Elements of Geometry |
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Page iii
... spherical isoperimetrical polygons , and on the regular poly- edrons , are inserted in this at the end of the fourth section of the second part . ust Hit ド Also an improved demonstration of the theorem for the solidity.
... spherical isoperimetrical polygons , and on the regular poly- edrons , are inserted in this at the end of the fourth section of the second part . ust Hit ド Also an improved demonstration of the theorem for the solidity.
Page 3
... demonstration . A Problem is a question proposed which requires a solution . A Lemma is a subsidiary truth employed in the demonstration of a theorem , or in the solution of a problem . The common name of Proposition is given ...
... demonstration . A Problem is a question proposed which requires a solution . A Lemma is a subsidiary truth employed in the demonstration of a theorem , or in the solution of a problem . The common name of Proposition is given ...
Page 4
... Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB , GE , GF , equal to each other , the distance AB will be ...
... Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB , GE , GF , equal to each other , the distance AB will be ...
Page 5
... Demonstration . Let the two points , which are common to the two lines , be A and B ( fig . 19 ) . In the first place it is evident Fig . 19 . that they must coincide entirely between A and B ; otherwise , two straight lines could be ...
... Demonstration . Let the two points , which are common to the two lines , be A and B ( fig . 19 ) . In the first place it is evident Fig . 19 . that they must coincide entirely between A and B ; otherwise , two straight lines could be ...
Page 6
... Demonstration . For if CB is not the line AC produced , let CE be that line produced ; then , ACE being a straight line , the angles ACD , DCE , are together equal to two right angles ( 28 ) ; but , by hypothesis , the angles ACD , DCB ...
... Demonstration . For if CB is not the line AC produced , let CE be that line produced ; then , ACE being a straight line , the angles ACD , DCE , are together equal to two right angles ( 28 ) ; but , by hypothesis , the angles ACD , DCB ...
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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