Elementary Geometry

  title={Elementary Geometry},
  author={William Desborough Cooley},
YOUR correspondent, “A Father,” has in view a very desirable object—to teach a young child geometry—but I fear that he is likely to miss altogether the path by which it may be reached. His principle, that “a child must of necessity commit to memory much that he does not comprehend,” appears to me to be totally erroneous, and not entitled to be called a fact. To this time-hallowed principle it is due that a large proportion of all who go to school learn nothing at all, while those more… 
In colloquial language the term elementary geometry is used loosely to refer to the body of notions and theorems which, following the tradition of Euclid's Elements, form the subject matter of
Geometrical Semantics for Spatial Prepositions
A classification of the kinds of geometry that underlie the basic meaning of various spatial prepositions and distinguishes between spatial preposition requiring a point of view and those that do not and places this distinction, along with others, in a geometrical framework.
This paper focuses on a specific case study which has been the subject of such an effort, namely the foundational analysis of the plane version of Desargues' theorem on homological triangles and its implications for the relationship between plane and solid geometry.
Axiomatizing changing conceptions of the geometric continuuum
We begin with a general account of the goals of axiomatization, introducing a variant (modest) on Detlefsen’s notion of ‘complete descriptive axiomatization’. We examine the distinctions between the
The Essential but Implicit Role of Modal Concepts in Science
  • P. Suppes
  • PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
  • 1972
When J. C. C. McKinsey and I were working on the foundations of mechanics many years ago, we thought it important to give a rigorous axiomatization within standard set theory, and we therefore
Carving Up Space: Existential Axioms for a Formal Theory of Spatial Regions
In this paper I investigate how one might arrive at a set of existential axioms that would specify a complete 1st-order theory of spatial regions. In such a theory all formulae would be true or false
A computational account of conceptual blending in basic mathematics
"The whole is greater than the part": Mereology in Euclid's elements
The present article provides a mereological analysis of Euclid’s planar geometry as presented in the first two books of his Elements . As a standard of comparison, a brief survey of the basic
Kant on geometry and spatial intuition
It is argued that diagrammatic interpretations of Kant's theory of geometrical intuition can, at best, capture only part of what Kant’s conception involves and that, for example, they cannot explain why Kant takes geometric constructions in the style of Euclid to provide us with an a priori framework for physical space.
Finding Proofs in Tarskian Geometry
  • M. Beeson, L. Wos
  • Computer Science, Mathematics
    Journal of Automated Reasoning
  • 2016
A methodology for the automated preparation and checking of the input files for the theorems in Tarskian geometry, to ensure that no human error has corrupted the formal development of an entire theory as embodied in two hundred input files and proofs.