A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Side 22
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , B and the other angles shall be equal each to each , to which the equal sides are opposite , namely , the angle ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , B and the other angles shall be equal each to each , to which the equal sides are opposite , namely , the angle ...
Side 23
... triangle upon the other . First he shows that AB exactly coincides with DE . Next , that the angle BAC coincides with EDF . Thirdly , that the line AC coincides with DF . And lastly , from these he shows that BC must coincide with EF ...
... triangle upon the other . First he shows that AB exactly coincides with DE . Next , that the angle BAC coincides with EDF . Thirdly , that the line AC coincides with DF . And lastly , from these he shows that BC must coincide with EF ...
Side 28
... angle BAC shall be equal to the angle EDF . B For if the triangle ABC be applied to the 2 , 3 . triangle DEF , so that the point B may be on E , and the straight line BC on the straight line EF , the point C will also coincide with the ...
... angle BAC shall be equal to the angle EDF . B For if the triangle ABC be applied to the 2 , 3 . triangle DEF , so that the point B may be on E , and the straight line BC on the straight line EF , the point C will also coincide with the ...
Side 29
... angle BAG = BGA because BA = BG , and the angle GAC - AGC because AC - GC . Therefore the whole angle BAC BGC , that is EDF . Q.E.D. Ex . 1. The diagonal of a rhombus bisects each of the angles through which it passes . Hence show that ...
... angle BAG = BGA because BA = BG , and the angle GAC - AGC because AC - GC . Therefore the whole angle BAC BGC , that is EDF . Q.E.D. Ex . 1. The diagonal of a rhombus bisects each of the angles through which it passes . Hence show that ...
Side 30
Euclides Charles Mansford. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given recti- 1. lineal angle . It is required to bisect it . 2 . Take any point D in AB ...
Euclides Charles Mansford. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given recti- 1. lineal angle . It is required to bisect it . 2 . Take any point D in AB ...
Andre utgaver - Vis alle
A School Euclid. Being Books I. & II. of Euclid's Elements, with Notes ... Euclid,Charles Mansford Uten tilgangsbegrensning - 1875 |
A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ... Euclides Uten tilgangsbegrensning - 1874 |
A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 28 - If two triangles have two sides of the one equal to two sides of the...
Side 41 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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.