The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
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Page 28
... fixed points A and B , and also equidistant from two other fixed points C and D. ( The point will be the intersection of two lines , each of which is a locus ) . Ex . 11. - Find a point equidistant from three given points . Ex . 12 ...
... fixed points A and B , and also equidistant from two other fixed points C and D. ( The point will be the intersection of two lines , each of which is a locus ) . Ex . 11. - Find a point equidistant from three given points . Ex . 12 ...
Page 51
... is at the intersection of tʊo loci . ) Ex . 39. - If any straight line be drawn through the mid - point of the join of two fixed points , it is equidistant from them . DEF . - Parallel straight lines are such as are Book I. Prop . 26 . 51.
... is at the intersection of tʊo loci . ) Ex . 39. - If any straight line be drawn through the mid - point of the join of two fixed points , it is equidistant from them . DEF . - Parallel straight lines are such as are Book I. Prop . 26 . 51.
Page 78
... fixed straight line AD is bisected by any other straight line BF . On BF are taken any equal segments BC , EF . triangles ABC , DEF are equivalent . Ex . 88. - Find a set of lines such that any segment of any one of them is the base of ...
... fixed straight line AD is bisected by any other straight line BF . On BF are taken any equal segments BC , EF . triangles ABC , DEF are equivalent . Ex . 88. - Find a set of lines such that any segment of any one of them is the base of ...
Page 111
... fixed , another is taken anywhere on a given straight line . Show that the locus of the third vertex is a pair of straight lines . Hence describe an equilateral triangle with one vertex at a fixed point , and the other two one on each ...
... fixed , another is taken anywhere on a given straight line . Show that the locus of the third vertex is a pair of straight lines . Hence describe an equilateral triangle with one vertex at a fixed point , and the other two one on each ...
Page 112
... fixed point , and P any point on a given straight line ; PO is produced to Q , so that OQ is equal to OP . Show that the locus of Q is a straight line parallel to the given one . Hence find two points one on each of two given ...
... fixed point , and P any point on a given straight line ; PO is produced to Q , so that OQ is equal to OP . Show that the locus of Q is a straight line parallel to the given one . Hence find two points one on each of two given ...
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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...