A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página vi
Now such a crease does not belong to either half of the paper , but simply divides one half from the other . Further , although it has appreciable width , we can imagine these two halves of the leaf to meet in the middle of the crease ...
Now such a crease does not belong to either half of the paper , but simply divides one half from the other . Further , although it has appreciable width , we can imagine these two halves of the leaf to meet in the middle of the crease ...
Página 65
And the triangle ABC is half of the parallelogram EBCA , because the diameter AB bisects it ; [ I. 34. ] and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects it . [ I. 34. ] But the B halves of equal ...
And the triangle ABC is half of the parallelogram EBCA , because the diameter AB bisects it ; [ I. 34. ] and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects it . [ I. 34. ] But the B halves of equal ...
Página 66
and the triangle DEF is half of the parallelogram DEFH , because the diameter DF bisects it . But the halves of equal things are equal . [ Ax . 7. ] Therefore the triangle ABC is equal to the triangle DEF . Therefore , triangles , & c .
and the triangle DEF is half of the parallelogram DEFH , because the diameter DF bisects it . But the halves of equal things are equal . [ Ax . 7. ] Therefore the triangle ABC is equal to the triangle DEF . Therefore , triangles , & c .
Página 69
Q.E.D. Hence the area of a triangle is half that of a rectangle having the same base and altitude . PROPOSITION 42. PROBLEM . To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a ...
Q.E.D. Hence the area of a triangle is half that of a rectangle having the same base and altitude . PROPOSITION 42. PROBLEM . To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a ...
Página 87
CB ) and the sq . on AC and the latter of GE ( = rect . AC . CB ) and the sq . on BC . Ex . 1. Prove that HF is a square . 2. The square on a line is four times the square on half the line . PROPOSITION 5. THEOREM .
CB ) and the sq . on AC and the latter of GE ( = rect . AC . CB ) and the sq . on BC . Ex . 1. Prove that HF is a square . 2. The square on a line is four times the square on half the line . PROPOSITION 5. THEOREM .
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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 |