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
11 . All right angles are equal to one another . 12. Two straight lines which cut one another cannot both be parallel to a third straight line . PROPOSITION 1. PROBLEM . To describe an equilateral triangle on 18 ECCLID'S ELEMENTS .
11 . All right angles are equal to one another . 12. Two straight lines which cut one another cannot both be parallel to a third straight line . PROPOSITION 1. PROBLEM . To describe an equilateral triangle on 18 ECCLID'S ELEMENTS .
Página 19
To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line . It is re1 . quired to describe an equilateral triangle on AB . From the centre A , at the distance AB , describe 2. the circle BCD ...
To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line . It is re1 . quired to describe an equilateral triangle on AB . From the centre A , at the distance AB , describe 2. the circle BCD ...
Página 20
and on it describe the equilateral triangle DAB , [ I. 1. ) and produce the straight lines DA , DB to E and F. [ Post . 2. ] From the centre B , at the distance BC , describe the circle CGH , meeting DF in G. [ Post . 3. ] ...
and on it describe the equilateral triangle DAB , [ I. 1. ) and produce the straight lines DA , DB to E and F. [ Post . 2. ] From the centre B , at the distance BC , describe the circle CGH , meeting DF in G. [ Post . 3. ] ...
Página 21
From the point 2 . A draw the straight line AD equal to C ; [ I. 2. ] and from the centre A , at the distance AD , describe A the circle DEF . [ Post . 3. ] AE shall be equal to C. Because the point A is the centre of the circle 3 .
From the point 2 . A draw the straight line AD equal to C ; [ I. 2. ] and from the centre A , at the distance AD , describe A the circle DEF . [ Post . 3. ] AE shall be equal to C. Because the point A is the centre of the circle 3 .
Página 30
Take any point D in AB , 2 . and from AC cut off AE equal to AD [ I. 3 ] ; join DE , and on DE on E the side remote from A describe the equilateral triangle DEF . ( 1. 1. ] Join AF . The straight line AF shall bisect the angle BAC . 3 .
Take any point D in AB , 2 . and from AC cut off AE equal to AD [ I. 3 ] ; join DE , and on DE on E the side remote from A describe the equilateral triangle DEF . ( 1. 1. ] Join AF . The straight line AF shall bisect the angle BAC . 3 .
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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 |