Elements of Geometry |
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Page 37
... contained by them , to construct the triangle . Solution . Draw the indefinite line DE , and make at the point D the angle EDF equal to the given angle A ; then take DG = B , DHC , and draw GH ; DGH will be the triangle required ( 36 ) ...
... contained by them , to construct the triangle . Solution . Draw the indefinite line DE , and make at the point D the angle EDF equal to the given angle A ; then take DG = B , DHC , and draw GH ; DGH will be the triangle required ( 36 ) ...
Page 41
... contained exactly twice in FD , GB will be the common measure of the two proposed lines . Let GB = 1 , we have FD = 2 ; but EB contains FD once plus GB ; therefore EB = 3 ; CD contains EB once plus FD ; there- fore CD = 5 ; AB contains ...
... contained exactly twice in FD , GB will be the common measure of the two proposed lines . Let GB = 1 , we have FD = 2 ; but EB contains FD once plus GB ; therefore EB = 3 ; CD contains EB once plus FD ; there- fore CD = 5 ; AB contains ...
Page 44
... contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rect- angle AEFD , as 7 is to 4 , or as AB is to AE . The same rea- soning may be applied to any other ratio beside that 44 ...
... contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rect- angle AEFD , as 7 is to 4 , or as AB is to AE . The same rea- soning may be applied to any other ratio beside that 44 ...
Page 46
... contained in the base , and the number of linear units contained in the altitude . This measure , however , is not absolute , but relative ; it sup- poses that we estimate , in a similar manner , another rectangle by measuring its sides ...
... contained in the base , and the number of linear units contained in the altitude . This measure , however , is not absolute , but relative ; it sup- poses that we estimate , in a similar manner , another rectangle by measuring its sides ...
Page 48
... contain the square described upon the part AB , plus the square described upon the other part BC , plus twice the rectangle contained by the two parts AB , BC ; which may be thus expressed , -2 2 -2 2 AC or ( AB + BC ) = AB + BC + 2 AB ...
... contain the square described upon the part AB , plus the square described upon the other part BC , plus twice the rectangle contained by the two parts AB , BC ; which may be thus expressed , -2 2 -2 2 AC or ( AB + BC ) = AB + BC + 2 AB ...
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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