Elements of GeometryGinn and Heath, 1877 - 250 σελίδες |
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Σελίδα 3
... extremities or limits . A Solid , as the term is used in Geometry , is a limited por- tion of space . After we acquire a clear notion of surfaces as boundaries of solids , we can easily conceive of surfaces apart from solids , and ...
... extremities or limits . A Solid , as the term is used in Geometry , is a limited por- tion of space . After we acquire a clear notion of surfaces as boundaries of solids , we can easily conceive of surfaces apart from solids , and ...
Σελίδα 5
... ( extremities ) of lines are points . The limits ( boundaries ) of surfaces are lines . The limits ( boundaries ) of solids are surfaces . 7. DEF . Extension is also called Magnitude . When reference is had to extent , lines , surfaces ...
... ( extremities ) of lines are points . The limits ( boundaries ) of surfaces are lines . The limits ( boundaries ) of solids are surfaces . 7. DEF . Extension is also called Magnitude . When reference is had to extent , lines , surfaces ...
Σελίδα 11
... extremities coincide . Two angles are equal , if they can be so placed that their vertices coincide in position and their sides in direction . In applying this test of equality , we assume that a line may be moved from one place to ...
... extremities coincide . Two angles are equal , if they can be so placed that their vertices coincide in position and their sides in direction . In applying this test of equality , we assume that a line may be moved from one place to ...
Σελίδα 17
... extremities in the same points ) . ..CFFE = = 2 C F , CO + OE 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance between two points ) . Substitute and 2 CO for CO + OE , 2 CF for CF + FE ; then we have 2 CO2 CF. .CO ...
... extremities in the same points ) . ..CFFE = = 2 C F , CO + OE 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance between two points ) . Substitute and 2 CO for CO + OE , 2 CF for CF + FE ; then we have 2 CO2 CF. .CO ...
Σελίδα 18
... . Point A will fall upon point 0 , ( FA = FO , by hyp . ) . ... line CA - line CO , ( their extremities being the same points ) . $ 18 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 GEOMETRY . — BOOK I.
... . Point A will fall upon point 0 , ( FA = FO , by hyp . ) . ... line CA - line CO , ( their extremities being the same points ) . $ 18 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 GEOMETRY . — BOOK I.
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A B C AABC AACB ABCD adjacent angles alt.-int altitude apothem arc A B bisect centre circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon exterior angles figure given line given point given polygon given straight line greater homologous sides hypotenuse isosceles triangle Let A B Let ABC limit line A B measured by arc middle point number of sides parallelogram perimeter perpendicular plane PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct rhombus right angles right triangle SCHOLIUM segment sides of equal sides of similar similar polygons subtend tangent THEOREM third side triangle ABC variable vertex vertices