Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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<
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præterea ſit rectilineum ABCD, ex puncto E, dato in latere AB, di-
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uidendum in duas partes, quarum prior ad B, vergens ad poſteriorem partem
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habeat proportionem datam K, ad L. </
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<
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xml:space
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">Ductis ex dato puncto E, ad omnes an-
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gulos oppoſitos rectis diuidentibus rectilineum in tot triangula vno minus,
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quotlatera figura habet; </
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<
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">inueniantur rectæ FH, HI, IG, triangulis EBC, ECD, EDA, proportionales. </
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<
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">Secta deindetota FG, in M, ſecundum datam propor-
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tionem K, ad L: </
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">quoniam diuiſionis punctum M, incidit in primam linea F H,
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diuidemus primi trianguli E B C, baſem BC, dato puncto E, oppoſitam in X, vt
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FH, ſecta eſt in M. </
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<
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">Iuncta namq; </
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<
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">recta EX, erit triangulum EBX, ad
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EXCDAE, vt FM, ad MG, hoc eſt, vt K, ad L: </
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<
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">propterea quod triangula E B C,
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ECD, EDA, rectis FH, HI, IG, proportionalia ſunt ex conſtructione; </
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<
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">primæ
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partes EBC, FH, ſectæ ſunt per rectam EX, & </
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">in M, proportionaliter; </
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">1. ſexti.</
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EBX, ad EXC, vt BX, ad XC, hoc eſt, vt FM, ad MH. </
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proportio data ſit N, ad O; </
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">ſecta FG, in P, ſecundum proportionem N,
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ad O, cadet diuiſionis punctum P, in ſecundam lineam HI. </
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">Igitur ſi ſecundi tri-
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anguli ECD, baſis CD, dato puncto E, oppoſita ſecetur in Q, vt ſecta eſt HI, in
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P, nectatur que recta EQ, erit rurſus figura EBCQE, ad figuram EQDA, vt
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ad PG, hoc eſt, vt N, ad O.</
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<
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denique data ſit proportio R, ad S; </
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<
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">ſecta FG, in V, ſecundum proportio-
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nem R, ad S, cadet diuiſionis punctum V, in tertiam lineam I G. </
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ſi tertij trianguli EDA, baſis DA, dato puncto E, oppoſita ſecetur in T, vt ſecta
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eſt IG, in V, iungaturque recta ET; </
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<
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"> erit rurſus figura EBCDTE, ad
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ETA, vt FV, ad VG, hoc eſt, vt R, ad S.</
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<
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hac via procedendum eſt in omnibus alijs figuris, quæ latera toti-
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dem habeant, quot angulos, id eſt, in quibus omnes anguli introrſum vergant.</
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<
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hoc problema efficiemus in rectilineo, cuius anguli partim extror-
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ſum vergant, & </
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<
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">partim introrſum, dummodo ab angulo, vel puncto dato in la-
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tere ducipoſsint lineæ rectæ diuidentes rectilineum in triangula quæ nullũ ipſi-
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us latus ſecent. </
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<
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">Vt in hac figura octo laterum ABCDEFGH, cuius quinque an-
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guli B, C, D, F, H, introrſum vergunt, & </
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<
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</
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<
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