Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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IO. BAPT. BENED.
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80
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file
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0080
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xlink:href
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g. & permutando
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ad
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hoc eſt ad
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vt
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ad
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hoc eſt
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. </
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<
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xml:space
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">Quamobrem ea-
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dem erit proportio
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ad
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quæ
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ad
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>.n.x</
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. </
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<
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xml:space
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">Abfoluantur itaque duo rectangu
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la
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et
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ita tamen vt
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rectangulum
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type
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<
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cogitetur ęquale rectangulo
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>.x.i.</
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cuius
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>.x.i.</
var
>
<
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ſuperficialis numerus ex communi conceptione lineari
<
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>.n.i.</
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æqualis erit, </
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<
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xml:space
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">quare ex
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eadem
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communi conceptione, numerus ſuperficialis
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>.u.z.</
var
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lineari
<
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>.n.i.</
var
>
æqualis erit, qui
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quidem numerus in figura rectangu-
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la ſuperficialis cognitandus erit, cum
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diuidendus ſit per
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>.h.</
var
>
hoc eſt per
<
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>.n.u.</
var
>
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/>
ex quo proueniens ex huiuſmodi di
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uiſione erit numerus
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>.n.z.</
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>
ex ijs
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quæ .10. theoremate dicta fuerunt.
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</
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<
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xml:space
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">Sed ex .15. fexti aut .20. ſepti-
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mi eadem eſt proportio
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ad
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>.n.z.</
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quæ
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>.n.u.</
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ad
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>.n.x.</
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hoc eſt
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>.o.r.</
var
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ad
<
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>.m.s.</
var
>
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videlicet vt
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>.n.i.</
var
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ad aggregatum reli-
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quorum omnium terminorum
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>.c.a</
var
>
:
<
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>f.
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r</
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>
: </
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<
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xml:space
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">m.s. ex præcedenti theoremate, & ex .11. quinti Euclidis. </
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xml:space
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">Itaque ex .9. eiuf-
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dem numerus
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æqualis erit ſummæ trium terminorum
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>.c.a</
var
>
: f. num
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>.s.</
var
>
cui coniuncto
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quarto termino
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var
>
propoſitum obtinetur.</
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>
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<
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xml:space
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">THEOREMA
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value
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num
>
.</
head
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<
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xml:space
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">PRopoſuere veteres quæſita nonnulla de itineribus
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type
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">interq́;</
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hoc vnum fuit. </
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<
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xml:space
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">Po-
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namus duos iter agere per eandem viam quorum alter quatuor milliaria ſin-
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gulis diebus conficiat, alter verò prima die milliare vnum, ſecunda duo, tertia tria,
<
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atque ita ſingulis diebus milliare addit; </
s
>
<
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xml:space
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">quærimus quot dierum ſpacio ſocium con
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ſequetur.</
s
>
</
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<
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<
s
xml:id
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xml:space
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">Quamobrem numerus milliarium primi viatoris duplicatur, ſic ſunt .8. milliaria.
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</
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<
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xml:space
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">ex quo ſemper vnitas detrahicur, quæ in præſenti exemplo erit .7.
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dies erunt
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quibus ſocius ſocium conſequetur, & milliarium numerum æqualem abſoluerit.</
s
>
</
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<
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<
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xml:space
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">Cuius rei facilis erit ſpeculatio, ſi ſubſcripta figura diligenter conſideretur, in
<
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qua primus viator, die prima, quatuor milliaria linea
<
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var
>
ſignificata conficit, at-
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que illa ipſa die alter vnum tantum defignatum per
<
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>.d.</
var
>
perficit, ita vt primus via-
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tor tribus milliaribus ſocium anteceſſerit, altera verò die fecundus uiator cum duo
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milliaria
<
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type
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, excedètur à primo duobus milliaribus tantummodo, quę cum tri-
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bus primæ diei quinque erunt; </
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<
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xml:space
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">tertia die ijſdem de cauſis primus ſex tantum millia-
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ribus à ſecundo diſtabit, cum verò quarta die tot ſecundus quot primus milliaria
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conficiat, primus à ſecundo amplius quam antea non diſtabit; </
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<
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xml:space
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">quinta verò cum ſe
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cundus vnum milliare amplius quam primus conficiat. </
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<
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xml:space
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">propius accedit ad primum
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vno ex ſex milliaribus, quibus anteà diſtabat, tum ſexta cum duobus primum ſupe-
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ret, detrahet ex ſex milliaribus præteritæ diſtantiæ tria, ſeptima tandem illa ſex
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detraxerit. </
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<
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xml:space
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">In quo conſiderandum eſt ſecundum viatorem iter agere progreſſio-
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ne arithmetica continua naturali
<
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>.d.c.f.</
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>
primum autem per rectangulum
<
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>.q.f.</
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>
<
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norm
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quarum
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duarum figurarum
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>
pars
<
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eſſe reperitur, quæ quantitates ſi inuicem
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æquales eſſe debent, neceſſe eſt ſeparatas partes
<
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>.u.q.n.</
var
>
et
<
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>.t.i.c.</
var
>
inter ſe æquales eſſe,
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& quoniam quarta die (hoc eſt die ſic diſtante à primo, nempè numero milliarium </
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