## Elements of Geometry |

### From inside the book

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**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

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**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

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**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

... oblique line , and the perpendicular let fall from the centre upon this tangent would be less than CA ; therefore this supposed tangent would

... 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 . THEOREM . Fig . 55 . Fig . 56 . Of the Circle . 29. Page 30

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**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 ...### Other editions - View all

### 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 JOHN CRERAR LIBRARY join less Let ABC let fall 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 three angles triangle ABC triangular prism triangular pyramids vertex vertices whence