The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 páginas |
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Página 28
... falling upon two other straight lines , make the alternate angles equal to one another , these two straight lines shall be parallel , Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles ...
... falling upon two other straight lines , make the alternate angles equal to one another , these two straight lines shall be parallel , Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles ...
Página 29
... fall upon two parallel straight lines , it makes the alter- nate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side ...
... fall upon two parallel straight lines , it makes the alter- nate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side ...
Página 30
... falling upon them , make the interior angles on the same side less than two right angles , will meet ( Ax . 12. ) together if continually produced ; therefore 3. The straight lines AB , CD , shall meet , if produced far enough ; but ...
... falling upon them , make the interior angles on the same side less than two right angles , will meet ( Ax . 12. ) together if continually produced ; therefore 3. The straight lines AB , CD , shall meet , if produced far enough ; but ...
Página 31
... falls upon them , 2. The exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3. The whole exterior angle ACD is equal to the two interior ...
... falls upon them , 2. The exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3. The whole exterior angle ACD is equal to the two interior ...
Página 41
... falls upon the parallels AH , EF , ( I. 29. ) 1. The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9. ) 2. The angles BHF , HFE , are less than two right angles ; but ( Ax . 12. ) straight lines which with ...
... falls upon the parallels AH , EF , ( I. 29. ) 1. The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9. ) 2. The angles BHF , HFE , are less than two right angles ; but ( Ax . 12. ) straight lines which with ...
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Términos y frases comunes
AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle