A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 19
... AC is equal to AB . [ Def . 15. ] And because the point B is the centre of the circle ACE , BC is equal to BA . [ Def . 15. ] But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB . But things which ...
... AC is equal to AB . [ Def . 15. ] And because the point B is the centre of the circle ACE , BC is equal to BA . [ Def . 15. ] But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB . But things which ...
Página 22
... equal , each to each , namely , those to which the equal sides are opposite . A Let ABC , DEF be two triangles which have the 1 . two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE and AC to DF ; and the ...
... equal , each to each , namely , those to which the equal sides are opposite . A Let ABC , DEF be two triangles which have the 1 . two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE and AC to DF ; and the ...
Página 23
... equal to it . [ Ax . 8. ] Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to ... AC coincides with DF . And lastly , from these he shows that BC must coincide with EF . Hence the triangle ABC ...
... equal to it . [ Ax . 8. ] Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to ... AC coincides with DF . And lastly , from these he shows that BC must coincide with EF . Hence the triangle ABC ...
Página 24
... equal 3. to AG , [ Con . ] and AB to AC , [ Hyp . ] the two sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the ...
... equal 3. to AG , [ Con . ] and AB to AC , [ Hyp . ] the two sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the ...
Página 25
... equal angles , shall be equal to one another . 1 . Let ABC be a triangle , having the angle ABC equal to the angle ACB . The side AC shall be equal to the side AB . A 2 . For if AC be not equal to AB , one of them is greater than the ...
... equal angles , shall be equal to one another . 1 . Let ABC be a triangle , having the angle ABC equal to the angle ACB . The side AC shall be equal to the side AB . A 2 . For if AC be not equal to AB , one of them is greater than the ...
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