## Elements of Geometry |

### From inside the book

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**radii**are all equal , and all the diameters also are equal , and double of the radius . 89. An arc of a circle is any portion of its circumference , as FHG . 90. The chord or subtense of an arc is the straight line FG , which joins its ... Page 25

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**radii**CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD ; that is , ADAB ( 88 ) . 100. Corollary . Hence the greatest straight line that can be ... Page 26

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**radii**CD , OG , be drawn , the two triangles ACD , EOG , will have the three sides of the one equal to the three sides of the other , each to each , namely , ACEO , CD OG and AD EG ; therefore these triangles are equal ( 43 ) ; hence ... Page 27

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**radii**CA , CB ; these**radii**are , with respect to the perpendicular CD , two equal oblique lines ; there- fore they are equally distant from the perpendicular ( 52 ) , and ᎯᎠ -- ᎠᏴ . Again , since AD = BD , and CG is a perpendicular ... Page 29

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**radii**CA , CD . The right - angled triangles CAF , DCG , have the hypothe- nuses CA , CD , equal ; moreover , the side AF , the half of AB , is equal to the side DG , the half of DE ; the triangles , then , are equal ( 56 ) , and ...### 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