Elements of Geometry |
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Page 24
... 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 . 89. An arc of ...
... 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 . 89. An arc of ...
Page 27
... 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 28
... 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 29
... 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 . THEOREM . Fig . 55. 112. Two parallels AB , Of the Circle . 29.
... 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 . THEOREM . Fig . 55. 112. Two parallels AB , Of the Circle . 29.
Page 30
... 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 BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle join less Let ABC let fall Let us suppose line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM third three angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Popular passages
Page 67 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 9 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 65 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 160 - ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be...
Page 168 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 157 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 8 - Any side of a triangle is less than the sum of the other two sides...
Page 82 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 29 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 182 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.