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 10
... common to the two triangles AFC , AGB ; therefore ( I. 4. ) 1. The base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to ...
... common to the two triangles AFC , AGB ; therefore ( I. 4. ) 1. The base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to ...
Σελίδα 11
... common to both , 1. The two sides DB , BC , are equal to the two AC , CB , each to each ; and the angle DBC is equal ( Hyp . ) to the angle ACB ; therefore , ( I. 4. ) 2. The base DC is equal to the base AB , and the triangle DBC is ...
... common to both , 1. The two sides DB , BC , are equal to the two AC , CB , each to each ; and the angle DBC is equal ( Hyp . ) to the angle ACB ; therefore , ( I. 4. ) 2. The base DC is equal to the base AB , and the triangle DBC is ...
Σελίδα 13
... Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; 1 . The two sides DA , AF , are equal to the two sides EA , AF , each to each ; and ( Constr . ) 2. The base DF is BOOK I. - PROP . VIII . IX . 13.
... Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; 1 . The two sides DA , AF , are equal to the two sides EA , AF , each to each ; and ( Constr . ) 2. The base DF is BOOK I. - PROP . VIII . IX . 13.
Σελίδα 14
... common to the two triangles ACD , BCD ; 1 . and ( Constr . ) The two sides AC , CD are equal to BC , CD , each to each ; 2. The angle ACD is equal to the angle BCD ; therefore ( I. 4. ) 3 . wherefore The base AD is equal to the base DB ...
... common to the two triangles ACD , BCD ; 1 . and ( Constr . ) The two sides AC , CD are equal to BC , CD , each to each ; 2. The angle ACD is equal to the angle BCD ; therefore ( I. 4. ) 3 . wherefore The base AD is equal to the base DB ...
Σελίδα 15
... common segment . If it be possible , 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 ...
... common segment . If it be possible , 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 ...
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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