Transactions of the Cambridge Philosophical Society..University Press, 1898 - Science |
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Common terms and phrases
a₁ aa aa abcd algebraically independent angles arbitrary functions ɑɑ B₁ B₂ circles touching circumcircles circumspheres coefficients concyclic concyclic points corresponding cos² denote derived differential equation displacements Euclid's Elements expression five four spheres geometry given Hart tetrads Hence hyperspheres intermediary integral intersection inverse tetrad k²pa² Latin Rectangles Latin Squares latitude line geometry linear complex magnitude meet multiples notation obtained operators P₁ partial differential equations permutations planes Prop PROPOSITION prove radial ratio result satisfied scale second order sin² solution supplementary angle surface forces symmetric function tetrahedron theorem U-conics U₁ u₁y V₁ values vanish w₁ x₁ Y₁ α₁ απ аф д д дв ди ди дф дх
Popular passages
Page 99 - ... a, b' and b, c' and c, d' and d' are the exterior-interior or corresponding angles.
Page 66 - ... surface varies as the cosine of the angle between the normal to the surface and the direction of the radiation.
Page 232 - ... a therefore and b are not unequal ; that is, they are equaL. Next, let c have the same ratio to each of the magnitudes a and b ) a is equal to b. For, if they are not, one of them is greater than the other ; let a be the greater ; therefore as was shewn in Prop.
Page 249 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 15 - ... 14, p. 308, and applies them to two classes of cases in which results of a general character are obtainable, the first class consisting of the vibrations of a solid sphere due to forces whose frequency is small compared to that of the fundamental free vibration of the same type , the second class of the forced vibrations of any frequency in a very thin spherical shell (p. 14 — 57). U 10 a. R.
Page 152 - ... spheres with 8 points on every sphere and 5 spheres through every point. Grace went on to show that starting from six spheres through a point we obtain a figure of 72 points and 27 spheres; and starting from seven spheres through a point we obtained a figure of 576 points and 126 spheres; and he remarks: 'Similar sets of points probably exist in which there are eight, nine . . . spheres through each point, but as the number of points increases the difficulties as to notation become very great.
Page 249 - ... required. Again, if we wish to find the ratio of two solids, A and B, we seek some unit of measure which is contained an exact number of times in each of them. If we take a cubic inch as the unit of measure, and we find it to be contained 9 times in A, and 13 times in B, then the ratio of A to B is the same as that of 9 to 13.
Page 261 - ... different letters appearing in each row and in each column. He and subsequent writers have called such squares " Latin Squares," and we have the question as to their enumeration for a given order. In regard to this matter he writes...
Page 236 - It is required to prove that if A, B, C, D are four magnitudes of the same kind, and if (A :B) = (C: D), and if A > C, then (AC:BD) = (A :B).
Page 263 - 2 + n — 2 relations between the coaxial minors of any determinant of the «th order (A certain class of generating functions in the theory of numbers, Phil. Trans., Vol. CLXXXV, p. 111 — 160). The relations are put in evidence for a particular determinant (p. 537—541). T 4 a , U 10. EP CULVERWELL. A Mode of Calculating a Limit to the Direct Effect of Great Eccentricity of the Earth's Orbit on Terrestrial Temperatures , showing the Inadequacy of the Astronomical...