## Proceedings of the Edinburgh Mathematical Society, Volume 2 |

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acid adiabatic arcs atoms bars base bisects centre CHRYSTAL circle coincide conic constant Construction contained continuous contour-lines corresponding curve Desargues described determine diagonal diminishes direction disques double draw drawn Edinburgh elector elements equal Euclid evidently external figure fixed formed Geometry given gives greater Hence hexagon increase indicated inscribed intersection isothermal join length less Mathematics meet moves MUIR obtained opposite sides optical original pair parallel parallelogram pass perpendicular plane polar pole position pressure problem produced Professor projective proof properties Proposition proved quadrant quadrilateral quantity region relation remain represents respectively result right angles segments Similarly small circles solid space sphere spherical triangle square straight line substance Suppose surface tangents temperature termed theorem third THOMAS tour triangle vertices volume voting

### Popular passages

Page 11 - Any two sides of a triangle are together greater than the third side.

Page 13 - The perpendiculars from the vertices of a triangle on the opposite sides are concurrent.

Page 11 - The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse.

Page 8 - The straight line, joining the points of bisection of two sides of a triangle, is parallel to the base.

Page 33 - The contour-line for a level immediately underneath that corresponding to the bar has a closed branch within the region of depression cut off. Thus the closed curve at I4, Fig. 24, is part of the contour-line ux. If a chart of an insular high-land be constructed as above indicated, a pass occurs at the node (see Fig. 24) of a figure-of-eight curve, (or out-loop curve, as Professor Cayley has termed it) ; while a bar occurs at the node of an in-loop curve. If, in Fig. 24, we interchange the summits...

Page 10 - В А С is equal to the angle В А' С, the angle BAG is likewise equal to the angle ED F. Therefore, &c. PROP. 1C. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each...

Page 11 - From this it follows at once, that the locus of the vertex of a triangle of constant area on a fixed base is a small circle.

Page 51 - If a perpendicular be drawn from the right angle to the hypotenuse of a right-angled triangle, and circles...

Page 14 - The perpendiculars from the vertices on the opposite sides of a triangle bisect the angles of the triangle formed by joining the feet of the perpendiculars.

Page 3 - This address will be found in The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science for January 1884, Fifth Series, vol.