Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page viii
... of a Prismoid , 144 Volumes of Regular Polyedrons , 146 LOGARITHMIC TABLES . Logarithms of Numbers from 1 to 10,000 .. Sines and Tangents .. 1-16 17-62 ELEMENTS OF GEOMETRY . INTRODUCTION . DEFINITIONS OF TERMS . viii CONTENTS .
... of a Prismoid , 144 Volumes of Regular Polyedrons , 146 LOGARITHMIC TABLES . Logarithms of Numbers from 1 to 10,000 .. Sines and Tangents .. 1-16 17-62 ELEMENTS OF GEOMETRY . INTRODUCTION . DEFINITIONS OF TERMS . viii CONTENTS .
Page 62
... TANGENT is a straight line which touches the circumference in one point only . This point is called , the point of contact , or the point of tangency . 12. Two circles are tangent to each other , when they touch each other in one point ...
... TANGENT is a straight line which touches the circumference in one point only . This point is called , the point of contact , or the point of tangency . 12. Two circles are tangent to each other , when they touch each other in one point ...
Page 70
... tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it is perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A : then is it ...
... tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it is perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A : then is it ...
Page 71
... tangent ; or , both may be tangents . 1o . Let the secants AB and DE be parallel : then the intercepted arcs MN and PQ are equal . For , draw the radius CH per- pendicular to the chord MP ; it is also perpendicular to NQ ( B. I. , P. XX ...
... tangent ; or , both may be tangents . 1o . Let the secants AB and DE be parallel : then the intercepted arcs MN and PQ are equal . For , draw the radius CH per- pendicular to the chord MP ; it is also perpendicular to NQ ( B. I. , P. XX ...
Page 72
... tangents DE and IL be parallel , and let H and K be their points of contact : then the intercepted arcs HMK and HPK are equal . For , draw the secant AB par- allel to DE ; then , from what has just been shown , we have HM equal to HP ...
... tangents DE and IL be parallel , and let H and K be their points of contact : then the intercepted arcs HMK and HPK are equal . For , draw the secant AB par- allel to DE ; then , from what has just been shown , we have HM equal to HP ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence