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]

Table of contents

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[4.18.] Quomodo dignoſcatur proportio uelocitatis duorum ſimilium corporum omogeniorum inaqualium. CAP. XVIII.
Page: 191 (179)
[4.19.] Quam ſit inanis ab Ariſtotele ſuſcepta demonſtratio quod uacuum non detur. CAP. XIX.
Page: 191 (179)
[4.20.] Non ſatis dilucidè Ariſtotelem de loco ratiocinatum fuiße. CAP. XX.
Page: 192 (180)
[4.21.] Vtrum bene Aristoteles ſenſerit de infinito. CAP. XXI.
Page: 193 (181)
[4.22.] Exagitatur ab Ariſtotele adductatemporis definitio. CAP. XXII.
Page: 194 (182)
[4.23.] Motum rectum eſſe continuum, uel dißentiente Ariſtotele. CAP. XXIII.
Page: 195 (183)
[4.24.] Idem uir grauisſimus an bene ſenſerit de motibus corporum uiolentis & natur alibus. CAP. XXIIII.
Page: 196 (184)
[4.25.] Motum rectum & natur alem non eſſe primo & per ſe quicquid Ariſtoteli uiſum ſit. CAP. XXV.
Page: 196 (184)
[4.26.] Omne corpus eſſe in loco proprio graue, ut Aristoteli placuit, non eft admittendum. CAP. XXVI.
Page: 197 (185)
[4.27.] Haud admittendam opinionem Principis Peripateticorum de circulo, & ſpbæra. CAP. XXVII.
Page: 197 (185)
[4.28.] Occultam fuiße grauisſimo Stagirit & canſam ſcintilla-tionis ſtellarum. CAP. XXVIII.
Page: 198 (186)
[4.29.] Daricontinuum infinitum motum ſuper rectam at que finitam lineam. CAP. XXIX.
Page: 198 (186)
[4.30.] Non eſſe ſolis calorem à motu localι ipſius corporis ſolaris, ut Ariſtoteli placuit. CAP. XXX.
Page: 199 (187)
[4.31.] Vnde caloris ſolis prode at incrementum & state, et byeme decrementum. CAP. XXXI.
Page: 200 (188)
[4.32.] Nullum corpus ſenſus expers à ſono offendi, præterquam Aristoteles crediderit. CAP. XXXII.
Page: 201 (189)
[4.33.] Pytagoreorum opinionem de ſonitu corporum cælestium non fuiſſe ab Aristotele ſublatam. CAP. XXXIII.
Page: 202 (190)
[4.34.] Deraro et denſo nonnulla, minus diligenter à Peripateticis perpenſa. CAP. XXXIIII.
Page: 203 (191)
[4.35.] Motum rectum curuo poſſe comparari etiam diſentiente Ariſtotele. CAP. XXXV.
Page: 206 (194)
[4.36.] Minus ſufficienter exploſam fuiſſe ab Ariſtotele opinionem cre-dentium plures mundos exiſtere. CAP. XXXVI.
Page: 207 (195)
[4.37.] Anrectè loquutus ſit Phyloſopbus de extenſione luminis per uacuum. CAP. XXXVII.
Page: 208 (196)
[4.38.] An rectè phyloſophiœ penus Ariſtoteles ſenſerit de loco im-pellendo à pyramide. CAP. XXXVIII.
Page: 208 (196)
[4.39.] Examinatur quam ualida ſit ratio Aristotelis de inalterabilitate Cœli. CAP. XXXIX.
Page: 209 (197)
[5.] IN QVINTVM EVCLIDIS LIBRVM
Page: 210 (198)
[Item 5.1.]
Page: 210 (198)
[5.1.1.] Horum autem primum est.
Page: 210 (198)
[5.1.2.] SECVNDVM.
Page: 210 (198)
[5.1.3.] TERTIVM. Quę est εuclidis ſeptima propoſitio.
Page: 210 (198)
[5.1.4.] QVARTVM. εuclidis uerò nona propoſitio.
Page: 211 (199)
[5.1.5.] QVINTVM. Euclidis uerò octaua propoſitio.
Page: 211 (199)
[5.1.6.] SEXTVM. εuclidis uerò decima propoſitio.
Page: 211 (199)
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            <div xml:id="echoid-div266" type="math:theorem" level="3" n="139">
              <p>
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                  <var>A.I.</var>
                vnde quadratum lineæ
                  <var>.A.I.</var>
                erit .100. idem dico de quadrato lineæ
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                <s xml:id="echoid-s1220" xml:space="preserve">quare
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                ex penultima primi
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                mo ferè. </s>
                <s xml:id="echoid-s1221" xml:space="preserve">quare
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                <s xml:id="echoid-s1222" xml:space="preserve">ſed
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                ex ſuppoſi-
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                <s xml:id="echoid-s1223" xml:space="preserve">qua
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                dempta ex
                  <var>.L.A.O.</var>
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                (nam
                  <var>.L.H.</var>
                cum
                  <var>.O.M.</var>
                æquatur ipſi
                  <var>.L.O.</var>
                ex .
                  <lb/>
                35. tertij ipſius Eucli. partium .8.
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                duabus ſeptimis. cuius
                  <reg norm="dimidium" type="context">dimidiũ</reg>
                hoc eſt
                  <var>.A.H.</var>
                erit
                  <lb/>
                4. cum una ſeptima, quod eſt propoſitum. </s>
                <s xml:id="echoid-s1224" xml:space="preserve">Reſpice figuram ipſius Tartaleæ.</s>
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            <div xml:id="echoid-div268" type="math:theorem" level="3" n="140">
              <head xml:id="echoid-head159" xml:space="preserve">THEOREMA
                <num value="140">CXL</num>
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              <p>
                <s xml:id="echoid-s1225" xml:space="preserve">QVadrageſimum nonum quæſitum ſimiliter poſſumus alio modo ſoluere, vt
                  <lb/>
                putà cum vnumquodque latus rhombi ſimul cum area cognitum, ſeu datum
                  <lb/>
                nobis ſit
                  <reg norm="cognitum" type="context">cognitũ</reg>
                ſimiliter nobis erit quadratum lateris
                  <var>.a.d.</var>
                hoc eſt ſumma duorum
                  <lb/>
                quadratorum
                  <var>.a.o.</var>
                et
                  <var>.o.d.</var>
                ex penultima primi Euclid. </s>
                <s xml:id="echoid-s1226" xml:space="preserve">cúmque nobis cognita etiam
                  <lb/>
                ſit totalis ſuperficies rhombi, cognita etiam nobis erit eius medietas, hoc eſt produ-
                  <lb/>
                ctum
                  <var>.o.d.</var>
                in
                  <var>.o.a.</var>
                vnde ex methodo .37. Theorematis cognoſcemus .a
                  <unsure/>
                  <var>.o.</var>
                et
                  <var>.o.d.</var>
                & ſic
                  <lb/>
                etiam eorum dupla, quod quærebatur.</s>
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            <div xml:id="echoid-div269" type="math:theorem" level="3" n="141">
              <head xml:id="echoid-head160" xml:space="preserve">THEOREMA
                <num value="141">CXLI</num>
              .</head>
              <p>
                <s xml:id="echoid-s1227" xml:space="preserve">PVlchrum quæſitum fuit id, quod Tartalea ponit pro .18. noni libri in quarto fo-
                  <lb/>
                lio, quod huiuſmodi eſt. </s>
                <s xml:id="echoid-s1228" xml:space="preserve">Aliquis habet dolium mero plenum, ex quo
                  <lb/>
                duas vrnas extrahit ipſius vini, ſed loco ipſius vini infundit duas vrnas aquæ. </s>
                <s xml:id="echoid-s1229" xml:space="preserve">Dein
                  <lb/>
                de poſt aliquot dies extrahit iterum alias duas vrnas illius miſti, & iterum infundit
                  <lb/>
                duas vrnas aquæ, & poſt alios aliquot dies idem facit, & hac vltima tertia vice in-
                  <lb/>
                uenit aquam tantam eſſe, quantum vinum. </s>
                <s xml:id="echoid-s1230" xml:space="preserve">Quæritur nunc quot vrnas capiat il-
                  <lb/>
                lud dolium.</s>
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              <p>
                <s xml:id="echoid-s1231" xml:space="preserve">Solutio ipſius Tartaleæ bona eſt, cum ſupponat illas quatuor quantitates vini eſſe
                  <lb/>
                inuicem continuas proportionales, vt putà primò totum vinum merum, poſteà re-
                  <lb/>
                ſiduum pro ſecunda quantitate, deinde pro tertia in ſecunda, & pro quarta in ter-
                  <lb/>
                tia extractione, hoc eſt quòd proportio totius vini meri ad vinum in prima ſit, vt hu
                  <lb/>
                ius ad vinum in ſecunda, & vt huius ad vinum in tertia miſtione. </s>
                <s xml:id="echoid-s1232" xml:space="preserve">Sed quia ipſe
                  <lb/>
                non probat hanc continuam proportionalitatem ex methodo ſcientifica, mihi
                  <reg norm="visum" type="context">visũ</reg>
                  <lb/>
                eſt hoc loco illam deſcribere.</s>
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              <p>
                <s xml:id="echoid-s1233" xml:space="preserve">Cogitemus igitur
                  <var>a.u.</var>
                pro capacitate dolij, et
                  <var>.a.i.</var>
                pro quantitate duarum vrna-
                  <lb/>
                rum. </s>
                <s xml:id="echoid-s1234" xml:space="preserve">Nunc uerò ſupponamus quamlibet partem huius miſti omogeneam eſſe ſuo
                  <lb/>
                toto, quapropter ſequetur eandem proportionem eſſe vini ad aquam in qualibet
                  <lb/>
                parte, quæ erit in toto, & ideò imaginemur
                  <var>.e.o.</var>
                æqualem
                  <var>.a.i</var>
                . </s>
                <s xml:id="echoid-s1235" xml:space="preserve">Sed in puncto
                  <var>.i.</var>
                tali
                  <lb/>
                modo diuiſam, vt proportio
                  <var>.i.e.</var>
                ad
                  <var>.i.o.</var>
                eadem ſit quæ
                  <var>.i.a.</var>
                ad
                  <var>.i.u</var>
                . </s>
                <s xml:id="echoid-s1236" xml:space="preserve">Supponamus
                  <reg norm="etiam" type="context">etiã</reg>
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