The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 8
... equal to BG ; and because D is the centre of the circle GLK , 2. DL is equal to DG ; 3 . and DA , DB , parts of them are equal ( Construction ) ; therefore , ( Ax . 3. ) The remainder AL is equal to the remainder BG . But it has been ...
... equal to BG ; and because D is the centre of the circle GLK , 2. DL is equal to DG ; 3 . and DA , DB , parts of them are equal ( Construction ) ; therefore , ( Ax . 3. ) The remainder AL is equal to the remainder BG . But it has been ...
Σελίδα 10
... equal to the angle ACB , and the angle CBD to the angle BCE . A B F G E D In BD take any point F , and from AE , the greater , cut off AG equal ( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to 4G , and ...
... equal to the angle ACB , and the angle CBD to the angle BCE . A B F G E D In BD take any point F , and from AE , the greater , cut off AG equal ( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to 4G , and ...
Σελίδα 13
... equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to ... same base EF , and upon the same side of it , there can be two triangles that have their ... ( Constr . ) 2. The base DF is BOOK I. - PROP . VIII . IX . 13.
... equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to ... same base EF , and upon the same side of it , there can be two triangles that have their ... ( Constr . ) 2. The base DF is BOOK I. - PROP . VIII . IX . 13.
Σελίδα 14
Euclid, Samuel A. GOOD. and ( Constr . ) 2. The base DF is equal to the base EF ; therefore ( I. 8. ) wherefore 3. The angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the straight line AF . Which was to be done ...
Euclid, Samuel A. GOOD. and ( Constr . ) 2. The base DF is equal to the base EF ; therefore ( I. 8. ) wherefore 3. The angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the straight line AF . Which was to be done ...
Σελίδα 15
... equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC , CF , each to each ; and ( Constr . ) 2 . therefore ( I. 8. ) 3 . The base DF is equal to the base EF ; The angle DCF is equal ...
... equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC , CF , each to each ; and ( Constr . ) 2 . therefore ( I. 8. ) 3 . The base DF is equal to the base EF ; The angle DCF is equal ...
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AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle