The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
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Page 6
... given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle on AB . A B From the centre A , at the distance AB , describe the circle BCD . From the centre B , at the distance BA ...
... given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle on AB . A B From the centre A , at the distance AB , describe the circle BCD . From the centre B , at the distance BA ...
Page 8
... given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given ... circle [ POST . 3 . From the centre D , at the distance DG , describe the circle GKL cutting DA produced in L ...
... given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given ... circle [ POST . 3 . From the centre D , at the distance DG , describe the circle GKL cutting DA produced in L ...
Page 9
... circle CGH , therefore BC is equal to BG ; But it has been shown that AL is ... given there are eight ways in which the problem might be solved . The ... circle may be described from any centre with a radius equal to any finite ...
... circle CGH , therefore BC is equal to BG ; But it has been shown that AL is ... given there are eight ways in which the problem might be solved . The ... circle may be described from any centre with a radius equal to any finite ...
Page 69
... given distance from a given straight line is a pair of parallels on opposite sides of the given straight line ... circle at a given distance from a given straight line . F The points required are at the intersection of the circle ...
... given distance from a given straight line is a pair of parallels on opposite sides of the given straight line ... circle at a given distance from a given straight line . F The points required are at the intersection of the circle ...
Page 107
... given point is the circumference of a circle having a radius equal to the given distance and its centre at the given point . 2. The locus of a point at a given distance from a given straight line is the pair of straight lines ...
... given point is the circumference of a circle having a radius equal to the given distance and its centre at the given point . 2. The locus of a point at a given distance from a given straight line is the pair of straight lines ...
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Common terms and phrases
bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices
Popular passages
Page 21 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 369 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Page 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 96 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 40 - Any two sides of a triangle are together greater than the third side.
Page 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Page 407 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 156 - 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, together •with the square...