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 3
... line , which is called the cir- cumference , and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another . XVI . And this point is called the centre of the circle . XVII ...
... line , which is called the cir- cumference , and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another . XVI . And this point is called the centre of the circle . XVII ...
Σελίδα 5
... straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a ...
... straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a ...
Σελίδα 7
... straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it ... draw ( Post . 1. ) the straight lines CA , CB , to the points 4 , B ; ABC shall be an equilateral triangle . C E ...
... straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it ... draw ( Post . 1. ) the straight lines CA , CB , to the points 4 , B ; ABC shall be an equilateral triangle . C E ...
Σελίδα 14
... straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be ... straight line FC drawn from the given point C ' 14 EUCLID'S ELEMENTS .
... straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be ... straight line FC drawn from the given point C ' 14 EUCLID'S ELEMENTS .
Σελίδα 15
Euclid, Samuel A. GOOD. straight line FC drawn from the given point C ' is at right angles to the given straight line AB F A D C E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF ...
Euclid, Samuel A. GOOD. straight line FC drawn from the given point C ' is at right angles to the given straight line AB F A D C E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF ...
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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