Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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A*PPENDIX*
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<
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">Demonstrationum ſupraſcriptarum nonnullas per nume@
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rosinstitutas, Mathematicas eſſe.</
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<
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xml:space
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">Mechanicæ demonſtrationis à doctis annotatur differen-
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tia, neque injuria. </
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<
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xml:space
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">Nam illa omnibus generalis eſt, & </
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<
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">rationem cur ita ſit
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penitus demonſtrat, hæc verò in ſubjecto duntaxat paradigmate numeris de-
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clarat. </
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<
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xml:space
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">Vt ſi demonſtraturus in rectangulo triangulo baſin recti æquè poſſe cru-
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ribus, aſſumat triangulum cujus minimum latus ſit 3, ſecundum 4, tertium 5 pe-
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dum, hocq́ue rectangulum eſſe deprehendatur; </
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<
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xml:space
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">tumq́ue oſtendat maximi la-
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teris quadratum 25, æquari reliquorum laterum quadratis 16 & </
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<
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<
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ſtratio hujuſmodi tantum eſt propoſiti exempli, unde non concluſeris omnibus
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rectangulis triangulis idem contingere, neque hinc cur id fiat evidens eſt; </
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quia opus hujuſmodi machinationein ſpeciali exemplo inſtituitur, mechanica
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demonſtratio appellatur: </
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<
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<
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tholica eſt & </
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<
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xml:space
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">univerſalis, cauſam repetens ab ipſis elementis cur ita neceſſariò, & </
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non aliter ſe habere poſſit: </
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<
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">hæc propter certitudinem in demonſtrando, & </
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<
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xml:space
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cendo infallibilem Mathematica dicitur; </
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<
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">ideoq́ue etiam ab ipſis Mathematicis
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potior cenſetur & </
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<
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">frequentiùs uſurpatur, quam illa per numeros mechanica.
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</
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<
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">Vnde objectionem mihi paratam intelligo, cur 4, 11, 12, 18 propoſitiones 2. </
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Elem. </
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">Cui occurritur,
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demonſtrationem in numeris dupliciter inſtitui; </
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<
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rationem, proportionemq́ue partium expoſitæ figuræ declarant; </
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<
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quantitatem. </
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<
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xml:space
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niat, & </
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<
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<
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rias. </
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<
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">Quain re Eutochius in ſuis in Apollonium cõmentariis 11 prop. </
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<
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<
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facit, dum ait: </
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">Non perturbentur qui in hæc inciderint, quodillud ex Arithmeticis de-
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monſtretur: </
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<
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men Mathematicæ potius ſunt, quam Arithmeticæpropter analogias. </
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tum Arithmeticam ſit; </
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mò numeris, ſecundo loco per numeros & </
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qui ita ſcripſit: </
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<
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">hoc eſt, hæ enim Ma-
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thematicæ diſciplinæ germanæ eſſe videntur. </
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Ptolomæi, Apollonii, & </
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">inter recentiores Comandini, Regiomontani, aliorumq́ue
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ſimilium propoſitionibus ipſam rationem, non autem rationis terminos in nu-
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meris nominatim proponi, quod à nobis factitatum ſit; </
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eſt & </
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<
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<
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pla, eodem in quam jure, citari etiam rationem duodecuplam, quale illud in di-
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cta 23 propoſ. </
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partientem vigeſimastertias ipſius A R ad R D in ſupraſcripta propoſitione 11,
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cum idem ſit rationem, & </
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<
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nearum in expoſitis figurarum illarum generibus alia ratio nulla eſt. </
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tem numerorum uſus ſit in perveſtigandis iſtiuſmodi figurarum proprietati-
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bus, ut his ducibus & </
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mus, etiam neceſſe fuit in illarum deſcriptione numeros eoſdem adſcribere, ne
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aliis obſcurum ſit, quod earum autoribus & </
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hæc ipſa eſt vera & </
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cauſis repetere.</
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