Discorsi Propositions 2/18-pr-05 Discorsi Proposition2/18-pr-05

 {236} PROBLEMA V, PROPOSITIO XVIII. {236} PROBLEM V, PROPOSITION XVIII Dato in perpendiculo quovis spatio a principio lationis signato, quod in dato tempore conficiatur, datoque quocunque alio tempore minori, aliud spatium in perpendiculo eodem reperire, quod in dato tempore minori conficiatur. Given the distance through which a body will fall vertically from rest during a given time-interval, and given also a smaller time-interval(Condition ) , it is required to locate another [equal] vertical distance which the body will traverse during this given smaller time-interval. Sit perpendiculum A, in quo detur spatium AB, cuius tempus ex principio A sit AB, sitque horizon CBE, et detur tempus ipso AB minus, cui in horizonte notetur aequale BC: oportet, in eodem perpendiculo spatium eidem AB aequale reperire, quod tempore BC conficiatur. Iungatur linea AC, cumque BC {10} minor sit BA, erit angulus BAC minor angulo BCA; constituatur ei aequalis CAE, et linea AE horizonti occurrat in puncto E, ad quam perpendicularis ponatur ED, secans perpendiculum in D, et linea DF ipsi BA secetur aequalis: dico, ipsam FD esse perpendiculi partem, in qua latio ex principio motus in A absolvitur tempore BC dato. Cum enim in triangulo rectangulo AED ab angulo recto E perpendicularis ad latus oppositum AD ducta sit EB, erit AE media inter DA, AB, et BE media inter DB, BA, seu inter FA, AB (est enim FA {20} ipsi DB aequalis); cumque ab positum sit esse tempus per A, erit AE, seu EC, tempus per totam AD, et EB tempus per AF; ergo reliqua BC erit tempus per reliquam FD: quod erat intentum. Let the vertical line be drawn through A, and on this line lay off the distance AB which is traversed by a body falling from rest at A, during a time which may also be represented by AB. Draw the horizontal line CBE, and on it lay off BC to represent the given interval of time which is shorter than AB. It is required to locate, in the perpendicular above mentioned, a distance which is equal to AB and which will be described in a time equal to BC. Join the points A and C; then, since BC(Condition 2/02-th-02-cor2) it follows that AE, or EC, will represent the time of fall through the entire distance AD, (Condition 202C) while EB will represent the time through AF. (Condition 2/11-th-11) Consequently the remainder BC will represent the time of fall through the remaining distance FD. Q. E. F.

 Discorsi Propositions 2/18-pr-05 Discorsi Proposition2/18-pr-05