Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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122102GEOMETRIE

COROLLARIVM.

_H_Inc liquet cuilibet abſciſſæ in proximis definitionibus propoſitæ li-
neæ reſpondere vnam ex reſiduis, ita vt tot ſint illæ, quæ dicun-
tur reſiduæ omnium abſciſſarum propoſitæ lineæ quot illæ, quæ dicun-
tur eiuſdem omnes abſciſſæ, ſiue recti, ſiue eiuſdem obliqui tranſitus, nam
reſiduæ omnium abſciſſarum propoſitælineæ interiacent inter reliquum
extremum eiuſdem punctum, & eadem illa puncta, inter quæ, & ex-
tremum primò dictum, interiacent omnes abſciſſæ.

VI.

SI pro qualibet earum, quæ dicuntur omnes abſciſſæ pro-
poſitæ rectæ lineæ, ipſa propoſita linea, ſiue eidem æ-
qualis, ſemel aſſumpta intelligatur, iſtæ ſimul collectæ di-
centur: Maximæ omnium abſciſſarum propoſitæ lineæ, vel
ſubintelligentur ſemper eſſe omnium, etiam ſi dicerentur ſo-
lummodò: Maximæ abſciſſarum.

COROLLARIVM.

_E_T quia omnes abſciſſæ tot ſunt, quot omnes reſidue, maximè verò
omnium abſciſſtrum tot ſunt, quot omnes abſciſſæ, nam cuilibet
abſciſſæ reſpondet vna maximarum, ideò maximæ omnium abſciſſarum
propoſitæ lineæ tot erunt, quot etiam reſiduæ omnium abſciſſarum, quot-
cumque ſint omnes abſciſſæ, vel reſiduæ : ideſt pro qualibet reſidua ha-
bebimus quoque vnam maximarum; ijs ſemper recti, vel eiuſdem obli-
qui tranſitus aſſumptis.

VII.

SI cuilibet omnium abſciſſarum propoſitæ rectæ lineæ ad-
iuncta intelligatur alia recta linea cuidam equalis, com-
poſitæ ex omnibus abſciſſis, & adiunctis, ſinul colle ctæ di-
centur : Omnes abſciſſæ propoſitæ lineæ adiuncta tali, nem-
pè adiuncta illa, cui, quę adiunguntur, ſunt ęquales. Sive-
rò fieret hęc adiunctio reſiduis, vel maximis omnium abſciſ-
ſarum, pariter dicerentur : Reſiduæ, vel Maximæ omnium
abſciſſarum adiuncta eadem; rectiſemper, veleiuſdem ob-
liqui tranſitus.

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