## Elements of Geometry |

### From inside the book

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**inscribed**in a circle , when its extremities are in the circumference of the circle , as AB ( fig 47 ) . 94. An**inscribed**angle is one whose vertex is in the circum- ference , and which is formed by two chords , as BAC . 95. An ... Page 25

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**inscribed**in the polygon . 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 curved ... Page 34

... the 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 . 126. The

... the 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 . 126. The

**inscribed**angle BAD ( fig . 34 Elements of Geometry . Page 35

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**inscribed**angle has for its measure the half of he 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 36

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**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 ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence