## Elements of Geometry |

### From inside the book

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**centre**. The circle is the space terminated by this curved line . * 88. Every straight line CA , CE , CD ( fig . 46 ) , & c . , drawn from the**centre**to the circumference , is called a radius or semi- diameter , and every straight line ... Page 25

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**centre**, which is contrary to the definition of a circle . THEOREM . 99. Every chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the**centre**to the extremities of the chord AD ... Page 27

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**centre**and the middle of the arc sub- tended by that chord . For this perpendicular is the same as that let fall from the**centre**upon the same chord , since they both pass through the middle of the chord ( 51 ) . THEOREM . 107. The ... Page 28

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**centre**O with the radius OB , will 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 three given points , which are not in the same straight line ; it remains ... Page 29

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**centre**; and , of two unequal chords , the less is at the greater distance from the**centre**. Demonstration 1. Let the chord AB = DE ( fig . 53 ) . Bisect Fig . 53 these chords by the perpendiculars CF , CG , and draw the radii ᏟᏁ , CD ...### 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 convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent 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 pyramid S-ABC 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