A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
Dentro del libro
Página 27
... angle ADC . [ I. 5. ] But the angle ACD is greater than the angle BCD [ Ax . 9 ] , therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to ...
... angle ADC . [ I. 5. ] But the angle ACD is greater than the angle BCD [ Ax . 9 ] , therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to ...
Página 31
... angle ACD is equal to the angle BCD [ Con . ] ; therefore the base AD is equal to the base DB . [ I. 4. ] Therefore the straight line AB is divided into two equal parts at the point D. Q.E.F. Ex . The straight line which bisects the ...
... angle ACD is equal to the angle BCD [ Con . ] ; therefore the base AD is equal to the base DB . [ I. 4. ] Therefore the straight line AB is divided into two equal parts at the point D. Q.E.F. Ex . The straight line which bisects the ...
Página 41
... angle ABC would be less than the angle ACB [ I. 18 ] ; but it is not [ Hyp . ] ; therefore AC is not less than AB ... BCD is greater than the angle ACD . [ Ax . 9. ] Therefore the angle BCD is greater than the angle BDC . And because the ...
... angle ABC would be less than the angle ACB [ I. 18 ] ; but it is not [ Hyp . ] ; therefore AC is not less than AB ... BCD is greater than the angle ACD . [ Ax . 9. ] Therefore the angle BCD is greater than the angle BDC . And because the ...
Página 61
... angle BCD ; therefore the base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles , each to each , to which the equal sides are opposite ; [ I. 4. ] therefore the angle ACB ...
... angle BCD ; therefore the base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles , each to each , to which the equal sides are opposite ; [ I. 4. ] therefore the angle ACB ...
Página 62
... BCD have two angles ABC BCA in the one , equal to two angles DCB , CBD in the other , each to each , and one side BC ... angle of the one to the third angle of the other , namely the side AB equal to the side CD , and the side AC equal ...
... BCD have two angles ABC BCA in the one , equal to two angles DCB , CBD in the other , each to each , and one side BC ... angle of the one to the third angle of the other , namely the side AB equal to the side CD , and the side AC equal ...
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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 DBA angle EDF angle equal angles are equal axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid EUCLID'S ELEMENTS 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 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
Pasajes populares
Página 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Página 28 - If two triangles have two sides of the one equal to two sides of the...
Página 41 - Any two sides of a triangle are together greater than the third side.
Página 57 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Página 72 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Página 75 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Página 55 - IF a straight line fall upon two parallel straight lines, it makes the alternate 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 together equal to two right angles...
Página 28 - A two triangles, having the two sides AB, AC, equal to the two sides \ DE, DF, each to each, viz: AB to DE, and AC to DF; and also the base BC equal to the base EF.
Página 69 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.