The Axioms of Descriptive Geometry
The Axioms of Descriptive Geometry
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In our eReader you can find the full English version of the book. Read The Axioms of Descriptive Geometry 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 The Axioms of Descriptive Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
(y) Two projective lines in a proper projective plane necessarily intersect.
For let m and n be the projective lines and a be the proper projective plane, and a^ its associated plane. Take any point outside ttj. Then two planes Om and On exist, with which re- spectively all projective points of m and n cohere. These planes intersect in a line through 0, /, say. Let A be any point in aj.
The plane Al intersects aj in a line, l\ say. The two lines I and V define a projective point which lies in b...oth the projective liries m and n.
(S) Desargues' Theorem holds for triangles formed by projective lines and projective points in a proper projective plane.
By (y) immediately above, no exception arises from non-intersec- tion. Then by taking a point external to the associated plane, two trihedrons can be formed for which the theorem holds. Hence the theorem holds for the proper projective plane.
(€) The projections upon a proper projective plane of three projective points belonging to the same projective line also belong to a projective line.
What to read after The Axioms of Descriptive Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Whitehead, Alfred North, 1861-1947 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(y) Two projective lines in a proper projective plane necessarily intersect.
For let m and n be the projective lines and a be the proper projective plane, and a^ its associated plane. Take any point outside ttj. Then two planes Om and On exist, with which re- spectively all projective points of m and n cohere. These planes intersect in a line through 0, /, say. Let A be any point in aj.
The plane Al intersects aj in a line, l\ say. The two lines I and V define a projective point which lies in b...oth the projective liries m and n.
(S) Desargues' Theorem holds for triangles formed by projective lines and projective points in a proper projective plane.
By (y) immediately above, no exception arises from non-intersec- tion. Then by taking a point external to the associated plane, two trihedrons can be formed for which the theorem holds. Hence the theorem holds for the proper projective plane.
(€) The projections upon a proper projective plane of three projective points belonging to the same projective line also belong to a projective line.
What to read after The Axioms of Descriptive Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Whitehead, Alfred North, 1861-1947 to read onlineMoreLess
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