## Elements of Geometry |

### From inside the book

Results 1-5 of 60

Page v

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**suppose**that there can be only one 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 ... Page xiv

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**suppose**one of these lines , or a fifth , if we please , to answer as a common measure to the whole , and to be taken for unity ; then A , B , C , D , will each represent a certain number of units , entire or frac- tional ... Page 4

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**suppose**, if it be pos- sible , that it falls upon a line CK , different from CD ; since , by hypothesis ( 10 ) , the angle EGH = HGF , it follows that Fig . 17 . But and besides , by hypothesis , hence ACK KCB . ACK > ACD , KCB BCD ... Page 5

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**suppose**, if it be possible , that the lines , when produced , separate from each other at a point C , the one becoming CD and the other CE . At the point C , let CF be drawn , so as to make the angle ACF a right angle ; then , ACD ... Page 13

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**suppose*** that AB is the greatest side , and BC the least , and that , consequently , ACB is the greatest angle , and BAC the least ( 49 ) . Through the point A , and the middle point I of the opposite side BC , draw the straight line ...### 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