Elements of Geometry and Trigonometry |
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Page 64
... extremity of the radius CB ; therefore it is a tan- gent . B Scholium . When the point A lies without the circle , there will evidently be always two equal tangents AB , AD , passing through the point A : they are equal , because the ...
... extremity of the radius CB ; therefore it is a tan- gent . B Scholium . When the point A lies without the circle , there will evidently be always two equal tangents AB , AD , passing through the point A : they are equal , because the ...
Page 65
... extremity , is a tangent ; and the same thing is true of the sides BC , AC . Scholium . The three lines which bisect the angles of a tri- angle meet in the same point . PROBLEM XVI . On a given straight line to describe a segment that ...
... extremity , is a tangent ; and the same thing is true of the sides BC , AC . Scholium . The three lines which bisect the angles of a tri- angle meet in the same point . PROBLEM XVI . On a given straight line to describe a segment that ...
Page 90
... extremities of a diameter BC , the triangle BAC will be right angled at A ( Book III . Prop . BD XVIII . Cor . 2. ) ; hence , first , the perpendicular AD is a mean proportional between the two segments BD , DC , of the diameter , or ...
... extremities of a diameter BC , the triangle BAC will be right angled at A ( Book III . Prop . BD XVIII . Cor . 2. ) ; hence , first , the perpendicular AD is a mean proportional between the two segments BD , DC , of the diameter , or ...
Page 98
... extremity B , by the straight line GB ; then draw CI parallel to GB : AI will be the fifth part of the line AB ; and ... extremities E and B ; and through the points C , & - A IF B A D , draw CI , DF , parallel to EB ; the line AB will ...
... extremity B , by the straight line GB ; then draw CI parallel to GB : AI will be the fifth part of the line AB ; and ... extremities E and B ; and through the points C , & - A IF B A D , draw CI , DF , parallel to EB ; the line AB will ...
Page 99
... A and B. PROBLEM IV . To divide a given line into two parts , such that the greater part shall be a mean proportional between the whole line and the other part . Let AB be the given line . At the extremity BOOK IV . 99.
... A and B. PROBLEM IV . To divide a given line into two parts , such that the greater part shall be a mean proportional between the whole line and the other part . Let AB be the given line . At the extremity BOOK IV . 99.
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex