A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 63
... reason EF is equal to BC ; therefore AD is equal to EF ; [ Ax . 1. ] therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF . [ Ax . 2 , 3. ] And AB is equal to DC ; [ I. 34. ] there- fore the two EA ...
... reason EF is equal to BC ; therefore AD is equal to EF ; [ Ax . 1. ] therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF . [ Ax . 2 , 3. ] And AB is equal to DC ; [ I. 34. ] there- fore the two EA ...
Página 65
... reason the parallelogram EFGH is equal to the same EBBH . Therefore the parallelogram ABCD is equal to the parallelogram EFGH . [ Ax . 1. ] Therefore , parallelograms , & c . Q.E.D. PROPOSITION 37. THEOREM . Triangles on the same base ...
... reason the parallelogram EFGH is equal to the same EBBH . Therefore the parallelogram ABCD is equal to the parallelogram EFGH . [ Ax . 1. ] Therefore , parallelograms , & c . Q.E.D. PROPOSITION 37. THEOREM . Triangles on the same base ...
Página 75
... reason , AB and AH are in the same straight line . Now the angle DBC is equal to the angle FBA , for each of them is a right angle . [ Ax . 11. ] Add to each the angle ABC . Therefore the whole angle DBA is equal to the whole angle FBC ...
... reason , AB and AH are in the same straight line . Now the angle DBC is equal to the angle FBA , for each of them is a right angle . [ Ax . 11. ] Add to each the angle ABC . Therefore the whole angle DBA is equal to the whole angle FBC ...
Página 81
... reasons : - 1. Because these methods of proof can only apply when the lines are commensurable , whereas the propositions are true for all divisions of the lines , whether commensurable or not . 2. Because in Arithmetic and Algebra we ...
... reasons : - 1. Because these methods of proof can only apply when the lines are commensurable , whereas the propositions are true for all divisions of the lines , whether commensurable or not . 2. Because in Arithmetic and Algebra we ...
Página 94
... reason each of the angles CEB , EBC is half a right angle . Therefore the whole angle AEB is a right angle . And because the angle GEF is half a right angle , and the angle EGF a right angle , for it is equal to the interior and ...
... reason each of the angles CEB , EBC is half a right angle . Therefore the whole angle AEB is a right angle . And because the angle GEF is half a right angle , and the angle EGF a right angle , for it is equal to the interior and ...
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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