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 páginas |
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Página 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 ...
Página 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 ...
Página 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 ...
Página 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 ...
Página 18
... ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD are likewise together equal to two ... Let the two straight lines AB , CD , cut one another in the point E ; the angle AEC shall be equal to the angle DEB ...
... ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD are likewise together equal to two ... 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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Términos y frases comunes
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