Elements of Geometry |
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Page v
... It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to established the entire edifice of the elements . 4 翼着 A 1 A 1 T ! It is necessary to the understanding of this work.
... It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to established the entire edifice of the elements . 4 翼着 A 1 A 1 T ! 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 4 and D , which is called also their rectangle , is nothing ...
... 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 4 and D , which is called also their rectangle , is nothing ...
Page 28
... 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 30
... 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 , what- ever numbers were substituted in the place of 7 and 4 ; there- fore , if the ratio of the angles ACB , DCE , can ...
... 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 , what- ever numbers were substituted in the place of 7 and 4 ; there- fore , if the ratio of the angles ACB , DCE , can ...
Page 31
Adrien Marie Legendre. 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. 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 BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence