Elements of Geometry, Theoretical and Practical: Containing a Full Explanation of the Construction and Use of Tables, and a New System of Surveying

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Pratt, Woodford, 1848 - 324 ページ
 

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目次

Multiplying or dividing dividend or divisor
34
A fraction an expression of division
35
Division by a fractionreciprocal
36
Fractions cleared of subdenominators
37
Scholia Signs common factors c
38
Elimination
39
ExponentsProportion Variation 1 Reciprocal powers
40
Root of a powerextension
41
and evolutionequal multiples
44
Inverse or reciprocal proportion
46
Continued proportiongeometrical progression
47
Variation definednotation
48
Inversion compositioninvolutionmultiples comparison com bined comparison
49
Analysis of Equations 1 A single equation resolvable into several distinct equations Ex amples
50
Quadraticsrule for solvingsum and product of roots
51
Classes of biquadratics solvable as quadratics
52
Rule for putting problems into equation
53
Discussion of the two values of the unknown quantity
55
Equation between constants and variables
57
Coëfficients equated
59
BOOK SECOND PLANE GEOMETRY DEPENDING ON THE RIGHT LINE SECTION I Comparison of Angles 1 Definitions Geometrysolids surfa...
63
Corollariesscholium on parallels
64
Sum of adjacent angles constant method
65
Corollariesright angles sum of adjacent angles lines forming one and the same straight line vertical angles sum of angles round a point
66
ApplicationsRightangle Surveyors Cross
67
Parallels method reversion and superposition
68
Corollariesthe converse conditions determined by the equality of alternate angles secant perpendicular lines parallel to the same angles having parallel...
69
Sum of external angles of polygon
70
Exercises
71
Relation of two sides of a triangle to the third
74
Consequencessimilar triangles c
80
Comparison of Plane Figures
90
BOOK THIRD
101
Inscribed anglesconsequences tangent
104
Exercises
112
Tangent and consequences
118
Scholiasignification of the symbol
124
CONTENTS
128
BOOK FIRST
131
Derivative of y fx Axa + B cb + Cart and the converse
137
Logarithms rules of operation
145
Development of y fx when av x computations
146
Interpolation
153
Exercises
158
Exponential theorem or development of y af
159
General Laws relating to the Development of Functions depending on a single Variable 1 Ratio of the increment of a continuous function to that of it...
162
Derivative of a polynomial and multiple function
163
Secant and tangent
172
Sine and cosine derivatives of
173
Sine and cosine developed in terms of arc
174
Sine and cosine of the sum and difference of two arcs
175
Corollariessin 2x cos 2x 1+cos 2x 1 cos 2x 1 + sin 2x 1 sin 2x 1 + sin 2x 1 sin 2x sin p + sin l sin p sin q cos p + cos q cos q cos psin p+singsin p ...
177
Tan a +b cotan a+b tan 2a cot 2a c
178
Denominate equationsradius restored
180
Arc developed in terms of tangent computed
181
Trigonometrical lines computed
183
Logarithmic sines and tangents
188
Are developed in terms of sine
190
Trigonometrical equations solved
191
Resolution of Triangles and Mensuration of Heights and Distances 1 Projection of one line upon another
192
CONTENTS 2 Fundamental relation between the sides and angles of a triangle
193
Sum of squares of two sidescorollary
194
Relation of sides and opposite angles
195
area of circle
201
arcs of similar sectors areas of circles circles and their like parts how related
202
Incremental ranishing arc of continuous curve
203
Segmental arca derirative of 204
204
Area of parabola
205
Proximate area of continuous eurre
206
Exercises
207
BOOK THIRD SURVEYING Section 1 Description and Use of Instruments 1 The chainlength division how used field notes
208
The surveyors crossconstruction and use
210
Vernier or nonius
211
Theodolitehow adjusted used
212
Variation of needle
214
Leveling
215
Plotting 1 Graphical problemsperpendiculars parallels c
216
Problems of constructionx a +b c
218
Graduation of the circlechords
220
To plot a field Diagonal scale sector
222
To plot a field Diagonal scale sector 2
224
Last side and diagonals of polygonal fields
225
Corollaries Similar figures and proportional lines the Pantograph
227
Exercises
229
Area of polygon in terms of the sides and their inclinations
231
Form of computation
234
BOOK FIRST
245
Surface of revolution derivative
251
Consequences ellipsoidal frustrum ellipsoid sphere Para
257
Orthographic projection consequences
280
BOOK THIRD
291
Time consequences
298
CourseMariners compass
304
II 312
312

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11 ページ - If two triangles have two sides of the one equal to two sides of the...
258 ページ - ... greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle, shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to...
64 ページ - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
189 ページ - As the sine of the angle opposite the given side, is to the sine of the angle opposite the required side ; so is the given side to the required side.
39 ページ - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
77 ページ - ... by four times the square of the line joining the middle points of the diagonals.
298 ページ - N. by E. NNE NE by N. NE NE by E. ENE E. by N. East E. by S. ESE SE by E. SE SE by S.
171 ページ - The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference.
258 ページ - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
74 ページ - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those angles equal which subtend the homologous sides.

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