Elements of Geometry |
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Page 22
... inscribed angle is one whose vertex is in the circumference , and which is formed by two chords , as BAC . An inscribed triangle is a triangle whose three angles have their vertices in the circumference of the circle , as BAC . * In ...
... inscribed angle is one whose vertex is in the circumference , and which is formed by two chords , as BAC . An inscribed triangle is a triangle whose three angles have their vertices in the circumference of the circle , as BAC . * In ...
Page 23
... inscribed in the polygon . 60 . . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects the circle and its cir- Fig . 49 . cumference . Demonstration . If the figure AEB be applied to AFB , so that the base AB may be common to both , the ...
... inscribed in the polygon . 60 . . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects the circle and its cir- Fig . 49 . cumference . Demonstration . If the figure AEB be applied to AFB , so that the base AB may be common to both , the ...
Page 32
... arcs of a circle , which are used as a measure of angles , will also serve as the measure of different sectors of the same circle or of equal circles . THEOREM . 65 . 126. The inscribed angle BAD ( 32 Elements of Geometry .
... arcs of a circle , which are used as a measure of angles , will also serve as the measure of different sectors of the same circle or of equal circles . THEOREM . 65 . 126. The inscribed angle BAD ( 32 Elements of Geometry .
Page 33
... inscribed angle has for its measure the half of the arc comprehended between its sides . 127. Corollary 1. All the angles BAC , BDC ( fig . 66 ) , & c . , Fig . 66 . inscribed in the same segment , are equal ; for they have each for ...
... inscribed angle has for its measure the half of the arc comprehended between its sides . 127. Corollary 1. All the angles BAC , BDC ( fig . 66 ) , & c . , Fig . 66 . inscribed in the same segment , are equal ; for they have each for ...
Page 34
... inscribed in a 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 ...
... inscribed in a 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 ...
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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