Elements of GeometryHilliard, Gray,, 1841 - 235 páginas |
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Página 24
... segment of a circle is the portion comprehended be- tween an arc and its chord . 92. A sector is the part of a ... segments ; but , in speaking of these , the smaller is always to be understood , when the contrary is not expressed . And ...
... segment of a circle is the portion comprehended be- tween an arc and its chord . 92. A sector is the part of a ... segments ; but , in speaking of these , the smaller is always to be understood , when the contrary is not expressed . And ...
Página 35
... segment , are equal ; for they have each for their measure the half of the same arc BOC . 128. Corollary 11. Every angle BAD ( fig . 67 ) , inscribed in Fig . 67 . a semicircle , is a right angle ; for it has for its measure the half of ...
... segment , are equal ; for they have each for their measure the half of the same arc BOC . 128. Corollary 11. Every angle BAD ( fig . 67 ) , inscribed in Fig . 67 . a semicircle , is a right angle ; for it has for its measure the half of ...
Página 36
... segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicir- cumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for ...
... segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicir- cumference . And every angle BOC , inscribed in a segment less than a semicircle , is an obtuse angle ; for ...
Página 42
... segment capable of containing a given angle C , that is , a segment such , that each of the angles , which may be inscribed in it , shall be equal to a given angle C. = Solution . Produce AB toward D , make at the point B the angle DBE ...
... segment capable of containing a given angle C , that is , a segment such , that each of the angles , which may be inscribed in it , shall be equal to a given angle C. = Solution . Produce AB toward D , make at the point B the angle DBE ...
Página 45
... segments , are such as correspond to equal angles at the centre . Thus , the angle A ( fig . 92 ) being equal to the angle Fig . 92 . O , the arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164. The altitude ...
... segments , are such as correspond to equal angles at the centre . Thus , the angle A ( fig . 92 ) being equal to the angle Fig . 92 . O , the arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164. The altitude ...
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Términos y frases comunes
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
Pasajes populares
Página 67 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 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.
Página 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'.
Página 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...
Página 168 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Página 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.
Página 8 - Any side of a triangle is less than the sum of the other two sides...
Página 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.
Página 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.
Página 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.