A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página 18
Things which are double of the same are equal to one another . 7. Things which are halves of the same are equal to one another . 8 . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to ...
Things which are double of the same are equal to one another . 7. Things which are halves of the same are equal to one another . 8 . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to ...
Página 45
Show how to make an angle double of a given angle . 2. Construct a triangle , having given two of its sides and the angle included by them . PROPOSITION 24 , THEOREM . If two triangles have two BOOK I. 23 . 45.
Show how to make an angle double of a given angle . 2. Construct a triangle , having given two of its sides and the angle included by them . PROPOSITION 24 , THEOREM . If two triangles have two BOOK I. 23 . 45.
Página 63
If the sides AD , DF A 3a . of the parallelograms ABCD , DBCF , opposite to the base BC , be terminated in the same point D , it is plair vhat each of the parallelograms is double of the triangle BDO ; [ I. 34. ] ...
If the sides AD , DF A 3a . of the parallelograms ABCD , DBCF , opposite to the base BC , be terminated in the same point D , it is plair vhat each of the parallelograms is double of the triangle BDO ; [ I. 34. ] ...
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 .
Página 93
If a straight line be divided into two equal , and also into two unequal parts , the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section . 1 .
If a straight line be divided into two equal , and also into two unequal parts , the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section . 1 .
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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 |