Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ILLUST. QUORUND. PROB. CONSTRUCT.
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<
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. V.</
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<
s
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">duobus contiguis lateribus
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productis, aptare ſub angulo interiori rectam
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magnitudine datam quæ per angulum oppoſitum
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tranſeat. </
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<
s
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xml:space
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quam ſit quadrati diameter dupla.</
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<
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<
s
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xml:space
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">Datum ſit quadratum A B, productaque latera A F, A E.</
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<
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Fig. 8.</
note
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<
s
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xml:space
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">Data verò linea K, non minor duplâ A B diametro. </
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<
s
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xml:space
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">Et
<
lb
/>
oporteat per angulum B ponere rectam D C ipſi K æqua-
<
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lem.</
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<
s
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xml:space
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">Si K æqualis fuerit duplæ A B, conſtructio manifeſta eſt;
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</
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<
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xml:space
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">tunc enim per B ducenda eſt quæ ſit ipſi A B ad angulos re-
<
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ctos, eaque propoſitum efficiet. </
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<
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xml:space
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">Cum verò major erit K quam
<
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dupla A B, conſtructio iiſdem verbis præcipitur atque in Pro-
<
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blemate præcedenti: </
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<
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xml:space
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">& </
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<
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">demonſtratio quoque eſt eadem.</
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</
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<
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<
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xml:space
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">Quod autem circumferentia B C G ſecabit productam A F
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hinc manifeſtum eſt. </
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<
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xml:space
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">Etenim quia K major eſt duplâ diame-
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tro A B, erit K quadratum majus octo quadratis E B. </
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<
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xml:space
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quadratum E G majus quam quadrata novem ex E B; </
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<
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inde E G major quam tripla E B. </
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<
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xml:space
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">Dimidia igitur B G, hoc
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eſt, radius deſcripti ſemicirculi major quam E B vel B F;
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<
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">unde neceſſe eſt rectam A C ſecari à circumferentia B C G.</
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<
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emph
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VI.</
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<
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">uno latere producto, aptare
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ſub angulo exteriori lineam magnitudine da-
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tam quæ ad oppoſitum angulum pertineat.</
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</
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<
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<
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xml:space
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<
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Fig. 1.</
note
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autem linea K. </
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pars intercepta D C ſit ipſi K æqualis.</
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<
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<
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dratis ex K & </
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<
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