Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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EPISTOL AE.
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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div758" type="section" level="3" n="44">
              <div xml:id="echoid-div758" type="letter" level="4" n="1">
                <pb o="409" rhead="EPISTOL AE." n="421" file="0421" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0421"/>
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            <div xml:id="echoid-div762" type="section" level="3" n="45">
              <div xml:id="echoid-div762" type="letter" level="4" n="1">
                <head xml:id="echoid-head568" xml:space="preserve">SOLVTIO CVIVSDAM QVÆSITI.</head>
                <head xml:id="echoid-head569" style="it" xml:space="preserve">Magnifico Ludouico Fauzzoni amico cariβimo.</head>
                <p>
                  <s xml:id="echoid-s4890" xml:space="preserve">TVI quæſiti ſolutio quam neſcio quis te docuit, valde diuerſa eſt à vera.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4891" xml:space="preserve">quæſitum enim tale fuit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4892" xml:space="preserve">Reperiuntur quatuor ſocij, Ludouicus, Hieronymus, Franciſcus, & Lau
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                  rentius quorum primus, Ludouicus ſcilicet, poſuit aureos .6000. Hierony
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                  mus verò aureos .5000. Franciſcus autem .2000. & Laurentius .1000. quorum ſum-
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                  ma faciebat aureos .14000. </s>
                  <s xml:id="echoid-s4893" xml:space="preserve">interim tamen de tali ſumma Ludouicus recepit aureos
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                  2000. Hieronymus verò .1000. Franciſcus autem .900. & Laurentius .800. quapro-
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                  pter in ſumma reſidua Ludouicus non habebat niſi aureos .4000. Hieronymus
                    <reg norm="etiam" type="context">etiã</reg>
                    <lb/>
                  4000. Franciſcus .1100. & Laurentius .200. quorum ſumma erat .9300. </s>
                  <s xml:id="echoid-s4894" xml:space="preserve">Nunc au-
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                  tem iſti ſocij cupiunt augere hanc ſummam per aureos .20000. tali tamen conditio-
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                  ne quod quilibet tantum tribuat vt in totali ſumma, tantam partem unus habeat,
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                  quantam alter.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4895" xml:space="preserve">Hoc autem problema tam ſacile eſt, & cum ſuo theoremate ita coniunctum, quod
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                  miror amicum noſtrum illud illico non vidiſſe.</s>
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                <p>
                  <s xml:id="echoid-s4896" xml:space="preserve">Accipe igitur illos aureos .20000. & eos collige cum ſumma .9300. vnde habebis
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                  aureos .29300. pro
                    <reg norm="summa" type="context">sũma</reg>
                  totali, cuius quarta pars erit .7325.
                    <reg norm="quam" type="context">quã</reg>
                    <reg norm="vnuſquisque" type="simple">vnuſquisq;</reg>
                  poſtea
                    <lb/>
                  habebit in dicta ſumma. </s>
                  <s xml:id="echoid-s4897" xml:space="preserve">Sed ut reperias quantitatem aureorum quam quilibet
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                  prius debet contribuere, vt poſtea habeat aureos .7325. in dicta ſocietate. </s>
                  <s xml:id="echoid-s4898" xml:space="preserve">Iubeo,
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                  vt Ludouicus demat illos aureos .4000. quos demum habebat, ex .7325. reliquum
                    <lb/>
                  autem erit .3325. qui quidem numerus erit aureorum nunc contribuendorum ipſius
                    <lb/>
                  Ludouici. </s>
                  <s xml:id="echoid-s4899" xml:space="preserve">Demptis ſimiliter aureis .4000. ex dictis .7325.
                    <reg norm="remanebunt" type="context">remanebũt</reg>
                  .3325. pro con
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                  tributione ipſius Hieronymi. </s>
                  <s xml:id="echoid-s4900" xml:space="preserve">Deinde ſi ex .7325. extracti fuerint aurei .1100. relin-
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                  quent .6225. pro contributione Franciſci. </s>
                  <s xml:id="echoid-s4901" xml:space="preserve">Demptis demum .200. ex .7325. reſidui
                    <lb/>
                  erunt .7125. pro contributione Laurentij, & ſic quilibet habebit æqualem portio-
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                  nem in totaliſumma.</s>
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              <div xml:id="echoid-div763" type="letter" level="4" n="2">
                <head xml:id="echoid-head570" style="it" xml:space="preserve">Speculatio cuiuſdam Methodire ductionis numiſmatum
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                unius ſpeciei in aliam.</head>
                <head xml:id="echoid-head571" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4902" xml:space="preserve">MIrum tibi videtur quo pacto verum ſit, quod ſumma
                    <reg norm="mendietatis" type="context">mẽdietatis</reg>
                  cuiuſuis
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                  numeri illorum numiſmatum, quæ hic vocantur Blanci, cum ſexta parte eiuſ
                    <lb/>
                  dem medietatis, ſemper ſit numerus florenorum huius prouinciæ. </s>
                  <s xml:id="echoid-s4903" xml:space="preserve">Vt exempli gra
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                  tia, quotieſcunque reducere voluerimus .48. Blancos in Florenos, ſi medietati ip-
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                  ſius .48. hoc eſt .24. adiecta fuerit ſexta pars ipſius medietatis, quæ eſt .4. </s>
                  <s xml:id="echoid-s4904" xml:space="preserve">tunc habebi
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                  mus .28. & ita dicemus quod .48. Blanci conſtituunt Florenos .28. quod quidem
                    <lb/>
                  verum eſt.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4905" xml:space="preserve">Huiuſmodi autem rei ſpeculatio ita ſe habet. </s>
                  <s xml:id="echoid-s4906" xml:space="preserve">Nam vnuſquiſque Blancus diuidi-
                    <lb/>
                  tur in .7. æquales partes, quarum .12. conſtituunt vnum Florenum, horum verò nu-
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                  miſmatum communis menſura, vocatur Groſſus, vt ſcis, ex quo ſequitur, quod ſi </s>
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