Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα iii
... diameter of 6 . , འང “ ཁ C V H C & C K BH = BK DK - DR AH = AR HC LAB & C K L B D A He 11 to B K & CK II to HB BH.C = B. K & CK = HB Add . ( HB = BK ) How ARE AH ) = AB - HB L DREDK ) = DB - BR AR + DR = AD = A B + DB - 2 HB 1. AD = AB ...
... diameter of 6 . , འང “ ཁ C V H C & C K BH = BK DK - DR AH = AR HC LAB & C K L B D A He 11 to B K & CK II to HB BH.C = B. K & CK = HB Add . ( HB = BK ) How ARE AH ) = AB - HB L DREDK ) = DB - BR AR + DR = AD = A B + DB - 2 HB 1. AD = AB ...
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 of a circle is greater than any other Let A B be the diameter of the circle AMB , and A E any other chord . M We are to prove ABA E. A 23 E B C From C , the centre of the O , draw C E. But СЕ CE = CB , ( being radii of the same ...
... diameter of a circle is greater than any other Let A B be the diameter of the circle AMB , and A E any other chord . M We are to prove ABA E. A 23 E B C From C , the centre of the O , draw C E. But СЕ CE = CB , ( being radii of the same ...
Σελίδα 95
... diameter BC P. PBA 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 ) . : . ZE BA is measured by arc E A. CASE III . In the circle BFP ( Fig . 3 ) , let the ...
... diameter BC P. PBA 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 ) . : . ZE BA is measured by arc E A. CASE III . In the circle BFP ( Fig . 3 ) , let the ...
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 30 96 GEOMETRY . BOOK II .
... 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 30 96 GEOMETRY . BOOK II .
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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