A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
Dentro del libro
Página 66
Q.E.D. Ex . If AC and DB cross each other at o in such a way that AB is parallel to CB ; shew that the triangle AOD is equal to the triangle BOC . PROPOSITION 38. THEOREM . Triangles on equal bases , and between the same parallels ...
Q.E.D. Ex . If AC and DB cross each other at o in such a way that AB is parallel to CB ; shew that the triangle AOD is equal to the triangle BOC . PROPOSITION 38. THEOREM . Triangles on equal bases , and between the same parallels ...
Página 77
... the triangles are equal in all respects . 3. The hypotenuses of three right - angled isosceles triangles are 80 placed as to form a right - angled triangle . Construct the figure and shew that the area of the triangle on the ...
... the triangles are equal in all respects . 3. The hypotenuses of three right - angled isosceles triangles are 80 placed as to form a right - angled triangle . Construct the figure and shew that the area of the triangle on the ...
Página 78
Shew that if the squares on BA and AC are less than the square on BC the angle BAC is acute ; but if greater than BAC is obtuse . 2. Make a square equal to the difference of two given squares . BOOK II . INTRODUCTION . above ways .
Shew that if the squares on BA and AC are less than the square on BC the angle BAC is acute ; but if greater than BAC is obtuse . 2. Make a square equal to the difference of two given squares . BOOK II . INTRODUCTION . above ways .
Página 84
Q.E.D. Ex . Put into words the arithmetical proposition corresponding to this , and if m = a + b , shew that its symbolical expression is md = an + bm . PROPOSITION 3. TEOREM . If a straight line be divided into any two parts ...
Q.E.D. Ex . Put into words the arithmetical proposition corresponding to this , and if m = a + b , shew that its symbolical expression is md = an + bm . PROPOSITION 3. TEOREM . If a straight line be divided into any two parts ...
Página 93
... is equal to the square on AD , that is to the square on the line made of AB and BC together . Therefore , if a straight line , & c . Q.E.D. If AB contains a lineal units and BC b lineal units , shew that this proposition may be ...
... is equal to the square on AD , that is to the square on the line made of AB and BC together . Therefore , if a straight line , & c . Q.E.D. If AB contains a lineal units and BC b lineal units , shew that this proposition may be ...
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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 |