Elements of Geometry |
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Page 12
... half of AF is less than AC half of AC + CF , that is , the perpendicular is less than any one of the oblique lines . 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right angle ABE = ABC , the triangle ...
... half of AF is less than AC half of AC + CF , that is , the perpendicular is less than any one of the oblique lines . 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right angle ABE = ABC , the triangle ...
Page 24
... half a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration . Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and ...
... half a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration . Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and ...
Page 27
... half of AB , is equal to the side DG , the half of DE ; the triangles then are equal ( 59 ) , and consequently the third side CF is equal to the third side CG ; therefore the two equal chords AB , DE , are at the same distance from the ...
... half of AB , is equal to the side DG , the half of DE ; the triangles then are equal ( 59 ) , and consequently the third side CF is equal to the third side CG ; therefore the two equal chords AB , DE , are at the same distance from the ...
Page 33
... half of the arc BD comprehended between its sides . Demonstration . Let us suppose , in the first place , that the ... half of BE . For a simi- lar reason the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD ...
... half of the arc BD comprehended between its sides . Demonstration . Let us suppose , in the first place , that the ... half of BE . For a simi- lar reason the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD ...
Page 34
... 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 semicircumference . 130 ...
... 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 semicircumference . 130 ...
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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