The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 σελίδες |
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Σελίδα 165
... chord of the circle . Hence the Corollary might be enunciated thus : - The perpendicular bisector of any chord of a circle passes through the centre of the circle . Ex . 265. - A circle cannot have two centres . Ex . 266. - Circles ...
... chord of the circle . Hence the Corollary might be enunciated thus : - The perpendicular bisector of any chord of a circle passes through the centre of the circle . Ex . 265. - A circle cannot have two centres . Ex . 266. - Circles ...
Σελίδα 169
... chords of a circle lie in a straight line . Ex . 271. — If a trapezoid be inscribed in a circle it must be symmetrical about one of its medians . In other words it must be an axe . ( See pp . 103 and 106. ) Ex . 272. An axe can always ...
... chords of a circle lie in a straight line . Ex . 271. — If a trapezoid be inscribed in a circle it must be symmetrical about one of its medians . In other words it must be an axe . ( See pp . 103 and 106. ) Ex . 272. An axe can always ...
Σελίδα 173
... chord AD of the larger of two concentric circles cuts the smaller in B and C. Show that ABCD . Show also that AB and CD subtend equal angles at the centre . PROPOSITION 7 . ( 1 ) If a point be Book III . Prop . 6 . 173.
... chord AD of the larger of two concentric circles cuts the smaller in B and C. Show that ABCD . Show also that AB and CD subtend equal angles at the centre . PROPOSITION 7 . ( 1 ) If a point be Book III . Prop . 6 . 173.
Σελίδα 186
... chords of a whose centre is E , and let EF , EG be drawn at rt . s to AB , CD and ... bisecting them in F , G. B ( 1 ) If AB = CD , then EF = EG , ... AB = CD , ... AF = CG . [ AB , CD are bisected . Now sqs . on EF , FA = sq . on EA ...
... chords of a whose centre is E , and let EF , EG be drawn at rt . s to AB , CD and ... bisecting them in F , G. B ( 1 ) If AB = CD , then EF = EG , ... AB = CD , ... AF = CG . [ AB , CD are bisected . Now sqs . on EF , FA = sq . on EA ...
Σελίδα 187
... chords of a circle lie on a concentric circle . Ex . 283. - Prove III . 14 by showing the congruence of the triangles EAB ... chord . ( A hint may be obtained from Ex . 287. ) DEF . When the perpendiculars from the centre on two Book III ...
... chords of a circle lie on a concentric circle . Ex . 283. - Prove III . 14 by showing the congruence of the triangles EAB ... chord . ( A hint may be obtained from Ex . 287. ) DEF . When the perpendiculars from the centre on two Book III ...
Άλλες εκδόσεις - Προβολή όλων
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Σελίδα 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 40 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...