A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
Dentro del libro
Resultados 1-5 de 12
Página 66
... shew that the triangle AOD is equal to the triangle BOC . PROPOSITION 38. THEOREM . Triangles on equal bases , and between the same par- allels , are equal to one another . 1 . Let the triangles ABC , DEF be on equal bases BC , EF and ...
... shew that the triangle AOD is equal to the triangle BOC . PROPOSITION 38. THEOREM . Triangles on equal bases , and between the same par- allels , are equal to one another . 1 . Let the triangles ABC , DEF be on equal bases BC , EF and ...
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 84
... shew that its symbolical expression is m2 = am + bm . PROPOSITION 3. THEOREM . If a straight line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two ...
... shew that its symbolical expression is m2 = am + bm . PROPOSITION 3. THEOREM . If a straight line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two ...
Página 93
... shew that this proposition may be expressed in symbols , thus : ( a + b ) - ( a - b ) 2 = 4ab . If AB and BC be considered as two lines , AD is their sum and AC their difference . Therefore four times the rectangle contained by two ...
... shew that this proposition may be expressed in symbols , thus : ( a + b ) - ( a - b ) 2 = 4ab . If AB and BC be considered as two lines , AD is their sum and AC their difference . Therefore four times the rectangle contained by two ...
Otras ediciones - Ver todas
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 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 Ах