Elements of GeometryHilliard, Gray,, 1841 - 235 páginas |
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Página v
... between he same points . It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to establish the entire edifice of the elements . It is necessary to the understanding of this work ,
... between he same points . It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to establish the entire edifice of the elements . It is necessary to the understanding of this work ,
Página xiv
... entire or frac- tional , commensurable or incommensurable , and the proportion among the lines A , B , C , D , becomes a proportion in numbers . Hence the product of two lines , A and D , which is called also their rectangle , is ...
... entire or frac- tional , commensurable or incommensurable , and the proportion among the lines A , B , C , D , becomes a proportion in numbers . Hence the product of two lines , A and D , which is called also their rectangle , is ...
Página 30
... entire arc HMK = HPK , and it is moreover evident , that each of these arcs is a semicircumfer- ence . Fig . 57 , 58 . THEOREM . 113. If the circumferences of two circles cut each other in two points , the line which passes through ...
... entire arc HMK = HPK , and it is moreover evident , that each of these arcs is a semicircumfer- ence . Fig . 57 , 58 . THEOREM . 113. If the circumferences of two circles cut each other in two points , the line which passes through ...
Página 32
... entire num- bers , the intercepted arcs AB , DE , will be to each other as the same numbers , and we shall have this ... entire arc AB will be to the entire arc DE as 7 to 4. Now it is evident , that the same reasoning might be used ...
... entire num- bers , the intercepted arcs AB , DE , will be to each other as the same numbers , and we shall have this ... entire arc AB will be to the entire arc DE as 7 to 4. Now it is evident , that the same reasoning might be used ...
Página 33
Adrien Marie Legendre. by entire numbers , the arcs AB , DE , will be to each other as the angles ACB , DCE . 121. Scholium : Reciprocally , if the arcs AB , DE , are to each other as two entire numbers , the angles ACB , DCE , will be ...
Adrien Marie Legendre. by entire numbers , the arcs AB , DE , will be to each other as the angles ACB , DCE . 121. Scholium : Reciprocally , if the arcs AB , DE , are to each other as two entire numbers , the angles ACB , DCE , will be ...
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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.