# A System of the Mathematics: Containing the Euclidean Geometry, Plane & Spherical Trigonometry ... Astronomy, the Use of the Globes & Navigation ... Also a Table of Meridional Parts ... Together with a Large & Very Useful Table of the Latitudes & Longitudes of Places, Volum 2

T. Page, W. & F. Mount, 1723

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Side 131 - As the sine of half the sum of the two sides is to the sine of half their difference so is the cotangent of half their contained angle to the tangent of half the difference of the other angles ; and again, 2.
Side 255 - The true cause of the variation of the seasons consists in the inclination of the axis of the earth to the plane of its orbit; or, in other words, to the ecliptic.
Side 134 - If, from an angle of a spherical triangle, there be drawn a perpendicular to the opposite side or base, the tangent of half the sum of the segments of the base is to the tangent of half the sum of the...
Side 58 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Side 59 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.
Side 131 - Is to the cosine of half their difference, So is the cotangent of half the contained angle To the tangent of half the sum of the other angle*.
Side 215 - Equator, e-kwaytur (Latin, œqueo, to divide equally). A great circle of the sphere, equally distant from the two poles of the world, and dividing it into two hemispheres, the northern and southern. It is called the equator, because when the sun is in this circle the days and nights are of equal duration in all parts of the world. From this circle the latitude of places, whether north or south, is reckoned, in degrees of the meridian ; the longitude of places is reckoned in degrees around this circle....
Side 8 - Projeftiott the Angles made by the Circles on the Surface of the Sphere are equal to the Angles made by their Reprefentatiyes on the plane of the Projection.
Side 63 - The exact length of the base being ascertained, and a system of triangles built upon it adapted to and covering the country to be surveyed, the lengths of all the other sides of the triangles in the system are inferred from the familiar theorem that " every triangle has six elements or functions, viz., three sides and three angles, any three of which being known (one being a side), the other unknown elements may be computed" with a degree of precision of the same order as that of the known elements.
Side 144 - Is to sine of one of the sides containing any angle, so is the sine of the other containing side, to a fourth sine. As...