A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 91
... difference , and it is proved that the square on AC is less than the squares on AB and BC by twice the rectangle AB , BC . Therefore the square on the difference of two lines is equal to the squares on the lines diminished by twice ...
... difference , and it is proved that the square on AC is less than the squares on AB and BC by twice the rectangle AB , BC . Therefore the square on the difference of two lines is equal to the squares on the lines diminished by twice ...
Página 93
... difference . Therefore four times the rectangle contained by two lines is less than the square on the sum of the two lines by the square on their difference . PROPOSITION 9. THEOREM . If a straight line be divided into two equal , and ...
... difference . Therefore four times the rectangle contained by two lines is less than the square on the sum of the two lines by the square on their difference . PROPOSITION 9. THEOREM . If a straight line be divided into two equal , and ...
Página 97
... difference is equal to twice the sum of the squares on the two lines . Ex . If AC contains m lineal units , and CD n such units , shew that this proposition may be thus stated , ( m + n ) 2 + ( m — n ) 2 = 2m2 + 2n2 . and prove that the ...
... difference is equal to twice the sum of the squares on the two lines . Ex . If AC contains m lineal units , and CD n such units , shew that this proposition may be thus stated , ( m + n ) 2 + ( m — n ) 2 = 2m2 + 2n2 . and prove that the ...
Página 112
... difference of the squares on AD and AE is equal to the difference of the squares on AB and AC . ER 5 FE 75 MUSEUM WILKINS AND ELLIS , PRINTERS , DERBY . BY CHARLES MANSFORD , B.A. A SCHOOL EUCLID . Being 112 EUCLID'S ELEMENTS .
... difference of the squares on AD and AE is equal to the difference of the squares on AB and AC . ER 5 FE 75 MUSEUM WILKINS AND ELLIS , PRINTERS , DERBY . BY CHARLES MANSFORD , B.A. A SCHOOL EUCLID . Being 112 EUCLID'S ELEMENTS .
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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