Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
"/>
hoc pacto. </
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>
<
s
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xml:space
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">Ex ſuperiori plano producto, hoc eſt, ex inferiori ſuperficie alicu-
<
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ius plani, quod corporis ſupremæ baſi imponeretur, ad planum baſis oppoſitæ
<
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perpendicularis demittatur. </
s
>
<
s
xml:id
="
echoid-s9566
"
xml:space
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preserve
">Hæc enim accuratè dimenſa altitudinem Icoſaedri
<
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dabit, eiuſque ſemiſsis altitudinem pyramidis, quæ quęritur. </
s
>
<
s
xml:id
="
echoid-s9567
"
xml:space
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preserve
">Quam Geome-
<
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tricè ita etiam explorabimus. </
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>
<
s
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echoid-s9568
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xml:space
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">Fiat pentagonum ex 5. </
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<
s
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echoid-s9569
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xml:space
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">lateribus Icoſaedri, inue-
<
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ſtigetur que eius ſemidiameter, & </
s
>
<
s
xml:id
="
echoid-s9570
"
xml:space
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">latus Decagoniin circulo illud pentagonum
<
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circumſcribente, in partibus, in quibus latus Icoſaedri datum eſt, hac ſcilicet ra-
<
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tione. </
s
>
<
s
xml:id
="
echoid-s9571
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xml:space
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">Concipiatur triangulum rectangulum, cuius baſis ſemidiameter dicti cir-
<
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/>
culi, latera verò ſemiſsis lateris pentagoni, hoc eſt, Icoſaedri, & </
s
>
<
s
xml:id
="
echoid-s9572
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xml:space
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">perpendicularis
<
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/>
è centro ad punctum medium dictilateris demiſſa. </
s
>
<
s
xml:id
="
echoid-s9573
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xml:space
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preserve
">Ita namque cognoſcetur ſe-
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midiameter, ex iis, quæ lib. </
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<
s
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xml:space
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">4. </
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<
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">cap. </
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<
s
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xml:space
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">5. </
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<
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xml:space
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">Num. </
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<
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xml:space
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">2. </
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<
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xml:space
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">tradita ſunt. </
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<
s
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xml:space
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">Latus verò Decagoni
<
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in eodem circulo deſcripti reperietur, vt paulo ante circa finem Num. </
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>
<
s
xml:id
="
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xml:space
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">4. </
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>
<
s
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">di-
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ctum eſt. </
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>
<
s
xml:id
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xml:space
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preserve
"> Et quia diameter ſphærę, ſiue Ico ſaedri potentia eſt
<
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symbol
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a
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position
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xlink:label
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note-242-01
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xlink:href
="
note-242-01a
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xml:space
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">1. corol. 16.
<
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tertiidec.</
note
>
tæ ſemidiametri; </
s
>
<
s
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xml:space
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">ſi quadratum ſemidiametri inuentę quintupletur, procreabi-
<
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/>
tur quadratum diametri Icoſaedri, cuius radix quadrata diametrum offeret,
<
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/>
ideoque & </
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>
<
s
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="
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"
xml:space
="
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">ſemidiameter Icoſaedri nota erit. </
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>
<
s
xml:id
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echoid-s9586
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xml:space
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">Vel aliter. </
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>
<
s
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xml:space
="
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"> Quoniam
<
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position
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xlink:label
="
note-242-02
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xlink:href
="
note-242-02a
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xml:space
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">2. corol. 16.
<
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tertiidec.</
note
>
ſphærę, id eſt, Icoſaedri, componitur ex latere Hexagoni, & </
s
>
<
s
xml:id
="
echoid-s9588
"
xml:space
="
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">duobus lateribus
<
lb
/>
decagoni in circulo pentagonum ex quinque lateribus Icoſaedri compoſitum
<
lb
/>
circumſcribente: </
s
>
<
s
xml:id
="
echoid-s9589
"
xml:space
="
preserve
">erit ſumma collecta ex ſemidiametro illius circuli, & </
s
>
<
s
xml:id
="
echoid-s9590
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xml:space
="
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">duobus
<
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/>
lateribus decagoni, diametro Icoſaedriæqualis: </
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>
<
s
xml:id
="
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xml:space
="
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">ideo que rurſus ſemidiameter
<
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Icoſaedrinota erit.</
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>
<
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</
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<
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<
emph
style
="
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">Hinc</
emph
>
patet, Orontium cum illis, qui ipſum ſequuntur, decipi, qui putat,
<
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/>
<
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position
="
left
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xlink:label
="
note-242-03
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xlink:href
="
note-242-03a
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xml:space
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">Error Oron-
<
lb
/>
tii.</
note
>
ex ſemiſſe ſemidiametri illius circuli, & </
s
>
<
s
xml:id
="
echoid-s9594
"
xml:space
="
preserve
">ex latere decagoni componi ſemiaxem
<
lb
/>
Icoſaedri, hoceſt, axem, vel altitudinem pyramidis, cuius baſis triangulum Ico-
<
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/>
ſaedri, & </
s
>
<
s
xml:id
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xml:space
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">vertex centrum ſp hæræ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Nam vt ex iis conſtat, quę proximè ſcripſi-
<
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/>
mus, eo modo componitur ſemidiameter ſphærę, vel Icoſaedri, quæ maior
<
lb
/>
eſt prędicto axe. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Semidiameter porro circuli prædictum pentagonum circum-
<
lb
/>
ſcribentis reperiri quo que poterit, vt ad finem Num. </
s
>
<
s
xml:id
="
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xml:space
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">4. </
s
>
<
s
xml:id
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xml:space
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">diximus, ſi nimirum
<
lb
/>
quadratum lateris decagoni ex quadrato lateris dicti pentagoni, quod à late-
<
lb
/>
re Icoſaedrinon differt, tollatur, & </
s
>
<
s
xml:id
="
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xml:space
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preserve
">reliqui numeri radix quadrata extrahatur:
<
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/>
</
s
>
<
s
xml:id
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xml:space
="
preserve
"> propterea quodlatus pentagoni poteſt latera decagoni, & </
s
>
<
s
xml:id
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xml:space
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">hexagoni
<
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xml:space
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">10. tertiidec.</
note
>
circuli.</
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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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">Iam</
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>
verò cognita ſemidiametro Icoſaedri, inueniemus altitudinem pyra-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-242-05
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xlink:href
="
note-242-05a
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xml:space
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">Perpendicu-
<
lb
/>
laris è centro
<
lb
/>
ſphæræ ad ba-
<
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ſem Icoſaedri.</
note
>
midis, cuius baſis eſt triangulum Icoſaedri, & </
s
>
<
s
xml:id
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xml:space
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">vertex eiuſdem centrum, hoc mo-
<
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do. </
s
>
<
s
xml:id
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"
xml:space
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">Quoniam diameter Icoſaedri, eiuſdemque altitudo ſeſein centro ſecant bi-
<
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/>
fariam, concipiatur triangulum rectangulum, cuius baſis eſt diameter Icoſaedri
<
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/>
proximè cognita, latera verò circa angulum rectum, altitudo pyramidis, & </
s
>
<
s
xml:id
="
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"
xml:space
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">ſe-
<
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midiameter circuli baſem Icoſaedri circumſcribentis. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Cum ergo hęc ſemidia-
<
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meter cognoſci poſsit ex iis, quæ lib. </
s
>
<
s
xml:id
="
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xml:space
="
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">4. </
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>
<
s
xml:id
="
echoid-s9610
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xml:space
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">cap. </
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>
<
s
xml:id
="
echoid-s9611
"
xml:space
="
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">5. </
s
>
<
s
xml:id
="
echoid-s9612
"
xml:space
="
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">docuimus, cognoſcetur
<
note
symbol
="
d
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position
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xlink:label
="
note-242-06
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xlink:href
="
note-242-06a
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xml:space
="
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">3. triang. re-
<
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ctil.</
note
>
latus reliquum pyramidis, videlicet altitudo, quæ inquiritur. </
s
>
<
s
xml:id
="
echoid-s9613
"
xml:space
="
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">Semidiameter
<
lb
/>
porro circuli baſem triangularem Icoſaedri circumſcribentis effi cietur hoc et-
<
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/>
iam pacto cognita. </
s
>
<
s
xml:id
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xml:space
="
preserve
"> Quoniam trianguli æquilaterilatus potentia triplum
<
note
symbol
="
e
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position
="
left
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xlink:label
="
note-242-07
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xlink:href
="
note-242-07a
"
xml:space
="
preserve
">12. tertiidec.
<
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/>
Semidiame-
<
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ter circuli tri-
<
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angulum Ico-
<
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/>
ſaedricircum
<
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/>
ſcribentis.</
note
>
ſemidiametri illius circuli; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſi quadratum lateris Icoſaedri diuidatur per 3. </
s
>
<
s
xml:id
="
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xml:space
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">erit
<
lb
/>
Quotientis radix quadrata ſemidiameter quæſita.</
s
>
<
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</
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<
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<
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">6. </
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>
<
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">
<
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style
="
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">Eadem</
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>
hacarte, quæ in Dodecaedro, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Icoſaedro expoſita eſt, areas
<
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/>
Tetraedri, cubi, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Octaedriinueſtigare licebit, ſi, lineis ex eorum centris ad o-
<
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/>
mnes angulos ductis, in pyramides æquales diſtribuantur. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Tetraedrum </
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