A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 58
... ABCD be any rectilineal figure having the 1. exterior angles A , B , C , D , these shall be together equal to four right angles . 2 . In BC take any point and draw from it lines parallel to the sides of the figure . Then by I. 29 the ...
... ABCD be any rectilineal figure having the 1. exterior angles A , B , C , D , these shall be together equal to four right angles . 2 . In BC take any point and draw from it lines parallel to the sides of the figure . Then by I. 29 the ...
Página 63
... ABCD , EBCF be on the same base BC , and between the same parallels AF , BC : the parallelogram ABCD shall be equal to the parallelogram EBCF . If the sides AD , DF ♬ 3a . of the parallelograms ABCD , DBCF , opposite to the base BC ...
... ABCD , EBCF be on the same base BC , and between the same parallels AF , BC : the parallelogram ABCD shall be equal to the parallelogram EBCF . If the sides AD , DF ♬ 3a . of the parallelograms ABCD , DBCF , opposite to the base BC ...
Página 64
... ABCD , EFGH be parallelograms on equal bases BC , FG , and between the same parallels AH , BG : the parallelogram ABCD shall be equal to the parallelogram EFGH . 2. Join BE , CH . A B F C Then , because BC is equal to FG , [ Hyp . ] and ...
... ABCD , EFGH be parallelograms on equal bases BC , FG , and between the same parallels AH , BG : the parallelogram ABCD shall be equal to the parallelogram EFGH . 2. Join BE , CH . A B F C Then , because BC is equal to FG , [ Hyp . ] and ...
Página 65
... ABCD , because they are on the same base BC , and between the same parallels BC , AH . [ I. 35. ] For the like reason the parallelogram EFGH is equal to the same EBBH . Therefore the parallelogram ABCD is equal to the parallelogram EFGH ...
... ABCD , because they are on the same base BC , and between the same parallels BC , AH . [ I. 35. ] For the like reason the parallelogram EFGH is equal to the same EBBH . Therefore the parallelogram ABCD is equal to the parallelogram EFGH ...
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 ...
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 CBA axioms base BC BC is equal 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 PROPOSITION 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