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
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . 11 .
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . 11 .
Página 22
And , AB coinciding with DE , AC will coincide with DF , because the angle BAC is equal to the angle EDF . [ Hyp . ] Therefore also the point C will coincide with the point F , because AC is equal to DF : [ Hyp . ] ...
And , AB coinciding with DE , AC will coincide with DF , because the angle BAC is equal to the angle EDF . [ Hyp . ] Therefore also the point C will coincide with the point F , because AC is equal to DF : [ Hyp . ] ...
Página 23
point E , therefore the base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Ax . 10. ] ...
point E , therefore the base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Ax . 10. ] ...
Página 28
... the point C will also coincide with the point F , because BC is equal to EF . [ Hyp . ] Therefore BC coinciding with EF , BA and AC will coincide with ED and DF . For if the base BC coincides with the base EF , 28 EUCLID'S ELEMENTS .
... the point C will also coincide with the point F , because BC is equal to EF . [ Hyp . ] Therefore BC coinciding with EF , BA and AC will coincide with ED and DF . For if the base BC coincides with the base EF , 28 EUCLID'S ELEMENTS .
Página 29
if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then on the same base and on the same side of it there will be two triangles having ...
if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then on the same base and on the same side of it there will be two triangles having ...
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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 |