An Elementary Treatise on Plane and Solid GeometryJ. Munroe, 1837 - 159 σελίδες |
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Σελίδα vii
... less than diameter ( 91 ) , Line inscribed in a circle ( 92 ) ; greatest inscribed line ( 93 ) , Line meets the circumference in only two points ( 94 ) , Angle measured by arc ( 95–98 , 100 ) , Infinitely small quantities ( 99 ) , 24 ...
... less than diameter ( 91 ) , Line inscribed in a circle ( 92 ) ; greatest inscribed line ( 93 ) , Line meets the circumference in only two points ( 94 ) , Angle measured by arc ( 95–98 , 100 ) , Infinitely small quantities ( 99 ) , 24 ...
Σελίδα xiv
... ) ; spherical seg- ment and zone , their bases and altitude ( 436 ) ; spherical sector ( 437 ) , · 135 One side of spherical triangle less than sum of other two ( 438 ) , 137 Sum of sides of spherical polygon ( 439 , 440 xiv CONTENTS .
... ) ; spherical seg- ment and zone , their bases and altitude ( 436 ) ; spherical sector ( 437 ) , · 135 One side of spherical triangle less than sum of other two ( 438 ) , 137 Sum of sides of spherical polygon ( 439 , 440 xiv CONTENTS .
Σελίδα xvi
... less than ASB ; for if ASD were equal to ASB , AD would , by art . 51 , be equal to AB ; and if it were greater , draw SF in the plane of ASD , making ASF = ASB , and SF = SB SD , whence , by art . 51 , AF AB . Join DF , and in the ...
... less than ASB ; for if ASD were equal to ASB , AD would , by art . 51 , be equal to AB ; and if it were greater , draw SF in the plane of ASD , making ASF = ASB , and SF = SB SD , whence , by art . 51 , AF AB . Join DF , and in the ...
Σελίδα xvii
... less than . Thus , A < B is A less than B. A2 indicates the second power of A , A3 the third pow- er , & c . A ratio or fraction is the quotient of one quantity divided by another , and is usually written with the sign ( :) . Thus the ...
... less than . Thus , A < B is A less than B. A2 indicates the second power of A , A3 the third pow- er , & c . A ratio or fraction is the quotient of one quantity divided by another , and is usually written with the sign ( :) . Thus the ...
Σελίδα 7
... less than a right angle , as A ( fig . 4 ) . An Obtuse angle is one greater than a right angle , as A ( fig . 6 ) . 22. Definitions . The Complement of an angle is the remainder , after subtracting it from a right angle . The Supplement ...
... less than a right angle , as A ( fig . 4 ) . An Obtuse angle is one greater than a right angle , as A ( fig . 6 ) . 22. Definitions . The Complement of an angle is the remainder , after subtracting it from a right angle . The Supplement ...
Άλλες εκδόσεις - Προβολή όλων
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°.