A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 97
... shew that this proposition may be thus stated , ( m + n ) 2 + ( m — n ) 2 = 2m2 + 2n2 . and prove that the equation is true . PROPOSITION 11. PROBLEM . To divide a given straight line into two parts , so that the rectangle contained by ...
... shew that this proposition may be thus stated , ( m + n ) 2 + ( m — n ) 2 = 2m2 + 2n2 . and prove that the equation is true . PROPOSITION 11. PROBLEM . To divide a given straight line into two parts , so that the rectangle contained by ...
Página 99
... shew that the square on BA will be four times the square on BC . 2. If the angle BAC = 135 ° , and BC contains 5 units and CA 8 units , shew that BA will contain very nearly 12 units . PROPOSITION 13. THEOREM . In every triangle , the ...
... shew that the square on BA will be four times the square on BC . 2. If the angle BAC = 135 ° , and BC contains 5 units and CA 8 units , shew that BA will contain very nearly 12 units . PROPOSITION 13. THEOREM . In every triangle , the ...
Página 104
... shew that since OB is common , the 26th proposition will connect the hypothesis with the conclusion , and the proof should be proceeded with accordingly . Any result involving the equality of the sides and angles of triangles would ...
... shew that since OB is common , the 26th proposition will connect the hypothesis with the conclusion , and the proof should be proceeded with accordingly . Any result involving the equality of the sides and angles of triangles would ...
Página 108
... Shew how to construct such a triangle . 34. Express as a fraction of a right angle the interior angle of each of the following regular figures , viz .: a hexagon , an octagon , and a decagon . 35. Show that three regular hexagons , four ...
... Shew how to construct such a triangle . 34. Express as a fraction of a right angle the interior angle of each of the following regular figures , viz .: a hexagon , an octagon , and a decagon . 35. Show that three regular hexagons , four ...
Página 109
... Shew 47. Any line passing through the middle point of the diagonal of a parallelogram divides the parallelogram into two equal parts . 48. To bisect a parallelogram by a straight line drawn from a given point in one of its sides . 49 ...
... Shew 47. Any line passing through the middle point of the diagonal of a parallelogram divides the parallelogram into two equal parts . 48. To bisect a parallelogram by a straight line drawn from a given point in one of its sides . 49 ...
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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