An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books

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James Munroe, 1846 - 161 sider
 

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One side of a triangle less than the sum of the other two
81
124 Value of one exterior angle of a triangle
82
The angles at the base of an isosceles triangle equal
83
The angles formed by producing the equal sides of an isosceles triangle are equal
84
The sides of a triangle which are opposite to equal angles are equal
85
Any point in a perpendicular to the middle of a straight line is at equal distances from extremities of that line
86
Greater side of a triangle opposite to greater angle
87
The converse
88
Section Page 145 Sum of the angles of a quadrilateral
89
151j Cases of equivalent parallelograms
90
Case of equivalent triangles
91
Value of each angle which may be formed at the middle of a polygon by drawing straight lines to its vertices
92
Table of the size of angles in a regular figure
94
Mensuration of a rectilineal figure Superficial unit Area and surface
95
a triangle
96
any regular polygon
97
A perpendicular to the middle of a chord bisects the arc and the angle
98
the centre of a circle
99
to Value of angles inscribed in segments 100
100
177 Value of the opposite angles of a quadrilateral
101
Radius may be drawn six times as a chord
102
Section Pge 182 To find the area of a circle
104
To find the area of a sector
105
Of Solids 187 Definition of a solid Of solids in general
106
Superficial contents of a prism
107
cone
108
regular solids
109
Unit of solidity Meaning of terms solidity solid content and volume
110
A right prism oblique prism parallelopiped rectangular parallelopiped
111
any parallelopiped
112
a triangular prism
113
a triangular pyramid
114
a sphere
115
Miscellaneous Propositions 209 To find the distance between two inaccessible objects
116
To draw a meridian line
125
To construct a triangle of which base altitude and an angle are given
126
Greater chord at least distance from the centre
127
about a regular polygon
128
To inscribe a circle in a triangle
129
Section Page VII Of Proportions 246 Meaning of terms ratio proportion geometrical proportion antecedent consequent extremes means mean propor...
130
Test of proportion
131
When figures are said to be similar Meaning of homolo gous
132
Ratio of triangles of equal altitude
133
triangles of equal bases
134
parallelograms in general to one another
136
such parallel line to the base
138
to What determines the similarity of triangles
139
270 To construct upon a given base a triangle similar to a given triangle
141
To determine a distance which cannot be exactly measured
142
To find the perpendicular height of a tower when it cannot be exactly measured
144
from the windows of a house the height of an object
145
the height of an object which cannot be approached very nearly
146
the distance between two inaccessible objects
147
Proportions formed by letting fall a perpendicular from the ver tex of a rightangled triangle
148
To find a mean proportional between two given lines
149
Ratio of the perimeters of similar triangles
150
homologous sides of similar triangles
151
Section Page 284 Similar polygons are divided by diagonals into similar trian gles
152
Construction of similar figures
153
To construct a diagram of a field upon a reduced scale
154
surfaces of similar figures
155
similar figures constructed on the three sides of a right triangle
156
Ratio of the parts of secants
157
To describe a circle the surface of which shall be equal to the surfaces of two given circles
158
Ratio of two cubes
159
solidity of a sphere to the solidity of a circum scribed cube
160
scribed cylinder
161

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Side 130 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Side 154 - 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.

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