An Elementary Treatise on Plane and Solid GeometryJ. Munroe, 1837 - 159 σελίδες |
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Σελίδα 5
... ABCD ( fig . 3 ) . - A Curved Line is one , the direction of which is constantly changing , as AB ( fig . 1 ) . 14. Definition . A Plane is a surface in which any two points being taken , the straight line joining those points lies ...
... ABCD ( fig . 3 ) . - A Curved Line is one , the direction of which is constantly changing , as AB ( fig . 1 ) . 14. Definition . A Plane is a surface in which any two points being taken , the straight line joining those points lies ...
Σελίδα 22
... ABCD ( fig . 39 ) be the parallelogram and AC its diagonal . = The two triangles ABC and ADC are equal , since they have the side AC common , the angle BAC = ACD , by art . 30 , on account of the parallels AB and CD , and BCA CAD , on ...
... ABCD ( fig . 39 ) be the parallelogram and AC its diagonal . = The two triangles ABC and ADC are equal , since they have the side AC common , the angle BAC = ACD , by art . 30 , on account of the parallels AB and CD , and BCA CAD , on ...
Σελίδα 23
... ABCD is a parallelogram . Demonstration . For the triangles ABC and ACD are equal , since they have the side AC common , the side = BC = AD , and the included angle BCA = CAD , on ac- count of the parallelism of BC and AD ; and ...
... ABCD is a parallelogram . Demonstration . For the triangles ABC and ACD are equal , since they have the side AC common , the side = BC = AD , and the included angle BCA = CAD , on ac- count of the parallelism of BC and AD ; and ...
Σελίδα 41
... ABCD is , by art . 79 , the parallelogram required . 147. Corollary . If the given angle is a right angle , the figure is a rectangle ; and , if the adjacent sides are also equal , the figure is a square . 148. To find the centre of a ...
... ABCD is , by art . 79 , the parallelogram required . 147. Corollary . If the given angle is a right angle , the figure is a rectangle ; and , if the adjacent sides are also equal , the figure is a square . 148. To find the centre of a ...
Σελίδα 57
... ABCD , & c . , A'B'C'D ' , & c . ( fig . 108 ) are composed of the same number of triangles ABC , ACD , & c . , A'B'C ' , A'C'D ' , & c . which are similar each to each and sim- ilarly disposed , the polygons are similar . Demonstration ...
... ABCD , & c . , A'B'C'D ' , & c . ( fig . 108 ) are composed of the same number of triangles ABC , ACD , & c . , A'B'C ' , A'C'D ' , & c . which are similar each to each and sim- ilarly disposed , the polygons are similar . Demonstration ...
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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°.