Elements of Geometry |
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Page 3
... respect to each other , when they have their sides equal , each to each , and placed in the same order , that is , when by proceeding round in the same direction the first in the one is equal to the first in the other , the second in ...
... respect to each other , when they have their sides equal , each to each , and placed in the same order , that is , when by proceeding round in the same direction the first in the one is equal to the first in the other , the second in ...
Page 16
... respect to the four obtuse angles AGE , BGH , GHC , DHF . It may be observ- ed , 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 ...
... respect to the four obtuse angles AGE , BGH , GHC , DHF . It may be observ- ed , 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 ...
Page 25
... respect to the perpendicular CD , two equal oblique lines , there- fore they are equally distant from the perpendicular ( 52 ) , and AD = DB . Again , since AD = BD , and CG is a perpendicular erected upon the middle of AB , each point ...
... respect to the perpendicular CD , two equal oblique lines , there- fore they are equally distant from the perpendicular ( 52 ) , and AD = DB . Again , since AD = BD , and CG is a perpendicular erected upon the middle of AB , each point ...
Page 27
... respect to this new tangent the radius CA would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be less than CA ; therefore this supposed tangent would pass into the circle and become a secant ...
... respect to this new tangent the radius CA would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be less than CA ; therefore this supposed tangent would pass into the circle and become a secant ...
Page 42
... respect to straight lines , that arcs also , which are compared , have not a common meas- ure ; we can then obtain , for the angles , only an approximate ratio in numbers , more or less exact , according to the degree to which the ...
... respect to straight lines , that arcs also , which are compared , have not a common meas- ure ; we can then obtain , for the angles , only an approximate ratio in numbers , more or less exact , according to the degree to which the ...
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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