Elements of GeometryHilliard, Gray,, 1841 - 235 páginas |
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Página vi
... entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular triangles , of similar figures , & c . We shall be found fault vi Preface .
... entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular triangles , of similar figures , & c . We shall be found fault vi Preface .
Página 3
... similar sense are to be understood two polygons equiangular with respect to each other . The equal sides in the first case , and the equal angles in the second , are called homologous ( A ) . 21. An Axiom is a proposition , the truth of ...
... similar sense are to be understood two polygons equiangular with respect to each other . The equal sides in the first case , and the equal angles in the second , are called homologous ( A ) . 21. An Axiom is a proposition , the truth of ...
Página 22
... similar reason , AB is parallel to CD ; therefore the quadrilateral ABCD is a parallelogram . THEOREM . 84. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral are equal and parallel , the two other sides will also be equal ...
... similar reason , AB is parallel to CD ; therefore the quadrilateral ABCD is a parallelogram . THEOREM . 84. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral are equal and parallel , the two other sides will also be equal ...
Página 28
... similar reason ; it will , then , be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is , therefore , only one circle , whose circum- ference can pass through three given ...
... similar reason ; it will , then , be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is , therefore , only one circle , whose circum- ference can pass through three given ...
Página 33
... similar , it may be shown , that the fourth term of the proportion cannot be less than AD ; The reference by Roman numerals is to the Introduction . GEOM . 5 therefore it is exactly AD , and we have the Of the Measure of Angles . 33.
... similar , it may be shown , that the fourth term of the proportion cannot be less than AD ; The reference by Roman numerals is to the Introduction . GEOM . 5 therefore it is exactly AD , and we have the Of the Measure of Angles . 33.
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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.