Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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duumin arcu abſciſſo contentorum. </
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<
s
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"
xml:space
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">Et ſi quid in diuiſione fueritreſidui, illud
<
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per 60. </
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>
<
s
xml:id
="
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"
xml:space
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">multiplicatum, atq; </
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>
<
s
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"
xml:space
="
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">in eundem diuiſorem, hoc eſt, in 128. </
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>
<
s
xml:id
="
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"
xml:space
="
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">diuiſum, dabit
<
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minuta graduum. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Et ſi adhuc quippiam remanſerit in hac diuiſione, illud eodem
<
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modo per 60. </
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>
<
s
xml:id
="
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"
xml:space
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">multiplicatum, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">in eundem diuiſorem 128, diuiſum, exhibebit
<
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ſecunda. </
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>
<
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xml:space
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">Atq; </
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<
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xml:space
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">hoc modo progrediendo, reperientur Tertia, Quarta, &</
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>
<
s
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="
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"
xml:space
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">c. </
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>
<
s
xml:id
="
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"
xml:space
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">do-
<
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/>
nec nihil in diuiſione ſuperſit. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Tunc enim vlterius progrediendum non eſt; </
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>
<
s
xml:id
="
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xml:space
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">Sed
<
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fatis eſt, ad ſecunda vſq; </
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>
<
s
xml:id
="
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xml:space
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">progredi. </
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>
<
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="
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">Exempligratia. </
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>
<
s
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xml:space
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">Ponatur ex Quadrante P Q,
<
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vſq; </
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>
<
s
xml:id
="
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"
xml:space
="
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">ad gradum 100. </
s
>
<
s
xml:id
="
echoid-s1195
"
xml:space
="
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">producto, qualis eſt duo decimus, filum perpendiculi ab-
<
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/>
<
handwritten
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="
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xlink:href
="
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number
="
15
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<
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="
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xlink:href
="
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number
="
16
"/>
<
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="
hd-048-1
"
xlink:href
="
hd-048-1a
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number
="
17
"/>
<
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="
hd-048-1
"
xlink:href
="
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number
="
18
"/>
<
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="
hd-048-1
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xlink:href
="
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number
="
19
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<
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ſcidiſſe partes 20. </
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<
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<
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">in quas totus arcus productus diſtributus eſt. </
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<
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">Fiat
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ergo, vt 128. </
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<
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xml:id
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">ad 20. </
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<
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">ita 100. </
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<
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">ad aliud; </
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<
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">inuenienturq; </
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<
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">gradus 15. </
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>
<
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">ſupereruntq; </
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>
<
s
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xml:space
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">in di-
<
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<
handwritten
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="
hd-048-1
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xlink:href
="
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number
="
15
"/>
<
handwritten
xlink:label
="
hd-048-1
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xlink:href
="
hd-048-1a
"
number
="
16
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
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number
="
17
"/>
<
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="
hd-048-1
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xlink:href
="
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number
="
18
"/>
<
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="
hd-048-1
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xlink:href
="
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number
="
19
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<
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="
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xlink:href
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="
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uiſione 80. </
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<
s
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">quę ducta in 60. </
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>
<
s
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">faciunt 4800. </
s
>
<
s
xml:id
="
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xml:space
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">quę diuiſa per 128. </
s
>
<
s
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xml:space
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">dant minuta 37, & </
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>
<
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<
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ſuperſunt adhuc 64. </
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<
s
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">quæ ſi ducãtur in 60. </
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>
<
s
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xml:space
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">& </
s
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<
s
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">productus numerus 3840. </
s
>
<
s
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="
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">diuida-
<
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tur per 128. </
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>
<
s
xml:id
="
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">prodibunt Sec. </
s
>
<
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">30. </
s
>
<
s
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">nihilq; </
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>
<
s
xml:id
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xml:space
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">in diuiſione ſupereſt. </
s
>
<
s
xml:id
="
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xml:space
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">Arcus ergo Q 20,
<
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/>
vel arcus Quadrantis BC, inter C, & </
s
>
<
s
xml:id
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xml:space
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">filum perpendiculi includit gr. </
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<
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">15. </
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>
<
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">Min. </
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<
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">37.
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</
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<
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">Sec. </
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<
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">30. </
s
>
<
s
xml:id
="
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xml:space
="
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">Rurſus ponamus ex octauo quadrante RS, vſq; </
s
>
<
s
xml:id
="
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xml:space
="
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">ad gradum 96. </
s
>
<
s
xml:id
="
echoid-s1228
"
xml:space
="
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">produ-
<
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/>
cto filum perpẽdiculi ab ſcidiſſe partes 96. </
s
>
<
s
xml:id
="
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xml:space
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">ex illis 128. </
s
>
<
s
xml:id
="
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xml:space
="
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">quæ in toto arcu producto
<
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/>
continentur. </
s
>
<
s
xml:id
="
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xml:space
="
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">Fiat ergo, vt 128. </
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<
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xml:id
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xml:space
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">ad 96. </
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<
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xml:id
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">ita 96. </
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<
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">ad aliud: </
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>
<
s
xml:id
="
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">reperientur que gradus 72. </
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<
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xml:space
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<
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pręcisè arcui abſciſſo conuenire. </
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>
<
s
xml:id
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xml:space
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">Item ceciderit filum in partem 64. </
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>
<
s
xml:id
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xml:space
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">Quadrantis
<
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ſextidecimi MN, vſque ad gradum 104. </
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<
s
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xml:space
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">producti. </
s
>
<
s
xml:id
="
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xml:space
="
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">Si ergo fiat, vt 128. </
s
>
<
s
xml:id
="
echoid-s1241
"
xml:space
="
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">ad 64. </
s
>
<
s
xml:id
="
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xml:space
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">ita
<
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104. </
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>
<
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xml:id
="
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xml:space
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">ad aliud, producentur quo que grad. </
s
>
<
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xml:id
="
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">52. </
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>
<
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>
<
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">atque ita de cæteris; </
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>
<
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xml:id
="
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xml:space
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">dum-
<
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/>
modo ſis memor, vt ſi quid in diuiſi onibus ſuperfuerit, reſidua diuiſionum mul-
<
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/>
tiplicentur per 60. </
s
>
<
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="
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xml:space
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">& </
s
>
<
s
xml:id
="
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"
xml:space
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">producti numeri per 128. </
s
>
<
s
xml:id
="
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xml:space
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">diuidantur, vt dictum eſt.</
s
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<
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</
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<
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<
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<
emph
style
="
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">Demonstratio</
emph
>
huius operationis perſpicua eſt. </
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<
s
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xml:space
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">Quoniam enim eſt, (in
<
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/>
vltimo exemplo) vt arcus N M, vſque ad grad. </
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>
<
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xml:id
="
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xml:space
="
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">104. </
s
>
<
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xml:id
="
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"
xml:space
="
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">productus, quatenus in
<
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/>
<
handwritten
xlink:label
="
hd-048-1
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xlink:href
="
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number
="
15
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
16
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
17
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
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"
number
="
18
"/>
<
handwritten
xlink:label
="
hd-048-1
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xlink:href
="
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number
="
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"/>
<
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="
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xlink:href
="
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number
="
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128. </
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>
<
s
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="
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xml:space
="
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">partes ſectus eſt, ad arcum N O, earundem partium 64. </
s
>
<
s
xml:id
="
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xml:space
="
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">vt idem arcus N M,
<
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/>
totus productus, quatenus grad. </
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>
<
s
xml:id
="
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"
xml:space
="
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">104. </
s
>
<
s
xml:id
="
echoid-s1259
"
xml:space
="
preserve
">complectitur, ad eundem arcum N O, re-
<
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/>
ſpectu eorundem graduum; </
s
>
<
s
xml:id
="
echoid-s1260
"
xml:space
="
preserve
">efficitur, vt ſi fiat quemadmodum partes 128, totius
<
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/>
arcus N M, vſque ad grad. </
s
>
<
s
xml:id
="
echoid-s1261
"
xml:space
="
preserve
">104. </
s
>
<
s
xml:id
="
echoid-s1262
"
xml:space
="
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">producti ad partes 64. </
s
>
<
s
xml:id
="
echoid-s1263
"
xml:space
="
preserve
">in arcu N O, contentas ita
<
lb
/>
idem arcus N M, productus graduum 104. </
s
>
<
s
xml:id
="
echoid-s1264
"
xml:space
="
preserve
">ad aliud, reperiantur gradus in eo dem
<
lb
/>
arcu N O, contenti, &</
s
>
<
s
xml:id
="
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"
xml:space
="
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">c.</
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>
<
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xml:id
="
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="
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"/>
</
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>
<
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>
<
s
xml:id
="
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xml:space
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">8. </
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>
<
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="
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="
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<
emph
style
="
sc
">In</
emph
>
gratiam autem ſtudio ſorum placet hic tabellam inſerere, in qua ex re-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-048-01
"
xlink:href
="
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"
xml:space
="
preserve
">Conſtructio
<
lb
/>
& vſ{us} tabel-
<
lb
/>
la pro minutis
<
lb
/>
& ſecundis.</
note
>
ſiduo primæ operationis regulæ aureæ, qua gradus eliciuntur, mox apparet,
<
lb
/>
quot minuta, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ſecunda illi reſi duo reſpondeant: </
s
>
<
s
xml:id
="
echoid-s1270
"
xml:space
="
preserve
">Ita vt opus ſit ſemel tantum
<
lb
/>
regulam auream adhibere. </
s
>
<
s
xml:id
="
echoid-s1271
"
xml:space
="
preserve
">Conſtruitur autem tabella, ſi ſingula reſidua, quæ
<
lb
/>
plura, quam 127, eſſe nequeunt, per 60. </
s
>
<
s
xml:id
="
echoid-s1272
"
xml:space
="
preserve
">multiplicentur, productique numeri per
<
lb
/>
128. </
s
>
<
s
xml:id
="
echoid-s1273
"
xml:space
="
preserve
">diuidantur. </
s
>
<
s
xml:id
="
echoid-s1274
"
xml:space
="
preserve
">Atque vt ſtructura, & </
s
>
<
s
xml:id
="
echoid-s1275
"
xml:space
="
preserve
">vſus huiuſce tabellæ facilius intelliga-
<
lb
/>
tur, apponemus vnum exemplum. </
s
>
<
s
xml:id
="
echoid-s1276
"
xml:space
="
preserve
">Cadat verbi gratia filum perpendiculi in
<
lb
/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
15
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
16
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
17
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
18
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
19
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
20
"/>
partem 29. </
s
>
<
s
xml:id
="
echoid-s1277
"
xml:space
="
preserve
">Quadrantis 32. </
s
>
<
s
xml:id
="
echoid-s1278
"
xml:space
="
preserve
">ad gradum vſque 120. </
s
>
<
s
xml:id
="
echoid-s1279
"
xml:space
="
preserve
">producti. </
s
>
<
s
xml:id
="
echoid-s1280
"
xml:space
="
preserve
">Fiat igitur vt 128.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1281
"
xml:space
="
preserve
">ad 29. </
s
>
<
s
xml:id
="
echoid-s1282
"
xml:space
="
preserve
">ita 120. </
s
>
<
s
xml:id
="
echoid-s1283
"
xml:space
="
preserve
">ad aliud; </
s
>
<
s
xml:id
="
echoid-s1284
"
xml:space
="
preserve
">producenturque grad. </
s
>
<
s
xml:id
="
echoid-s1285
"
xml:space
="
preserve
">27. </
s
>
<
s
xml:id
="
echoid-s1286
"
xml:space
="
preserve
">Quia verò in diuiſione ſu-
<
lb
/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
15
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
16
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
17
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
18
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
19
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
20
"/>
perſunt 24. </
s
>
<
s
xml:id
="
echoid-s1287
"
xml:space
="
preserve
">ſub quo numero in tabella ponuntur duo hi numeri 11. </
s
>
<
s
xml:id
="
echoid-s1288
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s1289
"
xml:space
="
preserve
">Prior
<
lb
/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
15
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
16
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
17
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
18
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
19
"/>
<
handwritten
xlink:label
="
hd-048-1
"
xlink:href
="
hd-048-1a
"
number
="
20
"/>
ergo dat minuta, & </
s
>
<
s
xml:id
="
echoid-s1290
"
xml:space
="
preserve
">poſterior ſecunda; </
s
>
<
s
xml:id
="
echoid-s1291
"
xml:space
="
preserve
">Ita vt arcus à filo abſciſſus complecta-
<
lb
/>
tur grad. </
s
>
<
s
xml:id
="
echoid-s1292
"
xml:space
="
preserve
">27: </
s
>
<
s
xml:id
="
echoid-s1293
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s1294
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s1295
"
xml:space
="
preserve
">ſec. </
s
>
<
s
xml:id
="
echoid-s1296
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s1297
"
xml:space
="
preserve
">Atque hæc minuta, & </
s
>
<
s
xml:id
="
echoid-s1298
"
xml:space
="
preserve
">Secunda producuntur, ſi reſi-
<
lb
/>
duum diuiſionis, nimirum 24. </
s
>
<
s
xml:id
="
echoid-s1299
"
xml:space
="
preserve
">ducatur in 60. </
s
>
<
s
xml:id
="
echoid-s1300
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1301
"
xml:space
="
preserve
">productus numerus per 128. </
s
>
<
s
xml:id
="
echoid-s1302
"
xml:space
="
preserve
">di-
<
lb
/>
uidatur, &</
s
>
<
s
xml:id
="
echoid-s1303
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s1304
"
xml:space
="
preserve
">Eadem ratio eſt dereliquis tabellę numeris. </
s
>
<
s
xml:id
="
echoid-s1305
"
xml:space
="
preserve
">Nam ſemper ſuperior
<
lb
/>
numerus eſt ille, qui in diuiſione remanſit: </
s
>
<
s
xml:id
="
echoid-s1306
"
xml:space
="
preserve
">Inferiorum autem numerorum prior
<
lb
/>
ad minuta, & </
s
>
<
s
xml:id
="
echoid-s1307
"
xml:space
="
preserve
">poſterior ad ſecunda ſpectat.</
s
>
<
s
xml:id
="
echoid-s1308
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div54
"
type
="
section
"
level
="
1
"
n
="
19
">
<
head
xml:id
="
echoid-head22
"
xml:space
="
preserve
">SEQVITVR TABELLA.</
head
>
</
div
>
</
text
>
</
echo
>
