A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 65
... parallelogram ABCD is equal to the parallelogram EFGH . [ Ax . 1. ] Therefore , parallelograms , & c . Q.E.D. PROPOSITION 37. THEOREM . Triangles on the same base , and between the same par- allels , are equal . Let the triangles ABC ...
... parallelogram ABCD is equal to the parallelogram EFGH . [ Ax . 1. ] Therefore , parallelograms , & c . Q.E.D. PROPOSITION 37. THEOREM . Triangles on the same base , and between the same par- allels , are equal . Let the triangles ABC ...
Página 66
... parallelogram . [ Def . ] And they are equal to one another because they are on equal bases BC , EF . and between the same parallels BF , GH . [ I. 36 ] . And the triangle ABC is half of the parallelogram GBCA , because the diameter AB ...
... parallelogram . [ Def . ] And they are equal to one another because they are on equal bases BC , EF . and between the same parallels BF , GH . [ I. 36 ] . And the triangle ABC is half of the parallelogram GBCA , because the diameter AB ...
Página 69
Euclides Charles Mansford. parallelogram . [ I. 34. ] Therefore the parallelogram ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q.E.D. Hence the area of a triangle is half that of a rectangle having the ...
Euclides Charles Mansford. parallelogram . [ I. 34. ] Therefore the parallelogram ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q.E.D. Hence the area of a triangle is half that of a rectangle having the ...
Página 71
... parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . 1 . Let AB be the given straight line , and C the given triangle , and D the given rectilineal angle : it is ...
... parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . 1 . Let AB be the given straight line , and C the given triangle , and D the given rectilineal angle : it is ...
Página 72
... parallelogram GM equal to the triangle DBC , and having the angle GHM equal to the angle E. [ I. 44. ] The figure FKML shall be the parallelogram required . Because the angle E is equal to each of the angles FKH , GHM , [ Const . ] the ...
... parallelogram GM equal to the triangle DBC , and having the angle GHM equal to the angle E. [ I. 44. ] The figure FKML shall be the parallelogram required . Because the angle E is equal to each of the angles FKH , GHM , [ Const . ] the ...
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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