Elements of Geometry And Conic Sections
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In our eReader you can find the full English version of the book. Read Elements of Geometry And Conic Sections Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of Geometry And Conic Sections
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Therefore ' if a straight line &c.
BOOK VII.
119 PROPOSITION XI. TFEOREM.
Two planes, which are perpendicular to the same straight line, are parallel to each other.
Let the planes MN, PQ be perpendicular to the line AB ; then will they be parallel to each other.
For if they are not parallel, they will meet if produced. Let them be produced and meet in C. Join AC, BC. Now the line AB, which is perpendicular to the plane MN, is perpendicular to the line AC drawn through its foot in that plane. Fo...r the same reason AB is perpendicular to BC. Therefore CA and CB are two perpendiculars let fall from the same point C upon the same straight line AB, which is impossible (Prop. XVI. , B. I. ). Hence the planes MN, PQ, can not meet when produced ; that is, they are parallel to each other. There- fore, two planes, &c.
PROPOSITION XII. THEOREM.
If two parallel planes are cut by a third plane, their common sections are parallel.
Let the parallel planes MN, PQ be cut by the plane ABDC ; and let their common sections with it be AB, CD ; then will AB be parallel to CD.
What to read after Elements of Geometry And Conic Sections?
You can find similar books in the "Read Also" column, or choose other free books by Elias Loomis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Therefore ' if a straight line &c.
BOOK VII.
119 PROPOSITION XI. TFEOREM.
Two planes, which are perpendicular to the same straight line, are parallel to each other.
Let the planes MN, PQ be perpendicular to the line AB ; then will they be parallel to each other.
For if they are not parallel, they will meet if produced. Let them be produced and meet in C. Join AC, BC. Now the line AB, which is perpendicular to the plane MN, is perpendicular to the line AC drawn through its foot in that plane. Fo...r the same reason AB is perpendicular to BC. Therefore CA and CB are two perpendiculars let fall from the same point C upon the same straight line AB, which is impossible (Prop. XVI. , B. I. ). Hence the planes MN, PQ, can not meet when produced ; that is, they are parallel to each other. There- fore, two planes, &c.
PROPOSITION XII. THEOREM.
If two parallel planes are cut by a third plane, their common sections are parallel.
Let the parallel planes MN, PQ be cut by the plane ABDC ; and let their common sections with it be AB, CD ; then will AB be parallel to CD.
What to read after Elements of Geometry And Conic Sections?
You can find similar books in the "Read Also" column, or choose other free books by Elias Loomis to read onlineMoreLess
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