An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis of Angular Sections

John Taylor, 1826 - Plane trigonometry - 313 pages

English mathematicians or the sexagesimal division notation	3

the circle to find the length of the corresponding	9

SECTION II	16

Cos mx	19

and cosecant of an angle	22

On the relations between angles and their sums and dif	28

SECTION IV	34

several trigonometrical terms deduced from their definitions	35

triangle to compute the area	144

sector of the vertical angle	148

circumscribes a spherical triangle	151

rical and plane triangles	155

of their longitudes	157

of error in the solution of triangles and to the corrections	162

nected with the position of a place on the terrestrial spheroid	205

SECTION XI	219

Title	An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis of Angular Sections
Author	Dionysius Lardner
Publisher	John Taylor, 1826
Original from	Harvard University
Digitized	6 Mar 2018
Length	313 pages

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angle	36

manner of deducing the former	40

66 General theory	42

twice the rectangle under them multiplied by the cosine of	46

area	47

of the other two sides to determine the remaining angles	49

least being a side the other three may be computed	52

gles to compute the angles and the remaining side	58

segments of that angle made by the bisector of the opposite side	61

SECTION I	67

bisects all parallels to its primary	69

termine the others	75

of three others the intersections of the latter will be the poles	76

condary to the base the triangle is isosceles	86

of a given triangle	91

triangles	97

102 Def Genesis of a sphere Its radii and centre	102

equal	108

major limit of the difference of the oblique angles of a right	109

SECTION VI	115

or greater than the hypothenuse according as it is less or greater	131

formulæ 1 by means of a subsidiary angle	225

230 Three systems of formulæ by which the remaining	230

of the sum of any number of angles General formulæ for	237

241 Three systems of formulæ for determining the	241

SECTION II	246

adjacent sides	250

Given two angles and the side opposed to one of them	256

COS x	258

which the perpendicular from its vertex divides the opposite	268

279 Investigation of a rule for determining the error in	279

SECTION III	280

On the summation of certain series of sines cosines c	289

sines of	290

any tract of country involves three problems	294

arithmetical progression	295

sines of x	300

SECTION V	301

manner of computing the true angles	302

differ but little from quadrants to compute the difference	311

tables	319

325 To determine the mean surface of the earth	325