Euclidian Geometry |
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Page 23
... D. Then ABC is < the exterior ACD ; ( 1. 13 ) .. LS ABC , ACB are together the 4s ACD , ACB , < and are .. < than two right angles . ( I. 9 ) PROPOSITION XIV . The greater side of every triangle has INEQUALITIES . 23.
... D. Then ABC is < the exterior ACD ; ( 1. 13 ) .. LS ABC , ACB are together the 4s ACD , ACB , < and are .. < than two right angles . ( I. 9 ) PROPOSITION XIV . The greater side of every triangle has INEQUALITIES . 23.
Page 24
Francis Cuthbertson (M.A.). PROPOSITION XIV . The greater side of every triangle has the greater angle opposite to it . Let ABC be a △ having the side AC greater than the side AB . Then shall the ABC be greater than the ACB . From AC ...
Francis Cuthbertson (M.A.). PROPOSITION XIV . The greater side of every triangle has the greater angle opposite to it . Let ABC be a △ having the side AC greater than the side AB . Then shall the ABC be greater than the ACB . From AC ...
Page 25
Francis Cuthbertson (M.A.). PROPOSITION XV . The greater angle of every triangle has the greater side opposite to it . B Let ABC be a △ having the ABC > the △ ACB , then shall the side AC be > the side AB . For if not , AC must either ...
Francis Cuthbertson (M.A.). PROPOSITION XV . The greater angle of every triangle has the greater side opposite to it . B Let ABC be a △ having the ABC > the △ ACB , then shall the side AC be > the side AB . For if not , AC must either ...
Page 26
... greater than the third . Let ABC be a △ . Then shall any two of its sides , as AB , AC , be together > BC . B Produce BA to K , making AK = AC , and join KC . Then . AK is = AC ; .. LACK is = LAKC ; ( 1. 2 ) BCK is > LACK ; but .. LBCK ...
... greater than the third . Let ABC be a △ . Then shall any two of its sides , as AB , AC , be together > BC . B Produce BA to K , making AK = AC , and join KC . Then . AK is = AC ; .. LACK is = LAKC ; ( 1. 2 ) BCK is > LACK ; but .. LBCK ...
Page 27
... greater than △ BAC . Produce BD to meet the side AC in E. Then BA and AE are together greater than BE ; add to each EC ; ( I. 16 ) .. BA and AC are together greater than BE and EC . Again , DE and EC are together greater than DC ...
... greater than △ BAC . Produce BD to meet the side AC in E. Then BA and AE are together greater than BE ; add to each EC ; ( I. 16 ) .. BA and AC are together greater than BE and EC . Again , DE and EC are together greater than DC ...
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Common terms and phrases
Algebra base Cambridge centre chord circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided draw a straight ELEMENTARY TREATISE English equiangular equilateral Euclid Extra fcap fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle Latin Let ABC line bisecting locus Mathematical meet opposite angles Owens College parallel parallelogram perimeter perpendicular plane polygon PROBLEM produced Professor proportional PROPOSITION ratio rect rectangle rectangle contained rectilineal figure regular polygon respectively rhombus right angles Schools Second Edition segment similar Similarly squares on AC straight line drawn straight line joining tangent THEOREM TRIGONOMETRY twice rectangle twice the squares vertex