The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 27
... bisector of the join of two given points it is equidistant from them . 2. If a point is equidistant from two given points it is on the perpen- dicular bisector of their join . The following enunciation is a concise statement equivalent ...
... bisector of the join of two given points it is equidistant from them . 2. If a point is equidistant from two given points it is on the perpen- dicular bisector of their join . The following enunciation is a concise statement equivalent ...
Página 28
... bisector of their join . Con- sequently the point required is the intersection of this perpendicular bisector with XY . ) Ex . 10. Find a point equidistant from two fixed points A and B , and also equidistant from two other fixed points ...
... bisector of their join . Con- sequently the point required is the intersection of this perpendicular bisector with XY . ) Ex . 10. Find a point equidistant from two fixed points A and B , and also equidistant from two other fixed points ...
Página 51
... bisector of the angle contained by them . For the same use of the word locus see Note on Ex . 8 . The following proposition is slightly more general : -- The locus of a point equidistant from two given intersecting straight lines is the ...
... bisector of the angle contained by them . For the same use of the word locus see Note on Ex . 8 . The following proposition is slightly more general : -- The locus of a point equidistant from two given intersecting straight lines is the ...
Página 99
... bisectors of the sides BC , CA of a △ ABC meet at a point O , which can be shown to be equidistant from △ and B , and is ... on the ir bisector of AB . NOTE . - This point is equidistant from A , B , and C ( so that a circle can be ...
... bisectors of the sides BC , CA of a △ ABC meet at a point O , which can be shown to be equidistant from △ and B , and is ... on the ir bisector of AB . NOTE . - This point is equidistant from A , B , and C ( so that a circle can be ...
Página 102
... bisector of the other . 2d . The axis bisects the angles at the vertices which it joins . 3d . The other two angles are equal . 4th . The axis divides it into two congruent triangles , with equal sides adjacent . 5th . The median lines ...
... bisector of the other . 2d . The axis bisects the angles at the vertices which it joins . 3d . The other two angles are equal . 4th . The axis divides it into two congruent triangles , with equal sides adjacent . 5th . The median lines ...
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The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Página 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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.
Página 40 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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.
Página 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...