A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 18
... 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 . All right angles are equal to one another . 11 ...
... 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 . All right angles are equal to one another . 11 ...
Página 22
... coincide with the point E , because AB is equal to DE . [ 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 will coincide with the point ...
... coincide with the point E , because AB is equal to DE . [ 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 will coincide with the point ...
Página 23
... coincides with the base EF , and is equal to it . [ Ax . 8. ] Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Ax . 8 ] And the other angles of the one coincide with the other angles of the ...
... coincides with the base EF , and is equal to it . [ Ax . 8. ] Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Ax . 8 ] And the other angles of the one coincide with the other angles of the ...
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 10 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 10 if the base BC coincides with the base EF 28 EUCLID'S ELEMENTS .
Página 29
... coincides with the base EF , the sides BA , AC must coincide with the sides ED , DF . Therefore also the angle BAC coincides with the angle EDF , and is equal to it . [ Ax . 8. ] Therefore , if two triangles & c . Q.E.D. Notice that ...
... coincides with the base EF , the sides BA , AC must coincide with the sides ED , DF . Therefore also the angle BAC coincides with the angle EDF , and is equal to it . [ Ax . 8. ] Therefore , if two triangles & c . Q.E.D. Notice that ...
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
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CBA axioms base BC BC is equal bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop PROPOSITION quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal