A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 38
... exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let one side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC ...
... exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let one side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC ...
Página 39
... angles are together less than two right angles . Produce BC to Then because 3 . ACD is the exterior angle of the triangle ABC , it is greater than the interior and opposite angle ABC . [ I. 16. ] To each of these add the angle ACB ...
... angles are together less than two right angles . Produce BC to Then because 3 . ACD is the exterior angle of the triangle ABC , it is greater than the interior and opposite angle ABC . [ I. 16. ] To each of these add the angle ACB ...
Página 40
... exterior angle of the triangle BDC , it is greater than the interior and opposite angle DCB . [ I. 16. ] But the angle ADB is equal to the angle ABD [ I. 5. ] , because the side AD is equal to the side AB . [ Const . ] Therefore the ...
... exterior angle of the triangle BDC , it is greater than the interior and opposite angle DCB . [ I. 16. ] But the angle ADB is equal to the angle ABD [ I. 5. ] , because the side AD is equal to the side AB . [ Const . ] Therefore the ...
Página 43
... exterior angle of any triangle 3. is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than the angle CED . [ I. 16. ] For the same reason , the exterior angle CEB of the triangle ABE ...
... exterior angle of any triangle 3. is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than the angle CED . [ I. 16. ] For the same reason , the exterior angle CEB of the triangle ABE ...
Página 51
Euclides Charles MANSFORD. angle ABH is equal to the angle DEF [ Hyp . ] ; therefore the base AH is equal to the base ... exterior angle BHA of the triangle AHC is equal to the interior and opposite angle BCA ; which is impossible . [ I ...
Euclides Charles MANSFORD. angle ABH is equal to the angle DEF [ Hyp . ] ; therefore the base AH is equal to the base ... exterior angle BHA of the triangle AHC is equal to the interior and opposite angle BCA ; which is impossible . [ I ...
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