An Elementary Treatise on Plane and Solid GeometryJ. Munroe, 1837 - 159 σελίδες |
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Σελίδα 9
... respectively the same as those of AC and AE , the di- rection of BD relatively to BF must be the same as that of AE relatively to AC ; so that , if BD is placed upon AC , BF will fall upon AE , and the angles will coincide . 30. Theorem ...
... respectively the same as those of AC and AE , the di- rection of BD relatively to BF must be the same as that of AE relatively to AC ; so that , if BD is placed upon AC , BF will fall upon AE , and the angles will coincide . 30. Theorem ...
Σελίδα 15
... respective- ly equal to two sides and the included angle of the other . Demonstration . In the two triangles ABC , DEF ( fig . 31 ) , let the angle A be equal to the angle D , and the sides AB , AC , respectively equal to DE , DF ...
... respective- ly equal to two sides and the included angle of the other . Demonstration . In the two triangles ABC , DEF ( fig . 31 ) , let the angle A be equal to the angle D , and the sides AB , AC , respectively equal to DE , DF ...
Σελίδα 16
... respectively equal to those of another , the other side and angles are also equal in the two triangles . 53. Theorem . Two triangles are equal , when a side and the two adjacent angles of one triangle are respectively equal to those of ...
... respectively equal to those of another , the other side and angles are also equal in the two triangles . 53. Theorem . Two triangles are equal , when a side and the two adjacent angles of one triangle are respectively equal to those of ...
Σελίδα 17
... respectively equal to the two sides BC , BD , and the included angle DBC ; and the angle A will be equal to C. 56. Corollary . An equilateral triangle is also equi- angular . 57. Theorem . The line BD ( fig . 32 ) , which bi- sects the ...
... respectively equal to the two sides BC , BD , and the included angle DBC ; and the angle A will be equal to C. 56. Corollary . An equilateral triangle is also equi- angular . 57. Theorem . The line BD ( fig . 32 ) , which bi- sects the ...
Σελίδα 18
... respectively equal to CA and CB , and terminate at the same extremities of AB . Demonstration . For , first , the vertex D of one triangle cannot fall within the other triangle ACB , as in fig . 19 , because , by art . 40 , AD + DB must ...
... respectively equal to CA and CB , and terminate at the same extremities of AB . Demonstration . For , first , the vertex D of one triangle cannot fall within the other triangle ACB , as in fig . 19 , because , by art . 40 , AD + DB must ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD &c AC AC adjacent angles altitude angle ABC angle BAC arc BC base and altitude bisect CD fig centre chord circumference convex surface Corollary cylinder DEF fig Definitions Demonstration denote diameter divided Draw equal arcs equal distances equilateral equivalent four right angles frustum given angle given circle given line given polygon given sides given square greater half the product Hence homologous sides hypothenuse infinitely small inscribed circle isoperimetrical isosceles Join AC Let ABCD line AB fig lines drawn mean proportional number of sides oblique lines parallel lines parallelogram parallelopiped perimeter perpendicular plane angles plane MN polygon ABCD prism Problem radii radius ratio rectangles regular polygon respectively equal right triangles Scholium secant sector segment side AC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle tangent Theorem triangles ABC triangular prism vertex vertices whence
Δημοφιλή αποσπάσματα
Σελίδα 148 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 90 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Σελίδα 24 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 40 - One side and two angles of a triangle being given, to construct the triangle. Solution.
Σελίδα 79 - Construct, by § 145, a right triangle, of which the hypothenuse BC (fig. 79) is equal to the side of the greater square, and the leg AB is equal to the side of the less square ; and AC is the side of the required square.
Σελίδα 142 - THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles; P and Q their polar triangles. Since the angles are equal in the triangles A and B, the sides will be equal in. their polar triangles P and Q (Prop.
Σελίδα 6 - The preface and commentary to the Antigone are even more creditable to Mr. Woolsey's ability than those to the Alcestis. The sketch of the poem, in the preface, is written with clearness and brevity. The difficulties in this play, that call for a commentator's explanation, are far more numerous than in the Alcestis.
Σελίδα 70 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 5 - A surface is that which has length and breadth, without thickness. 6. A plane is a surface, in which any two points being taken, the straight line joining those points lies wholly in that surface.
Σελίδα 137 - Each side of a spherical triangle is less than the sum of 'the other two sides. 48. The sum of the sides of a spherical polygon is less than 360°.