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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[5.1.7.] SEPTIMVM. Euclidis uerò undecima propoſitio.
[5.1.8.] OCTAVVM. εuclidis uerò duodecima propoſitio.
[5.1.9.] NONVM. Euclidis uero tertiadecima propoſitio.
[5.1.10.] DECIMVM.
[5.1.11.] VNDECIMVM.
[5.1.12.] DVODECIMVM.
[Item 5.2.]
[5.2.1.] THEOR.I. II. ET III.
[5.2.2.] THEOREM. IIII.
[5.2.3.] THEOR.V. ET VI.
[5.2.4.] THEOR. VII. VIII. IX.X. XI. XII. XIII.
[5.2.5.] THEOREM. XIIII.
[5.2.6.] THEOR. XV.
[5.2.7.] THEOREM. XVI.
[5.2.8.] THEOR. XVII.
[5.2.9.] THEOREM. XVIII.
[5.2.10.] THEOREM. XIX.
[5.2.11.] THEOREM. XX.
[5.2.12.] THEOREM. XXI.
[5.2.13.] THEOREM. XXII. XXIII.
[6.] PHYSICA, ET MATHEMATICA RESPONSA. FO. BAPTISTAE BεNεDICTI PATRITII Veneti, Philoſophi Mathematici.
[Item 6.1.]
[Item 6.2.]
[Item 6.3.]
[Item 6.4.]
[Item 6.5.]
[Item 6.6.]
[Item 6.7.]
[Item 6.8.]
[Item 6.9.]
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                <s xml:id="echoid-s1599" xml:space="preserve">
                  <pb o="132" rhead="IO. BAPT. BENED." n="144" file="0144" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0144"/>
                vnum ex lateribus anguli recti, ſeu normæ regulæ
                  <var>.B.C.</var>
                anniteretur, aliud verò
                  <lb/>
                per
                  <var>.m.</var>
                in rectitudine cuius ſignabam
                  <var>m.T.</var>
                interuallum æquale altitudini perfecti,
                  <lb/>
                ideſt punctum
                  <var>.T.</var>
                æqualiter diſtans ab
                  <var>.m.</var>
                tranſire faciebam, deinde regulam
                  <var>.o.Q.</var>
                  <lb/>
                per punctum
                  <var>.T.</var>
                tranſire quoque faciebam: </s>
                <s xml:id="echoid-s1600" xml:space="preserve">& notabam interſectionem ipſius cum
                  <lb/>
                linea
                  <var>.i.x.</var>
                in puncto
                  <var>.V.</var>
                efficiebam deinde vt vnum ex lateribus anguli recti, lateri ta-
                  <lb/>
                bulæ
                  <var>.B.C.</var>
                anniteretur, aliudq́ue per punctum
                  <var>.k.</var>
                tranſire faciebam, & in huiuſmodi
                  <lb/>
                rectitudine à puncto k. ſignabam quandam menſuram æ qualem lineæ
                  <var>.f.V.</var>
                quę erat
                  <lb/>
                  <var>k.R.</var>
                pro altitudine degradata.</s>
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              <head xml:id="echoid-head188" xml:space="preserve">ALITER IDEM.</head>
              <p>
                <s xml:id="echoid-s1601" xml:space="preserve">
                  <emph style="sc">MEdiante</emph>
                deinde figura
                  <var>.H.H.</var>
                vnum ex lateribus anguli recti, lateri tabu-
                  <lb/>
                  <var>.B.C.</var>
                vt anniteretur faciebam; </s>
                <s xml:id="echoid-s1602" xml:space="preserve">aliud verò per punctum
                  <var>.b.</var>
                perfecti, ideſt ba
                  <lb/>
                ſis eiuſdem perfecti tranſire faciebam. </s>
                <s xml:id="echoid-s1603" xml:space="preserve">Et in huiuſmodi rectitudine ſignabam
                  <var>.c.s.</var>
                  <lb/>
                æquale interuallum altitudini perfecti, ideſt punctum
                  <var>.s.</var>
                ita diſtans à
                  <var>.c.</var>
                efficiendo de
                  <lb/>
                inde, vt latus anguli recti, lateri
                  <var>.B.C.</var>
                tabulæ anniteretur, aliudq́ue per punctum
                  <var>.k.</var>
                  <lb/>
                tranſire faciens ſignabam
                  <var>.k.R.</var>
                indeterminatam. </s>
                <s xml:id="echoid-s1604" xml:space="preserve">Faciens deinde tranſire regulam
                  <lb/>
                  <var>i.M.</var>
                per punctum
                  <var>.s.</var>
                notabam punctum
                  <var>.R.</var>
                interſectionis eiuſdem cum linea
                  <var>.k.R.</var>
                  <reg norm="iam" type="context">iã</reg>
                  <lb/>
                ducta. </s>
                <s xml:id="echoid-s1605" xml:space="preserve">Itaque altitudinem
                  <var>.k.R.</var>
                degradatam habebam. </s>
                <s xml:id="echoid-s1606" xml:space="preserve">Hæc autem via aliquan-
                  <lb/>
                tulum breuior, expeditiorq́ue altera.</s>
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