Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration : Accompanied with All the Necessary Logarithmic and Trigonometric TablesD. Appleton, 1860 - 443 σελίδες |
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Σελίδα iii
... give a more extended and com prehensive course , better adapted to the use of Advanced Schools and Colleges . In the First Part of the work , which is confined to the theo- retical principles of Geometry , great care has been taken to ...
... give a more extended and com prehensive course , better adapted to the use of Advanced Schools and Colleges . In the First Part of the work , which is confined to the theo- retical principles of Geometry , great care has been taken to ...
Σελίδα 3
... gives a line , and any surface may be intersected by an infinite number of other distinct surfaces , it follows that On any surface whatever , we may conceive an infinite number of lines . The place of meeting , or of intersection of ...
... gives a line , and any surface may be intersected by an infinite number of other distinct surfaces , it follows that On any surface whatever , we may conceive an infinite number of lines . The place of meeting , or of intersection of ...
Σελίδα 34
... gives the angle ADB = CBD , which are alternate interior angles in reference to the sides AD and BC , hence these sides are parallel . Consequently the figure is a parallelogram ( D. XXV . ) . THEOREM XXX . If two opposite sides of a ...
... gives the angle ADB = CBD , which are alternate interior angles in reference to the sides AD and BC , hence these sides are parallel . Consequently the figure is a parallelogram ( D. XXV . ) . THEOREM XXX . If two opposite sides of a ...
Σελίδα 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 ...
Σελίδα 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 ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c 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 given angle given line gives greater half hence hypotenuse inches included angle inscribed circle 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
Δημοφιλή αποσπάσματα
Σελίδα 113 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Σελίδα 31 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 112 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Σελίδα 33 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 80 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 139 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Σελίδα 15 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Σελίδα 174 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Σελίδα 107 - ... similar figures are to each other as the squares of their homologous sides.
Σελίδα 180 - Every section of a sphere, made by a plane, is a circle.