## Elements of Geometry |

### From inside the book

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Page xiv

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**Hence**the product of two lines 4 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 this ... Page 4

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**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

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

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**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 20

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**Hence**two parallels AB , CD , comprehended between two other parallels AD , BC , are equal . THEOREM . 86. If , in a quadrilateral ABCD ( fig . 44 ) , the opposite sides are equal , namely , AB = CD , and AD = CB , the equal sides will ...### Other editions - View all

### 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