Elements of Euclid Adapted to Modern Methods in GeometryWilliam Collins, Sons,, 1874 - 216 σελίδες |
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Αποτελέσματα 1 - 5 από τα 26.
Σελίδα 13
... chord is a straight line joining the two extremities of an arc . 33. A segment of a circle is the figure contained by an arc and its chord . The chord is called the base of the segment . 34. A diameter of a circle is a chord which ...
... chord is a straight line joining the two extremities of an arc . 33. A segment of a circle is the figure contained by an arc and its chord . The chord is called the base of the segment . 34. A diameter of a circle is a chord which ...
Σελίδα 102
... chord through its middle point . E Let AB be any chord of the circle ABE , and let CE be a line drawn through its middle point C , at right angles to AB ; it is required to prove that the centre of the circle is in the perpendicular CE ...
... chord through its middle point . E Let AB be any chord of the circle ABE , and let CE be a line drawn through its middle point C , at right angles to AB ; it is required to prove that the centre of the circle is in the perpendicular CE ...
Σελίδα 103
... chord , bisects it . Let the line EC pass through the centre O of the circle ABF , and be at right angles to the chord AB , it shall pass through the middle point C of the chord . Join O , A and O , B. Then in the two triangles OCA , A ...
... chord , bisects it . Let the line EC pass through the centre O of the circle ABF , and be at right angles to the chord AB , it shall pass through the middle point C of the chord . Join O , A and O , B. Then in the two triangles OCA , A ...
Σελίδα 104
... chords than one . Let , if possible , C , which is not the centre , be the middle of the two chords AB and ED . Join C ... chord . PROP . II . THEOREM . ( EUC . III . 2 , in Part . ) . A straight line cannot cut a circle in more than two ...
... chords than one . Let , if possible , C , which is not the centre , be the middle of the two chords AB and ED . Join C ... chord . PROP . II . THEOREM . ( EUC . III . 2 , in Part . ) . A straight line cannot cut a circle in more than two ...
Σελίδα 106
... chord . For the distance AB in this case vanishes . 3. Let the given point A be within the circumference . Then AO and OE are greater than AE , that is , AC is greater than AE . Again , join O , D , and we have DA and AO greater than DO ...
... chord . For the distance AB in this case vanishes . 3. Let the given point A be within the circumference . Then AO and OE are greater than AE , that is , AC is greater than AE . Again , join O , D , and we have DA and AO greater than DO ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Euclid Adapted to Modern Methods in Geometry Euclid,James Bryce,David Munn (F.R.S.E.) Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1874 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AC and CB altitude angle AOB BA and AC bisecting the angle centre chord circles touch circumference cloth coincide Const conv Cor.-Hence diagonal diameter divided draw equal angles equal to BC equal to twice equiangular equilateral triangle Euclid exterior angle Fcap GEOGRAPHY geometrical given circle given line given point given straight line greater half the perimeter Hence hypotenuse inscribed intersecting isosceles triangle less Let ABC LL.D meet middle point multiple opposite sides parallel to BC parallelogram perpendicular polygon produced Proposition Q. E. D. Cor Q. E. D. PROP radius ratio rectangle contained rectilineal figure reflex angle remaining angles required to prove right angles right-angled triangle schol segments shew shewn side BC square on AC tangent THEOREM triangle ABC twice the rectangle twice the square whole line
Δημοφιλή αποσπάσματα
Σελίδα 68 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 77 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.
Σελίδα 87 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.
Σελίδα 30 - Any two sides of a triangle are together greater than the third side.
Σελίδα 204 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...
Σελίδα 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 98 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.