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 47
... 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 , which are at the opposite angles of the parallelograms which ...
... 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 , which are at the opposite angles of the parallelograms which ...
Σελίδα 52
... gnomon CMG ; therefore 4. The gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( II . 4. Cor . ) to the square of CD ; therefore 5. The gnomon CMG , together with LG , is equal to the rectangle AD ...
... gnomon CMG ; therefore 4. The gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( II . 4. Cor . ) to the square of CD ; therefore 5. The gnomon CMG , together with LG , is equal to the rectangle AD ...
Σελίδα 53
... gnomon AKF , together with the square CK ; there- fore but 3 . The gnomon AKF , together with the square CK , is double of AK ; 4. Twice the rectangle AB , BC , is double of AK , for BK is equal ( II . 4. Cor . ) to BC ; therefore 5. The ...
... gnomon AKF , together with the square CK ; there- fore but 3 . The gnomon AKF , together with the square CK , is double of AK ; 4. Twice the rectangle AB , BC , is double of AK , for BK is equal ( II . 4. Cor . ) to BC ; therefore 5. The ...
Σελίδα 54
Euclid, Samuel A. GOOD. up but the gnomon AKF , together with the squares CK , HF , make the whole figure ADEB and CK , which are the squares of AB and BC ; therefore 7. The squares of AB and BC are equal to twice the rectangle AB , BC ...
Euclid, Samuel A. GOOD. up but the gnomon AKF , together with the squares CK , HF , make the whole figure ADEB and CK , which are the squares of AB and BC ; therefore 7. The squares of AB and BC are equal to twice the rectangle AB , BC ...
Σελίδα 55
... gnomon AOH was demonstrated to be quadruple of AK ; there- fore 12. Four times the rectangle AB , BC , is equal to the gnomon AOH ; to each of these add XH , which is equal ( II . 4. Cor . ) to the square of AC ; therefore 13. Four ...
... gnomon AOH was demonstrated to be quadruple of AK ; there- fore 12. Four times the rectangle AB , BC , is equal to the gnomon AOH ; to each of these add XH , which is equal ( II . 4. Cor . ) to the square of AC ; therefore 13. Four ...
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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