1 {1/2} # 0 # 1 # 2 # 0 # 1 # 2 # 10 {1/2} # 1 # 3 # 3 {1/2} # 1 # 3 # 14 <lb/>Bra. # 2 # 2 # 2 # 0 # 2 # 3 # 0 # 3 # 0 # 0 # 3 # 1 # 6 # 3 # 2 # 7 # 3 # 3 # 10 {1/2} <lb/>Bra. # 3 # 3 # 3 # 0 # 4 # {1/2} # 0 # 4 # 2 # 0 # 5 # 0 # 0 # 5 # 1 # 10 {1/2} # 5 # 3 # 7 <lb/>Bra. # 4 # 5 # 0 # 0 # 5 # 2 # 0 # 6 # 0 # 0 # 6 # 2 # 7 # 7 # 2 # 0 # 7 # 3 # 0 <lb/>Bra. # 5 # 6 # 1 # 0 # 6 # 3 {1/2} # 0 # 7 # 2 # 0 # 8 # 1 # 0 # 9 # 0 # 0 # 9 # 3 # 0 <lb/>Bra. # 6 # 7 # 2 # 0 # 8 # 1 # 0 # 9 # 0 # 0 # 9 # 3 # 6 # 10 # 3 # 3 {1/2} # 11 # 3 # 0 <lb/></note> <pb o="28" file="181" n="181" rhead="SECONDO."/> </div> <div xml:id="echoid-div115" type="section" level="1" n="99"> <head xml:id="echoid-head127" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 13 # # # 13 {1/2} # # # 14 # # # 14 {1/2} # # # 15 # # # 15 {1<unsure/>/2} <lb/># # Z. # S. # B # Z # S. # B. # Z. # S. # B. # Z. # S. # B. # Z. # S. # B.<unsure/> # Z. # S. # B. <lb/>On. # {1/2} # 0 # 0 # 6 # 0 # {1/2} # 0 # 0 # {1/2} # 0 # 0 # {1/2} # 0 # 0 # {1/2} # 0 # 0 # {1/2} # 0 <lb/>On. # 1 # 0 # 0 # 12 # 0 # 0 # 15 # 0 # 0 # 15 # 0 # 0 # 15 # 0 # 1 # 0 # 0 # 1 # 0 <lb/>On. # 2 # 0 # 1 {1/2} # 0 # 0 # 1 {1/2} # 0 # 0 # 1 # 14 # 0 # 1 # 12 # 0 # 2 # 0 # 0 # 2 # 0 <lb/>On. # 3 # 0 # 2 # 0 # 0 # 2 # 4 {1/2} # 0 # 2 # 4 {1/2} # 0 # 2 # 12 # 0 # 2 # 14 # 0 # 3 # 0 <lb/>On. # 4 # 0 # 2 # 14 # 0 # 3 # 0 # 0 # 3 # 6 # 0 # 3 {1/2} # 0 # 0 # 3 # 14 # 1 # 0 # 0 <lb/>On. # 5 # 0 # 3 {1/2} # 0 # 0 # 3 # 14 {1/2} # 1 # 0 # 0 # 1 # 0 # 6 # 1 # {1/2} # 0 # 1 # 0 # 13 {1/2} <lb/>On. # 6 # 1 # 0 # 3 {1/2} # 1 # {1/2} # 0 # 1 # 1 # 0 # 1 # 1 # 3 {1/2} # 1 # 2 # 0 # 1 # 2 # 3 {1/2} <lb/>On. # 7 # 1 # 0 # 13 {1/2} # 1 # 1 # 0 # 1 # 1 # 12 # 1 # 2 # 0 # 1 # 2 {1/2} # 0 # 1 # 2 # 15 <lb/>On. # 8 # 1 # 1 # 12 # 1 # 2 # 0 # 1 # 2 # 6 # 1 # 2 # 12 # 1 # 3 {1/2} # 0 # 2 # 0 # 0 <lb/>On. # 9 # 1 # 2 # 6 # 1 # 2 # 12 # 1 # 3 # 3 # 1 # 3 # 12 # 2 # 0 # 6 # 2 # 1 # 0 <lb/>On. # 10 # 1 # 3 # 0 # 1 # 3 {1/2} # 0 # 2 # 0 # 3 # 2 # 0 # 12 # 2 # 1 # 6 # 2 # 2 # 0 <lb/>On. # 11 # 1 # 3 # 14 # 2 # 0 # 6 # 2 # 1 # 0 # 2 # 1 {1/2} # 0 # 2 # 2 # 12 # 2 # 3 # 0 <lb/>Bra. # 1 # 2 # {1/2} # 0 # 2 # 1 # 1 {1/2} # 2 # 1 # 14 # 2 # 2 {1/2} # 9 # 2 # 3 # 4 {1/2} # 3 # 0 # 0 <lb/>Bra. # 2 # 4 # 1 # 0 # 4 # 2 # 1 {1/2} # 4 # 3 # 10 {1/2} # 5 # 1 # 0 # 5 # 2 {1/2} # 0 # 6 # 0 # 0 <lb/>Bra. # 3 # 6 # 1 {1/2} # 0 # 6 # 3 # 5 # 7 # 1 # 7 # 7 # 3 {1/2} # 0 # 8 # 1 # 13 {1/2} # 9 # 0 # 0 <lb/>Bra. # 4 # 8 # 2 # 0 # 9 # 0 # 12 # 9 # 3 # 0 # 10 # 2 # 0 # 11 # 1 # 0 # 12 # 0 # 0 <lb/>Bra. # 5 # 10 # 2 {1/2} # 0 # 11 # 1 {1/2} # 0 # 12 # 1 # 0 # 13 # {1/2} # 0 # 14 # 0 # 4 {1/2} # 15 # 0 # 0 <lb/>Bra. # 6 # 12 # 3 # 0 # 13 # 2 # 10 {6<unsure/>/1} # 14 # 3 # 0 # 15 # 3 # 0 # 16 # 3 {1/2} # 0 # 18 # 0 # 0 <lb/></note> <pb file="182" n="182" rhead="LIBRO"/> </div> <div xml:id="echoid-div116" type="section" level="1" n="100"> <head xml:id="echoid-head128" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 16 # # # 16 {1/2} # # # 17 # # # 17 {1/2} # # # 18 # # # 18 {1/2} <lb/># # Z # S. # B. # Z. # S # B. # Z. # S # B # Z. # S. # B.<unsure/> # Z. # S. # B. # Z. # S. # B <lb/>On. # {1/2} # 0 # {1/2} # 0 # 0 # {1/2}<unsure/> # 0 # 0 # 0 # 12 # 0 # 0 # 12 # 0 # 0 # 12 # 0 # 0 # 12 <lb/>On. # 1 # 0 # 1 # 0 # 0 # 1 # 0 # 0 # 1 # 3 {1/2} # 0 # 1 # 3 {1/2} # 0 # 1 # 4 {1/2} # 0 # 1 # 6 <lb/>On. # 2 # 0 # 2 # 3 # 0 # 2 # 4 {1/2} # 0 # 2 # 7 # 0 # 2 # 7 # 0 # 2 # 13 {1/2} # 0 # 2 # 13 {1/2} <lb/>On. # 3 # 0 # 3 # 4 {1/2} # 0 # 3 # 6 # 0 # 3 # 12 # 0 # 3 # 14 # 1 # 0 # 0 # 1 # 0 # 3 <lb/>On. # 4 # 1 # 0 # 6 # 1 # {1/2} # 0 # 1 # 0 # 15 # 1 # 1 # 0 # 1 # 1 # 6 # 1 # 1 {1/2} # 0 <lb/>On. # 5 # 1 # 1 # 6 # 1 # 1 # 12 # 1 # 2 # 0 # 1 # 2 # 6 # 1 # 2 # 13 {1/2} # 1 # 3 # 0 <lb/>On. # 6 # 1 # 2 {1/2} # 0 # 1 # 2 # 12 # 1 # 3 # 3 {1/2} # 1 # 3 {1/2} # 0 # 2 # 0 # 0 # 2 # 0 # 6 <lb/>On. # 7 # 1 # 3 # 6 # 1 # 3 # 12 # 2 # 0 # 6 # 2 # 0 # 12 # 2 # 1 # 6 # 2 # 1 # 12 <lb/>On. # 8 # 2 # 0 # 14 # 2 # 1 # 0 # 2 # 1 # 6 # 2 # 2 # 0 # 2 # 2 # 14 # 2 # 3 # 3 <lb/>On. # 9 # 2 # 1 {1/2} # 0 # 2 # 2 # 3 # 2 # 2 {1/2} # 0 # 2 # 3 {1/2} # 0 # 3 # 0 # 3 # 3 # 0 # 12 <lb/>On. # 10 # 2 # 2 # 12 # 2 # 3 # 6 # 3 # 0 # 0 # 3 # 0 # 12 # 3 # 1 # 6 # 3 # 2 # 3 {1/2} <lb/>On. # 11 # 2 # 3 # 12 # 3 # 0 # 12 # 3 # 1 # 3 {1/2} # 3 # 2 # 0 # 3 # 3 # 4 {1/2} # 3 # 3 # 12 <lb/>Bra. # 1 # 3 # 0 # 14 # 3 # 1 # 13 {1/2} # 3 # 2 {1/2} # 0 # 3 # 3 # 6 # 4 # 0 # 3 {1/2} # 4 # 1 # 1 {1/2} <lb/>Bra. # 2 # 6 # 1 # 10 {1/2} # 6 # 3 {1/2} # 0 # 7 # 1 # 0 # 7 # 2 # 10 {1/2} # 8 # 0 # 7 # 8 # 2 # 10 {1/2} <lb/>Bra. # 3 # 9 # 2 # 7 # 10 # 1 # 4 {1/2} # 10 # 3 {1/2} # 0 # 11 # 2 # 0 # 12 # 0 # 10 {1/2} # 13 # 0 # 0 <lb/>Bra. # 4 # 12 # 3 # 3 {1/2} # 13 # 3 # 0 # 14 # 1 # 0 # 15 # 1 # 3 {1/2} # 16 # 1 # 0 # 17 # 0 # 7 <lb/>Bra. # 5 # 16 # 0 # 0 # 17 # 0 # 13 {1/2} # 18 # {1/2} # 0 # 19 # {1/2} # 0 # 20 # 1 # 0 # 21 # 1 {1/2} # 0 <lb/>Bra # 6 # 19 # 1 # 0 # 20 # 2 {1/2} # 0 # 21 # 3 # 0 # 22 # 3 # 14 # 24 # 1 # 3 {1/2} # 25 # 2 # 10 {1/2} <lb/></note> <pb o="29" file="183" n="183" rhead="SECONDO."/> </div> <div xml:id="echoid-div117" type="section" level="1" n="101"> <head xml:id="echoid-head129" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 19 # # # 19 {1/2} # # # 20 # # # 20 {1/2} # # # 21 # # # 21 {1/2} <lb/># # Z. # S. # B. # Z. # S. # B. # Z. # S. # B # Z. # S. # B. # Z. # S. # B. # Z. # S.<unsure/> # B. <lb/>On. # {1/2} # 0 # 0 # 12 # 0 # 0 # 12 # 0 # 0 # 15 # 0 # 0 # 15 # 0 # 1 # 0 # 0 # 1 # 0 <lb/>On. # 1 # 0 # 1 {1/2} # 0 # 0 # 1 {1/2} # 0 # 0 # 1 # 12 # 0 # 1 # 12 # 0 # 1 # 15 # 0 # 2 # 0 <lb/>On. # 2 # 0 # 3 # 0 # 0 # 3 # 0 # 0 # 3 # 6 # 0 # 3 # 6 # 0 # 3 # 14 # 0 # 3 # 14 <lb/>On. # 3 # 1 # {1/2} # 0 # 1 # 0 # 14 # 1 # 1 # 0 # 1 # 1 # 3 # 1 # 1 # 6 # 1 # 1 # 14 <lb/>On. # 4 # 1 # 1 # 15 # 1 # 2 # 3 # 1 # 2 # 12 # 1 # 2 # 15 # 1 # 3 # 3 # 1 # 3 # 12 <lb/>On. # 5 # 1 # 3 {1/2} # 0 # 2 # 0 # 0 # 2 # 0 # 13 {1/2} # 2 # 0 # 14 # 2 # 1 # 0 # 2 # 1 {1/2} # 0 <lb/>On. # 6 # 2 # 1 # 0 # 2 # 1 {1/2} # 0 # 2 # 2 # 0 # 2 # 2 {1/2} # 0 # 2 # 3 # 0 # 2 # 3 {1/2} # 0 <lb/>On. # 7 # 2 # 2 {1/2} # 0 # 2 # 3 # 0 # 3 # 0 # 0 # 3 # 0 # 12 # 3 # 1 # 0 # 3 # 1 {1/2} # 0 <lb/>On. # 8 # 3 # 0 # 0 # 3 # {1/2} # 0 # 3 # 1 # 6 # 3 # 1 # 12 # 3 # 2 # 12 # 3 # 3 # 3 <lb/>On. # 9 # 3 # 1 {1/2} # 0 # 3 # 2 # 3 # 3 # 3 # 0 # 3 # 3 # 12 # 4 # {1/2} # 0 # 4 # 1 # 0 <lb/>On. # 10 # 3 # 3 # 0 # 4 # 0 # 0 # 4 # 0 # 12 # 4 # 1 {1/2} # 0 # 4 # 2 {1/2} # 0 # 4 # 3 # 3 {1/2} <lb/>On. # 11 # 4 # {1/2} # 0 # 4 # 1 # 6 # 4 # 2 # 6 # 4 # 3 # 3 {1/2} # 5 # 0 # 3 # 5 # 1 {1/2} # 0 <lb/>Bra # 1 # 4 # 2 # 0 # 4 # 3 # 0 # 5 # 0 # 0 # 5 # 1 # 0 # 5 # 2 # 0 # 5 # 3 # 0 <lb/>Bra. # 2 # 9 # 0 # 0 # 9 # 2 # 0 # 10 # 0 # 0 # 10 # 2 # 0 # 11 # 0 # 0 # 11 # 2 # 0 <lb/>Bra. # 3 # 13 # 2 # 0 # 14 # 1 # 0 # 15 # 0 # 0 # 15 # 3 # 0 # 16 # 2 # 0 # 17 # 1 # 0 <lb/>Bra. # 4 # 18 # 0 # 0 # 19 # 0 # 0 # 20 # 0 # 0 # 21 # 0 # 0 # 22 # 0 # 0 # 23 # 0 # 0 <lb/>Bra. # 5 # 22 # 2 # 0 # 23 # 0 # 0 # 25 # 0 # 0 # 26 # 1 # 0 # 27 # 2 # 0 # 28 # 3 # 0 <lb/>Bra. # 6 # 27 # 0 # 0 # 28 # 2 # 0 # 30 # 0 # 0 # 32 # 2 # 0 # 33 # 0 # 0 # 34 # 2 # 0 <lb/></note> <pb file="184" n="184" rhead="LIBRO"/> </div> <div xml:id="echoid-div118" type="section" level="1" n="102"> <head xml:id="echoid-head130" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 22 # # # 22 {1/2} # # # 23 # # # 23 {1/2} # # # 24 # # # 24 {1/2} <lb/># # Z # S. # B. # Z. # S. # B # Z. # S. # B # Z. # S. # B. # Z. # S. # B. # Z. # S. # B. <lb/>On. # {1/2} # 0 # 1 # 0 # 0 # 1 # 0 # 0 # 1 # 3 # 0 # 1 # 3 # 0 # 1 # 3 # 0 # 1 # 3 {1/2} <lb/>On. # 1 # 0 # 2 # 0 # 0 # 2 # 0 # 0 # 2 # 3 # 0 # 2 # 3 {1/2} # 0 # 2 # 6 # 0 # 2 {1/2} # 0 <lb/>On. # 2 # 1 # 0 # 0 # 1 # 0 # 0 # 1 # 0 # 6 # 1 # 0 # 12 # 1 # 0 # 12 # 1 # 1 # 0 <lb/>On. # 3 # 1 # 2 # 0 # 1 # 2 # 6<unsure/> # 1 # 2 {1/2} # 0 # 1 # 2 # 14 # 1 # 3 # 0 # 1 # 3 {1/2} # 0 <lb/>On. # 4 # 2 # 0 # 0 # 2 # {1/2} # 0 # 2 # 0 # 14 # 2 # 1 # 3 # 2 # 1 {1/2} # 0 # 2 # 1 # 14 <lb/>On. # 5 # 2 # 2 # 0 # 2 # 2 {1/2} # 0 # 2 # 3 # 0 # 2 # 3 {1/2} # 0 # 3 # 0 # 0 # 3 # {1/2} # 0 <lb/>On. # 6 # 3 # 0 # 0 # 3 # {1/2} # 0 # 3 # 1 # 0 # 3 # 1 {1/2} # 0 # 3 # 2 # 6 # 3 # 3 # 0 <lb/>On. # 7 # 3 # 2 # 0 # 3 # 2 # 13 {1/2} # 4 # 0 # 0 # 4 # {1/2} # 0 # 4 # 1 # 0 # 4 # 1 # 13 {1/2} <lb/>On. # 8 # 4 # 0 # 0 # 4 # 3 # 0 # 4 # 1 # 12 # 4 # 2 # 3 # 4 # 3 # 0 # 4 # 3 # 14 <lb/>On. # 9 # 4 # 2 # 3 # 4 # 3 # 0 # 4 # 3 # 3 # 5 # 0 # 12 # 5 # 1 {1/2} # 0 # 5 # 2 {1/2} # 0 <lb/>On. # 10 # 5 # 0 # 3 # 5 # 1 # 0 # 5 # 1 # 14 # 5 # 3 # 0 # 6 # 0 # 0 # 6 # 1 # 0 <lb/>On. # 11 # 5 # 2 # 3 # 5 # 3 # 3 # 6 # 0 # 3 {1/2} # 6 # 1 # 6 # 6 # 2 {1/2} # 0 # 6 # 3 {1/2} # 0 <lb/>Bra. # 1 # 6 # 0 # 3 {1/2} # 6 # 1 # 6 # 6 # 2 {1/2} # 0 # 6 # 3 # 10 {1/2} # 7 # 0 # 14 # 7 # 2 # 0 <lb/>Bra. # 2 # 12 # 0 # 7 # 12 # 2 {1/2} # 0 # 13 # 1 # 0 # 13 # 3 # 6 # 14 # 1 # 14 # 15 # 0 # 0 <lb/>Bra. # 3 # 18 # 0 # 10 {1/2} # 19 # 0 # 0 # 19 # 3 {1/2} # 0 # 20 # 3 # 0 # 21 # 2 # 12 # 22 # 2 # 0 <lb/>Bra. # 4 # 24 # 0 # 14 # 25 # 1 # 3 {1/2} # 26 # 2 # 0 # 27 # 2 # 7 # 28 # 3 # 3 {1/2} # 30 # 0 # 0 <lb/>Bra. # 5 # 30 # 1 # 0 # 31 # 2 {1/2} # 0 # 33 # {1/2} # 0 # 34 # 2 # 0 # 36 # 0 # 0 # 37 # 2 # 0 <lb/>Bra. # 6 # 36 # 1 # 3 {1/2} # 38 # 0 # 0 # 39 # 3 # 0 # 41 # 1 # 10 {1/2} # 43 # 1 # 0 # 45 # 0 # 0 <lb/></note> <pb o="30" file="185" n="185" rhead="SECONDO."/> </div> <div xml:id="echoid-div119" type="section" level="1" n="103"> <head xml:id="echoid-head131" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 25 # # # 25 {1/2} # # # 26 # # # 26 {1/2} # # # 27 # # # 27 {1/2} <lb/># # Z. # S. # B. # Z. # S. # B. # Z. # S. # B # Z. # S. # B. # Z. # S. # B. # Z. # S. # B <lb/>On. # {1/2} # 0 # 1 # 4 {1/2} # 0 # 1 # 6 # 0 # 1 {1/2} # 0 # 0 # 1 {1/2} # 0 # 0 # 1 # 12 # 0 # 1 # 12 <lb/>On. # 1 # 0 # 2 # 12 # 0 # 2 # 12 # 0 # 2 # 12 # 0 # 2 # 15 # 0 # 3 # 0 # 0 # 3 # 0 <lb/>On. # 2 # 1 # 1 # 6 # 1 # 1 # 6 # 1 # 1 {1/2} # 0 # 1 # 1 # 14 # 1 # 2 # 0 # 1 # 2 # 3 <lb/>On. # 3 # 1 # 3 # 14 # 2 # 0 # 0 # 2 # 0 # 12 # 2 # 0 # 14 # 2 # 1 # 0 # 2 # 1 {1/2} # 0 <lb/>On. # 4 # 2 # 2 # 3 # 2 # 2 # 14 # 2 # 3 # 0 # 2 # 3 {1/2} # 0 # 3 # 0 # 3 # 3 # {1/2} # 0 <lb/>On. # 5 # 3 # 1 # 0 # 3 # 1 {1/2} # 0 # 3 # 2 # 0 # 3 # 2 {1/2} # 0 # 3 # 3 # 3 # 3 # 3 {1/2} # 0 <lb/>On. # 6 # 3 # 3 {1/2} # 0 # 4 # 0 # 3 # 4 # 1 # 0 # 4 # 1 {1/2} # 0 # 4 # 2 # 3 # 4 # 3 # 0 <lb/>On. # 7 # 4 # 2 # 3 # 4 # 2 # 13 {1/2} # 4 # 3 # 13 {1/2} # 5 # 0 # 6 # 5 # 1 # 0 # 5 # 2 # 0 <lb/>On. # 8 # 5 # 1 # 0 # 5 # 1 # 12 # 5 # 2 {1/2} # 0 # 5 # 3 # 0 # 6 # 0 # 6 # 6 # 1 # 3 <lb/>On. # 9 # 5 # 3 # 6 # 6 # 0 # 6 # 6 # 1 # 6 # 6 # 2 # 6 # 6 # 3 # 6 # 7 # 0 # 3 <lb/>On. # 10 # 6 # 2 # 0 # 6 # 3 # 0 # 7 # 0 # 0 # 7 # 1 # 3 {1/2} # 7 # 2 # 6 # 7 # 3 {1/2} # 0 <lb/>On. # 11 # 7 # {1/2} # 0 # 7 # 1 # 12 # 7 # 3 # 0 # 8 # 0 # 3 # 8 # 1 # 6 # 8 # 2 {1/2} # 0 <lb/>Bra. # 1 # 7 # 3 # 4 {1/2} # 8 # {1/2} # 0 # 8 # 1 # 14 # 8 # 3 # 1 {1/2} # 9 # {1/2} # 0 # 9 # 1 # 14 <lb/>Bra. # 2 # 15 # 2 {1/2} # 0 # 16 # 1 # 0 # 16 # 3 # 10 {1/2} # 17 # 2 # 1 {1/2} # 18 # 1 # 0 # 18 # 3 # 7 <lb/>Bra. # 3 # 23 # 1 # 13 {1/2} # 24 # 1 {1/2} # 0 # 25 # 1 # 12 # 26 # 1 # 6 # 27 # 1 {1/2} # 0 # 28 # 1 # 7 <lb/>Bra. # 4 # 31 # 1 # 0 # 32 # 2 # 0 # 33 # 3 # 6 # 35 # 0 # 3 {1/2} # 36 # 2 # 0 # 37 # 3 # 6 <lb/>Bra. # 5 # 39 # 0 # 4 {1/2} # 40 # 1 {1/2} # 0 # 42 # 1 # 0 # 43 # 3 {1/2} # 0 # 45 # 1 {1/2} # 0 # 47 # 1 # 0 <lb/>Bra. # 6 # 46 # 3 {1/2} # 0 # 48 # 3 # 0 # 50 # 3 # 0 # 52 # 2 # 10 {1/2} # 54 # 3 # 0 # 56 # 3 # 0 <lb/></note> <pb file="186" n="186" rhead="LIBRO"/> </div> <div xml:id="echoid-div120" type="section" level="1" n="104"> <head xml:id="echoid-head132" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 28 # # # 28 {1/2} # # # 29 # # # 29 {1/2} # # # 30 # # # 30 {1/2} <lb/># # Z. # S. # B. # Z. # S. # B # Z. # S # B. # Z. # S. # B # Z. # S. # B. # Z. # S. # B. <lb/>On. # {1/2} # 0 # 1 # 12 # 0 # 1 # 12 # 0 # 1 # 12 # 0 # 1 # 14 # 0 # 2 # 0 # 0 # 2 # 0 <lb/>On. # 1 # 0 # 3 # 3 {1/2} # 0 # 3 # 6 # 0 # 3 {1/2} # 0 # 0 # 3 {1/2} # 0 # 0 # 3 # 12 # 0 # 3 # 12 <lb/>On. # 2 # 1 # 2 # 12 # 1 # 2 # 12 # 1 # 3 # 0 # 1 # 3 # 4 {1/2} # 1 # 3 {1/2} # 0 # 1 # 3 # 13 {1/2} <lb/>On. # 3 # 2 # 1 # 14 # 2 # 2 # 0 # 2 # 2 {1/2} # 0 # 2 # 2 # 14 # 2 # 3 # 0 # 2 # 3 # 12 <lb/>On. # 4 # 3 # 1 # 0 # 3 # 1 {1/2} # 0 # 3 # 2 # 0 # 3 # 2 {1/2} # 0 # 3 # 3 # 0 # 3 # 3 {1/2} # 0 <lb/>On. # 5 # 4 # 0 # 3 {1/2} # 4 # 0 # 15 # 4 # 1 {1/2} # 0 # 4 # 2 # 0 # 4 # 2 # 12 # 4 # 3 # 3 <lb/>On. # 6 # 4 # 3 {1/2} # 0 # 5 # {1/2} # 0 # 5 # 1 # 12 # 5 # 2 # 0 # 5 # 2 # 12 # 5 # 3 # 6 <lb/>On. # 7 # 5 # 2 # 12 # 5 # 3 {1/2} # 0 # 6 # {1/2} # 0 # 6 # 1 # 6 # 6 # 2 # 3 {1/2} # 6 # 3 # 0 <lb/>On. # 8 # 6 # 1 # 12 # 6 # 2 # 3 # 7 # 0 # 0 # 7 # 1 # 0 # 7 # 2 # 0 # 7 # 3 # 0 <lb/>On. # 9 # 7 # 1 # 6 # 7 # 2 # 6 # 7 # 3 {1/2} # 0 # 8 # {1/2} # 2 # 8 # 1 # 12 # 8 # 3 # 0 <lb/>On. # 10 # 8 # 0 # 6 # 8 # 1 # 12 # 8 # 3 # 0 # 9 # 0 # 3 {1/2} # 9 # 1 {1/2} # 0 # 9 # 2 # 12 <lb/>On. # 11 # 9 # 0 # 0 # 9 # 1 # 0 # 9 # 2 {1/2} # 0 # 9 # 3 # 14 # 10 # 1 # 4 {1/2} # 10 # 2 {1/2} # 0 <lb/>Bra. # 1 # 9 # 3 # 3 {1/2} # 10 # 0 # 10 {1/2} # 10 # 2 # 0 # 10 # 3 {1/2} # 0 # 11 # 1 # 0 # 11 # 2 {1/2} # 0 <lb/>Bra. # 2 # 19 # 2 # 7 # 20 # 1 # 6 # 21 # 0 # 0 # 21 # 3 # 0 # 22 # 2 # 0 # 23 # 1 # 0 <lb/>Bra. # 3 # 29 # 1 # 10 {1/2} # 30 # 2 # 0 # 31 # 2 # 0 # 32 # 2 {1/2} # 0 # 33 # 3 # 0 # 34 # 3 {1/2} # 0 <lb/>Bra. # 4 # 39 # 0 # 14 # 40 # 2 # 12 # 42 # 0 # 0 # 43 # 2 # 0 # 45 # 0 # 0 # 46 # 2 # 0 <lb/>Bra. # 5 # 49 # 0 # 0 # 50 # 3 # 0 # 52 # 2 # 0 # 54 # 1 {1/2} # 0 # 56 # 1 # 0 # 58 # {1/2} # 0 <lb/>Bra. # 6 # 58 # 3 # 3 {1/2} # 60 # 3 {1/2} # 0 # 63 # 0 # 0 # 65 # 1 # 0 # 67 # 2 # 0 # 69 # 3 # 0 <lb/></note> <pb o="31" file="187" n="187" rhead="SECONDO."/> </div> <div xml:id="echoid-div121" type="section" level="1" n="105"> <head xml:id="echoid-head133" xml:space="preserve">Tauole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 31 # # # 31 {1/2} # # # 32 # # # 32 {1/2} # # # 33 # # # 33 {1/2} <lb/># # Z. # S. # B. # Z # S. # B. # Z. # S. # B. # Z. # S. # B # Z. # S. # B. # Z. # S. # B. <lb/>On. # {1/2} # 0 # 2 # 0 # 0 # 2 # 0 # 0 # 2 # 0 # 0 # 2 # 3 # 0 # 2 # 3 {1/2} # 0 # 2 # 6 <lb/>On. # 1 # 1 # 0 # 0 # 1 # 0 # 3 {1/2} # 1 # 0 # 6 # 1 # 2 # 0 # 1 # {1/2} # 0 # 1 # 0 # 12 <lb/>On. # 2 # 2 # 0 # 0 # 2 # 0 # 3 # 2 # {1/2} # 0 # 2 # 0 # 14 # 2 # 1 # 0 # 2 # 1 # 4 {1/2} <lb/>On. # 3 # 3 # 0 # 0 # 3 # 0 # 6 # 3 # 0 # 14 # 3 # 1 # 0 # 3 # 1 # 12 # 3 # 2 # 0 <lb/>On. # 4 # 4 # 0 # 0 # 4 # {1/2} # 0 # 4 # 1 # 0 # 4 # 1 {1/2} # 0 # 4 # 2 # 0 # 4 # 2 {1/2} # 0 <lb/>On. # 5 # 5 # 0 # 0 # 5 # 0 # 12 # 5 # 1 # 6 # 5 # 2 # 0 # 5 # 2 # 12 # 5 # 3 # 3 <lb/>On. # 6 # 6 # 0 # 0 # 6 # 0 # 13 {1/2} # 6 # 1 {1/2} # 0 # 6 # 2 # 6 # 6 # 3 # 6 # 7 # 0 # 0 <lb/>On. # 7 # 7 # 0 # 0 # 7 # 1 # 0 # 7 # 2 # 0 # 7 # 3 # 0 # 8 # 0 # 0 # 8 # 0 # 12 <lb/>On. # 8 # 8 # 0 # 0 # 8 # 1 # 0 # 8 # 2 # 0 # 8 # 3 # 0 # 9 # 0 # 6 # 9 # 1 {1/2} # 0 <lb/>On. # 9 # 9 # 0 # 0 # 9 # 1 # 0 # 9 # 1 # 12 # 9 # 3 {1/2} # 0 # 10 # 1 # 0 # 10 # 2 # 0 <lb/>On. # 10 # 10 # 0 # 0 # 10 # 1 # 3 {1/2} # 10 # 2 # 12 # 11 # 0 # 0 # 11 # 1 # 6 # 11 # 2 # 12 <lb/>On. # 11 # 11 # 0 # 0 # 11 # 1 # 6 # 11 # 3 # 0 # 12 # 0 # 6 # 12 # 2 # 0 # 12 # 3 # 6 <lb/>Bra. # 1 # 12 # 0 # 0 # 12 # 1 # 6 # 12 # 3 # 3 {1/2} # 13 # 0 # 14 # 13 # 2 {1/2} # 0 # 14 # 0 # 1 {1/2} <lb/>Bra. # 2 # 24 # 0 # 0 # 24 # 3 # 0 # 25 # 2 # 7 # 26 # 1 # 10 {1/2} # 27 # 1 # 0 # 28 # 0 # 1 {1/2} <lb/>Bra. # 3 # 36 # 0 # 0 # 37 # {1/2} # 0 # 38 # 1 # 10 {1/2} # 39 # 2 # 7 # 40 # 3 {1/2} # 0 # 42 # 0 # 5 <lb/>Bra. # 4 # 48 # 0 # 0 # 49 # 2 # 0 # 51 # 0 # 14 # 52 # 3 # 3 {1/2} # 54 # 2 # 0 # 56 # 0 # 3 {1/2} <lb/>Bra. # 5 # 60 # 0 # 0 # 61 # 3 {1/2} # 0 # 64 # 0 # 0 # 66 # 0 # 0 # 68 # {1/2} # 0 # 70 # {1/2} # 0 <lb/>Bra. # 6 # 72 # 0 # 0 # 74 # 1 # 0 # 76 # 3 # 3 {1/2} # 79 # 1 # 0 # 81 # 3 # 0 # 84 # 0 # 10 {1/2} <lb/></note> <pb file="188" n="188" rhead="LIBRO"/> </div> <div xml:id="echoid-div122" type="section" level="1" n="106"> <head xml:id="echoid-head134" xml:space="preserve">Tanole dell’Imbottare.</head> <note position="right" xml:space="preserve"> <lb/># # # # # 34 # # # 34 {1/2} # # # 35 # # # 35 {1/2} # # # 36 # # # 36 {1/2} <lb/># # Z # S. # B. # Z. # S. # B. # Z. # S. # B # Z. # S. # B. # Z. # S. # B. # Z. # S. # B. <lb/>On. # {1/2} # 0 # 2 # 6 # 0 # 2 {1/2} # 0 # 0 # 2 {1/2} # 0 # 0 # 2 # 12 # 0 # 2 # 12 # 0 # 2 # 15 <lb/>On. # 1 # 1 # 0 # 12 # 1 # 1 # 0 # 1 # 1 # 0 # 1 # 1 # 3 {1/2} # 1 # 1 # 6 # 1 # 1 {1/2} # 0 <lb/>On. # 2 # 2 # 1 # 12 # 2 # 1 # 14 # 2 # 2 # 3 # 2 # 2 # 6 # 2 # 2 # 14 # 2 # 3 # 0 <lb/>On. # 3 # 3 # 2 {1/2} # 0 # 3 # 3 # 0 # 3 # 3 # 6 # 3 # 3 {1/2} # 0 # 4 # 0 # 3 # 4 # {1/2} # 0 <lb/>On. # 4 # 4 # 3 # 3 # 4 # 3 # 12 # 5 # 0 # 3 # 5 # 0 # 12 # 5 # 1 # 0 # 5 # 1 # 14 <lb/>On. # 5 # 6 # 0 # 0 # 6 # 0 # 12 # 6 # 1 # 6 # 6 # 2 # 3 # 6 # 3 # 0 # 6 # 3 # 12 <lb/>On. # 6 # 7 # 1 # 0 # 7 # 2 # 0 # 7 # 2 {1/2} # 0 # 7 # 3 {1/2} # 0 # 8 # 3 # 0 # 8 # 1 # 12 <lb/>On. # 7 # 8 # 1 {1/2} # 0 # 8 # 2 # 4 {1/2} # 8 # 3 # 12 # 9 # 0 # 12 # 9 # 1 # 12 # 9 # 2 {1/2} # 0 <lb/>On. # 8 # 9 # 2 # 12 # 10 # 0 # 0 # 10 # 1 # 0 # 10 # 2 # 0 # 10 # 3 # 0 # 11 # 0 # 0 <lb/>On. # 9 # 10 # 3 # 6 # 11 # 1 # 0 # 11 # 2 # 0 # 11 # 3 # 0 # 12 # {1/2} # 0 # 12 # 0 # 14 <lb/>On. # 10 # 12 # 0 # 3 # 12 # 1 # 12 # 12 # 3 # 0 # 13 # {1/2} # 0 # 13 # 2 # 0 # 13 # 3 # 0 <lb/>On. # 11 # 13 # 1 # 0 # 13 # 3 # 3 {1/2} # 14 # 0 # 0 # 14 # 1 # 12 # 14 # 3 # 6 # 14 # 1 # 0 <lb/>Bra. # 1 # 14 # 1 # 14 # 15 # 0 # 3 {1/2} # 15 # 1 # 4 {1/2} # 15 # 3 # 0 # 16 # 0 # 14 # 16 # 2 # 12 <lb/>Bra. # 2 # 28 # 3 # 10 {1/2} # 29 # 0 # 7 # 30 # 2 {1/2} # 0 # 31 # 2 # 0 # 32 # 1 # 6 # 33 # 1 # 6 <lb/>Bra. # 3 # 43 # 1 # 7 # 45 # 0 # 10 {1/2} # 45 # 3 # 13 {1/2} # 47 # 1 # 0 # 48 # 2 # 7 # 50 # 0 # 0 <lb/>Bra. # 4 # 57 # 3 # 7 # 60 # 0 # 14 # 61 # 1 # 0 # 63 # 0 # 0 # 64 # 3 # 3 {1/2} # 66 # 2 # 7 <lb/>Bra. # 5 # 72 # 1 # 0 # 75 # 1 # 0 # 76 # 2 # 4 {1/2} # 78 # 3 # 0 # 81 # 0 # 0 # 83 # 1 # 0 <lb/>Bra. # 6 # 86 # 3 # 0 # 90 # 1 {1/2} # 0 # 91 # 3 {1/2} # 0 # 94 # 2 # 0 # 97 # 1 # 0 # 99 # 3 # 10 {1/2} <lb/></note> <pb o="32" file="189" n="189" rhead="SECONDO"/> </div> <div xml:id="echoid-div123" type="section" level="1" n="107"> <head xml:id="echoid-head135" xml:space="preserve">Ancora qui ſequentemente, ſi darà eſſempio del <lb/>miſurare le Biade, & vini.</head> <head xml:id="echoid-head136" xml:space="preserve">PRIMO ESSEMPIO.</head> <p> <s xml:id="echoid-s2857" xml:space="preserve"><emph style="sc">Ho r</emph> pongo hauer di diametro d’una piramide, d’un mõ <lb/>tone di biada da miſurare, ch’è onc. </s> <s xml:id="echoid-s2858" xml:space="preserve">73. </s> <s xml:id="echoid-s2859" xml:space="preserve">Prima di 73, ſi torrà <lb/>la metà, che ſarà 36, e mezo; </s> <s xml:id="echoid-s2860" xml:space="preserve">poi ſi torrà la terza parte del-<lb/>l’altezza della piramide, che ſarà brac. </s> <s xml:id="echoid-s2861" xml:space="preserve">2, on. </s> <s xml:id="echoid-s2862" xml:space="preserve">3; </s> <s xml:id="echoid-s2863" xml:space="preserve">ouer bra. </s> <s xml:id="echoid-s2864" xml:space="preserve">2 <lb/>onc. </s> <s xml:id="echoid-s2865" xml:space="preserve">3, ſarà la lunghezza d’una botte, & </s> <s xml:id="echoid-s2866" xml:space="preserve">per voler ſaper la <lb/>quantità della biada, ouer vino in vna botte, ſi piglieranno <lb/>le onc. </s> <s xml:id="echoid-s2867" xml:space="preserve">36, e meza, diſopra alle tauole, & </s> <s xml:id="echoid-s2868" xml:space="preserve">all’incontro di <lb/>brac. </s> <s xml:id="echoid-s2869" xml:space="preserve">2, ſiritrouerà ſegnato 33, 1, e 6; </s> <s xml:id="echoid-s2870" xml:space="preserve">il 33, ſaranno quarte <lb/>di biada 132, ouer di vino zerle 33; </s> <s xml:id="echoid-s2871" xml:space="preserve">& </s> <s xml:id="echoid-s2872" xml:space="preserve">lo 1, ſarà vna quarta <lb/>di biada, o vna ſecchia di vino; </s> <s xml:id="echoid-s2873" xml:space="preserve">& </s> <s xml:id="echoid-s2874" xml:space="preserve">il 6, ſarà ſtoppelli 6, di <lb/>biada, ouer boccali 6, di vino; </s> <s xml:id="echoid-s2875" xml:space="preserve">all’incontro di oncie 3, <lb/>ſotto al 36, e mezo, ſarà ſegnato 4, e mezzo; </s> <s xml:id="echoid-s2876" xml:space="preserve">il 4, ſono <lb/>quarte di biada 16, & </s> <s xml:id="echoid-s2877" xml:space="preserve">di vino zerle 4, & </s> <s xml:id="echoid-s2878" xml:space="preserve">il mezo, ſono cop. </s> <s xml:id="echoid-s2879" xml:space="preserve">2 <lb/>di biada, di vino il mezo ſarà meza ſecchia; </s> <s xml:id="echoid-s2880" xml:space="preserve">& </s> <s xml:id="echoid-s2881" xml:space="preserve">ſommato tut <lb/>to inſieme faranno di biada intorno a quarte 150; </s> <s xml:id="echoid-s2882" xml:space="preserve">& </s> <s xml:id="echoid-s2883" xml:space="preserve">di vi-<lb/>no intorno à zerle 37, & </s> <s xml:id="echoid-s2884" xml:space="preserve">ſecchie 2; </s> <s xml:id="echoid-s2885" xml:space="preserve">& </s> <s xml:id="echoid-s2886" xml:space="preserve">l’vno, & </s> <s xml:id="echoid-s2887" xml:space="preserve">l’altro ſi mol-<lb/>tiplicaranno per 4, & </s> <s xml:id="echoid-s2888" xml:space="preserve">faranno di biada quarte 600; </s> <s xml:id="echoid-s2889" xml:space="preserve">& </s> <s xml:id="echoid-s2890" xml:space="preserve">divi-<lb/>no intorno à zerle 150, & </s> <s xml:id="echoid-s2891" xml:space="preserve">coſi non ſolo alla quantità del <lb/>vino, come ancor delle biade ſeruiranno le oncie 73; </s> <s xml:id="echoid-s2892" xml:space="preserve">cioè <lb/>le onc. </s> <s xml:id="echoid-s2893" xml:space="preserve">73, ſaranno diametro d’una piramiderotonda, & </s> <s xml:id="echoid-s2894" xml:space="preserve">an <lb/>cora le oncie 73, s’intenderanno per la metà del diametro <lb/>del fondo, al cocone d’un vaſſello, ouer d’un tinazzo.</s> <s xml:id="echoid-s2895" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div124" type="section" level="1" n="108"> <head xml:id="echoid-head137" xml:space="preserve">SECONDO ESSEMPI O.</head> <p> <s xml:id="echoid-s2896" xml:space="preserve">Auuertendo anchora, che ſe ſi haueſſe di diametro oncie <lb/>50, e meza, perche ſopra le tauole non ſi ritroua queſto nu-<lb/>mero, ſarà biſogno pigliar le parti, cioè oncie 25, & </s> <s xml:id="echoid-s2897" xml:space="preserve">le on-<lb/>cie 25, e mezza, & </s> <s xml:id="echoid-s2898" xml:space="preserve">non il 25, e vn quarto, come ancor di <pb file="190" n="190" rhead="LIBRO"/> ſopra s’è detto; </s> <s xml:id="echoid-s2899" xml:space="preserve">& </s> <s xml:id="echoid-s2900" xml:space="preserve">ſe anchora la terza parte dell’altezza <lb/>della perpendicolare della piramide di biada, fuſſe brac-<lb/>cia 1, oncie 8; </s> <s xml:id="echoid-s2901" xml:space="preserve">ouer la lunghezza della botte, ſi piglierà <lb/>25, & </s> <s xml:id="echoid-s2902" xml:space="preserve">25, emezo, ſopra alle tauole, & </s> <s xml:id="echoid-s2903" xml:space="preserve">da mano ſiniſtra nel-<lb/>la prima colonna, ſi piglierà brac. </s> <s xml:id="echoid-s2904" xml:space="preserve">1. </s> <s xml:id="echoid-s2905" xml:space="preserve">on. </s> <s xml:id="echoid-s2906" xml:space="preserve">8; </s> <s xml:id="echoid-s2907" xml:space="preserve">& </s> <s xml:id="echoid-s2908" xml:space="preserve">all’incontro <lb/>dibrac. </s> <s xml:id="echoid-s2909" xml:space="preserve">1, ſotto al 25, ſi ritrouerà ſegnato zerle 7, ſecchie <lb/>3, et boccali 4, e mezo di vino; </s> <s xml:id="echoid-s2910" xml:space="preserve">& </s> <s xml:id="echoid-s2911" xml:space="preserve">all incontro di oncie 8, <lb/>ſotto al 25, ſi ritrouerà ſegnato zerle 5, eſecchia 1, di vino; <lb/></s> <s xml:id="echoid-s2912" xml:space="preserve">che ſommato il tutto inſieme faranno zerle 13; </s> <s xml:id="echoid-s2913" xml:space="preserve">ſecchie 0, e <lb/>boccali 4, e mezo di vino; </s> <s xml:id="echoid-s2914" xml:space="preserve">& </s> <s xml:id="echoid-s2915" xml:space="preserve">zerle 13, ſecchie 0, e boccali <lb/>4, mezo di vino, ſi raddoppieranno, che faranno zerle 26, <lb/>e|<unsure/>meza ſecchia di vino, hor per le 25, e meza oncie, che ſi <lb/>pigliano ſopra alle tauole, s’ha da pigliare vn braccio nella <lb/>prima colonna, & </s> <s xml:id="echoid-s2916" xml:space="preserve">ſotto al 25, e mezo, allo incontro del 1, <lb/>ſi trouerà ſegnato zerle 8, e meza ſecchia di vino; </s> <s xml:id="echoid-s2917" xml:space="preserve">& </s> <s xml:id="echoid-s2918" xml:space="preserve">all’in-<lb/>contro del 8, ſotto al 25, e mezo, ſi trouerà ſegnato zerle 5, <lb/>ſecchie 1, bocc. </s> <s xml:id="echoid-s2919" xml:space="preserve">12; </s> <s xml:id="echoid-s2920" xml:space="preserve">ilche ſommato inſieme, faranno di vi-<lb/>no zerle 13, ſecchie 2, e boccali 3; </s> <s xml:id="echoid-s2921" xml:space="preserve">doppiate faranno zerle <lb/>27, ſecchie 0, e bocc. </s> <s xml:id="echoid-s2922" xml:space="preserve">6; </s> <s xml:id="echoid-s2923" xml:space="preserve">& </s> <s xml:id="echoid-s2924" xml:space="preserve">ſommato il doppio delle on. </s> <s xml:id="echoid-s2925" xml:space="preserve">25, <lb/>& </s> <s xml:id="echoid-s2926" xml:space="preserve">quello delle oncie. </s> <s xml:id="echoid-s2927" xml:space="preserve">25, e meza, faranno zerle 53, & </s> <s xml:id="echoid-s2928" xml:space="preserve">quaſi <lb/>ſecchia 1, di vino, & </s> <s xml:id="echoid-s2929" xml:space="preserve">di biada quarte 213.</s> <s xml:id="echoid-s2930" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div125" type="section" level="1" n="109"> <head xml:id="echoid-head138" xml:space="preserve">TERZO ESSEMPIO.</head> <p> <s xml:id="echoid-s2931" xml:space="preserve">Auuertendo, che ſe’l diametro della piramide rotonda, <lb/>ouer la ſomma di due diametri, cioè del fondo, & </s> <s xml:id="echoid-s2932" xml:space="preserve">del coco-<lb/>ne d’una botta, fuſſero ſtate on. </s> <s xml:id="echoid-s2933" xml:space="preserve">49, e meza; </s> <s xml:id="echoid-s2934" xml:space="preserve">ſitorrebbe on-<lb/>cie 24, e meza, & </s> <s xml:id="echoid-s2935" xml:space="preserve">oncie 25, & </s> <s xml:id="echoid-s2936" xml:space="preserve">ſi farà come diſopra; </s> <s xml:id="echoid-s2937" xml:space="preserve">hauen-<lb/>do però nota la lunghezza della botte, ouer l’altezza del ti-<lb/>nazzo, oueramenre la terza parte dell’altezza d’una pira-<lb/>mide rotonda; </s> <s xml:id="echoid-s2938" xml:space="preserve">come ſaria per eſſempio, che la lunghezza <lb/>d’una botte, ſia brac. </s> <s xml:id="echoid-s2939" xml:space="preserve">3, on. </s> <s xml:id="echoid-s2940" xml:space="preserve">2; </s> <s xml:id="echoid-s2941" xml:space="preserve">ouer l’altezza d’un tinazzo; <lb/></s> <s xml:id="echoid-s2942" xml:space="preserve">ò la terza parte dell’altezza d’un montone di biada, à mo’<unsure/> <lb/>do di piramide rotonda; </s> <s xml:id="echoid-s2943" xml:space="preserve">ſi piglieran le on. </s> <s xml:id="echoid-s2944" xml:space="preserve">24, e meza, & </s> <s xml:id="echoid-s2945" xml:space="preserve">le <pb o="33" file="191" n="191" rhead="SECONDO"/> onc. </s> <s xml:id="echoid-s2946" xml:space="preserve">25, ſopra le tauole, & </s> <s xml:id="echoid-s2947" xml:space="preserve">allo incontro di brac. </s> <s xml:id="echoid-s2948" xml:space="preserve">3, ſ<unsure/>otto al <lb/>24, e mezo, & </s> <s xml:id="echoid-s2949" xml:space="preserve">al 25, ſoto alle on. </s> <s xml:id="echoid-s2950" xml:space="preserve">24, e meza, ſi trouerà ſegna <lb/>to zerle 22, e ſecchie 2; </s> <s xml:id="echoid-s2951" xml:space="preserve">& </s> <s xml:id="echoid-s2952" xml:space="preserve">ſotto al 25, ſi trouerà ſegnato zer-<lb/>le 23, & </s> <s xml:id="echoid-s2953" xml:space="preserve">ſecchie 1, e boccali 13, e mezo; </s> <s xml:id="echoid-s2954" xml:space="preserve">& </s> <s xml:id="echoid-s2955" xml:space="preserve">all’incontro del-<lb/>le onc. </s> <s xml:id="echoid-s2956" xml:space="preserve">2, ſotto al 24, e mezzo, & </s> <s xml:id="echoid-s2957" xml:space="preserve">25; </s> <s xml:id="echoid-s2958" xml:space="preserve">ſotto al 24, e mezzo, <lb/>ſitrouerà ſegnato zerle 1, ſecchie 1, & </s> <s xml:id="echoid-s2959" xml:space="preserve">ſotto al 25, zerle 1, <lb/>ſecchie 2, e boccali 6; </s> <s xml:id="echoid-s2960" xml:space="preserve">hor ſommando inſieme quello che <lb/>hanno datto on. </s> <s xml:id="echoid-s2961" xml:space="preserve">24, e mezza, & </s> <s xml:id="echoid-s2962" xml:space="preserve">ancor quello che han dato <lb/>le 25; </s> <s xml:id="echoid-s2963" xml:space="preserve">faranno per le oncie 24, e mezza zerle 23, e ſecchie 2; <lb/></s> <s xml:id="echoid-s2964" xml:space="preserve">& </s> <s xml:id="echoid-s2965" xml:space="preserve">per le onc. </s> <s xml:id="echoid-s2966" xml:space="preserve">25, zerle 24, ſecchie 3, hor raddoppiate l’una, <lb/>& </s> <s xml:id="echoid-s2967" xml:space="preserve">l’altra; </s> <s xml:id="echoid-s2968" xml:space="preserve">quelle del 24, e mezzo, faranno zerle 47, e ſec-<lb/>chie 2; </s> <s xml:id="echoid-s2969" xml:space="preserve">& </s> <s xml:id="echoid-s2970" xml:space="preserve">quello del 25, faranno zerle 49, eſecchie 2; </s> <s xml:id="echoid-s2971" xml:space="preserve">& </s> <s xml:id="echoid-s2972" xml:space="preserve"><lb/>di nouo ſi ſommaranno quelle dell’vno, & </s> <s xml:id="echoid-s2973" xml:space="preserve">l’altro inſie-<lb/>me, & </s> <s xml:id="echoid-s2974" xml:space="preserve">faranno zerle 97, di vino, & </s> <s xml:id="echoid-s2975" xml:space="preserve">di biada ſaranno quar-<lb/>te 388; </s> <s xml:id="echoid-s2976" xml:space="preserve">coſiſi potrà dire, che trouandoſi oncie 49, e mezza, <lb/>la metà del fondo; </s> <s xml:id="echoid-s2977" xml:space="preserve">& </s> <s xml:id="echoid-s2978" xml:space="preserve">del cocone d’una botte, & </s> <s xml:id="echoid-s2979" xml:space="preserve">la ſua lun-<lb/>ghezza brac. </s> <s xml:id="echoid-s2980" xml:space="preserve">3, on. </s> <s xml:id="echoid-s2981" xml:space="preserve">2, che la botte tenerà di vino zerle 97; </s> <s xml:id="echoid-s2982" xml:space="preserve"><lb/>il medeſimo miſurando vn tinazzo, cioè il diametro del fon <lb/>do, & </s> <s xml:id="echoid-s2983" xml:space="preserve">il diametro della bocca di ſoprauia (laſciando però <lb/>fuora le doue ouer aſsi del tinazzo, come ancor quelle del-<lb/>la botte) & </s> <s xml:id="echoid-s2984" xml:space="preserve">quelli due diametri del tinazzo, ſommati in-<lb/>ſieme, & </s> <s xml:id="echoid-s2985" xml:space="preserve">di quella ſomma tuorne la metà; </s> <s xml:id="echoid-s2986" xml:space="preserve">quel medeſimo <lb/>che ſi fa del diametro del fondo, & </s> <s xml:id="echoid-s2987" xml:space="preserve">del cocone d’una botte; </s> <s xml:id="echoid-s2988" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s2989" xml:space="preserve">l’altezza del tinazzo fuſſe brac. </s> <s xml:id="echoid-s2990" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s2991" xml:space="preserve">2, come ſe fuſſe <lb/>la lunghezza d’una botte; </s> <s xml:id="echoid-s2992" xml:space="preserve">coſi il tinazzo haurebbe tenuto <lb/>zerle 97, di vino, com’vna botte. </s> <s xml:id="echoid-s2993" xml:space="preserve">Ancora ſe fuſſe vn mon <lb/>tone di biada à modo di piramide rotonda, & </s> <s xml:id="echoid-s2994" xml:space="preserve">che’l diame-<lb/>tro della baſe fuſſe onc. </s> <s xml:id="echoid-s2995" xml:space="preserve">49, e mezza; </s> <s xml:id="echoid-s2996" xml:space="preserve">& </s> <s xml:id="echoid-s2997" xml:space="preserve">la terza parte del-<lb/>l’altezza fuſſe brac, 3, on. </s> <s xml:id="echoid-s2998" xml:space="preserve">2; </s> <s xml:id="echoid-s2999" xml:space="preserve">ſarebbe quella piramide di bia <lb/>da quarte 388; </s> <s xml:id="echoid-s3000" xml:space="preserve">Io<unsure/> anchora ho dichiarato il modo di torre <lb/>la metà delle oncie, che paſſano quelle che ſono ſopra alle <lb/>tauole, cioè a oncie 36, e meza. </s> <s xml:id="echoid-s3001" xml:space="preserve">Auuertendo ancora, che <lb/>pigliando la metà delle oncie, che auanzano 36, e mezo, <lb/>non ſi deue pigliare quella metà, che auanza l’altra metà <pb file="192" n="192" rhead="LIBRO"/> più di mezzo; </s> <s xml:id="echoid-s3002" xml:space="preserve">ne meno di mezo; </s> <s xml:id="echoid-s3003" xml:space="preserve">come diſopra ſiè detto, che <lb/>non ſi deue pigliare il quarto. </s> <s xml:id="echoid-s3004" xml:space="preserve">Auuertendo anchora che <lb/>quel numero che ſi ha da torre la metà, non paſsi il numero <lb/>dion. </s> <s xml:id="echoid-s3005" xml:space="preserve">73.</s> <s xml:id="echoid-s3006" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3007" xml:space="preserve">Parmi hauer detto aſſai del miſurare le biade in pirami-<lb/>derotonda, & </s> <s xml:id="echoid-s3008" xml:space="preserve">anco del vino, con le ſopradette tauole: </s> <s xml:id="echoid-s3009" xml:space="preserve">Qui <lb/>ſeguendo io dirò del miſurare il vino con breuità ſenza le <lb/>tauole.</s> <s xml:id="echoid-s3010" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div126" type="section" level="1" n="110"> <head xml:id="echoid-head139" xml:space="preserve">ESSEMPIO DI MISVRARE IL VINO</head> <head xml:id="echoid-head140" xml:space="preserve">ſenza le Tauole.</head> <p> <s xml:id="echoid-s3011" xml:space="preserve"><emph style="sc">Hor</emph> volendo miſurarevna botte, che fuſſe di diametro <lb/>al cocone onc. </s> <s xml:id="echoid-s3012" xml:space="preserve">32, & </s> <s xml:id="echoid-s3013" xml:space="preserve">al fondo onc. </s> <s xml:id="echoid-s3014" xml:space="preserve">29, ſi ſommeranno in-<lb/>ſieme, come diſopra s’è detto, & </s> <s xml:id="echoid-s3015" xml:space="preserve">faranno onc. </s> <s xml:id="echoid-s3016" xml:space="preserve">61, & </s> <s xml:id="echoid-s3017" xml:space="preserve">dion. <lb/></s> <s xml:id="echoid-s3018" xml:space="preserve">61, ſi piglierà la metà, che ſarà 30 e mezzo, & </s> <s xml:id="echoid-s3019" xml:space="preserve">30, e mezzo ſi <lb/>moltiplicherà in ſe medeſimo farãno pun. </s> <s xml:id="echoid-s3020" xml:space="preserve">930, evn quarto, <lb/>& </s> <s xml:id="echoid-s3021" xml:space="preserve">pun. </s> <s xml:id="echoid-s3022" xml:space="preserve">930, evn quarto ſi partiranno, per pun. </s> <s xml:id="echoid-s3023" xml:space="preserve">20, nevenirà <lb/>ſecchie 46, e mezza; </s> <s xml:id="echoid-s3024" xml:space="preserve">& </s> <s xml:id="echoid-s3025" xml:space="preserve">ſec chie 46, e mezza, ſi moltipliche-<lb/>ranno per bracc. </s> <s xml:id="echoid-s3026" xml:space="preserve">2, onc. </s> <s xml:id="echoid-s3027" xml:space="preserve">9, lunghezza della botte, & </s> <s xml:id="echoid-s3028" xml:space="preserve">neve-<lb/>nirà intorno a ſecchie 128, & </s> <s xml:id="echoid-s3029" xml:space="preserve">ſecchie 128, di vino tenirà la <lb/>ſopradetta botte; </s> <s xml:id="echoid-s3030" xml:space="preserve">& </s> <s xml:id="echoid-s3031" xml:space="preserve">volendo far ſecchie 128, in zerle, ſi par <lb/>tiranno ſecchie 128, per ſecchie 4, & </s> <s xml:id="echoid-s3032" xml:space="preserve">ne venirãno zerle 32; </s> <s xml:id="echoid-s3033" xml:space="preserve"><lb/>il medeſimo ſi farebbe nel miſurare vn tinazzo, tolendo <lb/>le ſue miſure, come diſopra ſi è detto nel miſurare vn tinaz <lb/>zo, con le ſopradette tauole.</s> <s xml:id="echoid-s3034" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div127" type="section" level="1" n="111"> <head xml:id="echoid-head141" xml:space="preserve">SECONDO ESSEMPIO</head> <head xml:id="echoid-head142" xml:space="preserve">di miſurare il vino con breuità.</head> <p> <s xml:id="echoid-s3035" xml:space="preserve">Auuertendo ancora, che iſopradetti conti d’una botte, <lb/>& </s> <s xml:id="echoid-s3036" xml:space="preserve">d’un tinazzo, ſi poſſono fare con più breuità, come diſo-<lb/>pra ſi è inſegnato nel voler miſurare vn mo ntone di biada, <lb/>in piramide rotonda.</s> <s xml:id="echoid-s3037" xml:space="preserve"/> </p> <pb o="34" file="193" n="193" rhead="SECONDO"/> <figure> <image file="193-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/193-01"/> </figure> <p> <s xml:id="echoid-s3038" xml:space="preserve">Auuertendo ancora, che ſe fuſſe vna botte che haueſſe vn <lb/>fondo più grande che l’altro ſi ſommeranno li due diametri <lb/>de’loro fondi, & </s> <s xml:id="echoid-s3039" xml:space="preserve">di quella ſomma ſe ne piglierà la metà, & </s> <s xml:id="echoid-s3040" xml:space="preserve"><lb/>quella metà ſi ſommerà col diametro della botte.</s> <s xml:id="echoid-s3041" xml:space="preserve"/> </p> <pb file="194" n="194" rhead="LIBRO"/> </div> <div xml:id="echoid-div128" type="section" level="1" n="112"> <head xml:id="echoid-head143" xml:space="preserve">REGOIA PER SAPERE PROPOR-<unsure/></head> <head xml:id="echoid-head144" xml:space="preserve">tionare vna Bacchetta, con laquale ſi poſſa <lb/>miſurare il vino nelle botte.</head> <p> <s xml:id="echoid-s3042" xml:space="preserve"><emph style="sc">Et</emph> volendo proportionare tal bacchetta, prima ſi ſe-<lb/>gnarà la bacchetta à oncie, & </s> <s xml:id="echoid-s3043" xml:space="preserve">meze; </s> <s xml:id="echoid-s3044" xml:space="preserve">poi ſi deue pigliare ſo-<lb/>pra à eſſa bacchetta le minor oncie, ouer meze comunate <lb/>della metà del diametro del fondo, & </s> <s xml:id="echoid-s3045" xml:space="preserve">del cocone d’una <lb/>botta, & </s> <s xml:id="echoid-s3046" xml:space="preserve">ponerò che ſi comincia alle onc. </s> <s xml:id="echoid-s3047" xml:space="preserve">5, & </s> <s xml:id="echoid-s3048" xml:space="preserve">iui ſi ſegnarà <lb/>vna ſecchia, & </s> <s xml:id="echoid-s3049" xml:space="preserve">bocc. </s> <s xml:id="echoid-s3050" xml:space="preserve">4, e mezzo, alle on. </s> <s xml:id="echoid-s3051" xml:space="preserve">5, e mezza ſe gli ſe-<lb/>gnarà vna ſecchia, e bocc. </s> <s xml:id="echoid-s3052" xml:space="preserve">9; </s> <s xml:id="echoid-s3053" xml:space="preserve">alle on. </s> <s xml:id="echoid-s3054" xml:space="preserve">6, iui ſi ſegnarà vna ſec <lb/>chia, & </s> <s xml:id="echoid-s3055" xml:space="preserve">boccali 14, e mezzo; </s> <s xml:id="echoid-s3056" xml:space="preserve">& </s> <s xml:id="echoid-s3057" xml:space="preserve">alle oncie 6, e mezza; </s> <s xml:id="echoid-s3058" xml:space="preserve">iui ſe <lb/>gli ſegnarà ſecchie 2, boccali 2; </s> <s xml:id="echoid-s3059" xml:space="preserve">alle onc. </s> <s xml:id="echoid-s3060" xml:space="preserve">7, iui ſe gli ſegne-<lb/>rà ſecchie 2, boccali 9; </s> <s xml:id="echoid-s3061" xml:space="preserve">alle oncie 7, e mezza, iui ſe gli ſe-<lb/>gnarà ſecchie 2, boccali 14; </s> <s xml:id="echoid-s3062" xml:space="preserve">& </s> <s xml:id="echoid-s3063" xml:space="preserve">alle oncie 8, iui ſe gli ſegne-<lb/>rà ſecchie 3, boccali 3, e mezo; </s> <s xml:id="echoid-s3064" xml:space="preserve">& </s> <s xml:id="echoid-s3065" xml:space="preserve">di mano in mano, alle on-<lb/>cie, & </s> <s xml:id="echoid-s3066" xml:space="preserve">meze oncie, ſegnate ſopra la bacchetta, s’andaranno <lb/>ſegnando le zerle, ſecchie, & </s> <s xml:id="echoid-s3067" xml:space="preserve">boccali, quel tanto che daran <lb/>no le oncie, & </s> <s xml:id="echoid-s3068" xml:space="preserve">meze comunate, della metà del diametro del <lb/>fondo, & </s> <s xml:id="echoid-s3069" xml:space="preserve">del cocone d’una botta; </s> <s xml:id="echoid-s3070" xml:space="preserve">& </s> <s xml:id="echoid-s3071" xml:space="preserve">queſta tal bacchetta nõ <lb/>vorrebbe eſſere lunga meno de braccia quattro, diuiſa in <lb/>braccie, oncie, & </s> <s xml:id="echoid-s3072" xml:space="preserve">meze oncie; </s> <s xml:id="echoid-s3073" xml:space="preserve">Etpoi che ſi hauerà ſegna-<lb/>to zerle, ſecchie, & </s> <s xml:id="echoid-s3074" xml:space="preserve">boccali alle on. </s> <s xml:id="echoid-s3075" xml:space="preserve">& </s> <s xml:id="echoid-s3076" xml:space="preserve">meze onc. </s> <s xml:id="echoid-s3077" xml:space="preserve">comunate; <lb/></s> <s xml:id="echoid-s3078" xml:space="preserve">altro non ſi deue fare che pigliare la lunghezza della botta, <lb/>& </s> <s xml:id="echoid-s3079" xml:space="preserve">quella moltiplicarla, con le zerle, ſecchie, & </s> <s xml:id="echoid-s3080" xml:space="preserve">boccali, che <lb/>ſi ritrouerãno ſegnate a quelle oncie comunate, ſopra a eſſa <lb/>bacchetta, & </s> <s xml:id="echoid-s3081" xml:space="preserve">quello che ne venirà d’eſſa multiplicatione, <lb/>ſarà la tenuta della botta, & </s> <s xml:id="echoid-s3082" xml:space="preserve">di queſto ſe ne darà eſſempio.</s> <s xml:id="echoid-s3083" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div129" type="section" level="1" n="113"> <head xml:id="echoid-head145" xml:space="preserve">ESSEMPIO.</head> <p> <s xml:id="echoid-s3084" xml:space="preserve">Pono che s’habbia vna botta che ſia di diametro al coco <lb/>ne oncie 28, & </s> <s xml:id="echoid-s3085" xml:space="preserve">a vn di fondi di diametro oncie 26; </s> <s xml:id="echoid-s3086" xml:space="preserve">ſi ſom-<lb/>merà inſieme 28, con 26, faranno oncie 54, & </s> <s xml:id="echoid-s3087" xml:space="preserve">di 54, ſi pi- <pb o="35" file="195" n="195" rhead="SECONDO"/> go<unsure/>lierà la metà che ſarà oncie 27, & </s> <s xml:id="echoid-s3088" xml:space="preserve">oncie 27, ſi adimanda-<lb/>no<unsure/> oncie comunate, & </s> <s xml:id="echoid-s3089" xml:space="preserve">oncie 27, comunate, ſe ritroueranno <lb/>ſopra la Bachetta, & </s> <s xml:id="echoid-s3090" xml:space="preserve">iui gli ſarà ſegnato ſecchie 36, boc-<lb/>cali 9, poiſi trouerà la lunghezza della botta, & </s> <s xml:id="echoid-s3091" xml:space="preserve">pongo che <lb/>ſia brac. </s> <s xml:id="echoid-s3092" xml:space="preserve">2, on. </s> <s xml:id="echoid-s3093" xml:space="preserve">5, & </s> <s xml:id="echoid-s3094" xml:space="preserve">brac. </s> <s xml:id="echoid-s3095" xml:space="preserve">2, onc. </s> <s xml:id="echoid-s3096" xml:space="preserve">5, ſi moltiplicheranno con <lb/>ſecchie 36, boccali 9, come diſopra s’è inſegnato nel miſu-<lb/>rare del vino, & </s> <s xml:id="echoid-s3097" xml:space="preserve">ſi ritrouerà che ſaranno zerle 22, ſecchie o, <lb/>boccali 3, e mezo; </s> <s xml:id="echoid-s3098" xml:space="preserve">& </s> <s xml:id="echoid-s3099" xml:space="preserve">tanto tenerà la detta botta; </s> <s xml:id="echoid-s3100" xml:space="preserve">il medeſi-<lb/>mo ſi ſarebbe fatto ſe ne le oncie comunate li fuſſe ſtato me <lb/>za oncia, cioè oncie comunate 27, e mezza, & </s> <s xml:id="echoid-s3101" xml:space="preserve">oncie 27, e <lb/>mezza ſi haurebbono ritrouato ſopra la bacchetta, & </s> <s xml:id="echoid-s3102" xml:space="preserve">iui ſi <lb/>ritrouarebbe ſegnato ſecchie 37, boccali 14; </s> <s xml:id="echoid-s3103" xml:space="preserve">& </s> <s xml:id="echoid-s3104" xml:space="preserve">poi ſi piglia <lb/>rebbe la miſura della lunghezza della botta, & </s> <s xml:id="echoid-s3105" xml:space="preserve">moltiplica-<lb/>re quella con ſecchie 37, boccali 14, ne venirebbe la tenu-<lb/>ta della botta; </s> <s xml:id="echoid-s3106" xml:space="preserve">& </s> <s xml:id="echoid-s3107" xml:space="preserve">con queſta regola ſi potrà ſapere ancora <lb/>la tenuta d’un tinazzo, ponendo la metà del diametro del <lb/>fondo, cõ la metà del diametro della bocca di ſoprauia del <lb/>tinazzo per le oncie comunate, & </s> <s xml:id="echoid-s3108" xml:space="preserve">per la lunghezza l’altez-<lb/>za del vacuo di dentrouia del tinazzo, & </s> <s xml:id="echoid-s3109" xml:space="preserve">oſſeruare l’ordine <lb/>come diſopra, nel ſapere la tenuta d’una botta, ſi ſaperà la <lb/>tenuta ancor d’un tinazzo.</s> <s xml:id="echoid-s3110" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div130" type="section" level="1" n="114"> <head xml:id="echoid-head146" xml:space="preserve">TERZO ESSEMPIO DI MISVRARE</head> <head xml:id="echoid-head147" xml:space="preserve">vn ſacco di biada.</head> <p> <s xml:id="echoid-s3111" xml:space="preserve">Et volendo miſurare vn ſacco di biada, ſi torrà la larghez-<lb/>za della boca del ſacco, & </s> <s xml:id="echoid-s3112" xml:space="preserve">di quella circonferenza ſe ne pi-<lb/>gliarà la terza parte, & </s> <s xml:id="echoid-s3113" xml:space="preserve">quella terza parte ſi farà tutt’à oncie; <lb/></s> <s xml:id="echoid-s3114" xml:space="preserve">& </s> <s xml:id="echoid-s3115" xml:space="preserve">quelle oncie ſaranno il diametro del ſacco; </s> <s xml:id="echoid-s3116" xml:space="preserve">& </s> <s xml:id="echoid-s3117" xml:space="preserve">ſe’l ſacco <lb/>ſarà largo alla bocca oncie 15, raddoppiando oncie 15, fa-<lb/>ranno onc. </s> <s xml:id="echoid-s3118" xml:space="preserve">30, & </s> <s xml:id="echoid-s3119" xml:space="preserve">di onc. </s> <s xml:id="echoid-s3120" xml:space="preserve">30, ſe ne toglia la terza parte, che <lb/>ſono on. </s> <s xml:id="echoid-s3121" xml:space="preserve">10, & </s> <s xml:id="echoid-s3122" xml:space="preserve">eſſendo alto il ſacco brac. </s> <s xml:id="echoid-s3123" xml:space="preserve">2, onc. </s> <s xml:id="echoid-s3124" xml:space="preserve">9, d’altezza <lb/>ſe gli darà d’ogni braccio mezz’oncia d’auantaggio, per-<lb/>che la grauezza del grano fa abbaſſare il ſacco.</s> <s xml:id="echoid-s3125" xml:space="preserve"/> </p> <pb file="196" n="196" rhead="LIBRO"/> <p> <s xml:id="echoid-s3126" xml:space="preserve">Hor ſi farà il conto quanto tiene di grano il ſacco della <lb/>ſopradetta miſura.</s> <s xml:id="echoid-s3127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3128" xml:space="preserve">Prima ſimoltiplicherà oncie 10, in ſe, & </s> <s xml:id="echoid-s3129" xml:space="preserve">faranno punti <lb/>100, & </s> <s xml:id="echoid-s3130" xml:space="preserve">punti 100, ſi partiranno per punti 20, & </s> <s xml:id="echoid-s3131" xml:space="preserve">ne venirà <lb/>quarte 5, di biada, ouer ſi moltiplicherà le decenein ſe, fa-<lb/>ranno 1; </s> <s xml:id="echoid-s3132" xml:space="preserve">& </s> <s xml:id="echoid-s3133" xml:space="preserve">1, ſi moltiplicherà per quarte 5, & </s> <s xml:id="echoid-s3134" xml:space="preserve">faranno pur <lb/>quarte 5, come ho detto. </s> <s xml:id="echoid-s3135" xml:space="preserve">Poi ſi moltiplicherà quarte 5, con <lb/>braccia 2, on. </s> <s xml:id="echoid-s3136" xml:space="preserve">9, dell’altezza del ſacco, come qui ſotto ſive <lb/>de, & </s> <s xml:id="echoid-s3137" xml:space="preserve">faranno quarte 13, cop. </s> <s xml:id="echoid-s3138" xml:space="preserve">3; </s> <s xml:id="echoid-s3139" xml:space="preserve">& </s> <s xml:id="echoid-s3140" xml:space="preserve">tanto tenerà il ſacco.</s> <s xml:id="echoid-s3141" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Brac. # 2, # on. # 9, <lb/>Quar. # 5, <lb/>Quar. # 10, <lb/>Quar. # 3, # cop. # 3, <lb/>Quar. # 13, # cop. # 3, <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Proua. <lb/>oncie # 5, # 2, # onc. di cop. <lb/>cop. # 6, # 2, # onc. di cop. <lb/></note> <note position="right" xml:space="preserve"> <lb/># oncie # 9 # auanza onc. di quar. 9, ſi fa- \\ ranno in onc. di cop. molti- \\ plicando per 4, & farāno 36, \\ onc. di cop. partendo per 12, \\ ſono cop. 3. <lb/># quar. # 5 <lb/># # oncie di quar. # 45 <lb/># partir’per # 12 <lb/># quar. # 3 cop. 3 <lb/></note> <p> <s xml:id="echoid-s3142" xml:space="preserve">Facendo il conto in due modi, come diſopra s’è inſegna <lb/>to nelle ragioni delle biade, tenerà il ſacco quarte 13, cop-<lb/>pi 3, di biada; </s> <s xml:id="echoid-s3143" xml:space="preserve">hor il medeſimo conto ſi farà con le noſtre ta <pb o="36" file="197" n="197" rhead="SECONDO"/> uole, pigliando on. </s> <s xml:id="echoid-s3144" xml:space="preserve">10, di diametro ſopra alle tauole; </s> <s xml:id="echoid-s3145" xml:space="preserve">& </s> <s xml:id="echoid-s3146" xml:space="preserve">da <lb/>mano ſiniſtra nella prima colonna brac. </s> <s xml:id="echoid-s3147" xml:space="preserve">2, on. </s> <s xml:id="echoid-s3148" xml:space="preserve">9, all’incon-<lb/>tro di brac. </s> <s xml:id="echoid-s3149" xml:space="preserve">2, ſotto a on. </s> <s xml:id="echoid-s3150" xml:space="preserve">10, ſi trouerà ſegnato zerle 2, ſec-<lb/>chie 2, che ſaranno quarte 10, di biada; </s> <s xml:id="echoid-s3151" xml:space="preserve">& </s> <s xml:id="echoid-s3152" xml:space="preserve">all’incontro di <lb/>onc. </s> <s xml:id="echoid-s3153" xml:space="preserve">9, ſotto à onc. </s> <s xml:id="echoid-s3154" xml:space="preserve">10, ſitrouerà ſegnato ſecchie 3, e bocc. <lb/></s> <s xml:id="echoid-s3155" xml:space="preserve">13, e mezzo, che ſono di biada quarte 3, coppi 3; </s> <s xml:id="echoid-s3156" xml:space="preserve">che ſom-<lb/>mato il tutto inſieme faranno, come di ſopra quarte 13, & </s> <s xml:id="echoid-s3157" xml:space="preserve"><lb/>coppi 3; </s> <s xml:id="echoid-s3158" xml:space="preserve">& </s> <s xml:id="echoid-s3159" xml:space="preserve">tanto tenerà il ſopradetto ſacco.</s> <s xml:id="echoid-s3160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3161" xml:space="preserve">Volendo miſurare le biade in vna caſſa, ſi farà il medeſi-<lb/>mo, come s’è detto nella prima miſura di biada à modo di <lb/>quadrangolo; </s> <s xml:id="echoid-s3162" xml:space="preserve">ſi torrà la lunghezza, la larghezza, & </s> <s xml:id="echoid-s3163" xml:space="preserve">l’altez-<lb/>za, eccetto che la biada nella caſſa non fa ſcarpa.</s> <s xml:id="echoid-s3164" xml:space="preserve"/> </p> <figure> <image file="197-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/197-01"/> </figure> <p> <s xml:id="echoid-s3165" xml:space="preserve">Et perche alle volte occorre à miſurare del vino, & </s> <s xml:id="echoid-s3166" xml:space="preserve">della <lb/>biada, nelle botte, & </s> <s xml:id="echoid-s3167" xml:space="preserve">non ſi vorrebbe leuare il cocone@; </s> <s xml:id="echoid-s3168" xml:space="preserve">però <lb/>ſi piglierà il diametro della botte al cocone di fuoriuia in <pb file="198" n="198" rhead="LIBRO"/> queſto modo; </s> <s xml:id="echoid-s3169" xml:space="preserve">ſi piglierà vno ſpago, ouero altra coſa, & </s> <s xml:id="echoid-s3170" xml:space="preserve">ſi mi <lb/>ſurerà intorno al vaſo, ouer botta, & </s> <s xml:id="echoid-s3171" xml:space="preserve">di quella miſura, che ſa <lb/>rà la circonferenza del vaſo, ſi ritrouerà il diametro, & </s> <s xml:id="echoid-s3172" xml:space="preserve">mol <lb/>tiplicando quella miſura, per 7, & </s> <s xml:id="echoid-s3173" xml:space="preserve">quel che è ſi parte per 22, <lb/>& </s> <s xml:id="echoid-s3174" xml:space="preserve">ne venirà di tal partimento il diametro della circonferen <lb/>za della botte; </s> <s xml:id="echoid-s3175" xml:space="preserve">Ma volendo il diametro di dentrouia della <lb/>botte, ſi cauarà la groſſezza di due doue, ouer aſsi, & </s> <s xml:id="echoid-s3176" xml:space="preserve">quel-<lb/>lo che reſterà ſarà il diametro di dentrouia; </s> <s xml:id="echoid-s3177" xml:space="preserve">il medeſimo ſi <lb/>farà al diametro da baſſo d’un tinazzo; </s> <s xml:id="echoid-s3178" xml:space="preserve">che per meglio eſſe-<lb/>re inteſo darò vno eſſempio. </s> <s xml:id="echoid-s3179" xml:space="preserve">Sia la circonferenza <emph style="sc">A B C D</emph>, <lb/>di fuorauia della botte brac. </s> <s xml:id="echoid-s3180" xml:space="preserve">3, oncie 6, ſi moltiplicheran-<lb/>no brac. </s> <s xml:id="echoid-s3181" xml:space="preserve">3, on. </s> <s xml:id="echoid-s3182" xml:space="preserve">6, per 7, che faranno brac. </s> <s xml:id="echoid-s3183" xml:space="preserve">24, on. </s> <s xml:id="echoid-s3184" xml:space="preserve">6, & </s> <s xml:id="echoid-s3185" xml:space="preserve">brac. <lb/></s> <s xml:id="echoid-s3186" xml:space="preserve">24, on. </s> <s xml:id="echoid-s3187" xml:space="preserve">6, ſi partiranno per 22, venendone brac. </s> <s xml:id="echoid-s3188" xml:space="preserve">1, on. </s> <s xml:id="echoid-s3189" xml:space="preserve">1, & </s> <s xml:id="echoid-s3190" xml:space="preserve"><lb/>intorno à punti 4, e vn terzo, & </s> <s xml:id="echoid-s3191" xml:space="preserve">punti 4, e vn terzo ſi piglie-<lb/>ranno per mezza oncia, che ſaranno in tutto onc. </s> <s xml:id="echoid-s3192" xml:space="preserve">13, e mez <lb/>za, ſi cauarà poi on. </s> <s xml:id="echoid-s3193" xml:space="preserve">3, per la groſſezza delle doue, cioè <emph style="sc">A H</emph>, <lb/>& </s> <s xml:id="echoid-s3194" xml:space="preserve"><emph style="sc">F C</emph>, reſtando il diametro di dentrouia <emph style="sc">E F</emph>, poi ſi proce-<lb/>derà, come diſopra, & </s> <s xml:id="echoid-s3195" xml:space="preserve">ſi hauerà la tenuta della botte. </s> <s xml:id="echoid-s3196" xml:space="preserve">Vero <lb/>è che il prattico non vuol far quella manifattura di molti-<lb/>plicare per 7, & </s> <s xml:id="echoid-s3197" xml:space="preserve">partire per 22, ma ſolo piglia la terza par-<lb/>te di brac. </s> <s xml:id="echoid-s3198" xml:space="preserve">3, on. </s> <s xml:id="echoid-s3199" xml:space="preserve">6, che ſono oncie 14, & </s> <s xml:id="echoid-s3200" xml:space="preserve">dion. </s> <s xml:id="echoid-s3201" xml:space="preserve">14, ne caua <lb/>la groſſezza delle due aſsi, ouer doue, che ſono on. </s> <s xml:id="echoid-s3202" xml:space="preserve">3, reſtan <lb/>do on. </s> <s xml:id="echoid-s3203" xml:space="preserve">11, per il diametro del cocone della botte, ouer per <lb/>il diametro di dentrouia del fondo d’un tinazzo.</s> <s xml:id="echoid-s3204" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3205" xml:space="preserve">Il medeſimo ſi puo fare volendo il diametro della baſe <lb/>d’una piramide rotonda; </s> <s xml:id="echoid-s3206" xml:space="preserve">ponendo come diſopra, che la ſua <lb/>circonferenza della baſe ſia brac. </s> <s xml:id="echoid-s3207" xml:space="preserve">3, on. </s> <s xml:id="echoid-s3208" xml:space="preserve">6, che moltiplican-<lb/>doſi per 7, ſi partirà per 22, & </s> <s xml:id="echoid-s3209" xml:space="preserve">ne venirà onc. </s> <s xml:id="echoid-s3210" xml:space="preserve">13, e mezza, <lb/>come diſopra ſiè detto; </s> <s xml:id="echoid-s3211" xml:space="preserve">& </s> <s xml:id="echoid-s3212" xml:space="preserve">oncie 13, e mezza ſaranno il dia <lb/>metro della baſe della piramide rotonda; </s> <s xml:id="echoid-s3213" xml:space="preserve">& </s> <s xml:id="echoid-s3214" xml:space="preserve">al modo del <lb/>prattico, come diſopra, il diametro ſarà onc. </s> <s xml:id="echoid-s3215" xml:space="preserve">14, ma in que-<lb/>ſta non ſi caua coſa alcuna. </s> <s xml:id="echoid-s3216" xml:space="preserve">Mi pare aſſai hauere detto del <lb/>miſurar le biade, & </s> <s xml:id="echoid-s3217" xml:space="preserve">parte del miſurar del vino; </s> <s xml:id="echoid-s3218" xml:space="preserve">reſta ſolo à <lb/>dar tre eſſempi della miſura del vino, ſenza doperar tauole.</s> <s xml:id="echoid-s3219" xml:space="preserve"/> </p> <pb o="37" file="199" n="199" rhead="SECONDO."/> </div> <div xml:id="echoid-div131" type="section" level="1" n="115"> <head xml:id="echoid-head148" xml:space="preserve">ESSEMPIO PRIMO.</head> <p> <s xml:id="echoid-s3220" xml:space="preserve">Sia vna botte di diametro al cocone oncie 26, & </s> <s xml:id="echoid-s3221" xml:space="preserve">al fon-<lb/>do oncie 24, di queſte due miſure ſi ritrouerà la media pro-<lb/>portionale, in queſto modo; </s> <s xml:id="echoid-s3222" xml:space="preserve">moltiplicando on. </s> <s xml:id="echoid-s3223" xml:space="preserve">24, con on-<lb/>cie 26, faranno pun. </s> <s xml:id="echoid-s3224" xml:space="preserve">624, & </s> <s xml:id="echoid-s3225" xml:space="preserve">624, raddoppiã doſi farāno pun. <lb/></s> <s xml:id="echoid-s3226" xml:space="preserve">1248, poi ſi quadrarà onc. </s> <s xml:id="echoid-s3227" xml:space="preserve">24, & </s> <s xml:id="echoid-s3228" xml:space="preserve">on. </s> <s xml:id="echoid-s3229" xml:space="preserve">26, che faranno punti <lb/>576, & </s> <s xml:id="echoid-s3230" xml:space="preserve">punti 676; </s> <s xml:id="echoid-s3231" xml:space="preserve">hor 576, con 676, ſi aggiungeranno à <lb/>pũti 1248, che faranno punti 2490, de i quali ſi piglierà la <lb/>quarta parte, che ſarà pũti 622, e mezzo ſuperficiali, & </s> <s xml:id="echoid-s3232" xml:space="preserve">di <lb/>pũti 622, e mezo, ſi piglierà vndeci quat or decimi, cioè, mol <lb/>tiplicādo 622, e mezzo p 11, & </s> <s xml:id="echoid-s3233" xml:space="preserve">quello che venirà partir per <lb/>14, & </s> <s xml:id="echoid-s3234" xml:space="preserve">ſi hauerà la ſuperficie media proportionale della bot <lb/>te, & </s> <s xml:id="echoid-s3235" xml:space="preserve">quella ſuperficie ſim oltiplicherà per la lũghezza della <lb/>botte, & </s> <s xml:id="echoid-s3236" xml:space="preserve">quello che venirà ſarà la tenuta di tutta la botte.</s> <s xml:id="echoid-s3237" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3238" xml:space="preserve">Hortogliendo li vndeci quatordecimi di punti 622, e <lb/>mezzo, ne veniran pun. </s> <s xml:id="echoid-s3239" xml:space="preserve">489, ouer poco di più, & </s> <s xml:id="echoid-s3240" xml:space="preserve">punti 489, <lb/>ſi faranno in oncie, & </s> <s xml:id="echoid-s3241" xml:space="preserve">braccia, che ſaranno brac. </s> <s xml:id="echoid-s3242" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s3243" xml:space="preserve">4, <lb/>pun. </s> <s xml:id="echoid-s3244" xml:space="preserve">9; </s> <s xml:id="echoid-s3245" xml:space="preserve">poi ſi moltiplicheranno con brac.</s> <s xml:id="echoid-s3246" xml:space="preserve"><unsure/> 2. </s> <s xml:id="echoid-s3247" xml:space="preserve">onc. </s> <s xml:id="echoid-s3248" xml:space="preserve">3, che fa-<lb/>ranno cerca à zerle 17, ſecchie o, e tre quarti di vino; </s> <s xml:id="echoid-s3249" xml:space="preserve">& </s> <s xml:id="echoid-s3250" xml:space="preserve">di <lb/>biada quarte 68, cop. </s> <s xml:id="echoid-s3251" xml:space="preserve">3, come di ſotto ſi vede.</s> <s xml:id="echoid-s3252" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3253" xml:space="preserve">Auertendo che ogni quadretto s’ha d’intendere quarte 9, <lb/>di biada ouero ſecchie 9, di vino, come anco ſi è detto.</s> <s xml:id="echoid-s3254" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Brac. # 3. # on. # 4, # pun. # 9, <lb/>Brac. # 2, # on. # 3, <lb/>Quadretti # 6, <lb/>Quadretti # 0, # on. # 8, <lb/>Quadretti # 0, # on # 1, # pun. # 6, <lb/>Quadretti # 0, # on. # 9, <lb/>Quadretti # 0, # on. # 1, <lb/>Quadretti # 0, # on. # 0, # pun. # 2, # at. # 3, <lb/>Quadretti # 7, # on. # 7, # pun. # 8, # at. # 3. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # pun. # 6, # 1, # ato. <lb/># pun. # 6, # 1, # ato. <lb/></note> <pb file="200" n="200" rhead="LIBRO"/> </div> <div xml:id="echoid-div132" type="section" level="1" n="116"> <head xml:id="echoid-head149" xml:space="preserve">SECONDO ESSEMPIO.</head> <p> <s xml:id="echoid-s3255" xml:space="preserve">Et volendo far ciò, con la prattica, ſi farà in queſto modo, <lb/>ſi moltiplicarà la metà di due diametri in ſe medeſimi, cioè <lb/>on. </s> <s xml:id="echoid-s3256" xml:space="preserve">25, con on. </s> <s xml:id="echoid-s3257" xml:space="preserve">25, faranno punti 625, & </s> <s xml:id="echoid-s3258" xml:space="preserve">punti 625, ſi par-<lb/>tiranno per pun. </s> <s xml:id="echoid-s3259" xml:space="preserve">20, & </s> <s xml:id="echoid-s3260" xml:space="preserve">faranno 31, e vn quarto di ſecchia, <lb/>come diſopra della biada, parlando ho inſegnato; </s> <s xml:id="echoid-s3261" xml:space="preserve">& </s> <s xml:id="echoid-s3262" xml:space="preserve">ſecch. <lb/></s> <s xml:id="echoid-s3263" xml:space="preserve">31, e vn quarto ſi moltiplicheranno con la lunghezza della <lb/>botta, cioè con brac. </s> <s xml:id="echoid-s3264" xml:space="preserve">2, onc. </s> <s xml:id="echoid-s3265" xml:space="preserve">3, & </s> <s xml:id="echoid-s3266" xml:space="preserve">faranno intorno a ſecchie <lb/>69; </s> <s xml:id="echoid-s3267" xml:space="preserve">& </s> <s xml:id="echoid-s3268" xml:space="preserve">ta nto tenerà la botte, come ſi vede al ſuo conto.</s> <s xml:id="echoid-s3269" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># on. # 26 <lb/># on. # 24 <lb/>ſomma # # 50 <lb/>metà # # 25 <lb/># moltiplica # 25 <lb/># in ſe, # 25 <lb/># # 125 <lb/># # 50 <lb/>punti # # 625 <lb/># partir per # 20, <lb/># # 62 5 <lb/>ſecchie # # 31, e vn quar. <lb/></note> <note position="right" xml:space="preserve"> <lb/># ſecchie # 31, e vn qnar. <lb/># brac. # 2, on. 3 <lb/># # 62 e mezzo <lb/># # 7 <lb/>ſecch. # # 70, intorno. <lb/></note> </div> <div xml:id="echoid-div133" type="section" level="1" n="117"> <head xml:id="echoid-head150" xml:space="preserve">TERZO ESSEMPIO <lb/>più breue.</head> <p> <s xml:id="echoid-s3270" xml:space="preserve">Volendo fare cõ breuità la ſopradetta miſura, ouer cõto, <lb/>ſi ſommeran le on. </s> <s xml:id="echoid-s3271" xml:space="preserve">24, del diametro del fondo, con le on. </s> <s xml:id="echoid-s3272" xml:space="preserve">26 <lb/>diametro del cocone, che farãno on. </s> <s xml:id="echoid-s3273" xml:space="preserve">50, e di on. </s> <s xml:id="echoid-s3274" xml:space="preserve">50, ſi piglie <lb/>rà la metà, che ſono onc. </s> <s xml:id="echoid-s3275" xml:space="preserve">25, & </s> <s xml:id="echoid-s3276" xml:space="preserve">onc. </s> <s xml:id="echoid-s3277" xml:space="preserve">25, ſi moltiplicheran-<lb/>no le ſue decene in ſe, & </s> <s xml:id="echoid-s3278" xml:space="preserve">faranno 4; </s> <s xml:id="echoid-s3279" xml:space="preserve">poi ſi moltiplicherà 4, <lb/>con ſecchie 5, faranno ſecchie 20; </s> <s xml:id="echoid-s3280" xml:space="preserve">poi moltiplicando le <lb/>decene col numero, cioè 2, con 5, faranno ſecchie 10; </s> <s xml:id="echoid-s3281" xml:space="preserve">ol- <pb o="38" file="201" n="201" rhead="SECONDO."/> tra di queſto moltiplicheraſsi numero, con numero, cioè, <lb/>5, con 5, che faranno punti 25, che ſono vna ſecchia, & </s> <s xml:id="echoid-s3282" xml:space="preserve">vn <lb/>quarto di ſecchia, ilche ſommato tutto inſieme faranno <lb/>ſecchie 32, e vn quarto, come qui ſeguente ſivede; </s> <s xml:id="echoid-s3283" xml:space="preserve">Poi <lb/>ſecchie 31, e vn quarto ſi moltiplicheranno per brac. </s> <s xml:id="echoid-s3284" xml:space="preserve">2, on. <lb/></s> <s xml:id="echoid-s3285" xml:space="preserve">3, & </s> <s xml:id="echoid-s3286" xml:space="preserve">faranno ſecchie 70, intorno.</s> <s xml:id="echoid-s3287" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># on. # 26 <lb/># on. # 24 <lb/>ſomma # # 50 <lb/>metà on. # # 25 <lb/># on. # 25 <lb/># on. # 25 <lb/># ſecchie # 20 <lb/># ſecchie # 10 <lb/># ſecchie # 1, e vn quar. <lb/>ſecchie # 31, e vn quar. <lb/></note> <note position="right" xml:space="preserve"> <lb/># ſecchie # 31, e vn q@ar <lb/># brac. # 2, on. 3 <lb/># ſecchie # 62 e meza <lb/># # ſecchie # 8 <lb/>ſecchie # 70, e vn terzo <lb/># intorno. <lb/></note> <p> <s xml:id="echoid-s3288" xml:space="preserve">Et queſte pratiche ſeruono à far i conti tanto del vino, <lb/>quanto delle biade; </s> <s xml:id="echoid-s3289" xml:space="preserve">come diſopra ho detto.</s> <s xml:id="echoid-s3290" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div134" type="section" level="1" n="118"> <head xml:id="echoid-head151" xml:space="preserve">REGOLA PER SAPERE LA PARTE <lb/>del ſemo, & quella del pieno <lb/>d’una Botta.</head> <p> <s xml:id="echoid-s3291" xml:space="preserve">Volendo ſapere la parte del ſemo, ouer quella del pieno <lb/>d’una botta; </s> <s xml:id="echoid-s3292" xml:space="preserve">Si farà in queſto modo, l’altezza del diame-<lb/>tro ch’è al cocone della botta, ſi farà a oncie; </s> <s xml:id="echoid-s3293" xml:space="preserve">il medeſimo ſi <lb/>farà la parte del ſemo, ouer quella del pieno: </s> <s xml:id="echoid-s3294" xml:space="preserve">fatto queſto <lb/>le on. </s> <s xml:id="echoid-s3295" xml:space="preserve">della parte del ſemo, ouer quella del pieno, ſi caue-<lb/>ranno dalle onc. </s> <s xml:id="echoid-s3296" xml:space="preserve">che ſono dell’altezza del diametro, che ſi <lb/>piglia al cocone; </s> <s xml:id="echoid-s3297" xml:space="preserve">& </s> <s xml:id="echoid-s3298" xml:space="preserve">di quelle oncie che rimaneranno ſe ne <pb file="202" n="202" rhead="LIBRO"/> piglierà la metà; </s> <s xml:id="echoid-s3299" xml:space="preserve">il medeſimo ſi hauerà da pigliare la metà <lb/>della tenuta bella botta;</s> <s xml:id="echoid-s3300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3301" xml:space="preserve">Poi fatto come di @opra, s’intrerà nelle tauole del parti <lb/>re, nella prima colõna da mano ſiniſtra, & </s> <s xml:id="echoid-s3302" xml:space="preserve">iui ſi piglierà quel <lb/>la metà delle oncie ſopradette; </s> <s xml:id="echoid-s3303" xml:space="preserve">& </s> <s xml:id="echoid-s3304" xml:space="preserve">ancora ſopra à eſſe tauo-<lb/>le ſi piglierà la metà della tenuta della botta; </s> <s xml:id="echoid-s3305" xml:space="preserve">& </s> <s xml:id="echoid-s3306" xml:space="preserve">ſotto à eſſa <lb/>metà, all’incontro della metà delle oncie, tolte nella prima <lb/>col@nna da mano ſiniſtra, ſi trouera ſegnato zerle, ſecchie, <lb/>boccali, & </s> <s xml:id="echoid-s3307" xml:space="preserve">oncie de boccali; </s> <s xml:id="echoid-s3308" xml:space="preserve">& </s> <s xml:id="echoid-s3309" xml:space="preserve">queſto numero di zerle, ſec-<lb/>chie, boccali, & </s> <s xml:id="echoid-s3310" xml:space="preserve">oncie de boccali, ſi piglieranno ſopra alle <lb/>tauole del moltiplicare; </s> <s xml:id="echoid-s3311" xml:space="preserve">& </s> <s xml:id="echoid-s3312" xml:space="preserve">trouato che ſarà tal numero, ſi <lb/>piglierà da mano ſiniſtra nella prima colonna, il numero <lb/>ch’è metà delle oncie di quella parte del ſemo, ouer quella <lb/>del pieno della botta; </s> <s xml:id="echoid-s3313" xml:space="preserve">& </s> <s xml:id="echoid-s3314" xml:space="preserve">ſotto alle zerle, ſecchie, boccali, <lb/>& </s> <s xml:id="echoid-s3315" xml:space="preserve">oncie de boccali, all’incontro delle oncie trouate nella <lb/>prima colonna da mano ſiniſtra; </s> <s xml:id="echoid-s3316" xml:space="preserve">ſi trouerà ſegnato quanto <lb/>è quella parte di ſemo, & </s> <s xml:id="echoid-s3317" xml:space="preserve">quanto ſarà quella del pieno <lb/>della botta.</s> <s xml:id="echoid-s3318" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div135" type="section" level="1" n="119"> <head xml:id="echoid-head152" xml:space="preserve">PRIMO ESSEMPIO.</head> <p> <s xml:id="echoid-s3319" xml:space="preserve">Pono che io habbia vna botta alta di diametro al coco-<lb/>ne oncie 28, & </s> <s xml:id="echoid-s3320" xml:space="preserve">la parte ſema oncie 4; </s> <s xml:id="echoid-s3321" xml:space="preserve">& </s> <s xml:id="echoid-s3322" xml:space="preserve">eſſa botta tiene zer <lb/>le 36, volendo vedere quanto è la parte ſema; </s> <s xml:id="echoid-s3323" xml:space="preserve">prima ſi ca-<lb/>uerà oncie 4, ſema, da oncie 28, dia metro al cocone, reſte-<lb/>rà oncie 24; </s> <s xml:id="echoid-s3324" xml:space="preserve">& </s> <s xml:id="echoid-s3325" xml:space="preserve">de oncie 24, ſe ne piglierà la metà, che ſaran <lb/>no oncie 12; </s> <s xml:id="echoid-s3326" xml:space="preserve">& </s> <s xml:id="echoid-s3327" xml:space="preserve">oncie 12, ſi troueranno nelle tauole del par <lb/>tire, nella prima colonna da mano ſiniſtra, & </s> <s xml:id="echoid-s3328" xml:space="preserve">ſopra à eſſe ta <lb/>uole ſi piglierà la metà de zerle 36, che ſono zerle 18; </s> <s xml:id="echoid-s3329" xml:space="preserve">& </s> <s xml:id="echoid-s3330" xml:space="preserve">non <lb/>eſſendo ſopra le tauole zerle 18, ſi piglierà zerle 10, & </s> <s xml:id="echoid-s3331" xml:space="preserve">zer-<lb/>le 8, & </s> <s xml:id="echoid-s3332" xml:space="preserve">all’incontro de on. </s> <s xml:id="echoid-s3333" xml:space="preserve">12, ſotto al 10, & </s> <s xml:id="echoid-s3334" xml:space="preserve">al 8, ſi trouerà <lb/>ſegnato vna zerla & </s> <s xml:id="echoid-s3335" xml:space="preserve">meza; </s> <s xml:id="echoid-s3336" xml:space="preserve">& </s> <s xml:id="echoid-s3337" xml:space="preserve">zerla 1, ſecchie 2, ſi piglieran <lb/>no ſopra alle tauole del moltiplicare; </s> <s xml:id="echoid-s3338" xml:space="preserve">& </s> <s xml:id="echoid-s3339" xml:space="preserve">ſotto à zerla 1, ſec-<lb/>chie 2, all’incontro de oncie 2, metà de oncie 4, del ſemo <pb o="39" file="203" n="203" rhead="SECONDO"/> tolte nella prima colonna da mano ſiniſtra, ſi trouerà ſe-<lb/>gnato zerle 3, & </s> <s xml:id="echoid-s3340" xml:space="preserve">zerle 3, ſarà la parte del ſemo della botta.</s> <s xml:id="echoid-s3341" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3342" xml:space="preserve">Auuertendo ſe la botta fuſſe ſema più della metà, ſi pi-<lb/>glierà l’altezza del pieno per il ſemo.</s> <s xml:id="echoid-s3343" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div136" type="section" level="1" n="120"> <head xml:id="echoid-head153" xml:space="preserve">SECONDO ESSEMPIO.</head> <p> <s xml:id="echoid-s3344" xml:space="preserve">Verbi gratia il pieno è alto oncie 4; </s> <s xml:id="echoid-s3345" xml:space="preserve">& </s> <s xml:id="echoid-s3346" xml:space="preserve">l’altezza del dia <lb/>metro al cocone è oncie 28; </s> <s xml:id="echoid-s3347" xml:space="preserve">& </s> <s xml:id="echoid-s3348" xml:space="preserve">la tenuta della botta è <lb/>zerle 36; </s> <s xml:id="echoid-s3349" xml:space="preserve">cauo oncie 4, altezza del pieno, da oncie 28 <lb/>altezza del diametro al cocone, reſterà oncie 24; </s> <s xml:id="echoid-s3350" xml:space="preserve">& </s> <s xml:id="echoid-s3351" xml:space="preserve">del-<lb/>le oncie 24, ne piglio la metà, che ſaranno oncie 12, & </s> <s xml:id="echoid-s3352" xml:space="preserve">on-<lb/>cie 12, ſe piglieranno nelle tauole del partire, nella prima <lb/>colonna da mano ſiniſtra; </s> <s xml:id="echoid-s3353" xml:space="preserve">& </s> <s xml:id="echoid-s3354" xml:space="preserve">la metà de zerle 36, che ſono <lb/>zerle 18; </s> <s xml:id="echoid-s3355" xml:space="preserve">& </s> <s xml:id="echoid-s3356" xml:space="preserve">zerle 18, ſi piglieranno ſopra à eſſe tauole, & </s> <s xml:id="echoid-s3357" xml:space="preserve"><lb/>non trouando ſopra à eſſe tauole del partire zerle 18, ſi pi-<lb/>glierà zerle 10, & </s> <s xml:id="echoid-s3358" xml:space="preserve">zerle 8; </s> <s xml:id="echoid-s3359" xml:space="preserve">& </s> <s xml:id="echoid-s3360" xml:space="preserve">all’incontro de oncie 12, ſi tro <lb/>uerà<unsure/> ſegnato zerla 1, ſecchie 2; </s> <s xml:id="echoid-s3361" xml:space="preserve">& </s> <s xml:id="echoid-s3362" xml:space="preserve">zerla 1, ſecchie 2, ſi pi-<lb/>glieranno ſopra alle tauole del moltiplicare; </s> <s xml:id="echoid-s3363" xml:space="preserve">& </s> <s xml:id="echoid-s3364" xml:space="preserve">in eſſe ta-<lb/>uole, da mano ſiniſtra, nella prima colonna ſi piglierà on-<lb/>cie 2, metà delle oncie 4, altezza del pieno, & </s> <s xml:id="echoid-s3365" xml:space="preserve">ſotto a zer <lb/>la 1, ſecchie 2, all’incontro de oncie, 2, ſi trouerà ſegnato <lb/>zerle 3, & </s> <s xml:id="echoid-s3366" xml:space="preserve">zerle 3, o di vino ouer altro licore è il pieno della <lb/>botta: </s> <s xml:id="echoid-s3367" xml:space="preserve">& </s> <s xml:id="echoid-s3368" xml:space="preserve">con queſti due eſſempij, non tanto ſi potrà hauere <lb/>la parte del pieno, come ancor quella del ſemo d’una botta.</s> <s xml:id="echoid-s3369" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3370" xml:space="preserve">Auuertendo ancora ſe per caſo ſi ritrouaſſe qualche par <lb/>te d’oncia nella parte, che reſta del diametro; </s> <s xml:id="echoid-s3371" xml:space="preserve">tal parte s’ha <lb/>da pigliare della differenza, ch’è fra l’un’oncia, & </s> <s xml:id="echoid-s3372" xml:space="preserve">l’altra, <lb/>che ſono nella prima colonna da mano ſiniſtra, nelle tauo-<lb/>le del moltiplicare.</s> <s xml:id="echoid-s3373" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div137" type="section" level="1" n="121"> <head xml:id="echoid-head154" xml:space="preserve">TERZO ESSEMPIO.</head> <p> <s xml:id="echoid-s3374" xml:space="preserve">Verbi gratia, mi ritrouo vna botta ch’è di diametro al <pb file="204" n="204" rhead="LIBRO"/> cocone oncie 25, & </s> <s xml:id="echoid-s3375" xml:space="preserve">è ſema oncie 6, & </s> <s xml:id="echoid-s3376" xml:space="preserve">tiene di vino zerle <lb/>32; </s> <s xml:id="echoid-s3377" xml:space="preserve">ſi cauerà on. </s> <s xml:id="echoid-s3378" xml:space="preserve">6, da on. </s> <s xml:id="echoid-s3379" xml:space="preserve">25, di diametro, ’reſterà oncie 19, <lb/>& </s> <s xml:id="echoid-s3380" xml:space="preserve">dalle oncie 19, ſi piglierà la metà che ſono oncie 9, e mez <lb/>za; </s> <s xml:id="echoid-s3381" xml:space="preserve">poi ſi torrà la metà delle zerle 32, tenuta della botta, <lb/>che ſarà zerle 16, & </s> <s xml:id="echoid-s3382" xml:space="preserve">zerle 16, ſi piglieranno ſopra alle tauo-<lb/>le del partire, & </s> <s xml:id="echoid-s3383" xml:space="preserve">non ritrouan do di ſopra alle tauole del par <lb/>tire il 16, ſi piglierà zerle 10, è 5, & </s> <s xml:id="echoid-s3384" xml:space="preserve">1, & </s> <s xml:id="echoid-s3385" xml:space="preserve">da mano ſiniſtra nel <lb/>la prima colonna ſi trouerà oncie 9, & </s> <s xml:id="echoid-s3386" xml:space="preserve">ſotto il 10, all’incon-<lb/>tro de oncie 9, ſi trouerà ſegnato zerla 1, boccali 8, & </s> <s xml:id="echoid-s3387" xml:space="preserve">ſotto <lb/>il 5, ſecchie 2, boccali 4, & </s> <s xml:id="echoid-s3388" xml:space="preserve">ſotto lo 1, boccali 8, & </s> <s xml:id="echoid-s3389" xml:space="preserve">queſte <lb/>tre partite ſi ſommaranno inſieme, & </s> <s xml:id="echoid-s3390" xml:space="preserve">faranno zerla 1, ſec-<lb/>chie 3, boccali 2; </s> <s xml:id="echoid-s3391" xml:space="preserve">Fatto queſto per la meza oncia, ſi piglierà <lb/>la differenza da oncie 9, a oncie 10, che ſaranno per le zer-<lb/>le 10, boc. </s> <s xml:id="echoid-s3392" xml:space="preserve">8; </s> <s xml:id="echoid-s3393" xml:space="preserve">e per le zerle 5, boc. </s> <s xml:id="echoid-s3394" xml:space="preserve">4; </s> <s xml:id="echoid-s3395" xml:space="preserve">& </s> <s xml:id="echoid-s3396" xml:space="preserve">per vna zerlaon. </s> <s xml:id="echoid-s3397" xml:space="preserve">de <lb/>boc. </s> <s xml:id="echoid-s3398" xml:space="preserve">19; </s> <s xml:id="echoid-s3399" xml:space="preserve">hor ſommato inſieme, faranno boccali 12, & </s> <s xml:id="echoid-s3400" xml:space="preserve">on. <lb/></s> <s xml:id="echoid-s3401" xml:space="preserve">de boccali 19; </s> <s xml:id="echoid-s3402" xml:space="preserve">& </s> <s xml:id="echoid-s3403" xml:space="preserve">di tãto ſe ne piglierà la metà, che ſarãno in <lb/>cerca a boc. </s> <s xml:id="echoid-s3404" xml:space="preserve">6, on. </s> <s xml:id="echoid-s3405" xml:space="preserve">9, de boc. </s> <s xml:id="echoid-s3406" xml:space="preserve">& </s> <s xml:id="echoid-s3407" xml:space="preserve">boccali 6, & </s> <s xml:id="echoid-s3408" xml:space="preserve">on. </s> <s xml:id="echoid-s3409" xml:space="preserve">de boccali 9, <lb/>ſi cauerãno da zerla 1, ſeccihie 3, boccali 2, & </s> <s xml:id="echoid-s3410" xml:space="preserve">reſtarãno zer <lb/>la 1, ſecchie 2, boccali 13, & </s> <s xml:id="echoid-s3411" xml:space="preserve">one. </s> <s xml:id="echoid-s3412" xml:space="preserve">de boccali 15; </s> <s xml:id="echoid-s3413" xml:space="preserve">& </s> <s xml:id="echoid-s3414" xml:space="preserve">tãto ſi pi-<lb/>glierà ſopra’ alle tauole del moltiplicare, che ſotto alla zer-<lb/>la, all’incõtro de on. </s> <s xml:id="echoid-s3415" xml:space="preserve">3, metà del ſemo, ſi trouerà ſegnato zer <lb/>le 3. </s> <s xml:id="echoid-s3416" xml:space="preserve">& </s> <s xml:id="echoid-s3417" xml:space="preserve">ſotto a ſecchie 2, all’incõtro de oncie 3, ſi trouerà ſe-<lb/>gnato zerla 1, ſecchie 2, & </s> <s xml:id="echoid-s3418" xml:space="preserve">ſotto a boccali 13, che ſarà 7, e <lb/>6, ſotto al 7, & </s> <s xml:id="echoid-s3419" xml:space="preserve">al 6, all’incontro de oncie 3, ſotto al 7, ſi tro-<lb/>uerà ſegnato ſecchie 1, boc. </s> <s xml:id="echoid-s3420" xml:space="preserve">3, & </s> <s xml:id="echoid-s3421" xml:space="preserve">ſotto al 6, ſecc. </s> <s xml:id="echoid-s3422" xml:space="preserve">1, & </s> <s xml:id="echoid-s3423" xml:space="preserve">ſotto a <lb/>onc. </s> <s xml:id="echoid-s3424" xml:space="preserve">15, che ſarà 12, & </s> <s xml:id="echoid-s3425" xml:space="preserve">3, all’incontro de oncie 3, ſotto al <lb/>12, ſi trouarà ſegnato bocc. </s> <s xml:id="echoid-s3426" xml:space="preserve">1, onc. </s> <s xml:id="echoid-s3427" xml:space="preserve">12, & </s> <s xml:id="echoid-s3428" xml:space="preserve">ſotto al 3, ſi troue-<lb/>rà ſegnato onc. </s> <s xml:id="echoid-s3429" xml:space="preserve">9, che ſommato il tutto inſieme, faranno <lb/>zerle 5, ſecc. </s> <s xml:id="echoid-s3430" xml:space="preserve">o, boc. </s> <s xml:id="echoid-s3431" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s3432" xml:space="preserve">21, & </s> <s xml:id="echoid-s3433" xml:space="preserve">tanto ſarà ſemma la ſopra <lb/>detta botta. </s> <s xml:id="echoid-s3434" xml:space="preserve">Et ſe per caſo nel torre la metà delle oncie, del <lb/>ſemo, ouer del pieno, gli fuſſe ſtato metà, ouero altra parte, <lb/>ſi pigliarebbe la meta delle differenze, come ſi è fatto nelle <lb/>tauole del partire; </s> <s xml:id="echoid-s3435" xml:space="preserve">ma però la meta delle differenze, in que <lb/>ſte tauole del moltiplicare, ſi aggiongeno; </s> <s xml:id="echoid-s3436" xml:space="preserve">& </s> <s xml:id="echoid-s3437" xml:space="preserve">in quelle tauo <pb o="40" file="205" n="205" rhead="SECONDO"/> le del partire ſi cauano.</s> <s xml:id="echoid-s3438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3439" xml:space="preserve">Auuerten doui ancora, ſe bene s’è detto ſolo della metà <lb/>dell’oncia, s’ha d’intendere d’ogn’altra parte d’oncia, non <lb/>in tutto, incerca coſi nelle tauole del partire, come quelle <lb/>del moltiplicare; </s> <s xml:id="echoid-s3440" xml:space="preserve">& </s> <s xml:id="echoid-s3441" xml:space="preserve">con queſto faccio fine; </s> <s xml:id="echoid-s3442" xml:space="preserve">perche sò, <lb/>che con gli eſſempi datti diſopra, ſi potrà ſapere ogn’altro <lb/>ſemo, ouero pieno di botta.</s> <s xml:id="echoid-s3443" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div138" type="section" level="1" n="122"> <head xml:id="echoid-head155" xml:space="preserve">Qui ſe guente ſegueno le Tauole per ſapere quant’è <lb/>la parte del ſemo, & quella del pieno <lb/>d’una Botta.</head> <pb file="206" n="206" rhead="LIBRO"/> </div> <div xml:id="echoid-div139" type="section" level="1" n="123"> <head xml:id="echoid-head156" xml:space="preserve">Tauola del partire di ſemi.</head> <note position="right" xml:space="preserve"> <lb/># # # # # Boc. # # # # Boc. # # # # Boc. # # # # Sec. # # # # Sec. <lb/># # # # # 3 # # # # 6 # # # # 9 # # # # 1 # # # # 2 <lb/># Z. # S. # B. # O # Z. # S. # B. # O # Z. # S. # B. # O # Z. # S. # B. # O # Z. # S. # B # O <lb/>2 # # # 1 # 12 # # # 3 # # # # 4 # 12 # # # 9 # # # 1 <lb/>3 # # # 1 # # # # 2 # # # # 3 # # # # 6 # # # # 12 <lb/>4 # # # # 18 # # # 1 # 12 # # # 2 # 6 # # # 4 # 12 # # # 9 <lb/>5 # # # # 14 # # # 1 # 5 # # # 1 # 19 # # # 3 # 14 # # # 7 # 5 <lb/>6 # # # # 12 # # # 1 # # # # 1 # 12 # # # 3 # # # # 6 <lb/>7 # # # # 10 # # # # 20 # # # 1 # 7 # # # 2 # 14 # # # 5 # 4 <lb/>8 # # # # 9 # # # # 18 # # # 1 # 3 # # # 2 # 6 # # # 4 # 12 <lb/>9 # # # # 8 # # # # 16 # # # 1 # # # # 2 # # # # 4 <lb/>10 # # # # 7 # # # # 14 # # # # 22 # # # 1 # 19 # # # 3 # 14 <lb/>11 # # # # 7 # # # # 13 # # # # 20 # # # 1 # 15 # # # 3 # 7 <lb/>12 # # # # 6 # # # # 12 # # # # 18 # # # 1 # 12 # # # 3 <lb/>13 # # # # 6 # # # # 11 # # # # 17 # # # 1 # 9 # # # 2 # 18 <lb/>14 # # # # 5 # # # # 10 # # # # 15 # # # 1 # 7 # # # 2 # 14 <lb/>15 # # # # 5 # # # # 10 # # # # 15 # # # 1 # 5 # # # 2 # 10 <lb/>16 # # # # 5 # # # # 9 # # # # 14 # # # 1 # 3 # # # 2 # 6 <lb/>17 # # # # 4 # # # # 8 # # # # 13 # # # 1 # 1 # # # 2 # 3 <lb/>18 # # # # 4 # # # # 8 # # # # 12 # # # 1 # # # # 2 <lb/>19 # # # # 4 # # # # 8 # # # # 11 # # # # 23 # # # 1 # 21 <lb/>20 # # # # 4 # # # # 7 # # # # 11 # # # # 22 # # # 1 # 20 <lb/></note> <pb o="41" file="207" n="207" rhead="SECONDO."/> </div> <div xml:id="echoid-div140" type="section" level="1" n="124"> <head xml:id="echoid-head157" xml:space="preserve">Tauola del partire di ſemi.</head> <note position="right" xml:space="preserve"> <lb/># # # # # Sec. # # # # Zer. # # # # Zer. # # # # Zer. # # # # Zer. <lb/># # # # # 3 # # # # 1 # # # # 2 # # # # 3 # # # # 4 <lb/># Z. # S. # B. # O # Z. # S. # B # O # Z. # S # B. # O # Z. # S. # B. # O # Z. # S. # B. # O <lb/>2 # # 1 # 9 # # # 2 # # # 1 # # # # 1 # 2 # # # 2 <lb/>3 # # 1 # # # # 1 # 6 # # # 2 # 12 # # 1 # # # # 1 # 1 # 6 <lb/>4 # # # 13 # 12 # # 1 # # # # 2 # # # # 3 # # # 1 <lb/>5 # # # 10 # 19 # # # 14 # 9 # # 1 # 10 # 18 # # 2 # 7 # 3 # # 3 # 3 # 14 <lb/>6 # # # 9 # # # # 12 # # # 1 # 6 # # # 2 # # # # 2 # 12 <lb/>7 # # # 7 # 10 # # # 10 # 7 # # 1 # 2 # 14 # # 1 # 12 # 20 # # 2 # 5 # 3 <lb/>8 # # # 6 # 18 # # # 9 # # # 1 # # # # 1 # 9 # # # 2 <lb/>9 # # # 6 # # # # 8 # # # # 16 # # # 1 # 6 # # # 1 # 14 <lb/>10 # # # 5 # 9 # # # 7 # 5 # # # 14 # 10 # # 1 # 3 # 14 # # 1 # 10 # 19 <lb/>11 # # # 4 # 21 # # # 6 # 13 # # # 13 # 2 # # 1 # 1 # 15 # # 1 # 8 # 4 <lb/>12 # # # 4 # 12 # # # 6 # # # # 12 # # # 1 # # # # 1 # 6 <lb/>13 # # # 4 # 3 # # # 5 # 13 # # # 11 # 2 # # # 16 # 15 # # 1 # 4 # 4 <lb/>14 # # # 3 # 21 # # # 5 # 4 # # # 10 # 7 # # # 15 # 10 # # 1 # 2 # 14 <lb/>15 # # # 3 # 15 # # # 4 # 19 # # # 9 # 14 # # # 14 # 9 # # 1 # 1 # 4 <lb/>16 # # # 3 # 9 # # # 4 # 12 # # # 9 # # # # 13 # 12 # # 1 <lb/>17 # # # 3 # 4 # # # 4 # 6 # # # 8 # 11 # # # 12 # 17 # # # 16 # 22 <lb/>18 # # # 3 # # # # 4 # # # # 8 # # # # 12 # # # # 16 <lb/>19 # # # 2 # 20 # # # 3 # 19 # # # 7 # 14 # # # 11 # 9 # # # 15 # 4 <lb/>20 # # # 2 # 17 # # # 3 # 15 # # # 7 # 5 # # # 10 # 19 # # # 14 # 10 <lb/></note> <pb file="208" n="208" rhead="LIBRO"/> </div> <div xml:id="echoid-div141" type="section" level="1" n="125"> <head xml:id="echoid-head158" xml:space="preserve">Tauola del partire di ſemi.</head> <note position="right" xml:space="preserve"> <lb/># # # # # Zer. # # # # Zer. # # # # Zer. # # # # Zer. # # # # Zer. <lb/># # # # # 5 # # # # 10 # # # # 20 # # # # 30 # # # # 40 <lb/># Z. # S. # B. # O # Z. # S # B. # O # Z. # S. # B. # O # Z. # S. # B. # O # Z. # S. # B. # O <lb/>2 # 2 # 2 # # # 5 # # # # 10 # # # # 15 # # # # 20 <lb/>3 # 1 # 2 # 12 # # 2 # 1 # 6 # # 6 # 2 # 12 # # 10 # # # # 13 # 1 # 6 <lb/>4 # 1 # 1 # # # 2 # 2 # # # 5 # # # # 7 # 2 # # # 10 <lb/>5 # 1 # # # # 2 # # # # 4 # # # # 6 # # # # 8 <lb/>6 # # 3 # 6 # # 1 # 2 # 12 # # 3 # 1 # 6 # # 5 # # # # 6 # 2 # 12 <lb/>7 # # 2 # 15 # 10 # 1 # 1 # 12 # 20 # 2 # 3 # 7 # 17 # 4 # 1 # 2 # 14 # 5 # 2 # 15 # 10 <lb/>8 # # 2 # 9 # # 1 # 1 # # # 2 # 2 # # # 3 # 3 # # # 5 <lb/>9 # # 2 # 4 # # 1 # # 8 # # 2 # # 16 # # 3 # 1 # 6 # # 4 # 1 # 14 <lb/>10 # # 2 # # # 1 # # # # 2 # # # # 3 # # # # 4 <lb/>11 # # 1 # 14 # 17 # # 3 # 11 # 10 # 1 # 3 # 4 # 22 # 2 # 2 # 16 # 8 # 3 # 2 # 9 # 20 <lb/>12 # # 1 # 12 # # # 3 # 6 # # 1 # 2 # 12 # # 2 # 2 # # # 3 # 1 # 6 <lb/>13 # # 1 # 9 # 17 # # 3 # 1 # 9 # 1 # 2 # 2 # 19 # 2 # 1 # 4 # 4 # 3 # # 5 # 14 <lb/>14 # # 1 # 7 # 17 # # 2 # 15 # 10 # 1 # 1 # 12 # 20 # 2 # # 10 # 7 # 2 # 3 # 7 # 17 <lb/>15 # # 1 # 6 # # # 2 # 12 # # 1 # 1 # 6 # # 2 # # # # 2 # 2 # 12 <lb/>16 # # 1 # 4 # 12 # # 2 # 9 # # 1 # 1 # # # 1 # 3 # 9 # # 2 # 2 <lb/>17 # # 1 # 3 # 4 # # 2 # 6 # 8 # 1 # # 12 # 16 # 1 # 3 # 1 # 1 # 2 # 1 # 7 # 8 <lb/>18 # # 1 # 2 # # # 2 # 4 # # 1 # # 8 # # 1 # 2 # 12 # # 2 # # 16 <lb/>19 # # 1 # # 23 # # 2 # 1 # 22 # 1 # # 3 # 19 # 1 # 2 # 5 # 17 # 2 # # 7 # 14 <lb/>20 # # 1 # # # # 2 # # # 1 # # # # 1 # 2 # # # 2 <lb/></note> <pb o="42" file="209" n="209" rhead="SECONDO."/> </div> <div xml:id="echoid-div142" type="section" level="1" n="126"> <head xml:id="echoid-head159" xml:space="preserve">Tauola del moltiplicare diſemi.</head> <note position="right" xml:space="preserve"> <lb/># # # Onc # # Onc. # # Onc. # # Onc. # # Onc. # # Onc. # # Onc. # # Boc. <lb/># # # 1 # # 2 # # 3 # # 4 # # 5 # # 6 # # 12 # # 1 <lb/># B. # O # B. # O # B # O # B # O # B. # O # B # O # B. # O # B. # O <lb/>1 # # 1 # # 2 # # 3 # # 4 # # 5 # # 6 # # 12 # 1 <lb/>2 # # 2 # # 4 # # 6 # # 8 # # 10 # # 12 # 1 # # 2 <lb/>3 # # 3 # # 6 # # 9 # # 12 # # 15 # # 18 # 1 # 12 # 3 <lb/>4 # # 4 # # 8 # # 12 # # 16 # # 20 # 1 # # 2 # # 4 <lb/>5 # # 5 # # 10 # # 15 # # 20 # 1 # 1 # 1 # 6 # 2 # 12 # 5 <lb/>6 # # 6 # # 12 # # 18 # 1 # # 1 # 6 # 1 # 12 # 3 # # 6 <lb/>7 # # 7 # # 14 # # 21 # 1 # 4 # 1 # 11 # 1 # 18 # 3 # 12 # 7 <lb/>8 # # 8 # # 16 # 1 # # 1 # 8 # 1 # 16 # 2 # # 4 # # 8 <lb/>9 # # 9 # # 18 # 1 # 3 # 1 # 12 # 1 # 21 # 2 # 6 # 4 # 12 # 9 <lb/>10 # # 10 # # 20 # 1 # 6 # 1 # 16 # 2 # 2 # 2 # 12 # 5 # # 10 <lb/>11 # # 11 # # 22 # 1 # 9 # 1 # 20 # 2 # 7 # 2 # 18 # 5 # 12 # 11 <lb/>12 # # 12 # 1 # # 1 # 12 # 2 # # 2 # 12 # 3 # # 6 # # 12 <lb/></note> <pb file="210" n="210" rhead="LIBRO"/> </div> <div xml:id="echoid-div143" type="section" level="1" n="127"> <head xml:id="echoid-head160" xml:space="preserve">Tauola del moltiplicare diſemi.</head> <note position="right" xml:space="preserve"> <lb/># # # Boc. # # Boc. # # Boc. # # Boc. # # Boc # # Boc. # # Boc. # # Boc. <lb/># # # 2 # # 3 # # 4 # # 5 # # 6 # # 7 # # 8 # # 9 <lb/># S. # B. # S. # B # S. # B. # S. # B. # S. # B. # S. # B. # S. # B. # S. # B. <lb/>1 # # 2 # # 3 # # 4 # # 5 # # 6 # # 7 # # 8 # # 9 <lb/>2 # # 4 # # 6 # # 8 # # 10 # # 12 # # 14 # # 16 # 1 <lb/>3 # # 6 # # 9 # # 12 # # 15 # 1 # # 1 # 3 # 1 # 6 # 1 # 9 <lb/>4 # # 8 # # 12 # # 16 # 1 # 2 # 1 # 6 # 1 # 10 # 1 # 14 # 2 <lb/>5 # # 10 # # 15 # 1 # 2 # 1 # 7 # 1 # 12 # 1 # 17 # 2 # 4 # 2 # 9 <lb/>6 # # 12 # 1 # # 1 # 6 # 1 # 12 # 2 # # 2 # 6 # 2 # 12 # 3 <lb/>7 # # 14 # 1 # 3 # 1 # 10 # 1 # 17 # 2 # 6 # 2 # 13 # 3 # 2 # 3 # 9 <lb/>8 # # 16 # 1 # 6 # 1 # 14 # 2 # 4 # 2 # 12 # 3 # 2 # 3 # 10 # 4 <lb/>9 # 1 # # 1 # 9 # 2 # # 2 # 9 # 3 # # 3 # 9 # 4 # # 4 # 9 <lb/>10 # 1 # 2 # 1 # 12 # 2 # 4 # 2 # 14 # 3 # 6 # 3 # 16 # 4 # 8 # 5 <lb/>11 # 1 # 4 # 1 # 15 # 2 # 8 # 3 # 1 # 3 # 12 # 4 # 5 # 4 # 16 # 5 # 9 <lb/>12 # 1 # 6 # 2 # # 2 # 12 # 3 # 6 # 4 # # 4 # 12 # 5 # 6 # 6 <lb/></note> <pb o="43" file="211" n="211" rhead="SECONDO."/> </div> <div xml:id="echoid-div144" type="section" level="1" n="128"> <head xml:id="echoid-head161" xml:space="preserve">Tauola del moltiplicare di ſemi.</head> <note position="right" xml:space="preserve"> <lb/># # Sec. # # Sec. # # Sec. # # Zer. # # Zer. # # Zer. # # Zer. # # Zer. <lb/># # 1 # # 2 # # 3 # # 1 # # 2 # # 3 # # 4 # # 5 <lb/># Z. # S # Z. # S # Z. # S. # Z. # S. # Z. # S. # Z. # S. # Z. # S. # Z. # S. <lb/>1 # # 1 # # 2 # # 3 # 1 # # 2 # # 3 # # 4 # # 5 <lb/>2 # # 2 # 1 # # 1 # 2 # 2 # # 4 # # 6 # # 8 # # 10 <lb/>3 # # 3 # 1 # 2 # 2 # 1 # 3 # # 6 # # 9 # # 12 # # 15 <lb/>4 # 1 # # 2 # # 3 # # 4 # # 8 # # 12 # # 16 # # 20 <lb/>5 # 1 # 1 # 2 # 2 # 3 # 3 # 5 # # 10 # # 15 # # 20 # # 25 <lb/>6 # 1 # 2 # 3 # # 4 # 2 # 6 # # 12 # # 18 # # 24 # # 30 <lb/>7 # 1 # 3 # 3 # 2 # 5 # 1 # 7 # # 14 # # 21 # # 28 # # 35 <lb/>8 # 2 # # 4 # # 6 # # 8 # # 16 # # 24 # # 32 # # 40 <lb/>9 # 2 # 1 # 4 # 2 # 6 # 3 # 9 # # 18 # # 27 # # 36 # # 45 <lb/>10 # 2 # 2 # 5 # # 7 # 2 # 10 # # 20 # # 30 # # 40 # # 50 <lb/>11 # 2 # 3 # 5 # 2 # 8 # 1 # 11 # # 22 # # 33 # # 44 # # 55 <lb/>12 # 4 # # 6 # # 9 # # 12 # # 24 # # 36 # # 48 # # 60 <lb/># # # # 2 <lb/></note> <pb file="212" n="212" rhead="LIBRO"/> </div> <div xml:id="echoid-div145" type="section" level="1" n="129"> <head xml:id="echoid-head162" xml:space="preserve">REGOLA PER FARE LI CONTI CHE <lb/>conuengono al miſurare del feno.</head> <p> <s xml:id="echoid-s3444" xml:space="preserve">IL miſurare del feno, & </s> <s xml:id="echoid-s3445" xml:space="preserve">delle mura è vna ma-<lb/>niera medeſima; </s> <s xml:id="echoid-s3446" xml:space="preserve">Ma però s’ha d’aduertire <lb/>che’l miſurator del feno, biſogna che habbia <lb/>buona prattica in conoſcerla qualità del fe-<lb/>no; </s> <s xml:id="echoid-s3447" xml:space="preserve">cioè ſe’l feno è magro, ò graſſo, ouer ſe è <lb/>ſituato doue habitano ſotto beſtiami, ouer non; </s> <s xml:id="echoid-s3448" xml:space="preserve">& </s> <s xml:id="echoid-s3449" xml:space="preserve">ancora <lb/>s’ è poco, ouer aſſai graſſo; </s> <s xml:id="echoid-s3450" xml:space="preserve">ouer poco, ò aſſai magro, & </s> <s xml:id="echoid-s3451" xml:space="preserve">ſe è <lb/>calcato, ouer mal calcato, & </s> <s xml:id="echoid-s3452" xml:space="preserve">tenendo alcune di queſte qua <lb/>lità, ouer conditioni, il miſuratore ſia molto diligente in co <lb/>noſcerle; </s> <s xml:id="echoid-s3453" xml:space="preserve">& </s> <s xml:id="echoid-s3454" xml:space="preserve">ſecondo la qualità che’l feno haurà, biſogna <lb/>che lo miſuri, & </s> <s xml:id="echoid-s3455" xml:space="preserve">conuenendo miſurar feno ſopra fenili, à toc <lb/>co alle mura ſi laſſerà circa due oncie; </s> <s xml:id="echoid-s3456" xml:space="preserve">perche il feno ſi vien <lb/>reſtringendo nel centro; </s> <s xml:id="echoid-s3457" xml:space="preserve">& </s> <s xml:id="echoid-s3458" xml:space="preserve">miſurato che ſia, il meglio che <lb/>poſſa fare il miſuratore è miſurarne vn quadretto in luogo <lb/>che ſia proportionato à tutto il fenile, che ſi miſurerà, cioè il <lb/>quadretto ſia miſurato nel mezzo, che non habbia ne del <lb/>troppo calcato, ne del poco calcato, & </s> <s xml:id="echoid-s3459" xml:space="preserve">queſto quadretto ſia <lb/>miſurato con diligenza, & </s> <s xml:id="echoid-s3460" xml:space="preserve">raccolto ſottilmente il feno con <lb/>vn lenzolo, ò altra coſa; </s> <s xml:id="echoid-s3461" xml:space="preserve">& </s> <s xml:id="echoid-s3462" xml:space="preserve">fatto queſto, quel feno raccolto <lb/>ſia peſato; </s> <s xml:id="echoid-s3463" xml:space="preserve">poi perla regola della proportione ſi farà queſto <lb/>conto, ſe tanta miſura mi dà di peſo peſi, libre, & </s> <s xml:id="echoid-s3464" xml:space="preserve">oncie, <lb/>quanto mi darà la miſura di tutto il fenile? </s> <s xml:id="echoid-s3465" xml:space="preserve">& </s> <s xml:id="echoid-s3466" xml:space="preserve">per queſta re-<lb/>gola, ſi trouerà preſſo à poco quanto feno ſia ſopra quel fe-<lb/>nile; </s> <s xml:id="echoid-s3467" xml:space="preserve">& </s> <s xml:id="echoid-s3468" xml:space="preserve">queſto modo ſarà miglior che miſurarlo a ventura. <lb/></s> <s xml:id="echoid-s3469" xml:space="preserve">Volẽdo miſurar ancora vn brozzo, ò carro di feno, biſogna <lb/>hauer conſideratione, ſe’l feno è magro ouer graſſo, ſe fuſſe <lb/>graſſo, ſi da di callo fin a dieci per cento, & </s> <s xml:id="echoid-s3470" xml:space="preserve">ſe fuſſe magro ſi <lb/>laſſa in ſùo eſſere, intendẽdo queſto quando ſi miſura ſopra <lb/>il carro, ouer brozzo, & </s> <s xml:id="echoid-s3471" xml:space="preserve">le miſure del carro, ouer brozzo, <lb/>s’hanno da pigliare in queſta forma; </s> <s xml:id="echoid-s3472" xml:space="preserve">prima ſi miſurerà la lun <lb/>ghezza del carro, ouer brozzo, calcando da vn capo all’al- <pb o="44" file="213" n="213" rhead="SECONDO"/> tro del carro, ouerbrozzo, con vn palo; </s> <s xml:id="echoid-s3473" xml:space="preserve">poi per larghezza ſi <lb/>piglieranno tre miſure l’vna nel mezo, radoppiata, & </s> <s xml:id="echoid-s3474" xml:space="preserve">que-<lb/>ſta miſura raddoppiata, ſi piglierà fra due pertiche, che ſi <lb/>metteranno da vna parte, & </s> <s xml:id="echoid-s3475" xml:space="preserve">dall’altra del carro, ouer broz-<lb/>zo; </s> <s xml:id="echoid-s3476" xml:space="preserve">poi l’altre due ſi piglieranno l’vna da vn capo, & </s> <s xml:id="echoid-s3477" xml:space="preserve">l’altra <lb/>dall’altro capo del carro, ouer brozzo, fra le due pertiche, & </s> <s xml:id="echoid-s3478" xml:space="preserve"><lb/>queſte due miſure s’aggiungono col doppio di quella di <lb/>mezzo, & </s> <s xml:id="echoid-s3479" xml:space="preserve">di queſta ſomma ſi piglia la quarta parte la qual ſa <lb/>rà la larghezza del carro, ouer brozzo; </s> <s xml:id="echoid-s3480" xml:space="preserve">poiper l’altezza ſi pi <lb/>glierà dall’un capo, & </s> <s xml:id="echoid-s3481" xml:space="preserve">dall’altro delle ſcale in ſuſo, fino al <lb/>perticale del carro, ouer brozzo, che riſtringe di ſoprauia il <lb/>feno; </s> <s xml:id="echoid-s3482" xml:space="preserve">& </s> <s xml:id="echoid-s3483" xml:space="preserve">queſte due miſure ſi ſommerãno inſieme, & </s> <s xml:id="echoid-s3484" xml:space="preserve">ſi piglie <lb/>rà la metà, & </s> <s xml:id="echoid-s3485" xml:space="preserve">queſta metà ſarà l’altezza del carro, ouer broz-<lb/>zo; </s> <s xml:id="echoid-s3486" xml:space="preserve">hora che moſtrate ſono le miſure d’un fenile, & </s> <s xml:id="echoid-s3487" xml:space="preserve">d’un car <lb/>ro, ouer brozzo di ſotto moſtrerò il modo di far i ſuoi conti.</s> <s xml:id="echoid-s3488" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3489" xml:space="preserve">Hauendo di ſopra detto il modo di far i conti de’ muri, <lb/>che ſon’ il medeſimo con queſti del feno non ſi farà altra de <lb/>chiaratione; </s> <s xml:id="echoid-s3490" xml:space="preserve">ma li ſuoi conti ſi faranno ſimplicemente.</s> <s xml:id="echoid-s3491" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Lungo brac. # 12, # on. # 4. # }Alto brac. 5, on. 7. <lb/>Largo brac. # 8, # on. # 5. <lb/>Brac. # 12, # on.4, <lb/>Brac. # 8, # on. # 5, <lb/>Brac. # 96, <lb/>Brac. # 2, # on. # 8, <lb/>Brac. # 5, # on. # 1, # pun. # 8, <lb/>Brac. # 103, # on. # 9, # pun. # 8, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # on. # 1, # 3, # pun. <lb/># on. # 3, # 3, # pun. <lb/></note> <pb file="214" n="214" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/>Brac. # 103, # on. # 9, # pun. # 8, <lb/>Brac. # 5, # on. # 7, <lb/>Quadretti # 515, <lb/>Quadretti # 3, # on. # 9, <lb/>Quadretti # 0, # on, # 3, # pun. # 4, <lb/>Quadretti # 60, # on. # 1, <lb/>Quadretti # 0, # on, # 5, # pun. # 3, <lb/>Quadretti # 0, # on, # 0, # pun. # 4, # at. # 8, <lb/>Quadretti # 579, # on. # 6, # pun. # 11, # at. # 8. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # pun. # 3, # 5, # ato. <lb/># onc. # 4, # 5, # ato. <lb/></note> <p> <s xml:id="echoid-s3492" xml:space="preserve">Coſi il feno nel fenile ſarebbe quadretti 579, onc. </s> <s xml:id="echoid-s3493" xml:space="preserve">6, <lb/>pun. </s> <s xml:id="echoid-s3494" xml:space="preserve">11, at. </s> <s xml:id="echoid-s3495" xml:space="preserve">8. </s> <s xml:id="echoid-s3496" xml:space="preserve">che partendo quadr. </s> <s xml:id="echoid-s3497" xml:space="preserve">579, per peſi 100, ne veni <lb/>rà carra 5, peſi 79, dando però vn peſo di feno per ogni qua-<lb/>dretto, com’è l’ordine, ſenz’altra conſideratione, hauendo <lb/>però miſurato come ho detto vn quadretto in luogo propor <lb/>tionato del finile, che ſiritroui eſſer lungo brac. </s> <s xml:id="echoid-s3498" xml:space="preserve">1, oncie 4, <lb/>largo brac. </s> <s xml:id="echoid-s3499" xml:space="preserve">1, onc. </s> <s xml:id="echoid-s3500" xml:space="preserve">2, alto bracc. </s> <s xml:id="echoid-s3501" xml:space="preserve">1, onc. </s> <s xml:id="echoid-s3502" xml:space="preserve">3; </s> <s xml:id="echoid-s3503" xml:space="preserve">Et queſto conto, <lb/>ſarà quadretto 1, onc. </s> <s xml:id="echoid-s3504" xml:space="preserve">11, punti 4; </s> <s xml:id="echoid-s3505" xml:space="preserve">& </s> <s xml:id="echoid-s3506" xml:space="preserve">a peſo, peſi 2, libre 3, <lb/>onc. </s> <s xml:id="echoid-s3507" xml:space="preserve">4, & </s> <s xml:id="echoid-s3508" xml:space="preserve">con queſta ragione vorrei ſapere hauuto il conto <lb/>dei detti quadretti 579, onc. </s> <s xml:id="echoid-s3509" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s3510" xml:space="preserve">11, at. </s> <s xml:id="echoid-s3511" xml:space="preserve">8, quanto feno <lb/>ſarà a peſo: </s> <s xml:id="echoid-s3512" xml:space="preserve">il che ſi può ſapere coſi facendo; </s> <s xml:id="echoid-s3513" xml:space="preserve">ſi partiranno pe <lb/>ſi 2, libre 3, onc. </s> <s xml:id="echoid-s3514" xml:space="preserve">4, per quadretti 1, onc. </s> <s xml:id="echoid-s3515" xml:space="preserve">11, punti 4, & </s> <s xml:id="echoid-s3516" xml:space="preserve">quel <lb/>tanto ne verrà che peſa vn quadretto, che ſia vn brac. </s> <s xml:id="echoid-s3517" xml:space="preserve">lungo, <lb/>largo, & </s> <s xml:id="echoid-s3518" xml:space="preserve">alto. </s> <s xml:id="echoid-s3519" xml:space="preserve">Et volendo ciò ſapere ſi ri durrà tutto à punti, <lb/>cioè il peſo, & </s> <s xml:id="echoid-s3520" xml:space="preserve">la miſura; </s> <s xml:id="echoid-s3521" xml:space="preserve">& </s> <s xml:id="echoid-s3522" xml:space="preserve">ſi ritrouerà che vn quadretto di <lb/>feno peſerà libre 27, onc. </s> <s xml:id="echoid-s3523" xml:space="preserve">5, punti 2; </s> <s xml:id="echoid-s3524" xml:space="preserve">& </s> <s xml:id="echoid-s3525" xml:space="preserve">vn’onc. </s> <s xml:id="echoid-s3526" xml:space="preserve">peſarà libre <lb/>2, onc. </s> <s xml:id="echoid-s3527" xml:space="preserve">3, punti 5; </s> <s xml:id="echoid-s3528" xml:space="preserve">Vn punto peſarà onc. </s> <s xml:id="echoid-s3529" xml:space="preserve">2, punti 3, e mezo; <lb/></s> <s xml:id="echoid-s3530" xml:space="preserve">Coſi moltiplicando i quadretti 579, onc. </s> <s xml:id="echoid-s3531" xml:space="preserve">6, punti 11, at. </s> <s xml:id="echoid-s3532" xml:space="preserve">8, <lb/>per libre 27, onc. </s> <s xml:id="echoid-s3533" xml:space="preserve">5, punti 2; </s> <s xml:id="echoid-s3534" xml:space="preserve">i quadretri, 579, peſaranno in- <pb o="45" file="215" n="215" rhead="SECONDO"/> torno a peſi 635, lìbre 7, & </s> <s xml:id="echoid-s3535" xml:space="preserve">tāto feno peſarà quadretti 579, <lb/>onc. </s> <s xml:id="echoid-s3536" xml:space="preserve">6, punti 11, atomi 8, per più chiarezza ecco il modo <lb/>da far le ragioni ſopradette; </s> <s xml:id="echoid-s3537" xml:space="preserve">prima ſi deue vedere quãto dia <lb/>a peſo vn quadretto di vn’oncia, & </s> <s xml:id="echoid-s3538" xml:space="preserve">vn punto, a miſura; </s> <s xml:id="echoid-s3539" xml:space="preserve">ilche <lb/>per vedere ho fatto di ſopra quella miſura del quadrettto <lb/>tagliato nel finile tutt’à punti, cioè quadr. </s> <s xml:id="echoid-s3540" xml:space="preserve">1, on. </s> <s xml:id="echoid-s3541" xml:space="preserve">11, punti 4, <lb/>che ſono punti 280; </s> <s xml:id="echoid-s3542" xml:space="preserve">Ancorhò fatto quello che peſa il qua-<lb/>dretto pur tagliato nel finile, medeſimamente tutt’à punti, <lb/>cioè peſi 2, lib. </s> <s xml:id="echoid-s3543" xml:space="preserve">3, on. </s> <s xml:id="echoid-s3544" xml:space="preserve">4, come di ſopra; </s> <s xml:id="echoid-s3545" xml:space="preserve">che ſono punti 7680, <lb/>& </s> <s xml:id="echoid-s3546" xml:space="preserve">punti 7680, ſono partiti per punti 280, onde ne vengono <lb/>libre 27, & </s> <s xml:id="echoid-s3547" xml:space="preserve">auanzan libre 120, le quali facendo in oncie, & </s> <s xml:id="echoid-s3548" xml:space="preserve"><lb/>moltiplicandole per oncie 12, farano oncie 1440, & </s> <s xml:id="echoid-s3549" xml:space="preserve">oncie <lb/>1440, ſi partiranno pur per 280, & </s> <s xml:id="echoid-s3550" xml:space="preserve">ne veniranno oncie 5, & </s> <s xml:id="echoid-s3551" xml:space="preserve"><lb/>auanzano, on. </s> <s xml:id="echoid-s3552" xml:space="preserve">40, le quali facendo in punti, & </s> <s xml:id="echoid-s3553" xml:space="preserve">moltiplican-<lb/>dole per punti 12, faranno punti 480, & </s> <s xml:id="echoid-s3554" xml:space="preserve">punti 480, ſi parto-<lb/>no per 280, onde ne veniranno, intorno a punti 2; </s> <s xml:id="echoid-s3555" xml:space="preserve">& </s> <s xml:id="echoid-s3556" xml:space="preserve">coſi vn <lb/>quadretto cubo, cioè lungo vn braccio, largo vn braccio, & </s> <s xml:id="echoid-s3557" xml:space="preserve"><lb/>alto vn braccio, peſerà di feno libre 27, onc. </s> <s xml:id="echoid-s3558" xml:space="preserve">5, punti 2; </s> <s xml:id="echoid-s3559" xml:space="preserve">& </s> <s xml:id="echoid-s3560" xml:space="preserve">vo <lb/>lendo vedere quanto peſerà vn’oncia cuba à peſo ſi partiran <lb/>no libre 27, onc. </s> <s xml:id="echoid-s3561" xml:space="preserve">5, punti 2, per onc. </s> <s xml:id="echoid-s3562" xml:space="preserve">12, cube, & </s> <s xml:id="echoid-s3563" xml:space="preserve">prima il 12, <lb/>in 27, entra fiate 2, & </s> <s xml:id="echoid-s3564" xml:space="preserve">auanza 3, libre, che ſono onc. </s> <s xml:id="echoid-s3565" xml:space="preserve">36, & </s> <s xml:id="echoid-s3566" xml:space="preserve">a <lb/>onc. </s> <s xml:id="echoid-s3567" xml:space="preserve">36, ſi giungerà onc. </s> <s xml:id="echoid-s3568" xml:space="preserve">5, che faranno onc. </s> <s xml:id="echoid-s3569" xml:space="preserve">41, il 12, in 41, <lb/>entra fiate 3, che ſono onc. </s> <s xml:id="echoid-s3570" xml:space="preserve">3, & </s> <s xml:id="echoid-s3571" xml:space="preserve">auanza onc. </s> <s xml:id="echoid-s3572" xml:space="preserve">5, & </s> <s xml:id="echoid-s3573" xml:space="preserve">onc. </s> <s xml:id="echoid-s3574" xml:space="preserve">5, fat-<lb/>te in punti ſaranno punti 60, ai quali punti 60, aggiungẽdo <lb/>punti 2, faranno punti 62, & </s> <s xml:id="echoid-s3575" xml:space="preserve">li 62, ſi partiranno per 12, & </s> <s xml:id="echoid-s3576" xml:space="preserve">ne <lb/>veniranno punti 5, auanzando punti 2; </s> <s xml:id="echoid-s3577" xml:space="preserve">& </s> <s xml:id="echoid-s3578" xml:space="preserve">i punti 2, ſi faran-<lb/>no in atomi, che faranno at. </s> <s xml:id="echoid-s3579" xml:space="preserve">24, & </s> <s xml:id="echoid-s3580" xml:space="preserve">li 24, partendo per 12, ne <lb/>veniranno at. </s> <s xml:id="echoid-s3581" xml:space="preserve">2, coſi vn’onc. </s> <s xml:id="echoid-s3582" xml:space="preserve">cuba vuole di feno a peſo libre <lb/>2, onc. </s> <s xml:id="echoid-s3583" xml:space="preserve">3, punti 5, at. </s> <s xml:id="echoid-s3584" xml:space="preserve">2; </s> <s xml:id="echoid-s3585" xml:space="preserve">& </s> <s xml:id="echoid-s3586" xml:space="preserve">volendo vedere quanto vorà di fe <lb/>no, vn punto a peſo, ſi dee partire libre 2, onc. </s> <s xml:id="echoid-s3587" xml:space="preserve">3, punti 5, at. <lb/></s> <s xml:id="echoid-s3588" xml:space="preserve">2, per punti 12, come di ſopra, & </s> <s xml:id="echoid-s3589" xml:space="preserve">ne venirà intorno a onc. </s> <s xml:id="echoid-s3590" xml:space="preserve">2, <lb/>punti 3, e mezo, & </s> <s xml:id="echoid-s3591" xml:space="preserve">tanto vorà vn punto cubo di feno à peſo; </s> <s xml:id="echoid-s3592" xml:space="preserve"><lb/>hauuto che ſi hauerà a peſo di feno vn quadretto, vn’oncia, <lb/>& </s> <s xml:id="echoid-s3593" xml:space="preserve">vn punto cubo; </s> <s xml:id="echoid-s3594" xml:space="preserve">appreſſo ſi vedrà quanto feno a peſo vorà <pb file="216" n="216" rhead="LIBRO"/> quadretti 579, onc. </s> <s xml:id="echoid-s3595" xml:space="preserve">6, punti 11, at. </s> <s xml:id="echoid-s3596" xml:space="preserve">8, come qui ſotto ſivedrà, <lb/>a parte, per parte, & </s> <s xml:id="echoid-s3597" xml:space="preserve">ſi ritrouerà che veneranno intorno a pe <lb/>ſi 636, di feno, & </s> <s xml:id="echoid-s3598" xml:space="preserve">tanto ſi potrà dire, che peſa la ſopradetta <lb/>miſura del fenile; </s> <s xml:id="echoid-s3599" xml:space="preserve">come qui ſotto a parte per parte moſtre-<lb/>raſsi.</s> <s xml:id="echoid-s3600" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Quadretti # 579, <lb/>Peſo # 1, # lib. # 2, # on. # 5, # pun. # 2, <lb/>Peſi # 579, <lb/>Peſi # 46, # lib. # 8, <lb/>Peſi # 9, # lib. # 16, # on. # 3, <lb/>Peſi # 0, # lib. # 8, # on. # 0, # pun. # 6, <lb/>Peſi # 635, # lib. # 7, # on. # 3, # pun. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # quadr. # 5, # 3, # punti. <lb/># punti # 2, # 3, # punti. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Oncie # 6, <lb/>Libre # 2, # on. # 3, # pun. # 5, <lb/>Libre # 12, # on. # 0, <lb/>Libre # 1, # on. # 6, <lb/>Libre # 0, # on. # 2, # pun. # 6, <lb/>Libre # 13, # on. # 8, # pun. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # onc. # 6, # 0, # punti. <lb/># punti # 0, # 0, # punti. <lb/></note> <pb o="46" file="217" n="217" rhead="SECONDO"/> <note position="right" xml:space="preserve"> <lb/>Punti # 11, <lb/>Oncie # 2, # punti # 3, # e mezzo. <lb/>Oncie # 22, <lb/># 3, # pun. # 2, # e mezzo. <lb/>Libre # 2, # on. # 1, # pun. # 2, # e mezzo. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # punti # 4, # 3, # mezi pun. <lb/># mezi pun. # 6, # 3, # mezi pun. <lb/></note> <p> <s xml:id="echoid-s3601" xml:space="preserve">Di ſopra ſi vede che moltiplicando peſo 1, libre 2, onc. </s> <s xml:id="echoid-s3602" xml:space="preserve">5, <lb/>punti 2, con quadretti 579, fanno peſi 635, libre 7, oncie 3, <lb/>punti 6, di feno.</s> <s xml:id="echoid-s3603" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3604" xml:space="preserve">Et moltiplicando libre 2, onc. </s> <s xml:id="echoid-s3605" xml:space="preserve">3, punti 5, con oncie 6, fan <lb/>no libre 13, oncie 8, punti 6, di feno.</s> <s xml:id="echoid-s3606" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3607" xml:space="preserve">Ancora moltiplicando oncie 2, punti 3, e mezo, con pun <lb/>ti 11. </s> <s xml:id="echoid-s3608" xml:space="preserve">fanno libre 2, onc. </s> <s xml:id="echoid-s3609" xml:space="preserve">1, punti 2 e mezo di feno, & </s> <s xml:id="echoid-s3610" xml:space="preserve">ſomma <lb/>ti queſti tre conti inſieme fanno, come qui ſotto ſi vede, in-<lb/>torno a peſi 636, di feno.</s> <s xml:id="echoid-s3611" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Peſi # 635, # libre # 7, # onc. # 3, # pun. # 6. <lb/>Peſi # 0, # libre # 13, # onc. # 8, # pun. # 6. <lb/>Peſi # 0, # libre # 2, # onc. # 1, # pun. # 2, # e mezo. <lb/>Peſi # 635, # libre # 23, # onc. # 1. # pun. # 2, # e mezo. <lb/></note> <p> <s xml:id="echoid-s3612" xml:space="preserve">Ancora il conto ſopradetto del feno, ſi poteua fare per la <lb/>regola del tre, acconciando la regola in queſto modo, ſe <lb/>quadr. </s> <s xml:id="echoid-s3613" xml:space="preserve">1, onc. </s> <s xml:id="echoid-s3614" xml:space="preserve">11, pun. </s> <s xml:id="echoid-s3615" xml:space="preserve">4, a miſura, da a peſo di feno peſi 2, <lb/>libre 3, onc. </s> <s xml:id="echoid-s3616" xml:space="preserve">4, quanto daranno quadretti 579, onc. </s> <s xml:id="echoid-s3617" xml:space="preserve">6, punti <lb/>11, at. </s> <s xml:id="echoid-s3618" xml:space="preserve">8, a peſo; </s> <s xml:id="echoid-s3619" xml:space="preserve">ſi trouerà che daranno intorno a peſi 636, <lb/>come di ſopra.</s> <s xml:id="echoid-s3620" xml:space="preserve"/> </p> <pb file="218" n="218" rhead="LIBRO"/> <p> <s xml:id="echoid-s3621" xml:space="preserve">Il medeſimo ſi farà, volendo miſurare ogn’altro fenile di <lb/>feno; </s> <s xml:id="echoid-s3622" xml:space="preserve">baſta aſſai del miſurare il feno ſopra i fenili, qui ſi re-<lb/>plicherà di inſegnar’à miſurarlo ſopra i carri, ouer brozzi; <lb/></s> <s xml:id="echoid-s3623" xml:space="preserve">Pongo dunque che’l ſia vn carro, ouer brozzo, tolta la lun-<lb/>ghezza, larghezza, & </s> <s xml:id="echoid-s3624" xml:space="preserve">altezza, come di ſopra s’è inſegnato; </s> <s xml:id="echoid-s3625" xml:space="preserve"><lb/>lungo braccia 8, onc. </s> <s xml:id="echoid-s3626" xml:space="preserve">6, largo brac. </s> <s xml:id="echoid-s3627" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s3628" xml:space="preserve">3, alto brac. </s> <s xml:id="echoid-s3629" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s3630" xml:space="preserve"><lb/>8; </s> <s xml:id="echoid-s3631" xml:space="preserve">vorei ſapere quanto feno a peſo ſi ritrouerà conciarai la <lb/>regola, come qui ſotto.</s> <s xml:id="echoid-s3632" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Lungo brac. # 8, # on. # 6. # } # Alto brac. # 3, # on. # 8. <lb/>Largo brac. # 4, # on. # 3. <lb/>Brac. # 32, <lb/>Brac. # 2, <lb/>Brac. # 2, <lb/>Brac. # 0, # on. # 1, # pun. # 6, <lb/>Brac. # 36, # on. # 1, # pun. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # on. # 4, # 1, # pun. <lb/># on. # 2, # 1, # pun. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Brac. # 36, # on. # 1, # pun. # 6, <lb/>Brac. # 3, # on. # 8, <lb/>Quadretti # 108, # on. # 3, <lb/>Quadretti # 24, # on. # 1, # pun. # 6, <lb/>Quadretti # 0, # on. # 0, # pun. # 8, <lb/>Quadretti # 0, # on. # 0, # pun. # 4, <lb/>Quadretti # 132, # on. # 5, # pun. # 6, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # pun. # 1, # 2, # ato. <lb/># onc. # 2, # 2, # ato. <lb/></note> <pb o="47" file="219" n="219" rhead="SECONDO."/> <p> <s xml:id="echoid-s3633" xml:space="preserve">Che ſaranno di feno intorno à peſi 133; </s> <s xml:id="echoid-s3634" xml:space="preserve">& </s> <s xml:id="echoid-s3635" xml:space="preserve">peſi 133, di <lb/>feno ſi potrà dire, che ſia di miſura il ſopradetto carro, ouer <lb/>brozzo. </s> <s xml:id="echoid-s3636" xml:space="preserve">Il medeſimo ſi farà volendo miſurare ogn’altro <lb/>carro, ouer brozzo, non ponendo altra conditione di peſo <lb/>al quadretto; </s> <s xml:id="echoid-s3637" xml:space="preserve">come di ſopra del fenile ſi è detto.</s> <s xml:id="echoid-s3638" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3639" xml:space="preserve">Le rappreſentationi de’ numeri, moltiplicando l’un l’al-<lb/>tro del feno, è il medeſimo di quelle delle mura; </s> <s xml:id="echoid-s3640" xml:space="preserve">& </s> <s xml:id="echoid-s3641" xml:space="preserve">per que <lb/>ſto non ne ho voluto mettere altro eſſempio.</s> <s xml:id="echoid-s3642" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3643" xml:space="preserve">Moſtrato il modo che ſi deue tenere del miſurare il feno <lb/>d’un fenile, & </s> <s xml:id="echoid-s3644" xml:space="preserve">quello d’un carro, ouerbrozzo; </s> <s xml:id="echoid-s3645" xml:space="preserve">appreſſo ſi <lb/>moſtrarà miſurarlo à modo di Piramide rotõda, come ſi vſà <lb/>nelle montagne. </s> <s xml:id="echoid-s3646" xml:space="preserve">Et ſia per eſſempio la Piramide rotonda <lb/><emph style="sc">A B C</emph>, il diametro <emph style="sc">A C</emph>, ſia brac. </s> <s xml:id="echoid-s3647" xml:space="preserve">7, on. </s> <s xml:id="echoid-s3648" xml:space="preserve">6, la perpẽdicolare <emph style="sc">B D</emph>, <lb/> <anchor type="figure" xlink:label="fig-219-01a" xlink:href="fig-219-01"/> <pb file="220" n="220" rhead="LIBRO"/> ſia brac. </s> <s xml:id="echoid-s3649" xml:space="preserve">7, on. </s> <s xml:id="echoid-s3650" xml:space="preserve">6, la perpendicolare <emph style="sc">B D</emph>, brac. </s> <s xml:id="echoid-s3651" xml:space="preserve">9, onc. </s> <s xml:id="echoid-s3652" xml:space="preserve">7; </s> <s xml:id="echoid-s3653" xml:space="preserve">di-<lb/>mando quanto feno à peſo ſarà la piramide rotonda.</s> <s xml:id="echoid-s3654" xml:space="preserve"/> </p> <div xml:id="echoid-div145" type="float" level="2" n="1"> <figure xlink:label="fig-219-01" xlink:href="fig-219-01a"> <image file="219-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/219-01"/> </figure> </div> <p> <s xml:id="echoid-s3655" xml:space="preserve">Prima ſi quadrarà il cerchio <emph style="sc">A E C F</emph>; </s> <s xml:id="echoid-s3656" xml:space="preserve">moltiplicando brac. <lb/></s> <s xml:id="echoid-s3657" xml:space="preserve">7, on. </s> <s xml:id="echoid-s3658" xml:space="preserve">6, in ſe medeſimo, come qui ſotto ſi vede;</s> <s xml:id="echoid-s3659" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Brac. # 7, # on. # 6, <lb/>Brac. # 7, # on. # 6, <lb/>Brac. # 49, <lb/>Brac. # 3, # on. # 6, <lb/>Brac. # 3, # on. # 6, <lb/>Brac. # 3, # on. # 3, <lb/>Quadr. # 56, # on. # 3, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # on. # 6, # 1, # pun. <lb/># on. # 6, # 1, # pun. <lb/></note> <p> <s xml:id="echoid-s3660" xml:space="preserve">Coſi moltiplicando il diametro in ſe farà brac. </s> <s xml:id="echoid-s3661" xml:space="preserve">56, on. </s> <s xml:id="echoid-s3662" xml:space="preserve">3, <lb/>& </s> <s xml:id="echoid-s3663" xml:space="preserve">di brac. </s> <s xml:id="echoid-s3664" xml:space="preserve">56, onc. </s> <s xml:id="echoid-s3665" xml:space="preserve">3, ſe ne torrà li vndeci quatordecimi, <lb/>cioè moltiplicando bracc. </s> <s xml:id="echoid-s3666" xml:space="preserve">56, onc. </s> <s xml:id="echoid-s3667" xml:space="preserve">3, per 11, ne veniranno<unsure/> <lb/>brac. </s> <s xml:id="echoid-s3668" xml:space="preserve">618, on. </s> <s xml:id="echoid-s3669" xml:space="preserve">9; </s> <s xml:id="echoid-s3670" xml:space="preserve">& </s> <s xml:id="echoid-s3671" xml:space="preserve">brac. </s> <s xml:id="echoid-s3672" xml:space="preserve">618, on. </s> <s xml:id="echoid-s3673" xml:space="preserve">9, ſi partiranno per 14, & </s> <s xml:id="echoid-s3674" xml:space="preserve"><lb/>ne veniran brac. </s> <s xml:id="echoid-s3675" xml:space="preserve">44, on. </s> <s xml:id="echoid-s3676" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s3677" xml:space="preserve">4; </s> <s xml:id="echoid-s3678" xml:space="preserve">& </s> <s xml:id="echoid-s3679" xml:space="preserve">tanto ſarà la ſuperacie <lb/>della baſe della pirami de <emph style="sc">A B C</emph>; </s> <s xml:id="echoid-s3680" xml:space="preserve">cioè, del cerchio <emph style="sc">A E C F</emph>; <lb/></s> <s xml:id="echoid-s3681" xml:space="preserve">Poi brac. </s> <s xml:id="echoid-s3682" xml:space="preserve">44, on. </s> <s xml:id="echoid-s3683" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s3684" xml:space="preserve">4, ſi moltiplicheranno con la terza <lb/>parte della perpendicolare, ouer altezza della piramide, <lb/>cioè con brac. </s> <s xml:id="echoid-s3685" xml:space="preserve">3, on. </s> <s xml:id="echoid-s3686" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s3687" xml:space="preserve">4, come qui ſeguente ſi vede, <lb/>conciando la miſura l’una ſotto l’altra.</s> <s xml:id="echoid-s3688" xml:space="preserve"/> </p> <pb o="48" file="221" n="221" rhead="SECONDO."/> <note position="right" xml:space="preserve"> <lb/>Brac. # 44, # on. # 2, # pun. # 4, <lb/>Brac. # 3, # on. # 2, # pun. # 4, <lb/>Quadretti # 132, <lb/>Quadretti # 0, # on. # 6, <lb/>Quadretti # 0, # on. # 1, <lb/>Quadretti # 7, # on. # 4, <lb/>Quadretti # 0, # on. # 0, # pun. # 4, <lb/>Quadretti # 0, # on. # 0, # pun. # 0, # at. # 8, <lb/>Quadretti # 1, # on. # 2, # pun. # 8, <lb/>Quadretti # 0, # on. # 0, # pun. # 0, # at. # 8, <lb/>Quadretti # 0, # on. # 0, # pun. # 0, # at. # 1, # mi.<unsure/> # 4, <lb/>Quadretti # 141, # on. # 2, # pun. # 1, # at. # 5, # mi. # 4, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua # pun. # 1, # 5, # mi. <lb/># pun. # 5, # 5, # mi. <lb/></note> <p> <s xml:id="echoid-s3689" xml:space="preserve">Poi moltiplicato brac. </s> <s xml:id="echoid-s3690" xml:space="preserve">3, on. </s> <s xml:id="echoid-s3691" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s3692" xml:space="preserve">4, conbrac. </s> <s xml:id="echoid-s3693" xml:space="preserve">44, on. <lb/></s> <s xml:id="echoid-s3694" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s3695" xml:space="preserve">4, fanno di cubicità quadretti 141, onc. </s> <s xml:id="echoid-s3696" xml:space="preserve">2, punto 1, <lb/>at. </s> <s xml:id="echoid-s3697" xml:space="preserve">5, min. </s> <s xml:id="echoid-s3698" xml:space="preserve">4; </s> <s xml:id="echoid-s3699" xml:space="preserve">onde quadretti 141, ſono di feno peſi 141, nõ <lb/>facendo altra conuentione, che le oncie, punti, atomi, & </s> <s xml:id="echoid-s3700" xml:space="preserve"><lb/>minuti non ſi mettono in conto.</s> <s xml:id="echoid-s3701" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3702" xml:space="preserve">Ancora per regola più breue, ſi hauerà la quantità del <lb/>feno, della piramide ſopradetta; </s> <s xml:id="echoid-s3703" xml:space="preserve">riducẽdo il diametro della <lb/>baſe della piramide in oncie, che ſaranno on. </s> <s xml:id="echoid-s3704" xml:space="preserve">90, & </s> <s xml:id="echoid-s3705" xml:space="preserve">on. </s> <s xml:id="echoid-s3706" xml:space="preserve">90. <lb/></s> <s xml:id="echoid-s3707" xml:space="preserve">ſe ſi moltiplicheranno in ſe faranno punti 8100, & </s> <s xml:id="echoid-s3708" xml:space="preserve">punti <lb/>8100, ſi partirãno per punti 20, & </s> <s xml:id="echoid-s3709" xml:space="preserve">ne venirà noni di qua-<lb/>dretti, ouer noni di peſi 405, & </s> <s xml:id="echoid-s3710" xml:space="preserve">405, ſi moltiplicarà cõ brac. </s> <s xml:id="echoid-s3711" xml:space="preserve"><lb/>3, on. </s> <s xml:id="echoid-s3712" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s3713" xml:space="preserve">4, terza parte dell’altezza, faranno noni di <lb/>quadretti, ouer di peſi 1295. </s> <s xml:id="echoid-s3714" xml:space="preserve">onc. </s> <s xml:id="echoid-s3715" xml:space="preserve">9, & </s> <s xml:id="echoid-s3716" xml:space="preserve">noni di quadretti, <lb/>ouer di peſi 1295, on. </s> <s xml:id="echoid-s3717" xml:space="preserve">9, ſi partiranno per 9, & </s> <s xml:id="echoid-s3718" xml:space="preserve">ne venirà cir-<lb/>ca quadretti ouer peſi 141, intorno & </s> <s xml:id="echoid-s3719" xml:space="preserve">tanto feno ſarà, come <lb/>qui ſe guente ſe ne vedrà la proua.</s> <s xml:id="echoid-s3720" xml:space="preserve"/> </p> <pb file="222" n="222" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/>Noni di quadr. # 405, <lb/>Braccia # 3, # on. # 2, # pun. # 4, <lb/>Noni di quadr. # 1215, <lb/>Noni di quadr. # 67, # on. # 6, <lb/>Noni di quadr. # 11, # on. # 3, <lb/>Noni di quad. # 1293, # on. # 9, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # quadr. # 6, # 2, # punti. <lb/># pun. # 5, # 2, # punti <lb/></note> <p> <s xml:id="echoid-s3721" xml:space="preserve">Et 1293, onc. </s> <s xml:id="echoid-s3722" xml:space="preserve">9, ſi faranno 1294; </s> <s xml:id="echoid-s3723" xml:space="preserve">hor ſi partirà 1294, <lb/>per 9, & </s> <s xml:id="echoid-s3724" xml:space="preserve">ne veniran peſi 144, à miſura Breſciana, & </s> <s xml:id="echoid-s3725" xml:space="preserve">à miſu-<lb/>ra Bergamaſca, eſſendo il cauezzo Breſciano di più del ca-<lb/>uezzo Bergamaſco on. </s> <s xml:id="echoid-s3726" xml:space="preserve">6; </s> <s xml:id="echoid-s3727" xml:space="preserve">Et volẽdo ridurli alla miſura Ber <lb/>gamaſca, quadretti 144, ſi moltiplicheranno per libre 7, <lb/>on. </s> <s xml:id="echoid-s3728" xml:space="preserve">26, eſſendo la libra Bergamaſca onc. </s> <s xml:id="echoid-s3729" xml:space="preserve">30, & </s> <s xml:id="echoid-s3730" xml:space="preserve">il quadret-<lb/>to libre 7, onc. </s> <s xml:id="echoid-s3731" xml:space="preserve">26, à miſura Bergamaſca; </s> <s xml:id="echoid-s3732" xml:space="preserve">per vedere quan-<lb/>ti peſi ſono, ſi moltiplicheranno i quadretti 144, con li-<lb/>bre 7, onc. </s> <s xml:id="echoid-s3733" xml:space="preserve">26, come qui ſotto ſi vede.</s> <s xml:id="echoid-s3734" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Quadretti # 144, <lb/>Libre. # 7, # on. # 26, <lb/>Libre # 1008, <lb/>Libre # 124, # on. # 24, <lb/>Libre # 1132, # on. # 24, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # quadr. # 4, # 6, # onc. <lb/># onc. # 5, # 6, # onc. <lb/></note> <p> <s xml:id="echoid-s3735" xml:space="preserve">Et libre 1132, on. </s> <s xml:id="echoid-s3736" xml:space="preserve">24, ſi partiranno per libre 10, che ſono <lb/>vn peſo Bergamaſco, & </s> <s xml:id="echoid-s3737" xml:space="preserve">ſi trouarà, che ſaranno intorno à <pb o="49" file="223" n="223" rhead="SECONDO"/> peſi 113, libre 2, on. </s> <s xml:id="echoid-s3738" xml:space="preserve">24, Bergamaſchi; </s> <s xml:id="echoid-s3739" xml:space="preserve">& </s> <s xml:id="echoid-s3740" xml:space="preserve">è differenza da pe <lb/>ſi 144, Breſciani, ài 113, libre 2, onc. </s> <s xml:id="echoid-s3741" xml:space="preserve">24, Bergamaſchi, peſi <lb/>30, libre 7, onc. </s> <s xml:id="echoid-s3742" xml:space="preserve">6, che ſono faſci 5, libre 7, on. </s> <s xml:id="echoid-s3743" xml:space="preserve">6, perche <lb/>vn faſcio in Bergamaſca ſono peſi 6, coſi in queſta miſura di <lb/>feno, la miſura Breſciana è di piu faſci 5, lib. </s> <s xml:id="echoid-s3744" xml:space="preserve">7, on. </s> <s xml:id="echoid-s3745" xml:space="preserve">6, Berga <lb/>maſchi, di quella Bergamaſca.</s> <s xml:id="echoid-s3746" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div147" type="section" level="1" n="130"> <head xml:id="echoid-head163" xml:space="preserve">DEL MISVRAR DELLE ASSI.</head> <p> <s xml:id="echoid-s3747" xml:space="preserve">Detto diſopra aſſai del feno, qui ſeguitando ſi dirà del <lb/>miſurare delle Aſsi; </s> <s xml:id="echoid-s3748" xml:space="preserve">le rappreſentationi di vn numero, à <lb/>moltiplicarlo con l’altro fanno il medeſimo di quello delle <lb/>mura, & </s> <s xml:id="echoid-s3749" xml:space="preserve">biade; </s> <s xml:id="echoid-s3750" xml:space="preserve">hor volendo miſurar le aſsi, ſi torrà vno ſpa <lb/>go, ouer riforzino, & </s> <s xml:id="echoid-s3751" xml:space="preserve">con quello s’anderà miſurando la <lb/>larghezza delle aſsi, che ſono neceſſarie da miſurare; </s> <s xml:id="echoid-s3752" xml:space="preserve">fatto <lb/>queſto ſi miſurerà quello ſpago, ouer riforzino con la mi-<lb/>ſura del Paeſe; </s> <s xml:id="echoid-s3753" xml:space="preserve">& </s> <s xml:id="echoid-s3754" xml:space="preserve">ſi ſaprà quante brac. </s> <s xml:id="echoid-s3755" xml:space="preserve">on. </s> <s xml:id="echoid-s3756" xml:space="preserve">& </s> <s xml:id="echoid-s3757" xml:space="preserve">punti ſarà quel <lb/>riforzino, ouero ſpago; </s> <s xml:id="echoid-s3758" xml:space="preserve">& </s> <s xml:id="echoid-s3759" xml:space="preserve">quelle brac. </s> <s xml:id="echoid-s3760" xml:space="preserve">on. </s> <s xml:id="echoid-s3761" xml:space="preserve">& </s> <s xml:id="echoid-s3762" xml:space="preserve">punti ſi ſegna-<lb/>ranno; </s> <s xml:id="echoid-s3763" xml:space="preserve">appreſſo di queſto ſi vedrà quanto ſia la lunghezza <lb/>delle aſsi, di che s’ètolto la larghezza; </s> <s xml:id="echoid-s3764" xml:space="preserve">perche è neceſſario, <lb/>che habbiano una medeſima lunghezza; </s> <s xml:id="echoid-s3765" xml:space="preserve">& </s> <s xml:id="echoid-s3766" xml:space="preserve">ſe haueſſero di-<lb/>uerſe lunghezze, ſarebbe neceſſario far diuerſe miſure; </s> <s xml:id="echoid-s3767" xml:space="preserve">hor <lb/>poniamo che la larghezza delle aſsi corte, ſia brac. </s> <s xml:id="echoid-s3768" xml:space="preserve">7, onc. <lb/></s> <s xml:id="echoid-s3769" xml:space="preserve">5, & </s> <s xml:id="echoid-s3770" xml:space="preserve">le aſsi lunghe brac. </s> <s xml:id="echoid-s3771" xml:space="preserve">5, on. </s> <s xml:id="echoid-s3772" xml:space="preserve">7, vorrei ſaper quante bra. </s> <s xml:id="echoid-s3773" xml:space="preserve"><lb/>ſaranno, farai la ſua moltiplicatione, come s’e fatto delli <lb/>muri, & </s> <s xml:id="echoid-s3774" xml:space="preserve">feni; </s> <s xml:id="echoid-s3775" xml:space="preserve">& </s> <s xml:id="echoid-s3776" xml:space="preserve">come ancor qui ſotto ſi vedrà.</s> <s xml:id="echoid-s3777" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Larghe brac. # 7, # on. # 5. <lb/>Lunghe brac. # 5, # on. # 8. <lb/>Brac. # 35, <lb/>Brac. # 2, # on. # 1, <lb/>Brac. # 4, # on. # 8, <lb/>Brac. # 0, # on. # 3, # pun. # 4, <lb/>Brac. # 42, # on. # 0, # pun. # 4, <lb/></note> <note position="right" xml:space="preserve"> <lb/>Proua. # oncie # 5, # 4, # punti. <lb/># oncie # 5, # 4, # punti. <lb/></note> <pb file="224" n="224" rhead="LIBRO"/> <p> <s xml:id="echoid-s3778" xml:space="preserve">Coſi ſi vede che moltiplicando brac. </s> <s xml:id="echoid-s3779" xml:space="preserve">7, on. </s> <s xml:id="echoid-s3780" xml:space="preserve">5, con brac. </s> <s xml:id="echoid-s3781" xml:space="preserve">5, <lb/>on. </s> <s xml:id="echoid-s3782" xml:space="preserve">8, fanno brac. </s> <s xml:id="echoid-s3783" xml:space="preserve">42, onc. </s> <s xml:id="echoid-s3784" xml:space="preserve">o, pun. </s> <s xml:id="echoid-s3785" xml:space="preserve">4; </s> <s xml:id="echoid-s3786" xml:space="preserve">& </s> <s xml:id="echoid-s3787" xml:space="preserve">brac. </s> <s xml:id="echoid-s3788" xml:space="preserve">42, on. </s> <s xml:id="echoid-s3789" xml:space="preserve">o, pun. <lb/></s> <s xml:id="echoid-s3790" xml:space="preserve">4, ſi partiranno per tanta lunghezza, come ſi vorrà che ſia <lb/>vn braccio lungo, ſecondo la miſura del paeſe, perche chi <lb/>pone vna miſura, & </s> <s xml:id="echoid-s3791" xml:space="preserve">chi ne mette vn’altra, il Breſciano vo-<lb/>gliono il ſuo braccio d’aſsi, che ſia lungo brac. </s> <s xml:id="echoid-s3792" xml:space="preserve">6; </s> <s xml:id="echoid-s3793" xml:space="preserve">il Berga-<lb/>maſco braccia 5; </s> <s xml:id="echoid-s3794" xml:space="preserve">coſi ſecondo ipaeſi, fannoſi diuerſe miſu-<lb/>re. </s> <s xml:id="echoid-s3795" xml:space="preserve">Horpartiremo brac. </s> <s xml:id="echoid-s3796" xml:space="preserve">42, on. </s> <s xml:id="echoid-s3797" xml:space="preserve">o, pun. </s> <s xml:id="echoid-s3798" xml:space="preserve">3; </s> <s xml:id="echoid-s3799" xml:space="preserve">per brac. </s> <s xml:id="echoid-s3800" xml:space="preserve">6, ſe-<lb/>condo il coſtume di Breſcia, & </s> <s xml:id="echoid-s3801" xml:space="preserve">ne venirà brac. </s> <s xml:id="echoid-s3802" xml:space="preserve">7, & </s> <s xml:id="echoid-s3803" xml:space="preserve">di quelli <lb/>punti non ſe ne tien conto alcuno. </s> <s xml:id="echoid-s3804" xml:space="preserve">Coſi le aſsi miſurate di <lb/>ſopra, o ſecondo il coſtume Breſciano ſono brac. </s> <s xml:id="echoid-s3805" xml:space="preserve">7; </s> <s xml:id="echoid-s3806" xml:space="preserve">& </s> <s xml:id="echoid-s3807" xml:space="preserve">ſe le <lb/>voleſsimo ſecondo il coſtume Bergamaſco, partiriano bra. </s> <s xml:id="echoid-s3808" xml:space="preserve"><lb/>42, perbrac. </s> <s xml:id="echoid-s3809" xml:space="preserve">5, che ſarebbono brac. </s> <s xml:id="echoid-s3810" xml:space="preserve">8, onc. </s> <s xml:id="echoid-s3811" xml:space="preserve">5, li intorno di <lb/>aſsi, alla Bergamaſca; </s> <s xml:id="echoid-s3812" xml:space="preserve">il medeſimo ſi farebbe in ogn’altro <lb/>luogo, hauendo però riſpetto alla lunghezza del cauezzo, <lb/>detto del miſurare le aſsi, ſi dirà del miſurar le legne; </s> <s xml:id="echoid-s3813" xml:space="preserve">le ſue <lb/>rappreſentationi ſono come quelli di ſopra, che s’è detto <lb/>de i muri, & </s> <s xml:id="echoid-s3814" xml:space="preserve">del feno; </s> <s xml:id="echoid-s3815" xml:space="preserve">Le legne ſul Breſciano à miſure ſi <lb/>fanno à mete, vna meda di legna è quadretti 72, cioèbra. </s> <s xml:id="echoid-s3816" xml:space="preserve">6, <lb/>larga, & </s> <s xml:id="echoid-s3817" xml:space="preserve">altri tanti alta, & </s> <s xml:id="echoid-s3818" xml:space="preserve">la legna vole eſſere braccia 2, lun <lb/>ga, & </s> <s xml:id="echoid-s3819" xml:space="preserve">à queſta miſura ſaranno quadretti 72; </s> <s xml:id="echoid-s3820" xml:space="preserve">ouer ſapendo il <lb/>ſuo ordinario della lunghezza della legna, cioèbrac. </s> <s xml:id="echoid-s3821" xml:space="preserve">2, lun <lb/>ga, non ſi miſura ſolo la larghezza, & </s> <s xml:id="echoid-s3822" xml:space="preserve">altezza, & </s> <s xml:id="echoid-s3823" xml:space="preserve">quadretti <lb/>36, faranno vna meda di legna, come diſopra.</s> <s xml:id="echoid-s3824" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3825" xml:space="preserve">Il modo Bergamaſco, ſarà vn carro di legna largo brac. <lb/></s> <s xml:id="echoid-s3826" xml:space="preserve">3, alto brac. </s> <s xml:id="echoid-s3827" xml:space="preserve">3, lungo brac. </s> <s xml:id="echoid-s3828" xml:space="preserve">3, & </s> <s xml:id="echoid-s3829" xml:space="preserve">oncie 4, ouer longo quarti <lb/>dieci, perche vn braccio è lungo quarti 3.</s> <s xml:id="echoid-s3830" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3831" xml:space="preserve">Auuertendo ancora che le proue ſopradette ſi poteuano <lb/>fare per vn’altro modo, ſecondo Euclide; </s> <s xml:id="echoid-s3832" xml:space="preserve">perche Euclide <lb/>in queſto modo, nella vigeſima propoſitione del ſettimo li <lb/>bro, dice ſe ſaranno quattro numeri proportionali; </s> <s xml:id="echoid-s3833" xml:space="preserve">quello <lb/>che vien produtto dal primo nell’ultimo, ſarà eguale à quel <lb/>lo che vien produtto dal ſecondo nel terzo. </s> <s xml:id="echoid-s3834" xml:space="preserve">Queſte mede-<lb/>ſime parole eſſo Euclide dice ancora nella quintadecima <pb o="50" file="225" n="225" rhead="SECONDO"/> propoſitione del ſeſto libro, di quattro linee proportionali; <lb/></s> <s xml:id="echoid-s3835" xml:space="preserve">ma noi habbiamo da ſeruirſi ſolo di quella del ſettimo per <lb/>li numeri; </s> <s xml:id="echoid-s3836" xml:space="preserve">coſi tutte le ragioni Aritmetiche, & </s> <s xml:id="echoid-s3837" xml:space="preserve">Geometri-<lb/>che delle miſure, tutte riuſciranno in quattro quantità pro <lb/>portionali, ò continua, ouer diſcontinua, coſi le ſopradet-<lb/>te ragioni haueranno quella proportione, ſe ſaranno eſſe <lb/>ragioni ben fatte.</s> <s xml:id="echoid-s3838" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3839" xml:space="preserve">Auuertendo ancora, che tutte le ragioni, di che s’hanno <lb/>da far le ſue proue, ha da eſſere la prima, & </s> <s xml:id="echoid-s3840" xml:space="preserve">la terza d’una <lb/>medeſima natura; </s> <s xml:id="echoid-s3841" xml:space="preserve">& </s> <s xml:id="echoid-s3842" xml:space="preserve">ancor la ſeconda, & </s> <s xml:id="echoid-s3843" xml:space="preserve">la quarta pur d’una <lb/>medeſima natura; </s> <s xml:id="echoid-s3844" xml:space="preserve">perche tutte le ragioni fatte ſe deueno <lb/>eſſer buone, s’hanno da ritrouar quattro quantità propor-<lb/>tionali, come dice eſſo Euclide nella vigeſima proportio-<lb/>ne del ſettimo libro.</s> <s xml:id="echoid-s3845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3846" xml:space="preserve">Verbi gratia io pongo da fare la proua, della nona ra-<lb/>gione delle biade, che è a miſura, come qui ſotto ſi vede.</s> <s xml:id="echoid-s3847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3848" xml:space="preserve">Brac. </s> <s xml:id="echoid-s3849" xml:space="preserve">5, on. </s> <s xml:id="echoid-s3850" xml:space="preserve">7, pun. </s> <s xml:id="echoid-s3851" xml:space="preserve">0, e4, ſettimi. </s> <s xml:id="echoid-s3852" xml:space="preserve">\\ Brac. </s> <s xml:id="echoid-s3853" xml:space="preserve">1, on. </s> <s xml:id="echoid-s3854" xml:space="preserve">2, pun. </s> <s xml:id="echoid-s3855" xml:space="preserve">0,}quad. </s> <s xml:id="echoid-s3856" xml:space="preserve">6, on, 6, pũ. </s> <s xml:id="echoid-s3857" xml:space="preserve">2, at. </s> <s xml:id="echoid-s3858" xml:space="preserve">2</s> </p> <p> <s xml:id="echoid-s3859" xml:space="preserve">Io conciarò per la prima quantità vn quadretto; </s> <s xml:id="echoid-s3860" xml:space="preserve">per la <lb/>ſeconda brac. </s> <s xml:id="echoid-s3861" xml:space="preserve">5, on. </s> <s xml:id="echoid-s3862" xml:space="preserve">7, pun. </s> <s xml:id="echoid-s3863" xml:space="preserve">o, e4, ſettimi, per la terza bra. </s> <s xml:id="echoid-s3864" xml:space="preserve">1 <lb/>on. </s> <s xml:id="echoid-s3865" xml:space="preserve">2; </s> <s xml:id="echoid-s3866" xml:space="preserve">& </s> <s xml:id="echoid-s3867" xml:space="preserve">per la quarta quadretti 6, onc. </s> <s xml:id="echoid-s3868" xml:space="preserve">6, pun. </s> <s xml:id="echoid-s3869" xml:space="preserve">2, atomi 2.</s> <s xml:id="echoid-s3870" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3871" xml:space="preserve">Et volendo far la proua di queſte quattro quantità, ſe ſo-<lb/>no proportionali, ouer veder ſe la ragione ſtà bene, èneceſ <lb/>ſario di far la prima, & </s> <s xml:id="echoid-s3872" xml:space="preserve">la terza d’una me deſima natura, ſi fa-<lb/>rà 1, quadretto à on. </s> <s xml:id="echoid-s3873" xml:space="preserve">com’è la terza, che ſono on. </s> <s xml:id="echoid-s3874" xml:space="preserve">12; </s> <s xml:id="echoid-s3875" xml:space="preserve">& </s> <s xml:id="echoid-s3876" xml:space="preserve">la <lb/>ſeconda ſettimi d’atomi, ſi farà ancor la quarta à ſettimi <lb/>d’atomi, ponendo il ſettimo alli atomi della quarta in que <lb/>ſto modo, niun ſettimi, & </s> <s xml:id="echoid-s3877" xml:space="preserve">ſtarà coſi quadretti 6, onc. </s> <s xml:id="echoid-s3878" xml:space="preserve">6, <lb/>punti 2, atomi 2, e niun ſettimi; </s> <s xml:id="echoid-s3879" xml:space="preserve">& </s> <s xml:id="echoid-s3880" xml:space="preserve">ſi andarà conciando di <lb/>nouo la regola come qui drieto ſi vede.</s> <s xml:id="echoid-s3881" xml:space="preserve"/> </p> <pb file="226" n="226" rhead="LIBRO"/> <note position="right" xml:space="preserve"> <lb/># Prima <lb/>Brac. # 0, # on. # 12, <lb/># Seconda. <lb/>Brac. # 5, # on. # 7, # pun. # 0, # at. # @, # e ſei ſettimi. <lb/># Terza. <lb/>Brac. # 1, # on. # 2, <lb/># Quarta. <lb/>Quadr. # 6, # on. # 6, # pun. # 2, # at. # 2, # e niun ſettimi: <lb/></note> </div> <div xml:id="echoid-div148" type="section" level="1" n="131"> <head xml:id="echoid-head164" xml:space="preserve">Proua della prima, & quarta.</head> <note position="right" xml:space="preserve"> <lb/>Prima, # oncie. # 5, # 0, # ſettimi d’atomi. <lb/>Quarta, # ſettimi d’at. # 0, <lb/></note> </div> <div xml:id="echoid-div149" type="section" level="1" n="132"> <head xml:id="echoid-head165" xml:space="preserve">Proua della ſeconda, & terza.</head> <note position="right" xml:space="preserve"> <lb/>Seconda, # oncie. # 0, # 0, # ſettimi d’atomi. <lb/>Terza, # ſettimi d’at. # 6, <lb/></note> <p> <s xml:id="echoid-s3882" xml:space="preserve">Et coſi ſi vede, che tanto è à moltiplicare la proua della <lb/>prima nella quarta, come à moltiplicare la proua della ſe-<lb/>conda nella terza; </s> <s xml:id="echoid-s3883" xml:space="preserve">coſi ſi farà ogn’altra proua di ragione, <lb/>non tanto Geometrica, come ancora Aritmetica; </s> <s xml:id="echoid-s3884" xml:space="preserve">& </s> <s xml:id="echoid-s3885" xml:space="preserve">queſto <lb/>è il vero modo di fare le proue alle ragioni.</s> <s xml:id="echoid-s3886" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3887" xml:space="preserve">Io non mi eſtenderò piu in lungo, in volere inſegnare à <lb/>far le proue delle ragioni, perche mi pare di hauerne detto <lb/>à ſofficienza.</s> <s xml:id="echoid-s3888" xml:space="preserve"/> </p> <pb o="51" file="227" n="227" rhead="SECONDO."/> </div> <div xml:id="echoid-div150" type="section" level="1" n="133"> <head xml:id="echoid-head166" xml:space="preserve">DEL LIVELLAR <lb/>dell’Acque.</head> <p> <s xml:id="echoid-s3889" xml:space="preserve"><emph style="sc">HAvendo</emph> detto intorno alla prattica della <lb/>Geometria, conſeguentemente io dirò del <lb/>liuellare dell’acque.</s> <s xml:id="echoid-s3890" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3891" xml:space="preserve">Hauendo da liuellare vn’acqua, che ſivo-<lb/>leſſe condur da vn luogo ad vn’altro; </s> <s xml:id="echoid-s3892" xml:space="preserve">la pri-<lb/>ma coſa che ſi dee fare;</s> <s xml:id="echoid-s3893" xml:space="preserve">è conſiderar bene il vaſo doue ſi ha <lb/>da cauarla; </s> <s xml:id="echoid-s3894" xml:space="preserve">poi conſiderare il luogo a parte, a parte, doue ſi <lb/>vuol condurla; </s> <s xml:id="echoid-s3895" xml:space="preserve">& </s> <s xml:id="echoid-s3896" xml:space="preserve">andar ponendo qualche ſegno per guida, <lb/>accioche quando ſi vorrà liuellare, ſi poſſa caminar per drit <lb/>to ordine doue s’ha da condur l’Acqua. </s> <s xml:id="echoid-s3897" xml:space="preserve">Oltra di queſto ſi <lb/>habbiano preparate due aſte dritte, con ferro appuntato da <lb/>vn capo, per poterle ficcare nella ſuperficie della terra; </s> <s xml:id="echoid-s3898" xml:space="preserve">& </s> <s xml:id="echoid-s3899" xml:space="preserve"><lb/>quelle ſiano ſegnate, a bracc. </s> <s xml:id="echoid-s3900" xml:space="preserve">on. </s> <s xml:id="echoid-s3901" xml:space="preserve">& </s> <s xml:id="echoid-s3902" xml:space="preserve">piu minutamente ſe <lb/>ſarà poſsibile; </s> <s xml:id="echoid-s3903" xml:space="preserve">poi or dinato il tutto, ſi pianterà vna di quel-<lb/>le aſte nel vaſo, doue ſihaurà da cauar l’acqua piu dritta, che <lb/>ſia poſsibile, cioè perpendicolare alla ſuperficie dell’acqua: <lb/></s> <s xml:id="echoid-s3904" xml:space="preserve">Fatto queſto ſi pianterà il ſuo liuello lõtano almeno diece, <lb/>fin’ à 15, cauezzi; </s> <s xml:id="echoid-s3905" xml:space="preserve">& </s> <s xml:id="echoid-s3906" xml:space="preserve">quel tanto che ſi poſſa ben comprende-<lb/>re vn punto, che ſi ſegnerà nell’aſta col veder che ſi fà alla <lb/>ſuperficie delliuello, & </s> <s xml:id="echoid-s3907" xml:space="preserve">con vna corda d’archetto; </s> <s xml:id="echoid-s3908" xml:space="preserve">& </s> <s xml:id="echoid-s3909" xml:space="preserve">com-<lb/>modato, che ſarà il liuello, ſi guarderà con l’occhio da vn <lb/>capo, all’altro, per la ſuperſicie di ſoprauia di eſſo liuello; </s> <s xml:id="echoid-s3910" xml:space="preserve">& </s> <s xml:id="echoid-s3911" xml:space="preserve"><lb/>à quel capo, doue non ſiritroua l’occhio, ſi terrà vn’archet-<lb/>to, che la ſua corda ſia d’una ſeta di coda di Cauallo; </s> <s xml:id="echoid-s3912" xml:space="preserve">accio-<lb/>che guardando per la ſuperficie di ſoprauia del liuello, ſi <lb/>poſſa anchora vedere eſſa corda che giace all’altro capo di <lb/>eſſo liuello; </s> <s xml:id="echoid-s3913" xml:space="preserve">& </s> <s xml:id="echoid-s3914" xml:space="preserve">guardando per la ſuperficie del liuello a eſſa <lb/>corda, ſtendaſi la viſta fin nell’aſta piantata nell’acqua, & </s> <s xml:id="echoid-s3915" xml:space="preserve"><lb/>iui doue batte il guardo della viſta accompagnata nella ſu-<lb/>perficie del liuello nell’aſta ſi farà vn ſegno di carta bianca, <lb/>attaccata con poco di cera da ſigillare, & </s> <s xml:id="echoid-s3916" xml:space="preserve">fermar eſſa carta <pb file="228" n="228" rhead="LIBRO"/> conla cera diligentemente, & </s> <s xml:id="echoid-s3917" xml:space="preserve">quanto piu detto ſegno di <lb/>carta ſarà picciolo meglio è, & </s> <s xml:id="echoid-s3918" xml:space="preserve">per queſto ſono neceſſarie <lb/>le ſtationi propinque; </s> <s xml:id="echoid-s3919" xml:space="preserve">ma ſe fuſſe poſsibile, che doue guar-<lb/>da l’occhio nell’aſta, ad vn punto fatto con vno ſpuntarolo <lb/>di ſpada guardaſſe, ſarebbe meglio. </s> <s xml:id="echoid-s3920" xml:space="preserve">Si dee poi miſurare dal <lb/>punto ſegnato dell’Aſta fina alla ſuperficie dell’acqua, & </s> <s xml:id="echoid-s3921" xml:space="preserve"><lb/>non al fondo dell’acqua, percioche pigliando la miſura fin <lb/>al fondo ſi farian due errori, l’uno perche’l fondo mai non <lb/>ſi troua eguale; </s> <s xml:id="echoid-s3922" xml:space="preserve">& </s> <s xml:id="echoid-s3923" xml:space="preserve">l’altro perche ficcando nel fondo l’aſta <lb/>non ſi ſapria quanto fuſſe l’altezza; </s> <s xml:id="echoid-s3924" xml:space="preserve">& </s> <s xml:id="echoid-s3925" xml:space="preserve">la ſuperficie dell’ac-<lb/>qua non può ingannare, perche ſi ritroua piana, & </s> <s xml:id="echoid-s3926" xml:space="preserve">equidi-<lb/>ſtante al fondo del vaſo. </s> <s xml:id="echoid-s3927" xml:space="preserve">Oltre di ciò, ſi andrà con l’occhio <lb/>all’altro capo del liuello, doue ſi ritrouerà l’archetto, & </s> <s xml:id="echoid-s3928" xml:space="preserve">iui <lb/>ſi affiſſarà l’occhio, ponendo l’archetto dall’altro capo, & </s> <s xml:id="echoid-s3929" xml:space="preserve"><lb/>guardando per la ſuperficie delliuello, alla corda dell’ar-<lb/>chetto non mouendo però il liuello guardando fin alla ſe-<lb/>conda aſta, piantata inanzi al liuello, doue ſi dee condur <lb/>l’acqua; </s> <s xml:id="echoid-s3930" xml:space="preserve">& </s> <s xml:id="echoid-s3931" xml:space="preserve">iui nell’aſta ſi farà vn ſegno con diligenza; </s> <s xml:id="echoid-s3932" xml:space="preserve">come <lb/>s’è fatto nella prima aſta piantata nell’acqua; </s> <s xml:id="echoid-s3933" xml:space="preserve">poi ſi miſurerà <lb/>da vn’aſta all’altra, & </s> <s xml:id="echoid-s3934" xml:space="preserve">quella miſura ſi ſegnarà ſopra la carta; <lb/></s> <s xml:id="echoid-s3935" xml:space="preserve">& </s> <s xml:id="echoid-s3936" xml:space="preserve">ancora ſi miſurerà dal punto fatto nella ſeconda aſta, a <lb/>lungo dell’aſta, fina alla ſuperficie della terra, & </s> <s xml:id="echoid-s3937" xml:space="preserve">ancor quel <lb/>la miſura ſi ſegnarà ſopra alla carta. </s> <s xml:id="echoid-s3938" xml:space="preserve">Fatto queſto ſileue-<lb/>rà il liuello, & </s> <s xml:id="echoid-s3939" xml:space="preserve">ſi porterà inanzi alla ſeconda aſta, da dieci, <lb/>in dodeci paſsi, ò tanto come diſopra s’è detto diritto fin <lb/>doue s’ha da condur l’acqua, non mouendo però la ſeconda <lb/>aſta; </s> <s xml:id="echoid-s3940" xml:space="preserve">Et di nouo ſi guarderà nella ſeconda aſta, per la ſuper <lb/>ficie del liuello, col veder la corda dall’archetto, & </s> <s xml:id="echoid-s3941" xml:space="preserve">doue ſi <lb/>vedrà nella ſeconda aſta, per il guardo che ſi fa nella ſuper-<lb/>ficie del liuello, iui ſi ſegnerà; </s> <s xml:id="echoid-s3942" xml:space="preserve">come diſopra s’è detto.</s> <s xml:id="echoid-s3943" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3944" xml:space="preserve">Et con queſto ammaeſtramento s’andrà mettendo vna <lb/>aſta inanzi al liuello, & </s> <s xml:id="echoid-s3945" xml:space="preserve">vna ſi laſcierà di dietro, col miſu-<lb/>rare, & </s> <s xml:id="echoid-s3946" xml:space="preserve">ſcriuere ſopra la carta, & </s> <s xml:id="echoid-s3947" xml:space="preserve">oſſeruando l’ordine mo-<lb/>ſtrato diſopra, ſi potrà condurre le acque da vn luogo ad <pb o="52" file="229" n="229" rhead="SECONDO."/> vn’altro, pur che ſi poſſa condurre; </s> <s xml:id="echoid-s3948" xml:space="preserve">come quiſeguente per li <lb/>noſtri diſſegni meglio ſi potrà comprendere.</s> <s xml:id="echoid-s3949" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div151" type="section" level="1" n="134"> <head xml:id="echoid-head167" xml:space="preserve">LIVELLO.</head> <figure> <image file="229-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/229-01"/> </figure> <p> <s xml:id="echoid-s3950" xml:space="preserve">L’archetto vorrei che fuſſe piccolo, & </s> <s xml:id="echoid-s3951" xml:space="preserve">greue; </s> <s xml:id="echoid-s3952" xml:space="preserve">& </s> <s xml:id="echoid-s3953" xml:space="preserve">s’eſſo foſ <lb/>ſe fatto di aciaio, ouero altro metallo greue, ſaria buono, <lb/>la corda ſua vorrei foſſe di filo diramme ſottiliſsima, come <lb/>la piu ſottile dell’arpicordo; </s> <s xml:id="echoid-s3954" xml:space="preserve">& </s> <s xml:id="echoid-s3955" xml:space="preserve">queſta grauezza, ſi fà per <lb/>riſpetto del vento, che non lo impediſca, nello adope-<lb/>perarlo.</s> <s xml:id="echoid-s3956" xml:space="preserve"/> </p> <pb file="230" n="230" rhead="LIBRO"/> <figure> <image file="230-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/230-01"/> </figure> <pb o="53" file="231" n="231" rhead="SECONDO"/> <figure> <image file="231-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/231-01"/> </figure> </div> <div xml:id="echoid-div152" type="section" level="1" n="135"> <head xml:id="echoid-head168" xml:space="preserve">PRIMO ESSEMPIO. <lb/>del Liuellare.</head> <p> <s xml:id="echoid-s3957" xml:space="preserve">Il Vaſo, ouer Seriola <emph style="sc">M N</emph>, <lb/>è doue ſi deue cauar l’acqua <lb/>per condurla al punto o; </s> <s xml:id="echoid-s3958" xml:space="preserve">l’<emph style="sc">A</emph>, <lb/>ſignifica la prima aſta, & </s> <s xml:id="echoid-s3959" xml:space="preserve">il <emph style="sc">B</emph>, <lb/>ſignifica la ſeconda aſta; </s> <s xml:id="echoid-s3960" xml:space="preserve">& </s> <s xml:id="echoid-s3961" xml:space="preserve">il <lb/><emph style="sc">C</emph>, ſignifica il liuello. </s> <s xml:id="echoid-s3962" xml:space="preserve">Il pun-<lb/>to <emph style="sc">D</emph>, ſignifica la prima ſtatio-<lb/>ne; </s> <s xml:id="echoid-s3963" xml:space="preserve">il ponto <emph style="sc">F</emph>, ſignifica la ſe <lb/>conda ſtatione; </s> <s xml:id="echoid-s3964" xml:space="preserve">il punto <emph style="sc">H</emph>, <lb/>la terza ſtatione; </s> <s xml:id="echoid-s3965" xml:space="preserve">il punto <emph style="sc">K</emph>, <lb/>la quarta ſtatione; </s> <s xml:id="echoid-s3966" xml:space="preserve">le linee <lb/>appuntate, ſignificano le li-<lb/>nee viſuali, che ſi fan riguar-<lb/>dando per laſuperficie del li <lb/>uello, che uà a dare di punta <lb/>nelle due aſte equidiſtante <lb/>all’orizóte, & </s> <s xml:id="echoid-s3967" xml:space="preserve">è ancora equi-<lb/>diſtante alla <emph style="sc">D</emph> o, & </s> <s xml:id="echoid-s3968" xml:space="preserve">con que <lb/>ſto medeſimo ordine ſi potrà <lb/>andar di mano in mano, con <lb/>la prima, & </s> <s xml:id="echoid-s3969" xml:space="preserve">ſeconda aſta, fa <lb/>cendo le due ſtationi, & </s> <s xml:id="echoid-s3970" xml:space="preserve">ri-<lb/>portando il ſuo liuello nel <lb/>mezzo ſe ſi può, fra l’una ſta-<lb/>tione, & </s> <s xml:id="echoid-s3971" xml:space="preserve">l’altra, come diſopra <lb/>ſi vede nel primo eſſempio, <lb/><emph style="sc">D</emph>, & </s> <s xml:id="echoid-s3972" xml:space="preserve"><emph style="sc">F</emph>, ſono le due ſtatio-<lb/>ni formate dalle due aſte <emph style="sc">A</emph>, <lb/>& </s> <s xml:id="echoid-s3973" xml:space="preserve"><emph style="sc">B</emph>, il liuello <emph style="sc">C</emph>, è nel mezo <lb/>nel punto <emph style="sc">E</emph>; </s> <s xml:id="echoid-s3974" xml:space="preserve">la prima aſta, <emph style="sc">A</emph>, <lb/>è riportata dal punto <emph style="sc">D</emph>, al <pb file="232" n="232" rhead="LIBRO"/> punto <emph style="sc">H</emph>, & </s> <s xml:id="echoid-s3975" xml:space="preserve">ſono fatte le due ſtationi <emph style="sc">F, H,</emph> il liuello <emph style="sc">C</emph>, è ripor <lb/>tato dal punto <emph style="sc">E</emph>, al punto <emph style="sc">G</emph>, fra le due ſtationi <emph style="sc">F</emph>, & </s> <s xml:id="echoid-s3976" xml:space="preserve"><emph style="sc">H</emph>; </s> <s xml:id="echoid-s3977" xml:space="preserve">di nouo <lb/>l’Aſta <emph style="sc">B</emph>, è riportata dal punto <emph style="sc">F</emph>, al punto <emph style="sc">K</emph>, medeſimamente <lb/>il liuello <emph style="sc">C</emph>, è riportato dal punto <emph style="sc">G</emph>, al punto 1, fra le due <lb/>ſtationi <emph style="sc">H</emph>, & </s> <s xml:id="echoid-s3978" xml:space="preserve"><emph style="sc">K</emph>, & </s> <s xml:id="echoid-s3979" xml:space="preserve">queſto è l’ordine, che ſi deue tenere, in ri-<lb/>portare le due Aſte, & </s> <s xml:id="echoid-s3980" xml:space="preserve">il liuello; </s> <s xml:id="echoid-s3981" xml:space="preserve">andando guardando per la <lb/>ſuperficie di ſoprauia del liuello, con la corda del ſuo ar-<lb/>chetto; </s> <s xml:id="echoid-s3982" xml:space="preserve">col miſurar dalla ſuperficie della terra fina al punto, <lb/>che fa la linea uiſuale nelle due Aſte; </s> <s xml:id="echoid-s3983" xml:space="preserve">& </s> <s xml:id="echoid-s3984" xml:space="preserve">miſurare ancora il <lb/>piano della ſuperficie della terra, fra l’una Aſta, ouer fra <lb/>l’vna ſtatione, & </s> <s xml:id="echoid-s3985" xml:space="preserve">l’alrra, & </s> <s xml:id="echoid-s3986" xml:space="preserve">ſcriuendo il tutto ſopra di vna car <lb/>ta, come di ſopra s’è detto. </s> <s xml:id="echoid-s3987" xml:space="preserve">Qui di ſotto ſi metterà vna ta-<lb/>uoletta, del modo che deue tenere il buon liuelladore nel <lb/>ſegnare le ſue miſure; </s> <s xml:id="echoid-s3988" xml:space="preserve">cioè le braccia, & </s> <s xml:id="echoid-s3989" xml:space="preserve">le oncie che ſono <lb/>dal pian dell’orizonte, fin al punto delle due Aſte, ſegnato <lb/>della linea viſuale; </s> <s xml:id="echoid-s3990" xml:space="preserve">come moſtra la linea appuntata equidi-<lb/>ſtante al piano dell’orizonte; </s> <s xml:id="echoid-s3991" xml:space="preserve">& </s> <s xml:id="echoid-s3992" xml:space="preserve">ancora li cauezzi bracc. </s> <s xml:id="echoid-s3993" xml:space="preserve">& </s> <s xml:id="echoid-s3994" xml:space="preserve"><lb/>oncie tra l’vna ſtatione & </s> <s xml:id="echoid-s3995" xml:space="preserve">l’altra.</s> <s xml:id="echoid-s3996" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div153" type="section" level="1" n="136"> <head xml:id="echoid-head169" xml:space="preserve">TAVOLA:</head> <note style="it" position="right" xml:space="preserve"> <lb/>De hauere. # Miſura ch’è tra l’una \\ ſtatione & l’altra. # Riceuuto. <lb/>Prima Brac. 4, on. 2. # Cau. 19, br. 3, on. 4. # Brac. 3, on. 8, ſeconda. <lb/>Secõda Brac. 3, on. 10. # Cau. 21, br. 2, on. 7. # Brac. 3, on. 11, terza. <lb/>Terza Brac. 4, on. 5. # Cau. 18, br. 4, on. 6. # Brac. 4, on. 9, quarta. <lb/>Brac. 12, on. 5 # Cau. 59, br. 4, on. 5. # Brac. 12, on 4, <lb/></note> <p> <s xml:id="echoid-s3997" xml:space="preserve">Sommate le miſure dell’hauuto, & </s> <s xml:id="echoid-s3998" xml:space="preserve">del riceuuto; </s> <s xml:id="echoid-s3999" xml:space="preserve">ſi cauerà <lb/>il minore dal maggiore e reſterà quello che ſi hauerà d’haue <lb/>re; </s> <s xml:id="echoid-s4000" xml:space="preserve">Verbi gratia la ſomma del de hauere, è bracc. </s> <s xml:id="echoid-s4001" xml:space="preserve">12, onc. <lb/></s> <s xml:id="echoid-s4002" xml:space="preserve">5, & </s> <s xml:id="echoid-s4003" xml:space="preserve">quello ch’è riceuuto, ſono brac. </s> <s xml:id="echoid-s4004" xml:space="preserve">12, onc. </s> <s xml:id="echoid-s4005" xml:space="preserve">4; </s> <s xml:id="echoid-s4006" xml:space="preserve">Onde eſſen-<lb/>do minore il receuuto, di quello che s’ha d’hauere; </s> <s xml:id="echoid-s4007" xml:space="preserve">ſi caue- <pb o="54" file="233" n="233" rhead="SECONDO"/> ran bracc. </s> <s xml:id="echoid-s4008" xml:space="preserve">12, onc. </s> <s xml:id="echoid-s4009" xml:space="preserve">4, da bracc. </s> <s xml:id="echoid-s4010" xml:space="preserve">12, onc. </s> <s xml:id="echoid-s4011" xml:space="preserve">5, reſterà onc. </s> <s xml:id="echoid-s4012" xml:space="preserve">1, adun <lb/>que ſi deue hauer di diſcaduta un’oncia, & </s> <s xml:id="echoid-s4013" xml:space="preserve">perche la ſomma <lb/>delle miſure, che ſono fra l’vna ſtatione & </s> <s xml:id="echoid-s4014" xml:space="preserve">l’altra, ſono ca-<lb/>uezzi 59, brac. </s> <s xml:id="echoid-s4015" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4016" xml:space="preserve">5, ſi darà a cau. </s> <s xml:id="echoid-s4017" xml:space="preserve">59, brac. </s> <s xml:id="echoid-s4018" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4019" xml:space="preserve">5, di <lb/>diſcaduta intorno a onc. </s> <s xml:id="echoid-s4020" xml:space="preserve">2, e meza, & </s> <s xml:id="echoid-s4021" xml:space="preserve">le 2, e meza, ſi piglia-<lb/>no, perche è coſtume di dar d’ogni cauezzi 100, di lunghez <lb/>za onc. </s> <s xml:id="echoid-s4022" xml:space="preserve">4, di diſcaduta, & </s> <s xml:id="echoid-s4023" xml:space="preserve">per ciò ſi danno a cauezzi 59, brac. <lb/></s> <s xml:id="echoid-s4024" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4025" xml:space="preserve">5, intorno ad onc. </s> <s xml:id="echoid-s4026" xml:space="preserve">2, emeza, & </s> <s xml:id="echoid-s4027" xml:space="preserve">con onc. </s> <s xml:id="echoid-s4028" xml:space="preserve">1, che di ſo-<lb/>pra ſi haueua di differenza del hauere, & </s> <s xml:id="echoid-s4029" xml:space="preserve">riceuuto faranno <lb/>onc. </s> <s xml:id="echoid-s4030" xml:space="preserve">3, e meza, & </s> <s xml:id="echoid-s4031" xml:space="preserve">tanto ſi darà di diſcaduta dal punto <emph style="sc">D</emph>, al <lb/>punto 0, doue ſi condurrà l’acqua. </s> <s xml:id="echoid-s4032" xml:space="preserve">Et per ſapere a parte, per <lb/>parte, il modo che ſi deue tener per cauare il vaſo, per cui ſi <lb/>condurrà l’acqua, ſi cominciarà dalla prima ſtatione, alla <lb/>ſeconda, & </s> <s xml:id="echoid-s4033" xml:space="preserve">ſi trouerà che ſono onc. </s> <s xml:id="echoid-s4034" xml:space="preserve">6, & </s> <s xml:id="echoid-s4035" xml:space="preserve">tanto ſi cauerà al li-<lb/>uello, con quaſi un’onc. </s> <s xml:id="echoid-s4036" xml:space="preserve">di più per la lunghezza ch’è fra la <lb/>prima, & </s> <s xml:id="echoid-s4037" xml:space="preserve">ſeconda ſtatione; </s> <s xml:id="echoid-s4038" xml:space="preserve">poi aggiungendo onc. </s> <s xml:id="echoid-s4039" xml:space="preserve">7, a brac. </s> <s xml:id="echoid-s4040" xml:space="preserve"><lb/>3, onc. </s> <s xml:id="echoid-s4041" xml:space="preserve">10, faranno brac. </s> <s xml:id="echoid-s4042" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4043" xml:space="preserve">5, & </s> <s xml:id="echoid-s4044" xml:space="preserve">a bracc. </s> <s xml:id="echoid-s4045" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4046" xml:space="preserve">5, ſi ag-<lb/>giungerà quaſi vn’oncia di deſcaduta per la diſtanza ch’è <lb/>fra la ſeconda, & </s> <s xml:id="echoid-s4047" xml:space="preserve">terza ſtatione, che ſaranno brac. </s> <s xml:id="echoid-s4048" xml:space="preserve">4, oncie 6, <lb/>& </s> <s xml:id="echoid-s4049" xml:space="preserve">di brac. </s> <s xml:id="echoid-s4050" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4051" xml:space="preserve">6, ſi caueran bracc. </s> <s xml:id="echoid-s4052" xml:space="preserve">3, onc. </s> <s xml:id="echoid-s4053" xml:space="preserve">11, & </s> <s xml:id="echoid-s4054" xml:space="preserve">reſteran <lb/>onc. </s> <s xml:id="echoid-s4055" xml:space="preserve">7, & </s> <s xml:id="echoid-s4056" xml:space="preserve">onc. </s> <s xml:id="echoid-s4057" xml:space="preserve">7, ſi cauera dalla ſeconda ſtatione alla terza, <lb/>di terreno ſeguendo il piano ch’è fra la prima & </s> <s xml:id="echoid-s4058" xml:space="preserve">ſeconda <lb/>ſtatione; </s> <s xml:id="echoid-s4059" xml:space="preserve">oltra di queſto ſi aggiungerà meza onc. </s> <s xml:id="echoid-s4060" xml:space="preserve">a onc. </s> <s xml:id="echoid-s4061" xml:space="preserve">7, <lb/>che faranno onc. </s> <s xml:id="echoid-s4062" xml:space="preserve">7, e meza, & </s> <s xml:id="echoid-s4063" xml:space="preserve">onc. </s> <s xml:id="echoid-s4064" xml:space="preserve">7, e meza, ſi aggiungeran <lb/>no con brac. </s> <s xml:id="echoid-s4065" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4066" xml:space="preserve">5, & </s> <s xml:id="echoid-s4067" xml:space="preserve">faranno brac. </s> <s xml:id="echoid-s4068" xml:space="preserve">5, onc. </s> <s xml:id="echoid-s4069" xml:space="preserve">0 e meza, & </s> <s xml:id="echoid-s4070" xml:space="preserve"><lb/>la meza onc. </s> <s xml:id="echoid-s4071" xml:space="preserve">che s’è aggiunta, ſiè per la diſcaduta che ſi dà <lb/>della diſtanza di cau. </s> <s xml:id="echoid-s4072" xml:space="preserve">18, bracc. </s> <s xml:id="echoid-s4073" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4074" xml:space="preserve">6, dalla terza, alla <lb/>quarta ſtatione: </s> <s xml:id="echoid-s4075" xml:space="preserve">hor cauando brac. </s> <s xml:id="echoid-s4076" xml:space="preserve">4, onc. </s> <s xml:id="echoid-s4077" xml:space="preserve">9, da bracc. </s> <s xml:id="echoid-s4078" xml:space="preserve">5, onc. </s> <s xml:id="echoid-s4079" xml:space="preserve"><lb/>0, e meza, reſteranno onc. </s> <s xml:id="echoid-s4080" xml:space="preserve">3, e meza, & </s> <s xml:id="echoid-s4081" xml:space="preserve">onc. </s> <s xml:id="echoid-s4082" xml:space="preserve">3, e meza, ſi ca-<lb/>ueran fina alla quarta ſtatione, ſeguitando il piano della ſe-<lb/>conda, & </s> <s xml:id="echoid-s4083" xml:space="preserve">terza ſtatione; </s> <s xml:id="echoid-s4084" xml:space="preserve">come di ſopra ſi è detto: </s> <s xml:id="echoid-s4085" xml:space="preserve">Il medeſi-<lb/>mo ſi farebbe ſe fuſſero più ſtationi; </s> <s xml:id="echoid-s4086" xml:space="preserve">& </s> <s xml:id="echoid-s4087" xml:space="preserve">ſe ſi voleſſe ſaper la <lb/>proportione piu propinqua del terreno, che ſi deue cauare, <lb/>ſi torrà la miſura del liuello, & </s> <s xml:id="echoid-s4088" xml:space="preserve">ſi farà come di ſopra, comin- <pb file="234" n="234" rhead="LIBRO"/> ciando dalla prima ſtatione fino al liuello, & </s> <s xml:id="echoid-s4089" xml:space="preserve">dal liuello al-<lb/>la ſeconda ſtatione; </s> <s xml:id="echoid-s4090" xml:space="preserve">& </s> <s xml:id="echoid-s4091" xml:space="preserve">ſeguitando l’ordine di mano in ma <lb/>no infino doue ſi vuol condur l’acqua, oſſeruando l’ordi-<lb/>ne di ſopra. </s> <s xml:id="echoid-s4092" xml:space="preserve">Si è detto aſſai del liuellare dell’acque; </s> <s xml:id="echoid-s4093" xml:space="preserve">hora <lb/>ſi dirà dell’ordine che ſi deetener intorno del vẽdere, ouer <lb/>comprare qualche parte d’acqua, del fabricarle bocche, & </s> <s xml:id="echoid-s4094" xml:space="preserve"><lb/>i loro vaſi.</s> <s xml:id="echoid-s4095" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div154" type="section" level="1" n="137"> <head xml:id="echoid-head170" xml:space="preserve">COME SI FABRICANO LE BOCCHE, <lb/>&i vaſi delle acque, quando ſi eſtraggon da i vaſi <lb/>maeſtrali, ò ſeriole; per venderle, ò <lb/>comprarle, à ragion di qua-<lb/>dretto, ò rota.</head> <p> <s xml:id="echoid-s4096" xml:space="preserve"><emph style="sc">Perche</emph> ſogliono la piu parte delle ſeriole maeſtrali, <lb/>lequali ò ſono cauate da groſsi fiumi, ò ſono generate dal <lb/>le vnioni di diuerſe ſortiue, eſſer diuiſe ò vendute da chi le <lb/>conducano, à chi vn quadretto, ò rota, ch’è l’iſteſſo, & </s> <s xml:id="echoid-s4097" xml:space="preserve">à <lb/>chi due, & </s> <s xml:id="echoid-s4098" xml:space="preserve">coſi diſcorrendo, ſecondo la volontà di diſpen <lb/>ſatori, ò venditori; </s> <s xml:id="echoid-s4099" xml:space="preserve">però m’è parſo di darne alcuna regola <lb/>(fra tanto che ſi darà in luce vn’opra, nella quale ſi tratterà, <lb/>del condurre, diuidere, vendere, & </s> <s xml:id="echoid-s4100" xml:space="preserve">differenze, col leuar <lb/>quelle ſi per forza di antichi, come di nuoui inſtrumenti) <lb/>& </s> <s xml:id="echoid-s4101" xml:space="preserve">maſsime quello che ſi vſa nel territorio Breſciano, ò che <lb/>ſi è vſato fin ad hora, da periti conduttieri, compartitori, <lb/>o venditori d’acque; </s> <s xml:id="echoid-s4102" xml:space="preserve">però cominciando, & </s> <s xml:id="echoid-s4103" xml:space="preserve">proponendo <lb/>che ſi voglia cauare una rota, ouer vn quadretto, d’alcuna <lb/>delle maeſtrali ſeriole, lequali ſogliono per il meno eſſere <lb/>per larghezza di bracc. </s> <s xml:id="echoid-s4104" xml:space="preserve">6, in 8, & </s> <s xml:id="echoid-s4105" xml:space="preserve">nel cui vaſo, & </s> <s xml:id="echoid-s4106" xml:space="preserve">per la piu <lb/>parte è l’acqua alta un braccio, cioè onc. </s> <s xml:id="echoid-s4107" xml:space="preserve">12; </s> <s xml:id="echoid-s4108" xml:space="preserve">Fabricaraſsi <lb/>una bocca alla riua della maeſtrale ſeriola, ſecondo la diſpo <lb/>ſition del vaſo, che ſi vuol fare; </s> <s xml:id="echoid-s4109" xml:space="preserve">percioche ſe la ſeriola ca <lb/>minerà (come quaſi ſogliono tutte) ò dal Ponente in Le-<lb/>uante, ò d’Aquilone almezo dì, conſi il vaſo del quadretto, <pb o="55" file="235" n="235" rhead="SECONDO."/> ò più miſura, è forza (ſe non ui è altro oſtaculo) caminare <lb/>ſimilmente dietro il vaſo maeſtrale, quanto capiſca la miſu <lb/>ra di cauezzi 150, come ſi dirà da qui inanzi.</s> <s xml:id="echoid-s4110" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4111" xml:space="preserve">Però come è detto, fabricaraſsi il vaſo <emph style="sc">A K</emph>; </s> <s xml:id="echoid-s4112" xml:space="preserve">diſtante dal-<lb/>la maeſtrale ſeriola almeno per vn cauezzo, largo on-<lb/>cie 12, & </s> <s xml:id="echoid-s4113" xml:space="preserve">piu, e meno, ſecõdo la proportione dell’acqua, <lb/>che ſi vuol condurre, ma ſe ſi vorrà cauare due quadretti, <lb/>ſia fatto largo due braccia, & </s> <s xml:id="echoid-s4114" xml:space="preserve">ſe ſi cauerà tre quadretti, ſi <lb/>farà largo braccia tre; </s> <s xml:id="echoid-s4115" xml:space="preserve">& </s> <s xml:id="echoid-s4116" xml:space="preserve">coſi ſeguitando la larghezza, ſe-<lb/>condo la quantità de’quadretti che ſi caueranno. </s> <s xml:id="echoid-s4117" xml:space="preserve">Il fondo <lb/>di queſto vaſo nel luogo, cioè nella ſoglia <emph style="sc">B</emph>, ſarà a liuello <lb/>al fondo della ſeriola maeſtrale nel punto <emph style="sc">T</emph>, & </s> <s xml:id="echoid-s4118" xml:space="preserve"><emph style="sc">M</emph>, Nel fon-<lb/>do <emph style="sc">B</emph>, poneraſsi vna ſoglia di pietra larga, almeno on 6, con <lb/>le ſue ſponde, lequali ſieno dell’iſteſſa larghezza; </s> <s xml:id="echoid-s4119" xml:space="preserve">ma ben <lb/>ſieno tanto lunghe ch’un braccio oltra la ſoglia penetri ſot <lb/>to terra; </s> <s xml:id="echoid-s4120" xml:space="preserve">& </s> <s xml:id="echoid-s4121" xml:space="preserve">vn braccio, & </s> <s xml:id="echoid-s4122" xml:space="preserve">mezzo ſia ſopra la ſoglia. </s> <s xml:id="echoid-s4123" xml:space="preserve">lequali <lb/>ſoglia & </s> <s xml:id="echoid-s4124" xml:space="preserve">ſponde ſono coſi come moſtra la ſoglia <emph style="sc">N</emph>, & </s> <s xml:id="echoid-s4125" xml:space="preserve">le <lb/>ſponde o,</s> </p> <figure> <image file="235-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/235-01"/> </figure> <pb file="236" n="236" rhead="LIBRO"/> <p> <s xml:id="echoid-s4126" xml:space="preserve">Fatto queſto fabricaraſsivn muro di quà, & </s> <s xml:id="echoid-s4127" xml:space="preserve">di là della ri-<lb/>pa, tanto alto che ſia eguale alla ſommità del vaſo, & </s> <s xml:id="echoid-s4128" xml:space="preserve">lun-<lb/>go dal <emph style="sc">B</emph>, ſin’al <emph style="sc">A</emph>; </s> <s xml:id="echoid-s4129" xml:space="preserve">che ſarà cauezzi tre, cioè brac. </s> <s xml:id="echoid-s4130" xml:space="preserve">18, & </s> <s xml:id="echoid-s4131" xml:space="preserve">al-<lb/>tro tanto da <emph style="sc">B</emph>, ſin in <emph style="sc">C</emph>; </s> <s xml:id="echoid-s4132" xml:space="preserve">& </s> <s xml:id="echoid-s4133" xml:space="preserve">in lungo ſia ſolato il fondo frà il <lb/><emph style="sc">B</emph>, & </s> <s xml:id="echoid-s4134" xml:space="preserve"><emph style="sc">A</emph>, di laſtre di pietra uiua, ò cotta, in modo che queſta <lb/>ſolatura ſia corriſpondente per liuello al fondo <emph style="sc">T</emph>, & </s> <s xml:id="echoid-s4135" xml:space="preserve"><emph style="sc">M</emph>; </s> <s xml:id="echoid-s4136" xml:space="preserve">& </s> <s xml:id="echoid-s4137" xml:space="preserve"><lb/>queſta ſarà la prima operatione.</s> <s xml:id="echoid-s4138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4139" xml:space="preserve">Fatto tutto ciò, dalla ſoglia <emph style="sc">B</emph>, inſin’al <emph style="sc">E</emph>, miſurerai cauez <lb/>zi 50, & </s> <s xml:id="echoid-s4140" xml:space="preserve">iui ponerai la ſeconda ſoglia con li ſuoi muri di <lb/>quà, & </s> <s xml:id="echoid-s4141" xml:space="preserve">di là, lunghi per tre cauezzi, & </s> <s xml:id="echoid-s4142" xml:space="preserve">queſta ſi farà come <lb/>la prima; </s> <s xml:id="echoid-s4143" xml:space="preserve">& </s> <s xml:id="echoid-s4144" xml:space="preserve">poi dalla detta ſoglia <emph style="sc">E</emph>, miſurerai altri 50, ca-<lb/>uezzi, & </s> <s xml:id="echoid-s4145" xml:space="preserve">iui ſiponerà la terza ſoglia, che ſarà in punto <emph style="sc">H</emph>; </s> <s xml:id="echoid-s4146" xml:space="preserve">& </s> <s xml:id="echoid-s4147" xml:space="preserve"><lb/>fabricheraſsi, come la prima, & </s> <s xml:id="echoid-s4148" xml:space="preserve">ſeconda ſoglia; </s> <s xml:id="echoid-s4149" xml:space="preserve">ma auuer-<lb/>tirai, perche qui ſtà tutto il fatto dell’operatione, che la <lb/>ſoglia <emph style="sc">H</emph>, ſia più baſſa del giuſto liuello della ſoglia <emph style="sc">B</emph>, per <lb/>oncie quattro, & </s> <s xml:id="echoid-s4150" xml:space="preserve">coſi la ſeconda ſoglia <emph style="sc">E</emph>, alla ſua por-<lb/>tione. </s> <s xml:id="echoid-s4151" xml:space="preserve">Poi dalla ſoglia <emph style="sc">B</emph>, ſin’al <emph style="sc">C</emph>, ſolerai il fondo di laſtre <lb/>quanto tien il muro ſin’al <emph style="sc">C</emph>, che ſaran cauezzi 3, con la pro <lb/>portione di caduta delle on. </s> <s xml:id="echoid-s4152" xml:space="preserve">4, che ſi dà di cauezzi 100; </s> <s xml:id="echoid-s4153" xml:space="preserve">& </s> <s xml:id="echoid-s4154" xml:space="preserve"><lb/>coſi ſi farà alla ſoglia <emph style="sc">E</emph>; </s> <s xml:id="echoid-s4155" xml:space="preserve">cioè frà <emph style="sc">D</emph>, & </s> <s xml:id="echoid-s4156" xml:space="preserve"><emph style="sc">F</emph>, & </s> <s xml:id="echoid-s4157" xml:space="preserve">alla ſoglia <emph style="sc">H</emph>, frà <lb/><emph style="sc">G</emph>, & </s> <s xml:id="echoid-s4158" xml:space="preserve"><emph style="sc">K</emph>; </s> <s xml:id="echoid-s4159" xml:space="preserve">oltre paſſati altri cauezzi 50, alla ſoglia <emph style="sc">H</emph>; </s> <s xml:id="echoid-s4160" xml:space="preserve">l’acqua <lb/>di detto vaſo potrà cadere tanto quanto ſarà in piacere al <lb/>compratore, ò compartecipe, & </s> <s xml:id="echoid-s4161" xml:space="preserve">non più propinquo alla <lb/>ſoglia <emph style="sc">H</emph>.</s> <s xml:id="echoid-s4162" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4163" xml:space="preserve">La detta acqua ò quadretto, ò più quadretti, coſi con-<lb/>dotta ſarà miſurata da compratori (ſe ſarà venduta, & </s> <s xml:id="echoid-s4164" xml:space="preserve">non <lb/>diuiſa) nella ſoglia <emph style="sc">E</emph>, la doue ſe ui ſi ritrouerà l’acqua alta <lb/>onc. </s> <s xml:id="echoid-s4165" xml:space="preserve">12, ſarà giuſto il quadretto, ò più quadretti, ò rote, che <lb/>vogliam dire d’acqua; </s> <s xml:id="echoid-s4166" xml:space="preserve">Queſte miſure per il più ſi ſoglion <lb/>fare à mezzo di Maggio, Giugno, Luglio, & </s> <s xml:id="echoid-s4167" xml:space="preserve">Agoſto, & </s> <s xml:id="echoid-s4168" xml:space="preserve">nel <lb/>detto tempo ſi deue mantenere l’acqua da venditori.</s> <s xml:id="echoid-s4169" xml:space="preserve"/> </p> <pb o="56" file="237" n="237" rhead="SECONDO."/> <p> <s xml:id="echoid-s4170" xml:space="preserve">Ma ſe per caſo l’acqua nella Seriola <lb/> <anchor type="figure" xlink:label="fig-237-01a" xlink:href="fig-237-01"/> maeſtrale non fuſſe alta vn braccio, ma <lb/>ſolamente onc. </s> <s xml:id="echoid-s4171" xml:space="preserve">8, ò piu ò manco, & </s> <s xml:id="echoid-s4172" xml:space="preserve">che <lb/>per ciò nõ ſi poteſſe hauere la portiõ ſua <lb/>del quadretto, circa ciò ui ſono varie opi <lb/>nioni, fra l’altre, l’una dellequali è, che ſi <lb/>abbaſsi il fondo della ſeriola <emph style="sc">A</emph>, onc. </s> <s xml:id="echoid-s4173" xml:space="preserve">4, <lb/>di piu4; </s> <s xml:id="echoid-s4174" xml:space="preserve">del fondo della ſeriola Maeſtrale <lb/>doue ſi caua l’acqua; </s> <s xml:id="echoid-s4175" xml:space="preserve">L’altra che ſi faccia <lb/>oncie 18, larga la ſeriola, che ſi conduce <lb/>l’acqua, alla portion del quadretto; </s> <s xml:id="echoid-s4176" xml:space="preserve">Et <lb/>l’altra che diſotto alla bocca della ſerio-<lb/>la, che ſi caua, cioè in punto <emph style="sc">T</emph>, ſi faccia vn <lb/>riparo, ò briglia, ouero ingorgamento, <lb/>quel tanto che l’acqua venga alzandoſi <lb/>nella ſeriola Maeſtrale dell’onc. </s> <s xml:id="echoid-s4177" xml:space="preserve">4, cioe, <lb/>alla portion del quadretto, & </s> <s xml:id="echoid-s4178" xml:space="preserve">di queſto <lb/>ſe n’ha da fare eſperienza per le meſole, <lb/>per accreſcere, ò minuire tali ripari, co-<lb/>me farà biſogno. </s> <s xml:id="echoid-s4179" xml:space="preserve">Et dell’ordine che s ha <lb/>detto diſopra d’un quadretto, ſi deue in-<lb/>tendere d’ogn’altra quãtità d’acqua che <lb/>ſi vorrà cauare.</s> <s xml:id="echoid-s4180" xml:space="preserve"/> </p> <div xml:id="echoid-div154" type="float" level="2" n="1"> <figure xlink:label="fig-237-01" xlink:href="fig-237-01a"> <image file="237-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/237-01"/> </figure> </div> <p> <s xml:id="echoid-s4181" xml:space="preserve">L’alrra ancora, che ſe ſi ritrouaſſe l’ac <lb/>qua nella ſeriola Maeſtrale, più alta d’un <lb/>braccio, ſi farà pur il fondo <emph style="sc">A</emph>, della ſerio <lb/>la che ſi caua, alla ſuperficie del fondo <lb/>della ſerio la Maeſtrale; </s> <s xml:id="echoid-s4182" xml:space="preserve">& </s> <s xml:id="echoid-s4183" xml:space="preserve">alla bocca del <lb/>la ſeriola, oue ſi caua l’acqua dalla ſerio-<lb/>la Maeſtrale ſi ſtopperà di ſoprauia, di <lb/>eſſa bocca quel tãto che ſarà di piu d’un <lb/>brac. </s> <s xml:id="echoid-s4184" xml:space="preserve">d’altezza nella ſeriola Maeſtrale <lb/>l’acqua.</s> <s xml:id="echoid-s4185" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4186" xml:space="preserve">Delle quali opinioni, meglio & </s> <s xml:id="echoid-s4187" xml:space="preserve">piu <pb file="238" n="238" rhead="LIBRO"/> <anchor type="figure" xlink:label="fig-238-01a" xlink:href="fig-238-01"/> ſottilmente ſi trattarà in vno libro che ſi darà fuori della <lb/>ragion delle acque, come ho anco detto diſopra.</s> <s xml:id="echoid-s4188" xml:space="preserve"/> </p> <div xml:id="echoid-div155" type="float" level="2" n="2"> <figure xlink:label="fig-238-01" xlink:href="fig-238-01a"> <image file="238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/238-01"/> </figure> </div> <p> <s xml:id="echoid-s4189" xml:space="preserve">Hauendo fin qui detto aſſai del Liuellare, Vendere, & </s> <s xml:id="echoid-s4190" xml:space="preserve"><lb/>Comprare dell’acque, qui diſotto ſi moſtrerà il modo di <lb/>creſcere, & </s> <s xml:id="echoid-s4191" xml:space="preserve">minuire vna ſpina d’acque à modo d’un circo-<lb/>lo alla ſua bocca.</s> <s xml:id="echoid-s4192" xml:space="preserve"/> </p> <figure> <image file="238-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/238-02"/> </figure> <p> <s xml:id="echoid-s4193" xml:space="preserve">Sia dunque il circolo <emph style="sc">A</emph>, ilqual ſi voglia minuire, ouer <lb/>creſcere la quinta parte; </s> <s xml:id="echoid-s4194" xml:space="preserve">prima ponerò di volerlo minuire <lb/>la quinta parte; </s> <s xml:id="echoid-s4195" xml:space="preserve">ſi farà in queſto modo, pigliaraitre volte, il <lb/>diamerro di eſſo cercolo, & </s> <s xml:id="echoid-s4196" xml:space="preserve">la ſettima parte di eſſo diame-<lb/>tro, & </s> <s xml:id="echoid-s4197" xml:space="preserve">ſi farà vna ſollinea; </s> <s xml:id="echoid-s4198" xml:space="preserve">La linea <emph style="sc">D E</emph>, è tre volte il diametro <lb/>del cerchio <emph style="sc">A</emph>, poi ſi torrà vna linea eguale al diametro <emph style="sc">B, C</emph>, <lb/>& </s> <s xml:id="echoid-s4199" xml:space="preserve">tal linea ſi diuiderà in ſette parti eguali, come ſi vede qui <lb/>auanti, la linea <emph style="sc">F G</emph>, eguale al diametro del cerchio <emph style="sc">A</emph>; </s> <s xml:id="echoid-s4200" xml:space="preserve">& </s> <s xml:id="echoid-s4201" xml:space="preserve"><lb/>volendo diuidere tal linea in ſette parti eguali, ſi faran due <lb/>angoli eguali, l’uno da vna banda, & </s> <s xml:id="echoid-s4202" xml:space="preserve">l’altro dall’altra nel <lb/>capo della linea, come moſtra i due angoli <emph style="sc">H I</emph>, & </s> <s xml:id="echoid-s4203" xml:space="preserve"><emph style="sc">K L</emph>; </s> <s xml:id="echoid-s4204" xml:space="preserve">fatto <lb/>queſto ſi tirerà le due linee equidiſtanti <emph style="sc">G M</emph>, & </s> <s xml:id="echoid-s4205" xml:space="preserve"><emph style="sc">F N</emph>, & </s> <s xml:id="echoid-s4206" xml:space="preserve">dalle <lb/>due linee equidiſtanti ſi piglieranno ſei parti eguali, manco <lb/>vna di quello che ſi hauerà da diuidere la linea; </s> <s xml:id="echoid-s4207" xml:space="preserve">& </s> <s xml:id="echoid-s4208" xml:space="preserve">dai punti <pb o="57" file="239" n="239" rhead="SECONDO"/> delle diuiſioni, ſi tireranno di nuouo le linee equidiſtanti, <lb/>& </s> <s xml:id="echoid-s4209" xml:space="preserve">quelle tali linee diuideranno la linea <emph style="sc">F G</emph>, in ſette parti <lb/>eguali, come ſi vede.</s> <s xml:id="echoid-s4210" xml:space="preserve"/> </p> <figure> <image file="239-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/239-01"/> </figure> <p> <s xml:id="echoid-s4211" xml:space="preserve">Ilmedeſimo ſi farà, volendo diuidere ogn’altra linea in <pb file="240" n="240" rhead="LIBRO"/> <anchor type="figure" xlink:label="fig-240-01a" xlink:href="fig-240-01"/> quante parti ſi vorrà eguali. </s> <s xml:id="echoid-s4212" xml:space="preserve">Et vna di queſte parti ſi aggiun <lb/>gerà alla linea <emph style="sc">D E</emph>, ch’è vna delle ſette parti del diametro <lb/>del cerchio <emph style="sc">A</emph>; </s> <s xml:id="echoid-s4213" xml:space="preserve">come ſi vede qui in margine nella linèa <emph style="sc">O P</emph>, <lb/>Et la linea <emph style="sc">O P</emph>, ſarà la propinqua circonferenza del cerchio <lb/><emph style="sc">A</emph>; </s> <s xml:id="echoid-s4214" xml:space="preserve">come moſtra Archimede Siracuſano, & </s> <s xml:id="echoid-s4215" xml:space="preserve">la linea <emph style="sc">O P</emph>, ſi di <lb/>uiderà in due parti eguali in punto <emph style="sc">Q</emph>;</s> <s xml:id="echoid-s4216" xml:space="preserve"/> </p> <div xml:id="echoid-div156" type="float" level="2" n="3"> <figure xlink:label="fig-240-01" xlink:href="fig-240-01a"> <image file="240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/240-01"/> </figure> </div> <p> <s xml:id="echoid-s4217" xml:space="preserve">Poi ſi torrà la metà della linea <emph style="sc">O P</emph>; </s> <s xml:id="echoid-s4218" xml:space="preserve">che ſarà la linea <lb/> <anchor type="figure" xlink:label="fig-240-02a" xlink:href="fig-240-02"/> Et ſopra alla linea <emph style="sc">R S</emph>, ſi formerà vn quadrangolo ret-<lb/>t’angolo; </s> <s xml:id="echoid-s4219" xml:space="preserve">la lunghezza di eſſo quadrangolo ſarà eguale alla <lb/>metà della circonferenza del cerchio <emph style="sc">A</emph>; </s> <s xml:id="echoid-s4220" xml:space="preserve">& </s> <s xml:id="echoid-s4221" xml:space="preserve">ancora eguale <lb/>alla linea <emph style="sc">R S</emph>, & </s> <s xml:id="echoid-s4222" xml:space="preserve">la larghezza di eſſo quadrangolo ſarà egua <lb/>le alla metà del diametro del cerchio <emph style="sc">A</emph>, che ſarà il qua-<lb/>drangolo <emph style="sc">T V X Y</emph>; </s> <s xml:id="echoid-s4223" xml:space="preserve">& </s> <s xml:id="echoid-s4224" xml:space="preserve">il quadrangolo rett’angolo <emph style="sc">T V X Y</emph>, <lb/> <anchor type="figure" xlink:label="fig-240-03a" xlink:href="fig-240-03"/> Sarà ancora eguale al cerchio <emph style="sc">A</emph>, come moſtra Archimede <lb/>Siracuſano; </s> <s xml:id="echoid-s4225" xml:space="preserve">& </s> <s xml:id="echoid-s4226" xml:space="preserve">eſſo quadrangolo rett’angolo ſi diuiderà in <lb/>cinque parti eguali; </s> <s xml:id="echoid-s4227" xml:space="preserve">come qui drieto ſi può vedere.</s> <s xml:id="echoid-s4228" xml:space="preserve"/> </p> <div xml:id="echoid-div157" type="float" level="2" n="4"> <figure xlink:label="fig-240-02" xlink:href="fig-240-02a"> <image file="240-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/240-02"/> </figure> <figure xlink:label="fig-240-03" xlink:href="fig-240-03a"> <image file="240-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/240-03"/> </figure> </div> <p> <s xml:id="echoid-s4229" xml:space="preserve">Poi ſi pigliaran quattro di quelle parti, che ſarà il qua-<lb/>drangolo rett’angolo <emph style="sc">A B C D</emph>; </s> <s xml:id="echoid-s4230" xml:space="preserve">poi ſi allungarà il lato <emph style="sc">B D</emph>, <lb/>fina in punto <emph style="sc">E</emph>, che ſarà la linea <emph style="sc">D E</emph>, eguale alla linea <emph style="sc">D C</emph>, <lb/>& </s> <s xml:id="echoid-s4231" xml:space="preserve">la linea <emph style="sc">B E</emph>, ſi diuiderà in due parti eguali in punto <emph style="sc">F</emph>, <pb o="58" file="241" n="241" rhead="SECONDO"/> <anchor type="figure" xlink:label="fig-241-01a" xlink:href="fig-241-01"/> & </s> <s xml:id="echoid-s4232" xml:space="preserve">il punto <emph style="sc">F</emph>, ſi farà centro d’un cerchio, & </s> <s xml:id="echoid-s4233" xml:space="preserve">per la lunghez <lb/>za della linea <emph style="sc">F B</emph>, ouer della <emph style="sc">F E</emph>, ſi deſcriuerà il ſemicerchio <lb/><emph style="sc">B G E</emph>, poi ſi allungherà la linea <emph style="sc">D C</emph>, fina alla circonferenza <lb/>del ſemicerchio in punto <emph style="sc">H</emph>; </s> <s xml:id="echoid-s4234" xml:space="preserve">& </s> <s xml:id="echoid-s4235" xml:space="preserve">la linea <emph style="sc">D H</emph>, ſarà il lato del <lb/>quadrato, che ſarà eguale à i quattro quinti del cerchio <emph style="sc">A</emph>, <lb/>che ſarà il quadrato rett’angolo <emph style="sc">I K L M</emph>, & </s> <s xml:id="echoid-s4236" xml:space="preserve">il quadrato ret-<lb/>t’angolo <emph style="sc">I K L M</emph>, ſarà eguale à i quattro quinti del cerchio <emph style="sc">A</emph>,</s> </p> <div xml:id="echoid-div158" type="float" level="2" n="5"> <figure xlink:label="fig-241-01" xlink:href="fig-241-01a"> <image file="241-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/241-01"/> </figure> </div> <figure> <image file="241-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/241-02"/> </figure> <p> <s xml:id="echoid-s4237" xml:space="preserve">Hor ſi farà del quadretto <emph style="sc">I K L M</emph>, in vn cerchio; </s> <s xml:id="echoid-s4238" xml:space="preserve">in queſto <lb/>modo ſi diuiderà il lato <emph style="sc">L M</emph>, del quadrato in vndeci parti <lb/>eguali, come diſopra ſi è moſtrato & </s> <s xml:id="echoid-s4239" xml:space="preserve">come meglio qui ſe-<lb/>guente ſi potrà vedere.</s> <s xml:id="echoid-s4240" xml:space="preserve"/> </p> <pb file="242" n="242" rhead="LIBRO"/> <p> <s xml:id="echoid-s4241" xml:space="preserve">Auuertẽdo che volendo diuidere le due linee equidiſtãti <lb/>ſi potrà torre che apertura di compaſſo ſi vorrà; </s> <s xml:id="echoid-s4242" xml:space="preserve">ma che quel <lb/>le parti che ſi vorranno fare in quelle due linee equidiſtāti, <lb/>con quella apertura di compaſſo, poſſano capire ſopra del-<lb/>la carta, doue ſi vuole far l’operatione.</s> <s xml:id="echoid-s4243" xml:space="preserve"/> </p> <figure> <image file="242-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/242-01"/> </figure> <p> <s xml:id="echoid-s4244" xml:space="preserve">Hor diuiſo il lato <emph style="sc">L M</emph>, del quadrato <emph style="sc">I K L M</emph>, in vndeci <lb/>parti eguali; </s> <s xml:id="echoid-s4245" xml:space="preserve">ſi piglierà due lati del quadrato, & </s> <s xml:id="echoid-s4246" xml:space="preserve">tre parti di <lb/>quelle vndici, & </s> <s xml:id="echoid-s4247" xml:space="preserve">ſi farà vna ſol linea, come qui ſotto ſi ve-<lb/>de, <emph style="sc">N O</emph>;</s> <s xml:id="echoid-s4248" xml:space="preserve"/> </p> <figure> <image file="242-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/242-02"/> </figure> <p> <s xml:id="echoid-s4249" xml:space="preserve">Et la linea <emph style="sc">N O</emph>, ſi diuiderà in due parti eguali in punto <emph style="sc">P</emph>, <pb o="59" file="243" n="243" rhead="SECONDO."/> come qui ſotto ſi vede; </s> <s xml:id="echoid-s4250" xml:space="preserve">& </s> <s xml:id="echoid-s4251" xml:space="preserve">il punto <emph style="sc">P</emph>, ſi farà centro d’un cer-<lb/>chio, & </s> <s xml:id="echoid-s4252" xml:space="preserve">per la lunghezza della linea <emph style="sc">P N</emph>, ouer <emph style="sc">P O</emph>, ſi deſcri <lb/>uerà il ſemicerchio <emph style="sc">N R O</emph>; </s> <s xml:id="echoid-s4253" xml:space="preserve">&</s> <s xml:id="echoid-s4254" xml:space="preserve">del punto <emph style="sc">Q</emph>, ch’è la eſtremità <lb/> <anchor type="figure" xlink:label="fig-243-01a" xlink:href="fig-243-01"/> del quadrato <emph style="sc">N Q</emph>, perche <emph style="sc">N Q</emph>, è eguale al lato <emph style="sc">L M</emph>, del qua-<lb/>drato <emph style="sc">I K L M</emph>, ſi tirerà vna perpendicolare <emph style="sc">Q R</emph>; </s> <s xml:id="echoid-s4255" xml:space="preserve">& </s> <s xml:id="echoid-s4256" xml:space="preserve"><emph style="sc">Q R</emph>, ſarà <lb/>diametro del cerchio, che ſarà la quinta parte minore del <lb/>cerchio <emph style="sc">A</emph>, ch’è quello, che ſi douerà fare; </s> <s xml:id="echoid-s4257" xml:space="preserve">come qui ſotto <lb/>ſi vede.</s> <s xml:id="echoid-s4258" xml:space="preserve"/> </p> <div xml:id="echoid-div159" type="float" level="2" n="6"> <figure xlink:label="fig-243-01" xlink:href="fig-243-01a"> <image file="243-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/243-01"/> </figure> </div> <figure> <image file="243-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/243-02"/> </figure> <p> <s xml:id="echoid-s4259" xml:space="preserve">II cerchio <emph style="sc">B</emph>, ſi è i quattro quinti del cerchio <emph style="sc">A</emph>.</s> <s xml:id="echoid-s4260" xml:space="preserve"/> </p> <pb file="244" n="244" rhead="LIERO"/> <figure> <image file="244-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/244-01"/> </figure> <p> <s xml:id="echoid-s4261" xml:space="preserve">Nel cerchio <emph style="sc">A</emph>, egliè in ſcritto il cerchio <emph style="sc">B</emph>, ch’è li quat-<lb/>tro quinti del cerchio <emph style="sc">A</emph>,</s> </p> <p> <s xml:id="echoid-s4262" xml:space="preserve">Detto ſi è aſſai del minuire vna ſuperficie d’un cerchio, <lb/>hora ſi dirà del creſcerlo.</s> <s xml:id="echoid-s4263" xml:space="preserve"/> </p> <figure> <image file="244-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/244-02"/> </figure> <p> <s xml:id="echoid-s4264" xml:space="preserve">Pono dunque di volerlo creſcer la quinta parte; </s> <s xml:id="echoid-s4265" xml:space="preserve">ſi piglie <lb/>rà il cerchio <emph style="sc">A</emph>, diſopra, & </s> <s xml:id="echoid-s4266" xml:space="preserve">fatto il cerchio in vn quadrango <lb/>lo rett’angolo; </s> <s xml:id="echoid-s4267" xml:space="preserve">come di ſopra s’è inſegnato; </s> <s xml:id="echoid-s4268" xml:space="preserve">che ſarà il qua <lb/>drangolo rettangolo <emph style="sc">B C D E</emph>;</s> <s xml:id="echoid-s4269" xml:space="preserve"> <pb o="60" file="245" n="245" rhead="SECONDO."/> <anchor type="figure" xlink:label="fig-245-01a" xlink:href="fig-245-01"/> Et il quadrangolo rett’angolo, ſi diuiderà in cinque parti <lb/>eguali, come moſtra il quadrangolo rett’angolo <emph style="sc">F G H I</emph>, <lb/> <anchor type="figure" xlink:label="fig-245-02a" xlink:href="fig-245-02"/> Et poi al quadrangolo rett’angolo <emph style="sc">F G H I</emph>, ſi aggiũgerà vna <lb/>di quelle parti; </s> <s xml:id="echoid-s4270" xml:space="preserve">come moſtra il quadrangolo rett’angolo <lb/><emph style="sc">K L M N</emph>.</s> <s xml:id="echoid-s4271" xml:space="preserve"/> </p> <div xml:id="echoid-div160" type="float" level="2" n="7"> <figure xlink:label="fig-245-01" xlink:href="fig-245-01a"> <image file="245-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/245-01"/> </figure> <figure xlink:label="fig-245-02" xlink:href="fig-245-02a"> <image file="245-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/245-02"/> </figure> </div> <figure> <image file="245-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/245-03"/> </figure> <p> <s xml:id="echoid-s4272" xml:space="preserve">Fatto queſto ſi allungarà il lato <emph style="sc">M N</emph>, fina in punto <emph style="sc">O</emph>, che <lb/>la linea <emph style="sc">N O</emph>, ſia eguale alla linea <emph style="sc">N L</emph>, lato del quadrangolo: <lb/></s> <s xml:id="echoid-s4273" xml:space="preserve">come qui dietro in figura ſi vede.</s> <s xml:id="echoid-s4274" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4275" xml:space="preserve">Oltra di queſto ſi diuiderà la linea in due parti eguali in <lb/>punto <emph style="sc">P</emph>; </s> <s xml:id="echoid-s4276" xml:space="preserve">Poi ſi farà centro d’un cerchio il punto <emph style="sc">P</emph>, & </s> <s xml:id="echoid-s4277" xml:space="preserve">ſi de <lb/>ſcriuerà il ſemicerchio <emph style="sc">M Q O</emph>, come qui ſeguente ſi vede <pb file="246" n="246" rhead="LIBRO"/> <anchor type="figure" xlink:label="fig-246-01a" xlink:href="fig-246-01"/> Poi ſi allungarà il lato <emph style="sc">L N</emph>, fin in pũto <emph style="sc">Q</emph>; </s> <s xml:id="echoid-s4278" xml:space="preserve">coſi la linea <emph style="sc">N Q</emph>, ſarà <lb/>lato del quadrato, che ſarà eguale al quadrangolo rett’an-<lb/>golo <emph style="sc">K L M N</emph>, che ſarà il quadrato rett’angolo <emph style="sc">R S T V</emph>, & </s> <s xml:id="echoid-s4279" xml:space="preserve">del <lb/>quadrato rett’angolo <emph style="sc">R S T V</emph>; </s> <s xml:id="echoid-s4280" xml:space="preserve">ſi farà in vn cerchio, come di <lb/>ſopra s’è moſtrato, del lato del quadrato <emph style="sc">I K L M</emph>.</s> <s xml:id="echoid-s4281" xml:space="preserve"/> </p> <div xml:id="echoid-div161" type="float" level="2" n="8"> <figure xlink:label="fig-246-01" xlink:href="fig-246-01a"> <image file="246-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/246-01"/> </figure> </div> <figure> <image file="246-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/246-02"/> </figure> <pb o="61" file="247" n="247" rhead="SECONDO."/> <p> <s xml:id="echoid-s4282" xml:space="preserve">Il lato del quadrato ſiè diuiſo in vndici parti eguali; </s> <s xml:id="echoid-s4283" xml:space="preserve">poi ſi <lb/>è tolto due volte il lato del quadrato, có tre di quelle parti <lb/>del lato del quadrato, che s’è diuiſo in vndeci parti eguali, <lb/> <anchor type="figure" xlink:label="fig-247-01a" xlink:href="fig-247-01"/> & </s> <s xml:id="echoid-s4284" xml:space="preserve">s’è fatto vna ſol linea, come moſtra la linea <emph style="sc">X Y</emph>; </s> <s xml:id="echoid-s4285" xml:space="preserve">& </s> <s xml:id="echoid-s4286" xml:space="preserve">la li-<lb/>nea <emph style="sc">X Y</emph>, ſi diuiderà in due parti eguali in punto <emph style="sc">Z</emph>; </s> <s xml:id="echoid-s4287" xml:space="preserve">& </s> <s xml:id="echoid-s4288" xml:space="preserve">il punto <lb/><emph style="sc">Z</emph>, ſi farà centro d’un cerchio, & </s> <s xml:id="echoid-s4289" xml:space="preserve">per la lunghezza della li-<lb/>nea <emph style="sc">Z X</emph>, ouer <emph style="sc">Z Y</emph>, ſi deſcriuerà il ſemicercolo <emph style="sc">X</emph> & </s> <s xml:id="echoid-s4290" xml:space="preserve"><emph style="sc">Y</emph>; </s> <s xml:id="echoid-s4291" xml:space="preserve">et del <lb/>la eſtremità ε, della linea ε <emph style="sc">Y</emph>, ch’è eguale allato del qua-<lb/>drato, ſi tirerà vna perpendicolare, che ſarà la linea ε &</s> <s xml:id="echoid-s4292" xml:space="preserve">; <lb/>et la linea ε &</s> <s xml:id="echoid-s4293" xml:space="preserve">, ſarà il diametro del cerchio, che ſarà egua <lb/>le al quadrangolo rett’angolo <emph style="sc">K L M N</emph>, & </s> <s xml:id="echoid-s4294" xml:space="preserve">al quadrato <emph style="sc">G</emph>, che <lb/>ſarà il cercolo <emph style="sc">E</emph>;</s> <s xml:id="echoid-s4295" xml:space="preserve"/> </p> <div xml:id="echoid-div162" type="float" level="2" n="9"> <figure xlink:label="fig-247-01" xlink:href="fig-247-01a"> <image file="247-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/247-01"/> </figure> </div> <pb file="248" n="248" rhead="LIBRO"/> <figure> <image file="248-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/248-01"/> </figure> <p> <s xml:id="echoid-s4296" xml:space="preserve">Et il cercolo <emph style="sc">E</emph>, ſarà vn quinto maggiore del cercolo <emph style="sc">A</emph>; </s> <s xml:id="echoid-s4297" xml:space="preserve">che <lb/>quello che ſi doueua fare. </s> <s xml:id="echoid-s4298" xml:space="preserve">Hor ſi ſcriuerà il cerchio <emph style="sc">A</emph>, nel <lb/>cerchio <emph style="sc">E</emph>; </s> <s xml:id="echoid-s4299" xml:space="preserve">come ſi vede: </s> <s xml:id="echoid-s4300" xml:space="preserve">& </s> <s xml:id="echoid-s4301" xml:space="preserve">queſto ſcriuere vn cerchio in <lb/>vn’altro ſi fa ſolo, per far vedere quello che manca, & </s> <s xml:id="echoid-s4302" xml:space="preserve">cre <lb/>ſce, minuendo, ouer creſcendo vna parte del cerchio; </s> <s xml:id="echoid-s4303" xml:space="preserve">mo-<lb/>ſtrato diſopra il minuire, & </s> <s xml:id="echoid-s4304" xml:space="preserve">creſcere vna quinta parte d’un <lb/>cerchio; </s> <s xml:id="echoid-s4305" xml:space="preserve">il medeſimo ſi potrà fare volendo minuire, ouer <lb/>creſcere qualunque altra parte, per lo ammaeſtramento in-<lb/>ſegnato diſopra.</s> <s xml:id="echoid-s4306" xml:space="preserve"/> </p> <pb o="62" file="249" n="249" rhead="SECONDO"/> </div> <div xml:id="echoid-div164" type="section" level="1" n="138"> <head xml:id="echoid-head171" xml:space="preserve">REGOLA PER SAPERE QVANTA</head> <head xml:id="echoid-head172" xml:space="preserve">proportione creſce, & calla d’acqua <lb/>vna Seriola.</head> <p> <s xml:id="echoid-s4307" xml:space="preserve">Volendo ſapere, quanto creſce vna parte d’acqua cor-<lb/>rendo però eſſa acqua proportionalmente cauandola fuori <lb/>d’una ſeriola, ouer altro vaſo, per il creſcere che fa la detta <lb/>ſeriola, ouer altro vaſo, ſi farà in queſto modo, ponendo che <lb/>ſi caui vna parte d’acqua, che ſia quadretti quattro, & </s> <s xml:id="echoid-s4308" xml:space="preserve">ſia al <lb/>ta l’acqua nel vaſo, ouer ſeriola oncie 5; </s> <s xml:id="echoid-s4309" xml:space="preserve">& </s> <s xml:id="echoid-s4310" xml:space="preserve">ſe occorre che <lb/>ad eſſo vaſo, ouer ſeriola, creſca alta l’acqua vn’oncia di <lb/>piu delle oncie 5, volendo ſaper quanto è l’altezza dell’ac-<lb/>qua nella ſeriola, che ſiè ſuppoſta alta oncie 5, ſi numerarà <lb/>da vno fin’a 5; </s> <s xml:id="echoid-s4311" xml:space="preserve">Al medeſimo ſi farà <lb/> <anchor type="note" xlink:label="note-249-01a" xlink:href="note-249-01"/> coſi, ſi conterà da vno fin’a 6, come <lb/>ſi vede; </s> <s xml:id="echoid-s4312" xml:space="preserve">& </s> <s xml:id="echoid-s4313" xml:space="preserve">ſommati il numerato da <lb/>vno fin’a 5, fa 15, & </s> <s xml:id="echoid-s4314" xml:space="preserve">quello d’uno fin’ <lb/>a 6, fa 21. </s> <s xml:id="echoid-s4315" xml:space="preserve">Poi ſi dirà per la regola del <lb/>tre, ſe 15, dà quadretti 4, quanto da-<lb/>rà 21, ſi moltiplicherà 4, con 21, & </s> <s xml:id="echoid-s4316" xml:space="preserve">fa-<lb/>ranno 84, & </s> <s xml:id="echoid-s4317" xml:space="preserve">84, ſi partirà per 15, & </s> <s xml:id="echoid-s4318" xml:space="preserve"><lb/>ne venirà quadretti 5, & </s> <s xml:id="echoid-s4319" xml:space="preserve">delle cinque <lb/>parti le tre d’un qua dretto; </s> <s xml:id="echoid-s4320" xml:space="preserve">& </s> <s xml:id="echoid-s4321" xml:space="preserve">coſi ſi potrà dire che eſſendo <lb/>alzato l’acqua nella ſeriola, vn’oncia, la parte che ſi piglia <lb/>d’acqua, ancor ella ſarà creſciuta vn quadretto, & </s> <s xml:id="echoid-s4322" xml:space="preserve">delle cin <lb/>que parti le tre d’un quadretto.</s> <s xml:id="echoid-s4323" xml:space="preserve"/> </p> <div xml:id="echoid-div164" type="float" level="2" n="1"> <note position="right" xlink:label="note-249-01" xlink:href="note-249-01a" xml:space="preserve"> <lb/>1 # 1 <lb/>2 # 2 <lb/>3 # 3 <lb/>4 # 4 <lb/>5 # 5 <lb/># 6 <lb/>15 # 21 <lb/></note> </div> <p> <s xml:id="echoid-s4324" xml:space="preserve">Et con queſto ammaeſtramento ſi potrà fare volendo ve <lb/>dere quanto creſce ogn’altra parte d’acqua, per l’occaſione <lb/>che fa il creſcere del vaſo, doue ſi piglia la parte; </s> <s xml:id="echoid-s4325" xml:space="preserve">& </s> <s xml:id="echoid-s4326" xml:space="preserve">il mede-<lb/>ſimo ordine ancora ſi potrà oſſeruare ſapendo il calare del-<lb/>l’acqua, quanto ancora calerà la parte che ſi piglia. </s> <s xml:id="echoid-s4327" xml:space="preserve">Et que <lb/>ſto ſi ha da intendere, che caminando proportionalmente <lb/>tal ſeriola, ò vaſo, doue ſi caua l’acqua. </s> <s xml:id="echoid-s4328" xml:space="preserve">Con ilche facendo <lb/>fine alla preſente ſeconda parte à laude di Dio, à vtile de gli <pb file="250" n="250" rhead="LIBRO"/> huomini, & </s> <s xml:id="echoid-s4329" xml:space="preserve">à gloria, & </s> <s xml:id="echoid-s4330" xml:space="preserve">honore del ſempre mio maggior Pa <lb/>tron honorando il Sig. </s> <s xml:id="echoid-s4331" xml:space="preserve">Nicolò Barbogli, Algiſi, & </s> <s xml:id="echoid-s4332" xml:space="preserve">Gaion-<lb/>celli, con i ſuoi Signori fratelli; </s> <s xml:id="echoid-s4333" xml:space="preserve">& </s> <s xml:id="echoid-s4334" xml:space="preserve">in particolare del Signor <lb/>Capitano Giacomo, famoſo nell’arme, & </s> <s xml:id="echoid-s4335" xml:space="preserve">nelle operationi <lb/>appartenenti à vn’honorato Gentil’huomo di guerra; </s> <s xml:id="echoid-s4336" xml:space="preserve">co-<lb/>me eſpreſſamente ne ha datto ſegno (oltre l’altre coſe ſue <lb/>ſegnalate) in queſte impreſe contra Turchi, nel ſeruitio de <lb/>gli Illuſtriſsimi Signori Venetiani; </s> <s xml:id="echoid-s4337" xml:space="preserve">doue per la fede & </s> <s xml:id="echoid-s4338" xml:space="preserve">per <lb/>la gran deuotione di ſeruir i ſuoi Patroni, fu fatto prigione <lb/>da eſsi Turchi; </s> <s xml:id="echoid-s4339" xml:space="preserve">ma col ſuo prudente ingegno s’è poi anco <lb/>(merce Diuina) dalle loro crude mani liberato; </s> <s xml:id="echoid-s4340" xml:space="preserve">quantun-<lb/>que ne ibeni di fortuna gli ſia ſtata grandiſs. </s> <s xml:id="echoid-s4341" xml:space="preserve">perdita; </s> <s xml:id="echoid-s4342" xml:space="preserve">ma do <lb/>ue hoggidi i pari ſuoi può meglio impiegare la ſua vita, le <lb/>virtù ſue, & </s> <s xml:id="echoid-s4343" xml:space="preserve">le ſue ricchezze di quel che ha fatto lui, poi che <lb/>tutte queſte coſe egli ha eſpoſte ſolo per Chriſto, per la fe-<lb/>de, & </s> <s xml:id="echoid-s4344" xml:space="preserve">per la Patria? </s> <s xml:id="echoid-s4345" xml:space="preserve">Il Signor ancora Gio: </s> <s xml:id="echoid-s4346" xml:space="preserve">Battiſta, & </s> <s xml:id="echoid-s4347" xml:space="preserve">il Si <lb/>gnor Gioſefo ambi ſuoi fratelli, non meno meritano lode, <lb/>& </s> <s xml:id="echoid-s4348" xml:space="preserve">honore; </s> <s xml:id="echoid-s4349" xml:space="preserve">ma non mi ſentendo io ſufficiente a lodarli a ba <lb/>ſtan za dirò ſolo, che eſsi, & </s> <s xml:id="echoid-s4350" xml:space="preserve">gli altri due inſieme ſono Gen-<lb/>til’huomini tali, che illuſtrano colle ſue virtù la ſua Città <lb/>honorata di Breſcia, dellaquale ſono honorati Cittadini, <lb/>& </s> <s xml:id="echoid-s4351" xml:space="preserve">nobili; </s> <s xml:id="echoid-s4352" xml:space="preserve">iquali per ſtar alieni dalle ambitioni vulgari, ha-<lb/>bitano hora nella amena, & </s> <s xml:id="echoid-s4353" xml:space="preserve">felice terra di Louere, nella-<lb/>quale il Signor Dio li conſerui lieti, & </s> <s xml:id="echoid-s4354" xml:space="preserve">felici.</s> <s xml:id="echoid-s4355" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div166" type="section" level="1" n="139"> <head xml:id="echoid-head173" xml:space="preserve">IL FINE.</head> <pb file="251" n="251" rhead="TAVOLA DELLE COSE CONTENVTE"/> </div> <div xml:id="echoid-div167" type="section" level="1" n="140"> <head xml:id="echoid-head174" xml:space="preserve">nella preſente Opera.</head> <figure> <image file="251-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/251-01"/> </figure> <p style="it"> <s xml:id="echoid-s4356" xml:space="preserve">ALLA prima carta, nella ſeconda ſaccia fina a carte 14 <lb/>gliè del miſurare le muraglie, in più modi.</s> <s xml:id="echoid-s4357" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4358" xml:space="preserve">Da carte 14, fino à carte 26, gliè del miſurare le <lb/>Biade in più modi.</s> <s xml:id="echoid-s4359" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4360" xml:space="preserve">Da carte 26, fino a carte 27, gliè il miſurare del Vino, <lb/>& </s> <s xml:id="echoid-s4361" xml:space="preserve">delle Biade, con le tauole.</s> <s xml:id="echoid-s4362" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4363" xml:space="preserve">Da carte 27, fino a carte 32, gliè le Tauole da miſurar le Biade in Pira-<lb/>mida, & </s> <s xml:id="echoid-s4364" xml:space="preserve">il Vino nelle Botte.</s> <s xml:id="echoid-s4365" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4366" xml:space="preserve">Da carte 32, fino a carte 34, gliè del miſurare le Biade in Piramide il Vi/<unsure/> <lb/>no nelle Botte, & </s> <s xml:id="echoid-s4367" xml:space="preserve">nelli tinazzi, non tanto per le Tauole, come ancor <lb/>in piu prattiche.</s> <s xml:id="echoid-s4368" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4369" xml:space="preserve">Da carte 34, fino a carte 38, gliè da formare la Bacchetta doue s’im-<lb/>botta, il miſurare le Biade in Piramida, & </s> <s xml:id="echoid-s4370" xml:space="preserve">in triangolo, & </s> <s xml:id="echoid-s4371" xml:space="preserve">il Vino nel-<lb/>le Botte; </s> <s xml:id="echoid-s4372" xml:space="preserve">col miſurar’ un ſacco di grano, & </s> <s xml:id="echoid-s4373" xml:space="preserve">in una caſſa, & </s> <s xml:id="echoid-s4374" xml:space="preserve">nelli tinaz-<lb/>zi, con le tauole, & </s> <s xml:id="echoid-s4375" xml:space="preserve">per prattica.</s> <s xml:id="echoid-s4376" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4377" xml:space="preserve">Da carte 38, fino a cartte 43, gliè il miſurar del uino quanto è ſemmo in <lb/>una botta, con le tauole, & </s> <s xml:id="echoid-s4378" xml:space="preserve">per prattica.</s> <s xml:id="echoid-s4379" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4380" xml:space="preserve">Da carte 43, fino a carte 49, gliè il miſurare del fieno in più modi.</s> <s xml:id="echoid-s4381" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4382" xml:space="preserve">A carte 49, gliè il miſurare le aßi, & </s> <s xml:id="echoid-s4383" xml:space="preserve">le legne.</s> <s xml:id="echoid-s4384" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4385" xml:space="preserve">A carte 51. </s> <s xml:id="echoid-s4386" xml:space="preserve">gliè il liuellare dell’ acque.</s> <s xml:id="echoid-s4387" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4388" xml:space="preserve">A carte 54, gliè il modo da formare le meſole, & </s> <s xml:id="echoid-s4389" xml:space="preserve">le ſoglie dell’acque.</s> <s xml:id="echoid-s4390" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4391" xml:space="preserve">A carte 56, giè il modo, che s’inſegna a creſcere, ouero minuire una ſpi-<lb/>na d’acqua.</s> <s xml:id="echoid-s4392" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div168" type="section" level="1" n="141"> <head xml:id="echoid-head175" xml:space="preserve">IL FINE.</head> <figure> <image file="251-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/251-02"/> </figure> <pb file="252" n="252" rhead="ERRORI OCCORSI."/> <p> <s xml:id="echoid-s4393" xml:space="preserve">A carte 3. </s> <s xml:id="echoid-s4394" xml:space="preserve">prima faccia, righe 13. </s> <s xml:id="echoid-s4395" xml:space="preserve">oue dice quadretti, ſi dica paſsi.</s> <s xml:id="echoid-s4396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4397" xml:space="preserve">Nella terza, & </s> <s xml:id="echoid-s4398" xml:space="preserve">quarta figura gli mancano le lettere.</s> <s xml:id="echoid-s4399" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4400" xml:space="preserve">A car. </s> <s xml:id="echoid-s4401" xml:space="preserve">12. </s> <s xml:id="echoid-s4402" xml:space="preserve">fac. </s> <s xml:id="echoid-s4403" xml:space="preserve">2. </s> <s xml:id="echoid-s4404" xml:space="preserve">nella prima riga gli manca ſarà.</s> <s xml:id="echoid-s4405" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4406" xml:space="preserve">A car. </s> <s xml:id="echoid-s4407" xml:space="preserve">13. </s> <s xml:id="echoid-s4408" xml:space="preserve">fac. </s> <s xml:id="echoid-s4409" xml:space="preserve">2. </s> <s xml:id="echoid-s4410" xml:space="preserve">righe 1. </s> <s xml:id="echoid-s4411" xml:space="preserve">ſeſti, dica ſettimi.</s> <s xml:id="echoid-s4412" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4413" xml:space="preserve">A car. </s> <s xml:id="echoid-s4414" xml:space="preserve">14. </s> <s xml:id="echoid-s4415" xml:space="preserve">fac. </s> <s xml:id="echoid-s4416" xml:space="preserve">1. </s> <s xml:id="echoid-s4417" xml:space="preserve">righe 20. </s> <s xml:id="echoid-s4418" xml:space="preserve">s’e detto, dica ſi dirà.</s> <s xml:id="echoid-s4419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4420" xml:space="preserve">A car. </s> <s xml:id="echoid-s4421" xml:space="preserve">15. </s> <s xml:id="echoid-s4422" xml:space="preserve">fac. </s> <s xml:id="echoid-s4423" xml:space="preserve">2. </s> <s xml:id="echoid-s4424" xml:space="preserve">alla moltiplicatione ſotto la proua, li mancala moltiplica-<lb/>tione dion. </s> <s xml:id="echoid-s4425" xml:space="preserve">2, con on. </s> <s xml:id="echoid-s4426" xml:space="preserve">7, che fanno punti 14.</s> <s xml:id="echoid-s4427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4428" xml:space="preserve">A car. </s> <s xml:id="echoid-s4429" xml:space="preserve">17. </s> <s xml:id="echoid-s4430" xml:space="preserve">fac. </s> <s xml:id="echoid-s4431" xml:space="preserve">1. </s> <s xml:id="echoid-s4432" xml:space="preserve">righe 5. </s> <s xml:id="echoid-s4433" xml:space="preserve">gli manca la i<unsure/>l<unsure/>nea, che ha da ſeparar il conto del-<lb/>la ſomma.</s> <s xml:id="echoid-s4434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4435" xml:space="preserve">A car. </s> <s xml:id="echoid-s4436" xml:space="preserve">20. </s> <s xml:id="echoid-s4437" xml:space="preserve">fac. </s> <s xml:id="echoid-s4438" xml:space="preserve">2. </s> <s xml:id="echoid-s4439" xml:space="preserve">righe 12. </s> <s xml:id="echoid-s4440" xml:space="preserve">detto aſſai del far i conti delle Biade, dica, detto <lb/>aſſai del miſurar le Biade in quadrangolo, col far i conti; </s> <s xml:id="echoid-s4441" xml:space="preserve">qui.</s> <s xml:id="echoid-s4442" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4443" xml:space="preserve">A car. </s> <s xml:id="echoid-s4444" xml:space="preserve">22. </s> <s xml:id="echoid-s4445" xml:space="preserve">fac. </s> <s xml:id="echoid-s4446" xml:space="preserve">1. </s> <s xml:id="echoid-s4447" xml:space="preserve">righe 18. </s> <s xml:id="echoid-s4448" xml:space="preserve">nella ſomma della ſettima ragione, coppi 2. <lb/></s> <s xml:id="echoid-s4449" xml:space="preserve">dica, coppi 1.</s> <s xml:id="echoid-s4450" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4451" xml:space="preserve">A car. </s> <s xml:id="echoid-s4452" xml:space="preserve">24. </s> <s xml:id="echoid-s4453" xml:space="preserve">fac. </s> <s xml:id="echoid-s4454" xml:space="preserve">1. </s> <s xml:id="echoid-s4455" xml:space="preserve">righe 15. </s> <s xml:id="echoid-s4456" xml:space="preserve">37. </s> <s xml:id="echoid-s4457" xml:space="preserve">dica, 32.</s> <s xml:id="echoid-s4458" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4459" xml:space="preserve">A car. </s> <s xml:id="echoid-s4460" xml:space="preserve">25. </s> <s xml:id="echoid-s4461" xml:space="preserve">fac. </s> <s xml:id="echoid-s4462" xml:space="preserve">1. </s> <s xml:id="echoid-s4463" xml:space="preserve">righe 4. </s> <s xml:id="echoid-s4464" xml:space="preserve">A B C, dica A E C F,</s> </p> <p> <s xml:id="echoid-s4465" xml:space="preserve">A car. </s> <s xml:id="echoid-s4466" xml:space="preserve">35. </s> <s xml:id="echoid-s4467" xml:space="preserve">fac. </s> <s xml:id="echoid-s4468" xml:space="preserve">1. </s> <s xml:id="echoid-s4469" xml:space="preserve">righe 1. </s> <s xml:id="echoid-s4470" xml:space="preserve">golierà, dica, glierà</s> </p> <p> <s xml:id="echoid-s4471" xml:space="preserve">A car. </s> <s xml:id="echoid-s4472" xml:space="preserve">35. </s> <s xml:id="echoid-s4473" xml:space="preserve">fac. </s> <s xml:id="echoid-s4474" xml:space="preserve">1. </s> <s xml:id="echoid-s4475" xml:space="preserve">righe 2. </s> <s xml:id="echoid-s4476" xml:space="preserve">n oncie dica, no oncie.</s> <s xml:id="echoid-s4477" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4478" xml:space="preserve">A car. </s> <s xml:id="echoid-s4479" xml:space="preserve">37. </s> <s xml:id="echoid-s4480" xml:space="preserve">fac. </s> <s xml:id="echoid-s4481" xml:space="preserve">2. </s> <s xml:id="echoid-s4482" xml:space="preserve">Terzo eſſempio, dica, Secondo eſſempio, & </s> <s xml:id="echoid-s4483" xml:space="preserve">il <lb/>Secondo uà caſſo.</s> <s xml:id="echoid-s4484" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4485" xml:space="preserve">A car. </s> <s xml:id="echoid-s4486" xml:space="preserve">38. </s> <s xml:id="echoid-s4487" xml:space="preserve">fac. </s> <s xml:id="echoid-s4488" xml:space="preserve">2. </s> <s xml:id="echoid-s4489" xml:space="preserve">righe 2. </s> <s xml:id="echoid-s4490" xml:space="preserve">bella dica, della.</s> <s xml:id="echoid-s4491" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4492" xml:space="preserve">A car. </s> <s xml:id="echoid-s4493" xml:space="preserve">44. </s> <s xml:id="echoid-s4494" xml:space="preserve">fac. </s> <s xml:id="echoid-s4495" xml:space="preserve">2. </s> <s xml:id="echoid-s4496" xml:space="preserve">righa ultima, i quadretti 579. </s> <s xml:id="echoid-s4497" xml:space="preserve">dica, quadretti 579. </s> <s xml:id="echoid-s4498" xml:space="preserve">one. </s> <s xml:id="echoid-s4499" xml:space="preserve">6. <lb/></s> <s xml:id="echoid-s4500" xml:space="preserve">punti 11. </s> <s xml:id="echoid-s4501" xml:space="preserve">atomi 8.</s> <s xml:id="echoid-s4502" xml:space="preserve"/> </p> <figure> <image file="252-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/252-01"/> </figure> <pb file="253" n="253" rhead="IN BRESCIA,"/> </div> <div xml:id="echoid-div169" type="section" level="1" n="142"> <head xml:id="echoid-head176" xml:space="preserve">APPRESSO VICENZO SABBIO;</head> <head xml:id="echoid-head177" xml:space="preserve">Ad inſtantia di Franceſco, t<unsure/> Piet: Maria <lb/>di Marchetti, Fratelli.</head> <head xml:id="echoid-head178" xml:space="preserve">M. D. LXXII.</head> <pb file="254" n="254"/> <pb file="255" n="255"/> <pb file="256" n="256"/> <pb file="257" n="257"/> <handwritten/> <pb file="258" n="258"/> </div></text> </echo>