The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 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 ...
Página 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 ...
Página 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.
Página 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 ...
Página 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 ...
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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...