Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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maiora ſuntlatere AC; </
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<
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drata AD, DC, minora duobus quadratis AB, BC. </
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<
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minus duplo quadratorum AD, DC: </
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<
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quadratis AD, DC, vna cum rectangulo bis ſub AD, DC; </
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<
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gulum bis, minus eſt duobus quadratis AD, DC, ex Lemmate propoſ. </
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quod erat demonſtrandum.</
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<
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tremæ à media æqualiter diſtant, rectam lineam ducere, & </
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per datum punctum in media, ſi omnes tres in vno puncto conue-
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niant; </
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qualia, vel datam habeant proportionem.</
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tres rectæ AB, CD, EF. </
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tres. </
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">qua ſecta bifariamin G, ſi quidem punctum G, cadet in mediam, factum
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erit, quodiubetur. </
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">Si verò G, cadet extra lineam mediam CD, agatur per G,
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alteri extremarum, nimirum ipſi EF, (dummodo einon æquidiſtet media CD)
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parallela AG, ſecans mediam in C. </
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enim CD, ponatur non æquidiſtareipſi
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EF, ſecabit vtique productam EF, & </
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inde eius quoque parallelam AG. </
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ſi CD, ipſi EF, æquidiſtaret, ducenda eſſet
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per G, ipſi AB, parallela. </
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puncto ductæ rectæ BF, ſumpto in extre-
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ma AB, cui non æquidiſtat AG, ducatur
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per C, vbi parallela AG, mediam CD, ſe-
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cat, recta BC, ſecans EF, in E. </
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ctas BC, CE, æquales eſſe. </
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triangulo BEF, recta CG, ſit baſi EF, parallela: </
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ad CE; </
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æqualis erit.</
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ſi per G, agatur ipſi AB, parallela GI, ſecans mediam CD, in I; </
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ducta FIK, ſecta quoque bifariam in I: </
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GI, baſi BK, æquidiſtat; </
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que FK, in I, bifariam ſecabitur.</
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his patet, cur media linea non debeat vtrique extremæ æquidiſtare, ſed
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vel neutri, vel alteri tantum. </
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<
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parallela alterutra extremarum, æquidiſtaret quoque mediæ, ac proinde eam
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non ſecaret. </
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extremarum. </
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rallela.</
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<
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verò ſi tres datæ rectæ coeant in eodem puncto productæ, vt in H,
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facilius erit problema, etiamſi in media linea detur punctum C, per quod </
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