The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
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Page 78
... 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 two equivalent triangles , having two given points as vertices . The set consists of two ...
... 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 two equivalent triangles , having two given points as vertices . The set consists of two ...
Page 90
... segment adjacent to that side . ( Rectangle BL = sq . on AB . ) Ex . 93. Construct a square whose area shall be twice , three times , four times a given square . · Make ABL a right angle . Make BC AB , BD = AC , BE = AD , BF AE , and so ...
... segment adjacent to that side . ( Rectangle BL = sq . on AB . ) Ex . 93. Construct a square whose area shall be twice , three times , four times a given square . · Make ABL a right angle . Make BC AB , BD = AC , BE = AD , BF AE , and so ...
Page 97
... Segment of a circle is the figure contained by a straight line and the circumference it cuts off . 20. Rectilineal Figures are those which are contained by straight lines . 21. Trilateral Figures , or Triangles , by three straight lines ...
... Segment of a circle is the figure contained by a straight line and the circumference it cuts off . 20. Rectilineal Figures are those which are contained by straight lines . 21. Trilateral Figures , or Triangles , by three straight lines ...
Page 156
... segments into which it divides the hypotenuse . Ex . 225. - A point O is taken in AB , such that AO - 3 OB . If P be any other point whatever , show that AP2 + 3 BP2 = AO2 + 3 BO2 + 4 OP2 . Apply II . 12 and 13 to AS AOP , BOP , and ...
... segments into which it divides the hypotenuse . Ex . 225. - A point O is taken in AB , such that AO - 3 OB . If P be any other point whatever , show that AP2 + 3 BP2 = AO2 + 3 BO2 + 4 OP2 . Apply II . 12 and 13 to AS AOP , BOP , and ...
Page 159
... segments into which the perpendicular from the right angle to the hypotenuse divides the base is four times the other . ( R. & de C. , Traité de Géométrie Élémen- taire . ) Ex . 244. - The shortest median of a triangle bisects the ...
... segments into which the perpendicular from the right angle to the hypotenuse divides the base is four times the other . ( R. & de C. , Traité de Géométrie Élémen- taire . ) Ex . 244. - The shortest median of a triangle bisects the ...
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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...