Euclidian GeometryMacmillan, 1874 - 349 sider |
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Side 21
... Produce AQ , and make the produced part QF = AQ . Join FR . Then AQR is a right 4 , .. 4 FQR is a right 4. ( 1.9 ) Hence in the As AQR , FQR , AQ , QR and AQR are respectively equal to FQ , QR , and FQR ; .. LARQ = L FRQ . ( I. 1 ) ...
... Produce AQ , and make the produced part QF = AQ . Join FR . Then AQR is a right 4 , .. 4 FQR is a right 4. ( 1.9 ) Hence in the As AQR , FQR , AQ , QR and AQR are respectively equal to FQ , QR , and FQR ; .. LARQ = L FRQ . ( I. 1 ) ...
Side 22
... produced to D. Then shall the ACD be > either of the S BAC , ABC . Bisect AC in E ; join BE and produce BE to F ... produced to G , that BCG is the ABC . But ACD is = L BCG ; ( 1.6 ) .. LACD is > the ABC . Hence it follows that Any two ...
... produced to D. Then shall the ACD be > either of the S BAC , ABC . Bisect AC in E ; join BE and produce BE to F ... produced to G , that BCG is the ABC . But ACD is = L BCG ; ( 1.6 ) .. LACD is > the ABC . Hence it follows that Any two ...
Side 23
... Produce BC to D. Then ABC is the exterior ACD ; ( 1 , 13 ) .. LS ABC , ACB are together < the 4s ACD , ACB , and are .. < than two right angles . ( 1.9 ) PROPOSITION XIV . The greater side of every triangle has INEQUALITIES . 23.
... Produce BC to D. Then ABC is the exterior ACD ; ( 1 , 13 ) .. LS ABC , ACB are together < the 4s ACD , ACB , and are .. < than two right angles . ( 1.9 ) PROPOSITION XIV . The greater side of every triangle has INEQUALITIES . 23.
Side 24
... produced to A , .. LADB is greater than 4 DCB ; ... also ABD is greater than △ DCB . ( I. 13 ) Much more then is ABC greater than DCB , i.e. LACB . PROPOSITION XV . The greater angle of every triangle has 24 INEQUALITIES .
... produced to A , .. LADB is greater than 4 DCB ; ... also ABD is greater than △ DCB . ( I. 13 ) Much more then is ABC greater than DCB , i.e. LACB . PROPOSITION XV . The greater angle of every triangle has 24 INEQUALITIES .
Side 26
... Produce BA to K , making AK = AC , and join KC . Then . AK is AC ; .. LACK is = L AKC ; ( 1. 2 ) = but BCK is > LACK ; .. L BCK is > L AKC , i.e. L BKC ; .. BK is BC ; but BK is = BA and AC together ; .. BA , AC are together > BC . ( 1 ...
... Produce BA to K , making AK = AC , and join KC . Then . AK is AC ; .. LACK is = L AKC ; ( 1. 2 ) = but BCK is > LACK ; .. L BCK is > L AKC , i.e. L BKC ; .. BK is BC ; but BK is = BA and AC together ; .. BA , AC are together > BC . ( 1 ...
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