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 39
... diameter AC divides it into two equal parts ; wherefore also 3. ABCD is double of the triangle EBC . Therefore , if a parallelogram , & c . Q.E.D. PROP . XLII . - PROBLEM . To describe a parallelogram that shall be equal to a given ...
... diameter AC divides it into two equal parts ; wherefore also 3. ABCD is double of the triangle EBC . Therefore , if a parallelogram , & c . Q.E.D. PROP . XLII . - PROBLEM . To describe a parallelogram that shall be equal to a given ...
Σελίδα 40
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG , the parallelograms about AC , that is , through which AC passes , and BK , KD , the other ...
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG , the parallelograms about AC , that is , through which AC passes , and BK , KD , the other ...
Σελίδα 41
... diameter is HK , and AG , ME , are the parallelograms about HK , and LB , BF , are the complements ; therefore ( I. 43. ) 4. LB is equal to BF . But BF is equal to the triangle C ; wherefore ( Ax . 1. ) 5. LB is equal to the triangle C ...
... diameter is HK , and AG , ME , are the parallelograms about HK , and LB , BF , are the complements ; therefore ( I. 43. ) 4. LB is equal to BF . But BF is equal to the triangle C ; wherefore ( Ax . 1. ) 5. LB is equal to the triangle C ...
Σελίδα 47
... diameter , together with the two complements , is called a gnomon . AE D HF B G C K " Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is more briefly expressed by the letters 4GK , or EHC ...
... diameter , together with the two complements , is called a gnomon . AE D HF B G C K " Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is more briefly expressed by the letters 4GK , or EHC ...
Σελίδα 51
... diameter of a square are likewise squares . PROP . V.THEOREM . If a straight line be divided into two equal parts , and also into two unequal parts , the rectangle contained by the unequal parts , together with the square of the line ...
... diameter of a square are likewise squares . PROP . V.THEOREM . If a straight line be divided into two equal parts , and also into two unequal parts , the rectangle contained by the unequal parts , together with the square of the line ...
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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