Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page 35
... gives AB = DC , and AD = BC ; that is , the opposite sides of a parallelogram are also equal . Cor . I. The diagonal of a parallelogram divides it into two equal parts . Cor . II . Two parallels included between two other parallels are ...
... gives AB = DC , and AD = BC ; that is , the opposite sides of a parallelogram are also equal . Cor . I. The diagonal of a parallelogram divides it into two equal parts . Cor . II . Two parallels included between two other parallels are ...
Page 44
... gives an ob- lique line greater than the radius ( B. I. , T. XII . ) . Hence , A is the only point common to the straight line and the circumference ; consequently , this line is tangent to the circumference ( D. IV . ) . Cor . I. If a ...
... gives an ob- lique line greater than the radius ( B. I. , T. XII . ) . Hence , A is the only point common to the straight line and the circumference ; consequently , this line is tangent to the circumference ( D. IV . ) . Cor . I. If a ...
Page 76
... gives these new propositions : AD + DB : DB : : AE + EC : EC , AB : AD :: AC : AE and AB : DB :: AC : EC . Conversely . If a straight line DE is so drawn as to give AB : AD :: AC : AE , we shall have , by division , AB - AD : AD ...
... gives these new propositions : AD + DB : DB : : AE + EC : EC , AB : AD :: AC : AE and AB : DB :: AC : EC . Conversely . If a straight line DE is so drawn as to give AB : AD :: AC : AE , we shall have , by division , AB - AD : AD ...
Page 99
... give rise to some new Theorems in regard to areas , with which we will close this Book . THEOREM XXX . The ... gives AE for the difference of these two lines . Construct the same figure as in the first case , and , in addition ...
... give rise to some new Theorems in regard to areas , with which we will close this Book . THEOREM XXX . The ... gives AE for the difference of these two lines . Construct the same figure as in the first case , and , in addition ...
Page 102
... give this proportion , PA : PB :: PB ' : PA ' . Scholium I. When one of the chords is a diameter , and the other ... gives ( B. III . , T. XIII . ) this pro- portion , PA : PB :: PB : PA ' . Scholium II . This same right - angled ...
... give this proportion , PA : PB :: PB ' : PA ' . Scholium I. When one of the chords is a diameter , and the other ... gives ( B. III . , T. XIII . ) this pro- portion , PA : PB :: PB : PA ' . Scholium II . This same right - angled ...
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume