Elements of Geometry |
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Page iii
... spherical isoperimetrical polygons , and on the regular poly- edrons , are inserted in this at the end of the fourth section of the second part . Also an improved demonstration of the theorem for the solidity retation Presented to.
... spherical isoperimetrical polygons , and on the regular poly- edrons , are inserted in this at the end of the fourth section of the second part . Also an improved demonstration of the theorem for the solidity retation Presented to.
Page vii
... spherical triangles . This treatise does not ordina- rily make a part of the elements of geometry ; still we have thought it proper to consider so much of it as may form an intro- duction to spherical trigonometry . The fourth section ...
... spherical triangles . This treatise does not ordina- rily make a part of the elements of geometry ; still we have thought it proper to consider so much of it as may form an intro- duction to spherical trigonometry . The fourth section ...
Page 155
... spherical triangle is a part of the surface of a sphere comprehended by three arcs of great circles . These arcs ... spherical triangle takes the name of right - angled , isos- celes and equilateral , like a plane triangle , and under ...
... spherical triangle is a part of the surface of a sphere comprehended by three arcs of great circles . These arcs ... spherical triangle takes the name of right - angled , isos- celes and equilateral , like a plane triangle , and under ...
Page 156
... spherical wedge the part of a sphere com- prehended between the halves of two great circles , and to which the lunary surface answers as a base . 447. A spherical pyramid is the part of a sphere comprehended between the planes of a ...
... spherical wedge the part of a sphere com- prehended between the halves of two great circles , and to which the lunary surface answers as a base . 447. A spherical pyramid is the part of a sphere comprehended between the planes of a ...
Page 157
... spherical triangle ABC ( fig . 222 ) either side is less Fig than the sum of the other two . Demonstration . Let O be the centre of the sphere , and let the radii OA , OB , OC , be drawn . If the planes AOB , AOC , COB , be supposed ...
... spherical triangle ABC ( fig . 222 ) either side is less Fig than the sum of the other two . Demonstration . Let O be the centre of the sphere , and let the radii OA , OB , OC , be drawn . If the planes AOB , AOC , COB , be supposed ...
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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