A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 20
... BC . Q.E.F. This problem admits of eight cases in the figure . 1. The given point may be joined with either extremity of the given line . 2. The equilateral triangle may be described on either side 20 EUCLID'S ELEMENTS .
... BC . Q.E.F. This problem admits of eight cases in the figure . 1. The given point may be joined with either extremity of the given line . 2. The equilateral triangle may be described on either side 20 EUCLID'S ELEMENTS .
Página 21
Euclides Charles Mansford. 2. The equilateral triangle may be described on either side of these two lines , giving four equilateral triangles . 3. In each of these possible triangles the sides may be pro- duced either through the vertex ...
Euclides Charles Mansford. 2. The equilateral triangle may be described on either side of these two lines , giving four equilateral triangles . 3. In each of these possible triangles the sides may be pro- duced either through the vertex ...
Página 22
... sides equal to one another , they shall also have their bases , or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to each , namely , those to which the equal sides are opposite ...
... sides equal to one another , they shall also have their bases , or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to each , namely , those to which the equal sides are opposite ...
Página 23
... sides be produced the angles on the other side of the base shall be equal to one another . Let ABC be an isosceles triangle , having the 1. side AB equal to the side AC , and let the straight lines AB , AC be produced to D and E ; the ...
... sides be produced the angles on the other side of the base shall be equal to one another . Let ABC be an isosceles triangle , having the 1. side AB equal to the side AC , and let the straight lines AB , AC be produced to D and E ; the ...
Página 24
... sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two tri- angles AFC , AGB ; there- fore the base FC is equal D to the base GB , and the triangle AFC to the triangle AGB ...
... sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two tri- angles AFC , AGB ; there- fore the base FC is equal D to the base GB , and the triangle AFC to the triangle AGB ...
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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