The Net Advance of Physics RETRO:
GEOMETRY

Geometry in the Long Nineteenth Century.

Most material in Net Advance Retro antedates 1920. It may be obsolete or incorrect.

• General: Introductory:
  • Elementary and Constructional Geometry by Edgar Hamilton Nichols [New York: Longmans, Green, 1896]

• General:
  • Leçons de mathématiques donneées a l'École Normale en 1795 by Pierre Simon Laplace [Journal de l'École Polytechnique , VII & VIII (1812)]
  • The First Six Books of Euclid's Elements, in Which Coloured Diagrams and Symbols are Used Instead of Letters for the Greater Ease of Learners by Oliver Byrne [London: Pickering, 1847]
  • Elementary Geometry: Congruent Figures by Olaus Henrici [London: Longmans, Green, 1879]
  • A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry, with Numerous Examples by John Casey [Dublin: Hodges and Figgis, 1886]
  • The Elements of Geometry by George Bruce Halsted [London: Macmillan, 1886]
  • Elementary Synthetic Geometry by George Bruce Halsted [New York: Wiley, 1896]
  • Planimetry by A. P. Kiselyov [1892] 236 pp. In Russian. The Glagolev edition of the famous geometry textbook, slightly revised by N. Ershov et al.
  • Rational Geometry: A Text-Book for the Science of Space Based on Hilbert's Foundations by George Bruce Halsted [New York: Wiley, 1904]
    • Reviews of Rational Geometry edited by George Bruce Halsted [n.d.] Not surprisingly, they all tend to be favourable ones.

• General: Philosophy:
  • Mr. Mill's Theory of Geometrical Reasoning Mathematically Tested by Wm. Robertson Smith [Proceedings of the Royal Society of Edinburgh 6, 477 (1869)] Hostile critique of Mill's Logic from an intuitionist standpoint.
  • Note on Professor Bain's Theory of Euclid I.4 by Wm. Robertson Smith [Proceedings of the Royal Society of Edinburgh 7, 176 (1870)] Attacks Bain's Mill-influenced work Logic.
  • Dr. Stirling, Hegel, and the Mathematicians by Wm. Robertson Smith [Fortnightly Review, (1873 April)] Stirling was a translator and defender of Hegel.

• Types: GEOMETRIC ALGEBRA; VECTOR;

• Type: ANALYTIC:
  • A Treatise on Conic Sections and the Application of Algebra to Geometry by J. Hymers, D.D. [Cambridge: Deighton, 1845]

• Type: CONSTRUCTIONS:
  • How to Draw a Straight Line; a Lecture on Linkages by Alfred Bray Kempe [London: Macmillan, 1877]

• Type: METRICAL:
  • Metrical Geometry: An Elementary Treatise on Mensuration by George Bruce Halsted [Boston: Ginn, 1890]

• Type: NON-EUCLIDEAN:
  • The New Ideas About Space by George Bruce Halsted [Popular Science 11, 364 (1877)]
  • Sidelights on Relativity by Albert Einstein [London: Methuen, 1922]

• Type: PROJECTIVE:
  • An Explanation of the Gnomonic Projection of the Sphere; and of Such Points of Astronomy as are Most Necessary in the Use of Astronomical Maps by Augustus De Morgan [London: Baldwin & Craddock, 1836]
  • An Elementary Treatise on Trilinear Co-ordinates, the Method of Reciprocal Polars, and the Theory of Projections by N. M. Ferrers [Cambridge: Macmillan, 1866]
  • Geometrical Conic Sections: An Elementary Treatise, in Which the Conic Sections are Defined as the Plane Sections of a Cone, and Treated by the Method of Projections by Rev. J. Stuart Jackson [London: Macmillan, 1872]
  • Quaternions and Projective Geometry by Charles Jasper Joly [Phil. Trans. R.S.L. A201, 223 (1903)]
  • Synthetic Projective Geometry by George Bruce Halsted [New York: Wiley, 1906] "Man, imprisoned in a little body with short-arm hands instead of wings, created for his guidance a mole geometry, a tactile space, codified by Euclid ... Yet man is no mole."

• Type: TRIANGULAR:
  • On a New Property of the Tangents of Three Arches Trisecting the Circumference of a Circle by Rev. Nevil Maskelyne [Phil. Trans. R. S. L. 98, 122 (1808)] "Arch" meaning "angle" and "tangent" meaning "tangent line-segment".
  • An Elementary Treatise on Trilinear Co-ordinates, the Method of Reciprocal Polars, and the Theory of Projections by Rev. N. M. Ferrers [Cambridge: Macmillan, 1861]
  • A Treatise on Trilinear Co-ordinates, Intended Chiefly for the Use of Junior Students by C. J. C. Price [Oxford: Henry and Parker, 1866]
  • Trilinear Coordinates and Other Methods of Modern Analytical Geometry of Two Dimensions by Rev. Wm. Allen Whitworth [Cambridge: Deighton, Bell, 1866]
  • Notes on the Geometry of the Plane Triangle by John Griffiths [Oxford: Jas. Parker, 1867]
  • Tracts Relating to the Modern Higher Mathematics: Trilinear Coordinates by Rev. W. J. Wright [London: Hodgson, 1875]
  • A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections by John Casey [Dublin: Hodges and Figgis, 1885]
  • The Modern Geometry of the Triangle by Wm. Gallatly [London: Hodgson, 1910]

• Aspects: FOUNDATIONS:
  • The Connexion of Number and Magnitude: An Attempt to Explain the Fifth Book of Euclid by Augustus De Morgan [London: Taylor and Walton, 1836]
  • Sidelights on Relativity by Albert Einstein [London: Methuen, 1922]

• Aspects: MECHANICAL DEVICES:
  • How to Draw a Straight Line; a Lecture on Linkages by Alfred Bray Kempe [London: Macmillan, 1877]
  • Katalog mathematischer und mathematisch-physikalischer Modelle, Apparate und Instrumente by Walther von Dyck [Munich: Wolf, 1892]

• Aspects: CIRCLE SQUARING:
  • The Quadrature of the Circle: Correspondence between an Eminent Mathematician [Augustus De Morgan] and James Smith, Esq. [London: Simpkin & Marshall, 1861] Smith evidently believed the value of pi to be exactly 3.125, and was astonished at the hostile reception which this idea received.
  • A Budget of Paradoxes by Augustus De Morgan [London: Longmans, Green, 1872]
  • The Squaring of the Circle: An Historical Sketch of the Problem from the Earliest Times to the Present Day by Hermann Schubert [Monist 1, 197 (1890)]

THE NET ADVANCE OF PHYSICS --- Retro