Elements of Geometry |
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Page 22
... passes through the centre and is terminated each way by the circumference , is called a diameter . By the definition of a circle the radii are all equal , and all the diameters also are equal and double of the radius . 92. An arc of a ...
... passes through the centre and is terminated each way by the circumference , is called a diameter . By the definition of a circle the radii are all equal , and all the diameters also are equal and double of the radius . 92. An arc of a ...
Page 25
... passes through any two of these points must necessarily pass through the third ; and must be perpendicular to the chord , It follows also , that a perpendicular erected upon the middle of a chord passes through the centre , and the ...
... passes through any two of these points must necessarily pass through the third ; and must be perpendicular to the chord , It follows also , that a perpendicular erected upon the middle of a chord passes through the centre , and the ...
Page 26
... pass through the same points . Demonstration . Join AB , BC , and bisect these two straight lines by the ... pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any ...
... pass through the same points . Demonstration . Join AB , BC , and bisect these two straight lines by the ... pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any ...
Page 27
... 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 . Fig . 55 . Fig . 56 . THEOREM . Of the Circle 27.
... 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 . Fig . 55 . Fig . 56 . THEOREM . Of the Circle 27.
Page 28
... passes through their centres will be perpen- dicular to the chord , which joins the points of intersection , and will ... pass through each of the centres C and D ( 106 ) . But through two given points only one straight line can be drawn ...
... passes through their centres will be perpen- dicular to the chord , which joins the points of intersection , and will ... pass through each of the centres C and D ( 106 ) . But through two given points only one straight line can be drawn ...
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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