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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[3.3.] Quòd quantit as cuiuſlibet ponderis, aut uirtus mouens re-ſpectu alterius quantitatis cognoſcatur beneficio perpendicularium ductarum à centro libr & ad line am inclinationis. CAP. III.
Page: 155 (143)
[3.4.] Quemadmodum exſupradictis cauſis omnes staterarum & uectium cauſæ dependeant. CAP. IIII.
Page: 156 (144)
[3.5.] De quibuſdam rebus animaduerſione dignis. CAP.V.
Page: 157 (145)
[3.6.] De ratione cuiuſdam uis adauctæ. CAP. VI.
Page: 158 (146)
[3.7.] De quibuſdam erroribus Nicolai Tartaleæ circa pondera corporum & eorum motus, quorum aliqui deſumpti fuerunt à fordano ſcriptore quodam antiquo. CAP. VII.
Page: 160 (148)
[3.8.] CAP. VIII.
Page: 161 (149)
[3.9.] Quòdſummaratione ſtateræper æqualia interualla ſint diuiſæ. CAP. IX.
Page: 163 (151)
[3.10.] Quòd line a circularis non habe at concauum cum con-uexo coniunctum, & quod Aristo. cir caproportio nes motuum aberrauerit. CAP.X.
Page: 164 (152)
[3.11.] Quod Aristo. in prima mechanicarum quæstionum eius quod inquir it, uer am cauſam non attulerit. CAP. XI.
Page: 165 (153)
[3.12.] De uer a cauſa ſecundæ, & tertiæ quæstionis mechanicæ ab Ariſtotele nonperſpecta. CAP. XII.
Page: 166 (154)
[3.13.] Quòd Ariſtotelisratio in 6. quæſtione poſit a non ſit admittenda. CAP. XIII.
Page: 167 (155)
[3.14.] Quòdrationes ab Ariſtotele de octaua quæstione confictæ ſufficient es non ſint. CAP. XIIII.
Page: 167 (155)
[3.15.] Quod Aristotelis ratio none queſtionis admittendanon ſit. CAP. XV.
Page: 171 (159)
[3.16.] Quod Aristotelis rationes de decima queſtione ſint reijciende. CAP. XVI.
Page: 171 (159)
[3.17.] De uer a cauſa .12. questionis mechanice. CAP. XVII.
Page: 172 (160)
[3.18.] De decimatertia questione. CAP. XVIII.
Page: 173 (161)
[3.19.] De decimaquart a queſtione. CAP. XIX.
Page: 173 (161)
[3.20.] De uer a r atione .17. queſtionis. CAP. XX.
Page: 174 (162)
[3.21.] De uera & intrinſeca cauſa trocble arum. CAP. XXI.
Page: 175 (163)
[3.22.] Depropria cauſa .24. quæſtionis. CAP. XXII.
Page: 177 (165)
[3.23.] De uer a cauſa .30. quæstionis. CAP. XXIIII.
Page: 179 (167)
[3.24.] Deratione .35. & ultimæ quæstionis. CAP. XXV.
Page: 179 (167)
[4.] DISPVTATIONES DE QVIBVSDAM PLACITIS ARISTOTELIS.
Page: 180 (168)
[4.1.] Qualiter & ubi Ariſtoteles de uelocitate motuum natura-lium localium aliter tractauerit quam nos ſentiamus. CAP.I.
Page: 180 (168)
[4.2.] Quædam ſupponenda ut conſtet cur circa uelocit atem motuum natur alium localium ab Ariſtotelis placitis recedamus. CAP. II.
Page: 181 (169)
[4.3.] Poſſe uelocitatem alicuius corporis proportionem contrariam in diuerſis medijs habere cum denſitate eorum. CAP. III.
Page: 182 (170)
[4.4.] Oſcitanter ab Ariſtotele nonnibil prolatum cap 8. lib. 4 Phyſicorum. CAP. IIII.
Page: 182 (170)
[4.5.] Exempla dictorum. CAP.V.
Page: 183 (171)
[4.6.] Quod proportiones ponderum eiuſdem corporis in diuerſis medijs pro portiones eorum mediorum denſit atum non ſeruant. Unde ne-ceßariò inæquales proportiones uelocitatum producuntur. CAP. VI.
Page: 184 (172)
[4.7.] Corpora grauia aut leuia eiuſdem figur æ et materiæ ſed inæqualis magnitudinis, in ſuis motibus natur alibus uelocit atis, in eo dem medio, proportionem longè diuerſam ſeruatura eße quam Aristoteliuiſum fuerit. CAP. VII.
Page: 184 (172)
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                  puncto
                    <var>.i.</var>
                  ex communi conceptu, &
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                  parallcla erit ipſi
                    <var>.d.b.</var>
                  ex. ſecunda par-
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                  te ſecundæ ſexti, vnde ex prima parte
                    <lb/>
                  ciuſdem, ita eritipſius
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                  vt
                    <var>.d.
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                  ad
                    <var>.c.a.</var>
                  & coniunctim ita erit ipſius
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                  ad
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                  vt ipſius
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                  & permu
                    <lb/>
                  tatim ipſius
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                  erit, vt
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                  ſed cum
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                  maior ſit ipſa
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                  vt omne totum maius eſt ſua parte.
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                  <s xml:id="echoid-s4305" xml:space="preserve">maior proportio erit ipſius
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                    <var>.a.
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                    c.</var>
                  quam ipſius
                    <var>.a.i.</var>
                  ad
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                  ipſius
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                  ad
                    <var>.a.d</var>
                  . </s>
                  <s xml:id="echoid-s4306" xml:space="preserve">Verum igitur eſt
                    <lb/>
                  propoſitum.</s>
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                <head xml:id="echoid-head528" style="it" xml:space="preserve">De differentia caloris Solis reſpectu altitudinis ipſius.</head>
                <head xml:id="echoid-head529" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4307" xml:space="preserve">QVodà me poſtulas deinde, ita ſe habet. </s>
                  <s xml:id="echoid-s4308" xml:space="preserve">Inquis enim, quod cum differentia
                    <lb/>
                  inter maiorem,
                    <reg norm="minoremque" type="simple">minoremq́;</reg>
                  calorem, oriatur etiam ex differentia maioris
                    <lb/>
                  quantitatis vaporum ad minorem, per quam quantitatem vaporum rranſit lumen
                    <lb/>
                  Solis (vt alias etiam tibi dixi) velles nunc ſcire quantitatem ipſius differentię, quæ
                    <lb/>
                  inter duas Solis datas altitudines ſupra orizontem reperitur.</s>
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                <p>
                  <s xml:id="echoid-s4309" xml:space="preserve">Quapropter imaginemur circulum
                    <var>.a.e.</var>
                  pro magno terræ, et
                    <var>.z.b.d.</var>
                  pro magno
                    <lb/>
                  vaporum, ſupponatur etiam quod angulus
                    <var>.z.o.d.</var>
                  vel
                    <var>.z.a.b.</var>
                  qui ſunt inuicem fe-
                    <lb/>
                  rè æquales, ſit angulus diſtantiæ Solis à zenit,
                    <var>z.a.</var>
                  verò ſit ſpiſſitudo vaporum, et
                    <var>.a.
                      <lb/>
                    b.</var>
                  radius tranſiens per vapores dictos. </s>
                  <s xml:id="echoid-s4310" xml:space="preserve">nunc
                    <lb/>
                    <figure xlink:label="fig-0371-02" xlink:href="fig-0371-02a" number="411">
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                  quæratur proportio, quæ eſt inter
                    <var>.a.b.</var>
                  et
                    <var>.a.
                      <lb/>
                    z.</var>
                  qua inuenta, angulo
                    <var>.z.a.b.</var>
                  mediante,
                    <lb/>
                  quæremus eandem mediante angulo
                    <var>.z.a.b.</var>
                    <lb/>
                  maiore priori, velipſo minore, vnde cogno
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                  ſcemus differentiam duarum
                    <var>.a.b.</var>
                  quæ qui-
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                  dem inæquales inuicem erunt, eo quod ſup
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                  ponatur
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                  immutabilis, & hoc ita facie-
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                  mus. </s>
                  <s xml:id="echoid-s4311" xml:space="preserve">Imaginabimur
                    <var>.o.b.</var>
                  quæ claudat trian
                    <lb/>
                  gulum
                    <var>.a.b.o.</var>
                  & quia
                    <var>.a.z.</var>
                  cognita eſt quam
                    <lb/>
                  Alhazem docetinuenire, cognoſcimus
                    <reg norm="etiam" type="context">etiã</reg>
                    <lb/>
                    <var>o.a.</var>
                  vt ſemidiametrum terræ, vnde
                    <var>.o.b.</var>
                  et
                    <var>.
                      <lb/>
                    o.a.</var>
                  duo latera trianguli
                    <var>.a.o.b.</var>
                  cognita
                    <reg norm="erunt" type="context">erũt</reg>
                    <lb/>
                  ſimul cum angulo
                    <var>.o.a.b.</var>
                  reſiduo duorum re
                    <lb/>
                  ctorum, eo quod reliquus
                    <var>.z.a.b.</var>
                  datus eſt.
                    <lb/>
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                  <s xml:id="echoid-s4312" xml:space="preserve">Quare
                    <var>.a.b.</var>
                  cognita erit reſpectu
                    <var>.o.a.</var>
                  et
                    <var>.o.
                      <lb/>
                    b.</var>
                  et
                    <var>.a.z.</var>
                  quæ eſt eorum differentia. </s>
                  <s xml:id="echoid-s4313" xml:space="preserve">Nunc
                    <lb/>
                  ſi idem faciemus cum alia
                    <var>.a.b.</var>
                  ſub diuerſo
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                  angulo, habebimus propoſitum.</s>
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