An Elementary Treatise on Plane and Solid Geometry |
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Page vii
... tangent , point of contact , tangent circles ( 118 ) ; polygon circumscribed about circle ( 118 ) , Direction of tangent and curve at point of contact ( 119 ) , ( 119 ) , Tangent perpendicular to radius ( 120 ) , Measure of angle formed by ...
... tangent , point of contact , tangent circles ( 118 ) ; polygon circumscribed about circle ( 118 ) , Direction of tangent and curve at point of contact ( 119 ) , ( 119 ) , Tangent perpendicular to radius ( 120 ) , Measure of angle formed by ...
Page viii
... tangent to a circle ( 150 , 151 ) , To inscribe a circle in a triangle ( 152 , 153 ) , To describe a segment capable of containing a given angle ( 154 , 155 ) , • To find the common measure of two lines ( 156 ) ; or of two arcs ( 157 ) ...
... tangent to a circle ( 150 , 151 ) , To inscribe a circle in a triangle ( 152 , 153 ) , To describe a segment capable of containing a given angle ( 154 , 155 ) , • To find the common measure of two lines ( 156 ) ; or of two arcs ( 157 ) ...
Page ix
... Tangent drawn to a circle through a point is a mean proportional between the parts of the secant drawn through it ( 191 ) , To divide a line in extreme and mean ratio ( 192 ) , Case of similar polygons ( 193 ) , . To construct a polygon ...
... Tangent drawn to a circle through a point is a mean proportional between the parts of the secant drawn through it ( 191 ) , To divide a line in extreme and mean ratio ( 192 ) , Case of similar polygons ( 193 ) , . To construct a polygon ...
Page xiii
... tangent to sphere ( 435 ) , spherical segment and zone , their bases and altitude ( 436 ) ; spherical sector ( 437 ) , One side of spherical triangle less than sum of other two ( 438 ) , Sum of sides of spherical polygon ( 439 , 440 ) ...
... tangent to sphere ( 435 ) , spherical segment and zone , their bases and altitude ( 436 ) ; spherical sector ( 437 ) , One side of spherical triangle less than sum of other two ( 438 ) , Sum of sides of spherical polygon ( 439 , 440 ) ...
Page 32
... its extremities , that is , the chords AG and GB are equal ; and therefore , by § 113 , the arcs AG and GB are equal . Tangent to a Circle . 117. Corollary . The perpendicular 32 [ CH . VIII . § 116 . PLANE GEOMETRY .
... its extremities , that is , the chords AG and GB are equal ; and therefore , by § 113 , the arcs AG and GB are equal . Tangent to a Circle . 117. Corollary . The perpendicular 32 [ CH . VIII . § 116 . PLANE GEOMETRY .
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Common terms and phrases
ABC fig adjacent angles angle BAC arc BC base and altitude bisect centre chord circumference common altitude construct convex surface Corollary DEF fig Definitions denote diameter divided Draw equal arcs equal distances equiangular with respect equilateral equivalent frustum given angle given circle given line given polygon given sides given square gles greater half the product Hence homologous sides hypothenuse infinite number infinitely small Inscribed Angle inscribed circle isosceles Let ABCD line AB fig line BC lines drawn mean proportional number of sides oblique lines parallel lines parallel to BC parallelogram parallelopipeds perimeter perpendicular plane MN polyedron polygon ABCD &c Problem Proof pyramid or cone radii radius rectangles regular polygon right triangle Scholium sector segment side BC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle straight line tangent Theorem triangles ABC triangular prism vertex vertices whence
Popular passages
Page 68 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 127 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.
Page 71 - Rectangles of the same altitude are to each other as their bases, and rectangles of the same base are to each other as their altitudes. 245.
Page 20 - The sum of the three angles of any triangle is equal to two right angles.
Page xv - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 83 - ... we suppose the error A to be of any magnitude whatever. 286. Definition. Similar sectors and similar segments are such as correspond to similar arcs. 287. Theorem. Similar sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'OB ' (fig. 136) are, by the same reasoning as in t5 97, the same parts of their respective circles, which the angle O= O...
Page 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
Page 87 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Page 99 - B, from the plane. 320. Theorem. Oblique lines drawn from a point to a plane at equal distances from the perpendicular are equal; and of two oblique lines unequally distant the more remote is the greater.
Page 78 - Similar triangles are to each other as the squares of their homologous sides. Proof. In the similar .triangles ABC, A'B'C