A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
Dentro del libro
Página 29
The demonstration of this prop . may be conducted thus : For let the triangle DEF be applied to ABC so that the bases may coincide , and the vertices fall on opposite A D B sides ...
The demonstration of this prop . may be conducted thus : For let the triangle DEF be applied to ABC so that the bases may coincide , and the vertices fall on opposite A D B sides ...
Página 30
Q.E.F. If the equilateral triangle were not described on the side of DE remote from A the point F might fall either , 1. Within the angle BAC , as in the prop . 2. On the point 4 ; in which case the construction would fail ; or , 3.
Q.E.F. If the equilateral triangle were not described on the side of DE remote from A the point F might fall either , 1. Within the angle BAC , as in the prop . 2. On the point 4 ; in which case the construction would fail ; or , 3.
Página 44
Thus if B and C were not greater than A , then FH would not be greater than FD , and the circle described from centre F , with radius FD , would therefore pass through the point H , or fall beyond it . In either case one circle would ...
Thus if B and C were not greater than A , then FH would not be greater than FD , and the circle described from centre F , with radius FD , would therefore pass through the point H , or fall beyond it . In either case one circle would ...
Página 47
By starting from the side which is not greater than the other , the point G is made to fall above EF , otherwise there would be three cases to consider , viz .: 1. When G falls above EF , as in the proposition . 2. When G falls on EF ...
By starting from the side which is not greater than the other , the point G is made to fall above EF , otherwise there would be three cases to consider , viz .: 1. When G falls above EF , as in the proposition . 2. When G falls on EF ...
Página 52
If a straight line falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two A 1. straight lines AB ...
If a straight line falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two A 1. straight lines AB ...
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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 alternate angles 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 equal sides equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater 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 remainder 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 |