Ceva, Giovanni, Geometria motus, 1692

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              PROP. IX. THEOR. IX.
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              <s id="s.000217">REctangulum ſub altitudine, & baſi vnius auuerſarum
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              ad ipſam auuerſam figuram, eandem habet
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              ,
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              ac altera auuerſa figura ad rectangulum ex baſi in altitudi­
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              nem eiuſdem huius figuræ. </s>
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              Tab.
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              .
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              fig.
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              7.</s>
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              <s id="s.000220">Sint auuerſæ figuræ ACB, GFDEG. </s>
              <s id="s.000221">Dico rectangu­
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              lum DF in DE ad figuram GFDEG, eandem habere ratio­
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              nem ac figura ACBA ad rectangulum AB in BC. </s>
              <s id="s.000222">Sint pri­
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              mùm ABC, FDE anguli recti, & ducta qualibet HI paral­
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              lela BC, ſit BAC ad HIA vt DF ad KF, erit ob naturam
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              auuerſarum KL ad DE vt BC ad HI; itaque ſi ponatur eſſe
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              quidam motus ab F in D iuxta imaginem
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              BAC,
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              erit GFDEG imago temporis eiuſdem motus; nam imago
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              BAC ad imaginem HIA eſt vt ſpatium DF ad ſpatium FK
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              & velocitas BC ad
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              HI vt reciprocè KL ad DE.
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              </s>
              <s id="s.000223">Sit etiam alius motus, ſed æquabilis, cuius imago velocita­
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              tum æqualis ſit, & homogenea ipſi BAC, rectangulum
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                pe</expan>
              AB in BM, & ideo ſi fiat BM ad BC ſicut DE ad DN,
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              concipiaturque rectangulum FD in DN, erit hoc imago
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              temporis dicti motus æquabilis, homogenea, & æqualis
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              imagini GFDEG; nam
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              , ſcilicet imagines GFDEG,
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              FD in DN rectangulum componuntur ex rationibus ſpa­
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              tiorum, hoc eſt imaginum velocitatum interſe æqualium,
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              ABM, ACB, & reciproca æquatricum pariter æqualium
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              BM, BM. </s>
              <s id="s.000224">Cum igitur rectangulum FD in DN æquale ſit
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              imagini, ſeu figuræ GFDEG, habebit eadem figurą
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              GFDEG ad rectangulum FD in DE eandem rationem,
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              quam DN ad DE, hoc eſt quam BC ad BM, ſeu quam re­
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              ctangulum AB in BC ad rectangulum AB in BM, aut ad ei
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              æqualem figuram ABC; & conuertendo, manifeſtum eſt
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              quod propoſuimus, nempe rectangulum FD in DE ad fi­
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              guram GFDEG habere eandem
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              , ac figura ACBA </s>
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