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.]
[5.2. None]
[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.]
[6.1. None]
[6.2. None]
[6.3. None]
[6.4. None]
[6.5. None]
[6.6. None]
[6.7. None]
[6.8. None]
[6.9. None]
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IO. BAPT. BENED.
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                <head xml:id="echoid-head392" style="it" xml:space="preserve">Qualiter circulus deſignari poßit alios duos circulos
                  <lb/>
                propoſitos includens.</head>
                <head xml:id="echoid-head393" xml:space="preserve">CLARISS. PETRO PIZZAMANO.</head>
                <p>
                  <s xml:id="echoid-s3287" xml:space="preserve">SVperioribus diebus per tuas literas à me quæſiuiſti, vt modum tibi ſcribere vel-
                    <lb/>
                  lem, quo circulus deſignari poſſit circunſcribens alios duos propoſitos circulos.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3288" xml:space="preserve">Qua in re vt tibi ſatisfaciam quod maximè cupio ita rem accipe.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3289" xml:space="preserve">Propoſiti circuli ſint, aut inter ſe contigui, aut interſecantes vel ſeparati. </s>
                  <s xml:id="echoid-s3290" xml:space="preserve">Eſto
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                      <lb/>
                    mũ</reg>
                  contiguos eſſe, qui ſint
                    <var>.d.b.</var>
                  et
                    <var>.f.q.</var>
                    <reg norm="quorum" type="context">quorũ</reg>
                    <var>.d.b.</var>
                  maior ſit et
                    <var>.f.q.</var>
                  minor,
                    <reg norm="eorum" type="context">eorũ</reg>
                  vero
                    <lb/>
                  centra ſint .a et
                    <var>.o.</var>
                    <reg norm="punctum" type="context">punctũ</reg>
                  autem
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                  ſit
                    <var>.i</var>
                  . </s>
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                    <reg norm="Nunc" type="context">Nũc</reg>
                    <reg norm="protrahatur" type="simple simple">ꝓtrahat̃</reg>
                  .
                    <var>b.a.o.q.</var>
                  per
                    <reg norm="centra" type="context">cẽtra</reg>
                  eo
                    <lb/>
                  rum ab vna circunferentia ad aliam, quę quidem linea tranſibit per punctum
                    <var>.i.</var>
                  ex
                    <lb/>
                  11, tertij Eucli. </s>
                  <s xml:id="echoid-s3292" xml:space="preserve">deinde à diametro maiori abſcindatur
                    <var>.i.e.</var>
                  ad æqualitatem minoris
                    <lb/>
                  ſemidiametri, quo facto ſumatur diſtantia inter
                    <var>.e.</var>
                  et
                    <var>.b.</var>
                  circino mediante
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                  cen
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                  tro
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                  ſcindatur, alio circini pede, circunferentia maioris circuli in puncto
                    <var>.u.</var>
                  à quo ſi
                    <lb/>
                  mente concipiemus duas lineas
                    <var>.u.a.d.</var>
                  et
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                  tranſeuntes per eorum centra
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                  et
                    <var>.o.</var>
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                  vſque ad circunferentias in punctis
                    <var>.d.</var>
                  et
                    <var>.f.</var>
                  ipſę
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                  inuicem ęquales, eo quod
                    <var>.e.i.</var>
                    <reg norm="sum- pta" type="context">sũ-
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                    pta</reg>
                  fuit æqualis
                    <var>.o.f.</var>
                  et
                    <var>.o.u.</var>
                  æqualis
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                  </s>
                  <s xml:id="echoid-s3293" xml:space="preserve">quare
                    <var>.u.f.</var>
                  æqualis erit
                    <var>.b.i.</var>
                  ſed
                    <var>u.d.</var>
                    <reg norm="etiam" type="context">etiã</reg>
                  æqua
                    <lb/>
                  lis
                    <var>.b.i.</var>
                  ergo
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                  æqualis erit
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                  & circulus, cuius
                    <var>u.d.</var>
                  vel
                    <var>.u.f.</var>
                  erit ſemidiameter, con-
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                  tiguus erit ipſis propoſitis circulis ex conuerſo .11. iam dictæ. </s>
                  <s xml:id="echoid-s3294" xml:space="preserve">Idem dico pro circu-
                    <lb/>
                  lis ſe inuicem ſecantibus.</s>
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