A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 85
... rectangle AB , BC is equal to the rectangle AC , CB , together with the square on BC . Therefore , if a straight ... twice the rectangle contained by the two parts . 1 . Let the straight line AB be divided into any two parts at the point ...
... rectangle AB , BC is equal to the rectangle AC , CB , together with the square on BC . Therefore , if a straight ... twice the rectangle contained by the two parts . 1 . Let the straight line AB be divided into any two parts at the point ...
Página 91
... twice the rectangle AB , BC . To each of these equals add HF , which is equal to the square on AC . [ II . 4 , Cor . , and I. 34. ] Therefore the gnomon AKF , together with the squares CK , HF , is equal to twice the rectangle AB , BC ...
... twice the rectangle AB , BC . To each of these equals add HF , which is equal to the square on AC . [ II . 4 , Cor . , and I. 34. ] Therefore the gnomon AKF , together with the squares CK , HF , is equal to twice the rectangle AB , BC ...
Página 97
... twice the sum of the squares on the two lines . Ex . If AC contains m lineal units , and CD n such units , shew that ... rectangle contained by the whole and one of the parts be equal to the square on the other part . may Let AB be the given ...
... twice the sum of the squares on the two lines . Ex . If AC contains m lineal units , and CD n such units , shew that ... rectangle contained by the whole and one of the parts be equal to the square on the other part . may Let AB be the given ...
Página 99
... triangle , having 1 , 2. the obtuse angle ACB , and from the point A let AD be drawn perpendicular to BC produced : the square on AB shall be greater than the squares on AC , CB , by twice the rectangle BC , CD . 3 . Because the ...
... triangle , having 1 , 2. the obtuse angle ACB , and from the point A let AD be drawn perpendicular to BC produced : the square on AB shall be greater than the squares on AC , CB , by twice the rectangle BC , CD . 3 . Because the ...
Página 100
Euclides Charles Mansford. PROPOSITION 13. THEOREM . In every triangle , the square on the side subtending an acute angle , is less than the squares on the sides con- taining that angle , by twice the rectangle ... twice the rectangle CB , BD ...
Euclides Charles Mansford. PROPOSITION 13. THEOREM . In every triangle , the square on the side subtending an acute angle , is less than the squares on the sides con- taining that angle , by twice the rectangle ... twice the rectangle CB , BD ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join less Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal