Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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ipſi, FD, quæ eſi vna maximarum abſciſſarum ipſius, FD, vnde hac via
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colligemus omnes lineas trianguli, FCD, regula, CD, dum latus, FD,
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æquatur ipſi, DC, eſſe æquales omnibus abſciſſis ipſius, FD; </
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<
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_huius._</
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lineas trianguli, AFC, eſſe æquales reſiduis omnium abſciſſarum, FD,
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_huius._</
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& </
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FD, quæ dicuntur eiuſdem obliqui tranſitus, ſi angulus, CDF, non ſit
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_huius._</
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rectus, & </
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<
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logrammum, AD, duplum eſſe trianguli, FCD, vel, ACF, & </
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<
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de etiam omnes lineas, AD, regula CD duplas eſſe omnium linearum
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trianguli, FCD, vel, ACF, ſic etiam vt demonſtratum recipi potest
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propoſitæ linearectæ, vt ipſius, FD, vtcunque, maximas abſciſſarum,
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duplas eſſe omnium abſciſſarum eiuſdem, vel reſiduarum omnium abſciſ-
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ſarum, vnde & </
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<
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ſarum eiuſdem lineæ, ijs vel recti, vel eiuſdem obliqui tranſitus ſumptis,
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quæ ad ſequentium intelligentiam diligenter ſunt adnotanda.</
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latim ad vnamquamque, vt magnitudo, V, ad tot alias, P, S,
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ſingillatim ad vnamquamq; </
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vt, V, ad, P; </
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ad, E, O, ſimul eſſe, vt, V, ad, P, S, ſimul iun-
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ctas. </
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dam, A, vttertia, P, ad quartam, V, ſed etiam
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conuertendo quinta, O, eſt ad ſecundam, A, vt
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ſexta, S, ad quartam, V, ergo compoſita ex prima,
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E, & </
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ſita ex tertia, P, & </
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conuertendo, A, ad, EO, ſimul erit, vt, V, ad, P,
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huius.</
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S, ſimul iunctas, qui arguendi modus dicitur à me,
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colligere, ſeu colligendo.</
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tineatur, NE, pro vna ex ductis vtcunque parallela
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ipſi, CD, producta autem, CD, vtcunque in, M, comple-
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toque parallelogrammo, OD. </
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M, ad trapezium, FCMO, eſſe vt, CM, ad, MD, ſimul
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cum {1/2}, CD.</
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