# Trigonometry Improv'd, and Projection of the Sphere, Made Easy: Teaching the Projection of the Sphere Orthographick, and Stereographick: as Also, Trigonometry Plain and Spherical; with Plain and Intelligible Reasons for the Various and Most Useful Methods, Both in Projection and Calculation; with the Application of the Whole to Astronomy, Dialling, and Geography

H.P., 1720 - 192

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Strona 10 - Then as the sum of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference (Theor.
Strona 21 - TWo fides and an angle oppofite to one of them being given, To find the third fide and either of the other angles.
Strona 76 - Authors reckoned the 3d and 4th, where there are given two Sides and an Angle oppofite to one of them, to find the...
Strona 53 - Perpendicular, let it fall from the End of a given Side, and oppofite to a given Angle...
Strona 23 - ... the sum of any two sides is to their difference ; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference.
Strona 40 - With the Tangent of the given Angle, and one Foot in the Center defc1 ihe an Arch.
Strona 57 - RULE IV. The Tangents of the Sides, are reciprocally Proportional to the Co-fines of the Angles at the Vertex.
Strona 32 - 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.
Strona 34 - POLE, in spherics, a point equally distant from every part of the circumference of a great circle of the sphere, as the centre is a plane figure ; or it is a point of ninety degrees distant from the plane of a circle, and in a line, called the axis, passing perpendicularly through the centre. The zenith and nadir are the poles of the * horizon ; and the poles of the equator are the same with those of the sphere. POLES of the ecliptic, are two points on the surface of the sphere, 23° 30' distant...
Strona 59 - Log-Sines of that half Sum and Remainder, half the Total of thefe four Logarithms is the Sine Complement of half the Angle required.