Discorsi Propositions 2/23-pr-09-schol6 Discorsi Proposition2/23-pr-09-schol6

 Ex his igitur rationabiliter asserere possumus, quod si per aliquod planum inclinatum fiat descensus, post quem sequatur reflexio per planum {245} elevatum, mobile per impetum conceptum ascendet usque ad eandem altitudinem, seu elevationem ab horizonte; From this we may logically infer that a body which descends {245} along any inclined plane and continues its motion along a plane inclined upwards will, on account of the momentum acquired, ascend to an equal height above the horizontal; ut si fiat descensus per AB, feretur mobile per planum reflexum BC usque ad horizontalem ACD, non tantum si inclinationes planorum sint aequales, verum etiam si inaequales sint, qualis est plani BD: assumptum enim prius est, gradus {10} velocitatis esse aequales, qui super planis inaequaliter inclinatis acquiruntur, dum ipsorum planorum eadem fuerit supra horizontem elevatio.Si autem, existente eadem inclinatione planorum EB, BD, descensus per EB impellere valet mobile per planum BD usque ad D; cum talis impulsus fiat propter conceptum velocitatis impetum in puncto B, sitque idem impetus in B, seu descendat mobile per AB seu per EB; constat, quod expelletur pariter mobile per BD post descensum per AB, atque per EB. so that if the descent is along AB the body will be carried up the plane BC as far as the horizontal line ACD: and this is true whether the inclinations of the planes are the same or different, as in the case of the planes AB and BD. But by a previous postulate [p. 184] the speeds acquired by fall along variously inclined planes having the same vertical height are the same.If therefore the planes EB and BD have the same slope, the descent along EB will be able to drive the body along BD as far as D; and since this propulsion comes from the speed acquired on reaching the point B, it follows that this speed at B is the same whether the body has made its descent along AB or EB. Evidently then the body will be carried up BD whether the descent has been made along AB or along EB.

 Discorsi Propositions 2/23-pr-09-schol6 Discorsi Proposition2/23-pr-09-schol6