Elements of Geometry |
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Page 9
... base BC ; the two triangles ABD , ADC , will have the three sides of the one , equal to the three sides of the other , each to each , namely , AD common to both , AB = AC , by hypothesis , and BD = DC , by construction ; therefore ( 43 ) ...
... base BC ; the two triangles ABD , ADC , will have the three sides of the one , equal to the three sides of the other , each to each , namely , AD common to both , AB = AC , by hypothesis , and BD = DC , by construction ; therefore ( 43 ) ...
Page 10
... base , is perpendicular to the base , and divides the ver- tical angle into two equal parts . In a triangle that is not isosceles , any one of its sides may be taken indifferently for a base ; and then its vertex is that of the opposite ...
... base , is perpendicular to the base , and divides the ver- tical angle into two equal parts . In a triangle that is not isosceles , any one of its sides may be taken indifferently for a base ; and then its vertex is that of the opposite ...
Page 19
... bases the different sides of the polygon , except the two which form the angle BAG . We see , at the same time , that the sum of the angles of all these triangles does not differ from the sum of the angles of the poly- gon ; therefore ...
... bases the different sides of the polygon , except the two which form the angle BAG . We see , at the same time , that the sum of the angles of all these triangles does not differ from the sum of the angles of the poly- gon ; therefore ...
Page 23
... base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is contrary to the definition of a ...
... base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is contrary to the definition of a ...
Page 32
... bases of these sectors . It will be perceived therefore , that the arcs of a circle , which are used as a measure of angles , will also serve as the measure of different sectors of the same circle or of equal circles . THEOREM . 65 ...
... bases of these sectors . It will be perceived therefore , that the arcs of a circle , which are used as a measure of angles , will also serve as the measure of different sectors of the same circle or of equal circles . THEOREM . 65 ...
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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