A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página 52
Let the straight line EF , which falls on the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . A B 2 . Q.E.D For if it be not parallel , 52 EUCLID'S ELEMENTS .
Let the straight line EF , which falls on the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . A B 2 . Q.E.D For if it be not parallel , 52 EUCLID'S ELEMENTS .
Página 53
Q.E.D For if it be not parallel , AB and CD being produced , will meet either towards B , D , or towards A , D. Let them be produced and meet towards B , D in the point G. 3 . Then because GEF is a triangle , its exterior angle AEF is ...
Q.E.D For if it be not parallel , AB and CD being produced , will meet either towards B , D , or towards A , D. Let them be produced and meet towards B , D in the point G. 3 . Then because GEF is a triangle , its exterior angle AEF is ...
Página 54
Let the straight line EF fall on the two straight lines AB , CD , and make the interior angles BGH , GHD on the same side together equal to two right angles : AB shall be parallel to CD . Then because the angles BGH , GHD are together ...
Let the straight line EF fall on the two straight lines AB , CD , and make the interior angles BGH , GHD on the same side together equal to two right angles : AB shall be parallel to CD . Then because the angles BGH , GHD are together ...
Página 55
Let the straight line EF fall on the two parallel 1 . straight lines AB , CD : the alternate angles AGH , GHD shall be equal to one another , and the exterior angle EGB shall be equal to the interior and opposite angle on the same side ...
Let the straight line EF fall on the two parallel 1 . straight lines AB , CD : the alternate angles AGH , GHD shall be equal to one another , and the exterior angle EGB shall be equal to the interior and opposite angle on the same side ...
Página 56
1 . 3 . PROPOSITION 30 . THEOREM . Straight lines which are parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . 2.
1 . 3 . PROPOSITION 30 . THEOREM . Straight lines which are parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . 2.
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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 |