Clavius, Christoph
,
Geometria practica
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268
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GEOMETR. PRACT.
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totidem partes GI, IK, KL, LM, MH, illis ordine proportionales. </
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ſe, verbi gratia, duas partes AC, CD, ſimul ad reliquastres DE, EF, FB, ſimul, vt
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ſunt duæ GI, IK, ſimulad reliquas tres KL, LM, MH, ſimul, &</
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<
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eſt, vt AC, ad CD, ita GI, ad IK, erit componendo etiam, vt AD, ad CD, ita GK,
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ad IK: </
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<
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xml:space
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">Vtautem CD, ad DE, ita eſt IK, ad KL. </
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<
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xml:space
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">Igitur ex æqualitate erit, vt AD,
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ad DE, ita GK, ad KL.</
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quia conuertendo eſt, vt BF, ad F E, ita HM, ad ML; </
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<
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que componendo, vt BE, ad FE, ita HL, ad ML: </
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">Vtautem FE, ad ED, ita eſt
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ML; </
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<
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xml:id
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xml:space
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">ad LK. </
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<
s
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xml:space
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">Igitur ex æqualitate erit, vt B E, ad ED, ita HL, ad L K; </
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<
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fig-268-01
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ponendo, vt B D, ad E D, ita H K, ad L K; </
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<
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<
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xml:space
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">conuertendo, vt D E, ad D B, ita
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KL, ad KH. </
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<
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xml:space
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">Itaque cumoſtenſum ſit, eſſe vt AD, ad DE, ita vt GK, ad KL, & </
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<
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D E, ad D B, ita K L, ad K H; </
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<
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">erit ex æqualitate, vt A D, ad D B, ita G K,
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ad K H.</
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<
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aliter oſtendemus eſſe, vt AC, ad CB, ita GI, ad IH. </
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uertendo, componendo, & </
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">ex æqualitate erit vt B C, ad D C, ita HI, ad K I; </
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conuertendo, vt CD, ad CB, ita IK, ad IH. </
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<
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">Cum ergo ſit, vt AC, ad CD, ita GI,
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ad IK, & </
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<
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xml:space
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">vt CD, ad CB, ita IK, ad I H; </
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<
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">erit ex æqualitate, vt AC, ad CB, ita GI,
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ad I H.</
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<
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ratione erit, vt AF, ad FB, ita GM, ad MH. </
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ponendo, & </
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">ex æqualitate, vt AF, ad EF, ita GM, ad LM. </
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que, vt EF, ad FB, ita LM, ad MH: </
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">erit ex æqualitate, vt AF, ad FB, ita GM, ad
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MH; </
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<
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pars v. </
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<
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">tertia quo que pars KL, in duas KO, OL, illis proportionales. </
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que vt AN, ad NB, ita GO, ad OH. </
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">Erit enim conuertendo, vt EN, ad N D, ita
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L O, ad O K: </
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<
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">componendo, vt ED, ad DN, ita LK, ad K O. </
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<
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">Quare cum ſit,
<
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vt CD, ad DE, ita IK, ad KL, & </
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<
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<
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">erit ex æqualita-
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te, vt CD, ad DN, ita IK, ad KO, atque ita partes AC, CD, DN, partibus GI, IK,
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KO, proportionales ſunt.</
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<
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quia eſt conuertendo, vt FE, ad E D, ita ML, ad LK; </
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<
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<
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nendo, vt DE, ad NE, ita KL, ad OL; </
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<
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">erit exæqualitate, vt FE, ad E N, ita ML,
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ad LO; </
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<
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">conuertendo, vt NE, ad EF, ita OL, ad LM; </
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<
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tes AC, CD, DN, NE, EF, FB, omnibus partibus GI, IK, KO, OL, LM,
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M H, proportionales ſunt. </
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<
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tumeſt, erit vt AN, ad NB, ita GO, ad OH. </
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<
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ergo etiam ſecundum.</
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