It can be shown, for example, that for masonry having a density of 3, water being 1, the figure of minimum section is a right-angled triangle, with the water against its vertical face; while for a greater density the water face must lean towards the water, and for a less density away from the water, so that the water may lie upon it.

Menaechmus discussed three species of cones (distinguished by the magnitude of the vertical angle as obtuse-angled, right-angled and acuteangled), and the only section he treated was that made by a plane perpendicular to a generator of the cone; according to the species of the cone, he obtained the curves now known as the hyperbola, parabola and ellipse.

By adopting right-angled reflectionprisms above the eyepiece he completely erected the image.

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If the right-angled triangle abc, fig.

This triangle, for the convenience of calculation, we divide into two right-angled triangles.

Within the focus of the object-glass is a right-angled prism of total reflection, which diverts the converging rays from the object-glass at right angles to the axis of the telescope, and permits the observing micrometer n to be mounted in the very convenient position shown in the figure.

To say, for instance, that the area of a right-angled triangle is half the area of the rectangle contained by the two sides, is not to say what the area is, but what it is the half of.

Contains problems of finding rational right-angled triangles such that different functions of their parts (the sides and the area) are squares.

Constructing a square of twice the area of a given square (which follows as a corollary to the Pythagorean property of a right-angled triangle, viz.