A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 18
... angles are equal to one another . 11 . 12. Two straight lines which cut one another cannot both be parallel to a third straight line . PROPOSITION 1. PROBLEM . To describe an equilateral triangle on 18 EUCLID'S ELEMENTS .
... angles are equal to one another . 11 . 12. Two straight lines which cut one another cannot both be parallel to a third straight line . PROPOSITION 1. PROBLEM . To describe an equilateral triangle on 18 EUCLID'S ELEMENTS .
Página 19
... describe an equilateral triangle on AB . From the centre A , at the distance AB , describe the circle BCD . [ Post . 3. ] From the centre B , at the distance BA , describe the circle ACE . [ Post . 3. ] From the point C , in which the ...
... describe an equilateral triangle on AB . From the centre A , at the distance AB , describe the circle BCD . [ Post . 3. ] From the centre B , at the distance BA , describe the circle ACE . [ Post . 3. ] From the point C , in which the ...
Página 20
... describe the equilateral triangle DAB , [ I. 1. ] and produce the straight lines DA , DB to E and F. [ Post . 2. ] From the centre B , at the distance BC , describe the circle CGH , meeting DF in G. [ Post . 3. ] From the centre D , at ...
... describe the equilateral triangle DAB , [ I. 1. ] and produce the straight lines DA , DB to E and F. [ Post . 2. ] From the centre B , at the distance BC , describe the circle CGH , meeting DF in G. [ Post . 3. ] From the centre D , at ...
Página 21
... describe the circle DEF . [ Post . 3. ] AE shall be equal to C. ~ 14 A B Because the point A is the centre of the circle 3 . DEF , AE is equal to AD . [ Def . 15. ] But C is equal to AD . [ Const . ] Therefore AE and Care each of them ...
... describe the circle DEF . [ Post . 3. ] AE shall be equal to C. ~ 14 A B Because the point A is the centre of the circle 3 . DEF , AE is equal to AD . [ Def . 15. ] But C is equal to AD . [ Const . ] Therefore AE and Care each of them ...
Página 30
... describe the equilateral triangle DEF . [ I. 1. ] Join AF . The straight line AF shall bisect the angle BAC . B C 3 . Because AD is equal to AE [ Con . ] , and AF is common to the two triangles DAF , EAF , the two sides DA , AF are ...
... describe the equilateral triangle DEF . [ I. 1. ] Join AF . The straight line AF shall bisect the angle BAC . B C 3 . Because AD is equal to AE [ Con . ] , and AF is common to the two triangles DAF , EAF , the two sides DA , AF are ...
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