Elements of Geometry |
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Page 21
... consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig ...
... consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig ...
Page 27
... 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 centre . 2. Let the chord AH be greater than DE , the arc AKH will be greater than the arc DME ...
... 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 centre . 2. Let the chord AH be greater than DE , the arc AKH will be greater than the arc DME ...
Page 30
... consequently have AI = AB , or the part equal to the whole , which is impossible ; therefore the angle ACB = DCE . THEOREM . 120. In the same circle , or in equal circles , if two angles at the Fig . 62. centre ACB , DCE ( fig . 62 ) ...
... consequently have AI = AB , or the part equal to the whole , which is impossible ; therefore the angle ACB = DCE . THEOREM . 120. In the same circle , or in equal circles , if two angles at the Fig . 62. centre ACB , DCE ( fig . 62 ) ...
Page 38
... consequently be the greatest of the sides . 2. If the angle C ( fig . 81 ) is acute , and B greater than A , the construction is the same , and DEF is the triangle required . But if , while C ( fig . 82 ) is acute , the side B is less ...
... consequently be the greatest of the sides . 2. If the angle C ( fig . 81 ) is acute , and B greater than A , the construction is the same , and DEF is the triangle required . But if , while C ( fig . 82 ) is acute , the side B is less ...
Page 39
... the three sides of the triangle ; these lines will be equal to each other . For , by construc- tion , the angle DAO = OAF , and the right angle ADO = AFO ; 5 ¿ consequently the third angle AOD is equal to Problems . 39.
... the three sides of the triangle ; these lines will be equal to each other . For , by construc- tion , the angle DAO = OAF , and the right angle ADO = AFO ; 5 ¿ consequently the third angle AOD is equal to Problems . 39.
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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