Elements of GeometryHilliard, Gray,, 1841 - 235 σελίδες |
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Σελίδα 2
... opposite to the right angle is called the hypothenuse . Fig . 10. Thus ABC ( fig . 10 ) is a triangle right - angled at A , and the side BC is the hypothenuse . Fig . 11 . Fig . 12 . Fig . 13 . Fig . 14 . Fig . 15 . 17. Among ...
... opposite to the right angle is called the hypothenuse . Fig . 10. Thus ABC ( fig . 10 ) is a triangle right - angled at A , and the side BC is the hypothenuse . Fig . 11 . Fig . 12 . Fig . 13 . Fig . 14 . Fig . 15 . 17. Among ...
Σελίδα 6
... opposite angle BCE . It may be demonstrated , in like manner , that the angle ACE is equal to its opposite angle BCD . 35. Scholium . The four angles , formed about a point by two straight lines which cut each other , are together equal ...
... opposite angle BCE . It may be demonstrated , in like manner , that the angle ACE is equal to its opposite angle BCD . 35. Scholium . The four angles , formed about a point by two straight lines which cut each other , are together equal ...
Σελίδα 9
... opposite to equal sides ; thus , the equal angles A and D are op- posite to the equal sides BC and EF . THEOREM . 45. In an isosceles triangle , the angles opposite to the equal sides are equal . = Demonstration . Let the side AB AC ...
... opposite to equal sides ; thus , the equal angles A and D are op- posite to the equal sides BC and EF . THEOREM . 45. In an isosceles triangle , the angles opposite to the equal sides are equal . = Demonstration . Let the side AB AC ...
Σελίδα 10
... opposite to the greater angle ; and conversely , of the two angles of a triangle , that is the greater , which is opposite to the greater side . Demonstration . 1. Let the angle C > B ( fig . 30 ) , then will the side AB , opposite to ...
... opposite to the greater angle ; and conversely , of the two angles of a triangle , that is the greater , which is opposite to the greater side . Demonstration . 1. Let the angle C > B ( fig . 30 ) , then will the side AB , opposite to ...
Σελίδα 11
... opposite sides of the perpendicular , and at equal distances BC , BE , from it , are equal to one another ; 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote from the perpendicular is the greater ...
... opposite sides of the perpendicular , and at equal distances BC , BE , from it , are equal to one another ; 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote from the perpendicular is the greater ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle join less Let ABC let fall Let us suppose line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM third three angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Δημοφιλή αποσπάσματα
Σελίδα 67 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 9 - 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 65 - 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 160 - ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be...
Σελίδα 168 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 157 - 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 8 - Any side of a triangle is less than the sum of the other two sides...
Σελίδα 82 - 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 29 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Σελίδα 182 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.