Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα iii
... distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines of the figures are full lines , the lines employed.
... distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines of the figures are full lines , the lines employed.
Σελίδα 12
... fall on B ' , then if the side BA fall on B ' A ' , the angle ABC equals the angle A'B ' C " ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A ' B ' C " ; but if the side BA fall in the ...
... fall on B ' , then if the side BA fall on B ' A ' , the angle ABC equals the angle A'B ' C " ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A ' B ' C " ; but if the side BA fall in the ...
Σελίδα 17
... fall upon the point E , ( since 0 C0 E by cons . ) . .. line CF = line FE , ( having their extremities in the same points ) . = ..CFFE 2 CF , and But CO + OE 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance between ...
... fall upon the point E , ( since 0 C0 E by cons . ) . .. line CF = line FE , ( having their extremities in the same points ) . = ..CFFE 2 CF , and But CO + OE 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance between ...
Σελίδα 18
... being a rt . 2 ) . 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 BOOK I. GEOMETRY . ―
... being a rt . 2 ) . 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 BOOK I. GEOMETRY . ―
Σελίδα 21
... fall upon the point K ; otherwise one of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . $ 55 .. FE FK . = Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the ...
... fall upon the point K ; otherwise one of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . $ 55 .. FE FK . = Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A B C AABC AACB ABCD acute adjacent angles alt.-int altitude apothem arc A B BC² bisect centre chord A B circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon equivalent exterior angles figure given line given point given polygon greater homologous sides hypotenuse Iden isosceles triangle Let A B 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