A School Euclid. Being Books I. & II. of Euclid's Elements, with Notes, Exercises and Explanations Appended to Each Proposition1875 - 112 páginas |
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Página 77
... shew that the area of the triangle on the hypotenuse is equal to the area of the other two . PROPOSITION 48. THEOREM . If the square described on one of the sides of a tri- angle be equal to the squares described on the other two sides ...
... shew that the area of the triangle on the hypotenuse is equal to the area of the other two . PROPOSITION 48. THEOREM . If the square described on one of the sides of a tri- angle be equal to the squares described on the other two sides ...
Página 78
... Shew that if the squares on BA and AC are less than the square on BC the angle BAC is acute ; but if greater than BAC is obtuse . 2. Make a square equal to the difference of two given squares . BOOK II . INTRODUCTION . THE Second Book ...
... Shew that if the squares on BA and AC are less than the square on BC the angle BAC is acute ; but if greater than BAC is obtuse . 2. Make a square equal to the difference of two given squares . BOOK II . INTRODUCTION . THE Second Book ...
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 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 109
... Shew that the parallelogram AQ is equal to the trapezium ABCD . 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 ...
... Shew that the parallelogram AQ is equal to the trapezium ABCD . 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 ...
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
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 BC is equal bisect centre 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 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