A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 52
... triangles with the required parts , viz . , ADB , ACB . And it should be noticed that there is this difference between them : the angle ACB opposite AB in the one triangle is acute ( for DCB is an isosceles triangle ) , while ADB , the ...
... triangles with the required parts , viz . , ADB , ACB . And it should be noticed that there is this difference between them : the angle ACB opposite AB in the one triangle is acute ( for DCB is an isosceles triangle ) , while ADB , the ...
Página 77
... triangle , the triangles are equal in all respects . 3. The hypotenuses of three right - angled isosceles triangles are so placed as to form a right - angled triangle . Construct the figure and shew that the area of the triangle on the ...
... triangle , the triangles are equal in all respects . 3. The hypotenuses of three right - angled isosceles triangles are so placed as to form a right - angled triangle . Construct the figure and shew that the area of the triangle on the ...
Página 99
... triangles , & c . Q.E.D. Ex . 1. If BCA is two - thirds of two right angles , and the triangle is isosceles , shew that the square on BA will be four times the square on BC . 2. If the angle BAC = 135 ° , and BC contains 5 units and CA ...
... triangles , & c . Q.E.D. Ex . 1. If BCA is two - thirds of two right angles , and the triangle is isosceles , shew that the square on BA will be four times the square on BC . 2. If the angle BAC = 135 ° , and BC contains 5 units and CA ...
Página 106
... isosceles triangle ABC are bisected by the straight lines AO , BO intersecting in 0 . If 40 be joined show that it will bisect the vertical angle ACB . 5. In any isosceles triangle if a straight line be drawn from the vertex to the base ...
... isosceles triangle ABC are bisected by the straight lines AO , BO intersecting in 0 . If 40 be joined show that it will bisect the vertical angle ACB . 5. In any isosceles triangle if a straight line be drawn from the vertex to the base ...
Página 107
... triangle are together greater than twice the line joining the vertex with the middle point of the base . 17. The sum ... isosceles triangle will be parallel to the base . 23. If 40 bisects the base of an isosceles triangle ABC and a ...
... triangle are together greater than twice the line joining the vertex with the middle point of the base . 17. The sum ... isosceles triangle will be parallel to the base . 23. If 40 bisects the base of an isosceles triangle ABC and a ...
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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