The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
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Page 26
... external point to the second line ( as in Prop . 12 ) ; the latter when the first line is looked upon as drawn from a point in the second ( as in Prop . 11 ) . PROPOSITION 11 . PROBLEM . To draw a straight line at right angles to a ...
... external point to the second line ( as in Prop . 12 ) ; the latter when the first line is looked upon as drawn from a point in the second ( as in Prop . 11 ) . PROPOSITION 11 . PROBLEM . To draw a straight line at right angles to a ...
Page 100
... external point . a b A If OA , OB , OC , OD , OE , OF ( or these lines produced ) meet a straight line parallel to AF in a , b , c , d , e , f , show that ab , bc , cd , de , ef , are equal to one another . Hence obtain a practical ...
... external point . a b A If OA , OB , OC , OD , OE , OF ( or these lines produced ) meet a straight line parallel to AF in a , b , c , d , e , f , show that ab , bc , cd , de , ef , are equal to one another . Hence obtain a practical ...
Page 156
... . - ABCD is a square whose diagonals intersect in O ; AC is produced to E , so that CE is equal to AB ; prove that the square on AE is double the square on OE . Ex . 229. - Divide a line internally or externally 156 Euclid's Elements .
... . - ABCD is a square whose diagonals intersect in O ; AC is produced to E , so that CE is equal to AB ; prove that the square on AE is double the square on OE . Ex . 229. - Divide a line internally or externally 156 Euclid's Elements .
Page 157
... externally into two parts such that the difference between their squares shall be equal to a given square . Ex . 230 ... external point ; show that the difference of the squares on OA and OE is twice the difference of the squares on OB ...
... externally into two parts such that the difference between their squares shall be equal to a given square . Ex . 230 ... external point ; show that the difference of the squares on OA and OE is twice the difference of the squares on OB ...
Page 172
... the other , they are said to touch each other externally ; if one is wholly within the other , they are said to touch each other internally . PROPOSITION 6 . If two circles touch one another internally 172 Euclid's Elements .
... the other , they are said to touch each other externally ; if one is wholly within the other , they are said to touch each other internally . PROPOSITION 6 . If two circles touch one another internally 172 Euclid's Elements .
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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...