A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 20
... BC the given straight line . It is required to draw from the point A a straight line equal to BC . 2 . From the ... side 20 EUCLID'S ELEMENTS .
... BC the given straight line . It is required to draw from the point A a straight line equal to BC . 2 . From the ... side 20 EUCLID'S ELEMENTS .
Página 23
... BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Ax . 10 ... side of the base shall be equal to one another . Let ABC be an isosceles triangle , having the 1. side AB equal to the ...
... BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Ax . 10 ... side of the base shall be equal to one another . Let ABC be an isosceles triangle , having the 1. side AB equal to the ...
Página 25
... side of the base . Therefore the angles , & c . Q.E.D. Corollary . Hence every equilateral triangle is also ... BC is common to both , the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the BOOK I. 6 . 25.
... side of the base . Therefore the angles , & c . Q.E.D. Corollary . Hence every equilateral triangle is also ... BC is common to both , the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the BOOK I. 6 . 25.
Página 27
... side of it , let there be two triangles ACB , ADB , which have their sides ... BC is equal to BD [ Hyp . ] , the angle BDC is equal to the angle BCD . [ I ... side of the base CD , are equal to one another . [ I. 5. ] But the angle ECD is ...
... side of it , let there be two triangles ACB , ADB , which have their sides ... BC is equal to BD [ Hyp . ] , the angle BDC is equal to the angle BCD . [ I ... side of the base CD , are equal to one another . [ I. 5. ] But the angle ECD is ...
Página 28
... side of the other needs no demonstration . Therefore , on the same base & c . Q.E.D. This proposition is introduced ... BC equal to the base EF ; the angle BAC shall be equal to the angle EDF . A B For if the triangle ABC be applied to the 2 ...
... side of the other needs no demonstration . Therefore , on the same base & c . Q.E.D. This proposition is introduced ... BC equal to the base EF ; the angle BAC shall be equal to the angle EDF . A B For if the triangle ABC be applied to the 2 ...
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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