A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 52
... another . Let the straight line EF , which falls on the two A 1. straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . B For if it be not parallel , AB and CD 52 EUCLID'S ELEMENTS .
... another . Let the straight line EF , which falls on the two A 1. straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . B For if it be not parallel , AB and CD 52 EUCLID'S ELEMENTS .
Página 53
Euclides Charles MANSFORD. For if it be not parallel , AB and CD being pro2 . duced , will meet either towards B , D , or towards A , D. Let them be produced and meet towards B , D in the point G. 3 . Then because GEF is a triangle , its ...
Euclides Charles MANSFORD. For if it be not parallel , AB and CD being pro2 . duced , will meet either towards B , D , or towards A , D. Let them be produced and meet towards B , D in the point G. 3 . Then because GEF is a triangle , its ...
Página 54
... parallel to CD . Then because the angles BGH , GHD are to3 . gether equal to two right angles [ Hyp . ] , and that ... parallel to CD . [ I. 27. ] Therefore , if a straight line , & e . Q.E.D. Propositions 27 and 28 show that under ...
... parallel to CD . Then because the angles BGH , GHD are to3 . gether equal to two right angles [ Hyp . ] , and that ... parallel to CD . [ I. 27. ] Therefore , if a straight line , & e . Q.E.D. Propositions 27 and 28 show that under ...
Página 55
... parallel straight lines AB , CD : the alternate angles AGH , GHD shall be equal to one another , and the exterior angle EGB shall be equal to the interior and opposite angle on the same side , GHD , and the two interior angles on the ...
... parallel straight lines AB , CD : the alternate angles AGH , GHD shall be equal to one another , and the exterior angle EGB shall be equal to the interior and opposite angle on the same side , GHD , and the two interior angles on the ...
Página 56
... parallel to the same straight line are parallel to each other . 1 . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . 2. Let the straight line GHK cut AB , EF , CD . Because 3 . GHK cuts the parallel straight A ...
... parallel to the same straight line are parallel to each other . 1 . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . 2. Let the straight line GHK cut AB , EF , CD . Because 3 . GHK cuts the parallel straight A ...
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