Clavius, Christoph
,
Geometria practica
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LIBER QVINTVS.
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duo A D E H, B C F G, & </
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<
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ſe parallela, & </
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<
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">æqualia, dicitur parallelepipedum, Huius area ita inueſtigabitur.
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lepipedirectã-
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guli.</
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Sit primò propoſitum parallelepipedum rectangulum habens omnia ſex pa-
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rallelo gramma rectangula, ac proinde omnes eius angulos ſolidos rectos: </
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<
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que longitudo baſis AB, palm. </
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<
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<
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<
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<
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<
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">altitudo AH, palm. </
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<
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</
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<
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<
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<
s
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">vt producatur baſis palmorum
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<
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6. </
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<
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<
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<
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<
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<
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ducatur in altitudinem 4. </
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<
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<
s
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pipedo contineri 24 cubos, quorũ ſingula latera ſingulos palmos complectun-
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tur, quod ita planum faciemus. </
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<
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">Exponatur ſeorſum rectangulum I K L M, æ-
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quale baſi ABCD, intelligaturque altitudo per-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/235-01
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pendicularis L N, 4. </
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<
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<
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tus I M, palm. </
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<
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<
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<
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<
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baſis palmorum quadratorum 6. </
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<
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concipiantur extructi 6. </
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<
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bunt ij parallelepipedum vſq; </
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<
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mum L Q, altitudinis. </
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<
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<
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quales prioribus ſuperimp onantur, implebit@r parallelepipedum vſq; </
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<
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dum palmum altitudinis QP. </
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<
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<
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</
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<
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">tertium palmum P O, altitudinis implebunt. </
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<
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">Denique alij 6. </
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<
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tum parallelepipedum explebunt vſque ad quartũ altitudinis palmum O N. </
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<
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Conſtat ergo in toto parallelepipedo exiſtere toties 6. </
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<
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palmus in altitudine continetur, hoc eſt cubos 24.</
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</
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<
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<
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deinde parallelepipedum ABCE, cuius baſes ABCD,
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-
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lepipedi nõre
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-
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ctanguli.</
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EFGH, ſint Rhombi, vel Rhomboides, ac latera AH, DE, DE, BG, CF, ad ba-
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ſem A B C D, recta, ita vt altitudo ſit A H. </
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<
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ABCD, vt lib. </
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<
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<
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<
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<
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<
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<
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<
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catur. </
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<
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<
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">numerus erit parallelepipedi area. </
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<
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xml:space
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">Nam ſi fiat rectan-
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gulum IL, baſi AC, æquale, & </
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<
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">ſupra illud concipiatur parallelepipedũ rectan-
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gulũ, cuius altitudo LN, altitudini AH, ſit æqualis erit hoc
<
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parallelepipedo ACE, æquale. </
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<
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">Cum ergo parallelepipedum, cuius baſis rectan-
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gulum IL, & </
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<
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">altitudo LN, producatur ex altitudine LN, in baſem IL, vt oſten-
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ſem eſt, producetur quoque parallelepipedum ACE, ex altitudine AH, in ba-
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ſem AC, baſi IL, æqualem.</
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</
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<
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<
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nullum latus parallelepipedi rectum eſt ad baſem, demittenda erit ex ali-
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quo angulo ſupremi parallogrammi ad planum, in quo baſis, linea perpendi-
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cularis, pro altitudine parallelepipedi, eaque diligenter metienda. </
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<
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<
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baſis inueſtigetur vel per cap. </
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<
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<
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<
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<
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">quando eſt rectangula, vel per cap. </
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<
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</
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<
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<
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">quando non eſtrectangula, eaque in altitudinem inuentam duca-
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tur, producetur area propoſiti parallelepipedi. </
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<
s
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xml:space
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">Nam ſi ſupra baſem intelligatur
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parallelepipedum rectum eiuſdem altitudinis cum propoſito parallelepipedo,
<
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<
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">29. vel 30.
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vndec.</
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erunt duo hæc parallelepipeda inter ſeæqualia. </
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<
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<
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<
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">& </
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<
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">2.</
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<
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"> parallelepipedum rectum gigni ex ductu bafis in altitudinem.</
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<
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</
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<
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<
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<
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<
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, qui etiam parallelepipedum quoddam eſt rectangulum, eo dem
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<
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xlink:label
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">Area c ubi.</
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>
modo producitur, nimirum ex latere in ſe, & </
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<
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">iterum in productum. </
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<
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">Vt ſi latus
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cubi ſit 10. </
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<
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">erit eius area 1000. </
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<
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">quod decies decem decies procreent 1000.</
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<
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</
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<
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vndec.</
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<
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<
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<
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>
eſt figura ſolida, quæplanis continetur, quorum aduerſa </
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