File:2coni-sfera-comune.jpg
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Italiano: due coni con una sfera in comune - la genesi spaziale del polo di una retta p rispetto ad una circonferenza delta.
Da sempre si detto, nella geometria piana, che preso un punto V esterno ad una circonferenza delta e tracciati da esso due rette tangenti a delta, si ha due punti le cui unione e' la retta m detta polare del punto P rispetto a delta. Nello spazio considerando delta come circonferenza massima di una sfera K e appartenente al primo piano di proiezione pigreco1, e stabilito che il punto V sia il vertice del cono J tangente la sfera K (secondo la circonferenza B), si può osservare che la prima proiezione ortogonale di B e' la cosi detta retta polare m di V rispetto alla circonferenza delta. Bene !!!, preso un altro punto R' su pigreco1 come vertice di un secondo cono J' che tange la stessa sfera K, si ha che la prima proiezione della circonferenza di tangenza B' e' la polare m' del Polo R' rispetto alla circonferenza massima Delta. In questo modo il punto d'intersezione delle due rette polari m m', individua il polo P della polare p rispetto alla circonferenza delta. pertanto si fa osservare che la polare p e' la retta passante per i vertici R R' dei due coni J J'. Nello spazio, l'intersezione delle due circonferenze B B' (basi dei coni J J' sulla sfera K) e' una retta che interseca pigreco1 secondo il detto polo P. Quindi e' solo nello spazio che si può giustificare la genesi del Polo di una polare p rispetto alla circonferenza. Secondo la sopraddetta interpretazione, il polo e' una proiezione ortogonale di due punti di tangenza ad una stessa sfera condotti da due piani aventi in comune una retta (polare). Quindi tutti i coni che hanno vertici appartenenti ad una stessa retta (polare) e inviluppano una sfera K, sono tangenti K secondo due stessi punti.العربية: مخروطين مشتركين بنفس الكرة -- النشأة التكوينية لقطب خط مستقيم بالنسبة لدائرة
بالتالي, يلاحظ أن الخط القطبي بي يمر بقمتي المخروطين جي وجي‘. في الفراغ ، تقاطع الدائرتين ب ب‘ (قاعدتي المخاريط جي وجي‘ على الكرة كبا) تمثل الخط الذي يتقاطع مع المستوى باي وفقا للقطب المذكور. "لذلك فقط في الفراغ يمكن أن نبرر نشأة قطب خط بالنسبة لدائرة. وفقا للتفسير المذكور آنفا، القطب هو إسقاط عمودي لنقطتي تماس الكرة أجريتا بمستويين خطهما المشترك الخط القطبي. وبالتالي يمكن القول ان جميع المخاريط التي قممها تنتمي للخط القطبي ، ومتماسة للكرة كبا , تكون متماسة لمستويين يمسان الكرة وفقا لنقطتين فقط. |
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Source | Own work |
Author | Hasanisawi |
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File change date and time | 01:12, 18 October 2011 |
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Date and time of digitizing | 03:12, 18 October 2011 |
Date metadata was last modified | 03:12, 18 October 2011 |