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 13
Euclid, Samuel A. GOOD. Let ABC , DEF , be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and also the base BC equal to the base EF . The angle BAC is equal to ...
Euclid, Samuel A. GOOD. Let ABC , DEF , be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and also the base BC equal to the base EF . The angle BAC is equal to ...
Σελίδα 14
... Let AB be the given straight line ; it is required to divide it into two equal parts . 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 ...
... Let AB be the given straight line ; it is required to divide it into two equal parts . 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 ...
Σελίδα 15
... let the two straight lines ABC , ABD , have the seg- ment AB common to both of them . E A B Ꭰ C From the point B draw BE at right angles to AB ; and becanse ABC is a straight line , ( Def . 10. ) 1. The angle CBE is equal to the angle ...
... let the two straight lines ABC , ABD , have the seg- ment AB common to both of them . E A B Ꭰ C From the point B draw BE at right angles to AB ; and becanse ABC is a straight line , ( Def . 10. ) 1. The angle CBE is equal to the angle ...
Σελίδα 17
... ABC ; therefore ( Ax . 2. ) 3. The angles DBA , ABC , are equal to the three angles DBE , EBA , ABC ; but the angles ... let the two straight lines BC , BD , upon the opposite sides of AB , make the adjacent angles ABC , ABD , equal ...
... ABC ; therefore ( Ax . 2. ) 3. The angles DBA , ABC , are equal to the three angles DBE , EBA , ABC ; but the angles ... let the two straight lines BC , BD , upon the opposite sides of AB , make the adjacent angles ABC , ABD , equal ...
Σελίδα 18
... AB makes angles with the straight line CBE , upon one side of it , ( I. 13. ) 1. The angles ABC , ABE , are together ... Let the two straight lines AB , CD , cut one another in the point E ; the angle AEC shall be equal to the angle DEB ...
... AB makes angles with the straight line CBE , upon one side of it , ( I. 13. ) 1. The angles ABC , ABE , are together ... Let the two straight lines AB , CD , cut one another in the point E ; the angle AEC shall be equal to the angle DEB ...
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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