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 52
Euclid, Samuel A. GOOD. But AH is the rectangle contained by AD , BD , for DH is equal ( II . 4. Cor . ) to DB ; and DF , together with CH , is the gnomon CMG ; therefore 4. The gnomon CMG is equal to the rectangle AD , DB : to each of ...
Euclid, Samuel A. GOOD. But AH is the rectangle contained by AD , BD , for DH is equal ( II . 4. Cor . ) to DB ; and DF , together with CH , is the gnomon CMG ; therefore 4. The gnomon CMG is equal to the rectangle AD , DB : to each of ...
Página 53
... rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided into any two parts in the point C ; the squares of AB , BC , are equal to twice the rectangle AB , BC ...
... rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided into any two parts in the point C ; the squares of AB , BC , are equal to twice the rectangle AB , BC ...
Página 54
... rectangle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q.E.D. PROP . VIII . - THEOREM . If a straight line be divided into any two parts , four times the rectangle contained by the whole line , and ...
... rectangle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q.E.D. PROP . VIII . - THEOREM . If a straight line be divided into any two parts , four times the rectangle contained by the whole line , and ...
Página 55
... rectangle contained by AB , BC , for BK is equal to BC , therefore 11. Four times the rectangle AB , BC , is quadruple of AK ; but the gnomon AOH was demonstrated to be quadruple of AK ; there- fore 12. Four times the rectangle AB , BC ...
... rectangle contained by AB , BC , for BK is equal to BC , therefore 11. Four times the rectangle AB , BC , is quadruple of AK ; but the gnomon AOH was demonstrated to be quadruple of AK ; there- fore 12. Four times the rectangle AB , BC ...
Página 60
... rectangle contained by AB , BH , for AB is equal to BD ; and FH is the square of AH ; therefore 7. The rectangle AB , BH , is equal to the square of AH . Wherefore the straight line AB is divided in H , so that the rectangle AB , BH ...
... rectangle contained by AB , BH , for AB is equal to BD ; and FH is the square of AH ; therefore 7. The rectangle AB , BH , is equal to the square of AH . Wherefore the straight line AB is divided in H , so that the rectangle AB , BH ...
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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