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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THEOREM. ARIT.
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75
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file
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0075
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0075
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ras confideranti ſpeculari licebit, Diametros harum figurarum notaui literis ſiue
<
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characteribus
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.</
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103
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0075-01
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0075-02
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xlink:href
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<
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xml:space
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">THEOREMA
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num
value
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95
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num
>
.</
head
>
<
p
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<
s
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xml:space
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">IN progreſſionibus, quæ ab alio termino quam vnitate incohantur, idipſum vt
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monuimus accidit, hoc tamen notato, quòd ex conſequenti quælibet pars dia-
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metri
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norm
="
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type
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">parallelogrãmi</
reg
>
, minimo termino æqualis erit, prout in progreſſionibus quæ
<
lb
/>
ab vnitate originem ducunt, ſingulæ partes diametri, vnitati ſui primi termini æ-
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quales ſunt. </
s
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<
s
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xml:space
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preserve
">At in reliquis progreſſionibus, vt in figura patet, eadem eſt propor-
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lb
/>
tio totius diametri ad
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var
>.o.n.</
var
>
quæ minimi termini ad vnitatem ex .13. quinti, nempe
<
var
>.
<
lb
/>
a.o.</
var
>
ad
<
var
>.o.n.</
var
>
vt
<
var
>.n.n.n.n.</
var
>
ad
<
var
>.n</
var
>
. </
s
>
<
s
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xml:space
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">In eiuſmodi progreſſionibus accidit quoque
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lb
/>
grãmum</
reg
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à diametro in tres partes diuidi, quarum vnam ipſe occupat, reliquæ ve-
<
lb
/>
ro inter ſe æquales ipſum ambiunt. </
s
>
<
s
xml:id
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xml:space
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preserve
">Ex quo illud etiam ſequitur, productum
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var
>.a.o.</
var
>
in
<
lb
/>
dimidium
<
var
>.o.n.</
var
>
æquale eſſe dimidio
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type
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, quod minus eſt ſumma progreſ-
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ſionis dimidio diametri, quod dimidum ſi inuenire voluerimus, minimum
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<
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>.
<
lb
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n.n.n.n.</
var
>
per dimidium
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var
>
multiplicabimus, & ex .18. aut .19. ſeptimi ipſum habe-
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bimus,
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minimo termino per totum
<
var
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var
>
multiplicato profertur integer
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diameter ex .20. prædicti. </
s
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<
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xml:id
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xml:space
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">Etenim vt diximus, eadem eſt proportio totius diame-
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tri ad
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var
>
quæ minimi termini ad vnitatem. </
s
>
<
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xml:space
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preserve
">Ita etiam dico ex dicta .20. ſeptimi.
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<
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xml:space
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">idem dimidium diametri oriri, ſi quis dimidium minimi termini nempè
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var
>.n.n.</
var
>
per to
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lb
/>
tum
<
var
>.o.n.</
var
>
multiplicauerit. </
s
>
<
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xml:space
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">Quamobrem qui ſtatim ſummam propoſitæ progreſſionis
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cognoſcere voluerit,
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0075-03
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xlink:href
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ſemper primum termi
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num
<
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>.n.n.n.n.</
var
>
cum
<
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>.a.o.</
var
>
<
lb
/>
coniunget, qua ſumma
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lb
/>
per
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type
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<
var
>.o.n.</
var
>
mul-
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tiplicata, aut
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var
>.o.n.</
var
>
per
<
lb
/>
dimidium dictæ ſum-
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mæ, ex prædictis rationibus propofitum conſequemur.</
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<
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<
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xml:space
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">CVR ſi quis numerum terminorum inuenire velit, cognitis tantummodo pri
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mo atque vltimo, rectè vltimum per primum diuidet, ex quo proueniens </
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