Elements of Geometry |
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Page 36
... taken together , have for their measure the half of the circumference ; therefore their sum is equal to two right angles . THEOREM . 131. The angle BAC ( fig . 69 ) , formed by a tangent and a chord , has for its measure the half of the ...
... taken together , have for their measure the half of the circumference ; therefore their sum is equal to two right angles . THEOREM . 131. The angle BAC ( fig . 69 ) , formed by a tangent and a chord , has for its measure the half of the ...
Page 45
... taken for a base . Fig . 93 . Fig . 94 . The altitude of a trapezoid is the perpendicular EF ( fig . 95 ) Fig . 95 ... taken from DE , there will remain CE ; and if FE , equal to DC , be taken also from DE , there will remain DF ...
... taken for a base . Fig . 93 . Fig . 94 . The altitude of a trapezoid is the perpendicular EF ( fig . 95 ) Fig . 95 ... taken from DE , there will remain CE ; and if FE , equal to DC , be taken also from DE , there will remain DF ...
Page 46
... taken , there will remain the parallelogram ABEF ; and if , from the same quadrilateral ABED , the triangle CBE , equal to the former , be taken , there will remain the parallelogram ABCD ; therefore the two parallelograms ABCD , ABEF ...
... taken , there will remain the parallelogram ABEF ; and if , from the same quadrilateral ABED , the triangle CBE , equal to the former , be taken , there will remain the parallelogram ABCD ; therefore the two parallelograms ABCD , ABEF ...
Page 51
... taken equal to AB ; the second IGDH is the square described upon BC ; for , since AC AE , and ABAF , the difference AC - AB — AE — AF , which gives BC = EF ; but , on account of the parallels , IG = BC , and DG EF , therefore HIGD is ...
... taken equal to AB ; the second IGDH is the square described upon BC ; for , since AC AE , and ABAF , the difference AC - AB — AE — AF , which gives BC = EF ; but , on account of the parallels , IG = BC , and DG EF , therefore HIGD is ...
Page 53
... taken together , make the square BCGF ; therefore the square BCGF , described upon the hypothenuse , is equal to the sum of the squares ABHL , ACIK , described upon the two other sides ; or , BC = AB + AC 187. Corollary 1. The square of ...
... taken together , make the square BCGF ; therefore the square BCGF , described upon the hypothenuse , is equal to the sum of the squares ABHL , ACIK , described upon the two other sides ; or , BC = AB + AC 187. Corollary 1. The square of ...
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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