Annals of MathematicsPrinceton University Press, 1902 - Electronic journals |
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Common terms and phrases
a₁ analytic function anchor ring angle aßy axis C₁ Calculus of Variations cardioid Cauchy-Kowalewski theorem characteristic curves characteristic strip circle coefficients conic conjugate constant continued fractions corresponding cusps cyclic group defined denote derivative double points Duhamel's Theorem elements equations 15 geodesic line geometric group of isomorphisms group-determinant group-matrix Hence hyperbola identically imaginary infinitesimal inner equator integral curves integral strip integral surface intersection linear locus Math moment of inertia multiple points obtained open curves ORMOND STONE P₁ partial differential equation positive problem proof quadric quadruple points relation respectively S₁ S₂ satisfied substituted sufficient condition surfaces of translation t₁ t₁ mod t₂ three parameter family tion transformation triangle tricuspidal quartic v₁ values w₁ Wilson's theorem x₁ Y₁ zero дх
Popular passages
Page 17 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 49 - LOGARITHMS. 1. The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 49 - The logarithm of any number to a given base is the index of the power to which the base must be raised in order to equal the given number.
Page 163 - ... altitude. Now let us mark one apex 100 copper, another 100 tin, and the third 100 zinc, and the opposite sides zero copper, tin and zinc. Then any point in the triangle represents one alloy, and all the possible points represent all the possible alloys of the three metals. Now divide each altitude into ten parts, and through the points of division draw lines parallel to the three sides. The crossing points of these lines represent all the alloys whose constituents are even multiples of ten per...
Page 87 - A variable line which moves always parallel to itself cuts two fixed lines in P and Q ; the locus of the middle point of PQ is a straight line through the point of intersection of the two fixed lines.
Page 17 - ... second is the polar triangle of the first. PROPOSITION XI. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. PROPOSITION XII. PROPOSITION XIII. Two triangles on the same sphere are either equal or symmetrical when a side and the two adjacent angles of one are respectively equal to a side and the two adjacent angles of the other.
Page 49 - Therefore ф(х) becomes positively infinite as x increases indefinitely, and thus the first part of the theorem is proved. To prove the second part of the theorem, put ¿
Page 25 - Any positive rational number can be expressed in one and only one way in the form a, a. a,. 1.2 1.2.3 1.2.3. ..k' where al, a,, ..., ot are integers, and Oga1, 0^a,<2, Ogos<3, .... 0<at<fc.
Page 88 - Prove that the ordinate of the point of intersection of two tangents to a parabola is the arithmetical mean between the ordinates of the points of contact of the tangents.