Elements of Geometry |
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Page vi
... four of which treat of plane geometry , and four of solid geometry . The first section , entitled first principles , & c . contains the pro- perties of straight lines which meet those of perpendiculars , the theorem upon the sum of the ...
... four of which treat of plane geometry , and four of solid geometry . The first section , entitled first principles , & c . contains the pro- perties of straight lines which meet those of perpendiculars , the theorem upon the sum of the ...
Page xiv
... four proportional quantities form a new proportion . By multiplying the proportion by we shall have A2 : B2 :: C2 D3 A B :: C : D , A3 : B 3 3 :: C3 : D3 , that is , the cubes of four proportional quantities form a new pro- portion . VI ...
... four proportional quantities form a new proportion . By multiplying the proportion by we shall have A2 : B2 :: C2 D3 A B :: C : D , A3 : B 3 3 :: C3 : D3 , that is , the cubes of four proportional quantities form a new pro- portion . VI ...
Page 2
... four sides is called a quadrilateral ; that of five sides , a pentagon ; that of six , a hexa- gon , & c . 15. A triangle is denominated equilateral ( fig . 7 ) , when the Fig , 8. three sides are equal , isosceles ( fig . 8 ) , when ...
... four sides is called a quadrilateral ; that of five sides , a pentagon ; that of six , a hexa- gon , & c . 15. A triangle is denominated equilateral ( fig . 7 ) , when the Fig , 8. three sides are equal , isosceles ( fig . 8 ) , when ...
Page 4
... four distances CA , CB , GE , GF , equal to each other , the distance AB will be equal to the distance EF , and the line EF may be applied to AB , so that the point E will fall upon A , and the point F upon B. These two lines , thus ...
... four distances CA , CB , GE , GF , equal to each other , the distance AB will be equal to the distance EF , and the line EF may be applied to AB , so that the point E will fall upon A , and the point F upon B. These two lines , thus ...
Page 6
... four right angles . For , if at the point C , four right angles be formed by two lines perpendicular to each other , they will comprehend the same space as the successive angles , ACB , BCD , & c . These are often called vertical angles ...
... four right angles . For , if at the point C , four right angles be formed by two lines perpendicular to each other , they will comprehend the same space as the successive angles , ACB , BCD , & c . These are often called vertical angles ...
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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