Euclid's Elements of Geometry, Bücher 1-6;Bücher 11Henry Martyn Taylor The University Press, 1895 - 657 Seiten |
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Seite 169
... line DCE pass through the point C , but do not intersect there : they touch at the point C , and DE is a tangent to the circle at the point C. Α B C D E T. E. 12 In the diagram the circles PRS , QRS meet at DEFINITIONS . 169.
... line DCE pass through the point C , but do not intersect there : they touch at the point C , and DE is a tangent to the circle at the point C. Α B C D E T. E. 12 In the diagram the circles PRS , QRS meet at DEFINITIONS . 169.
Seite 213
... tangent at B , AB bisects the angle CAP . 5. Prove that although no straight line can be drawn to pass between a circle and its tangent , yet any number of circles can be described to do so . 6. Circles , which have a common tangent at ...
... tangent at B , AB bisects the angle CAP . 5. Prove that although no straight line can be drawn to pass between a circle and its tangent , yet any number of circles can be described to do so . 6. Circles , which have a common tangent at ...
Seite 214
... tangent to the circle ABC . First , let the point D be on the circle . CONSTRUCTION . Find the centre E ; ( Prop . 5. ) ( I. Prop . 11. ) draw ED , and draw DF at right angles to DE ; then DF is a tangent drawn as re- quired . PROOF ...
... tangent to the circle ABC . First , let the point D be on the circle . CONSTRUCTION . Find the centre E ; ( Prop . 5. ) ( I. Prop . 11. ) draw ED , and draw DF at right angles to DE ; then DF is a tangent drawn as re- quired . PROOF ...
Seite 215
... tangent to the circle ABC at G. Both the construction in the Proposition and the alternative con- struction point out that two and only two tangents can be drawn to a circle through an external point , one through a point on the circle ...
... tangent to the circle ABC at G. Both the construction in the Proposition and the alternative con- struction point out that two and only two tangents can be drawn to a circle through an external point , one through a point on the circle ...
Seite 216
... DCE were not at right angles to CF , DCE would cut the circle ( Prop . 16 ) ; but it does not : therefore DCE is at right angles to CF. Wherefore , if a straight line & c . THE TANGENT AS THE LIMIT OF THE SECANT . Let 216 BOOK III .
... DCE were not at right angles to CF , DCE would cut the circle ( Prop . 16 ) ; but it does not : therefore DCE is at right angles to CF. Wherefore , if a straight line & c . THE TANGENT AS THE LIMIT OF THE SECANT . Let 216 BOOK III .
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Häufige Begriffe und Wortgruppen
ABCD ADDITIONAL PROPOSITION AE is equal angle ABC angle ACB angle BAC angular points bisected bisectors centre of similitude chord circle ABC circumscribed circle coincide CONSTRUCTION Coroll cut the circle describe a circle diagonals diameter equal angles equiangular equilateral triangle Euclid EXERCISES figure fixed point given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed circle intersect isosceles triangle Let ABC locus magnitudes meet middle points opposite sides pairs parallel parallelepiped parallelogram perpendicular plane angles polygon PROOF Prop quadrilateral radical axis radius rectangle contained regular polygon required to prove respectively rhombus right angles right-angled triangle shew side BC Similarly solid angle sphere square on AC straight line drawn straight line joining tangent tetrahedron theorem triangle ABC triangles are equal trihedral angle twice the rectangle vertex vertices Wherefore
Beliebte Passagen
Seite 70 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 218 - The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.
Seite 279 - 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...
Seite 148 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.
Seite 137 - 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.
Seite 372 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Seite 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Seite 303 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Seite 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Seite 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.