Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Schema for vertical declining dials graphical techniques were used to derive formula_1 and formula_2 and from it formula_3. There are four basic angles that are needed to construct a vertical declining dial, Waugh described them such: The four basic calculation have a certain symmetry. At this point only three lines matter, the vertical, the substyle length and substyle height. A circle marked off in 15° angles is needed (circular protractor). Before the protractor became ubiquitous, compasses and the Scale of Chords were used for laying out an angle. This method originally used them. At this point only three lines matter, the vertical, the substyle length