Clavius, Christoph
,
Geometria practica
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LIBER SEXTVS.
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part
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es æquales, detrahenda primum erit per lineam rectam ex dato puncto du-
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ctam pars denominata à numero partium, in quas diuidendum eſt triangulum.
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Deinde duæ tales partes: </
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">poſtea tres, atque ita deinceps, donec tot partes, vna
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minus, detractæ ſint, in quot partes diuidendum proponitur triangulum. </
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<
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triangulum ABC, ex puncto D, diuidendum ſit in quinque partes æquales, diui-
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demus latus BC, in quo datum punctum eſt, in quinque partes æquales, in pun-
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ctis E, F, G, H. </
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<
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">Iuncta deinderecta DA, ducemus ei parallelas EI, FK, GL, HM.
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</
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<
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">Sinamque connectantur rectæ D I, D K, D L, D M, diuiſum erit triangulum in
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quinque partes æquales. </
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<
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">Nam vt in dicta propoſ. </
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Euclid. </
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">oſtenſum eſt, triangulum DBI, eſt {@/5}. </
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<
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">totius trianguli, hoc eſt, ita ſe ha-
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bet DBI, ad ABC, vt BE, ad BC. </
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<
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">Triangulum autem DBK, continet {2/3}. </
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xml:space
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">totius
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trianguli, id eſt, ita ſe habet D B K, ad A B C, vt B F, ad B C. </
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<
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DBL, complectitur {3/5}. </
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<
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">totius trianguli, id eſt, ita ſe habet DBL, ad ABC, vt BG,
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ad BC. </
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">totius trianguli, hoc
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eſt, ita ſe habet ABDM, ad ABC, vt B H, ad B C. </
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<
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xml:space
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">Ex quo fit, reliquum triangu-
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lum DMC, eſſe {1/5}. </
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">eiuſdem trianguli ABC.</
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punctum datum eſt in vno angulo, manifeſtum eſt, ſi latus op-
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poſitum in tot partes ſecetur, in quot triangulum diuidendum eſt, rectas
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eo angulo ad puncta diuiſionum eductas ſecare triangulum in propoſitas par-
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tes æquales.</
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quales partes diuidere,</
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triangulum A B C, diuidendum verbi gratia in quatuor partes æquales
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perlineas lateri BC, æquidiſtantes. </
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mirum A B, in 4. </
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">partes æquales, in tot videlicet, in quot triangulũ diuidendum
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eſt, in punctis D, E, F. </
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