A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 52
... parallel to one another . Let the straight line EF , which falls on the two 1 . straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . B 2 . For if it be not parallel , AB 52 ...
... parallel to one another . Let the straight line EF , which falls on the two 1 . straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . B 2 . For if it be not parallel , AB 52 ...
Página 53
... parallel . [ Def . 35. ] Therefore AB is parallel to CD . Therefore , if a straight line , & c . Q.E.D PROPOSITION 28. THEOREM . If a straight line falling on two other straight lines , make the exterior angle equal to the interior and ...
... parallel . [ Def . 35. ] Therefore AB is parallel to CD . Therefore , if a straight line , & c . Q.E.D PROPOSITION 28. THEOREM . If a straight line falling on two other straight lines , make the exterior angle equal to the interior and ...
Página 54
... parallel to CD . [ I. 27. ] Therefore , if a straight line , & e . Q.E.D. Propositions 27 and 28 show that under certain conditions lines are parallel to each other . These conditions are : 1. That the alternate angles are equal ; or ...
... parallel to CD . [ I. 27. ] Therefore , if a straight line , & e . Q.E.D. Propositions 27 and 28 show that under certain conditions lines are parallel to each other . These conditions are : 1. That the alternate angles are equal ; or ...
Página 55
... parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together equal to two ...
... parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together equal to two ...
Página 56
... parallel lines are themselves parallel . 2. If the angle ABC be equal to PQR , and AB be parallel to PQ , then if BC and QR lie on the same side of AB and PQ respectively BC shall also be parallel to QR . 3. Any straight line drawn ...
... parallel lines are themselves parallel . 2. If the angle ABC be equal to PQR , and AB be parallel to PQ , then if BC and QR lie on the same side of AB and PQ respectively BC shall also be parallel to QR . 3. Any straight line drawn ...
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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