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 7
... straight lines CA , CB , to the points 4 , B ; ABC shall be an equilateral triangle . C E Because the point A is the centre of the circle BCD , ( Definition 15. ) 1. AC is equal to AB ; and because the point B is the centre of the ...
... straight lines CA , CB , to the points 4 , B ; ABC shall be an equilateral triangle . C E Because the point A is the centre of the circle BCD , ( Definition 15. ) 1. AC is equal to AB ; and because the point B is the centre of the ...
Σελίδα 8
... A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given ...
... A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given ...
Σελίδα 9
... A may be on D , and the straight line AB upon DE ; 1 . The point B shall coincide with the point E , because AB is equal to DE . And AB coinciding with DE , 2 . AC shall coincide with DF , because the angle BAC is equal to the angle EDF ...
... A may be on D , and the straight line AB upon DE ; 1 . The point B shall coincide with the point E , because AB is equal to DE . And AB coinciding with DE , 2 . AC shall coincide with DF , because the angle BAC is equal to the angle EDF ...
Σελίδα 13
... straight line BC upon EF ; 1 . The point C shall coincide with the point F , because BC is equal to EF ; therefore BC coinciding with EF , 2 . BA and AC shall coincide with ED and DF ; for , if the base BC coincide with the base EF ...
... straight line BC upon EF ; 1 . The point C shall coincide with the point F , because BC is equal to EF ; therefore BC coinciding with EF , 2 . BA and AC shall coincide with ED and DF ; for , if the base BC coincide with the base EF ...
Σελίδα 14
... straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is ... AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 . and ( Constr . ) The two sides AC , CD are ...
... straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is ... AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 . and ( Constr . ) The two sides AC , CD are ...
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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