Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα 17
... between two points ) . Substitute and 2 CO for CO + OE , 2 CF for CF + FE ; then we have 2 CO < 2C F. ..CO < CF. $ 18 . Cons . $ 18 Q E. D. PROPOSITION IV . THEOREM . 53. Two oblique lines drawn PERPENDICULAR AND OBLIQUE LINES . 17.
... between two points ) . Substitute and 2 CO for CO + OE , 2 CF for CF + FE ; then we have 2 CO < 2C F. ..CO < CF. $ 18 . Cons . $ 18 Q E. D. PROPOSITION IV . THEOREM . 53. Two oblique lines drawn PERPENDICULAR AND OBLIQUE LINES . 17.
Σελίδα 19
... + OE > OA + OE + O B. Substitute for CE + BE its equal C B , and take away OE from each side of the inequality . We have CA + CBOA + O B. Q. E. D. PROPOSITION VI . THEOREM . 55. Of two oblique lines PERPENDICULAR AND OBLIQUE LINES . 19.
... + OE > OA + OE + O B. Substitute for CE + BE its equal C B , and take away OE from each side of the inequality . We have CA + CBOA + O B. Q. E. D. PROPOSITION VI . THEOREM . 55. Of two oblique lines PERPENDICULAR AND OBLIQUE LINES . 19.
Σελίδα 23
... Substitute for DB its equal DA , then CB < CD + DA . = CD + DA CA , ..CB CA. § 18 Ax . 9 . Q. E. D .. 59. The Locus of a point is a line , straight or curved , con- taining all the points which possess a common property . Thus , the ...
... Substitute for DB its equal DA , then CB < CD + DA . = CD + DA CA , ..CB CA. § 18 Ax . 9 . Q. E. D .. 59. The Locus of a point is a line , straight or curved , con- taining all the points which possess a common property . Thus , the ...
Σελίδα 31
... . - adj . ) . But = ZEHB LHKD , $ 34 § 70 ( being ext . - int . £ ) . Substitute HKD for EHB in the first equality ; ZBHK + Z HKD = 2 rt . s . Q. E. D. PROPOSITION XVI . THEOREM . 74. CONVERSELY : When two PARALLEL LINES . 31.
... . - adj . ) . But = ZEHB LHKD , $ 34 § 70 ( being ext . - int . £ ) . Substitute HKD for EHB in the first equality ; ZBHK + Z HKD = 2 rt . s . Q. E. D. PROPOSITION XVI . THEOREM . 74. CONVERSELY : When two PARALLEL LINES . 31.
Σελίδα 40
... Substitute for ECF and BCE their equal , A and B. Then ZA + ZB + Z BCA = 2 rt . s . Q. E. D. 99. COROLLARY 1. If the sum of two angles of a triangle be known , the third angle can be found by taking this sum from two right angles . 100 ...
... Substitute for ECF and BCE their equal , A and B. Then ZA + ZB + Z BCA = 2 rt . s . Q. E. D. 99. COROLLARY 1. If the sum of two angles of a triangle be known , the third angle can be found by taking this sum from two right angles . 100 ...
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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