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 11
... equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base ... ( Hyp . ) to the angle ACB ; therefore , ( I. 4. ) 2. The base DC is equal to the base AB , and the triangle DBC is ...
... equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base ... ( Hyp . ) to the angle ACB ; therefore , ( I. 4. ) 2. The base DC is equal to the base AB , and the triangle DBC is ...
Página 18
... equal to two right angles ( Hyp . ) ; therefore ( Ax . 1. ) 2. The angles CBA , ABE , are equal to the angles CBA , ABD . Take away the common angle ABC , and ( Ax . 3. ) 3 . The remaining angle ABE is equal to the remaining angle ...
... equal to two right angles ( Hyp . ) ; therefore ( Ax . 1. ) 2. The angles CBA , ABE , are equal to the angles CBA , ABD . Take away the common angle ABC , and ( Ax . 3. ) 3 . The remaining angle ABE is equal to the remaining angle ...
Página 27
... equal ( Hyp . ) to EF ; therefore The two AB , BC , are equal to the two DE , EF , each 6 . to each ; and the angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the third ...
... equal ( Hyp . ) to EF ; therefore The two AB , BC , are equal to the two DE , EF , each 6 . to each ; and the angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the third ...
Página 29
... equal ( I. 15. ) to the angle AGH , 1 . The angle AGH is equal to the angle GHD , and they are alternate angles ; therefore ( I. 27. ) 2. AB is parallel to CD . Again , because the angles BGH , GHD , are equal ( Hyp . ) to two right ...
... equal ( I. 15. ) to the angle AGH , 1 . The angle AGH is equal to the angle GHD , and they are alternate angles ; therefore ( I. 27. ) 2. AB is parallel to CD . Again , because the angles BGH , GHD , are equal ( Hyp . ) to two right ...
Página 35
... equal to one another . But if the sides 4D , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not ... ( Hyp . ) parallels , and joined towards the same parts by the straight lines BE , CH . But straight lines which join equal ...
... equal to one another . But if the sides 4D , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not ... ( Hyp . ) parallels , and joined towards the same parts by the straight lines BE , CH . But straight lines which join equal ...
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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