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 6
... straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . " PROPOSITION I. - PROBLEM . To describe an equilateral triangle 6 EUCLID'S ELEMENTS .
... straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . " PROPOSITION I. - PROBLEM . To describe an equilateral triangle 6 EUCLID'S ELEMENTS .
Σελίδα 7
... describe an equi- lateral triangle upon it . From the centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the ...
... describe an equi- lateral triangle upon it . From the centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the ...
Σελίδα 8
... describe ( Post . 3. ) the circle DEF : AE shall be equal to C. D E B Because A is the centre of the circle DEF , ( Def . 15. ) 1. AE is equal to AD ; but the straight line C is likewise equal to AD ( Constr . ) ; whence AE and Care ...
... describe ( Post . 3. ) the circle DEF : AE shall be equal to C. D E B Because A is the centre of the circle DEF , ( Def . 15. ) 1. AE is equal to AD ; but the straight line C is likewise equal to AD ( Constr . ) ; whence AE and Care ...
Σελίδα 13
... describe ( I. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the triangle BAC . D F B C Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; 1 . The two sides DA , AF , are equal ...
... describe ( I. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the triangle BAC . D F B C Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; 1 . The two sides DA , AF , are equal ...
Σελίδα 14
... Describe ( I. 1. ) upon it an equilateral triangle ABC , and bisect ( I. 9. ) the angle 4CB by the straight line CD . AB is cut into two equal parts in the point D. C A. D B Because AC is equal to CB , and CD common to the two triangles ...
... Describe ( I. 1. ) upon it an equilateral triangle ABC , and bisect ( I. 9. ) the angle 4CB by the straight line CD . AB is cut into two equal parts in the point D. C A. D B Because AC is equal to CB , and CD common to the two triangles ...
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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