A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página 23
Prove by the method used in this proposition that the two triangles into which a square is divided by its diagonal ... Let ABC be an isosceles triangle , having the side AB equal to the side AC , and let the straight lines AB , AC be ...
Prove by the method used in this proposition that the two triangles into which a square is divided by its diagonal ... Let ABC be an isosceles triangle , having the side AB equal to the side AC , and let the straight lines AB , AC be ...
Página 29
Therefore if the base BC coincides with the base EF , the sides BA , AC must coincide with the sides ED , DF . Therefore also the angle BAC coincides with ... The diagon : rls of a square bisect cach other at right angles . [ Prop . 4. ] ...
Therefore if the base BC coincides with the base EF , the sides BA , AC must coincide with the sides ED , DF . Therefore also the angle BAC coincides with ... The diagon : rls of a square bisect cach other at right angles . [ Prop . 4. ] ...
Página 41
... AC is greater than AB . Therefore , the greater angle , & c . Q.E.D. Ex . 1. The perpendicular is shorter than any other line which can be drawn from a given point to a given line . 2. Any point is taken in the side of a square .
... AC is greater than AB . Therefore , the greater angle , & c . Q.E.D. Ex . 1. The perpendicular is shorter than any other line which can be drawn from a given point to a given line . 2. Any point is taken in the side of a square .
Página 74
To describe a square on a given straight line . Let AB be the given straight line : it is required 1 . to describe a square on AB . From the point A draw AC at right angles to AB ; [ I. 11. ] and make AD equal to AB ; [ 1. 3. ] ...
To describe a square on a given straight line . Let AB be the given straight line : it is required 1 . to describe a square on AB . From the point A draw AC at right angles to AB ; [ I. 11. ] and make AD equal to AB ; [ 1. 3. ] ...
Página 75
On BC de2 . scribe the square BDEC , and on BA , AC describe the squares GB , HC ; [ I. 46. ] through A draw AL parallel to K BD or CE ; [ I. 31. ] and join AD , FC . Then , be3 . the angle BAC is a right angle , [ Hyp . ] ...
On BC de2 . scribe the square BDEC , and on BA , AC describe the squares GB , HC ; [ I. 46. ] through A draw AL parallel to K BD or CE ; [ I. 31. ] and join AD , FC . Then , be3 . the angle BAC is a right angle , [ Hyp . ] ...
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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 |