Elements of Geometry |
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Page 3
... surfaces , 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.
... surfaces , 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 24
... surface which has length and breadth , while the circumference is only a line . + The same chord , as FG , corresponds to two arcs , and consequent- ly to two segments ; but , in speaking of these , the smaller is always to be ...
... surface which has length and breadth , while the circumference is only a line . + The same chord , as FG , corresponds to two arcs , and consequent- ly to two segments ; but , in speaking of these , the smaller is always to be ...
Page 44
... surfaces are equal . Two figures may be equivalent , however dissimilar ; thus a circle may be equivalent to a square , a triangle to a rectangle , & c . The denomination of equal figures will be restricted to those , which , being ...
... surfaces are equal . Two figures may be equivalent , however dissimilar ; thus a circle may be equivalent to a square , a triangle to a rectangle , & c . The denomination of equal figures will be restricted to those , which , being ...
Page 45
... surface of a figure are terms nearly synonymous . Area , however , is more particularly used to de- note the superficial extent of the figure considered as measured , or compared with other surfaces . THEOREM . 166. Parallelograms ...
... surface of a figure are terms nearly synonymous . Area , however , is more particularly used to de- note the superficial extent of the figure considered as measured , or compared with other surfaces . THEOREM . 166. Parallelograms ...
Page 48
... surface ; and that square has been preferred , whose side is the unit of length ; the measure , therefore , which we have regarded as simply relative , becomes absolute . The number 30 , for example , by which we have measured the ...
... surface ; and that square has been preferred , whose side is the unit of length ; the measure , therefore , which we have regarded as simply relative , becomes absolute . The number 30 , for example , by which we have measured the ...
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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