Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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xml:space
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">_E_X hoc habetur ſingula puncta recti tranſitus, vel obliqui, inciden-
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tis lineæ, nedum eſſe communes ſectiones illius, & </
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<
s
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xml:space
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">ſingulorum,
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quæ collecta dicuntur, omnia plana propoſiti ſolidi, ſed etiam, ſi per
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talem incidentem extendatur planum, eſſe communes ſectiones illius,
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& </
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<
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">ſingularum, quæ collectæ dicuntur : </
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<
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xml:space
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">Omnes lineæ planæ figuræ, cuius
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oppoſitætangentes ſunt communes ſectiones plani eiuſdem figuræ, & </
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oppoſitarum tangentium dicti ſolidi : </
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<
s
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xml:space
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">nam motum planum deſignat in
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plano ſecante rectam lineam, & </
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<
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">inſimul punctum in ineidente, quod
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reperitur in illa recta linea, & </
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">ideò idem punctum eſt communis ſectio
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tum moti plani & </
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<
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">rectæ incidentis, tum vnius earum, quæ dicuntur om-
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nes lineæ datæ figuræ planæ (ita tamen productæ, vt hanc incidentem ſe-
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care poſſint) & </
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<
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lineæ, & </
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<
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xml:space
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">ſingula puncta, quæ ſimul collecta dicuntur
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omnia puncta recti, veleiuſdem obliqui tranſitus eiuſdem,
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fumamus interiacentes lineas, dicantur iſtæ ſimul collectæ:
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</
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<
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xml:space
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">Omnes abſciſſæ propoſitæ lineæ, quas (etiam ſi non expri-
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matur) vocari ſupponemus recti tranſitus, ſi puncta ſint recti
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tranſitus, vel eiuſdem obliqui tranſitus, ſi puncta ſint eiu-
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ſdem obliqui tranſitus.</
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linea inter eadem puncta, & </
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<
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teria centes, dicentur: </
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">Reſiduæ omnium abſciſſarum propo-
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ſitæ lineæ recti tranſitus, ſi puncta ſint rectitranſitus, vel eiu-
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idem obliquitranſitus, ſi ſumpta puncta ſint eiuſdem obliqui
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tranſitus.</
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