Elements of Geometry and Trigonometry |
From inside the book
Page 54
... measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that ... measured by the arc BE ; hence BAC will be measured by the half of BE . For a like reason , the angle CAD will be ...
... measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that ... measured by the arc BE ; hence BAC will be measured by the half of BE . For a like reason , the angle CAD will be ...
Page 55
... measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ... measured by half of the arc BOC , less than a semicircumference . And every angle BOC , inscribed in a segment less ...
... measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ... measured by half of the arc BOC , less than a semicircumference . And every angle BOC , inscribed in a segment less ...
Page 56
... measured by half the arc FDB ( Prop . XVIII . ) ; therefore , DEB E C D B is measured by half of FDB ; that is , by half of DB + DF , or half of DB + AC . In the same manner it might be proved that the angle AED is measured by half of ...
... measured by half the arc FDB ( Prop . XVIII . ) ; therefore , DEB E C D B is measured by half of FDB ; that is , by half of DB + DF , or half of DB + AC . In the same manner it might be proved that the angle AED is measured by half of ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
14 other sections not shown
Other editions - View all
Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex