## Elements of Geometry |

### From inside the book

Results 1-5 of 31

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

... 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 ... 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 ... 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 ... Page 33

Adrien Marie Legendre. by

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 ...### Other editions - View all

### 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