Elements of Geometry |
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Page 3
... common name of Proposition is given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone ...
... common name of Proposition is given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone ...
Page 5
... common , coin- cide throughout , and form one and the same straight line . 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 ...
... common , coin- cide throughout , and form one and the same straight line . 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 ...
Page 6
... common angle ACD , and there will remain the part DCB equal to the whole DCE , which is impossible ; there- fore CB is the line AC produced . Fig . 21 . Fig 22 . THEOREM . 34. Whenever two straight lines AB , DE ( fig . 21 ) , cut each ...
... common angle ACD , and there will remain the part DCB equal to the whole DCE , which is impossible ; there- fore CB is the line AC produced . Fig . 21 . Fig 22 . THEOREM . 34. Whenever two straight lines AB , DE ( fig . 21 ) , cut each ...
Page 9
... common to both , AB = = AC , by hypothesis , and BD = DC , by construction ; therefore ( 43 ) the angle B is equal to the angle C. 46. Corollary . An equilateral triangle is also equiangular ; that is , it has its angles equal . GEOH 2 ...
... common to both , AB = = AC , by hypothesis , and BD = DC , by construction ; therefore ( 43 ) the angle B is equal to the angle C. 46. Corollary . An equilateral triangle is also equiangular ; that is , it has its angles equal . GEOH 2 ...
Page 12
... common , and the side BF = BA ; therefore the third side CF is equal to the third side AC ( 36 ) . But AF < AC + CF ( 40 ) , and AB half of AF is less than AC half of AC + CF ; that is , the perpendicular is less than any one of the ...
... common , and the side BF = BA ; therefore the third side CF is equal to the third side AC ( 36 ) . But AF < AC + CF ( 40 ) , and AB half of AF is less than AC half of AC + CF ; that is , the perpendicular is less than any one of the ...
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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