## Elements of Geometry |

### From inside the book

Results 1-5 of 20

Page 35

...

...

**measure the half**of the arc BD comprehended between its sides . = Demonstration . Let us suppose , in the first ... measure the arc BE ; therefore the angle BAC has for its**measure the half**of BE . For a similar reason , the angle CAD ... Page 36

...

...

**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 it has for its**measure the half**of the arc BAC greater than a ... Page 42

...

...

**measure the half**of the arc AKB ( 131 ) ; besides , the angle AMB , as an inscribed angle , has also for its**measure the half**of the arc AKB ; con- sequently the angle AMB = ABF = EBD = C ; therefore = = each of the angles inscribed in ... Page 49

...

...

**measure**AB × BE ( 173 ) ; therefore AB × BE is equal to the area of the parallelogram ABCD . 175. Corollary ...**half**of its altitude . Demonstration . The triangle ABC ( fig . 104 ) is**half**of the Fig . 104 . parallelogram ABCE , which ... Page 50

...

...

**measure**EF × AL . But AL = DK ; and , since the triangle IBL is equal to the triangle KCI , the side BL = CK ; therefore AB + CD = AL + DK = 2 AL ; thus AL is**half**the sum of the sides AB , CD ; and consequently the area of the ...### 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