Elements of Geometry |
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Page iii
... Moreover the work is divided into two parts , one treating of plane figures and the other of solids ; and the subdivisions of each part are denominated sections . As a knowledge of algebraical signs and the theory of propor- tions is ...
... Moreover the work is divided into two parts , one treating of plane figures and the other of solids ; and the subdivisions of each part are denominated sections . As a knowledge of algebraical signs and the theory of propor- tions is ...
Page xii
... Moreover the two ratios A : C , B : D , being common to the two proportions above obtained , it follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing ...
... Moreover the two ratios A : C , B : D , being common to the two proportions above obtained , it follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing ...
Page 7
... moreover DF is equal to AC ; therefore the point F will fall upon C , and the third side EF will exactly coincide with the third side BC ; therefore the triangle DEF is equal to the triangle ABC ( 26 ) . 37. Corollary . When , in two ...
... moreover DF is equal to AC ; therefore the point F will fall upon C , and the third side EF will exactly coincide with the third side BC ; therefore the triangle DEF is equal to the triangle ABC ( 26 ) . 37. Corollary . When , in two ...
Page 14
... moreover , that if the figure is constructed with care , and AL be taken double of AF , we shall find that AM is exactly double of AG ; also , if AL be taken triple of AF , we shall find that AG is triple of AG , and in general there ...
... moreover , that if the figure is constructed with care , and AL be taken double of AF , we shall find that AM is exactly double of AG ; also , if AL be taken triple of AF , we shall find that AG is triple of AG , and in general there ...
Page 16
... moreover , that by adding one of the four acute angles to one of the four obtuse angles , the sum will always be equal to two right angles . 67. Scholium . The angles of which we have been speaking , compared , two and two , take ...
... moreover , that by adding one of the four acute angles to one of the four obtuse angles , the sum will always be equal to two right angles . 67. Scholium . The angles of which we have been speaking , compared , two and two , take ...
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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