## Elements of Geometry |

### From inside the book

Results 1-5 of 85

Page xiv

...

...

**Hence**the product of two lines , A and D , which is called also their rectangle , is nothing else than the number of linear units . contained in A multiplied by the number of linear units con- tained in B ; and we can easily conceive ... Page 4

...

...

**hence**ACK KCB . ACK > ACD , KCB BCD ; ACD BCD ; ACK KCB ; and the line GH cannot fall upon a line CK different from CD ; consequently it falls upon CD , and the angle EGH upon ACD , and EGH is equal to ACD ; therefore all right angles ... Page 10

...

...

**Hence**a straight line , drawn from the vertex of an isosceles triangle to the middle of the base , is perpendicular to that base , and divides the vertical angle into two equal parts . In a triangle that is not isosceles , any one of ... Page 11

...

...

**hence**it would follow , that two straight lines ACF , ABF , might be drawn between the same two points A and F , which is impossible ( 25 ) ; it is , then , equally impossible to draw two perpendiculars from the same point to the same ... Page 14

...

...

**hence**follows , 1. that the angle AC'B ' , designated by C ' , is composed of two angles , equal , respectively , to the two angles B and C , of the triangle ABC , and that , accordingly , we have C ' = B + C ; 2. that the angle A of ...### 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