A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 78
... square on AC . Therefore the squares on DA , AC are equal to the squares on BA , B squares AC . [ Ax . 2. ] But because the angle DAC is a right angle , [ Const . ] the square on DC is equal to the on DA , AC . [ I. 47. ] And , by ...
... square on AC . Therefore the squares on DA , AC are equal to the squares on BA , B squares AC . [ Ax . 2. ] But because the angle DAC is a right angle , [ Const . ] the square on DC is equal to the on DA , AC . [ I. 47. ] And , by ...
Página 81
... square units re- peated 4 times , and the A whole figure consequently contains 3 x 4 or 12 square D units . F 81 Similarly if AB contains a units , and AD , b units , then the area of AC will be ab square units . From this we see that ...
... square units re- peated 4 times , and the A whole figure consequently contains 3 x 4 or 12 square D units . F 81 Similarly if AB contains a units , and AD , b units , then the area of AC will be ab square units . From this we see that ...
Página 83
... square on the whole line . 1 . Let the straight line AB be divided into any two parts at the point C : the rectangle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square on AB . 2 . On AB describe ...
... square on the whole line . 1 . Let the straight line AB be divided into any two parts at the point C : the rectangle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square on AB . 2 . On AB describe ...
Página 84
... AC , of which DA is equal to BA ; and CE is contained by AB , BC , for BE is equal to AB . There- fore the rectangle AB , AC , together with the rectangle AB , BC , is equal to the square on AB . Therefore , if a straight line , & c ...
... AC , of which DA is equal to BA ; and CE is contained by AB , BC , for BE is equal to AB . There- fore the rectangle AB , AC , together with the rectangle AB , BC , is equal to the square on AB . Therefore , if a straight line , & c ...
Página 85
... rectangle AB , AC is equal to the rectangle AC , CB together with the square on AC . PROPOSITION 4. THEOREM . If a straight line be divided into any two parts , the square on the whole line is equal to the squares on the two parts ...
... rectangle AB , AC is equal to the rectangle AC , CB together with the square on AC . PROPOSITION 4. THEOREM . If a straight line be divided into any two parts , the square on the whole line is equal to the squares on the two parts ...
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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