Valerio, Luca, De centro gravitatis solidorvm libri tres

Table of figures

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              AD parabolam AE: baſes autem æquales BC, DE pa­
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              rallelas parabolarum diametres per A, & in vna recta li­
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              nea CE ſegmento BD interiecto: vtriuſque autem ſe­
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              ctionis AC, AE concauitas ſpectet extra figuram ACE:
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              ſecta autem CE bifariam in F, iunctaque AF, ponatur
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              AG tripla ipſius GF. </s>
              <s>Dico compoſiti ex triangulis A
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              BC, ADE centrum grauitatis eſſe G. </s>
              <s>Poſita enimvtra­
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              que ſeſquialtera, CH ipſius HB, & EK ipſius KD,
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              iunctisque AH, AK, ducatur per punctum G ipſi CE
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              parallela ſecans AH, AK in punctis L, M. </s>
              <s>Quoniam
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              igitur LM ipſi CE parallela ſecat eas quæ ex puncto A
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              ad rectam CD du­
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              cuntur rectas lineas
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              in eaſdem rationes, &
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              eſt AG tripla ipſius
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              GF; tripla erit vtra­
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              que AL ipſius LH,
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              & AM ipſius MK:
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              ſeſquialtera autem eſt
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              CH ipſius HB, &
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              EK ipſius KD; erit
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              igitur L centrum gra
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              uitatis trianguli AB
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              C, & M trianguli A
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              DE per præceden­
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              tem. </s>
              <s>Rurſus quoniam abſoluantur triangula rectilineæ
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              ACB, AEK, & æqualia erunt propter æquales baſes,
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              poſita inter eaſdem parallelas, & vtrumque ſeſquialterum
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              eius trianguli mixti, quod comprehendit, ex demonſtra­
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              tione antecedentis; æqualia igitur erunt triangula mixta
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              ABC, ADE, ſiquidem ſunt æqualium ſubſeſquialtera.
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              <s>Et quoniam componendo, & permutando eſt vt CB ad
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              DE ita BH ad DK, æqualis erit BH ipſi DK: ſed ſi ab
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              æqualibus poſitis CF, FE ipſas CB, DE æquales au-</s>
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