## Elements of Geometry |

### From inside the book

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... , or solids , are equal , when , being

... , or solids , are equal , when , being

**applied**the one to the other , they coin- cide with each other entirely ; that is , when they exactly fill the same space . Fig . 42 PART FIRST . OF PLANE FIGURES . SECTION FIRST . Axioms . 3. Page 4

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**applied**to AB , so that the point E will fall upon A , and the point F upon B. These two lines , thus placed , will co- incide with each other throughout ; otherwise there would be two straight lines between A and B , which is ... Page 25

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**applied**to AFB , so that the base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is ... Page 26

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**applied**exactly to the semicircle ENGF , and then the curved line AMDB will coincide entirely with the curved line ENGF ; but the portion AMD being sup- posed equal to the portion ENG , the point D will fall upon G ; therefore the chord ... Page 44

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**applied**to an arc of the same radius , as a straight line is**applied**to a straight line . We shall thus obtain a common measure of the arcs CD , EF , if they have one , and their ratio in numbers . This ratio will be the same as that 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