Elements of Geometry |
From inside the book
Results 1-5 of 22
Page 22
... segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a ... segments ; but , in speaking of these , the smaller is always to be understood , when the contrary is not expressed , In ...
... segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a ... segments ; but , in speaking of these , the smaller is always to be understood , when the contrary is not expressed , In ...
Page 33
... segment , are equal ; for they have each for their measure the half of the same arc BOC . 128. Corollary 11. Every angle BAD ( fig . 67 ) , inscribed in Fig . 67 . a semicircle , is a right angle ; for it has for its measure the half of ...
... segment , are equal ; for they have each for their measure the half of the same arc BOC . 128. Corollary 11. Every angle BAD ( fig . 67 ) , inscribed in Fig . 67 . a semicircle , is a right angle ; for it has for its measure the half of ...
Page 34
... segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicir- cumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for ...
... segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicir- cumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for ...
Page 40
... segment capable of containing a given angle C , that is a segment 89 . such , that each of the angles , which may be inscribed in it , shall be equal to a given angle C. Solution . Produce AB toward D , make at the point B the angle DBE ...
... segment capable of containing a given angle C , that is a segment 89 . such , that each of the angles , which may be inscribed in it , shall be equal to a given angle C. Solution . Produce AB toward D , make at the point B the angle DBE ...
Page 43
... segments , are such as correspond to equal angles at the cen- tre . Thus , the angle A ( fig . 92 ) being equal to the angle O , the Fig . 92 . arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164. The altitude ...
... segments , are such as correspond to equal angles at the cen- tre . Thus , the angle A ( fig . 92 ) being equal to the angle O , the Fig . 92 . arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164. The altitude ...
Other editions - View all
Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence