My cousin built his house on the **vertex** of the highest hill in the county.

The **vertex** of my roof needs some serious repair.

It may be noticed that if the scales of x and be properly adjusted, the curve of positions in the present problem is the portion of a cycloid extending from a **vertex** to a cusp.

The **vertex** of the Washington Monument is made of aluminum, an extremely expensive material at the time of its construction.

Each **vertex** is singly enclosed by the five faces; the centre of each face is doubly enclosed by the succession of faces about the face; and the centre of the solid is doubly enclosed by the faces.

The [ox's] horns are of nearly equal size in both sexes, are placed on or near the **vertex** of the skull, and may be either rounded or angulated, while their direction is more or less outwards, with an upward direction near the tips, and conspicuous knobs or ridges are never developed on their surface.

The solid angles subtended by all normal sections of a cone at the **vertex** are therefore equal, and since the attractions of these sections on a particle at the **vertex** are proportional to their distances from the **vertex**, they are numerically equal to one another and to the solid angle of the cone.

It may be shown to be the locus of the **vertex** of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.

To comprehend more exactly the discovery of Apollonius, imagine an oblique cone on a circular base, of which the line joining the **vertex** to the centre of the base is the axis.

With a **vertex** much more distant the desired effect would be impaired, and with one nearer neither of the poles would be seen, whilst the exaggeration of China would have been too gross for a professed representation of the hemisphere.

The cube may have originated by placing three equal squares at a common **vertex**, so as to form a trihedral angle.

If three equilateral triangles be placed at a common **vertex** with their covertical sides coincident in pairs, it is seen that the base is an equal equilateral triangle; hence four equal equilateral triangles enclose a space.

Each **vertex** is singly enclosed by the succession of faces about it; and the centre of the solid is quadruply enclosed by the faces.

Each **vertex** is doubly enclosed by the succession of covertical faces, while the centre of the solid is triply enclosed by the faces.