A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página 58
Let ABCD be any rectilineal figure having the 1 . exterior angles A , B , C , D , these shall be together equal to four right angles . In BC take any 2 . point and draw from it lines parallel to the sides of the figure .
Let ABCD be any rectilineal figure having the 1 . exterior angles A , B , C , D , these shall be together equal to four right angles . In BC take any 2 . point and draw from it lines parallel to the sides of the figure .
Página 63
Let the parallelograms 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 A 3a . of the parallelograms ABCD ...
Let the parallelograms 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 A 3a . of the parallelograms ABCD ...
Página 64
that is , the parallelogram ABCD is equal to the parallelogram EBCF . Therefore , parallelograms on the same base , & c . Q.E.D. In the phrase the whole or remainder , which occurs in the demonstration , the whole refers to the left ...
that is , the parallelogram ABCD is equal to the parallelogram EBCF . Therefore , parallelograms on the same base , & c . Q.E.D. In the phrase the whole or remainder , which occurs in the demonstration , the whole refers to the left ...
Página 65
And it is equal to 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 ...
And it is equal to 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 ...
Página 69
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 same base and altitude . PROPOSITION 42. PROBLEM .
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 same base and altitude . PROPOSITION 42. PROBLEM .
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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
ABCD AC is equal angle ABC angle ACB angle BAC angle BCD angle EDF angle equal apply axioms base BC bisect BOOK called centre circle coincide common Const construction definitions demonstration describe diagonals diameter difference divided double draw drawn equal sides equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater half Hence isosceles triangle join length less Let ABC meet method namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained rectilineal figure result right angles side BC sides square on AC Take THEOREM things triangle ABC true truths twice the rectangle unequal units whole
Información bibliográfica
| Título | A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
| Autor | Euclides |
| Editor | Charles MANSFORD |
| Publicado | 1874 |
| Procedencia del original | Biblioteca Británica |
| Digitalizado | 27 Nov. 2020 |
| Exportar cita | BiBTeX EndNote RefMan |