A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 32
... common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is equal to the base EF [ Def . 24. ] ; therefore the angle DCF is equal to the angle ECF [ I. 8 ] , and ...
... common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is equal to the base EF [ Def . 24. ] ; therefore the angle DCF is equal to the angle ECF [ I. 8 ] , and ...
Página 33
... common to the two triangles FHC , GHC ; the two sides FH , HC are equal to the two sides GH , HC , each to each ; and the base CF is equal to the base CG [ Def . ] ; therefore the angle CHF is equal to the angle CHG [ I. 8. ] ; and they ...
... common to the two triangles FHC , GHC ; the two sides FH , HC are equal to the two sides GH , HC , each to each ; and the base CF is equal to the base CG [ Def . ] ; therefore the angle CHF is equal to the angle CHG [ I. 8. ] ; and they ...
Página 36
... common angle ABC , and the remaining angle ABE is equal to the remaining angle ABD , [ Ax . 3. ] the less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . there- And in like manner it may be ...
... common angle ABC , and the remaining angle ABE is equal to the remaining angle ABD , [ Ax . 3. ] the less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . there- And in like manner it may be ...
Página 37
... common angle AED , and the remaining angle CEA is equal to the remaining angle DEB . [ Ax . 3. ] In the same manner it can be proved that the angle CEB is equal to the angle AED . Therefore , if two straight lines , & c . Q.E.D. ...
... common angle AED , and the remaining angle CEA is equal to the remaining angle DEB . [ Ax . 3. ] In the same manner it can be proved that the angle CEB is equal to the angle AED . Therefore , if two straight lines , & c . Q.E.D. ...
Página 54
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHI ) [ Ax . 3 ] ; and they are alternate angles ; therefore AB is parallel to CD . [ I. 27. ] Therefore , if a straight line , & e . Q.E.D. ...
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHI ) [ Ax . 3 ] ; and they are alternate angles ; therefore AB is parallel to CD . [ I. 27. ] Therefore , if a straight line , & e . Q.E.D. ...
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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 CEA axioms base BC 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 less Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop 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