# Robert Franklin Muirhead's papers

We list below as many of Robert Franklin Muirhead's papers as we can find. If anyone knows of further papers by Muirhead, please let us know so we can add them to our list.

- Robert Franklin Muirhead, On a Substitute for Euclid's Third Postulate,
*Proceedings of the Royal Philosophical Society of Glasgow***12**(1880), 112-118.

- Robert Franklin Muirhead, Report by R F Muirhead to the British Association,
*Proceedings of the Royal Philosophical Society of Glasgow***13**(1) (1880), 93-95.

- Robert Franklin Muirhead, The laws of motion,
*The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science*(5)**13**(1887), 473-489.

- Robert Franklin Muirhead, Demonstration on dilatancy,
*Proceedings of the Royal Philosophical Society of Glasgow***18**(1887), 400; 418.

- Robert Franklin Muirhead, On E Carpenter's proof of Taylor's theorem,
*Proceedings of the Edinburgh Mathematical Society***12**(1894), 114-117.

- Robert Franklin Muirhead, Proof of a theorem in conics,
*Proceedings of the Edinburgh Mathematical Society***13**(1895), 156-159.

- Robert Franklin Muirhead, Note on triangle transformations 1,
*Proceedings of the Edinburgh Mathematical Society***13**(1895), 112-114.

- Robert Franklin Muirhead, Note on triangle transformations 2,
*Proceedings of the Edinburgh Mathematical Society***13**(1895), 129-131.

- Robert Franklin Muirhead, Some suggestions in mathematical terminology,
*Proceedings of the Edinburgh Mathematical Society***13**(1895), 143.

- Robert Franklin Muirhead, On some suggestions in mathematical terminology,
*The Mathematical Gazette***1**(6) (1895), 57.

- Robert Franklin Muirhead, On the number and nature of the solutions of the Apollonian contact problem,
*Proceedings of the Edinburgh Mathematical Society***14**(1896), 135-147.

- Robert Franklin Muirhead, On superposition by the act of dissection,
*Proceedings of the Edinburgh Mathematical Society***14**(1896), 109-112.

- Robert Franklin Muirhead, On deducing the properties of the trigonometrical functions from their addition equations,
*Proceedings of the Edinburgh Mathematical Society***14**(1896), 127-134.

- Robert Franklin Muirhead, Notes on elementary dynamics I,
*The Mathematical Gazette***1**(8) (1896), 32-34.

- Robert Franklin Muirhead, Notes on elementary dynamics II,
*The Mathematical Gazette***1**(9) (1896), 60-64.

- Robert Franklin Muirhead, Notes on elementary dynamics III,
*The Mathematical Gazette***1**(10) (1897), 78-81.

- Robert Franklin Muirhead, Notes on elementary dynamics IV. The parallelogram of velocities, and relative velocities,
*The Mathematical Gazette***1**(12) (1897), 123-126.

- Robert Franklin Muirhead, On a method of studying displacement,
*Proceedings of the Edinburgh Mathematical Society***15**(1897), 119-128.

- Robert Franklin Muirhead, On the proof of the formula $s = ut + \large\frac{1}{2}\normalsize at^{2}$,
*The Mathematical Gazette***1**(11) (1897), 106.

- Robert Franklin Muirhead, On the transformation sequence,
*Proceedings of the Edinburgh Mathematical Society***16**(1898), 70-76.

- Robert Franklin Muirhead, Notes on elementary dynamics V,
*The Mathematical Gazette***1**(14) (1898), 180-184.

- Robert Franklin Muirhead, Permutations: Alternative proofs of elementary formulas,
*Proceedings of the Edinburgh Mathematical Society***16**(1898), 68-69.

- Robert Franklin Muirhead, Question 13651,
*Educational Times***69**(1898), 52-54.

- Robert Franklin Muirhead, A proof of the binomial theorem when the exponent is a positive integer,
*Proceedings of the Edinburgh Mathematical Society***17**(1899), 42.

- Robert Franklin Muirhead, Against Euler's proof of the binomial theorem for negative and fractional exponents,
*Proceedings of the Edinburgh Mathematical Society***17**(1899), 38-39.

- Robert Franklin Muirhead, Note on continued fractions,
*Proceedings of the Edinburgh Mathematical Society***17**(1899), 39-41.

- Robert Franklin Muirhead, Question 13735,
*Educational Times***70**(1899), 84-86.

- Robert Franklin Muirhead, Question 13651,
*Educational Times***71**(1899), 121-122.

- Robert Franklin Muirhead, Remark on Dr. Peddie's proof,
*Proceedings of the Edinburgh Mathematical Society***18**(1900), 32.

- Robert Franklin Muirhead, The dissection of any two triangles into mutually similar pairs of triangles,
*Proceedings of the Edinburgh Mathematical Society***18**(1900), 5-10; 100.

- Robert Franklin Muirhead, Stress - its definition,
*Nature***64**(1901), 207.

- Robert Franklin Muirhead, Inequalities relating to some algebraic means,
*Proceedings of the Edinburgh Mathematical Society***19**(1901), 36-45.

- Robert Franklin Muirhead, The teaching of mathematics,
*The Mathematical Gazette***2**(29) (1901), 81-83.

- Robert Franklin Muirhead, Note on the theory of the rolling of one rigid surface on another,
*Proceedings of the Edinburgh Mathematical Society***20**(1902), 8-10.

- Robert Franklin Muirhead, Notes on the theorems of Menelaus and Ceva,
*Proceedings of the Edinburgh Mathematical Society***20**(1902), 62-66.

- Robert Franklin Muirhead, Geometry of the isosceles trapezium and the contra-parallelogram, with applications to the geometry of the ellipse,
*Proceedings of the Edinburgh Mathematical Society***20**(1902), 70-72.

- Robert Franklin Muirhead, Constructions connected with Euclid VI, 3 and 4, and the circle of Apollonius,
*Proceedings of the Edinburgh Mathematical Society***20**(1902), 67-69.

- Robert Franklin Muirhead, Mathematical Note 114,
*The Mathematical Gazette***2**(35) (1902), 201.

- Robert Franklin Muirhead, On a Model for Exhibiting a Classification of the Consonantal Sounds of the English Language,
*Proceedings of the Royal Philosophical Society of Glasgow***33**(1902), 232-234.

- Robert Franklin Muirhead, The axial dioptric system,
*The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science*(6)**6**(1903), 326-343.

- Robert Franklin Muirhead, Construction connected with the locus of a point at which two segments of a straight line subtend equal angles,
*Proceedings of the Edinburgh Mathematical Society***21**(1903), 158.

- Robert Franklin Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters,
*Proceedings of the Edinburgh Mathematical Society***21**(1903), 143-157.

- Robert Franklin Muirhead, Proofs that the arithmetic mean is greater than the geometric mean,
*The Mathematical Gazette***2**(39) (1903), 283-287.

- Robert Franklin Muirhead, Two trigonometric notes,
*The Mathematical Gazette***2**(41) (1903), 340-341.

- Robert Franklin Muirhead, Note on Mr Roseveare's "Chapter on Algebra",
*The Mathematical Gazette***2**(41) (1903), 341-342.

- Robert Franklin Muirhead, Minimum deviation through a prism, etc,
*Proceedings of the Edinburgh Mathematical Society***22**(1904), 76-79.

- Robert Franklin Muirhead, On the use of the term
*"*Power*"*in Geometry, and on the treatment of the*"*doubtful sign*"*,*Proceedings of the Edinburgh Mathematical Society***22**(1904), 68-73.

- Robert Franklin Muirhead, Solution of a geometrical problem,
*Proceedings of the Edinburgh Mathematical Society***22**(1904), 74-75.

- Robert Franklin Muirhead, Definitions of trigonometrical ratios, and general proof of addition-theorems for sine and cosine,
*The Mathematical Gazette***3**(47) (1904), 89-90.

- Robert Franklin Muirhead, Constructions with straight-edge and dividers,
*The Mathematical Gazette***3**(1905), 209-210.

- Robert Franklin Muirhead, A proof of Waring's expression for $\Sigma a_{r}$ in terms of the coefficients of the equation,
*Proceedings of the Edinburgh Mathematical Society***23**(1905), 71-74.

- Robert Franklin Muirhead, Some proofs of Newton's theorem on sums of powers of roots,
*Proceedings of the Edinburgh Mathematical Society***23**(1905), 66-70.

- Robert Franklin Muirhead, A proof of the multiplication theorem for determinants,
*The Messenger of Mathematics*(2)**35**(1905), 151-152.

- Robert Franklin Muirhead, Proof of an inequality,
*Proceedings of the Edinburgh Mathematical Society***24**(1906), 45-50.

- Robert Franklin Muirhead, The teaching of mechanics,
*The Mathematical Gazette***3**(55) (1906), 265-266.

- Robert Franklin Muirhead, Elementary methods for calculating first and second moments of simple configurations,
*Proceedings of the Edinburgh Mathematical Society***25**(1907), 107-113.

- Robert Franklin Muirhead, Convenient rules for elementary calculations as to thin lenses,
*The Mathematical Gazette***4**(65) (1907), 110-111.

- Robert Franklin Muirhead, A proof of the theorem that the vector-sum of the 'axes' of two couples is the 'axis' of their resultant,
*The Mathematical Gazette***4**(66) (1907), 129.

- Robert Franklin Muirhead, A method of calculating approximately high powers and roots of numbers without the aid of tables,
*The Mathematical Gazette***4**(1908), 302-306.

- Robert Franklin Muirhead, To express a determinant of the $n$th order in terms of compound determinants of the 2nd order, and vice-versa,
*Proceedings of the Edinburgh Mathematical Society***26**(1908), 15-17.

- Robert Franklin Muirhead, A graphic method of solving n simultaneous linear equations involving n unknowns,
*Proceedings of the Edinburgh Mathematical Society***26**(1908), 30-36.

- Robert Franklin Muirhead, Some considerations on Scottish Universities, with Special Reference to Needed Reforms,
*Proceedings of the Edinburgh Mathematical Society***40**(1909), 66-87.

- Robert Franklin Muirhead, Some proofs of the theorem that a chord of a circle passing through a point is divided harmonically by that point and its polar, etc,
*The Mathematical Gazette***5**(83) (1910), 182-185.

- Robert Franklin Muirhead, The anharmonic ratio of four points in a line,
*Proceedings of the Edinburgh Mathematical Society***28**(1910), 14-22.

- Robert Franklin Muirhead, On Wilkinson's method of treating the ninepoints circle with generalizations,
*Proceedings of the Edinburgh Mathematical Society***28**(1910), 129-147.

- Robert Franklin Muirhead, A method for successive graphic integrations,
*Proceedings of the Edinburgh Mathematical Society***29**(1911), 78-82.

- Robert Franklin Muirhead, Note on the use of the protractor,
*The Mathematical Gazette***6**(94) (1911), 156-157.

- Robert Franklin Muirhead, A mechanism for solving equations of the $n$th degree,
*Proceedings of the Edinburgh Mathematical Society***30**(1912), 69-74.

- Robert Franklin Muirhead, Notes on algebraic inequalities,
*Edinburgh Mathematical Society Notes***1912/13**(1913), 129-132.

- Robert Franklin Muirhead, Two theorems on determinants and their application to the proof of the volume-formula for tetrahedra,
*Edinburgh Mathematical Society Notes***1912/13**(1913), 151-153.

- Robert Franklin Muirhead, Notes on mathematical induction,
*Proceedings of the Edinburgh Mathematical Society***31**(1913), 47-53.

- Robert Franklin Muirhead, On superposition as a basis for geometry - its logic, and its relation to the doctrine of continuous quantity,
*Proceedings Fifth International Congress of Mathematicians***2**(1913), 505-511.

- Robert Franklin Muirhead, Some graphical methods for determining centres of gravity,
*Proceedings of the Edinburgh Mathematical Society***32**(1914), 36-43.

- Robert Franklin Muirhead, The anharmonic ratio of four points in space and the discord of two pairs of points,
*The Mathematical Gazette***7**(1914), 326-328.

- Robert Franklin Muirhead, Theorems analogues to Newton's theorems on symmetric functions, with elementary proofs,
*Proceedings of the Edinburgh Mathematical Society***32**(1914), 44-48.

- Robert Franklin Muirhead, Centre of curvature,
*Edinburgh Mathematical Society Notes***20**(1916), 235-237.

- Robert Franklin Muirhead, Rolling loads: a new graphical method,
*Proceedings of the Edinburgh Mathematical Society***36**(1917), 96-102.

- Robert Franklin Muirhead, A trigonometrical lubrication,
*The Mathematical Gazette***10**(1920), 66-68.

- Robert Franklin Muirhead, A proof of the formula for a volume of a tetrahedron, in terms of the rectangular coordinates of its vertices,
*The Mathematical Gazette***10**(154) (1921), 324-325.

- Robert Franklin Muirhead, On curvature, tortuosity, and higher flexures of a curve in flat space of $n$ dimensions,
*The Messenger of Mathematics*(2)**52**(1922), 45-48.

- Robert Franklin Muirhead, Extension of some definitions and propositions in Euclid's book XI, and remarks,
*The Mathematical Gazette***11**(1923), 332-333.

- Robert Franklin Muirhead, Direct method for finding $\log_{10}3$,
*The Mathematical Gazette***11**(166) (1923), 389.

- Robert Franklin Muirhead, The Stroud system,
*The Mathematical Gazette***12**(172) (1924), 207-208.

- Robert Franklin Muirhead, Note on topics of regions separated by boundaries,
*Proceedings of the Edinburgh Mathematical Society***43**(1925), 111-114.

- Robert Franklin Muirhead, New proof of the theorem that the arithmetic mean of n positive numbers is greater than their geometric mean, if the numbers are not all equal,
*The Mathematical Gazette***12**(1925), 390-391.

- Robert Franklin Muirhead, Theorems on limits,
*The Mathematical Gazette***13**(1926), 200-201.

- Robert Franklin Muirhead, Note on the geometry of the parabola,
*The Mathematical Gazette***14**(1929), 359-361.

- Robert Franklin Muirhead, Curvature of a roulette. Elementary proof of a formula,
*The Mathematical Gazette***14**(1929), 506-507.

- Robert Franklin Muirhead, A footnote to Euclid, book III,
*Edinburgh Mathematical Society Notes***24**(1929), 8-11.

- Robert Franklin Muirhead, Elementary proof of a theorem about maxima and minima of $f (x)$,
*Edinburgh Mathematical Society Notes***24**(1929), 7-8.

- Robert Franklin Muirhead, A proof of the binomial theorem for a positive integral index,
*The Mathematical Gazette***15**(1930), 165-166.

- Robert Franklin Muirhead, How ought a logarithm to be defined?,
*The Mathematical Gazette***15**(216) (1931), 488-489.

- Robert Franklin Muirhead, Proof of the formula for acceleration of a point moving with uniform speed in the circumference of a circle,
*The Mathematical Gazette***15**(1931), 360.

- Robert Franklin Muirhead, Approximating to a square root,
*The Mathematical Gazette***17**(1933), 84-86.

- Robert Franklin Muirhead, Note on the decimal point,
*The Mathematical Gazette***19**(232) (1935), 42-43.

- Robert Franklin Muirhead, Solution of the triangle, Given $a, b, A$ (The "Ambiguous Case"),
*The Mathematical Gazette***20**(237) (1936), 55.

- Robert Franklin Muirhead, A proof of the binomial theorem for a positive integral exponent,
*The Mathematical Gazette***23**(1939), 473-475.

- Robert Franklin Muirhead, An algebraic note,
*The Mathematical Gazette***23**(1939), 471-473.

Last Updated March 2021