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 49
... rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . 30. ) to AB ; and 2 ... twice the rectangle contained by the parts . 1 Let the straight line AB be divided into any 3 BOOK II . - PROP ...
... rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . 30. ) to AB ; and 2 ... twice the rectangle contained by the parts . 1 Let the straight line AB be divided into any 3 BOOK II . - PROP ...
Σελίδα 50
... twice the rectangle contained by AC , CB . ୯ B G H K twice Селе , де , СВ D FE Upon AB describe ( I. 46. ) the square ADEB , and join BD ; and through C draw ( I. 31. ) CGF parallel to AD or BE ; and through G draw HK parallel to AB or ...
... twice the rectangle contained by AC , CB . ୯ B G H K twice Селе , де , СВ D FE Upon AB describe ( I. 46. ) the square ADEB , and join BD ; and through C draw ( I. 31. ) CGF parallel to AD or BE ; and through G draw HK parallel to AB or ...
Σελίδα 51
... rectangle AC , CB ; wherefore F 14 . AG , GE , are equal to twice the rectangle AC , CB : and HF , CK , are the squares of AC , CB ; wherefore 15. The four figures HF , CK , AG , GE , are equal to the squares of AC , CB , and to twice the ...
... rectangle AC , CB ; wherefore F 14 . AG , GE , are equal to twice the rectangle AC , CB : and HF , CK , are the squares of AC , CB ; wherefore 15. The four figures HF , CK , AG , GE , are equal to the squares of AC , CB , and to twice the ...
Σελίδα 53
... twice the rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided into any two parts in the point C ; the squares of AB , BC , are equal to twice the rectangle AB ...
... twice the rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided into any two parts in the point C ; the squares of AB , BC , are equal to twice the rectangle AB ...
Σελίδα 54
... twice the rectangle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q.E.D. PROP . VIII . - THEOREM . If a straight line be divided into any two parts , four times the rectangle contained by the whole ...
... twice the rectangle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q.E.D. PROP . VIII . - THEOREM . If a straight line be divided into any two parts , four times the rectangle contained by the whole ...
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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