Elements of Geometry |
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Page 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 ,
Page 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 ...
Page 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 ...
Page 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 ...
Page 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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Common terms and phrases
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 JOHN CRERAR LIBRARY join less Let ABC let fall 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 three angles triangle ABC triangular prism triangular pyramids vertex vertices whence