## Proceedings of the Edinburgh Mathematical Society, Volumes 15-16 |

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### Common terms and phrases

a₁ algebraic angles applied axes axis B.Sc B₁ base centre circle College complete conic constant containing corresponding curve definition denote direction displacement distance Edinburgh elliptic integral equal equation Euclid's example expression factors figure force function geometrical George given gives Glasgow Hence infinite integral JOHN kind l'on lemniscate limit magnitudes Mathematics means meet method Note obtained parallel perpendicular plane position possible problem produced Professor proof proved quantities racines ratio relation represented respectively result satisfied School seen sequence sides similar Similarly solid solution space square suppose surface symbol theorem theory tractions transformation triangle unit University values zero α₁

### Popular passages

Page 81 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.

Page 115 - In the three sides of an equiangular field stand three trees at the distances of 10, 12, and 16 chains from one another ; to find the content of the field, it being the greatest the data will admit of.

Page 26 - Formeln und Lehrsätze zum Gebrauche der elliptischen Functionen, nach Vorlesungen und Aufzeichnungen des Herrn K.

Page 102 - The quantuplicity of A with respect to B may be estimated by examining how the multiples of A are distributed among the multiples of B, when both are arranged in ascending order of magnitude and the series of multiples continued without limit.

Page 39 - In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them.

Page 100 - II. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less, that is, ' when the greater contains the less a certain number of times exactly.' III. " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.

Page 102 - If CP and BP be produced to E and F, it will appear from Art. 35. and 36. that the Sine of BPE muft be to that of APE, as a to b; and the Sine of CPF (BPE) to that of APF, as a to r.

Page 76 - ... Nine-points Circle. If any conic be inscribed in a given triangle and a confocal to it pass through the circumcentre , then the circle through the intersection of these two confocals touches the nine-points circle of the triangle (p. 74—75). S 2 CHS CARSLAW. The Steady Motion of a Spherical Vortex. The possibility of the steady motion of a spherical vortex of constant vorticity in an infinite homogeneous liquid was first pointed out by Hill in the Phil. Trans., 1894, p. 213—245 (Rev. sem....

Page 47 - Stewart's theorem enables us to resolve easily the following problem : " To draw a circle touching another given circle and passing through two given points.