Elements of GeometryGinn, Heath & Company, 1884 |
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Σελίδα 73
... Diameter of a circle is any straight line pass- ing through the centre and having its extremities in the circum- ference , as A B , Fig . 2 . By the definition of a circle , all its radii are equal . Hence , all its diameters are equal ...
... Diameter of a circle is any straight line pass- ing through the centre and having its extremities in the circum- ference , as A B , Fig . 2 . By the definition of a circle , all its radii are equal . Hence , all its diameters are equal ...
Σελίδα 75
... diameter bisects the circle and its circumference . For if we fold over the segment AMB on A B as an axis until it ... diameter of a circle is greater than any other chord . Let A B be the diameter of the circle AM B , and A E any other ...
... diameter bisects the circle and its circumference . For if we fold over the segment AMB on A B as an axis until it ... diameter of a circle is greater than any other chord . Let A B be the diameter of the circle AM B , and A E any other ...
Σελίδα 95
... diameter B C P. ZPBA is measured by arc PA , ( Case I. ) PBE is measured by arc PE , ( Case I. ) : . Z PBA + Z PBE is measured by ( arc PA + arc P E ) . .. △ E BA is measured by 1⁄2 arc E A. CASE III . In the circle BFP ( Fig . 3 ) ...
... diameter B C P. ZPBA is measured by arc PA , ( Case I. ) PBE is measured by arc PE , ( Case I. ) : . Z PBA + Z PBE is measured by ( arc PA + arc P E ) . .. △ E BA is measured by 1⁄2 arc E A. CASE III . In the circle BFP ( Fig . 3 ) ...
Σελίδα 96
... arc B D. Q. E. D. Ex . Show that the least chord that can be drawn through a given point in a circle is perpendicular to the diameter drawn through the point . PROPOSITION XVI . THEOREM . 209. An angle formed by 96 BOOK II . GEOMETRY .
... arc B D. Q. E. D. Ex . Show that the least chord that can be drawn through a given point in a circle is perpendicular to the diameter drawn through the point . PROPOSITION XVI . THEOREM . 209. An angle formed by 96 BOOK II . GEOMETRY .
Σελίδα 97
... diameter A C F. FAM is a rt . △ , $ 186 ( the radius drawn to a tangent at the point of contact is to it ) . △ FA M , being a rt . Z , is measured by the semi - circum- ference A EF . FAH is measured by arc FH , ( an inscribed is ...
... diameter A C F. FAM is a rt . △ , $ 186 ( the radius drawn to a tangent at the point of contact is to it ) . △ FA M , being a rt . Z , is measured by the semi - circum- ference A EF . FAH is measured by arc FH , ( an inscribed is ...
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A B C AABC 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 equivalent exterior angles figure given line given point given polygon greater homologous sides hypotenuse isosceles triangle Let A B Let ABC limit line A B Mailing price measured by arc middle point number of sides parallelogram perimeter perpendicular PHILLIPS EXETER ACADEMY 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 vertex vertices Wentworth