The axioms of descriptive geometry, by A.N. Whitehead.
16 DESARGUES' PERSPECTIVE THEOREMS [CH. II Bl lies between the planes B21 and Al, or the plane B 1 lies between the planes B1l and Al, or the planes Bl and B21 are identical. But in either of the first two cases the intermediate plane intersects both semi-rays al and a2. Hence a plane is found through 1, intersecting both a1 and a2. Call it the plane B,'l. Again take any point B3 on as; and the same argument shews that at least one of B2'l and B31 intersects a,, a2, and a,. Proceeding in this way, a plane is finally found which intersects each of the n semi-rays. 17. Desargues' Perspective theorems* can be enunciated in the following modified forms: (1) If two coplanar triangles ABC and A'B'C' are such that the lines AA', BB', CC' are concurrent in a point 0, then the three inter sections of BC and B'C', CA and C'A', AB and A'B', if they exist, are collinear. * Cf. Proj. Geom. ~ 7.
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About this Item
- Title
- The axioms of descriptive geometry, by A.N. Whitehead.
- Author
- Whitehead, Alfred North, 1861-1947.
- Canvas
- Page 16
- Publication
- Cambridge,: University press,
- 1907.
- Subject terms
- Geometry, Descriptive
Technical Details
- Link to this Item
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https://name.umdl.umich.edu/abn2643.0001.001
- Link to this scan
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https://quod.lib.umich.edu/u/umhistmath/abn2643.0001.001/26
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IIIF
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https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:abn2643.0001.001
Cite this Item
- Full citation
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"The axioms of descriptive geometry, by A.N. Whitehead." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/abn2643.0001.001. University of Michigan Library Digital Collections. Accessed June 20, 2025.