Clavius, Christoph
,
Geometria practica
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rhead
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GEOMETR. PRACT.
"/>
<
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<
s
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xml:space
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"> inſuper Secunda, Tertia, Quarta, &</
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<
s
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<
s
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xml:space
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">vt earum areas conſequi poſsimus. </
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>
<
s
xml:id
="
echoid-s7456
"
xml:space
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">Nam
<
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ex latere cuiuſcunque figurę regularis cognito in partibus diametri circuli cir-
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cumſcripti, vel ſinus totius, veniemus per ea, quæ cap. </
s
>
<
s
xml:id
="
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xml:space
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">2. </
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<
s
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xml:space
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">Num. </
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<
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="
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xml:space
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">2. </
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<
s
xml:id
="
echoid-s7460
"
xml:space
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">ſcripſimus, in
<
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cognitionem lineæ perpendicularis ex centro in vnum latus deductę, ac proin-
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de totam aream nanciſcemur, vt paulo ante Num. </
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<
s
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="
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xml:space
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">1. </
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<
s
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="
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xml:space
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">docuimus. </
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<
s
xml:id
="
echoid-s7463
"
xml:space
="
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">Latera igitur in
<
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quam plurimis figuris in tabula pręcedenti expoſita habes, quæ omnia veris la-
<
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teribus ſunt paulò minora; </
s
>
<
s
xml:id
="
echoid-s7464
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7465
"
xml:space
="
preserve
">ſi adieceris vnitatem, fient paulò maiora veris;
<
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/>
</
s
>
<
s
xml:id
="
echoid-s7466
"
xml:space
="
preserve
">ita vt verum latus trianguli æquilateri inter hos duos numeros 17320508. </
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<
s
xml:id
="
echoid-s7467
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xml:space
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">
<
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17320509. </
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<
s
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xml:space
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">conſiſtat.</
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>
<
s
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"
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</
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<
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position
="
left
"
xml:space
="
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">Ex cognita ſe-
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midiametro
<
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circuli inue-
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nire lat{us} fi-
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guræregula-
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ris in eo circu-
<
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lo deſcriptæ.</
note
>
<
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<
s
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xml:space
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">4. </
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<
s
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<
emph
style
="
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">Iam</
emph
>
verò cognita ſemidiametro alicuius circuli in partibus cuiuſcunque
<
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/>
menſuræ, reperiemus in iiſdem partibus latus figurę regularis, cuius laterum nu-
<
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merus maior non eſt, quam 80. </
s
>
<
s
xml:id
="
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"
xml:space
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">beneficio præcedentis tabulę: </
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>
<
s
xml:id
="
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"
xml:space
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">ſi nimirum fiat,
<
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vt ſinus totus 10000000. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">ad latus figurę propoſitæ in præcedenti tabula, ita ſe-
<
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midiamer circuli propoſiti data ad aliud. </
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>
<
s
xml:id
="
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xml:space
="
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">Sit verbi gratia, ſemidiameter alicuius
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circuli 12. </
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>
<
s
xml:id
="
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xml:space
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">& </
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<
s
xml:id
="
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"
xml:space
="
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">inueniendum ſit latus decagoni reſpectu dictæ ſemidiametri: </
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>
<
s
xml:id
="
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xml:space
="
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">Fiat
<
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vt 10000000. </
s
>
<
s
xml:id
="
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xml:space
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">ſinus totus ad 6180339. </
s
>
<
s
xml:id
="
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"
xml:space
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">latus Decagoni; </
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>
<
s
xml:id
="
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xml:space
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">ita 12. </
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<
s
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="
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"
xml:space
="
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">ſemidiameter da-
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ta ad aliud; </
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>
<
s
xml:id
="
echoid-s7483
"
xml:space
="
preserve
">exibitque latus quæſitum 8 {164068/10000000}. </
s
>
<
s
xml:id
="
echoid-s7484
"
xml:space
="
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">vel in minoribus numeris
<
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8 {41017/2500000}.</
s
>
<
s
xml:id
="
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"/>
</
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>
<
note
position
="
left
"
xml:space
="
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">Fractionem
<
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magnam ad
<
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/>
minorem ferè
<
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/>
æquiualentem
<
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/>
reducere.</
note
>
<
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<
s
xml:id
="
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xml:space
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<
emph
style
="
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">Et</
emph
>
ſi moleſtum videatur operari cum fractione tam magna, reduces eam ad
<
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minorem quaſi æquiualentem hoc modo. </
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>
<
s
xml:id
="
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"
xml:space
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">Elige pro Numeratore quemuis nu-
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merum, vt 10. </
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>
<
s
xml:id
="
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xml:space
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">Et fiat vt Numerator 164068. </
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>
<
s
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="
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xml:space
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">ad ſuum Denominatorẽ 10000000.
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</
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>
<
s
xml:id
="
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xml:space
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">ita Numerator electus 10. </
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>
<
s
xml:id
="
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xml:space
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">ad aliud, reperieſque Denominatorem 609 {82588/164068}. </
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<
s
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="
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xml:space
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<
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Ita vt relicta hac fractione, Denominator 609. </
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<
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xml:space
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">ſit minor quam verus; </
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<
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xml:space
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">& </
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<
s
xml:id
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">610. </
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<
s
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="
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<
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maior, hoc eſt, fractio {10/609}. </
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>
<
s
xml:id
="
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xml:space
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">ſit maior fractione {164068/10000000}. </
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>
<
s
xml:id
="
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xml:space
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">fractio autem
<
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<
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position
="
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xlink:label
="
note-208-03
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xlink:href
="
note-208-03a
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xml:space
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">Inter du{as}
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fractiones in-
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uenire mediã.</
note
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{10/610}. </
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<
s
xml:id
="
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xml:space
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">minor Inter has autẽ duas fractiones {10/609}. </
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<
s
xml:id
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xml:space
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">{10/610}. </
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>
<
s
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">produces mediã {20/1219}. </
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<
s
xml:id
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">cuius
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Numerator ex Numeratoribus, & </
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<
s
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">Denominator ex Denominatoribus confla-
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tus eſt. </
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<
s
xml:id
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xml:space
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">Erit que fractio inuenta ferè maiori illi æqualis.</
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<
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</
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<
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<
s
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<
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style
="
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porrò, cuius Numerator ex duobus Numeratoribus, & </
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<
s
xml:id
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xml:space
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">De-
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nominator ex Denominatoribus duarum minutiarum componitur, eſſe maio-
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rem minore, & </
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>
<
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xml:id
="
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xml:space
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">minorem maiore, demonſtrabimus lib. </
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<
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xml:space
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<
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<
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<
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</
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<
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position
="
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xml:space
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">Ex cognito
<
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latere figuræ
<
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regularis, in-
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uenire ſemi-
<
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/>
diam{et}rum
<
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/>
circuli cir-
<
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cumſcripti.</
note
>
<
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<
s
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<
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style
="
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>
ex dato latere cuiuslibet figuræ regularis cognoſcemus ſemi-
<
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diametrum circuli circumſcribentis: </
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>
<
s
xml:id
="
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xml:space
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">ſi fiat, vt latus propoſitæ figuræ in tabula
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antecedente ad 10000000. </
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>
<
s
xml:id
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xml:space
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">ita latus datum ad aliud. </
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>
<
s
xml:id
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xml:space
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">Vt ſi latus Pentagoni de-
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tur 12. </
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>
<
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xml:id
="
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xml:space
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">& </
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<
s
xml:id
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">fiat, vt 11755705. </
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<
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">ad 10000000. </
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<
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">ita 12. </
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>
<
s
xml:id
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xml:space
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">ad aliud, reperietur ſemidiame-
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ter circuli circumſcripti 10 {2442950/11755705}. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Et ſi fiat, vt Numerator huius fractionis ad
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ſuum Denominatorem: </
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>
<
s
xml:id
="
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xml:space
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">Ita Numerator electus quicunque, nimirum 1. </
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>
<
s
xml:id
="
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xml:space
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">ad a-
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liud, inuenietur Denominator ſequens 4 {1983905/2442950}. </
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>
<
s
xml:id
="
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xml:space
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">ita vt fractio {1/4}. </
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<
s
xml:id
="
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xml:space
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">ſit maior,
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quã {2442950/11755705}. </
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<
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xml:id
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">at {1/5}. </
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<
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xml:id
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">minor Ex additione numeratorũ 1. </
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<
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">1. </
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<
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<
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rum 4. </
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<
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">5. </
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<
s
xml:id
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">inter ſe, efficies fractionem {2/9}. </
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>
<
s
xml:id
="
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xml:space
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">mediam, quæ adhuc maior eſt, quam
<
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{2442950/11755705}. </
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<
s
xml:id
="
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xml:space
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">Media autem inter {1/5}. </
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<
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xml:id
="
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xml:space
="
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">& </
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<
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xml:id
="
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xml:space
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">{2/9}. </
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<
s
xml:id
="
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xml:space
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">eſt {3/14}. </
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<
s
xml:id
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xml:space
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">quæ parum ab illa differt: </
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>
<
s
xml:id
="
echoid-s7540
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xml:space
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">ita vt
<
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ſemidiameter quæſita dici poſsit eſſe 10 {3/14}. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Atque in hunc modum per mino-
<
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res numeros operationes fieri poſſunt, quamuis non omnino ex quiſitè, quod
<
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/>
fractiones aſſumptę non ſint omnino veræ; </
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>
<
s
xml:id
="
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xml:space
="
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">ſed hic error in dimenſionibus cam-
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porum tolerabilis eſt.</
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<
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</
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<
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<
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">5. </
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<
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<
emph
style
="
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">Anteqvam</
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>
rectilinearum figurarum dimenſionem concludam, lubet
<
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/>
regulam attexere, qua ex cognita area cuiuſcunque figuræ latus habentis </
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>
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