A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 27
... angle ADC . [ I. 5. ] But the angle ACD is greater than the angle BCD [ Ax . 9 ] , therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . But if one of the vertices as 2 ...
... angle ADC . [ I. 5. ] But the angle ACD is greater than the angle BCD [ Ax . 9 ] , therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . But if one of the vertices as 2 ...
Página 31
... angle ACD is equal to the angle BCD [ Con . ] ; therefore the base AD is equal to the base DB . [ I. 4. ] Therefore the straight line AB is divided into two equal parts at the point D. Q.E.F. Ex . The straight line which bisects the ...
... angle ACD is equal to the angle BCD [ Con . ] ; therefore the base AD is equal to the base DB . [ I. 4. ] Therefore the straight line AB is divided into two equal parts at the point D. Q.E.F. Ex . The straight line which bisects the ...
Página 41
... angle ABC would be less than the angle ACB [ I. 18 ] ; but it is not [ Hyp . ] ; therefore AC is not less than AB ... BCD is greater than the angle ACD . [ Ax . 9. ] Therefore the angle BCD is greater than the angle BDC . And because the ...
... angle ABC would be less than the angle ACB [ I. 18 ] ; but it is not [ Hyp . ] ; therefore AC is not less than AB ... BCD is greater than the angle ACD . [ Ax . 9. ] Therefore the angle BCD is greater than the angle BDC . And because the ...
Página 62
... BCD have two angles ABC BCA in the one , equal to two angles DCB , CBD in the other , each to each , and one side BC is ... angle BCD ; therefore the triangle ABC is equal to the triangle BCD , [ I. 4. and the diameter BC divides the ...
... BCD have two angles ABC BCA in the one , equal to two angles DCB , CBD in the other , each to each , and one side BC is ... angle BCD ; therefore the triangle ABC is equal to the triangle BCD , [ I. 4. and the diameter BC divides the ...
Página 107
... Angles of Triangles . Conditions of Inequality . Props . 18 , 19 , 20 , 21 , 24 , 25 . 13. If AD is the longest side and BC the shortest of a quadrilateral ABCD , then the angle ABC is greater than ADC , and the angle BCD greater than ...
... Angles of Triangles . Conditions of Inequality . Props . 18 , 19 , 20 , 21 , 24 , 25 . 13. If AD is the longest side and BC the shortest of a quadrilateral ABCD , then the angle ABC is greater than ADC , and the angle BCD greater than ...
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