A Text-book of Geometrical DeductionsLongmans, Green and Company, 1891 - Geometry |
From inside the book
Results 1-5 of 11
Page 26
... circle , and through B a point within the circle CD is drawn perpendicular to AB , meeting the circum- ference in C and D. Show that CB = DB . Use Ex . 1 . 9. If the bisectors of the exterior angles of the △ ABC be produced to form a ...
... circle , and through B a point within the circle CD is drawn perpendicular to AB , meeting the circum- ference in C and D. Show that CB = DB . Use Ex . 1 . 9. If the bisectors of the exterior angles of the △ ABC be produced to form a ...
Page 57
... circle is described cutting DB produced in E. From AE AF is cut off equal to AC , and CF is joined . Show that CF bisects AB . 24. If the mid - points of two opposite sides of a parallelogram are also the mid - points of two opposite ...
... circle is described cutting DB produced in E. From AE AF is cut off equal to AC , and CF is joined . Show that CF bisects AB . 24. If the mid - points of two opposite sides of a parallelogram are also the mid - points of two opposite ...
Page 58
... circle on a fixed straight line which does not cut the circle is constant . Use Ex . 8 . Examine the case when the fixed line cuts the circle . 31. The sum of the distances of the vertices of a quadrilateral from a straight line which ...
... circle on a fixed straight line which does not cut the circle is constant . Use Ex . 8 . Examine the case when the fixed line cuts the circle . 31. The sum of the distances of the vertices of a quadrilateral from a straight line which ...
Page 92
... circle whose centre is C , and whose radius is equal to AB . This circle is therefore the place where all such points are to be found ; and if we suppose a point to start from D and move round the circle , it will at every position ...
... circle whose centre is C , and whose radius is equal to AB . This circle is therefore the place where all such points are to be found ; and if we suppose a point to start from D and move round the circle , it will at every position ...
Page 93
... circle ; and ( 2 ) that every point on that circle satisfies the condition . 3. Find the locus of a point whose distance from 823 ] 93 Book I. - Problems.
... circle ; and ( 2 ) that every point on that circle satisfies the condition . 3. Find the locus of a point whose distance from 823 ] 93 Book I. - Problems.
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A Text-Book of Geometrical Deductions: Book I. Corresponding to ..., Book 1 James Blaikie,W. Thomson No preview available - 2017 |
Common terms and phrases
26 to show 38 to show ABCD altitude angle equal angular points apply Euc bisect bisectors Bookwork centre Compare Ex Construct a right-angled Construct a triangle Construct an isosceles convex polygon diagonals Draw a straight drawn parallel equal angles equilateral triangle EUCLID exterior angles Find a point Find the locus fixed point given line given point given square given straight line given the base given triangle hypotenuse isosceles triangle joining the mid-points LADC Let ABC line which joins lines be drawn median meet BC method of Ex mid-point of BC obtuse opposite angles opposite sides parallel straight lines parallelogram perimeter point in BC previous Ex quadrilateral quadrilateral ABCD rectangle required to prove respectively equal rhombus right angles right-angled triangle satisfies the condition Standard Theorem straight line drawn trapezium triangle required Trisect vertex vertical angle
Popular passages
Page 81 - In every triangle, the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Page 27 - If two triangles have two sides of the one equal to two sides of the...
Page 135 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Page 136 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 138 - If the square described on one side of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these two sides is a right angle.
Page 81 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Page 137 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Page 50 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
Page 137 - ... upon the same side together equal to two right angles; the two straight lines shall be parallel to one another.
Page 135 - The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced the angles on the other side of the base shall be equal to one another.